From 53bff2f22bfe373cf8b04694be5790c4007bb184 Mon Sep 17 00:00:00 2001
From: King-sj <King-sj@users.noreply.github.com>
Date: Wed, 6 Nov 2024 18:09:26 +0000
Subject: [PATCH] deploy:
 King-sj/KBlog@d4e7e5986fa6d73ebda4abc0c8d318abce877562

---
 404.html                                      |   8 +-
 article/index.html                            |  23 +--
 ...{0.html-BMihHxnS.js => 0.html-CC8GZdvL.js} |   2 +-
 ...{1.html-B2woGSgL.js => 1.html-C8e1pvTo.js} |   2 +-
 ...{2.html-DuLx7xSk.js => 2.html-CfN7D4gf.js} |   2 +-
 ...{3.html-CZB5joNY.js => 3.html-D9pPtuiP.js} |   2 +-
 ...{4.html-C8TuLMaF.js => 4.html-DavKkBaH.js} |   2 +-
 ....html-BC0rHQLu.js => 404.html-CGMXaJuv.js} |   2 +-
 ...{5.html-qLlLbRlw.js => 5.html-DpkUOZDe.js} |   2 +-
 ...{6.html-BPGbpgjm.js => 6.html-4dTDTOb4.js} |   2 +-
 ...{7.html-DopH3hey.js => 7.html-BzOHeKw-.js} |   2 +-
 ...{8.html-D1TnfZgI.js => 8.html-C-sA1tiy.js} |   2 +-
 ...{9.html-CGdd1xtP.js => 9.html-DOIgY3Qt.js} |   2 +-
 ...8.js => DesignPrinciples.html-BAjp9viD.js} |   2 +-
 ...5\256\211\350\243\205Qt5.html-DdU1Gd4z.js" |   2 +-
 assets/SearchResult-DAas8KH8.js               |   1 +
 assets/SearchResult-DUP77o_D.js               |   1 -
 ...qp.js => abstractFactory.html-D_oh5f2L.js} |   2 +-
 ...l-B2UlYWFL.js => adapter.html-x6kHt0VN.js} |   2 +-
 ...\346\215\242\346\272\220.html-DkRIM6mj.js" |   2 +-
 assets/{app-B69Gl_S-.js => app-B4LGNJZ0.js}   | 142 +++++++++---------
 assets/{arc-BCmLGSVu.js => arc-DWlpCdAw.js}   |   2 +-
 ...2.js => blockDiagram-a8a0820c-DvOSxzpN.js} |   2 +-
 ...ml-LTDknqB7.js => bridge.html-DzkNbynT.js} |   2 +-
 ...l-Ba33pTyP.js => builder.html-B7MALN7e.js} |   2 +-
 ...sQW3.js => c4Diagram-dc8f04df-DWstOjwk.js} |   2 +-
 assets/carrobot.html-B7set7IG.js              |   1 +
 ...=> chainOfResponsibility.html-CpbeYqOk.js} |   2 +-
 assets/channel-DJsAcM5I.js                    |   1 -
 assets/channel-yU22lAlC.js                    |   1 +
 ...html-CedraPRV.js => cicd.html-BxLHD3yn.js} |   2 +-
 ...u.js => classDiagram-8298e144-DKojaSxZ.js} |   2 +-
 ...s => classDiagram-v2-296fb1cd-DTrZkQpq.js} |   2 +-
 assets/clone-C3EvpqoY.js                      |   1 +
 assets/clone-CI3kFeqi.js                      |   1 -
 ...l-d4IhdjVF.js => command.html-Bzqk5uGA.js} |   2 +-
 ...DOBxYen3.js => composite.html-D89dw1yo.js} |   2 +-
 ...XUz.js => createText-4a4f35c9-CISzj231.js} |   2 +-
 ...FfT8RlFX.js => decorator.html-0jwtowLH.js} |   2 +-
 ...ml-B-hYGcsZ.js => docker.html-DtdutZB7.js} |   2 +-
 ...\351\241\271\347\233\256.html-CZONKQdf.js" |   2 +-
 ...B19hLEst.js => edges-5962ec63-ApWhby2b.js} |   2 +-
 ....html-De4ifiEs.js => end.html-CkqhlgwJ.js} |   2 +-
 ...-GEp.js => erDiagram-51d2b61e-D5StoYmd.js} |   2 +-
 ...ml-Cj3lyBcS.js => facade.html-BODpRH45.js} |   2 +-
 ...xz9.js => factory_method.html-NuMbQ7is.js} |   2 +-
 ...ME-hebA.js => figure_bed.html-vyc89ngd.js} |   2 +-
 ...3mEtQas.js => flowDb-0da60e67-XaXEQp9e.js} |   2 +-
 ...aS.js => flowDiagram-622f9fc1-BpT3eoaF.js} |   2 +-
 assets/flowDiagram-v2-a33b4996-BQrZXIe9.js    |   1 +
 assets/flowDiagram-v2-a33b4996-BVubizbB.js    |   1 -
 ...chart-elk-definition-930acc39-D2d6YT5I.js} |   2 +-
 ...CWx8TgTS.js => flyweight.html-DUTi0_Qx.js} |   2 +-
 ...C.js => ganttDiagram-a649f789-B7dFucT2.js} |   2 +-
 ...s => gitGraphDiagram-23af1bdb-Dd7cNN9F.js} |   2 +-
 ...\344\275\234\346\265\201.html-DJORqAx-.js" |   2 +-
 .../{graph-T5JS4vfK.js => graph-B1296pfd.js}  |   2 +-
 assets/image-Dc9IOqtq.png                     | Bin 0 -> 196365 bytes
 ...B8uh0R2i.js => index-9620d214-BlfbO5wW.js} |   2 +-
 ...tml-CZDJXbd3.js => index.html-B1eL3fl0.js} |   2 +-
 ...tml-B7IKPS0E.js => index.html-BCqj2PVi.js} |   2 +-
 ...tml-0LHdE1Bw.js => index.html-BFj2MrdQ.js} |   2 +-
 ...tml-BlxatHgv.js => index.html-BJX9B5Ij.js} |   2 +-
 ...tml-Bb8RnxYT.js => index.html-BOaWfYA8.js} |   2 +-
 ...tml-DRlrhC7d.js => index.html-BgifGsNR.js} |   2 +-
 assets/index.html-BjAw7f-F.js                 |   1 -
 assets/index.html-BjDh3PHW.js                 |   1 -
 ...tml-C8X5E5_U.js => index.html-BjeRhPA4.js} |   2 +-
 ...tml-CXhg3e64.js => index.html-BlsqD0oa.js} |   2 +-
 assets/index.html-Bq7J9cN0.js                 |   1 +
 ...tml-CLOegCHC.js => index.html-BwXv95cV.js} |   2 +-
 ...tml-BtJnl_OK.js => index.html-C9AeqWIc.js} |   2 +-
 ...tml-BK-iNYKv.js => index.html-CE6ffKsf.js} |   2 +-
 ...tml-ZxSgoRoh.js => index.html-CL479cux.js} |   2 +-
 ...tml-B3D_5fpm.js => index.html-COyA9Sec.js} |   2 +-
 ...tml-DDeLtmuh.js => index.html-CVNN5Fwq.js} |   2 +-
 ...tml-DzsdPiFk.js => index.html-CYOJa5u_.js} |   2 +-
 assets/index.html-CdwZ1P48.js                 |   1 +
 ...tml-Dakgazin.js => index.html-CqYdKjYM.js} |   2 +-
 ...tml-B2T3kUK3.js => index.html-CryaZFG_.js} |   2 +-
 ...tml-BZLD09T1.js => index.html-Cw9y1ZOg.js} |   2 +-
 ...tml-DDn6tClc.js => index.html-CzSwk-A5.js} |   2 +-
 ...tml-BKjCcFT0.js => index.html-D8p9fsJ8.js} |   2 +-
 ...tml-VMxXqaQ8.js => index.html-DCZKDe-x.js} |   2 +-
 ...tml-DeH2SCB3.js => index.html-DERlmHfl.js} |   2 +-
 ...tml-BXtqeyHq.js => index.html-DOXbY5aY.js} |   2 +-
 ...tml-B71I-yvI.js => index.html-DOZrz5tX.js} |   2 +-
 ...tml-DR-PJoSN.js => index.html-DW1c3ODz.js} |   2 +-
 ...tml-CcgdDCiF.js => index.html-DYx5t_sy.js} |   2 +-
 ...tml-D2pTqZFy.js => index.html-DeNCk-ye.js} |   2 +-
 ...tml-BSJr7qwh.js => index.html-DhCS_0vf.js} |   2 +-
 ...tml-B5GIg4Ij.js => index.html-Dj_dWWjR.js} |   2 +-
 ...tml-BHNGjpbb.js => index.html-DklcXGYl.js} |   2 +-
 ...tml-Dh_a7h_3.js => index.html-DottIbHL.js} |   2 +-
 ...tml-CGsa9ffM.js => index.html-Dpy8imS-.js} |   2 +-
 ...tml-Dv6rE_pN.js => index.html-DtPJaw_H.js} |   2 +-
 ...tml-BLuB_Eoc.js => index.html-DwPUACaS.js} |   2 +-
 assets/index.html-DzJoMr4P.js                 |   1 -
 ...tml-ayClYbZ3.js => index.html-F61LMFJS.js} |   2 +-
 ...tml-CRzs15I0.js => index.html-JQfnAIea.js} |   2 +-
 ...tml-kOhwCTdr.js => index.html-NUfXNLwU.js} |   2 +-
 ...tml-BvZSJ2r-.js => index.html-SMm58lXr.js} |   2 +-
 ...tml-Ak5uwHrg.js => index.html-SwHQd6yQ.js} |   2 +-
 ...tml-CO8-8uSt.js => index.html-TRJ6qSMT.js} |   2 +-
 ...tml-UrkKwESw.js => index.html-ZzlVKqB8.js} |   2 +-
 ...tml-BNAyU6dK.js => index.html-auYNF0Cp.js} |   2 +-
 ...tml-DZYdDCPP.js => index.html-hPg6lxSo.js} |   2 +-
 ...tml-QNuKjuoZ.js => index.html-i5A_pLCb.js} |   2 +-
 assets/index.html-jwKIpsPi.js                 |   1 +
 ...tml-bipylPNF.js => index.html-mplfcIL_.js} |   2 +-
 ...tml-CSRSsNOG.js => index.html-rivgPJ9m.js} |   2 +-
 ...tml-BpjUVtkj.js => index.html-y8ELyp0v.js} |   2 +-
 ...tml-9q-r5JHT.js => index.html-yUxPRBBH.js} |   2 +-
 assets/index.html-ybZqFA4D.js                 |   1 +
 ...He.js => infoDiagram-f86e0131-BvySRD9D.js} |   2 +-
 ...nsycaD.js => interpreter.html-DfDQyPSV.js} |   2 +-
 ...tml-CEHYbhC9.js => intro.html-DcelwrZW.js} |   2 +-
 ...-USsHv5Pr.js => iterator.html-9EjNXcsT.js} |   2 +-
 ...js => journeyDiagram-de0d04b7-bCIGoTun.js} |   2 +-
 ...{layout-DUYLy6Ue.js => layout-qMafh1ee.js} |   2 +-
 assets/{line-D0jG_HZ-.js => line-BqHmcuby.js} |   2 +-
 ...{linear-CRQH6hcv.js => linear-Cb1OAgs3.js} |   2 +-
 ...ITZCknd.js => mailserver.html-DO5Xbwgi.js} |   2 +-
 ...-RBFBa63Z.js => mediator.html-C5vte2nl.js} |   2 +-
 ...l-CbbBldep.js => memento.html-Dw4vFzUb.js} |   2 +-
 ...e-ChLYKTZm.js => mermaid.core-DNo_7Q2B.js} |   8 +-
 ...> mindmap-definition-b08d3ac4-CtqZ8Vgk.js} |   2 +-
 ...ml-M2GwLZ2U.js => modint.html-DNrISIPe.js} |   2 +-
 ...-BvrPoU9w.js => observer.html-DCoBW7Y-.js} |   2 +-
 ...fQ6.js => pieDiagram-31d824a1-BIcjeA1S.js} |   2 +-
 ...Boe-0El2.js => prototype.html-Be3THUal.js} |   2 +-
 ...tml-CSHBH0Xk.js => proxy.html-DydmfTHY.js} |   2 +-
 ...js => python_requrements.html-D_iboyN4.js} |   2 +-
 ...s => quadrantDiagram-a712a7d9-CNklQ4II.js} |   2 +-
 ...> requirementDiagram-eb878fee-OFUpKWxv.js} |   2 +-
 ....js => sankeyDiagram-c599f8ec-Ss3oz1oB.js} |   2 +-
 ...s => sequenceDiagram-66748113-sH_v1_cD.js} |   2 +-
 ...Pzh1ZzrO.js => singleton.html-CJylCsqx.js} |   2 +-
 ...tml-DsXXtCU9.js => state.html-D0BJywlY.js} |   2 +-
 ...X.js => stateDiagram-35d39939-D7FEhrYs.js} |   2 +-
 ...s => stateDiagram-v2-6c43c13a-C7zU9Dfv.js} |   2 +-
 ...\345\274\200\345\217\221.html-BnsNbJlM.js" |   2 +-
 ...-Cprd53d9.js => strategy.html-BeQd57Ga.js} |   2 +-
 ...tml-CXxr9xzn.js => style.html-4qtN5eOW.js} |   2 +-
 ...XxGUMW8.js => styles-422bd1c9-CFsDtXUv.js} |   2 +-
 ...jk-EQ8n.js => styles-de3becd0-D7QN2-IT.js} |   2 +-
 ...YWOaoPC.js => styles-e2b9d258-CoUUuHq5.js} |   2 +-
 ....js => svgDrawCommon-9d162435-DBc9TLjw.js} |   2 +-
 ...Sl.js => template_method.html-B7oRZ-kS.js} |   2 +-
 ...\350\270\251\345\235\221.html-CtBHw7dX.js" |   2 +-
 ... timeline-definition-6eaa3543-CYqJxmAu.js} |   2 +-
 ...\346\277\200\346\264\273.html-DUOLfN6Y.js" |   2 +-
 ...l-C6V612X1.js => visitor.html-DaIekGHb.js} |   2 +-
 ...\345\260\217\350\256\260.html-BytDpa8J.js" |   2 +-
 ...js => xychartDiagram-4a8b8217-DS1INfpk.js} |   2 +-
 ...\347\204\266\346\225\260.html-NHamcIiY.js" |   2 +-
 ...10\260mobile\347\253\257.html-CKHKQibh.js" |   2 +-
 ...\345\212\240\351\224\201.html-gfcHinKw.js" |   2 +-
 ...\345\215\217\347\250\213.html-BovqfV_l.js" |   2 +-
 ...\351\241\273\346\234\211.html-B46pNP68.js" |   2 +-
 ...5\221\230\347\232\204PPT.html-D4bbFarZ.js" |   2 +-
 ...\347\216\260\347\261\273.html-CeWxsqOK.js" |   2 +-
 category/build-tools/index.html               |   8 +-
 category/cicd/index.html                      |   8 +-
 category/docker/index.html                    |   8 +-
 category/index.html                           |   8 +-
 category/nginx/index.html                     |   8 +-
 category/oi/index.html                        |   8 +-
 category/python/index.html                    |   8 +-
 .../index.html"                               |   8 +-
 .../\346\225\260\345\255\246/index.html"      |   8 +-
 .../index.html"                               |   8 +-
 .../index.html"                               |   8 +-
 .../\351\243\216\346\240\274/index.html"      |   8 +-
 essays/index.html                             |   8 +-
 ...\347\273\210\351\241\273\346\234\211.html" |   6 +-
 index.html                                    |  23 +--
 intro.html                                    |   6 +-
 projects/carrobot.html                        |  40 +++++
 projects/index.html                           |   8 +-
 resources/compile/index.html                  |  40 +++++
 resources/html2md/index.html                  |   8 +-
 resources/index.html                          |   8 +-
 search-pro.worker.js                          |   2 +-
 sitemap.xml                                   |   2 +-
 star/index.html                               |   8 +-
 tag/c/index.html                              |   8 +-
 tag/cicd/index.html                           |   8 +-
 tag/docker/index.html                         |   8 +-
 tag/index.html                                |   8 +-
 tag/mobile/index.html                         |   8 +-
 tag/modint/index.html                         |   8 +-
 tag/typescript/index.html                     |   8 +-
 .../index.html"                               |   8 +-
 .../index.html"                               |   8 +-
 .../index.html"                               |   8 +-
 .../index.html"                               |   8 +-
 .../index.html"                               |   8 +-
 .../index.html"                               |   8 +-
 .../index.html"                               |   8 +-
 "tag/\346\277\200\346\264\273/index.html"     |   8 +-
 .../index.html"                               |   8 +-
 .../index.html"                               |   8 +-
 .../index.html"                               |   8 +-
 .../index.html"                               |   8 +-
 .../index.html"                               |   8 +-
 .../index.html"                               |   8 +-
 .../index.html"                               |   8 +-
 .../index.html"                               |   8 +-
 .../index.html"                               |   8 +-
 .../index.html"                               |   8 +-
 "tag/\351\203\250\347\275\262/index.html"     |   8 +-
 "tag/\351\243\216\346\240\274/index.html"     |   8 +-
 tech/DesignPatterns/DesignPrinciples.html     |   6 +-
 tech/DesignPatterns/abstractFactory.html      |   6 +-
 tech/DesignPatterns/adapter.html              |   6 +-
 tech/DesignPatterns/bridge.html               |   6 +-
 tech/DesignPatterns/builder.html              |   6 +-
 .../DesignPatterns/chainOfResponsibility.html |   6 +-
 tech/DesignPatterns/command.html              |   6 +-
 tech/DesignPatterns/composite.html            |   6 +-
 tech/DesignPatterns/decorator.html            |   6 +-
 tech/DesignPatterns/end.html                  |   6 +-
 tech/DesignPatterns/facade.html               |   6 +-
 tech/DesignPatterns/factory_method.html       |   6 +-
 tech/DesignPatterns/flyweight.html            |   6 +-
 tech/DesignPatterns/index.html                |   6 +-
 tech/DesignPatterns/interpreter.html          |   6 +-
 tech/DesignPatterns/iterator.html             |   6 +-
 tech/DesignPatterns/mediator.html             |   6 +-
 tech/DesignPatterns/memento.html              |   6 +-
 tech/DesignPatterns/observer.html             |   6 +-
 tech/DesignPatterns/prototype.html            |   6 +-
 tech/DesignPatterns/proxy.html                |   6 +-
 tech/DesignPatterns/singleton.html            |   6 +-
 tech/DesignPatterns/state.html                |   6 +-
 tech/DesignPatterns/strategy.html             |   6 +-
 tech/DesignPatterns/template_method.html      |   6 +-
 tech/DesignPatterns/visitor.html              |   6 +-
 ...0\203\275\345\256\211\350\243\205Qt5.html" |   6 +-
 ...droid studio\346\215\242\346\272\220.html" |   6 +-
 tech/cicd.html                                |   6 +-
 tech/designASimpileCCompiler/0.html           |   6 +-
 tech/designASimpileCCompiler/1.html           |   6 +-
 tech/designASimpileCCompiler/2.html           |   6 +-
 tech/designASimpileCCompiler/3.html           |   6 +-
 tech/designASimpileCCompiler/4.html           |   6 +-
 tech/designASimpileCCompiler/5.html           |   6 +-
 tech/designASimpileCCompiler/6.html           |   6 +-
 tech/designASimpileCCompiler/7.html           |   6 +-
 tech/designASimpileCCompiler/8.html           |   6 +-
 tech/designASimpileCCompiler/9.html           |   6 +-
 tech/designASimpileCCompiler/index.html       |   6 +-
 tech/docker.html                              |   6 +-
 ...7\275\262web\351\241\271\347\233\256.html" |   6 +-
 tech/figure_bed.html                          |   6 +-
 ...\345\267\245\344\275\234\346\265\201.html" |   6 +-
 tech/index.html                               |   6 +-
 tech/mailserver.html                          |   6 +-
 tech/modint.html                              |   6 +-
 tech/python_requrements.html                  |   6 +-
 ...\347\273\204\345\274\200\345\217\221.html" |   6 +-
 tech/style.html                               |   6 +-
 .../tensorflow\350\270\251\345\235\221.html"  |   6 +-
 ...\345\217\221\345\260\217\350\256\260.html" |   6 +-
 ...\350\207\252\347\204\266\346\225\260.html" |   6 +-
 ...47\273\345\210\260mobile\347\253\257.html" |   6 +-
 ...\350\246\201\345\212\240\351\224\201.html" |   6 +-
 "tech/\345\215\217\347\250\213.html"          |   6 +-
 ...5\272\217\345\221\230\347\232\204PPT.html" |   6 +-
 ...\345\256\236\347\216\260\347\261\273.html" |   6 +-
 timeline/index.html                           |   8 +-
 tutorials/index.html                          |   6 +-
 .../typora\346\277\200\346\264\273.html"      |   6 +-
 274 files changed, 707 insertions(+), 611 deletions(-)
 rename assets/{0.html-BMihHxnS.js => 0.html-CC8GZdvL.js} (99%)
 rename assets/{1.html-B2woGSgL.js => 1.html-C8e1pvTo.js} (99%)
 rename assets/{2.html-DuLx7xSk.js => 2.html-CfN7D4gf.js} (99%)
 rename assets/{3.html-CZB5joNY.js => 3.html-D9pPtuiP.js} (99%)
 rename assets/{4.html-C8TuLMaF.js => 4.html-DavKkBaH.js} (99%)
 rename assets/{404.html-BC0rHQLu.js => 404.html-CGMXaJuv.js} (93%)
 rename assets/{5.html-qLlLbRlw.js => 5.html-DpkUOZDe.js} (99%)
 rename assets/{6.html-BPGbpgjm.js => 6.html-4dTDTOb4.js} (99%)
 rename assets/{7.html-DopH3hey.js => 7.html-BzOHeKw-.js} (99%)
 rename assets/{8.html-D1TnfZgI.js => 8.html-C-sA1tiy.js} (99%)
 rename assets/{9.html-CGdd1xtP.js => 9.html-DOIgY3Qt.js} (99%)
 rename assets/{DesignPrinciples.html-BLnXHGN8.js => DesignPrinciples.html-BAjp9viD.js} (99%)
 rename "assets/Qt6 Maintence tools\344\270\215\350\203\275\345\256\211\350\243\205Qt5.html-CTk8exni.js" => "assets/Qt6 Maintence tools\344\270\215\350\203\275\345\256\211\350\243\205Qt5.html-DdU1Gd4z.js" (97%)
 create mode 100644 assets/SearchResult-DAas8KH8.js
 delete mode 100644 assets/SearchResult-DUP77o_D.js
 rename assets/{abstractFactory.html-DS3CgVqp.js => abstractFactory.html-D_oh5f2L.js} (99%)
 rename assets/{adapter.html-B2UlYWFL.js => adapter.html-x6kHt0VN.js} (99%)
 rename "assets/android studio\346\215\242\346\272\220.html-CxjDu5df.js" => "assets/android studio\346\215\242\346\272\220.html-DkRIM6mj.js" (98%)
 rename assets/{app-B69Gl_S-.js => app-B4LGNJZ0.js} (63%)
 rename assets/{arc-BCmLGSVu.js => arc-DWlpCdAw.js} (96%)
 rename assets/{blockDiagram-a8a0820c-1CGnBiz2.js => blockDiagram-a8a0820c-DvOSxzpN.js} (98%)
 rename assets/{bridge.html-LTDknqB7.js => bridge.html-DzkNbynT.js} (99%)
 rename assets/{builder.html-Ba33pTyP.js => builder.html-B7MALN7e.js} (99%)
 rename assets/{c4Diagram-dc8f04df-CiA8sQW3.js => c4Diagram-dc8f04df-DWstOjwk.js} (99%)
 create mode 100644 assets/carrobot.html-B7set7IG.js
 rename assets/{chainOfResponsibility.html-DhJtx4gW.js => chainOfResponsibility.html-CpbeYqOk.js} (99%)
 delete mode 100644 assets/channel-DJsAcM5I.js
 create mode 100644 assets/channel-yU22lAlC.js
 rename assets/{cicd.html-CedraPRV.js => cicd.html-BxLHD3yn.js} (98%)
 rename assets/{classDiagram-8298e144-w121JOWu.js => classDiagram-8298e144-DKojaSxZ.js} (97%)
 rename assets/{classDiagram-v2-296fb1cd-BmyNy9b3.js => classDiagram-v2-296fb1cd-DTrZkQpq.js} (92%)
 create mode 100644 assets/clone-C3EvpqoY.js
 delete mode 100644 assets/clone-CI3kFeqi.js
 rename assets/{command.html-d4IhdjVF.js => command.html-Bzqk5uGA.js} (99%)
 rename assets/{composite.html-DOBxYen3.js => composite.html-D89dw1yo.js} (99%)
 rename assets/{createText-4a4f35c9-BuT3nXUz.js => createText-4a4f35c9-CISzj231.js} (99%)
 rename assets/{decorator.html-FfT8RlFX.js => decorator.html-0jwtowLH.js} (99%)
 rename assets/{docker.html-B-hYGcsZ.js => docker.html-DtdutZB7.js} (99%)
 rename "assets/docker_nginx\351\203\250\347\275\262web\351\241\271\347\233\256.html-4IxhKq9E.js" => "assets/docker_nginx\351\203\250\347\275\262web\351\241\271\347\233\256.html-CZONKQdf.js" (99%)
 rename assets/{edges-5962ec63-B19hLEst.js => edges-5962ec63-ApWhby2b.js} (99%)
 rename assets/{end.html-De4ifiEs.js => end.html-CkqhlgwJ.js} (97%)
 rename assets/{erDiagram-51d2b61e-BxYe-GEp.js => erDiagram-51d2b61e-D5StoYmd.js} (99%)
 rename assets/{facade.html-Cj3lyBcS.js => facade.html-BODpRH45.js} (99%)
 rename assets/{factory_method.html-B20phxz9.js => factory_method.html-NuMbQ7is.js} (99%)
 rename assets/{figure_bed.html-BME-hebA.js => figure_bed.html-vyc89ngd.js} (96%)
 rename assets/{flowDb-0da60e67-C3mEtQas.js => flowDb-0da60e67-XaXEQp9e.js} (99%)
 rename assets/{flowDiagram-622f9fc1-C8iBq7aS.js => flowDiagram-622f9fc1-BpT3eoaF.js} (97%)
 create mode 100644 assets/flowDiagram-v2-a33b4996-BQrZXIe9.js
 delete mode 100644 assets/flowDiagram-v2-a33b4996-BVubizbB.js
 rename assets/{flowchart-elk-definition-930acc39-Q-ihdrlR.js => flowchart-elk-definition-930acc39-D2d6YT5I.js} (99%)
 rename assets/{flyweight.html-CWx8TgTS.js => flyweight.html-DUTi0_Qx.js} (99%)
 rename assets/{ganttDiagram-a649f789-B8bnTgqC.js => ganttDiagram-a649f789-B7dFucT2.js} (99%)
 rename assets/{gitGraphDiagram-23af1bdb-BuC3CTB9.js => gitGraphDiagram-23af1bdb-Dd7cNN9F.js} (99%)
 rename "assets/github \345\267\245\344\275\234\346\265\201.html-CFTCrRk5.js" => "assets/github \345\267\245\344\275\234\346\265\201.html-DJORqAx-.js" (97%)
 rename assets/{graph-T5JS4vfK.js => graph-B1296pfd.js} (99%)
 create mode 100644 assets/image-Dc9IOqtq.png
 rename assets/{index-9620d214-B8uh0R2i.js => index-9620d214-BlfbO5wW.js} (96%)
 rename assets/{index.html-CZDJXbd3.js => index.html-B1eL3fl0.js} (94%)
 rename assets/{index.html-B7IKPS0E.js => index.html-BCqj2PVi.js} (94%)
 rename assets/{index.html-0LHdE1Bw.js => index.html-BFj2MrdQ.js} (94%)
 rename assets/{index.html-BlxatHgv.js => index.html-BJX9B5Ij.js} (94%)
 rename assets/{index.html-Bb8RnxYT.js => index.html-BOaWfYA8.js} (93%)
 rename assets/{index.html-DRlrhC7d.js => index.html-BgifGsNR.js} (94%)
 delete mode 100644 assets/index.html-BjAw7f-F.js
 delete mode 100644 assets/index.html-BjDh3PHW.js
 rename assets/{index.html-C8X5E5_U.js => index.html-BjeRhPA4.js} (94%)
 rename assets/{index.html-CXhg3e64.js => index.html-BlsqD0oa.js} (96%)
 create mode 100644 assets/index.html-Bq7J9cN0.js
 rename assets/{index.html-CLOegCHC.js => index.html-BwXv95cV.js} (94%)
 rename assets/{index.html-BtJnl_OK.js => index.html-C9AeqWIc.js} (96%)
 rename assets/{index.html-BK-iNYKv.js => index.html-CE6ffKsf.js} (93%)
 rename assets/{index.html-ZxSgoRoh.js => index.html-CL479cux.js} (94%)
 rename assets/{index.html-B3D_5fpm.js => index.html-COyA9Sec.js} (94%)
 rename assets/{index.html-DDeLtmuh.js => index.html-CVNN5Fwq.js} (93%)
 rename assets/{index.html-DzsdPiFk.js => index.html-CYOJa5u_.js} (94%)
 create mode 100644 assets/index.html-CdwZ1P48.js
 rename assets/{index.html-Dakgazin.js => index.html-CqYdKjYM.js} (93%)
 rename assets/{index.html-B2T3kUK3.js => index.html-CryaZFG_.js} (95%)
 rename assets/{index.html-BZLD09T1.js => index.html-Cw9y1ZOg.js} (94%)
 rename assets/{index.html-DDn6tClc.js => index.html-CzSwk-A5.js} (94%)
 rename assets/{index.html-BKjCcFT0.js => index.html-D8p9fsJ8.js} (93%)
 rename assets/{index.html-VMxXqaQ8.js => index.html-DCZKDe-x.js} (94%)
 rename assets/{index.html-DeH2SCB3.js => index.html-DERlmHfl.js} (93%)
 rename assets/{index.html-BXtqeyHq.js => index.html-DOXbY5aY.js} (93%)
 rename assets/{index.html-B71I-yvI.js => index.html-DOZrz5tX.js} (94%)
 rename assets/{index.html-DR-PJoSN.js => index.html-DW1c3ODz.js} (93%)
 rename assets/{index.html-CcgdDCiF.js => index.html-DYx5t_sy.js} (94%)
 rename assets/{index.html-D2pTqZFy.js => index.html-DeNCk-ye.js} (93%)
 rename assets/{index.html-BSJr7qwh.js => index.html-DhCS_0vf.js} (94%)
 rename assets/{index.html-B5GIg4Ij.js => index.html-Dj_dWWjR.js} (95%)
 rename assets/{index.html-BHNGjpbb.js => index.html-DklcXGYl.js} (95%)
 rename assets/{index.html-Dh_a7h_3.js => index.html-DottIbHL.js} (93%)
 rename assets/{index.html-CGsa9ffM.js => index.html-Dpy8imS-.js} (94%)
 rename assets/{index.html-Dv6rE_pN.js => index.html-DtPJaw_H.js} (98%)
 rename assets/{index.html-BLuB_Eoc.js => index.html-DwPUACaS.js} (94%)
 delete mode 100644 assets/index.html-DzJoMr4P.js
 rename assets/{index.html-ayClYbZ3.js => index.html-F61LMFJS.js} (94%)
 rename assets/{index.html-CRzs15I0.js => index.html-JQfnAIea.js} (94%)
 rename assets/{index.html-kOhwCTdr.js => index.html-NUfXNLwU.js} (94%)
 rename assets/{index.html-BvZSJ2r-.js => index.html-SMm58lXr.js} (93%)
 rename assets/{index.html-Ak5uwHrg.js => index.html-SwHQd6yQ.js} (94%)
 rename assets/{index.html-CO8-8uSt.js => index.html-TRJ6qSMT.js} (93%)
 rename assets/{index.html-UrkKwESw.js => index.html-ZzlVKqB8.js} (94%)
 rename assets/{index.html-BNAyU6dK.js => index.html-auYNF0Cp.js} (94%)
 rename assets/{index.html-DZYdDCPP.js => index.html-hPg6lxSo.js} (94%)
 rename assets/{index.html-QNuKjuoZ.js => index.html-i5A_pLCb.js} (94%)
 create mode 100644 assets/index.html-jwKIpsPi.js
 rename assets/{index.html-bipylPNF.js => index.html-mplfcIL_.js} (93%)
 rename assets/{index.html-CSRSsNOG.js => index.html-rivgPJ9m.js} (94%)
 rename assets/{index.html-BpjUVtkj.js => index.html-y8ELyp0v.js} (93%)
 rename assets/{index.html-9q-r5JHT.js => index.html-yUxPRBBH.js} (94%)
 create mode 100644 assets/index.html-ybZqFA4D.js
 rename assets/{infoDiagram-f86e0131-BJ_tgdHe.js => infoDiagram-f86e0131-BvySRD9D.js} (98%)
 rename assets/{interpreter.html-CansycaD.js => interpreter.html-DfDQyPSV.js} (99%)
 rename assets/{intro.html-CEHYbhC9.js => intro.html-DcelwrZW.js} (97%)
 rename assets/{iterator.html-USsHv5Pr.js => iterator.html-9EjNXcsT.js} (99%)
 rename assets/{journeyDiagram-de0d04b7-DXj0d_vq.js => journeyDiagram-de0d04b7-bCIGoTun.js} (98%)
 rename assets/{layout-DUYLy6Ue.js => layout-qMafh1ee.js} (99%)
 rename assets/{line-D0jG_HZ-.js => line-BqHmcuby.js} (93%)
 rename assets/{linear-CRQH6hcv.js => linear-Cb1OAgs3.js} (99%)
 rename assets/{mailserver.html-DITZCknd.js => mailserver.html-DO5Xbwgi.js} (99%)
 rename assets/{mediator.html-RBFBa63Z.js => mediator.html-C5vte2nl.js} (99%)
 rename assets/{memento.html-CbbBldep.js => memento.html-Dw4vFzUb.js} (99%)
 rename assets/{mermaid.core-ChLYKTZm.js => mermaid.core-DNo_7Q2B.js} (98%)
 rename assets/{mindmap-definition-b08d3ac4-DYSC8IDG.js => mindmap-definition-b08d3ac4-CtqZ8Vgk.js} (99%)
 rename assets/{modint.html-M2GwLZ2U.js => modint.html-DNrISIPe.js} (99%)
 rename assets/{observer.html-BvrPoU9w.js => observer.html-DCoBW7Y-.js} (99%)
 rename assets/{pieDiagram-31d824a1-CV6f6fQ6.js => pieDiagram-31d824a1-BIcjeA1S.js} (98%)
 rename assets/{prototype.html-Boe-0El2.js => prototype.html-Be3THUal.js} (99%)
 rename assets/{proxy.html-CSHBH0Xk.js => proxy.html-DydmfTHY.js} (99%)
 rename assets/{python_requrements.html-Va55tBYB.js => python_requrements.html-D_iboyN4.js} (97%)
 rename assets/{quadrantDiagram-a712a7d9-Bu83u7Zz.js => quadrantDiagram-a712a7d9-CNklQ4II.js} (99%)
 rename assets/{requirementDiagram-eb878fee-DPiNb9b5.js => requirementDiagram-eb878fee-OFUpKWxv.js} (98%)
 rename assets/{sankeyDiagram-c599f8ec-BGnWqC27.js => sankeyDiagram-c599f8ec-Ss3oz1oB.js} (99%)
 rename assets/{sequenceDiagram-66748113-MIUFy2Oj.js => sequenceDiagram-66748113-sH_v1_cD.js} (99%)
 rename assets/{singleton.html-Pzh1ZzrO.js => singleton.html-CJylCsqx.js} (99%)
 rename assets/{state.html-DsXXtCU9.js => state.html-D0BJywlY.js} (99%)
 rename assets/{stateDiagram-35d39939-BlCBJSJX.js => stateDiagram-35d39939-D7FEhrYs.js} (97%)
 rename assets/{stateDiagram-v2-6c43c13a-CtOdsXqX.js => stateDiagram-v2-6c43c13a-C7zU9Dfv.js} (90%)
 rename "assets/steam\346\250\241\347\273\204\345\274\200\345\217\221.html-DQKsmuFu.js" => "assets/steam\346\250\241\347\273\204\345\274\200\345\217\221.html-BnsNbJlM.js" (98%)
 rename assets/{strategy.html-Cprd53d9.js => strategy.html-BeQd57Ga.js} (99%)
 rename assets/{style.html-CXxr9xzn.js => style.html-4qtN5eOW.js} (98%)
 rename assets/{styles-422bd1c9-CXxGUMW8.js => styles-422bd1c9-CFsDtXUv.js} (98%)
 rename assets/{styles-de3becd0-Bjk-EQ8n.js => styles-de3becd0-D7QN2-IT.js} (99%)
 rename assets/{styles-e2b9d258-TYWOaoPC.js => styles-e2b9d258-CoUUuHq5.js} (99%)
 rename assets/{svgDrawCommon-9d162435-DXbPg0E8.js => svgDrawCommon-9d162435-DBc9TLjw.js} (95%)
 rename assets/{template_method.html-Do5aF6Sl.js => template_method.html-B7oRZ-kS.js} (99%)
 rename "assets/tensorflow\350\270\251\345\235\221.html-BAaphJ4H.js" => "assets/tensorflow\350\270\251\345\235\221.html-CtBHw7dX.js" (97%)
 rename assets/{timeline-definition-6eaa3543-BApSUGyX.js => timeline-definition-6eaa3543-CYqJxmAu.js} (99%)
 rename "assets/typora\346\277\200\346\264\273.html-BuwKOD8g.js" => "assets/typora\346\277\200\346\264\273.html-DUOLfN6Y.js" (98%)
 rename assets/{visitor.html-C6V612X1.js => visitor.html-DaIekGHb.js} (99%)
 rename "assets/vsocde\346\217\222\344\273\266\345\274\200\345\217\221\345\260\217\350\256\260.html-DtdCKw5q.js" => "assets/vsocde\346\217\222\344\273\266\345\274\200\345\217\221\345\260\217\350\256\260.html-BytDpa8J.js" (97%)
 rename assets/{xychartDiagram-4a8b8217-CYu3f7i9.js => xychartDiagram-4a8b8217-DS1INfpk.js} (99%)
 rename "assets/\343\200\214\347\256\227\346\234\257\345\205\254\347\220\206\347\263\273\347\273\237 1\343\200\215\350\207\252\347\204\266\346\225\260.html-CtzEDcR8.js" => "assets/\343\200\214\347\256\227\346\234\257\345\205\254\347\220\206\347\263\273\347\273\237 1\343\200\215\350\207\252\347\204\266\346\225\260.html-NHamcIiY.js" (99%)
 rename "assets/\344\275\277\347\224\250capacitor\345\222\214ionic\345\260\206vue\351\241\271\347\233\256\350\277\201\347\247\273\345\210\260mobile\347\253\257.html-CjY4pFX9.js" => "assets/\344\275\277\347\224\250capacitor\345\222\214ionic\345\260\206vue\351\241\271\347\233\256\350\277\201\347\247\273\345\210\260mobile\347\253\257.html-CKHKQibh.js" (98%)
 rename "assets/\345\215\217\347\250\213(asyncio)\345\210\260\345\272\225\351\234\200\344\270\215\351\234\200\350\246\201\345\212\240\351\224\201.html-CTO2grll.js" => "assets/\345\215\217\347\250\213(asyncio)\345\210\260\345\272\225\351\234\200\344\270\215\351\234\200\350\246\201\345\212\240\351\224\201.html-gfcHinKw.js" (99%)
 rename "assets/\345\215\217\347\250\213.html-LdIMvjSl.js" => "assets/\345\215\217\347\250\213.html-BovqfV_l.js" (93%)
 rename "assets/\345\221\275\351\207\214\346\234\211\346\227\266\347\273\210\351\241\273\346\234\211.html-DOvT7-xg.js" => "assets/\345\221\275\351\207\214\346\234\211\346\227\266\347\273\210\351\241\273\346\234\211.html-B46pNP68.js" (97%)
 rename "assets/\347\250\213\345\272\217\345\221\230\347\232\204PPT.html-CmGk8DAJ.js" => "assets/\347\250\213\345\272\217\345\221\230\347\232\204PPT.html-D4bbFarZ.js" (98%)
 rename "assets/\351\227\255\345\214\205\345\256\236\347\216\260\347\261\273.html-DjTAmLiV.js" => "assets/\351\227\255\345\214\205\345\256\236\347\216\260\347\261\273.html-CeWxsqOK.js" (99%)
 create mode 100644 projects/carrobot.html
 create mode 100644 resources/compile/index.html

diff --git a/404.html b/404.html
index 53300cf..7b45a30 100644
--- a/404.html
+++ b/404.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/404.html"><meta property="og:site_name" content="blog"><meta property="og:description" content="404 Not Found"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"","description":"404 Not Found"}</script><title>blog</title><meta name="description" content="404 Not Found">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/404.html-BC0rHQLu.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/404.html-CGMXaJuv.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
-    <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page not-found"><div class="not-found-hint"><p class="error-code">404</p><h1 class="error-title">页面不存在</h1><p class="error-hint">我们是怎么来到这儿的？</p></div><div class="actions"><button type="button" class="action-button">返回上一页</button><button type="button" class="action-button">带我回家</button></div></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page not-found"><div class="not-found-hint"><p class="error-code">404</p><h1 class="error-title">页面不存在</h1><p class="error-hint">这 是 四 零 四 !</p></div><div class="actions"><button type="button" class="action-button">返回上一页</button><button type="button" class="action-button">带我回家</button></div></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/article/index.html b/article/index.html
index 7665a35..4314d62 100644
--- a/article/index.html
+++ b/article/index.html
@@ -30,11 +30,19 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/article/"><meta property="og:site_name" content="blog"><meta property="og:title" content="文章"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"文章"}</script><title>文章 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-DeH2SCB3.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-DERlmHfl.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
-    <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="vp-article-type-wrapper"><li class="vp-article-type active"><a class="route-link" href="/article/">全部</a></li><li class="vp-article-type"><a class="route-link" href="/star/">星标</a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/figure_bed.html"><header class="vp-article-title"><!----><!----><span property="headline">github 图床</span></header></a><div class="vp-article-excerpt"><p>参考</p>
+    <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="vp-article-type-wrapper"><li class="vp-article-type active"><a class="route-link" href="/article/">全部</a></li><li class="vp-article-type"><a class="route-link" href="/star/">星标</a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/projects/carrobot.html"><header class="vp-article-title"><!----><!----><span property="headline">北京邮电大学创新创业智能车循迹python版</span></header></a><div class="vp-article-excerpt"><p><a href="https://github.com/king-sj/carrobot" target="_blank" rel="noopener noreferrer">项目源码</a></p>
+<p><s>因为想要创新学分，所以选了创新创业智能车课程</s>，项目要求完成智能车的循迹和避障。</p>
+<p>由于笔者不喜欢使用VPL的图形化（<s>报用qWq</s>）, 故而使用手写代码的方式实现。</p>
+</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-11-07T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 4 分钟</span><meta property="timeRequired" content="PT4M"></span><!----><!----></div></article></div><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/resources/compile/"><header class="vp-article-title"><!----><!----><span property="headline">编译原理相关</span></header></a><div class="vp-article-excerpt"><ul>
+<li>anltr.grammar</li>
+<li>bison/yacc</li>
+<li>flex</li>
+</ul>
+</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-11-06T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><!----></div></article></div><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/figure_bed.html"><header class="vp-article-title"><!----><!----><span property="headline">github 图床</span></header></a><div class="vp-article-excerpt"><p>参考</p>
 <ul>
 <li>https://zhuanlan.zhihu.com/p/347342082</li>
 </ul>
@@ -64,12 +72,7 @@ <h2>示例代码</h2>
 <li><strong>简化语法解析</strong>：通过定义文法规则，可以轻松解析和执行特定的语言或指令集。</li>
 <li><strong>可扩展性</strong>：可以轻松添加新的语法规则或指令，而无需修改现有代码。</li>
 <li><strong>代码复用</strong>：通过将不同的语法规则封装在不同的类中，可以提高代码的复用性和可维护性。</li>
-</ol></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-29T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 3 分钟</span><meta property="timeRequired" content="PT3M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag1 clickable" role="navigation">用类实现</span><!--]--><meta property="keywords" content="设计模式,TypeScript,用类实现"></span></div></article></div><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/DesignPatterns/proxy.html"><header class="vp-article-title"><!----><!----><span property="headline">Proxy 模式</span></header></a><div class="vp-article-excerpt"><h2>为什么使用代理模式</h2>
-<p>在面向对象编程中，“本人”和“代理人”都是对象。如果“本人”对象太忙了．有些工作无法自己亲自完成，就将其交给“代理人"对象负责。</p>
-</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-29T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag5 clickable" role="navigation">避免浪费</span><!--]--><meta property="keywords" content="设计模式,TypeScript,避免浪费"></span></div></article></div><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/DesignPatterns/flyweight.html"><header class="vp-article-title"><!----><!----><span property="headline">Flyweight 模式</span></header></a><div class="vp-article-excerpt"><h2>为什么使用 Flyweight 模式</h2>
-<p>Flyweight 模式是一种结构型设计模式，它通过共享尽可能多的相同对象来减少内存使用，从而提高性能。在需要生成大量细粒度对象的场景中，Flyweight 模式非常有用。通过共享对象，Flyweight 模式可以显著减少内存消耗，并提高应用程序的效率。</p>
-<h2>实例代码</h2>
-<img src="https://www.plantuml.com/plantuml/svg/RL7B2i8m4BpdA_ROKli3GKfH43nuyYWUrZJMG4rAinL4_7VJz5rxMsPsPcTtKqjOKVqic2ZGMjYfVF_02ZuC80RXIerFoS5IfNJkmRlHb27X18oWT1K58OUNKHdxihdT0GMPwjsvbiOK74vORbk3JT-MUDeb8YN0EgQGP3HVkBJ9Z7RYkW62q2VePBcaewDG2zd4-PD6JKU71ilzHi5iXRCdk_GtbJSoExHUhjvsciWLW-NwUHQ7YUDac3mEdA3z0giaIwNEt0z_" alt=""></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-28T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 8 分钟</span><meta property="timeRequired" content="PT8M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag5 clickable" role="navigation">避免浪费</span><!--]--><meta property="keywords" content="设计模式,TypeScript,避免浪费"></span></div></article></div><div class="vp-pagination"><nav class="vp-pagination-list"><div class="vp-pagination-number"><!----><!----><!--[--><div class="active" role="navigation">1</div><div class="" role="navigation">2</div><div class="" role="navigation">3</div><div class="" role="navigation">4</div><div class="" role="navigation">5</div><!--]--><!--[--><div class="ellipsis">...</div><div role="navigation">7</div><!--]--><div class="next" role="navigation" unselectable="on">下一页</div></div><div class="vp-pagination-nav"><label for="navigation-text">跳转到: </label><input id="navigation-text" value><button class="vp-pagination-button" type="button" role="navigation" title="前往">前往</button></div></nav></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</ol></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-29T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 3 分钟</span><meta property="timeRequired" content="PT3M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag1 clickable" role="navigation">用类实现</span><!--]--><meta property="keywords" content="设计模式,TypeScript,用类实现"></span></div></article></div><div class="vp-pagination"><nav class="vp-pagination-list"><div class="vp-pagination-number"><!----><!----><!--[--><div class="active" role="navigation">1</div><div class="" role="navigation">2</div><div class="" role="navigation">3</div><div class="" role="navigation">4</div><div class="" role="navigation">5</div><!--]--><!--[--><div class="ellipsis">...</div><div role="navigation">7</div><!--]--><div class="next" role="navigation" unselectable="on">下一页</div></div><div class="vp-pagination-nav"><label for="navigation-text">跳转到: </label><input id="navigation-text" value><button class="vp-pagination-button" type="button" role="navigation" title="前往">前往</button></div></nav></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/assets/0.html-BMihHxnS.js b/assets/0.html-CC8GZdvL.js
similarity index 99%
rename from assets/0.html-BMihHxnS.js
rename to assets/0.html-CC8GZdvL.js
index 94991b6..13be91d 100644
--- a/assets/0.html-BMihHxnS.js
+++ b/assets/0.html-CC8GZdvL.js
@@ -1 +1 @@
-import{_ as l,r as a,o as i,c as p,b as e,e as t,d as n,f as o}from"./app-B69Gl_S-.js";const s={},h=e("h1",{id:"转载声明",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#转载声明"},[e("span",null,"转载声明")])],-1),c=e("strong",null,"手把手教你构建 C 语言编译器（0）- 前言",-1),d=e("strong",null,"三点水",-1),_={href:"https://lotabout.me/2015/write-a-C-interpreter-0/",target:"_blank",rel:"noopener noreferrer"},u={href:"https://devtool.tech/html-md",target:"_blank",rel:"noopener noreferrer"},f={href:"https://www.helloworld.net/html2md",target:"_blank",rel:"noopener noreferrer"},m=e("h1",{id:"原文内容",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#原文内容"},[e("span",null,"原文内容")])],-1),g=e("p",null,"“手把手教你构建 C 语言编译器” 这一系列教程将带你从头编写一个 C 语言的编译器。希望通过这个系列，我们能对编译器的构建有一定的了解，同时，我们也将构建出一个能用的 C 语言编译器，尽管有许多语法并不支持。",-1),C=e("p",null,"手把手教你构建 C 语言编译器系列共有10个部分：",-1),b={href:"http://lotabout.me/2015/write-a-C-interpreter-0/",target:"_blank",rel:"noopener noreferrer"},E={href:"http://lotabout.me/2015/write-a-C-interpreter-1/",target:"_blank",rel:"noopener noreferrer"},k={href:"http://lotabout.me/2015/write-a-C-interpreter-2/",target:"_blank",rel:"noopener noreferrer"},w={href:"http://lotabout.me/2015/write-a-C-interpreter-3/",target:"_blank",rel:"noopener noreferrer"},B={href:"http://lotabout.me/2016/write-a-C-interpreter-4/",target:"_blank",rel:"noopener noreferrer"},x={href:"http://lotabout.me/2016/write-a-C-interpreter-5/",target:"_blank",rel:"noopener noreferrer"},A={href:"http://lotabout.me/2016/write-a-C-interpreter-6/",target:"_blank",rel:"noopener noreferrer"},v={href:"http://lotabout.me/2016/write-a-C-interpreter-7/",target:"_blank",rel:"noopener noreferrer"},y={href:"http://lotabout.me/2016/write-a-C-interpreter-8/",target:"_blank",rel:"noopener noreferrer"},L={href:"http://lotabout.me/2016/write-a-C-interpreter-9/",target:"_blank",rel:"noopener noreferrer"},D=o('<p>在开始进入正题之前，本篇是一些闲聊，谈谈这个系列的初衷。如果你急切地想进入正篇，请跳过本章。</p><h2 id="为什么要学编译原理" tabindex="-1"><a class="header-anchor" href="#为什么要学编译原理"><span><a href="#%E4%B8%BA%E4%BB%80%E4%B9%88%E8%A6%81%E5%AD%A6%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86"></a>为什么要学编译原理</span></a></h2><p>如果要我说计算机专业最重要的三门课，我会说是《数据结构》、《算法》和《编译原理》。在我看来，能不能理解“递归”像是程序员的第一道门槛，而会不会写编译器则是第二道。</p><p>（当然，并不是说是没写过编译器就不是好程序员，只能说它是一个相当大的挑战吧）</p><p>以前人们会说，学习了编译原理，你就能写出更加高效的代码，但随着计算机性能的提升，代码是否高效显得就不那么重要了。那么为什么要学习编译原理呢？</p><p>原因只有一个：装B。</p><p>好吧，也许现在还想学习编译原理的人只可能是因为兴趣了。一方面想了解它的工作原理；另一方面希望挑战一下自己，看看自己能走多远。</p><h2 id="理论很复杂-实现也很复杂" tabindex="-1"><a class="header-anchor" href="#理论很复杂-实现也很复杂"><span><a href="#%E7%90%86%E8%AE%BA%E5%BE%88%E5%A4%8D%E6%9D%82-%E5%AE%9E%E7%8E%B0%E4%B9%9F%E5%BE%88%E5%A4%8D%E6%9D%82%EF%BC%9F"></a>理论很复杂，实现也很复杂？</span></a></h2><p>我对编译器一直心存敬佩。所以当学校开《编译原理》的课程后，我是抱着满腔热情去上课的，但是两节课后我就放弃了。原因是太复杂了，听不懂。</p><p>一般编译原理的课程会说一些：</p><ol><li>如何表示语法（BNF什么的）</li><li>词法分析，用什么有穷自动机和无穷自动机</li><li>语法分析，递归下降法，什么 <code>LL(k)</code>，LALR 分析。</li><li>中间代码的表示</li><li>代码的生成</li><li>代码优化</li></ol><p>我相信绝大多数（98％）的学生顶多学到语法分析就结束了。并且最重要的是，学了这么多也没用！依旧帮助不了我们学习编译器！这其中最主要的原因是《编译原理》试图教会我们的是如何构造“编译器生成器”，即构造一个工具，根据文法来生成编译器（如 lex/yacc）等等。</p><p>这些理论试图教会我们如何用通用的方法来自动解决问题，它们有很强的实际意义，只是对于一般的学生或程序员来说，它们过于强大，内容过于复杂。如果你尝试阅读 lex/yacc （或 flex/bison）的代码，就会发现太可怕了。</p><p>然而如果你能跟我一样，真正来实现一个简单的编译器，那么你会发现，比起可怕的《编译原理》，这点复杂度还是不算什么的（因为好多理论根本用不上）。</p><h2 id="项目的初衷" tabindex="-1"><a class="header-anchor" href="#项目的初衷"><span><a href="#%E9%A1%B9%E7%9B%AE%E7%9A%84%E5%88%9D%E8%A1%B7"></a>项目的初衷</span></a></h2>',15),F={href:"https://github.com/rswier/c4",target:"_blank",rel:"noopener noreferrer"},N=e("p",null,"一般的编译器相关的教程要么就十分简单（如实现四则运算），要么就是借助了自动生成的工具（如 flex/bison）。而 c4 的代码完全是手工实现的，不用外部工具。可惜的是它的代码初衷是代码最小化，所以写得很乱，很难懂。所以本项目的主要目的：",-1),S=e("ol",null,[e("li",null,"实现一个功能完善的 C 语言编译器"),e("li",null,"通过教程来说明这个过程。")],-1),j={href:"https://github.com/lotabout/write-a-C-interpreter",target:"_blank",rel:"noopener noreferrer"},I=o('<p>声明：本项目中的代码逻辑绝大多数取自 c4 ，但确为自己重写。</p><h2 id="做好心理准备" tabindex="-1"><a class="header-anchor" href="#做好心理准备"><span><a href="#%E5%81%9A%E5%A5%BD%E5%BF%83%E7%90%86%E5%87%86%E5%A4%87"></a>做好心理准备</span></a></h2><p>在写编译器的时候会遇到两个主要问题：</p><ol><li>繁琐，会有许多相似的代码，写起来很无聊。</li><li>难以调试，一方面没有很好的测试用例，另一方面需要对照生成的代码来调试（遇到的时候就知道了）。</li></ol><p>所以我希望你有足够的耐心和时间来学习，相信当你真正完成的时候会像我一样，十分有成就感。</p><p>PS. 第一篇完全没有正题相关的内容也是希望你能有所心理准备再开始学习。</p><h2 id="参考资料" tabindex="-1"><a class="header-anchor" href="#参考资料"><span><a href="#%E5%8F%82%E8%80%83%E8%B5%84%E6%96%99"></a>参考资料</span></a></h2><p>最后想介绍几个资料：</p>',8),K={href:"http://compilers.iecc.com/crenshaw/",target:"_blank",rel:"noopener noreferrer"},P={href:"http://www.hwaci.com/sw/lemon/",target:"_blank",rel:"noopener noreferrer"},V=e("p",null,"由于本人水平一般，文章、代码难免会有错误，敬请批评指正！",-1),J=e("p",null,"最后祝你学得愉快。",-1),O=e("h1",{id:"转载者注",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#转载者注"},[e("span",null,"转载者注")])],-1),T=e("p",null,"这篇博客并没有使用诸如 flex、bison 等工具来编写 token 和文法的定义，因而灵活性较差。相反，它通过定义自己的指令集并支持该指令集的虚拟机来模拟编译的部分过程，具有一定的参考价值。不过，我仍然认为通过定义 token 和文法并编写解析算法（如 regex、LL(k) 等）可能会更具普适性。",-1),z=e("div",{class:"hint-container info"},[e("p",{class:"hint-container-title"},"相关信息"),e("p",null,"不过据说c、cpp、java这些成熟的语言都是手动实现的？还没仔细了解过。 TODO")],-1);function G(R,M){const r=a("ExternalLinkIcon");return i(),p("div",null,[h,e("p",null,[t("本文转载自 "),c,t("，原作者 "),d,t("，原文链接："),e("a",_,[t("原文链接"),n(r)]),t("，如有侵权，请联系删除。")]),e("p",null,[t("转载工具:"),e("a",u,[t("devtool"),n(r)]),t("、"),e("a",f,[t("helloworld"),n(r)])]),m,g,C,e("ol",null,[e("li",null,[e("a",b,[t("手把手教你构建 C 语言编译器（0）——前言"),n(r)])]),e("li",null,[e("a",E,[t("手把手教你构建 C 语言编译器（1）——设计"),n(r)])]),e("li",null,[e("a",k,[t("手把手教你构建 C 语言编译器（2）——虚拟机"),n(r)])]),e("li",null,[e("a",w,[t("手把手教你构建 C 语言编译器（3）——词法分析器"),n(r)])]),e("li",null,[e("a",B,[t("手把手教你构建 C 语言编译器（4）——递归下降"),n(r)])]),e("li",null,[e("a",x,[t("手把手教你构建 C 语言编译器（5）——变量定义"),n(r)])]),e("li",null,[e("a",A,[t("手把手教你构建 C 语言编译器（6）——函数定义"),n(r)])]),e("li",null,[e("a",v,[t("手把手教你构建 C 语言编译器（7）——语句"),n(r)])]),e("li",null,[e("a",y,[t("手把手教你构建 C 语言编译器（8）——表达式"),n(r)])]),e("li",null,[e("a",L,[t("手把手教你构建 C 语言编译器（9）——总结"),n(r)])])]),D,e("p",null,[t("有一次在 Github 上看到了一个项目（当时很火的），名叫 "),e("a",F,[t("c4"),n(r)]),t("，号称用 4 个函数来实现了一个小的 C 语言编译器。它最让我震惊的是能够自举，即能自己编译自己。并且它用很少的代码就完成了一个功能相当完善的 C 语言编译器。")]),N,S,e("p",null,[t("c4 大致500+行。重写的代码历时一周，总共代码加注释1400行。项目地址: "),e("a",j,[t("Write a C Interpreter"),n(r)]),t("。")]),I,e("ol",null,[e("li",null,[e("a",K,[t("Let’s Build a Compiler"),n(r)]),t(" 很好的初学者教程，英文的。")]),e("li",null,[e("a",P,[t("Lemon Parser Generator"),n(r)]),t("，一个语法分析器生成器，对照《编译原理》观看效果更佳。")])]),V,J,O,T,z])}const q=l(s,[["render",G],["__file","0.html.vue"]]),H=JSON.parse('{"path":"/tech/designASimpileCCompiler/0.html","title":"手把手教你构建 C 语言编译器（0）- 前言","lang":"zh-CN","frontmatter":{"title":"手把手教你构建 C 语言编译器（0）- 前言","category":["编译原理"],"tag":["c","编译器","解释器"],"description":"转载声明 本文转载自 手把手教你构建 C 语言编译器（0）- 前言，原作者 三点水，原文链接：原文链接，如有侵权，请联系删除。 转载工具:devtool、helloworld 原文内容 “手把手教你构建 C 语言编译器” 这一系列教程将带你从头编写一个 C 语言的编译器。希望通过这个系列，我们能对编译器的构建有一定的了解，同时，我们也将构建出一个能用的...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/designASimpileCCompiler/0.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"手把手教你构建 C 语言编译器（0）- 前言"}],["meta",{"property":"og:description","content":"转载声明 本文转载自 手把手教你构建 C 语言编译器（0）- 前言，原作者 三点水，原文链接：原文链接，如有侵权，请联系删除。 转载工具:devtool、helloworld 原文内容 “手把手教你构建 C 语言编译器” 这一系列教程将带你从头编写一个 C 语言的编译器。希望通过这个系列，我们能对编译器的构建有一定的了解，同时，我们也将构建出一个能用的..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"c"}],["meta",{"property":"article:tag","content":"编译器"}],["meta",{"property":"article:tag","content":"解释器"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"手把手教你构建 C 语言编译器（0）- 前言\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"为什么要学编译原理","slug":"为什么要学编译原理","link":"#为什么要学编译原理","children":[]},{"level":2,"title":"理论很复杂，实现也很复杂？","slug":"理论很复杂-实现也很复杂","link":"#理论很复杂-实现也很复杂","children":[]},{"level":2,"title":"项目的初衷","slug":"项目的初衷","link":"#项目的初衷","children":[]},{"level":2,"title":"做好心理准备","slug":"做好心理准备","link":"#做好心理准备","children":[]},{"level":2,"title":"参考资料","slug":"参考资料","link":"#参考资料","children":[]}],"readingTime":{"minutes":6.12,"words":1835},"filePathRelative":"tech/designASimpileCCompiler/0.md","excerpt":"\\n<p>本文转载自 <strong>手把手教你构建 C 语言编译器（0）- 前言</strong>，原作者 <strong>三点水</strong>，原文链接：<a href=\\"https://lotabout.me/2015/write-a-C-interpreter-0/\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">原文链接</a>，如有侵权，请联系删除。</p>\\n<p>转载工具:<a href=\\"https://devtool.tech/html-md\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">devtool</a>、<a href=\\"https://www.helloworld.net/html2md\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">helloworld</a></p>","autoDesc":true}');export{q as comp,H as data};
+import{_ as l,r as a,o as i,c as p,b as e,e as t,d as n,f as o}from"./app-B4LGNJZ0.js";const s={},h=e("h1",{id:"转载声明",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#转载声明"},[e("span",null,"转载声明")])],-1),c=e("strong",null,"手把手教你构建 C 语言编译器（0）- 前言",-1),d=e("strong",null,"三点水",-1),_={href:"https://lotabout.me/2015/write-a-C-interpreter-0/",target:"_blank",rel:"noopener noreferrer"},u={href:"https://devtool.tech/html-md",target:"_blank",rel:"noopener noreferrer"},f={href:"https://www.helloworld.net/html2md",target:"_blank",rel:"noopener noreferrer"},m=e("h1",{id:"原文内容",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#原文内容"},[e("span",null,"原文内容")])],-1),g=e("p",null,"“手把手教你构建 C 语言编译器” 这一系列教程将带你从头编写一个 C 语言的编译器。希望通过这个系列，我们能对编译器的构建有一定的了解，同时，我们也将构建出一个能用的 C 语言编译器，尽管有许多语法并不支持。",-1),C=e("p",null,"手把手教你构建 C 语言编译器系列共有10个部分：",-1),b={href:"http://lotabout.me/2015/write-a-C-interpreter-0/",target:"_blank",rel:"noopener noreferrer"},E={href:"http://lotabout.me/2015/write-a-C-interpreter-1/",target:"_blank",rel:"noopener noreferrer"},k={href:"http://lotabout.me/2015/write-a-C-interpreter-2/",target:"_blank",rel:"noopener noreferrer"},w={href:"http://lotabout.me/2015/write-a-C-interpreter-3/",target:"_blank",rel:"noopener noreferrer"},B={href:"http://lotabout.me/2016/write-a-C-interpreter-4/",target:"_blank",rel:"noopener noreferrer"},x={href:"http://lotabout.me/2016/write-a-C-interpreter-5/",target:"_blank",rel:"noopener noreferrer"},A={href:"http://lotabout.me/2016/write-a-C-interpreter-6/",target:"_blank",rel:"noopener noreferrer"},v={href:"http://lotabout.me/2016/write-a-C-interpreter-7/",target:"_blank",rel:"noopener noreferrer"},y={href:"http://lotabout.me/2016/write-a-C-interpreter-8/",target:"_blank",rel:"noopener noreferrer"},L={href:"http://lotabout.me/2016/write-a-C-interpreter-9/",target:"_blank",rel:"noopener noreferrer"},D=o('<p>在开始进入正题之前，本篇是一些闲聊，谈谈这个系列的初衷。如果你急切地想进入正篇，请跳过本章。</p><h2 id="为什么要学编译原理" tabindex="-1"><a class="header-anchor" href="#为什么要学编译原理"><span><a href="#%E4%B8%BA%E4%BB%80%E4%B9%88%E8%A6%81%E5%AD%A6%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86"></a>为什么要学编译原理</span></a></h2><p>如果要我说计算机专业最重要的三门课，我会说是《数据结构》、《算法》和《编译原理》。在我看来，能不能理解“递归”像是程序员的第一道门槛，而会不会写编译器则是第二道。</p><p>（当然，并不是说是没写过编译器就不是好程序员，只能说它是一个相当大的挑战吧）</p><p>以前人们会说，学习了编译原理，你就能写出更加高效的代码，但随着计算机性能的提升，代码是否高效显得就不那么重要了。那么为什么要学习编译原理呢？</p><p>原因只有一个：装B。</p><p>好吧，也许现在还想学习编译原理的人只可能是因为兴趣了。一方面想了解它的工作原理；另一方面希望挑战一下自己，看看自己能走多远。</p><h2 id="理论很复杂-实现也很复杂" tabindex="-1"><a class="header-anchor" href="#理论很复杂-实现也很复杂"><span><a href="#%E7%90%86%E8%AE%BA%E5%BE%88%E5%A4%8D%E6%9D%82-%E5%AE%9E%E7%8E%B0%E4%B9%9F%E5%BE%88%E5%A4%8D%E6%9D%82%EF%BC%9F"></a>理论很复杂，实现也很复杂？</span></a></h2><p>我对编译器一直心存敬佩。所以当学校开《编译原理》的课程后，我是抱着满腔热情去上课的，但是两节课后我就放弃了。原因是太复杂了，听不懂。</p><p>一般编译原理的课程会说一些：</p><ol><li>如何表示语法（BNF什么的）</li><li>词法分析，用什么有穷自动机和无穷自动机</li><li>语法分析，递归下降法，什么 <code>LL(k)</code>，LALR 分析。</li><li>中间代码的表示</li><li>代码的生成</li><li>代码优化</li></ol><p>我相信绝大多数（98％）的学生顶多学到语法分析就结束了。并且最重要的是，学了这么多也没用！依旧帮助不了我们学习编译器！这其中最主要的原因是《编译原理》试图教会我们的是如何构造“编译器生成器”，即构造一个工具，根据文法来生成编译器（如 lex/yacc）等等。</p><p>这些理论试图教会我们如何用通用的方法来自动解决问题，它们有很强的实际意义，只是对于一般的学生或程序员来说，它们过于强大，内容过于复杂。如果你尝试阅读 lex/yacc （或 flex/bison）的代码，就会发现太可怕了。</p><p>然而如果你能跟我一样，真正来实现一个简单的编译器，那么你会发现，比起可怕的《编译原理》，这点复杂度还是不算什么的（因为好多理论根本用不上）。</p><h2 id="项目的初衷" tabindex="-1"><a class="header-anchor" href="#项目的初衷"><span><a href="#%E9%A1%B9%E7%9B%AE%E7%9A%84%E5%88%9D%E8%A1%B7"></a>项目的初衷</span></a></h2>',15),F={href:"https://github.com/rswier/c4",target:"_blank",rel:"noopener noreferrer"},N=e("p",null,"一般的编译器相关的教程要么就十分简单（如实现四则运算），要么就是借助了自动生成的工具（如 flex/bison）。而 c4 的代码完全是手工实现的，不用外部工具。可惜的是它的代码初衷是代码最小化，所以写得很乱，很难懂。所以本项目的主要目的：",-1),S=e("ol",null,[e("li",null,"实现一个功能完善的 C 语言编译器"),e("li",null,"通过教程来说明这个过程。")],-1),j={href:"https://github.com/lotabout/write-a-C-interpreter",target:"_blank",rel:"noopener noreferrer"},I=o('<p>声明：本项目中的代码逻辑绝大多数取自 c4 ，但确为自己重写。</p><h2 id="做好心理准备" tabindex="-1"><a class="header-anchor" href="#做好心理准备"><span><a href="#%E5%81%9A%E5%A5%BD%E5%BF%83%E7%90%86%E5%87%86%E5%A4%87"></a>做好心理准备</span></a></h2><p>在写编译器的时候会遇到两个主要问题：</p><ol><li>繁琐，会有许多相似的代码，写起来很无聊。</li><li>难以调试，一方面没有很好的测试用例，另一方面需要对照生成的代码来调试（遇到的时候就知道了）。</li></ol><p>所以我希望你有足够的耐心和时间来学习，相信当你真正完成的时候会像我一样，十分有成就感。</p><p>PS. 第一篇完全没有正题相关的内容也是希望你能有所心理准备再开始学习。</p><h2 id="参考资料" tabindex="-1"><a class="header-anchor" href="#参考资料"><span><a href="#%E5%8F%82%E8%80%83%E8%B5%84%E6%96%99"></a>参考资料</span></a></h2><p>最后想介绍几个资料：</p>',8),K={href:"http://compilers.iecc.com/crenshaw/",target:"_blank",rel:"noopener noreferrer"},P={href:"http://www.hwaci.com/sw/lemon/",target:"_blank",rel:"noopener noreferrer"},V=e("p",null,"由于本人水平一般，文章、代码难免会有错误，敬请批评指正！",-1),J=e("p",null,"最后祝你学得愉快。",-1),O=e("h1",{id:"转载者注",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#转载者注"},[e("span",null,"转载者注")])],-1),T=e("p",null,"这篇博客并没有使用诸如 flex、bison 等工具来编写 token 和文法的定义，因而灵活性较差。相反，它通过定义自己的指令集并支持该指令集的虚拟机来模拟编译的部分过程，具有一定的参考价值。不过，我仍然认为通过定义 token 和文法并编写解析算法（如 regex、LL(k) 等）可能会更具普适性。",-1),z=e("div",{class:"hint-container info"},[e("p",{class:"hint-container-title"},"相关信息"),e("p",null,"不过据说c、cpp、java这些成熟的语言都是手动实现的？还没仔细了解过。 TODO")],-1);function G(R,M){const r=a("ExternalLinkIcon");return i(),p("div",null,[h,e("p",null,[t("本文转载自 "),c,t("，原作者 "),d,t("，原文链接："),e("a",_,[t("原文链接"),n(r)]),t("，如有侵权，请联系删除。")]),e("p",null,[t("转载工具:"),e("a",u,[t("devtool"),n(r)]),t("、"),e("a",f,[t("helloworld"),n(r)])]),m,g,C,e("ol",null,[e("li",null,[e("a",b,[t("手把手教你构建 C 语言编译器（0）——前言"),n(r)])]),e("li",null,[e("a",E,[t("手把手教你构建 C 语言编译器（1）——设计"),n(r)])]),e("li",null,[e("a",k,[t("手把手教你构建 C 语言编译器（2）——虚拟机"),n(r)])]),e("li",null,[e("a",w,[t("手把手教你构建 C 语言编译器（3）——词法分析器"),n(r)])]),e("li",null,[e("a",B,[t("手把手教你构建 C 语言编译器（4）——递归下降"),n(r)])]),e("li",null,[e("a",x,[t("手把手教你构建 C 语言编译器（5）——变量定义"),n(r)])]),e("li",null,[e("a",A,[t("手把手教你构建 C 语言编译器（6）——函数定义"),n(r)])]),e("li",null,[e("a",v,[t("手把手教你构建 C 语言编译器（7）——语句"),n(r)])]),e("li",null,[e("a",y,[t("手把手教你构建 C 语言编译器（8）——表达式"),n(r)])]),e("li",null,[e("a",L,[t("手把手教你构建 C 语言编译器（9）——总结"),n(r)])])]),D,e("p",null,[t("有一次在 Github 上看到了一个项目（当时很火的），名叫 "),e("a",F,[t("c4"),n(r)]),t("，号称用 4 个函数来实现了一个小的 C 语言编译器。它最让我震惊的是能够自举，即能自己编译自己。并且它用很少的代码就完成了一个功能相当完善的 C 语言编译器。")]),N,S,e("p",null,[t("c4 大致500+行。重写的代码历时一周，总共代码加注释1400行。项目地址: "),e("a",j,[t("Write a C Interpreter"),n(r)]),t("。")]),I,e("ol",null,[e("li",null,[e("a",K,[t("Let’s Build a Compiler"),n(r)]),t(" 很好的初学者教程，英文的。")]),e("li",null,[e("a",P,[t("Lemon Parser Generator"),n(r)]),t("，一个语法分析器生成器，对照《编译原理》观看效果更佳。")])]),V,J,O,T,z])}const q=l(s,[["render",G],["__file","0.html.vue"]]),H=JSON.parse('{"path":"/tech/designASimpileCCompiler/0.html","title":"手把手教你构建 C 语言编译器（0）- 前言","lang":"zh-CN","frontmatter":{"title":"手把手教你构建 C 语言编译器（0）- 前言","category":["编译原理"],"tag":["c","编译器","解释器"],"description":"转载声明 本文转载自 手把手教你构建 C 语言编译器（0）- 前言，原作者 三点水，原文链接：原文链接，如有侵权，请联系删除。 转载工具:devtool、helloworld 原文内容 “手把手教你构建 C 语言编译器” 这一系列教程将带你从头编写一个 C 语言的编译器。希望通过这个系列，我们能对编译器的构建有一定的了解，同时，我们也将构建出一个能用的...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/designASimpileCCompiler/0.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"手把手教你构建 C 语言编译器（0）- 前言"}],["meta",{"property":"og:description","content":"转载声明 本文转载自 手把手教你构建 C 语言编译器（0）- 前言，原作者 三点水，原文链接：原文链接，如有侵权，请联系删除。 转载工具:devtool、helloworld 原文内容 “手把手教你构建 C 语言编译器” 这一系列教程将带你从头编写一个 C 语言的编译器。希望通过这个系列，我们能对编译器的构建有一定的了解，同时，我们也将构建出一个能用的..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"c"}],["meta",{"property":"article:tag","content":"编译器"}],["meta",{"property":"article:tag","content":"解释器"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"手把手教你构建 C 语言编译器（0）- 前言\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"为什么要学编译原理","slug":"为什么要学编译原理","link":"#为什么要学编译原理","children":[]},{"level":2,"title":"理论很复杂，实现也很复杂？","slug":"理论很复杂-实现也很复杂","link":"#理论很复杂-实现也很复杂","children":[]},{"level":2,"title":"项目的初衷","slug":"项目的初衷","link":"#项目的初衷","children":[]},{"level":2,"title":"做好心理准备","slug":"做好心理准备","link":"#做好心理准备","children":[]},{"level":2,"title":"参考资料","slug":"参考资料","link":"#参考资料","children":[]}],"readingTime":{"minutes":6.12,"words":1835},"filePathRelative":"tech/designASimpileCCompiler/0.md","excerpt":"\\n<p>本文转载自 <strong>手把手教你构建 C 语言编译器（0）- 前言</strong>，原作者 <strong>三点水</strong>，原文链接：<a href=\\"https://lotabout.me/2015/write-a-C-interpreter-0/\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">原文链接</a>，如有侵权，请联系删除。</p>\\n<p>转载工具:<a href=\\"https://devtool.tech/html-md\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">devtool</a>、<a href=\\"https://www.helloworld.net/html2md\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">helloworld</a></p>","autoDesc":true}');export{q as comp,H as data};
diff --git a/assets/1.html-B2woGSgL.js b/assets/1.html-C8e1pvTo.js
similarity index 99%
rename from assets/1.html-B2woGSgL.js
rename to assets/1.html-C8e1pvTo.js
index 277485a..bbd3632 100644
--- a/assets/1.html-B2woGSgL.js
+++ b/assets/1.html-C8e1pvTo.js
@@ -1 +1 @@
-import{_ as t,r as p,o as r,c as o,b as s,e as a,d as e,f as l}from"./app-B69Gl_S-.js";const i={},c=s("h1",{id:"转载声明",tabindex:"-1"},[s("a",{class:"header-anchor",href:"#转载声明"},[s("span",null,"转载声明")])],-1),b={href:"https://lotabout.me/2015/write-a-C-interpreter-1/",target:"_blank",rel:"noopener noreferrer"},d=l('<h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-1-设计" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-1-设计"><span>手把手教你构建 C 语言编译器（1）- 设计</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#%E7%BC%96%E8%AF%91%E5%99%A8%E7%9A%84%E6%9E%84%E5%BB%BA%E6%B5%81%E7%A8%8B">1. 编译器的构建流程</a></li><li><a href="about:blank#%E7%BC%96%E8%AF%91%E5%99%A8%E6%A1%86%E6%9E%B6">2. 编译器框架</a></li></ol><p>这是“手把手教你构建 C 语言编译器”系列的第二篇，我们要从整体上讲解如何设计我们的 C 语言编译器。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p>',6),h={href:"http://lotabout.me/2015/write-a-C-interpreter-0/",target:"_blank",rel:"noopener noreferrer"},u={href:"http://lotabout.me/2015/write-a-C-interpreter-1/",target:"_blank",rel:"noopener noreferrer"},m={href:"http://lotabout.me/2015/write-a-C-interpreter-2/",target:"_blank",rel:"noopener noreferrer"},_={href:"http://lotabout.me/2015/write-a-C-interpreter-3/",target:"_blank",rel:"noopener noreferrer"},f={href:"http://lotabout.me/2016/write-a-C-interpreter-4/",target:"_blank",rel:"noopener noreferrer"},g={href:"http://lotabout.me/2016/write-a-C-interpreter-5/",target:"_blank",rel:"noopener noreferrer"},C={href:"http://lotabout.me/2016/write-a-C-interpreter-6/",target:"_blank",rel:"noopener noreferrer"},E={href:"http://lotabout.me/2016/write-a-C-interpreter-7/",target:"_blank",rel:"noopener noreferrer"},k={href:"http://lotabout.me/2016/write-a-C-interpreter-8/",target:"_blank",rel:"noopener noreferrer"},y={href:"http://lotabout.me/2016/write-a-C-interpreter-9/",target:"_blank",rel:"noopener noreferrer"},w=l('<p>首先要说明的是，虽然标题是编译器，但实际上我们构建的是 C 语言的解释器，这意味着我们可以像运行脚本一样去运行 C 语言的源代码文件。这么做的理由有两点：</p><ol><li>解释器与编译器仅在代码生成阶段有区别，而其它方面如词法分析、语法分析是一样的。</li><li>解释器需要我们实现自己的虚拟机与指令集，而这部分能帮助我们了解计算机的工作原理。</li></ol><h2 id="编译器的构建流程" tabindex="-1"><a class="header-anchor" href="#编译器的构建流程"><span><a href="about:blank#%E7%BC%96%E8%AF%91%E5%99%A8%E7%9A%84%E6%9E%84%E5%BB%BA%E6%B5%81%E7%A8%8B"></a>编译器的构建流程</span></a></h2><p>一般而言，编译器的编写分为 3 个步骤：</p><ol><li>词法分析器，用于将字符串转化成内部的表示结构。</li><li>语法分析器，将词法分析得到的标记流（token）生成一棵语法树。</li><li>目标代码的生成，将语法树转化成目标代码。</li></ol><p>已经有许多工具能帮助我们处理阶段1和2，如 flex 用于词法分析，bison 用于语法分析。只是它们的功能都过于强大，屏蔽了许多实现上的细节，对于学习构建编译器帮助不大。所以我们要完全手写这些功能。</p><p>所以我们会依照以下步骤来构建我们的编译器：</p><ol><li>构建我们自己的虚拟机以及指令集。这后生成的目标代码便是我们的指令集。</li><li>构建我们的词法分析器</li><li>构建语法分析器</li></ol><h2 id="编译器框架" tabindex="-1"><a class="header-anchor" href="#编译器框架"><span><a href="about:blank#%E7%BC%96%E8%AF%91%E5%99%A8%E6%A1%86%E6%9E%B6"></a>编译器框架</span></a></h2><p>我们的编译器主要包括 4 个函数：</p><ol><li><code>next()</code> 用于词法分析，获取下一个标记，它将自动忽略空白字符。</li><li><code>program()</code> 语法分析的入口，分析整个 C 语言程序。</li><li><code>expression(level)</code> 用于解析一个表达式。</li><li><code>eval()</code> 虚拟机的入口，用于解释目标代码。</li></ol><p>这里有一个单独用于解析“表达式”的函数 <code>expression</code> 是因为表达式在语法分析中相对独立并且比较复杂，所以我们将它单独作为一个模块（函数）。下面是相应的源代码：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;stdio.h&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;stdlib.h&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;memory.h&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;string.h&gt;</span></span></span><br><span class="line"></span><br><span class="line"><span class="type">int</span> token;            <span class="comment">// current token</span></span><br><span class="line"><span class="type">char</span> *src, *old_src;  <span class="comment">// pointer to source code string;</span></span><br><span class="line"><span class="type">int</span> poolsize;         <span class="comment">// default size of text/data/stack</span></span><br><span class="line"><span class="type">int</span> line;             <span class="comment">// line number</span></span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">next</span><span class="params">()</span> {</span><br><span class="line">    token = *src++;</span><br><span class="line">    <span class="keyword">return</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">expression</span><span class="params">(<span class="type">int</span> level)</span> {</span><br><span class="line">    <span class="comment">// do nothing</span></span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">program</span><span class="params">()</span> {</span><br><span class="line">    next();                  <span class="comment">// get next token</span></span><br><span class="line">    <span class="keyword">while</span> (token &gt; <span class="number">0</span>) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;token is: %c\\n&quot;</span>, token);</span><br><span class="line">        next();</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">eval</span><span class="params">()</span> { <span class="comment">// do nothing yet</span></span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">main</span><span class="params">(<span class="type">int</span> argc, <span class="type">char</span> **argv)</span></span><br><span class="line">{</span><br><span class="line">    <span class="type">int</span> i, fd;</span><br><span class="line"></span><br><span class="line">    argc--;</span><br><span class="line">    argv++;</span><br><span class="line"></span><br><span class="line">    poolsize = <span class="number">256</span> * <span class="number">1024</span>; <span class="comment">// arbitrary size</span></span><br><span class="line">    line = <span class="number">1</span>;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> ((fd = open(*argv, <span class="number">0</span>)) &lt; <span class="number">0</span>) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;could not open(%s)\\n&quot;</span>, *argv);</span><br><span class="line">        <span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (!(src = old_src = <span class="built_in">malloc</span>(poolsize))) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;could not malloc(%d) for source area\\n&quot;</span>, poolsize);</span><br><span class="line">        <span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="comment">// read the source file</span></span><br><span class="line">    <span class="keyword">if</span> ((i = read(fd, src, poolsize<span class="number">-1</span>)) &lt;= <span class="number">0</span>) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;read() returned %d\\n&quot;</span>, i);</span><br><span class="line">        <span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">    }</span><br><span class="line">    src[i] = <span class="number">0</span>; <span class="comment">// add EOF character</span></span><br><span class="line">    close(fd);</span><br><span class="line"></span><br><span class="line">    program();</span><br><span class="line">    <span class="keyword">return</span> eval();</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>上面的代码看上去挺复杂，但其实内容不多。它的流程为：读取一个文件（内容为 C 语言代码），逐个读取文件中的字符，并输出。这里需要的是注意每个函数的作用，后面的文章中，我们将逐个填充每个函数的功能，最终构建起我们的编译器。</p>',14),A={href:"https://github.com/lotabout/write-a-C-interpreter/tree/step-0",target:"_blank",rel:"noopener noreferrer"},B=s("table",null,[s("tbody",null,[s("tr",null,[s("td",{class:"code"},[s("pre",null,[s("span",{class:"line"},"git clone -b step-0 https://github.com/lotabout/write-a-C-interpreter"),s("br")])])])])],-1),x=s("p",null,[a("这样我们就有了一个最简单的编译器：什么都不干的编译器，下一章中，我们将实现其中的"),s("code",null,"eval"),a("函数，即我们自己的虚拟机。")],-1);function v(z,q){const n=p("ExternalLinkIcon");return r(),o("div",null,[c,s("p",null,[a("本文转自 "),s("a",b,[a("https://lotabout.me/2015/write-a-C-interpreter-1/"),e(n)]),a("，如有侵权，请联系删除。")]),d,s("ol",null,[s("li",null,[s("a",h,[a("手把手教你构建 C 语言编译器（0）——前言"),e(n)])]),s("li",null,[s("a",u,[a("手把手教你构建 C 语言编译器（1）——设计"),e(n)])]),s("li",null,[s("a",m,[a("手把手教你构建 C 语言编译器（2）——虚拟机"),e(n)])]),s("li",null,[s("a",_,[a("手把手教你构建 C 语言编译器（3）——词法分析器"),e(n)])]),s("li",null,[s("a",f,[a("手把手教你构建 C 语言编译器（4）——递归下降"),e(n)])]),s("li",null,[s("a",g,[a("手把手教你构建 C 语言编译器（5）——变量定义"),e(n)])]),s("li",null,[s("a",C,[a("手把手教你构建 C 语言编译器（6）——函数定义"),e(n)])]),s("li",null,[s("a",E,[a("手把手教你构建 C 语言编译器（7）——语句"),e(n)])]),s("li",null,[s("a",k,[a("手把手教你构建 C 语言编译器（8）——表达式"),e(n)])]),s("li",null,[s("a",y,[a("手把手教你构建 C 语言编译器（9）——总结"),e(n)])])]),w,s("p",null,[a("本节的代码可以在 "),s("a",A,[a("Github"),e(n)]),a(" 上下载，也可以直接 clone")]),B,x])}const N=t(i,[["render",v],["__file","1.html.vue"]]),S=JSON.parse('{"path":"/tech/designASimpileCCompiler/1.html","title":"手把手教你构建 C 语言编译器（1）- 设计","lang":"zh-CN","frontmatter":{"title":"手把手教你构建 C 语言编译器（1）- 设计","description":"转载声明 本文转自 https://lotabout.me/2015/write-a-C-interpreter-1/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（1）- 设计 Table of Contents 1. 编译器的构建流程 2. 编译器框架 这是“手把手教你构建 C 语言编译器”系列的第二篇，我们要从整体上讲解如何设...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/designASimpileCCompiler/1.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"手把手教你构建 C 语言编译器（1）- 设计"}],["meta",{"property":"og:description","content":"转载声明 本文转自 https://lotabout.me/2015/write-a-C-interpreter-1/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（1）- 设计 Table of Contents 1. 编译器的构建流程 2. 编译器框架 这是“手把手教你构建 C 语言编译器”系列的第二篇，我们要从整体上讲解如何设..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"手把手教你构建 C 语言编译器（1）- 设计\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"编译器的构建流程","slug":"编译器的构建流程","link":"#编译器的构建流程","children":[]},{"level":2,"title":"编译器框架","slug":"编译器框架","link":"#编译器框架","children":[]}],"readingTime":{"minutes":6.74,"words":2023},"filePathRelative":"tech/designASimpileCCompiler/1.md","excerpt":"\\n<p>本文转自 <a href=\\"https://lotabout.me/2015/write-a-C-interpreter-1/\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">https://lotabout.me/2015/write-a-C-interpreter-1/</a>，如有侵权，请联系删除。</p>\\n<h1>原文内容</h1>\\n<h1>手把手教你构建 C 语言编译器（1）- 设计</h1>\\n<p>Table of Contents</p>\\n<ol>\\n<li><a href=\\"about:blank#%E7%BC%96%E8%AF%91%E5%99%A8%E7%9A%84%E6%9E%84%E5%BB%BA%E6%B5%81%E7%A8%8B\\">1. 编译器的构建流程</a></li>\\n<li><a href=\\"about:blank#%E7%BC%96%E8%AF%91%E5%99%A8%E6%A1%86%E6%9E%B6\\">2. 编译器框架</a></li>\\n</ol>","autoDesc":true}');export{N as comp,S as data};
+import{_ as t,r as p,o as r,c as o,b as s,e as a,d as e,f as l}from"./app-B4LGNJZ0.js";const i={},c=s("h1",{id:"转载声明",tabindex:"-1"},[s("a",{class:"header-anchor",href:"#转载声明"},[s("span",null,"转载声明")])],-1),b={href:"https://lotabout.me/2015/write-a-C-interpreter-1/",target:"_blank",rel:"noopener noreferrer"},d=l('<h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-1-设计" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-1-设计"><span>手把手教你构建 C 语言编译器（1）- 设计</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#%E7%BC%96%E8%AF%91%E5%99%A8%E7%9A%84%E6%9E%84%E5%BB%BA%E6%B5%81%E7%A8%8B">1. 编译器的构建流程</a></li><li><a href="about:blank#%E7%BC%96%E8%AF%91%E5%99%A8%E6%A1%86%E6%9E%B6">2. 编译器框架</a></li></ol><p>这是“手把手教你构建 C 语言编译器”系列的第二篇，我们要从整体上讲解如何设计我们的 C 语言编译器。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p>',6),h={href:"http://lotabout.me/2015/write-a-C-interpreter-0/",target:"_blank",rel:"noopener noreferrer"},u={href:"http://lotabout.me/2015/write-a-C-interpreter-1/",target:"_blank",rel:"noopener noreferrer"},m={href:"http://lotabout.me/2015/write-a-C-interpreter-2/",target:"_blank",rel:"noopener noreferrer"},_={href:"http://lotabout.me/2015/write-a-C-interpreter-3/",target:"_blank",rel:"noopener noreferrer"},f={href:"http://lotabout.me/2016/write-a-C-interpreter-4/",target:"_blank",rel:"noopener noreferrer"},g={href:"http://lotabout.me/2016/write-a-C-interpreter-5/",target:"_blank",rel:"noopener noreferrer"},C={href:"http://lotabout.me/2016/write-a-C-interpreter-6/",target:"_blank",rel:"noopener noreferrer"},E={href:"http://lotabout.me/2016/write-a-C-interpreter-7/",target:"_blank",rel:"noopener noreferrer"},k={href:"http://lotabout.me/2016/write-a-C-interpreter-8/",target:"_blank",rel:"noopener noreferrer"},y={href:"http://lotabout.me/2016/write-a-C-interpreter-9/",target:"_blank",rel:"noopener noreferrer"},w=l('<p>首先要说明的是，虽然标题是编译器，但实际上我们构建的是 C 语言的解释器，这意味着我们可以像运行脚本一样去运行 C 语言的源代码文件。这么做的理由有两点：</p><ol><li>解释器与编译器仅在代码生成阶段有区别，而其它方面如词法分析、语法分析是一样的。</li><li>解释器需要我们实现自己的虚拟机与指令集，而这部分能帮助我们了解计算机的工作原理。</li></ol><h2 id="编译器的构建流程" tabindex="-1"><a class="header-anchor" href="#编译器的构建流程"><span><a href="about:blank#%E7%BC%96%E8%AF%91%E5%99%A8%E7%9A%84%E6%9E%84%E5%BB%BA%E6%B5%81%E7%A8%8B"></a>编译器的构建流程</span></a></h2><p>一般而言，编译器的编写分为 3 个步骤：</p><ol><li>词法分析器，用于将字符串转化成内部的表示结构。</li><li>语法分析器，将词法分析得到的标记流（token）生成一棵语法树。</li><li>目标代码的生成，将语法树转化成目标代码。</li></ol><p>已经有许多工具能帮助我们处理阶段1和2，如 flex 用于词法分析，bison 用于语法分析。只是它们的功能都过于强大，屏蔽了许多实现上的细节，对于学习构建编译器帮助不大。所以我们要完全手写这些功能。</p><p>所以我们会依照以下步骤来构建我们的编译器：</p><ol><li>构建我们自己的虚拟机以及指令集。这后生成的目标代码便是我们的指令集。</li><li>构建我们的词法分析器</li><li>构建语法分析器</li></ol><h2 id="编译器框架" tabindex="-1"><a class="header-anchor" href="#编译器框架"><span><a href="about:blank#%E7%BC%96%E8%AF%91%E5%99%A8%E6%A1%86%E6%9E%B6"></a>编译器框架</span></a></h2><p>我们的编译器主要包括 4 个函数：</p><ol><li><code>next()</code> 用于词法分析，获取下一个标记，它将自动忽略空白字符。</li><li><code>program()</code> 语法分析的入口，分析整个 C 语言程序。</li><li><code>expression(level)</code> 用于解析一个表达式。</li><li><code>eval()</code> 虚拟机的入口，用于解释目标代码。</li></ol><p>这里有一个单独用于解析“表达式”的函数 <code>expression</code> 是因为表达式在语法分析中相对独立并且比较复杂，所以我们将它单独作为一个模块（函数）。下面是相应的源代码：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;stdio.h&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;stdlib.h&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;memory.h&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;string.h&gt;</span></span></span><br><span class="line"></span><br><span class="line"><span class="type">int</span> token;            <span class="comment">// current token</span></span><br><span class="line"><span class="type">char</span> *src, *old_src;  <span class="comment">// pointer to source code string;</span></span><br><span class="line"><span class="type">int</span> poolsize;         <span class="comment">// default size of text/data/stack</span></span><br><span class="line"><span class="type">int</span> line;             <span class="comment">// line number</span></span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">next</span><span class="params">()</span> {</span><br><span class="line">    token = *src++;</span><br><span class="line">    <span class="keyword">return</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">expression</span><span class="params">(<span class="type">int</span> level)</span> {</span><br><span class="line">    <span class="comment">// do nothing</span></span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">program</span><span class="params">()</span> {</span><br><span class="line">    next();                  <span class="comment">// get next token</span></span><br><span class="line">    <span class="keyword">while</span> (token &gt; <span class="number">0</span>) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;token is: %c\\n&quot;</span>, token);</span><br><span class="line">        next();</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">eval</span><span class="params">()</span> { <span class="comment">// do nothing yet</span></span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">main</span><span class="params">(<span class="type">int</span> argc, <span class="type">char</span> **argv)</span></span><br><span class="line">{</span><br><span class="line">    <span class="type">int</span> i, fd;</span><br><span class="line"></span><br><span class="line">    argc--;</span><br><span class="line">    argv++;</span><br><span class="line"></span><br><span class="line">    poolsize = <span class="number">256</span> * <span class="number">1024</span>; <span class="comment">// arbitrary size</span></span><br><span class="line">    line = <span class="number">1</span>;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> ((fd = open(*argv, <span class="number">0</span>)) &lt; <span class="number">0</span>) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;could not open(%s)\\n&quot;</span>, *argv);</span><br><span class="line">        <span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (!(src = old_src = <span class="built_in">malloc</span>(poolsize))) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;could not malloc(%d) for source area\\n&quot;</span>, poolsize);</span><br><span class="line">        <span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="comment">// read the source file</span></span><br><span class="line">    <span class="keyword">if</span> ((i = read(fd, src, poolsize<span class="number">-1</span>)) &lt;= <span class="number">0</span>) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;read() returned %d\\n&quot;</span>, i);</span><br><span class="line">        <span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">    }</span><br><span class="line">    src[i] = <span class="number">0</span>; <span class="comment">// add EOF character</span></span><br><span class="line">    close(fd);</span><br><span class="line"></span><br><span class="line">    program();</span><br><span class="line">    <span class="keyword">return</span> eval();</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>上面的代码看上去挺复杂，但其实内容不多。它的流程为：读取一个文件（内容为 C 语言代码），逐个读取文件中的字符，并输出。这里需要的是注意每个函数的作用，后面的文章中，我们将逐个填充每个函数的功能，最终构建起我们的编译器。</p>',14),A={href:"https://github.com/lotabout/write-a-C-interpreter/tree/step-0",target:"_blank",rel:"noopener noreferrer"},B=s("table",null,[s("tbody",null,[s("tr",null,[s("td",{class:"code"},[s("pre",null,[s("span",{class:"line"},"git clone -b step-0 https://github.com/lotabout/write-a-C-interpreter"),s("br")])])])])],-1),x=s("p",null,[a("这样我们就有了一个最简单的编译器：什么都不干的编译器，下一章中，我们将实现其中的"),s("code",null,"eval"),a("函数，即我们自己的虚拟机。")],-1);function v(z,q){const n=p("ExternalLinkIcon");return r(),o("div",null,[c,s("p",null,[a("本文转自 "),s("a",b,[a("https://lotabout.me/2015/write-a-C-interpreter-1/"),e(n)]),a("，如有侵权，请联系删除。")]),d,s("ol",null,[s("li",null,[s("a",h,[a("手把手教你构建 C 语言编译器（0）——前言"),e(n)])]),s("li",null,[s("a",u,[a("手把手教你构建 C 语言编译器（1）——设计"),e(n)])]),s("li",null,[s("a",m,[a("手把手教你构建 C 语言编译器（2）——虚拟机"),e(n)])]),s("li",null,[s("a",_,[a("手把手教你构建 C 语言编译器（3）——词法分析器"),e(n)])]),s("li",null,[s("a",f,[a("手把手教你构建 C 语言编译器（4）——递归下降"),e(n)])]),s("li",null,[s("a",g,[a("手把手教你构建 C 语言编译器（5）——变量定义"),e(n)])]),s("li",null,[s("a",C,[a("手把手教你构建 C 语言编译器（6）——函数定义"),e(n)])]),s("li",null,[s("a",E,[a("手把手教你构建 C 语言编译器（7）——语句"),e(n)])]),s("li",null,[s("a",k,[a("手把手教你构建 C 语言编译器（8）——表达式"),e(n)])]),s("li",null,[s("a",y,[a("手把手教你构建 C 语言编译器（9）——总结"),e(n)])])]),w,s("p",null,[a("本节的代码可以在 "),s("a",A,[a("Github"),e(n)]),a(" 上下载，也可以直接 clone")]),B,x])}const N=t(i,[["render",v],["__file","1.html.vue"]]),S=JSON.parse('{"path":"/tech/designASimpileCCompiler/1.html","title":"手把手教你构建 C 语言编译器（1）- 设计","lang":"zh-CN","frontmatter":{"title":"手把手教你构建 C 语言编译器（1）- 设计","description":"转载声明 本文转自 https://lotabout.me/2015/write-a-C-interpreter-1/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（1）- 设计 Table of Contents 1. 编译器的构建流程 2. 编译器框架 这是“手把手教你构建 C 语言编译器”系列的第二篇，我们要从整体上讲解如何设...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/designASimpileCCompiler/1.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"手把手教你构建 C 语言编译器（1）- 设计"}],["meta",{"property":"og:description","content":"转载声明 本文转自 https://lotabout.me/2015/write-a-C-interpreter-1/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（1）- 设计 Table of Contents 1. 编译器的构建流程 2. 编译器框架 这是“手把手教你构建 C 语言编译器”系列的第二篇，我们要从整体上讲解如何设..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"手把手教你构建 C 语言编译器（1）- 设计\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"编译器的构建流程","slug":"编译器的构建流程","link":"#编译器的构建流程","children":[]},{"level":2,"title":"编译器框架","slug":"编译器框架","link":"#编译器框架","children":[]}],"readingTime":{"minutes":6.74,"words":2023},"filePathRelative":"tech/designASimpileCCompiler/1.md","excerpt":"\\n<p>本文转自 <a href=\\"https://lotabout.me/2015/write-a-C-interpreter-1/\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">https://lotabout.me/2015/write-a-C-interpreter-1/</a>，如有侵权，请联系删除。</p>\\n<h1>原文内容</h1>\\n<h1>手把手教你构建 C 语言编译器（1）- 设计</h1>\\n<p>Table of Contents</p>\\n<ol>\\n<li><a href=\\"about:blank#%E7%BC%96%E8%AF%91%E5%99%A8%E7%9A%84%E6%9E%84%E5%BB%BA%E6%B5%81%E7%A8%8B\\">1. 编译器的构建流程</a></li>\\n<li><a href=\\"about:blank#%E7%BC%96%E8%AF%91%E5%99%A8%E6%A1%86%E6%9E%B6\\">2. 编译器框架</a></li>\\n</ol>","autoDesc":true}');export{N as comp,S as data};
diff --git a/assets/2.html-DuLx7xSk.js b/assets/2.html-CfN7D4gf.js
similarity index 99%
rename from assets/2.html-DuLx7xSk.js
rename to assets/2.html-CfN7D4gf.js
index 5d04dae..7a5900e 100644
--- a/assets/2.html-DuLx7xSk.js
+++ b/assets/2.html-CfN7D4gf.js
@@ -1 +1 @@
-import{_ as l,r as t,o as c,c as r,b as s,e as a,d as n,f as p}from"./app-B69Gl_S-.js";const o={},i=s("hr",null,null,-1),d=s("p",null,'title: "手把手教你构建 C 语言编译器（2）——虚拟机" category:',-1),b=s("ul",null,[s("li",null,"编译原理 tag:"),s("li",null,"c"),s("li",null,"编译器"),s("li",null,"解释器")],-1),h=s("hr",null,null,-1),u=s("h1",{id:"转载声明",tabindex:"-1"},[s("a",{class:"header-anchor",href:"#转载声明"},[s("span",null,"转载声明")])],-1),m={href:"https://lotabout.me/2015/write-a-C-interpreter-2/",target:"_blank",rel:"noopener noreferrer"},y=p('<h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-2-虚拟机" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-2-虚拟机"><span>手把手教你构建 C 语言编译器（2）- 虚拟机</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E5%86%85%E9%83%A8%E5%B7%A5%E4%BD%9C%E5%8E%9F%E7%90%86">1. 计算机的内部工作原理</a><ol><li><a href="about:blank#%E5%86%85%E5%AD%98">1.1. 内存</a></li><li><a href="about:blank#%E5%AF%84%E5%AD%98%E5%99%A8">1.2. 寄存器</a></li></ol></li><li><a href="about:blank#%E6%8C%87%E4%BB%A4%E9%9B%86">2. 指令集</a><ol><li><a href="about:blank#mov">2.1. MOV</a></li><li><a href="about:blank#push">2.2. PUSH</a></li><li><a href="about:blank#jmp">2.3. JMP</a></li><li><a href="about:blank#jz-jnz">2.4. JZ/JNZ</a></li><li><a href="about:blank#%E5%AD%90%E5%87%BD%E6%95%B0%E8%B0%83%E7%94%A8">2.5. 子函数调用</a></li><li><a href="about:blank#ent">2.6. ENT</a></li><li><a href="about:blank#adj">2.7. ADJ</a></li><li><a href="about:blank#lev">2.8. LEV</a></li><li><a href="about:blank#lea">2.9. LEA</a></li><li><a href="about:blank#%E8%BF%90%E7%AE%97%E7%AC%A6%E6%8C%87%E4%BB%A4">2.10. 运算符指令</a></li><li><a href="about:blank#%E5%86%85%E7%BD%AE%E5%87%BD%E6%95%B0">2.11. 内置函数</a></li></ol></li><li><a href="about:blank#%E6%B5%8B%E8%AF%95">3. 测试</a></li><li><a href="about:blank#%E5%B0%8F%E7%BB%93">4. 小结</a></li></ol><p>这是“手把手教你构建 C 语言编译器”系列的第三篇，本章我们要构建一台虚拟的电脑，设计我们自己的指令集，运行我们的指令集，说得通俗一点就是自己实现一套汇编语言。它们将作为我们的编译器最终输出的目标代码。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p>',6),f={href:"http://lotabout.me/2015/write-a-C-interpreter-0/",target:"_blank",rel:"noopener noreferrer"},k={href:"http://lotabout.me/2015/write-a-C-interpreter-1/",target:"_blank",rel:"noopener noreferrer"},x={href:"http://lotabout.me/2015/write-a-C-interpreter-2/",target:"_blank",rel:"noopener noreferrer"},E={href:"http://lotabout.me/2015/write-a-C-interpreter-3/",target:"_blank",rel:"noopener noreferrer"},g={href:"http://lotabout.me/2016/write-a-C-interpreter-4/",target:"_blank",rel:"noopener noreferrer"},w={href:"http://lotabout.me/2016/write-a-C-interpreter-5/",target:"_blank",rel:"noopener noreferrer"},_={href:"http://lotabout.me/2016/write-a-C-interpreter-6/",target:"_blank",rel:"noopener noreferrer"},C={href:"http://lotabout.me/2016/write-a-C-interpreter-7/",target:"_blank",rel:"noopener noreferrer"},A={href:"http://lotabout.me/2016/write-a-C-interpreter-8/",target:"_blank",rel:"noopener noreferrer"},v={href:"http://lotabout.me/2016/write-a-C-interpreter-9/",target:"_blank",rel:"noopener noreferrer"},L=p('<h2 id="计算机的内部工作原理" tabindex="-1"><a class="header-anchor" href="#计算机的内部工作原理"><span><a href="about:blank#%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E5%86%85%E9%83%A8%E5%B7%A5%E4%BD%9C%E5%8E%9F%E7%90%86"></a>计算机的内部工作原理</span></a></h2><p>计算机中有三个基本部件需要我们关注：CPU、寄存器及内存。代码（汇编指令）以二进制的形式保存在内存中；CPU 从中一条条地加载指令执行；程序运行的状态保存在寄存器中。</p><h3 id="内存" tabindex="-1"><a class="header-anchor" href="#内存"><span><a href="about:blank#%E5%86%85%E5%AD%98"></a>内存</span></a></h3><p>内存用于存储数据，这里的数据可以是代码，也可以是其它的数据。现代操作系统在操作内存时，并不是直接处理”物理内存“，而是操作”虚拟内存“。虚拟内存可以理解为一种映射，它的作用是屏蔽了物理的细节。例如 32 位的机器中，我们可以使用的内存地址为 <code>2^32 = 4G</code>，而电脑上的实际内存可能只有 <code>256 M</code>。操作系统将我们使用的虚拟地址映射到了到实际的内存上。</p><p>当然，我们这里并不需要了解太多，但需要了解的是：进程的内存会被分成几个段：</p><ol><li>代码段（text）用于存放代码（指令）。</li><li>数据段（data）用于存放初始化了的数据，如<code>int i = 10;</code>，就需要存放到数据段中。</li><li>未初始化数据段（bss）用于存放未初始化的数据，如 <code>int i[1000];</code>，因为不关心其中的真正数值，所以单独存放可以节省空间，减少程序的体积。</li><li>栈（stack）用于处理函数调用相关的数据，如调用帧（calling frame）或是函数的局部变量等。</li><li>堆（heap）用于为程序动态分配内存。</li></ol><p>它们在内存中的位置类似于下图：</p><table><tbody><tr><td class="code"><pre><span class="line">+------------------+</span><br><span class="line">|    stack   |     |      high address</span><br><span class="line">|    ...     v     |</span><br><span class="line">|                  |</span><br><span class="line">|                  |</span><br><span class="line">|                  |</span><br><span class="line">|                  |</span><br><span class="line">|    ...     ^     |</span><br><span class="line">|    heap    |     |</span><br><span class="line">+------------------+</span><br><span class="line">| bss  segment     |</span><br><span class="line">+------------------+</span><br><span class="line">| data segment     |</span><br><span class="line">+------------------+</span><br><span class="line">| text segment     |      low address</span><br><span class="line">+------------------+</span><br></pre></td></tr></tbody></table><p>我们的虚拟机并不打算模拟完整的计算机，因此简单起见，我们只关心三个内容：代码段、数据段以及栈。其中的数据段我们只用来存放字符串，因为我们的编译器并不支持初始化变量，因此我们也不需要未初始化数据段。</p><p>当用户的程序需要分配内存时，理论上我们的虚拟机需要维护一个堆用于内存分配，但实际实现上较为复杂且与编译无关，故我们引入一个指令<code>MSET</code>，使我们能直接使用编译器（解释器）中的内存。</p><p>综上，我们需要首先在全局添加如下代码：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> *text,            <span class="comment">// text segment</span></span><br><span class="line">    *old_text,        <span class="comment">// for dump text segment</span></span><br><span class="line">    *<span class="built_in">stack</span>;           <span class="comment">// stack</span></span><br><span class="line"><span class="type">char</span> *data;           <span class="comment">// data segment</span></span><br></pre></td></tr></tbody></table><p>注意这里的类型，虽然是<code>int</code>型，但理解起来应该作为无符号的整型，因为我们会在代码段（text）中存放如指针/内存地址的数据，它们就是无符号的。其中数据段（data）由于只存放字符串，所以是 <code>char *</code> 型的。</p><p>接着，在<code>main</code>函数中加入初始化代码，真正为其分配内存：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> <span class="title function_">main</span><span class="params">()</span> {</span><br><span class="line">    close(fd);</span><br><span class="line">    ...</span><br><span class="line"></span><br><span class="line">    <span class="comment">// allocate memory for virtual machine</span></span><br><span class="line">    <span class="keyword">if</span> (!(text = old_text = <span class="built_in">malloc</span>(poolsize))) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;could not malloc(%d) for text area\\n&quot;</span>, poolsize);</span><br><span class="line">        <span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">if</span> (!(data = <span class="built_in">malloc</span>(poolsize))) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;could not malloc(%d) for data area\\n&quot;</span>, poolsize);</span><br><span class="line">        <span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">if</span> (!(<span class="built_in">stack</span> = <span class="built_in">malloc</span>(poolsize))) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;could not malloc(%d) for stack area\\n&quot;</span>, poolsize);</span><br><span class="line">        <span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="built_in">memset</span>(text, <span class="number">0</span>, poolsize);</span><br><span class="line">    <span class="built_in">memset</span>(data, <span class="number">0</span>, poolsize);</span><br><span class="line">    <span class="built_in">memset</span>(<span class="built_in">stack</span>, <span class="number">0</span>, poolsize);</span><br><span class="line"></span><br><span class="line">    ...</span><br><span class="line">    program();</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="寄存器" tabindex="-1"><a class="header-anchor" href="#寄存器"><span><a href="about:blank#%E5%AF%84%E5%AD%98%E5%99%A8"></a>寄存器</span></a></h3><p>计算机中的寄存器用于存放计算机的运行状态，真正的计算机中有许多不同种类的寄存器，但我们的虚拟机中只使用 4 个寄存器，分别如下：</p><ol><li><code>PC</code> 程序计数器，它存放的是一个内存地址，该地址中存放着 <strong>下一条</strong> 要执行的计算机指令。</li><li><code>SP</code> 指针寄存器，永远指向当前的栈顶。注意的是由于栈是位于高地址并向低地址增长的，所以入栈时 <code>SP</code> 的值减小。</li><li><code>BP</code> 基址指针。也是用于指向栈的某些位置，在调用函数时会使用到它。</li><li><code>AX</code> 通用寄存器，我们的虚拟机中，它用于存放一条指令执行后的结果。</li></ol><p>要理解这些寄存器的作用，需要去理解程序运行中会有哪些状态。而这些寄存器只是用于保存这些状态的。</p><p>在全局中加入如下定义：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> *pc, *bp, *sp, ax, cycle; <span class="comment">// virtual machine registers</span></span><br></pre></td></tr></tbody></table><p>在 <code>main</code> 函数中加入初始化代码，注意的是<code>PC</code>在初始应指向目标代码中的<code>main</code>函数，但我们还没有写任何编译相关的代码，因此先不处理。代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="built_in">memset</span>(<span class="built_in">stack</span>, <span class="number">0</span>, poolsize);</span><br><span class="line">...</span><br><span class="line"></span><br><span class="line">bp = sp = (<span class="type">int</span> *)((<span class="type">int</span>)<span class="built_in">stack</span> + poolsize);</span><br><span class="line">ax = <span class="number">0</span>;</span><br><span class="line"></span><br><span class="line">...</span><br><span class="line">program();</span><br></pre></td></tr></tbody></table><p>与 CPU 相关的是指令集，我们将专门作为一个小节。</p><h2 id="指令集" tabindex="-1"><a class="header-anchor" href="#指令集"><span><a href="about:blank#%E6%8C%87%E4%BB%A4%E9%9B%86"></a>指令集</span></a></h2><p>指令集是 CPU 能识别的命令的集合，也可以说是 CPU 能理解的语言。这里我们要为我们的虚拟机构建自己的指令集。它们基于 x86 的指令集，但更为简单。</p><p>首先在全局变量中加入一个枚举类型，这是我们要支持的全部指令：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="comment">// instructions</span></span><br><span class="line"><span class="class"><span class="keyword">enum</span> {</span> LEA ,IMM ,JMP ,CALL,JZ  ,JNZ ,ENT ,ADJ ,LEV ,LI  ,LC  ,SI  ,SC  ,PUSH,</span><br><span class="line">       OR  ,XOR ,AND ,EQ  ,NE  ,LT  ,GT  ,LE  ,GE  ,SHL ,SHR ,ADD ,SUB ,MUL ,DIV ,MOD ,</span><br><span class="line">       OPEN,READ,CLOS,PRTF,MALC,MSET,MCMP,EXIT };</span><br></pre></td></tr></tbody></table><p>这些指令的顺序安排是有意的，稍后你会看到，带有参数的指令在前，没有参数的指令在后。这种顺序的唯一作用就是在打印调试信息时更加方便。但我们讲解的顺序并不依据它。</p><h3 id="mov" tabindex="-1"><a class="header-anchor" href="#mov"><span><a href="about:blank#mov"></a>MOV</span></a></h3><p><code>MOV</code> 是所有指令中最基础的一个，它用于将数据放进寄存器或内存地址，有点类似于 C 语言中的赋值语句。x86 的 <code>MOV</code> 指令有两个参数，分别是源地址和目标地址：<code>MOV dest, source</code> （Intel 风格），表示将 <code>source</code> 的内容放在 <code>dest</code> 中，它们可以是一个数、寄存器或是一个内存地址。</p><p>一方面，我们的虚拟机只有一个寄存器，另一方面，识别这些参数的类型（是数据还是地址）是比较困难的，因此我们将 <code>MOV</code> 指令拆分成 5 个指令，这些指令只接受一个参数，如下：</p><ol><li><code>IMM &lt;num&gt;</code> 将 <code>&lt;num&gt;</code> 放入寄存器 <code>ax</code> 中。</li><li><code>LC</code> 将对应地址中的字符载入 <code>ax</code> 中，要求 <code>ax</code> 中存放地址。</li><li><code>LI</code> 将对应地址中的整数载入 <code>ax</code> 中，要求 <code>ax</code> 中存放地址。</li><li><code>SC</code> 将 <code>ax</code> 中的数据作为字符存放入地址中，要求栈顶存放地址。</li><li><code>SI</code> 将 <code>ax</code> 中的数据作为整数存放入地址中，要求栈顶存放地址。</li></ol><p>你可能会觉得将一个指令变成了许多指令，整个系统就变得复杂了，但实际情况并非如此。首先是 x86 的 <code>MOV</code> 指令其实有许多变种，根据类型的不同有 <code>MOVB</code>, <code>MOVW</code> 等指令，我们这里的 <code>LC/SC</code> 和 <code>LI/SI</code> 就是对应字符型和整型的存取操作。</p><p>但最为重要的是，通过将 <code>MOV</code> 指令拆分成这些指令，只有 <code>IMM</code> 需要有参数，且不需要判断类型，所以大大简化了实现的难度。</p><p>在 <code>eval()</code> 函数中加入下列代码：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">eval</span><span class="params">()</span> {</span><br><span class="line">    <span class="type">int</span> op, *tmp;</span><br><span class="line">    <span class="keyword">while</span> (<span class="number">1</span>) {</span><br><span class="line">        <span class="keyword">if</span> (op == IMM)       {ax = *pc++;}                                     <span class="comment">// load immediate value to ax</span></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (op == LC)   {ax = *(<span class="type">char</span> *)ax;}                               <span class="comment">// load character to ax, address in ax</span></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (op == LI)   {ax = *(<span class="type">int</span> *)ax;}                                <span class="comment">// load integer to ax, address in ax</span></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (op == SC)   {ax = *(<span class="type">char</span> *)*sp++ = ax;}                       <span class="comment">// save character to address, value in ax, address on stack</span></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (op == SI)   {*(<span class="type">int</span> *)*sp++ = ax;}                             <span class="comment">// save integer to address, value in ax, address on stack</span></span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    ...</span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>其中的 <code>*sp++</code> 的作用是退栈，相当于 <code>POP</code> 操作。</p><p>这里要解释的一点是，为什么 <code>SI/SC</code> 指令中，地址存放在栈中，而 <code>LI/LC</code> 中，地址存放在 <code>ax</code> 中？原因是默认计算的结果是存放在 <code>ax</code> 中的，而地址通常是需要通过计算获得，所以执行 <code>LI/LC</code> 时直接从 <code>ax</code> 取值会更高效。另一点是我们的 <code>PUSH</code> 指令只能将 <code>ax</code> 的值放到栈上，而不能以值作为参数，详细见下文。</p><h3 id="push" tabindex="-1"><a class="header-anchor" href="#push"><span><a href="about:blank#push"></a>PUSH</span></a></h3><p>在 x86 中，<code>PUSH</code> 的作用是将值或寄存器，而在我们的虚拟机中，它的作用是将 <code>ax</code> 的值放入栈中。这样做的主要原因是为了简化虚拟机的实现，并且我们也只有一个寄存器 <code>ax</code> 。代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == PUSH) {*--sp = ax;}                                     <span class="comment">// push the value of ax onto the stack</span></span><br></pre></td></tr></tbody></table><h3 id="jmp" tabindex="-1"><a class="header-anchor" href="#jmp"><span><a href="about:blank#jmp"></a>JMP</span></a></h3><p><code>JMP &lt;addr&gt;</code> 是跳转指令，无条件地将当前的 <code>PC</code> 寄存器设置为指定的 <code>&lt;addr&gt;</code>，实现如下：</p><table><tbody><tr><td class="code"><pre><span class="line">else if (op == JMP)  {pc = (int *)*pc;}                                // jump to the address</span><br></pre></td></tr></tbody></table><p>需要注意的是，<code>pc</code> 寄存器指向的是 <strong>下一条</strong> 指令。所以此时它存放的是 <code>JMP</code> 指令的参数，即 <code>&lt;addr&gt;</code> 的值。</p><h3 id="jz-jnz" tabindex="-1"><a class="header-anchor" href="#jz-jnz"><span><a href="about:blank#jz-jnz"></a>JZ/JNZ</span></a></h3><p>为了实现 <code>if</code> 语句，我们需要条件判断相关的指令。这里我们只实现两个最简单的条件判断，即结果（<code>ax</code>）为零或不为零情况下的跳转。</p><p>实现如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == JZ)   {pc = ax ? pc + <span class="number">1</span> : (<span class="type">int</span> *)*pc;}                   <span class="comment">// jump if ax is zero</span></span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == JNZ)  {pc = ax ? (<span class="type">int</span> *)*pc : pc + <span class="number">1</span>;}                   <span class="comment">// jump if ax is not zero</span></span><br></pre></td></tr></tbody></table><h3 id="子函数调用" tabindex="-1"><a class="header-anchor" href="#子函数调用"><span><a href="about:blank#%E5%AD%90%E5%87%BD%E6%95%B0%E8%B0%83%E7%94%A8"></a>子函数调用</span></a></h3><p>这是汇编中最难理解的部分，所以合在一起说，要引入的命令有 <code>CALL</code>, <code>ENT</code>, <code>ADJ</code> 及 <code>LEV</code>。</p><p>首先我们介绍 <code>CALL &lt;addr&gt;</code> 与 <code>RET</code> 指令，<code>CALL</code> 的作用是跳转到地址为 <code>&lt;addr&gt;</code> 的子函数，<code>RET</code> 则用于从子函数中返回。</p><p>为什么不能直接使用 <code>JMP</code> 指令呢？原因是当我们从子函数中返回时，程序需要回到跳转之前的地方继续运行，这就需要事先将这个位置信息存储起来。反过来，子函数要返回时，就需要获取并恢复这个信息。因此实际中我们将 <code>PC</code> 保存在栈中。如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == CALL) {*--sp = (<span class="type">int</span>)(pc+<span class="number">1</span>); pc = (<span class="type">int</span> *)*pc;}           <span class="comment">// call subroutine</span></span><br><span class="line"><span class="comment">//else if (op == RET)  {pc = (int *)*sp++;}                              // return from subroutine;</span></span><br></pre></td></tr></tbody></table><p>这里我们把 <code>RET</code> 相关的内容注释了，是因为之后我们将用 <code>LEV</code> 指令来代替它。</p><p>在实际调用函数时，不仅要考虑函数的地址，还要考虑如何传递参数和如何返回结果。这里我们约定，如果子函数有返回结果，那么就在返回时保存在 <code>ax</code> 中，它可以是一个值，也可以是一个地址。那么参数的传递呢？</p><p>各种编程语言关于如何调用子函数有不同的约定，例如 C 语言的调用标准是：</p><ol><li>由调用者将参数入栈。</li><li>调用结束时，由调用者将参数出栈。</li><li>参数逆序入栈。</li></ol>',59),B={href:"https://en.wikipedia.org/wiki/X86_calling_conventions",target:"_blank",rel:"noopener noreferrer"},M=p('<table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> <span class="title function_">callee</span><span class="params">(<span class="type">int</span>, <span class="type">int</span>, <span class="type">int</span>)</span>;</span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">caller</span><span class="params">(<span class="type">void</span>)</span></span><br><span class="line">{</span><br><span class="line">	<span class="type">int</span> i, ret;</span><br><span class="line"></span><br><span class="line">	ret = callee(<span class="number">1</span>, <span class="number">2</span>, <span class="number">3</span>);</span><br><span class="line">	ret += <span class="number">5</span>;</span><br><span class="line">	<span class="keyword">return</span> ret;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>会生成如下的 x86 汇编代码：</p><table><tbody><tr><td class="code"><pre><span class="line">caller:</span><br><span class="line">	; make new call frame</span><br><span class="line">	push    ebp</span><br><span class="line">	mov     ebp, esp</span><br><span class="line">        sub     1, esp       ; save stack for variable: i</span><br><span class="line">	; push call arguments</span><br><span class="line">	push    3</span><br><span class="line">	push    2</span><br><span class="line">	push    1</span><br><span class="line">	; call subroutine &#39;callee&#39;</span><br><span class="line">	call    callee</span><br><span class="line">	; remove arguments from frame</span><br><span class="line">	add     esp, 12</span><br><span class="line">	; use subroutine result</span><br><span class="line">	add     eax, 5</span><br><span class="line">	; restore old call frame</span><br><span class="line">        mov     esp, ebp</span><br><span class="line">	pop     ebp</span><br><span class="line">	; return</span><br><span class="line">	ret</span><br></pre></td></tr></tbody></table><p>上面这段代码在我们自己的虚拟机里会有几个问题：</p><ol><li><code>push ebp</code>，但我们的 <code>PUSH</code> 指令并无法指定寄存器。</li><li><code>mov ebp, esp</code>，我们的 <code>MOV</code> 指令同样功能不足。</li><li><code>add esp, 12</code>，也是一样的问题（尽管我们还没定义）。</li></ol><p>也就是说由于我们的指令过于简单（如只能操作<code>ax</code>寄存器），所以用上面提到的指令，我们连函数调用都无法实现。而我们又不希望扩充现有指令的功能，因为这样实现起来就会变得复杂，因此我们采用的方法是增加指令集。毕竟我们不是真正的计算机，增加指令会消耗许多资源（钱）。</p><h3 id="ent" tabindex="-1"><a class="header-anchor" href="#ent"><span><a href="about:blank#ent"></a>ENT</span></a></h3><p><code>ENT &lt;size&gt;</code> 指的是 <code>enter</code>，用于实现 ‘make new call frame’ 的功能，即保存当前的栈指针，同时在栈上保留一定的空间，用以存放局部变量。对应的汇编代码为：</p><table><tbody><tr><td class="code"><pre><span class="line">; make new call frame</span><br><span class="line">push    ebp</span><br><span class="line">mov     ebp, esp</span><br><span class="line">       sub     1, esp       ; save stack for variable: i</span><br></pre></td></tr></tbody></table><p>实现如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == ENT)  {*--sp = (<span class="type">int</span>)bp; bp = sp; sp = sp - *pc++;}      <span class="comment">// make new stack frame</span></span><br></pre></td></tr></tbody></table><h3 id="adj" tabindex="-1"><a class="header-anchor" href="#adj"><span><a href="about:blank#adj"></a>ADJ</span></a></h3><p><code>ADJ &lt;size&gt;</code> 用于实现 ‘remove arguments from frame’。在将调用子函数时压入栈中的数据清除，本质上是因为我们的 <code>ADD</code> 指令功能有限。对应的汇编代码为：</p><table><tbody><tr><td class="code"><pre><span class="line">; remove arguments from frame</span><br><span class="line">add     esp, 12</span><br></pre></td></tr></tbody></table><p>实现如下：</p><table><tbody><tr><td class="code"><pre><span class="line">else if (op == ADJ)  {sp = sp + *pc++;}                                // add esp, &lt;size&gt;</span><br></pre></td></tr></tbody></table><h3 id="lev" tabindex="-1"><a class="header-anchor" href="#lev"><span><a href="about:blank#lev"></a>LEV</span></a></h3><p>本质上这个指令并不是必需的，只是我们的指令集中并没有 <code>POP</code> 指令。并且三条指令写来比较麻烦且浪费空间，所以用一个指令代替。对应的汇编指令为：</p><table><tbody><tr><td class="code"><pre><span class="line">; restore old call frame</span><br><span class="line">       mov     esp, ebp</span><br><span class="line">pop     ebp</span><br><span class="line">; return</span><br><span class="line">ret</span><br></pre></td></tr></tbody></table><p>具体的实现如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == LEV)  {sp = bp; bp = (<span class="type">int</span> *)*sp++; pc = (<span class="type">int</span> *)*sp++;}  <span class="comment">// restore call frame and PC</span></span><br></pre></td></tr></tbody></table><p>注意的是，<code>LEV</code> 已经把 <code>RET</code> 的功能包含了，所以我们不再需要 <code>RET</code> 指令。</p><h3 id="lea" tabindex="-1"><a class="header-anchor" href="#lea"><span><a href="about:blank#lea"></a>LEA</span></a></h3><p>上面的一些指令解决了调用帧的问题，但还有一个问题是如何在子函数中获得传入的参数。这里我们首先要了解的是当参数调用时，栈中的调用帧是什么样的。我们依旧用上面的例子（只是现在用“顺序”调用参数）：</p><table><tbody><tr><td class="code"><pre><span class="line">sub_function(arg1, arg2, arg3);</span><br><span class="line"></span><br><span class="line">|    ....       | high address</span><br><span class="line">+---------------+</span><br><span class="line">| arg: 1        |    new_bp + 4</span><br><span class="line">+---------------+</span><br><span class="line">| arg: 2        |    new_bp + 3</span><br><span class="line">+---------------+</span><br><span class="line">| arg: 3        |    new_bp + 2</span><br><span class="line">+---------------+</span><br><span class="line">|return address |    new_bp + 1</span><br><span class="line">+---------------+</span><br><span class="line">| old BP        | &lt;- new BP</span><br><span class="line">+---------------+</span><br><span class="line">| local var 1   |    new_bp - 1</span><br><span class="line">+---------------+</span><br><span class="line">| local var 2   |    new_bp - 2</span><br><span class="line">+---------------+</span><br><span class="line">|    ....       |  low address</span><br></pre></td></tr></tbody></table><p>所以为了获取第一个参数，我们需要得到 <code>new_bp + 4</code>，但就如上面的说，我们的 <code>ADD</code> 指令无法操作除 <code>ax</code> 外的寄存器，所以我们提供了一个新的指令：<code>LEA &lt;offset&gt;</code></p><p>实现如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == LEA)  {ax = (<span class="type">int</span>)(bp + *pc++);}                         <span class="comment">// load address for arguments.</span></span><br></pre></td></tr></tbody></table><p>以上就是我们为了实现函数调用需要的指令了。</p><h3 id="运算符指令" tabindex="-1"><a class="header-anchor" href="#运算符指令"><span><a href="about:blank#%E8%BF%90%E7%AE%97%E7%AC%A6%E6%8C%87%E4%BB%A4"></a>运算符指令</span></a></h3><p>我们为 C 语言中支持的运算符都提供对应汇编指令。每个运算符都是二元的，即有两个参数，第一个参数放在栈顶，第二个参数放在 <code>ax</code> 中。这个顺序要特别注意。因为像 <code>-</code>，<code>/</code> 之类的运算符是与参数顺序有关的。计算后会将栈顶的参数退栈，结果存放在寄存器 <code>ax</code> 中。因此计算结束后，两个参数都无法取得了（汇编的意义上，存在内存地址上就另当别论）。</p><p>实现如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == OR)  ax = *sp++ | ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == XOR) ax = *sp++ ^ ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == AND) ax = *sp++ &amp; ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == EQ)  ax = *sp++ == ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == NE)  ax = *sp++ != ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == LT)  ax = *sp++ &lt; ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == LE)  ax = *sp++ &lt;= ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == GT)  ax = *sp++ &gt;  ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == GE)  ax = *sp++ &gt;= ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == SHL) ax = *sp++ &lt;&lt; ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == SHR) ax = *sp++ &gt;&gt; ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == ADD) ax = *sp++ + ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == SUB) ax = *sp++ - ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == MUL) ax = *sp++ * ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == DIV) ax = *sp++ / ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == MOD) ax = *sp++ % ax;</span><br></pre></td></tr></tbody></table><h3 id="内置函数" tabindex="-1"><a class="header-anchor" href="#内置函数"><span><a href="about:blank#%E5%86%85%E7%BD%AE%E5%87%BD%E6%95%B0"></a>内置函数</span></a></h3><p>写的程序要”有用“，除了核心的逻辑外还需要输入输出，例如 C 语言中我们经常使用的 <code>printf</code> 函数就是用于输出。但是 <code>printf</code> 函数的实现本身就十分复杂，如果我们的编译器要达到自举，就势必要实现 <code>printf</code> 之类的函数，但它又与编译器没有太大的联系，因此我们继续实现新的指令，从虚拟机的角度予以支持。</p><p>编译器中我们需要用到的函数有：<code>exit</code>, <code>open</code>, <code>close</code>, <code>read</code>, <code>printf</code>, <code>malloc</code>, <code>memset</code> 及 <code>memcmp</code>。代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == EXIT) { <span class="built_in">printf</span>(<span class="string">&quot;exit(%d)&quot;</span>, *sp); <span class="keyword">return</span> *sp;}</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == OPEN) { ax = open((<span class="type">char</span> *)sp[<span class="number">1</span>], sp[<span class="number">0</span>]); }</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == CLOS) { ax = close(*sp);}</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == READ) { ax = read(sp[<span class="number">2</span>], (<span class="type">char</span> *)sp[<span class="number">1</span>], *sp); }</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == PRTF) { tmp = sp + pc[<span class="number">1</span>]; ax = <span class="built_in">printf</span>((<span class="type">char</span> *)tmp[<span class="number">-1</span>], tmp[<span class="number">-2</span>], tmp[<span class="number">-3</span>], tmp[<span class="number">-4</span>], tmp[<span class="number">-5</span>], tmp[<span class="number">-6</span>]); }</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == MALC) { ax = (<span class="type">int</span>)<span class="built_in">malloc</span>(*sp);}</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == MSET) { ax = (<span class="type">int</span>)<span class="built_in">memset</span>((<span class="type">char</span> *)sp[<span class="number">2</span>], sp[<span class="number">1</span>], *sp);}</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == MCMP) { ax = <span class="built_in">memcmp</span>((<span class="type">char</span> *)sp[<span class="number">2</span>], (<span class="type">char</span> *)sp[<span class="number">1</span>], *sp);}</span><br></pre></td></tr></tbody></table><p>这里的原理是，我们的电脑上已经有了这些函数的实现，因此编译编译器时，这些函数的二进制代码就被编译进了我们的编译器，因此在我们的编译器/虚拟机上运行我们提供的这些指令时，这些函数就是可用的。换句话说就是不需要我们自己去实现了。</p><p>最后再加上一个错误判断：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> {</span><br><span class="line">    <span class="built_in">printf</span>(<span class="string">&quot;unknown instruction:%d\\n&quot;</span>, op);</span><br><span class="line">    <span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h2 id="测试" tabindex="-1"><a class="header-anchor" href="#测试"><span><a href="about:blank#%E6%B5%8B%E8%AF%95"></a>测试</span></a></h2><p>下面我们用我们的汇编写一小段程序，来计算 <code>10+20</code>，在 <code>main</code> 函数中加入下列代码：</p><table><tbody><tr><td class="code"><pre><span class="line">int main(int argc, char *argv[])</span><br><span class="line">{</span><br><span class="line">    ax = 0;</span><br><span class="line">    ...</span><br><span class="line"></span><br><span class="line">    i = 0;</span><br><span class="line">    text[i++] = IMM;</span><br><span class="line">    text[i++] = 10;</span><br><span class="line">    text[i++] = PUSH;</span><br><span class="line">    text[i++] = IMM;</span><br><span class="line">    text[i++] = 20;</span><br><span class="line">    text[i++] = ADD;</span><br><span class="line">    text[i++] = PUSH;</span><br><span class="line">    text[i++] = EXIT;</span><br><span class="line">    pc = text;</span><br><span class="line"></span><br><span class="line">    ...</span><br><span class="line">    program();</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>编译程序 <code>gcc xc-tutor.c</code>，运行程序：<code>./a.out hello.c</code>。输出</p><table><tbody><tr><td class="code"><pre><span class="line">exit(30)</span><br></pre></td></tr></tbody></table><p>另外，我们的代码里有一些指针的强制转换，默认是 32 位的，因此在 64 位机器下，会出现 <code>segmentation fault</code>，解决方法（二选一）：</p><ol><li>编译时加上 <code>-m32</code> 参数：<code>gcc -m32 xc-tutor.c</code></li><li>在代码的开头，增加 <code>#define int long long</code>，<code>long long</code> 是 64 位的，不会出现强制转换后的问题。</li></ol><p>注意我们的之前的程序需要指令一个源文件，只是现在还用不着，但从结果可以看出，我们的虚拟机还是工作良好的。</p><h2 id="小结" tabindex="-1"><a class="header-anchor" href="#小结"><span><a href="about:blank#%E5%B0%8F%E7%BB%93"></a>小结</span></a></h2><p>本章中我们回顾了计算机的内部运行原理，并仿照 x86 汇编指令设计并实现了我们自己的指令集。希望通过本章的学习，你能对计算机程序的原理有一定的了解，同时能对汇编语言有一定的概念，因为汇编语言就是 C 编译器的输出。</p>',50),P={href:"https://github.com/lotabout/write-a-C-interpreter/tree/step-1",target:"_blank",rel:"noopener noreferrer"},D=s("table",null,[s("tbody",null,[s("tr",null,[s("td",{class:"code"},[s("pre",null,[s("span",{class:"line"},"git clone -b step-1 https://github.com/lotabout/write-a-C-interpreter"),s("br")])])])])],-1),S=s("p",null,"实际计算机中，添加一个新的指令需要设计许多新的电路，会增加许多的成本，但我们的虚拟机中，新的指令几乎不消耗资源，因此我们可以利用这一点，用更多的指令来完成更多的功能，从而简化具体的实现。",-1);function j(z,T){const e=t("ExternalLinkIcon");return c(),r("div",null,[i,d,b,h,u,s("p",null,[a("本文转自 "),s("a",m,[a("https://lotabout.me/2015/write-a-C-interpreter-2/"),n(e)]),a("，如有侵权，请联系删除。")]),y,s("ol",null,[s("li",null,[s("a",f,[a("手把手教你构建 C 语言编译器（0）——前言"),n(e)])]),s("li",null,[s("a",k,[a("手把手教你构建 C 语言编译器（1）——设计"),n(e)])]),s("li",null,[s("a",x,[a("手把手教你构建 C 语言编译器（2）——虚拟机"),n(e)])]),s("li",null,[s("a",E,[a("手把手教你构建 C 语言编译器（3）——词法分析器"),n(e)])]),s("li",null,[s("a",g,[a("手把手教你构建 C 语言编译器（4）——递归下降"),n(e)])]),s("li",null,[s("a",w,[a("手把手教你构建 C 语言编译器（5）——变量定义"),n(e)])]),s("li",null,[s("a",_,[a("手把手教你构建 C 语言编译器（6）——函数定义"),n(e)])]),s("li",null,[s("a",C,[a("手把手教你构建 C 语言编译器（7）——语句"),n(e)])]),s("li",null,[s("a",A,[a("手把手教你构建 C 语言编译器（8）——表达式"),n(e)])]),s("li",null,[s("a",v,[a("手把手教你构建 C 语言编译器（9）——总结"),n(e)])])]),L,s("p",null,[a("事先声明一下，我们的编译器参数是顺序入栈的，下面的例子（C 语言调用标准）取自 "),s("a",B,[a("维基百科"),n(e)]),a("：")]),M,s("p",null,[a("本章的代码可以在 "),s("a",P,[a("Github"),n(e)]),a(" 上下载，也可以直接 clone")]),D,S])}const I=l(o,[["render",j],["__file","2.html.vue"]]),V=JSON.parse('{"path":"/tech/designASimpileCCompiler/2.html","title":"转载声明","lang":"zh-CN","frontmatter":{"description":"title: \\"手把手教你构建 C 语言编译器（2）——虚拟机\\" category: 编译原理 tag: c 编译器 解释器 转载声明 本文转自 https://lotabout.me/2015/write-a-C-interpreter-2/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（2）- 虚拟机 Table of Cont...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/designASimpileCCompiler/2.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"转载声明"}],["meta",{"property":"og:description","content":"title: \\"手把手教你构建 C 语言编译器（2）——虚拟机\\" category: 编译原理 tag: c 编译器 解释器 转载声明 本文转自 https://lotabout.me/2015/write-a-C-interpreter-2/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（2）- 虚拟机 Table of Cont..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"转载声明\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"计算机的内部工作原理","slug":"计算机的内部工作原理","link":"#计算机的内部工作原理","children":[{"level":3,"title":"内存","slug":"内存","link":"#内存","children":[]},{"level":3,"title":"寄存器","slug":"寄存器","link":"#寄存器","children":[]}]},{"level":2,"title":"指令集","slug":"指令集","link":"#指令集","children":[{"level":3,"title":"MOV","slug":"mov","link":"#mov","children":[]},{"level":3,"title":"PUSH","slug":"push","link":"#push","children":[]},{"level":3,"title":"JMP","slug":"jmp","link":"#jmp","children":[]},{"level":3,"title":"JZ/JNZ","slug":"jz-jnz","link":"#jz-jnz","children":[]},{"level":3,"title":"子函数调用","slug":"子函数调用","link":"#子函数调用","children":[]},{"level":3,"title":"ENT","slug":"ent","link":"#ent","children":[]},{"level":3,"title":"ADJ","slug":"adj","link":"#adj","children":[]},{"level":3,"title":"LEV","slug":"lev","link":"#lev","children":[]},{"level":3,"title":"LEA","slug":"lea","link":"#lea","children":[]},{"level":3,"title":"运算符指令","slug":"运算符指令","link":"#运算符指令","children":[]},{"level":3,"title":"内置函数","slug":"内置函数","link":"#内置函数","children":[]}]},{"level":2,"title":"测试","slug":"测试","link":"#测试","children":[]},{"level":2,"title":"小结","slug":"小结","link":"#小结","children":[]}],"readingTime":{"minutes":25.04,"words":7511},"filePathRelative":"tech/designASimpileCCompiler/2.md","excerpt":"<hr>\\n<p>title: \\"手把手教你构建 C 语言编译器（2）——虚拟机\\"\\ncategory:</p>\\n<ul>\\n<li>编译原理\\ntag:</li>\\n<li>c</li>\\n<li>编译器</li>\\n<li>解释器</li>\\n</ul>\\n<hr>\\n<h1>转载声明</h1>\\n<p>本文转自 <a href=\\"https://lotabout.me/2015/write-a-C-interpreter-2/\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">https://lotabout.me/2015/write-a-C-interpreter-2/</a>，如有侵权，请联系删除。</p>","autoDesc":true}');export{I as comp,V as data};
+import{_ as l,r as t,o as c,c as r,b as s,e as a,d as n,f as p}from"./app-B4LGNJZ0.js";const o={},i=s("hr",null,null,-1),d=s("p",null,'title: "手把手教你构建 C 语言编译器（2）——虚拟机" category:',-1),b=s("ul",null,[s("li",null,"编译原理 tag:"),s("li",null,"c"),s("li",null,"编译器"),s("li",null,"解释器")],-1),h=s("hr",null,null,-1),u=s("h1",{id:"转载声明",tabindex:"-1"},[s("a",{class:"header-anchor",href:"#转载声明"},[s("span",null,"转载声明")])],-1),m={href:"https://lotabout.me/2015/write-a-C-interpreter-2/",target:"_blank",rel:"noopener noreferrer"},y=p('<h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-2-虚拟机" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-2-虚拟机"><span>手把手教你构建 C 语言编译器（2）- 虚拟机</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E5%86%85%E9%83%A8%E5%B7%A5%E4%BD%9C%E5%8E%9F%E7%90%86">1. 计算机的内部工作原理</a><ol><li><a href="about:blank#%E5%86%85%E5%AD%98">1.1. 内存</a></li><li><a href="about:blank#%E5%AF%84%E5%AD%98%E5%99%A8">1.2. 寄存器</a></li></ol></li><li><a href="about:blank#%E6%8C%87%E4%BB%A4%E9%9B%86">2. 指令集</a><ol><li><a href="about:blank#mov">2.1. MOV</a></li><li><a href="about:blank#push">2.2. PUSH</a></li><li><a href="about:blank#jmp">2.3. JMP</a></li><li><a href="about:blank#jz-jnz">2.4. JZ/JNZ</a></li><li><a href="about:blank#%E5%AD%90%E5%87%BD%E6%95%B0%E8%B0%83%E7%94%A8">2.5. 子函数调用</a></li><li><a href="about:blank#ent">2.6. ENT</a></li><li><a href="about:blank#adj">2.7. ADJ</a></li><li><a href="about:blank#lev">2.8. LEV</a></li><li><a href="about:blank#lea">2.9. LEA</a></li><li><a href="about:blank#%E8%BF%90%E7%AE%97%E7%AC%A6%E6%8C%87%E4%BB%A4">2.10. 运算符指令</a></li><li><a href="about:blank#%E5%86%85%E7%BD%AE%E5%87%BD%E6%95%B0">2.11. 内置函数</a></li></ol></li><li><a href="about:blank#%E6%B5%8B%E8%AF%95">3. 测试</a></li><li><a href="about:blank#%E5%B0%8F%E7%BB%93">4. 小结</a></li></ol><p>这是“手把手教你构建 C 语言编译器”系列的第三篇，本章我们要构建一台虚拟的电脑，设计我们自己的指令集，运行我们的指令集，说得通俗一点就是自己实现一套汇编语言。它们将作为我们的编译器最终输出的目标代码。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p>',6),f={href:"http://lotabout.me/2015/write-a-C-interpreter-0/",target:"_blank",rel:"noopener noreferrer"},k={href:"http://lotabout.me/2015/write-a-C-interpreter-1/",target:"_blank",rel:"noopener noreferrer"},x={href:"http://lotabout.me/2015/write-a-C-interpreter-2/",target:"_blank",rel:"noopener noreferrer"},E={href:"http://lotabout.me/2015/write-a-C-interpreter-3/",target:"_blank",rel:"noopener noreferrer"},g={href:"http://lotabout.me/2016/write-a-C-interpreter-4/",target:"_blank",rel:"noopener noreferrer"},w={href:"http://lotabout.me/2016/write-a-C-interpreter-5/",target:"_blank",rel:"noopener noreferrer"},_={href:"http://lotabout.me/2016/write-a-C-interpreter-6/",target:"_blank",rel:"noopener noreferrer"},C={href:"http://lotabout.me/2016/write-a-C-interpreter-7/",target:"_blank",rel:"noopener noreferrer"},A={href:"http://lotabout.me/2016/write-a-C-interpreter-8/",target:"_blank",rel:"noopener noreferrer"},v={href:"http://lotabout.me/2016/write-a-C-interpreter-9/",target:"_blank",rel:"noopener noreferrer"},L=p('<h2 id="计算机的内部工作原理" tabindex="-1"><a class="header-anchor" href="#计算机的内部工作原理"><span><a href="about:blank#%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E5%86%85%E9%83%A8%E5%B7%A5%E4%BD%9C%E5%8E%9F%E7%90%86"></a>计算机的内部工作原理</span></a></h2><p>计算机中有三个基本部件需要我们关注：CPU、寄存器及内存。代码（汇编指令）以二进制的形式保存在内存中；CPU 从中一条条地加载指令执行；程序运行的状态保存在寄存器中。</p><h3 id="内存" tabindex="-1"><a class="header-anchor" href="#内存"><span><a href="about:blank#%E5%86%85%E5%AD%98"></a>内存</span></a></h3><p>内存用于存储数据，这里的数据可以是代码，也可以是其它的数据。现代操作系统在操作内存时，并不是直接处理”物理内存“，而是操作”虚拟内存“。虚拟内存可以理解为一种映射，它的作用是屏蔽了物理的细节。例如 32 位的机器中，我们可以使用的内存地址为 <code>2^32 = 4G</code>，而电脑上的实际内存可能只有 <code>256 M</code>。操作系统将我们使用的虚拟地址映射到了到实际的内存上。</p><p>当然，我们这里并不需要了解太多，但需要了解的是：进程的内存会被分成几个段：</p><ol><li>代码段（text）用于存放代码（指令）。</li><li>数据段（data）用于存放初始化了的数据，如<code>int i = 10;</code>，就需要存放到数据段中。</li><li>未初始化数据段（bss）用于存放未初始化的数据，如 <code>int i[1000];</code>，因为不关心其中的真正数值，所以单独存放可以节省空间，减少程序的体积。</li><li>栈（stack）用于处理函数调用相关的数据，如调用帧（calling frame）或是函数的局部变量等。</li><li>堆（heap）用于为程序动态分配内存。</li></ol><p>它们在内存中的位置类似于下图：</p><table><tbody><tr><td class="code"><pre><span class="line">+------------------+</span><br><span class="line">|    stack   |     |      high address</span><br><span class="line">|    ...     v     |</span><br><span class="line">|                  |</span><br><span class="line">|                  |</span><br><span class="line">|                  |</span><br><span class="line">|                  |</span><br><span class="line">|    ...     ^     |</span><br><span class="line">|    heap    |     |</span><br><span class="line">+------------------+</span><br><span class="line">| bss  segment     |</span><br><span class="line">+------------------+</span><br><span class="line">| data segment     |</span><br><span class="line">+------------------+</span><br><span class="line">| text segment     |      low address</span><br><span class="line">+------------------+</span><br></pre></td></tr></tbody></table><p>我们的虚拟机并不打算模拟完整的计算机，因此简单起见，我们只关心三个内容：代码段、数据段以及栈。其中的数据段我们只用来存放字符串，因为我们的编译器并不支持初始化变量，因此我们也不需要未初始化数据段。</p><p>当用户的程序需要分配内存时，理论上我们的虚拟机需要维护一个堆用于内存分配，但实际实现上较为复杂且与编译无关，故我们引入一个指令<code>MSET</code>，使我们能直接使用编译器（解释器）中的内存。</p><p>综上，我们需要首先在全局添加如下代码：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> *text,            <span class="comment">// text segment</span></span><br><span class="line">    *old_text,        <span class="comment">// for dump text segment</span></span><br><span class="line">    *<span class="built_in">stack</span>;           <span class="comment">// stack</span></span><br><span class="line"><span class="type">char</span> *data;           <span class="comment">// data segment</span></span><br></pre></td></tr></tbody></table><p>注意这里的类型，虽然是<code>int</code>型，但理解起来应该作为无符号的整型，因为我们会在代码段（text）中存放如指针/内存地址的数据，它们就是无符号的。其中数据段（data）由于只存放字符串，所以是 <code>char *</code> 型的。</p><p>接着，在<code>main</code>函数中加入初始化代码，真正为其分配内存：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> <span class="title function_">main</span><span class="params">()</span> {</span><br><span class="line">    close(fd);</span><br><span class="line">    ...</span><br><span class="line"></span><br><span class="line">    <span class="comment">// allocate memory for virtual machine</span></span><br><span class="line">    <span class="keyword">if</span> (!(text = old_text = <span class="built_in">malloc</span>(poolsize))) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;could not malloc(%d) for text area\\n&quot;</span>, poolsize);</span><br><span class="line">        <span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">if</span> (!(data = <span class="built_in">malloc</span>(poolsize))) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;could not malloc(%d) for data area\\n&quot;</span>, poolsize);</span><br><span class="line">        <span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">if</span> (!(<span class="built_in">stack</span> = <span class="built_in">malloc</span>(poolsize))) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;could not malloc(%d) for stack area\\n&quot;</span>, poolsize);</span><br><span class="line">        <span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="built_in">memset</span>(text, <span class="number">0</span>, poolsize);</span><br><span class="line">    <span class="built_in">memset</span>(data, <span class="number">0</span>, poolsize);</span><br><span class="line">    <span class="built_in">memset</span>(<span class="built_in">stack</span>, <span class="number">0</span>, poolsize);</span><br><span class="line"></span><br><span class="line">    ...</span><br><span class="line">    program();</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="寄存器" tabindex="-1"><a class="header-anchor" href="#寄存器"><span><a href="about:blank#%E5%AF%84%E5%AD%98%E5%99%A8"></a>寄存器</span></a></h3><p>计算机中的寄存器用于存放计算机的运行状态，真正的计算机中有许多不同种类的寄存器，但我们的虚拟机中只使用 4 个寄存器，分别如下：</p><ol><li><code>PC</code> 程序计数器，它存放的是一个内存地址，该地址中存放着 <strong>下一条</strong> 要执行的计算机指令。</li><li><code>SP</code> 指针寄存器，永远指向当前的栈顶。注意的是由于栈是位于高地址并向低地址增长的，所以入栈时 <code>SP</code> 的值减小。</li><li><code>BP</code> 基址指针。也是用于指向栈的某些位置，在调用函数时会使用到它。</li><li><code>AX</code> 通用寄存器，我们的虚拟机中，它用于存放一条指令执行后的结果。</li></ol><p>要理解这些寄存器的作用，需要去理解程序运行中会有哪些状态。而这些寄存器只是用于保存这些状态的。</p><p>在全局中加入如下定义：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> *pc, *bp, *sp, ax, cycle; <span class="comment">// virtual machine registers</span></span><br></pre></td></tr></tbody></table><p>在 <code>main</code> 函数中加入初始化代码，注意的是<code>PC</code>在初始应指向目标代码中的<code>main</code>函数，但我们还没有写任何编译相关的代码，因此先不处理。代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="built_in">memset</span>(<span class="built_in">stack</span>, <span class="number">0</span>, poolsize);</span><br><span class="line">...</span><br><span class="line"></span><br><span class="line">bp = sp = (<span class="type">int</span> *)((<span class="type">int</span>)<span class="built_in">stack</span> + poolsize);</span><br><span class="line">ax = <span class="number">0</span>;</span><br><span class="line"></span><br><span class="line">...</span><br><span class="line">program();</span><br></pre></td></tr></tbody></table><p>与 CPU 相关的是指令集，我们将专门作为一个小节。</p><h2 id="指令集" tabindex="-1"><a class="header-anchor" href="#指令集"><span><a href="about:blank#%E6%8C%87%E4%BB%A4%E9%9B%86"></a>指令集</span></a></h2><p>指令集是 CPU 能识别的命令的集合，也可以说是 CPU 能理解的语言。这里我们要为我们的虚拟机构建自己的指令集。它们基于 x86 的指令集，但更为简单。</p><p>首先在全局变量中加入一个枚举类型，这是我们要支持的全部指令：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="comment">// instructions</span></span><br><span class="line"><span class="class"><span class="keyword">enum</span> {</span> LEA ,IMM ,JMP ,CALL,JZ  ,JNZ ,ENT ,ADJ ,LEV ,LI  ,LC  ,SI  ,SC  ,PUSH,</span><br><span class="line">       OR  ,XOR ,AND ,EQ  ,NE  ,LT  ,GT  ,LE  ,GE  ,SHL ,SHR ,ADD ,SUB ,MUL ,DIV ,MOD ,</span><br><span class="line">       OPEN,READ,CLOS,PRTF,MALC,MSET,MCMP,EXIT };</span><br></pre></td></tr></tbody></table><p>这些指令的顺序安排是有意的，稍后你会看到，带有参数的指令在前，没有参数的指令在后。这种顺序的唯一作用就是在打印调试信息时更加方便。但我们讲解的顺序并不依据它。</p><h3 id="mov" tabindex="-1"><a class="header-anchor" href="#mov"><span><a href="about:blank#mov"></a>MOV</span></a></h3><p><code>MOV</code> 是所有指令中最基础的一个，它用于将数据放进寄存器或内存地址，有点类似于 C 语言中的赋值语句。x86 的 <code>MOV</code> 指令有两个参数，分别是源地址和目标地址：<code>MOV dest, source</code> （Intel 风格），表示将 <code>source</code> 的内容放在 <code>dest</code> 中，它们可以是一个数、寄存器或是一个内存地址。</p><p>一方面，我们的虚拟机只有一个寄存器，另一方面，识别这些参数的类型（是数据还是地址）是比较困难的，因此我们将 <code>MOV</code> 指令拆分成 5 个指令，这些指令只接受一个参数，如下：</p><ol><li><code>IMM &lt;num&gt;</code> 将 <code>&lt;num&gt;</code> 放入寄存器 <code>ax</code> 中。</li><li><code>LC</code> 将对应地址中的字符载入 <code>ax</code> 中，要求 <code>ax</code> 中存放地址。</li><li><code>LI</code> 将对应地址中的整数载入 <code>ax</code> 中，要求 <code>ax</code> 中存放地址。</li><li><code>SC</code> 将 <code>ax</code> 中的数据作为字符存放入地址中，要求栈顶存放地址。</li><li><code>SI</code> 将 <code>ax</code> 中的数据作为整数存放入地址中，要求栈顶存放地址。</li></ol><p>你可能会觉得将一个指令变成了许多指令，整个系统就变得复杂了，但实际情况并非如此。首先是 x86 的 <code>MOV</code> 指令其实有许多变种，根据类型的不同有 <code>MOVB</code>, <code>MOVW</code> 等指令，我们这里的 <code>LC/SC</code> 和 <code>LI/SI</code> 就是对应字符型和整型的存取操作。</p><p>但最为重要的是，通过将 <code>MOV</code> 指令拆分成这些指令，只有 <code>IMM</code> 需要有参数，且不需要判断类型，所以大大简化了实现的难度。</p><p>在 <code>eval()</code> 函数中加入下列代码：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">eval</span><span class="params">()</span> {</span><br><span class="line">    <span class="type">int</span> op, *tmp;</span><br><span class="line">    <span class="keyword">while</span> (<span class="number">1</span>) {</span><br><span class="line">        <span class="keyword">if</span> (op == IMM)       {ax = *pc++;}                                     <span class="comment">// load immediate value to ax</span></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (op == LC)   {ax = *(<span class="type">char</span> *)ax;}                               <span class="comment">// load character to ax, address in ax</span></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (op == LI)   {ax = *(<span class="type">int</span> *)ax;}                                <span class="comment">// load integer to ax, address in ax</span></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (op == SC)   {ax = *(<span class="type">char</span> *)*sp++ = ax;}                       <span class="comment">// save character to address, value in ax, address on stack</span></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (op == SI)   {*(<span class="type">int</span> *)*sp++ = ax;}                             <span class="comment">// save integer to address, value in ax, address on stack</span></span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    ...</span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>其中的 <code>*sp++</code> 的作用是退栈，相当于 <code>POP</code> 操作。</p><p>这里要解释的一点是，为什么 <code>SI/SC</code> 指令中，地址存放在栈中，而 <code>LI/LC</code> 中，地址存放在 <code>ax</code> 中？原因是默认计算的结果是存放在 <code>ax</code> 中的，而地址通常是需要通过计算获得，所以执行 <code>LI/LC</code> 时直接从 <code>ax</code> 取值会更高效。另一点是我们的 <code>PUSH</code> 指令只能将 <code>ax</code> 的值放到栈上，而不能以值作为参数，详细见下文。</p><h3 id="push" tabindex="-1"><a class="header-anchor" href="#push"><span><a href="about:blank#push"></a>PUSH</span></a></h3><p>在 x86 中，<code>PUSH</code> 的作用是将值或寄存器，而在我们的虚拟机中，它的作用是将 <code>ax</code> 的值放入栈中。这样做的主要原因是为了简化虚拟机的实现，并且我们也只有一个寄存器 <code>ax</code> 。代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == PUSH) {*--sp = ax;}                                     <span class="comment">// push the value of ax onto the stack</span></span><br></pre></td></tr></tbody></table><h3 id="jmp" tabindex="-1"><a class="header-anchor" href="#jmp"><span><a href="about:blank#jmp"></a>JMP</span></a></h3><p><code>JMP &lt;addr&gt;</code> 是跳转指令，无条件地将当前的 <code>PC</code> 寄存器设置为指定的 <code>&lt;addr&gt;</code>，实现如下：</p><table><tbody><tr><td class="code"><pre><span class="line">else if (op == JMP)  {pc = (int *)*pc;}                                // jump to the address</span><br></pre></td></tr></tbody></table><p>需要注意的是，<code>pc</code> 寄存器指向的是 <strong>下一条</strong> 指令。所以此时它存放的是 <code>JMP</code> 指令的参数，即 <code>&lt;addr&gt;</code> 的值。</p><h3 id="jz-jnz" tabindex="-1"><a class="header-anchor" href="#jz-jnz"><span><a href="about:blank#jz-jnz"></a>JZ/JNZ</span></a></h3><p>为了实现 <code>if</code> 语句，我们需要条件判断相关的指令。这里我们只实现两个最简单的条件判断，即结果（<code>ax</code>）为零或不为零情况下的跳转。</p><p>实现如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == JZ)   {pc = ax ? pc + <span class="number">1</span> : (<span class="type">int</span> *)*pc;}                   <span class="comment">// jump if ax is zero</span></span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == JNZ)  {pc = ax ? (<span class="type">int</span> *)*pc : pc + <span class="number">1</span>;}                   <span class="comment">// jump if ax is not zero</span></span><br></pre></td></tr></tbody></table><h3 id="子函数调用" tabindex="-1"><a class="header-anchor" href="#子函数调用"><span><a href="about:blank#%E5%AD%90%E5%87%BD%E6%95%B0%E8%B0%83%E7%94%A8"></a>子函数调用</span></a></h3><p>这是汇编中最难理解的部分，所以合在一起说，要引入的命令有 <code>CALL</code>, <code>ENT</code>, <code>ADJ</code> 及 <code>LEV</code>。</p><p>首先我们介绍 <code>CALL &lt;addr&gt;</code> 与 <code>RET</code> 指令，<code>CALL</code> 的作用是跳转到地址为 <code>&lt;addr&gt;</code> 的子函数，<code>RET</code> 则用于从子函数中返回。</p><p>为什么不能直接使用 <code>JMP</code> 指令呢？原因是当我们从子函数中返回时，程序需要回到跳转之前的地方继续运行，这就需要事先将这个位置信息存储起来。反过来，子函数要返回时，就需要获取并恢复这个信息。因此实际中我们将 <code>PC</code> 保存在栈中。如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == CALL) {*--sp = (<span class="type">int</span>)(pc+<span class="number">1</span>); pc = (<span class="type">int</span> *)*pc;}           <span class="comment">// call subroutine</span></span><br><span class="line"><span class="comment">//else if (op == RET)  {pc = (int *)*sp++;}                              // return from subroutine;</span></span><br></pre></td></tr></tbody></table><p>这里我们把 <code>RET</code> 相关的内容注释了，是因为之后我们将用 <code>LEV</code> 指令来代替它。</p><p>在实际调用函数时，不仅要考虑函数的地址，还要考虑如何传递参数和如何返回结果。这里我们约定，如果子函数有返回结果，那么就在返回时保存在 <code>ax</code> 中，它可以是一个值，也可以是一个地址。那么参数的传递呢？</p><p>各种编程语言关于如何调用子函数有不同的约定，例如 C 语言的调用标准是：</p><ol><li>由调用者将参数入栈。</li><li>调用结束时，由调用者将参数出栈。</li><li>参数逆序入栈。</li></ol>',59),B={href:"https://en.wikipedia.org/wiki/X86_calling_conventions",target:"_blank",rel:"noopener noreferrer"},M=p('<table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> <span class="title function_">callee</span><span class="params">(<span class="type">int</span>, <span class="type">int</span>, <span class="type">int</span>)</span>;</span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">caller</span><span class="params">(<span class="type">void</span>)</span></span><br><span class="line">{</span><br><span class="line">	<span class="type">int</span> i, ret;</span><br><span class="line"></span><br><span class="line">	ret = callee(<span class="number">1</span>, <span class="number">2</span>, <span class="number">3</span>);</span><br><span class="line">	ret += <span class="number">5</span>;</span><br><span class="line">	<span class="keyword">return</span> ret;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>会生成如下的 x86 汇编代码：</p><table><tbody><tr><td class="code"><pre><span class="line">caller:</span><br><span class="line">	; make new call frame</span><br><span class="line">	push    ebp</span><br><span class="line">	mov     ebp, esp</span><br><span class="line">        sub     1, esp       ; save stack for variable: i</span><br><span class="line">	; push call arguments</span><br><span class="line">	push    3</span><br><span class="line">	push    2</span><br><span class="line">	push    1</span><br><span class="line">	; call subroutine &#39;callee&#39;</span><br><span class="line">	call    callee</span><br><span class="line">	; remove arguments from frame</span><br><span class="line">	add     esp, 12</span><br><span class="line">	; use subroutine result</span><br><span class="line">	add     eax, 5</span><br><span class="line">	; restore old call frame</span><br><span class="line">        mov     esp, ebp</span><br><span class="line">	pop     ebp</span><br><span class="line">	; return</span><br><span class="line">	ret</span><br></pre></td></tr></tbody></table><p>上面这段代码在我们自己的虚拟机里会有几个问题：</p><ol><li><code>push ebp</code>，但我们的 <code>PUSH</code> 指令并无法指定寄存器。</li><li><code>mov ebp, esp</code>，我们的 <code>MOV</code> 指令同样功能不足。</li><li><code>add esp, 12</code>，也是一样的问题（尽管我们还没定义）。</li></ol><p>也就是说由于我们的指令过于简单（如只能操作<code>ax</code>寄存器），所以用上面提到的指令，我们连函数调用都无法实现。而我们又不希望扩充现有指令的功能，因为这样实现起来就会变得复杂，因此我们采用的方法是增加指令集。毕竟我们不是真正的计算机，增加指令会消耗许多资源（钱）。</p><h3 id="ent" tabindex="-1"><a class="header-anchor" href="#ent"><span><a href="about:blank#ent"></a>ENT</span></a></h3><p><code>ENT &lt;size&gt;</code> 指的是 <code>enter</code>，用于实现 ‘make new call frame’ 的功能，即保存当前的栈指针，同时在栈上保留一定的空间，用以存放局部变量。对应的汇编代码为：</p><table><tbody><tr><td class="code"><pre><span class="line">; make new call frame</span><br><span class="line">push    ebp</span><br><span class="line">mov     ebp, esp</span><br><span class="line">       sub     1, esp       ; save stack for variable: i</span><br></pre></td></tr></tbody></table><p>实现如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == ENT)  {*--sp = (<span class="type">int</span>)bp; bp = sp; sp = sp - *pc++;}      <span class="comment">// make new stack frame</span></span><br></pre></td></tr></tbody></table><h3 id="adj" tabindex="-1"><a class="header-anchor" href="#adj"><span><a href="about:blank#adj"></a>ADJ</span></a></h3><p><code>ADJ &lt;size&gt;</code> 用于实现 ‘remove arguments from frame’。在将调用子函数时压入栈中的数据清除，本质上是因为我们的 <code>ADD</code> 指令功能有限。对应的汇编代码为：</p><table><tbody><tr><td class="code"><pre><span class="line">; remove arguments from frame</span><br><span class="line">add     esp, 12</span><br></pre></td></tr></tbody></table><p>实现如下：</p><table><tbody><tr><td class="code"><pre><span class="line">else if (op == ADJ)  {sp = sp + *pc++;}                                // add esp, &lt;size&gt;</span><br></pre></td></tr></tbody></table><h3 id="lev" tabindex="-1"><a class="header-anchor" href="#lev"><span><a href="about:blank#lev"></a>LEV</span></a></h3><p>本质上这个指令并不是必需的，只是我们的指令集中并没有 <code>POP</code> 指令。并且三条指令写来比较麻烦且浪费空间，所以用一个指令代替。对应的汇编指令为：</p><table><tbody><tr><td class="code"><pre><span class="line">; restore old call frame</span><br><span class="line">       mov     esp, ebp</span><br><span class="line">pop     ebp</span><br><span class="line">; return</span><br><span class="line">ret</span><br></pre></td></tr></tbody></table><p>具体的实现如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == LEV)  {sp = bp; bp = (<span class="type">int</span> *)*sp++; pc = (<span class="type">int</span> *)*sp++;}  <span class="comment">// restore call frame and PC</span></span><br></pre></td></tr></tbody></table><p>注意的是，<code>LEV</code> 已经把 <code>RET</code> 的功能包含了，所以我们不再需要 <code>RET</code> 指令。</p><h3 id="lea" tabindex="-1"><a class="header-anchor" href="#lea"><span><a href="about:blank#lea"></a>LEA</span></a></h3><p>上面的一些指令解决了调用帧的问题，但还有一个问题是如何在子函数中获得传入的参数。这里我们首先要了解的是当参数调用时，栈中的调用帧是什么样的。我们依旧用上面的例子（只是现在用“顺序”调用参数）：</p><table><tbody><tr><td class="code"><pre><span class="line">sub_function(arg1, arg2, arg3);</span><br><span class="line"></span><br><span class="line">|    ....       | high address</span><br><span class="line">+---------------+</span><br><span class="line">| arg: 1        |    new_bp + 4</span><br><span class="line">+---------------+</span><br><span class="line">| arg: 2        |    new_bp + 3</span><br><span class="line">+---------------+</span><br><span class="line">| arg: 3        |    new_bp + 2</span><br><span class="line">+---------------+</span><br><span class="line">|return address |    new_bp + 1</span><br><span class="line">+---------------+</span><br><span class="line">| old BP        | &lt;- new BP</span><br><span class="line">+---------------+</span><br><span class="line">| local var 1   |    new_bp - 1</span><br><span class="line">+---------------+</span><br><span class="line">| local var 2   |    new_bp - 2</span><br><span class="line">+---------------+</span><br><span class="line">|    ....       |  low address</span><br></pre></td></tr></tbody></table><p>所以为了获取第一个参数，我们需要得到 <code>new_bp + 4</code>，但就如上面的说，我们的 <code>ADD</code> 指令无法操作除 <code>ax</code> 外的寄存器，所以我们提供了一个新的指令：<code>LEA &lt;offset&gt;</code></p><p>实现如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == LEA)  {ax = (<span class="type">int</span>)(bp + *pc++);}                         <span class="comment">// load address for arguments.</span></span><br></pre></td></tr></tbody></table><p>以上就是我们为了实现函数调用需要的指令了。</p><h3 id="运算符指令" tabindex="-1"><a class="header-anchor" href="#运算符指令"><span><a href="about:blank#%E8%BF%90%E7%AE%97%E7%AC%A6%E6%8C%87%E4%BB%A4"></a>运算符指令</span></a></h3><p>我们为 C 语言中支持的运算符都提供对应汇编指令。每个运算符都是二元的，即有两个参数，第一个参数放在栈顶，第二个参数放在 <code>ax</code> 中。这个顺序要特别注意。因为像 <code>-</code>，<code>/</code> 之类的运算符是与参数顺序有关的。计算后会将栈顶的参数退栈，结果存放在寄存器 <code>ax</code> 中。因此计算结束后，两个参数都无法取得了（汇编的意义上，存在内存地址上就另当别论）。</p><p>实现如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == OR)  ax = *sp++ | ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == XOR) ax = *sp++ ^ ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == AND) ax = *sp++ &amp; ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == EQ)  ax = *sp++ == ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == NE)  ax = *sp++ != ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == LT)  ax = *sp++ &lt; ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == LE)  ax = *sp++ &lt;= ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == GT)  ax = *sp++ &gt;  ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == GE)  ax = *sp++ &gt;= ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == SHL) ax = *sp++ &lt;&lt; ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == SHR) ax = *sp++ &gt;&gt; ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == ADD) ax = *sp++ + ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == SUB) ax = *sp++ - ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == MUL) ax = *sp++ * ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == DIV) ax = *sp++ / ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == MOD) ax = *sp++ % ax;</span><br></pre></td></tr></tbody></table><h3 id="内置函数" tabindex="-1"><a class="header-anchor" href="#内置函数"><span><a href="about:blank#%E5%86%85%E7%BD%AE%E5%87%BD%E6%95%B0"></a>内置函数</span></a></h3><p>写的程序要”有用“，除了核心的逻辑外还需要输入输出，例如 C 语言中我们经常使用的 <code>printf</code> 函数就是用于输出。但是 <code>printf</code> 函数的实现本身就十分复杂，如果我们的编译器要达到自举，就势必要实现 <code>printf</code> 之类的函数，但它又与编译器没有太大的联系，因此我们继续实现新的指令，从虚拟机的角度予以支持。</p><p>编译器中我们需要用到的函数有：<code>exit</code>, <code>open</code>, <code>close</code>, <code>read</code>, <code>printf</code>, <code>malloc</code>, <code>memset</code> 及 <code>memcmp</code>。代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == EXIT) { <span class="built_in">printf</span>(<span class="string">&quot;exit(%d)&quot;</span>, *sp); <span class="keyword">return</span> *sp;}</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == OPEN) { ax = open((<span class="type">char</span> *)sp[<span class="number">1</span>], sp[<span class="number">0</span>]); }</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == CLOS) { ax = close(*sp);}</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == READ) { ax = read(sp[<span class="number">2</span>], (<span class="type">char</span> *)sp[<span class="number">1</span>], *sp); }</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == PRTF) { tmp = sp + pc[<span class="number">1</span>]; ax = <span class="built_in">printf</span>((<span class="type">char</span> *)tmp[<span class="number">-1</span>], tmp[<span class="number">-2</span>], tmp[<span class="number">-3</span>], tmp[<span class="number">-4</span>], tmp[<span class="number">-5</span>], tmp[<span class="number">-6</span>]); }</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == MALC) { ax = (<span class="type">int</span>)<span class="built_in">malloc</span>(*sp);}</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == MSET) { ax = (<span class="type">int</span>)<span class="built_in">memset</span>((<span class="type">char</span> *)sp[<span class="number">2</span>], sp[<span class="number">1</span>], *sp);}</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == MCMP) { ax = <span class="built_in">memcmp</span>((<span class="type">char</span> *)sp[<span class="number">2</span>], (<span class="type">char</span> *)sp[<span class="number">1</span>], *sp);}</span><br></pre></td></tr></tbody></table><p>这里的原理是，我们的电脑上已经有了这些函数的实现，因此编译编译器时，这些函数的二进制代码就被编译进了我们的编译器，因此在我们的编译器/虚拟机上运行我们提供的这些指令时，这些函数就是可用的。换句话说就是不需要我们自己去实现了。</p><p>最后再加上一个错误判断：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> {</span><br><span class="line">    <span class="built_in">printf</span>(<span class="string">&quot;unknown instruction:%d\\n&quot;</span>, op);</span><br><span class="line">    <span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h2 id="测试" tabindex="-1"><a class="header-anchor" href="#测试"><span><a href="about:blank#%E6%B5%8B%E8%AF%95"></a>测试</span></a></h2><p>下面我们用我们的汇编写一小段程序，来计算 <code>10+20</code>，在 <code>main</code> 函数中加入下列代码：</p><table><tbody><tr><td class="code"><pre><span class="line">int main(int argc, char *argv[])</span><br><span class="line">{</span><br><span class="line">    ax = 0;</span><br><span class="line">    ...</span><br><span class="line"></span><br><span class="line">    i = 0;</span><br><span class="line">    text[i++] = IMM;</span><br><span class="line">    text[i++] = 10;</span><br><span class="line">    text[i++] = PUSH;</span><br><span class="line">    text[i++] = IMM;</span><br><span class="line">    text[i++] = 20;</span><br><span class="line">    text[i++] = ADD;</span><br><span class="line">    text[i++] = PUSH;</span><br><span class="line">    text[i++] = EXIT;</span><br><span class="line">    pc = text;</span><br><span class="line"></span><br><span class="line">    ...</span><br><span class="line">    program();</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>编译程序 <code>gcc xc-tutor.c</code>，运行程序：<code>./a.out hello.c</code>。输出</p><table><tbody><tr><td class="code"><pre><span class="line">exit(30)</span><br></pre></td></tr></tbody></table><p>另外，我们的代码里有一些指针的强制转换，默认是 32 位的，因此在 64 位机器下，会出现 <code>segmentation fault</code>，解决方法（二选一）：</p><ol><li>编译时加上 <code>-m32</code> 参数：<code>gcc -m32 xc-tutor.c</code></li><li>在代码的开头，增加 <code>#define int long long</code>，<code>long long</code> 是 64 位的，不会出现强制转换后的问题。</li></ol><p>注意我们的之前的程序需要指令一个源文件，只是现在还用不着，但从结果可以看出，我们的虚拟机还是工作良好的。</p><h2 id="小结" tabindex="-1"><a class="header-anchor" href="#小结"><span><a href="about:blank#%E5%B0%8F%E7%BB%93"></a>小结</span></a></h2><p>本章中我们回顾了计算机的内部运行原理，并仿照 x86 汇编指令设计并实现了我们自己的指令集。希望通过本章的学习，你能对计算机程序的原理有一定的了解，同时能对汇编语言有一定的概念，因为汇编语言就是 C 编译器的输出。</p>',50),P={href:"https://github.com/lotabout/write-a-C-interpreter/tree/step-1",target:"_blank",rel:"noopener noreferrer"},D=s("table",null,[s("tbody",null,[s("tr",null,[s("td",{class:"code"},[s("pre",null,[s("span",{class:"line"},"git clone -b step-1 https://github.com/lotabout/write-a-C-interpreter"),s("br")])])])])],-1),S=s("p",null,"实际计算机中，添加一个新的指令需要设计许多新的电路，会增加许多的成本，但我们的虚拟机中，新的指令几乎不消耗资源，因此我们可以利用这一点，用更多的指令来完成更多的功能，从而简化具体的实现。",-1);function j(z,T){const e=t("ExternalLinkIcon");return c(),r("div",null,[i,d,b,h,u,s("p",null,[a("本文转自 "),s("a",m,[a("https://lotabout.me/2015/write-a-C-interpreter-2/"),n(e)]),a("，如有侵权，请联系删除。")]),y,s("ol",null,[s("li",null,[s("a",f,[a("手把手教你构建 C 语言编译器（0）——前言"),n(e)])]),s("li",null,[s("a",k,[a("手把手教你构建 C 语言编译器（1）——设计"),n(e)])]),s("li",null,[s("a",x,[a("手把手教你构建 C 语言编译器（2）——虚拟机"),n(e)])]),s("li",null,[s("a",E,[a("手把手教你构建 C 语言编译器（3）——词法分析器"),n(e)])]),s("li",null,[s("a",g,[a("手把手教你构建 C 语言编译器（4）——递归下降"),n(e)])]),s("li",null,[s("a",w,[a("手把手教你构建 C 语言编译器（5）——变量定义"),n(e)])]),s("li",null,[s("a",_,[a("手把手教你构建 C 语言编译器（6）——函数定义"),n(e)])]),s("li",null,[s("a",C,[a("手把手教你构建 C 语言编译器（7）——语句"),n(e)])]),s("li",null,[s("a",A,[a("手把手教你构建 C 语言编译器（8）——表达式"),n(e)])]),s("li",null,[s("a",v,[a("手把手教你构建 C 语言编译器（9）——总结"),n(e)])])]),L,s("p",null,[a("事先声明一下，我们的编译器参数是顺序入栈的，下面的例子（C 语言调用标准）取自 "),s("a",B,[a("维基百科"),n(e)]),a("：")]),M,s("p",null,[a("本章的代码可以在 "),s("a",P,[a("Github"),n(e)]),a(" 上下载，也可以直接 clone")]),D,S])}const I=l(o,[["render",j],["__file","2.html.vue"]]),V=JSON.parse('{"path":"/tech/designASimpileCCompiler/2.html","title":"转载声明","lang":"zh-CN","frontmatter":{"description":"title: \\"手把手教你构建 C 语言编译器（2）——虚拟机\\" category: 编译原理 tag: c 编译器 解释器 转载声明 本文转自 https://lotabout.me/2015/write-a-C-interpreter-2/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（2）- 虚拟机 Table of Cont...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/designASimpileCCompiler/2.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"转载声明"}],["meta",{"property":"og:description","content":"title: \\"手把手教你构建 C 语言编译器（2）——虚拟机\\" category: 编译原理 tag: c 编译器 解释器 转载声明 本文转自 https://lotabout.me/2015/write-a-C-interpreter-2/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（2）- 虚拟机 Table of Cont..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"转载声明\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"计算机的内部工作原理","slug":"计算机的内部工作原理","link":"#计算机的内部工作原理","children":[{"level":3,"title":"内存","slug":"内存","link":"#内存","children":[]},{"level":3,"title":"寄存器","slug":"寄存器","link":"#寄存器","children":[]}]},{"level":2,"title":"指令集","slug":"指令集","link":"#指令集","children":[{"level":3,"title":"MOV","slug":"mov","link":"#mov","children":[]},{"level":3,"title":"PUSH","slug":"push","link":"#push","children":[]},{"level":3,"title":"JMP","slug":"jmp","link":"#jmp","children":[]},{"level":3,"title":"JZ/JNZ","slug":"jz-jnz","link":"#jz-jnz","children":[]},{"level":3,"title":"子函数调用","slug":"子函数调用","link":"#子函数调用","children":[]},{"level":3,"title":"ENT","slug":"ent","link":"#ent","children":[]},{"level":3,"title":"ADJ","slug":"adj","link":"#adj","children":[]},{"level":3,"title":"LEV","slug":"lev","link":"#lev","children":[]},{"level":3,"title":"LEA","slug":"lea","link":"#lea","children":[]},{"level":3,"title":"运算符指令","slug":"运算符指令","link":"#运算符指令","children":[]},{"level":3,"title":"内置函数","slug":"内置函数","link":"#内置函数","children":[]}]},{"level":2,"title":"测试","slug":"测试","link":"#测试","children":[]},{"level":2,"title":"小结","slug":"小结","link":"#小结","children":[]}],"readingTime":{"minutes":25.04,"words":7511},"filePathRelative":"tech/designASimpileCCompiler/2.md","excerpt":"<hr>\\n<p>title: \\"手把手教你构建 C 语言编译器（2）——虚拟机\\"\\ncategory:</p>\\n<ul>\\n<li>编译原理\\ntag:</li>\\n<li>c</li>\\n<li>编译器</li>\\n<li>解释器</li>\\n</ul>\\n<hr>\\n<h1>转载声明</h1>\\n<p>本文转自 <a href=\\"https://lotabout.me/2015/write-a-C-interpreter-2/\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">https://lotabout.me/2015/write-a-C-interpreter-2/</a>，如有侵权，请联系删除。</p>","autoDesc":true}');export{I as comp,V as data};
diff --git a/assets/3.html-CZB5joNY.js b/assets/3.html-D9pPtuiP.js
similarity index 99%
rename from assets/3.html-CZB5joNY.js
rename to assets/3.html-D9pPtuiP.js
index 576c6fb..9d3ca87 100644
--- a/assets/3.html-CZB5joNY.js
+++ b/assets/3.html-D9pPtuiP.js
@@ -1 +1 @@
-import{_ as l,r,o as c,c as t,b as s,e as a,d as e,f as p}from"./app-B69Gl_S-.js";const i={},o=s("h1",{id:"转载声明",tabindex:"-1"},[s("a",{class:"header-anchor",href:"#转载声明"},[s("span",null,"转载声明")])],-1),b={href:"https://lotabout.me/2015/write-a-C-interpreter-3/",target:"_blank",rel:"noopener noreferrer"},d=p('<h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-3-词法分析器" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-3-词法分析器"><span>手把手教你构建 C 语言编译器（3）- 词法分析器</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#%E4%BB%80%E4%B9%88%E6%98%AF%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8">1. 什么是词法分析器</a></li><li><a href="about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8%E4%B8%8E%E7%BC%96%E8%AF%91%E5%99%A8">2. 词法分析器与编译器</a></li><li><a href="about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8%E7%9A%84%E5%AE%9E%E7%8E%B0">3. 词法分析器的实现</a><ol><li><a href="about:blank#%E6%94%AF%E6%8C%81%E7%9A%84%E6%A0%87%E8%AE%B0">3.1. 支持的标记</a></li><li><a href="about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8%E7%9A%84%E6%A1%86%E6%9E%B6">3.2. 词法分析器的框架</a></li><li><a href="about:blank#%E6%8D%A2%E8%A1%8C%E7%AC%A6">3.3. 换行符</a></li><li><a href="about:blank#%E5%AE%8F%E5%AE%9A%E4%B9%89">3.4. 宏定义</a></li><li><a href="about:blank#%E6%A0%87%E8%AF%86%E7%AC%A6%E4%B8%8E%E7%AC%A6%E5%8F%B7%E8%A1%A8">3.5. 标识符与符号表</a></li><li><a href="about:blank#%E6%95%B0%E5%AD%97">3.6. 数字</a></li><li><a href="about:blank#%E5%AD%97%E7%AC%A6%E4%B8%B2">3.7. 字符串</a></li><li><a href="about:blank#%E6%B3%A8%E9%87%8A">3.8. 注释</a></li><li><a href="about:blank#%E5%85%B6%E5%AE%83">3.9. 其它</a></li><li><a href="about:blank#%E5%85%B3%E9%94%AE%E5%AD%97%E4%B8%8E%E5%86%85%E7%BD%AE%E5%87%BD%E6%95%B0">3.10. 关键字与内置函数</a></li></ol></li><li><a href="about:blank#%E4%BB%A3%E7%A0%81">4. 代码</a></li><li><a href="about:blank#%E5%B0%8F%E7%BB%93">5. 小结</a></li></ol><p>本章我们要讲解如何构建词法分析器。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p>',6),k={href:"http://lotabout.me/2015/write-a-C-interpreter-0/",target:"_blank",rel:"noopener noreferrer"},h={href:"http://lotabout.me/2015/write-a-C-interpreter-1/",target:"_blank",rel:"noopener noreferrer"},E={href:"http://lotabout.me/2015/write-a-C-interpreter-2/",target:"_blank",rel:"noopener noreferrer"},m={href:"http://lotabout.me/2015/write-a-C-interpreter-3/",target:"_blank",rel:"noopener noreferrer"},u={href:"http://lotabout.me/2016/write-a-C-interpreter-4/",target:"_blank",rel:"noopener noreferrer"},y={href:"http://lotabout.me/2016/write-a-C-interpreter-5/",target:"_blank",rel:"noopener noreferrer"},f={href:"http://lotabout.me/2016/write-a-C-interpreter-6/",target:"_blank",rel:"noopener noreferrer"},g={href:"http://lotabout.me/2016/write-a-C-interpreter-7/",target:"_blank",rel:"noopener noreferrer"},A={href:"http://lotabout.me/2016/write-a-C-interpreter-8/",target:"_blank",rel:"noopener noreferrer"},w={href:"http://lotabout.me/2016/write-a-C-interpreter-9/",target:"_blank",rel:"noopener noreferrer"},_=p('<h2 id="什么是词法分析器" tabindex="-1"><a class="header-anchor" href="#什么是词法分析器"><span><a href="about:blank#%E4%BB%80%E4%B9%88%E6%98%AF%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8"></a>什么是词法分析器</span></a></h2><p>简而言之，词法分析器用于对源码字符串做预处理，以减少语法分析器的复杂程度。</p><p>词法分析器以源码字符串为输入，输出为标记流（token stream），即一连串的标记，每个标记通常包括： <code>(token, token value)</code> 即标记本身和标记的值。例如，源码中若包含一个数字 <code>&#39;998&#39;</code> ，词法分析器将输出 <code>(Number, 998)</code>，即（数字，998）。再例如：</p><table><tbody><tr><td class="code"><pre><span class="line">2 + 3 * (4 - 5)</span><br><span class="line">=&gt;</span><br><span class="line">(Number, 2) Add (Number, 3) Multiply Left-Bracket (Number, 4) Subtract (Number, 5) Right-Bracket</span><br></pre></td></tr></tbody></table><p>通过词法分析器的预处理，语法分析器的复杂度会大大降低，这点在后面的语法分析器我们就能体会。</p><h2 id="词法分析器与编译器" tabindex="-1"><a class="header-anchor" href="#词法分析器与编译器"><span><a href="about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8%E4%B8%8E%E7%BC%96%E8%AF%91%E5%99%A8"></a>词法分析器与编译器</span></a></h2><p>要是深入词法分析器，你就会发现，它的本质上也是编译器。我们的编译器是以标记流为输入，输出汇编代码，而词法分析器则是以源码字符串为输入，输出标记流。</p><table><tbody><tr><td class="code"><pre><span class="line">                   +-------+                      +--------+</span><br><span class="line">-- source code --&gt; | lexer | --&gt; token stream --&gt; | parser | --&gt; assembly</span><br><span class="line">                   +-------+                      +--------+</span><br></pre></td></tr></tbody></table><p>在这个前提下，我们可以这样认为：直接从源代码编译成汇编代码是很困难的，因为输入的字符串比较难处理。所以我们先编写一个较为简单的编译器（词法分析器）来将字符串转换成标记流，而标记流对于语法分析器而言就容易处理得多了。</p><h2 id="词法分析器的实现" tabindex="-1"><a class="header-anchor" href="#词法分析器的实现"><span><a href="about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8%E7%9A%84%E5%AE%9E%E7%8E%B0"></a>词法分析器的实现</span></a></h2><p>由于词法分析的工作很常见，但又枯燥且容易出错，所以人们已经开发出了许多工具来生成词法分析器，如 <code>lex, flex</code>。这些工具允许我们通过正则表达式来识别标记。</p><p>这里注意的是，我们并不会一次性地将所有源码全部转换成标记流，原因有二：</p><ol><li>字符串转换成标记流有时是有状态的，即与代码的上下文是有关系的。</li><li>保存所有的标记流没有意义且浪费空间。</li></ol><p>所以实际的处理方法是提供一个函数（即前几篇中提到的 <code>next()</code>），每次调用该函数则返回下一个标记。</p><h3 id="支持的标记" tabindex="-1"><a class="header-anchor" href="#支持的标记"><span><a href="about:blank#%E6%94%AF%E6%8C%81%E7%9A%84%E6%A0%87%E8%AE%B0"></a>支持的标记</span></a></h3><p>在全局中添加如下定义：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="comment">// tokens and classes (operators last and in precedence order)</span></span><br><span class="line"><span class="class"><span class="keyword">enum</span> {</span></span><br><span class="line">  Num = <span class="number">128</span>, Fun, Sys, Glo, Loc, Id,</span><br><span class="line">  Char, Else, Enum, If, Int, Return, Sizeof, While,</span><br><span class="line">  Assign, Cond, Lor, Lan, Or, Xor, And, Eq, Ne, Lt, Gt, Le, Ge, Shl, Shr, Add, Sub, Mul, Div, Mod, Inc, Dec, Brak</span><br><span class="line">};</span><br></pre></td></tr></tbody></table><p>这些就是我们要支持的标记符。例如，我们会将 <code>=</code> 解析为 <code>Assign</code>；将 <code>==</code> 解析为 <code>Eq</code>；将 <code>!=</code> 解析为 <code>Ne</code> 等等。</p><p>所以这里我们会有这样的印象，一个标记（token）可能包含多个字符，且多数情况下如此。而词法分析器能减小语法分析复杂度的原因，正是因为它相当于通过一定的编码（更多的标记）来压缩了源码字符串。</p><p>当然，上面这些标记是有顺序的，跟它们在 C 语言中的优先级有关，如 <code>*(Mul)</code> 的优先级就要高于 <code>+(Add)</code>。它们的具体使用在后面的语法分析中会提到。</p><p>最后要注意的是还有一些字符，它们自己就构成了标记，如右方括号 <code>]</code> 或波浪号 <code>~</code> 等。我们不另外处理它们的原因是：</p><ol><li>它们是单字符的，即并不是多个字符共同构成标记（如 <code>==</code> 需要两个字符）；</li><li>它们不涉及优先级关系。</li></ol><h3 id="词法分析器的框架" tabindex="-1"><a class="header-anchor" href="#词法分析器的框架"><span><a href="about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8%E7%9A%84%E6%A1%86%E6%9E%B6"></a>词法分析器的框架</span></a></h3><p>即 <code>next()</code> 函数的主体：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">next</span><span class="params">()</span> {</span><br><span class="line">    <span class="type">char</span> *last_pos;</span><br><span class="line">    <span class="type">int</span> hash;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">while</span> (token = *src) {</span><br><span class="line">        ++src;</span><br><span class="line">        <span class="comment">// parse token here</span></span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">return</span>;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>这里的一个问题是，为什么要用 <code>while</code> 循环呢？这就涉及到编译器（记得我们说过词法分析器也是某种意义上的编译器）的一个问题：如何处理错误？</p><p>对词法分析器而言，若碰到了一个我们不认识的字符该怎么处理？一般处理的方法有两种：</p><ol><li>指出错误发生的位置，并退出整个程序</li><li>指出错误发生的位置，跳过当前错误并继续编译</li></ol><p>这个 <code>while</code> 循环的作用就是跳过这些我们不识别的字符，我们同时还用它来处理空白字符。我们知道，C 语言中空格是用来作为分隔用的，并不作为语法的一部分。因此在实现中我们将它作为“不识别”的字符，这个 <code>while</code> 循环可以用来跳过它。</p><h3 id="换行符" tabindex="-1"><a class="header-anchor" href="#换行符"><span><a href="about:blank#%E6%8D%A2%E8%A1%8C%E7%AC%A6"></a>换行符</span></a></h3><p>换行符和空格类似，但有一点不同，每次遇到换行符，我们需要将当前的行号加一：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="comment">// parse token here</span></span><br><span class="line">...</span><br><span class="line"></span><br><span class="line"><span class="keyword">if</span> (token == <span class="string">&#39;\\n&#39;</span>) {</span><br><span class="line">    ++line;</span><br><span class="line">}</span><br><span class="line">...</span><br></pre></td></tr></tbody></table><h3 id="宏定义" tabindex="-1"><a class="header-anchor" href="#宏定义"><span><a href="about:blank#%E5%AE%8F%E5%AE%9A%E4%B9%89"></a>宏定义</span></a></h3><p>C 语言的宏定义以字符 <code>#</code> 开头，如 <code># include &lt;stdio.h&gt;</code>。我们的编译器并不支持宏定义，所以直接跳过它们。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;#&#39;</span>) {</span><br><span class="line">    <span class="comment">// skip macro, because we will not support it</span></span><br><span class="line">    <span class="keyword">while</span> (*src != <span class="number">0</span> &amp;&amp; *src != <span class="string">&#39;\\n&#39;</span>) {</span><br><span class="line">        src++;</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="标识符与符号表" tabindex="-1"><a class="header-anchor" href="#标识符与符号表"><span><a href="about:blank#%E6%A0%87%E8%AF%86%E7%AC%A6%E4%B8%8E%E7%AC%A6%E5%8F%B7%E8%A1%A8"></a>标识符与符号表</span></a></h3><p>标识符（identifier）可以理解为变量名。对于语法分析而言，我们并不关心一个变量具体叫什么名字，而只关心这个变量名代表的唯一标识。例如 <code>int a;</code> 定义了变量 <code>a</code>，而之后的语句 <code>a = 10</code>，我们需要知道这两个 <code>a</code> 指向的是同一个变量。</p><p>基于这个理由，词法分析器会把扫描到的标识符全都保存到一张表中，遇到新的标识符就去查这张表，如果标识符已经存在，就返回它的唯一标识。</p><p>那么我们怎么表示标识符呢？如下：</p><table><tbody><tr><td class="code"><pre><span class="line">struct identifier {</span><br><span class="line">    int token;</span><br><span class="line">    int hash;</span><br><span class="line">    char * name;</span><br><span class="line">    int class;</span><br><span class="line">    int type;</span><br><span class="line">    int value;</span><br><span class="line">    int Bclass;</span><br><span class="line">    int Btype;</span><br><span class="line">    int Bvalue;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>这里解释一下具体的含义：</p><ol><li><code>token</code>：该标识符返回的标记，理论上所有的变量返回的标记都应该是 <code>Id</code>，但实际上由于我们还将在符号表中加入关键字如 <code>if</code>, <code>while</code> 等，它们都有对应的标记。</li><li><code>hash</code>：顾名思义，就是这个标识符的哈希值，用于标识符的快速比较。</li><li><code>name</code>：存放标识符本身的字符串。</li><li><code>class</code>：该标识符的类别，如数字，全局变量或局部变量等。</li><li><code>type</code>：标识符的类型，即如果它是个变量，变量是 <code>int</code> 型、<code>char</code> 型还是指针型。</li><li><code>value</code>：存放这个标识符的值，如标识符是函数，刚存放函数的地址。</li><li><code>BXXXX</code>：C 语言中标识符可以是全局的也可以是局部的，当局部标识符的名字与全局标识符相同时，用作保存全局标识符的信息。</li></ol><p>由上可以看出，我们实现的词法分析器与传统意义上的词法分析器不太相同。传统意义上的符号表只需要知道标识符的唯一标识即可，而我们还存放了一些只有语法分析器才会得到的信息，如 <code>type</code> 。</p><p>由于我们的目标是能自举，而我们定义的语法不支持 <code>struct</code>，故而使用下列方式。</p><table><tbody><tr><td class="code"><pre><span class="line">Symbol table:</span><br><span class="line">----+-----+----+----+----+-----+-----+-----+------+------+----</span><br><span class="line"> .. |token|hash|name|type|class|value|btype|bclass|bvalue| ..</span><br><span class="line">----+-----+----+----+----+-----+-----+-----+------+------+----</span><br><span class="line">    |&lt;---       one single identifier                ---&gt;|</span><br></pre></td></tr></tbody></table><p>即用一个整型数组来保存相关的ID信息。每个ID占用数组中的9个空间，分析标识符的相关代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> token_val;                <span class="comment">// value of current token (mainly for number)</span></span><br><span class="line"><span class="type">int</span> *current_id,              <span class="comment">// current parsed ID</span></span><br><span class="line">    *symbols;                 <span class="comment">// symbol table</span></span><br><span class="line"></span><br><span class="line"><span class="comment">// fields of identifier</span></span><br><span class="line"><span class="class"><span class="keyword">enum</span> {</span>Token, Hash, Name, Type, Class, Value, BType, BClass, BValue, IdSize};</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">next</span><span class="params">()</span> {</span><br><span class="line">        ...</span><br><span class="line"></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> ((token &gt;= <span class="string">&#39;a&#39;</span> &amp;&amp; token &lt;= <span class="string">&#39;z&#39;</span>) || (token &gt;= <span class="string">&#39;A&#39;</span> &amp;&amp; token &lt;= <span class="string">&#39;Z&#39;</span>) || (token == <span class="string">&#39;_&#39;</span>)) {</span><br><span class="line"></span><br><span class="line">            <span class="comment">// parse identifier</span></span><br><span class="line">            last_pos = src - <span class="number">1</span>;</span><br><span class="line">            hash = token;</span><br><span class="line"></span><br><span class="line">            <span class="keyword">while</span> ((*src &gt;= <span class="string">&#39;a&#39;</span> &amp;&amp; *src &lt;= <span class="string">&#39;z&#39;</span>) || (*src &gt;= <span class="string">&#39;A&#39;</span> &amp;&amp; *src &lt;= <span class="string">&#39;Z&#39;</span>) || (*src &gt;= <span class="string">&#39;0&#39;</span> &amp;&amp; *src &lt;= <span class="string">&#39;9&#39;</span>) || (*src == <span class="string">&#39;_&#39;</span>)) {</span><br><span class="line">                hash = hash * <span class="number">147</span> + *src;</span><br><span class="line">                src++;</span><br><span class="line">            }</span><br><span class="line"></span><br><span class="line">            <span class="comment">// look for existing identifier, linear search</span></span><br><span class="line">            current_id = symbols;</span><br><span class="line">            <span class="keyword">while</span> (current_id[Token]) {</span><br><span class="line">                <span class="keyword">if</span> (current_id[Hash] == hash &amp;&amp; !<span class="built_in">memcmp</span>((<span class="type">char</span> *)current_id[Name], last_pos, src - last_pos)) {</span><br><span class="line">                    <span class="comment">//found one, return</span></span><br><span class="line">                    token = current_id[Token];</span><br><span class="line">                    <span class="keyword">return</span>;</span><br><span class="line">                }</span><br><span class="line">                current_id = current_id + IdSize;</span><br><span class="line">            }</span><br><span class="line"></span><br><span class="line"></span><br><span class="line">            <span class="comment">// store new ID</span></span><br><span class="line">            current_id[Name] = (<span class="type">int</span>)last_pos;</span><br><span class="line">            current_id[Hash] = hash;</span><br><span class="line">            token = current_id[Token] = Id;</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        ...</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>查找已有标识符的方法是线性查找 <code>symbols</code> 表。</p><h3 id="数字" tabindex="-1"><a class="header-anchor" href="#数字"><span><a href="about:blank#%E6%95%B0%E5%AD%97"></a>数字</span></a></h3><p>数字中较为复杂的一点是需要支持十进制、十六进制及八进制。逻辑也较为直接，可能唯一不好理解的是获取十六进制的值相关的代码。</p><table><tbody><tr><td class="code"><pre><span class="line">token_val = token_val * 16 + (token &amp; 15) + (token &gt;= &#39;A&#39; ? 9 : 0);</span><br></pre></td></tr></tbody></table><p>这里要注意的是在ASCII码中，字符<code>a</code>对应的十六进制值是 <code>61</code>, <code>A</code>是<code>41</code>，故通过 <code>(token &amp; 15)</code> 可以得到个位数的值。其它就不多说了，这里这样写的目的是装B（其实是抄 c4 的源代码的）。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">next</span><span class="params">()</span> {</span><br><span class="line">        ...</span><br><span class="line"></span><br><span class="line"></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token &gt;= <span class="string">&#39;0&#39;</span> &amp;&amp; token &lt;= <span class="string">&#39;9&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse number, three kinds: dec(123) hex(0x123) oct(017)</span></span><br><span class="line">            token_val = token - <span class="string">&#39;0&#39;</span>;</span><br><span class="line">            <span class="keyword">if</span> (token_val &gt; <span class="number">0</span>) {</span><br><span class="line">                <span class="comment">// dec, starts with [1-9]</span></span><br><span class="line">                <span class="keyword">while</span> (*src &gt;= <span class="string">&#39;0&#39;</span> &amp;&amp; *src &lt;= <span class="string">&#39;9&#39;</span>) {</span><br><span class="line">                    token_val = token_val*<span class="number">10</span> + *src++ - <span class="string">&#39;0&#39;</span>;</span><br><span class="line">                }</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                <span class="comment">// starts with number 0</span></span><br><span class="line">                <span class="keyword">if</span> (*src == <span class="string">&#39;x&#39;</span> || *src == <span class="string">&#39;X&#39;</span>) {</span><br><span class="line">                    <span class="comment">//hex</span></span><br><span class="line">                    token = *++src;</span><br><span class="line">                    <span class="keyword">while</span> ((token &gt;= <span class="string">&#39;0&#39;</span> &amp;&amp; token &lt;= <span class="string">&#39;9&#39;</span>) || (token &gt;= <span class="string">&#39;a&#39;</span> &amp;&amp; token &lt;= <span class="string">&#39;f&#39;</span>) || (token &gt;= <span class="string">&#39;A&#39;</span> &amp;&amp; token &lt;= <span class="string">&#39;F&#39;</span>)) {</span><br><span class="line">                        token_val = token_val * <span class="number">16</span> + (token &amp; <span class="number">15</span>) + (token &gt;= <span class="string">&#39;A&#39;</span> ? <span class="number">9</span> : <span class="number">0</span>);</span><br><span class="line">                        token = *++src;</span><br><span class="line">                    }</span><br><span class="line">                } <span class="keyword">else</span> {</span><br><span class="line">                    <span class="comment">// oct</span></span><br><span class="line">                    <span class="keyword">while</span> (*src &gt;= <span class="string">&#39;0&#39;</span> &amp;&amp; *src &lt;= <span class="string">&#39;7&#39;</span>) {</span><br><span class="line">                        token_val = token_val*<span class="number">8</span> + *src++ - <span class="string">&#39;0&#39;</span>;</span><br><span class="line">                    }</span><br><span class="line">                }</span><br><span class="line">            }</span><br><span class="line"></span><br><span class="line">            token = Num;</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        ...</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="字符串" tabindex="-1"><a class="header-anchor" href="#字符串"><span><a href="about:blank#%E5%AD%97%E7%AC%A6%E4%B8%B2"></a>字符串</span></a></h3><p>在分析时，如果分析到字符串，我们需要将它存放到前一篇文章中说的 <code>data</code> 段中。然后返回它在 <code>data</code> 段中的地址。另一个特殊的地方是我们需要支持转义符。例如用 <code>\\n</code> 表示换行符。由于本编译器的目的是达到自己编译自己，所以代码中并没有支持除 <code>\\n</code> 的转义符，如 <code>\\t</code>, <code>\\r</code> 等，但仍支持 <code>\\a</code> 表示字符 <code>a</code> 的语法，如 <code>\\&quot;</code> 表示 <code>&quot;</code>。</p><p>在分析时，我们将同时分析单个字符如 <code>&#39;a&#39;</code> 和字符串如 <code>&quot;a string&quot;</code>。若得到的是单个字符，我们以 <code>Num</code> 的形式返回。相关代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">next</span><span class="params">()</span> {</span><br><span class="line">        ...</span><br><span class="line"></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;&quot;&#39;</span> || token == <span class="string">&#39;\\&#39;&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse string literal, currently, the only supported escape</span></span><br><span class="line">            <span class="comment">// character is &#39;\\n&#39;, store the string literal into data.</span></span><br><span class="line">            last_pos = data;</span><br><span class="line">            <span class="keyword">while</span> (*src != <span class="number">0</span> &amp;&amp; *src != token) {</span><br><span class="line">                token_val = *src++;</span><br><span class="line">                <span class="keyword">if</span> (token_val == <span class="string">&#39;\\\\&#39;</span>) {</span><br><span class="line">                    <span class="comment">// escape character</span></span><br><span class="line">                    token_val = *src++;</span><br><span class="line">                    <span class="keyword">if</span> (token_val == <span class="string">&#39;n&#39;</span>) {</span><br><span class="line">                        token_val = <span class="string">&#39;\\n&#39;</span>;</span><br><span class="line">                    }</span><br><span class="line">                }</span><br><span class="line"></span><br><span class="line">                <span class="keyword">if</span> (token == <span class="string">&#39;&quot;&#39;</span>) {</span><br><span class="line">                    *data++ = token_val;</span><br><span class="line">                }</span><br><span class="line">            }</span><br><span class="line"></span><br><span class="line">            src++;</span><br><span class="line">            <span class="comment">// if it is a single character, return Num token</span></span><br><span class="line">            <span class="keyword">if</span> (token == <span class="string">&#39;&quot;&#39;</span>) {</span><br><span class="line">                token_val = (<span class="type">int</span>)last_pos;</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                token = Num;</span><br><span class="line">            }</span><br><span class="line"></span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="注释" tabindex="-1"><a class="header-anchor" href="#注释"><span><a href="about:blank#%E6%B3%A8%E9%87%8A"></a>注释</span></a></h3><p>在我们的 C 语言中，只支持 <code>//</code> 类型的注释，不支持 <code>/* comments */</code> 的注释。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">next</span><span class="params">()</span> {</span><br><span class="line">        ...</span><br><span class="line"></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;/&#39;</span>) {</span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;/&#39;</span>) {</span><br><span class="line">                <span class="comment">// skip comments</span></span><br><span class="line">                <span class="keyword">while</span> (*src != <span class="number">0</span> &amp;&amp; *src != <span class="string">&#39;\\n&#39;</span>) {</span><br><span class="line">                    ++src;</span><br><span class="line">                }</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                <span class="comment">// divide operator</span></span><br><span class="line">                token = Div;</span><br><span class="line">                <span class="keyword">return</span>;</span><br><span class="line">            }</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        ...</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>这里我们要额外介绍 <code>lookahead</code> 的概念，即提前看多个字符。上述代码中我们看到，除了跳过注释，我们还可能返回除号 <code>/(Div)</code> 标记。</p><p>提前看字符的原理是：有一个或多个标记是以同样的字符开头的（如本小节中的注释与除号），因此只凭当前的字符我们并无法确定具体应该解释成哪一个标记，所以只能再向前查看字符，如本例需向前查看一个字符，若是 <code>/</code> 则说明是注释，反之则是除号。</p><p>我们之前说过，词法分析器本质上也是编译器，其实提前看字符的概念也存在于编译器，只是这时就是提前看k个“标记”而不是“字符”了。平时听到的 <code>LL(k)</code> 中的 <code>k</code> 就是需要向前看的标记的个数了。</p><p>另外，我们用词法分析器将源码转换成标记流，能减小语法分析复杂度，原因之一就是减少了语法分析器需要“向前看”的字符个数。</p><h3 id="其它" tabindex="-1"><a class="header-anchor" href="#其它"><span><a href="about:blank#%E5%85%B6%E5%AE%83"></a>其它</span></a></h3><p>其它的标记的解析就相对容易一些了，我们直接贴上代码：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">next</span><span class="params">()</span> {</span><br><span class="line">        ...</span><br><span class="line"></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;=&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse &#39;==&#39; and &#39;=&#39;</span></span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;=&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Eq;</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                token = Assign;</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;+&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse &#39;+&#39; and &#39;++&#39;</span></span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;+&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Inc;</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                token = Add;</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;-&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse &#39;-&#39; and &#39;--&#39;</span></span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;-&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Dec;</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                token = Sub;</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;!&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse &#39;!=&#39;</span></span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;=&#39;</span>) {</span><br><span class="line">                src++;</span><br><span class="line">                token = Ne;</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;&lt;&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse &#39;&lt;=&#39;, &#39;&lt;&lt;&#39; or &#39;&lt;&#39;</span></span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;=&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Le;</span><br><span class="line">            } <span class="keyword">else</span> <span class="keyword">if</span> (*src == <span class="string">&#39;&lt;&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Shl;</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                token = Lt;</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;&gt;&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse &#39;&gt;=&#39;, &#39;&gt;&gt;&#39; or &#39;&gt;&#39;</span></span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;=&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Ge;</span><br><span class="line">            } <span class="keyword">else</span> <span class="keyword">if</span> (*src == <span class="string">&#39;&gt;&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Shr;</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                token = Gt;</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;|&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse &#39;|&#39; or &#39;||&#39;</span></span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;|&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Lor;</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                token = Or;</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;&amp;&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse &#39;&amp;&#39; and &#39;&amp;&amp;&#39;</span></span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;&amp;&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Lan;</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                token = And;</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;^&#39;</span>) {</span><br><span class="line">            token = Xor;</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;%&#39;</span>) {</span><br><span class="line">            token = Mod;</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;*&#39;</span>) {</span><br><span class="line">            token = Mul;</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;[&#39;</span>) {</span><br><span class="line">            token = Brak;</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;?&#39;</span>) {</span><br><span class="line">            token = Cond;</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;~&#39;</span> || token == <span class="string">&#39;;&#39;</span> || token == <span class="string">&#39;{&#39;</span> || token == <span class="string">&#39;}&#39;</span> || token == <span class="string">&#39;(&#39;</span> || token == <span class="string">&#39;)&#39;</span> || token == <span class="string">&#39;]&#39;</span> || token == <span class="string">&#39;,&#39;</span> || token == <span class="string">&#39;:&#39;</span>) {</span><br><span class="line">            <span class="comment">// directly return the character as token;</span></span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        ...</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>代码较多，但主要逻辑就是向前看一个字符来确定真正的标记。</p><h3 id="关键字与内置函数" tabindex="-1"><a class="header-anchor" href="#关键字与内置函数"><span><a href="about:blank#%E5%85%B3%E9%94%AE%E5%AD%97%E4%B8%8E%E5%86%85%E7%BD%AE%E5%87%BD%E6%95%B0"></a>关键字与内置函数</span></a></h3><p>虽然上面写完了词法分析器，但还有一个问题需要考虑，那就是“关键字”，例如 <code>if</code>, <code>while</code>, <code>return</code> 等。它们不能被作为普通的标识符，因为有特殊的含义。</p><p>一般有两种处理方法：</p><ol><li>词法分析器中直接解析这些关键字。</li><li>在语法分析前将关键字提前加入符号表。</li></ol><p>这里我们就采用第二种方法，将它们加入符号表，并提前为它们赋予必要的信息（还记得前面说的标识符 <code>Token</code> 字段吗？）。这样当源代码中出现关键字时，它们会被解析成标识符，但由于符号表中已经有了相关的信息，我们就能知道它们是特殊的关键字。</p><p>内置函数的行为也和关键字类似，不同的只是赋值的信息，在<code>main</code>函数中进行初始化如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="comment">// types of variable/function</span></span><br><span class="line"><span class="class"><span class="keyword">enum</span> {</span> CHAR, INT, PTR };</span><br><span class="line"><span class="type">int</span> *idmain;                  <span class="comment">// the `main` function</span></span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">main</span><span class="params">()</span> {</span><br><span class="line">    ...</span><br><span class="line"></span><br><span class="line">    src = <span class="string">&quot;char else enum if int return sizeof while &quot;</span></span><br><span class="line">          <span class="string">&quot;open read close printf malloc memset memcmp exit void main&quot;</span>;</span><br><span class="line"></span><br><span class="line">     <span class="comment">// add keywords to symbol table</span></span><br><span class="line">    i = Char;</span><br><span class="line">    <span class="keyword">while</span> (i &lt;= While) {</span><br><span class="line">        next();</span><br><span class="line">        current_id[Token] = i++;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="comment">// add library to symbol table</span></span><br><span class="line">    i = OPEN;</span><br><span class="line">    <span class="keyword">while</span> (i &lt;= EXIT) {</span><br><span class="line">        next();</span><br><span class="line">        current_id[Class] = Sys;</span><br><span class="line">        current_id[Type] = INT;</span><br><span class="line">        current_id[Value] = i++;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    next(); current_id[Token] = Char; <span class="comment">// handle void type</span></span><br><span class="line">    next(); idmain = current_id; <span class="comment">// keep track of main</span></span><br><span class="line"></span><br><span class="line">    ...</span><br><span class="line">    program();</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h2 id="代码" tabindex="-1"><a class="header-anchor" href="#代码"><span><a href="about:blank#%E4%BB%A3%E7%A0%81"></a>代码</span></a></h2>',76),B={href:"https://github.com/lotabout/write-a-C-interpreter/tree/step-2",target:"_blank",rel:"noopener noreferrer"},C=p('<table><tbody><tr><td class="code"><pre><span class="line">git clone -b step-2 https://github.com/lotabout/write-a-C-interpreter</span><br></pre></td></tr></tbody></table><p>上面的代码运行后会出现 ‘Segmentation Falt’，这是正常的，因为它会尝试运行我们上一章创建的虚拟机，但其中并没有任何汇编代码。</p><h2 id="小结" tabindex="-1"><a class="header-anchor" href="#小结"><span><a href="about:blank#%E5%B0%8F%E7%BB%93"></a>小结</span></a></h2><p>本章我们为我们的编译器构建了词法分析器，通过本章的学习，我认为有几个要点需要强调：</p><ol><li>词法分析器的作用是对源码字符串进行预处理，作用是减小语法分析器的复杂程度。</li><li>词法分析器本身可以认为是一个编译器，输入是源码，输出是标记流。</li><li><code>lookahead(k)</code> 的概念，即向前看 <code>k</code> 个字符或标记。</li><li>词法分析中如何处理标识符与符号表。</li></ol><p>下一章中，我们将介绍递归下降的语法分析器。我们下一章见。</p>',6);function v(x,D){const n=r("ExternalLinkIcon");return c(),t("div",null,[o,s("p",null,[a("本文转自 "),s("a",b,[a("https://lotabout.me/2015/write-a-C-interpreter-3/"),e(n)]),a("，如有侵权，请联系删除。")]),d,s("ol",null,[s("li",null,[s("a",k,[a("手把手教你构建 C 语言编译器（0）——前言"),e(n)])]),s("li",null,[s("a",h,[a("手把手教你构建 C 语言编译器（1）——设计"),e(n)])]),s("li",null,[s("a",E,[a("手把手教你构建 C 语言编译器（2）——虚拟机"),e(n)])]),s("li",null,[s("a",m,[a("手把手教你构建 C 语言编译器（3）——词法分析器"),e(n)])]),s("li",null,[s("a",u,[a("手把手教你构建 C 语言编译器（4）——递归下降"),e(n)])]),s("li",null,[s("a",y,[a("手把手教你构建 C 语言编译器（5）——变量定义"),e(n)])]),s("li",null,[s("a",f,[a("手把手教你构建 C 语言编译器（6）——函数定义"),e(n)])]),s("li",null,[s("a",g,[a("手把手教你构建 C 语言编译器（7）——语句"),e(n)])]),s("li",null,[s("a",A,[a("手把手教你构建 C 语言编译器（8）——表达式"),e(n)])]),s("li",null,[s("a",w,[a("手把手教你构建 C 语言编译器（9）——总结"),e(n)])])]),_,s("p",null,[a("本章的代码可以在 "),s("a",B,[a("Github"),e(n)]),a(" 上下载，也可以直接 clone")]),C])}const N=l(i,[["render",v],["__file","3.html.vue"]]),S=JSON.parse('{"path":"/tech/designASimpileCCompiler/3.html","title":"手把手教你构建 C 语言编译器（3）——词法分析器","lang":"zh-CN","frontmatter":{"title":"手把手教你构建 C 语言编译器（3）——词法分析器","category":["编译原理"],"tag":["c","编译器","解释器"],"description":"转载声明 本文转自 https://lotabout.me/2015/write-a-C-interpreter-3/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（3）- 词法分析器 Table of Contents 1. 什么是词法分析器 2. 词法分析器与编译器 3. 词法分析器的实现 3.1. 支持的标记 3.2. 词法分...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/designASimpileCCompiler/3.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"手把手教你构建 C 语言编译器（3）——词法分析器"}],["meta",{"property":"og:description","content":"转载声明 本文转自 https://lotabout.me/2015/write-a-C-interpreter-3/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（3）- 词法分析器 Table of Contents 1. 什么是词法分析器 2. 词法分析器与编译器 3. 词法分析器的实现 3.1. 支持的标记 3.2. 词法分..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"c"}],["meta",{"property":"article:tag","content":"编译器"}],["meta",{"property":"article:tag","content":"解释器"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"手把手教你构建 C 语言编译器（3）——词法分析器\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"什么是词法分析器","slug":"什么是词法分析器","link":"#什么是词法分析器","children":[]},{"level":2,"title":"词法分析器与编译器","slug":"词法分析器与编译器","link":"#词法分析器与编译器","children":[]},{"level":2,"title":"词法分析器的实现","slug":"词法分析器的实现","link":"#词法分析器的实现","children":[{"level":3,"title":"支持的标记","slug":"支持的标记","link":"#支持的标记","children":[]},{"level":3,"title":"词法分析器的框架","slug":"词法分析器的框架","link":"#词法分析器的框架","children":[]},{"level":3,"title":"换行符","slug":"换行符","link":"#换行符","children":[]},{"level":3,"title":"宏定义","slug":"宏定义","link":"#宏定义","children":[]},{"level":3,"title":"标识符与符号表","slug":"标识符与符号表","link":"#标识符与符号表","children":[]},{"level":3,"title":"数字","slug":"数字","link":"#数字","children":[]},{"level":3,"title":"字符串","slug":"字符串","link":"#字符串","children":[]},{"level":3,"title":"注释","slug":"注释","link":"#注释","children":[]},{"level":3,"title":"其它","slug":"其它","link":"#其它","children":[]},{"level":3,"title":"关键字与内置函数","slug":"关键字与内置函数","link":"#关键字与内置函数","children":[]}]},{"level":2,"title":"代码","slug":"代码","link":"#代码","children":[]},{"level":2,"title":"小结","slug":"小结","link":"#小结","children":[]}],"readingTime":{"minutes":25.21,"words":7563},"filePathRelative":"tech/designASimpileCCompiler/3.md","excerpt":"\\n<p>本文转自 <a href=\\"https://lotabout.me/2015/write-a-C-interpreter-3/\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">https://lotabout.me/2015/write-a-C-interpreter-3/</a>，如有侵权，请联系删除。</p>\\n<h1>原文内容</h1>\\n<h1>手把手教你构建 C 语言编译器（3）- 词法分析器</h1>\\n<p>Table of Contents</p>\\n<ol>\\n<li><a href=\\"about:blank#%E4%BB%80%E4%B9%88%E6%98%AF%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8\\">1. 什么是词法分析器</a></li>\\n<li><a href=\\"about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8%E4%B8%8E%E7%BC%96%E8%AF%91%E5%99%A8\\">2. 词法分析器与编译器</a></li>\\n<li><a href=\\"about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8%E7%9A%84%E5%AE%9E%E7%8E%B0\\">3. 词法分析器的实现</a>\\n<ol>\\n<li><a href=\\"about:blank#%E6%94%AF%E6%8C%81%E7%9A%84%E6%A0%87%E8%AE%B0\\">3.1. 支持的标记</a></li>\\n<li><a href=\\"about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8%E7%9A%84%E6%A1%86%E6%9E%B6\\">3.2. 词法分析器的框架</a></li>\\n<li><a href=\\"about:blank#%E6%8D%A2%E8%A1%8C%E7%AC%A6\\">3.3. 换行符</a></li>\\n<li><a href=\\"about:blank#%E5%AE%8F%E5%AE%9A%E4%B9%89\\">3.4. 宏定义</a></li>\\n<li><a href=\\"about:blank#%E6%A0%87%E8%AF%86%E7%AC%A6%E4%B8%8E%E7%AC%A6%E5%8F%B7%E8%A1%A8\\">3.5. 标识符与符号表</a></li>\\n<li><a href=\\"about:blank#%E6%95%B0%E5%AD%97\\">3.6. 数字</a></li>\\n<li><a href=\\"about:blank#%E5%AD%97%E7%AC%A6%E4%B8%B2\\">3.7. 字符串</a></li>\\n<li><a href=\\"about:blank#%E6%B3%A8%E9%87%8A\\">3.8. 注释</a></li>\\n<li><a href=\\"about:blank#%E5%85%B6%E5%AE%83\\">3.9. 其它</a></li>\\n<li><a href=\\"about:blank#%E5%85%B3%E9%94%AE%E5%AD%97%E4%B8%8E%E5%86%85%E7%BD%AE%E5%87%BD%E6%95%B0\\">3.10. 关键字与内置函数</a></li>\\n</ol>\\n</li>\\n<li><a href=\\"about:blank#%E4%BB%A3%E7%A0%81\\">4. 代码</a></li>\\n<li><a href=\\"about:blank#%E5%B0%8F%E7%BB%93\\">5. 小结</a></li>\\n</ol>","autoDesc":true}');export{N as comp,S as data};
+import{_ as l,r,o as c,c as t,b as s,e as a,d as e,f as p}from"./app-B4LGNJZ0.js";const i={},o=s("h1",{id:"转载声明",tabindex:"-1"},[s("a",{class:"header-anchor",href:"#转载声明"},[s("span",null,"转载声明")])],-1),b={href:"https://lotabout.me/2015/write-a-C-interpreter-3/",target:"_blank",rel:"noopener noreferrer"},d=p('<h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-3-词法分析器" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-3-词法分析器"><span>手把手教你构建 C 语言编译器（3）- 词法分析器</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#%E4%BB%80%E4%B9%88%E6%98%AF%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8">1. 什么是词法分析器</a></li><li><a href="about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8%E4%B8%8E%E7%BC%96%E8%AF%91%E5%99%A8">2. 词法分析器与编译器</a></li><li><a href="about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8%E7%9A%84%E5%AE%9E%E7%8E%B0">3. 词法分析器的实现</a><ol><li><a href="about:blank#%E6%94%AF%E6%8C%81%E7%9A%84%E6%A0%87%E8%AE%B0">3.1. 支持的标记</a></li><li><a href="about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8%E7%9A%84%E6%A1%86%E6%9E%B6">3.2. 词法分析器的框架</a></li><li><a href="about:blank#%E6%8D%A2%E8%A1%8C%E7%AC%A6">3.3. 换行符</a></li><li><a href="about:blank#%E5%AE%8F%E5%AE%9A%E4%B9%89">3.4. 宏定义</a></li><li><a href="about:blank#%E6%A0%87%E8%AF%86%E7%AC%A6%E4%B8%8E%E7%AC%A6%E5%8F%B7%E8%A1%A8">3.5. 标识符与符号表</a></li><li><a href="about:blank#%E6%95%B0%E5%AD%97">3.6. 数字</a></li><li><a href="about:blank#%E5%AD%97%E7%AC%A6%E4%B8%B2">3.7. 字符串</a></li><li><a href="about:blank#%E6%B3%A8%E9%87%8A">3.8. 注释</a></li><li><a href="about:blank#%E5%85%B6%E5%AE%83">3.9. 其它</a></li><li><a href="about:blank#%E5%85%B3%E9%94%AE%E5%AD%97%E4%B8%8E%E5%86%85%E7%BD%AE%E5%87%BD%E6%95%B0">3.10. 关键字与内置函数</a></li></ol></li><li><a href="about:blank#%E4%BB%A3%E7%A0%81">4. 代码</a></li><li><a href="about:blank#%E5%B0%8F%E7%BB%93">5. 小结</a></li></ol><p>本章我们要讲解如何构建词法分析器。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p>',6),k={href:"http://lotabout.me/2015/write-a-C-interpreter-0/",target:"_blank",rel:"noopener noreferrer"},h={href:"http://lotabout.me/2015/write-a-C-interpreter-1/",target:"_blank",rel:"noopener noreferrer"},E={href:"http://lotabout.me/2015/write-a-C-interpreter-2/",target:"_blank",rel:"noopener noreferrer"},m={href:"http://lotabout.me/2015/write-a-C-interpreter-3/",target:"_blank",rel:"noopener noreferrer"},u={href:"http://lotabout.me/2016/write-a-C-interpreter-4/",target:"_blank",rel:"noopener noreferrer"},y={href:"http://lotabout.me/2016/write-a-C-interpreter-5/",target:"_blank",rel:"noopener noreferrer"},f={href:"http://lotabout.me/2016/write-a-C-interpreter-6/",target:"_blank",rel:"noopener noreferrer"},g={href:"http://lotabout.me/2016/write-a-C-interpreter-7/",target:"_blank",rel:"noopener noreferrer"},A={href:"http://lotabout.me/2016/write-a-C-interpreter-8/",target:"_blank",rel:"noopener noreferrer"},w={href:"http://lotabout.me/2016/write-a-C-interpreter-9/",target:"_blank",rel:"noopener noreferrer"},_=p('<h2 id="什么是词法分析器" tabindex="-1"><a class="header-anchor" href="#什么是词法分析器"><span><a href="about:blank#%E4%BB%80%E4%B9%88%E6%98%AF%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8"></a>什么是词法分析器</span></a></h2><p>简而言之，词法分析器用于对源码字符串做预处理，以减少语法分析器的复杂程度。</p><p>词法分析器以源码字符串为输入，输出为标记流（token stream），即一连串的标记，每个标记通常包括： <code>(token, token value)</code> 即标记本身和标记的值。例如，源码中若包含一个数字 <code>&#39;998&#39;</code> ，词法分析器将输出 <code>(Number, 998)</code>，即（数字，998）。再例如：</p><table><tbody><tr><td class="code"><pre><span class="line">2 + 3 * (4 - 5)</span><br><span class="line">=&gt;</span><br><span class="line">(Number, 2) Add (Number, 3) Multiply Left-Bracket (Number, 4) Subtract (Number, 5) Right-Bracket</span><br></pre></td></tr></tbody></table><p>通过词法分析器的预处理，语法分析器的复杂度会大大降低，这点在后面的语法分析器我们就能体会。</p><h2 id="词法分析器与编译器" tabindex="-1"><a class="header-anchor" href="#词法分析器与编译器"><span><a href="about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8%E4%B8%8E%E7%BC%96%E8%AF%91%E5%99%A8"></a>词法分析器与编译器</span></a></h2><p>要是深入词法分析器，你就会发现，它的本质上也是编译器。我们的编译器是以标记流为输入，输出汇编代码，而词法分析器则是以源码字符串为输入，输出标记流。</p><table><tbody><tr><td class="code"><pre><span class="line">                   +-------+                      +--------+</span><br><span class="line">-- source code --&gt; | lexer | --&gt; token stream --&gt; | parser | --&gt; assembly</span><br><span class="line">                   +-------+                      +--------+</span><br></pre></td></tr></tbody></table><p>在这个前提下，我们可以这样认为：直接从源代码编译成汇编代码是很困难的，因为输入的字符串比较难处理。所以我们先编写一个较为简单的编译器（词法分析器）来将字符串转换成标记流，而标记流对于语法分析器而言就容易处理得多了。</p><h2 id="词法分析器的实现" tabindex="-1"><a class="header-anchor" href="#词法分析器的实现"><span><a href="about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8%E7%9A%84%E5%AE%9E%E7%8E%B0"></a>词法分析器的实现</span></a></h2><p>由于词法分析的工作很常见，但又枯燥且容易出错，所以人们已经开发出了许多工具来生成词法分析器，如 <code>lex, flex</code>。这些工具允许我们通过正则表达式来识别标记。</p><p>这里注意的是，我们并不会一次性地将所有源码全部转换成标记流，原因有二：</p><ol><li>字符串转换成标记流有时是有状态的，即与代码的上下文是有关系的。</li><li>保存所有的标记流没有意义且浪费空间。</li></ol><p>所以实际的处理方法是提供一个函数（即前几篇中提到的 <code>next()</code>），每次调用该函数则返回下一个标记。</p><h3 id="支持的标记" tabindex="-1"><a class="header-anchor" href="#支持的标记"><span><a href="about:blank#%E6%94%AF%E6%8C%81%E7%9A%84%E6%A0%87%E8%AE%B0"></a>支持的标记</span></a></h3><p>在全局中添加如下定义：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="comment">// tokens and classes (operators last and in precedence order)</span></span><br><span class="line"><span class="class"><span class="keyword">enum</span> {</span></span><br><span class="line">  Num = <span class="number">128</span>, Fun, Sys, Glo, Loc, Id,</span><br><span class="line">  Char, Else, Enum, If, Int, Return, Sizeof, While,</span><br><span class="line">  Assign, Cond, Lor, Lan, Or, Xor, And, Eq, Ne, Lt, Gt, Le, Ge, Shl, Shr, Add, Sub, Mul, Div, Mod, Inc, Dec, Brak</span><br><span class="line">};</span><br></pre></td></tr></tbody></table><p>这些就是我们要支持的标记符。例如，我们会将 <code>=</code> 解析为 <code>Assign</code>；将 <code>==</code> 解析为 <code>Eq</code>；将 <code>!=</code> 解析为 <code>Ne</code> 等等。</p><p>所以这里我们会有这样的印象，一个标记（token）可能包含多个字符，且多数情况下如此。而词法分析器能减小语法分析复杂度的原因，正是因为它相当于通过一定的编码（更多的标记）来压缩了源码字符串。</p><p>当然，上面这些标记是有顺序的，跟它们在 C 语言中的优先级有关，如 <code>*(Mul)</code> 的优先级就要高于 <code>+(Add)</code>。它们的具体使用在后面的语法分析中会提到。</p><p>最后要注意的是还有一些字符，它们自己就构成了标记，如右方括号 <code>]</code> 或波浪号 <code>~</code> 等。我们不另外处理它们的原因是：</p><ol><li>它们是单字符的，即并不是多个字符共同构成标记（如 <code>==</code> 需要两个字符）；</li><li>它们不涉及优先级关系。</li></ol><h3 id="词法分析器的框架" tabindex="-1"><a class="header-anchor" href="#词法分析器的框架"><span><a href="about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8%E7%9A%84%E6%A1%86%E6%9E%B6"></a>词法分析器的框架</span></a></h3><p>即 <code>next()</code> 函数的主体：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">next</span><span class="params">()</span> {</span><br><span class="line">    <span class="type">char</span> *last_pos;</span><br><span class="line">    <span class="type">int</span> hash;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">while</span> (token = *src) {</span><br><span class="line">        ++src;</span><br><span class="line">        <span class="comment">// parse token here</span></span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">return</span>;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>这里的一个问题是，为什么要用 <code>while</code> 循环呢？这就涉及到编译器（记得我们说过词法分析器也是某种意义上的编译器）的一个问题：如何处理错误？</p><p>对词法分析器而言，若碰到了一个我们不认识的字符该怎么处理？一般处理的方法有两种：</p><ol><li>指出错误发生的位置，并退出整个程序</li><li>指出错误发生的位置，跳过当前错误并继续编译</li></ol><p>这个 <code>while</code> 循环的作用就是跳过这些我们不识别的字符，我们同时还用它来处理空白字符。我们知道，C 语言中空格是用来作为分隔用的，并不作为语法的一部分。因此在实现中我们将它作为“不识别”的字符，这个 <code>while</code> 循环可以用来跳过它。</p><h3 id="换行符" tabindex="-1"><a class="header-anchor" href="#换行符"><span><a href="about:blank#%E6%8D%A2%E8%A1%8C%E7%AC%A6"></a>换行符</span></a></h3><p>换行符和空格类似，但有一点不同，每次遇到换行符，我们需要将当前的行号加一：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="comment">// parse token here</span></span><br><span class="line">...</span><br><span class="line"></span><br><span class="line"><span class="keyword">if</span> (token == <span class="string">&#39;\\n&#39;</span>) {</span><br><span class="line">    ++line;</span><br><span class="line">}</span><br><span class="line">...</span><br></pre></td></tr></tbody></table><h3 id="宏定义" tabindex="-1"><a class="header-anchor" href="#宏定义"><span><a href="about:blank#%E5%AE%8F%E5%AE%9A%E4%B9%89"></a>宏定义</span></a></h3><p>C 语言的宏定义以字符 <code>#</code> 开头，如 <code># include &lt;stdio.h&gt;</code>。我们的编译器并不支持宏定义，所以直接跳过它们。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;#&#39;</span>) {</span><br><span class="line">    <span class="comment">// skip macro, because we will not support it</span></span><br><span class="line">    <span class="keyword">while</span> (*src != <span class="number">0</span> &amp;&amp; *src != <span class="string">&#39;\\n&#39;</span>) {</span><br><span class="line">        src++;</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="标识符与符号表" tabindex="-1"><a class="header-anchor" href="#标识符与符号表"><span><a href="about:blank#%E6%A0%87%E8%AF%86%E7%AC%A6%E4%B8%8E%E7%AC%A6%E5%8F%B7%E8%A1%A8"></a>标识符与符号表</span></a></h3><p>标识符（identifier）可以理解为变量名。对于语法分析而言，我们并不关心一个变量具体叫什么名字，而只关心这个变量名代表的唯一标识。例如 <code>int a;</code> 定义了变量 <code>a</code>，而之后的语句 <code>a = 10</code>，我们需要知道这两个 <code>a</code> 指向的是同一个变量。</p><p>基于这个理由，词法分析器会把扫描到的标识符全都保存到一张表中，遇到新的标识符就去查这张表，如果标识符已经存在，就返回它的唯一标识。</p><p>那么我们怎么表示标识符呢？如下：</p><table><tbody><tr><td class="code"><pre><span class="line">struct identifier {</span><br><span class="line">    int token;</span><br><span class="line">    int hash;</span><br><span class="line">    char * name;</span><br><span class="line">    int class;</span><br><span class="line">    int type;</span><br><span class="line">    int value;</span><br><span class="line">    int Bclass;</span><br><span class="line">    int Btype;</span><br><span class="line">    int Bvalue;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>这里解释一下具体的含义：</p><ol><li><code>token</code>：该标识符返回的标记，理论上所有的变量返回的标记都应该是 <code>Id</code>，但实际上由于我们还将在符号表中加入关键字如 <code>if</code>, <code>while</code> 等，它们都有对应的标记。</li><li><code>hash</code>：顾名思义，就是这个标识符的哈希值，用于标识符的快速比较。</li><li><code>name</code>：存放标识符本身的字符串。</li><li><code>class</code>：该标识符的类别，如数字，全局变量或局部变量等。</li><li><code>type</code>：标识符的类型，即如果它是个变量，变量是 <code>int</code> 型、<code>char</code> 型还是指针型。</li><li><code>value</code>：存放这个标识符的值，如标识符是函数，刚存放函数的地址。</li><li><code>BXXXX</code>：C 语言中标识符可以是全局的也可以是局部的，当局部标识符的名字与全局标识符相同时，用作保存全局标识符的信息。</li></ol><p>由上可以看出，我们实现的词法分析器与传统意义上的词法分析器不太相同。传统意义上的符号表只需要知道标识符的唯一标识即可，而我们还存放了一些只有语法分析器才会得到的信息，如 <code>type</code> 。</p><p>由于我们的目标是能自举，而我们定义的语法不支持 <code>struct</code>，故而使用下列方式。</p><table><tbody><tr><td class="code"><pre><span class="line">Symbol table:</span><br><span class="line">----+-----+----+----+----+-----+-----+-----+------+------+----</span><br><span class="line"> .. |token|hash|name|type|class|value|btype|bclass|bvalue| ..</span><br><span class="line">----+-----+----+----+----+-----+-----+-----+------+------+----</span><br><span class="line">    |&lt;---       one single identifier                ---&gt;|</span><br></pre></td></tr></tbody></table><p>即用一个整型数组来保存相关的ID信息。每个ID占用数组中的9个空间，分析标识符的相关代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> token_val;                <span class="comment">// value of current token (mainly for number)</span></span><br><span class="line"><span class="type">int</span> *current_id,              <span class="comment">// current parsed ID</span></span><br><span class="line">    *symbols;                 <span class="comment">// symbol table</span></span><br><span class="line"></span><br><span class="line"><span class="comment">// fields of identifier</span></span><br><span class="line"><span class="class"><span class="keyword">enum</span> {</span>Token, Hash, Name, Type, Class, Value, BType, BClass, BValue, IdSize};</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">next</span><span class="params">()</span> {</span><br><span class="line">        ...</span><br><span class="line"></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> ((token &gt;= <span class="string">&#39;a&#39;</span> &amp;&amp; token &lt;= <span class="string">&#39;z&#39;</span>) || (token &gt;= <span class="string">&#39;A&#39;</span> &amp;&amp; token &lt;= <span class="string">&#39;Z&#39;</span>) || (token == <span class="string">&#39;_&#39;</span>)) {</span><br><span class="line"></span><br><span class="line">            <span class="comment">// parse identifier</span></span><br><span class="line">            last_pos = src - <span class="number">1</span>;</span><br><span class="line">            hash = token;</span><br><span class="line"></span><br><span class="line">            <span class="keyword">while</span> ((*src &gt;= <span class="string">&#39;a&#39;</span> &amp;&amp; *src &lt;= <span class="string">&#39;z&#39;</span>) || (*src &gt;= <span class="string">&#39;A&#39;</span> &amp;&amp; *src &lt;= <span class="string">&#39;Z&#39;</span>) || (*src &gt;= <span class="string">&#39;0&#39;</span> &amp;&amp; *src &lt;= <span class="string">&#39;9&#39;</span>) || (*src == <span class="string">&#39;_&#39;</span>)) {</span><br><span class="line">                hash = hash * <span class="number">147</span> + *src;</span><br><span class="line">                src++;</span><br><span class="line">            }</span><br><span class="line"></span><br><span class="line">            <span class="comment">// look for existing identifier, linear search</span></span><br><span class="line">            current_id = symbols;</span><br><span class="line">            <span class="keyword">while</span> (current_id[Token]) {</span><br><span class="line">                <span class="keyword">if</span> (current_id[Hash] == hash &amp;&amp; !<span class="built_in">memcmp</span>((<span class="type">char</span> *)current_id[Name], last_pos, src - last_pos)) {</span><br><span class="line">                    <span class="comment">//found one, return</span></span><br><span class="line">                    token = current_id[Token];</span><br><span class="line">                    <span class="keyword">return</span>;</span><br><span class="line">                }</span><br><span class="line">                current_id = current_id + IdSize;</span><br><span class="line">            }</span><br><span class="line"></span><br><span class="line"></span><br><span class="line">            <span class="comment">// store new ID</span></span><br><span class="line">            current_id[Name] = (<span class="type">int</span>)last_pos;</span><br><span class="line">            current_id[Hash] = hash;</span><br><span class="line">            token = current_id[Token] = Id;</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        ...</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>查找已有标识符的方法是线性查找 <code>symbols</code> 表。</p><h3 id="数字" tabindex="-1"><a class="header-anchor" href="#数字"><span><a href="about:blank#%E6%95%B0%E5%AD%97"></a>数字</span></a></h3><p>数字中较为复杂的一点是需要支持十进制、十六进制及八进制。逻辑也较为直接，可能唯一不好理解的是获取十六进制的值相关的代码。</p><table><tbody><tr><td class="code"><pre><span class="line">token_val = token_val * 16 + (token &amp; 15) + (token &gt;= &#39;A&#39; ? 9 : 0);</span><br></pre></td></tr></tbody></table><p>这里要注意的是在ASCII码中，字符<code>a</code>对应的十六进制值是 <code>61</code>, <code>A</code>是<code>41</code>，故通过 <code>(token &amp; 15)</code> 可以得到个位数的值。其它就不多说了，这里这样写的目的是装B（其实是抄 c4 的源代码的）。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">next</span><span class="params">()</span> {</span><br><span class="line">        ...</span><br><span class="line"></span><br><span class="line"></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token &gt;= <span class="string">&#39;0&#39;</span> &amp;&amp; token &lt;= <span class="string">&#39;9&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse number, three kinds: dec(123) hex(0x123) oct(017)</span></span><br><span class="line">            token_val = token - <span class="string">&#39;0&#39;</span>;</span><br><span class="line">            <span class="keyword">if</span> (token_val &gt; <span class="number">0</span>) {</span><br><span class="line">                <span class="comment">// dec, starts with [1-9]</span></span><br><span class="line">                <span class="keyword">while</span> (*src &gt;= <span class="string">&#39;0&#39;</span> &amp;&amp; *src &lt;= <span class="string">&#39;9&#39;</span>) {</span><br><span class="line">                    token_val = token_val*<span class="number">10</span> + *src++ - <span class="string">&#39;0&#39;</span>;</span><br><span class="line">                }</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                <span class="comment">// starts with number 0</span></span><br><span class="line">                <span class="keyword">if</span> (*src == <span class="string">&#39;x&#39;</span> || *src == <span class="string">&#39;X&#39;</span>) {</span><br><span class="line">                    <span class="comment">//hex</span></span><br><span class="line">                    token = *++src;</span><br><span class="line">                    <span class="keyword">while</span> ((token &gt;= <span class="string">&#39;0&#39;</span> &amp;&amp; token &lt;= <span class="string">&#39;9&#39;</span>) || (token &gt;= <span class="string">&#39;a&#39;</span> &amp;&amp; token &lt;= <span class="string">&#39;f&#39;</span>) || (token &gt;= <span class="string">&#39;A&#39;</span> &amp;&amp; token &lt;= <span class="string">&#39;F&#39;</span>)) {</span><br><span class="line">                        token_val = token_val * <span class="number">16</span> + (token &amp; <span class="number">15</span>) + (token &gt;= <span class="string">&#39;A&#39;</span> ? <span class="number">9</span> : <span class="number">0</span>);</span><br><span class="line">                        token = *++src;</span><br><span class="line">                    }</span><br><span class="line">                } <span class="keyword">else</span> {</span><br><span class="line">                    <span class="comment">// oct</span></span><br><span class="line">                    <span class="keyword">while</span> (*src &gt;= <span class="string">&#39;0&#39;</span> &amp;&amp; *src &lt;= <span class="string">&#39;7&#39;</span>) {</span><br><span class="line">                        token_val = token_val*<span class="number">8</span> + *src++ - <span class="string">&#39;0&#39;</span>;</span><br><span class="line">                    }</span><br><span class="line">                }</span><br><span class="line">            }</span><br><span class="line"></span><br><span class="line">            token = Num;</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        ...</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="字符串" tabindex="-1"><a class="header-anchor" href="#字符串"><span><a href="about:blank#%E5%AD%97%E7%AC%A6%E4%B8%B2"></a>字符串</span></a></h3><p>在分析时，如果分析到字符串，我们需要将它存放到前一篇文章中说的 <code>data</code> 段中。然后返回它在 <code>data</code> 段中的地址。另一个特殊的地方是我们需要支持转义符。例如用 <code>\\n</code> 表示换行符。由于本编译器的目的是达到自己编译自己，所以代码中并没有支持除 <code>\\n</code> 的转义符，如 <code>\\t</code>, <code>\\r</code> 等，但仍支持 <code>\\a</code> 表示字符 <code>a</code> 的语法，如 <code>\\&quot;</code> 表示 <code>&quot;</code>。</p><p>在分析时，我们将同时分析单个字符如 <code>&#39;a&#39;</code> 和字符串如 <code>&quot;a string&quot;</code>。若得到的是单个字符，我们以 <code>Num</code> 的形式返回。相关代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">next</span><span class="params">()</span> {</span><br><span class="line">        ...</span><br><span class="line"></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;&quot;&#39;</span> || token == <span class="string">&#39;\\&#39;&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse string literal, currently, the only supported escape</span></span><br><span class="line">            <span class="comment">// character is &#39;\\n&#39;, store the string literal into data.</span></span><br><span class="line">            last_pos = data;</span><br><span class="line">            <span class="keyword">while</span> (*src != <span class="number">0</span> &amp;&amp; *src != token) {</span><br><span class="line">                token_val = *src++;</span><br><span class="line">                <span class="keyword">if</span> (token_val == <span class="string">&#39;\\\\&#39;</span>) {</span><br><span class="line">                    <span class="comment">// escape character</span></span><br><span class="line">                    token_val = *src++;</span><br><span class="line">                    <span class="keyword">if</span> (token_val == <span class="string">&#39;n&#39;</span>) {</span><br><span class="line">                        token_val = <span class="string">&#39;\\n&#39;</span>;</span><br><span class="line">                    }</span><br><span class="line">                }</span><br><span class="line"></span><br><span class="line">                <span class="keyword">if</span> (token == <span class="string">&#39;&quot;&#39;</span>) {</span><br><span class="line">                    *data++ = token_val;</span><br><span class="line">                }</span><br><span class="line">            }</span><br><span class="line"></span><br><span class="line">            src++;</span><br><span class="line">            <span class="comment">// if it is a single character, return Num token</span></span><br><span class="line">            <span class="keyword">if</span> (token == <span class="string">&#39;&quot;&#39;</span>) {</span><br><span class="line">                token_val = (<span class="type">int</span>)last_pos;</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                token = Num;</span><br><span class="line">            }</span><br><span class="line"></span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="注释" tabindex="-1"><a class="header-anchor" href="#注释"><span><a href="about:blank#%E6%B3%A8%E9%87%8A"></a>注释</span></a></h3><p>在我们的 C 语言中，只支持 <code>//</code> 类型的注释，不支持 <code>/* comments */</code> 的注释。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">next</span><span class="params">()</span> {</span><br><span class="line">        ...</span><br><span class="line"></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;/&#39;</span>) {</span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;/&#39;</span>) {</span><br><span class="line">                <span class="comment">// skip comments</span></span><br><span class="line">                <span class="keyword">while</span> (*src != <span class="number">0</span> &amp;&amp; *src != <span class="string">&#39;\\n&#39;</span>) {</span><br><span class="line">                    ++src;</span><br><span class="line">                }</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                <span class="comment">// divide operator</span></span><br><span class="line">                token = Div;</span><br><span class="line">                <span class="keyword">return</span>;</span><br><span class="line">            }</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        ...</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>这里我们要额外介绍 <code>lookahead</code> 的概念，即提前看多个字符。上述代码中我们看到，除了跳过注释，我们还可能返回除号 <code>/(Div)</code> 标记。</p><p>提前看字符的原理是：有一个或多个标记是以同样的字符开头的（如本小节中的注释与除号），因此只凭当前的字符我们并无法确定具体应该解释成哪一个标记，所以只能再向前查看字符，如本例需向前查看一个字符，若是 <code>/</code> 则说明是注释，反之则是除号。</p><p>我们之前说过，词法分析器本质上也是编译器，其实提前看字符的概念也存在于编译器，只是这时就是提前看k个“标记”而不是“字符”了。平时听到的 <code>LL(k)</code> 中的 <code>k</code> 就是需要向前看的标记的个数了。</p><p>另外，我们用词法分析器将源码转换成标记流，能减小语法分析复杂度，原因之一就是减少了语法分析器需要“向前看”的字符个数。</p><h3 id="其它" tabindex="-1"><a class="header-anchor" href="#其它"><span><a href="about:blank#%E5%85%B6%E5%AE%83"></a>其它</span></a></h3><p>其它的标记的解析就相对容易一些了，我们直接贴上代码：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">next</span><span class="params">()</span> {</span><br><span class="line">        ...</span><br><span class="line"></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;=&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse &#39;==&#39; and &#39;=&#39;</span></span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;=&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Eq;</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                token = Assign;</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;+&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse &#39;+&#39; and &#39;++&#39;</span></span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;+&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Inc;</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                token = Add;</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;-&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse &#39;-&#39; and &#39;--&#39;</span></span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;-&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Dec;</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                token = Sub;</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;!&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse &#39;!=&#39;</span></span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;=&#39;</span>) {</span><br><span class="line">                src++;</span><br><span class="line">                token = Ne;</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;&lt;&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse &#39;&lt;=&#39;, &#39;&lt;&lt;&#39; or &#39;&lt;&#39;</span></span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;=&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Le;</span><br><span class="line">            } <span class="keyword">else</span> <span class="keyword">if</span> (*src == <span class="string">&#39;&lt;&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Shl;</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                token = Lt;</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;&gt;&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse &#39;&gt;=&#39;, &#39;&gt;&gt;&#39; or &#39;&gt;&#39;</span></span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;=&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Ge;</span><br><span class="line">            } <span class="keyword">else</span> <span class="keyword">if</span> (*src == <span class="string">&#39;&gt;&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Shr;</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                token = Gt;</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;|&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse &#39;|&#39; or &#39;||&#39;</span></span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;|&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Lor;</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                token = Or;</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;&amp;&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse &#39;&amp;&#39; and &#39;&amp;&amp;&#39;</span></span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;&amp;&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Lan;</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                token = And;</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;^&#39;</span>) {</span><br><span class="line">            token = Xor;</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;%&#39;</span>) {</span><br><span class="line">            token = Mod;</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;*&#39;</span>) {</span><br><span class="line">            token = Mul;</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;[&#39;</span>) {</span><br><span class="line">            token = Brak;</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;?&#39;</span>) {</span><br><span class="line">            token = Cond;</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;~&#39;</span> || token == <span class="string">&#39;;&#39;</span> || token == <span class="string">&#39;{&#39;</span> || token == <span class="string">&#39;}&#39;</span> || token == <span class="string">&#39;(&#39;</span> || token == <span class="string">&#39;)&#39;</span> || token == <span class="string">&#39;]&#39;</span> || token == <span class="string">&#39;,&#39;</span> || token == <span class="string">&#39;:&#39;</span>) {</span><br><span class="line">            <span class="comment">// directly return the character as token;</span></span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        ...</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>代码较多，但主要逻辑就是向前看一个字符来确定真正的标记。</p><h3 id="关键字与内置函数" tabindex="-1"><a class="header-anchor" href="#关键字与内置函数"><span><a href="about:blank#%E5%85%B3%E9%94%AE%E5%AD%97%E4%B8%8E%E5%86%85%E7%BD%AE%E5%87%BD%E6%95%B0"></a>关键字与内置函数</span></a></h3><p>虽然上面写完了词法分析器，但还有一个问题需要考虑，那就是“关键字”，例如 <code>if</code>, <code>while</code>, <code>return</code> 等。它们不能被作为普通的标识符，因为有特殊的含义。</p><p>一般有两种处理方法：</p><ol><li>词法分析器中直接解析这些关键字。</li><li>在语法分析前将关键字提前加入符号表。</li></ol><p>这里我们就采用第二种方法，将它们加入符号表，并提前为它们赋予必要的信息（还记得前面说的标识符 <code>Token</code> 字段吗？）。这样当源代码中出现关键字时，它们会被解析成标识符，但由于符号表中已经有了相关的信息，我们就能知道它们是特殊的关键字。</p><p>内置函数的行为也和关键字类似，不同的只是赋值的信息，在<code>main</code>函数中进行初始化如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="comment">// types of variable/function</span></span><br><span class="line"><span class="class"><span class="keyword">enum</span> {</span> CHAR, INT, PTR };</span><br><span class="line"><span class="type">int</span> *idmain;                  <span class="comment">// the `main` function</span></span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">main</span><span class="params">()</span> {</span><br><span class="line">    ...</span><br><span class="line"></span><br><span class="line">    src = <span class="string">&quot;char else enum if int return sizeof while &quot;</span></span><br><span class="line">          <span class="string">&quot;open read close printf malloc memset memcmp exit void main&quot;</span>;</span><br><span class="line"></span><br><span class="line">     <span class="comment">// add keywords to symbol table</span></span><br><span class="line">    i = Char;</span><br><span class="line">    <span class="keyword">while</span> (i &lt;= While) {</span><br><span class="line">        next();</span><br><span class="line">        current_id[Token] = i++;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="comment">// add library to symbol table</span></span><br><span class="line">    i = OPEN;</span><br><span class="line">    <span class="keyword">while</span> (i &lt;= EXIT) {</span><br><span class="line">        next();</span><br><span class="line">        current_id[Class] = Sys;</span><br><span class="line">        current_id[Type] = INT;</span><br><span class="line">        current_id[Value] = i++;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    next(); current_id[Token] = Char; <span class="comment">// handle void type</span></span><br><span class="line">    next(); idmain = current_id; <span class="comment">// keep track of main</span></span><br><span class="line"></span><br><span class="line">    ...</span><br><span class="line">    program();</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h2 id="代码" tabindex="-1"><a class="header-anchor" href="#代码"><span><a href="about:blank#%E4%BB%A3%E7%A0%81"></a>代码</span></a></h2>',76),B={href:"https://github.com/lotabout/write-a-C-interpreter/tree/step-2",target:"_blank",rel:"noopener noreferrer"},C=p('<table><tbody><tr><td class="code"><pre><span class="line">git clone -b step-2 https://github.com/lotabout/write-a-C-interpreter</span><br></pre></td></tr></tbody></table><p>上面的代码运行后会出现 ‘Segmentation Falt’，这是正常的，因为它会尝试运行我们上一章创建的虚拟机，但其中并没有任何汇编代码。</p><h2 id="小结" tabindex="-1"><a class="header-anchor" href="#小结"><span><a href="about:blank#%E5%B0%8F%E7%BB%93"></a>小结</span></a></h2><p>本章我们为我们的编译器构建了词法分析器，通过本章的学习，我认为有几个要点需要强调：</p><ol><li>词法分析器的作用是对源码字符串进行预处理，作用是减小语法分析器的复杂程度。</li><li>词法分析器本身可以认为是一个编译器，输入是源码，输出是标记流。</li><li><code>lookahead(k)</code> 的概念，即向前看 <code>k</code> 个字符或标记。</li><li>词法分析中如何处理标识符与符号表。</li></ol><p>下一章中，我们将介绍递归下降的语法分析器。我们下一章见。</p>',6);function v(x,D){const n=r("ExternalLinkIcon");return c(),t("div",null,[o,s("p",null,[a("本文转自 "),s("a",b,[a("https://lotabout.me/2015/write-a-C-interpreter-3/"),e(n)]),a("，如有侵权，请联系删除。")]),d,s("ol",null,[s("li",null,[s("a",k,[a("手把手教你构建 C 语言编译器（0）——前言"),e(n)])]),s("li",null,[s("a",h,[a("手把手教你构建 C 语言编译器（1）——设计"),e(n)])]),s("li",null,[s("a",E,[a("手把手教你构建 C 语言编译器（2）——虚拟机"),e(n)])]),s("li",null,[s("a",m,[a("手把手教你构建 C 语言编译器（3）——词法分析器"),e(n)])]),s("li",null,[s("a",u,[a("手把手教你构建 C 语言编译器（4）——递归下降"),e(n)])]),s("li",null,[s("a",y,[a("手把手教你构建 C 语言编译器（5）——变量定义"),e(n)])]),s("li",null,[s("a",f,[a("手把手教你构建 C 语言编译器（6）——函数定义"),e(n)])]),s("li",null,[s("a",g,[a("手把手教你构建 C 语言编译器（7）——语句"),e(n)])]),s("li",null,[s("a",A,[a("手把手教你构建 C 语言编译器（8）——表达式"),e(n)])]),s("li",null,[s("a",w,[a("手把手教你构建 C 语言编译器（9）——总结"),e(n)])])]),_,s("p",null,[a("本章的代码可以在 "),s("a",B,[a("Github"),e(n)]),a(" 上下载，也可以直接 clone")]),C])}const N=l(i,[["render",v],["__file","3.html.vue"]]),S=JSON.parse('{"path":"/tech/designASimpileCCompiler/3.html","title":"手把手教你构建 C 语言编译器（3）——词法分析器","lang":"zh-CN","frontmatter":{"title":"手把手教你构建 C 语言编译器（3）——词法分析器","category":["编译原理"],"tag":["c","编译器","解释器"],"description":"转载声明 本文转自 https://lotabout.me/2015/write-a-C-interpreter-3/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（3）- 词法分析器 Table of Contents 1. 什么是词法分析器 2. 词法分析器与编译器 3. 词法分析器的实现 3.1. 支持的标记 3.2. 词法分...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/designASimpileCCompiler/3.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"手把手教你构建 C 语言编译器（3）——词法分析器"}],["meta",{"property":"og:description","content":"转载声明 本文转自 https://lotabout.me/2015/write-a-C-interpreter-3/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（3）- 词法分析器 Table of Contents 1. 什么是词法分析器 2. 词法分析器与编译器 3. 词法分析器的实现 3.1. 支持的标记 3.2. 词法分..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"c"}],["meta",{"property":"article:tag","content":"编译器"}],["meta",{"property":"article:tag","content":"解释器"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"手把手教你构建 C 语言编译器（3）——词法分析器\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"什么是词法分析器","slug":"什么是词法分析器","link":"#什么是词法分析器","children":[]},{"level":2,"title":"词法分析器与编译器","slug":"词法分析器与编译器","link":"#词法分析器与编译器","children":[]},{"level":2,"title":"词法分析器的实现","slug":"词法分析器的实现","link":"#词法分析器的实现","children":[{"level":3,"title":"支持的标记","slug":"支持的标记","link":"#支持的标记","children":[]},{"level":3,"title":"词法分析器的框架","slug":"词法分析器的框架","link":"#词法分析器的框架","children":[]},{"level":3,"title":"换行符","slug":"换行符","link":"#换行符","children":[]},{"level":3,"title":"宏定义","slug":"宏定义","link":"#宏定义","children":[]},{"level":3,"title":"标识符与符号表","slug":"标识符与符号表","link":"#标识符与符号表","children":[]},{"level":3,"title":"数字","slug":"数字","link":"#数字","children":[]},{"level":3,"title":"字符串","slug":"字符串","link":"#字符串","children":[]},{"level":3,"title":"注释","slug":"注释","link":"#注释","children":[]},{"level":3,"title":"其它","slug":"其它","link":"#其它","children":[]},{"level":3,"title":"关键字与内置函数","slug":"关键字与内置函数","link":"#关键字与内置函数","children":[]}]},{"level":2,"title":"代码","slug":"代码","link":"#代码","children":[]},{"level":2,"title":"小结","slug":"小结","link":"#小结","children":[]}],"readingTime":{"minutes":25.21,"words":7563},"filePathRelative":"tech/designASimpileCCompiler/3.md","excerpt":"\\n<p>本文转自 <a href=\\"https://lotabout.me/2015/write-a-C-interpreter-3/\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">https://lotabout.me/2015/write-a-C-interpreter-3/</a>，如有侵权，请联系删除。</p>\\n<h1>原文内容</h1>\\n<h1>手把手教你构建 C 语言编译器（3）- 词法分析器</h1>\\n<p>Table of Contents</p>\\n<ol>\\n<li><a href=\\"about:blank#%E4%BB%80%E4%B9%88%E6%98%AF%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8\\">1. 什么是词法分析器</a></li>\\n<li><a href=\\"about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8%E4%B8%8E%E7%BC%96%E8%AF%91%E5%99%A8\\">2. 词法分析器与编译器</a></li>\\n<li><a href=\\"about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8%E7%9A%84%E5%AE%9E%E7%8E%B0\\">3. 词法分析器的实现</a>\\n<ol>\\n<li><a href=\\"about:blank#%E6%94%AF%E6%8C%81%E7%9A%84%E6%A0%87%E8%AE%B0\\">3.1. 支持的标记</a></li>\\n<li><a href=\\"about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8%E7%9A%84%E6%A1%86%E6%9E%B6\\">3.2. 词法分析器的框架</a></li>\\n<li><a href=\\"about:blank#%E6%8D%A2%E8%A1%8C%E7%AC%A6\\">3.3. 换行符</a></li>\\n<li><a href=\\"about:blank#%E5%AE%8F%E5%AE%9A%E4%B9%89\\">3.4. 宏定义</a></li>\\n<li><a href=\\"about:blank#%E6%A0%87%E8%AF%86%E7%AC%A6%E4%B8%8E%E7%AC%A6%E5%8F%B7%E8%A1%A8\\">3.5. 标识符与符号表</a></li>\\n<li><a href=\\"about:blank#%E6%95%B0%E5%AD%97\\">3.6. 数字</a></li>\\n<li><a href=\\"about:blank#%E5%AD%97%E7%AC%A6%E4%B8%B2\\">3.7. 字符串</a></li>\\n<li><a href=\\"about:blank#%E6%B3%A8%E9%87%8A\\">3.8. 注释</a></li>\\n<li><a href=\\"about:blank#%E5%85%B6%E5%AE%83\\">3.9. 其它</a></li>\\n<li><a href=\\"about:blank#%E5%85%B3%E9%94%AE%E5%AD%97%E4%B8%8E%E5%86%85%E7%BD%AE%E5%87%BD%E6%95%B0\\">3.10. 关键字与内置函数</a></li>\\n</ol>\\n</li>\\n<li><a href=\\"about:blank#%E4%BB%A3%E7%A0%81\\">4. 代码</a></li>\\n<li><a href=\\"about:blank#%E5%B0%8F%E7%BB%93\\">5. 小结</a></li>\\n</ol>","autoDesc":true}');export{N as comp,S as data};
diff --git a/assets/4.html-C8TuLMaF.js b/assets/4.html-DavKkBaH.js
similarity index 99%
rename from assets/4.html-C8TuLMaF.js
rename to assets/4.html-DavKkBaH.js
index 55b0054..b52bced 100644
--- a/assets/4.html-C8TuLMaF.js
+++ b/assets/4.html-DavKkBaH.js
@@ -1 +1 @@
-import{_ as t,r as p,o as r,c,b as s,e as a,d as e,f as l}from"./app-B69Gl_S-.js";const i={},o=s("p",null,"[]",-1),b=s("h1",{id:"转载声明",tabindex:"-1"},[s("a",{class:"header-anchor",href:"#转载声明"},[s("span",null,"转载声明")])],-1),d={href:"https://lotabout.me/2016/write-a-C-interpreter-4/",target:"_blank",rel:"noopener noreferrer"},h=l('<h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-4-递归下降" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-4-递归下降"><span>手把手教你构建 C 语言编译器（4）- 递归下降</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#%E4%BB%80%E4%B9%88%E6%98%AF%E9%80%92%E5%BD%92%E4%B8%8B%E9%99%8D">1. 什么是递归下降</a></li><li><a href="about:blank#%E7%BB%88%E7%BB%93%E7%AC%A6%E4%B8%8E%E9%9D%9E%E7%BB%88%E7%BB%93%E7%AC%A6">2. 终结符与非终结符</a></li><li><a href="about:blank#%E5%9B%9B%E5%88%99%E8%BF%90%E7%AE%97%E7%9A%84%E9%80%92%E5%BD%92%E4%B8%8B%E9%99%8D">3. 四则运算的递归下降</a></li><li><a href="about:blank#%E4%B8%BA%E4%BB%80%E4%B9%88%E9%80%89%E6%8B%A9%E9%80%92%E5%BD%92%E4%B8%8B%E9%99%8D">4. 为什么选择递归下降</a></li><li><a href="about:blank#%E5%B7%A6%E9%80%92%E5%BD%92">5. 左递归</a></li><li><a href="about:blank#%E5%9B%9B%E5%88%99%E8%BF%90%E7%AE%97%E7%9A%84%E5%AE%9E%E7%8E%B0">6. 四则运算的实现</a></li><li><a href="about:blank#%E5%B0%8F%E7%BB%93">7. 小结</a></li></ol><p>本章我们将讲解递归下降的方法，并用它完成一个基本的四则运算的语法分析器。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p>',6),E={href:"http://lotabout.me/2015/write-a-C-interpreter-0/",target:"_blank",rel:"noopener noreferrer"},g={href:"http://lotabout.me/2015/write-a-C-interpreter-1/",target:"_blank",rel:"noopener noreferrer"},u={href:"http://lotabout.me/2015/write-a-C-interpreter-2/",target:"_blank",rel:"noopener noreferrer"},m={href:"http://lotabout.me/2015/write-a-C-interpreter-3/",target:"_blank",rel:"noopener noreferrer"},B={href:"http://lotabout.me/2016/write-a-C-interpreter-4/",target:"_blank",rel:"noopener noreferrer"},f={href:"http://lotabout.me/2016/write-a-C-interpreter-5/",target:"_blank",rel:"noopener noreferrer"},k={href:"http://lotabout.me/2016/write-a-C-interpreter-6/",target:"_blank",rel:"noopener noreferrer"},_={href:"http://lotabout.me/2016/write-a-C-interpreter-7/",target:"_blank",rel:"noopener noreferrer"},y={href:"http://lotabout.me/2016/write-a-C-interpreter-8/",target:"_blank",rel:"noopener noreferrer"},C={href:"http://lotabout.me/2016/write-a-C-interpreter-9/",target:"_blank",rel:"noopener noreferrer"},w=l('<h2 id="什么是递归下降" tabindex="-1"><a class="header-anchor" href="#什么是递归下降"><span><a href="about:blank#%E4%BB%80%E4%B9%88%E6%98%AF%E9%80%92%E5%BD%92%E4%B8%8B%E9%99%8D"></a>什么是递归下降</span></a></h2><p>传统上，编写语法分析器有两种方法，一种是自顶向下，一种是自底向上。自顶向下是从起始非终结符开始，不断地对非终结符进行分解，直到匹配输入的终结符；自底向上是不断地将终结符进行合并，直到合并成起始的非终结符。</p><p>其中的自顶向下方法就是我们所说的递归下降。</p><h2 id="终结符与非终结符" tabindex="-1"><a class="header-anchor" href="#终结符与非终结符"><span><a href="about:blank#%E7%BB%88%E7%BB%93%E7%AC%A6%E4%B8%8E%E9%9D%9E%E7%BB%88%E7%BB%93%E7%AC%A6"></a>终结符与非终结符</span></a></h2>',4),x={href:"https://zh.wikipedia.org/wiki/%E5%B7%B4%E7%A7%91%E6%96%AF%E8%8C%83%E5%BC%8F",target:"_blank",rel:"noopener noreferrer"},A=l('<table><tbody><tr><td class="code"><pre><span class="line">&lt;expr&gt; ::= &lt;expr&gt; + &lt;term&gt;</span><br><span class="line">         | &lt;expr&gt; - &lt;term&gt;</span><br><span class="line">         | &lt;term&gt;</span><br><span class="line"></span><br><span class="line">&lt;term&gt; ::= &lt;term&gt; * &lt;factor&gt;</span><br><span class="line">         | &lt;term&gt; / &lt;factor&gt;</span><br><span class="line">         | &lt;factor&gt;</span><br><span class="line"></span><br><span class="line">&lt;factor&gt; ::= ( &lt;expr&gt; )</span><br><span class="line">           | Num</span><br></pre></td></tr></tbody></table><p>用尖括号 <code>&lt;&gt;</code> 括起来的就称作 <strong>非终结符</strong> ，因为它们可以用 <code>::=</code> 右侧的式子代替。<code>|</code> 表示选择，如 <code>&lt;expr&gt;</code> 可以是 <code>&lt;expr&gt; + &lt;term&gt;</code>、<code>&lt;expr&gt; - &lt;term&gt;</code>或 <code>&lt;term&gt;</code> 中的一种。而没有出现在<code>::=</code>左边的就称作 <strong>终结符</strong> ，一般终结符对应于词法分析器输出的标记。</p><h2 id="四则运算的递归下降" tabindex="-1"><a class="header-anchor" href="#四则运算的递归下降"><span><a href="about:blank#%E5%9B%9B%E5%88%99%E8%BF%90%E7%AE%97%E7%9A%84%E9%80%92%E5%BD%92%E4%B8%8B%E9%99%8D"></a>四则运算的递归下降</span></a></h2><p>例如，我们对 <code>3 * (4 + 2)</code> 进行语法分析。我们假设词法分析器已经正确地将其中的数字识别成了标记 <code>Num</code>。</p><p>递归下降是从起始的非终结符开始（顶），本例中是 <code>&lt;expr&gt;</code>，实际中可以自己指定，不指定的话一般认为是第一个出现的非终结符。</p><table><tbody><tr><td class="code"><pre><span class="line">1. &lt;expr&gt; =&gt; &lt;expr&gt;</span><br><span class="line">2.           =&gt; &lt;term&gt;        * &lt;factor&gt;</span><br><span class="line">3.              =&gt; &lt;factor&gt;     |</span><br><span class="line">4.                 =&gt; Num (3)   |</span><br><span class="line">5.                              =&gt; ( &lt;expr&gt; )</span><br><span class="line">6.                                   =&gt; &lt;expr&gt;           + &lt;term&gt;</span><br><span class="line">7.                                      =&gt; &lt;term&gt;          |</span><br><span class="line">8.                                         =&gt; &lt;factor&gt;     |</span><br><span class="line">9.                                            =&gt; Num (4)   |</span><br><span class="line">10.                                                        =&gt; &lt;factor&gt;</span><br><span class="line">11.                                                           =&gt; Num (2)</span><br></pre></td></tr></tbody></table><p>可以看到，整个解析的过程是在不断对非终结符进行替换（向下），直到遇见了终结符（底）。而我们可以从解析的过程中看出，一些非终结符如<code>&lt;expr&gt;</code>被递归地使用了。</p><h2 id="为什么选择递归下降" tabindex="-1"><a class="header-anchor" href="#为什么选择递归下降"><span><a href="about:blank#%E4%B8%BA%E4%BB%80%E4%B9%88%E9%80%89%E6%8B%A9%E9%80%92%E5%BD%92%E4%B8%8B%E9%99%8D"></a>为什么选择递归下降</span></a></h2><p>从上小节对四则运算的递归下降解析可以看出，整个解析的过程和语法的 BNF 表示是十分接近的，更为重要的是，我们可以很容易地直接将 BNF 表示转换成实际的代码。方法是为每个产生式（即 <code>非终结符 ::= ...</code>）生成一个同名的函数。</p><p>这里会有一个疑问，就是上例中，当一个终结符有多个选择时，如何确定具体选择哪一个？如为什么用 <code>&lt;expr&gt; ::= &lt;term&gt; * &lt;factor&gt;</code> 而不是 <code>&lt;expr&gt; ::= &lt;term&gt; / &lt;factor&gt;</code> ？这就用到了上一章中提到的“向前看 k 个标记”的概念了。我们向前看一个标记，发现是 <code>*</code>，而这个标记足够让我们确定用哪个表达式了。</p><p>另外，递归下下降方法对 BNF 方法本身有一定的要求，否则会有一些问题，如经典的“左递归”问题。</p><h2 id="左递归" tabindex="-1"><a class="header-anchor" href="#左递归"><span><a href="about:blank#%E5%B7%A6%E9%80%92%E5%BD%92"></a>左递归</span></a></h2><p>原则上我们是不讲这么深入，但我们上面的四则运算的文法就是左递归的，而左递归的语法是没法直接使用递归下降的方法实现的。因此我们要消除左递归，消除后的文法如下：</p><table><tbody><tr><td class="code"><pre><span class="line">&lt;expr&gt; ::= &lt;term&gt; &lt;expr_tail&gt;</span><br><span class="line">&lt;expr_tail&gt; ::= + &lt;term&gt; &lt;expr_tail&gt;</span><br><span class="line">              | - &lt;term&gt; &lt;expr_tail&gt;</span><br><span class="line">              | &lt;empty&gt;</span><br><span class="line"></span><br><span class="line">&lt;term&gt; ::= &lt;factor&gt; &lt;term_tail&gt;</span><br><span class="line">&lt;term_tail&gt; ::= * &lt;factor&gt; &lt;term_tail&gt;</span><br><span class="line">              | / &lt;factor&gt; &lt;term_tail&gt;</span><br><span class="line">              | &lt;empty&gt;</span><br><span class="line"></span><br><span class="line">&lt;factor&gt; ::= ( &lt;expr&gt; )</span><br><span class="line">           | Num</span><br></pre></td></tr></tbody></table><p>消除左递归的相关方法，这里不再多说，请自行查阅相关的资料。</p><h2 id="四则运算的实现" tabindex="-1"><a class="header-anchor" href="#四则运算的实现"><span><a href="about:blank#%E5%9B%9B%E5%88%99%E8%BF%90%E7%AE%97%E7%9A%84%E5%AE%9E%E7%8E%B0"></a>四则运算的实现</span></a></h2><p>本节中我们专注语法分析器部分的实现，具体实现很容易，我们直接贴上代码，就是上述的消除左递归后的文法直接转换而来的：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> <span class="title function_">expr</span><span class="params">()</span>;</span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">factor</span><span class="params">()</span> {</span><br><span class="line">    <span class="type">int</span> value = <span class="number">0</span>;</span><br><span class="line">    <span class="keyword">if</span> (token == <span class="string">&#39;(&#39;</span>) {</span><br><span class="line">        match(<span class="string">&#39;(&#39;</span>);</span><br><span class="line">        value = expr();</span><br><span class="line">        match(<span class="string">&#39;)&#39;</span>);</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        value = token_val;</span><br><span class="line">        match(Num);</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">return</span> value;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">term_tail</span><span class="params">(<span class="type">int</span> lvalue)</span> {</span><br><span class="line">    <span class="keyword">if</span> (token == <span class="string">&#39;*&#39;</span>) {</span><br><span class="line">        match(<span class="string">&#39;*&#39;</span>);</span><br><span class="line">        <span class="type">int</span> value = lvalue * factor();</span><br><span class="line">        <span class="keyword">return</span> term_tail(value);</span><br><span class="line">    } <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;/&#39;</span>) {</span><br><span class="line">        match(<span class="string">&#39;/&#39;</span>);</span><br><span class="line">        <span class="type">int</span> value = lvalue / factor();</span><br><span class="line">        <span class="keyword">return</span> term_tail(value);</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="keyword">return</span> lvalue;</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">term</span><span class="params">()</span> {</span><br><span class="line">    <span class="type">int</span> lvalue = factor();</span><br><span class="line">    <span class="keyword">return</span> term_tail(lvalue);</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">expr_tail</span><span class="params">(<span class="type">int</span> lvalue)</span> {</span><br><span class="line">    <span class="keyword">if</span> (token == <span class="string">&#39;+&#39;</span>) {</span><br><span class="line">        match(<span class="string">&#39;+&#39;</span>);</span><br><span class="line">        <span class="type">int</span> value = lvalue + term();</span><br><span class="line">        <span class="keyword">return</span> expr_tail(value);</span><br><span class="line">    } <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;-&#39;</span>) {</span><br><span class="line">        match(<span class="string">&#39;-&#39;</span>);</span><br><span class="line">        <span class="type">int</span> value = lvalue - term();</span><br><span class="line">        <span class="keyword">return</span> expr_tail(value);</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="keyword">return</span> lvalue;</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">expr</span><span class="params">()</span> {</span><br><span class="line">    <span class="type">int</span> lvalue = term();</span><br><span class="line">    <span class="keyword">return</span> expr_tail(lvalue);</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>可以看到，有了BNF方法后，采用递归向下的方法来实现编译器是很直观的。</p><p>我们把词法分析器的代码一并贴上：</p><table><tbody><tr><td class="code"><pre><span class="line">#<span class="meta">#<span class="keyword">include</span> <span class="string">&lt;stdio.h&gt;</span></span></span><br><span class="line">#<span class="meta">#<span class="keyword">include</span> <span class="string">&lt;stdlib.h&gt;</span></span></span><br><span class="line"></span><br><span class="line"><span class="class"><span class="keyword">enum</span> {</span>Num};</span><br><span class="line"><span class="type">int</span> token;</span><br><span class="line"><span class="type">int</span> token_val;</span><br><span class="line"><span class="type">char</span> *line = <span class="literal">NULL</span>;</span><br><span class="line"><span class="type">char</span> *src = <span class="literal">NULL</span>;</span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">next</span><span class="params">()</span> {</span><br><span class="line">    <span class="comment">// skip white space</span></span><br><span class="line">    <span class="keyword">while</span> (*src == <span class="string">&#39; &#39;</span> || *src == <span class="string">&#39;\\t&#39;</span>) {</span><br><span class="line">        src ++;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    token = *src++;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (token &gt;= <span class="string">&#39;0&#39;</span> &amp;&amp; token &lt;= <span class="string">&#39;9&#39;</span> ) {</span><br><span class="line">        token_val = token - <span class="string">&#39;0&#39;</span>;</span><br><span class="line">        token = Num;</span><br><span class="line"></span><br><span class="line">        <span class="keyword">while</span> (*src &gt;= <span class="string">&#39;0&#39;</span> &amp;&amp; *src &lt;= <span class="string">&#39;9&#39;</span>) {</span><br><span class="line">            token_val = token_val*<span class="number">10</span> + *src - <span class="string">&#39;0&#39;</span>;</span><br><span class="line">            src ++;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">return</span>;</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">match</span><span class="params">(<span class="type">int</span> tk)</span> {</span><br><span class="line">    <span class="keyword">if</span> (token != tk) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;expected token: %d(%c), got: %d(%c)\\n&quot;</span>, tk, tk, token, token);</span><br><span class="line">        <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line">    next();</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>最后是<code>main</code>函数：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> <span class="title function_">main</span><span class="params">(<span class="type">int</span> argc, <span class="type">char</span> *argv[])</span></span><br><span class="line">{</span><br><span class="line">    <span class="type">size_t</span> linecap = <span class="number">0</span>;</span><br><span class="line">    <span class="type">ssize_t</span> linelen;</span><br><span class="line">    <span class="keyword">while</span> ((linelen = getline(&amp;line, &amp;linecap, <span class="built_in">stdin</span>)) &gt; <span class="number">0</span>) {</span><br><span class="line">        src = line;</span><br><span class="line">        next();</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%d\\n&quot;</span>, expr());</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h2 id="小结" tabindex="-1"><a class="header-anchor" href="#小结"><span><a href="about:blank#%E5%B0%8F%E7%BB%93"></a>小结</span></a></h2><p>本章中我们介绍了递归下降的方法，并用它来实现了四则运算的语法分析器。</p><p>花这么大精力讲解递归下降方法，是因为几乎所有手工编写的语法分析器都或多或少地有它的影子。换句话说，掌握了递归下降的方法，就可以应付大多数的语法分析器编写。</p><p>同时我们也用实例看到了理论（BNF 语法，左递归的消除）是如何帮助我们的工程实现的。尽管理论不是必需的，但如果能掌握它，对于提高我们的水平还是很有帮助的。</p>',27);function v(D,N){const n=p("ExternalLinkIcon");return r(),c("div",null,[o,b,s("p",null,[a("本文转自 "),s("a",d,[a("https://lotabout.me/2016/write-a-C-interpreter-4/"),e(n)]),a("，如有侵权，请联系删除。")]),h,s("ol",null,[s("li",null,[s("a",E,[a("手把手教你构建 C 语言编译器（0）——前言"),e(n)])]),s("li",null,[s("a",g,[a("手把手教你构建 C 语言编译器（1）——设计"),e(n)])]),s("li",null,[s("a",u,[a("手把手教你构建 C 语言编译器（2）——虚拟机"),e(n)])]),s("li",null,[s("a",m,[a("手把手教你构建 C 语言编译器（3）——词法分析器"),e(n)])]),s("li",null,[s("a",B,[a("手把手教你构建 C 语言编译器（4）——递归下降"),e(n)])]),s("li",null,[s("a",f,[a("手把手教你构建 C 语言编译器（5）——变量定义"),e(n)])]),s("li",null,[s("a",k,[a("手把手教你构建 C 语言编译器（6）——函数定义"),e(n)])]),s("li",null,[s("a",_,[a("手把手教你构建 C 语言编译器（7）——语句"),e(n)])]),s("li",null,[s("a",y,[a("手把手教你构建 C 语言编译器（8）——表达式"),e(n)])]),s("li",null,[s("a",C,[a("手把手教你构建 C 语言编译器（9）——总结"),e(n)])])]),w,s("p",null,[a("没有学过编译原理的话可能并不知道什么是“终结符”，“非终结符”。这里我简单介绍一下。首先是 "),s("a",x,[a("BNF"),e(n)]),a(" 范式，就是一种用来描述语法的语言，例如，四则运算的规则可以表示如下：")]),A])}const S=t(i,[["render",v],["__file","4.html.vue"]]),L=JSON.parse('{"path":"/tech/designASimpileCCompiler/4.html","title":"手把手教你构建 C 语言编译器（4）——递归下降","lang":"zh-CN","frontmatter":{"title":"手把手教你构建 C 语言编译器（4）——递归下降","category":["编译原理"],"tag":["c","编译器","解释器"],"description":"[] 转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-4/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（4）- 递归下降 Table of Contents 1. 什么是递归下降 2. 终结符与非终结符 3. 四则运算的递归下降 4. 为什么选择递归下降 5. 左递...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/designASimpileCCompiler/4.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"手把手教你构建 C 语言编译器（4）——递归下降"}],["meta",{"property":"og:description","content":"[] 转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-4/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（4）- 递归下降 Table of Contents 1. 什么是递归下降 2. 终结符与非终结符 3. 四则运算的递归下降 4. 为什么选择递归下降 5. 左递..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"c"}],["meta",{"property":"article:tag","content":"编译器"}],["meta",{"property":"article:tag","content":"解释器"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"手把手教你构建 C 语言编译器（4）——递归下降\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"什么是递归下降","slug":"什么是递归下降","link":"#什么是递归下降","children":[]},{"level":2,"title":"终结符与非终结符","slug":"终结符与非终结符","link":"#终结符与非终结符","children":[]},{"level":2,"title":"四则运算的递归下降","slug":"四则运算的递归下降","link":"#四则运算的递归下降","children":[]},{"level":2,"title":"为什么选择递归下降","slug":"为什么选择递归下降","link":"#为什么选择递归下降","children":[]},{"level":2,"title":"左递归","slug":"左递归","link":"#左递归","children":[]},{"level":2,"title":"四则运算的实现","slug":"四则运算的实现","link":"#四则运算的实现","children":[]},{"level":2,"title":"小结","slug":"小结","link":"#小结","children":[]}],"readingTime":{"minutes":11.33,"words":3399},"filePathRelative":"tech/designASimpileCCompiler/4.md","excerpt":"<p>[]</p>\\n<h1>转载声明</h1>\\n<p>本文转自 <a href=\\"https://lotabout.me/2016/write-a-C-interpreter-4/\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">https://lotabout.me/2016/write-a-C-interpreter-4/</a>，如有侵权，请联系删除。</p>\\n<h1>原文内容</h1>\\n<h1>手把手教你构建 C 语言编译器（4）- 递归下降</h1>\\n<p>Table of Contents</p>\\n<ol>\\n<li><a href=\\"about:blank#%E4%BB%80%E4%B9%88%E6%98%AF%E9%80%92%E5%BD%92%E4%B8%8B%E9%99%8D\\">1. 什么是递归下降</a></li>\\n<li><a href=\\"about:blank#%E7%BB%88%E7%BB%93%E7%AC%A6%E4%B8%8E%E9%9D%9E%E7%BB%88%E7%BB%93%E7%AC%A6\\">2. 终结符与非终结符</a></li>\\n<li><a href=\\"about:blank#%E5%9B%9B%E5%88%99%E8%BF%90%E7%AE%97%E7%9A%84%E9%80%92%E5%BD%92%E4%B8%8B%E9%99%8D\\">3. 四则运算的递归下降</a></li>\\n<li><a href=\\"about:blank#%E4%B8%BA%E4%BB%80%E4%B9%88%E9%80%89%E6%8B%A9%E9%80%92%E5%BD%92%E4%B8%8B%E9%99%8D\\">4. 为什么选择递归下降</a></li>\\n<li><a href=\\"about:blank#%E5%B7%A6%E9%80%92%E5%BD%92\\">5. 左递归</a></li>\\n<li><a href=\\"about:blank#%E5%9B%9B%E5%88%99%E8%BF%90%E7%AE%97%E7%9A%84%E5%AE%9E%E7%8E%B0\\">6. 四则运算的实现</a></li>\\n<li><a href=\\"about:blank#%E5%B0%8F%E7%BB%93\\">7. 小结</a></li>\\n</ol>","autoDesc":true}');export{S as comp,L as data};
+import{_ as t,r as p,o as r,c,b as s,e as a,d as e,f as l}from"./app-B4LGNJZ0.js";const i={},o=s("p",null,"[]",-1),b=s("h1",{id:"转载声明",tabindex:"-1"},[s("a",{class:"header-anchor",href:"#转载声明"},[s("span",null,"转载声明")])],-1),d={href:"https://lotabout.me/2016/write-a-C-interpreter-4/",target:"_blank",rel:"noopener noreferrer"},h=l('<h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-4-递归下降" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-4-递归下降"><span>手把手教你构建 C 语言编译器（4）- 递归下降</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#%E4%BB%80%E4%B9%88%E6%98%AF%E9%80%92%E5%BD%92%E4%B8%8B%E9%99%8D">1. 什么是递归下降</a></li><li><a href="about:blank#%E7%BB%88%E7%BB%93%E7%AC%A6%E4%B8%8E%E9%9D%9E%E7%BB%88%E7%BB%93%E7%AC%A6">2. 终结符与非终结符</a></li><li><a href="about:blank#%E5%9B%9B%E5%88%99%E8%BF%90%E7%AE%97%E7%9A%84%E9%80%92%E5%BD%92%E4%B8%8B%E9%99%8D">3. 四则运算的递归下降</a></li><li><a href="about:blank#%E4%B8%BA%E4%BB%80%E4%B9%88%E9%80%89%E6%8B%A9%E9%80%92%E5%BD%92%E4%B8%8B%E9%99%8D">4. 为什么选择递归下降</a></li><li><a href="about:blank#%E5%B7%A6%E9%80%92%E5%BD%92">5. 左递归</a></li><li><a href="about:blank#%E5%9B%9B%E5%88%99%E8%BF%90%E7%AE%97%E7%9A%84%E5%AE%9E%E7%8E%B0">6. 四则运算的实现</a></li><li><a href="about:blank#%E5%B0%8F%E7%BB%93">7. 小结</a></li></ol><p>本章我们将讲解递归下降的方法，并用它完成一个基本的四则运算的语法分析器。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p>',6),E={href:"http://lotabout.me/2015/write-a-C-interpreter-0/",target:"_blank",rel:"noopener noreferrer"},g={href:"http://lotabout.me/2015/write-a-C-interpreter-1/",target:"_blank",rel:"noopener noreferrer"},u={href:"http://lotabout.me/2015/write-a-C-interpreter-2/",target:"_blank",rel:"noopener noreferrer"},m={href:"http://lotabout.me/2015/write-a-C-interpreter-3/",target:"_blank",rel:"noopener noreferrer"},B={href:"http://lotabout.me/2016/write-a-C-interpreter-4/",target:"_blank",rel:"noopener noreferrer"},f={href:"http://lotabout.me/2016/write-a-C-interpreter-5/",target:"_blank",rel:"noopener noreferrer"},k={href:"http://lotabout.me/2016/write-a-C-interpreter-6/",target:"_blank",rel:"noopener noreferrer"},_={href:"http://lotabout.me/2016/write-a-C-interpreter-7/",target:"_blank",rel:"noopener noreferrer"},y={href:"http://lotabout.me/2016/write-a-C-interpreter-8/",target:"_blank",rel:"noopener noreferrer"},C={href:"http://lotabout.me/2016/write-a-C-interpreter-9/",target:"_blank",rel:"noopener noreferrer"},w=l('<h2 id="什么是递归下降" tabindex="-1"><a class="header-anchor" href="#什么是递归下降"><span><a href="about:blank#%E4%BB%80%E4%B9%88%E6%98%AF%E9%80%92%E5%BD%92%E4%B8%8B%E9%99%8D"></a>什么是递归下降</span></a></h2><p>传统上，编写语法分析器有两种方法，一种是自顶向下，一种是自底向上。自顶向下是从起始非终结符开始，不断地对非终结符进行分解，直到匹配输入的终结符；自底向上是不断地将终结符进行合并，直到合并成起始的非终结符。</p><p>其中的自顶向下方法就是我们所说的递归下降。</p><h2 id="终结符与非终结符" tabindex="-1"><a class="header-anchor" href="#终结符与非终结符"><span><a href="about:blank#%E7%BB%88%E7%BB%93%E7%AC%A6%E4%B8%8E%E9%9D%9E%E7%BB%88%E7%BB%93%E7%AC%A6"></a>终结符与非终结符</span></a></h2>',4),x={href:"https://zh.wikipedia.org/wiki/%E5%B7%B4%E7%A7%91%E6%96%AF%E8%8C%83%E5%BC%8F",target:"_blank",rel:"noopener noreferrer"},A=l('<table><tbody><tr><td class="code"><pre><span class="line">&lt;expr&gt; ::= &lt;expr&gt; + &lt;term&gt;</span><br><span class="line">         | &lt;expr&gt; - &lt;term&gt;</span><br><span class="line">         | &lt;term&gt;</span><br><span class="line"></span><br><span class="line">&lt;term&gt; ::= &lt;term&gt; * &lt;factor&gt;</span><br><span class="line">         | &lt;term&gt; / &lt;factor&gt;</span><br><span class="line">         | &lt;factor&gt;</span><br><span class="line"></span><br><span class="line">&lt;factor&gt; ::= ( &lt;expr&gt; )</span><br><span class="line">           | Num</span><br></pre></td></tr></tbody></table><p>用尖括号 <code>&lt;&gt;</code> 括起来的就称作 <strong>非终结符</strong> ，因为它们可以用 <code>::=</code> 右侧的式子代替。<code>|</code> 表示选择，如 <code>&lt;expr&gt;</code> 可以是 <code>&lt;expr&gt; + &lt;term&gt;</code>、<code>&lt;expr&gt; - &lt;term&gt;</code>或 <code>&lt;term&gt;</code> 中的一种。而没有出现在<code>::=</code>左边的就称作 <strong>终结符</strong> ，一般终结符对应于词法分析器输出的标记。</p><h2 id="四则运算的递归下降" tabindex="-1"><a class="header-anchor" href="#四则运算的递归下降"><span><a href="about:blank#%E5%9B%9B%E5%88%99%E8%BF%90%E7%AE%97%E7%9A%84%E9%80%92%E5%BD%92%E4%B8%8B%E9%99%8D"></a>四则运算的递归下降</span></a></h2><p>例如，我们对 <code>3 * (4 + 2)</code> 进行语法分析。我们假设词法分析器已经正确地将其中的数字识别成了标记 <code>Num</code>。</p><p>递归下降是从起始的非终结符开始（顶），本例中是 <code>&lt;expr&gt;</code>，实际中可以自己指定，不指定的话一般认为是第一个出现的非终结符。</p><table><tbody><tr><td class="code"><pre><span class="line">1. &lt;expr&gt; =&gt; &lt;expr&gt;</span><br><span class="line">2.           =&gt; &lt;term&gt;        * &lt;factor&gt;</span><br><span class="line">3.              =&gt; &lt;factor&gt;     |</span><br><span class="line">4.                 =&gt; Num (3)   |</span><br><span class="line">5.                              =&gt; ( &lt;expr&gt; )</span><br><span class="line">6.                                   =&gt; &lt;expr&gt;           + &lt;term&gt;</span><br><span class="line">7.                                      =&gt; &lt;term&gt;          |</span><br><span class="line">8.                                         =&gt; &lt;factor&gt;     |</span><br><span class="line">9.                                            =&gt; Num (4)   |</span><br><span class="line">10.                                                        =&gt; &lt;factor&gt;</span><br><span class="line">11.                                                           =&gt; Num (2)</span><br></pre></td></tr></tbody></table><p>可以看到，整个解析的过程是在不断对非终结符进行替换（向下），直到遇见了终结符（底）。而我们可以从解析的过程中看出，一些非终结符如<code>&lt;expr&gt;</code>被递归地使用了。</p><h2 id="为什么选择递归下降" tabindex="-1"><a class="header-anchor" href="#为什么选择递归下降"><span><a href="about:blank#%E4%B8%BA%E4%BB%80%E4%B9%88%E9%80%89%E6%8B%A9%E9%80%92%E5%BD%92%E4%B8%8B%E9%99%8D"></a>为什么选择递归下降</span></a></h2><p>从上小节对四则运算的递归下降解析可以看出，整个解析的过程和语法的 BNF 表示是十分接近的，更为重要的是，我们可以很容易地直接将 BNF 表示转换成实际的代码。方法是为每个产生式（即 <code>非终结符 ::= ...</code>）生成一个同名的函数。</p><p>这里会有一个疑问，就是上例中，当一个终结符有多个选择时，如何确定具体选择哪一个？如为什么用 <code>&lt;expr&gt; ::= &lt;term&gt; * &lt;factor&gt;</code> 而不是 <code>&lt;expr&gt; ::= &lt;term&gt; / &lt;factor&gt;</code> ？这就用到了上一章中提到的“向前看 k 个标记”的概念了。我们向前看一个标记，发现是 <code>*</code>，而这个标记足够让我们确定用哪个表达式了。</p><p>另外，递归下下降方法对 BNF 方法本身有一定的要求，否则会有一些问题，如经典的“左递归”问题。</p><h2 id="左递归" tabindex="-1"><a class="header-anchor" href="#左递归"><span><a href="about:blank#%E5%B7%A6%E9%80%92%E5%BD%92"></a>左递归</span></a></h2><p>原则上我们是不讲这么深入，但我们上面的四则运算的文法就是左递归的，而左递归的语法是没法直接使用递归下降的方法实现的。因此我们要消除左递归，消除后的文法如下：</p><table><tbody><tr><td class="code"><pre><span class="line">&lt;expr&gt; ::= &lt;term&gt; &lt;expr_tail&gt;</span><br><span class="line">&lt;expr_tail&gt; ::= + &lt;term&gt; &lt;expr_tail&gt;</span><br><span class="line">              | - &lt;term&gt; &lt;expr_tail&gt;</span><br><span class="line">              | &lt;empty&gt;</span><br><span class="line"></span><br><span class="line">&lt;term&gt; ::= &lt;factor&gt; &lt;term_tail&gt;</span><br><span class="line">&lt;term_tail&gt; ::= * &lt;factor&gt; &lt;term_tail&gt;</span><br><span class="line">              | / &lt;factor&gt; &lt;term_tail&gt;</span><br><span class="line">              | &lt;empty&gt;</span><br><span class="line"></span><br><span class="line">&lt;factor&gt; ::= ( &lt;expr&gt; )</span><br><span class="line">           | Num</span><br></pre></td></tr></tbody></table><p>消除左递归的相关方法，这里不再多说，请自行查阅相关的资料。</p><h2 id="四则运算的实现" tabindex="-1"><a class="header-anchor" href="#四则运算的实现"><span><a href="about:blank#%E5%9B%9B%E5%88%99%E8%BF%90%E7%AE%97%E7%9A%84%E5%AE%9E%E7%8E%B0"></a>四则运算的实现</span></a></h2><p>本节中我们专注语法分析器部分的实现，具体实现很容易，我们直接贴上代码，就是上述的消除左递归后的文法直接转换而来的：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> <span class="title function_">expr</span><span class="params">()</span>;</span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">factor</span><span class="params">()</span> {</span><br><span class="line">    <span class="type">int</span> value = <span class="number">0</span>;</span><br><span class="line">    <span class="keyword">if</span> (token == <span class="string">&#39;(&#39;</span>) {</span><br><span class="line">        match(<span class="string">&#39;(&#39;</span>);</span><br><span class="line">        value = expr();</span><br><span class="line">        match(<span class="string">&#39;)&#39;</span>);</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        value = token_val;</span><br><span class="line">        match(Num);</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">return</span> value;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">term_tail</span><span class="params">(<span class="type">int</span> lvalue)</span> {</span><br><span class="line">    <span class="keyword">if</span> (token == <span class="string">&#39;*&#39;</span>) {</span><br><span class="line">        match(<span class="string">&#39;*&#39;</span>);</span><br><span class="line">        <span class="type">int</span> value = lvalue * factor();</span><br><span class="line">        <span class="keyword">return</span> term_tail(value);</span><br><span class="line">    } <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;/&#39;</span>) {</span><br><span class="line">        match(<span class="string">&#39;/&#39;</span>);</span><br><span class="line">        <span class="type">int</span> value = lvalue / factor();</span><br><span class="line">        <span class="keyword">return</span> term_tail(value);</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="keyword">return</span> lvalue;</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">term</span><span class="params">()</span> {</span><br><span class="line">    <span class="type">int</span> lvalue = factor();</span><br><span class="line">    <span class="keyword">return</span> term_tail(lvalue);</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">expr_tail</span><span class="params">(<span class="type">int</span> lvalue)</span> {</span><br><span class="line">    <span class="keyword">if</span> (token == <span class="string">&#39;+&#39;</span>) {</span><br><span class="line">        match(<span class="string">&#39;+&#39;</span>);</span><br><span class="line">        <span class="type">int</span> value = lvalue + term();</span><br><span class="line">        <span class="keyword">return</span> expr_tail(value);</span><br><span class="line">    } <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;-&#39;</span>) {</span><br><span class="line">        match(<span class="string">&#39;-&#39;</span>);</span><br><span class="line">        <span class="type">int</span> value = lvalue - term();</span><br><span class="line">        <span class="keyword">return</span> expr_tail(value);</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="keyword">return</span> lvalue;</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">expr</span><span class="params">()</span> {</span><br><span class="line">    <span class="type">int</span> lvalue = term();</span><br><span class="line">    <span class="keyword">return</span> expr_tail(lvalue);</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>可以看到，有了BNF方法后，采用递归向下的方法来实现编译器是很直观的。</p><p>我们把词法分析器的代码一并贴上：</p><table><tbody><tr><td class="code"><pre><span class="line">#<span class="meta">#<span class="keyword">include</span> <span class="string">&lt;stdio.h&gt;</span></span></span><br><span class="line">#<span class="meta">#<span class="keyword">include</span> <span class="string">&lt;stdlib.h&gt;</span></span></span><br><span class="line"></span><br><span class="line"><span class="class"><span class="keyword">enum</span> {</span>Num};</span><br><span class="line"><span class="type">int</span> token;</span><br><span class="line"><span class="type">int</span> token_val;</span><br><span class="line"><span class="type">char</span> *line = <span class="literal">NULL</span>;</span><br><span class="line"><span class="type">char</span> *src = <span class="literal">NULL</span>;</span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">next</span><span class="params">()</span> {</span><br><span class="line">    <span class="comment">// skip white space</span></span><br><span class="line">    <span class="keyword">while</span> (*src == <span class="string">&#39; &#39;</span> || *src == <span class="string">&#39;\\t&#39;</span>) {</span><br><span class="line">        src ++;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    token = *src++;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (token &gt;= <span class="string">&#39;0&#39;</span> &amp;&amp; token &lt;= <span class="string">&#39;9&#39;</span> ) {</span><br><span class="line">        token_val = token - <span class="string">&#39;0&#39;</span>;</span><br><span class="line">        token = Num;</span><br><span class="line"></span><br><span class="line">        <span class="keyword">while</span> (*src &gt;= <span class="string">&#39;0&#39;</span> &amp;&amp; *src &lt;= <span class="string">&#39;9&#39;</span>) {</span><br><span class="line">            token_val = token_val*<span class="number">10</span> + *src - <span class="string">&#39;0&#39;</span>;</span><br><span class="line">            src ++;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">return</span>;</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">match</span><span class="params">(<span class="type">int</span> tk)</span> {</span><br><span class="line">    <span class="keyword">if</span> (token != tk) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;expected token: %d(%c), got: %d(%c)\\n&quot;</span>, tk, tk, token, token);</span><br><span class="line">        <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line">    next();</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>最后是<code>main</code>函数：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> <span class="title function_">main</span><span class="params">(<span class="type">int</span> argc, <span class="type">char</span> *argv[])</span></span><br><span class="line">{</span><br><span class="line">    <span class="type">size_t</span> linecap = <span class="number">0</span>;</span><br><span class="line">    <span class="type">ssize_t</span> linelen;</span><br><span class="line">    <span class="keyword">while</span> ((linelen = getline(&amp;line, &amp;linecap, <span class="built_in">stdin</span>)) &gt; <span class="number">0</span>) {</span><br><span class="line">        src = line;</span><br><span class="line">        next();</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%d\\n&quot;</span>, expr());</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h2 id="小结" tabindex="-1"><a class="header-anchor" href="#小结"><span><a href="about:blank#%E5%B0%8F%E7%BB%93"></a>小结</span></a></h2><p>本章中我们介绍了递归下降的方法，并用它来实现了四则运算的语法分析器。</p><p>花这么大精力讲解递归下降方法，是因为几乎所有手工编写的语法分析器都或多或少地有它的影子。换句话说，掌握了递归下降的方法，就可以应付大多数的语法分析器编写。</p><p>同时我们也用实例看到了理论（BNF 语法，左递归的消除）是如何帮助我们的工程实现的。尽管理论不是必需的，但如果能掌握它，对于提高我们的水平还是很有帮助的。</p>',27);function v(D,N){const n=p("ExternalLinkIcon");return r(),c("div",null,[o,b,s("p",null,[a("本文转自 "),s("a",d,[a("https://lotabout.me/2016/write-a-C-interpreter-4/"),e(n)]),a("，如有侵权，请联系删除。")]),h,s("ol",null,[s("li",null,[s("a",E,[a("手把手教你构建 C 语言编译器（0）——前言"),e(n)])]),s("li",null,[s("a",g,[a("手把手教你构建 C 语言编译器（1）——设计"),e(n)])]),s("li",null,[s("a",u,[a("手把手教你构建 C 语言编译器（2）——虚拟机"),e(n)])]),s("li",null,[s("a",m,[a("手把手教你构建 C 语言编译器（3）——词法分析器"),e(n)])]),s("li",null,[s("a",B,[a("手把手教你构建 C 语言编译器（4）——递归下降"),e(n)])]),s("li",null,[s("a",f,[a("手把手教你构建 C 语言编译器（5）——变量定义"),e(n)])]),s("li",null,[s("a",k,[a("手把手教你构建 C 语言编译器（6）——函数定义"),e(n)])]),s("li",null,[s("a",_,[a("手把手教你构建 C 语言编译器（7）——语句"),e(n)])]),s("li",null,[s("a",y,[a("手把手教你构建 C 语言编译器（8）——表达式"),e(n)])]),s("li",null,[s("a",C,[a("手把手教你构建 C 语言编译器（9）——总结"),e(n)])])]),w,s("p",null,[a("没有学过编译原理的话可能并不知道什么是“终结符”，“非终结符”。这里我简单介绍一下。首先是 "),s("a",x,[a("BNF"),e(n)]),a(" 范式，就是一种用来描述语法的语言，例如，四则运算的规则可以表示如下：")]),A])}const S=t(i,[["render",v],["__file","4.html.vue"]]),L=JSON.parse('{"path":"/tech/designASimpileCCompiler/4.html","title":"手把手教你构建 C 语言编译器（4）——递归下降","lang":"zh-CN","frontmatter":{"title":"手把手教你构建 C 语言编译器（4）——递归下降","category":["编译原理"],"tag":["c","编译器","解释器"],"description":"[] 转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-4/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（4）- 递归下降 Table of Contents 1. 什么是递归下降 2. 终结符与非终结符 3. 四则运算的递归下降 4. 为什么选择递归下降 5. 左递...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/designASimpileCCompiler/4.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"手把手教你构建 C 语言编译器（4）——递归下降"}],["meta",{"property":"og:description","content":"[] 转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-4/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（4）- 递归下降 Table of Contents 1. 什么是递归下降 2. 终结符与非终结符 3. 四则运算的递归下降 4. 为什么选择递归下降 5. 左递..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"c"}],["meta",{"property":"article:tag","content":"编译器"}],["meta",{"property":"article:tag","content":"解释器"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"手把手教你构建 C 语言编译器（4）——递归下降\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"什么是递归下降","slug":"什么是递归下降","link":"#什么是递归下降","children":[]},{"level":2,"title":"终结符与非终结符","slug":"终结符与非终结符","link":"#终结符与非终结符","children":[]},{"level":2,"title":"四则运算的递归下降","slug":"四则运算的递归下降","link":"#四则运算的递归下降","children":[]},{"level":2,"title":"为什么选择递归下降","slug":"为什么选择递归下降","link":"#为什么选择递归下降","children":[]},{"level":2,"title":"左递归","slug":"左递归","link":"#左递归","children":[]},{"level":2,"title":"四则运算的实现","slug":"四则运算的实现","link":"#四则运算的实现","children":[]},{"level":2,"title":"小结","slug":"小结","link":"#小结","children":[]}],"readingTime":{"minutes":11.33,"words":3399},"filePathRelative":"tech/designASimpileCCompiler/4.md","excerpt":"<p>[]</p>\\n<h1>转载声明</h1>\\n<p>本文转自 <a href=\\"https://lotabout.me/2016/write-a-C-interpreter-4/\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">https://lotabout.me/2016/write-a-C-interpreter-4/</a>，如有侵权，请联系删除。</p>\\n<h1>原文内容</h1>\\n<h1>手把手教你构建 C 语言编译器（4）- 递归下降</h1>\\n<p>Table of Contents</p>\\n<ol>\\n<li><a href=\\"about:blank#%E4%BB%80%E4%B9%88%E6%98%AF%E9%80%92%E5%BD%92%E4%B8%8B%E9%99%8D\\">1. 什么是递归下降</a></li>\\n<li><a href=\\"about:blank#%E7%BB%88%E7%BB%93%E7%AC%A6%E4%B8%8E%E9%9D%9E%E7%BB%88%E7%BB%93%E7%AC%A6\\">2. 终结符与非终结符</a></li>\\n<li><a href=\\"about:blank#%E5%9B%9B%E5%88%99%E8%BF%90%E7%AE%97%E7%9A%84%E9%80%92%E5%BD%92%E4%B8%8B%E9%99%8D\\">3. 四则运算的递归下降</a></li>\\n<li><a href=\\"about:blank#%E4%B8%BA%E4%BB%80%E4%B9%88%E9%80%89%E6%8B%A9%E9%80%92%E5%BD%92%E4%B8%8B%E9%99%8D\\">4. 为什么选择递归下降</a></li>\\n<li><a href=\\"about:blank#%E5%B7%A6%E9%80%92%E5%BD%92\\">5. 左递归</a></li>\\n<li><a href=\\"about:blank#%E5%9B%9B%E5%88%99%E8%BF%90%E7%AE%97%E7%9A%84%E5%AE%9E%E7%8E%B0\\">6. 四则运算的实现</a></li>\\n<li><a href=\\"about:blank#%E5%B0%8F%E7%BB%93\\">7. 小结</a></li>\\n</ol>","autoDesc":true}');export{S as comp,L as data};
diff --git a/assets/404.html-BC0rHQLu.js b/assets/404.html-CGMXaJuv.js
similarity index 93%
rename from assets/404.html-BC0rHQLu.js
rename to assets/404.html-CGMXaJuv.js
index 5e5e7ad..7fd665f 100644
--- a/assets/404.html-BC0rHQLu.js
+++ b/assets/404.html-CGMXaJuv.js
@@ -1 +1 @@
-import{_ as t,o as e,c as o,b as n}from"./app-B69Gl_S-.js";const r={},a=n("p",null,"404 Not Found",-1),c=[a];function p(s,i){return e(),o("div",null,c)}const d=t(r,[["render",p],["__file","404.html.vue"]]),m=JSON.parse('{"path":"/404.html","title":"","lang":"zh-CN","frontmatter":{"layout":"NotFound","description":"404 Not Found","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/404.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:description","content":"404 Not Found"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"\\",\\"description\\":\\"404 Not Found\\"}"]]},"headers":[],"readingTime":{"minutes":0.01,"words":3},"filePathRelative":null,"excerpt":"<p>404 Not Found</p>\\n","autoDesc":true}');export{d as comp,m as data};
+import{_ as t,o as e,c as o,b as n}from"./app-B4LGNJZ0.js";const r={},a=n("p",null,"404 Not Found",-1),c=[a];function p(s,i){return e(),o("div",null,c)}const d=t(r,[["render",p],["__file","404.html.vue"]]),m=JSON.parse('{"path":"/404.html","title":"","lang":"zh-CN","frontmatter":{"layout":"NotFound","description":"404 Not Found","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/404.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:description","content":"404 Not Found"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"\\",\\"description\\":\\"404 Not Found\\"}"]]},"headers":[],"readingTime":{"minutes":0.01,"words":3},"filePathRelative":null,"excerpt":"<p>404 Not Found</p>\\n","autoDesc":true}');export{d as comp,m as data};
diff --git a/assets/5.html-qLlLbRlw.js b/assets/5.html-DpkUOZDe.js
similarity index 99%
rename from assets/5.html-qLlLbRlw.js
rename to assets/5.html-DpkUOZDe.js
index 04ceab3..77dc916 100644
--- a/assets/5.html-qLlLbRlw.js
+++ b/assets/5.html-DpkUOZDe.js
@@ -1 +1 @@
-import{_ as p,r as t,o as r,c as i,b as a,e as s,d as e,f as l}from"./app-B69Gl_S-.js";const c={},o=a("h1",{id:"转载声明",tabindex:"-1"},[a("a",{class:"header-anchor",href:"#转载声明"},[a("span",null,"转载声明")])],-1),b={href:"https://lotabout.me/2016/write-a-C-interpreter-5/",target:"_blank",rel:"noopener noreferrer"},d=l('<h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-5-变量定义" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-5-变量定义"><span>手把手教你构建 C 语言编译器（5）- 变量定义</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#ebnf-%E8%A1%A8%E7%A4%BA">1. EBNF 表示</a></li><li><a href="about:blank#%E8%A7%A3%E6%9E%90%E5%8F%98%E9%87%8F%E7%9A%84%E5%AE%9A%E4%B9%89">2. 解析变量的定义</a><ol><li><a href="about:blank#program">2.1. program()</a></li><li><a href="about:blank#global-declaration">2.2. global_declaration()</a></li><li><a href="about:blank#enum-declaration">2.3. enum_declaration()</a></li><li><a href="about:blank#%E5%85%B6%E5%AE%83">2.4. 其它</a></li></ol></li><li><a href="about:blank#%E4%BB%A3%E7%A0%81">3. 代码</a></li><li><a href="about:blank#%E5%B0%8F%E7%BB%93">4. 小结</a></li></ol><p>本章中我们用 EBNF 来大致描述我们实现的 C 语言的文法，并实现其中解析变量定义部分。</p><p>由于语法分析本身比较复杂，所以我们将它拆分成 3 个部分进行讲解，分别是：变量定义、函数定义、表达式。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p>',7),m={href:"http://lotabout.me/2015/write-a-C-interpreter-0/",target:"_blank",rel:"noopener noreferrer"},h={href:"http://lotabout.me/2015/write-a-C-interpreter-1/",target:"_blank",rel:"noopener noreferrer"},u={href:"http://lotabout.me/2015/write-a-C-interpreter-2/",target:"_blank",rel:"noopener noreferrer"},_={href:"http://lotabout.me/2015/write-a-C-interpreter-3/",target:"_blank",rel:"noopener noreferrer"},f={href:"http://lotabout.me/2016/write-a-C-interpreter-4/",target:"_blank",rel:"noopener noreferrer"},g={href:"http://lotabout.me/2016/write-a-C-interpreter-5/",target:"_blank",rel:"noopener noreferrer"},y={href:"http://lotabout.me/2016/write-a-C-interpreter-6/",target:"_blank",rel:"noopener noreferrer"},k={href:"http://lotabout.me/2016/write-a-C-interpreter-7/",target:"_blank",rel:"noopener noreferrer"},E={href:"http://lotabout.me/2016/write-a-C-interpreter-8/",target:"_blank",rel:"noopener noreferrer"},C={href:"http://lotabout.me/2016/write-a-C-interpreter-9/",target:"_blank",rel:"noopener noreferrer"},w=l('<h2 id="ebnf-表示" tabindex="-1"><a class="header-anchor" href="#ebnf-表示"><span><a href="about:blank#ebnf-%E8%A1%A8%E7%A4%BA"></a>EBNF 表示</span></a></h2><p>EBNF 是对前一章提到的 BNF 的扩展，它的语法更容易理解，实现起来也更直观。但真正看起来还是很烦，如果不想看可以跳过。</p><table><tbody><tr><td class="code"><pre><span class="line">program ::= {global_declaration}+</span><br><span class="line"></span><br><span class="line">global_declaration ::= enum_decl | variable_decl | function_decl</span><br><span class="line"></span><br><span class="line">enum_decl ::= &#39;enum&#39; [id] &#39;{&#39; id [&#39;=&#39; &#39;num&#39;] {&#39;,&#39; id [&#39;=&#39; &#39;num&#39;] &#39;}&#39;</span><br><span class="line"></span><br><span class="line">variable_decl ::= type {&#39;*&#39;} id { &#39;,&#39; {&#39;*&#39;} id } &#39;;&#39;</span><br><span class="line"></span><br><span class="line">function_decl ::= type {&#39;*&#39;} id &#39;(&#39; parameter_decl &#39;)&#39; &#39;{&#39; body_decl &#39;}&#39;</span><br><span class="line"></span><br><span class="line">parameter_decl ::= type {&#39;*&#39;} id {&#39;,&#39; type {&#39;*&#39;} id}</span><br><span class="line"></span><br><span class="line">body_decl ::= {variable_decl}, {statement}</span><br><span class="line"></span><br><span class="line">statement ::= non_empty_statement | empty_statement</span><br><span class="line"></span><br><span class="line">non_empty_statement ::= if_statement | while_statement | &#39;{&#39; statement &#39;}&#39;</span><br><span class="line">                     | &#39;return&#39; expression | expression &#39;;&#39;</span><br><span class="line"></span><br><span class="line">if_statement ::= &#39;if&#39; &#39;(&#39; expression &#39;)&#39; statement [&#39;else&#39; non_empty_statement]</span><br><span class="line"></span><br><span class="line">while_statement ::= &#39;while&#39; &#39;(&#39; expression &#39;)&#39; non_empty_statement</span><br></pre></td></tr></tbody></table><p>其中 <code>expression</code> 相关的内容我们放到后面解释，主要原因是我们的语言不支持跨函数递归，而为了实现自举，实际上我们也不能使用递归（亏我们说了一章的递归下降）。</p><p>P.S. 我是先写程序再总结上面的文法，所以实际上它们间的对应关系并不是特别明显。</p><h2 id="解析变量的定义" tabindex="-1"><a class="header-anchor" href="#解析变量的定义"><span><a href="about:blank#%E8%A7%A3%E6%9E%90%E5%8F%98%E9%87%8F%E7%9A%84%E5%AE%9A%E4%B9%89"></a>解析变量的定义</span></a></h2><p>本章要讲解的就是上节文法中的 <code>enum_decl</code> 和 <code>variable_decl</code> 部分。</p><h3 id="program" tabindex="-1"><a class="header-anchor" href="#program"><span><a href="about:blank#program"></a>program()</span></a></h3><p>首先是之前定义过的 <code>program</code> 函数，将它改成：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">program</span><span class="params">()</span> {</span><br><span class="line">    <span class="comment">// get next token</span></span><br><span class="line">    next();</span><br><span class="line">    <span class="keyword">while</span> (token &gt; <span class="number">0</span>) {</span><br><span class="line">        global_declaration();</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>我知道 <code>global_declaration</code> 函数还没有出现过，但没有关系，采用自顶向下的编写方法就是要不断地实现我们需要的内容。下面是 <code>global_declaration</code> 函数的内容：</p><h3 id="global-declaration" tabindex="-1"><a class="header-anchor" href="#global-declaration"><span><a href="about:blank#global-declaration"></a>global_declaration()</span></a></h3><p>即全局的定义语句，包括变量定义，类型定义（只支持枚举）及函数定义。代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> basetype;    <span class="comment">// the type of a declaration, make it global for convenience</span></span><br><span class="line"><span class="type">int</span> expr_type;   <span class="comment">// the type of an expression</span></span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">global_declaration</span><span class="params">()</span> {</span><br><span class="line">    <span class="comment">// global_declaration ::= enum_decl | variable_decl | function_decl</span></span><br><span class="line">    <span class="comment">//</span></span><br><span class="line">    <span class="comment">// enum_decl ::= &#39;enum&#39; [id] &#39;{&#39; id [&#39;=&#39; &#39;num&#39;] {&#39;,&#39; id [&#39;=&#39; &#39;num&#39;} &#39;}&#39;</span></span><br><span class="line">    <span class="comment">//</span></span><br><span class="line">    <span class="comment">// variable_decl ::= type {&#39;*&#39;} id { &#39;,&#39; {&#39;*&#39;} id } &#39;;&#39;</span></span><br><span class="line">    <span class="comment">//</span></span><br><span class="line">    <span class="comment">// function_decl ::= type {&#39;*&#39;} id &#39;(&#39; parameter_decl &#39;)&#39; &#39;{&#39; body_decl &#39;}&#39;</span></span><br><span class="line"></span><br><span class="line"></span><br><span class="line">    <span class="type">int</span> type; <span class="comment">// tmp, actual type for variable</span></span><br><span class="line">    <span class="type">int</span> i; <span class="comment">// tmp</span></span><br><span class="line"></span><br><span class="line">    basetype = INT;</span><br><span class="line"></span><br><span class="line">    <span class="comment">// parse enum, this should be treated alone.</span></span><br><span class="line">    <span class="keyword">if</span> (token == Enum) {</span><br><span class="line">        <span class="comment">// enum [id] { a = 10, b = 20, ... }</span></span><br><span class="line">        match(Enum);</span><br><span class="line">        <span class="keyword">if</span> (token != <span class="string">&#39;{&#39;</span>) {</span><br><span class="line">            match(Id); <span class="comment">// skip the [id] part</span></span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">if</span> (token == <span class="string">&#39;{&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse the assign part</span></span><br><span class="line">            match(<span class="string">&#39;{&#39;</span>);</span><br><span class="line">            enum_declaration();</span><br><span class="line">            match(<span class="string">&#39;}&#39;</span>);</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        match(<span class="string">&#39;;&#39;</span>);</span><br><span class="line">        <span class="keyword">return</span>;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="comment">// parse type information</span></span><br><span class="line">    <span class="keyword">if</span> (token == Int) {</span><br><span class="line">        match(Int);</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">else</span> <span class="keyword">if</span> (token == Char) {</span><br><span class="line">        match(Char);</span><br><span class="line">        basetype = CHAR;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="comment">// parse the comma seperated variable declaration.</span></span><br><span class="line">    <span class="keyword">while</span> (token != <span class="string">&#39;;&#39;</span> &amp;&amp; token != <span class="string">&#39;}&#39;</span>) {</span><br><span class="line">        type = basetype;</span><br><span class="line">        <span class="comment">// parse pointer type, note that there may exist `int ****x;`</span></span><br><span class="line">        <span class="keyword">while</span> (token == Mul) {</span><br><span class="line">            match(Mul);</span><br><span class="line">            type = type + PTR;</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        <span class="keyword">if</span> (token != Id) {</span><br><span class="line">            <span class="comment">// invalid declaration</span></span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot;%d: bad global declaration\\n&quot;</span>, line);</span><br><span class="line">            <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">if</span> (current_id[Class]) {</span><br><span class="line">            <span class="comment">// identifier exists</span></span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot;%d: duplicate global declaration\\n&quot;</span>, line);</span><br><span class="line">            <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">        }</span><br><span class="line">        match(Id);</span><br><span class="line">        current_id[Type] = type;</span><br><span class="line"></span><br><span class="line">        <span class="keyword">if</span> (token == <span class="string">&#39;(&#39;</span>) {</span><br><span class="line">            current_id[Class] = Fun;</span><br><span class="line">            current_id[Value] = (<span class="type">int</span>)(text + <span class="number">1</span>); <span class="comment">// the memory address of function</span></span><br><span class="line">            function_declaration();</span><br><span class="line">        } <span class="keyword">else</span> {</span><br><span class="line">            <span class="comment">// variable declaration</span></span><br><span class="line">            current_id[Class] = Glo; <span class="comment">// global variable</span></span><br><span class="line">            current_id[Value] = (<span class="type">int</span>)data; <span class="comment">// assign memory address</span></span><br><span class="line">            data = data + <span class="keyword">sizeof</span>(<span class="type">int</span>);</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        <span class="keyword">if</span> (token == <span class="string">&#39;,&#39;</span>) {</span><br><span class="line">            match(<span class="string">&#39;,&#39;</span>);</span><br><span class="line">        }</span><br><span class="line">    }</span><br><span class="line">    next();</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>看了上面的代码，能大概理解吗？这里我们讲解其中的一些细节。</p><p><strong>向前看标记</strong> ：其中的 <code>if (token == xxx)</code> 语句就是用来向前查看标记以确定使用哪一个产生式，例如只要遇到 <code>enum</code> 我们就知道是需要解析枚举类型。而如果只解析到类型，如 <code>int identifier</code> 时我们并不能确定 <code>identifier</code> 是一个普通的变量还是一个函数，所以还需要继续查看后续的标记，如果遇到 <code>(</code> 则可以断定是函数了，反之则是变量。</p><p><strong>变量类型的表示</strong> ：我们的编译器支持指针类型，那意味着也支持指针的指针，如 <code>int **data;</code>。那么我们如何表示指针类型呢？前文中我们定义了支持的类型：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="comment">// types of variable/function</span></span><br><span class="line"><span class="class"><span class="keyword">enum</span> {</span> CHAR, INT, PTR };</span><br></pre></td></tr></tbody></table><p>所以一个类型首先有基本类型，如 <code>CHAR</code> 或 <code>INT</code>，当它是一个指向基本类型的指针时，如 <code>int *data</code>，我们就将它的类型加上 <code>PTR</code> 即代码中的：<code>type = type + PTR;</code>。同理，如果是指针的指针，则再加上 <code>PTR</code>。</p><h3 id="enum-declaration" tabindex="-1"><a class="header-anchor" href="#enum-declaration"><span><a href="about:blank#enum-declaration"></a>enum_declaration()</span></a></h3><p>用于解析枚举类型的定义。主要的逻辑用于解析用逗号（<code>,</code>）分隔的变量，值得注意的是在编译器中如何保存枚举变量的信息。</p><p>即我们将该变量的类别设置成了 <code>Num</code>，这样它就成了全局的常量了，而注意到上节中，正常的全局变量的类别则是 <code>Glo</code>，类别信息在后面章节中解析 <code>expression</code> 会使用到。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">enum_declaration</span><span class="params">()</span> {</span><br><span class="line">    <span class="comment">// parse enum [id] { a = 1, b = 3, ...}</span></span><br><span class="line">    <span class="type">int</span> i;</span><br><span class="line">    i = <span class="number">0</span>;</span><br><span class="line">    <span class="keyword">while</span> (token != <span class="string">&#39;}&#39;</span>) {</span><br><span class="line">        <span class="keyword">if</span> (token != Id) {</span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot;%d: bad enum identifier %d\\n&quot;</span>, line, token);</span><br><span class="line">            <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">        }</span><br><span class="line">        next();</span><br><span class="line">        <span class="keyword">if</span> (token == Assign) {</span><br><span class="line">            <span class="comment">// like {a=10}</span></span><br><span class="line">            next();</span><br><span class="line">            <span class="keyword">if</span> (token != Num) {</span><br><span class="line">                <span class="built_in">printf</span>(<span class="string">&quot;%d: bad enum initializer\\n&quot;</span>, line);</span><br><span class="line">                <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">            }</span><br><span class="line">            i = token_val;</span><br><span class="line">            next();</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        current_id[Class] = Num;</span><br><span class="line">        current_id[Type] = INT;</span><br><span class="line">        current_id[Value] = i++;</span><br><span class="line"></span><br><span class="line">        <span class="keyword">if</span> (token == <span class="string">&#39;,&#39;</span>) {</span><br><span class="line">            next();</span><br><span class="line">        }</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="其它" tabindex="-1"><a class="header-anchor" href="#其它"><span><a href="about:blank#%E5%85%B6%E5%AE%83"></a>其它</span></a></h3><p>其中的 <code>function_declaration</code> 函数我们将放到下一章中讲解。<code>match</code> 函数是一个辅助函数：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">match</span><span class="params">(<span class="type">int</span> tk)</span> {</span><br><span class="line">    <span class="keyword">if</span> (token == tk) {</span><br><span class="line">        next();</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%d: expected token: %d\\n&quot;</span>, line, tk);</span><br><span class="line">        <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>它将 <code>next</code> 函数包装起来，如果不是预期的标记则报错并退出。</p><h2 id="代码" tabindex="-1"><a class="header-anchor" href="#代码"><span><a href="about:blank#%E4%BB%A3%E7%A0%81"></a>代码</span></a></h2>',28),x={href:"https://github.com/lotabout/write-a-C-interpreter/tree/step-3",target:"_blank",rel:"noopener noreferrer"},A=l('<table><tbody><tr><td class="code"><pre><span class="line">git clone -b step-3 https://github.com/lotabout/write-a-C-interpreter</span><br></pre></td></tr></tbody></table><p>本章的代码还无法正常运行，因为还有许多功能没有实现，但如果有兴趣的话，可以自己先试着去实现它。</p><h2 id="小结" tabindex="-1"><a class="header-anchor" href="#小结"><span><a href="about:blank#%E5%B0%8F%E7%BB%93"></a>小结</span></a></h2><p>本章的内容应该不难，除了开头的 EBNF 表达式可能相对不好理解一些，但如果你查看了 EBNF 的具体表示方法后就不难理解了。</p><p>剩下的内容就是按部就班地将 EBNF 的产生式转换成函数的过程，如果你理解了上一章中的内容，相信这部分也不难理解。</p><p>下一章中我们将介绍如何解析函数的定义，敬请期待。</p>',6);function B(v,N){const n=t("ExternalLinkIcon");return r(),i("div",null,[o,a("p",null,[s("本文转自 "),a("a",b,[s("https://lotabout.me/2016/write-a-C-interpreter-5/"),e(n)]),s("，如有侵权，请联系删除。")]),d,a("ol",null,[a("li",null,[a("a",m,[s("手把手教你构建 C 语言编译器（0）——前言"),e(n)])]),a("li",null,[a("a",h,[s("手把手教你构建 C 语言编译器（1）——设计"),e(n)])]),a("li",null,[a("a",u,[s("手把手教你构建 C 语言编译器（2）——虚拟机"),e(n)])]),a("li",null,[a("a",_,[s("手把手教你构建 C 语言编译器（3）——词法分析器"),e(n)])]),a("li",null,[a("a",f,[s("手把手教你构建 C 语言编译器（4）——递归下降"),e(n)])]),a("li",null,[a("a",g,[s("手把手教你构建 C 语言编译器（5）——变量定义"),e(n)])]),a("li",null,[a("a",y,[s("手把手教你构建 C 语言编译器（6）——函数定义"),e(n)])]),a("li",null,[a("a",k,[s("手把手教你构建 C 语言编译器（7）——语句"),e(n)])]),a("li",null,[a("a",E,[s("手把手教你构建 C 语言编译器（8）——表达式"),e(n)])]),a("li",null,[a("a",C,[s("手把手教你构建 C 语言编译器（9）——总结"),e(n)])])]),w,a("p",null,[s("本章的代码可以在 "),a("a",x,[s("Github"),e(n)]),s(" 上下载，也可以直接 clone")]),A])}const T=p(c,[["render",B],["__file","5.html.vue"]]),I=JSON.parse('{"path":"/tech/designASimpileCCompiler/5.html","title":"手把手教你构建 C 语言编译器（5）——变量定义","lang":"zh-CN","frontmatter":{"title":"手把手教你构建 C 语言编译器（5）——变量定义","category":["编译原理"],"tag":["c","编译器","解释器"],"description":"转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-5/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（5）- 变量定义 Table of Contents 1. EBNF 表示 2. 解析变量的定义 2.1. program() 2.2. global_declarat...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/designASimpileCCompiler/5.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"手把手教你构建 C 语言编译器（5）——变量定义"}],["meta",{"property":"og:description","content":"转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-5/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（5）- 变量定义 Table of Contents 1. EBNF 表示 2. 解析变量的定义 2.1. program() 2.2. global_declarat..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"c"}],["meta",{"property":"article:tag","content":"编译器"}],["meta",{"property":"article:tag","content":"解释器"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"手把手教你构建 C 语言编译器（5）——变量定义\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"EBNF 表示","slug":"ebnf-表示","link":"#ebnf-表示","children":[]},{"level":2,"title":"解析变量的定义","slug":"解析变量的定义","link":"#解析变量的定义","children":[{"level":3,"title":"program()","slug":"program","link":"#program","children":[]},{"level":3,"title":"global_declaration()","slug":"global-declaration","link":"#global-declaration","children":[]},{"level":3,"title":"enum_declaration()","slug":"enum-declaration","link":"#enum-declaration","children":[]},{"level":3,"title":"其它","slug":"其它","link":"#其它","children":[]}]},{"level":2,"title":"代码","slug":"代码","link":"#代码","children":[]},{"level":2,"title":"小结","slug":"小结","link":"#小结","children":[]}],"readingTime":{"minutes":10.71,"words":3212},"filePathRelative":"tech/designASimpileCCompiler/5.md","excerpt":"\\n<p>本文转自 <a href=\\"https://lotabout.me/2016/write-a-C-interpreter-5/\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">https://lotabout.me/2016/write-a-C-interpreter-5/</a>，如有侵权，请联系删除。</p>\\n<h1>原文内容</h1>\\n<h1>手把手教你构建 C 语言编译器（5）- 变量定义</h1>\\n<p>Table of Contents</p>\\n<ol>\\n<li><a href=\\"about:blank#ebnf-%E8%A1%A8%E7%A4%BA\\">1. EBNF 表示</a></li>\\n<li><a href=\\"about:blank#%E8%A7%A3%E6%9E%90%E5%8F%98%E9%87%8F%E7%9A%84%E5%AE%9A%E4%B9%89\\">2. 解析变量的定义</a>\\n<ol>\\n<li><a href=\\"about:blank#program\\">2.1. program()</a></li>\\n<li><a href=\\"about:blank#global-declaration\\">2.2. global_declaration()</a></li>\\n<li><a href=\\"about:blank#enum-declaration\\">2.3. enum_declaration()</a></li>\\n<li><a href=\\"about:blank#%E5%85%B6%E5%AE%83\\">2.4. 其它</a></li>\\n</ol>\\n</li>\\n<li><a href=\\"about:blank#%E4%BB%A3%E7%A0%81\\">3. 代码</a></li>\\n<li><a href=\\"about:blank#%E5%B0%8F%E7%BB%93\\">4. 小结</a></li>\\n</ol>","autoDesc":true}');export{T as comp,I as data};
+import{_ as p,r as t,o as r,c as i,b as a,e as s,d as e,f as l}from"./app-B4LGNJZ0.js";const c={},o=a("h1",{id:"转载声明",tabindex:"-1"},[a("a",{class:"header-anchor",href:"#转载声明"},[a("span",null,"转载声明")])],-1),b={href:"https://lotabout.me/2016/write-a-C-interpreter-5/",target:"_blank",rel:"noopener noreferrer"},d=l('<h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-5-变量定义" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-5-变量定义"><span>手把手教你构建 C 语言编译器（5）- 变量定义</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#ebnf-%E8%A1%A8%E7%A4%BA">1. EBNF 表示</a></li><li><a href="about:blank#%E8%A7%A3%E6%9E%90%E5%8F%98%E9%87%8F%E7%9A%84%E5%AE%9A%E4%B9%89">2. 解析变量的定义</a><ol><li><a href="about:blank#program">2.1. program()</a></li><li><a href="about:blank#global-declaration">2.2. global_declaration()</a></li><li><a href="about:blank#enum-declaration">2.3. enum_declaration()</a></li><li><a href="about:blank#%E5%85%B6%E5%AE%83">2.4. 其它</a></li></ol></li><li><a href="about:blank#%E4%BB%A3%E7%A0%81">3. 代码</a></li><li><a href="about:blank#%E5%B0%8F%E7%BB%93">4. 小结</a></li></ol><p>本章中我们用 EBNF 来大致描述我们实现的 C 语言的文法，并实现其中解析变量定义部分。</p><p>由于语法分析本身比较复杂，所以我们将它拆分成 3 个部分进行讲解，分别是：变量定义、函数定义、表达式。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p>',7),m={href:"http://lotabout.me/2015/write-a-C-interpreter-0/",target:"_blank",rel:"noopener noreferrer"},h={href:"http://lotabout.me/2015/write-a-C-interpreter-1/",target:"_blank",rel:"noopener noreferrer"},u={href:"http://lotabout.me/2015/write-a-C-interpreter-2/",target:"_blank",rel:"noopener noreferrer"},_={href:"http://lotabout.me/2015/write-a-C-interpreter-3/",target:"_blank",rel:"noopener noreferrer"},f={href:"http://lotabout.me/2016/write-a-C-interpreter-4/",target:"_blank",rel:"noopener noreferrer"},g={href:"http://lotabout.me/2016/write-a-C-interpreter-5/",target:"_blank",rel:"noopener noreferrer"},y={href:"http://lotabout.me/2016/write-a-C-interpreter-6/",target:"_blank",rel:"noopener noreferrer"},k={href:"http://lotabout.me/2016/write-a-C-interpreter-7/",target:"_blank",rel:"noopener noreferrer"},E={href:"http://lotabout.me/2016/write-a-C-interpreter-8/",target:"_blank",rel:"noopener noreferrer"},C={href:"http://lotabout.me/2016/write-a-C-interpreter-9/",target:"_blank",rel:"noopener noreferrer"},w=l('<h2 id="ebnf-表示" tabindex="-1"><a class="header-anchor" href="#ebnf-表示"><span><a href="about:blank#ebnf-%E8%A1%A8%E7%A4%BA"></a>EBNF 表示</span></a></h2><p>EBNF 是对前一章提到的 BNF 的扩展，它的语法更容易理解，实现起来也更直观。但真正看起来还是很烦，如果不想看可以跳过。</p><table><tbody><tr><td class="code"><pre><span class="line">program ::= {global_declaration}+</span><br><span class="line"></span><br><span class="line">global_declaration ::= enum_decl | variable_decl | function_decl</span><br><span class="line"></span><br><span class="line">enum_decl ::= &#39;enum&#39; [id] &#39;{&#39; id [&#39;=&#39; &#39;num&#39;] {&#39;,&#39; id [&#39;=&#39; &#39;num&#39;] &#39;}&#39;</span><br><span class="line"></span><br><span class="line">variable_decl ::= type {&#39;*&#39;} id { &#39;,&#39; {&#39;*&#39;} id } &#39;;&#39;</span><br><span class="line"></span><br><span class="line">function_decl ::= type {&#39;*&#39;} id &#39;(&#39; parameter_decl &#39;)&#39; &#39;{&#39; body_decl &#39;}&#39;</span><br><span class="line"></span><br><span class="line">parameter_decl ::= type {&#39;*&#39;} id {&#39;,&#39; type {&#39;*&#39;} id}</span><br><span class="line"></span><br><span class="line">body_decl ::= {variable_decl}, {statement}</span><br><span class="line"></span><br><span class="line">statement ::= non_empty_statement | empty_statement</span><br><span class="line"></span><br><span class="line">non_empty_statement ::= if_statement | while_statement | &#39;{&#39; statement &#39;}&#39;</span><br><span class="line">                     | &#39;return&#39; expression | expression &#39;;&#39;</span><br><span class="line"></span><br><span class="line">if_statement ::= &#39;if&#39; &#39;(&#39; expression &#39;)&#39; statement [&#39;else&#39; non_empty_statement]</span><br><span class="line"></span><br><span class="line">while_statement ::= &#39;while&#39; &#39;(&#39; expression &#39;)&#39; non_empty_statement</span><br></pre></td></tr></tbody></table><p>其中 <code>expression</code> 相关的内容我们放到后面解释，主要原因是我们的语言不支持跨函数递归，而为了实现自举，实际上我们也不能使用递归（亏我们说了一章的递归下降）。</p><p>P.S. 我是先写程序再总结上面的文法，所以实际上它们间的对应关系并不是特别明显。</p><h2 id="解析变量的定义" tabindex="-1"><a class="header-anchor" href="#解析变量的定义"><span><a href="about:blank#%E8%A7%A3%E6%9E%90%E5%8F%98%E9%87%8F%E7%9A%84%E5%AE%9A%E4%B9%89"></a>解析变量的定义</span></a></h2><p>本章要讲解的就是上节文法中的 <code>enum_decl</code> 和 <code>variable_decl</code> 部分。</p><h3 id="program" tabindex="-1"><a class="header-anchor" href="#program"><span><a href="about:blank#program"></a>program()</span></a></h3><p>首先是之前定义过的 <code>program</code> 函数，将它改成：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">program</span><span class="params">()</span> {</span><br><span class="line">    <span class="comment">// get next token</span></span><br><span class="line">    next();</span><br><span class="line">    <span class="keyword">while</span> (token &gt; <span class="number">0</span>) {</span><br><span class="line">        global_declaration();</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>我知道 <code>global_declaration</code> 函数还没有出现过，但没有关系，采用自顶向下的编写方法就是要不断地实现我们需要的内容。下面是 <code>global_declaration</code> 函数的内容：</p><h3 id="global-declaration" tabindex="-1"><a class="header-anchor" href="#global-declaration"><span><a href="about:blank#global-declaration"></a>global_declaration()</span></a></h3><p>即全局的定义语句，包括变量定义，类型定义（只支持枚举）及函数定义。代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> basetype;    <span class="comment">// the type of a declaration, make it global for convenience</span></span><br><span class="line"><span class="type">int</span> expr_type;   <span class="comment">// the type of an expression</span></span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">global_declaration</span><span class="params">()</span> {</span><br><span class="line">    <span class="comment">// global_declaration ::= enum_decl | variable_decl | function_decl</span></span><br><span class="line">    <span class="comment">//</span></span><br><span class="line">    <span class="comment">// enum_decl ::= &#39;enum&#39; [id] &#39;{&#39; id [&#39;=&#39; &#39;num&#39;] {&#39;,&#39; id [&#39;=&#39; &#39;num&#39;} &#39;}&#39;</span></span><br><span class="line">    <span class="comment">//</span></span><br><span class="line">    <span class="comment">// variable_decl ::= type {&#39;*&#39;} id { &#39;,&#39; {&#39;*&#39;} id } &#39;;&#39;</span></span><br><span class="line">    <span class="comment">//</span></span><br><span class="line">    <span class="comment">// function_decl ::= type {&#39;*&#39;} id &#39;(&#39; parameter_decl &#39;)&#39; &#39;{&#39; body_decl &#39;}&#39;</span></span><br><span class="line"></span><br><span class="line"></span><br><span class="line">    <span class="type">int</span> type; <span class="comment">// tmp, actual type for variable</span></span><br><span class="line">    <span class="type">int</span> i; <span class="comment">// tmp</span></span><br><span class="line"></span><br><span class="line">    basetype = INT;</span><br><span class="line"></span><br><span class="line">    <span class="comment">// parse enum, this should be treated alone.</span></span><br><span class="line">    <span class="keyword">if</span> (token == Enum) {</span><br><span class="line">        <span class="comment">// enum [id] { a = 10, b = 20, ... }</span></span><br><span class="line">        match(Enum);</span><br><span class="line">        <span class="keyword">if</span> (token != <span class="string">&#39;{&#39;</span>) {</span><br><span class="line">            match(Id); <span class="comment">// skip the [id] part</span></span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">if</span> (token == <span class="string">&#39;{&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse the assign part</span></span><br><span class="line">            match(<span class="string">&#39;{&#39;</span>);</span><br><span class="line">            enum_declaration();</span><br><span class="line">            match(<span class="string">&#39;}&#39;</span>);</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        match(<span class="string">&#39;;&#39;</span>);</span><br><span class="line">        <span class="keyword">return</span>;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="comment">// parse type information</span></span><br><span class="line">    <span class="keyword">if</span> (token == Int) {</span><br><span class="line">        match(Int);</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">else</span> <span class="keyword">if</span> (token == Char) {</span><br><span class="line">        match(Char);</span><br><span class="line">        basetype = CHAR;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="comment">// parse the comma seperated variable declaration.</span></span><br><span class="line">    <span class="keyword">while</span> (token != <span class="string">&#39;;&#39;</span> &amp;&amp; token != <span class="string">&#39;}&#39;</span>) {</span><br><span class="line">        type = basetype;</span><br><span class="line">        <span class="comment">// parse pointer type, note that there may exist `int ****x;`</span></span><br><span class="line">        <span class="keyword">while</span> (token == Mul) {</span><br><span class="line">            match(Mul);</span><br><span class="line">            type = type + PTR;</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        <span class="keyword">if</span> (token != Id) {</span><br><span class="line">            <span class="comment">// invalid declaration</span></span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot;%d: bad global declaration\\n&quot;</span>, line);</span><br><span class="line">            <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">if</span> (current_id[Class]) {</span><br><span class="line">            <span class="comment">// identifier exists</span></span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot;%d: duplicate global declaration\\n&quot;</span>, line);</span><br><span class="line">            <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">        }</span><br><span class="line">        match(Id);</span><br><span class="line">        current_id[Type] = type;</span><br><span class="line"></span><br><span class="line">        <span class="keyword">if</span> (token == <span class="string">&#39;(&#39;</span>) {</span><br><span class="line">            current_id[Class] = Fun;</span><br><span class="line">            current_id[Value] = (<span class="type">int</span>)(text + <span class="number">1</span>); <span class="comment">// the memory address of function</span></span><br><span class="line">            function_declaration();</span><br><span class="line">        } <span class="keyword">else</span> {</span><br><span class="line">            <span class="comment">// variable declaration</span></span><br><span class="line">            current_id[Class] = Glo; <span class="comment">// global variable</span></span><br><span class="line">            current_id[Value] = (<span class="type">int</span>)data; <span class="comment">// assign memory address</span></span><br><span class="line">            data = data + <span class="keyword">sizeof</span>(<span class="type">int</span>);</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        <span class="keyword">if</span> (token == <span class="string">&#39;,&#39;</span>) {</span><br><span class="line">            match(<span class="string">&#39;,&#39;</span>);</span><br><span class="line">        }</span><br><span class="line">    }</span><br><span class="line">    next();</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>看了上面的代码，能大概理解吗？这里我们讲解其中的一些细节。</p><p><strong>向前看标记</strong> ：其中的 <code>if (token == xxx)</code> 语句就是用来向前查看标记以确定使用哪一个产生式，例如只要遇到 <code>enum</code> 我们就知道是需要解析枚举类型。而如果只解析到类型，如 <code>int identifier</code> 时我们并不能确定 <code>identifier</code> 是一个普通的变量还是一个函数，所以还需要继续查看后续的标记，如果遇到 <code>(</code> 则可以断定是函数了，反之则是变量。</p><p><strong>变量类型的表示</strong> ：我们的编译器支持指针类型，那意味着也支持指针的指针，如 <code>int **data;</code>。那么我们如何表示指针类型呢？前文中我们定义了支持的类型：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="comment">// types of variable/function</span></span><br><span class="line"><span class="class"><span class="keyword">enum</span> {</span> CHAR, INT, PTR };</span><br></pre></td></tr></tbody></table><p>所以一个类型首先有基本类型，如 <code>CHAR</code> 或 <code>INT</code>，当它是一个指向基本类型的指针时，如 <code>int *data</code>，我们就将它的类型加上 <code>PTR</code> 即代码中的：<code>type = type + PTR;</code>。同理，如果是指针的指针，则再加上 <code>PTR</code>。</p><h3 id="enum-declaration" tabindex="-1"><a class="header-anchor" href="#enum-declaration"><span><a href="about:blank#enum-declaration"></a>enum_declaration()</span></a></h3><p>用于解析枚举类型的定义。主要的逻辑用于解析用逗号（<code>,</code>）分隔的变量，值得注意的是在编译器中如何保存枚举变量的信息。</p><p>即我们将该变量的类别设置成了 <code>Num</code>，这样它就成了全局的常量了，而注意到上节中，正常的全局变量的类别则是 <code>Glo</code>，类别信息在后面章节中解析 <code>expression</code> 会使用到。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">enum_declaration</span><span class="params">()</span> {</span><br><span class="line">    <span class="comment">// parse enum [id] { a = 1, b = 3, ...}</span></span><br><span class="line">    <span class="type">int</span> i;</span><br><span class="line">    i = <span class="number">0</span>;</span><br><span class="line">    <span class="keyword">while</span> (token != <span class="string">&#39;}&#39;</span>) {</span><br><span class="line">        <span class="keyword">if</span> (token != Id) {</span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot;%d: bad enum identifier %d\\n&quot;</span>, line, token);</span><br><span class="line">            <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">        }</span><br><span class="line">        next();</span><br><span class="line">        <span class="keyword">if</span> (token == Assign) {</span><br><span class="line">            <span class="comment">// like {a=10}</span></span><br><span class="line">            next();</span><br><span class="line">            <span class="keyword">if</span> (token != Num) {</span><br><span class="line">                <span class="built_in">printf</span>(<span class="string">&quot;%d: bad enum initializer\\n&quot;</span>, line);</span><br><span class="line">                <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">            }</span><br><span class="line">            i = token_val;</span><br><span class="line">            next();</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        current_id[Class] = Num;</span><br><span class="line">        current_id[Type] = INT;</span><br><span class="line">        current_id[Value] = i++;</span><br><span class="line"></span><br><span class="line">        <span class="keyword">if</span> (token == <span class="string">&#39;,&#39;</span>) {</span><br><span class="line">            next();</span><br><span class="line">        }</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="其它" tabindex="-1"><a class="header-anchor" href="#其它"><span><a href="about:blank#%E5%85%B6%E5%AE%83"></a>其它</span></a></h3><p>其中的 <code>function_declaration</code> 函数我们将放到下一章中讲解。<code>match</code> 函数是一个辅助函数：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">match</span><span class="params">(<span class="type">int</span> tk)</span> {</span><br><span class="line">    <span class="keyword">if</span> (token == tk) {</span><br><span class="line">        next();</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%d: expected token: %d\\n&quot;</span>, line, tk);</span><br><span class="line">        <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>它将 <code>next</code> 函数包装起来，如果不是预期的标记则报错并退出。</p><h2 id="代码" tabindex="-1"><a class="header-anchor" href="#代码"><span><a href="about:blank#%E4%BB%A3%E7%A0%81"></a>代码</span></a></h2>',28),x={href:"https://github.com/lotabout/write-a-C-interpreter/tree/step-3",target:"_blank",rel:"noopener noreferrer"},A=l('<table><tbody><tr><td class="code"><pre><span class="line">git clone -b step-3 https://github.com/lotabout/write-a-C-interpreter</span><br></pre></td></tr></tbody></table><p>本章的代码还无法正常运行，因为还有许多功能没有实现，但如果有兴趣的话，可以自己先试着去实现它。</p><h2 id="小结" tabindex="-1"><a class="header-anchor" href="#小结"><span><a href="about:blank#%E5%B0%8F%E7%BB%93"></a>小结</span></a></h2><p>本章的内容应该不难，除了开头的 EBNF 表达式可能相对不好理解一些，但如果你查看了 EBNF 的具体表示方法后就不难理解了。</p><p>剩下的内容就是按部就班地将 EBNF 的产生式转换成函数的过程，如果你理解了上一章中的内容，相信这部分也不难理解。</p><p>下一章中我们将介绍如何解析函数的定义，敬请期待。</p>',6);function B(v,N){const n=t("ExternalLinkIcon");return r(),i("div",null,[o,a("p",null,[s("本文转自 "),a("a",b,[s("https://lotabout.me/2016/write-a-C-interpreter-5/"),e(n)]),s("，如有侵权，请联系删除。")]),d,a("ol",null,[a("li",null,[a("a",m,[s("手把手教你构建 C 语言编译器（0）——前言"),e(n)])]),a("li",null,[a("a",h,[s("手把手教你构建 C 语言编译器（1）——设计"),e(n)])]),a("li",null,[a("a",u,[s("手把手教你构建 C 语言编译器（2）——虚拟机"),e(n)])]),a("li",null,[a("a",_,[s("手把手教你构建 C 语言编译器（3）——词法分析器"),e(n)])]),a("li",null,[a("a",f,[s("手把手教你构建 C 语言编译器（4）——递归下降"),e(n)])]),a("li",null,[a("a",g,[s("手把手教你构建 C 语言编译器（5）——变量定义"),e(n)])]),a("li",null,[a("a",y,[s("手把手教你构建 C 语言编译器（6）——函数定义"),e(n)])]),a("li",null,[a("a",k,[s("手把手教你构建 C 语言编译器（7）——语句"),e(n)])]),a("li",null,[a("a",E,[s("手把手教你构建 C 语言编译器（8）——表达式"),e(n)])]),a("li",null,[a("a",C,[s("手把手教你构建 C 语言编译器（9）——总结"),e(n)])])]),w,a("p",null,[s("本章的代码可以在 "),a("a",x,[s("Github"),e(n)]),s(" 上下载，也可以直接 clone")]),A])}const T=p(c,[["render",B],["__file","5.html.vue"]]),I=JSON.parse('{"path":"/tech/designASimpileCCompiler/5.html","title":"手把手教你构建 C 语言编译器（5）——变量定义","lang":"zh-CN","frontmatter":{"title":"手把手教你构建 C 语言编译器（5）——变量定义","category":["编译原理"],"tag":["c","编译器","解释器"],"description":"转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-5/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（5）- 变量定义 Table of Contents 1. EBNF 表示 2. 解析变量的定义 2.1. program() 2.2. global_declarat...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/designASimpileCCompiler/5.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"手把手教你构建 C 语言编译器（5）——变量定义"}],["meta",{"property":"og:description","content":"转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-5/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（5）- 变量定义 Table of Contents 1. EBNF 表示 2. 解析变量的定义 2.1. program() 2.2. global_declarat..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"c"}],["meta",{"property":"article:tag","content":"编译器"}],["meta",{"property":"article:tag","content":"解释器"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"手把手教你构建 C 语言编译器（5）——变量定义\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"EBNF 表示","slug":"ebnf-表示","link":"#ebnf-表示","children":[]},{"level":2,"title":"解析变量的定义","slug":"解析变量的定义","link":"#解析变量的定义","children":[{"level":3,"title":"program()","slug":"program","link":"#program","children":[]},{"level":3,"title":"global_declaration()","slug":"global-declaration","link":"#global-declaration","children":[]},{"level":3,"title":"enum_declaration()","slug":"enum-declaration","link":"#enum-declaration","children":[]},{"level":3,"title":"其它","slug":"其它","link":"#其它","children":[]}]},{"level":2,"title":"代码","slug":"代码","link":"#代码","children":[]},{"level":2,"title":"小结","slug":"小结","link":"#小结","children":[]}],"readingTime":{"minutes":10.71,"words":3212},"filePathRelative":"tech/designASimpileCCompiler/5.md","excerpt":"\\n<p>本文转自 <a href=\\"https://lotabout.me/2016/write-a-C-interpreter-5/\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">https://lotabout.me/2016/write-a-C-interpreter-5/</a>，如有侵权，请联系删除。</p>\\n<h1>原文内容</h1>\\n<h1>手把手教你构建 C 语言编译器（5）- 变量定义</h1>\\n<p>Table of Contents</p>\\n<ol>\\n<li><a href=\\"about:blank#ebnf-%E8%A1%A8%E7%A4%BA\\">1. EBNF 表示</a></li>\\n<li><a href=\\"about:blank#%E8%A7%A3%E6%9E%90%E5%8F%98%E9%87%8F%E7%9A%84%E5%AE%9A%E4%B9%89\\">2. 解析变量的定义</a>\\n<ol>\\n<li><a href=\\"about:blank#program\\">2.1. program()</a></li>\\n<li><a href=\\"about:blank#global-declaration\\">2.2. global_declaration()</a></li>\\n<li><a href=\\"about:blank#enum-declaration\\">2.3. enum_declaration()</a></li>\\n<li><a href=\\"about:blank#%E5%85%B6%E5%AE%83\\">2.4. 其它</a></li>\\n</ol>\\n</li>\\n<li><a href=\\"about:blank#%E4%BB%A3%E7%A0%81\\">3. 代码</a></li>\\n<li><a href=\\"about:blank#%E5%B0%8F%E7%BB%93\\">4. 小结</a></li>\\n</ol>","autoDesc":true}');export{T as comp,I as data};
diff --git a/assets/6.html-BPGbpgjm.js b/assets/6.html-4dTDTOb4.js
similarity index 99%
rename from assets/6.html-BPGbpgjm.js
rename to assets/6.html-4dTDTOb4.js
index a0a3092..d10c062 100644
--- a/assets/6.html-BPGbpgjm.js
+++ b/assets/6.html-4dTDTOb4.js
@@ -1 +1 @@
-import{_ as p,r as t,o as r,c,b as s,e as a,d as e,f as l}from"./app-B69Gl_S-.js";const i={},o=s("h1",{id:"转载声明",tabindex:"-1"},[s("a",{class:"header-anchor",href:"#转载声明"},[s("span",null,"转载声明")])],-1),b={href:"https://lotabout.me/2016/write-a-C-interpreter-6/",target:"_blank",rel:"noopener noreferrer"},d=l('<h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-6-函数定义" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-6-函数定义"><span>手把手教你构建 C 语言编译器（6）- 函数定义</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#ebnf-%E8%A1%A8%E7%A4%BA">1. EBNF 表示</a></li><li><a href="about:blank#%E8%A7%A3%E6%9E%90%E5%87%BD%E6%95%B0%E7%9A%84%E5%AE%9A%E4%B9%89">2. 解析函数的定义</a><ol><li><a href="about:blank#%E5%87%BD%E6%95%B0%E5%8F%82%E6%95%B0%E4%B8%8E%E6%B1%87%E7%BC%96%E4%BB%A3%E7%A0%81">2.1. 函数参数与汇编代码</a></li><li><a href="about:blank#%E5%87%BD%E6%95%B0%E5%AE%9A%E4%B9%89%E7%9A%84%E8%A7%A3%E6%9E%90">2.2. 函数定义的解析</a></li><li><a href="about:blank#%E8%A7%A3%E6%9E%90%E5%8F%82%E6%95%B0">2.3. 解析参数</a></li><li><a href="about:blank#%E5%87%BD%E6%95%B0%E4%BD%93%E7%9A%84%E8%A7%A3%E6%9E%90">2.4. 函数体的解析</a></li></ol></li><li><a href="about:blank#%E4%BB%A3%E7%A0%81">3. 代码</a></li><li><a href="about:blank#%E5%B0%8F%E7%BB%93">4. 小结</a></li></ol><p>由于语法分析本身比较复杂，所以我们将它拆分成 3 个部分进行讲解，分别是：变量定义、函数定义、表达式。本章讲解函数定义相关的内容。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p>',6),h={href:"http://lotabout.me/2015/write-a-C-interpreter-0/",target:"_blank",rel:"noopener noreferrer"},m={href:"http://lotabout.me/2015/write-a-C-interpreter-1/",target:"_blank",rel:"noopener noreferrer"},u={href:"http://lotabout.me/2015/write-a-C-interpreter-2/",target:"_blank",rel:"noopener noreferrer"},_={href:"http://lotabout.me/2015/write-a-C-interpreter-3/",target:"_blank",rel:"noopener noreferrer"},E={href:"http://lotabout.me/2016/write-a-C-interpreter-4/",target:"_blank",rel:"noopener noreferrer"},f={href:"http://lotabout.me/2016/write-a-C-interpreter-5/",target:"_blank",rel:"noopener noreferrer"},y={href:"http://lotabout.me/2016/write-a-C-interpreter-6/",target:"_blank",rel:"noopener noreferrer"},B={href:"http://lotabout.me/2016/write-a-C-interpreter-7/",target:"_blank",rel:"noopener noreferrer"},k={href:"http://lotabout.me/2016/write-a-C-interpreter-8/",target:"_blank",rel:"noopener noreferrer"},g={href:"http://lotabout.me/2016/write-a-C-interpreter-9/",target:"_blank",rel:"noopener noreferrer"},A=l('<h2 id="ebnf-表示" tabindex="-1"><a class="header-anchor" href="#ebnf-表示"><span><a href="about:blank#ebnf-%E8%A1%A8%E7%A4%BA"></a>EBNF 表示</span></a></h2><p>这是上一章的 EBNF 方法中与函数定义相关的内容。</p><table><tbody><tr><td class="code"><pre><span class="line">variable_decl ::= type {&#39;*&#39;} id { &#39;,&#39; {&#39;*&#39;} id } &#39;;&#39;</span><br><span class="line"></span><br><span class="line">function_decl ::= type {&#39;*&#39;} id &#39;(&#39; parameter_decl &#39;)&#39; &#39;{&#39; body_decl &#39;}&#39;</span><br><span class="line"></span><br><span class="line">parameter_decl ::= type {&#39;*&#39;} id {&#39;,&#39; type {&#39;*&#39;} id}</span><br><span class="line"></span><br><span class="line">body_decl ::= {variable_decl}, {statement}</span><br><span class="line"></span><br><span class="line">statement ::= non_empty_statement | empty_statement</span><br><span class="line"></span><br><span class="line">non_empty_statement ::= if_statement | while_statement | &#39;{&#39; statement &#39;}&#39;</span><br><span class="line">                     | &#39;return&#39; expression | expression &#39;;&#39;</span><br><span class="line"></span><br><span class="line">if_statement ::= &#39;if&#39; &#39;(&#39; expression &#39;)&#39; statement [&#39;else&#39; non_empty_statement]</span><br><span class="line"></span><br><span class="line">while_statement ::= &#39;while&#39; &#39;(&#39; expression &#39;)&#39; non_empty_statement</span><br></pre></td></tr></tbody></table><h2 id="解析函数的定义" tabindex="-1"><a class="header-anchor" href="#解析函数的定义"><span><a href="about:blank#%E8%A7%A3%E6%9E%90%E5%87%BD%E6%95%B0%E7%9A%84%E5%AE%9A%E4%B9%89"></a>解析函数的定义</span></a></h2><p>上一章的代码中，我们已经知道了什么时候开始解析函数的定义，相关的代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line">...</span><br><span class="line"><span class="keyword">if</span> (token == <span class="string">&#39;(&#39;</span>) {</span><br><span class="line">    current_id[Class] = Fun;</span><br><span class="line">    current_id[Value] = (<span class="type">int</span>)(text + <span class="number">1</span>); <span class="comment">// the memory address of function</span></span><br><span class="line">    function_declaration();</span><br><span class="line">} <span class="keyword">else</span> {</span><br><span class="line">...</span><br></pre></td></tr></tbody></table><p>即在这断代码之前，我们已经为当前的标识符（identifier）设置了正确的类型，上面这断代码为当前的标识符设置了正确的类别（Fun），以及该函数在代码段（text segment）中的位置。接下来开始解析函数定义相关的内容：<code>parameter_decl</code> 及 <code>body_decl</code>。</p><h3 id="函数参数与汇编代码" tabindex="-1"><a class="header-anchor" href="#函数参数与汇编代码"><span><a href="about:blank#%E5%87%BD%E6%95%B0%E5%8F%82%E6%95%B0%E4%B8%8E%E6%B1%87%E7%BC%96%E4%BB%A3%E7%A0%81"></a>函数参数与汇编代码</span></a></h3><p>现在我们要回忆如何将“函数”转换成对应的汇编代码，因为这决定了在解析时我们需要哪些相关的信息。考虑下列函数：</p><table><tbody><tr><td class="code"><pre><span class="line">int demo(int param_a, int *param_b) {</span><br><span class="line">    int local_1;</span><br><span class="line">    char local_2;</span><br><span class="line"></span><br><span class="line">    ...</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>那么它应该被转换成什么样的汇编代码呢？在思考这个问题之前，我们需要了解当 <code>demo</code>函数被调用时，计算机的栈的状态，如下（参照第三章讲解的虚拟机）：</p><table><tbody><tr><td class="code"><pre><span class="line">|    ....       | high address</span><br><span class="line">+---------------+</span><br><span class="line">| arg: param_a  |    new_bp + 3</span><br><span class="line">+---------------+</span><br><span class="line">| arg: param_b  |    new_bp + 2</span><br><span class="line">+---------------+</span><br><span class="line">|return address |    new_bp + 1</span><br><span class="line">+---------------+</span><br><span class="line">| old BP        | &lt;- new BP</span><br><span class="line">+---------------+</span><br><span class="line">| local_1       |    new_bp - 1</span><br><span class="line">+---------------+</span><br><span class="line">| local_2       |    new_bp - 2</span><br><span class="line">+---------------+</span><br><span class="line">|    ....       |  low address</span><br></pre></td></tr></tbody></table><p>这里最为重要的一点是，无论是函数的参数（如 <code>param_a</code>）还是函数的局部变量（如 <code>local_1</code>）都是存放在计算机的 <strong>栈</strong> 上的。因此，与存放在 <strong>数据段</strong> 中的全局变量不同，在函数内访问它们是通过 <code>new_bp</code> 指针和对应的位移量进行的。因此，在解析的过程中，我们需要知道参数的个数，各个参数的位移量。</p><h3 id="函数定义的解析" tabindex="-1"><a class="header-anchor" href="#函数定义的解析"><span><a href="about:blank#%E5%87%BD%E6%95%B0%E5%AE%9A%E4%B9%89%E7%9A%84%E8%A7%A3%E6%9E%90"></a>函数定义的解析</span></a></h3><p>这相当于是整个函数定义的语法解析的框架，代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">function_declaration</span><span class="params">()</span> {</span><br><span class="line">    <span class="comment">// type func_name (...) {...}</span></span><br><span class="line">    <span class="comment">//               | this part</span></span><br><span class="line"></span><br><span class="line">    match(<span class="string">&#39;(&#39;</span>);</span><br><span class="line">    function_parameter();</span><br><span class="line">    match(<span class="string">&#39;)&#39;</span>);</span><br><span class="line">    match(<span class="string">&#39;{&#39;</span>);</span><br><span class="line">    function_body();</span><br><span class="line">    <span class="comment">//match(&#39;}&#39;);                 //  ①</span></span><br><span class="line"></span><br><span class="line">    <span class="comment">// ②</span></span><br><span class="line">    <span class="comment">// unwind local variable declarations for all local variables.</span></span><br><span class="line">    current_id = symbols;</span><br><span class="line">    <span class="keyword">while</span> (current_id[Token]) {</span><br><span class="line">        <span class="keyword">if</span> (current_id[Class] == Loc) {</span><br><span class="line">            current_id[Class] = current_id[BClass];</span><br><span class="line">            current_id[Type]  = current_id[BType];</span><br><span class="line">            current_id[Value] = current_id[BValue];</span><br><span class="line">        }</span><br><span class="line">        current_id = current_id + IdSize;</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>其中①中我们没有消耗最后的<code>}</code>字符。这么做的原因是：<code>variable_decl</code> 与 <code>function_decl</code> 是放在一起解析的，而 <code>variable_decl</code> 是以字符 <code>;</code> 结束的。而 <code>function_decl</code> 是以字符 <code>}</code> 结束的，若在此通过 <code>match</code> 消耗了 ‘;’ 字符，那么外层的 <code>while</code> 循环就没法准确地知道函数定义已经结束。所以我们将结束符的解析放在了外层的 <code>while</code> 循环中。</p><p>而②中的代码是用于将符号表中的信息恢复成全局的信息。这是因为，局部变量是可以和全局变量同名的，一旦同名，在函数体内局部变量就会覆盖全局变量，出了函数体，全局变量就恢复了原先的作用。这段代码线性地遍历所有标识符，并将保存在 <code>BXXX</code> 中的信息还原。</p><h3 id="解析参数" tabindex="-1"><a class="header-anchor" href="#解析参数"><span><a href="about:blank#%E8%A7%A3%E6%9E%90%E5%8F%82%E6%95%B0"></a>解析参数</span></a></h3><table><tbody><tr><td class="code"><pre><span class="line">parameter_decl ::= type {&#39;*&#39;} id {&#39;,&#39; type {&#39;*&#39;} id}</span><br></pre></td></tr></tbody></table><p>解析函数的参数就是解析以逗号分隔的一个个标识符，同时记录它们的位置与类型。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> index_of_bp; <span class="comment">// index of bp pointer on stack</span></span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">function_parameter</span><span class="params">()</span> {</span><br><span class="line">    <span class="type">int</span> type;</span><br><span class="line">    <span class="type">int</span> params;</span><br><span class="line">    params = <span class="number">0</span>;</span><br><span class="line">    <span class="keyword">while</span> (token != <span class="string">&#39;)&#39;</span>) {</span><br><span class="line">        <span class="comment">// ①</span></span><br><span class="line"></span><br><span class="line">        <span class="comment">// int name, ...</span></span><br><span class="line">        type = INT;</span><br><span class="line">        <span class="keyword">if</span> (token == Int) {</span><br><span class="line">            match(Int);</span><br><span class="line">        } <span class="keyword">else</span> <span class="keyword">if</span> (token == Char) {</span><br><span class="line">            type = CHAR;</span><br><span class="line">            match(Char);</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        <span class="comment">// pointer type</span></span><br><span class="line">        <span class="keyword">while</span> (token == Mul) {</span><br><span class="line">            match(Mul);</span><br><span class="line">            type = type + PTR;</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        <span class="comment">// parameter name</span></span><br><span class="line">        <span class="keyword">if</span> (token != Id) {</span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot;%d: bad parameter declaration\\n&quot;</span>, line);</span><br><span class="line">            <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">if</span> (current_id[Class] == Loc) {</span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot;%d: duplicate parameter declaration\\n&quot;</span>, line);</span><br><span class="line">            <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        match(Id);</span><br><span class="line"></span><br><span class="line">        <span class="comment">//②</span></span><br><span class="line">        <span class="comment">// store the local variable</span></span><br><span class="line">        current_id[BClass] = current_id[Class]; current_id[Class]  = Loc;</span><br><span class="line">        current_id[BType]  = current_id[Type];  current_id[Type]   = type;</span><br><span class="line">        current_id[BValue] = current_id[Value]; current_id[Value]  = params++;   <span class="comment">// index of current parameter</span></span><br><span class="line"></span><br><span class="line">        <span class="keyword">if</span> (token == <span class="string">&#39;,&#39;</span>) {</span><br><span class="line">            match(<span class="string">&#39;,&#39;</span>);</span><br><span class="line">        }</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="comment">// ③</span></span><br><span class="line">    index_of_bp = params+<span class="number">1</span>;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>其中①与全局变量定义的解析十分一样，用于解析该参数的类型。</p><p>而②则与上节中提到的“局部变量覆盖全局变量”相关，先将全局变量的信息保存（无论是是否真的在全局中用到了这个变量）在 <code>BXXX</code> 中，再赋上局部变量相关的信息，如 <code>Value</code> 中存放的是参数的位置（是第几个参数）。</p><p>③则与汇编代码的生成有关，<code>index_of_bp</code> 就是前文提到的 <code>new_bp</code> 的位置。</p><h3 id="函数体的解析" tabindex="-1"><a class="header-anchor" href="#函数体的解析"><span><a href="about:blank#%E5%87%BD%E6%95%B0%E4%BD%93%E7%9A%84%E8%A7%A3%E6%9E%90"></a>函数体的解析</span></a></h3><p>我们实现的 C 语言与现代的 C 语言不太一致，我们需要所有的变量定义出现在所有的语句之前。函数体的代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">function_body</span><span class="params">()</span> {</span><br><span class="line">    <span class="comment">// type func_name (...) {...}</span></span><br><span class="line">    <span class="comment">//                   --&gt;|   |&lt;--</span></span><br><span class="line"></span><br><span class="line">    <span class="comment">// ... {</span></span><br><span class="line">    <span class="comment">// 1. local declarations</span></span><br><span class="line">    <span class="comment">// 2. statements</span></span><br><span class="line">    <span class="comment">// }</span></span><br><span class="line"></span><br><span class="line">    <span class="type">int</span> pos_local; <span class="comment">// position of local variables on the stack.</span></span><br><span class="line">    <span class="type">int</span> type;</span><br><span class="line">    pos_local = index_of_bp;</span><br><span class="line"></span><br><span class="line">    <span class="comment">// ①</span></span><br><span class="line">    <span class="keyword">while</span> (token == Int || token == Char) {</span><br><span class="line">        <span class="comment">// local variable declaration, just like global ones.</span></span><br><span class="line">        basetype = (token == Int) ? INT : CHAR;</span><br><span class="line">        match(token);</span><br><span class="line"></span><br><span class="line">        <span class="keyword">while</span> (token != <span class="string">&#39;;&#39;</span>) {</span><br><span class="line">            type = basetype;</span><br><span class="line">            <span class="keyword">while</span> (token == Mul) {</span><br><span class="line">                match(Mul);</span><br><span class="line">                type = type + PTR;</span><br><span class="line">            }</span><br><span class="line"></span><br><span class="line">            <span class="keyword">if</span> (token != Id) {</span><br><span class="line">                <span class="comment">// invalid declaration</span></span><br><span class="line">                <span class="built_in">printf</span>(<span class="string">&quot;%d: bad local declaration\\n&quot;</span>, line);</span><br><span class="line">                <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">if</span> (current_id[Class] == Loc) {</span><br><span class="line">                <span class="comment">// identifier exists</span></span><br><span class="line">                <span class="built_in">printf</span>(<span class="string">&quot;%d: duplicate local declaration\\n&quot;</span>, line);</span><br><span class="line">                <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">            }</span><br><span class="line">            match(Id);</span><br><span class="line"></span><br><span class="line">            <span class="comment">// store the local variable</span></span><br><span class="line">            current_id[BClass] = current_id[Class]; current_id[Class]  = Loc;</span><br><span class="line">            current_id[BType]  = current_id[Type];  current_id[Type]   = type;</span><br><span class="line">            current_id[BValue] = current_id[Value]; current_id[Value]  = ++pos_local;   <span class="comment">// index of current parameter</span></span><br><span class="line"></span><br><span class="line">            <span class="keyword">if</span> (token == <span class="string">&#39;,&#39;</span>) {</span><br><span class="line">                match(<span class="string">&#39;,&#39;</span>);</span><br><span class="line">            }</span><br><span class="line">        }</span><br><span class="line">        match(<span class="string">&#39;;&#39;</span>);</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="comment">// ②</span></span><br><span class="line">    <span class="comment">// save the stack size for local variables</span></span><br><span class="line">    *++text = ENT;</span><br><span class="line">    *++text = pos_local - index_of_bp;</span><br><span class="line"></span><br><span class="line">    <span class="comment">// statements</span></span><br><span class="line">    <span class="keyword">while</span> (token != <span class="string">&#39;}&#39;</span>) {</span><br><span class="line">        statement();</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="comment">// emit code for leaving the sub function</span></span><br><span class="line">    *++text = LEV;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>其中①用于解析函数体内的局部变量的定义，代码与全局的变量定义几乎一样。</p><p>而②则用于生成汇编代码，我们在第三章的虚拟机中提到过，我们需要在栈上为局部变量预留空间，这两行代码起的就是这个作用。</p><h2 id="代码" tabindex="-1"><a class="header-anchor" href="#代码"><span><a href="about:blank#%E4%BB%A3%E7%A0%81"></a>代码</span></a></h2>',31),C={href:"https://github.com/lotabout/write-a-C-interpreter/tree/step-4",target:"_blank",rel:"noopener noreferrer"},w=l('<table><tbody><tr><td class="code"><pre><span class="line">git clone -b step-4 https://github.com/lotabout/write-a-C-interpreter</span><br></pre></td></tr></tbody></table><p>本章的代码依旧无法运行，还有两个重要函数没有完成：<code>statement</code> 及 <code>expression</code>，感兴趣的话可以尝试自己实现它们。</p><h2 id="小结" tabindex="-1"><a class="header-anchor" href="#小结"><span><a href="about:blank#%E5%B0%8F%E7%BB%93"></a>小结</span></a></h2><p>本章中我们用了不多的代码完成了函数定义的解析。大部分的代码依旧是用于解析变量：参数和局部变量，而它们的逻辑和全局变量的解析几乎一致，最大的区别就是保存的信息不同。</p><p>当然，要理解函数定义的解析过程，最重要的是理解我们会为函数生成怎样的汇编代码，因为这决定了我们需要从解析中获取什么样的信息（例如参数的位置，个数等），而这些可能需要你重新回顾一下“虚拟机”这一章，或是重新学习学习汇编相关的知识。</p><p>下一章中我们将讲解语句的解析，敬请期待。</p>',6);function x(v,T){const n=t("ExternalLinkIcon");return r(),c("div",null,[o,s("p",null,[a("本文转自 "),s("a",b,[a("https://lotabout.me/2016/write-a-C-interpreter-6/"),e(n)]),a("，如有侵权，请联系删除。")]),d,s("ol",null,[s("li",null,[s("a",h,[a("手把手教你构建 C 语言编译器（0）——前言"),e(n)])]),s("li",null,[s("a",m,[a("手把手教你构建 C 语言编译器（1）——设计"),e(n)])]),s("li",null,[s("a",u,[a("手把手教你构建 C 语言编译器（2）——虚拟机"),e(n)])]),s("li",null,[s("a",_,[a("手把手教你构建 C 语言编译器（3）——词法分析器"),e(n)])]),s("li",null,[s("a",E,[a("手把手教你构建 C 语言编译器（4）——递归下降"),e(n)])]),s("li",null,[s("a",f,[a("手把手教你构建 C 语言编译器（5）——变量定义"),e(n)])]),s("li",null,[s("a",y,[a("手把手教你构建 C 语言编译器（6）——函数定义"),e(n)])]),s("li",null,[s("a",B,[a("手把手教你构建 C 语言编译器（7）——语句"),e(n)])]),s("li",null,[s("a",k,[a("手把手教你构建 C 语言编译器（8）——表达式"),e(n)])]),s("li",null,[s("a",g,[a("手把手教你构建 C 语言编译器（9）——总结"),e(n)])])]),A,s("p",null,[a("本章的代码可以在 "),s("a",C,[a("Github"),e(n)]),a(" 上下载，也可以直接 clone")]),w])}const N=p(i,[["render",x],["__file","6.html.vue"]]),D=JSON.parse('{"path":"/tech/designASimpileCCompiler/6.html","title":"手把手教你构建 C 语言编译器（6）——函数定义","lang":"zh-CN","frontmatter":{"title":"手把手教你构建 C 语言编译器（6）——函数定义","category":["编译原理"],"tag":["c","编译器","解释器"],"description":"转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-6/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（6）- 函数定义 Table of Contents 1. EBNF 表示 2. 解析函数的定义 2.1. 函数参数与汇编代码 2.2. 函数定义的解析 2.3. 解析...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/designASimpileCCompiler/6.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"手把手教你构建 C 语言编译器（6）——函数定义"}],["meta",{"property":"og:description","content":"转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-6/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（6）- 函数定义 Table of Contents 1. EBNF 表示 2. 解析函数的定义 2.1. 函数参数与汇编代码 2.2. 函数定义的解析 2.3. 解析..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"c"}],["meta",{"property":"article:tag","content":"编译器"}],["meta",{"property":"article:tag","content":"解释器"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"手把手教你构建 C 语言编译器（6）——函数定义\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"EBNF 表示","slug":"ebnf-表示","link":"#ebnf-表示","children":[]},{"level":2,"title":"解析函数的定义","slug":"解析函数的定义","link":"#解析函数的定义","children":[{"level":3,"title":"函数参数与汇编代码","slug":"函数参数与汇编代码","link":"#函数参数与汇编代码","children":[]},{"level":3,"title":"函数定义的解析","slug":"函数定义的解析","link":"#函数定义的解析","children":[]},{"level":3,"title":"解析参数","slug":"解析参数","link":"#解析参数","children":[]},{"level":3,"title":"函数体的解析","slug":"函数体的解析","link":"#函数体的解析","children":[]}]},{"level":2,"title":"代码","slug":"代码","link":"#代码","children":[]},{"level":2,"title":"小结","slug":"小结","link":"#小结","children":[]}],"readingTime":{"minutes":12.61,"words":3783},"filePathRelative":"tech/designASimpileCCompiler/6.md","excerpt":"\\n<p>本文转自 <a href=\\"https://lotabout.me/2016/write-a-C-interpreter-6/\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">https://lotabout.me/2016/write-a-C-interpreter-6/</a>，如有侵权，请联系删除。</p>\\n<h1>原文内容</h1>\\n<h1>手把手教你构建 C 语言编译器（6）- 函数定义</h1>\\n<p>Table of Contents</p>\\n<ol>\\n<li><a href=\\"about:blank#ebnf-%E8%A1%A8%E7%A4%BA\\">1. EBNF 表示</a></li>\\n<li><a href=\\"about:blank#%E8%A7%A3%E6%9E%90%E5%87%BD%E6%95%B0%E7%9A%84%E5%AE%9A%E4%B9%89\\">2. 解析函数的定义</a>\\n<ol>\\n<li><a href=\\"about:blank#%E5%87%BD%E6%95%B0%E5%8F%82%E6%95%B0%E4%B8%8E%E6%B1%87%E7%BC%96%E4%BB%A3%E7%A0%81\\">2.1. 函数参数与汇编代码</a></li>\\n<li><a href=\\"about:blank#%E5%87%BD%E6%95%B0%E5%AE%9A%E4%B9%89%E7%9A%84%E8%A7%A3%E6%9E%90\\">2.2. 函数定义的解析</a></li>\\n<li><a href=\\"about:blank#%E8%A7%A3%E6%9E%90%E5%8F%82%E6%95%B0\\">2.3. 解析参数</a></li>\\n<li><a href=\\"about:blank#%E5%87%BD%E6%95%B0%E4%BD%93%E7%9A%84%E8%A7%A3%E6%9E%90\\">2.4. 函数体的解析</a></li>\\n</ol>\\n</li>\\n<li><a href=\\"about:blank#%E4%BB%A3%E7%A0%81\\">3. 代码</a></li>\\n<li><a href=\\"about:blank#%E5%B0%8F%E7%BB%93\\">4. 小结</a></li>\\n</ol>","autoDesc":true}');export{N as comp,D as data};
+import{_ as p,r as t,o as r,c,b as s,e as a,d as e,f as l}from"./app-B4LGNJZ0.js";const i={},o=s("h1",{id:"转载声明",tabindex:"-1"},[s("a",{class:"header-anchor",href:"#转载声明"},[s("span",null,"转载声明")])],-1),b={href:"https://lotabout.me/2016/write-a-C-interpreter-6/",target:"_blank",rel:"noopener noreferrer"},d=l('<h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-6-函数定义" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-6-函数定义"><span>手把手教你构建 C 语言编译器（6）- 函数定义</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#ebnf-%E8%A1%A8%E7%A4%BA">1. EBNF 表示</a></li><li><a href="about:blank#%E8%A7%A3%E6%9E%90%E5%87%BD%E6%95%B0%E7%9A%84%E5%AE%9A%E4%B9%89">2. 解析函数的定义</a><ol><li><a href="about:blank#%E5%87%BD%E6%95%B0%E5%8F%82%E6%95%B0%E4%B8%8E%E6%B1%87%E7%BC%96%E4%BB%A3%E7%A0%81">2.1. 函数参数与汇编代码</a></li><li><a href="about:blank#%E5%87%BD%E6%95%B0%E5%AE%9A%E4%B9%89%E7%9A%84%E8%A7%A3%E6%9E%90">2.2. 函数定义的解析</a></li><li><a href="about:blank#%E8%A7%A3%E6%9E%90%E5%8F%82%E6%95%B0">2.3. 解析参数</a></li><li><a href="about:blank#%E5%87%BD%E6%95%B0%E4%BD%93%E7%9A%84%E8%A7%A3%E6%9E%90">2.4. 函数体的解析</a></li></ol></li><li><a href="about:blank#%E4%BB%A3%E7%A0%81">3. 代码</a></li><li><a href="about:blank#%E5%B0%8F%E7%BB%93">4. 小结</a></li></ol><p>由于语法分析本身比较复杂，所以我们将它拆分成 3 个部分进行讲解，分别是：变量定义、函数定义、表达式。本章讲解函数定义相关的内容。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p>',6),h={href:"http://lotabout.me/2015/write-a-C-interpreter-0/",target:"_blank",rel:"noopener noreferrer"},m={href:"http://lotabout.me/2015/write-a-C-interpreter-1/",target:"_blank",rel:"noopener noreferrer"},u={href:"http://lotabout.me/2015/write-a-C-interpreter-2/",target:"_blank",rel:"noopener noreferrer"},_={href:"http://lotabout.me/2015/write-a-C-interpreter-3/",target:"_blank",rel:"noopener noreferrer"},E={href:"http://lotabout.me/2016/write-a-C-interpreter-4/",target:"_blank",rel:"noopener noreferrer"},f={href:"http://lotabout.me/2016/write-a-C-interpreter-5/",target:"_blank",rel:"noopener noreferrer"},y={href:"http://lotabout.me/2016/write-a-C-interpreter-6/",target:"_blank",rel:"noopener noreferrer"},B={href:"http://lotabout.me/2016/write-a-C-interpreter-7/",target:"_blank",rel:"noopener noreferrer"},k={href:"http://lotabout.me/2016/write-a-C-interpreter-8/",target:"_blank",rel:"noopener noreferrer"},g={href:"http://lotabout.me/2016/write-a-C-interpreter-9/",target:"_blank",rel:"noopener noreferrer"},A=l('<h2 id="ebnf-表示" tabindex="-1"><a class="header-anchor" href="#ebnf-表示"><span><a href="about:blank#ebnf-%E8%A1%A8%E7%A4%BA"></a>EBNF 表示</span></a></h2><p>这是上一章的 EBNF 方法中与函数定义相关的内容。</p><table><tbody><tr><td class="code"><pre><span class="line">variable_decl ::= type {&#39;*&#39;} id { &#39;,&#39; {&#39;*&#39;} id } &#39;;&#39;</span><br><span class="line"></span><br><span class="line">function_decl ::= type {&#39;*&#39;} id &#39;(&#39; parameter_decl &#39;)&#39; &#39;{&#39; body_decl &#39;}&#39;</span><br><span class="line"></span><br><span class="line">parameter_decl ::= type {&#39;*&#39;} id {&#39;,&#39; type {&#39;*&#39;} id}</span><br><span class="line"></span><br><span class="line">body_decl ::= {variable_decl}, {statement}</span><br><span class="line"></span><br><span class="line">statement ::= non_empty_statement | empty_statement</span><br><span class="line"></span><br><span class="line">non_empty_statement ::= if_statement | while_statement | &#39;{&#39; statement &#39;}&#39;</span><br><span class="line">                     | &#39;return&#39; expression | expression &#39;;&#39;</span><br><span class="line"></span><br><span class="line">if_statement ::= &#39;if&#39; &#39;(&#39; expression &#39;)&#39; statement [&#39;else&#39; non_empty_statement]</span><br><span class="line"></span><br><span class="line">while_statement ::= &#39;while&#39; &#39;(&#39; expression &#39;)&#39; non_empty_statement</span><br></pre></td></tr></tbody></table><h2 id="解析函数的定义" tabindex="-1"><a class="header-anchor" href="#解析函数的定义"><span><a href="about:blank#%E8%A7%A3%E6%9E%90%E5%87%BD%E6%95%B0%E7%9A%84%E5%AE%9A%E4%B9%89"></a>解析函数的定义</span></a></h2><p>上一章的代码中，我们已经知道了什么时候开始解析函数的定义，相关的代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line">...</span><br><span class="line"><span class="keyword">if</span> (token == <span class="string">&#39;(&#39;</span>) {</span><br><span class="line">    current_id[Class] = Fun;</span><br><span class="line">    current_id[Value] = (<span class="type">int</span>)(text + <span class="number">1</span>); <span class="comment">// the memory address of function</span></span><br><span class="line">    function_declaration();</span><br><span class="line">} <span class="keyword">else</span> {</span><br><span class="line">...</span><br></pre></td></tr></tbody></table><p>即在这断代码之前，我们已经为当前的标识符（identifier）设置了正确的类型，上面这断代码为当前的标识符设置了正确的类别（Fun），以及该函数在代码段（text segment）中的位置。接下来开始解析函数定义相关的内容：<code>parameter_decl</code> 及 <code>body_decl</code>。</p><h3 id="函数参数与汇编代码" tabindex="-1"><a class="header-anchor" href="#函数参数与汇编代码"><span><a href="about:blank#%E5%87%BD%E6%95%B0%E5%8F%82%E6%95%B0%E4%B8%8E%E6%B1%87%E7%BC%96%E4%BB%A3%E7%A0%81"></a>函数参数与汇编代码</span></a></h3><p>现在我们要回忆如何将“函数”转换成对应的汇编代码，因为这决定了在解析时我们需要哪些相关的信息。考虑下列函数：</p><table><tbody><tr><td class="code"><pre><span class="line">int demo(int param_a, int *param_b) {</span><br><span class="line">    int local_1;</span><br><span class="line">    char local_2;</span><br><span class="line"></span><br><span class="line">    ...</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>那么它应该被转换成什么样的汇编代码呢？在思考这个问题之前，我们需要了解当 <code>demo</code>函数被调用时，计算机的栈的状态，如下（参照第三章讲解的虚拟机）：</p><table><tbody><tr><td class="code"><pre><span class="line">|    ....       | high address</span><br><span class="line">+---------------+</span><br><span class="line">| arg: param_a  |    new_bp + 3</span><br><span class="line">+---------------+</span><br><span class="line">| arg: param_b  |    new_bp + 2</span><br><span class="line">+---------------+</span><br><span class="line">|return address |    new_bp + 1</span><br><span class="line">+---------------+</span><br><span class="line">| old BP        | &lt;- new BP</span><br><span class="line">+---------------+</span><br><span class="line">| local_1       |    new_bp - 1</span><br><span class="line">+---------------+</span><br><span class="line">| local_2       |    new_bp - 2</span><br><span class="line">+---------------+</span><br><span class="line">|    ....       |  low address</span><br></pre></td></tr></tbody></table><p>这里最为重要的一点是，无论是函数的参数（如 <code>param_a</code>）还是函数的局部变量（如 <code>local_1</code>）都是存放在计算机的 <strong>栈</strong> 上的。因此，与存放在 <strong>数据段</strong> 中的全局变量不同，在函数内访问它们是通过 <code>new_bp</code> 指针和对应的位移量进行的。因此，在解析的过程中，我们需要知道参数的个数，各个参数的位移量。</p><h3 id="函数定义的解析" tabindex="-1"><a class="header-anchor" href="#函数定义的解析"><span><a href="about:blank#%E5%87%BD%E6%95%B0%E5%AE%9A%E4%B9%89%E7%9A%84%E8%A7%A3%E6%9E%90"></a>函数定义的解析</span></a></h3><p>这相当于是整个函数定义的语法解析的框架，代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">function_declaration</span><span class="params">()</span> {</span><br><span class="line">    <span class="comment">// type func_name (...) {...}</span></span><br><span class="line">    <span class="comment">//               | this part</span></span><br><span class="line"></span><br><span class="line">    match(<span class="string">&#39;(&#39;</span>);</span><br><span class="line">    function_parameter();</span><br><span class="line">    match(<span class="string">&#39;)&#39;</span>);</span><br><span class="line">    match(<span class="string">&#39;{&#39;</span>);</span><br><span class="line">    function_body();</span><br><span class="line">    <span class="comment">//match(&#39;}&#39;);                 //  ①</span></span><br><span class="line"></span><br><span class="line">    <span class="comment">// ②</span></span><br><span class="line">    <span class="comment">// unwind local variable declarations for all local variables.</span></span><br><span class="line">    current_id = symbols;</span><br><span class="line">    <span class="keyword">while</span> (current_id[Token]) {</span><br><span class="line">        <span class="keyword">if</span> (current_id[Class] == Loc) {</span><br><span class="line">            current_id[Class] = current_id[BClass];</span><br><span class="line">            current_id[Type]  = current_id[BType];</span><br><span class="line">            current_id[Value] = current_id[BValue];</span><br><span class="line">        }</span><br><span class="line">        current_id = current_id + IdSize;</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>其中①中我们没有消耗最后的<code>}</code>字符。这么做的原因是：<code>variable_decl</code> 与 <code>function_decl</code> 是放在一起解析的，而 <code>variable_decl</code> 是以字符 <code>;</code> 结束的。而 <code>function_decl</code> 是以字符 <code>}</code> 结束的，若在此通过 <code>match</code> 消耗了 ‘;’ 字符，那么外层的 <code>while</code> 循环就没法准确地知道函数定义已经结束。所以我们将结束符的解析放在了外层的 <code>while</code> 循环中。</p><p>而②中的代码是用于将符号表中的信息恢复成全局的信息。这是因为，局部变量是可以和全局变量同名的，一旦同名，在函数体内局部变量就会覆盖全局变量，出了函数体，全局变量就恢复了原先的作用。这段代码线性地遍历所有标识符，并将保存在 <code>BXXX</code> 中的信息还原。</p><h3 id="解析参数" tabindex="-1"><a class="header-anchor" href="#解析参数"><span><a href="about:blank#%E8%A7%A3%E6%9E%90%E5%8F%82%E6%95%B0"></a>解析参数</span></a></h3><table><tbody><tr><td class="code"><pre><span class="line">parameter_decl ::= type {&#39;*&#39;} id {&#39;,&#39; type {&#39;*&#39;} id}</span><br></pre></td></tr></tbody></table><p>解析函数的参数就是解析以逗号分隔的一个个标识符，同时记录它们的位置与类型。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> index_of_bp; <span class="comment">// index of bp pointer on stack</span></span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">function_parameter</span><span class="params">()</span> {</span><br><span class="line">    <span class="type">int</span> type;</span><br><span class="line">    <span class="type">int</span> params;</span><br><span class="line">    params = <span class="number">0</span>;</span><br><span class="line">    <span class="keyword">while</span> (token != <span class="string">&#39;)&#39;</span>) {</span><br><span class="line">        <span class="comment">// ①</span></span><br><span class="line"></span><br><span class="line">        <span class="comment">// int name, ...</span></span><br><span class="line">        type = INT;</span><br><span class="line">        <span class="keyword">if</span> (token == Int) {</span><br><span class="line">            match(Int);</span><br><span class="line">        } <span class="keyword">else</span> <span class="keyword">if</span> (token == Char) {</span><br><span class="line">            type = CHAR;</span><br><span class="line">            match(Char);</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        <span class="comment">// pointer type</span></span><br><span class="line">        <span class="keyword">while</span> (token == Mul) {</span><br><span class="line">            match(Mul);</span><br><span class="line">            type = type + PTR;</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        <span class="comment">// parameter name</span></span><br><span class="line">        <span class="keyword">if</span> (token != Id) {</span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot;%d: bad parameter declaration\\n&quot;</span>, line);</span><br><span class="line">            <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">if</span> (current_id[Class] == Loc) {</span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot;%d: duplicate parameter declaration\\n&quot;</span>, line);</span><br><span class="line">            <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        match(Id);</span><br><span class="line"></span><br><span class="line">        <span class="comment">//②</span></span><br><span class="line">        <span class="comment">// store the local variable</span></span><br><span class="line">        current_id[BClass] = current_id[Class]; current_id[Class]  = Loc;</span><br><span class="line">        current_id[BType]  = current_id[Type];  current_id[Type]   = type;</span><br><span class="line">        current_id[BValue] = current_id[Value]; current_id[Value]  = params++;   <span class="comment">// index of current parameter</span></span><br><span class="line"></span><br><span class="line">        <span class="keyword">if</span> (token == <span class="string">&#39;,&#39;</span>) {</span><br><span class="line">            match(<span class="string">&#39;,&#39;</span>);</span><br><span class="line">        }</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="comment">// ③</span></span><br><span class="line">    index_of_bp = params+<span class="number">1</span>;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>其中①与全局变量定义的解析十分一样，用于解析该参数的类型。</p><p>而②则与上节中提到的“局部变量覆盖全局变量”相关，先将全局变量的信息保存（无论是是否真的在全局中用到了这个变量）在 <code>BXXX</code> 中，再赋上局部变量相关的信息，如 <code>Value</code> 中存放的是参数的位置（是第几个参数）。</p><p>③则与汇编代码的生成有关，<code>index_of_bp</code> 就是前文提到的 <code>new_bp</code> 的位置。</p><h3 id="函数体的解析" tabindex="-1"><a class="header-anchor" href="#函数体的解析"><span><a href="about:blank#%E5%87%BD%E6%95%B0%E4%BD%93%E7%9A%84%E8%A7%A3%E6%9E%90"></a>函数体的解析</span></a></h3><p>我们实现的 C 语言与现代的 C 语言不太一致，我们需要所有的变量定义出现在所有的语句之前。函数体的代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">function_body</span><span class="params">()</span> {</span><br><span class="line">    <span class="comment">// type func_name (...) {...}</span></span><br><span class="line">    <span class="comment">//                   --&gt;|   |&lt;--</span></span><br><span class="line"></span><br><span class="line">    <span class="comment">// ... {</span></span><br><span class="line">    <span class="comment">// 1. local declarations</span></span><br><span class="line">    <span class="comment">// 2. statements</span></span><br><span class="line">    <span class="comment">// }</span></span><br><span class="line"></span><br><span class="line">    <span class="type">int</span> pos_local; <span class="comment">// position of local variables on the stack.</span></span><br><span class="line">    <span class="type">int</span> type;</span><br><span class="line">    pos_local = index_of_bp;</span><br><span class="line"></span><br><span class="line">    <span class="comment">// ①</span></span><br><span class="line">    <span class="keyword">while</span> (token == Int || token == Char) {</span><br><span class="line">        <span class="comment">// local variable declaration, just like global ones.</span></span><br><span class="line">        basetype = (token == Int) ? INT : CHAR;</span><br><span class="line">        match(token);</span><br><span class="line"></span><br><span class="line">        <span class="keyword">while</span> (token != <span class="string">&#39;;&#39;</span>) {</span><br><span class="line">            type = basetype;</span><br><span class="line">            <span class="keyword">while</span> (token == Mul) {</span><br><span class="line">                match(Mul);</span><br><span class="line">                type = type + PTR;</span><br><span class="line">            }</span><br><span class="line"></span><br><span class="line">            <span class="keyword">if</span> (token != Id) {</span><br><span class="line">                <span class="comment">// invalid declaration</span></span><br><span class="line">                <span class="built_in">printf</span>(<span class="string">&quot;%d: bad local declaration\\n&quot;</span>, line);</span><br><span class="line">                <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">if</span> (current_id[Class] == Loc) {</span><br><span class="line">                <span class="comment">// identifier exists</span></span><br><span class="line">                <span class="built_in">printf</span>(<span class="string">&quot;%d: duplicate local declaration\\n&quot;</span>, line);</span><br><span class="line">                <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">            }</span><br><span class="line">            match(Id);</span><br><span class="line"></span><br><span class="line">            <span class="comment">// store the local variable</span></span><br><span class="line">            current_id[BClass] = current_id[Class]; current_id[Class]  = Loc;</span><br><span class="line">            current_id[BType]  = current_id[Type];  current_id[Type]   = type;</span><br><span class="line">            current_id[BValue] = current_id[Value]; current_id[Value]  = ++pos_local;   <span class="comment">// index of current parameter</span></span><br><span class="line"></span><br><span class="line">            <span class="keyword">if</span> (token == <span class="string">&#39;,&#39;</span>) {</span><br><span class="line">                match(<span class="string">&#39;,&#39;</span>);</span><br><span class="line">            }</span><br><span class="line">        }</span><br><span class="line">        match(<span class="string">&#39;;&#39;</span>);</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="comment">// ②</span></span><br><span class="line">    <span class="comment">// save the stack size for local variables</span></span><br><span class="line">    *++text = ENT;</span><br><span class="line">    *++text = pos_local - index_of_bp;</span><br><span class="line"></span><br><span class="line">    <span class="comment">// statements</span></span><br><span class="line">    <span class="keyword">while</span> (token != <span class="string">&#39;}&#39;</span>) {</span><br><span class="line">        statement();</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="comment">// emit code for leaving the sub function</span></span><br><span class="line">    *++text = LEV;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>其中①用于解析函数体内的局部变量的定义，代码与全局的变量定义几乎一样。</p><p>而②则用于生成汇编代码，我们在第三章的虚拟机中提到过，我们需要在栈上为局部变量预留空间，这两行代码起的就是这个作用。</p><h2 id="代码" tabindex="-1"><a class="header-anchor" href="#代码"><span><a href="about:blank#%E4%BB%A3%E7%A0%81"></a>代码</span></a></h2>',31),C={href:"https://github.com/lotabout/write-a-C-interpreter/tree/step-4",target:"_blank",rel:"noopener noreferrer"},w=l('<table><tbody><tr><td class="code"><pre><span class="line">git clone -b step-4 https://github.com/lotabout/write-a-C-interpreter</span><br></pre></td></tr></tbody></table><p>本章的代码依旧无法运行，还有两个重要函数没有完成：<code>statement</code> 及 <code>expression</code>，感兴趣的话可以尝试自己实现它们。</p><h2 id="小结" tabindex="-1"><a class="header-anchor" href="#小结"><span><a href="about:blank#%E5%B0%8F%E7%BB%93"></a>小结</span></a></h2><p>本章中我们用了不多的代码完成了函数定义的解析。大部分的代码依旧是用于解析变量：参数和局部变量，而它们的逻辑和全局变量的解析几乎一致，最大的区别就是保存的信息不同。</p><p>当然，要理解函数定义的解析过程，最重要的是理解我们会为函数生成怎样的汇编代码，因为这决定了我们需要从解析中获取什么样的信息（例如参数的位置，个数等），而这些可能需要你重新回顾一下“虚拟机”这一章，或是重新学习学习汇编相关的知识。</p><p>下一章中我们将讲解语句的解析，敬请期待。</p>',6);function x(v,T){const n=t("ExternalLinkIcon");return r(),c("div",null,[o,s("p",null,[a("本文转自 "),s("a",b,[a("https://lotabout.me/2016/write-a-C-interpreter-6/"),e(n)]),a("，如有侵权，请联系删除。")]),d,s("ol",null,[s("li",null,[s("a",h,[a("手把手教你构建 C 语言编译器（0）——前言"),e(n)])]),s("li",null,[s("a",m,[a("手把手教你构建 C 语言编译器（1）——设计"),e(n)])]),s("li",null,[s("a",u,[a("手把手教你构建 C 语言编译器（2）——虚拟机"),e(n)])]),s("li",null,[s("a",_,[a("手把手教你构建 C 语言编译器（3）——词法分析器"),e(n)])]),s("li",null,[s("a",E,[a("手把手教你构建 C 语言编译器（4）——递归下降"),e(n)])]),s("li",null,[s("a",f,[a("手把手教你构建 C 语言编译器（5）——变量定义"),e(n)])]),s("li",null,[s("a",y,[a("手把手教你构建 C 语言编译器（6）——函数定义"),e(n)])]),s("li",null,[s("a",B,[a("手把手教你构建 C 语言编译器（7）——语句"),e(n)])]),s("li",null,[s("a",k,[a("手把手教你构建 C 语言编译器（8）——表达式"),e(n)])]),s("li",null,[s("a",g,[a("手把手教你构建 C 语言编译器（9）——总结"),e(n)])])]),A,s("p",null,[a("本章的代码可以在 "),s("a",C,[a("Github"),e(n)]),a(" 上下载，也可以直接 clone")]),w])}const N=p(i,[["render",x],["__file","6.html.vue"]]),D=JSON.parse('{"path":"/tech/designASimpileCCompiler/6.html","title":"手把手教你构建 C 语言编译器（6）——函数定义","lang":"zh-CN","frontmatter":{"title":"手把手教你构建 C 语言编译器（6）——函数定义","category":["编译原理"],"tag":["c","编译器","解释器"],"description":"转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-6/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（6）- 函数定义 Table of Contents 1. EBNF 表示 2. 解析函数的定义 2.1. 函数参数与汇编代码 2.2. 函数定义的解析 2.3. 解析...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/designASimpileCCompiler/6.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"手把手教你构建 C 语言编译器（6）——函数定义"}],["meta",{"property":"og:description","content":"转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-6/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（6）- 函数定义 Table of Contents 1. EBNF 表示 2. 解析函数的定义 2.1. 函数参数与汇编代码 2.2. 函数定义的解析 2.3. 解析..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"c"}],["meta",{"property":"article:tag","content":"编译器"}],["meta",{"property":"article:tag","content":"解释器"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"手把手教你构建 C 语言编译器（6）——函数定义\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"EBNF 表示","slug":"ebnf-表示","link":"#ebnf-表示","children":[]},{"level":2,"title":"解析函数的定义","slug":"解析函数的定义","link":"#解析函数的定义","children":[{"level":3,"title":"函数参数与汇编代码","slug":"函数参数与汇编代码","link":"#函数参数与汇编代码","children":[]},{"level":3,"title":"函数定义的解析","slug":"函数定义的解析","link":"#函数定义的解析","children":[]},{"level":3,"title":"解析参数","slug":"解析参数","link":"#解析参数","children":[]},{"level":3,"title":"函数体的解析","slug":"函数体的解析","link":"#函数体的解析","children":[]}]},{"level":2,"title":"代码","slug":"代码","link":"#代码","children":[]},{"level":2,"title":"小结","slug":"小结","link":"#小结","children":[]}],"readingTime":{"minutes":12.61,"words":3783},"filePathRelative":"tech/designASimpileCCompiler/6.md","excerpt":"\\n<p>本文转自 <a href=\\"https://lotabout.me/2016/write-a-C-interpreter-6/\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">https://lotabout.me/2016/write-a-C-interpreter-6/</a>，如有侵权，请联系删除。</p>\\n<h1>原文内容</h1>\\n<h1>手把手教你构建 C 语言编译器（6）- 函数定义</h1>\\n<p>Table of Contents</p>\\n<ol>\\n<li><a href=\\"about:blank#ebnf-%E8%A1%A8%E7%A4%BA\\">1. EBNF 表示</a></li>\\n<li><a href=\\"about:blank#%E8%A7%A3%E6%9E%90%E5%87%BD%E6%95%B0%E7%9A%84%E5%AE%9A%E4%B9%89\\">2. 解析函数的定义</a>\\n<ol>\\n<li><a href=\\"about:blank#%E5%87%BD%E6%95%B0%E5%8F%82%E6%95%B0%E4%B8%8E%E6%B1%87%E7%BC%96%E4%BB%A3%E7%A0%81\\">2.1. 函数参数与汇编代码</a></li>\\n<li><a href=\\"about:blank#%E5%87%BD%E6%95%B0%E5%AE%9A%E4%B9%89%E7%9A%84%E8%A7%A3%E6%9E%90\\">2.2. 函数定义的解析</a></li>\\n<li><a href=\\"about:blank#%E8%A7%A3%E6%9E%90%E5%8F%82%E6%95%B0\\">2.3. 解析参数</a></li>\\n<li><a href=\\"about:blank#%E5%87%BD%E6%95%B0%E4%BD%93%E7%9A%84%E8%A7%A3%E6%9E%90\\">2.4. 函数体的解析</a></li>\\n</ol>\\n</li>\\n<li><a href=\\"about:blank#%E4%BB%A3%E7%A0%81\\">3. 代码</a></li>\\n<li><a href=\\"about:blank#%E5%B0%8F%E7%BB%93\\">4. 小结</a></li>\\n</ol>","autoDesc":true}');export{N as comp,D as data};
diff --git a/assets/7.html-DopH3hey.js b/assets/7.html-BzOHeKw-.js
similarity index 99%
rename from assets/7.html-DopH3hey.js
rename to assets/7.html-BzOHeKw-.js
index 7b6d505..cb78404 100644
--- a/assets/7.html-DopH3hey.js
+++ b/assets/7.html-BzOHeKw-.js
@@ -1 +1 @@
-import{_ as l,r,o as p,c as i,b as e,e as a,d as n,f as t}from"./app-B69Gl_S-.js";const o={},c=e("h1",{id:"转载声明",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#转载声明"},[e("span",null,"转载声明")])],-1),b={href:"https://lotabout.me/2016/write-a-C-interpreter-7/",target:"_blank",rel:"noopener noreferrer"},h=t('<h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-7-语句" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-7-语句"><span>手把手教你构建 C 语言编译器（7）- 语句</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#%E8%AF%AD%E5%8F%A5">1. 语句</a><ol><li><a href="about:blank#if-%E8%AF%AD%E5%8F%A5">1.1. IF 语句</a></li><li><a href="about:blank#while-%E8%AF%AD%E5%8F%A5">1.2. While 语句</a></li><li><a href="about:blank#return-%E8%AF%AD%E5%8F%A5">1.3. Return 语句</a></li><li><a href="about:blank#%E5%85%B6%E5%AE%83%E8%AF%AD%E5%8F%A5">1.4. 其它语句</a></li></ol></li><li><a href="about:blank#%E4%BB%A3%E7%A0%81">2. 代码</a></li><li><a href="about:blank#%E5%B0%8F%E7%BB%93">3. 小结</a></li></ol><p>整个编译器还剩下最后两个部分：语句和表达式的解析。它们的内容比较多，主要涉及如何将语句和表达式编译成汇编代码。这章讲解语句的解析，相对于表达式来说它还是较为容易的。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p>',6),d={href:"http://lotabout.me/2015/write-a-C-interpreter-0/",target:"_blank",rel:"noopener noreferrer"},m={href:"http://lotabout.me/2015/write-a-C-interpreter-1/",target:"_blank",rel:"noopener noreferrer"},u={href:"http://lotabout.me/2015/write-a-C-interpreter-2/",target:"_blank",rel:"noopener noreferrer"},f={href:"http://lotabout.me/2015/write-a-C-interpreter-3/",target:"_blank",rel:"noopener noreferrer"},g={href:"http://lotabout.me/2016/write-a-C-interpreter-4/",target:"_blank",rel:"noopener noreferrer"},_={href:"http://lotabout.me/2016/write-a-C-interpreter-5/",target:"_blank",rel:"noopener noreferrer"},k={href:"http://lotabout.me/2016/write-a-C-interpreter-6/",target:"_blank",rel:"noopener noreferrer"},A={href:"http://lotabout.me/2016/write-a-C-interpreter-7/",target:"_blank",rel:"noopener noreferrer"},E={href:"http://lotabout.me/2016/write-a-C-interpreter-8/",target:"_blank",rel:"noopener noreferrer"},C={href:"http://lotabout.me/2016/write-a-C-interpreter-9/",target:"_blank",rel:"noopener noreferrer"},y=t('<h2 id="语句" tabindex="-1"><a class="header-anchor" href="#语句"><span><a href="about:blank#%E8%AF%AD%E5%8F%A5"></a>语句</span></a></h2><p>C 语言区分“语句”（statement）和“表达式”（expression）两个概念。简单地说，可以认为语句就是表达式加上末尾的分号。</p><p>在我们的编译器中共识别 6 种语句：</p><ol><li><code>if (...) &lt;statement&gt; [else &lt;statement&gt;]</code></li><li><code>while (...) &lt;statement&gt;</code></li><li><code>{ &lt;statement&gt; }</code></li><li><code>return xxx;</code></li><li><code>&lt;empty statement&gt;</code>;</li><li><code>expression;</code> (expression end with semicolon)</li></ol><p>它们的语法分析都相对容易，重要的是去理解如何将这些语句编译成汇编代码，下面我们逐一解释。</p><h3 id="if-语句" tabindex="-1"><a class="header-anchor" href="#if-语句"><span><a href="about:blank#if-%E8%AF%AD%E5%8F%A5"></a>IF 语句</span></a></h3><p>IF 语句的作用是跳转，跟据条件表达式决定跳转的位置。我们看看下面的伪代码：</p><table><tbody><tr><td class="code"><pre><span class="line">if (...) &lt;statement&gt; [else &lt;statement&gt;]</span><br><span class="line"></span><br><span class="line">  if (&lt;cond&gt;)                   &lt;cond&gt;</span><br><span class="line">                                JZ a</span><br><span class="line">    &lt;true_statement&gt;   ===&gt;     &lt;true_statement&gt;</span><br><span class="line">  else:                         JMP b</span><br><span class="line">a:                           a:</span><br><span class="line">    &lt;false_statement&gt;           &lt;false_statement&gt;</span><br><span class="line">b:                           b:</span><br></pre></td></tr></tbody></table><p>对应的汇编代码流程为：</p><ol><li>执行条件表达式 <code>&lt;cond&gt;</code>。</li><li>如果条件失败，则跳转到 <code>a</code> 的位置，执行 <code>else</code> 语句。这里 <code>else</code> 语句是可以省略的，此时 <code>a</code> 和 <code>b</code> 都指向 IF 语句后方的代码。</li><li>因为汇编代码是顺序排列的，所以如果执行了 <code>true_statement</code>，为了防止因为顺序排列而执行了 <code>false_statement</code>，所以需要无条件跳转 <code>JMP b</code>。</li></ol><p>对应的 C 代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">if</span> (token == If) {</span><br><span class="line">    match(If);</span><br><span class="line">    match(<span class="string">&#39;(&#39;</span>);</span><br><span class="line">    expression(Assign);  <span class="comment">// parse condition</span></span><br><span class="line">    match(<span class="string">&#39;)&#39;</span>);</span><br><span class="line"></span><br><span class="line">    *++text = JZ;</span><br><span class="line">    b = ++text;</span><br><span class="line"></span><br><span class="line">    statement();         <span class="comment">// parse statement</span></span><br><span class="line">    <span class="keyword">if</span> (token == Else) { <span class="comment">// parse else</span></span><br><span class="line">        match(Else);</span><br><span class="line"></span><br><span class="line">        <span class="comment">// emit code for JMP B</span></span><br><span class="line">        *b = (<span class="type">int</span>)(text + <span class="number">3</span>);</span><br><span class="line">        *++text = JMP;</span><br><span class="line">        b = ++text;</span><br><span class="line"></span><br><span class="line">        statement();</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    *b = (<span class="type">int</span>)(text + <span class="number">1</span>);</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="while-语句" tabindex="-1"><a class="header-anchor" href="#while-语句"><span><a href="about:blank#while-%E8%AF%AD%E5%8F%A5"></a>While 语句</span></a></h3><p>While 语句比 If 语句简单，它对应的汇编代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line">a:                     a:</span><br><span class="line">   while (&lt;cond&gt;)        &lt;cond&gt;</span><br><span class="line">                         JZ b</span><br><span class="line">    &lt;statement&gt;          &lt;statement&gt;</span><br><span class="line">                         JMP a</span><br><span class="line">b:                     b:</span><br></pre></td></tr></tbody></table><p>没有什么值得说明的内容，它的 C 代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == While) {</span><br><span class="line">    match(While);</span><br><span class="line"></span><br><span class="line">    a = text + <span class="number">1</span>;</span><br><span class="line"></span><br><span class="line">    match(<span class="string">&#39;(&#39;</span>);</span><br><span class="line">    expression(Assign);</span><br><span class="line">    match(<span class="string">&#39;)&#39;</span>);</span><br><span class="line"></span><br><span class="line">    *++text = JZ;</span><br><span class="line">    b = ++text;</span><br><span class="line"></span><br><span class="line">    statement();</span><br><span class="line"></span><br><span class="line">    *++text = JMP;</span><br><span class="line">    *++text = (<span class="type">int</span>)a;</span><br><span class="line">    *b = (<span class="type">int</span>)(text + <span class="number">1</span>);</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="return-语句" tabindex="-1"><a class="header-anchor" href="#return-语句"><span><a href="about:blank#return-%E8%AF%AD%E5%8F%A5"></a>Return 语句</span></a></h3><p>Return 唯一特殊的地方是：一旦遇到了 Return 语句，则意味着函数要退出了，所以需要生成汇编代码 <code>LEV</code> 来表示退出。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Return) {</span><br><span class="line">    <span class="comment">// return [expression];</span></span><br><span class="line">    match(Return);</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (token != <span class="string">&#39;;&#39;</span>) {</span><br><span class="line">        expression(Assign);</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    match(<span class="string">&#39;;&#39;</span>);</span><br><span class="line"></span><br><span class="line">    <span class="comment">// emit code for return</span></span><br><span class="line">    *++text = LEV;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="其它语句" tabindex="-1"><a class="header-anchor" href="#其它语句"><span><a href="about:blank#%E5%85%B6%E5%AE%83%E8%AF%AD%E5%8F%A5"></a>其它语句</span></a></h3><p>其它语句并不直接生成汇编代码，所以不多做说明，代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;{&#39;</span>) {</span><br><span class="line">    <span class="comment">// { &lt;statement&gt; ... }</span></span><br><span class="line">    match(<span class="string">&#39;{&#39;</span>);</span><br><span class="line"></span><br><span class="line">    <span class="keyword">while</span> (token != <span class="string">&#39;}&#39;</span>) {</span><br><span class="line">        statement();</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    match(<span class="string">&#39;}&#39;</span>);</span><br><span class="line">}</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;;&#39;</span>) {</span><br><span class="line">    <span class="comment">// empty statement</span></span><br><span class="line">    match(<span class="string">&#39;;&#39;</span>);</span><br><span class="line">}</span><br><span class="line"><span class="keyword">else</span> {</span><br><span class="line">    <span class="comment">// a = b; or function_call();</span></span><br><span class="line">    expression(Assign);</span><br><span class="line">    match(<span class="string">&#39;;&#39;</span>);</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h2 id="代码" tabindex="-1"><a class="header-anchor" href="#代码"><span><a href="about:blank#%E4%BB%A3%E7%A0%81"></a>代码</span></a></h2>',24),w={href:"https://github.com/lotabout/write-a-C-interpreter/tree/step-5",target:"_blank",rel:"noopener noreferrer"},x=t('<table><tbody><tr><td class="code"><pre><span class="line">git clone -b step-5 https://github.com/lotabout/write-a-C-interpreter</span><br></pre></td></tr></tbody></table><p>本章的代码依旧无法运行，还剩最后一部分没有完成：<code>expression</code>。</p><h2 id="小结" tabindex="-1"><a class="header-anchor" href="#小结"><span><a href="about:blank#%E5%B0%8F%E7%BB%93"></a>小结</span></a></h2><p>本章讲解了如何将语句编译成汇编代码，内容相对容易一些，关键就是去理解汇编代码的执行原理。</p><p>同时值得一提的是，编译器的语法分析部分其实是很简单的，而真正的难点是如何在语法分析时收集足够多的信息，最终把源代码转换成目标代码（汇编）。我认为这也是初学者实现编译器的一大难点，往往比词法分析/语法分析更困难。</p><p>所以建议如果没有学过汇编，可以学习学习，它本身不难，但对理解计算机的原理有很大帮助。</p>',6);function F(B,D){const s=r("ExternalLinkIcon");return p(),i("div",null,[c,e("p",null,[a("本文转自 "),e("a",b,[a("https://lotabout.me/2016/write-a-C-interpreter-7/"),n(s)]),a("，如有侵权，请联系删除。")]),h,e("ol",null,[e("li",null,[e("a",d,[a("手把手教你构建 C 语言编译器（0）——前言"),n(s)])]),e("li",null,[e("a",m,[a("手把手教你构建 C 语言编译器（1）——设计"),n(s)])]),e("li",null,[e("a",u,[a("手把手教你构建 C 语言编译器（2）——虚拟机"),n(s)])]),e("li",null,[e("a",f,[a("手把手教你构建 C 语言编译器（3）——词法分析器"),n(s)])]),e("li",null,[e("a",g,[a("手把手教你构建 C 语言编译器（4）——递归下降"),n(s)])]),e("li",null,[e("a",_,[a("手把手教你构建 C 语言编译器（5）——变量定义"),n(s)])]),e("li",null,[e("a",k,[a("手把手教你构建 C 语言编译器（6）——函数定义"),n(s)])]),e("li",null,[e("a",A,[a("手把手教你构建 C 语言编译器（7）——语句"),n(s)])]),e("li",null,[e("a",E,[a("手把手教你构建 C 语言编译器（8）——表达式"),n(s)])]),e("li",null,[e("a",C,[a("手把手教你构建 C 语言编译器（9）——总结"),n(s)])])]),y,e("p",null,[a("本章的代码可以在 "),e("a",w,[a("Github"),n(s)]),a(" 上下载，也可以直接 clone")]),x])}const J=l(o,[["render",F],["__file","7.html.vue"]]),v=JSON.parse('{"path":"/tech/designASimpileCCompiler/7.html","title":"手把手教你构建 C 语言编译器（7）——语句","lang":"zh-CN","frontmatter":{"title":"手把手教你构建 C 语言编译器（7）——语句","category":["编译原理"],"tag":["c","编译器","解释器"],"description":"转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-7/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（7）- 语句 Table of Contents 1. 语句 1.1. IF 语句 1.2. While 语句 1.3. Return 语句 1.4. 其它语句 2. ...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/designASimpileCCompiler/7.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"手把手教你构建 C 语言编译器（7）——语句"}],["meta",{"property":"og:description","content":"转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-7/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（7）- 语句 Table of Contents 1. 语句 1.1. IF 语句 1.2. While 语句 1.3. Return 语句 1.4. 其它语句 2. ..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"c"}],["meta",{"property":"article:tag","content":"编译器"}],["meta",{"property":"article:tag","content":"解释器"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"手把手教你构建 C 语言编译器（7）——语句\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"语句","slug":"语句","link":"#语句","children":[{"level":3,"title":"IF 语句","slug":"if-语句","link":"#if-语句","children":[]},{"level":3,"title":"While 语句","slug":"while-语句","link":"#while-语句","children":[]},{"level":3,"title":"Return 语句","slug":"return-语句","link":"#return-语句","children":[]},{"level":3,"title":"其它语句","slug":"其它语句","link":"#其它语句","children":[]}]},{"level":2,"title":"代码","slug":"代码","link":"#代码","children":[]},{"level":2,"title":"小结","slug":"小结","link":"#小结","children":[]}],"readingTime":{"minutes":6.99,"words":2097},"filePathRelative":"tech/designASimpileCCompiler/7.md","excerpt":"\\n<p>本文转自 <a href=\\"https://lotabout.me/2016/write-a-C-interpreter-7/\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">https://lotabout.me/2016/write-a-C-interpreter-7/</a>，如有侵权，请联系删除。</p>\\n<h1>原文内容</h1>\\n<h1>手把手教你构建 C 语言编译器（7）- 语句</h1>\\n<p>Table of Contents</p>\\n<ol>\\n<li><a href=\\"about:blank#%E8%AF%AD%E5%8F%A5\\">1. 语句</a>\\n<ol>\\n<li><a href=\\"about:blank#if-%E8%AF%AD%E5%8F%A5\\">1.1. IF 语句</a></li>\\n<li><a href=\\"about:blank#while-%E8%AF%AD%E5%8F%A5\\">1.2. While 语句</a></li>\\n<li><a href=\\"about:blank#return-%E8%AF%AD%E5%8F%A5\\">1.3. Return 语句</a></li>\\n<li><a href=\\"about:blank#%E5%85%B6%E5%AE%83%E8%AF%AD%E5%8F%A5\\">1.4. 其它语句</a></li>\\n</ol>\\n</li>\\n<li><a href=\\"about:blank#%E4%BB%A3%E7%A0%81\\">2. 代码</a></li>\\n<li><a href=\\"about:blank#%E5%B0%8F%E7%BB%93\\">3. 小结</a></li>\\n</ol>","autoDesc":true}');export{J as comp,v as data};
+import{_ as l,r,o as p,c as i,b as e,e as a,d as n,f as t}from"./app-B4LGNJZ0.js";const o={},c=e("h1",{id:"转载声明",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#转载声明"},[e("span",null,"转载声明")])],-1),b={href:"https://lotabout.me/2016/write-a-C-interpreter-7/",target:"_blank",rel:"noopener noreferrer"},h=t('<h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-7-语句" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-7-语句"><span>手把手教你构建 C 语言编译器（7）- 语句</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#%E8%AF%AD%E5%8F%A5">1. 语句</a><ol><li><a href="about:blank#if-%E8%AF%AD%E5%8F%A5">1.1. IF 语句</a></li><li><a href="about:blank#while-%E8%AF%AD%E5%8F%A5">1.2. While 语句</a></li><li><a href="about:blank#return-%E8%AF%AD%E5%8F%A5">1.3. Return 语句</a></li><li><a href="about:blank#%E5%85%B6%E5%AE%83%E8%AF%AD%E5%8F%A5">1.4. 其它语句</a></li></ol></li><li><a href="about:blank#%E4%BB%A3%E7%A0%81">2. 代码</a></li><li><a href="about:blank#%E5%B0%8F%E7%BB%93">3. 小结</a></li></ol><p>整个编译器还剩下最后两个部分：语句和表达式的解析。它们的内容比较多，主要涉及如何将语句和表达式编译成汇编代码。这章讲解语句的解析，相对于表达式来说它还是较为容易的。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p>',6),d={href:"http://lotabout.me/2015/write-a-C-interpreter-0/",target:"_blank",rel:"noopener noreferrer"},m={href:"http://lotabout.me/2015/write-a-C-interpreter-1/",target:"_blank",rel:"noopener noreferrer"},u={href:"http://lotabout.me/2015/write-a-C-interpreter-2/",target:"_blank",rel:"noopener noreferrer"},f={href:"http://lotabout.me/2015/write-a-C-interpreter-3/",target:"_blank",rel:"noopener noreferrer"},g={href:"http://lotabout.me/2016/write-a-C-interpreter-4/",target:"_blank",rel:"noopener noreferrer"},_={href:"http://lotabout.me/2016/write-a-C-interpreter-5/",target:"_blank",rel:"noopener noreferrer"},k={href:"http://lotabout.me/2016/write-a-C-interpreter-6/",target:"_blank",rel:"noopener noreferrer"},A={href:"http://lotabout.me/2016/write-a-C-interpreter-7/",target:"_blank",rel:"noopener noreferrer"},E={href:"http://lotabout.me/2016/write-a-C-interpreter-8/",target:"_blank",rel:"noopener noreferrer"},C={href:"http://lotabout.me/2016/write-a-C-interpreter-9/",target:"_blank",rel:"noopener noreferrer"},y=t('<h2 id="语句" tabindex="-1"><a class="header-anchor" href="#语句"><span><a href="about:blank#%E8%AF%AD%E5%8F%A5"></a>语句</span></a></h2><p>C 语言区分“语句”（statement）和“表达式”（expression）两个概念。简单地说，可以认为语句就是表达式加上末尾的分号。</p><p>在我们的编译器中共识别 6 种语句：</p><ol><li><code>if (...) &lt;statement&gt; [else &lt;statement&gt;]</code></li><li><code>while (...) &lt;statement&gt;</code></li><li><code>{ &lt;statement&gt; }</code></li><li><code>return xxx;</code></li><li><code>&lt;empty statement&gt;</code>;</li><li><code>expression;</code> (expression end with semicolon)</li></ol><p>它们的语法分析都相对容易，重要的是去理解如何将这些语句编译成汇编代码，下面我们逐一解释。</p><h3 id="if-语句" tabindex="-1"><a class="header-anchor" href="#if-语句"><span><a href="about:blank#if-%E8%AF%AD%E5%8F%A5"></a>IF 语句</span></a></h3><p>IF 语句的作用是跳转，跟据条件表达式决定跳转的位置。我们看看下面的伪代码：</p><table><tbody><tr><td class="code"><pre><span class="line">if (...) &lt;statement&gt; [else &lt;statement&gt;]</span><br><span class="line"></span><br><span class="line">  if (&lt;cond&gt;)                   &lt;cond&gt;</span><br><span class="line">                                JZ a</span><br><span class="line">    &lt;true_statement&gt;   ===&gt;     &lt;true_statement&gt;</span><br><span class="line">  else:                         JMP b</span><br><span class="line">a:                           a:</span><br><span class="line">    &lt;false_statement&gt;           &lt;false_statement&gt;</span><br><span class="line">b:                           b:</span><br></pre></td></tr></tbody></table><p>对应的汇编代码流程为：</p><ol><li>执行条件表达式 <code>&lt;cond&gt;</code>。</li><li>如果条件失败，则跳转到 <code>a</code> 的位置，执行 <code>else</code> 语句。这里 <code>else</code> 语句是可以省略的，此时 <code>a</code> 和 <code>b</code> 都指向 IF 语句后方的代码。</li><li>因为汇编代码是顺序排列的，所以如果执行了 <code>true_statement</code>，为了防止因为顺序排列而执行了 <code>false_statement</code>，所以需要无条件跳转 <code>JMP b</code>。</li></ol><p>对应的 C 代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">if</span> (token == If) {</span><br><span class="line">    match(If);</span><br><span class="line">    match(<span class="string">&#39;(&#39;</span>);</span><br><span class="line">    expression(Assign);  <span class="comment">// parse condition</span></span><br><span class="line">    match(<span class="string">&#39;)&#39;</span>);</span><br><span class="line"></span><br><span class="line">    *++text = JZ;</span><br><span class="line">    b = ++text;</span><br><span class="line"></span><br><span class="line">    statement();         <span class="comment">// parse statement</span></span><br><span class="line">    <span class="keyword">if</span> (token == Else) { <span class="comment">// parse else</span></span><br><span class="line">        match(Else);</span><br><span class="line"></span><br><span class="line">        <span class="comment">// emit code for JMP B</span></span><br><span class="line">        *b = (<span class="type">int</span>)(text + <span class="number">3</span>);</span><br><span class="line">        *++text = JMP;</span><br><span class="line">        b = ++text;</span><br><span class="line"></span><br><span class="line">        statement();</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    *b = (<span class="type">int</span>)(text + <span class="number">1</span>);</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="while-语句" tabindex="-1"><a class="header-anchor" href="#while-语句"><span><a href="about:blank#while-%E8%AF%AD%E5%8F%A5"></a>While 语句</span></a></h3><p>While 语句比 If 语句简单，它对应的汇编代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line">a:                     a:</span><br><span class="line">   while (&lt;cond&gt;)        &lt;cond&gt;</span><br><span class="line">                         JZ b</span><br><span class="line">    &lt;statement&gt;          &lt;statement&gt;</span><br><span class="line">                         JMP a</span><br><span class="line">b:                     b:</span><br></pre></td></tr></tbody></table><p>没有什么值得说明的内容，它的 C 代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == While) {</span><br><span class="line">    match(While);</span><br><span class="line"></span><br><span class="line">    a = text + <span class="number">1</span>;</span><br><span class="line"></span><br><span class="line">    match(<span class="string">&#39;(&#39;</span>);</span><br><span class="line">    expression(Assign);</span><br><span class="line">    match(<span class="string">&#39;)&#39;</span>);</span><br><span class="line"></span><br><span class="line">    *++text = JZ;</span><br><span class="line">    b = ++text;</span><br><span class="line"></span><br><span class="line">    statement();</span><br><span class="line"></span><br><span class="line">    *++text = JMP;</span><br><span class="line">    *++text = (<span class="type">int</span>)a;</span><br><span class="line">    *b = (<span class="type">int</span>)(text + <span class="number">1</span>);</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="return-语句" tabindex="-1"><a class="header-anchor" href="#return-语句"><span><a href="about:blank#return-%E8%AF%AD%E5%8F%A5"></a>Return 语句</span></a></h3><p>Return 唯一特殊的地方是：一旦遇到了 Return 语句，则意味着函数要退出了，所以需要生成汇编代码 <code>LEV</code> 来表示退出。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Return) {</span><br><span class="line">    <span class="comment">// return [expression];</span></span><br><span class="line">    match(Return);</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (token != <span class="string">&#39;;&#39;</span>) {</span><br><span class="line">        expression(Assign);</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    match(<span class="string">&#39;;&#39;</span>);</span><br><span class="line"></span><br><span class="line">    <span class="comment">// emit code for return</span></span><br><span class="line">    *++text = LEV;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="其它语句" tabindex="-1"><a class="header-anchor" href="#其它语句"><span><a href="about:blank#%E5%85%B6%E5%AE%83%E8%AF%AD%E5%8F%A5"></a>其它语句</span></a></h3><p>其它语句并不直接生成汇编代码，所以不多做说明，代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;{&#39;</span>) {</span><br><span class="line">    <span class="comment">// { &lt;statement&gt; ... }</span></span><br><span class="line">    match(<span class="string">&#39;{&#39;</span>);</span><br><span class="line"></span><br><span class="line">    <span class="keyword">while</span> (token != <span class="string">&#39;}&#39;</span>) {</span><br><span class="line">        statement();</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    match(<span class="string">&#39;}&#39;</span>);</span><br><span class="line">}</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;;&#39;</span>) {</span><br><span class="line">    <span class="comment">// empty statement</span></span><br><span class="line">    match(<span class="string">&#39;;&#39;</span>);</span><br><span class="line">}</span><br><span class="line"><span class="keyword">else</span> {</span><br><span class="line">    <span class="comment">// a = b; or function_call();</span></span><br><span class="line">    expression(Assign);</span><br><span class="line">    match(<span class="string">&#39;;&#39;</span>);</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h2 id="代码" tabindex="-1"><a class="header-anchor" href="#代码"><span><a href="about:blank#%E4%BB%A3%E7%A0%81"></a>代码</span></a></h2>',24),w={href:"https://github.com/lotabout/write-a-C-interpreter/tree/step-5",target:"_blank",rel:"noopener noreferrer"},x=t('<table><tbody><tr><td class="code"><pre><span class="line">git clone -b step-5 https://github.com/lotabout/write-a-C-interpreter</span><br></pre></td></tr></tbody></table><p>本章的代码依旧无法运行，还剩最后一部分没有完成：<code>expression</code>。</p><h2 id="小结" tabindex="-1"><a class="header-anchor" href="#小结"><span><a href="about:blank#%E5%B0%8F%E7%BB%93"></a>小结</span></a></h2><p>本章讲解了如何将语句编译成汇编代码，内容相对容易一些，关键就是去理解汇编代码的执行原理。</p><p>同时值得一提的是，编译器的语法分析部分其实是很简单的，而真正的难点是如何在语法分析时收集足够多的信息，最终把源代码转换成目标代码（汇编）。我认为这也是初学者实现编译器的一大难点，往往比词法分析/语法分析更困难。</p><p>所以建议如果没有学过汇编，可以学习学习，它本身不难，但对理解计算机的原理有很大帮助。</p>',6);function F(B,D){const s=r("ExternalLinkIcon");return p(),i("div",null,[c,e("p",null,[a("本文转自 "),e("a",b,[a("https://lotabout.me/2016/write-a-C-interpreter-7/"),n(s)]),a("，如有侵权，请联系删除。")]),h,e("ol",null,[e("li",null,[e("a",d,[a("手把手教你构建 C 语言编译器（0）——前言"),n(s)])]),e("li",null,[e("a",m,[a("手把手教你构建 C 语言编译器（1）——设计"),n(s)])]),e("li",null,[e("a",u,[a("手把手教你构建 C 语言编译器（2）——虚拟机"),n(s)])]),e("li",null,[e("a",f,[a("手把手教你构建 C 语言编译器（3）——词法分析器"),n(s)])]),e("li",null,[e("a",g,[a("手把手教你构建 C 语言编译器（4）——递归下降"),n(s)])]),e("li",null,[e("a",_,[a("手把手教你构建 C 语言编译器（5）——变量定义"),n(s)])]),e("li",null,[e("a",k,[a("手把手教你构建 C 语言编译器（6）——函数定义"),n(s)])]),e("li",null,[e("a",A,[a("手把手教你构建 C 语言编译器（7）——语句"),n(s)])]),e("li",null,[e("a",E,[a("手把手教你构建 C 语言编译器（8）——表达式"),n(s)])]),e("li",null,[e("a",C,[a("手把手教你构建 C 语言编译器（9）——总结"),n(s)])])]),y,e("p",null,[a("本章的代码可以在 "),e("a",w,[a("Github"),n(s)]),a(" 上下载，也可以直接 clone")]),x])}const J=l(o,[["render",F],["__file","7.html.vue"]]),v=JSON.parse('{"path":"/tech/designASimpileCCompiler/7.html","title":"手把手教你构建 C 语言编译器（7）——语句","lang":"zh-CN","frontmatter":{"title":"手把手教你构建 C 语言编译器（7）——语句","category":["编译原理"],"tag":["c","编译器","解释器"],"description":"转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-7/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（7）- 语句 Table of Contents 1. 语句 1.1. IF 语句 1.2. While 语句 1.3. Return 语句 1.4. 其它语句 2. ...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/designASimpileCCompiler/7.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"手把手教你构建 C 语言编译器（7）——语句"}],["meta",{"property":"og:description","content":"转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-7/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（7）- 语句 Table of Contents 1. 语句 1.1. IF 语句 1.2. While 语句 1.3. Return 语句 1.4. 其它语句 2. ..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"c"}],["meta",{"property":"article:tag","content":"编译器"}],["meta",{"property":"article:tag","content":"解释器"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"手把手教你构建 C 语言编译器（7）——语句\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"语句","slug":"语句","link":"#语句","children":[{"level":3,"title":"IF 语句","slug":"if-语句","link":"#if-语句","children":[]},{"level":3,"title":"While 语句","slug":"while-语句","link":"#while-语句","children":[]},{"level":3,"title":"Return 语句","slug":"return-语句","link":"#return-语句","children":[]},{"level":3,"title":"其它语句","slug":"其它语句","link":"#其它语句","children":[]}]},{"level":2,"title":"代码","slug":"代码","link":"#代码","children":[]},{"level":2,"title":"小结","slug":"小结","link":"#小结","children":[]}],"readingTime":{"minutes":6.99,"words":2097},"filePathRelative":"tech/designASimpileCCompiler/7.md","excerpt":"\\n<p>本文转自 <a href=\\"https://lotabout.me/2016/write-a-C-interpreter-7/\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">https://lotabout.me/2016/write-a-C-interpreter-7/</a>，如有侵权，请联系删除。</p>\\n<h1>原文内容</h1>\\n<h1>手把手教你构建 C 语言编译器（7）- 语句</h1>\\n<p>Table of Contents</p>\\n<ol>\\n<li><a href=\\"about:blank#%E8%AF%AD%E5%8F%A5\\">1. 语句</a>\\n<ol>\\n<li><a href=\\"about:blank#if-%E8%AF%AD%E5%8F%A5\\">1.1. IF 语句</a></li>\\n<li><a href=\\"about:blank#while-%E8%AF%AD%E5%8F%A5\\">1.2. While 语句</a></li>\\n<li><a href=\\"about:blank#return-%E8%AF%AD%E5%8F%A5\\">1.3. Return 语句</a></li>\\n<li><a href=\\"about:blank#%E5%85%B6%E5%AE%83%E8%AF%AD%E5%8F%A5\\">1.4. 其它语句</a></li>\\n</ol>\\n</li>\\n<li><a href=\\"about:blank#%E4%BB%A3%E7%A0%81\\">2. 代码</a></li>\\n<li><a href=\\"about:blank#%E5%B0%8F%E7%BB%93\\">3. 小结</a></li>\\n</ol>","autoDesc":true}');export{J as comp,v as data};
diff --git a/assets/8.html-D1TnfZgI.js b/assets/8.html-C-sA1tiy.js
similarity index 99%
rename from assets/8.html-D1TnfZgI.js
rename to assets/8.html-C-sA1tiy.js
index e9ef834..3f906ea 100644
--- a/assets/8.html-D1TnfZgI.js
+++ b/assets/8.html-C-sA1tiy.js
@@ -1 +1 @@
-import{_ as l,r as t,o as c,c as r,b as s,e as a,d as e,f as p}from"./app-B69Gl_S-.js";const i={},o=s("h1",{id:"转载声明",tabindex:"-1"},[s("a",{class:"header-anchor",href:"#转载声明"},[s("span",null,"转载声明")])],-1),b={href:"https://blog.csdn.net/xzp740813/article/details/142961332?spm=1001.2014.3001.5501",target:"_blank",rel:"noopener noreferrer"},d=p('<h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-8-表达式" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-8-表达式"><span>手把手教你构建 C 语言编译器（8）- 表达式</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#%E8%BF%90%E7%AE%97%E7%AC%A6%E7%9A%84%E4%BC%98%E5%85%88%E7%BA%A7">1. 运算符的优先级</a></li><li><a href="about:blank#%E4%B8%80%E5%85%83%E8%BF%90%E7%AE%97%E7%AC%A6">2. 一元运算符</a><ol><li><a href="about:blank#%E5%B8%B8%E9%87%8F">2.1. 常量</a></li><li><a href="about:blank#sizeof">2.2. sizeof</a></li><li><a href="about:blank#%E5%8F%98%E9%87%8F%E4%B8%8E%E5%87%BD%E6%95%B0%E8%B0%83%E7%94%A8">2.3. 变量与函数调用</a></li><li><a href="about:blank#%E5%BC%BA%E5%88%B6%E8%BD%AC%E6%8D%A2">2.4. 强制转换</a></li><li><a href="about:blank#%E6%8C%87%E9%92%88%E5%8F%96%E5%80%BC">2.5. 指针取值</a></li><li><a href="about:blank#%E5%8F%96%E5%9D%80%E6%93%8D%E4%BD%9C">2.6. 取址操作</a></li><li><a href="about:blank#%E9%80%BB%E8%BE%91%E5%8F%96%E5%8F%8D">2.7. 逻辑取反</a></li><li><a href="about:blank#%E6%8C%89%E4%BD%8D%E5%8F%96%E5%8F%8D">2.8. 按位取反</a></li><li><a href="about:blank#%E6%AD%A3%E8%B4%9F%E5%8F%B7">2.9. 正负号</a></li><li><a href="about:blank#%E8%87%AA%E5%A2%9E%E8%87%AA%E5%87%8F">2.10. 自增自减</a></li></ol></li><li><a href="about:blank#%E4%BA%8C%E5%85%83%E8%BF%90%E7%AE%97%E7%AC%A6">3. 二元运算符</a><ol><li><a href="about:blank#%E8%B5%8B%E5%80%BC%E6%93%8D%E4%BD%9C">3.1. 赋值操作</a></li><li><a href="about:blank#%E4%B8%89%E7%9B%AE%E8%BF%90%E7%AE%97%E7%AC%A6">3.2. 三目运算符</a></li><li><a href="about:blank#%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6">3.3. 逻辑运算符</a></li><li><a href="about:blank#%E6%95%B0%E5%AD%A6%E8%BF%90%E7%AE%97%E7%AC%A6">3.4. 数学运算符</a></li><li><a href="about:blank#%E8%87%AA%E5%A2%9E%E8%87%AA%E5%87%8F-v2">3.5. 自增自减</a></li><li><a href="about:blank#%E6%95%B0%E7%BB%84%E5%8F%96%E5%80%BC%E6%93%8D%E4%BD%9C">3.6. 数组取值操作</a></li></ol></li><li><a href="about:blank#%E4%BB%A3%E7%A0%81">4. 代码</a></li><li><a href="about:blank#%E5%B0%8F%E7%BB%93">5. 小结</a></li></ol><p>这是整个编译器的最后一部分，解析表达式。什么是表达式？表达式是将各种语言要素的一个组合，用来求值。例如：函数调用、变量赋值、运算符运算等等。</p><p>表达式的解析难点有二：一是运算符的优先级问题，二是如何将表达式编译成目标代码。我们就来逐一说明。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p>',7),h={href:"http://lotabout.me/2015/write-a-C-interpreter-0/",target:"_blank",rel:"noopener noreferrer"},m={href:"http://lotabout.me/2015/write-a-C-interpreter-1/",target:"_blank",rel:"noopener noreferrer"},y={href:"http://lotabout.me/2015/write-a-C-interpreter-2/",target:"_blank",rel:"noopener noreferrer"},x={href:"http://lotabout.me/2015/write-a-C-interpreter-3/",target:"_blank",rel:"noopener noreferrer"},u={href:"http://lotabout.me/2016/write-a-C-interpreter-4/",target:"_blank",rel:"noopener noreferrer"},f={href:"http://lotabout.me/2016/write-a-C-interpreter-5/",target:"_blank",rel:"noopener noreferrer"},k={href:"http://lotabout.me/2016/write-a-C-interpreter-6/",target:"_blank",rel:"noopener noreferrer"},E={href:"http://lotabout.me/2016/write-a-C-interpreter-7/",target:"_blank",rel:"noopener noreferrer"},g={href:"http://lotabout.me/2016/write-a-C-interpreter-8/",target:"_blank",rel:"noopener noreferrer"},C={href:"http://lotabout.me/2016/write-a-C-interpreter-9/",target:"_blank",rel:"noopener noreferrer"},_=p('<h2 id="运算符的优先级" tabindex="-1"><a class="header-anchor" href="#运算符的优先级"><span><a href="about:blank#%E8%BF%90%E7%AE%97%E7%AC%A6%E7%9A%84%E4%BC%98%E5%85%88%E7%BA%A7"></a>运算符的优先级</span></a></h2><p>运算符的优先级决定了表达式的运算顺序，如在普通的四则运算中，乘法 <code>*</code> 优先级高于加法 <code>+</code>，这就意味着表达式 <code>2 + 3 * 4</code> 的实际运行顺序是 <code>2 + (3 * 4)</code> 而不是 <code>(2 + 3) * 4</code>。</p>',2),A={href:"http://en.cppreference.com/w/c/language/operator_precedence",target:"_blank",rel:"noopener noreferrer"},w=p('<p>传统的编程书籍会用“逆波兰式”实现四则运算来讲解优先级问题。实际上，优先级关心的就是哪个运算符先计算，哪个运算符后计算（毕竟叫做“优先级”嘛）。而这就意味着我们需要决定先为哪个运算符生成目标代码（汇编），因为汇编代码是顺序排列的，我们必须先计算优先级高的运算符。</p><p>那么如何确定运算符的优先级呢？答曰：栈（递归调用的实质也是栈的处理）。</p><p>举一个例子：<code>2 + 3 - 4 * 5</code>，它的运算顺序是这样的：</p><ol><li>将 <code>2</code> 入栈</li><li>遇到运算符 <code>+</code>，入栈，此时我们期待的是<code>+</code>的另一个参数</li><li>遇到数字 <code>3</code>，原则上我们需要立即计算 <code>2+3</code>的值，但我们不确定数字 <code>3</code> 是否属于优先级更高的运算符，所以先将它入栈。</li><li>遇到运算符 <code>-</code>，它的优先级和 <code>+</code> 相同，此时判断参数 <code>3</code> 属于这前的 <code>+</code>。将运算符 <code>+</code> 出栈，并将之前的 <code>2</code> 和 <code>3</code> 出栈，计算 <code>2+3</code> 的结果，得到 <code>5</code> 入栈。同时将运算符 <code>-</code> 入栈。</li><li>遇到数字<code>4</code>，同样不能确定是否能立即计算，入栈</li><li>遇到运算符 <code>*</code> 优先级大于 <code>-</code>，入栈</li><li>遇到数字<code>5</code>，依旧不能确定是否立即计算，入栈</li><li>表达式结束，运算符出栈，为 <code>*</code>，将参数出栈，计算 <code>4*5</code> 得到结果 <code>20</code> 入栈。</li><li>运算符出栈，为 <code>-</code>，将参数出栈，计算 <code>5-20</code>，得到 <code>-15</code> 入栈。</li><li>此时运算符栈为空，因此得到结果 <code>-15</code>。</li></ol><table><tbody><tr><td class="code"><pre><span class="line">// after step 1, 2</span><br><span class="line">|      |</span><br><span class="line">+------+</span><br><span class="line">| 3    |   |      |</span><br><span class="line">+------+   +------+</span><br><span class="line">| 2    |   | +    |</span><br><span class="line">+------+   +------+</span><br><span class="line"></span><br><span class="line">// after step 4</span><br><span class="line">|      |   |      |</span><br><span class="line">+------+   +------+</span><br><span class="line">| 5    |   | -    |</span><br><span class="line">+------+   +------+</span><br><span class="line"></span><br><span class="line">// after step 7</span><br><span class="line">|      |</span><br><span class="line">+------+</span><br><span class="line">| 5    |</span><br><span class="line">+------+   +------+</span><br><span class="line">| 4    |   | *    |</span><br><span class="line">+------+   +------+</span><br><span class="line">| 5    |   | -    |</span><br><span class="line">+------+   +------+</span><br></pre></td></tr></tbody></table><p>综上，在计算一个运算符‘x’之前，必须先查看它的右方，找出并计算所有优先级大于‘x’的运算符，之后再计算运算符‘x’。</p><p>最后注意的是优先通常只与多元运算符相关，单元运算符往往没有这个问题（因为只有一个参数）。也可以认为“优先级”的实质就是两个运算符在抢参数。</p><h2 id="一元运算符" tabindex="-1"><a class="header-anchor" href="#一元运算符"><span><a href="about:blank#%E4%B8%80%E5%85%83%E8%BF%90%E7%AE%97%E7%AC%A6"></a>一元运算符</span></a></h2><p>上节中说到了运算符的优先级，也提到了优先级一般只与多元运算符有关，这也意味着一元运算符的优先级总是高于多元运算符。因为我们需要先对它们进行解析。</p><p>当然，这部分也将同时解析参数本身（如变量、数字、字符串等等）。</p><p>关于表达式的解析，与语法分析相关的部分就是上文所说的优先级问题了，而剩下的较难较烦的部分是与目标代码的生成有关的。因此对于需要讲解的运算符，我们主要从它的目标代码入手。</p><h3 id="常量" tabindex="-1"><a class="header-anchor" href="#常量"><span><a href="about:blank#%E5%B8%B8%E9%87%8F"></a>常量</span></a></h3><p>首先是数字，用 <code>IMM</code> 指令将它加载到 <code>AX</code> 中即可：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">if</span> (token == Num) {</span><br><span class="line">    match(Num);</span><br><span class="line"></span><br><span class="line">    <span class="comment">// emit code</span></span><br><span class="line">    *++text = IMM;</span><br><span class="line">    *++text = token_val;</span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br><span class="line"></span><br></pre></td></tr></tbody></table><p>接着是字符串常量。它比较特殊的一点是 C 语言的字符串常量支持如下风格：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">char</span> *p;</span><br><span class="line">p = <span class="string">&quot;first line&quot;</span></span><br><span class="line">    <span class="string">&quot;second line&quot;</span>;</span><br></pre></td></tr></tbody></table><p>即跨行的字符串拼接，它相当于：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">char</span> *p;</span><br><span class="line">p = <span class="string">&quot;first linesecond line&quot;</span>;</span><br></pre></td></tr></tbody></table><p>所以解析的时候要注意这一点：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;&quot;&#39;</span>) {</span><br><span class="line">    <span class="comment">// emit code</span></span><br><span class="line">    *++text = IMM;</span><br><span class="line">    *++text = token_val;</span><br><span class="line"></span><br><span class="line">    match(<span class="string">&#39;&quot;&#39;</span>);</span><br><span class="line">    <span class="comment">// store the rest strings</span></span><br><span class="line">    <span class="keyword">while</span> (token == <span class="string">&#39;&quot;&#39;</span>) {</span><br><span class="line">        match(<span class="string">&#39;&quot;&#39;</span>);</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="comment">// append the end of string character &#39;\\0&#39;, all the data are default</span></span><br><span class="line">    <span class="comment">// to 0, so just move data one position forward.</span></span><br><span class="line">    data = (<span class="type">char</span> *)(((<span class="type">int</span>)data + <span class="keyword">sizeof</span>(<span class="type">int</span>)) &amp; (-<span class="keyword">sizeof</span>(<span class="type">int</span>)));</span><br><span class="line">    expr_type = PTR;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="sizeof" tabindex="-1"><a class="header-anchor" href="#sizeof"><span><a href="about:blank#sizeof"></a>sizeof</span></a></h3><p><code>sizeof</code> 是一个一元运算符，我们需要知道后面参数的类型，类型的解析在前面的文章中我们已经很熟悉了。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Sizeof) {</span><br><span class="line">    <span class="comment">// sizeof is actually an unary operator</span></span><br><span class="line">    <span class="comment">// now only `sizeof(int)`, `sizeof(char)` and `sizeof(*...)` are</span></span><br><span class="line">    <span class="comment">// supported.</span></span><br><span class="line">    match(Sizeof);</span><br><span class="line">    match(<span class="string">&#39;(&#39;</span>);</span><br><span class="line">    expr_type = INT;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (token == Int) {</span><br><span class="line">        match(Int);</span><br><span class="line">    } <span class="keyword">else</span> <span class="keyword">if</span> (token == Char) {</span><br><span class="line">        match(Char);</span><br><span class="line">        expr_type = CHAR;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="keyword">while</span> (token == Mul) {</span><br><span class="line">        match(Mul);</span><br><span class="line">        expr_type = expr_type + PTR;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    match(<span class="string">&#39;)&#39;</span>);</span><br><span class="line"></span><br><span class="line">    <span class="comment">// emit code</span></span><br><span class="line">    *++text = IMM;</span><br><span class="line">    *++text = (expr_type == CHAR) ? <span class="keyword">sizeof</span>(<span class="type">char</span>) : <span class="keyword">sizeof</span>(<span class="type">int</span>);</span><br><span class="line"></span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>注意的是只支持 <code>sizeof(int)</code>，<code>sizeof(char)</code> 及 <code>sizeof(pointer type...)</code>。并且它的结果是 <code>int</code> 型。</p><h3 id="变量与函数调用" tabindex="-1"><a class="header-anchor" href="#变量与函数调用"><span><a href="about:blank#%E5%8F%98%E9%87%8F%E4%B8%8E%E5%87%BD%E6%95%B0%E8%B0%83%E7%94%A8"></a>变量与函数调用</span></a></h3><p>由于取变量的值与函数的调用都是以 <code>Id</code> 标记开头的，因此将它们放在一起处理。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Id) {</span><br><span class="line">    <span class="comment">// there are several type when occurs to Id</span></span><br><span class="line">    <span class="comment">// but this is unit, so it can only be</span></span><br><span class="line">    <span class="comment">// 1. function call</span></span><br><span class="line">    <span class="comment">// 2. Enum variable</span></span><br><span class="line">    <span class="comment">// 3. global/local variable</span></span><br><span class="line">    match(Id);</span><br><span class="line"></span><br><span class="line">    id = current_id;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (token == <span class="string">&#39;(&#39;</span>) {</span><br><span class="line">        <span class="comment">// function call</span></span><br><span class="line">        match(<span class="string">&#39;(&#39;</span>);</span><br><span class="line"></span><br><span class="line">        <span class="comment">// ①</span></span><br><span class="line">        <span class="comment">// pass in arguments</span></span><br><span class="line">        tmp = <span class="number">0</span>; <span class="comment">// number of arguments</span></span><br><span class="line">        <span class="keyword">while</span> (token != <span class="string">&#39;)&#39;</span>) {</span><br><span class="line">            expression(Assign);</span><br><span class="line">            *++text = PUSH;</span><br><span class="line">            tmp ++;</span><br><span class="line"></span><br><span class="line">            <span class="keyword">if</span> (token == <span class="string">&#39;,&#39;</span>) {</span><br><span class="line">                match(<span class="string">&#39;,&#39;</span>);</span><br><span class="line">            }</span><br><span class="line">        }</span><br><span class="line">        match(<span class="string">&#39;)&#39;</span>);</span><br><span class="line"></span><br><span class="line">        <span class="comment">// ②</span></span><br><span class="line">        <span class="comment">// emit code</span></span><br><span class="line">        <span class="keyword">if</span> (id[Class] == Sys) {</span><br><span class="line">            <span class="comment">// system functions</span></span><br><span class="line">            *++text = id[Value];</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (id[Class] == Fun) {</span><br><span class="line">            <span class="comment">// function call</span></span><br><span class="line">            *++text = CALL;</span><br><span class="line">            *++text = id[Value];</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> {</span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot;%d: bad function call\\n&quot;</span>, line);</span><br><span class="line">            <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        <span class="comment">// ③</span></span><br><span class="line">        <span class="comment">// clean the stack for arguments</span></span><br><span class="line">        <span class="keyword">if</span> (tmp &gt; <span class="number">0</span>) {</span><br><span class="line">            *++text = ADJ;</span><br><span class="line">            *++text = tmp;</span><br><span class="line">        }</span><br><span class="line">        expr_type = id[Type];</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">else</span> <span class="keyword">if</span> (id[Class] == Num) {</span><br><span class="line">        <span class="comment">// ④</span></span><br><span class="line">        <span class="comment">// enum variable</span></span><br><span class="line">        *++text = IMM;</span><br><span class="line">        *++text = id[Value];</span><br><span class="line">        expr_type = INT;</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">else</span> {</span><br><span class="line">        <span class="comment">// ⑤</span></span><br><span class="line">        <span class="comment">// variable</span></span><br><span class="line">        <span class="keyword">if</span> (id[Class] == Loc) {</span><br><span class="line">            *++text = LEA;</span><br><span class="line">            *++text = index_of_bp - id[Value];</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (id[Class] == Glo) {</span><br><span class="line">            *++text = IMM;</span><br><span class="line">            *++text = id[Value];</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> {</span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot;%d: undefined variable\\n&quot;</span>, line);</span><br><span class="line">            <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        <span class="comment">//⑥</span></span><br><span class="line">        <span class="comment">// emit code, default behaviour is to load the value of the</span></span><br><span class="line">        <span class="comment">// address which is stored in `ax`</span></span><br><span class="line">        expr_type = id[Type];</span><br><span class="line">        *++text = (expr_type == Char) ? LC : LI;</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>①中注意我们是顺序将参数入栈，这和第三章：虚拟机中讲解的指令是对应的。与之不同，标准 C 是逆序将参数入栈的。</p><p>②中判断函数的类型，同样在第三章：“虚拟机”中我们介绍过内置函数的支持，如 <code>printf</code>, <code>read</code>, <code>malloc</code> 等等。内置函数有对应的汇编指令，而普通的函数则编译成 <code>CALL &lt;addr&gt;</code> 的形式。</p><p>③用于清除入栈的参数。因为我们不在乎出栈的值，所以直接修改栈指针的大小即可。</p><p>④：当该标识符是全局定义的枚举类型时，直接将对应的值用 <code>IMM</code> 指令存入 <code>AX</code> 即可。</p><p>⑤则是用于加载变量的值，如果是局部变量则采用与 <code>bp</code> 指针相对位置的形式（参见第 7章函数定义）。而如果是全局变量则用 <code>IMM</code> 加载变量的地址。</p><p>⑥：无论是全局还是局部变量，最终都根据它们的类型用 <code>LC</code> 或 <code>LI</code> 指令加载对应的值。</p><p>关于变量，你可能有疑问，如果遇到标识符就用 <code>LC/LI</code> 载入相应的值，那诸如 <code>a[10]</code> 之类的表达式要如何实现呢？后面我们会看到，根据标识符后的运算符，我们可能会修改或删除现有的 <code>LC/LI</code> 指令。</p><h3 id="强制转换" tabindex="-1"><a class="header-anchor" href="#强制转换"><span><a href="about:blank#%E5%BC%BA%E5%88%B6%E8%BD%AC%E6%8D%A2"></a>强制转换</span></a></h3><p>虽然我们前面没有提到，但我们一直用 <code>expr_type</code> 来保存一个表达式的类型，强制转换的作用是获取转换的类型，并直接修改 <code>expr_type</code> 的值。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;(&#39;</span>) {</span><br><span class="line">    <span class="comment">// cast or parenthesis</span></span><br><span class="line">    match(<span class="string">&#39;(&#39;</span>);</span><br><span class="line">    <span class="keyword">if</span> (token == Int || token == Char) {</span><br><span class="line">        tmp = (token == Char) ? CHAR : INT; <span class="comment">// cast type</span></span><br><span class="line">        match(token);</span><br><span class="line">        <span class="keyword">while</span> (token == Mul) {</span><br><span class="line">            match(Mul);</span><br><span class="line">            tmp = tmp + PTR;</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        match(<span class="string">&#39;)&#39;</span>);</span><br><span class="line"></span><br><span class="line">        expression(Inc); <span class="comment">// cast has precedence as Inc(++)</span></span><br><span class="line"></span><br><span class="line">        expr_type  = tmp;</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="comment">// normal parenthesis</span></span><br><span class="line">        expression(Assign);</span><br><span class="line">        match(<span class="string">&#39;)&#39;</span>);</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="指针取值" tabindex="-1"><a class="header-anchor" href="#指针取值"><span><a href="about:blank#%E6%8C%87%E9%92%88%E5%8F%96%E5%80%BC"></a>指针取值</span></a></h3><p>诸如 <code>*a</code> 的指针取值，关键是判断 <code>a</code> 的类型，而就像上节中提到的，当一个表达式解析结束时，它的类型保存在变量 <code>expr_type</code> 中。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Mul) {</span><br><span class="line">    <span class="comment">// dereference *&lt;addr&gt;</span></span><br><span class="line">    match(Mul);</span><br><span class="line">    expression(Inc); <span class="comment">// dereference has the same precedence as Inc(++)</span></span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (expr_type &gt;= PTR) {</span><br><span class="line">        expr_type = expr_type - PTR;</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%d: bad dereference\\n&quot;</span>, line);</span><br><span class="line">        <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    *++text = (expr_type == CHAR) ? LC : LI;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="取址操作" tabindex="-1"><a class="header-anchor" href="#取址操作"><span><a href="about:blank#%E5%8F%96%E5%9D%80%E6%93%8D%E4%BD%9C"></a>取址操作</span></a></h3><p>这里我们就能看到“变量与函数调用”一节中所说的修改或删除 <code>LC/LI</code> 指令了。前文中我们说到，对于变量，我们会先加载它的地址，并根据它们类型使用 <code>LC/LI</code> 指令加载实际内容，例如对变量 <code>a</code>：</p><table><tbody><tr><td class="code"><pre><span class="line">IMM &lt;addr&gt;</span><br><span class="line">LI</span><br></pre></td></tr></tbody></table><p>那么对变量 <code>a</code> 取址，其实只要不执行 <code>LC/LI</code> 即可。因此我们删除相应的指令。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == And) {</span><br><span class="line">    <span class="comment">// get the address of</span></span><br><span class="line">    match(And);</span><br><span class="line">    expression(Inc); <span class="comment">// get the address of</span></span><br><span class="line">    <span class="keyword">if</span> (*text == LC || *text == LI) {</span><br><span class="line">        text --;</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%d: bad address of\\n&quot;</span>, line);</span><br><span class="line">        <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    expr_type = expr_type + PTR;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="逻辑取反" tabindex="-1"><a class="header-anchor" href="#逻辑取反"><span><a href="about:blank#%E9%80%BB%E8%BE%91%E5%8F%96%E5%8F%8D"></a>逻辑取反</span></a></h3><p>我们没有直接的逻辑取反指令，因此我们判断它是否与数字 0 相等。而数字 0 代表了逻辑 “False”。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;!&#39;</span>) {</span><br><span class="line">    <span class="comment">// not</span></span><br><span class="line">    match(<span class="string">&#39;!&#39;</span>);</span><br><span class="line">    expression(Inc);</span><br><span class="line"></span><br><span class="line">    <span class="comment">// emit code, use &lt;expr&gt; == 0</span></span><br><span class="line">    *++text = PUSH;</span><br><span class="line">    *++text = IMM;</span><br><span class="line">    *++text = <span class="number">0</span>;</span><br><span class="line">    *++text = EQ;</span><br><span class="line"></span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="按位取反" tabindex="-1"><a class="header-anchor" href="#按位取反"><span><a href="about:blank#%E6%8C%89%E4%BD%8D%E5%8F%96%E5%8F%8D"></a>按位取反</span></a></h3><p>同样我们没有相应的指令，所以我们用异或来实现，即 <code>~a = a ^ 0xFFFF</code>。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;~&#39;</span>) {</span><br><span class="line">    <span class="comment">// bitwise not</span></span><br><span class="line">    match(<span class="string">&#39;~&#39;</span>);</span><br><span class="line">    expression(Inc);</span><br><span class="line"></span><br><span class="line">    <span class="comment">// emit code, use &lt;expr&gt; XOR -1</span></span><br><span class="line">    *++text = PUSH;</span><br><span class="line">    *++text = IMM;</span><br><span class="line">    *++text = <span class="number">-1</span>;</span><br><span class="line">    *++text = XOR;</span><br><span class="line"></span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="正负号" tabindex="-1"><a class="header-anchor" href="#正负号"><span><a href="about:blank#%E6%AD%A3%E8%B4%9F%E5%8F%B7"></a>正负号</span></a></h3><p>注意这里并不是四则运算中的加减法，而是单个数字的取正取负操作。同样，我们没有取负的操作，用 <code>0 - x</code> 来实现 <code>-x</code>。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Add) {</span><br><span class="line">    <span class="comment">// +var, do nothing</span></span><br><span class="line">    match(Add);</span><br><span class="line">    expression(Inc);</span><br><span class="line"></span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Sub) {</span><br><span class="line">    <span class="comment">// -var</span></span><br><span class="line">    match(Sub);</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (token == Num) {</span><br><span class="line">        *++text = IMM;</span><br><span class="line">        *++text = -token_val;</span><br><span class="line">        match(Num);</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line"></span><br><span class="line">        *++text = IMM;</span><br><span class="line">        *++text = <span class="number">-1</span>;</span><br><span class="line">        *++text = PUSH;</span><br><span class="line">        expression(Inc);</span><br><span class="line">        *++text = MUL;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="自增自减" tabindex="-1"><a class="header-anchor" href="#自增自减"><span><a href="about:blank#%E8%87%AA%E5%A2%9E%E8%87%AA%E5%87%8F"></a>自增自减</span></a></h3><p>注意的是自增自减操作的优先级是和它的位置有关的。如 <code>++p</code> 的优先级高于 <code>p++</code>，这里我们解析的就是类似 <code>++p</code> 的操作。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Inc || token == Dec) {</span><br><span class="line">    tmp = token;</span><br><span class="line">    match(token);</span><br><span class="line">    expression(Inc);</span><br><span class="line">    <span class="comment">// ①</span></span><br><span class="line">    <span class="keyword">if</span> (*text == LC) {</span><br><span class="line">        *text = PUSH;  <span class="comment">// to duplicate the address</span></span><br><span class="line">        *++text = LC;</span><br><span class="line">    } <span class="keyword">else</span> <span class="keyword">if</span> (*text == LI) {</span><br><span class="line">        *text = PUSH;</span><br><span class="line">        *++text = LI;</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%d: bad lvalue of pre-increment\\n&quot;</span>, line);</span><br><span class="line">        <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line">    *++text = PUSH;</span><br><span class="line">    *++text = IMM;</span><br><span class="line">    <span class="comment">// ②</span></span><br><span class="line">    *++text = (expr_type &gt; PTR) ? <span class="keyword">sizeof</span>(<span class="type">int</span>) : <span class="keyword">sizeof</span>(<span class="type">char</span>);</span><br><span class="line">    *++text = (tmp == Inc) ? ADD : SUB;</span><br><span class="line">    *++text = (expr_type == CHAR) ? SC : SI;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>对应的汇编代码也比较直观，只是在实现 <code>++p</code>时，我们要使用变量 <code>p</code> 的地址两次，所以我们需要先 <code>PUSH</code> （①）。</p><p>②则是因为自增自减操作还需要处理是指针的情形。</p><h2 id="二元运算符" tabindex="-1"><a class="header-anchor" href="#二元运算符"><span><a href="about:blank#%E4%BA%8C%E5%85%83%E8%BF%90%E7%AE%97%E7%AC%A6"></a>二元运算符</span></a></h2><p>这里，我们需要处理多运算符的优先级问题，就如前文的“优先级”一节提到的，我们需要不断地向右扫描，直到遇到优先级 <strong>小于</strong> 当前优先级的运算符。</p><p>回想起我们之前定义过的各个标记，它们是以优先级从低到高排列的，即 <code>Assign</code> 的优先级最低，而 <code>Brak</code>（<code>[</code>） 的优先级最高。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="class"><span class="keyword">enum</span> {</span></span><br><span class="line">  Num = <span class="number">128</span>, Fun, Sys, Glo, Loc, Id,</span><br><span class="line">  Char, Else, Enum, If, Int, Return, Sizeof, While,</span><br><span class="line">  Assign, Cond, Lor, Lan, Or, Xor, And, Eq, Ne, Lt, Gt, Le, Ge, Shl, Shr, Add, Sub, Mul, Div, Mod, Inc, Dec, Brak</span><br><span class="line">};</span><br></pre></td></tr></tbody></table><p>所以，当我们调用 <code>expression(level)</code> 进行解析的时候，我们其实通过了参数 <code>level</code> 指定了当前的优先级。在前文的一元运算符处理中也用到了这一点。</p><p>所以，此时的二元运算符的解析的框架为：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">while</span> (token &gt;= level) {</span><br><span class="line">    <span class="comment">// parse token for binary operator and postfix operator</span></span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>解决了优先级的问题，让我们继续讲解如何把运算符编译成汇编代码吧。</p><h3 id="赋值操作" tabindex="-1"><a class="header-anchor" href="#赋值操作"><span><a href="about:blank#%E8%B5%8B%E5%80%BC%E6%93%8D%E4%BD%9C"></a>赋值操作</span></a></h3><p>赋值操作是优先级最低的运算符。考虑诸如 <code>a = (expession)</code> 的表达式，在解析 <code>=</code> 之前，我们已经为变量 <code>a</code> 生成了如下的汇编代码：</p><table><tbody><tr><td class="code"><pre><span class="line">IMM &lt;addr&gt;</span><br><span class="line">LC/LI</span><br></pre></td></tr></tbody></table><p>当解析完<code>=</code>右边的表达式后，相应的值会存放在 <code>ax</code> 中，此时，为了实际将这个值保存起来，我们需要类似下面的汇编代码：</p><table><tbody><tr><td class="code"><pre><span class="line">IMM &lt;addr&gt;</span><br><span class="line">PUSH</span><br><span class="line">SC/SI</span><br></pre></td></tr></tbody></table><p>明白了这点，也就能理解下面的源代码了：</p><table><tbody><tr><td class="code"><pre><span class="line">tmp = expr_type;</span><br><span class="line"><span class="keyword">if</span> (token == Assign) {</span><br><span class="line">    <span class="comment">// var = expr;</span></span><br><span class="line">    match(Assign);</span><br><span class="line">    <span class="keyword">if</span> (*text == LC || *text == LI) {</span><br><span class="line">        *text = PUSH; <span class="comment">// save the lvalue&#39;s pointer</span></span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%d: bad lvalue in assignment\\n&quot;</span>, line);</span><br><span class="line">        <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line">    expression(Assign);</span><br><span class="line"></span><br><span class="line">    expr_type = tmp;</span><br><span class="line">    *++text = (expr_type == CHAR) ? SC : SI;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="三目运算符" tabindex="-1"><a class="header-anchor" href="#三目运算符"><span><a href="about:blank#%E4%B8%89%E7%9B%AE%E8%BF%90%E7%AE%97%E7%AC%A6"></a>三目运算符</span></a></h3><p>这是 C 语言中唯一的一个三元运算符： <code>? :</code>，它相当于一个小型的 If 语句，所以生成的代码也类似于 If 语句，这里就不多作解释。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Cond) {</span><br><span class="line">    <span class="comment">// expr ? a : b;</span></span><br><span class="line">    match(Cond);</span><br><span class="line">    *++text = JZ;</span><br><span class="line">    addr = ++text;</span><br><span class="line">    expression(Assign);</span><br><span class="line">    <span class="keyword">if</span> (token == <span class="string">&#39;:&#39;</span>) {</span><br><span class="line">        match(<span class="string">&#39;:&#39;</span>);</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%d: missing colon in conditional\\n&quot;</span>, line);</span><br><span class="line">        <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line">    *addr = (<span class="type">int</span>)(text + <span class="number">3</span>);</span><br><span class="line">    *++text = JMP;</span><br><span class="line">    addr = ++text;</span><br><span class="line">    expression(Cond);</span><br><span class="line">    *addr = (<span class="type">int</span>)(text + <span class="number">1</span>);</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="逻辑运算符" tabindex="-1"><a class="header-anchor" href="#逻辑运算符"><span><a href="about:blank#%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6"></a>逻辑运算符</span></a></h3><p>这包括 <code>||</code> 和 <code>&amp;&amp;</code>。它们对应的汇编代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line">&lt;expr1&gt; || &lt;expr2&gt;     &lt;expr1&gt; &amp;&amp; &lt;expr2&gt;</span><br><span class="line"></span><br><span class="line">  ...&lt;expr1&gt;...          ...&lt;expr1&gt;...</span><br><span class="line">  JNZ b                  JZ b</span><br><span class="line">  ...&lt;expr2&gt;...          ...&lt;expr2&gt;...</span><br><span class="line">b:                     b:</span><br></pre></td></tr></tbody></table><p>所以源码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Lor) {</span><br><span class="line">    <span class="comment">// logic or</span></span><br><span class="line">    match(Lor);</span><br><span class="line">    *++text = JNZ;</span><br><span class="line">    addr = ++text;</span><br><span class="line">    expression(Lan);</span><br><span class="line">    *addr = (<span class="type">int</span>)(text + <span class="number">1</span>);</span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Lan) {</span><br><span class="line">    <span class="comment">// logic and</span></span><br><span class="line">    match(Lan);</span><br><span class="line">    *++text = JZ;</span><br><span class="line">    addr = ++text;</span><br><span class="line">    expression(Or);</span><br><span class="line">    *addr = (<span class="type">int</span>)(text + <span class="number">1</span>);</span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="数学运算符" tabindex="-1"><a class="header-anchor" href="#数学运算符"><span><a href="about:blank#%E6%95%B0%E5%AD%A6%E8%BF%90%E7%AE%97%E7%AC%A6"></a>数学运算符</span></a></h3><p>它们包括 <code>|</code>, <code>^</code>, <code>&amp;</code>, <code>==</code>, <code>!=</code> <code>&lt;=</code>, <code>&gt;=</code>, <code>&lt;</code>, <code>&gt;</code>, <code>&lt;&lt;</code>, <code>&gt;&gt;</code>, <code>+</code>, <code>-</code>, <code>*</code>, <code>/</code>, <code>%</code>。它们的实现都很类似，我们以异或 <code>^</code> 为例：</p><table><tbody><tr><td class="code"><pre><span class="line">&lt;expr1&gt; ^ &lt;expr2&gt;</span><br><span class="line"></span><br><span class="line">...&lt;expr1&gt;...          &lt;- now the result is on ax</span><br><span class="line">PUSH</span><br><span class="line">...&lt;expr2&gt;...          &lt;- now the value of &lt;expr2&gt; is on ax</span><br><span class="line">XOR</span><br></pre></td></tr></tbody></table><p>所以它对应的代码为：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Xor) {</span><br><span class="line">    <span class="comment">// bitwise xor</span></span><br><span class="line">    match(Xor);</span><br><span class="line">    *++text = PUSH;</span><br><span class="line">    expression(And);</span><br><span class="line">    *++text = XOR;</span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>其它的我们便不再详述。但这当中还有一个问题，就是指针的加减。在 C 语言中，指针加上数值等于将指针移位，且根据不同的类型移动的位移不同。如 <code>a + 1</code>，如果 <code>a</code> 是 <code>char *</code> 型，则移动一字节，而如果 <code>a</code> 是 <code>int *</code> 型，则移动 4 个字节（32位系统）。</p><p>另外，在作指针减法时，如果是两个指针相减（相同类型），则结果是两个指针间隔的元素个数。因此要有特殊的处理。</p><p>下面以加法为例，对应的汇编代码为：</p><table><tbody><tr><td class="code"><pre><span class="line">&lt;expr1&gt; + &lt;expr2&gt;</span><br><span class="line"></span><br><span class="line">normal         pointer</span><br><span class="line"></span><br><span class="line">&lt;expr1&gt;        &lt;expr1&gt;</span><br><span class="line">PUSH           PUSH</span><br><span class="line">&lt;expr2&gt;        &lt;expr2&gt;     |</span><br><span class="line">ADD            PUSH        | &lt;expr2&gt; * &lt;unit&gt;</span><br><span class="line">               IMM &lt;unit&gt;  |</span><br><span class="line">               MUL         |</span><br><span class="line">               ADD</span><br></pre></td></tr></tbody></table><p>即当 <code>&lt;expr1&gt;</code> 是指针时，要根据它的类型放大 <code>&lt;expr2&gt;</code> 的值，因此对应的源码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Add) {</span><br><span class="line">    <span class="comment">// add</span></span><br><span class="line">    match(Add);</span><br><span class="line">    *++text = PUSH;</span><br><span class="line">    expression(Mul);</span><br><span class="line"></span><br><span class="line">    expr_type = tmp;</span><br><span class="line">    <span class="keyword">if</span> (expr_type &gt; PTR) {</span><br><span class="line">        <span class="comment">// pointer type, and not `char *`</span></span><br><span class="line">        *++text = PUSH;</span><br><span class="line">        *++text = IMM;</span><br><span class="line">        *++text = <span class="keyword">sizeof</span>(<span class="type">int</span>);</span><br><span class="line">        *++text = MUL;</span><br><span class="line">    }</span><br><span class="line">    *++text = ADD;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>相应的减法的代码就不贴了，可以自己实现看看，也可以看文末给出的链接。</p><h3 id="自增自减-1" tabindex="-1"><a class="header-anchor" href="#自增自减-1"><span><a href="about:blank#%E8%87%AA%E5%A2%9E%E8%87%AA%E5%87%8F-v2"></a>自增自减</span></a></h3><p>这次是后缀形式的，即 <code>p++</code> 或 <code>p--</code>。与前缀形式不同的是，在执行自增自减后， <code>ax</code>上需要保留原来的值。所以我们首先执行类似前缀自增自减的操作，再将 <code>ax</code> 中的值执行减/增的操作。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="comment">// 前缀形式 生成汇编代码</span></span><br><span class="line">*++text = PUSH;</span><br><span class="line">*++text = IMM;</span><br><span class="line">*++text = (expr_type &gt; PTR) ? <span class="keyword">sizeof</span>(<span class="type">int</span>) : <span class="keyword">sizeof</span>(<span class="type">char</span>);</span><br><span class="line">*++text = (tmp == Inc) ? ADD : SUB;</span><br><span class="line">*++text = (expr_type == CHAR) ? SC : SI;</span><br><span class="line"></span><br><span class="line"><span class="comment">// 后缀形式 生成汇编代码</span></span><br><span class="line">*++text = PUSH;</span><br><span class="line">*++text = IMM;</span><br><span class="line">*++text = (expr_type &gt; PTR) ? <span class="keyword">sizeof</span>(<span class="type">int</span>) : <span class="keyword">sizeof</span>(<span class="type">char</span>);</span><br><span class="line">*++text = (token == Inc) ? ADD : SUB;</span><br><span class="line">*++text = (expr_type == CHAR) ? SC : SI;</span><br><span class="line">*++text = PUSH;                                             <span class="comment">//</span></span><br><span class="line">*++text = IMM;                                              <span class="comment">// 执行相反的增/减操作</span></span><br><span class="line">*++text = (expr_type &gt; PTR) ? <span class="keyword">sizeof</span>(<span class="type">int</span>) : <span class="keyword">sizeof</span>(<span class="type">char</span>);   <span class="comment">//</span></span><br><span class="line">*++text = (token == Inc) ? SUB : ADD;                       <span class="comment">//</span></span><br></pre></td></tr></tbody></table><h3 id="数组取值操作" tabindex="-1"><a class="header-anchor" href="#数组取值操作"><span><a href="about:blank#%E6%95%B0%E7%BB%84%E5%8F%96%E5%80%BC%E6%93%8D%E4%BD%9C"></a>数组取值操作</span></a></h3><p>在学习 C 语言的时候你可能已经知道了，诸如 <code>a[10]</code> 的操作等价于 <code>*(a + 10)</code>。因此我们要做的就是生成类似的汇编代码：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Brak) {</span><br><span class="line">    <span class="comment">// array access var[xx]</span></span><br><span class="line">    match(Brak);</span><br><span class="line">    *++text = PUSH;</span><br><span class="line">    expression(Assign);</span><br><span class="line">    match(<span class="string">&#39;]&#39;</span>);</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (tmp &gt; PTR) {</span><br><span class="line">        <span class="comment">// pointer, `not char *`</span></span><br><span class="line">        *++text = PUSH;</span><br><span class="line">        *++text = IMM;</span><br><span class="line">        *++text = <span class="keyword">sizeof</span>(<span class="type">int</span>);</span><br><span class="line">        *++text = MUL;</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">else</span> <span class="keyword">if</span> (tmp &lt; PTR) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%d: pointer type expected\\n&quot;</span>, line);</span><br><span class="line">        <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line">    expr_type = tmp - PTR;</span><br><span class="line">    *++text = ADD;</span><br><span class="line">    *++text = (expr_type == CHAR) ? LC : LI;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h2 id="代码" tabindex="-1"><a class="header-anchor" href="#代码"><span><a href="about:blank#%E4%BB%A3%E7%A0%81"></a>代码</span></a></h2><p>除了上述对表达式的解析外，我们还需要初始化虚拟机的栈，我们可以正确调用 <code>main</code> 函数，且当 <code>main</code> 函数结束时退出进程。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> *tmp;</span><br><span class="line"><span class="comment">// setup stack</span></span><br><span class="line">sp = (<span class="type">int</span> *)((<span class="type">int</span>)<span class="built_in">stack</span> + poolsize);</span><br><span class="line">*--sp = EXIT; <span class="comment">// call exit if main returns</span></span><br><span class="line">*--sp = PUSH; tmp = sp;</span><br><span class="line">*--sp = argc;</span><br><span class="line">*--sp = (<span class="type">int</span>)argv;</span><br><span class="line">*--sp = (<span class="type">int</span>)tmp;</span><br></pre></td></tr></tbody></table><p>当然，最后要注意的一点是：所有的变量定义必须放在语句之前。</p>',104),B={href:"https://github.com/lotabout/write-a-C-interpreter/tree/step-6",target:"_blank",rel:"noopener noreferrer"},I=p('<table><tbody><tr><td class="code"><pre><span class="line">git clone -b step-6 https://github.com/lotabout/write-a-C-interpreter</span><br></pre></td></tr></tbody></table><p>通过 <code>gcc -o xc-tutor xc-tutor.c</code> 进行编译。并执行 <code>./xc-tutor hello.c</code> 查看结果。</p><p>正如我们保证的那样，我们的代码是自举的，能自己编译自己，所以你可以执行 <code>./xc-tutor xc-tutor.c hello.c</code>。可以看到和之前有同样的输出。</p><h2 id="小结" tabindex="-1"><a class="header-anchor" href="#小结"><span><a href="about:blank#%E5%B0%8F%E7%BB%93"></a>小结</span></a></h2><p>本章我们进行了最后的解析，解析表达式。本章有两个难点：</p><ol><li>如何通过递归调用 <code>expression</code> 来实现运算符的优先级。</li><li>如何为每个运算符生成对应的汇编代码。</li></ol><p>尽管代码看起来比较简单（虽然多），但其中用到的原理还是需要仔细推敲的。</p><p>最后，恭喜你！通过一步步的学习，自己实现了一个C语言的编译器（好吧，是解释器）。</p>',8);function M(S,v){const n=t("ExternalLinkIcon");return c(),r("div",null,[o,s("p",null,[a("本文转自 "),s("a",b,[a("https://blog.csdn.net/xzp740813/article/details/142961332?spm=1001.2014.3001.5501"),e(n)]),a("，如有侵权，请联系删除。")]),d,s("ol",null,[s("li",null,[s("a",h,[a("手把手教你构建 C 语言编译器（0）——前言"),e(n)])]),s("li",null,[s("a",m,[a("手把手教你构建 C 语言编译器（1）——设计"),e(n)])]),s("li",null,[s("a",y,[a("手把手教你构建 C 语言编译器（2）——虚拟机"),e(n)])]),s("li",null,[s("a",x,[a("手把手教你构建 C 语言编译器（3）——词法分析器"),e(n)])]),s("li",null,[s("a",u,[a("手把手教你构建 C 语言编译器（4）——递归下降"),e(n)])]),s("li",null,[s("a",f,[a("手把手教你构建 C 语言编译器（5）——变量定义"),e(n)])]),s("li",null,[s("a",k,[a("手把手教你构建 C 语言编译器（6）——函数定义"),e(n)])]),s("li",null,[s("a",E,[a("手把手教你构建 C 语言编译器（7）——语句"),e(n)])]),s("li",null,[s("a",g,[a("手把手教你构建 C 语言编译器（8）——表达式"),e(n)])]),s("li",null,[s("a",C,[a("手把手教你构建 C 语言编译器（9）——总结"),e(n)])])]),_,s("p",null,[a("C 语言定义了各种表达式的优先级，可以参考 "),s("a",A,[a("C 语言运算符优先级"),e(n)]),a("。")]),w,s("p",null,[a("本章的代码可以在 "),s("a",B,[a("Github"),e(n)]),a(" 上下载，也可以直接 clone")]),I])}const L=l(i,[["render",M],["__file","8.html.vue"]]),F=JSON.parse('{"path":"/tech/designASimpileCCompiler/8.html","title":"手把手教你构建 C 语言编译器（8）——表达式","lang":"zh-CN","frontmatter":{"title":"手把手教你构建 C 语言编译器（8）——表达式","category":["编译原理"],"tag":["c","编译器","解释器"],"description":"转载声明 本文转自 https://blog.csdn.net/xzp740813/article/details/142961332?spm=1001.2014.3001.5501，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（8）- 表达式 Table of Contents 1. 运算符的优先级 2. 一元运算符 2.1. 常...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/designASimpileCCompiler/8.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"手把手教你构建 C 语言编译器（8）——表达式"}],["meta",{"property":"og:description","content":"转载声明 本文转自 https://blog.csdn.net/xzp740813/article/details/142961332?spm=1001.2014.3001.5501，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（8）- 表达式 Table of Contents 1. 运算符的优先级 2. 一元运算符 2.1. 常..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"c"}],["meta",{"property":"article:tag","content":"编译器"}],["meta",{"property":"article:tag","content":"解释器"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"手把手教你构建 C 语言编译器（8）——表达式\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"运算符的优先级","slug":"运算符的优先级","link":"#运算符的优先级","children":[]},{"level":2,"title":"一元运算符","slug":"一元运算符","link":"#一元运算符","children":[{"level":3,"title":"常量","slug":"常量","link":"#常量","children":[]},{"level":3,"title":"sizeof","slug":"sizeof","link":"#sizeof","children":[]},{"level":3,"title":"变量与函数调用","slug":"变量与函数调用","link":"#变量与函数调用","children":[]},{"level":3,"title":"强制转换","slug":"强制转换","link":"#强制转换","children":[]},{"level":3,"title":"指针取值","slug":"指针取值","link":"#指针取值","children":[]},{"level":3,"title":"取址操作","slug":"取址操作","link":"#取址操作","children":[]},{"level":3,"title":"逻辑取反","slug":"逻辑取反","link":"#逻辑取反","children":[]},{"level":3,"title":"按位取反","slug":"按位取反","link":"#按位取反","children":[]},{"level":3,"title":"正负号","slug":"正负号","link":"#正负号","children":[]},{"level":3,"title":"自增自减","slug":"自增自减","link":"#自增自减","children":[]}]},{"level":2,"title":"二元运算符","slug":"二元运算符","link":"#二元运算符","children":[{"level":3,"title":"赋值操作","slug":"赋值操作","link":"#赋值操作","children":[]},{"level":3,"title":"三目运算符","slug":"三目运算符","link":"#三目运算符","children":[]},{"level":3,"title":"逻辑运算符","slug":"逻辑运算符","link":"#逻辑运算符","children":[]},{"level":3,"title":"数学运算符","slug":"数学运算符","link":"#数学运算符","children":[]},{"level":3,"title":"自增自减","slug":"自增自减-1","link":"#自增自减-1","children":[]},{"level":3,"title":"数组取值操作","slug":"数组取值操作","link":"#数组取值操作","children":[]}]},{"level":2,"title":"代码","slug":"代码","link":"#代码","children":[]},{"level":2,"title":"小结","slug":"小结","link":"#小结","children":[]}],"readingTime":{"minutes":29.67,"words":8900},"filePathRelative":"tech/designASimpileCCompiler/8.md","excerpt":"\\n<p>本文转自 <a href=\\"https://blog.csdn.net/xzp740813/article/details/142961332?spm=1001.2014.3001.5501\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">https://blog.csdn.net/xzp740813/article/details/142961332?spm=1001.2014.3001.5501</a>，如有侵权，请联系删除。</p>\\n<h1>原文内容</h1>\\n<h1>手把手教你构建 C 语言编译器（8）- 表达式</h1>\\n<p>Table of Contents</p>","autoDesc":true}');export{L as comp,F as data};
+import{_ as l,r as t,o as c,c as r,b as s,e as a,d as e,f as p}from"./app-B4LGNJZ0.js";const i={},o=s("h1",{id:"转载声明",tabindex:"-1"},[s("a",{class:"header-anchor",href:"#转载声明"},[s("span",null,"转载声明")])],-1),b={href:"https://blog.csdn.net/xzp740813/article/details/142961332?spm=1001.2014.3001.5501",target:"_blank",rel:"noopener noreferrer"},d=p('<h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-8-表达式" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-8-表达式"><span>手把手教你构建 C 语言编译器（8）- 表达式</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#%E8%BF%90%E7%AE%97%E7%AC%A6%E7%9A%84%E4%BC%98%E5%85%88%E7%BA%A7">1. 运算符的优先级</a></li><li><a href="about:blank#%E4%B8%80%E5%85%83%E8%BF%90%E7%AE%97%E7%AC%A6">2. 一元运算符</a><ol><li><a href="about:blank#%E5%B8%B8%E9%87%8F">2.1. 常量</a></li><li><a href="about:blank#sizeof">2.2. sizeof</a></li><li><a href="about:blank#%E5%8F%98%E9%87%8F%E4%B8%8E%E5%87%BD%E6%95%B0%E8%B0%83%E7%94%A8">2.3. 变量与函数调用</a></li><li><a href="about:blank#%E5%BC%BA%E5%88%B6%E8%BD%AC%E6%8D%A2">2.4. 强制转换</a></li><li><a href="about:blank#%E6%8C%87%E9%92%88%E5%8F%96%E5%80%BC">2.5. 指针取值</a></li><li><a href="about:blank#%E5%8F%96%E5%9D%80%E6%93%8D%E4%BD%9C">2.6. 取址操作</a></li><li><a href="about:blank#%E9%80%BB%E8%BE%91%E5%8F%96%E5%8F%8D">2.7. 逻辑取反</a></li><li><a href="about:blank#%E6%8C%89%E4%BD%8D%E5%8F%96%E5%8F%8D">2.8. 按位取反</a></li><li><a href="about:blank#%E6%AD%A3%E8%B4%9F%E5%8F%B7">2.9. 正负号</a></li><li><a href="about:blank#%E8%87%AA%E5%A2%9E%E8%87%AA%E5%87%8F">2.10. 自增自减</a></li></ol></li><li><a href="about:blank#%E4%BA%8C%E5%85%83%E8%BF%90%E7%AE%97%E7%AC%A6">3. 二元运算符</a><ol><li><a href="about:blank#%E8%B5%8B%E5%80%BC%E6%93%8D%E4%BD%9C">3.1. 赋值操作</a></li><li><a href="about:blank#%E4%B8%89%E7%9B%AE%E8%BF%90%E7%AE%97%E7%AC%A6">3.2. 三目运算符</a></li><li><a href="about:blank#%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6">3.3. 逻辑运算符</a></li><li><a href="about:blank#%E6%95%B0%E5%AD%A6%E8%BF%90%E7%AE%97%E7%AC%A6">3.4. 数学运算符</a></li><li><a href="about:blank#%E8%87%AA%E5%A2%9E%E8%87%AA%E5%87%8F-v2">3.5. 自增自减</a></li><li><a href="about:blank#%E6%95%B0%E7%BB%84%E5%8F%96%E5%80%BC%E6%93%8D%E4%BD%9C">3.6. 数组取值操作</a></li></ol></li><li><a href="about:blank#%E4%BB%A3%E7%A0%81">4. 代码</a></li><li><a href="about:blank#%E5%B0%8F%E7%BB%93">5. 小结</a></li></ol><p>这是整个编译器的最后一部分，解析表达式。什么是表达式？表达式是将各种语言要素的一个组合，用来求值。例如：函数调用、变量赋值、运算符运算等等。</p><p>表达式的解析难点有二：一是运算符的优先级问题，二是如何将表达式编译成目标代码。我们就来逐一说明。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p>',7),h={href:"http://lotabout.me/2015/write-a-C-interpreter-0/",target:"_blank",rel:"noopener noreferrer"},m={href:"http://lotabout.me/2015/write-a-C-interpreter-1/",target:"_blank",rel:"noopener noreferrer"},y={href:"http://lotabout.me/2015/write-a-C-interpreter-2/",target:"_blank",rel:"noopener noreferrer"},x={href:"http://lotabout.me/2015/write-a-C-interpreter-3/",target:"_blank",rel:"noopener noreferrer"},u={href:"http://lotabout.me/2016/write-a-C-interpreter-4/",target:"_blank",rel:"noopener noreferrer"},f={href:"http://lotabout.me/2016/write-a-C-interpreter-5/",target:"_blank",rel:"noopener noreferrer"},k={href:"http://lotabout.me/2016/write-a-C-interpreter-6/",target:"_blank",rel:"noopener noreferrer"},E={href:"http://lotabout.me/2016/write-a-C-interpreter-7/",target:"_blank",rel:"noopener noreferrer"},g={href:"http://lotabout.me/2016/write-a-C-interpreter-8/",target:"_blank",rel:"noopener noreferrer"},C={href:"http://lotabout.me/2016/write-a-C-interpreter-9/",target:"_blank",rel:"noopener noreferrer"},_=p('<h2 id="运算符的优先级" tabindex="-1"><a class="header-anchor" href="#运算符的优先级"><span><a href="about:blank#%E8%BF%90%E7%AE%97%E7%AC%A6%E7%9A%84%E4%BC%98%E5%85%88%E7%BA%A7"></a>运算符的优先级</span></a></h2><p>运算符的优先级决定了表达式的运算顺序，如在普通的四则运算中，乘法 <code>*</code> 优先级高于加法 <code>+</code>，这就意味着表达式 <code>2 + 3 * 4</code> 的实际运行顺序是 <code>2 + (3 * 4)</code> 而不是 <code>(2 + 3) * 4</code>。</p>',2),A={href:"http://en.cppreference.com/w/c/language/operator_precedence",target:"_blank",rel:"noopener noreferrer"},w=p('<p>传统的编程书籍会用“逆波兰式”实现四则运算来讲解优先级问题。实际上，优先级关心的就是哪个运算符先计算，哪个运算符后计算（毕竟叫做“优先级”嘛）。而这就意味着我们需要决定先为哪个运算符生成目标代码（汇编），因为汇编代码是顺序排列的，我们必须先计算优先级高的运算符。</p><p>那么如何确定运算符的优先级呢？答曰：栈（递归调用的实质也是栈的处理）。</p><p>举一个例子：<code>2 + 3 - 4 * 5</code>，它的运算顺序是这样的：</p><ol><li>将 <code>2</code> 入栈</li><li>遇到运算符 <code>+</code>，入栈，此时我们期待的是<code>+</code>的另一个参数</li><li>遇到数字 <code>3</code>，原则上我们需要立即计算 <code>2+3</code>的值，但我们不确定数字 <code>3</code> 是否属于优先级更高的运算符，所以先将它入栈。</li><li>遇到运算符 <code>-</code>，它的优先级和 <code>+</code> 相同，此时判断参数 <code>3</code> 属于这前的 <code>+</code>。将运算符 <code>+</code> 出栈，并将之前的 <code>2</code> 和 <code>3</code> 出栈，计算 <code>2+3</code> 的结果，得到 <code>5</code> 入栈。同时将运算符 <code>-</code> 入栈。</li><li>遇到数字<code>4</code>，同样不能确定是否能立即计算，入栈</li><li>遇到运算符 <code>*</code> 优先级大于 <code>-</code>，入栈</li><li>遇到数字<code>5</code>，依旧不能确定是否立即计算，入栈</li><li>表达式结束，运算符出栈，为 <code>*</code>，将参数出栈，计算 <code>4*5</code> 得到结果 <code>20</code> 入栈。</li><li>运算符出栈，为 <code>-</code>，将参数出栈，计算 <code>5-20</code>，得到 <code>-15</code> 入栈。</li><li>此时运算符栈为空，因此得到结果 <code>-15</code>。</li></ol><table><tbody><tr><td class="code"><pre><span class="line">// after step 1, 2</span><br><span class="line">|      |</span><br><span class="line">+------+</span><br><span class="line">| 3    |   |      |</span><br><span class="line">+------+   +------+</span><br><span class="line">| 2    |   | +    |</span><br><span class="line">+------+   +------+</span><br><span class="line"></span><br><span class="line">// after step 4</span><br><span class="line">|      |   |      |</span><br><span class="line">+------+   +------+</span><br><span class="line">| 5    |   | -    |</span><br><span class="line">+------+   +------+</span><br><span class="line"></span><br><span class="line">// after step 7</span><br><span class="line">|      |</span><br><span class="line">+------+</span><br><span class="line">| 5    |</span><br><span class="line">+------+   +------+</span><br><span class="line">| 4    |   | *    |</span><br><span class="line">+------+   +------+</span><br><span class="line">| 5    |   | -    |</span><br><span class="line">+------+   +------+</span><br></pre></td></tr></tbody></table><p>综上，在计算一个运算符‘x’之前，必须先查看它的右方，找出并计算所有优先级大于‘x’的运算符，之后再计算运算符‘x’。</p><p>最后注意的是优先通常只与多元运算符相关，单元运算符往往没有这个问题（因为只有一个参数）。也可以认为“优先级”的实质就是两个运算符在抢参数。</p><h2 id="一元运算符" tabindex="-1"><a class="header-anchor" href="#一元运算符"><span><a href="about:blank#%E4%B8%80%E5%85%83%E8%BF%90%E7%AE%97%E7%AC%A6"></a>一元运算符</span></a></h2><p>上节中说到了运算符的优先级，也提到了优先级一般只与多元运算符有关，这也意味着一元运算符的优先级总是高于多元运算符。因为我们需要先对它们进行解析。</p><p>当然，这部分也将同时解析参数本身（如变量、数字、字符串等等）。</p><p>关于表达式的解析，与语法分析相关的部分就是上文所说的优先级问题了，而剩下的较难较烦的部分是与目标代码的生成有关的。因此对于需要讲解的运算符，我们主要从它的目标代码入手。</p><h3 id="常量" tabindex="-1"><a class="header-anchor" href="#常量"><span><a href="about:blank#%E5%B8%B8%E9%87%8F"></a>常量</span></a></h3><p>首先是数字，用 <code>IMM</code> 指令将它加载到 <code>AX</code> 中即可：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">if</span> (token == Num) {</span><br><span class="line">    match(Num);</span><br><span class="line"></span><br><span class="line">    <span class="comment">// emit code</span></span><br><span class="line">    *++text = IMM;</span><br><span class="line">    *++text = token_val;</span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br><span class="line"></span><br></pre></td></tr></tbody></table><p>接着是字符串常量。它比较特殊的一点是 C 语言的字符串常量支持如下风格：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">char</span> *p;</span><br><span class="line">p = <span class="string">&quot;first line&quot;</span></span><br><span class="line">    <span class="string">&quot;second line&quot;</span>;</span><br></pre></td></tr></tbody></table><p>即跨行的字符串拼接，它相当于：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">char</span> *p;</span><br><span class="line">p = <span class="string">&quot;first linesecond line&quot;</span>;</span><br></pre></td></tr></tbody></table><p>所以解析的时候要注意这一点：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;&quot;&#39;</span>) {</span><br><span class="line">    <span class="comment">// emit code</span></span><br><span class="line">    *++text = IMM;</span><br><span class="line">    *++text = token_val;</span><br><span class="line"></span><br><span class="line">    match(<span class="string">&#39;&quot;&#39;</span>);</span><br><span class="line">    <span class="comment">// store the rest strings</span></span><br><span class="line">    <span class="keyword">while</span> (token == <span class="string">&#39;&quot;&#39;</span>) {</span><br><span class="line">        match(<span class="string">&#39;&quot;&#39;</span>);</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="comment">// append the end of string character &#39;\\0&#39;, all the data are default</span></span><br><span class="line">    <span class="comment">// to 0, so just move data one position forward.</span></span><br><span class="line">    data = (<span class="type">char</span> *)(((<span class="type">int</span>)data + <span class="keyword">sizeof</span>(<span class="type">int</span>)) &amp; (-<span class="keyword">sizeof</span>(<span class="type">int</span>)));</span><br><span class="line">    expr_type = PTR;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="sizeof" tabindex="-1"><a class="header-anchor" href="#sizeof"><span><a href="about:blank#sizeof"></a>sizeof</span></a></h3><p><code>sizeof</code> 是一个一元运算符，我们需要知道后面参数的类型，类型的解析在前面的文章中我们已经很熟悉了。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Sizeof) {</span><br><span class="line">    <span class="comment">// sizeof is actually an unary operator</span></span><br><span class="line">    <span class="comment">// now only `sizeof(int)`, `sizeof(char)` and `sizeof(*...)` are</span></span><br><span class="line">    <span class="comment">// supported.</span></span><br><span class="line">    match(Sizeof);</span><br><span class="line">    match(<span class="string">&#39;(&#39;</span>);</span><br><span class="line">    expr_type = INT;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (token == Int) {</span><br><span class="line">        match(Int);</span><br><span class="line">    } <span class="keyword">else</span> <span class="keyword">if</span> (token == Char) {</span><br><span class="line">        match(Char);</span><br><span class="line">        expr_type = CHAR;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="keyword">while</span> (token == Mul) {</span><br><span class="line">        match(Mul);</span><br><span class="line">        expr_type = expr_type + PTR;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    match(<span class="string">&#39;)&#39;</span>);</span><br><span class="line"></span><br><span class="line">    <span class="comment">// emit code</span></span><br><span class="line">    *++text = IMM;</span><br><span class="line">    *++text = (expr_type == CHAR) ? <span class="keyword">sizeof</span>(<span class="type">char</span>) : <span class="keyword">sizeof</span>(<span class="type">int</span>);</span><br><span class="line"></span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>注意的是只支持 <code>sizeof(int)</code>，<code>sizeof(char)</code> 及 <code>sizeof(pointer type...)</code>。并且它的结果是 <code>int</code> 型。</p><h3 id="变量与函数调用" tabindex="-1"><a class="header-anchor" href="#变量与函数调用"><span><a href="about:blank#%E5%8F%98%E9%87%8F%E4%B8%8E%E5%87%BD%E6%95%B0%E8%B0%83%E7%94%A8"></a>变量与函数调用</span></a></h3><p>由于取变量的值与函数的调用都是以 <code>Id</code> 标记开头的，因此将它们放在一起处理。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Id) {</span><br><span class="line">    <span class="comment">// there are several type when occurs to Id</span></span><br><span class="line">    <span class="comment">// but this is unit, so it can only be</span></span><br><span class="line">    <span class="comment">// 1. function call</span></span><br><span class="line">    <span class="comment">// 2. Enum variable</span></span><br><span class="line">    <span class="comment">// 3. global/local variable</span></span><br><span class="line">    match(Id);</span><br><span class="line"></span><br><span class="line">    id = current_id;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (token == <span class="string">&#39;(&#39;</span>) {</span><br><span class="line">        <span class="comment">// function call</span></span><br><span class="line">        match(<span class="string">&#39;(&#39;</span>);</span><br><span class="line"></span><br><span class="line">        <span class="comment">// ①</span></span><br><span class="line">        <span class="comment">// pass in arguments</span></span><br><span class="line">        tmp = <span class="number">0</span>; <span class="comment">// number of arguments</span></span><br><span class="line">        <span class="keyword">while</span> (token != <span class="string">&#39;)&#39;</span>) {</span><br><span class="line">            expression(Assign);</span><br><span class="line">            *++text = PUSH;</span><br><span class="line">            tmp ++;</span><br><span class="line"></span><br><span class="line">            <span class="keyword">if</span> (token == <span class="string">&#39;,&#39;</span>) {</span><br><span class="line">                match(<span class="string">&#39;,&#39;</span>);</span><br><span class="line">            }</span><br><span class="line">        }</span><br><span class="line">        match(<span class="string">&#39;)&#39;</span>);</span><br><span class="line"></span><br><span class="line">        <span class="comment">// ②</span></span><br><span class="line">        <span class="comment">// emit code</span></span><br><span class="line">        <span class="keyword">if</span> (id[Class] == Sys) {</span><br><span class="line">            <span class="comment">// system functions</span></span><br><span class="line">            *++text = id[Value];</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (id[Class] == Fun) {</span><br><span class="line">            <span class="comment">// function call</span></span><br><span class="line">            *++text = CALL;</span><br><span class="line">            *++text = id[Value];</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> {</span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot;%d: bad function call\\n&quot;</span>, line);</span><br><span class="line">            <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        <span class="comment">// ③</span></span><br><span class="line">        <span class="comment">// clean the stack for arguments</span></span><br><span class="line">        <span class="keyword">if</span> (tmp &gt; <span class="number">0</span>) {</span><br><span class="line">            *++text = ADJ;</span><br><span class="line">            *++text = tmp;</span><br><span class="line">        }</span><br><span class="line">        expr_type = id[Type];</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">else</span> <span class="keyword">if</span> (id[Class] == Num) {</span><br><span class="line">        <span class="comment">// ④</span></span><br><span class="line">        <span class="comment">// enum variable</span></span><br><span class="line">        *++text = IMM;</span><br><span class="line">        *++text = id[Value];</span><br><span class="line">        expr_type = INT;</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">else</span> {</span><br><span class="line">        <span class="comment">// ⑤</span></span><br><span class="line">        <span class="comment">// variable</span></span><br><span class="line">        <span class="keyword">if</span> (id[Class] == Loc) {</span><br><span class="line">            *++text = LEA;</span><br><span class="line">            *++text = index_of_bp - id[Value];</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (id[Class] == Glo) {</span><br><span class="line">            *++text = IMM;</span><br><span class="line">            *++text = id[Value];</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> {</span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot;%d: undefined variable\\n&quot;</span>, line);</span><br><span class="line">            <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        <span class="comment">//⑥</span></span><br><span class="line">        <span class="comment">// emit code, default behaviour is to load the value of the</span></span><br><span class="line">        <span class="comment">// address which is stored in `ax`</span></span><br><span class="line">        expr_type = id[Type];</span><br><span class="line">        *++text = (expr_type == Char) ? LC : LI;</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>①中注意我们是顺序将参数入栈，这和第三章：虚拟机中讲解的指令是对应的。与之不同，标准 C 是逆序将参数入栈的。</p><p>②中判断函数的类型，同样在第三章：“虚拟机”中我们介绍过内置函数的支持，如 <code>printf</code>, <code>read</code>, <code>malloc</code> 等等。内置函数有对应的汇编指令，而普通的函数则编译成 <code>CALL &lt;addr&gt;</code> 的形式。</p><p>③用于清除入栈的参数。因为我们不在乎出栈的值，所以直接修改栈指针的大小即可。</p><p>④：当该标识符是全局定义的枚举类型时，直接将对应的值用 <code>IMM</code> 指令存入 <code>AX</code> 即可。</p><p>⑤则是用于加载变量的值，如果是局部变量则采用与 <code>bp</code> 指针相对位置的形式（参见第 7章函数定义）。而如果是全局变量则用 <code>IMM</code> 加载变量的地址。</p><p>⑥：无论是全局还是局部变量，最终都根据它们的类型用 <code>LC</code> 或 <code>LI</code> 指令加载对应的值。</p><p>关于变量，你可能有疑问，如果遇到标识符就用 <code>LC/LI</code> 载入相应的值，那诸如 <code>a[10]</code> 之类的表达式要如何实现呢？后面我们会看到，根据标识符后的运算符，我们可能会修改或删除现有的 <code>LC/LI</code> 指令。</p><h3 id="强制转换" tabindex="-1"><a class="header-anchor" href="#强制转换"><span><a href="about:blank#%E5%BC%BA%E5%88%B6%E8%BD%AC%E6%8D%A2"></a>强制转换</span></a></h3><p>虽然我们前面没有提到，但我们一直用 <code>expr_type</code> 来保存一个表达式的类型，强制转换的作用是获取转换的类型，并直接修改 <code>expr_type</code> 的值。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;(&#39;</span>) {</span><br><span class="line">    <span class="comment">// cast or parenthesis</span></span><br><span class="line">    match(<span class="string">&#39;(&#39;</span>);</span><br><span class="line">    <span class="keyword">if</span> (token == Int || token == Char) {</span><br><span class="line">        tmp = (token == Char) ? CHAR : INT; <span class="comment">// cast type</span></span><br><span class="line">        match(token);</span><br><span class="line">        <span class="keyword">while</span> (token == Mul) {</span><br><span class="line">            match(Mul);</span><br><span class="line">            tmp = tmp + PTR;</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        match(<span class="string">&#39;)&#39;</span>);</span><br><span class="line"></span><br><span class="line">        expression(Inc); <span class="comment">// cast has precedence as Inc(++)</span></span><br><span class="line"></span><br><span class="line">        expr_type  = tmp;</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="comment">// normal parenthesis</span></span><br><span class="line">        expression(Assign);</span><br><span class="line">        match(<span class="string">&#39;)&#39;</span>);</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="指针取值" tabindex="-1"><a class="header-anchor" href="#指针取值"><span><a href="about:blank#%E6%8C%87%E9%92%88%E5%8F%96%E5%80%BC"></a>指针取值</span></a></h3><p>诸如 <code>*a</code> 的指针取值，关键是判断 <code>a</code> 的类型，而就像上节中提到的，当一个表达式解析结束时，它的类型保存在变量 <code>expr_type</code> 中。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Mul) {</span><br><span class="line">    <span class="comment">// dereference *&lt;addr&gt;</span></span><br><span class="line">    match(Mul);</span><br><span class="line">    expression(Inc); <span class="comment">// dereference has the same precedence as Inc(++)</span></span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (expr_type &gt;= PTR) {</span><br><span class="line">        expr_type = expr_type - PTR;</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%d: bad dereference\\n&quot;</span>, line);</span><br><span class="line">        <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    *++text = (expr_type == CHAR) ? LC : LI;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="取址操作" tabindex="-1"><a class="header-anchor" href="#取址操作"><span><a href="about:blank#%E5%8F%96%E5%9D%80%E6%93%8D%E4%BD%9C"></a>取址操作</span></a></h3><p>这里我们就能看到“变量与函数调用”一节中所说的修改或删除 <code>LC/LI</code> 指令了。前文中我们说到，对于变量，我们会先加载它的地址，并根据它们类型使用 <code>LC/LI</code> 指令加载实际内容，例如对变量 <code>a</code>：</p><table><tbody><tr><td class="code"><pre><span class="line">IMM &lt;addr&gt;</span><br><span class="line">LI</span><br></pre></td></tr></tbody></table><p>那么对变量 <code>a</code> 取址，其实只要不执行 <code>LC/LI</code> 即可。因此我们删除相应的指令。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == And) {</span><br><span class="line">    <span class="comment">// get the address of</span></span><br><span class="line">    match(And);</span><br><span class="line">    expression(Inc); <span class="comment">// get the address of</span></span><br><span class="line">    <span class="keyword">if</span> (*text == LC || *text == LI) {</span><br><span class="line">        text --;</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%d: bad address of\\n&quot;</span>, line);</span><br><span class="line">        <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    expr_type = expr_type + PTR;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="逻辑取反" tabindex="-1"><a class="header-anchor" href="#逻辑取反"><span><a href="about:blank#%E9%80%BB%E8%BE%91%E5%8F%96%E5%8F%8D"></a>逻辑取反</span></a></h3><p>我们没有直接的逻辑取反指令，因此我们判断它是否与数字 0 相等。而数字 0 代表了逻辑 “False”。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;!&#39;</span>) {</span><br><span class="line">    <span class="comment">// not</span></span><br><span class="line">    match(<span class="string">&#39;!&#39;</span>);</span><br><span class="line">    expression(Inc);</span><br><span class="line"></span><br><span class="line">    <span class="comment">// emit code, use &lt;expr&gt; == 0</span></span><br><span class="line">    *++text = PUSH;</span><br><span class="line">    *++text = IMM;</span><br><span class="line">    *++text = <span class="number">0</span>;</span><br><span class="line">    *++text = EQ;</span><br><span class="line"></span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="按位取反" tabindex="-1"><a class="header-anchor" href="#按位取反"><span><a href="about:blank#%E6%8C%89%E4%BD%8D%E5%8F%96%E5%8F%8D"></a>按位取反</span></a></h3><p>同样我们没有相应的指令，所以我们用异或来实现，即 <code>~a = a ^ 0xFFFF</code>。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;~&#39;</span>) {</span><br><span class="line">    <span class="comment">// bitwise not</span></span><br><span class="line">    match(<span class="string">&#39;~&#39;</span>);</span><br><span class="line">    expression(Inc);</span><br><span class="line"></span><br><span class="line">    <span class="comment">// emit code, use &lt;expr&gt; XOR -1</span></span><br><span class="line">    *++text = PUSH;</span><br><span class="line">    *++text = IMM;</span><br><span class="line">    *++text = <span class="number">-1</span>;</span><br><span class="line">    *++text = XOR;</span><br><span class="line"></span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="正负号" tabindex="-1"><a class="header-anchor" href="#正负号"><span><a href="about:blank#%E6%AD%A3%E8%B4%9F%E5%8F%B7"></a>正负号</span></a></h3><p>注意这里并不是四则运算中的加减法，而是单个数字的取正取负操作。同样，我们没有取负的操作，用 <code>0 - x</code> 来实现 <code>-x</code>。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Add) {</span><br><span class="line">    <span class="comment">// +var, do nothing</span></span><br><span class="line">    match(Add);</span><br><span class="line">    expression(Inc);</span><br><span class="line"></span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Sub) {</span><br><span class="line">    <span class="comment">// -var</span></span><br><span class="line">    match(Sub);</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (token == Num) {</span><br><span class="line">        *++text = IMM;</span><br><span class="line">        *++text = -token_val;</span><br><span class="line">        match(Num);</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line"></span><br><span class="line">        *++text = IMM;</span><br><span class="line">        *++text = <span class="number">-1</span>;</span><br><span class="line">        *++text = PUSH;</span><br><span class="line">        expression(Inc);</span><br><span class="line">        *++text = MUL;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="自增自减" tabindex="-1"><a class="header-anchor" href="#自增自减"><span><a href="about:blank#%E8%87%AA%E5%A2%9E%E8%87%AA%E5%87%8F"></a>自增自减</span></a></h3><p>注意的是自增自减操作的优先级是和它的位置有关的。如 <code>++p</code> 的优先级高于 <code>p++</code>，这里我们解析的就是类似 <code>++p</code> 的操作。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Inc || token == Dec) {</span><br><span class="line">    tmp = token;</span><br><span class="line">    match(token);</span><br><span class="line">    expression(Inc);</span><br><span class="line">    <span class="comment">// ①</span></span><br><span class="line">    <span class="keyword">if</span> (*text == LC) {</span><br><span class="line">        *text = PUSH;  <span class="comment">// to duplicate the address</span></span><br><span class="line">        *++text = LC;</span><br><span class="line">    } <span class="keyword">else</span> <span class="keyword">if</span> (*text == LI) {</span><br><span class="line">        *text = PUSH;</span><br><span class="line">        *++text = LI;</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%d: bad lvalue of pre-increment\\n&quot;</span>, line);</span><br><span class="line">        <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line">    *++text = PUSH;</span><br><span class="line">    *++text = IMM;</span><br><span class="line">    <span class="comment">// ②</span></span><br><span class="line">    *++text = (expr_type &gt; PTR) ? <span class="keyword">sizeof</span>(<span class="type">int</span>) : <span class="keyword">sizeof</span>(<span class="type">char</span>);</span><br><span class="line">    *++text = (tmp == Inc) ? ADD : SUB;</span><br><span class="line">    *++text = (expr_type == CHAR) ? SC : SI;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>对应的汇编代码也比较直观，只是在实现 <code>++p</code>时，我们要使用变量 <code>p</code> 的地址两次，所以我们需要先 <code>PUSH</code> （①）。</p><p>②则是因为自增自减操作还需要处理是指针的情形。</p><h2 id="二元运算符" tabindex="-1"><a class="header-anchor" href="#二元运算符"><span><a href="about:blank#%E4%BA%8C%E5%85%83%E8%BF%90%E7%AE%97%E7%AC%A6"></a>二元运算符</span></a></h2><p>这里，我们需要处理多运算符的优先级问题，就如前文的“优先级”一节提到的，我们需要不断地向右扫描，直到遇到优先级 <strong>小于</strong> 当前优先级的运算符。</p><p>回想起我们之前定义过的各个标记，它们是以优先级从低到高排列的，即 <code>Assign</code> 的优先级最低，而 <code>Brak</code>（<code>[</code>） 的优先级最高。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="class"><span class="keyword">enum</span> {</span></span><br><span class="line">  Num = <span class="number">128</span>, Fun, Sys, Glo, Loc, Id,</span><br><span class="line">  Char, Else, Enum, If, Int, Return, Sizeof, While,</span><br><span class="line">  Assign, Cond, Lor, Lan, Or, Xor, And, Eq, Ne, Lt, Gt, Le, Ge, Shl, Shr, Add, Sub, Mul, Div, Mod, Inc, Dec, Brak</span><br><span class="line">};</span><br></pre></td></tr></tbody></table><p>所以，当我们调用 <code>expression(level)</code> 进行解析的时候，我们其实通过了参数 <code>level</code> 指定了当前的优先级。在前文的一元运算符处理中也用到了这一点。</p><p>所以，此时的二元运算符的解析的框架为：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">while</span> (token &gt;= level) {</span><br><span class="line">    <span class="comment">// parse token for binary operator and postfix operator</span></span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>解决了优先级的问题，让我们继续讲解如何把运算符编译成汇编代码吧。</p><h3 id="赋值操作" tabindex="-1"><a class="header-anchor" href="#赋值操作"><span><a href="about:blank#%E8%B5%8B%E5%80%BC%E6%93%8D%E4%BD%9C"></a>赋值操作</span></a></h3><p>赋值操作是优先级最低的运算符。考虑诸如 <code>a = (expession)</code> 的表达式，在解析 <code>=</code> 之前，我们已经为变量 <code>a</code> 生成了如下的汇编代码：</p><table><tbody><tr><td class="code"><pre><span class="line">IMM &lt;addr&gt;</span><br><span class="line">LC/LI</span><br></pre></td></tr></tbody></table><p>当解析完<code>=</code>右边的表达式后，相应的值会存放在 <code>ax</code> 中，此时，为了实际将这个值保存起来，我们需要类似下面的汇编代码：</p><table><tbody><tr><td class="code"><pre><span class="line">IMM &lt;addr&gt;</span><br><span class="line">PUSH</span><br><span class="line">SC/SI</span><br></pre></td></tr></tbody></table><p>明白了这点，也就能理解下面的源代码了：</p><table><tbody><tr><td class="code"><pre><span class="line">tmp = expr_type;</span><br><span class="line"><span class="keyword">if</span> (token == Assign) {</span><br><span class="line">    <span class="comment">// var = expr;</span></span><br><span class="line">    match(Assign);</span><br><span class="line">    <span class="keyword">if</span> (*text == LC || *text == LI) {</span><br><span class="line">        *text = PUSH; <span class="comment">// save the lvalue&#39;s pointer</span></span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%d: bad lvalue in assignment\\n&quot;</span>, line);</span><br><span class="line">        <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line">    expression(Assign);</span><br><span class="line"></span><br><span class="line">    expr_type = tmp;</span><br><span class="line">    *++text = (expr_type == CHAR) ? SC : SI;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="三目运算符" tabindex="-1"><a class="header-anchor" href="#三目运算符"><span><a href="about:blank#%E4%B8%89%E7%9B%AE%E8%BF%90%E7%AE%97%E7%AC%A6"></a>三目运算符</span></a></h3><p>这是 C 语言中唯一的一个三元运算符： <code>? :</code>，它相当于一个小型的 If 语句，所以生成的代码也类似于 If 语句，这里就不多作解释。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Cond) {</span><br><span class="line">    <span class="comment">// expr ? a : b;</span></span><br><span class="line">    match(Cond);</span><br><span class="line">    *++text = JZ;</span><br><span class="line">    addr = ++text;</span><br><span class="line">    expression(Assign);</span><br><span class="line">    <span class="keyword">if</span> (token == <span class="string">&#39;:&#39;</span>) {</span><br><span class="line">        match(<span class="string">&#39;:&#39;</span>);</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%d: missing colon in conditional\\n&quot;</span>, line);</span><br><span class="line">        <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line">    *addr = (<span class="type">int</span>)(text + <span class="number">3</span>);</span><br><span class="line">    *++text = JMP;</span><br><span class="line">    addr = ++text;</span><br><span class="line">    expression(Cond);</span><br><span class="line">    *addr = (<span class="type">int</span>)(text + <span class="number">1</span>);</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="逻辑运算符" tabindex="-1"><a class="header-anchor" href="#逻辑运算符"><span><a href="about:blank#%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6"></a>逻辑运算符</span></a></h3><p>这包括 <code>||</code> 和 <code>&amp;&amp;</code>。它们对应的汇编代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line">&lt;expr1&gt; || &lt;expr2&gt;     &lt;expr1&gt; &amp;&amp; &lt;expr2&gt;</span><br><span class="line"></span><br><span class="line">  ...&lt;expr1&gt;...          ...&lt;expr1&gt;...</span><br><span class="line">  JNZ b                  JZ b</span><br><span class="line">  ...&lt;expr2&gt;...          ...&lt;expr2&gt;...</span><br><span class="line">b:                     b:</span><br></pre></td></tr></tbody></table><p>所以源码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Lor) {</span><br><span class="line">    <span class="comment">// logic or</span></span><br><span class="line">    match(Lor);</span><br><span class="line">    *++text = JNZ;</span><br><span class="line">    addr = ++text;</span><br><span class="line">    expression(Lan);</span><br><span class="line">    *addr = (<span class="type">int</span>)(text + <span class="number">1</span>);</span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Lan) {</span><br><span class="line">    <span class="comment">// logic and</span></span><br><span class="line">    match(Lan);</span><br><span class="line">    *++text = JZ;</span><br><span class="line">    addr = ++text;</span><br><span class="line">    expression(Or);</span><br><span class="line">    *addr = (<span class="type">int</span>)(text + <span class="number">1</span>);</span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="数学运算符" tabindex="-1"><a class="header-anchor" href="#数学运算符"><span><a href="about:blank#%E6%95%B0%E5%AD%A6%E8%BF%90%E7%AE%97%E7%AC%A6"></a>数学运算符</span></a></h3><p>它们包括 <code>|</code>, <code>^</code>, <code>&amp;</code>, <code>==</code>, <code>!=</code> <code>&lt;=</code>, <code>&gt;=</code>, <code>&lt;</code>, <code>&gt;</code>, <code>&lt;&lt;</code>, <code>&gt;&gt;</code>, <code>+</code>, <code>-</code>, <code>*</code>, <code>/</code>, <code>%</code>。它们的实现都很类似，我们以异或 <code>^</code> 为例：</p><table><tbody><tr><td class="code"><pre><span class="line">&lt;expr1&gt; ^ &lt;expr2&gt;</span><br><span class="line"></span><br><span class="line">...&lt;expr1&gt;...          &lt;- now the result is on ax</span><br><span class="line">PUSH</span><br><span class="line">...&lt;expr2&gt;...          &lt;- now the value of &lt;expr2&gt; is on ax</span><br><span class="line">XOR</span><br></pre></td></tr></tbody></table><p>所以它对应的代码为：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Xor) {</span><br><span class="line">    <span class="comment">// bitwise xor</span></span><br><span class="line">    match(Xor);</span><br><span class="line">    *++text = PUSH;</span><br><span class="line">    expression(And);</span><br><span class="line">    *++text = XOR;</span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>其它的我们便不再详述。但这当中还有一个问题，就是指针的加减。在 C 语言中，指针加上数值等于将指针移位，且根据不同的类型移动的位移不同。如 <code>a + 1</code>，如果 <code>a</code> 是 <code>char *</code> 型，则移动一字节，而如果 <code>a</code> 是 <code>int *</code> 型，则移动 4 个字节（32位系统）。</p><p>另外，在作指针减法时，如果是两个指针相减（相同类型），则结果是两个指针间隔的元素个数。因此要有特殊的处理。</p><p>下面以加法为例，对应的汇编代码为：</p><table><tbody><tr><td class="code"><pre><span class="line">&lt;expr1&gt; + &lt;expr2&gt;</span><br><span class="line"></span><br><span class="line">normal         pointer</span><br><span class="line"></span><br><span class="line">&lt;expr1&gt;        &lt;expr1&gt;</span><br><span class="line">PUSH           PUSH</span><br><span class="line">&lt;expr2&gt;        &lt;expr2&gt;     |</span><br><span class="line">ADD            PUSH        | &lt;expr2&gt; * &lt;unit&gt;</span><br><span class="line">               IMM &lt;unit&gt;  |</span><br><span class="line">               MUL         |</span><br><span class="line">               ADD</span><br></pre></td></tr></tbody></table><p>即当 <code>&lt;expr1&gt;</code> 是指针时，要根据它的类型放大 <code>&lt;expr2&gt;</code> 的值，因此对应的源码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Add) {</span><br><span class="line">    <span class="comment">// add</span></span><br><span class="line">    match(Add);</span><br><span class="line">    *++text = PUSH;</span><br><span class="line">    expression(Mul);</span><br><span class="line"></span><br><span class="line">    expr_type = tmp;</span><br><span class="line">    <span class="keyword">if</span> (expr_type &gt; PTR) {</span><br><span class="line">        <span class="comment">// pointer type, and not `char *`</span></span><br><span class="line">        *++text = PUSH;</span><br><span class="line">        *++text = IMM;</span><br><span class="line">        *++text = <span class="keyword">sizeof</span>(<span class="type">int</span>);</span><br><span class="line">        *++text = MUL;</span><br><span class="line">    }</span><br><span class="line">    *++text = ADD;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>相应的减法的代码就不贴了，可以自己实现看看，也可以看文末给出的链接。</p><h3 id="自增自减-1" tabindex="-1"><a class="header-anchor" href="#自增自减-1"><span><a href="about:blank#%E8%87%AA%E5%A2%9E%E8%87%AA%E5%87%8F-v2"></a>自增自减</span></a></h3><p>这次是后缀形式的，即 <code>p++</code> 或 <code>p--</code>。与前缀形式不同的是，在执行自增自减后， <code>ax</code>上需要保留原来的值。所以我们首先执行类似前缀自增自减的操作，再将 <code>ax</code> 中的值执行减/增的操作。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="comment">// 前缀形式 生成汇编代码</span></span><br><span class="line">*++text = PUSH;</span><br><span class="line">*++text = IMM;</span><br><span class="line">*++text = (expr_type &gt; PTR) ? <span class="keyword">sizeof</span>(<span class="type">int</span>) : <span class="keyword">sizeof</span>(<span class="type">char</span>);</span><br><span class="line">*++text = (tmp == Inc) ? ADD : SUB;</span><br><span class="line">*++text = (expr_type == CHAR) ? SC : SI;</span><br><span class="line"></span><br><span class="line"><span class="comment">// 后缀形式 生成汇编代码</span></span><br><span class="line">*++text = PUSH;</span><br><span class="line">*++text = IMM;</span><br><span class="line">*++text = (expr_type &gt; PTR) ? <span class="keyword">sizeof</span>(<span class="type">int</span>) : <span class="keyword">sizeof</span>(<span class="type">char</span>);</span><br><span class="line">*++text = (token == Inc) ? ADD : SUB;</span><br><span class="line">*++text = (expr_type == CHAR) ? SC : SI;</span><br><span class="line">*++text = PUSH;                                             <span class="comment">//</span></span><br><span class="line">*++text = IMM;                                              <span class="comment">// 执行相反的增/减操作</span></span><br><span class="line">*++text = (expr_type &gt; PTR) ? <span class="keyword">sizeof</span>(<span class="type">int</span>) : <span class="keyword">sizeof</span>(<span class="type">char</span>);   <span class="comment">//</span></span><br><span class="line">*++text = (token == Inc) ? SUB : ADD;                       <span class="comment">//</span></span><br></pre></td></tr></tbody></table><h3 id="数组取值操作" tabindex="-1"><a class="header-anchor" href="#数组取值操作"><span><a href="about:blank#%E6%95%B0%E7%BB%84%E5%8F%96%E5%80%BC%E6%93%8D%E4%BD%9C"></a>数组取值操作</span></a></h3><p>在学习 C 语言的时候你可能已经知道了，诸如 <code>a[10]</code> 的操作等价于 <code>*(a + 10)</code>。因此我们要做的就是生成类似的汇编代码：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Brak) {</span><br><span class="line">    <span class="comment">// array access var[xx]</span></span><br><span class="line">    match(Brak);</span><br><span class="line">    *++text = PUSH;</span><br><span class="line">    expression(Assign);</span><br><span class="line">    match(<span class="string">&#39;]&#39;</span>);</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (tmp &gt; PTR) {</span><br><span class="line">        <span class="comment">// pointer, `not char *`</span></span><br><span class="line">        *++text = PUSH;</span><br><span class="line">        *++text = IMM;</span><br><span class="line">        *++text = <span class="keyword">sizeof</span>(<span class="type">int</span>);</span><br><span class="line">        *++text = MUL;</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">else</span> <span class="keyword">if</span> (tmp &lt; PTR) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%d: pointer type expected\\n&quot;</span>, line);</span><br><span class="line">        <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line">    expr_type = tmp - PTR;</span><br><span class="line">    *++text = ADD;</span><br><span class="line">    *++text = (expr_type == CHAR) ? LC : LI;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h2 id="代码" tabindex="-1"><a class="header-anchor" href="#代码"><span><a href="about:blank#%E4%BB%A3%E7%A0%81"></a>代码</span></a></h2><p>除了上述对表达式的解析外，我们还需要初始化虚拟机的栈，我们可以正确调用 <code>main</code> 函数，且当 <code>main</code> 函数结束时退出进程。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> *tmp;</span><br><span class="line"><span class="comment">// setup stack</span></span><br><span class="line">sp = (<span class="type">int</span> *)((<span class="type">int</span>)<span class="built_in">stack</span> + poolsize);</span><br><span class="line">*--sp = EXIT; <span class="comment">// call exit if main returns</span></span><br><span class="line">*--sp = PUSH; tmp = sp;</span><br><span class="line">*--sp = argc;</span><br><span class="line">*--sp = (<span class="type">int</span>)argv;</span><br><span class="line">*--sp = (<span class="type">int</span>)tmp;</span><br></pre></td></tr></tbody></table><p>当然，最后要注意的一点是：所有的变量定义必须放在语句之前。</p>',104),B={href:"https://github.com/lotabout/write-a-C-interpreter/tree/step-6",target:"_blank",rel:"noopener noreferrer"},I=p('<table><tbody><tr><td class="code"><pre><span class="line">git clone -b step-6 https://github.com/lotabout/write-a-C-interpreter</span><br></pre></td></tr></tbody></table><p>通过 <code>gcc -o xc-tutor xc-tutor.c</code> 进行编译。并执行 <code>./xc-tutor hello.c</code> 查看结果。</p><p>正如我们保证的那样，我们的代码是自举的，能自己编译自己，所以你可以执行 <code>./xc-tutor xc-tutor.c hello.c</code>。可以看到和之前有同样的输出。</p><h2 id="小结" tabindex="-1"><a class="header-anchor" href="#小结"><span><a href="about:blank#%E5%B0%8F%E7%BB%93"></a>小结</span></a></h2><p>本章我们进行了最后的解析，解析表达式。本章有两个难点：</p><ol><li>如何通过递归调用 <code>expression</code> 来实现运算符的优先级。</li><li>如何为每个运算符生成对应的汇编代码。</li></ol><p>尽管代码看起来比较简单（虽然多），但其中用到的原理还是需要仔细推敲的。</p><p>最后，恭喜你！通过一步步的学习，自己实现了一个C语言的编译器（好吧，是解释器）。</p>',8);function M(S,v){const n=t("ExternalLinkIcon");return c(),r("div",null,[o,s("p",null,[a("本文转自 "),s("a",b,[a("https://blog.csdn.net/xzp740813/article/details/142961332?spm=1001.2014.3001.5501"),e(n)]),a("，如有侵权，请联系删除。")]),d,s("ol",null,[s("li",null,[s("a",h,[a("手把手教你构建 C 语言编译器（0）——前言"),e(n)])]),s("li",null,[s("a",m,[a("手把手教你构建 C 语言编译器（1）——设计"),e(n)])]),s("li",null,[s("a",y,[a("手把手教你构建 C 语言编译器（2）——虚拟机"),e(n)])]),s("li",null,[s("a",x,[a("手把手教你构建 C 语言编译器（3）——词法分析器"),e(n)])]),s("li",null,[s("a",u,[a("手把手教你构建 C 语言编译器（4）——递归下降"),e(n)])]),s("li",null,[s("a",f,[a("手把手教你构建 C 语言编译器（5）——变量定义"),e(n)])]),s("li",null,[s("a",k,[a("手把手教你构建 C 语言编译器（6）——函数定义"),e(n)])]),s("li",null,[s("a",E,[a("手把手教你构建 C 语言编译器（7）——语句"),e(n)])]),s("li",null,[s("a",g,[a("手把手教你构建 C 语言编译器（8）——表达式"),e(n)])]),s("li",null,[s("a",C,[a("手把手教你构建 C 语言编译器（9）——总结"),e(n)])])]),_,s("p",null,[a("C 语言定义了各种表达式的优先级，可以参考 "),s("a",A,[a("C 语言运算符优先级"),e(n)]),a("。")]),w,s("p",null,[a("本章的代码可以在 "),s("a",B,[a("Github"),e(n)]),a(" 上下载，也可以直接 clone")]),I])}const L=l(i,[["render",M],["__file","8.html.vue"]]),F=JSON.parse('{"path":"/tech/designASimpileCCompiler/8.html","title":"手把手教你构建 C 语言编译器（8）——表达式","lang":"zh-CN","frontmatter":{"title":"手把手教你构建 C 语言编译器（8）——表达式","category":["编译原理"],"tag":["c","编译器","解释器"],"description":"转载声明 本文转自 https://blog.csdn.net/xzp740813/article/details/142961332?spm=1001.2014.3001.5501，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（8）- 表达式 Table of Contents 1. 运算符的优先级 2. 一元运算符 2.1. 常...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/designASimpileCCompiler/8.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"手把手教你构建 C 语言编译器（8）——表达式"}],["meta",{"property":"og:description","content":"转载声明 本文转自 https://blog.csdn.net/xzp740813/article/details/142961332?spm=1001.2014.3001.5501，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（8）- 表达式 Table of Contents 1. 运算符的优先级 2. 一元运算符 2.1. 常..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"c"}],["meta",{"property":"article:tag","content":"编译器"}],["meta",{"property":"article:tag","content":"解释器"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"手把手教你构建 C 语言编译器（8）——表达式\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"运算符的优先级","slug":"运算符的优先级","link":"#运算符的优先级","children":[]},{"level":2,"title":"一元运算符","slug":"一元运算符","link":"#一元运算符","children":[{"level":3,"title":"常量","slug":"常量","link":"#常量","children":[]},{"level":3,"title":"sizeof","slug":"sizeof","link":"#sizeof","children":[]},{"level":3,"title":"变量与函数调用","slug":"变量与函数调用","link":"#变量与函数调用","children":[]},{"level":3,"title":"强制转换","slug":"强制转换","link":"#强制转换","children":[]},{"level":3,"title":"指针取值","slug":"指针取值","link":"#指针取值","children":[]},{"level":3,"title":"取址操作","slug":"取址操作","link":"#取址操作","children":[]},{"level":3,"title":"逻辑取反","slug":"逻辑取反","link":"#逻辑取反","children":[]},{"level":3,"title":"按位取反","slug":"按位取反","link":"#按位取反","children":[]},{"level":3,"title":"正负号","slug":"正负号","link":"#正负号","children":[]},{"level":3,"title":"自增自减","slug":"自增自减","link":"#自增自减","children":[]}]},{"level":2,"title":"二元运算符","slug":"二元运算符","link":"#二元运算符","children":[{"level":3,"title":"赋值操作","slug":"赋值操作","link":"#赋值操作","children":[]},{"level":3,"title":"三目运算符","slug":"三目运算符","link":"#三目运算符","children":[]},{"level":3,"title":"逻辑运算符","slug":"逻辑运算符","link":"#逻辑运算符","children":[]},{"level":3,"title":"数学运算符","slug":"数学运算符","link":"#数学运算符","children":[]},{"level":3,"title":"自增自减","slug":"自增自减-1","link":"#自增自减-1","children":[]},{"level":3,"title":"数组取值操作","slug":"数组取值操作","link":"#数组取值操作","children":[]}]},{"level":2,"title":"代码","slug":"代码","link":"#代码","children":[]},{"level":2,"title":"小结","slug":"小结","link":"#小结","children":[]}],"readingTime":{"minutes":29.67,"words":8900},"filePathRelative":"tech/designASimpileCCompiler/8.md","excerpt":"\\n<p>本文转自 <a href=\\"https://blog.csdn.net/xzp740813/article/details/142961332?spm=1001.2014.3001.5501\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">https://blog.csdn.net/xzp740813/article/details/142961332?spm=1001.2014.3001.5501</a>，如有侵权，请联系删除。</p>\\n<h1>原文内容</h1>\\n<h1>手把手教你构建 C 语言编译器（8）- 表达式</h1>\\n<p>Table of Contents</p>","autoDesc":true}');export{L as comp,F as data};
diff --git a/assets/9.html-CGdd1xtP.js b/assets/9.html-DOIgY3Qt.js
similarity index 99%
rename from assets/9.html-CGdd1xtP.js
rename to assets/9.html-DOIgY3Qt.js
index ae7d14e..df18252 100644
--- a/assets/9.html-CGdd1xtP.js
+++ b/assets/9.html-DOIgY3Qt.js
@@ -1 +1 @@
-import{_ as o,r as l,o as i,c as p,b as e,e as t,d as a,f as n}from"./app-B69Gl_S-.js";const h={},s=e("h1",{id:"转载声明",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#转载声明"},[e("span",null,"转载声明")])],-1),c={href:"https://lotabout.me/2016/write-a-C-interpreter-9/",target:"_blank",rel:"noopener noreferrer"},E=n('<h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-9-总结" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-9-总结"><span>手把手教你构建 C 语言编译器（9）- 总结</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#%E8%99%9A%E6%8B%9F%E6%9C%BA%E4%B8%8E%E7%9B%AE%E6%A0%87%E4%BB%A3%E7%A0%81">1. 虚拟机与目标代码</a></li><li><a href="about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90">2. 词法分析</a></li><li><a href="about:blank#%E8%AF%AD%E6%B3%95%E5%88%86%E6%9E%90">3. 语法分析</a></li><li><a href="about:blank#%E5%85%B3%E4%BA%8E%E7%BC%96%E4%BB%A3%E7%A0%81">4. 关于编代码</a></li><li><a href="about:blank#%E7%BB%93%E8%AF%AD">5. 结语</a></li></ol><p>恭喜你完成了自己的 C 语言编译器，本章中我们发一发牢骚，说一说编写编译器值得注意的一些问题；编写编译器时遇到的一些难题。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p>',6),b={href:"http://lotabout.me/2015/write-a-C-interpreter-0/",target:"_blank",rel:"noopener noreferrer"},d={href:"http://lotabout.me/2015/write-a-C-interpreter-1/",target:"_blank",rel:"noopener noreferrer"},u={href:"http://lotabout.me/2015/write-a-C-interpreter-2/",target:"_blank",rel:"noopener noreferrer"},f={href:"http://lotabout.me/2015/write-a-C-interpreter-3/",target:"_blank",rel:"noopener noreferrer"},C={href:"http://lotabout.me/2016/write-a-C-interpreter-4/",target:"_blank",rel:"noopener noreferrer"},_={href:"http://lotabout.me/2016/write-a-C-interpreter-5/",target:"_blank",rel:"noopener noreferrer"},m={href:"http://lotabout.me/2016/write-a-C-interpreter-6/",target:"_blank",rel:"noopener noreferrer"},B={href:"http://lotabout.me/2016/write-a-C-interpreter-7/",target:"_blank",rel:"noopener noreferrer"},A={href:"http://lotabout.me/2016/write-a-C-interpreter-8/",target:"_blank",rel:"noopener noreferrer"},g={href:"http://lotabout.me/2016/write-a-C-interpreter-9/",target:"_blank",rel:"noopener noreferrer"},k=n('<h2 id="虚拟机与目标代码" tabindex="-1"><a class="header-anchor" href="#虚拟机与目标代码"><span><a href="about:blank#%E8%99%9A%E6%8B%9F%E6%9C%BA%E4%B8%8E%E7%9B%AE%E6%A0%87%E4%BB%A3%E7%A0%81"></a>虚拟机与目标代码</span></a></h2><p>整个系列的一开始，我们就着手虚拟机的实现。不知道你是否有同感，这部分对于整个编译器的编写其实是十分重要的。我认为至少占了重要程度的50%。</p><p>这里要说明这样一个观点，学习编译原理时常常着眼于词法分析和语法分析，而忽略了同样重要的代码生成。对于学习或考试而言或许可以，但实际编译项目时，最为重要的是能“跑起来”，所以我们需要给予代码生成高度的重视。</p><p>同时我们也看到，在后期解析语句和表达式时，难点已经不再是语法分析了，而是如何为运算符生成相应的汇编代码。</p><h2 id="词法分析" tabindex="-1"><a class="header-anchor" href="#词法分析"><span><a href="about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90"></a>词法分析</span></a></h2><p>我们用了很暴力的手段编写了我们的词法分析器，我认为这并无不可。</p><p>但你依旧可以学习相关的知识，了解自动生成词法分析器的原理，它涉及到了“正则表达式”，“状态机”等等知识。相信这部分的知识能够很大程度上提高你的编程水平。</p><p>同时，如果今后你仍然想编写编译器，不妨试试这些自动生成工具。</p><h2 id="语法分析" tabindex="-1"><a class="header-anchor" href="#语法分析"><span><a href="about:blank#%E8%AF%AD%E6%B3%95%E5%88%86%E6%9E%90"></a>语法分析</span></a></h2><p>长期以来，语法分析对我而言一直是迷一样的存在，直到真正用递归下降的方式实现了一个。</p><p>我们用了专门的一章讲解了“递归下降”与 BNF 文法的关系。希望能减少你对理论的厌恶。至少，实现起来并不是太难。</p><p>如果有兴趣，可以学习学习这些文法，因为已经有许多自动生成的工具支持它们。这样你就不需要重复造轮子。可以看看 yacc 等工具，更先进的版本是 <code>bsion</code>。同时其它语言也有许多类似的支持。</p><p>题外话，最近知道了一个叫“PEG 文法”的表示方法，无论是读起来，还是实现起来，都比 BNF 要容易，你也可以学习看看。</p><h2 id="关于编代码" tabindex="-1"><a class="header-anchor" href="#关于编代码"><span><a href="about:blank#%E5%85%B3%E4%BA%8E%E7%BC%96%E4%BB%A3%E7%A0%81"></a>关于编代码</span></a></h2><p>这也是我自己的感慨吧。无论多好的教程，想要完全理解它，最好的方式恐怕还是要自己实现它。</p><p>只是在编写代码的过程中，我们会遇到许多的挫折，例如需要考虑许多细节，或是调试起来十分困难。但也只有真正静下心来去克服它，我们才能有所成长吧。</p><p>例如在编写表达式的解析时，大量重复的代码特别让人崩溃。还有就是调试编译器，简直痛苦地无话可说。</p><p>P.S. 如果你按这个系列自己编写代码，记得事先写一些用于输出汇编代码的函数，很有帮助的。</p><p>还有就是写这个系列的文章，开始的冲动过了之后，每写一篇都特别心烦，希望文章本身没有受我的这种情绪影响吧。</p><h2 id="结语" tabindex="-1"><a class="header-anchor" href="#结语"><span><a href="about:blank#%E7%BB%93%E8%AF%AD"></a>结语</span></a></h2><p>编程有趣又无趣，只有身在其中的我们才能体会吧。</p>',21);function w(x,y){const r=l("ExternalLinkIcon");return i(),p("div",null,[s,e("p",null,[t("本文转自 "),e("a",c,[t("https://lotabout.me/2016/write-a-C-interpreter-9/"),a(r)]),t("，如有侵权，请联系删除。")]),E,e("ol",null,[e("li",null,[e("a",b,[t("手把手教你构建 C 语言编译器（0）——前言"),a(r)])]),e("li",null,[e("a",d,[t("手把手教你构建 C 语言编译器（1）——设计"),a(r)])]),e("li",null,[e("a",u,[t("手把手教你构建 C 语言编译器（2）——虚拟机"),a(r)])]),e("li",null,[e("a",f,[t("手把手教你构建 C 语言编译器（3）——词法分析器"),a(r)])]),e("li",null,[e("a",C,[t("手把手教你构建 C 语言编译器（4）——递归下降"),a(r)])]),e("li",null,[e("a",_,[t("手把手教你构建 C 语言编译器（5）——变量定义"),a(r)])]),e("li",null,[e("a",m,[t("手把手教你构建 C 语言编译器（6）——函数定义"),a(r)])]),e("li",null,[e("a",B,[t("手把手教你构建 C 语言编译器（7）——语句"),a(r)])]),e("li",null,[e("a",A,[t("手把手教你构建 C 语言编译器（8）——表达式"),a(r)])]),e("li",null,[e("a",g,[t("手把手教你构建 C 语言编译器（9）——总结"),a(r)])])]),k])}const D=o(h,[["render",w],["__file","9.html.vue"]]),v=JSON.parse('{"path":"/tech/designASimpileCCompiler/9.html","title":"手把手教你构建 C 语言编译器（9）——总结","lang":"zh-CN","frontmatter":{"title":"手把手教你构建 C 语言编译器（9）——总结","category":["编译原理"],"tag":["c","编译器","解释器"],"description":"转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-9/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（9）- 总结 Table of Contents 1. 虚拟机与目标代码 2. 词法分析 3. 语法分析 4. 关于编代码 5. 结语 恭喜你完成了自己的 C 语言编译...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/designASimpileCCompiler/9.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"手把手教你构建 C 语言编译器（9）——总结"}],["meta",{"property":"og:description","content":"转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-9/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（9）- 总结 Table of Contents 1. 虚拟机与目标代码 2. 词法分析 3. 语法分析 4. 关于编代码 5. 结语 恭喜你完成了自己的 C 语言编译..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"c"}],["meta",{"property":"article:tag","content":"编译器"}],["meta",{"property":"article:tag","content":"解释器"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"手把手教你构建 C 语言编译器（9）——总结\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"虚拟机与目标代码","slug":"虚拟机与目标代码","link":"#虚拟机与目标代码","children":[]},{"level":2,"title":"词法分析","slug":"词法分析","link":"#词法分析","children":[]},{"level":2,"title":"语法分析","slug":"语法分析","link":"#语法分析","children":[]},{"level":2,"title":"关于编代码","slug":"关于编代码","link":"#关于编代码","children":[]},{"level":2,"title":"结语","slug":"结语","link":"#结语","children":[]}],"readingTime":{"minutes":4.66,"words":1397},"filePathRelative":"tech/designASimpileCCompiler/9.md","excerpt":"\\n<p>本文转自 <a href=\\"https://lotabout.me/2016/write-a-C-interpreter-9/\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">https://lotabout.me/2016/write-a-C-interpreter-9/</a>，如有侵权，请联系删除。</p>\\n<h1>原文内容</h1>\\n<h1>手把手教你构建 C 语言编译器（9）- 总结</h1>\\n<p>Table of Contents</p>\\n<ol>\\n<li><a href=\\"about:blank#%E8%99%9A%E6%8B%9F%E6%9C%BA%E4%B8%8E%E7%9B%AE%E6%A0%87%E4%BB%A3%E7%A0%81\\">1. 虚拟机与目标代码</a></li>\\n<li><a href=\\"about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90\\">2. 词法分析</a></li>\\n<li><a href=\\"about:blank#%E8%AF%AD%E6%B3%95%E5%88%86%E6%9E%90\\">3. 语法分析</a></li>\\n<li><a href=\\"about:blank#%E5%85%B3%E4%BA%8E%E7%BC%96%E4%BB%A3%E7%A0%81\\">4. 关于编代码</a></li>\\n<li><a href=\\"about:blank#%E7%BB%93%E8%AF%AD\\">5. 结语</a></li>\\n</ol>","autoDesc":true}');export{D as comp,v as data};
+import{_ as o,r as l,o as i,c as p,b as e,e as t,d as a,f as n}from"./app-B4LGNJZ0.js";const h={},s=e("h1",{id:"转载声明",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#转载声明"},[e("span",null,"转载声明")])],-1),c={href:"https://lotabout.me/2016/write-a-C-interpreter-9/",target:"_blank",rel:"noopener noreferrer"},E=n('<h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-9-总结" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-9-总结"><span>手把手教你构建 C 语言编译器（9）- 总结</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#%E8%99%9A%E6%8B%9F%E6%9C%BA%E4%B8%8E%E7%9B%AE%E6%A0%87%E4%BB%A3%E7%A0%81">1. 虚拟机与目标代码</a></li><li><a href="about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90">2. 词法分析</a></li><li><a href="about:blank#%E8%AF%AD%E6%B3%95%E5%88%86%E6%9E%90">3. 语法分析</a></li><li><a href="about:blank#%E5%85%B3%E4%BA%8E%E7%BC%96%E4%BB%A3%E7%A0%81">4. 关于编代码</a></li><li><a href="about:blank#%E7%BB%93%E8%AF%AD">5. 结语</a></li></ol><p>恭喜你完成了自己的 C 语言编译器，本章中我们发一发牢骚，说一说编写编译器值得注意的一些问题；编写编译器时遇到的一些难题。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p>',6),b={href:"http://lotabout.me/2015/write-a-C-interpreter-0/",target:"_blank",rel:"noopener noreferrer"},d={href:"http://lotabout.me/2015/write-a-C-interpreter-1/",target:"_blank",rel:"noopener noreferrer"},u={href:"http://lotabout.me/2015/write-a-C-interpreter-2/",target:"_blank",rel:"noopener noreferrer"},f={href:"http://lotabout.me/2015/write-a-C-interpreter-3/",target:"_blank",rel:"noopener noreferrer"},C={href:"http://lotabout.me/2016/write-a-C-interpreter-4/",target:"_blank",rel:"noopener noreferrer"},_={href:"http://lotabout.me/2016/write-a-C-interpreter-5/",target:"_blank",rel:"noopener noreferrer"},m={href:"http://lotabout.me/2016/write-a-C-interpreter-6/",target:"_blank",rel:"noopener noreferrer"},B={href:"http://lotabout.me/2016/write-a-C-interpreter-7/",target:"_blank",rel:"noopener noreferrer"},A={href:"http://lotabout.me/2016/write-a-C-interpreter-8/",target:"_blank",rel:"noopener noreferrer"},g={href:"http://lotabout.me/2016/write-a-C-interpreter-9/",target:"_blank",rel:"noopener noreferrer"},k=n('<h2 id="虚拟机与目标代码" tabindex="-1"><a class="header-anchor" href="#虚拟机与目标代码"><span><a href="about:blank#%E8%99%9A%E6%8B%9F%E6%9C%BA%E4%B8%8E%E7%9B%AE%E6%A0%87%E4%BB%A3%E7%A0%81"></a>虚拟机与目标代码</span></a></h2><p>整个系列的一开始，我们就着手虚拟机的实现。不知道你是否有同感，这部分对于整个编译器的编写其实是十分重要的。我认为至少占了重要程度的50%。</p><p>这里要说明这样一个观点，学习编译原理时常常着眼于词法分析和语法分析，而忽略了同样重要的代码生成。对于学习或考试而言或许可以，但实际编译项目时，最为重要的是能“跑起来”，所以我们需要给予代码生成高度的重视。</p><p>同时我们也看到，在后期解析语句和表达式时，难点已经不再是语法分析了，而是如何为运算符生成相应的汇编代码。</p><h2 id="词法分析" tabindex="-1"><a class="header-anchor" href="#词法分析"><span><a href="about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90"></a>词法分析</span></a></h2><p>我们用了很暴力的手段编写了我们的词法分析器，我认为这并无不可。</p><p>但你依旧可以学习相关的知识，了解自动生成词法分析器的原理，它涉及到了“正则表达式”，“状态机”等等知识。相信这部分的知识能够很大程度上提高你的编程水平。</p><p>同时，如果今后你仍然想编写编译器，不妨试试这些自动生成工具。</p><h2 id="语法分析" tabindex="-1"><a class="header-anchor" href="#语法分析"><span><a href="about:blank#%E8%AF%AD%E6%B3%95%E5%88%86%E6%9E%90"></a>语法分析</span></a></h2><p>长期以来，语法分析对我而言一直是迷一样的存在，直到真正用递归下降的方式实现了一个。</p><p>我们用了专门的一章讲解了“递归下降”与 BNF 文法的关系。希望能减少你对理论的厌恶。至少，实现起来并不是太难。</p><p>如果有兴趣，可以学习学习这些文法，因为已经有许多自动生成的工具支持它们。这样你就不需要重复造轮子。可以看看 yacc 等工具，更先进的版本是 <code>bsion</code>。同时其它语言也有许多类似的支持。</p><p>题外话，最近知道了一个叫“PEG 文法”的表示方法，无论是读起来，还是实现起来，都比 BNF 要容易，你也可以学习看看。</p><h2 id="关于编代码" tabindex="-1"><a class="header-anchor" href="#关于编代码"><span><a href="about:blank#%E5%85%B3%E4%BA%8E%E7%BC%96%E4%BB%A3%E7%A0%81"></a>关于编代码</span></a></h2><p>这也是我自己的感慨吧。无论多好的教程，想要完全理解它，最好的方式恐怕还是要自己实现它。</p><p>只是在编写代码的过程中，我们会遇到许多的挫折，例如需要考虑许多细节，或是调试起来十分困难。但也只有真正静下心来去克服它，我们才能有所成长吧。</p><p>例如在编写表达式的解析时，大量重复的代码特别让人崩溃。还有就是调试编译器，简直痛苦地无话可说。</p><p>P.S. 如果你按这个系列自己编写代码，记得事先写一些用于输出汇编代码的函数，很有帮助的。</p><p>还有就是写这个系列的文章，开始的冲动过了之后，每写一篇都特别心烦，希望文章本身没有受我的这种情绪影响吧。</p><h2 id="结语" tabindex="-1"><a class="header-anchor" href="#结语"><span><a href="about:blank#%E7%BB%93%E8%AF%AD"></a>结语</span></a></h2><p>编程有趣又无趣，只有身在其中的我们才能体会吧。</p>',21);function w(x,y){const r=l("ExternalLinkIcon");return i(),p("div",null,[s,e("p",null,[t("本文转自 "),e("a",c,[t("https://lotabout.me/2016/write-a-C-interpreter-9/"),a(r)]),t("，如有侵权，请联系删除。")]),E,e("ol",null,[e("li",null,[e("a",b,[t("手把手教你构建 C 语言编译器（0）——前言"),a(r)])]),e("li",null,[e("a",d,[t("手把手教你构建 C 语言编译器（1）——设计"),a(r)])]),e("li",null,[e("a",u,[t("手把手教你构建 C 语言编译器（2）——虚拟机"),a(r)])]),e("li",null,[e("a",f,[t("手把手教你构建 C 语言编译器（3）——词法分析器"),a(r)])]),e("li",null,[e("a",C,[t("手把手教你构建 C 语言编译器（4）——递归下降"),a(r)])]),e("li",null,[e("a",_,[t("手把手教你构建 C 语言编译器（5）——变量定义"),a(r)])]),e("li",null,[e("a",m,[t("手把手教你构建 C 语言编译器（6）——函数定义"),a(r)])]),e("li",null,[e("a",B,[t("手把手教你构建 C 语言编译器（7）——语句"),a(r)])]),e("li",null,[e("a",A,[t("手把手教你构建 C 语言编译器（8）——表达式"),a(r)])]),e("li",null,[e("a",g,[t("手把手教你构建 C 语言编译器（9）——总结"),a(r)])])]),k])}const D=o(h,[["render",w],["__file","9.html.vue"]]),v=JSON.parse('{"path":"/tech/designASimpileCCompiler/9.html","title":"手把手教你构建 C 语言编译器（9）——总结","lang":"zh-CN","frontmatter":{"title":"手把手教你构建 C 语言编译器（9）——总结","category":["编译原理"],"tag":["c","编译器","解释器"],"description":"转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-9/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（9）- 总结 Table of Contents 1. 虚拟机与目标代码 2. 词法分析 3. 语法分析 4. 关于编代码 5. 结语 恭喜你完成了自己的 C 语言编译...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/designASimpileCCompiler/9.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"手把手教你构建 C 语言编译器（9）——总结"}],["meta",{"property":"og:description","content":"转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-9/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（9）- 总结 Table of Contents 1. 虚拟机与目标代码 2. 词法分析 3. 语法分析 4. 关于编代码 5. 结语 恭喜你完成了自己的 C 语言编译..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"c"}],["meta",{"property":"article:tag","content":"编译器"}],["meta",{"property":"article:tag","content":"解释器"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"手把手教你构建 C 语言编译器（9）——总结\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"虚拟机与目标代码","slug":"虚拟机与目标代码","link":"#虚拟机与目标代码","children":[]},{"level":2,"title":"词法分析","slug":"词法分析","link":"#词法分析","children":[]},{"level":2,"title":"语法分析","slug":"语法分析","link":"#语法分析","children":[]},{"level":2,"title":"关于编代码","slug":"关于编代码","link":"#关于编代码","children":[]},{"level":2,"title":"结语","slug":"结语","link":"#结语","children":[]}],"readingTime":{"minutes":4.66,"words":1397},"filePathRelative":"tech/designASimpileCCompiler/9.md","excerpt":"\\n<p>本文转自 <a href=\\"https://lotabout.me/2016/write-a-C-interpreter-9/\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">https://lotabout.me/2016/write-a-C-interpreter-9/</a>，如有侵权，请联系删除。</p>\\n<h1>原文内容</h1>\\n<h1>手把手教你构建 C 语言编译器（9）- 总结</h1>\\n<p>Table of Contents</p>\\n<ol>\\n<li><a href=\\"about:blank#%E8%99%9A%E6%8B%9F%E6%9C%BA%E4%B8%8E%E7%9B%AE%E6%A0%87%E4%BB%A3%E7%A0%81\\">1. 虚拟机与目标代码</a></li>\\n<li><a href=\\"about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90\\">2. 词法分析</a></li>\\n<li><a href=\\"about:blank#%E8%AF%AD%E6%B3%95%E5%88%86%E6%9E%90\\">3. 语法分析</a></li>\\n<li><a href=\\"about:blank#%E5%85%B3%E4%BA%8E%E7%BC%96%E4%BB%A3%E7%A0%81\\">4. 关于编代码</a></li>\\n<li><a href=\\"about:blank#%E7%BB%93%E8%AF%AD\\">5. 结语</a></li>\\n</ol>","autoDesc":true}');export{D as comp,v as data};
diff --git a/assets/DesignPrinciples.html-BLnXHGN8.js b/assets/DesignPrinciples.html-BAjp9viD.js
similarity index 99%
rename from assets/DesignPrinciples.html-BLnXHGN8.js
rename to assets/DesignPrinciples.html-BAjp9viD.js
index 8ba4c1e..86b27e4 100644
--- a/assets/DesignPrinciples.html-BLnXHGN8.js
+++ b/assets/DesignPrinciples.html-BAjp9viD.js
@@ -1,4 +1,4 @@
-import{_ as a,o as e,c as t,a as n,b as l,f as s}from"./app-B69Gl_S-.js";const i={},p=l("p",null,"类的设计原则有七个，包括：开闭原则、里氏代换原则、迪米特原则（最少知道原则）、单一职责原则、接口分隔原则、依赖倒置原则、组合/聚合复用原则。",-1),c=s('<h2 id="关系" tabindex="-1"><a class="header-anchor" href="#关系"><span>关系</span></a></h2><p>七大原则之间并不是相互孤立的，而是相互关联的。一个原则可以是另一个原则的加强或基础。违反其中一个原则，可能同时违反其他原则。</p><p>开闭原则是面向对象可复用设计的基石，其他设计原则是实现开闭原则的手段和工具。</p><p>通常，可以将这七个原则分为以下两部分：</p><ul><li>设计目标：开闭原则、里氏代换原则、迪米特原则</li><li>设计方法：单一职责原则、接口分隔原则、依赖倒置原则、组合/聚合复用原则</li></ul><h2 id="开闭原则" tabindex="-1"><a class="header-anchor" href="#开闭原则"><span>开闭原则</span></a></h2><ul><li>对扩展开放</li><li>对修改关闭</li></ul><p>根据开闭原则，在设计一个系统模块的时候，应该可以在不修改原模块的基础上，扩展其功能。</p><h3 id="实现方法" tabindex="-1"><a class="header-anchor" href="#实现方法"><span>实现方法</span></a></h3><ol><li>使用抽象类和接口：通过定义抽象类和接口，可以在不修改现有代码的情况下，增加新的实现。</li><li>使用设计模式：例如策略模式、装饰者模式等，可以在不改变原有代码的情况下，动态地扩展对象的行为。</li><li>遵循单一职责原则：确保每个类只有一个职责，这样在扩展功能时，不会影响其他功能。</li></ol>',10),o=s(`<img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuIh9BCb9LNY-PjdJ2HrFzpIydBxsQT_yfnqpkJBpIbABqXAJKnKSaug3KulAKeiKghaK5BGLYa4S3Kq5AuMWrEBId1AkMYwkv9p4uc85vvpCrBmIi39TXTnAg2uhX0bQO0DIyeFpSrD3CZBpqZKq4RgB8SepSmjoKdE1vXGJOpFKIbrTBOHgBeVKl1IWvm00" alt=""><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuIh9BCb9LNYoe_VvccLF9tGytTFmSlhQfttpdtRCv4hEIImkLd3EoKpDAr6evb9Gq5N8hGnEBIfBBLAmKe0mj832sWef-S7vkQaX6PbvwHgQNBLGdSKGfTLW9M2EXYPGOr1gSMbE2L0Lr6HTNIseKYw7rBmKeAi0" alt=""><h2 id="里氏代换原则" tabindex="-1"><a class="header-anchor" href="#里氏代换原则"><span>里氏代换原则</span></a></h2><h3 id="里氏代换原则-1" tabindex="-1"><a class="header-anchor" href="#里氏代换原则-1"><span>里氏代换原则</span></a></h3><ul><li>里氏代换原则规定子类不得重写父类的普通方法，只能重写父类的抽象方法；即子类可以扩展父类的功能，但是不能改变父类原有的功能。</li><li>派生类应当可以替换基类并出现在基类能够出现的任何地方，或者说如果我们把代码中使用基类的地方用它的派生类所代替，代码还能正常工作。</li></ul><h3 id="实现方法-1" tabindex="-1"><a class="header-anchor" href="#实现方法-1"><span>实现方法</span></a></h3><ol><li>使用抽象类和接口：确保子类实现父类的抽象方法，而不是重写父类的具体方法。</li><li>遵循契约：子类的方法签名应与父类一致，返回类型应与父类相同或是其子类型。</li><li>遵循行为一致性：子类应保持父类的行为，不应引入违反父类预期的新行为。</li></ol><h3 id="示例" tabindex="-1"><a class="header-anchor" href="#示例"><span>示例</span></a></h3><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuIh9BCb9LNY-PjdJ2HqlstkURUX_idlnizv5J_lcF-sOoPMOL5nIb9XSef2SarXShE2KMPIYKCsbeA2ja9PJgQ6fOALGbf-PmbNBnGLH45oGM5IKNwwGMb6IcfT2X0QGWl34akICr2Aekd8GJoC9fD4AB8si2LcvhguTM9xB0MWLq2y0" alt=""><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuIh9BCb9LNYoe_VvccLF9tIyREzvjg7_oUx5pteNFUsR_xHZ9bTYKd59KM9oYK9oJc9niO9JPb6AGZMNWeAsGbfEfOQcWfL2MNvc2bSj5nT4WJzGUMPoXa9gHKbgNWfE3GhL2YKPHVdb2dcfvGgXUSMb1GNvHIMfAVu5gKM99PdvUQuLoQa588Q6fhL2BS9ya7dXYIN96Qb5K6FBGJoD990zLc1fP4SXAzVLjGFBSpa0NGRqFG00" alt=""><h2 id="迪米特原则" tabindex="-1"><a class="header-anchor" href="#迪米特原则"><span>迪米特原则</span></a></h2><h3 id="迪米特原则-1" tabindex="-1"><a class="header-anchor" href="#迪米特原则-1"><span>迪米特原则</span></a></h3><p>一个实体应当尽量少地与其他实体之间发生相互作用，使得系统功能模块相对独立；降低类之间的耦合度，提高模块的相对独立性。</p><h3 id="实现方法-2" tabindex="-1"><a class="header-anchor" href="#实现方法-2"><span>实现方法</span></a></h3><ol><li><strong>引入中介者模式</strong>：通过中介者对象来管理对象之间的交互，减少对象之间的直接依赖。</li><li><strong>使用门面模式</strong>：通过门面对象提供统一的接口，隐藏系统的复杂性，减少对象之间的直接交互。</li><li><strong>限制公开方法</strong>：尽量减少类的公开方法，避免不必要的外部依赖。</li></ol><h2 id="单一职责原则" tabindex="-1"><a class="header-anchor" href="#单一职责原则"><span>单一职责原则</span></a></h2><ul><li>一个类只对应一个职责，其职责是引起该类变化的原因。</li><li>如果一个类需要改变，改变它的理由永远只有一个。如果存在多个改变它的理由，就需要重新设计该类。</li></ul><h3 id="实现方法-3" tabindex="-1"><a class="header-anchor" href="#实现方法-3"><span>实现方法</span></a></h3><ol><li><strong>职责分离</strong>：将不同的职责分离到不同的类中，每个类只负责一个职责。</li><li><strong>模块化设计</strong>：通过模块化设计，将不同的功能模块分开，确保每个模块只负责一个功能。</li><li><strong>重构</strong>：在发现类有多个职责时，及时进行重构，将不同的职责分离到不同的类中。</li></ol><h3 id="示例-1" tabindex="-1"><a class="header-anchor" href="#示例-1"><span>示例</span></a></h3><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// 不符合单一职责原则的类</span>
+import{_ as a,o as e,c as t,a as n,b as l,f as s}from"./app-B4LGNJZ0.js";const i={},p=l("p",null,"类的设计原则有七个，包括：开闭原则、里氏代换原则、迪米特原则（最少知道原则）、单一职责原则、接口分隔原则、依赖倒置原则、组合/聚合复用原则。",-1),c=s('<h2 id="关系" tabindex="-1"><a class="header-anchor" href="#关系"><span>关系</span></a></h2><p>七大原则之间并不是相互孤立的，而是相互关联的。一个原则可以是另一个原则的加强或基础。违反其中一个原则，可能同时违反其他原则。</p><p>开闭原则是面向对象可复用设计的基石，其他设计原则是实现开闭原则的手段和工具。</p><p>通常，可以将这七个原则分为以下两部分：</p><ul><li>设计目标：开闭原则、里氏代换原则、迪米特原则</li><li>设计方法：单一职责原则、接口分隔原则、依赖倒置原则、组合/聚合复用原则</li></ul><h2 id="开闭原则" tabindex="-1"><a class="header-anchor" href="#开闭原则"><span>开闭原则</span></a></h2><ul><li>对扩展开放</li><li>对修改关闭</li></ul><p>根据开闭原则，在设计一个系统模块的时候，应该可以在不修改原模块的基础上，扩展其功能。</p><h3 id="实现方法" tabindex="-1"><a class="header-anchor" href="#实现方法"><span>实现方法</span></a></h3><ol><li>使用抽象类和接口：通过定义抽象类和接口，可以在不修改现有代码的情况下，增加新的实现。</li><li>使用设计模式：例如策略模式、装饰者模式等，可以在不改变原有代码的情况下，动态地扩展对象的行为。</li><li>遵循单一职责原则：确保每个类只有一个职责，这样在扩展功能时，不会影响其他功能。</li></ol>',10),o=s(`<img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuIh9BCb9LNY-PjdJ2HrFzpIydBxsQT_yfnqpkJBpIbABqXAJKnKSaug3KulAKeiKghaK5BGLYa4S3Kq5AuMWrEBId1AkMYwkv9p4uc85vvpCrBmIi39TXTnAg2uhX0bQO0DIyeFpSrD3CZBpqZKq4RgB8SepSmjoKdE1vXGJOpFKIbrTBOHgBeVKl1IWvm00" alt=""><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuIh9BCb9LNYoe_VvccLF9tGytTFmSlhQfttpdtRCv4hEIImkLd3EoKpDAr6evb9Gq5N8hGnEBIfBBLAmKe0mj832sWef-S7vkQaX6PbvwHgQNBLGdSKGfTLW9M2EXYPGOr1gSMbE2L0Lr6HTNIseKYw7rBmKeAi0" alt=""><h2 id="里氏代换原则" tabindex="-1"><a class="header-anchor" href="#里氏代换原则"><span>里氏代换原则</span></a></h2><h3 id="里氏代换原则-1" tabindex="-1"><a class="header-anchor" href="#里氏代换原则-1"><span>里氏代换原则</span></a></h3><ul><li>里氏代换原则规定子类不得重写父类的普通方法，只能重写父类的抽象方法；即子类可以扩展父类的功能，但是不能改变父类原有的功能。</li><li>派生类应当可以替换基类并出现在基类能够出现的任何地方，或者说如果我们把代码中使用基类的地方用它的派生类所代替，代码还能正常工作。</li></ul><h3 id="实现方法-1" tabindex="-1"><a class="header-anchor" href="#实现方法-1"><span>实现方法</span></a></h3><ol><li>使用抽象类和接口：确保子类实现父类的抽象方法，而不是重写父类的具体方法。</li><li>遵循契约：子类的方法签名应与父类一致，返回类型应与父类相同或是其子类型。</li><li>遵循行为一致性：子类应保持父类的行为，不应引入违反父类预期的新行为。</li></ol><h3 id="示例" tabindex="-1"><a class="header-anchor" href="#示例"><span>示例</span></a></h3><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuIh9BCb9LNY-PjdJ2HqlstkURUX_idlnizv5J_lcF-sOoPMOL5nIb9XSef2SarXShE2KMPIYKCsbeA2ja9PJgQ6fOALGbf-PmbNBnGLH45oGM5IKNwwGMb6IcfT2X0QGWl34akICr2Aekd8GJoC9fD4AB8si2LcvhguTM9xB0MWLq2y0" alt=""><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuIh9BCb9LNYoe_VvccLF9tIyREzvjg7_oUx5pteNFUsR_xHZ9bTYKd59KM9oYK9oJc9niO9JPb6AGZMNWeAsGbfEfOQcWfL2MNvc2bSj5nT4WJzGUMPoXa9gHKbgNWfE3GhL2YKPHVdb2dcfvGgXUSMb1GNvHIMfAVu5gKM99PdvUQuLoQa588Q6fhL2BS9ya7dXYIN96Qb5K6FBGJoD990zLc1fP4SXAzVLjGFBSpa0NGRqFG00" alt=""><h2 id="迪米特原则" tabindex="-1"><a class="header-anchor" href="#迪米特原则"><span>迪米特原则</span></a></h2><h3 id="迪米特原则-1" tabindex="-1"><a class="header-anchor" href="#迪米特原则-1"><span>迪米特原则</span></a></h3><p>一个实体应当尽量少地与其他实体之间发生相互作用，使得系统功能模块相对独立；降低类之间的耦合度，提高模块的相对独立性。</p><h3 id="实现方法-2" tabindex="-1"><a class="header-anchor" href="#实现方法-2"><span>实现方法</span></a></h3><ol><li><strong>引入中介者模式</strong>：通过中介者对象来管理对象之间的交互，减少对象之间的直接依赖。</li><li><strong>使用门面模式</strong>：通过门面对象提供统一的接口，隐藏系统的复杂性，减少对象之间的直接交互。</li><li><strong>限制公开方法</strong>：尽量减少类的公开方法，避免不必要的外部依赖。</li></ol><h2 id="单一职责原则" tabindex="-1"><a class="header-anchor" href="#单一职责原则"><span>单一职责原则</span></a></h2><ul><li>一个类只对应一个职责，其职责是引起该类变化的原因。</li><li>如果一个类需要改变，改变它的理由永远只有一个。如果存在多个改变它的理由，就需要重新设计该类。</li></ul><h3 id="实现方法-3" tabindex="-1"><a class="header-anchor" href="#实现方法-3"><span>实现方法</span></a></h3><ol><li><strong>职责分离</strong>：将不同的职责分离到不同的类中，每个类只负责一个职责。</li><li><strong>模块化设计</strong>：通过模块化设计，将不同的功能模块分开，确保每个模块只负责一个功能。</li><li><strong>重构</strong>：在发现类有多个职责时，及时进行重构，将不同的职责分离到不同的类中。</li></ol><h3 id="示例-1" tabindex="-1"><a class="header-anchor" href="#示例-1"><span>示例</span></a></h3><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// 不符合单一职责原则的类</span>
 <span class="token keyword">class</span> <span class="token class-name">User</span> <span class="token punctuation">{</span>
   <span class="token function">login</span><span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
     <span class="token comment">// 登录逻辑</span>
diff --git "a/assets/Qt6 Maintence tools\344\270\215\350\203\275\345\256\211\350\243\205Qt5.html-CTk8exni.js" "b/assets/Qt6 Maintence tools\344\270\215\350\203\275\345\256\211\350\243\205Qt5.html-DdU1Gd4z.js"
similarity index 97%
rename from "assets/Qt6 Maintence tools\344\270\215\350\203\275\345\256\211\350\243\205Qt5.html-CTk8exni.js"
rename to "assets/Qt6 Maintence tools\344\270\215\350\203\275\345\256\211\350\243\205Qt5.html-DdU1Gd4z.js"
index 4152b48..7462137 100644
--- "a/assets/Qt6 Maintence tools\344\270\215\350\203\275\345\256\211\350\243\205Qt5.html-CTk8exni.js"	
+++ "b/assets/Qt6 Maintence tools\344\270\215\350\203\275\345\256\211\350\243\205Qt5.html-DdU1Gd4z.js"	
@@ -1 +1 @@
-import{_ as t,o as e,c as n,f as o}from"./app-B69Gl_S-.js";const i={},s=o('<h1 id="qt" tabindex="-1"><a class="header-anchor" href="#qt"><span>Qt</span></a></h1><h2 id="some-solutions-to-questions-about-qt" tabindex="-1"><a class="header-anchor" href="#some-solutions-to-questions-about-qt"><span>Some Solutions to Questions about Qt</span></a></h2><h3 id="the-qt-5-isn-t-in-qt-maintenance-tools" tabindex="-1"><a class="header-anchor" href="#the-qt-5-isn-t-in-qt-maintenance-tools"><span>The qt-5 isn&#39;t in Qt Maintenance tools</span></a></h3><ol><li>Open the Qt Maintenance Tools.</li><li>click the Archive in the Select-Component section.</li><li>click the filter button and you can see the qt-5 in the list.</li></ol>',4),a=[s];function l(c,h){return e(),n("div",null,a)}const p=t(i,[["render",l],["__file","Qt6 Maintence tools不能安装Qt5.html.vue"]]),u=JSON.parse(`{"path":"/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html","title":"Qt","lang":"zh-CN","frontmatter":{"title":"Qt","date":"2024-08-31T00:00:00.000Z","draft":false,"description":"Qt Some Solutions to Questions about Qt The qt-5 isn't in Qt Maintenance tools Open the Qt Maintenance Tools. click the Archive in the Select-Component section. click the filter...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"Qt"}],["meta",{"property":"og:description","content":"Qt Some Solutions to Questions about Qt The qt-5 isn't in Qt Maintenance tools Open the Qt Maintenance Tools. click the Archive in the Select-Component section. click the filter..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:published_time","content":"2024-08-31T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"Qt\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-08-31T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"Some Solutions to Questions about Qt","slug":"some-solutions-to-questions-about-qt","link":"#some-solutions-to-questions-about-qt","children":[{"level":3,"title":"The qt-5 isn't in Qt Maintenance tools","slug":"the-qt-5-isn-t-in-qt-maintenance-tools","link":"#the-qt-5-isn-t-in-qt-maintenance-tools","children":[]}]}],"readingTime":{"minutes":0.18,"words":54},"filePathRelative":"tech/Qt6 Maintence tools不能安装Qt5.md","localizedDate":"2024年8月31日","excerpt":"\\n<h2>Some Solutions to Questions about Qt</h2>\\n<h3>The qt-5 isn't in Qt Maintenance tools</h3>\\n<ol>\\n<li>Open the Qt Maintenance Tools.</li>\\n<li>click the Archive in the Select-Component section.</li>\\n<li>click the filter button and you can see the qt-5 in the list.</li>\\n</ol>\\n","autoDesc":true}`);export{p as comp,u as data};
+import{_ as t,o as e,c as n,f as o}from"./app-B4LGNJZ0.js";const i={},s=o('<h1 id="qt" tabindex="-1"><a class="header-anchor" href="#qt"><span>Qt</span></a></h1><h2 id="some-solutions-to-questions-about-qt" tabindex="-1"><a class="header-anchor" href="#some-solutions-to-questions-about-qt"><span>Some Solutions to Questions about Qt</span></a></h2><h3 id="the-qt-5-isn-t-in-qt-maintenance-tools" tabindex="-1"><a class="header-anchor" href="#the-qt-5-isn-t-in-qt-maintenance-tools"><span>The qt-5 isn&#39;t in Qt Maintenance tools</span></a></h3><ol><li>Open the Qt Maintenance Tools.</li><li>click the Archive in the Select-Component section.</li><li>click the filter button and you can see the qt-5 in the list.</li></ol>',4),a=[s];function l(c,h){return e(),n("div",null,a)}const p=t(i,[["render",l],["__file","Qt6 Maintence tools不能安装Qt5.html.vue"]]),u=JSON.parse(`{"path":"/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html","title":"Qt","lang":"zh-CN","frontmatter":{"title":"Qt","date":"2024-08-31T00:00:00.000Z","draft":false,"description":"Qt Some Solutions to Questions about Qt The qt-5 isn't in Qt Maintenance tools Open the Qt Maintenance Tools. click the Archive in the Select-Component section. click the filter...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"Qt"}],["meta",{"property":"og:description","content":"Qt Some Solutions to Questions about Qt The qt-5 isn't in Qt Maintenance tools Open the Qt Maintenance Tools. click the Archive in the Select-Component section. click the filter..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:published_time","content":"2024-08-31T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"Qt\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-08-31T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"Some Solutions to Questions about Qt","slug":"some-solutions-to-questions-about-qt","link":"#some-solutions-to-questions-about-qt","children":[{"level":3,"title":"The qt-5 isn't in Qt Maintenance tools","slug":"the-qt-5-isn-t-in-qt-maintenance-tools","link":"#the-qt-5-isn-t-in-qt-maintenance-tools","children":[]}]}],"readingTime":{"minutes":0.18,"words":54},"filePathRelative":"tech/Qt6 Maintence tools不能安装Qt5.md","localizedDate":"2024年8月31日","excerpt":"\\n<h2>Some Solutions to Questions about Qt</h2>\\n<h3>The qt-5 isn't in Qt Maintenance tools</h3>\\n<ol>\\n<li>Open the Qt Maintenance Tools.</li>\\n<li>click the Archive in the Select-Component section.</li>\\n<li>click the filter button and you can see the qt-5 in the list.</li>\\n</ol>\\n","autoDesc":true}`);export{p as comp,u as data};
diff --git a/assets/SearchResult-DAas8KH8.js b/assets/SearchResult-DAas8KH8.js
new file mode 100644
index 0000000..d2db279
--- /dev/null
+++ b/assets/SearchResult-DAas8KH8.js
@@ -0,0 +1 @@
+import{u as U,g as te,h as se,i as M,j as ae,P as le,t as re,k as ie,l as x,m as F,n as ne,p as Y,q as s,s as ce,R as O,v as oe,x as Ee,y as ue,C as he,z as me,A as Be,B as pe,D as ge,E as Ae,F as de,G as ve,H as T,I as $,J as ye,K as f,L as De}from"./app-B4LGNJZ0.js";const Ce=["/","/intro.html","/essays/","/essays/%E5%91%BD%E9%87%8C%E6%9C%89%E6%97%B6%E7%BB%88%E9%A1%BB%E6%9C%89.html","/projects/carrobot.html","/projects/","/resources/","/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html","/tech/android%20studio%E6%8D%A2%E6%BA%90.html","/tech/cicd.html","/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html","/tech/docker.html","/tech/figure_bed.html","/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html","/tech/","/tech/mailserver.html","/tech/modint.html","/tech/python_requrements.html","/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html","/tech/style.html","/tech/tensorflow%E8%B8%A9%E5%9D%91.html","/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html","/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html","/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html","/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html","/tech/%E5%8D%8F%E7%A8%8B.html","/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html","/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html","/tutorials/","/tutorials/typora%E6%BF%80%E6%B4%BB.html","/resources/compile/","/resources/html2md/","/tech/DesignPatterns/DesignPrinciples.html","/tech/DesignPatterns/abstractFactory.html","/tech/DesignPatterns/adapter.html","/tech/DesignPatterns/bridge.html","/tech/DesignPatterns/builder.html","/tech/DesignPatterns/chainOfResponsibility.html","/tech/DesignPatterns/command.html","/tech/DesignPatterns/composite.html","/tech/DesignPatterns/decorator.html","/tech/DesignPatterns/end.html","/tech/DesignPatterns/facade.html","/tech/DesignPatterns/factory_method.html","/tech/DesignPatterns/flyweight.html","/tech/DesignPatterns/","/tech/DesignPatterns/interpreter.html","/tech/DesignPatterns/iterator.html","/tech/DesignPatterns/mediator.html","/tech/DesignPatterns/memento.html","/tech/DesignPatterns/observer.html","/tech/DesignPatterns/prototype.html","/tech/DesignPatterns/proxy.html","/tech/DesignPatterns/singleton.html","/tech/DesignPatterns/state.html","/tech/DesignPatterns/strategy.html","/tech/DesignPatterns/template_method.html","/tech/DesignPatterns/visitor.html","/tech/designASimpileCCompiler/0.html","/tech/designASimpileCCompiler/1.html","/tech/designASimpileCCompiler/2.html","/tech/designASimpileCCompiler/3.html","/tech/designASimpileCCompiler/4.html","/tech/designASimpileCCompiler/5.html","/tech/designASimpileCCompiler/6.html","/tech/designASimpileCCompiler/7.html","/tech/designASimpileCCompiler/8.html","/tech/designASimpileCCompiler/9.html","/404.html","/tech/designASimpileCCompiler/","/category/","/category/build-tools/","/category/cicd/","/category/nginx/","/category/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/","/category/docker/","/category/oi/","/category/python/","/category/%E9%A3%8E%E6%A0%BC/","/category/%E6%95%B0%E5%AD%A6/","/category/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/","/category/%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86/","/tag/","/tag/cicd/","/tag/%E9%83%A8%E7%BD%B2/","/tag/docker/","/tag/modint/","/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/","/tag/%E9%A3%8E%E6%A0%BC/","/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/","/tag/mobile/","/tag/%E6%BF%80%E6%B4%BB/","/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/","/tag/typescript/","/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/","/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/","/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/","/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/","/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/","/tag/%E7%AE%80%E5%8D%95%E5%8C%96/","/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/","/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/","/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/","/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/","/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/","/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/","/tag/c/","/tag/%E7%BC%96%E8%AF%91%E5%99%A8/","/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/","/article/","/star/","/timeline/"],Pe="SEARCH_PRO_QUERY_HISTORY",A=U(Pe,[]),Fe=()=>{const{queryHistoryCount:a}=f,l=a>0;return{enabled:l,queryHistory:A,addQueryHistory:r=>{l&&(A.value=Array.from(new Set([r,...A.value.slice(0,a-1)])))},removeQueryHistory:r=>{A.value=[...A.value.slice(0,r),...A.value.slice(r+1)]}}},q=a=>Ce[a.id]+("anchor"in a?`#${a.anchor}`:""),fe="SEARCH_PRO_RESULT_HISTORY",{resultHistoryCount:I}=f,d=U(fe,[]),He=()=>{const a=I>0;return{enabled:a,resultHistory:d,addResultHistory:l=>{if(a){const r={link:q(l),display:l.display};"header"in l&&(r.header=l.header),d.value=[r,...d.value.slice(0,I-1)]}},removeResultHistory:l=>{d.value=[...d.value.slice(0,l),...d.value.slice(l+1)]}}},Se=a=>{const l=he(),r=M(),H=me(),n=x(0),D=F(()=>n.value>0),B=Be([]);return pe(()=>{const{search:p,terminate:S}=ge(),v=ye(E=>{const y=E.join(" "),{searchFilter:k=m=>m,splitWord:R,suggestionsFilter:L,...g}=l.value;y?(n.value+=1,p(E.join(" "),r.value,g).then(m=>k(m,y,r.value,H.value)).then(m=>{n.value-=1,B.value=m}).catch(m=>{console.warn(m),n.value-=1,n.value||(B.value=[])})):B.value=[]},f.searchDelay-f.suggestDelay);Y([a,r],([E])=>v(E),{immediate:!0}),Ae(()=>{S()})}),{isSearching:D,results:B}};var Re=te({name:"SearchResult",props:{queries:{type:Array,required:!0},isFocusing:Boolean},emits:["close","updateQuery"],setup(a,{emit:l}){const r=se(),H=M(),n=ae(le),{enabled:D,addQueryHistory:B,queryHistory:p,removeQueryHistory:S}=Fe(),{enabled:v,resultHistory:E,addResultHistory:y,removeResultHistory:k}=He(),R=D||v,L=re(a,"queries"),{results:g,isSearching:m}=Se(L),i=ie({isQuery:!0,index:0}),u=x(0),h=x(0),_=F(()=>R&&(p.value.length>0||E.value.length>0)),b=F(()=>g.value.length>0),w=F(()=>g.value[u.value]||null),z=()=>{const{isQuery:e,index:t}=i;t===0?(i.isQuery=!e,i.index=e?E.value.length-1:p.value.length-1):i.index=t-1},G=()=>{const{isQuery:e,index:t}=i;t===(e?p.value.length-1:E.value.length-1)?(i.isQuery=!e,i.index=0):i.index=t+1},J=()=>{u.value=u.value>0?u.value-1:g.value.length-1,h.value=w.value.contents.length-1},K=()=>{u.value=u.value<g.value.length-1?u.value+1:0,h.value=0},V=()=>{h.value<w.value.contents.length-1?h.value+=1:K()},N=()=>{h.value>0?h.value-=1:J()},Q=e=>e.map(t=>De(t)?t:s(t[0],t[1])),W=e=>{if(e.type==="customField"){const t=de[e.index]||"$content",[c,P=""]=ve(t)?t[H.value].split("$content"):t.split("$content");return e.display.map(o=>s("div",Q([c,...o,P])))}return e.display.map(t=>s("div",Q(t)))},C=()=>{u.value=0,h.value=0,l("updateQuery",""),l("close")},X=()=>D?s("ul",{class:"search-pro-result-list"},s("li",{class:"search-pro-result-list-item"},[s("div",{class:"search-pro-result-title"},n.value.queryHistory),p.value.map((e,t)=>s("div",{class:["search-pro-result-item",{active:i.isQuery&&i.index===t}],onClick:()=>{l("updateQuery",e)}},[s(T,{class:"search-pro-result-type"}),s("div",{class:"search-pro-result-content"},e),s("button",{class:"search-pro-remove-icon",innerHTML:$,onClick:c=>{c.preventDefault(),c.stopPropagation(),S(t)}})]))])):null,Z=()=>v?s("ul",{class:"search-pro-result-list"},s("li",{class:"search-pro-result-list-item"},[s("div",{class:"search-pro-result-title"},n.value.resultHistory),E.value.map((e,t)=>s(O,{to:e.link,class:["search-pro-result-item",{active:!i.isQuery&&i.index===t}],onClick:()=>{C()}},()=>[s(T,{class:"search-pro-result-type"}),s("div",{class:"search-pro-result-content"},[e.header?s("div",{class:"content-header"},e.header):null,s("div",e.display.map(c=>Q(c)).flat())]),s("button",{class:"search-pro-remove-icon",innerHTML:$,onClick:c=>{c.preventDefault(),c.stopPropagation(),k(t)}})]))])):null;return ne("keydown",e=>{if(a.isFocusing){if(b.value){if(e.key==="ArrowUp")N();else if(e.key==="ArrowDown")V();else if(e.key==="Enter"){const t=w.value.contents[h.value];B(a.queries.join(" ")),y(t),r.push(q(t)),C()}}else if(v){if(e.key==="ArrowUp")z();else if(e.key==="ArrowDown")G();else if(e.key==="Enter"){const{index:t}=i;i.isQuery?(l("updateQuery",p.value[t]),e.preventDefault()):(r.push(E.value[t].link),C())}}}}),Y([u,h],()=>{var e;(e=document.querySelector(".search-pro-result-list-item.active .search-pro-result-item.active"))==null||e.scrollIntoView(!1)},{flush:"post"}),()=>s("div",{class:["search-pro-result-wrapper",{empty:a.queries.length?!b.value:!_.value}],id:"search-pro-results"},a.queries.length?m.value?s(ce,{hint:n.value.searching}):b.value?s("ul",{class:"search-pro-result-list"},g.value.map(({title:e,contents:t},c)=>{const P=u.value===c;return s("li",{class:["search-pro-result-list-item",{active:P}]},[s("div",{class:"search-pro-result-title"},e||n.value.defaultTitle),t.map((o,ee)=>{const j=P&&h.value===ee;return s(O,{to:q(o),class:["search-pro-result-item",{active:j,"aria-selected":j}],onClick:()=>{B(a.queries.join(" ")),y(o),C()}},()=>[o.type==="text"?null:s(o.type==="title"?oe:o.type==="heading"?Ee:ue,{class:"search-pro-result-type"}),s("div",{class:"search-pro-result-content"},[o.type==="text"&&o.header?s("div",{class:"content-header"},o.header):null,s("div",W(o))])])})])})):n.value.emptyResult:R?_.value?[X(),Z()]:n.value.emptyHistory:n.value.emptyResult)}});export{Re as default};
diff --git a/assets/SearchResult-DUP77o_D.js b/assets/SearchResult-DUP77o_D.js
deleted file mode 100644
index 30669e9..0000000
--- a/assets/SearchResult-DUP77o_D.js
+++ /dev/null
@@ -1 +0,0 @@
-import{u as U,g as te,h as se,i as M,j as ae,P as le,t as re,k as ie,l as x,m as F,n as ne,p as Y,q as s,s as ce,R as T,v as Ee,x as oe,y as ue,C as he,z as me,A as Be,B as pe,D as ge,E as Ae,F as de,G as ve,H as j,I as $,J as ye,K as f,L as De}from"./app-B69Gl_S-.js";const Ce=["/","/intro.html","/essays/","/essays/%E5%91%BD%E9%87%8C%E6%9C%89%E6%97%B6%E7%BB%88%E9%A1%BB%E6%9C%89.html","/projects/","/resources/","/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html","/tech/android%20studio%E6%8D%A2%E6%BA%90.html","/tech/cicd.html","/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html","/tech/docker.html","/tech/figure_bed.html","/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html","/tech/","/tech/mailserver.html","/tech/modint.html","/tech/python_requrements.html","/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html","/tech/style.html","/tech/tensorflow%E8%B8%A9%E5%9D%91.html","/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html","/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html","/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html","/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html","/tech/%E5%8D%8F%E7%A8%8B.html","/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html","/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html","/tutorials/","/tutorials/typora%E6%BF%80%E6%B4%BB.html","/resources/html2md/","/tech/DesignPatterns/DesignPrinciples.html","/tech/DesignPatterns/abstractFactory.html","/tech/DesignPatterns/adapter.html","/tech/DesignPatterns/bridge.html","/tech/DesignPatterns/builder.html","/tech/DesignPatterns/chainOfResponsibility.html","/tech/DesignPatterns/command.html","/tech/DesignPatterns/composite.html","/tech/DesignPatterns/decorator.html","/tech/DesignPatterns/end.html","/tech/DesignPatterns/facade.html","/tech/DesignPatterns/factory_method.html","/tech/DesignPatterns/flyweight.html","/tech/DesignPatterns/","/tech/DesignPatterns/interpreter.html","/tech/DesignPatterns/iterator.html","/tech/DesignPatterns/mediator.html","/tech/DesignPatterns/memento.html","/tech/DesignPatterns/observer.html","/tech/DesignPatterns/prototype.html","/tech/DesignPatterns/proxy.html","/tech/DesignPatterns/singleton.html","/tech/DesignPatterns/state.html","/tech/DesignPatterns/strategy.html","/tech/DesignPatterns/template_method.html","/tech/DesignPatterns/visitor.html","/tech/designASimpileCCompiler/0.html","/tech/designASimpileCCompiler/1.html","/tech/designASimpileCCompiler/2.html","/tech/designASimpileCCompiler/3.html","/tech/designASimpileCCompiler/4.html","/tech/designASimpileCCompiler/5.html","/tech/designASimpileCCompiler/6.html","/tech/designASimpileCCompiler/7.html","/tech/designASimpileCCompiler/8.html","/tech/designASimpileCCompiler/9.html","/404.html","/tech/designASimpileCCompiler/","/category/","/category/build-tools/","/category/cicd/","/category/nginx/","/category/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/","/category/docker/","/category/oi/","/category/python/","/category/%E9%A3%8E%E6%A0%BC/","/category/%E6%95%B0%E5%AD%A6/","/category/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/","/category/%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86/","/tag/","/tag/cicd/","/tag/%E9%83%A8%E7%BD%B2/","/tag/docker/","/tag/modint/","/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/","/tag/%E9%A3%8E%E6%A0%BC/","/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/","/tag/mobile/","/tag/%E6%BF%80%E6%B4%BB/","/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/","/tag/typescript/","/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/","/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/","/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/","/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/","/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/","/tag/%E7%AE%80%E5%8D%95%E5%8C%96/","/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/","/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/","/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/","/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/","/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/","/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/","/tag/c/","/tag/%E7%BC%96%E8%AF%91%E5%99%A8/","/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/","/article/","/star/","/timeline/"],Pe="SEARCH_PRO_QUERY_HISTORY",A=U(Pe,[]),Fe=()=>{const{queryHistoryCount:a}=f,l=a>0;return{enabled:l,queryHistory:A,addQueryHistory:r=>{l&&(A.value=Array.from(new Set([r,...A.value.slice(0,a-1)])))},removeQueryHistory:r=>{A.value=[...A.value.slice(0,r),...A.value.slice(r+1)]}}},q=a=>Ce[a.id]+("anchor"in a?`#${a.anchor}`:""),fe="SEARCH_PRO_RESULT_HISTORY",{resultHistoryCount:I}=f,d=U(fe,[]),He=()=>{const a=I>0;return{enabled:a,resultHistory:d,addResultHistory:l=>{if(a){const r={link:q(l),display:l.display};"header"in l&&(r.header=l.header),d.value=[r,...d.value.slice(0,I-1)]}},removeResultHistory:l=>{d.value=[...d.value.slice(0,l),...d.value.slice(l+1)]}}},Se=a=>{const l=he(),r=M(),H=me(),n=x(0),D=F(()=>n.value>0),B=Be([]);return pe(()=>{const{search:p,terminate:S}=ge(),v=ye(o=>{const y=o.join(" "),{searchFilter:k=m=>m,splitWord:R,suggestionsFilter:L,...g}=l.value;y?(n.value+=1,p(o.join(" "),r.value,g).then(m=>k(m,y,r.value,H.value)).then(m=>{n.value-=1,B.value=m}).catch(m=>{console.warn(m),n.value-=1,n.value||(B.value=[])})):B.value=[]},f.searchDelay-f.suggestDelay);Y([a,r],([o])=>v(o),{immediate:!0}),Ae(()=>{S()})}),{isSearching:D,results:B}};var Re=te({name:"SearchResult",props:{queries:{type:Array,required:!0},isFocusing:Boolean},emits:["close","updateQuery"],setup(a,{emit:l}){const r=se(),H=M(),n=ae(le),{enabled:D,addQueryHistory:B,queryHistory:p,removeQueryHistory:S}=Fe(),{enabled:v,resultHistory:o,addResultHistory:y,removeResultHistory:k}=He(),R=D||v,L=re(a,"queries"),{results:g,isSearching:m}=Se(L),i=ie({isQuery:!0,index:0}),u=x(0),h=x(0),_=F(()=>R&&(p.value.length>0||o.value.length>0)),b=F(()=>g.value.length>0),w=F(()=>g.value[u.value]||null),z=()=>{const{isQuery:e,index:t}=i;t===0?(i.isQuery=!e,i.index=e?o.value.length-1:p.value.length-1):i.index=t-1},G=()=>{const{isQuery:e,index:t}=i;t===(e?p.value.length-1:o.value.length-1)?(i.isQuery=!e,i.index=0):i.index=t+1},J=()=>{u.value=u.value>0?u.value-1:g.value.length-1,h.value=w.value.contents.length-1},K=()=>{u.value=u.value<g.value.length-1?u.value+1:0,h.value=0},V=()=>{h.value<w.value.contents.length-1?h.value+=1:K()},N=()=>{h.value>0?h.value-=1:J()},Q=e=>e.map(t=>De(t)?t:s(t[0],t[1])),W=e=>{if(e.type==="customField"){const t=de[e.index]||"$content",[c,P=""]=ve(t)?t[H.value].split("$content"):t.split("$content");return e.display.map(E=>s("div",Q([c,...E,P])))}return e.display.map(t=>s("div",Q(t)))},C=()=>{u.value=0,h.value=0,l("updateQuery",""),l("close")},X=()=>D?s("ul",{class:"search-pro-result-list"},s("li",{class:"search-pro-result-list-item"},[s("div",{class:"search-pro-result-title"},n.value.queryHistory),p.value.map((e,t)=>s("div",{class:["search-pro-result-item",{active:i.isQuery&&i.index===t}],onClick:()=>{l("updateQuery",e)}},[s(j,{class:"search-pro-result-type"}),s("div",{class:"search-pro-result-content"},e),s("button",{class:"search-pro-remove-icon",innerHTML:$,onClick:c=>{c.preventDefault(),c.stopPropagation(),S(t)}})]))])):null,Z=()=>v?s("ul",{class:"search-pro-result-list"},s("li",{class:"search-pro-result-list-item"},[s("div",{class:"search-pro-result-title"},n.value.resultHistory),o.value.map((e,t)=>s(T,{to:e.link,class:["search-pro-result-item",{active:!i.isQuery&&i.index===t}],onClick:()=>{C()}},()=>[s(j,{class:"search-pro-result-type"}),s("div",{class:"search-pro-result-content"},[e.header?s("div",{class:"content-header"},e.header):null,s("div",e.display.map(c=>Q(c)).flat())]),s("button",{class:"search-pro-remove-icon",innerHTML:$,onClick:c=>{c.preventDefault(),c.stopPropagation(),k(t)}})]))])):null;return ne("keydown",e=>{if(a.isFocusing){if(b.value){if(e.key==="ArrowUp")N();else if(e.key==="ArrowDown")V();else if(e.key==="Enter"){const t=w.value.contents[h.value];B(a.queries.join(" ")),y(t),r.push(q(t)),C()}}else if(v){if(e.key==="ArrowUp")z();else if(e.key==="ArrowDown")G();else if(e.key==="Enter"){const{index:t}=i;i.isQuery?(l("updateQuery",p.value[t]),e.preventDefault()):(r.push(o.value[t].link),C())}}}}),Y([u,h],()=>{var e;(e=document.querySelector(".search-pro-result-list-item.active .search-pro-result-item.active"))==null||e.scrollIntoView(!1)},{flush:"post"}),()=>s("div",{class:["search-pro-result-wrapper",{empty:a.queries.length?!b.value:!_.value}],id:"search-pro-results"},a.queries.length?m.value?s(ce,{hint:n.value.searching}):b.value?s("ul",{class:"search-pro-result-list"},g.value.map(({title:e,contents:t},c)=>{const P=u.value===c;return s("li",{class:["search-pro-result-list-item",{active:P}]},[s("div",{class:"search-pro-result-title"},e||n.value.defaultTitle),t.map((E,ee)=>{const O=P&&h.value===ee;return s(T,{to:q(E),class:["search-pro-result-item",{active:O,"aria-selected":O}],onClick:()=>{B(a.queries.join(" ")),y(E),C()}},()=>[E.type==="text"?null:s(E.type==="title"?Ee:E.type==="heading"?oe:ue,{class:"search-pro-result-type"}),s("div",{class:"search-pro-result-content"},[E.type==="text"&&E.header?s("div",{class:"content-header"},E.header):null,s("div",W(E))])])})])})):n.value.emptyResult:R?_.value?[X(),Z()]:n.value.emptyHistory:n.value.emptyResult)}});export{Re as default};
diff --git a/assets/abstractFactory.html-DS3CgVqp.js b/assets/abstractFactory.html-D_oh5f2L.js
similarity index 99%
rename from assets/abstractFactory.html-DS3CgVqp.js
rename to assets/abstractFactory.html-D_oh5f2L.js
index 27ab4cf..f932ca9 100644
--- a/assets/abstractFactory.html-DS3CgVqp.js
+++ b/assets/abstractFactory.html-D_oh5f2L.js
@@ -1,4 +1,4 @@
-import{_ as s,o as a,c as t,a as p,b as n,f as o}from"./app-B69Gl_S-.js";const e={},c=n("h2",{id:"为什么要使用抽象工厂模式",tabindex:"-1"},[n("a",{class:"header-anchor",href:"#为什么要使用抽象工厂模式"},[n("span",null,"为什么要使用抽象工厂模式")])],-1),l=n("p",null,"抽象工厂模式提供一个接口，用于创建相关或依赖对象的家族，而无需明确指定具体类。它通过定义一个创建对象的接口来实现，这样子类可以决定实例化哪个类。抽象工厂模式使得一个类的实例化延迟到其子类。",-1),i=o(`<ol><li><strong>解耦</strong>：抽象工厂模式通过将对象的创建过程抽象化，减少了客户端代码与具体类之间的耦合。</li><li><strong>一致性</strong>：确保同一工厂创建的一系列对象具有一致的接口和行为。</li><li><strong>扩展性</strong>：可以方便地增加新的产品族而不影响现有代码。</li></ol><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/dLJBJiCm4BptA_QO0k43Ske9WLGa3hqX3ajY5Qk94zaRH8JuTzPvsiQfIWyvT7TdTcSopSuGQcghSgEm4gR1N02-6zAOqmC_jUxWUmDp3V8IZG6t1N0BkHP8OY_LAScn8Lch31WWrV4EMbrEFxOPs1aFTD3OXI2UisLlxWMF8Y59fLYeiQMFMZieEyIedytVavz8LEEzAGJxnaKLdiJZuNcVR9r6ZCkA0F55GXK1iIDs1Mk5nR4yrMLzwVLjl0YB8f5S6CfyrcSjYnLYgttXSeqQQxvRanErubFemhssLxVKj9JunHNh-CubLxoANoK9DpoJdsPEssHDaCBxwoCNCbqQmH1tNIH35ZUYYtelKR63Pzth8LtOl8p5PFoBhG_M6fkJkZCfc5vUcjuCVvvijD3hz9T5E_sMkUF6PM0S3JmxuRF79lmjEzRB7yPV" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// factory.ts</span>
+import{_ as s,o as a,c as t,a as p,b as n,f as o}from"./app-B4LGNJZ0.js";const e={},c=n("h2",{id:"为什么要使用抽象工厂模式",tabindex:"-1"},[n("a",{class:"header-anchor",href:"#为什么要使用抽象工厂模式"},[n("span",null,"为什么要使用抽象工厂模式")])],-1),l=n("p",null,"抽象工厂模式提供一个接口，用于创建相关或依赖对象的家族，而无需明确指定具体类。它通过定义一个创建对象的接口来实现，这样子类可以决定实例化哪个类。抽象工厂模式使得一个类的实例化延迟到其子类。",-1),i=o(`<ol><li><strong>解耦</strong>：抽象工厂模式通过将对象的创建过程抽象化，减少了客户端代码与具体类之间的耦合。</li><li><strong>一致性</strong>：确保同一工厂创建的一系列对象具有一致的接口和行为。</li><li><strong>扩展性</strong>：可以方便地增加新的产品族而不影响现有代码。</li></ol><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/dLJBJiCm4BptA_QO0k43Ske9WLGa3hqX3ajY5Qk94zaRH8JuTzPvsiQfIWyvT7TdTcSopSuGQcghSgEm4gR1N02-6zAOqmC_jUxWUmDp3V8IZG6t1N0BkHP8OY_LAScn8Lch31WWrV4EMbrEFxOPs1aFTD3OXI2UisLlxWMF8Y59fLYeiQMFMZieEyIedytVavz8LEEzAGJxnaKLdiJZuNcVR9r6ZCkA0F55GXK1iIDs1Mk5nR4yrMLzwVLjl0YB8f5S6CfyrcSjYnLYgttXSeqQQxvRanErubFemhssLxVKj9JunHNh-CubLxoANoK9DpoJdsPEssHDaCBxwoCNCbqQmH1tNIH35ZUYYtelKR63Pzth8LtOl8p5PFoBhG_M6fkJkZCfc5vUcjuCVvvijD3hz9T5E_sMkUF6PM0S3JmxuRF79lmjEzRB7yPV" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// factory.ts</span>
 <span class="token comment">// 抽象工厂</span>
 <span class="token keyword">import</span> <span class="token punctuation">{</span> Link <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&#39;./link&#39;</span><span class="token punctuation">;</span>
 <span class="token keyword">import</span> <span class="token punctuation">{</span> Tray <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&#39;./tray&#39;</span><span class="token punctuation">;</span>
diff --git a/assets/adapter.html-B2UlYWFL.js b/assets/adapter.html-x6kHt0VN.js
similarity index 99%
rename from assets/adapter.html-B2UlYWFL.js
rename to assets/adapter.html-x6kHt0VN.js
index 2716586..ee6cf2e 100644
--- a/assets/adapter.html-B2UlYWFL.js
+++ b/assets/adapter.html-x6kHt0VN.js
@@ -1,4 +1,4 @@
-import{_ as n,o as s,c as a,f as t}from"./app-B69Gl_S-.js";const p={},e=t(`<h2 id="适配器模式" tabindex="-1"><a class="header-anchor" href="#适配器模式"><span>适配器模式</span></a></h2><p>适配器模式（Adapter Pattern）是一种结构型设计模式，它允许将一个类的接口转换成客户希望的另一个接口。适配器模式使得原本由于接口不兼容而不能一起工作的那些类可以一起工作。</p><h3 id="为什么要用适配器模式" tabindex="-1"><a class="header-anchor" href="#为什么要用适配器模式"><span>为什么要用适配器模式</span></a></h3><p>在软件开发中，经常会遇到需要使用一些现有的类，但它们的接口并不符合当前系统的需求。适配器模式通过创建一个适配器类，将现有类的接口转换为所需的接口，从而使得现有类可以在新的环境中使用。</p><h3 id="类比" tabindex="-1"><a class="header-anchor" href="#类比"><span>类比</span></a></h3><h3 id="类比-1" tabindex="-1"><a class="header-anchor" href="#类比-1"><span>类比</span></a></h3><table><thead><tr><th></th><th>比喻</th><th>示例程序</th></tr></thead><tbody><tr><td>实际需求</td><td>交流100V</td><td>Banner</td></tr><tr><td>变换装置</td><td>适配器</td><td>PrintBanner</td></tr><tr><td>需求</td><td>直流12V</td><td>Print</td></tr></tbody></table><h3 id="示例程序" tabindex="-1"><a class="header-anchor" href="#示例程序"><span>示例程序</span></a></h3><p>Adapter 有两种方式实现</p><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuIh9BCb9jL9uldlviyxzN9bv9Qb5QOd9gGe1HK2sGZMNWe9s0OWPdfgOhQ49vmQN5ENdfGC5QhcuadCIYuiLd1BpybAB83gAC_BBmpDBCW8IYrBp8BfWGex5G1kGzO4jWcfEhIX9pKk1cvMPMv2JcfkQLr9CWdCSW2O0FGO0" alt=""><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuIh9BCb9jL9ukdpAiyuPN8b9nIL5YSab2iavYSN52W55cNab2jLS2WhQ1I1cU6fYjeOcd1jSKfIVbmuKgENYWcXmIipBIos2w2ZEo2yFpop924WiIis3w889EHQNf1OXwmDR1DMSMb6IcfS25GEPf9i4bh22caw4Qv2DqzNLWZaBxaq7e0L0pmC0" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// banner.ts</span>
+import{_ as n,o as s,c as a,f as t}from"./app-B4LGNJZ0.js";const p={},e=t(`<h2 id="适配器模式" tabindex="-1"><a class="header-anchor" href="#适配器模式"><span>适配器模式</span></a></h2><p>适配器模式（Adapter Pattern）是一种结构型设计模式，它允许将一个类的接口转换成客户希望的另一个接口。适配器模式使得原本由于接口不兼容而不能一起工作的那些类可以一起工作。</p><h3 id="为什么要用适配器模式" tabindex="-1"><a class="header-anchor" href="#为什么要用适配器模式"><span>为什么要用适配器模式</span></a></h3><p>在软件开发中，经常会遇到需要使用一些现有的类，但它们的接口并不符合当前系统的需求。适配器模式通过创建一个适配器类，将现有类的接口转换为所需的接口，从而使得现有类可以在新的环境中使用。</p><h3 id="类比" tabindex="-1"><a class="header-anchor" href="#类比"><span>类比</span></a></h3><h3 id="类比-1" tabindex="-1"><a class="header-anchor" href="#类比-1"><span>类比</span></a></h3><table><thead><tr><th></th><th>比喻</th><th>示例程序</th></tr></thead><tbody><tr><td>实际需求</td><td>交流100V</td><td>Banner</td></tr><tr><td>变换装置</td><td>适配器</td><td>PrintBanner</td></tr><tr><td>需求</td><td>直流12V</td><td>Print</td></tr></tbody></table><h3 id="示例程序" tabindex="-1"><a class="header-anchor" href="#示例程序"><span>示例程序</span></a></h3><p>Adapter 有两种方式实现</p><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuIh9BCb9jL9uldlviyxzN9bv9Qb5QOd9gGe1HK2sGZMNWe9s0OWPdfgOhQ49vmQN5ENdfGC5QhcuadCIYuiLd1BpybAB83gAC_BBmpDBCW8IYrBp8BfWGex5G1kGzO4jWcfEhIX9pKk1cvMPMv2JcfkQLr9CWdCSW2O0FGO0" alt=""><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuIh9BCb9jL9ukdpAiyuPN8b9nIL5YSab2iavYSN52W55cNab2jLS2WhQ1I1cU6fYjeOcd1jSKfIVbmuKgENYWcXmIipBIos2w2ZEo2yFpop924WiIis3w889EHQNf1OXwmDR1DMSMb6IcfS25GEPf9i4bh22caw4Qv2DqzNLWZaBxaq7e0L0pmC0" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// banner.ts</span>
 <span class="token keyword">export</span> <span class="token keyword">class</span> <span class="token class-name">Banner</span> <span class="token punctuation">{</span>
   <span class="token keyword">private</span> <span class="token builtin">string</span><span class="token operator">:</span> <span class="token builtin">string</span><span class="token punctuation">;</span>
   <span class="token function">constructor</span><span class="token punctuation">(</span><span class="token builtin">string</span><span class="token operator">:</span> <span class="token builtin">string</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
diff --git "a/assets/android studio\346\215\242\346\272\220.html-CxjDu5df.js" "b/assets/android studio\346\215\242\346\272\220.html-DkRIM6mj.js"
similarity index 98%
rename from "assets/android studio\346\215\242\346\272\220.html-CxjDu5df.js"
rename to "assets/android studio\346\215\242\346\272\220.html-DkRIM6mj.js"
index b5e0927..b8dde58 100644
--- "a/assets/android studio\346\215\242\346\272\220.html-CxjDu5df.js"	
+++ "b/assets/android studio\346\215\242\346\272\220.html-DkRIM6mj.js"	
@@ -1,4 +1,4 @@
-import{_ as i,r as o,o as a,c as l,b as e,e as n,d as r,f as s}from"./app-B69Gl_S-.js";const d={},u=e("h1",{id:"gradle",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#gradle"},[e("span",null,"gradle")])],-1),c={href:"https://mirrors.cloud.tencent.com/gradle/",target:"_blank",rel:"noopener noreferrer"},p=e("p",null,"Android Studio下载gradle太慢可换源",-1),m={href:"https://blog.csdn.net/qq_43811536/article/details/139447518",target:"_blank",rel:"noopener noreferrer"},v=s(`<p><strong>修改 settings.gradle.kts</strong></p><div class="language-text line-numbers-mode" data-ext="text" data-title="text"><pre class="language-text"><code>pluginManagement {
+import{_ as i,r as o,o as a,c as l,b as e,e as n,d as r,f as s}from"./app-B4LGNJZ0.js";const d={},u=e("h1",{id:"gradle",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#gradle"},[e("span",null,"gradle")])],-1),c={href:"https://mirrors.cloud.tencent.com/gradle/",target:"_blank",rel:"noopener noreferrer"},p=e("p",null,"Android Studio下载gradle太慢可换源",-1),m={href:"https://blog.csdn.net/qq_43811536/article/details/139447518",target:"_blank",rel:"noopener noreferrer"},v=s(`<p><strong>修改 settings.gradle.kts</strong></p><div class="language-text line-numbers-mode" data-ext="text" data-title="text"><pre class="language-text"><code>pluginManagement {
     repositories {
         maven { url=uri (&quot;https://jitpack.io&quot;) }
         maven { url=uri (&quot;https://maven.aliyun.com/repository/releases&quot;) }
diff --git a/assets/app-B69Gl_S-.js b/assets/app-B4LGNJZ0.js
similarity index 63%
rename from assets/app-B69Gl_S-.js
rename to assets/app-B4LGNJZ0.js
index 89e4f2c..aba8b3f 100644
--- a/assets/app-B69Gl_S-.js
+++ b/assets/app-B4LGNJZ0.js
@@ -14,15 +14,18 @@
 * @vue/runtime-dom v3.4.27
 * (c) 2018-present Yuxi (Evan) You and Vue contributors
 * @license MIT
-**/const K0="http://www.w3.org/2000/svg",J0="http://www.w3.org/1998/Math/MathML",Yt=typeof document<"u"?document:null,bs=Yt&&Yt.createElement("template"),Q0={insert:(e,t,n)=>{t.insertBefore(e,n||null)},remove:e=>{const t=e.parentNode;t&&t.removeChild(e)},createElement:(e,t,n,r)=>{const a=t==="svg"?Yt.createElementNS(K0,e):t==="mathml"?Yt.createElementNS(J0,e):Yt.createElement(e,n?{is:n}:void 0);return e==="select"&&r&&r.multiple!=null&&a.setAttribute("multiple",r.multiple),a},createText:e=>Yt.createTextNode(e),createComment:e=>Yt.createComment(e),setText:(e,t)=>{e.nodeValue=t},setElementText:(e,t)=>{e.textContent=t},parentNode:e=>e.parentNode,nextSibling:e=>e.nextSibling,querySelector:e=>Yt.querySelector(e),setScopeId(e,t){e.setAttribute(t,"")},insertStaticContent(e,t,n,r,a,o){const l=n?n.previousSibling:t.lastChild;if(a&&(a===o||a.nextSibling))for(;t.insertBefore(a.cloneNode(!0),n),!(a===o||!(a=a.nextSibling)););else{bs.innerHTML=r==="svg"?`<svg>${e}</svg>`:r==="mathml"?`<math>${e}</math>`:e;const i=bs.content;if(r==="svg"||r==="mathml"){const c=i.firstChild;for(;c.firstChild;)i.appendChild(c.firstChild);i.removeChild(c)}t.insertBefore(i,n)}return[l?l.nextSibling:t.firstChild,n?n.previousSibling:t.lastChild]}},zt="transition",Qn="animation",Hn=Symbol("_vtc"),Rt=(e,{slots:t})=>s(a0,Tc(e),t);Rt.displayName="Transition";const kc={name:String,type:String,css:{type:Boolean,default:!0},duration:[String,Number,Object],enterFromClass:String,enterActiveClass:String,enterToClass:String,appearFromClass:String,appearActiveClass:String,appearToClass:String,leaveFromClass:String,leaveActiveClass:String,leaveToClass:String},Y0=Rt.props=Pe({},Xi,kc),fn=(e,t=[])=>{te(e)?e.forEach(n=>n(...t)):e&&e(...t)},Es=e=>e?te(e)?e.some(t=>t.length>1):e.length>1:!1;function Tc(e){const t={};for(const R in e)R in kc||(t[R]=e[R]);if(e.css===!1)return t;const{name:n="v",type:r,duration:a,enterFromClass:o=`${n}-enter-from`,enterActiveClass:l=`${n}-enter-active`,enterToClass:i=`${n}-enter-to`,appearFromClass:c=o,appearActiveClass:u=l,appearToClass:d=i,leaveFromClass:f=`${n}-leave-from`,leaveActiveClass:p=`${n}-leave-active`,leaveToClass:h=`${n}-leave-to`}=e,v=Z0(a),_=v&&v[0],E=v&&v[1],{onBeforeEnter:b,onEnter:C,onEnterCancelled:y,onLeave:A,onLeaveCancelled:D,onBeforeAppear:P=b,onAppear:H=C,onAppearCancelled:O=y}=t,Q=(R,X,Le)=>{Wt(R,X?d:i),Wt(R,X?u:l),Le&&Le()},I=(R,X)=>{R._isLeaving=!1,Wt(R,f),Wt(R,h),Wt(R,p),X&&X()},U=R=>(X,Le)=>{const Ae=R?H:C,W=()=>Q(X,R,Le);fn(Ae,[X,W]),_s(()=>{Wt(X,R?c:o),Dt(X,R?d:i),Es(Ae)||ws(X,r,_,W)})};return Pe(t,{onBeforeEnter(R){fn(b,[R]),Dt(R,o),Dt(R,l)},onBeforeAppear(R){fn(P,[R]),Dt(R,c),Dt(R,u)},onEnter:U(!1),onAppear:U(!0),onLeave(R,X){R._isLeaving=!0;const Le=()=>I(R,X);Dt(R,f),Dt(R,p),xc(),_s(()=>{R._isLeaving&&(Wt(R,f),Dt(R,h),Es(A)||ws(R,r,E,Le))}),fn(A,[R,Le])},onEnterCancelled(R){Q(R,!1),fn(y,[R])},onAppearCancelled(R){Q(R,!0),fn(O,[R])},onLeaveCancelled(R){I(R),fn(D,[R])}})}function Z0(e){if(e==null)return null;if(Be(e))return[Ua(e.enter),Ua(e.leave)];{const t=Ua(e);return[t,t]}}function Ua(e){return n2(e)}function Dt(e,t){t.split(/\s+/).forEach(n=>n&&e.classList.add(n)),(e[Hn]||(e[Hn]=new Set)).add(t)}function Wt(e,t){t.split(/\s+/).forEach(r=>r&&e.classList.remove(r));const n=e[Hn];n&&(n.delete(t),n.size||(e[Hn]=void 0))}function _s(e){requestAnimationFrame(()=>{requestAnimationFrame(e)})}let X0=0;function ws(e,t,n,r){const a=e._endId=++X0,o=()=>{a===e._endId&&r()};if(n)return setTimeout(o,n);const{type:l,timeout:i,propCount:c}=Sc(e,t);if(!l)return r();const u=l+"end";let d=0;const f=()=>{e.removeEventListener(u,p),o()},p=h=>{h.target===e&&++d>=c&&f()};setTimeout(()=>{d<c&&f()},i+1),e.addEventListener(u,p)}function Sc(e,t){const n=window.getComputedStyle(e),r=v=>(n[v]||"").split(", "),a=r(`${zt}Delay`),o=r(`${zt}Duration`),l=As(a,o),i=r(`${Qn}Delay`),c=r(`${Qn}Duration`),u=As(i,c);let d=null,f=0,p=0;t===zt?l>0&&(d=zt,f=l,p=o.length):t===Qn?u>0&&(d=Qn,f=u,p=c.length):(f=Math.max(l,u),d=f>0?l>u?zt:Qn:null,p=d?d===zt?o.length:c.length:0);const h=d===zt&&/\b(transform|all)(,|$)/.test(r(`${zt}Property`).toString());return{type:d,timeout:f,propCount:p,hasTransform:h}}function As(e,t){for(;e.length<t.length;)e=e.concat(e);return Math.max(...t.map((n,r)=>Cs(n)+Cs(e[r])))}function Cs(e){return e==="auto"?0:Number(e.slice(0,-1).replace(",","."))*1e3}function xc(){return document.body.offsetHeight}function ed(e,t,n){const r=e[Hn];r&&(t=(t?[t,...r]:[...r]).join(" ")),t==null?e.removeAttribute("class"):n?e.setAttribute("class",t):e.className=t}const ks=Symbol("_vod"),td=Symbol("_vsh"),nd=Symbol(""),rd=/(^|;)\s*display\s*:/;function ad(e,t,n){const r=e.style,a=Re(n);let o=!1;if(n&&!a){if(t)if(Re(t))for(const l of t.split(";")){const i=l.slice(0,l.indexOf(":")).trim();n[i]==null&&sa(r,i,"")}else for(const l in t)n[l]==null&&sa(r,l,"");for(const l in n)l==="display"&&(o=!0),sa(r,l,n[l])}else if(a){if(t!==n){const l=r[nd];l&&(n+=";"+l),r.cssText=n,o=rd.test(n)}}else t&&e.removeAttribute("style");ks in e&&(e[ks]=o?r.display:"",e[td]&&(r.display="none"))}const Ts=/\s*!important$/;function sa(e,t,n){if(te(n))n.forEach(r=>sa(e,t,r));else if(n==null&&(n=""),t.startsWith("--"))e.setProperty(t,n);else{const r=od(e,t);Ts.test(n)?e.setProperty(jn(r),n.replace(Ts,""),"important"):e[r]=n}}const Ss=["Webkit","Moz","ms"],Wa={};function od(e,t){const n=Wa[t];if(n)return n;let r=qe(t);if(r!=="filter"&&r in e)return Wa[t]=r;r=_n(r);for(let a=0;a<Ss.length;a++){const o=Ss[a]+r;if(o in e)return Wa[t]=o}return t}const xs="http://www.w3.org/1999/xlink";function ld(e,t,n,r,a){if(r&&t.startsWith("xlink:"))n==null?e.removeAttributeNS(xs,t.slice(6,t.length)):e.setAttributeNS(xs,t,n);else{const o=c2(t);n==null||o&&!ki(n)?e.removeAttribute(t):e.setAttribute(t,o?"":n)}}function sd(e,t,n,r,a,o,l){if(t==="innerHTML"||t==="textContent"){r&&l(r,a,o),e[t]=n??"";return}const i=e.tagName;if(t==="value"&&i!=="PROGRESS"&&!i.includes("-")){const u=i==="OPTION"?e.getAttribute("value")||"":e.value,d=n??"";(u!==d||!("_value"in e))&&(e.value=d),n==null&&e.removeAttribute(t),e._value=n;return}let c=!1;if(n===""||n==null){const u=typeof e[t];u==="boolean"?n=ki(n):n==null&&u==="string"?(n="",c=!0):u==="number"&&(n=0,c=!0)}try{e[t]=n}catch{}c&&e.removeAttribute(t)}function id(e,t,n,r){e.addEventListener(t,n,r)}function cd(e,t,n,r){e.removeEventListener(t,n,r)}const Ls=Symbol("_vei");function ud(e,t,n,r,a=null){const o=e[Ls]||(e[Ls]={}),l=o[t];if(r&&l)l.value=r;else{const[i,c]=dd(t);if(r){const u=o[t]=hd(r,a);id(e,i,u,c)}else l&&(cd(e,i,l,c),o[t]=void 0)}}const Bs=/(?:Once|Passive|Capture)$/;function dd(e){let t;if(Bs.test(e)){t={};let r;for(;r=e.match(Bs);)e=e.slice(0,e.length-r[0].length),t[r[0].toLowerCase()]=!0}return[e[2]===":"?e.slice(3):jn(e.slice(2)),t]}let Ka=0;const fd=Promise.resolve(),pd=()=>Ka||(fd.then(()=>Ka=0),Ka=Date.now());function hd(e,t){const n=r=>{if(!r._vts)r._vts=Date.now();else if(r._vts<=n.attached)return;ft(md(r,n.value),t,5,[r])};return n.value=e,n.attached=pd(),n}function md(e,t){if(te(t)){const n=e.stopImmediatePropagation;return e.stopImmediatePropagation=()=>{n.call(e),e._stopped=!0},t.map(r=>a=>!a._stopped&&r&&r(a))}else return t}const Is=e=>e.charCodeAt(0)===111&&e.charCodeAt(1)===110&&e.charCodeAt(2)>96&&e.charCodeAt(2)<123,vd=(e,t,n,r,a,o,l,i,c)=>{const u=a==="svg";t==="class"?ed(e,r,u):t==="style"?ad(e,n,r):Sr(t)?Uo(t)||ud(e,t,n,r,l):(t[0]==="."?(t=t.slice(1),!0):t[0]==="^"?(t=t.slice(1),!1):gd(e,t,r,u))?sd(e,t,r,o,l,i,c):(t==="true-value"?e._trueValue=r:t==="false-value"&&(e._falseValue=r),ld(e,t,r,u))};function gd(e,t,n,r){if(r)return!!(t==="innerHTML"||t==="textContent"||t in e&&Is(t)&&re(n));if(t==="spellcheck"||t==="draggable"||t==="translate"||t==="form"||t==="list"&&e.tagName==="INPUT"||t==="type"&&e.tagName==="TEXTAREA")return!1;if(t==="width"||t==="height"){const a=e.tagName;if(a==="IMG"||a==="VIDEO"||a==="CANVAS"||a==="SOURCE")return!1}return Is(t)&&Re(n)?!1:t in e}const Lc=new WeakMap,Bc=new WeakMap,ga=Symbol("_moveCb"),Ps=Symbol("_enterCb"),Ic={name:"TransitionGroup",props:Pe({},Y0,{tag:String,moveClass:String}),setup(e,{slots:t}){const n=ln(),r=Zi();let a,o;return rc(()=>{if(!a.length)return;const l=e.moveClass||`${e.name||"v"}-move`;if(!Ad(a[0].el,n.vnode.el,l))return;a.forEach(Ed),a.forEach(_d);const i=a.filter(wd);xc(),i.forEach(c=>{const u=c.el,d=u.style;Dt(u,l),d.transform=d.webkitTransform=d.transitionDuration="";const f=u[ga]=p=>{p&&p.target!==u||(!p||/transform$/.test(p.propertyName))&&(u.removeEventListener("transitionend",f),u[ga]=null,Wt(u,l))};u.addEventListener("transitionend",f)})}),()=>{const l=pe(e),i=Tc(l);let c=l.tag||nt;if(a=[],o)for(let u=0;u<o.length;u++){const d=o[u];d.el&&d.el instanceof Element&&(a.push(d),gr(d,vr(d,i,r,n)),Lc.set(d,d.el.getBoundingClientRect()))}o=t.default?ll(t.default()):[];for(let u=0;u<o.length;u++){const d=o[u];d.key!=null&&gr(d,vr(d,i,r,n))}return Te(c,null,o)}}},yd=e=>delete e.mode;Ic.props;const bd=Ic;function Ed(e){const t=e.el;t[ga]&&t[ga](),t[Ps]&&t[Ps]()}function _d(e){Bc.set(e,e.el.getBoundingClientRect())}function wd(e){const t=Lc.get(e),n=Bc.get(e),r=t.left-n.left,a=t.top-n.top;if(r||a){const o=e.el.style;return o.transform=o.webkitTransform=`translate(${r}px,${a}px)`,o.transitionDuration="0s",e}}function Ad(e,t,n){const r=e.cloneNode(),a=e[Hn];a&&a.forEach(i=>{i.split(/\s+/).forEach(c=>c&&r.classList.remove(c))}),n.split(/\s+/).forEach(i=>i&&r.classList.add(i)),r.style.display="none";const o=t.nodeType===1?t:t.parentNode;o.appendChild(r);const{hasTransform:l}=Sc(r);return o.removeChild(r),l}const Cd=Pe({patchProp:vd},Q0);let Ja,Ds=!1;function kd(){return Ja=Ds?Ja:B0(Cd),Ds=!0,Ja}const Td=(...e)=>{const t=kd().createApp(...e),{mount:n}=t;return t.mount=r=>{const a=xd(r);if(a)return n(a,!0,Sd(a))},t};function Sd(e){if(e instanceof SVGElement)return"svg";if(typeof MathMLElement=="function"&&e instanceof MathMLElement)return"mathml"}function xd(e){return Re(e)?document.querySelector(e):e}var Ld=["link","meta","script","style","noscript","template"],Bd=["title","base"],Id=([e,t,n])=>Bd.includes(e)?e:Ld.includes(e)?e==="meta"&&t.name?`${e}.${t.name}`:e==="template"&&t.id?`${e}.${t.id}`:JSON.stringify([e,Object.entries(t).map(([r,a])=>typeof a=="boolean"?a?[r,""]:null:[r,a]).filter(r=>r!=null).sort(([r],[a])=>r.localeCompare(a)),n]):null,Pd=e=>{const t=new Set,n=[];return e.forEach(r=>{const a=Id(r);a&&!t.has(a)&&(t.add(a),n.push(r))}),n},Dd=e=>e[0]==="/"?e:`/${e}`,Pc=e=>e[e.length-1]==="/"||e.endsWith(".html")?e:`${e}/`,sn=e=>/^(https?:)?\/\//.test(e),Od=/.md((\?|#).*)?$/,xa=(e,t="/")=>!!(sn(e)||e.startsWith("/")&&!e.startsWith(t)&&!Od.test(e)),La=e=>/^[a-z][a-z0-9+.-]*:/.test(e),qn=e=>Object.prototype.toString.call(e)==="[object Object]",Md=e=>{const[t,...n]=e.split(/(\?|#)/);if(!t||t.endsWith("/"))return e;let r=t.replace(/(^|\/)README.md$/i,"$1index.html");return r.endsWith(".md")?r=r.substring(0,r.length-3)+".html":r.endsWith(".html")||(r=r+".html"),r.endsWith("/index.html")&&(r=r.substring(0,r.length-10)),r+n.join("")},pl=e=>e[e.length-1]==="/"?e.slice(0,-1):e,Dc=e=>e[0]==="/"?e.slice(1):e,Rd=(e,t)=>{const n=Object.keys(e).sort((r,a)=>{const o=a.split("/").length-r.split("/").length;return o!==0?o:a.length-r.length});for(const r of n)if(t.startsWith(r))return r;return"/"},$d=e=>typeof e=="function",we=e=>typeof e=="string";const Fd="modulepreload",Hd=function(e){return"/"+e},Os={},T=function(t,n,r){let a=Promise.resolve();if(n&&n.length>0){document.getElementsByTagName("link");const o=document.querySelector("meta[property=csp-nonce]"),l=(o==null?void 0:o.nonce)||(o==null?void 0:o.getAttribute("nonce"));a=Promise.all(n.map(i=>{if(i=Hd(i),i in Os)return;Os[i]=!0;const c=i.endsWith(".css"),u=c?'[rel="stylesheet"]':"";if(document.querySelector(`link[href="${i}"]${u}`))return;const d=document.createElement("link");if(d.rel=c?"stylesheet":Fd,c||(d.as="script",d.crossOrigin=""),d.href=i,l&&d.setAttribute("nonce",l),document.head.appendChild(d),c)return new Promise((f,p)=>{d.addEventListener("load",f),d.addEventListener("error",()=>p(new Error(`Unable to preload CSS for ${i}`)))})}))}return a.then(()=>t()).catch(o=>{const l=new Event("vite:preloadError",{cancelable:!0});if(l.payload=o,window.dispatchEvent(l),!l.defaultPrevented)throw o})},Nd=JSON.parse('{"/tech/docker+nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html":"/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html"}'),Vd=Object.fromEntries([["/",{loader:()=>T(()=>import("./index.html-BjAw7f-F.js"),[]),meta:{t:"主页",i:"home"}}],["/intro.html",{loader:()=>T(()=>import("./intro.html-CEHYbhC9.js"),[]),meta:{t:"介绍页",i:"circle-info"}}],["/essays/",{loader:()=>T(()=>import("./index.html-DzJoMr4P.js"),[]),meta:{d:17292096e5,l:"2024年10月18日",e:`
+**/const K0="http://www.w3.org/2000/svg",J0="http://www.w3.org/1998/Math/MathML",Yt=typeof document<"u"?document:null,bs=Yt&&Yt.createElement("template"),Q0={insert:(e,t,n)=>{t.insertBefore(e,n||null)},remove:e=>{const t=e.parentNode;t&&t.removeChild(e)},createElement:(e,t,n,r)=>{const a=t==="svg"?Yt.createElementNS(K0,e):t==="mathml"?Yt.createElementNS(J0,e):Yt.createElement(e,n?{is:n}:void 0);return e==="select"&&r&&r.multiple!=null&&a.setAttribute("multiple",r.multiple),a},createText:e=>Yt.createTextNode(e),createComment:e=>Yt.createComment(e),setText:(e,t)=>{e.nodeValue=t},setElementText:(e,t)=>{e.textContent=t},parentNode:e=>e.parentNode,nextSibling:e=>e.nextSibling,querySelector:e=>Yt.querySelector(e),setScopeId(e,t){e.setAttribute(t,"")},insertStaticContent(e,t,n,r,a,o){const l=n?n.previousSibling:t.lastChild;if(a&&(a===o||a.nextSibling))for(;t.insertBefore(a.cloneNode(!0),n),!(a===o||!(a=a.nextSibling)););else{bs.innerHTML=r==="svg"?`<svg>${e}</svg>`:r==="mathml"?`<math>${e}</math>`:e;const i=bs.content;if(r==="svg"||r==="mathml"){const c=i.firstChild;for(;c.firstChild;)i.appendChild(c.firstChild);i.removeChild(c)}t.insertBefore(i,n)}return[l?l.nextSibling:t.firstChild,n?n.previousSibling:t.lastChild]}},zt="transition",Qn="animation",Hn=Symbol("_vtc"),Rt=(e,{slots:t})=>s(a0,Tc(e),t);Rt.displayName="Transition";const kc={name:String,type:String,css:{type:Boolean,default:!0},duration:[String,Number,Object],enterFromClass:String,enterActiveClass:String,enterToClass:String,appearFromClass:String,appearActiveClass:String,appearToClass:String,leaveFromClass:String,leaveActiveClass:String,leaveToClass:String},Y0=Rt.props=Pe({},Xi,kc),fn=(e,t=[])=>{te(e)?e.forEach(n=>n(...t)):e&&e(...t)},Es=e=>e?te(e)?e.some(t=>t.length>1):e.length>1:!1;function Tc(e){const t={};for(const R in e)R in kc||(t[R]=e[R]);if(e.css===!1)return t;const{name:n="v",type:r,duration:a,enterFromClass:o=`${n}-enter-from`,enterActiveClass:l=`${n}-enter-active`,enterToClass:i=`${n}-enter-to`,appearFromClass:c=o,appearActiveClass:u=l,appearToClass:d=i,leaveFromClass:f=`${n}-leave-from`,leaveActiveClass:p=`${n}-leave-active`,leaveToClass:h=`${n}-leave-to`}=e,v=Z0(a),_=v&&v[0],E=v&&v[1],{onBeforeEnter:b,onEnter:C,onEnterCancelled:y,onLeave:A,onLeaveCancelled:D,onBeforeAppear:P=b,onAppear:H=C,onAppearCancelled:O=y}=t,Q=(R,X,Le)=>{Wt(R,X?d:i),Wt(R,X?u:l),Le&&Le()},I=(R,X)=>{R._isLeaving=!1,Wt(R,f),Wt(R,h),Wt(R,p),X&&X()},U=R=>(X,Le)=>{const Ae=R?H:C,W=()=>Q(X,R,Le);fn(Ae,[X,W]),_s(()=>{Wt(X,R?c:o),Dt(X,R?d:i),Es(Ae)||ws(X,r,_,W)})};return Pe(t,{onBeforeEnter(R){fn(b,[R]),Dt(R,o),Dt(R,l)},onBeforeAppear(R){fn(P,[R]),Dt(R,c),Dt(R,u)},onEnter:U(!1),onAppear:U(!0),onLeave(R,X){R._isLeaving=!0;const Le=()=>I(R,X);Dt(R,f),Dt(R,p),xc(),_s(()=>{R._isLeaving&&(Wt(R,f),Dt(R,h),Es(A)||ws(R,r,E,Le))}),fn(A,[R,Le])},onEnterCancelled(R){Q(R,!1),fn(y,[R])},onAppearCancelled(R){Q(R,!0),fn(O,[R])},onLeaveCancelled(R){I(R),fn(D,[R])}})}function Z0(e){if(e==null)return null;if(Be(e))return[Ua(e.enter),Ua(e.leave)];{const t=Ua(e);return[t,t]}}function Ua(e){return n2(e)}function Dt(e,t){t.split(/\s+/).forEach(n=>n&&e.classList.add(n)),(e[Hn]||(e[Hn]=new Set)).add(t)}function Wt(e,t){t.split(/\s+/).forEach(r=>r&&e.classList.remove(r));const n=e[Hn];n&&(n.delete(t),n.size||(e[Hn]=void 0))}function _s(e){requestAnimationFrame(()=>{requestAnimationFrame(e)})}let X0=0;function ws(e,t,n,r){const a=e._endId=++X0,o=()=>{a===e._endId&&r()};if(n)return setTimeout(o,n);const{type:l,timeout:i,propCount:c}=Sc(e,t);if(!l)return r();const u=l+"end";let d=0;const f=()=>{e.removeEventListener(u,p),o()},p=h=>{h.target===e&&++d>=c&&f()};setTimeout(()=>{d<c&&f()},i+1),e.addEventListener(u,p)}function Sc(e,t){const n=window.getComputedStyle(e),r=v=>(n[v]||"").split(", "),a=r(`${zt}Delay`),o=r(`${zt}Duration`),l=As(a,o),i=r(`${Qn}Delay`),c=r(`${Qn}Duration`),u=As(i,c);let d=null,f=0,p=0;t===zt?l>0&&(d=zt,f=l,p=o.length):t===Qn?u>0&&(d=Qn,f=u,p=c.length):(f=Math.max(l,u),d=f>0?l>u?zt:Qn:null,p=d?d===zt?o.length:c.length:0);const h=d===zt&&/\b(transform|all)(,|$)/.test(r(`${zt}Property`).toString());return{type:d,timeout:f,propCount:p,hasTransform:h}}function As(e,t){for(;e.length<t.length;)e=e.concat(e);return Math.max(...t.map((n,r)=>Cs(n)+Cs(e[r])))}function Cs(e){return e==="auto"?0:Number(e.slice(0,-1).replace(",","."))*1e3}function xc(){return document.body.offsetHeight}function ed(e,t,n){const r=e[Hn];r&&(t=(t?[t,...r]:[...r]).join(" ")),t==null?e.removeAttribute("class"):n?e.setAttribute("class",t):e.className=t}const ks=Symbol("_vod"),td=Symbol("_vsh"),nd=Symbol(""),rd=/(^|;)\s*display\s*:/;function ad(e,t,n){const r=e.style,a=Re(n);let o=!1;if(n&&!a){if(t)if(Re(t))for(const l of t.split(";")){const i=l.slice(0,l.indexOf(":")).trim();n[i]==null&&sa(r,i,"")}else for(const l in t)n[l]==null&&sa(r,l,"");for(const l in n)l==="display"&&(o=!0),sa(r,l,n[l])}else if(a){if(t!==n){const l=r[nd];l&&(n+=";"+l),r.cssText=n,o=rd.test(n)}}else t&&e.removeAttribute("style");ks in e&&(e[ks]=o?r.display:"",e[td]&&(r.display="none"))}const Ts=/\s*!important$/;function sa(e,t,n){if(te(n))n.forEach(r=>sa(e,t,r));else if(n==null&&(n=""),t.startsWith("--"))e.setProperty(t,n);else{const r=od(e,t);Ts.test(n)?e.setProperty(jn(r),n.replace(Ts,""),"important"):e[r]=n}}const Ss=["Webkit","Moz","ms"],Wa={};function od(e,t){const n=Wa[t];if(n)return n;let r=qe(t);if(r!=="filter"&&r in e)return Wa[t]=r;r=_n(r);for(let a=0;a<Ss.length;a++){const o=Ss[a]+r;if(o in e)return Wa[t]=o}return t}const xs="http://www.w3.org/1999/xlink";function ld(e,t,n,r,a){if(r&&t.startsWith("xlink:"))n==null?e.removeAttributeNS(xs,t.slice(6,t.length)):e.setAttributeNS(xs,t,n);else{const o=c2(t);n==null||o&&!ki(n)?e.removeAttribute(t):e.setAttribute(t,o?"":n)}}function sd(e,t,n,r,a,o,l){if(t==="innerHTML"||t==="textContent"){r&&l(r,a,o),e[t]=n??"";return}const i=e.tagName;if(t==="value"&&i!=="PROGRESS"&&!i.includes("-")){const u=i==="OPTION"?e.getAttribute("value")||"":e.value,d=n??"";(u!==d||!("_value"in e))&&(e.value=d),n==null&&e.removeAttribute(t),e._value=n;return}let c=!1;if(n===""||n==null){const u=typeof e[t];u==="boolean"?n=ki(n):n==null&&u==="string"?(n="",c=!0):u==="number"&&(n=0,c=!0)}try{e[t]=n}catch{}c&&e.removeAttribute(t)}function id(e,t,n,r){e.addEventListener(t,n,r)}function cd(e,t,n,r){e.removeEventListener(t,n,r)}const Ls=Symbol("_vei");function ud(e,t,n,r,a=null){const o=e[Ls]||(e[Ls]={}),l=o[t];if(r&&l)l.value=r;else{const[i,c]=dd(t);if(r){const u=o[t]=hd(r,a);id(e,i,u,c)}else l&&(cd(e,i,l,c),o[t]=void 0)}}const Bs=/(?:Once|Passive|Capture)$/;function dd(e){let t;if(Bs.test(e)){t={};let r;for(;r=e.match(Bs);)e=e.slice(0,e.length-r[0].length),t[r[0].toLowerCase()]=!0}return[e[2]===":"?e.slice(3):jn(e.slice(2)),t]}let Ka=0;const fd=Promise.resolve(),pd=()=>Ka||(fd.then(()=>Ka=0),Ka=Date.now());function hd(e,t){const n=r=>{if(!r._vts)r._vts=Date.now();else if(r._vts<=n.attached)return;ft(md(r,n.value),t,5,[r])};return n.value=e,n.attached=pd(),n}function md(e,t){if(te(t)){const n=e.stopImmediatePropagation;return e.stopImmediatePropagation=()=>{n.call(e),e._stopped=!0},t.map(r=>a=>!a._stopped&&r&&r(a))}else return t}const Is=e=>e.charCodeAt(0)===111&&e.charCodeAt(1)===110&&e.charCodeAt(2)>96&&e.charCodeAt(2)<123,vd=(e,t,n,r,a,o,l,i,c)=>{const u=a==="svg";t==="class"?ed(e,r,u):t==="style"?ad(e,n,r):Sr(t)?Uo(t)||ud(e,t,n,r,l):(t[0]==="."?(t=t.slice(1),!0):t[0]==="^"?(t=t.slice(1),!1):gd(e,t,r,u))?sd(e,t,r,o,l,i,c):(t==="true-value"?e._trueValue=r:t==="false-value"&&(e._falseValue=r),ld(e,t,r,u))};function gd(e,t,n,r){if(r)return!!(t==="innerHTML"||t==="textContent"||t in e&&Is(t)&&re(n));if(t==="spellcheck"||t==="draggable"||t==="translate"||t==="form"||t==="list"&&e.tagName==="INPUT"||t==="type"&&e.tagName==="TEXTAREA")return!1;if(t==="width"||t==="height"){const a=e.tagName;if(a==="IMG"||a==="VIDEO"||a==="CANVAS"||a==="SOURCE")return!1}return Is(t)&&Re(n)?!1:t in e}const Lc=new WeakMap,Bc=new WeakMap,ga=Symbol("_moveCb"),Ps=Symbol("_enterCb"),Ic={name:"TransitionGroup",props:Pe({},Y0,{tag:String,moveClass:String}),setup(e,{slots:t}){const n=ln(),r=Zi();let a,o;return rc(()=>{if(!a.length)return;const l=e.moveClass||`${e.name||"v"}-move`;if(!Ad(a[0].el,n.vnode.el,l))return;a.forEach(Ed),a.forEach(_d);const i=a.filter(wd);xc(),i.forEach(c=>{const u=c.el,d=u.style;Dt(u,l),d.transform=d.webkitTransform=d.transitionDuration="";const f=u[ga]=p=>{p&&p.target!==u||(!p||/transform$/.test(p.propertyName))&&(u.removeEventListener("transitionend",f),u[ga]=null,Wt(u,l))};u.addEventListener("transitionend",f)})}),()=>{const l=pe(e),i=Tc(l);let c=l.tag||nt;if(a=[],o)for(let u=0;u<o.length;u++){const d=o[u];d.el&&d.el instanceof Element&&(a.push(d),gr(d,vr(d,i,r,n)),Lc.set(d,d.el.getBoundingClientRect()))}o=t.default?ll(t.default()):[];for(let u=0;u<o.length;u++){const d=o[u];d.key!=null&&gr(d,vr(d,i,r,n))}return Te(c,null,o)}}},yd=e=>delete e.mode;Ic.props;const bd=Ic;function Ed(e){const t=e.el;t[ga]&&t[ga](),t[Ps]&&t[Ps]()}function _d(e){Bc.set(e,e.el.getBoundingClientRect())}function wd(e){const t=Lc.get(e),n=Bc.get(e),r=t.left-n.left,a=t.top-n.top;if(r||a){const o=e.el.style;return o.transform=o.webkitTransform=`translate(${r}px,${a}px)`,o.transitionDuration="0s",e}}function Ad(e,t,n){const r=e.cloneNode(),a=e[Hn];a&&a.forEach(i=>{i.split(/\s+/).forEach(c=>c&&r.classList.remove(c))}),n.split(/\s+/).forEach(i=>i&&r.classList.add(i)),r.style.display="none";const o=t.nodeType===1?t:t.parentNode;o.appendChild(r);const{hasTransform:l}=Sc(r);return o.removeChild(r),l}const Cd=Pe({patchProp:vd},Q0);let Ja,Ds=!1;function kd(){return Ja=Ds?Ja:B0(Cd),Ds=!0,Ja}const Td=(...e)=>{const t=kd().createApp(...e),{mount:n}=t;return t.mount=r=>{const a=xd(r);if(a)return n(a,!0,Sd(a))},t};function Sd(e){if(e instanceof SVGElement)return"svg";if(typeof MathMLElement=="function"&&e instanceof MathMLElement)return"mathml"}function xd(e){return Re(e)?document.querySelector(e):e}var Ld=["link","meta","script","style","noscript","template"],Bd=["title","base"],Id=([e,t,n])=>Bd.includes(e)?e:Ld.includes(e)?e==="meta"&&t.name?`${e}.${t.name}`:e==="template"&&t.id?`${e}.${t.id}`:JSON.stringify([e,Object.entries(t).map(([r,a])=>typeof a=="boolean"?a?[r,""]:null:[r,a]).filter(r=>r!=null).sort(([r],[a])=>r.localeCompare(a)),n]):null,Pd=e=>{const t=new Set,n=[];return e.forEach(r=>{const a=Id(r);a&&!t.has(a)&&(t.add(a),n.push(r))}),n},Dd=e=>e[0]==="/"?e:`/${e}`,Pc=e=>e[e.length-1]==="/"||e.endsWith(".html")?e:`${e}/`,sn=e=>/^(https?:)?\/\//.test(e),Od=/.md((\?|#).*)?$/,xa=(e,t="/")=>!!(sn(e)||e.startsWith("/")&&!e.startsWith(t)&&!Od.test(e)),La=e=>/^[a-z][a-z0-9+.-]*:/.test(e),qn=e=>Object.prototype.toString.call(e)==="[object Object]",Md=e=>{const[t,...n]=e.split(/(\?|#)/);if(!t||t.endsWith("/"))return e;let r=t.replace(/(^|\/)README.md$/i,"$1index.html");return r.endsWith(".md")?r=r.substring(0,r.length-3)+".html":r.endsWith(".html")||(r=r+".html"),r.endsWith("/index.html")&&(r=r.substring(0,r.length-10)),r+n.join("")},pl=e=>e[e.length-1]==="/"?e.slice(0,-1):e,Dc=e=>e[0]==="/"?e.slice(1):e,Rd=(e,t)=>{const n=Object.keys(e).sort((r,a)=>{const o=a.split("/").length-r.split("/").length;return o!==0?o:a.length-r.length});for(const r of n)if(t.startsWith(r))return r;return"/"},$d=e=>typeof e=="function",we=e=>typeof e=="string";const Fd="modulepreload",Hd=function(e){return"/"+e},Os={},T=function(t,n,r){let a=Promise.resolve();if(n&&n.length>0){document.getElementsByTagName("link");const o=document.querySelector("meta[property=csp-nonce]"),l=(o==null?void 0:o.nonce)||(o==null?void 0:o.getAttribute("nonce"));a=Promise.all(n.map(i=>{if(i=Hd(i),i in Os)return;Os[i]=!0;const c=i.endsWith(".css"),u=c?'[rel="stylesheet"]':"";if(document.querySelector(`link[href="${i}"]${u}`))return;const d=document.createElement("link");if(d.rel=c?"stylesheet":Fd,c||(d.as="script",d.crossOrigin=""),d.href=i,l&&d.setAttribute("nonce",l),document.head.appendChild(d),c)return new Promise((f,p)=>{d.addEventListener("load",f),d.addEventListener("error",()=>p(new Error(`Unable to preload CSS for ${i}`)))})}))}return a.then(()=>t()).catch(o=>{const l=new Event("vite:preloadError",{cancelable:!0});if(l.payload=o,window.dispatchEvent(l),!l.defaultPrevented)throw o})},Nd=JSON.parse('{"/tech/docker+nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html":"/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html"}'),Vd=Object.fromEntries([["/",{loader:()=>T(()=>import("./index.html-Bq7J9cN0.js"),[]),meta:{t:"主页",i:"home"}}],["/intro.html",{loader:()=>T(()=>import("./intro.html-DcelwrZW.js"),[]),meta:{t:"介绍页",i:"circle-info"}}],["/essays/",{loader:()=>T(()=>import("./index.html-CdwZ1P48.js"),[]),meta:{d:17292096e5,l:"2024年10月18日",e:`
 <p>这里是所有个人感想、生活记录等非技术类文章。</p>
-`,r:{minutes:.13,words:39},t:"随笔",y:"a"}}],["/essays/%E5%91%BD%E9%87%8C%E6%9C%89%E6%97%B6%E7%BB%88%E9%A1%BB%E6%9C%89.html",{loader:()=>T(()=>import("./命里有时终须有.html-DOvT7-xg.js"),[]),meta:{d:17302464e5,l:"2024年10月30日",e:`<figure><figcaption>alt text</figcaption></figure>
+`,r:{minutes:.13,words:40},t:"随笔",y:"a"}}],["/essays/%E5%91%BD%E9%87%8C%E6%9C%89%E6%97%B6%E7%BB%88%E9%A1%BB%E6%9C%89.html",{loader:()=>T(()=>import("./命里有时终须有.html-B46pNP68.js"),[]),meta:{d:17302464e5,l:"2024年10月30日",e:`<figure><figcaption>alt text</figcaption></figure>
 <p>昨日在玩“三国杀：一将成名”时，我抽奖一发就中了大奖——“清河公主”传说皮。这让我不禁感慨：“命里有时终须有，命里无时莫强求。”这句话真是道出了人生的真谛，有些事情是强求不来的，顺其自然反而能得到意想不到的收获。</p>
-`,r:{minutes:.35,words:104},t:"命里有时终须有",y:"a"}}],["/projects/",{loader:()=>T(()=>import("./index.html-BjDh3PHW.js"),[]),meta:{d:17292096e5,l:"2024年10月18日",e:`
+`,r:{minutes:.35,words:104},t:"命里有时终须有",y:"a"}}],["/projects/carrobot.html",{loader:()=>T(()=>import("./carrobot.html-B7set7IG.js"),[]),meta:{d:17309376e5,l:"2024年11月7日",e:`<p><a href="https://github.com/king-sj/carrobot" target="_blank" rel="noopener noreferrer">项目源码</a></p>
+<p><s>因为想要创新学分，所以选了创新创业智能车课程</s>，项目要求完成智能车的循迹和避障。</p>
+<p>由于笔者不喜欢使用VPL的图形化（<s>报用qWq</s>）, 故而使用手写代码的方式实现。</p>
+`,r:{minutes:4.03,words:1210},t:"北京邮电大学创新创业智能车循迹python版",y:"a"}}],["/projects/",{loader:()=>T(()=>import("./index.html-jwKIpsPi.js"),[]),meta:{d:17292096e5,l:"2024年10月18日",e:`
 <p>这里是你参与或开发的项目介绍和进展。</p>
-`,r:{minutes:.12,words:36},t:"项目",y:"a"}}],["/resources/",{loader:()=>T(()=>import("./index.html-Dv6rE_pN.js"),[]),meta:{d:17292096e5,l:"2024年10月18日",e:`
+`,r:{minutes:.12,words:37},t:"项目",y:"a"}}],["/resources/",{loader:()=>T(()=>import("./index.html-DtPJaw_H.js"),[]),meta:{d:17292096e5,l:"2024年10月18日",e:`
 <p>这里是推荐的书籍、网站、工具等资源。</p>
-`,r:{minutes:.58,words:175},t:"资源",y:"a"}}],["/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html",{loader:()=>T(()=>import("./Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js"),[]),meta:{d:17250624e5,l:"2024年8月31日",e:`
+`,r:{minutes:.58,words:175},t:"资源",y:"a"}}],["/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html",{loader:()=>T(()=>import("./Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js"),[]),meta:{d:17250624e5,l:"2024年8月31日",e:`
 <h2>Some Solutions to Questions about Qt</h2>
 <h3>The qt-5 isn't in Qt Maintenance tools</h3>
 <ol>
@@ -30,60 +33,60 @@
 <li>click the Archive in the Select-Component section.</li>
 <li>click the filter button and you can see the qt-5 in the list.</li>
 </ol>
-`,r:{minutes:.18,words:54},t:"Qt",y:"a"}}],["/tech/android%20studio%E6%8D%A2%E6%BA%90.html",{loader:()=>T(()=>import("./android studio换源.html-CxjDu5df.js"),[]),meta:{d:17225568e5,l:"2024年8月2日",c:["build-tools"],e:`
+`,r:{minutes:.18,words:54},t:"Qt",y:"a"}}],["/tech/android%20studio%E6%8D%A2%E6%BA%90.html",{loader:()=>T(()=>import("./android studio换源.html-DkRIM6mj.js"),[]),meta:{d:17225568e5,l:"2024年8月2日",c:["build-tools"],e:`
 <p><a href="https://mirrors.cloud.tencent.com/gradle/" target="_blank" rel="noopener noreferrer">国内镜像</a></p>
 <p>Android Studio下载gradle太慢可换源</p>
 <p><a href="https://blog.csdn.net/qq_43811536/article/details/139447518" target="_blank" rel="noopener noreferrer">android.plugin version 下载错误查看</a></p>
-<p><strong>修改 settings.gradle.kts</strong></p>`,r:{minutes:.46,words:139},t:"android studio换源",y:"a"}}],["/tech/cicd.html",{loader:()=>T(()=>import("./cicd.html-CedraPRV.js"),[]),meta:{d:17225568e5,l:"2024年8月2日",c:["CI/CD"],g:["CI/CD"],e:`
+<p><strong>修改 settings.gradle.kts</strong></p>`,r:{minutes:.46,words:139},t:"android studio换源",y:"a"}}],["/tech/cicd.html",{loader:()=>T(()=>import("./cicd.html-BxLHD3yn.js"),[]),meta:{d:17225568e5,l:"2024年8月2日",c:["CI/CD"],g:["CI/CD"],e:`
 <p>本地调试工具 <a href="https://github.com/nektos/act" target="_blank" rel="noopener noreferrer">act</a></p>
 <p>需要创建配置文件</p>
 <!-- TODO -->
 <p>也可另外指定</p>
 <div class="language-bash" data-ext="sh" data-title="sh"><pre class="language-bash"><code>act --var-file <span class="token string">"./.act/.vars"</span> --secret-file <span class="token string">"./.act/.secrets"</span> --env-file <span class="token string">"./.act/.env"</span> <span class="token punctuation">{</span><span class="token punctuation">{</span>other<span class="token punctuation">}</span><span class="token punctuation">}</span>
-</code></pre></div>`,r:{minutes:.16,words:48},t:"CI/CD",y:"a"}}],["/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html",{loader:()=>T(()=>import("./docker_nginx部署web项目.html-4IxhKq9E.js"),[]),meta:{a:"King-sj",d:17264448e5,l:"2024年9月16日",c:["nginx"],g:["部署"],e:`
+</code></pre></div>`,r:{minutes:.16,words:48},t:"CI/CD",y:"a"}}],["/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html",{loader:()=>T(()=>import("./docker_nginx部署web项目.html-CZONKQdf.js"),[]),meta:{a:"King-sj",d:17264448e5,l:"2024年9月16日",c:["nginx"],g:["部署"],e:`
 <p>本文将介绍如何使用 Docker、Nginx 和 acme.sh 部署一个 Vue 和 Flask 项目。我们将详细讲解环境配置、项目结构、Nginx 配置、Docker 配置以及如何升级到 HTTPS。</p>
-`,r:{minutes:2.63,words:789},t:"docker + nginx + acme.sh 部署 vue/flask 项目",y:"a"}}],["/tech/docker.html",{loader:()=>T(()=>import("./docker.html-B-hYGcsZ.js"),[]),meta:{d:17260992e5,l:"2024年9月12日",c:["奇技淫巧","docker"],g:["docker"],e:`<h2>GitHub Container Registry 加速</h2>
+`,r:{minutes:2.63,words:789},t:"docker + nginx + acme.sh 部署 vue/flask 项目",y:"a"}}],["/tech/docker.html",{loader:()=>T(()=>import("./docker.html-DtdutZB7.js"),[]),meta:{d:17260992e5,l:"2024年9月12日",c:["奇技淫巧","docker"],g:["docker"],e:`<h2>GitHub Container Registry 加速</h2>
 <h3>ghcr.io简介</h3>
 <ul>
 <li>ghcr.io 是 GitHub Container Registry 的域名。GitHub Container Registry 是 GitHub 提供的容器镜像注册表服务，允许开发者在 GitHub 上存储、管理和分享 Docker 镜像。它与 GitHub 代码仓库紧密集成，可以使用相同的权限管理、团队协作和版本控制工具来管理容器镜像。</li>
 <li>通过 GitHub Container Registry，开发者可以方便地将他们的容器镜像与代码仓库关联起来，这样就可以在同一个平台上管理代码和镜像。这种集成性使得持续集成/持续交付 (CI/CD) 流程更加简化和统一，开发团队可以更容易地构建、测试和部署应用程序。</li>
 <li>对于使用 GitHub 作为代码托管平台的开发者来说，GitHub Container Registry 提供一个便捷且强大的容器镜像管理解决方案。通过该服务，可以更轻松地构建和部署容器化的应用程序，从而加速开发和交付周期。</li>
-</ul>`,r:{minutes:1.11,words:334},t:"",y:"a"}}],["/tech/figure_bed.html",{loader:()=>T(()=>import("./figure_bed.html-BME-hebA.js"),[]),meta:{d:17304192e5,l:"2024年11月1日",e:`<p>参考</p>
+</ul>`,r:{minutes:1.11,words:334},t:"",y:"a"}}],["/tech/figure_bed.html",{loader:()=>T(()=>import("./figure_bed.html-vyc89ngd.js"),[]),meta:{d:17304192e5,l:"2024年11月1日",e:`<p>参考</p>
 <ul>
 <li>https://zhuanlan.zhihu.com/p/347342082</li>
 </ul>
-`,r:{minutes:.04,words:12},t:"github 图床",y:"a"}}],["/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html",{loader:()=>T(()=>import("./github 工作流.html-CFTCrRk5.js"),[]),meta:{e:`
+`,r:{minutes:.04,words:12},t:"github 图床",y:"a"}}],["/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html",{loader:()=>T(()=>import("./github 工作流.html-DJORqAx-.js"),[]),meta:{e:`
 <p><a href="https://www.bilibili.com/video/BV19e4y1q7JJ" target="_blank" rel="noopener noreferrer">十分钟学会正确的github工作流，和开源作者们使用同一套流程</a></p>
 <div class="hint-container info">
 <p class="hint-container-title">相关信息</p>
 <p>TODO</p>
 </div>
-`,r:{minutes:.11,words:34},t:"github 工作流程",y:"a"}}],["/tech/",{loader:()=>T(()=>import("./index.html-Dakgazin.js"),[]),meta:{d:17292096e5,l:"2024年10月18日",e:`
+`,r:{minutes:.11,words:34},t:"github 工作流程",y:"a"}}],["/tech/",{loader:()=>T(()=>import("./index.html-CqYdKjYM.js"),[]),meta:{d:17292096e5,l:"2024年10月18日",e:`
 <p>这里是所有与技术相关的文章，包括编程、工具使用、技术分享等内容。</p>
-`,r:{minutes:.16,words:49},t:"技术",y:"a"}}],["/tech/mailserver.html",{loader:()=>T(()=>import("./mailserver.html-DITZCknd.js"),[]),meta:{d:17304192e5,l:"2024年11月1日",e:`<p>参见:</p>
+`,r:{minutes:.16,words:49},t:"技术",y:"a"}}],["/tech/mailserver.html",{loader:()=>T(()=>import("./mailserver.html-DO5Xbwgi.js"),[]),meta:{d:17304192e5,l:"2024年11月1日",e:`<p>参见:</p>
 <ul>
 <li>https://docker-mailserver.github.io/docker-mailserver/latest/</li>
 <li>https://blog.csdn.net/qq_25866579/article/details/140717115</li>
 <li>https://zhuanlan.zhihu.com/p/609639797</li>
 </ul>
 <p>值得注意的是docker-mailserver 并不支持通过ui注册/修改等操作， 当可以自行实现（后端通过shell命令即可</p>
-<h2>使用python 发送示例</h2>`,r:{minutes:.55,words:164},t:"自建mail server",y:"a"}}],["/tech/modint.html",{loader:()=>T(()=>import("./modint.html-M2GwLZ2U.js"),[]),meta:{d:16909344e5,l:"2023年8月2日",c:["OI"],g:["MODInt"],e:`
+<h2>使用python 发送示例</h2>`,r:{minutes:.55,words:164},t:"自建mail server",y:"a"}}],["/tech/modint.html",{loader:()=>T(()=>import("./modint.html-DNrISIPe.js"),[]),meta:{d:16909344e5,l:"2023年8月2日",c:["OI"],g:["MODInt"],e:`
 <p>在 OI 中，有大量的题目要求对一些数字取模，这便是本文写作的背景。</p>
 <h2>背景介绍</h2>
 <p>这些题目要么是因为答案太大，不方便输出结果，例如许多计数 dp；要么是因为答案是浮点数，出题人不愿意写一个确定精度的 Special Judge，例如很多期望概率题；要么是因为这道题目直接考察了模的性质和运用，比如大量的 998244353 类的多项式题目。</p>
-`,r:{minutes:2.4,words:721},t:"「泛型与 OI」modint",y:"a"}}],["/tech/python_requrements.html",{loader:()=>T(()=>import("./python_requrements.html-Va55tBYB.js"),[]),meta:{d:173016e7,l:"2024年10月29日",c:["python"],g:["踩坑记录"],e:`<p>Python 生成 <code>requirements</code>有两种方式</p>
+`,r:{minutes:2.4,words:721},t:"「泛型与 OI」modint",y:"a"}}],["/tech/python_requrements.html",{loader:()=>T(()=>import("./python_requrements.html-D_iboyN4.js"),[]),meta:{d:173016e7,l:"2024年10月29日",c:["python"],g:["踩坑记录"],e:`<p>Python 生成 <code>requirements</code>有两种方式</p>
 <ul>
 <li><code>pip list --format=freeze &gt; requirements.txt</code> (推荐做法)</li>
 <li><code>pip freeze &gt; requirements.txt</code> (不推荐，会带有本地路径)</li>
 </ul>
-`,r:{minutes:.15,words:45},t:"python requirements.txt",y:"a"}}],["/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html",{loader:()=>T(()=>import("./steam模组开发.html-DQKsmuFu.js"),[]),meta:{d:172584e7,l:"2024年9月9日",e:`<p>This is the content of the game plugin post.</p>
+`,r:{minutes:.15,words:45},t:"python requirements.txt",y:"a"}}],["/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html",{loader:()=>T(()=>import("./steam模组开发.html-BnsNbJlM.js"),[]),meta:{d:172584e7,l:"2024年9月9日",e:`<p>This is the content of the game plugin post.</p>
 <ul>
 <li><a href="https://github.com/BepInEx/BepInEx" target="_blank" rel="noopener noreferrer">BepInEx</a></li>
 <li><a href="https://github.com/Perfare/AssetStudio" target="_blank" rel="noopener noreferrer">AssetStudioAssetStudio</a></li>
 <li><a href="https://github.com/dnSpy/dnSpy" target="_blank" rel="noopener noreferrer">dnSpy</a></li>
 <li><a href="https://github.com/pardeike/Harmony" target="_blank" rel="noopener noreferrer">Harmony</a></li>
 <li><a href="https://github.com/sinai-dev/UnityExplorer" target="_blank" rel="noopener noreferrer">UnityExplorer</a></li>
-</ul>`,r:{minutes:.12,words:36},t:"Game Plugin",y:"a"}}],["/tech/style.html",{loader:()=>T(()=>import("./style.html-CXxr9xzn.js"),[]),meta:{d:17245872e5,l:"2024年8月25日",c:"风格",g:"风格",e:`
+</ul>`,r:{minutes:.12,words:36},t:"Game Plugin",y:"a"}}],["/tech/style.html",{loader:()=>T(()=>import("./style.html-4qtN5eOW.js"),[]),meta:{d:17245872e5,l:"2024年8月25日",c:"风格",g:"风格",e:`
 <p>如何实现风格统一？
 可以使用*.editorconfig*文件来实现风格统一。</p>
 <ol>
@@ -98,8 +101,8 @@ end_of_line = lf
 charset = utf-8
 trim_trailing_whitespace = true
 insert_final_newline = true
-</code></pre></div>`,r:{minutes:.31,words:94},t:"风格统一",y:"a"}}],["/tech/tensorflow%E8%B8%A9%E5%9D%91.html",{loader:()=>T(()=>import("./tensorflow踩坑.html-BAaphJ4H.js"),[]),meta:{d:17304192e5,l:"2024年11月1日",e:`<p><strong>Pytorch 用于快速原型验证（学术研究）， TensorFlow 用于工业生产部署</strong></p>
-`,r:{minutes:.79,words:236},t:"tensorflow 踩坑记录",y:"a"}}],["/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html",{loader:()=>T(()=>import("./vsocde插件开发小记.html-DtdCKw5q.js"),[]),meta:{e:`
+</code></pre></div>`,r:{minutes:.31,words:94},t:"风格统一",y:"a"}}],["/tech/tensorflow%E8%B8%A9%E5%9D%91.html",{loader:()=>T(()=>import("./tensorflow踩坑.html-CtBHw7dX.js"),[]),meta:{d:17304192e5,l:"2024年11月1日",e:`<p><strong>Pytorch 用于快速原型验证（学术研究）， TensorFlow 用于工业生产部署</strong></p>
+`,r:{minutes:.79,words:236},t:"tensorflow 踩坑记录",y:"a"}}],["/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html",{loader:()=>T(()=>import("./vsocde插件开发小记.html-BytDpa8J.js"),[]),meta:{e:`
 <p>// TODO
 https://code.visualstudio.com/api/get-started/your-first-extension</p>
 <h1>tips</h1>
@@ -107,19 +110,19 @@ https://code.visualstudio.com/api/get-started/your-first-extension</p>
 <li>若activate function执行时间过长，会导致<code>Activating extension 'undefined_publisher.kcodetime' failed: AggregateError.</code>, 从而启动失败</li>
 <li>若deactivate function执行时间超过5s, 会被强行终止，导致插件无法正常退出。</li>
 <li>关闭vscode 不会触发onDidCloseTextDocument事件</li>
-</ul>`,r:{minutes:.23,words:69},t:"vscode plugin",y:"a"}}],["/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html",{loader:()=>T(()=>import("./「算术公理系统 1」自然数.html-CtzEDcR8.js"),[]),meta:{d:16888608e5,l:"2023年7月9日",c:["数学"],g:["公理系统"],e:`
+</ul>`,r:{minutes:.23,words:69},t:"vscode plugin",y:"a"}}],["/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html",{loader:()=>T(()=>import("./「算术公理系统 1」自然数.html-NHamcIiY.js"),[]),meta:{d:16888608e5,l:"2023年7月9日",c:["数学"],g:["公理系统"],e:`
 <p>假设存在一个算数系统的模型满足 Peano 公理，即假定 Peano 公理相容，在此承认次假设的基础之上，我们即可建立如今最常用的<strong>算术公理系统</strong>。<strong>自然数的定义</strong>则是构建此算术公理系统的第一步。</p>
-`,r:{minutes:18.04,words:5412},t:"「算术公理系统 1」自然数",y:"a"}}],["/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html",{loader:()=>T(()=>import("./使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js"),[]),meta:{g:["mobile"],e:`
+`,r:{minutes:18.04,words:5412},t:"「算术公理系统 1」自然数",y:"a"}}],["/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html",{loader:()=>T(()=>import("./使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js"),[]),meta:{g:["mobile"],e:`
 <p>当我们写完了vue项目后，想做一个一样的移动app，此时我们可以使用ionic无缝将其迁移到移动端。</p>
-`,r:{minutes:.73,words:218},t:"使用capacitor和ionic将vue项目迁移到mobile端",y:"a"}}],["/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html",{loader:()=>T(()=>import("./协程(asyncio)到底需不需要加锁.html-CTO2grll.js"),[]),meta:{e:`
+`,r:{minutes:.73,words:218},t:"使用capacitor和ionic将vue项目迁移到mobile端",y:"a"}}],["/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html",{loader:()=>T(()=>import("./协程(asyncio)到底需不需要加锁.html-gfcHinKw.js"),[]),meta:{e:`
 <p>原文转载自「刘悦的技术博客」<a href="https://link.segmentfault.com/?enc=8btt3pfGP%2FRxuxLguNqhrg%3D%3D.f%2BWWJlm9AsMAbAJjJZT%2BOQBqYNXwZgTYGW7Jx9l%2BpxQ%3D" target="_blank" rel="noopener noreferrer">https://v3u.cn/a_id_208</a></p>
-`,r:{minutes:10.04,words:3013},t:"并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3",y:"a"}}],["/tech/%E5%8D%8F%E7%A8%8B.html",{loader:()=>T(()=>import("./协程.html-LdIMvjSl.js"),[]),meta:{e:`
+`,r:{minutes:10.04,words:3013},t:"并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3",y:"a"}}],["/tech/%E5%8D%8F%E7%A8%8B.html",{loader:()=>T(()=>import("./协程.html-BovqfV_l.js"),[]),meta:{e:`
 <p><a href="https://course.rs/advance/async/getting-started.html#:~:text=async%20%E7%AE%80%E4%BB%8B." target="_blank" rel="noopener noreferrer">文档</a></p>
 <div class="hint-container important">
 <p class="hint-container-title">重要</p>
 <p>TODO</p>
 </div>
-`,r:{minutes:.06,words:18},t:"协程",y:"a"}}],["/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html",{loader:()=>T(()=>import("./程序员的PPT.html-CmGk8DAJ.js"),[]),meta:{e:`
+`,r:{minutes:.06,words:18},t:"协程",y:"a"}}],["/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html",{loader:()=>T(()=>import("./程序员的PPT.html-D4bbFarZ.js"),[]),meta:{e:`
 <p>复杂演示推荐</p>
 <h2>缺点</h2>
 <p>不支持导出pptx</p>
@@ -133,26 +136,31 @@ https://code.visualstudio.com/api/get-started/your-first-extension</p>
 <p>https://sspai.com/post/55718</p>
 <p>https://segmentfault.com/a/1190000040806239</p>
 <p>⚠️注意事项
-如果你的 VS Code 安装了 Markdown 渲染插件 Markdown Preview Enhanced，需要先将这个插件「禁用」或是「卸载」，转而使用 VS Code 后来集成的 Markdown 预览功能，才能正常看到渲染后的 PPT 页面。</p>`,r:{minutes:.35,words:105},t:"Slidev",y:"a"}}],["/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html",{loader:()=>T(()=>import("./闭包实现类.html-DjTAmLiV.js"),[]),meta:{d:16909344e5,l:"2023年8月2日",c:["OI"],g:["MODInt"],e:`
+如果你的 VS Code 安装了 Markdown 渲染插件 Markdown Preview Enhanced，需要先将这个插件「禁用」或是「卸载」，转而使用 VS Code 后来集成的 Markdown 预览功能，才能正常看到渲染后的 PPT 页面。</p>`,r:{minutes:.35,words:105},t:"Slidev",y:"a"}}],["/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html",{loader:()=>T(()=>import("./闭包实现类.html-CeWxsqOK.js"),[]),meta:{d:16909344e5,l:"2023年8月2日",c:["OI"],g:["MODInt"],e:`
 <p>你是否曾经想过，不用类也能封装数据和方法？这篇文章将带你走进闭包的奇妙世界，展示如何用闭包来实现这一点。通过一个有趣的代码示例，你将看到闭包是如何捕获变量并提供类似类的功能的。准备好了吗？让我们开始这段有趣的旅程吧！</p>
-`,r:{minutes:1.64,words:491},t:"闭包实现类",y:"a"}}],["/tutorials/",{loader:()=>T(()=>import("./index.html-BtJnl_OK.js"),[]),meta:{d:17292096e5,l:"2024年10月18日",e:`
+`,r:{minutes:1.64,words:491},t:"闭包实现类",y:"a"}}],["/tutorials/",{loader:()=>T(()=>import("./index.html-C9AeqWIc.js"),[]),meta:{d:17292096e5,l:"2024年10月18日",e:`
 <p>这里是所有详细的教程和指南。</p>
-`,r:{minutes:.12,words:35},t:"教程",y:"a"}}],["/tutorials/typora%E6%BF%80%E6%B4%BB.html",{loader:()=>T(()=>import("./typora激活.html-BuwKOD8g.js"),[]),meta:{d:17294688e5,l:"2024年10月21日",g:["激活"],e:`
+`,r:{minutes:.12,words:35},t:"教程",y:"a"}}],["/tutorials/typora%E6%BF%80%E6%B4%BB.html",{loader:()=>T(()=>import("./typora激活.html-DUOLfN6Y.js"),[]),meta:{d:17294688e5,l:"2024年10月21日",g:["激活"],e:`
 <p>Typora 是一款简洁高效的 Markdown 编辑器，支持实时预览和多种导出格式，适用于编写笔记、文档和博客等。</p>
 <h1>安装教程</h1>
 <ul>
 <li><a href="https://typora.io" target="_blank" rel="noopener noreferrer">Typora 官网</a></li>
 <li><a href="https://typoraio.cn" target="_blank" rel="noopener noreferrer">Typora 中文官网</a></li>
 </ul>
-<!-- TODO: 添加自己的静态服务 -->`,r:{minutes:.82,words:247},t:"Typora激活教程",y:"a"}}],["/resources/html2md/",{loader:()=>T(()=>import("./index.html-CXhg3e64.js"),[]),meta:{e:`
+<!-- TODO: 添加自己的静态服务 -->`,r:{minutes:.82,words:247},t:"Typora激活教程",y:"a"}}],["/resources/compile/",{loader:()=>T(()=>import("./index.html-ybZqFA4D.js"),[]),meta:{d:17308512e5,l:"2024年11月6日",e:`<ul>
+<li>anltr.grammar</li>
+<li>bison/yacc</li>
+<li>flex</li>
+</ul>
+`,r:{minutes:.05,words:14},t:"编译原理相关",y:"a"}}],["/resources/html2md/",{loader:()=>T(()=>import("./index.html-BlsqD0oa.js"),[]),meta:{e:`
 <ul>
 <li>https://github.com/mixmark-io/turndown</li>
 <li>https://github.com/aaronsw/html2text</li>
 </ul>
-`,r:{minutes:.03,words:10},t:"html 转 md 工具",y:"a"}}],["/tech/DesignPatterns/DesignPrinciples.html",{loader:()=>T(()=>import("./DesignPrinciples.html-BLnXHGN8.js"),[]),meta:{d:17294688e5,l:"2024年10月21日",c:["设计模式"],g:["设计模式","typescript"],e:`<p>类的设计原则有七个，包括：开闭原则、里氏代换原则、迪米特原则（最少知道原则）、单一职责原则、接口分隔原则、依赖倒置原则、组合/聚合复用原则。</p>
-`,r:{minutes:6.23,words:1868},t:"设计模式七大原则",y:"a"}}],["/tech/DesignPatterns/abstractFactory.html",{loader:()=>T(()=>import("./abstractFactory.html-DS3CgVqp.js"),[]),meta:{d:17298144e5,l:"2024年10月25日",c:["设计模式"],g:["设计模式","typescript","生成实例"],e:`<h2>为什么要使用抽象工厂模式</h2>
+`,r:{minutes:.03,words:10},t:"html 转 md 工具",y:"a"}}],["/tech/DesignPatterns/DesignPrinciples.html",{loader:()=>T(()=>import("./DesignPrinciples.html-BAjp9viD.js"),[]),meta:{d:17294688e5,l:"2024年10月21日",c:["设计模式"],g:["设计模式","typescript"],e:`<p>类的设计原则有七个，包括：开闭原则、里氏代换原则、迪米特原则（最少知道原则）、单一职责原则、接口分隔原则、依赖倒置原则、组合/聚合复用原则。</p>
+`,r:{minutes:6.23,words:1868},t:"设计模式七大原则",y:"a"}}],["/tech/DesignPatterns/abstractFactory.html",{loader:()=>T(()=>import("./abstractFactory.html-D_oh5f2L.js"),[]),meta:{d:17298144e5,l:"2024年10月25日",c:["设计模式"],g:["设计模式","typescript","生成实例"],e:`<h2>为什么要使用抽象工厂模式</h2>
 <p>抽象工厂模式提供一个接口，用于创建相关或依赖对象的家族，而无需明确指定具体类。它通过定义一个创建对象的接口来实现，这样子类可以决定实例化哪个类。抽象工厂模式使得一个类的实例化延迟到其子类。</p>
-`,r:{minutes:4.31,words:1293},t:"抽象工厂模式",y:"a"}}],["/tech/DesignPatterns/adapter.html",{loader:()=>T(()=>import("./adapter.html-B2UlYWFL.js"),[]),meta:{d:17294688e5,l:"2024年10月21日",c:["设计模式"],g:["设计模式","typescript"],e:`<h2>适配器模式</h2>
+`,r:{minutes:4.31,words:1293},t:"抽象工厂模式",y:"a"}}],["/tech/DesignPatterns/adapter.html",{loader:()=>T(()=>import("./adapter.html-x6kHt0VN.js"),[]),meta:{d:17294688e5,l:"2024年10月21日",c:["设计模式"],g:["设计模式","typescript"],e:`<h2>适配器模式</h2>
 <p>适配器模式（Adapter Pattern）是一种结构型设计模式，它允许将一个类的接口转换成客户希望的另一个接口。适配器模式使得原本由于接口不兼容而不能一起工作的那些类可以一起工作。</p>
 <h3>为什么要用适配器模式</h3>
 <p>在软件开发中，经常会遇到需要使用一些现有的类，但它们的接口并不符合当前系统的需求。适配器模式通过创建一个适配器类，将现有类的接口转换为所需的接口，从而使得现有类可以在新的环境中使用。</p>
@@ -183,47 +191,47 @@ https://code.visualstudio.com/api/get-started/your-first-extension</p>
 <td>Print</td>
 </tr>
 </tbody>
-</table>`,r:{minutes:1.52,words:456},t:"适配器模式",y:"a"}}],["/tech/DesignPatterns/bridge.html",{loader:()=>T(()=>import("./bridge.html-LTDknqB7.js"),[]),meta:{d:17298144e5,l:"2024年10月25日",c:["设计模式"],g:["设计模式","TypeScript","分开考虑"],e:`<p>Bridge 模式在“类的功能层次结构”和“类的实现层次结构”之间搭建桥梁。</p>
-`,r:{minutes:5.76,words:1728},t:"Bridge 模式",y:"a"}}],["/tech/DesignPatterns/builder.html",{loader:()=>T(()=>import("./builder.html-Ba33pTyP.js"),[]),meta:{d:17295552e5,l:"2024年10月22日",c:["设计模式"],g:["设计模式","typescript","生成实例"],e:`<h2>为什么要使用 Builder 模式</h2>
+</table>`,r:{minutes:1.52,words:456},t:"适配器模式",y:"a"}}],["/tech/DesignPatterns/bridge.html",{loader:()=>T(()=>import("./bridge.html-DzkNbynT.js"),[]),meta:{d:17298144e5,l:"2024年10月25日",c:["设计模式"],g:["设计模式","TypeScript","分开考虑"],e:`<p>Bridge 模式在“类的功能层次结构”和“类的实现层次结构”之间搭建桥梁。</p>
+`,r:{minutes:5.76,words:1728},t:"Bridge 模式",y:"a"}}],["/tech/DesignPatterns/builder.html",{loader:()=>T(()=>import("./builder.html-B7MALN7e.js"),[]),meta:{d:17295552e5,l:"2024年10月22日",c:["设计模式"],g:["设计模式","typescript","生成实例"],e:`<h2>为什么要使用 Builder 模式</h2>
 <p>Builder 模式通过将对象的构建过程与其表示分离，使得同样的构建过程可以创建不同的表示。它主要用于以下情况：</p>
 <ol>
 <li><strong>复杂对象的创建</strong>：当一个对象的构建过程非常复杂时，Builder 模式可以将构建过程分解为多个步骤，使代码更易于维护和理解。</li>
 <li><strong>不同的表示</strong>：当需要创建不同表示的对象时，Builder 模式允许使用相同的构建过程来生成不同的对象表示。</li>
 <li><strong>代码复用</strong>：通过将构建过程封装在 Director 类中，可以在不同的上下文中重用相同的构建逻辑。</li>
-</ol>`,r:{minutes:4.44,words:1333},t:"builder 模式",y:"a"}}],["/tech/DesignPatterns/chainOfResponsibility.html",{loader:()=>T(()=>import("./chainOfResponsibility.html-DhJtx4gW.js"),[]),meta:{d:17298144e5,l:"2024年10月25日",c:["设计模式"],g:["设计模式","TypeScript","推卸责任"],e:`<p>“推卸责任"听起来有些贬义的意思，但是有时候也确实存在需要“推卸责任"的情况。例如，当外部请求程序进行某个处理，但程序暂时无法直接决定由哪个对象负责处理时，就需要推卸责任。这种情况下，我们可以考虑将多个对象组成一条职责链，然后按照它们在职责链上的顺序一个一个地找出到底应该谁来负责处理。</p>
-`,r:{minutes:3.27,words:980},t:"chainOfResponsibility 模式",y:"a"}}],["/tech/DesignPatterns/command.html",{loader:()=>T(()=>import("./command.html-d4IhdjVF.js"),[]),meta:{d:173016e7,l:"2024年10月29日",c:["设计模式"],g:["设计模式","TypeScript","用类实现"],e:`<h2>为什么使用此模式</h2>
+</ol>`,r:{minutes:4.44,words:1333},t:"builder 模式",y:"a"}}],["/tech/DesignPatterns/chainOfResponsibility.html",{loader:()=>T(()=>import("./chainOfResponsibility.html-CpbeYqOk.js"),[]),meta:{d:17298144e5,l:"2024年10月25日",c:["设计模式"],g:["设计模式","TypeScript","推卸责任"],e:`<p>“推卸责任"听起来有些贬义的意思，但是有时候也确实存在需要“推卸责任"的情况。例如，当外部请求程序进行某个处理，但程序暂时无法直接决定由哪个对象负责处理时，就需要推卸责任。这种情况下，我们可以考虑将多个对象组成一条职责链，然后按照它们在职责链上的顺序一个一个地找出到底应该谁来负责处理。</p>
+`,r:{minutes:3.27,words:980},t:"chainOfResponsibility 模式",y:"a"}}],["/tech/DesignPatterns/command.html",{loader:()=>T(()=>import("./command.html-Bzqk5uGA.js"),[]),meta:{d:173016e7,l:"2024年10月29日",c:["设计模式"],g:["设计模式","TypeScript","用类实现"],e:`<h2>为什么使用此模式</h2>
 <p>Command 模式将请求封装成对象，使得可以用不同的请求、队列或者日志来参数化其他对象。Command 模式也支持可撤销的操作。</p>
 <h2>示例代码</h2>
-<img src="https://www.plantuml.com/plantuml/svg/bL992i8m5Dtt55bMj1VeGWfrwmd4nM_ofOKCag6sY7St7Va5kt2NzwStaC9vi3uecJJQetq0HrOQfK0BzauOEsA7F7XC3pbhJIEIJq8cBnPUK4cSHaL4QPSp7LI5ziJwvKbskGJdnhqIT0kEDUefKQ7sRdijgnldZOqthi2jcJKDD4-80bOz__FExWWnDPojXmRGKy2ZufnetubdegAgTxdu15o-b6_tqM5mTJhtrXOn7BGmD00k4Imj_5158i-oypPK6ilG91OBr2B-ZYy0" alt="">`,r:{minutes:2.91,words:874},t:"Command 模式",y:"a"}}],["/tech/DesignPatterns/composite.html",{loader:()=>T(()=>import("./composite.html-DOBxYen3.js"),[]),meta:{d:17298144e5,l:"2024年10月25日",c:["设计模式"],g:["设计模式","TypeScript","容器与内容的一致性"],e:`<h2>使用此设计模式的理由</h2>
+<img src="https://www.plantuml.com/plantuml/svg/bL992i8m5Dtt55bMj1VeGWfrwmd4nM_ofOKCag6sY7St7Va5kt2NzwStaC9vi3uecJJQetq0HrOQfK0BzauOEsA7F7XC3pbhJIEIJq8cBnPUK4cSHaL4QPSp7LI5ziJwvKbskGJdnhqIT0kEDUefKQ7sRdijgnldZOqthi2jcJKDD4-80bOz__FExWWnDPojXmRGKy2ZufnetubdegAgTxdu15o-b6_tqM5mTJhtrXOn7BGmD00k4Imj_5158i-oypPK6ilG91OBr2B-ZYy0" alt="">`,r:{minutes:2.91,words:874},t:"Command 模式",y:"a"}}],["/tech/DesignPatterns/composite.html",{loader:()=>T(()=>import("./composite.html-D89dw1yo.js"),[]),meta:{d:17298144e5,l:"2024年10月25日",c:["设计模式"],g:["设计模式","TypeScript","容器与内容的一致性"],e:`<h2>使用此设计模式的理由</h2>
 <p>Composite 模式允许你将对象组合成递归结构来表示“部分-整体”的层次结构。使用 Composite 模式，用户可以统一地对待单个对象和组合对象。例如，在文件系统中，目录和文件都可以被视为条目（Entry），目录可以包含其他目录和文件，而文件则是叶子节点。</p>
 <h2>示例代码</h2>
-<img src="https://www.plantuml.com/plantuml/svg/hPAn3e8m48Ptdk8I5mZX1OW3WpePOyBWO1mAFR495D8U1ZM-kwM0A77GnEcI_-xQxsiQQMAAwY9tMA99iPGWpPdMi9IaBd1p07p8a3QiGDSBmSm8cGrfBAusbNMHeB8fuzp5TZViZl3wQfkLMQQrqDGkdKl1JJeRqvsWqrRXKJHkPSjmtpZj0vMnpLvexexJGI-4mfHA0uuDeUIzHciH01-QFT7-O6DfpAPU_x3znUifi18vVcAVG0QW3SiRoVVKlu6DJpeFWhAtYmoV-JCF" alt="">`,r:{minutes:1.78,words:533},t:"Composite 模式",y:"a"}}],["/tech/DesignPatterns/decorator.html",{loader:()=>T(()=>import("./decorator.html-FfT8RlFX.js"),[]),meta:{d:17298144e5,l:"2024年10月25日",c:["设计模式"],g:["设计模式","TypeScript","容器与内容的一致性"],e:`<p>在这个示例中，我们使用装饰器模式来动态地给对象添加职责。装饰器模式允许我们通过将对象放入包含行为的特殊封装对象中来扩展对象的功能，而无需修改原始类的代码。</p>
-`,r:{minutes:5.79,words:1737},t:"Decorator 模式",y:"a"}}],["/tech/DesignPatterns/end.html",{loader:()=>T(()=>import("./end.html-De4ifiEs.js"),[]),meta:{d:173016e7,l:"2024年10月29日",c:["设计模式"],g:["设计模式","TypeScript"],e:`<p><a href="https://github.com/King-sj/DesignPatterns" target="_blank" rel="noopener noreferrer">教程源码示例</a></p>
+<img src="https://www.plantuml.com/plantuml/svg/hPAn3e8m48Ptdk8I5mZX1OW3WpePOyBWO1mAFR495D8U1ZM-kwM0A77GnEcI_-xQxsiQQMAAwY9tMA99iPGWpPdMi9IaBd1p07p8a3QiGDSBmSm8cGrfBAusbNMHeB8fuzp5TZViZl3wQfkLMQQrqDGkdKl1JJeRqvsWqrRXKJHkPSjmtpZj0vMnpLvexexJGI-4mfHA0uuDeUIzHciH01-QFT7-O6DfpAPU_x3znUifi18vVcAVG0QW3SiRoVVKlu6DJpeFWhAtYmoV-JCF" alt="">`,r:{minutes:1.78,words:533},t:"Composite 模式",y:"a"}}],["/tech/DesignPatterns/decorator.html",{loader:()=>T(()=>import("./decorator.html-0jwtowLH.js"),[]),meta:{d:17298144e5,l:"2024年10月25日",c:["设计模式"],g:["设计模式","TypeScript","容器与内容的一致性"],e:`<p>在这个示例中，我们使用装饰器模式来动态地给对象添加职责。装饰器模式允许我们通过将对象放入包含行为的特殊封装对象中来扩展对象的功能，而无需修改原始类的代码。</p>
+`,r:{minutes:5.79,words:1737},t:"Decorator 模式",y:"a"}}],["/tech/DesignPatterns/end.html",{loader:()=>T(()=>import("./end.html-CkqhlgwJ.js"),[]),meta:{d:173016e7,l:"2024年10月29日",c:["设计模式"],g:["设计模式","TypeScript"],e:`<p><a href="https://github.com/King-sj/DesignPatterns" target="_blank" rel="noopener noreferrer">教程源码示例</a></p>
 <p>使用设计模式的目的是重用代码，并在增加需求时尽量不修改已有的类。我们不应死记硬背这些设计模式，而应理解其背后的核心思想。设计模式的使用不是最终目的，而是为了更好地解决问题和优化代码结构。同时，我们也要避免过早地进行“工程化”，应根据实际需求灵活应用设计模式。</p>
-<p>设计模式提供了一种通用的解决方案，可以帮助我们应对软件开发中的常见问题。通过学习和应用设计模式，我们可以提高代码的可读性、可维护性和可扩展性。然而，设计模式并不是万能的，它们也有其局限性和适用范围。在实际开发中，我们需要根据具体情况选择合适的设计模式，而不是盲目地套用。</p>`,r:{minutes:1.48,words:445},t:"结语",y:"a"}}],["/tech/DesignPatterns/facade.html",{loader:()=>T(()=>import("./facade.html-Cj3lyBcS.js"),[]),meta:{d:17299008e5,l:"2024年10月26日",c:["设计模式"],g:["设计模式","TypeScript","简单化"],e:`<p>当某个程序员得意地说出"啊，在调用那个类之前需要先调用这个类。在调用那个方法之前需要先在这个类中注册一下"的时候，就意味着我们需要引人Facade了。</p>
+<p>设计模式提供了一种通用的解决方案，可以帮助我们应对软件开发中的常见问题。通过学习和应用设计模式，我们可以提高代码的可读性、可维护性和可扩展性。然而，设计模式并不是万能的，它们也有其局限性和适用范围。在实际开发中，我们需要根据具体情况选择合适的设计模式，而不是盲目地套用。</p>`,r:{minutes:1.48,words:445},t:"结语",y:"a"}}],["/tech/DesignPatterns/facade.html",{loader:()=>T(()=>import("./facade.html-BODpRH45.js"),[]),meta:{d:17299008e5,l:"2024年10月26日",c:["设计模式"],g:["设计模式","TypeScript","简单化"],e:`<p>当某个程序员得意地说出"啊，在调用那个类之前需要先调用这个类。在调用那个方法之前需要先在这个类中注册一下"的时候，就意味着我们需要引人Facade了。</p>
 <p>对于那些能够明确地用语言描述出来的知识，我们不应该将它们隐藏在自己脑袋中，而是应该用代码将它们表现出来。</p>
 <p style="text-align: right;">—————《图解设计模式》</p>
-`,r:{minutes:2.26,words:679},t:"facade 模式",y:"a"}}],["/tech/DesignPatterns/factory_method.html",{loader:()=>T(()=>import("./factory_method.html-B20phxz9.js"),[]),meta:{d:17294688e5,l:"2024年10月21日",c:["设计模式"],g:["设计模式","typescript","工厂方法","交给子类"],e:`<p>在 Factory Method 模式中，我们定义一个用于创建对象的接口，但由子类决定要实例化的类是哪一个。Factory Method 使一个类的实例化延迟到其子类。</p>
-`,r:{minutes:1.67,words:501},t:"Factory Method 模式",y:"a"}}],["/tech/DesignPatterns/flyweight.html",{loader:()=>T(()=>import("./flyweight.html-CWx8TgTS.js"),[]),meta:{d:17300736e5,l:"2024年10月28日",c:["设计模式"],g:["设计模式","TypeScript","避免浪费"],e:`<h2>为什么使用 Flyweight 模式</h2>
+`,r:{minutes:2.26,words:679},t:"facade 模式",y:"a"}}],["/tech/DesignPatterns/factory_method.html",{loader:()=>T(()=>import("./factory_method.html-NuMbQ7is.js"),[]),meta:{d:17294688e5,l:"2024年10月21日",c:["设计模式"],g:["设计模式","typescript","工厂方法","交给子类"],e:`<p>在 Factory Method 模式中，我们定义一个用于创建对象的接口，但由子类决定要实例化的类是哪一个。Factory Method 使一个类的实例化延迟到其子类。</p>
+`,r:{minutes:1.67,words:501},t:"Factory Method 模式",y:"a"}}],["/tech/DesignPatterns/flyweight.html",{loader:()=>T(()=>import("./flyweight.html-DUTi0_Qx.js"),[]),meta:{d:17300736e5,l:"2024年10月28日",c:["设计模式"],g:["设计模式","TypeScript","避免浪费"],e:`<h2>为什么使用 Flyweight 模式</h2>
 <p>Flyweight 模式是一种结构型设计模式，它通过共享尽可能多的相同对象来减少内存使用，从而提高性能。在需要生成大量细粒度对象的场景中，Flyweight 模式非常有用。通过共享对象，Flyweight 模式可以显著减少内存消耗，并提高应用程序的效率。</p>
 <h2>实例代码</h2>
-<img src="https://www.plantuml.com/plantuml/svg/RL7B2i8m4BpdA_ROKli3GKfH43nuyYWUrZJMG4rAinL4_7VJz5rxMsPsPcTtKqjOKVqic2ZGMjYfVF_02ZuC80RXIerFoS5IfNJkmRlHb27X18oWT1K58OUNKHdxihdT0GMPwjsvbiOK74vORbk3JT-MUDeb8YN0EgQGP3HVkBJ9Z7RYkW62q2VePBcaewDG2zd4-PD6JKU71ilzHi5iXRCdk_GtbJSoExHUhjvsciWLW-NwUHQ7YUDac3mEdA3z0giaIwNEt0z_" alt="">`,r:{minutes:8.16,words:2449},t:"Flyweight 模式",y:"a"}}],["/tech/DesignPatterns/",{loader:()=>T(()=>import("./index.html-B5GIg4Ij.js"),[]),meta:{d:17294688e5,l:"2024年10月21日",c:["设计模式"],g:["设计模式","typescript"],e:`<p>面向对象三大特性：封装、继承、多态。 设计模式需遵循面向对象的设计原则，由于笔者不太喜欢java, 并嫌弃cpp中没有interface, 遂使用ts作为实现语言(我才不用rust呢 😃 )</p>
-`,r:{minutes:.48,words:144},t:"设计模式",y:"a"}}],["/tech/DesignPatterns/interpreter.html",{loader:()=>T(()=>import("./interpreter.html-CansycaD.js"),[]),meta:{d:173016e7,l:"2024年10月29日",c:["设计模式"],g:["设计模式","TypeScript","用类实现"],e:`<h2>为什么使用此模式</h2>
+<img src="https://www.plantuml.com/plantuml/svg/RL7B2i8m4BpdA_ROKli3GKfH43nuyYWUrZJMG4rAinL4_7VJz5rxMsPsPcTtKqjOKVqic2ZGMjYfVF_02ZuC80RXIerFoS5IfNJkmRlHb27X18oWT1K58OUNKHdxihdT0GMPwjsvbiOK74vORbk3JT-MUDeb8YN0EgQGP3HVkBJ9Z7RYkW62q2VePBcaewDG2zd4-PD6JKU71ilzHi5iXRCdk_GtbJSoExHUhjvsciWLW-NwUHQ7YUDac3mEdA3z0giaIwNEt0z_" alt="">`,r:{minutes:8.16,words:2449},t:"Flyweight 模式",y:"a"}}],["/tech/DesignPatterns/",{loader:()=>T(()=>import("./index.html-Dj_dWWjR.js"),[]),meta:{d:17294688e5,l:"2024年10月21日",c:["设计模式"],g:["设计模式","typescript"],e:`<p>面向对象三大特性：封装、继承、多态。 设计模式需遵循面向对象的设计原则，由于笔者不太喜欢java, 并嫌弃cpp中没有interface, 遂使用ts作为实现语言(我才不用rust呢 😃 )</p>
+`,r:{minutes:.48,words:144},t:"设计模式",y:"a"}}],["/tech/DesignPatterns/interpreter.html",{loader:()=>T(()=>import("./interpreter.html-DfDQyPSV.js"),[]),meta:{d:173016e7,l:"2024年10月29日",c:["设计模式"],g:["设计模式","TypeScript","用类实现"],e:`<h2>为什么使用此模式</h2>
 <p>解释器模式（Interpreter Pattern）是一种行为设计模式，它定义了一种语言的文法表示，并定义一个解释器来解释该语言中的句子。使用解释器模式的原因包括：</p>
 <ol>
 <li><strong>简化语法解析</strong>：通过定义文法规则，可以轻松解析和执行特定的语言或指令集。</li>
 <li><strong>可扩展性</strong>：可以轻松添加新的语法规则或指令，而无需修改现有代码。</li>
 <li><strong>代码复用</strong>：通过将不同的语法规则封装在不同的类中，可以提高代码的复用性和可维护性。</li>
-</ol>`,r:{minutes:3.33,words:998},t:"Interpreter 模式",y:"a"}}],["/tech/DesignPatterns/iterator.html",{loader:()=>T(()=>import("./iterator.html-USsHv5Pr.js"),[]),meta:{d:17294688e5,l:"2024年10月21日",c:["设计模式"],g:["设计模式","typescript"],e:`<h2>为什么要使用迭代器模式</h2>
+</ol>`,r:{minutes:3.33,words:998},t:"Interpreter 模式",y:"a"}}],["/tech/DesignPatterns/iterator.html",{loader:()=>T(()=>import("./iterator.html-9EjNXcsT.js"),[]),meta:{d:17294688e5,l:"2024年10月21日",c:["设计模式"],g:["设计模式","typescript"],e:`<h2>为什么要使用迭代器模式</h2>
 <p>迭代器模式提供了一种方法来顺序访问集合中的元素，而无需暴露其底层表示。使用迭代器模式有以下几个优点：</p>
 <ol>
 <li><strong>简化代码</strong>：迭代器模式将遍历逻辑封装在迭代器对象中，使得客户端代码更加简洁和易读。</li>
 <li><strong>解耦集合和遍历</strong>：集合对象和遍历算法分离，增加了代码的灵活性和可维护性。可以在不修改集合对象的情况下，改变遍历算法。</li>
 <li><strong>统一接口</strong>：通过实现统一的迭代器接口，不同类型的集合可以使用相同的遍历方式，增强了代码的可扩展性。</li>
 <li><strong>支持多种遍历方式</strong>：可以根据需要实现不同的迭代器，以支持多种遍历方式，如正向遍历、反向遍历、过滤遍历等。</li>
-</ol>`,r:{minutes:2.86,words:857},t:"迭代器模式",y:"a"}}],["/tech/DesignPatterns/mediator.html",{loader:()=>T(()=>import("./mediator.html-RBFBa63Z.js"),[]),meta:{d:17299008e5,l:"2024年10月26日",c:["设计模式"],g:["设计模式","TypeScript","简单化"],e:`<h2>为什么使用此类</h2>
+</ol>`,r:{minutes:2.86,words:857},t:"迭代器模式",y:"a"}}],["/tech/DesignPatterns/mediator.html",{loader:()=>T(()=>import("./mediator.html-C5vte2nl.js"),[]),meta:{d:17299008e5,l:"2024年10月26日",c:["设计模式"],g:["设计模式","TypeScript","简单化"],e:`<h2>为什么使用此类</h2>
 <p>请大家想象一下一个乱糟糟的开发小组的工作状态。小组中的 10 个成员虽然一起协同工作，但是意见难以统一，总是互相指挥，导致工作进度始终滞后。不仅如此，他们还十分在意编码细节，经常为此争执不下。</p>
-`,r:{minutes:5.09,words:1526},t:"Mediator 模式",y:"a"}}],["/tech/DesignPatterns/memento.html",{loader:()=>T(()=>import("./memento.html-CbbBldep.js"),[]),meta:{d:17300736e5,l:"2024年10月28日",c:["设计模式"],g:["设计模式","TypeScript","管理状态"],e:`<h2>为什么使用 Memento 模式</h2>
+`,r:{minutes:5.09,words:1526},t:"Mediator 模式",y:"a"}}],["/tech/DesignPatterns/memento.html",{loader:()=>T(()=>import("./memento.html-Dw4vFzUb.js"),[]),meta:{d:17300736e5,l:"2024年10月28日",c:["设计模式"],g:["设计模式","TypeScript","管理状态"],e:`<h2>为什么使用 Memento 模式</h2>
 <p>Memento 模式的主要目的是在不破坏封装性的前提下，捕获和恢复对象的内部状态。它在以下情况下特别有用：</p>
 <ul>
 <li>需要保存和恢复对象的多个状态。</li>
@@ -231,11 +239,11 @@ https://code.visualstudio.com/api/get-started/your-first-extension</p>
 <li>需要在不暴露对象实现细节的情况下保存对象状态。</li>
 </ul>
 <h2>示例代码</h2>
-<p>在这个示例中，我们使用了 Memento 模式来管理 <code>Gamer</code> 对象的状态。Memento 模式允许我们在不暴露对象实现细节的情况下保存和恢复对象的状态。以下是示例代码：</p>`,r:{minutes:4.19,words:1257},t:"Memento 模式",y:"a"}}],["/tech/DesignPatterns/observer.html",{loader:()=>T(()=>import("./observer.html-BvrPoU9w.js"),[]),meta:{d:17299008e5,l:"2024年10月26日",c:["设计模式"],g:["设计模式","TypeScript","管理状态"],e:`<h2>为什么使用观察者模式</h2>
+<p>在这个示例中，我们使用了 Memento 模式来管理 <code>Gamer</code> 对象的状态。Memento 模式允许我们在不暴露对象实现细节的情况下保存和恢复对象的状态。以下是示例代码：</p>`,r:{minutes:4.19,words:1257},t:"Memento 模式",y:"a"}}],["/tech/DesignPatterns/observer.html",{loader:()=>T(()=>import("./observer.html-DCoBW7Y-.js"),[]),meta:{d:17299008e5,l:"2024年10月26日",c:["设计模式"],g:["设计模式","TypeScript","管理状态"],e:`<h2>为什么使用观察者模式</h2>
 <p>观察者模式非常适合用于需要自动更新的场景。例如，在图形用户界面（GUI）应用程序中，当数据模型发生变化时，所有显示该数据的视图都需要自动更新。通过使用观察者模式，我们可以将这些视图注册为观察者，当数据模型发生变化时，它们会自动收到通知并更新显示。</p>
 <h2>示例代码</h2>
 <p>在这个示例中，我们展示了如何使用观察者模式来管理状态变化。观察者模式定义了一种一对多的依赖关系，当一个对象的状态发生改变时，所有依赖于它的对象都会得到通知并自动更新。以下是 TypeScript 实现的代码示例：</p>
-<img src="https://www.plantuml.com/plantuml/svg/jL912i8m4Bpd5JbMf1_eoOFWJS4VR9kn1fgaRBP54VzkDRQKua4GRyliC3CxoIOAiNIkKTOB-4GLzA6Cu1wiRqhhTTSQ4cGrF9WaSA7tdIl1kn5O5ReFrgYxKbH6OQf4Lmt5k2GcFJ9cDCZ2UoWcpr5i81eq47p7zK7iwJekOZPRrP2Kumdwr_I4SK7L3NVDqgVGMrjRcIgmhctWu2N-K4iItZ6rvty87ycRu9PbuoBmvlCZvAc7UH_VrxGK37a-dQ0sW-Vmcnu0" alt="">`,r:{minutes:4.64,words:1392},t:"Observer 模式",y:"a"}}],["/tech/DesignPatterns/prototype.html",{loader:()=>T(()=>import("./prototype.html-Boe-0El2.js"),[]),meta:{d:17295552e5,l:"2024年10月22日",c:["设计模式"],g:["设计模式","typescript","生成实例"],e:`<h2>为什么要使用 Prototype 模式</h2>
+<img src="https://www.plantuml.com/plantuml/svg/jL912i8m4Bpd5JbMf1_eoOFWJS4VR9kn1fgaRBP54VzkDRQKua4GRyliC3CxoIOAiNIkKTOB-4GLzA6Cu1wiRqhhTTSQ4cGrF9WaSA7tdIl1kn5O5ReFrgYxKbH6OQf4Lmt5k2GcFJ9cDCZ2UoWcpr5i81eq47p7zK7iwJekOZPRrP2Kumdwr_I4SK7L3NVDqgVGMrjRcIgmhctWu2N-K4iItZ6rvty87ycRu9PbuoBmvlCZvAc7UH_VrxGK37a-dQ0sW-Vmcnu0" alt="">`,r:{minutes:4.64,words:1392},t:"Observer 模式",y:"a"}}],["/tech/DesignPatterns/prototype.html",{loader:()=>T(()=>import("./prototype.html-Be3THUal.js"),[]),meta:{d:17295552e5,l:"2024年10月22日",c:["设计模式"],g:["设计模式","typescript","生成实例"],e:`<h2>为什么要使用 Prototype 模式</h2>
 <p>Prototype 模式是一种创建型设计模式，它允许你复制现有对象而无需使代码依赖它们所属的类。使用 Prototype 模式可以：</p>
 <ul>
 <li>避免重复初始化对象的复杂过程。</li>
@@ -245,14 +253,14 @@ https://code.visualstudio.com/api/get-started/your-first-extension</p>
 <li>难以根据类生成实例</li>
 <li>解耦框架与生成的实例</li>
 </ul>
-`,r:{minutes:1.6,words:480},t:"Prototype 模式",y:"a"}}],["/tech/DesignPatterns/proxy.html",{loader:()=>T(()=>import("./proxy.html-CSHBH0Xk.js"),[]),meta:{d:173016e7,l:"2024年10月29日",c:["设计模式"],g:["设计模式","TypeScript","避免浪费"],e:`<h2>为什么使用代理模式</h2>
+`,r:{minutes:1.6,words:480},t:"Prototype 模式",y:"a"}}],["/tech/DesignPatterns/proxy.html",{loader:()=>T(()=>import("./proxy.html-DydmfTHY.js"),[]),meta:{d:173016e7,l:"2024年10月29日",c:["设计模式"],g:["设计模式","TypeScript","避免浪费"],e:`<h2>为什么使用代理模式</h2>
 <p>在面向对象编程中，“本人”和“代理人”都是对象。如果“本人”对象太忙了．有些工作无法自己亲自完成，就将其交给“代理人"对象负责。</p>
-`,r:{minutes:5.08,words:1524},t:"Proxy 模式",y:"a"}}],["/tech/DesignPatterns/singleton.html",{loader:()=>T(()=>import("./singleton.html-Pzh1ZzrO.js"),[]),meta:{d:17294688e5,l:"2024年10月21日",c:["设计模式"],g:["设计模式","typescript","生成实例"],e:`<h2>为什么要使用 Singleton 模式</h2>
+`,r:{minutes:5.08,words:1524},t:"Proxy 模式",y:"a"}}],["/tech/DesignPatterns/singleton.html",{loader:()=>T(()=>import("./singleton.html-CJylCsqx.js"),[]),meta:{d:17294688e5,l:"2024年10月21日",c:["设计模式"],g:["设计模式","typescript","生成实例"],e:`<h2>为什么要使用 Singleton 模式</h2>
 <p>Singleton 模式确保一个类只有一个实例，并提供一个全局访问点。它常用于需要控制资源访问的场景，例如数据库连接、日志记录器等。通过 Singleton 模式，可以避免创建多个实例带来的资源浪费和不一致性问题。</p>
-`,r:{minutes:1.52,words:457},t:"Singleton 模式",y:"a"}}],["/tech/DesignPatterns/state.html",{loader:()=>T(()=>import("./state.html-DsXXtCU9.js"),[]),meta:{d:17300736e5,l:"2024年10月28日",c:["设计模式"],g:["设计模式","TypeScript","管理状态"],e:`<h2>为什么使用 State 模式</h2>
+`,r:{minutes:1.52,words:457},t:"Singleton 模式",y:"a"}}],["/tech/DesignPatterns/state.html",{loader:()=>T(()=>import("./state.html-D0BJywlY.js"),[]),meta:{d:17300736e5,l:"2024年10月28日",c:["设计模式"],g:["设计模式","TypeScript","管理状态"],e:`<h2>为什么使用 State 模式</h2>
 <p>State 模式允许对象在其内部状态改变时改变其行为。它将与状态相关的行为封装在独立的类中，使得状态转换变得清晰且易于管理。使用 State 模式可以避免大量的条件语句，使代码更加简洁和可维护。</p>
 <h2>示例代码</h2>
-<img src="https://www.plantuml.com/plantuml/svg/vPJ1JeGm48RlF4MFaCeBS5g3CJ4nneJi0zGoMnhRZca7inlZkzi2AnXnqRCN0fq_q--VydSNI7ZghScq8_078O7L65-FnDuonW9GRL0-vntslcAkjq_WYugzecvZMNR2AMX84EGXFIisV2mKmfW6PEyrdMf8U-Gsg8e5yjgfMUT1ec_lKQsLtxC5th310DVYo2P7uEfCViNMQLlS1_YcNjQlZV3sekAnG_TpZmWgZGY1tOZJoAdjYm4RZOSHF75p1NJduhoSXBoOHXRNozWs6kybeS-B9FohGxvbaMzxv5iceuIm6GueqOz7DLj_qAgZ_sg-4GUuzS9-yJwrIExBPKfIius0yUs4yTz6Z5_CsEVyLkQrCf_vZpzV5rYMawqTk3PUAHy0" alt="">`,r:{minutes:11.72,words:3515},t:"State 模式",y:"a"}}],["/tech/DesignPatterns/strategy.html",{loader:()=>T(()=>import("./strategy.html-Cprd53d9.js"),[]),meta:{d:17298144e5,l:"2024年10月25日",c:["设计模式"],g:["设计模式","TypeScript","分开考虑","整体的替换算法"],e:`<h2>使用此设计模式的理由</h2>
+<img src="https://www.plantuml.com/plantuml/svg/vPJ1JeGm48RlF4MFaCeBS5g3CJ4nneJi0zGoMnhRZca7inlZkzi2AnXnqRCN0fq_q--VydSNI7ZghScq8_078O7L65-FnDuonW9GRL0-vntslcAkjq_WYugzecvZMNR2AMX84EGXFIisV2mKmfW6PEyrdMf8U-Gsg8e5yjgfMUT1ec_lKQsLtxC5th310DVYo2P7uEfCViNMQLlS1_YcNjQlZV3sekAnG_TpZmWgZGY1tOZJoAdjYm4RZOSHF75p1NJduhoSXBoOHXRNozWs6kybeS-B9FohGxvbaMzxv5iceuIm6GueqOz7DLj_qAgZ_sg-4GUuzS9-yJwrIExBPKfIius0yUs4yTz6Z5_CsEVyLkQrCf_vZpzV5rYMawqTk3PUAHy0" alt="">`,r:{minutes:11.72,words:3515},t:"State 模式",y:"a"}}],["/tech/DesignPatterns/strategy.html",{loader:()=>T(()=>import("./strategy.html-BeQd57Ga.js"),[]),meta:{d:17298144e5,l:"2024年10月25日",c:["设计模式"],g:["设计模式","TypeScript","分开考虑","整体的替换算法"],e:`<h2>使用此设计模式的理由</h2>
 <p>在这个示例程序中，我们使用了策略模式（Strategy Pattern）来实现不同的猜拳策略。策略模式的主要优点包括：</p>
 <ol>
 <li><strong>易于扩展</strong>：可以很容易地添加新的策略，而不需要修改现有的代码。</li>
@@ -260,11 +268,11 @@ https://code.visualstudio.com/api/get-started/your-first-extension</p>
 <li><strong>减少重复代码</strong>：通过使用策略模式，可以避免在多个地方重复相同的算法逻辑。</li>
 </ol>
 <h2>示例程序</h2>
-<p>下面我们来看一段使用了 strategy 模式的示例程序。这段示例程序的功能是让电脑玩“猜拳"游戏。</p>`,r:{minutes:4.53,words:1359},t:"Strategy 模式",y:"a"}}],["/tech/DesignPatterns/template_method.html",{loader:()=>T(()=>import("./template_method.html-Do5aF6Sl.js"),[]),meta:{d:17294688e5,l:"2024年10月21日",c:["设计模式"],g:["设计模式","typescript","交给子类"],e:`<p>在父类中定义处理流程的框架，在子类中实现具体处理。Template Method 模式的主要目的是为了定义一个算法的骨架，而将一些步骤的具体实现延迟到子类中。通过这种方式，子类可以在不改变算法结构的情况下，重新定义算法中的某些步骤。</p>
-`,r:{minutes:2.33,words:698},t:"Template Method 模式",y:"a"}}],["/tech/DesignPatterns/visitor.html",{loader:()=>T(()=>import("./visitor.html-C6V612X1.js"),[]),meta:{d:17298144e5,l:"2024年10月25日",c:["设计模式"],g:["设计模式","TypeScript","访问数据结构并处理数据"],e:`<p>在 Visitor 模式中，数据结构与处理被分离开来。我们编写一个表示“访问者”的类来访问数据结构中的元素，并把对各元素的处理交给访问者类。这样，当需要增加新的处理时，我们只需要编写新的访问者，然后让数据结构可以接受访问者的访问即可。</p>
-`,r:{minutes:6.29,words:1888},t:"Visitor 模式",y:"a"}}],["/tech/designASimpileCCompiler/0.html",{loader:()=>T(()=>import("./0.html-BMihHxnS.js"),[]),meta:{c:["编译原理"],g:["c","编译器","解释器"],e:`
+<p>下面我们来看一段使用了 strategy 模式的示例程序。这段示例程序的功能是让电脑玩“猜拳"游戏。</p>`,r:{minutes:4.53,words:1359},t:"Strategy 模式",y:"a"}}],["/tech/DesignPatterns/template_method.html",{loader:()=>T(()=>import("./template_method.html-B7oRZ-kS.js"),[]),meta:{d:17294688e5,l:"2024年10月21日",c:["设计模式"],g:["设计模式","typescript","交给子类"],e:`<p>在父类中定义处理流程的框架，在子类中实现具体处理。Template Method 模式的主要目的是为了定义一个算法的骨架，而将一些步骤的具体实现延迟到子类中。通过这种方式，子类可以在不改变算法结构的情况下，重新定义算法中的某些步骤。</p>
+`,r:{minutes:2.33,words:698},t:"Template Method 模式",y:"a"}}],["/tech/DesignPatterns/visitor.html",{loader:()=>T(()=>import("./visitor.html-DaIekGHb.js"),[]),meta:{d:17298144e5,l:"2024年10月25日",c:["设计模式"],g:["设计模式","TypeScript","访问数据结构并处理数据"],e:`<p>在 Visitor 模式中，数据结构与处理被分离开来。我们编写一个表示“访问者”的类来访问数据结构中的元素，并把对各元素的处理交给访问者类。这样，当需要增加新的处理时，我们只需要编写新的访问者，然后让数据结构可以接受访问者的访问即可。</p>
+`,r:{minutes:6.29,words:1888},t:"Visitor 模式",y:"a"}}],["/tech/designASimpileCCompiler/0.html",{loader:()=>T(()=>import("./0.html-CC8GZdvL.js"),[]),meta:{c:["编译原理"],g:["c","编译器","解释器"],e:`
 <p>本文转载自 <strong>手把手教你构建 C 语言编译器（0）- 前言</strong>，原作者 <strong>三点水</strong>，原文链接：<a href="https://lotabout.me/2015/write-a-C-interpreter-0/" target="_blank" rel="noopener noreferrer">原文链接</a>，如有侵权，请联系删除。</p>
-<p>转载工具:<a href="https://devtool.tech/html-md" target="_blank" rel="noopener noreferrer">devtool</a>、<a href="https://www.helloworld.net/html2md" target="_blank" rel="noopener noreferrer">helloworld</a></p>`,r:{minutes:6.12,words:1835},t:"手把手教你构建 C 语言编译器（0）- 前言",y:"a"}}],["/tech/designASimpileCCompiler/1.html",{loader:()=>T(()=>import("./1.html-B2woGSgL.js"),[]),meta:{e:`
+<p>转载工具:<a href="https://devtool.tech/html-md" target="_blank" rel="noopener noreferrer">devtool</a>、<a href="https://www.helloworld.net/html2md" target="_blank" rel="noopener noreferrer">helloworld</a></p>`,r:{minutes:6.12,words:1835},t:"手把手教你构建 C 语言编译器（0）- 前言",y:"a"}}],["/tech/designASimpileCCompiler/1.html",{loader:()=>T(()=>import("./1.html-C8e1pvTo.js"),[]),meta:{e:`
 <p>本文转自 <a href="https://lotabout.me/2015/write-a-C-interpreter-1/" target="_blank" rel="noopener noreferrer">https://lotabout.me/2015/write-a-C-interpreter-1/</a>，如有侵权，请联系删除。</p>
 <h1>原文内容</h1>
 <h1>手把手教你构建 C 语言编译器（1）- 设计</h1>
@@ -272,7 +280,7 @@ https://code.visualstudio.com/api/get-started/your-first-extension</p>
 <ol>
 <li><a href="about:blank#%E7%BC%96%E8%AF%91%E5%99%A8%E7%9A%84%E6%9E%84%E5%BB%BA%E6%B5%81%E7%A8%8B">1. 编译器的构建流程</a></li>
 <li><a href="about:blank#%E7%BC%96%E8%AF%91%E5%99%A8%E6%A1%86%E6%9E%B6">2. 编译器框架</a></li>
-</ol>`,r:{minutes:6.74,words:2023},t:"手把手教你构建 C 语言编译器（1）- 设计",y:"a"}}],["/tech/designASimpileCCompiler/2.html",{loader:()=>T(()=>import("./2.html-DuLx7xSk.js"),[]),meta:{e:`<hr>
+</ol>`,r:{minutes:6.74,words:2023},t:"手把手教你构建 C 语言编译器（1）- 设计",y:"a"}}],["/tech/designASimpileCCompiler/2.html",{loader:()=>T(()=>import("./2.html-CfN7D4gf.js"),[]),meta:{e:`<hr>
 <p>title: "手把手教你构建 C 语言编译器（2）——虚拟机"
 category:</p>
 <ul>
@@ -284,7 +292,7 @@ tag:</li>
 </ul>
 <hr>
 <h1>转载声明</h1>
-<p>本文转自 <a href="https://lotabout.me/2015/write-a-C-interpreter-2/" target="_blank" rel="noopener noreferrer">https://lotabout.me/2015/write-a-C-interpreter-2/</a>，如有侵权，请联系删除。</p>`,r:{minutes:25.04,words:7511},t:"转载声明",y:"a"}}],["/tech/designASimpileCCompiler/3.html",{loader:()=>T(()=>import("./3.html-CZB5joNY.js"),[]),meta:{c:["编译原理"],g:["c","编译器","解释器"],e:`
+<p>本文转自 <a href="https://lotabout.me/2015/write-a-C-interpreter-2/" target="_blank" rel="noopener noreferrer">https://lotabout.me/2015/write-a-C-interpreter-2/</a>，如有侵权，请联系删除。</p>`,r:{minutes:25.04,words:7511},t:"转载声明",y:"a"}}],["/tech/designASimpileCCompiler/3.html",{loader:()=>T(()=>import("./3.html-D9pPtuiP.js"),[]),meta:{c:["编译原理"],g:["c","编译器","解释器"],e:`
 <p>本文转自 <a href="https://lotabout.me/2015/write-a-C-interpreter-3/" target="_blank" rel="noopener noreferrer">https://lotabout.me/2015/write-a-C-interpreter-3/</a>，如有侵权，请联系删除。</p>
 <h1>原文内容</h1>
 <h1>手把手教你构建 C 语言编译器（3）- 词法分析器</h1>
@@ -308,7 +316,7 @@ tag:</li>
 </li>
 <li><a href="about:blank#%E4%BB%A3%E7%A0%81">4. 代码</a></li>
 <li><a href="about:blank#%E5%B0%8F%E7%BB%93">5. 小结</a></li>
-</ol>`,r:{minutes:25.21,words:7563},t:"手把手教你构建 C 语言编译器（3）——词法分析器",y:"a"}}],["/tech/designASimpileCCompiler/4.html",{loader:()=>T(()=>import("./4.html-C8TuLMaF.js"),[]),meta:{c:["编译原理"],g:["c","编译器","解释器"],e:`<p>[]</p>
+</ol>`,r:{minutes:25.21,words:7563},t:"手把手教你构建 C 语言编译器（3）——词法分析器",y:"a"}}],["/tech/designASimpileCCompiler/4.html",{loader:()=>T(()=>import("./4.html-DavKkBaH.js"),[]),meta:{c:["编译原理"],g:["c","编译器","解释器"],e:`<p>[]</p>
 <h1>转载声明</h1>
 <p>本文转自 <a href="https://lotabout.me/2016/write-a-C-interpreter-4/" target="_blank" rel="noopener noreferrer">https://lotabout.me/2016/write-a-C-interpreter-4/</a>，如有侵权，请联系删除。</p>
 <h1>原文内容</h1>
@@ -322,7 +330,7 @@ tag:</li>
 <li><a href="about:blank#%E5%B7%A6%E9%80%92%E5%BD%92">5. 左递归</a></li>
 <li><a href="about:blank#%E5%9B%9B%E5%88%99%E8%BF%90%E7%AE%97%E7%9A%84%E5%AE%9E%E7%8E%B0">6. 四则运算的实现</a></li>
 <li><a href="about:blank#%E5%B0%8F%E7%BB%93">7. 小结</a></li>
-</ol>`,r:{minutes:11.33,words:3399},t:"手把手教你构建 C 语言编译器（4）——递归下降",y:"a"}}],["/tech/designASimpileCCompiler/5.html",{loader:()=>T(()=>import("./5.html-qLlLbRlw.js"),[]),meta:{c:["编译原理"],g:["c","编译器","解释器"],e:`
+</ol>`,r:{minutes:11.33,words:3399},t:"手把手教你构建 C 语言编译器（4）——递归下降",y:"a"}}],["/tech/designASimpileCCompiler/5.html",{loader:()=>T(()=>import("./5.html-DpkUOZDe.js"),[]),meta:{c:["编译原理"],g:["c","编译器","解释器"],e:`
 <p>本文转自 <a href="https://lotabout.me/2016/write-a-C-interpreter-5/" target="_blank" rel="noopener noreferrer">https://lotabout.me/2016/write-a-C-interpreter-5/</a>，如有侵权，请联系删除。</p>
 <h1>原文内容</h1>
 <h1>手把手教你构建 C 语言编译器（5）- 变量定义</h1>
@@ -339,7 +347,7 @@ tag:</li>
 </li>
 <li><a href="about:blank#%E4%BB%A3%E7%A0%81">3. 代码</a></li>
 <li><a href="about:blank#%E5%B0%8F%E7%BB%93">4. 小结</a></li>
-</ol>`,r:{minutes:10.71,words:3212},t:"手把手教你构建 C 语言编译器（5）——变量定义",y:"a"}}],["/tech/designASimpileCCompiler/6.html",{loader:()=>T(()=>import("./6.html-BPGbpgjm.js"),[]),meta:{c:["编译原理"],g:["c","编译器","解释器"],e:`
+</ol>`,r:{minutes:10.71,words:3212},t:"手把手教你构建 C 语言编译器（5）——变量定义",y:"a"}}],["/tech/designASimpileCCompiler/6.html",{loader:()=>T(()=>import("./6.html-4dTDTOb4.js"),[]),meta:{c:["编译原理"],g:["c","编译器","解释器"],e:`
 <p>本文转自 <a href="https://lotabout.me/2016/write-a-C-interpreter-6/" target="_blank" rel="noopener noreferrer">https://lotabout.me/2016/write-a-C-interpreter-6/</a>，如有侵权，请联系删除。</p>
 <h1>原文内容</h1>
 <h1>手把手教你构建 C 语言编译器（6）- 函数定义</h1>
@@ -356,7 +364,7 @@ tag:</li>
 </li>
 <li><a href="about:blank#%E4%BB%A3%E7%A0%81">3. 代码</a></li>
 <li><a href="about:blank#%E5%B0%8F%E7%BB%93">4. 小结</a></li>
-</ol>`,r:{minutes:12.61,words:3783},t:"手把手教你构建 C 语言编译器（6）——函数定义",y:"a"}}],["/tech/designASimpileCCompiler/7.html",{loader:()=>T(()=>import("./7.html-DopH3hey.js"),[]),meta:{c:["编译原理"],g:["c","编译器","解释器"],e:`
+</ol>`,r:{minutes:12.61,words:3783},t:"手把手教你构建 C 语言编译器（6）——函数定义",y:"a"}}],["/tech/designASimpileCCompiler/7.html",{loader:()=>T(()=>import("./7.html-BzOHeKw-.js"),[]),meta:{c:["编译原理"],g:["c","编译器","解释器"],e:`
 <p>本文转自 <a href="https://lotabout.me/2016/write-a-C-interpreter-7/" target="_blank" rel="noopener noreferrer">https://lotabout.me/2016/write-a-C-interpreter-7/</a>，如有侵权，请联系删除。</p>
 <h1>原文内容</h1>
 <h1>手把手教你构建 C 语言编译器（7）- 语句</h1>
@@ -372,11 +380,11 @@ tag:</li>
 </li>
 <li><a href="about:blank#%E4%BB%A3%E7%A0%81">2. 代码</a></li>
 <li><a href="about:blank#%E5%B0%8F%E7%BB%93">3. 小结</a></li>
-</ol>`,r:{minutes:6.99,words:2097},t:"手把手教你构建 C 语言编译器（7）——语句",y:"a"}}],["/tech/designASimpileCCompiler/8.html",{loader:()=>T(()=>import("./8.html-D1TnfZgI.js"),[]),meta:{c:["编译原理"],g:["c","编译器","解释器"],e:`
+</ol>`,r:{minutes:6.99,words:2097},t:"手把手教你构建 C 语言编译器（7）——语句",y:"a"}}],["/tech/designASimpileCCompiler/8.html",{loader:()=>T(()=>import("./8.html-C-sA1tiy.js"),[]),meta:{c:["编译原理"],g:["c","编译器","解释器"],e:`
 <p>本文转自 <a href="https://blog.csdn.net/xzp740813/article/details/142961332?spm=1001.2014.3001.5501" target="_blank" rel="noopener noreferrer">https://blog.csdn.net/xzp740813/article/details/142961332?spm=1001.2014.3001.5501</a>，如有侵权，请联系删除。</p>
 <h1>原文内容</h1>
 <h1>手把手教你构建 C 语言编译器（8）- 表达式</h1>
-<p>Table of Contents</p>`,r:{minutes:29.67,words:8900},t:"手把手教你构建 C 语言编译器（8）——表达式",y:"a"}}],["/tech/designASimpileCCompiler/9.html",{loader:()=>T(()=>import("./9.html-CGdd1xtP.js"),[]),meta:{c:["编译原理"],g:["c","编译器","解释器"],e:`
+<p>Table of Contents</p>`,r:{minutes:29.67,words:8900},t:"手把手教你构建 C 语言编译器（8）——表达式",y:"a"}}],["/tech/designASimpileCCompiler/9.html",{loader:()=>T(()=>import("./9.html-DOIgY3Qt.js"),[]),meta:{c:["编译原理"],g:["c","编译器","解释器"],e:`
 <p>本文转自 <a href="https://lotabout.me/2016/write-a-C-interpreter-9/" target="_blank" rel="noopener noreferrer">https://lotabout.me/2016/write-a-C-interpreter-9/</a>，如有侵权，请联系删除。</p>
 <h1>原文内容</h1>
 <h1>手把手教你构建 C 语言编译器（9）- 总结</h1>
@@ -387,15 +395,15 @@ tag:</li>
 <li><a href="about:blank#%E8%AF%AD%E6%B3%95%E5%88%86%E6%9E%90">3. 语法分析</a></li>
 <li><a href="about:blank#%E5%85%B3%E4%BA%8E%E7%BC%96%E4%BB%A3%E7%A0%81">4. 关于编代码</a></li>
 <li><a href="about:blank#%E7%BB%93%E8%AF%AD">5. 结语</a></li>
-</ol>`,r:{minutes:4.66,words:1397},t:"手把手教你构建 C 语言编译器（9）——总结",y:"a"}}],["/404.html",{loader:()=>T(()=>import("./404.html-BC0rHQLu.js"),[]),meta:{t:""}}],["/tech/designASimpileCCompiler/",{loader:()=>T(()=>import("./index.html-Ak5uwHrg.js"),[]),meta:{t:"Design ASimpile CCompiler"}}],["/category/",{loader:()=>T(()=>import("./index.html-CO8-8uSt.js"),[]),meta:{t:"分类",I:!1}}],["/category/build-tools/",{loader:()=>T(()=>import("./index.html-B7IKPS0E.js"),[]),meta:{t:"build-tools 分类",I:!1}}],["/category/cicd/",{loader:()=>T(()=>import("./index.html-BK-iNYKv.js"),[]),meta:{t:"CI/CD 分类",I:!1}}],["/category/nginx/",{loader:()=>T(()=>import("./index.html-DDeLtmuh.js"),[]),meta:{t:"nginx 分类",I:!1}}],["/category/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/",{loader:()=>T(()=>import("./index.html-BSJr7qwh.js"),[]),meta:{t:"奇技淫巧 分类",I:!1}}],["/category/docker/",{loader:()=>T(()=>import("./index.html-DRlrhC7d.js"),[]),meta:{t:"docker 分类",I:!1}}],["/category/oi/",{loader:()=>T(()=>import("./index.html-BXtqeyHq.js"),[]),meta:{t:"OI 分类",I:!1}}],["/category/python/",{loader:()=>T(()=>import("./index.html-UrkKwESw.js"),[]),meta:{t:"python 分类",I:!1}}],["/category/%E9%A3%8E%E6%A0%BC/",{loader:()=>T(()=>import("./index.html-C8X5E5_U.js"),[]),meta:{t:"风格 分类",I:!1}}],["/category/%E6%95%B0%E5%AD%A6/",{loader:()=>T(()=>import("./index.html-CZDJXbd3.js"),[]),meta:{t:"数学 分类",I:!1}}],["/category/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/",{loader:()=>T(()=>import("./index.html-B71I-yvI.js"),[]),meta:{t:"设计模式 分类",I:!1}}],["/category/%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86/",{loader:()=>T(()=>import("./index.html-ZxSgoRoh.js"),[]),meta:{t:"编译原理 分类",I:!1}}],["/tag/",{loader:()=>T(()=>import("./index.html-bipylPNF.js"),[]),meta:{t:"标签",I:!1}}],["/tag/cicd/",{loader:()=>T(()=>import("./index.html-DR-PJoSN.js"),[]),meta:{t:"标签: CI/CD",I:!1}}],["/tag/%E9%83%A8%E7%BD%B2/",{loader:()=>T(()=>import("./index.html-DDn6tClc.js"),[]),meta:{t:"标签: 部署",I:!1}}],["/tag/docker/",{loader:()=>T(()=>import("./index.html-BvZSJ2r-.js"),[]),meta:{t:"标签: docker",I:!1}}],["/tag/modint/",{loader:()=>T(()=>import("./index.html-BKjCcFT0.js"),[]),meta:{t:"标签: MODInt",I:!1}}],["/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/",{loader:()=>T(()=>import("./index.html-CSRSsNOG.js"),[]),meta:{t:"标签: 踩坑记录",I:!1}}],["/tag/%E9%A3%8E%E6%A0%BC/",{loader:()=>T(()=>import("./index.html-BLuB_Eoc.js"),[]),meta:{t:"标签: 风格",I:!1}}],["/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/",{loader:()=>T(()=>import("./index.html-CLOegCHC.js"),[]),meta:{t:"标签: 公理系统",I:!1}}],["/tag/mobile/",{loader:()=>T(()=>import("./index.html-D2pTqZFy.js"),[]),meta:{t:"标签: mobile",I:!1}}],["/tag/%E6%BF%80%E6%B4%BB/",{loader:()=>T(()=>import("./index.html-DZYdDCPP.js"),[]),meta:{t:"标签: 激活",I:!1}}],["/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/",{loader:()=>T(()=>import("./index.html-DzsdPiFk.js"),[]),meta:{t:"标签: 设计模式",I:!1}}],["/tag/typescript/",{loader:()=>T(()=>import("./index.html-CRzs15I0.js"),[]),meta:{t:"标签: typescript",I:!1}}],["/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/",{loader:()=>T(()=>import("./index.html-BZLD09T1.js"),[]),meta:{t:"标签: 生成实例",I:!1}}],["/tag/typescript/",{loader:()=>T(()=>import("./index.html-CRzs15I0.js"),[]),meta:{t:"标签: TypeScript",I:!1}}],["/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/",{loader:()=>T(()=>import("./index.html-CGsa9ffM.js"),[]),meta:{t:"标签: 分开考虑",I:!1}}],["/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/",{loader:()=>T(()=>import("./index.html-QNuKjuoZ.js"),[]),meta:{t:"标签: 推卸责任",I:!1}}],["/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/",{loader:()=>T(()=>import("./index.html-9q-r5JHT.js"),[]),meta:{t:"标签: 用类实现",I:!1}}],["/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/",{loader:()=>T(()=>import("./index.html-BHNGjpbb.js"),[]),meta:{t:"标签: 容器与内容的一致性",I:!1}}],["/tag/%E7%AE%80%E5%8D%95%E5%8C%96/",{loader:()=>T(()=>import("./index.html-0LHdE1Bw.js"),[]),meta:{t:"标签: 简单化",I:!1}}],["/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/",{loader:()=>T(()=>import("./index.html-kOhwCTdr.js"),[]),meta:{t:"标签: 工厂方法",I:!1}}],["/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/",{loader:()=>T(()=>import("./index.html-BlxatHgv.js"),[]),meta:{t:"标签: 交给子类",I:!1}}],["/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/",{loader:()=>T(()=>import("./index.html-ayClYbZ3.js"),[]),meta:{t:"标签: 避免浪费",I:!1}}],["/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/",{loader:()=>T(()=>import("./index.html-B3D_5fpm.js"),[]),meta:{t:"标签: 管理状态",I:!1}}],["/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/",{loader:()=>T(()=>import("./index.html-CcgdDCiF.js"),[]),meta:{t:"标签: 整体的替换算法",I:!1}}],["/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/",{loader:()=>T(()=>import("./index.html-B2T3kUK3.js"),[]),meta:{t:"标签: 访问数据结构并处理数据",I:!1}}],["/tag/c/",{loader:()=>T(()=>import("./index.html-BpjUVtkj.js"),[]),meta:{t:"标签: c",I:!1}}],["/tag/%E7%BC%96%E8%AF%91%E5%99%A8/",{loader:()=>T(()=>import("./index.html-BNAyU6dK.js"),[]),meta:{t:"标签: 编译器",I:!1}}],["/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/",{loader:()=>T(()=>import("./index.html-VMxXqaQ8.js"),[]),meta:{t:"标签: 解释器",I:!1}}],["/article/",{loader:()=>T(()=>import("./index.html-DeH2SCB3.js"),[]),meta:{t:"文章",I:!1}}],["/star/",{loader:()=>T(()=>import("./index.html-Dh_a7h_3.js"),[]),meta:{t:"星标",I:!1}}],["/timeline/",{loader:()=>T(()=>import("./index.html-Bb8RnxYT.js"),[]),meta:{t:"时间轴",I:!1}}]]);/*!
+</ol>`,r:{minutes:4.66,words:1397},t:"手把手教你构建 C 语言编译器（9）——总结",y:"a"}}],["/404.html",{loader:()=>T(()=>import("./404.html-CGMXaJuv.js"),[]),meta:{t:""}}],["/tech/designASimpileCCompiler/",{loader:()=>T(()=>import("./index.html-SwHQd6yQ.js"),[]),meta:{t:"Design ASimpile CCompiler"}}],["/category/",{loader:()=>T(()=>import("./index.html-TRJ6qSMT.js"),[]),meta:{t:"分类",I:!1}}],["/category/build-tools/",{loader:()=>T(()=>import("./index.html-BCqj2PVi.js"),[]),meta:{t:"build-tools 分类",I:!1}}],["/category/cicd/",{loader:()=>T(()=>import("./index.html-CE6ffKsf.js"),[]),meta:{t:"CI/CD 分类",I:!1}}],["/category/nginx/",{loader:()=>T(()=>import("./index.html-CVNN5Fwq.js"),[]),meta:{t:"nginx 分类",I:!1}}],["/category/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/",{loader:()=>T(()=>import("./index.html-DhCS_0vf.js"),[]),meta:{t:"奇技淫巧 分类",I:!1}}],["/category/docker/",{loader:()=>T(()=>import("./index.html-BgifGsNR.js"),[]),meta:{t:"docker 分类",I:!1}}],["/category/oi/",{loader:()=>T(()=>import("./index.html-DOXbY5aY.js"),[]),meta:{t:"OI 分类",I:!1}}],["/category/python/",{loader:()=>T(()=>import("./index.html-ZzlVKqB8.js"),[]),meta:{t:"python 分类",I:!1}}],["/category/%E9%A3%8E%E6%A0%BC/",{loader:()=>T(()=>import("./index.html-BjeRhPA4.js"),[]),meta:{t:"风格 分类",I:!1}}],["/category/%E6%95%B0%E5%AD%A6/",{loader:()=>T(()=>import("./index.html-B1eL3fl0.js"),[]),meta:{t:"数学 分类",I:!1}}],["/category/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/",{loader:()=>T(()=>import("./index.html-DOZrz5tX.js"),[]),meta:{t:"设计模式 分类",I:!1}}],["/category/%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86/",{loader:()=>T(()=>import("./index.html-CL479cux.js"),[]),meta:{t:"编译原理 分类",I:!1}}],["/tag/",{loader:()=>T(()=>import("./index.html-mplfcIL_.js"),[]),meta:{t:"标签",I:!1}}],["/tag/cicd/",{loader:()=>T(()=>import("./index.html-DW1c3ODz.js"),[]),meta:{t:"标签: CI/CD",I:!1}}],["/tag/%E9%83%A8%E7%BD%B2/",{loader:()=>T(()=>import("./index.html-CzSwk-A5.js"),[]),meta:{t:"标签: 部署",I:!1}}],["/tag/docker/",{loader:()=>T(()=>import("./index.html-SMm58lXr.js"),[]),meta:{t:"标签: docker",I:!1}}],["/tag/modint/",{loader:()=>T(()=>import("./index.html-D8p9fsJ8.js"),[]),meta:{t:"标签: MODInt",I:!1}}],["/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/",{loader:()=>T(()=>import("./index.html-rivgPJ9m.js"),[]),meta:{t:"标签: 踩坑记录",I:!1}}],["/tag/%E9%A3%8E%E6%A0%BC/",{loader:()=>T(()=>import("./index.html-DwPUACaS.js"),[]),meta:{t:"标签: 风格",I:!1}}],["/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/",{loader:()=>T(()=>import("./index.html-BwXv95cV.js"),[]),meta:{t:"标签: 公理系统",I:!1}}],["/tag/mobile/",{loader:()=>T(()=>import("./index.html-DeNCk-ye.js"),[]),meta:{t:"标签: mobile",I:!1}}],["/tag/%E6%BF%80%E6%B4%BB/",{loader:()=>T(()=>import("./index.html-hPg6lxSo.js"),[]),meta:{t:"标签: 激活",I:!1}}],["/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/",{loader:()=>T(()=>import("./index.html-CYOJa5u_.js"),[]),meta:{t:"标签: 设计模式",I:!1}}],["/tag/typescript/",{loader:()=>T(()=>import("./index.html-JQfnAIea.js"),[]),meta:{t:"标签: typescript",I:!1}}],["/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/",{loader:()=>T(()=>import("./index.html-Cw9y1ZOg.js"),[]),meta:{t:"标签: 生成实例",I:!1}}],["/tag/typescript/",{loader:()=>T(()=>import("./index.html-JQfnAIea.js"),[]),meta:{t:"标签: TypeScript",I:!1}}],["/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/",{loader:()=>T(()=>import("./index.html-Dpy8imS-.js"),[]),meta:{t:"标签: 分开考虑",I:!1}}],["/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/",{loader:()=>T(()=>import("./index.html-i5A_pLCb.js"),[]),meta:{t:"标签: 推卸责任",I:!1}}],["/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/",{loader:()=>T(()=>import("./index.html-yUxPRBBH.js"),[]),meta:{t:"标签: 用类实现",I:!1}}],["/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/",{loader:()=>T(()=>import("./index.html-DklcXGYl.js"),[]),meta:{t:"标签: 容器与内容的一致性",I:!1}}],["/tag/%E7%AE%80%E5%8D%95%E5%8C%96/",{loader:()=>T(()=>import("./index.html-BFj2MrdQ.js"),[]),meta:{t:"标签: 简单化",I:!1}}],["/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/",{loader:()=>T(()=>import("./index.html-NUfXNLwU.js"),[]),meta:{t:"标签: 工厂方法",I:!1}}],["/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/",{loader:()=>T(()=>import("./index.html-BJX9B5Ij.js"),[]),meta:{t:"标签: 交给子类",I:!1}}],["/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/",{loader:()=>T(()=>import("./index.html-F61LMFJS.js"),[]),meta:{t:"标签: 避免浪费",I:!1}}],["/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/",{loader:()=>T(()=>import("./index.html-COyA9Sec.js"),[]),meta:{t:"标签: 管理状态",I:!1}}],["/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/",{loader:()=>T(()=>import("./index.html-DYx5t_sy.js"),[]),meta:{t:"标签: 整体的替换算法",I:!1}}],["/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/",{loader:()=>T(()=>import("./index.html-CryaZFG_.js"),[]),meta:{t:"标签: 访问数据结构并处理数据",I:!1}}],["/tag/c/",{loader:()=>T(()=>import("./index.html-y8ELyp0v.js"),[]),meta:{t:"标签: c",I:!1}}],["/tag/%E7%BC%96%E8%AF%91%E5%99%A8/",{loader:()=>T(()=>import("./index.html-auYNF0Cp.js"),[]),meta:{t:"标签: 编译器",I:!1}}],["/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/",{loader:()=>T(()=>import("./index.html-DCZKDe-x.js"),[]),meta:{t:"标签: 解释器",I:!1}}],["/article/",{loader:()=>T(()=>import("./index.html-DERlmHfl.js"),[]),meta:{t:"文章",I:!1}}],["/star/",{loader:()=>T(()=>import("./index.html-DottIbHL.js"),[]),meta:{t:"星标",I:!1}}],["/timeline/",{loader:()=>T(()=>import("./index.html-BOaWfYA8.js"),[]),meta:{t:"时间轴",I:!1}}]]);/*!
   * vue-router v4.3.2
   * (c) 2024 Eduardo San Martin Morote
   * @license MIT
   */const xn=typeof document<"u";function jd(e){return e.__esModule||e[Symbol.toStringTag]==="Module"}const me=Object.assign;function Qa(e,t){const n={};for(const r in t){const a=t[r];n[r]=Et(a)?a.map(e):e(a)}return n}const cr=()=>{},Et=Array.isArray,Oc=/#/g,zd=/&/g,qd=/\//g,Gd=/=/g,Ud=/\?/g,Mc=/\+/g,Wd=/%5B/g,Kd=/%5D/g,Rc=/%5E/g,Jd=/%60/g,$c=/%7B/g,Qd=/%7C/g,Fc=/%7D/g,Yd=/%20/g;function hl(e){return encodeURI(""+e).replace(Qd,"|").replace(Wd,"[").replace(Kd,"]")}function Zd(e){return hl(e).replace($c,"{").replace(Fc,"}").replace(Rc,"^")}function ko(e){return hl(e).replace(Mc,"%2B").replace(Yd,"+").replace(Oc,"%23").replace(zd,"%26").replace(Jd,"`").replace($c,"{").replace(Fc,"}").replace(Rc,"^")}function Xd(e){return ko(e).replace(Gd,"%3D")}function ef(e){return hl(e).replace(Oc,"%23").replace(Ud,"%3F")}function tf(e){return e==null?"":ef(e).replace(qd,"%2F")}function br(e){try{return decodeURIComponent(""+e)}catch{}return""+e}const nf=/\/$/,rf=e=>e.replace(nf,"");function Ya(e,t,n="/"){let r,a={},o="",l="";const i=t.indexOf("#");let c=t.indexOf("?");return i<c&&i>=0&&(c=-1),c>-1&&(r=t.slice(0,c),o=t.slice(c+1,i>-1?i:t.length),a=e(o)),i>-1&&(r=r||t.slice(0,i),l=t.slice(i,t.length)),r=sf(r??t,n),{fullPath:r+(o&&"?")+o+l,path:r,query:a,hash:br(l)}}function af(e,t){const n=t.query?e(t.query):"";return t.path+(n&&"?")+n+(t.hash||"")}function Ms(e,t){return!t||!e.toLowerCase().startsWith(t.toLowerCase())?e:e.slice(t.length)||"/"}function of(e,t,n){const r=t.matched.length-1,a=n.matched.length-1;return r>-1&&r===a&&Nn(t.matched[r],n.matched[a])&&Hc(t.params,n.params)&&e(t.query)===e(n.query)&&t.hash===n.hash}function Nn(e,t){return(e.aliasOf||e)===(t.aliasOf||t)}function Hc(e,t){if(Object.keys(e).length!==Object.keys(t).length)return!1;for(const n in e)if(!lf(e[n],t[n]))return!1;return!0}function lf(e,t){return Et(e)?Rs(e,t):Et(t)?Rs(t,e):e===t}function Rs(e,t){return Et(t)?e.length===t.length&&e.every((n,r)=>n===t[r]):e.length===1&&e[0]===t}function sf(e,t){if(e.startsWith("/"))return e;if(!e)return t;const n=t.split("/"),r=e.split("/"),a=r[r.length-1];(a===".."||a===".")&&r.push("");let o=n.length-1,l,i;for(l=0;l<r.length;l++)if(i=r[l],i!==".")if(i==="..")o>1&&o--;else break;return n.slice(0,o).join("/")+"/"+r.slice(l).join("/")}var Er;(function(e){e.pop="pop",e.push="push"})(Er||(Er={}));var ur;(function(e){e.back="back",e.forward="forward",e.unknown=""})(ur||(ur={}));function cf(e){if(!e)if(xn){const t=document.querySelector("base");e=t&&t.getAttribute("href")||"/",e=e.replace(/^\w+:\/\/[^\/]+/,"")}else e="/";return e[0]!=="/"&&e[0]!=="#"&&(e="/"+e),rf(e)}const uf=/^[^#]+#/;function df(e,t){return e.replace(uf,"#")+t}function ff(e,t){const n=document.documentElement.getBoundingClientRect(),r=e.getBoundingClientRect();return{behavior:t.behavior,left:r.left-n.left-(t.left||0),top:r.top-n.top-(t.top||0)}}const Ba=()=>({left:window.scrollX,top:window.scrollY});function pf(e){let t;if("el"in e){const n=e.el,r=typeof n=="string"&&n.startsWith("#"),a=typeof n=="string"?r?document.getElementById(n.slice(1)):document.querySelector(n):n;if(!a)return;t=ff(a,e)}else t=e;"scrollBehavior"in document.documentElement.style?window.scrollTo(t):window.scrollTo(t.left!=null?t.left:window.scrollX,t.top!=null?t.top:window.scrollY)}function $s(e,t){return(history.state?history.state.position-t:-1)+e}const To=new Map;function hf(e,t){To.set(e,t)}function mf(e){const t=To.get(e);return To.delete(e),t}let vf=()=>location.protocol+"//"+location.host;function Nc(e,t){const{pathname:n,search:r,hash:a}=t,o=e.indexOf("#");if(o>-1){let i=a.includes(e.slice(o))?e.slice(o).length:1,c=a.slice(i);return c[0]!=="/"&&(c="/"+c),Ms(c,"")}return Ms(n,e)+r+a}function gf(e,t,n,r){let a=[],o=[],l=null;const i=({state:p})=>{const h=Nc(e,location),v=n.value,_=t.value;let E=0;if(p){if(n.value=h,t.value=p,l&&l===v){l=null;return}E=_?p.position-_.position:0}else r(h);a.forEach(b=>{b(n.value,v,{delta:E,type:Er.pop,direction:E?E>0?ur.forward:ur.back:ur.unknown})})};function c(){l=n.value}function u(p){a.push(p);const h=()=>{const v=a.indexOf(p);v>-1&&a.splice(v,1)};return o.push(h),h}function d(){const{history:p}=window;p.state&&p.replaceState(me({},p.state,{scroll:Ba()}),"")}function f(){for(const p of o)p();o=[],window.removeEventListener("popstate",i),window.removeEventListener("beforeunload",d)}return window.addEventListener("popstate",i),window.addEventListener("beforeunload",d,{passive:!0}),{pauseListeners:c,listen:u,destroy:f}}function Fs(e,t,n,r=!1,a=!1){return{back:e,current:t,forward:n,replaced:r,position:window.history.length,scroll:a?Ba():null}}function yf(e){const{history:t,location:n}=window,r={value:Nc(e,n)},a={value:t.state};a.value||o(r.value,{back:null,current:r.value,forward:null,position:t.length-1,replaced:!0,scroll:null},!0);function o(c,u,d){const f=e.indexOf("#"),p=f>-1?(n.host&&document.querySelector("base")?e:e.slice(f))+c:vf()+e+c;try{t[d?"replaceState":"pushState"](u,"",p),a.value=u}catch(h){console.error(h),n[d?"replace":"assign"](p)}}function l(c,u){const d=me({},t.state,Fs(a.value.back,c,a.value.forward,!0),u,{position:a.value.position});o(c,d,!0),r.value=c}function i(c,u){const d=me({},a.value,t.state,{forward:c,scroll:Ba()});o(d.current,d,!0);const f=me({},Fs(r.value,c,null),{position:d.position+1},u);o(c,f,!1),r.value=c}return{location:r,state:a,push:i,replace:l}}function bf(e){e=cf(e);const t=yf(e),n=gf(e,t.state,t.location,t.replace);function r(o,l=!0){l||n.pauseListeners(),history.go(o)}const a=me({location:"",base:e,go:r,createHref:df.bind(null,e)},t,n);return Object.defineProperty(a,"location",{enumerable:!0,get:()=>t.location.value}),Object.defineProperty(a,"state",{enumerable:!0,get:()=>t.state.value}),a}function Ef(e){return typeof e=="string"||e&&typeof e=="object"}function Vc(e){return typeof e=="string"||typeof e=="symbol"}const Ot={path:"/",name:void 0,params:{},query:{},hash:"",fullPath:"/",matched:[],meta:{},redirectedFrom:void 0},jc=Symbol("");var Hs;(function(e){e[e.aborted=4]="aborted",e[e.cancelled=8]="cancelled",e[e.duplicated=16]="duplicated"})(Hs||(Hs={}));function Vn(e,t){return me(new Error,{type:e,[jc]:!0},t)}function Pt(e,t){return e instanceof Error&&jc in e&&(t==null||!!(e.type&t))}const Ns="[^/]+?",_f={sensitive:!1,strict:!1,start:!0,end:!0},wf=/[.+*?^${}()[\]/\\]/g;function Af(e,t){const n=me({},_f,t),r=[];let a=n.start?"^":"";const o=[];for(const u of e){const d=u.length?[]:[90];n.strict&&!u.length&&(a+="/");for(let f=0;f<u.length;f++){const p=u[f];let h=40+(n.sensitive?.25:0);if(p.type===0)f||(a+="/"),a+=p.value.replace(wf,"\\$&"),h+=40;else if(p.type===1){const{value:v,repeatable:_,optional:E,regexp:b}=p;o.push({name:v,repeatable:_,optional:E});const C=b||Ns;if(C!==Ns){h+=10;try{new RegExp(`(${C})`)}catch(A){throw new Error(`Invalid custom RegExp for param "${v}" (${C}): `+A.message)}}let y=_?`((?:${C})(?:/(?:${C}))*)`:`(${C})`;f||(y=E&&u.length<2?`(?:/${y})`:"/"+y),E&&(y+="?"),a+=y,h+=20,E&&(h+=-8),_&&(h+=-20),C===".*"&&(h+=-50)}d.push(h)}r.push(d)}if(n.strict&&n.end){const u=r.length-1;r[u][r[u].length-1]+=.7000000000000001}n.strict||(a+="/?"),n.end?a+="$":n.strict&&(a+="(?:/|$)");const l=new RegExp(a,n.sensitive?"":"i");function i(u){const d=u.match(l),f={};if(!d)return null;for(let p=1;p<d.length;p++){const h=d[p]||"",v=o[p-1];f[v.name]=h&&v.repeatable?h.split("/"):h}return f}function c(u){let d="",f=!1;for(const p of e){(!f||!d.endsWith("/"))&&(d+="/"),f=!1;for(const h of p)if(h.type===0)d+=h.value;else if(h.type===1){const{value:v,repeatable:_,optional:E}=h,b=v in u?u[v]:"";if(Et(b)&&!_)throw new Error(`Provided param "${v}" is an array but it is not repeatable (* or + modifiers)`);const C=Et(b)?b.join("/"):b;if(!C)if(E)p.length<2&&(d.endsWith("/")?d=d.slice(0,-1):f=!0);else throw new Error(`Missing required param "${v}"`);d+=C}}return d||"/"}return{re:l,score:r,keys:o,parse:i,stringify:c}}function Cf(e,t){let n=0;for(;n<e.length&&n<t.length;){const r=t[n]-e[n];if(r)return r;n++}return e.length<t.length?e.length===1&&e[0]===80?-1:1:e.length>t.length?t.length===1&&t[0]===80?1:-1:0}function kf(e,t){let n=0;const r=e.score,a=t.score;for(;n<r.length&&n<a.length;){const o=Cf(r[n],a[n]);if(o)return o;n++}if(Math.abs(a.length-r.length)===1){if(Vs(r))return 1;if(Vs(a))return-1}return a.length-r.length}function Vs(e){const t=e[e.length-1];return e.length>0&&t[t.length-1]<0}const Tf={type:0,value:""},Sf=/[a-zA-Z0-9_]/;function xf(e){if(!e)return[[]];if(e==="/")return[[Tf]];if(!e.startsWith("/"))throw new Error(`Invalid path "${e}"`);function t(h){throw new Error(`ERR (${n})/"${u}": ${h}`)}let n=0,r=n;const a=[];let o;function l(){o&&a.push(o),o=[]}let i=0,c,u="",d="";function f(){u&&(n===0?o.push({type:0,value:u}):n===1||n===2||n===3?(o.length>1&&(c==="*"||c==="+")&&t(`A repeatable param (${u}) must be alone in its segment. eg: '/:ids+.`),o.push({type:1,value:u,regexp:d,repeatable:c==="*"||c==="+",optional:c==="*"||c==="?"})):t("Invalid state to consume buffer"),u="")}function p(){u+=c}for(;i<e.length;){if(c=e[i++],c==="\\"&&n!==2){r=n,n=4;continue}switch(n){case 0:c==="/"?(u&&f(),l()):c===":"?(f(),n=1):p();break;case 4:p(),n=r;break;case 1:c==="("?n=2:Sf.test(c)?p():(f(),n=0,c!=="*"&&c!=="?"&&c!=="+"&&i--);break;case 2:c===")"?d[d.length-1]=="\\"?d=d.slice(0,-1)+c:n=3:d+=c;break;case 3:f(),n=0,c!=="*"&&c!=="?"&&c!=="+"&&i--,d="";break;default:t("Unknown state");break}}return n===2&&t(`Unfinished custom RegExp for param "${u}"`),f(),l(),a}function Lf(e,t,n){const r=Af(xf(e.path),n),a=me(r,{record:e,parent:t,children:[],alias:[]});return t&&!a.record.aliasOf==!t.record.aliasOf&&t.children.push(a),a}function Bf(e,t){const n=[],r=new Map;t=qs({strict:!1,end:!0,sensitive:!1},t);function a(d){return r.get(d)}function o(d,f,p){const h=!p,v=If(d);v.aliasOf=p&&p.record;const _=qs(t,d),E=[v];if("alias"in d){const y=typeof d.alias=="string"?[d.alias]:d.alias;for(const A of y)E.push(me({},v,{components:p?p.record.components:v.components,path:A,aliasOf:p?p.record:v}))}let b,C;for(const y of E){const{path:A}=y;if(f&&A[0]!=="/"){const D=f.record.path,P=D[D.length-1]==="/"?"":"/";y.path=f.record.path+(A&&P+A)}if(b=Lf(y,f,_),p?p.alias.push(b):(C=C||b,C!==b&&C.alias.push(b),h&&d.name&&!zs(b)&&l(d.name)),v.children){const D=v.children;for(let P=0;P<D.length;P++)o(D[P],b,p&&p.children[P])}p=p||b,(b.record.components&&Object.keys(b.record.components).length||b.record.name||b.record.redirect)&&c(b)}return C?()=>{l(C)}:cr}function l(d){if(Vc(d)){const f=r.get(d);f&&(r.delete(d),n.splice(n.indexOf(f),1),f.children.forEach(l),f.alias.forEach(l))}else{const f=n.indexOf(d);f>-1&&(n.splice(f,1),d.record.name&&r.delete(d.record.name),d.children.forEach(l),d.alias.forEach(l))}}function i(){return n}function c(d){let f=0;for(;f<n.length&&kf(d,n[f])>=0&&(d.record.path!==n[f].record.path||!zc(d,n[f]));)f++;n.splice(f,0,d),d.record.name&&!zs(d)&&r.set(d.record.name,d)}function u(d,f){let p,h={},v,_;if("name"in d&&d.name){if(p=r.get(d.name),!p)throw Vn(1,{location:d});_=p.record.name,h=me(js(f.params,p.keys.filter(C=>!C.optional).concat(p.parent?p.parent.keys.filter(C=>C.optional):[]).map(C=>C.name)),d.params&&js(d.params,p.keys.map(C=>C.name))),v=p.stringify(h)}else if(d.path!=null)v=d.path,p=n.find(C=>C.re.test(v)),p&&(h=p.parse(v),_=p.record.name);else{if(p=f.name?r.get(f.name):n.find(C=>C.re.test(f.path)),!p)throw Vn(1,{location:d,currentLocation:f});_=p.record.name,h=me({},f.params,d.params),v=p.stringify(h)}const E=[];let b=p;for(;b;)E.unshift(b.record),b=b.parent;return{name:_,path:v,params:h,matched:E,meta:Df(E)}}return e.forEach(d=>o(d)),{addRoute:o,resolve:u,removeRoute:l,getRoutes:i,getRecordMatcher:a}}function js(e,t){const n={};for(const r of t)r in e&&(n[r]=e[r]);return n}function If(e){return{path:e.path,redirect:e.redirect,name:e.name,meta:e.meta||{},aliasOf:void 0,beforeEnter:e.beforeEnter,props:Pf(e),children:e.children||[],instances:{},leaveGuards:new Set,updateGuards:new Set,enterCallbacks:{},components:"components"in e?e.components||null:e.component&&{default:e.component}}}function Pf(e){const t={},n=e.props||!1;if("component"in e)t.default=n;else for(const r in e.components)t[r]=typeof n=="object"?n[r]:n;return t}function zs(e){for(;e;){if(e.record.aliasOf)return!0;e=e.parent}return!1}function Df(e){return e.reduce((t,n)=>me(t,n.meta),{})}function qs(e,t){const n={};for(const r in e)n[r]=r in t?t[r]:e[r];return n}function zc(e,t){return t.children.some(n=>n===e||zc(e,n))}function Of(e){const t={};if(e===""||e==="?")return t;const r=(e[0]==="?"?e.slice(1):e).split("&");for(let a=0;a<r.length;++a){const o=r[a].replace(Mc," "),l=o.indexOf("="),i=br(l<0?o:o.slice(0,l)),c=l<0?null:br(o.slice(l+1));if(i in t){let u=t[i];Et(u)||(u=t[i]=[u]),u.push(c)}else t[i]=c}return t}function Gs(e){let t="";for(let n in e){const r=e[n];if(n=Xd(n),r==null){r!==void 0&&(t+=(t.length?"&":"")+n);continue}(Et(r)?r.map(o=>o&&ko(o)):[r&&ko(r)]).forEach(o=>{o!==void 0&&(t+=(t.length?"&":"")+n,o!=null&&(t+="="+o))})}return t}function Mf(e){const t={};for(const n in e){const r=e[n];r!==void 0&&(t[n]=Et(r)?r.map(a=>a==null?null:""+a):r==null?r:""+r)}return t}const Rf=Symbol(""),Us=Symbol(""),Ia=Symbol(""),ml=Symbol(""),So=Symbol("");function Yn(){let e=[];function t(r){return e.push(r),()=>{const a=e.indexOf(r);a>-1&&e.splice(a,1)}}function n(){e=[]}return{add:t,list:()=>e.slice(),reset:n}}function Zt(e,t,n,r,a,o=l=>l()){const l=r&&(r.enterCallbacks[a]=r.enterCallbacks[a]||[]);return()=>new Promise((i,c)=>{const u=p=>{p===!1?c(Vn(4,{from:n,to:t})):p instanceof Error?c(p):Ef(p)?c(Vn(2,{from:t,to:p})):(l&&r.enterCallbacks[a]===l&&typeof p=="function"&&l.push(p),i())},d=o(()=>e.call(r&&r.instances[a],t,n,u));let f=Promise.resolve(d);e.length<3&&(f=f.then(u)),f.catch(p=>c(p))})}function Za(e,t,n,r,a=o=>o()){const o=[];for(const l of e)for(const i in l.components){let c=l.components[i];if(!(t!=="beforeRouteEnter"&&!l.instances[i]))if($f(c)){const d=(c.__vccOpts||c)[t];d&&o.push(Zt(d,n,r,l,i,a))}else{let u=c();o.push(()=>u.then(d=>{if(!d)return Promise.reject(new Error(`Couldn't resolve component "${i}" at "${l.path}"`));const f=jd(d)?d.default:d;l.components[i]=f;const h=(f.__vccOpts||f)[t];return h&&Zt(h,n,r,l,i,a)()}))}}return o}function $f(e){return typeof e=="object"||"displayName"in e||"props"in e||"__vccOpts"in e}function Ws(e){const t=ve(Ia),n=ve(ml),r=w(()=>{const c=bt(e.to);return t.resolve(c)}),a=w(()=>{const{matched:c}=r.value,{length:u}=c,d=c[u-1],f=n.matched;if(!d||!f.length)return-1;const p=f.findIndex(Nn.bind(null,d));if(p>-1)return p;const h=Ks(c[u-2]);return u>1&&Ks(d)===h&&f[f.length-1].path!==h?f.findIndex(Nn.bind(null,c[u-2])):p}),o=w(()=>a.value>-1&&Vf(n.params,r.value.params)),l=w(()=>a.value>-1&&a.value===n.matched.length-1&&Hc(n.params,r.value.params));function i(c={}){return Nf(c)?t[bt(e.replace)?"replace":"push"](bt(e.to)).catch(cr):Promise.resolve()}return{route:r,href:w(()=>r.value.href),isActive:o,isExactActive:l,navigate:i}}const Ff=M({name:"RouterLink",compatConfig:{MODE:3},props:{to:{type:[String,Object],required:!0},replace:Boolean,activeClass:String,exactActiveClass:String,custom:Boolean,ariaCurrentValue:{type:String,default:"page"}},useLink:Ws,setup(e,{slots:t}){const n=Lr(Ws(e)),{options:r}=ve(Ia),a=w(()=>({[Js(e.activeClass,r.linkActiveClass,"router-link-active")]:n.isActive,[Js(e.exactActiveClass,r.linkExactActiveClass,"router-link-exact-active")]:n.isExactActive}));return()=>{const o=t.default&&t.default(n);return e.custom?o:s("a",{"aria-current":n.isExactActive?e.ariaCurrentValue:null,href:n.href,onClick:n.navigate,class:a.value},o)}}}),Hf=Ff;function Nf(e){if(!(e.metaKey||e.altKey||e.ctrlKey||e.shiftKey)&&!e.defaultPrevented&&!(e.button!==void 0&&e.button!==0)){if(e.currentTarget&&e.currentTarget.getAttribute){const t=e.currentTarget.getAttribute("target");if(/\b_blank\b/i.test(t))return}return e.preventDefault&&e.preventDefault(),!0}}function Vf(e,t){for(const n in t){const r=t[n],a=e[n];if(typeof r=="string"){if(r!==a)return!1}else if(!Et(a)||a.length!==r.length||r.some((o,l)=>o!==a[l]))return!1}return!0}function Ks(e){return e?e.aliasOf?e.aliasOf.path:e.path:""}const Js=(e,t,n)=>e??t??n,jf=M({name:"RouterView",inheritAttrs:!1,props:{name:{type:String,default:"default"},route:Object},compatConfig:{MODE:3},setup(e,{attrs:t,slots:n}){const r=ve(So),a=w(()=>e.route||r.value),o=ve(Us,0),l=w(()=>{let u=bt(o);const{matched:d}=a.value;let f;for(;(f=d[u])&&!f.components;)u++;return u}),i=w(()=>a.value.matched[l.value]);ht(Us,w(()=>l.value+1)),ht(Rf,i),ht(So,a);const c=z();return ae(()=>[c.value,i.value,e.name],([u,d,f],[p,h,v])=>{d&&(d.instances[f]=u,h&&h!==d&&u&&u===p&&(d.leaveGuards.size||(d.leaveGuards=h.leaveGuards),d.updateGuards.size||(d.updateGuards=h.updateGuards))),u&&d&&(!h||!Nn(d,h)||!p)&&(d.enterCallbacks[f]||[]).forEach(_=>_(u))},{flush:"post"}),()=>{const u=a.value,d=e.name,f=i.value,p=f&&f.components[d];if(!p)return Qs(n.default,{Component:p,route:u});const h=f.props[d],v=h?h===!0?u.params:typeof h=="function"?h(u):h:null,E=s(p,me({},v,t,{onVnodeUnmounted:b=>{b.component.isUnmounted&&(f.instances[d]=null)},ref:c}));return Qs(n.default,{Component:E,route:u})||E}}});function Qs(e,t){if(!e)return null;const n=e(t);return n.length===1?n[0]:n}const zf=jf;function qf(e){const t=Bf(e.routes,e),n=e.parseQuery||Of,r=e.stringifyQuery||Gs,a=e.history,o=Yn(),l=Yn(),i=Yn(),c=xe(Ot);let u=Ot;xn&&e.scrollBehavior&&"scrollRestoration"in history&&(history.scrollRestoration="manual");const d=Qa.bind(null,S=>""+S),f=Qa.bind(null,tf),p=Qa.bind(null,br);function h(S,q){let V,J;return Vc(S)?(V=t.getRecordMatcher(S),J=q):J=S,t.addRoute(J,V)}function v(S){const q=t.getRecordMatcher(S);q&&t.removeRoute(q)}function _(){return t.getRoutes().map(S=>S.record)}function E(S){return!!t.getRecordMatcher(S)}function b(S,q){if(q=me({},q||c.value),typeof S=="string"){const g=Ya(n,S,q.path),k=t.resolve({path:g.path},q),L=a.createHref(g.fullPath);return me(g,k,{params:p(k.params),hash:br(g.hash),redirectedFrom:void 0,href:L})}let V;if(S.path!=null)V=me({},S,{path:Ya(n,S.path,q.path).path});else{const g=me({},S.params);for(const k in g)g[k]==null&&delete g[k];V=me({},S,{params:f(g)}),q.params=f(q.params)}const J=t.resolve(V,q),ue=S.hash||"";J.params=d(p(J.params));const Ee=af(r,me({},S,{hash:Zd(ue),path:J.path})),m=a.createHref(Ee);return me({fullPath:Ee,hash:ue,query:r===Gs?Mf(S.query):S.query||{}},J,{redirectedFrom:void 0,href:m})}function C(S){return typeof S=="string"?Ya(n,S,c.value.path):me({},S)}function y(S,q){if(u!==S)return Vn(8,{from:q,to:S})}function A(S){return H(S)}function D(S){return A(me(C(S),{replace:!0}))}function P(S){const q=S.matched[S.matched.length-1];if(q&&q.redirect){const{redirect:V}=q;let J=typeof V=="function"?V(S):V;return typeof J=="string"&&(J=J.includes("?")||J.includes("#")?J=C(J):{path:J},J.params={}),me({query:S.query,hash:S.hash,params:J.path!=null?{}:S.params},J)}}function H(S,q){const V=u=b(S),J=c.value,ue=S.state,Ee=S.force,m=S.replace===!0,g=P(V);if(g)return H(me(C(g),{state:typeof g=="object"?me({},ue,g.state):ue,force:Ee,replace:m}),q||V);const k=V;k.redirectedFrom=q;let L;return!Ee&&of(r,J,V)&&(L=Vn(16,{to:k,from:J}),lt(J,J,!0,!1)),(L?Promise.resolve(L):I(k,J)).catch(x=>Pt(x)?Pt(x,2)?x:wt(x):K(x,k,J)).then(x=>{if(x){if(Pt(x,2))return H(me({replace:m},C(x.to),{state:typeof x.to=="object"?me({},ue,x.to.state):ue,force:Ee}),q||k)}else x=R(k,J,!0,m,ue);return U(k,J,x),x})}function O(S,q){const V=y(S,q);return V?Promise.reject(V):Promise.resolve()}function Q(S){const q=It.values().next().value;return q&&typeof q.runWithContext=="function"?q.runWithContext(S):S()}function I(S,q){let V;const[J,ue,Ee]=Gf(S,q);V=Za(J.reverse(),"beforeRouteLeave",S,q);for(const g of J)g.leaveGuards.forEach(k=>{V.push(Zt(k,S,q))});const m=O.bind(null,S,q);return V.push(m),Oe(V).then(()=>{V=[];for(const g of o.list())V.push(Zt(g,S,q));return V.push(m),Oe(V)}).then(()=>{V=Za(ue,"beforeRouteUpdate",S,q);for(const g of ue)g.updateGuards.forEach(k=>{V.push(Zt(k,S,q))});return V.push(m),Oe(V)}).then(()=>{V=[];for(const g of Ee)if(g.beforeEnter)if(Et(g.beforeEnter))for(const k of g.beforeEnter)V.push(Zt(k,S,q));else V.push(Zt(g.beforeEnter,S,q));return V.push(m),Oe(V)}).then(()=>(S.matched.forEach(g=>g.enterCallbacks={}),V=Za(Ee,"beforeRouteEnter",S,q,Q),V.push(m),Oe(V))).then(()=>{V=[];for(const g of l.list())V.push(Zt(g,S,q));return V.push(m),Oe(V)}).catch(g=>Pt(g,8)?g:Promise.reject(g))}function U(S,q,V){i.list().forEach(J=>Q(()=>J(S,q,V)))}function R(S,q,V,J,ue){const Ee=y(S,q);if(Ee)return Ee;const m=q===Ot,g=xn?history.state:{};V&&(J||m?a.replace(S.fullPath,me({scroll:m&&g&&g.scroll},ue)):a.push(S.fullPath,ue)),c.value=S,lt(S,q,V,m),wt()}let X;function Le(){X||(X=a.listen((S,q,V)=>{if(!At.listening)return;const J=b(S),ue=P(J);if(ue){H(me(ue,{replace:!0}),J).catch(cr);return}u=J;const Ee=c.value;xn&&hf($s(Ee.fullPath,V.delta),Ba()),I(J,Ee).catch(m=>Pt(m,12)?m:Pt(m,2)?(H(m.to,J).then(g=>{Pt(g,20)&&!V.delta&&V.type===Er.pop&&a.go(-1,!1)}).catch(cr),Promise.reject()):(V.delta&&a.go(-V.delta,!1),K(m,J,Ee))).then(m=>{m=m||R(J,Ee,!1),m&&(V.delta&&!Pt(m,8)?a.go(-V.delta,!1):V.type===Er.pop&&Pt(m,20)&&a.go(-1,!1)),U(J,Ee,m)}).catch(cr)}))}let Ae=Yn(),W=Yn(),ee;function K(S,q,V){wt(S);const J=W.list();return J.length?J.forEach(ue=>ue(S,q,V)):console.error(S),Promise.reject(S)}function De(){return ee&&c.value!==Ot?Promise.resolve():new Promise((S,q)=>{Ae.add([S,q])})}function wt(S){return ee||(ee=!S,Le(),Ae.list().forEach(([q,V])=>S?V(S):q()),Ae.reset()),S}function lt(S,q,V,J){const{scrollBehavior:ue}=e;if(!xn||!ue)return Promise.resolve();const Ee=!V&&mf($s(S.fullPath,0))||(J||!V)&&history.state&&history.state.scroll||null;return _t().then(()=>ue(S,q,Ee)).then(m=>m&&pf(m)).catch(m=>K(m,S,q))}const Fe=S=>a.go(S);let Xe;const It=new Set,At={currentRoute:c,listening:!0,addRoute:h,removeRoute:v,hasRoute:E,getRoutes:_,resolve:b,options:e,push:A,replace:D,go:Fe,back:()=>Fe(-1),forward:()=>Fe(1),beforeEach:o.add,beforeResolve:l.add,afterEach:i.add,onError:W.add,isReady:De,install(S){const q=this;S.component("RouterLink",Hf),S.component("RouterView",zf),S.config.globalProperties.$router=q,Object.defineProperty(S.config.globalProperties,"$route",{enumerable:!0,get:()=>bt(c)}),xn&&!Xe&&c.value===Ot&&(Xe=!0,A(a.location).catch(ue=>{}));const V={};for(const ue in Ot)Object.defineProperty(V,ue,{get:()=>c.value[ue],enumerable:!0});S.provide(Ia,q),S.provide(ml,Fi(V)),S.provide(So,c);const J=S.unmount;It.add(S),S.unmount=function(){It.delete(S),It.size<1&&(u=Ot,X&&X(),X=null,c.value=Ot,Xe=!1,ee=!1),J()}}};function Oe(S){return S.reduce((q,V)=>q.then(()=>Q(V)),Promise.resolve())}return At}function Gf(e,t){const n=[],r=[],a=[],o=Math.max(t.matched.length,e.matched.length);for(let l=0;l<o;l++){const i=t.matched[l];i&&(e.matched.find(u=>Nn(u,i))?r.push(i):n.push(i));const c=e.matched[l];c&&(t.matched.find(u=>Nn(u,c))||a.push(c))}return[n,r,a]}function wn(){return ve(Ia)}function Ht(){return ve(ml)}var vl=Symbol(""),Bt=()=>{const e=ve(vl);if(!e)throw new Error("useClientData() is called without provider.");return e},Uf=()=>Bt().pageComponent,ge=()=>Bt().pageData,he=()=>Bt().pageFrontmatter,Wf=()=>Bt().pageHead,Pa=()=>Bt().pageLang,Kf=()=>Bt().pageLayout,Ye=()=>Bt().routeLocale,Jf=()=>Bt().routes,qc=()=>Bt().siteData,Gn=()=>Bt().siteLocaleData,Qf=Symbol(""),xo=xe(Nd),_r=xe(Vd),Gc=e=>{const t=Md(e);if(_r.value[t])return t;const n=encodeURI(t);return _r.value[n]?n:xo.value[t]||xo.value[n]||t},xt=e=>{const t=Gc(e),n=_r.value[t]??{..._r.value["/404.html"],notFound:!0};return{path:t,notFound:!1,...n}},Or=M({name:"ClientOnly",setup(e,t){const n=z(!1);return se(()=>{n.value=!0}),()=>{var r,a;return n.value?(a=(r=t.slots).default)==null?void 0:a.call(r):null}}}),Uc=M({name:"Content",props:{path:{type:String,required:!1,default:""}},setup(e){const t=Uf(),n=w(()=>{if(!e.path)return t.value;const r=xt(e.path);return tc(()=>r.loader().then(({comp:a})=>a))});return()=>s(n.value)}}),Ze=(e={})=>e,be=e=>sn(e)?e:`/${Dc(e)}`,Yf=e=>{if(!(e.metaKey||e.altKey||e.ctrlKey||e.shiftKey)&&!e.defaultPrevented&&!(e.button!==void 0&&e.button!==0)){if(e.currentTarget){const t=e.currentTarget.getAttribute("target");if(t!=null&&t.match(/\b_blank\b/i))return}return e.preventDefault(),!0}},Ie=({active:e=!1,activeClass:t="route-link-active",to:n,...r},{slots:a})=>{var c;const o=wn(),l=Gc(n),i=l.startsWith("#")||l.startsWith("?")?l:be(l);return s("a",{...r,class:["route-link",{[t]:e}],href:i,onClick:(u={})=>{Yf(u)?o.push(n).catch():Promise.resolve()}},(c=a.default)==null?void 0:c.call(a))};Ie.displayName="RouteLink";Ie.props={active:Boolean,activeClass:String,to:String};var Zf="Layout",Xf="en-US",pn=Lr({resolveLayouts:e=>e.reduce((t,n)=>({...t,...n.layouts}),{}),resolvePageHead:(e,t,n)=>{const r=we(t.description)?t.description:n.description,a=[...Array.isArray(t.head)?t.head:[],...n.head,["title",{},e],["meta",{name:"description",content:r}]];return Pd(a)},resolvePageHeadTitle:(e,t)=>[e.title,t.title].filter(n=>!!n).join(" | "),resolvePageLang:(e,t)=>e.lang||t.lang||Xf,resolvePageLayout:(e,t)=>{const n=we(e.frontmatter.layout)?e.frontmatter.layout:Zf;if(!t[n])throw new Error(`[vuepress] Cannot resolve layout: ${n}`);return t[n]},resolveRouteLocale:(e,t)=>Rd(e,t),resolveSiteLocaleData:(e,t)=>{var n;return{...e,...e.locales[t],head:[...((n=e.locales[t])==null?void 0:n.head)??[],...e.head??[]]}}});const e3={};var rt=Uint8Array,In=Uint16Array,t3=Int32Array,Wc=new rt([0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,0,0,0,0]),Kc=new rt([0,0,0,0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13,0,0]),n3=new rt([16,17,18,0,8,7,9,6,10,5,11,4,12,3,13,2,14,1,15]),Jc=function(e,t){for(var n=new In(31),r=0;r<31;++r)n[r]=t+=1<<e[r-1];for(var a=new t3(n[30]),r=1;r<30;++r)for(var o=n[r];o<n[r+1];++o)a[o]=o-n[r]<<5|r;return{b:n,r:a}},Qc=Jc(Wc,2),Yc=Qc.b,r3=Qc.r;Yc[28]=258,r3[258]=28;var a3=Jc(Kc,0),o3=a3.b,Lo=new In(32768);for(var _e=0;_e<32768;++_e){var qt=(_e&43690)>>1|(_e&21845)<<1;qt=(qt&52428)>>2|(qt&13107)<<2,qt=(qt&61680)>>4|(qt&3855)<<4,Lo[_e]=((qt&65280)>>8|(qt&255)<<8)>>1}var dr=function(e,t,n){for(var r=e.length,a=0,o=new In(t);a<r;++a)e[a]&&++o[e[a]-1];var l=new In(t);for(a=1;a<t;++a)l[a]=l[a-1]+o[a-1]<<1;var i;if(n){i=new In(1<<t);var c=15-t;for(a=0;a<r;++a)if(e[a])for(var u=a<<4|e[a],d=t-e[a],f=l[e[a]-1]++<<d,p=f|(1<<d)-1;f<=p;++f)i[Lo[f]>>c]=u}else for(i=new In(r),a=0;a<r;++a)e[a]&&(i[a]=Lo[l[e[a]-1]++]>>15-e[a]);return i},Mr=new rt(288);for(var _e=0;_e<144;++_e)Mr[_e]=8;for(var _e=144;_e<256;++_e)Mr[_e]=9;for(var _e=256;_e<280;++_e)Mr[_e]=7;for(var _e=280;_e<288;++_e)Mr[_e]=8;var Zc=new rt(32);for(var _e=0;_e<32;++_e)Zc[_e]=5;var l3=dr(Mr,9,1),s3=dr(Zc,5,1),Xa=function(e){for(var t=e[0],n=1;n<e.length;++n)e[n]>t&&(t=e[n]);return t},vt=function(e,t,n){var r=t/8|0;return(e[r]|e[r+1]<<8)>>(t&7)&n},eo=function(e,t){var n=t/8|0;return(e[n]|e[n+1]<<8|e[n+2]<<16)>>(t&7)},i3=function(e){return(e+7)/8|0},Xc=function(e,t,n){return(t==null||t<0)&&(t=0),(n==null||n>e.length)&&(n=e.length),new rt(e.subarray(t,n))},c3=["unexpected EOF","invalid block type","invalid length/literal","invalid distance","stream finished","no stream handler",,"no callback","invalid UTF-8 data","extra field too long","date not in range 1980-2099","filename too long","stream finishing","invalid zip data"],ct=function(e,t,n){var r=new Error(t||c3[e]);if(r.code=e,Error.captureStackTrace&&Error.captureStackTrace(r,ct),!n)throw r;return r},u3=function(e,t,n,r){var a=e.length,o=0;if(!a||t.f&&!t.l)return n||new rt(0);var l=!n,i=l||t.i!=2,c=t.i;l&&(n=new rt(a*3));var u=function(ue){var Ee=n.length;if(ue>Ee){var m=new rt(Math.max(Ee*2,ue));m.set(n),n=m}},d=t.f||0,f=t.p||0,p=t.b||0,h=t.l,v=t.d,_=t.m,E=t.n,b=a*8;do{if(!h){d=vt(e,f,1);var C=vt(e,f+1,3);if(f+=3,C)if(C==1)h=l3,v=s3,_=9,E=5;else if(C==2){var P=vt(e,f,31)+257,H=vt(e,f+10,15)+4,O=P+vt(e,f+5,31)+1;f+=14;for(var Q=new rt(O),I=new rt(19),U=0;U<H;++U)I[n3[U]]=vt(e,f+U*3,7);f+=H*3;for(var R=Xa(I),X=(1<<R)-1,Le=dr(I,R,1),U=0;U<O;){var Ae=Le[vt(e,f,X)];f+=Ae&15;var y=Ae>>4;if(y<16)Q[U++]=y;else{var W=0,ee=0;for(y==16?(ee=3+vt(e,f,3),f+=2,W=Q[U-1]):y==17?(ee=3+vt(e,f,7),f+=3):y==18&&(ee=11+vt(e,f,127),f+=7);ee--;)Q[U++]=W}}var K=Q.subarray(0,P),De=Q.subarray(P);_=Xa(K),E=Xa(De),h=dr(K,_,1),v=dr(De,E,1)}else ct(1);else{var y=i3(f)+4,A=e[y-4]|e[y-3]<<8,D=y+A;if(D>a){c&&ct(0);break}i&&u(p+A),n.set(e.subarray(y,D),p),t.b=p+=A,t.p=f=D*8,t.f=d;continue}if(f>b){c&&ct(0);break}}i&&u(p+131072);for(var wt=(1<<_)-1,lt=(1<<E)-1,Fe=f;;Fe=f){var W=h[eo(e,f)&wt],Xe=W>>4;if(f+=W&15,f>b){c&&ct(0);break}if(W||ct(2),Xe<256)n[p++]=Xe;else if(Xe==256){Fe=f,h=null;break}else{var It=Xe-254;if(Xe>264){var U=Xe-257,At=Wc[U];It=vt(e,f,(1<<At)-1)+Yc[U],f+=At}var Oe=v[eo(e,f)&lt],S=Oe>>4;Oe||ct(3),f+=Oe&15;var De=o3[S];if(S>3){var At=Kc[S];De+=eo(e,f)&(1<<At)-1,f+=At}if(f>b){c&&ct(0);break}i&&u(p+131072);var q=p+It;if(p<De){var V=o-De,J=Math.min(De,q);for(V+p<0&&ct(3);p<J;++p)n[p]=r[V+p]}for(;p<q;++p)n[p]=n[p-De]}}t.l=h,t.p=Fe,t.b=p,t.f=d,h&&(d=1,t.m=_,t.d=v,t.n=E)}while(!d);return p!=n.length&&l?Xc(n,0,p):n.subarray(0,p)},d3=new rt(0),f3=function(e,t){return((e[0]&15)!=8||e[0]>>4>7||(e[0]<<8|e[1])%31)&&ct(6,"invalid zlib data"),(e[1]>>5&1)==+!t&&ct(6,"invalid zlib data: "+(e[1]&32?"need":"unexpected")+" dictionary"),(e[1]>>3&4)+2};function p3(e,t){return u3(e.subarray(f3(e,t),-4),{i:2},t,t)}var Bo=typeof TextDecoder<"u"&&new TextDecoder,h3=0;try{Bo.decode(d3,{stream:!0}),h3=1}catch{}var m3=function(e){for(var t="",n=0;;){var r=e[n++],a=(r>127)+(r>223)+(r>239);if(n+a>e.length)return{s:t,r:Xc(e,n-1)};a?a==3?(r=((r&15)<<18|(e[n++]&63)<<12|(e[n++]&63)<<6|e[n++]&63)-65536,t+=String.fromCharCode(55296|r>>10,56320|r&1023)):a&1?t+=String.fromCharCode((r&31)<<6|e[n++]&63):t+=String.fromCharCode((r&15)<<12|(e[n++]&63)<<6|e[n++]&63):t+=String.fromCharCode(r)}};function v3(e,t){{for(var n=new rt(e.length),r=0;r<e.length;++r)n[r]=e.charCodeAt(r);return n}for(var a=e.length,r=0;r<a;++r);}function g3(e,t){var n;if(Bo)return Bo.decode(e);var r=m3(e),a=r.s,n=r.r;return n.length&&ct(8),a}const to=(e,t)=>{var r;const n=(r=ln())==null?void 0:r.appContext.components;return n?e in n||qe(e)in n||_n(qe(e))in n:!1},y3=Object.keys;function eu(e,t){let n,r,a;const o=z(!0),l=()=>{o.value=!0,a()};ae(e,l,{flush:"sync"});const i=typeof t=="function"?t:t.get,c=typeof t=="function"?void 0:t.set,u=rl((d,f)=>(r=d,a=f,{get(){return o.value&&(n=i(),o.value=!1),r(),n},set(p){c==null||c(p)}}));return Object.isExtensible(u)&&(u.trigger=l),u}function Lt(e){return Ti()?(f2(e),!0):!1}function Me(e){return typeof e=="function"?e():bt(e)}const bn=typeof window<"u"&&typeof document<"u";typeof WorkerGlobalScope<"u"&&globalThis instanceof WorkerGlobalScope;const b3=e=>e!=null,E3=Object.prototype.toString,_3=e=>E3.call(e)==="[object Object]",St=()=>{},Io=w3();function w3(){var e,t;return bn&&((e=window==null?void 0:window.navigator)==null?void 0:e.userAgent)&&(/iP(ad|hone|od)/.test(window.navigator.userAgent)||((t=window==null?void 0:window.navigator)==null?void 0:t.maxTouchPoints)>2&&/iPad|Macintosh/.test(window==null?void 0:window.navigator.userAgent))}function gl(e,t){function n(...r){return new Promise((a,o)=>{Promise.resolve(e(()=>t.apply(this,r),{fn:t,thisArg:this,args:r})).then(a).catch(o)})}return n}const tu=e=>e();function A3(e,t={}){let n,r,a=St;const o=i=>{clearTimeout(i),a(),a=St};return i=>{const c=Me(e),u=Me(t.maxWait);return n&&o(n),c<=0||u!==void 0&&u<=0?(r&&(o(r),r=null),Promise.resolve(i())):new Promise((d,f)=>{a=t.rejectOnCancel?f:d,u&&!r&&(r=setTimeout(()=>{n&&o(n),r=null,d(i())},u)),n=setTimeout(()=>{r&&o(r),r=null,d(i())},c)})}}function C3(...e){let t=0,n,r=!0,a=St,o,l,i,c,u;!$e(e[0])&&typeof e[0]=="object"?{delay:l,trailing:i=!0,leading:c=!0,rejectOnCancel:u=!1}=e[0]:[l,i=!0,c=!0,u=!1]=e;const d=()=>{n&&(clearTimeout(n),n=void 0,a(),a=St)};return p=>{const h=Me(l),v=Date.now()-t,_=()=>o=p();return d(),h<=0?(t=Date.now(),_()):(v>h&&(c||!r)?(t=Date.now(),_()):i&&(o=new Promise((E,b)=>{a=u?b:E,n=setTimeout(()=>{t=Date.now(),r=!0,E(_()),d()},Math.max(0,h-v))})),!c&&!n&&(n=setTimeout(()=>r=!0,h)),r=!1,o)}}function k3(e=tu){const t=z(!0);function n(){t.value=!1}function r(){t.value=!0}const a=(...o)=>{t.value&&e(...o)};return{isActive:on(t),pause:n,resume:r,eventFilter:a}}function T3(e){let t;function n(){return t||(t=e()),t}return n.reset=async()=>{const r=t;t=void 0,r&&await r},n}function nu(e){return ln()}function S3(...e){if(e.length!==1)return zn(...e);const t=e[0];return typeof t=="function"?on(rl(()=>({get:t,set:St}))):z(t)}function ru(e,t=200,n={}){return gl(A3(t,n),e)}function x3(e,t=200,n=!1,r=!0,a=!1){return gl(C3(t,n,r,a),e)}function L3(e,t,n={}){const{eventFilter:r=tu,...a}=n;return ae(e,gl(r,t),a)}function B3(e,t,n={}){const{eventFilter:r,...a}=n,{eventFilter:o,pause:l,resume:i,isActive:c}=k3(r);return{stop:L3(e,t,{...a,eventFilter:o}),pause:l,resume:i,isActive:c}}function Da(e,t=!0,n){nu()?se(e,n):t?e():_t(e)}function I3(e,t){nu()&&Ft(e,t)}function P3(e,t=1e3,n={}){const{immediate:r=!0,immediateCallback:a=!1}=n;let o=null;const l=z(!1);function i(){o&&(clearInterval(o),o=null)}function c(){l.value=!1,i()}function u(){const d=Me(t);d<=0||(l.value=!0,a&&e(),i(),o=setInterval(e,d))}if(r&&bn&&u(),$e(t)||typeof t=="function"){const d=ae(t,()=>{l.value&&bn&&u()});Lt(d)}return Lt(c),{isActive:l,pause:c,resume:u}}function D3(e,t,n={}){const{immediate:r=!0}=n,a=z(!1);let o=null;function l(){o&&(clearTimeout(o),o=null)}function i(){a.value=!1,l()}function c(...u){l(),a.value=!0,o=setTimeout(()=>{a.value=!1,o=null,e(...u)},Me(t))}return r&&(a.value=!0,bn&&c()),Lt(i),{isPending:on(a),start:c,stop:i}}function wr(e=!1,t={}){const{truthyValue:n=!0,falsyValue:r=!1}=t,a=$e(e),o=z(e);function l(i){if(arguments.length)return o.value=i,o.value;{const c=Me(n);return o.value=o.value===c?Me(r):c,o.value}}return a?l:[o,l]}function Ke(e){var t;const n=Me(e);return(t=n==null?void 0:n.$el)!=null?t:n}const ot=bn?window:void 0,au=bn?window.document:void 0,ou=bn?window.navigator:void 0;function Se(...e){let t,n,r,a;if(typeof e[0]=="string"||Array.isArray(e[0])?([n,r,a]=e,t=ot):[t,n,r,a]=e,!t)return St;Array.isArray(n)||(n=[n]),Array.isArray(r)||(r=[r]);const o=[],l=()=>{o.forEach(d=>d()),o.length=0},i=(d,f,p,h)=>(d.addEventListener(f,p,h),()=>d.removeEventListener(f,p,h)),c=ae(()=>[Ke(t),Me(a)],([d,f])=>{if(l(),!d)return;const p=_3(f)?{...f}:f;o.push(...n.flatMap(h=>r.map(v=>i(d,h,v,p))))},{immediate:!0,flush:"post"}),u=()=>{c(),l()};return Lt(u),u}let Ys=!1;function lu(e,t,n={}){const{window:r=ot,ignore:a=[],capture:o=!0,detectIframe:l=!1}=n;if(!r)return St;Io&&!Ys&&(Ys=!0,Array.from(r.document.body.children).forEach(p=>p.addEventListener("click",St)),r.document.documentElement.addEventListener("click",St));let i=!0;const c=p=>a.some(h=>{if(typeof h=="string")return Array.from(r.document.querySelectorAll(h)).some(v=>v===p.target||p.composedPath().includes(v));{const v=Ke(h);return v&&(p.target===v||p.composedPath().includes(v))}}),d=[Se(r,"click",p=>{const h=Ke(e);if(!(!h||h===p.target||p.composedPath().includes(h))){if(p.detail===0&&(i=!c(p)),!i){i=!0;return}t(p)}},{passive:!0,capture:o}),Se(r,"pointerdown",p=>{const h=Ke(e);i=!c(p)&&!!(h&&!p.composedPath().includes(h))},{passive:!0}),l&&Se(r,"blur",p=>{setTimeout(()=>{var h;const v=Ke(e);((h=r.document.activeElement)==null?void 0:h.tagName)==="IFRAME"&&!(v!=null&&v.contains(r.document.activeElement))&&t(p)},0)})].filter(Boolean);return()=>d.forEach(p=>p())}function O3(){const e=z(!1),t=ln();return t&&se(()=>{e.value=!0},t),e}function Un(e){const t=O3();return w(()=>(t.value,!!e()))}function M3(e,t={}){const{immediate:n=!0,fpsLimit:r=void 0,window:a=ot}=t,o=z(!1),l=r?1e3/r:null;let i=0,c=null;function u(p){if(!o.value||!a)return;i||(i=p);const h=p-i;if(l&&h<l){c=a.requestAnimationFrame(u);return}i=p,e({delta:h,timestamp:p}),c=a.requestAnimationFrame(u)}function d(){!o.value&&a&&(o.value=!0,i=0,c=a.requestAnimationFrame(u))}function f(){o.value=!1,c!=null&&a&&(a.cancelAnimationFrame(c),c=null)}return n&&d(),Lt(f),{isActive:on(o),pause:f,resume:d}}function su(e,t={}){const{window:n=ot}=t,r=Un(()=>n&&"matchMedia"in n&&typeof n.matchMedia=="function");let a;const o=z(!1),l=u=>{o.value=u.matches},i=()=>{a&&("removeEventListener"in a?a.removeEventListener("change",l):a.removeListener(l))},c=Qi(()=>{r.value&&(i(),a=n.matchMedia(Me(e)),"addEventListener"in a?a.addEventListener("change",l):a.addListener(l),o.value=a.matches)});return Lt(()=>{c(),i(),a=void 0}),o}function Zs(e,t={}){const{controls:n=!1,navigator:r=ou}=t,a=Un(()=>r&&"permissions"in r);let o;const l=typeof e=="string"?{name:e}:e,i=z(),c=()=>{o&&(i.value=o.state)},u=T3(async()=>{if(a.value){if(!o)try{o=await r.permissions.query(l),Se(o,"change",c),c()}catch{i.value="prompt"}return o}});return u(),n?{state:i,isSupported:a,query:u}:i}function R3(e={}){const{navigator:t=ou,read:n=!1,source:r,copiedDuring:a=1500,legacy:o=!1}=e,l=Un(()=>t&&"clipboard"in t),i=Zs("clipboard-read"),c=Zs("clipboard-write"),u=w(()=>l.value||o),d=z(""),f=z(!1),p=D3(()=>f.value=!1,a);function h(){l.value&&b(i.value)?t.clipboard.readText().then(C=>{d.value=C}):d.value=E()}u.value&&n&&Se(["copy","cut"],h);async function v(C=Me(r)){u.value&&C!=null&&(l.value&&b(c.value)?await t.clipboard.writeText(C):_(C),d.value=C,f.value=!0,p.start())}function _(C){const y=document.createElement("textarea");y.value=C??"",y.style.position="absolute",y.style.opacity="0",document.body.appendChild(y),y.select(),document.execCommand("copy"),y.remove()}function E(){var C,y,A;return(A=(y=(C=document==null?void 0:document.getSelection)==null?void 0:C.call(document))==null?void 0:y.toString())!=null?A:""}function b(C){return C==="granted"||C==="prompt"}return{isSupported:u,text:d,copied:f,copy:v}}const Xr=typeof globalThis<"u"?globalThis:typeof window<"u"?window:typeof global<"u"?global:typeof self<"u"?self:{},ea="__vueuse_ssr_handlers__",$3=F3();function F3(){return ea in Xr||(Xr[ea]=Xr[ea]||{}),Xr[ea]}function H3(e,t){return $3[e]||t}function N3(e){return e==null?"any":e instanceof Set?"set":e instanceof Map?"map":e instanceof Date?"date":typeof e=="boolean"?"boolean":typeof e=="string"?"string":typeof e=="object"?"object":Number.isNaN(e)?"any":"number"}const V3={boolean:{read:e=>e==="true",write:e=>String(e)},object:{read:e=>JSON.parse(e),write:e=>JSON.stringify(e)},number:{read:e=>Number.parseFloat(e),write:e=>String(e)},any:{read:e=>e,write:e=>String(e)},string:{read:e=>e,write:e=>String(e)},map:{read:e=>new Map(JSON.parse(e)),write:e=>JSON.stringify(Array.from(e.entries()))},set:{read:e=>new Set(JSON.parse(e)),write:e=>JSON.stringify(Array.from(e))},date:{read:e=>new Date(e),write:e=>e.toISOString()}},Xs="vueuse-storage";function cn(e,t,n,r={}){var a;const{flush:o="pre",deep:l=!0,listenToStorageChanges:i=!0,writeDefaults:c=!0,mergeDefaults:u=!1,shallow:d,window:f=ot,eventFilter:p,onError:h=I=>{console.error(I)},initOnMounted:v}=r,_=(d?xe:z)(typeof t=="function"?t():t);if(!n)try{n=H3("getDefaultStorage",()=>{var I;return(I=ot)==null?void 0:I.localStorage})()}catch(I){h(I)}if(!n)return _;const E=Me(t),b=N3(E),C=(a=r.serializer)!=null?a:V3[b],{pause:y,resume:A}=B3(_,()=>P(_.value),{flush:o,deep:l,eventFilter:p});f&&i&&Da(()=>{Se(f,"storage",O),Se(f,Xs,Q),v&&O()}),v||O();function D(I,U){f&&f.dispatchEvent(new CustomEvent(Xs,{detail:{key:e,oldValue:I,newValue:U,storageArea:n}}))}function P(I){try{const U=n.getItem(e);if(I==null)D(U,null),n.removeItem(e);else{const R=C.write(I);U!==R&&(n.setItem(e,R),D(U,R))}}catch(U){h(U)}}function H(I){const U=I?I.newValue:n.getItem(e);if(U==null)return c&&E!=null&&n.setItem(e,C.write(E)),E;if(!I&&u){const R=C.read(U);return typeof u=="function"?u(R,E):b==="object"&&!Array.isArray(R)?{...E,...R}:R}else return typeof U!="string"?U:C.read(U)}function O(I){if(!(I&&I.storageArea!==n)){if(I&&I.key==null){_.value=E;return}if(!(I&&I.key!==e)){y();try{(I==null?void 0:I.newValue)!==C.write(_.value)&&(_.value=H(I))}catch(U){h(U)}finally{I?_t(A):A()}}}}function Q(I){O(I.detail)}return _}function j3(e){return su("(prefers-color-scheme: dark)",e)}function z3(e,t,n={}){const{window:r=ot,...a}=n;let o;const l=Un(()=>r&&"MutationObserver"in r),i=()=>{o&&(o.disconnect(),o=void 0)},c=w(()=>{const p=Me(e),h=(Array.isArray(p)?p:[p]).map(Ke).filter(b3);return new Set(h)}),u=ae(()=>c.value,p=>{i(),l.value&&r&&p.size&&(o=new MutationObserver(t),p.forEach(h=>o.observe(h,a)))},{immediate:!0,flush:"post"}),d=()=>o==null?void 0:o.takeRecords(),f=()=>{i(),u()};return Lt(f),{isSupported:l,stop:f,takeRecords:d}}function q3(e,t,n={}){const{window:r=ot,...a}=n;let o;const l=Un(()=>r&&"ResizeObserver"in r),i=()=>{o&&(o.disconnect(),o=void 0)},c=w(()=>Array.isArray(e)?e.map(f=>Ke(f)):[Ke(e)]),u=ae(c,f=>{if(i(),l.value&&r){o=new ResizeObserver(t);for(const p of f)p&&o.observe(p,a)}},{immediate:!0,flush:"post"}),d=()=>{i(),u()};return Lt(d),{isSupported:l,stop:d}}function G3(e,t={width:0,height:0},n={}){const{window:r=ot,box:a="content-box"}=n,o=w(()=>{var f,p;return(p=(f=Ke(e))==null?void 0:f.namespaceURI)==null?void 0:p.includes("svg")}),l=z(t.width),i=z(t.height),{stop:c}=q3(e,([f])=>{const p=a==="border-box"?f.borderBoxSize:a==="content-box"?f.contentBoxSize:f.devicePixelContentBoxSize;if(r&&o.value){const h=Ke(e);if(h){const v=r.getComputedStyle(h);l.value=Number.parseFloat(v.width),i.value=Number.parseFloat(v.height)}}else if(p){const h=Array.isArray(p)?p:[p];l.value=h.reduce((v,{inlineSize:_})=>v+_,0),i.value=h.reduce((v,{blockSize:_})=>v+_,0)}else l.value=f.contentRect.width,i.value=f.contentRect.height},n);Da(()=>{const f=Ke(e);f&&(l.value="offsetWidth"in f?f.offsetWidth:t.width,i.value="offsetHeight"in f?f.offsetHeight:t.height)});const u=ae(()=>Ke(e),f=>{l.value=f?t.width:0,i.value=f?t.height:0});function d(){c(),u()}return{width:l,height:i,stop:d}}const ei=["fullscreenchange","webkitfullscreenchange","webkitendfullscreen","mozfullscreenchange","MSFullscreenChange"];function yl(e,t={}){const{document:n=au,autoExit:r=!1}=t,a=w(()=>{var b;return(b=Ke(e))!=null?b:n==null?void 0:n.querySelector("html")}),o=z(!1),l=w(()=>["requestFullscreen","webkitRequestFullscreen","webkitEnterFullscreen","webkitEnterFullScreen","webkitRequestFullScreen","mozRequestFullScreen","msRequestFullscreen"].find(b=>n&&b in n||a.value&&b in a.value)),i=w(()=>["exitFullscreen","webkitExitFullscreen","webkitExitFullScreen","webkitCancelFullScreen","mozCancelFullScreen","msExitFullscreen"].find(b=>n&&b in n||a.value&&b in a.value)),c=w(()=>["fullScreen","webkitIsFullScreen","webkitDisplayingFullscreen","mozFullScreen","msFullscreenElement"].find(b=>n&&b in n||a.value&&b in a.value)),u=["fullscreenElement","webkitFullscreenElement","mozFullScreenElement","msFullscreenElement"].find(b=>n&&b in n),d=Un(()=>a.value&&n&&l.value!==void 0&&i.value!==void 0&&c.value!==void 0),f=()=>u?(n==null?void 0:n[u])===a.value:!1,p=()=>{if(c.value){if(n&&n[c.value]!=null)return n[c.value];{const b=a.value;if((b==null?void 0:b[c.value])!=null)return!!b[c.value]}}return!1};async function h(){if(!(!d.value||!o.value)){if(i.value)if((n==null?void 0:n[i.value])!=null)await n[i.value]();else{const b=a.value;(b==null?void 0:b[i.value])!=null&&await b[i.value]()}o.value=!1}}async function v(){if(!d.value||o.value)return;p()&&await h();const b=a.value;l.value&&(b==null?void 0:b[l.value])!=null&&(await b[l.value](),o.value=!0)}async function _(){await(o.value?h():v())}const E=()=>{const b=p();(!b||b&&f())&&(o.value=b)};return Se(n,ei,E,!1),Se(()=>Ke(a),ei,E,!1),r&&Lt(h),{isSupported:d,isFullscreen:o,enter:v,exit:h,toggle:_}}function no(e){return typeof Window<"u"&&e instanceof Window?e.document.documentElement:typeof Document<"u"&&e instanceof Document?e.documentElement:e}function J5(e,t,n={}){const{window:r=ot}=n;return cn(e,t,r==null?void 0:r.localStorage,n)}function U3(e={}){const{controls:t=!1,interval:n="requestAnimationFrame"}=e,r=z(new Date),a=()=>r.value=new Date,o=n==="requestAnimationFrame"?M3(a,{immediate:!0}):P3(a,n,{immediate:!0});return t?{now:r,...o}:r}function ro(e,t=St,n={}){const{immediate:r=!0,manual:a=!1,type:o="text/javascript",async:l=!0,crossOrigin:i,referrerPolicy:c,noModule:u,defer:d,document:f=au,attrs:p={}}=n,h=z(null);let v=null;const _=C=>new Promise((y,A)=>{const D=O=>(h.value=O,y(O),O);if(!f){y(!1);return}let P=!1,H=f.querySelector(`script[src="${Me(e)}"]`);H?H.hasAttribute("data-loaded")&&D(H):(H=f.createElement("script"),H.type=o,H.async=l,H.src=Me(e),d&&(H.defer=d),i&&(H.crossOrigin=i),u&&(H.noModule=u),c&&(H.referrerPolicy=c),Object.entries(p).forEach(([O,Q])=>H==null?void 0:H.setAttribute(O,Q)),P=!0),H.addEventListener("error",O=>A(O)),H.addEventListener("abort",O=>A(O)),H.addEventListener("load",()=>{H.setAttribute("data-loaded","true"),t(H),D(H)}),P&&(H=f.head.appendChild(H)),C||D(H)}),E=(C=!0)=>(v||(v=_(C)),v),b=()=>{if(!f)return;v=null,h.value&&(h.value=null);const C=f.querySelector(`script[src="${Me(e)}"]`);C&&f.head.removeChild(C)};return r&&!a&&Da(E),a||I3(b),{scriptTag:h,load:E,unload:b}}function iu(e){const t=window.getComputedStyle(e);if(t.overflowX==="scroll"||t.overflowY==="scroll"||t.overflowX==="auto"&&e.clientWidth<e.scrollWidth||t.overflowY==="auto"&&e.clientHeight<e.scrollHeight)return!0;{const n=e.parentNode;return!n||n.tagName==="BODY"?!1:iu(n)}}function W3(e){const t=e||window.event,n=t.target;return iu(n)?!1:t.touches.length>1?!0:(t.preventDefault&&t.preventDefault(),!1)}const ta=new WeakMap;function bl(e,t=!1){const n=z(t);let r=null;ae(S3(e),l=>{const i=no(Me(l));if(i){const c=i;ta.get(c)||ta.set(c,c.style.overflow),n.value&&(c.style.overflow="hidden")}},{immediate:!0});const a=()=>{const l=no(Me(e));!l||n.value||(Io&&(r=Se(l,"touchmove",i=>{W3(i)},{passive:!1})),l.style.overflow="hidden",n.value=!0)},o=()=>{var l;const i=no(Me(e));!i||!n.value||(Io&&(r==null||r()),i.style.overflow=(l=ta.get(i))!=null?l:"",ta.delete(i),n.value=!1)};return Lt(o),w({get(){return n.value},set(l){l?a():o()}})}function cu(e,t,n={}){const{window:r=ot}=n;return cn(e,t,r==null?void 0:r.sessionStorage,n)}function K3(e={}){const{window:t=ot,behavior:n="auto"}=e;if(!t)return{x:z(0),y:z(0)};const r=z(t.scrollX),a=z(t.scrollY),o=w({get(){return r.value},set(i){scrollTo({left:i,behavior:n})}}),l=w({get(){return a.value},set(i){scrollTo({top:i,behavior:n})}});return Se(t,"scroll",()=>{r.value=t.scrollX,a.value=t.scrollY},{capture:!1,passive:!0}),{x:o,y:l}}function J3(e={}){const{window:t=ot,initialWidth:n=Number.POSITIVE_INFINITY,initialHeight:r=Number.POSITIVE_INFINITY,listenOrientation:a=!0,includeScrollbar:o=!0}=e,l=z(n),i=z(r),c=()=>{t&&(o?(l.value=t.innerWidth,i.value=t.innerHeight):(l.value=t.document.documentElement.clientWidth,i.value=t.document.documentElement.clientHeight))};if(c(),Da(c),Se("resize",c,{passive:!0}),a){const u=su("(orientation: portrait)");ae(u,()=>c())}return{width:l,height:i}}var Q3=M({name:"FontIcon",props:{icon:{type:String,default:""},color:{type:String,default:""},size:{type:[String,Number],default:""}},setup(e){const t=w(()=>{const r=["font-icon icon"],a=`${e.icon}`;return r.push(a),r}),n=w(()=>{const r={};return e.color&&(r.color=e.color),e.size&&(r["font-size"]=Number.isNaN(Number(e.size))?e.size:`${e.size}px`),y3(r).length?r:null});return()=>e.icon?s("span",{key:e.icon,class:t.value,style:n.value}):null}});const uu=({type:e="info",text:t="",vertical:n,color:r},{slots:a})=>{var o;return s("span",{class:["vp-badge",e,{diy:r}],style:{verticalAlign:n??!1,backgroundColor:r??!1}},((o=a.default)==null?void 0:o.call(a))??t)};uu.displayName="Badge";const du=({title:e,desc:t="",logo:n,background:r,color:a,link:o})=>{const l=[n?s("img",{class:"vp-card-logo",src:be(n),loading:"lazy","no-view":""}):null,s("div",{class:"vp-card-content"},[s("div",{class:"vp-card-title",innerHTML:e}),s("hr"),s("div",{class:"vp-card-desc",innerHTML:t})])],i={};return r&&(i.background=r),a&&(i.color=a),o?xa(o)?s("a",{class:"vp-card",href:o,target:"_blank",style:i},l):s(Ie,{to:o,class:"vp-card",style:i},()=>l):s("div",{class:"vp-card",style:i},l)};du.displayName="VPCard";const Y3=Ze({enhance:({app:e})=>{to("FontIcon")||e.component("FontIcon",Q3),to("Badge")||e.component("Badge",uu),to("VPCard")||e.component("VPCard",du)},setup:()=>{ro("https://cdn.jsdelivr.net/npm/@fortawesome/fontawesome-free@6/js/brands.min.js",()=>{},{attrs:{"data-auto-replace-svg":"nest"}}),ro("https://cdn.jsdelivr.net/npm/@fortawesome/fontawesome-free@6/js/solid.min.js",()=>{},{attrs:{"data-auto-replace-svg":"nest"}}),ro("https://cdn.jsdelivr.net/npm/@fortawesome/fontawesome-free@6/js/fontawesome.min.js",()=>{},{attrs:{"data-auto-replace-svg":"nest"}})},rootComponents:[]}),ti=async(e,t)=>{const{path:n,query:r}=e.currentRoute.value,{scrollBehavior:a}=e.options;e.options.scrollBehavior=void 0,await e.replace({path:n,query:r,hash:t}),e.options.scrollBehavior=a},Z3=({headerLinkSelector:e,headerAnchorSelector:t,delay:n,offset:r=5})=>{const a=wn();Se("scroll",ru(()=>{var v,_;const l=Math.max(window.scrollY,document.documentElement.scrollTop,document.body.scrollTop);if(Math.abs(l-0)<r){ti(a,"");return}const c=window.innerHeight+l,u=Math.max(document.documentElement.scrollHeight,document.body.scrollHeight),d=Math.abs(u-c)<r,f=Array.from(document.querySelectorAll(e)),h=Array.from(document.querySelectorAll(t)).filter(E=>f.some(b=>b.hash===E.hash));for(let E=0;E<h.length;E++){const b=h[E],C=h[E+1],y=l>=(((v=b.parentElement)==null?void 0:v.offsetTop)??0)-r,A=!C||l<(((_=C.parentElement)==null?void 0:_.offsetTop)??0)-r;if(!(y&&A))continue;const P=decodeURIComponent(a.currentRoute.value.hash),H=decodeURIComponent(b.hash);if(P===H)return;if(d){for(let O=E+1;O<h.length;O++)if(P===decodeURIComponent(h[O].hash))return}ti(a,H);return}},n))},X3=".vp-sidebar-link, .vp-toc-link",ep=".header-anchor",tp=200,np=5,rp=Ze({setup(){Z3({headerLinkSelector:X3,headerAnchorSelector:ep,delay:tp,offset:np})}}),El=e=>{const t=Ye();return w(()=>e[t.value]??{})},ap=(e,t)=>{var r;const n=(r=(t==null?void 0:t._instance)||ln())==null?void 0:r.appContext.components;return n?e in n||qe(e)in n||_n(qe(e))in n:!1},ao=e=>typeof e=="number",ni=(e,t)=>we(e)&&e.startsWith(t),op=(e,t)=>we(e)&&e.endsWith(t),lp=Object.entries,sp=Object.keys,ip=e=>new Promise(t=>setTimeout(t,e));let fu=e=>we(e.title)?{title:e.title}:null;const pu=Symbol(""),cp=e=>{fu=e},up=()=>ve(pu),dp=e=>{e.provide(pu,fu)};var fp={"/":{title:"目录",empty:"暂无目录"}};const pp=M({name:"Catalog",props:{base:{type:String,default:""},level:{type:Number,default:3},index:Boolean,hideHeading:Boolean},setup(e){const t=up(),n=El(fp),r=ge(),a=Jf(),o=qc(),i=xe(lp(a.value).map(([u,{meta:d}])=>{const f=t(d);if(!f)return null;const p=u.split("/").length;return{level:op(u,"/")?p-2:p-1,base:u.replace(/\/[^/]+\/?$/,"/"),path:u,...f}}).filter(u=>qn(u)&&we(u.title))),c=w(()=>{const u=e.base?Dd(Pc(e.base)):r.value.path.replace(/\/[^/]+$/,"/"),d=u.split("/").length-2,f=[];return i.value.filter(({level:p,path:h})=>{if(!ni(h,u)||h===u)return!1;if(u==="/"){const v=sp(o.value.locales).filter(_=>_!=="/");if(h==="/404.html"||v.some(_=>ni(h,_)))return!1}return p-d<=e.level}).sort(({title:p,level:h,order:v},{title:_,level:E,order:b})=>{const C=h-E;return C||(ao(v)?ao(b)?v>0?b>0?v-b:-1:b<0?v-b:1:v:ao(b)?b:p.localeCompare(_))}).forEach(p=>{var _;const{base:h,level:v}=p;switch(v-d){case 1:{f.push(p);break}case 2:{const E=f.find(b=>b.path===h);E&&(E.children??(E.children=[])).push(p);break}default:{const E=f.find(b=>b.path===h.replace(/\/[^/]+\/$/,"/"));if(E){const b=(_=E.children)==null?void 0:_.find(C=>C.path===h);b&&(b.children??(b.children=[])).push(p)}}}}),f});return()=>{const u=c.value.some(d=>d.children);return s("div",{class:["vp-catalog-wrapper",{index:e.index}]},[e.hideHeading?null:s("h2",{class:"vp-catalog-main-title"},n.value.title),c.value.length?s(e.index?"ol":"ul",{class:["vp-catalogs",{deep:u}]},c.value.map(({children:d=[],title:f,path:p,content:h})=>{const v=s(Ie,{class:"vp-catalog-title",to:p},()=>h?s(h):f);return s("li",{class:"vp-catalog"},u?[s("h3",{id:f,class:["vp-catalog-child-title",{"has-children":d.length}]},[s("a",{href:`#${f}`,class:"vp-catalog-header-anchor","aria-hidden":!0},"#"),v]),d.length?s(e.index?"ol":"ul",{class:"vp-child-catalogs"},d.map(({children:_=[],content:E,path:b,title:C})=>s("li",{class:"vp-child-catalog"},[s("div",{class:["vp-catalog-sub-title",{"has-children":_.length}]},[s("a",{href:`#${C}`,class:"vp-catalog-header-anchor"},"#"),s(Ie,{class:"vp-catalog-title",to:b},()=>E?s(E):C)]),_.length?s(e.index?"ol":"div",{class:e.index?"vp-sub-catalogs":"vp-sub-catalogs-wrapper"},_.map(({content:y,path:A,title:D})=>e.index?s("li",{class:"vp-sub-catalog"},s(Ie,{to:A},()=>y?s(y):D)):s(Ie,{class:"vp-sub-catalog-link",to:A},()=>y?s(y):D))):null]))):null]:s("div",{class:"vp-catalog-child-title"},v))})):s("p",{class:"vp-empty-catalog"},n.value.empty)])}}}),hp=Ze({enhance:({app:e})=>{dp(e),ap("Catalog",e)||e.component("Catalog",pp)}}),hu=e=>{const t=Ye();return w(()=>e[t.value]??{})},Mn=(e,t)=>{var r;const n=(r=ln())==null?void 0:r.appContext.components;return n?e in n||qe(e)in n||_n(qe(e))in n:!1},Po=Array.isArray,Oa=(e,t)=>we(e)&&e.startsWith(t),Ma=Object.entries,En=Object.keys,_l=e=>{if(e){if(typeof e=="number")return new Date(e);const t=Date.parse(e.toString());if(!Number.isNaN(t))return new Date(t)}return null},Rr=e=>Oa(e,"/"),mp="http://.",vp=(e,t)=>{if(Rr(e)||typeof t!="string")return xt(e);const n=t.slice(0,t.lastIndexOf("/"));return xt(new URL(`${n}/${encodeURI(e)}`,mp).pathname)},gp=e=>new Promise(t=>setTimeout(t,e));var yp={"/":{backToTop:"返回顶部"}};const bp=M({name:"BackToTop",setup(){const e=he(),t=hu(yp),n=xe(),{height:r}=G3(n),{height:a}=J3(),{y:o}=K3(),l=w(()=>e.value.backToTop!==!1&&o.value>100),i=w(()=>o.value/(r.value-a.value)*100);return se(()=>{n.value=document.body}),()=>s(Rt,{name:"back-to-top"},()=>l.value?s("button",{type:"button",class:"vp-back-to-top-button","aria-label":t.value.backToTop,onClick:()=>{window.scrollTo({top:0,behavior:"smooth"})}},[s("span",{class:"vp-scroll-progress",role:"progressbar","aria-labelledby":"loadinglabel","aria-valuenow":i.value},s("svg",s("circle",{cx:"26",cy:"26",r:"24",fill:"none",stroke:"currentColor","stroke-width":"4","stroke-dasharray":`${Math.PI*i.value*.48} ${Math.PI*(100-i.value)*.48}`}))),s("div",{class:"back-to-top-icon"})]):null)}}),Ep=Ze({rootComponents:[bp]}),_p=s("svg",{class:"external-link-icon",xmlns:"http://www.w3.org/2000/svg","aria-hidden":"true",focusable:"false",x:"0px",y:"0px",viewBox:"0 0 100 100",width:"15",height:"15"},[s("path",{fill:"currentColor",d:"M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"}),s("polygon",{fill:"currentColor",points:"45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"})]),mu=M({name:"ExternalLinkIcon",props:{locales:{type:Object,default:()=>({})}},setup(e){const t=Ye(),n=w(()=>e.locales[t.value]??{openInNewWindow:"open in new window"});return()=>s("span",[_p,s("span",{class:"external-link-icon-sr-only"},n.value.openInNewWindow)])}});var wp={};const Ap=wp,Cp=Ze({enhance({app:e}){e.component("ExternalLinkIcon",s(mu,{locales:Ap}))}});/**
  * NProgress, (c) 2013, 2014 Rico Sta. Cruz - http://ricostacruz.com/nprogress
  * @license MIT
- */const de={settings:{minimum:.08,easing:"ease",speed:200,trickle:!0,trickleRate:.02,trickleSpeed:800,barSelector:'[role="bar"]',parent:"body",template:'<div class="bar" role="bar"></div>'},status:null,set:e=>{const t=de.isStarted();e=oo(e,de.settings.minimum,1),de.status=e===1?null:e;const n=de.render(!t),r=n.querySelector(de.settings.barSelector),a=de.settings.speed,o=de.settings.easing;return n.offsetWidth,kp(l=>{na(r,{transform:"translate3d("+ri(e)+"%,0,0)",transition:"all "+a+"ms "+o}),e===1?(na(n,{transition:"none",opacity:"1"}),n.offsetWidth,setTimeout(function(){na(n,{transition:"all "+a+"ms linear",opacity:"0"}),setTimeout(function(){de.remove(),l()},a)},a)):setTimeout(()=>l(),a)}),de},isStarted:()=>typeof de.status=="number",start:()=>{de.status||de.set(0);const e=()=>{setTimeout(()=>{de.status&&(de.trickle(),e())},de.settings.trickleSpeed)};return de.settings.trickle&&e(),de},done:e=>!e&&!de.status?de:de.inc(.3+.5*Math.random()).set(1),inc:e=>{let t=de.status;return t?(typeof e!="number"&&(e=(1-t)*oo(Math.random()*t,.1,.95)),t=oo(t+e,0,.994),de.set(t)):de.start()},trickle:()=>de.inc(Math.random()*de.settings.trickleRate),render:e=>{if(de.isRendered())return document.getElementById("nprogress");ai(document.documentElement,"nprogress-busy");const t=document.createElement("div");t.id="nprogress",t.innerHTML=de.settings.template;const n=t.querySelector(de.settings.barSelector),r=e?"-100":ri(de.status||0),a=document.querySelector(de.settings.parent);return na(n,{transition:"all 0 linear",transform:"translate3d("+r+"%,0,0)"}),a!==document.body&&ai(a,"nprogress-custom-parent"),a==null||a.appendChild(t),t},remove:()=>{oi(document.documentElement,"nprogress-busy"),oi(document.querySelector(de.settings.parent),"nprogress-custom-parent");const e=document.getElementById("nprogress");e&&Tp(e)},isRendered:()=>!!document.getElementById("nprogress")},oo=(e,t,n)=>e<t?t:e>n?n:e,ri=e=>(-1+e)*100,kp=function(){const e=[];function t(){const n=e.shift();n&&n(t)}return function(n){e.push(n),e.length===1&&t()}}(),na=function(){const e=["Webkit","O","Moz","ms"],t={};function n(l){return l.replace(/^-ms-/,"ms-").replace(/-([\da-z])/gi,function(i,c){return c.toUpperCase()})}function r(l){const i=document.body.style;if(l in i)return l;let c=e.length;const u=l.charAt(0).toUpperCase()+l.slice(1);let d;for(;c--;)if(d=e[c]+u,d in i)return d;return l}function a(l){return l=n(l),t[l]??(t[l]=r(l))}function o(l,i,c){i=a(i),l.style[i]=c}return function(l,i){for(const c in i){const u=i[c];u!==void 0&&Object.prototype.hasOwnProperty.call(i,c)&&o(l,c,u)}}}(),vu=(e,t)=>(typeof e=="string"?e:wl(e)).indexOf(" "+t+" ")>=0,ai=(e,t)=>{const n=wl(e),r=n+t;vu(n,t)||(e.className=r.substring(1))},oi=(e,t)=>{const n=wl(e);if(!vu(e,t))return;const r=n.replace(" "+t+" "," ");e.className=r.substring(1,r.length-1)},wl=e=>(" "+(e.className||"")+" ").replace(/\s+/gi," "),Tp=e=>{e&&e.parentNode&&e.parentNode.removeChild(e)},Sp=()=>{se(()=>{const e=wn(),t=new Set;t.add(e.currentRoute.value.path),e.beforeEach(n=>{t.has(n.path)||de.start()}),e.afterEach(n=>{t.add(n.path),de.done()})})},xp=Ze({setup(){Sp()}}),Lp=JSON.parse(`{"encrypt":{"config":{"/encrypt/":["$2a$10$ChYC07LQmX6Ilyl.Cqgv4enXptxrrlQMQUFIOQHpyoqxfTPK/jtn."]}},"author":{"name":"KSJ","url":"https://github.com/King-sj"},"logo":"/logo.svg","repo":"https://github.com/King-sj/KBlog","docsDir":"src","footer":"<a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ ","displayFooter":true,"copyright":"MPL-2.0 许可证","blog":{"description":"一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。","intro":"/intro.html","medias":{"Email":"mailto:2175616761@qq.com","GitHub":"https://github.com/King-sj","QQ":"https://wpa.qq.com/msgrd?v=3&uin=2175616761&site=qq&menu=yes"}},"locales":{"/":{"lang":"zh-CN","navbarLocales":{"langName":"简体中文","selectLangAriaLabel":"选择语言"},"metaLocales":{"author":"作者","date":"写作日期","origin":"原创","views":"访问量","category":"分类","tag":"标签","readingTime":"阅读时间","words":"字数","toc":"此页内容","prev":"上一页","next":"下一页","lastUpdated":"上次编辑于","contributors":"贡献者","editLink":"在 GitHub 上编辑此页","print":"打印"},"blogLocales":{"article":"文章","articleList":"文章列表","category":"分类","tag":"标签","timeline":"时间轴","timelineTitle":"昨日不在","all":"全部","intro":"个人介绍","star":"星标","empty":"$text 为空"},"paginationLocales":{"prev":"上一页","next":"下一页","navigate":"跳转到","action":"前往","errorText":"请输入 1 到 $page 之前的页码！"},"outlookLocales":{"themeColor":"主题色","darkmode":"外观","fullscreen":"全屏"},"encryptLocales":{"iconLabel":"文章已加密","placeholder":"输入密码","remember":"记住密码","errorHint":"请输入正确的密码"},"routeLocales":{"skipToContent":"跳至主要內容","notFoundTitle":"页面不存在","notFoundMsg":["这里什么也没有","我们是怎么来到这儿的？","这 是 四 零 四 !","看起来你访问了一个失效的链接"],"back":"返回上一页","home":"带我回家","openInNewWindow":"Open in new window"},"navbar":["/","/tech/","/essays/","/projects/","/tutorials/","/resources/",{"text":"友链","children":[{"text":"KSJ-Blog","link":"https://bupt.online"},{"text":"KSJ-Blog-GitHub","link":"https://king-sj.github.io"}]}],"sidebar":{"/":["","intro"],"/tech/":[{"text":"技术","children":"structure","collapsible":true}],"/essay/":[{"text":"随笔","children":"structure","collapsible":true}],"/tutorials/":[{"text":"教程","children":"structure","icon":"book","collapsible":true}],"/resources/":[{"text":"资源","children":"structure","icon":"book","collapsible":true}]}}}}`),Bp=z(Lp),gu=()=>Bp,yu=Symbol(""),Ip=()=>{const e=ve(yu);if(!e)throw new Error("useThemeLocaleData() is called without provider.");return e},Pp=(e,t)=>{const{locales:n,...r}=e;return{...r,...n==null?void 0:n[t]}},Dp=Ze({enhance({app:e}){const t=gu(),n=e._context.provides[vl],r=w(()=>Pp(t.value,n.routeLocale.value));e.provide(yu,r),Object.defineProperties(e.config.globalProperties,{$theme:{get(){return t.value}},$themeLocale:{get(){return r.value}}})}});var Op={provider:"Giscus",lightTheme:"https://unpkg.com/vuepress-theme-hope@2.0.0-rc.38/templates/giscus/light.css",darkTheme:"https://unpkg.com/vuepress-theme-hope@2.0.0-rc.38/templates/giscus/dark.css",repo:"King-sj/KBlog",repoId:"R_kgDOL41Gpw",category:"Q&A",categoryId:"DIC_kwDOL41Gp84CiYFP",lazyLoading:!0};const Mp=Op;let Rp=Mp;const bu=Symbol(""),Eu=()=>ve(bu),$p=Eu,Fp=e=>{e.provide(bu,Rp)},_u=()=>s("svg",{xmlns:"http://www.w3.org/2000/svg",width:"32",height:"32",preserveAspectRatio:"xMidYMid",viewBox:"0 0 100 100"},[s("circle",{cx:"28",cy:"75",r:"11",fill:"currentColor"},s("animate",{attributeName:"fill-opacity",begin:"0s",dur:"1s",keyTimes:"0;0.2;1",repeatCount:"indefinite",values:"0;1;1"})),s("path",{fill:"none",stroke:"#88baf0","stroke-width":"10",d:"M28 47a28 28 0 0 1 28 28"},s("animate",{attributeName:"stroke-opacity",begin:"0.1s",dur:"1s",keyTimes:"0;0.2;1",repeatCount:"indefinite",values:"0;1;1"})),s("path",{fill:"none",stroke:"#88baf0","stroke-width":"10",d:"M28 25a50 50 0 0 1 50 50"},s("animate",{attributeName:"stroke-opacity",begin:"0.2s",dur:"1s",keyTimes:"0;0.2;1",repeatCount:"indefinite",values:"0;1;1"}))]);_u.displayName="LoadingIcon";const li=["ar","ca","da","de","en","eo","es","fa","fr","he","id","it","ja","ko","nl","pl","pt","ro","ru","th","tr","uk","uz","vi","zh-CN","zh-TW"],Hp=M({name:"GiscusComment",props:{identifier:{type:String,required:!0},darkmode:Boolean},setup(e){const t=$p(),n=Pa(),r=!!(t.repo&&t.repoId&&t.category&&t.categoryId),{repo:a,repoId:o,category:l,categoryId:i}=t,c=z(!1),u=w(()=>{if(li.includes(n.value))return n.value;const f=n.value.split("-")[0];return li.includes(f)?f:"en"}),d=w(()=>({repo:a,repoId:o,category:l,categoryId:i,lang:u.value,theme:e.darkmode?t.darkTheme||"dark":t.lightTheme||"light",mapping:t.mapping||"pathname",term:e.identifier,inputPosition:t.inputPosition||"top",reactionsEnabled:t.reactionsEnabled===!1?"0":"1",strict:t.strict===!1?"0":"1",loading:t.lazyLoading===!1?"eager":"lazy",emitMetadata:"0"}));return se(async()=>{await T(()=>import("./giscus--_FS5kYt.js"),[]),c.value=!0}),()=>r?s("div",{id:"comment",class:["giscus-wrapper",{"input-top":t.inputPosition!=="bottom"}]},c.value?s("giscus-widget",d.value):s(_u)):null}}),Np=M({name:"CommentService",props:{darkmode:Boolean},setup(e){const t=Eu(),n=ge(),r=he(),a=t.comment!==!1,o=w(()=>r.value.comment||a&&r.value.comment!==!1);return()=>s(Hp,{id:"vp-comment",identifier:r.value.commentID||n.value.path,darkmode:e.darkmode,style:{display:o.value?"block":"none"}})}}),Vp=Ze({enhance:({app:e})=>{Fp(e),e.component("CommentService",Np)}}),jp=/\b(?:Android|webOS|iPhone|iPad|iPod|BlackBerry|IEMobile|Opera Mini)/i,zp=()=>typeof window<"u"&&window.navigator&&"userAgent"in window.navigator&&jp.test(navigator.userAgent),qp=({delay:e=500,duration:t=2e3,locales:n,selector:r,showInMobile:a})=>{const{copy:o,copied:l}=R3({legacy:!0,copiedDuring:t}),i=hu(n),c=ge(),u=p=>{if(!p.hasAttribute("copy-code-registered")){const h=document.createElement("button");h.type="button",h.classList.add("vp-copy-code-button"),h.innerHTML='<div class="vp-copy-icon" />',h.setAttribute("aria-label",i.value.copy),h.setAttribute("data-copied",i.value.copied),p.parentElement&&p.parentElement.insertBefore(h,p),p.setAttribute("copy-code-registered","")}},d=()=>{_t().then(()=>gp(e)).then(()=>{r.forEach(p=>{document.querySelectorAll(p).forEach(u)})})},f=(p,h,v)=>{let{innerText:_=""}=h;/language-(shellscript|shell|bash|sh|zsh)/.test(p.classList.toString())&&(_=_.replace(/^ *(\$|>) /gm,"")),o(_).then(()=>{v.classList.add("copied"),ae(l,()=>{v.classList.remove("copied"),v.blur()},{once:!0})})};se(()=>{const p=!zp()||a;p&&d(),Se("click",h=>{const v=h.target;if(v.matches('div[class*="language-"] > button.copy')){const _=v.parentElement,E=v.nextElementSibling;E&&f(_,E,v)}else if(v.matches('div[class*="language-"] div.vp-copy-icon')){const _=v.parentElement,E=_.parentElement,b=_.nextElementSibling;b&&f(E,b,_)}}),ae(()=>c.value.path,()=>{p&&d()})})};var Gp={"/":{copy:"复制代码",copied:"已复制"}},Up=['.theme-hope-content div[class*="language-"] pre'];const Wp=500,Kp=2e3,Jp=Gp,Qp=Up,Yp=!1,Zp=Ze({setup:()=>{qp({selector:Qp,locales:Jp,duration:Kp,delay:Wp,showInMobile:Yp})}}),ra=cn("VUEPRESS_CODE_TAB_STORE",{});var Xp=M({name:"CodeTabs",props:{active:{type:Number,default:0},data:{type:Array,required:!0},id:{type:String,required:!0},tabId:{type:String,default:""}},slots:Object,setup(e,{slots:t}){const n=z(e.active),r=xe([]),a=()=>{e.tabId&&(ra.value[e.tabId]=e.data[n.value].id)},o=(u=n.value)=>{n.value=u<r.value.length-1?u+1:0,r.value[n.value].focus()},l=(u=n.value)=>{n.value=u>0?u-1:r.value.length-1,r.value[n.value].focus()},i=(u,d)=>{u.key===" "||u.key==="Enter"?(u.preventDefault(),n.value=d):u.key==="ArrowRight"?(u.preventDefault(),o()):u.key==="ArrowLeft"&&(u.preventDefault(),l()),e.tabId&&(ra.value[e.tabId]=e.data[n.value].id)},c=()=>{if(e.tabId){const u=e.data.findIndex(({id:d})=>ra.value[e.tabId]===d);if(u!==-1)return u}return e.active};return se(()=>{n.value=c(),ae(()=>ra.value[e.tabId],(u,d)=>{if(e.tabId&&u!==d){const f=e.data.findIndex(({id:p})=>p===u);f!==-1&&(n.value=f)}})}),()=>e.data.length?s("div",{class:"vp-code-tabs"},[s("div",{class:"vp-code-tabs-nav",role:"tablist"},e.data.map(({id:u},d)=>{const f=d===n.value;return s("button",{type:"button",ref:p=>{p&&(r.value[d]=p)},class:["vp-code-tab-nav",{active:f}],role:"tab","aria-controls":`codetab-${e.id}-${d}`,"aria-selected":f,onClick:()=>{n.value=d,a()},onKeydown:p=>i(p,d)},t[`title${d}`]({value:u,isActive:f}))})),e.data.map(({id:u},d)=>{const f=d===n.value;return s("div",{class:["vp-code-tab",{active:f}],id:`codetab-${e.id}-${d}`,role:"tabpanel","aria-expanded":f},[s("div",{class:"vp-code-tab-title"},t[`title${d}`]({value:u,isActive:f})),t[`tab${d}`]({value:u,isActive:f})])})]):null}});const ya=e=>{const t=atob(e);return g3(p3(v3(t)))},e4=e=>typeof e<"u",wu=Object.keys,t4=e=>typeof e<"u",n4=Object.keys,ie=({name:e="",color:t="currentColor"},{slots:n})=>{var r;return s("svg",{xmlns:"http://www.w3.org/2000/svg",class:["icon",`${e}-icon`],viewBox:"0 0 1024 1024",fill:t,"aria-label":`${e} icon`},(r=n.default)==null?void 0:r.call(n))};ie.displayName="IconBase";const Al=({size:e=48,stroke:t=4,wrapper:n=!0,height:r=2*e})=>{const a=s("svg",{xmlns:"http://www.w3.org/2000/svg",width:e,height:e,preserveAspectRatio:"xMidYMid",viewBox:"25 25 50 50"},[s("animateTransform",{attributeName:"transform",type:"rotate",dur:"2s",keyTimes:"0;1",repeatCount:"indefinite",values:"0;360"}),s("circle",{cx:"50",cy:"50",r:"20",fill:"none",stroke:"currentColor","stroke-width":t,"stroke-linecap":"round"},[s("animate",{attributeName:"stroke-dasharray",dur:"1.5s",keyTimes:"0;0.5;1",repeatCount:"indefinite",values:"1,200;90,200;1,200"}),s("animate",{attributeName:"stroke-dashoffset",dur:"1.5s",keyTimes:"0;0.5;1",repeatCount:"indefinite",values:"0;-35px;-125px"})])]);return n?s("div",{class:"loading-icon-wrapper",style:`display:flex;align-items:center;justify-content:center;height:${r}px`},a):a};Al.displayName="LoadingIcon";const Au=(e,{slots:t})=>{var n;return(n=t.default)==null?void 0:n.call(t)},r4=e=>sn(e)?e:`https://github.com/${e}`,Cl=(e="")=>!sn(e)||/github\.com/.test(e)?"GitHub":/bitbucket\.org/.test(e)?"Bitbucket":/gitlab\.com/.test(e)?"GitLab":/gitee\.com/.test(e)?"Gitee":null,Cu=()=>s(ie,{name:"github"},()=>s("path",{d:"M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"}));Cu.displayName="GitHubIcon";const ku=()=>s(ie,{name:"gitee"},()=>s("path",{d:"M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm242.97-533.34H482.39a23.7 23.7 0 0 0-23.7 23.7l-.03 59.28c0 13.08 10.59 23.7 23.7 23.7h165.96a23.7 23.7 0 0 1 23.7 23.7v11.85a71.1 71.1 0 0 1-71.1 71.1H375.71a23.7 23.7 0 0 1-23.7-23.7V423.11a71.1 71.1 0 0 1 71.1-71.1h331.8a23.7 23.7 0 0 0 23.7-23.7l.06-59.25a23.73 23.73 0 0 0-23.7-23.73H423.11a177.78 177.78 0 0 0-177.78 177.75v331.83c0 13.08 10.62 23.7 23.7 23.7h349.62a159.99 159.99 0 0 0 159.99-159.99V482.33a23.7 23.7 0 0 0-23.7-23.7z"}));ku.displayName="GiteeIcon";const Tu=()=>s(ie,{name:"bitbucket"},()=>s("path",{d:"M575.256 490.862c6.29 47.981-52.005 85.723-92.563 61.147-45.714-20.004-45.714-92.562-1.133-113.152 38.29-23.442 93.696 7.424 93.696 52.005zm63.451-11.996c-10.276-81.152-102.29-134.839-177.152-101.156-47.433 21.138-79.433 71.424-77.129 124.562 2.853 69.705 69.157 126.866 138.862 120.576S647.3 548.571 638.708 478.83zm136.558-309.723c-25.161-33.134-67.986-38.839-105.728-45.13-106.862-17.151-216.576-17.7-323.438 1.134-35.438 5.706-75.447 11.996-97.719 43.996 36.572 34.304 88.576 39.424 135.424 45.129 84.553 10.862 171.447 11.447 256 .585 47.433-5.705 99.987-10.276 135.424-45.714zm32.585 591.433c-16.018 55.99-6.839 131.438-66.304 163.986-102.29 56.576-226.304 62.867-338.87 42.862-59.43-10.862-129.135-29.696-161.72-85.723-14.3-54.858-23.442-110.848-32.585-166.84l3.438-9.142 10.276-5.157c170.277 112.567 408.576 112.567 579.438 0 26.844 8.01 6.84 40.558 6.29 60.014zm103.424-549.157c-19.42 125.148-41.728 249.71-63.415 374.272-6.29 36.572-41.728 57.162-71.424 72.558-106.862 53.724-231.424 62.866-348.562 50.286-79.433-8.558-160.585-29.696-225.134-79.433-30.28-23.443-30.28-63.415-35.986-97.134-20.005-117.138-42.862-234.277-57.161-352.585 6.839-51.42 64.585-73.728 107.447-89.71 57.16-21.138 118.272-30.866 178.87-36.571 129.134-12.58 261.157-8.01 386.304 28.562 44.581 13.13 92.563 31.415 122.844 69.705 13.714 17.7 9.143 40.01 6.29 60.014z"}));Tu.displayName="BitbucketIcon";const Su=()=>s(ie,{name:"source"},()=>s("path",{d:"M601.92 475.2c0 76.428-8.91 83.754-28.512 99.594-14.652 11.88-43.956 14.058-78.012 16.434-18.81 1.386-40.392 2.97-62.172 6.534-18.612 2.97-36.432 9.306-53.064 17.424V299.772c37.818-21.978 63.36-62.766 63.36-109.692 0-69.894-56.826-126.72-126.72-126.72S190.08 120.186 190.08 190.08c0 46.926 25.542 87.714 63.36 109.692v414.216c-37.818 21.978-63.36 62.766-63.36 109.692 0 69.894 56.826 126.72 126.72 126.72s126.72-56.826 126.72-126.72c0-31.086-11.286-59.598-29.7-81.576 13.266-9.504 27.522-17.226 39.996-19.206 16.038-2.574 32.868-3.762 50.688-5.148 48.312-3.366 103.158-7.326 148.896-44.55 61.182-49.698 74.25-103.158 75.24-187.902V475.2h-126.72zM316.8 126.72c34.848 0 63.36 28.512 63.36 63.36s-28.512 63.36-63.36 63.36-63.36-28.512-63.36-63.36 28.512-63.36 63.36-63.36zm0 760.32c-34.848 0-63.36-28.512-63.36-63.36s28.512-63.36 63.36-63.36 63.36 28.512 63.36 63.36-28.512 63.36-63.36 63.36zM823.68 158.4h-95.04V63.36h-126.72v95.04h-95.04v126.72h95.04v95.04h126.72v-95.04h95.04z"}));Su.displayName="SourceIcon";const a4=({link:e,type:t=Cl(e??"")})=>{if(!t)return null;const n=t.toLowerCase();return s(n==="bitbucket"?Tu:n==="github"?Cu:n==="gitlab"?"GitLab":n==="gitee"?ku:Su)};function o4(){const e=z(!1),t=ln();return t&&se(()=>{e.value=!0},t),e}function l4(e){return o4(),w(()=>!!e())}const s4=()=>l4(()=>typeof window<"u"&&window.navigator&&"userAgent"in window.navigator),i4=()=>{const e=s4();return w(()=>e.value&&/\b(?:Android|iPhone)/i.test(navigator.userAgent))},c4=e=>[/\((ipad);[-\w),; ]+apple/i,/applecoremedia\/[\w.]+ \((ipad)/i,/\b(ipad)\d\d?,\d\d?[;\]].+ios/i].some(t=>t.test(e)),u4=e=>[/ip[honead]{2,4}\b(?:.*os ([\w]+) like mac|; opera)/i,/cfnetwork\/.+darwin/i].some(t=>t.test(e)),d4=e=>[/(mac os x) ?([\w. ]*)/i,/(macintosh|mac_powerpc\b)(?!.+haiku)/i].some(t=>t.test(e)),f4=(e,t=0)=>{let n=3735928559^t,r=1103547991^t;for(let a=0,o;a<e.length;a++)o=e.charCodeAt(a),n=Math.imul(n^o,2654435761),r=Math.imul(r^o,1597334677);return n=Math.imul(n^n>>>16,2246822507),n^=Math.imul(r^r>>>13,3266489909),r=Math.imul(r^r>>>16,2246822507),r^=Math.imul(n^n>>>13,3266489909),4294967296*(2097151&r)+(n>>>0)},Ra=(e,t)=>f4(e)%t;let p4=class{constructor(){this.messageElements={};const t="message-container",n=document.getElementById(t);n?this.containerElement=n:(this.containerElement=document.createElement("div"),this.containerElement.id=t,document.body.appendChild(this.containerElement))}pop(t,n=2e3){const r=document.createElement("div"),a=Date.now();return r.className="message move-in",r.innerHTML=t,this.containerElement.appendChild(r),this.messageElements[a]=r,n>0&&setTimeout(()=>{this.close(a)},n),a}close(t){if(t){const n=this.messageElements[t];n.classList.remove("move-in"),n.classList.add("move-out"),n.addEventListener("animationend",()=>{n.remove(),delete this.messageElements[t]})}else n4(this.messageElements).forEach(n=>this.close(Number(n)))}destroy(){document.body.removeChild(this.containerElement)}};const xu=/#.*$/u,h4=e=>{const t=xu.exec(e);return t?t[0]:""},si=e=>decodeURI(e).replace(xu,"").replace(/\/index\.html$/iu,"/").replace(/\.html$/iu,"").replace(/(README|index)?\.md$/iu,""),Lu=(e,t)=>{if(!t4(t))return!1;const n=si(e.path),r=si(t),a=h4(t);return a?a===e.hash&&(!r||n===r):n===r};var m4=e=>Object.prototype.toString.call(e)==="[object Object]",Ar=e=>typeof e=="string";const Bu=Array.isArray,ii=e=>m4(e)&&Ar(e.name),Cr=(e,t=!1)=>e?Bu(e)?e.map(n=>Ar(n)?{name:n}:ii(n)?n:null).filter(n=>n!==null):Ar(e)?[{name:e}]:ii(e)?[e]:(console.error(`Expect "author" to be \`AuthorInfo[] | AuthorInfo | string[] | string ${t?"":"| false"} | undefined\`, but got`,e),[]):[],Iu=(e,t)=>{if(e){if(Bu(e)&&e.every(Ar))return e;if(Ar(e))return[e];console.error(`Expect ${t} to be \`string[] | string | undefined\`, but got`,e)}return[]},Pu=e=>Iu(e,"category"),Du=e=>Iu(e,"tag"),v4='<svg class="codepen-icon" viewBox="0 0 1024 1024" xmlns="http://www.w3.org/2000/svg"><path d="M123.429 668L468 897.714V692.571L277.143 565.143zM88 585.714L198.286 512 88 438.286v147.428zm468 312L900.571 668 746.857 565.143 556 692.57v205.143zM512 616l155.429-104L512 408 356.571 512zM277.143 458.857L468 331.43V126.286L123.429 356zM825.714 512L936 585.714V438.286zm-78.857-53.143L900.571 356 556 126.286v205.143zM1024 356v312q0 23.429-19.429 36.571l-468 312Q524.571 1024 512 1024t-24.571-7.429l-468-312Q0 691.43 0 668V356q0-23.429 19.429-36.571l468-312Q499.429 0 512 0t24.571 7.429l468 312Q1024 332.57 1024 356z"/></svg>',g4='<svg class="jsfiddle-icon" viewBox="0 0 1170 1024" xmlns="http://www.w3.org/2000/svg"><path d="M1028.571 441.143q63.429 26.286 102.572 83.143t39.143 126.571q0 93.714-67.429 160.286T940 877.714q-2.286 0-6.571-.285t-6-.286H232q-97.143-5.714-164.571-71.714T0 645.143q0-62.857 31.429-116t84-84q-6.858-22.286-6.858-46.857 0-65.715 46.858-112T269.143 240q54.286 0 98.286 33.143 42.857-88 127.142-141.714t186.572-53.715q94.857 0 174.857 46t126.571 124.857 46.572 172q0 3.429-.286 10.286t-.286 10.286zm-761.142 152q0 69.714 48 110.286T434.286 744q78.285 0 137.143-56.571-9.143-11.429-27.143-32.286t-24.857-28.857q-38.286 37.143-82.286 37.143-31.429 0-53.429-19.143t-22-50q0-30.286 22-49.715T436 525.143q25.143 0 48.286 12T526 568.57t37.143 42.858 39.428 46.857 44 42.857T702 732.57t69.429 12q69.142 0 116.857-40.857T936 594.857q0-69.143-48-109.714T769.714 444.57Q688 444.571 632 500l53.143 61.714q37.714-36.571 81.143-36.571 29.714 0 52.571 18.857t22.857 48q0 32.571-21.143 52.286T766.857 664q-24.571 0-47.143-12t-41.143-31.429-37.428-42.857-39.714-46.857T557.143 488 502 456.571t-67.714-12q-69.715 0-118.286 40.286t-48.571 108.286z"/></svg>';var y4={useBabel:!1,jsLib:[],cssLib:[],codepenLayout:"left",codepenEditors:"101",babel:"https://unpkg.com/@babel/standalone/babel.min.js",vue:"https://unpkg.com/vue/dist/vue.global.prod.js",react:"https://unpkg.com/react/umd/react.production.min.js",reactDOM:"https://unpkg.com/react-dom/umd/react-dom.production.min.js"};const lo=y4,ci={html:{types:["html","slim","haml","md","markdown","vue"],map:{html:"none",vue:"none",md:"markdown"}},js:{types:["js","javascript","coffee","coffeescript","ts","typescript","ls","livescript"],map:{js:"none",javascript:"none",coffee:"coffeescript",ls:"livescript",ts:"typescript"}},css:{types:["css","less","sass","scss","stylus","styl"],map:{css:"none",styl:"stylus"}}},b4=(e,t,n)=>{const r=document.createElement(e);return qn(t)&&wu(t).forEach(a=>{if(a.indexOf("data"))r[a]=t[a];else{const o=a.replace("data","");r.dataset[o]=t[a]}}),r},kl=e=>({...lo,...e,jsLib:Array.from(new Set([...lo.jsLib||[],...e.jsLib??[]])),cssLib:Array.from(new Set([...lo.cssLib||[],...e.cssLib??[]]))}),Rn=(e,t)=>{if(e4(e[t]))return e[t];const n=new Promise(r=>{var o;const a=document.createElement("script");a.src=t,(o=document.querySelector("body"))==null||o.appendChild(a),a.onload=()=>{r()}});return e[t]=n,n},E4=(e,t)=>{if(t.css&&Array.from(e.childNodes).every(n=>n.nodeName!=="STYLE")){const n=b4("style",{innerHTML:t.css});e.appendChild(n)}},_4=(e,t,n)=>{const r=n.getScript();if(r&&Array.from(t.childNodes).every(a=>a.nodeName!=="SCRIPT")){const a=document.createElement("script");a.appendChild(document.createTextNode(`{const document=window.document.querySelector('#${e} .vp-code-demo-display').shadowRoot;
+ */const de={settings:{minimum:.08,easing:"ease",speed:200,trickle:!0,trickleRate:.02,trickleSpeed:800,barSelector:'[role="bar"]',parent:"body",template:'<div class="bar" role="bar"></div>'},status:null,set:e=>{const t=de.isStarted();e=oo(e,de.settings.minimum,1),de.status=e===1?null:e;const n=de.render(!t),r=n.querySelector(de.settings.barSelector),a=de.settings.speed,o=de.settings.easing;return n.offsetWidth,kp(l=>{na(r,{transform:"translate3d("+ri(e)+"%,0,0)",transition:"all "+a+"ms "+o}),e===1?(na(n,{transition:"none",opacity:"1"}),n.offsetWidth,setTimeout(function(){na(n,{transition:"all "+a+"ms linear",opacity:"0"}),setTimeout(function(){de.remove(),l()},a)},a)):setTimeout(()=>l(),a)}),de},isStarted:()=>typeof de.status=="number",start:()=>{de.status||de.set(0);const e=()=>{setTimeout(()=>{de.status&&(de.trickle(),e())},de.settings.trickleSpeed)};return de.settings.trickle&&e(),de},done:e=>!e&&!de.status?de:de.inc(.3+.5*Math.random()).set(1),inc:e=>{let t=de.status;return t?(typeof e!="number"&&(e=(1-t)*oo(Math.random()*t,.1,.95)),t=oo(t+e,0,.994),de.set(t)):de.start()},trickle:()=>de.inc(Math.random()*de.settings.trickleRate),render:e=>{if(de.isRendered())return document.getElementById("nprogress");ai(document.documentElement,"nprogress-busy");const t=document.createElement("div");t.id="nprogress",t.innerHTML=de.settings.template;const n=t.querySelector(de.settings.barSelector),r=e?"-100":ri(de.status||0),a=document.querySelector(de.settings.parent);return na(n,{transition:"all 0 linear",transform:"translate3d("+r+"%,0,0)"}),a!==document.body&&ai(a,"nprogress-custom-parent"),a==null||a.appendChild(t),t},remove:()=>{oi(document.documentElement,"nprogress-busy"),oi(document.querySelector(de.settings.parent),"nprogress-custom-parent");const e=document.getElementById("nprogress");e&&Tp(e)},isRendered:()=>!!document.getElementById("nprogress")},oo=(e,t,n)=>e<t?t:e>n?n:e,ri=e=>(-1+e)*100,kp=function(){const e=[];function t(){const n=e.shift();n&&n(t)}return function(n){e.push(n),e.length===1&&t()}}(),na=function(){const e=["Webkit","O","Moz","ms"],t={};function n(l){return l.replace(/^-ms-/,"ms-").replace(/-([\da-z])/gi,function(i,c){return c.toUpperCase()})}function r(l){const i=document.body.style;if(l in i)return l;let c=e.length;const u=l.charAt(0).toUpperCase()+l.slice(1);let d;for(;c--;)if(d=e[c]+u,d in i)return d;return l}function a(l){return l=n(l),t[l]??(t[l]=r(l))}function o(l,i,c){i=a(i),l.style[i]=c}return function(l,i){for(const c in i){const u=i[c];u!==void 0&&Object.prototype.hasOwnProperty.call(i,c)&&o(l,c,u)}}}(),vu=(e,t)=>(typeof e=="string"?e:wl(e)).indexOf(" "+t+" ")>=0,ai=(e,t)=>{const n=wl(e),r=n+t;vu(n,t)||(e.className=r.substring(1))},oi=(e,t)=>{const n=wl(e);if(!vu(e,t))return;const r=n.replace(" "+t+" "," ");e.className=r.substring(1,r.length-1)},wl=e=>(" "+(e.className||"")+" ").replace(/\s+/gi," "),Tp=e=>{e&&e.parentNode&&e.parentNode.removeChild(e)},Sp=()=>{se(()=>{const e=wn(),t=new Set;t.add(e.currentRoute.value.path),e.beforeEach(n=>{t.has(n.path)||de.start()}),e.afterEach(n=>{t.add(n.path),de.done()})})},xp=Ze({setup(){Sp()}}),Lp=JSON.parse(`{"encrypt":{"config":{"/encrypt/":["$2a$10$TtCknAj0RDydnax15B6bcOYS2MHBADKC.6SScgjDTfkWEcpxyvq7G"]}},"author":{"name":"KSJ","url":"https://github.com/King-sj"},"logo":"/logo.svg","repo":"https://github.com/King-sj/KBlog","docsDir":"src","footer":"<a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ ","displayFooter":true,"copyright":"MPL-2.0 许可证","blog":{"description":"一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。","intro":"/intro.html","medias":{"Email":"mailto:2175616761@qq.com","GitHub":"https://github.com/King-sj","QQ":"https://wpa.qq.com/msgrd?v=3&uin=2175616761&site=qq&menu=yes"}},"locales":{"/":{"lang":"zh-CN","navbarLocales":{"langName":"简体中文","selectLangAriaLabel":"选择语言"},"metaLocales":{"author":"作者","date":"写作日期","origin":"原创","views":"访问量","category":"分类","tag":"标签","readingTime":"阅读时间","words":"字数","toc":"此页内容","prev":"上一页","next":"下一页","lastUpdated":"上次编辑于","contributors":"贡献者","editLink":"在 GitHub 上编辑此页","print":"打印"},"blogLocales":{"article":"文章","articleList":"文章列表","category":"分类","tag":"标签","timeline":"时间轴","timelineTitle":"昨日不在","all":"全部","intro":"个人介绍","star":"星标","empty":"$text 为空"},"paginationLocales":{"prev":"上一页","next":"下一页","navigate":"跳转到","action":"前往","errorText":"请输入 1 到 $page 之前的页码！"},"outlookLocales":{"themeColor":"主题色","darkmode":"外观","fullscreen":"全屏"},"encryptLocales":{"iconLabel":"文章已加密","placeholder":"输入密码","remember":"记住密码","errorHint":"请输入正确的密码"},"routeLocales":{"skipToContent":"跳至主要內容","notFoundTitle":"页面不存在","notFoundMsg":["这里什么也没有","我们是怎么来到这儿的？","这 是 四 零 四 !","看起来你访问了一个失效的链接"],"back":"返回上一页","home":"带我回家","openInNewWindow":"Open in new window"},"navbar":["/","/tech/","/essays/","/projects/","/tutorials/","/resources/",{"text":"友链","children":[{"text":"KSJ-Blog","link":"https://bupt.online"},{"text":"KSJ-Blog-GitHub","link":"https://king-sj.github.io"}]}],"sidebar":{"/":["","intro"],"/tech/":[{"text":"技术","children":"structure","collapsible":true}],"/essay/":[{"text":"随笔","children":"structure","collapsible":true}],"/tutorials/":[{"text":"教程","children":"structure","icon":"book","collapsible":true}],"/resources/":[{"text":"资源","children":"structure","icon":"book","collapsible":true}]}}}}`),Bp=z(Lp),gu=()=>Bp,yu=Symbol(""),Ip=()=>{const e=ve(yu);if(!e)throw new Error("useThemeLocaleData() is called without provider.");return e},Pp=(e,t)=>{const{locales:n,...r}=e;return{...r,...n==null?void 0:n[t]}},Dp=Ze({enhance({app:e}){const t=gu(),n=e._context.provides[vl],r=w(()=>Pp(t.value,n.routeLocale.value));e.provide(yu,r),Object.defineProperties(e.config.globalProperties,{$theme:{get(){return t.value}},$themeLocale:{get(){return r.value}}})}});var Op={provider:"Giscus",lightTheme:"https://unpkg.com/vuepress-theme-hope@2.0.0-rc.38/templates/giscus/light.css",darkTheme:"https://unpkg.com/vuepress-theme-hope@2.0.0-rc.38/templates/giscus/dark.css",repo:"King-sj/KBlog",repoId:"R_kgDOL41Gpw",category:"Q&A",categoryId:"DIC_kwDOL41Gp84CiYFP",lazyLoading:!0};const Mp=Op;let Rp=Mp;const bu=Symbol(""),Eu=()=>ve(bu),$p=Eu,Fp=e=>{e.provide(bu,Rp)},_u=()=>s("svg",{xmlns:"http://www.w3.org/2000/svg",width:"32",height:"32",preserveAspectRatio:"xMidYMid",viewBox:"0 0 100 100"},[s("circle",{cx:"28",cy:"75",r:"11",fill:"currentColor"},s("animate",{attributeName:"fill-opacity",begin:"0s",dur:"1s",keyTimes:"0;0.2;1",repeatCount:"indefinite",values:"0;1;1"})),s("path",{fill:"none",stroke:"#88baf0","stroke-width":"10",d:"M28 47a28 28 0 0 1 28 28"},s("animate",{attributeName:"stroke-opacity",begin:"0.1s",dur:"1s",keyTimes:"0;0.2;1",repeatCount:"indefinite",values:"0;1;1"})),s("path",{fill:"none",stroke:"#88baf0","stroke-width":"10",d:"M28 25a50 50 0 0 1 50 50"},s("animate",{attributeName:"stroke-opacity",begin:"0.2s",dur:"1s",keyTimes:"0;0.2;1",repeatCount:"indefinite",values:"0;1;1"}))]);_u.displayName="LoadingIcon";const li=["ar","ca","da","de","en","eo","es","fa","fr","he","id","it","ja","ko","nl","pl","pt","ro","ru","th","tr","uk","uz","vi","zh-CN","zh-TW"],Hp=M({name:"GiscusComment",props:{identifier:{type:String,required:!0},darkmode:Boolean},setup(e){const t=$p(),n=Pa(),r=!!(t.repo&&t.repoId&&t.category&&t.categoryId),{repo:a,repoId:o,category:l,categoryId:i}=t,c=z(!1),u=w(()=>{if(li.includes(n.value))return n.value;const f=n.value.split("-")[0];return li.includes(f)?f:"en"}),d=w(()=>({repo:a,repoId:o,category:l,categoryId:i,lang:u.value,theme:e.darkmode?t.darkTheme||"dark":t.lightTheme||"light",mapping:t.mapping||"pathname",term:e.identifier,inputPosition:t.inputPosition||"top",reactionsEnabled:t.reactionsEnabled===!1?"0":"1",strict:t.strict===!1?"0":"1",loading:t.lazyLoading===!1?"eager":"lazy",emitMetadata:"0"}));return se(async()=>{await T(()=>import("./giscus--_FS5kYt.js"),[]),c.value=!0}),()=>r?s("div",{id:"comment",class:["giscus-wrapper",{"input-top":t.inputPosition!=="bottom"}]},c.value?s("giscus-widget",d.value):s(_u)):null}}),Np=M({name:"CommentService",props:{darkmode:Boolean},setup(e){const t=Eu(),n=ge(),r=he(),a=t.comment!==!1,o=w(()=>r.value.comment||a&&r.value.comment!==!1);return()=>s(Hp,{id:"vp-comment",identifier:r.value.commentID||n.value.path,darkmode:e.darkmode,style:{display:o.value?"block":"none"}})}}),Vp=Ze({enhance:({app:e})=>{Fp(e),e.component("CommentService",Np)}}),jp=/\b(?:Android|webOS|iPhone|iPad|iPod|BlackBerry|IEMobile|Opera Mini)/i,zp=()=>typeof window<"u"&&window.navigator&&"userAgent"in window.navigator&&jp.test(navigator.userAgent),qp=({delay:e=500,duration:t=2e3,locales:n,selector:r,showInMobile:a})=>{const{copy:o,copied:l}=R3({legacy:!0,copiedDuring:t}),i=hu(n),c=ge(),u=p=>{if(!p.hasAttribute("copy-code-registered")){const h=document.createElement("button");h.type="button",h.classList.add("vp-copy-code-button"),h.innerHTML='<div class="vp-copy-icon" />',h.setAttribute("aria-label",i.value.copy),h.setAttribute("data-copied",i.value.copied),p.parentElement&&p.parentElement.insertBefore(h,p),p.setAttribute("copy-code-registered","")}},d=()=>{_t().then(()=>gp(e)).then(()=>{r.forEach(p=>{document.querySelectorAll(p).forEach(u)})})},f=(p,h,v)=>{let{innerText:_=""}=h;/language-(shellscript|shell|bash|sh|zsh)/.test(p.classList.toString())&&(_=_.replace(/^ *(\$|>) /gm,"")),o(_).then(()=>{v.classList.add("copied"),ae(l,()=>{v.classList.remove("copied"),v.blur()},{once:!0})})};se(()=>{const p=!zp()||a;p&&d(),Se("click",h=>{const v=h.target;if(v.matches('div[class*="language-"] > button.copy')){const _=v.parentElement,E=v.nextElementSibling;E&&f(_,E,v)}else if(v.matches('div[class*="language-"] div.vp-copy-icon')){const _=v.parentElement,E=_.parentElement,b=_.nextElementSibling;b&&f(E,b,_)}}),ae(()=>c.value.path,()=>{p&&d()})})};var Gp={"/":{copy:"复制代码",copied:"已复制"}},Up=['.theme-hope-content div[class*="language-"] pre'];const Wp=500,Kp=2e3,Jp=Gp,Qp=Up,Yp=!1,Zp=Ze({setup:()=>{qp({selector:Qp,locales:Jp,duration:Kp,delay:Wp,showInMobile:Yp})}}),ra=cn("VUEPRESS_CODE_TAB_STORE",{});var Xp=M({name:"CodeTabs",props:{active:{type:Number,default:0},data:{type:Array,required:!0},id:{type:String,required:!0},tabId:{type:String,default:""}},slots:Object,setup(e,{slots:t}){const n=z(e.active),r=xe([]),a=()=>{e.tabId&&(ra.value[e.tabId]=e.data[n.value].id)},o=(u=n.value)=>{n.value=u<r.value.length-1?u+1:0,r.value[n.value].focus()},l=(u=n.value)=>{n.value=u>0?u-1:r.value.length-1,r.value[n.value].focus()},i=(u,d)=>{u.key===" "||u.key==="Enter"?(u.preventDefault(),n.value=d):u.key==="ArrowRight"?(u.preventDefault(),o()):u.key==="ArrowLeft"&&(u.preventDefault(),l()),e.tabId&&(ra.value[e.tabId]=e.data[n.value].id)},c=()=>{if(e.tabId){const u=e.data.findIndex(({id:d})=>ra.value[e.tabId]===d);if(u!==-1)return u}return e.active};return se(()=>{n.value=c(),ae(()=>ra.value[e.tabId],(u,d)=>{if(e.tabId&&u!==d){const f=e.data.findIndex(({id:p})=>p===u);f!==-1&&(n.value=f)}})}),()=>e.data.length?s("div",{class:"vp-code-tabs"},[s("div",{class:"vp-code-tabs-nav",role:"tablist"},e.data.map(({id:u},d)=>{const f=d===n.value;return s("button",{type:"button",ref:p=>{p&&(r.value[d]=p)},class:["vp-code-tab-nav",{active:f}],role:"tab","aria-controls":`codetab-${e.id}-${d}`,"aria-selected":f,onClick:()=>{n.value=d,a()},onKeydown:p=>i(p,d)},t[`title${d}`]({value:u,isActive:f}))})),e.data.map(({id:u},d)=>{const f=d===n.value;return s("div",{class:["vp-code-tab",{active:f}],id:`codetab-${e.id}-${d}`,role:"tabpanel","aria-expanded":f},[s("div",{class:"vp-code-tab-title"},t[`title${d}`]({value:u,isActive:f})),t[`tab${d}`]({value:u,isActive:f})])})]):null}});const ya=e=>{const t=atob(e);return g3(p3(v3(t)))},e4=e=>typeof e<"u",wu=Object.keys,t4=e=>typeof e<"u",n4=Object.keys,ie=({name:e="",color:t="currentColor"},{slots:n})=>{var r;return s("svg",{xmlns:"http://www.w3.org/2000/svg",class:["icon",`${e}-icon`],viewBox:"0 0 1024 1024",fill:t,"aria-label":`${e} icon`},(r=n.default)==null?void 0:r.call(n))};ie.displayName="IconBase";const Al=({size:e=48,stroke:t=4,wrapper:n=!0,height:r=2*e})=>{const a=s("svg",{xmlns:"http://www.w3.org/2000/svg",width:e,height:e,preserveAspectRatio:"xMidYMid",viewBox:"25 25 50 50"},[s("animateTransform",{attributeName:"transform",type:"rotate",dur:"2s",keyTimes:"0;1",repeatCount:"indefinite",values:"0;360"}),s("circle",{cx:"50",cy:"50",r:"20",fill:"none",stroke:"currentColor","stroke-width":t,"stroke-linecap":"round"},[s("animate",{attributeName:"stroke-dasharray",dur:"1.5s",keyTimes:"0;0.5;1",repeatCount:"indefinite",values:"1,200;90,200;1,200"}),s("animate",{attributeName:"stroke-dashoffset",dur:"1.5s",keyTimes:"0;0.5;1",repeatCount:"indefinite",values:"0;-35px;-125px"})])]);return n?s("div",{class:"loading-icon-wrapper",style:`display:flex;align-items:center;justify-content:center;height:${r}px`},a):a};Al.displayName="LoadingIcon";const Au=(e,{slots:t})=>{var n;return(n=t.default)==null?void 0:n.call(t)},r4=e=>sn(e)?e:`https://github.com/${e}`,Cl=(e="")=>!sn(e)||/github\.com/.test(e)?"GitHub":/bitbucket\.org/.test(e)?"Bitbucket":/gitlab\.com/.test(e)?"GitLab":/gitee\.com/.test(e)?"Gitee":null,Cu=()=>s(ie,{name:"github"},()=>s("path",{d:"M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"}));Cu.displayName="GitHubIcon";const ku=()=>s(ie,{name:"gitee"},()=>s("path",{d:"M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm242.97-533.34H482.39a23.7 23.7 0 0 0-23.7 23.7l-.03 59.28c0 13.08 10.59 23.7 23.7 23.7h165.96a23.7 23.7 0 0 1 23.7 23.7v11.85a71.1 71.1 0 0 1-71.1 71.1H375.71a23.7 23.7 0 0 1-23.7-23.7V423.11a71.1 71.1 0 0 1 71.1-71.1h331.8a23.7 23.7 0 0 0 23.7-23.7l.06-59.25a23.73 23.73 0 0 0-23.7-23.73H423.11a177.78 177.78 0 0 0-177.78 177.75v331.83c0 13.08 10.62 23.7 23.7 23.7h349.62a159.99 159.99 0 0 0 159.99-159.99V482.33a23.7 23.7 0 0 0-23.7-23.7z"}));ku.displayName="GiteeIcon";const Tu=()=>s(ie,{name:"bitbucket"},()=>s("path",{d:"M575.256 490.862c6.29 47.981-52.005 85.723-92.563 61.147-45.714-20.004-45.714-92.562-1.133-113.152 38.29-23.442 93.696 7.424 93.696 52.005zm63.451-11.996c-10.276-81.152-102.29-134.839-177.152-101.156-47.433 21.138-79.433 71.424-77.129 124.562 2.853 69.705 69.157 126.866 138.862 120.576S647.3 548.571 638.708 478.83zm136.558-309.723c-25.161-33.134-67.986-38.839-105.728-45.13-106.862-17.151-216.576-17.7-323.438 1.134-35.438 5.706-75.447 11.996-97.719 43.996 36.572 34.304 88.576 39.424 135.424 45.129 84.553 10.862 171.447 11.447 256 .585 47.433-5.705 99.987-10.276 135.424-45.714zm32.585 591.433c-16.018 55.99-6.839 131.438-66.304 163.986-102.29 56.576-226.304 62.867-338.87 42.862-59.43-10.862-129.135-29.696-161.72-85.723-14.3-54.858-23.442-110.848-32.585-166.84l3.438-9.142 10.276-5.157c170.277 112.567 408.576 112.567 579.438 0 26.844 8.01 6.84 40.558 6.29 60.014zm103.424-549.157c-19.42 125.148-41.728 249.71-63.415 374.272-6.29 36.572-41.728 57.162-71.424 72.558-106.862 53.724-231.424 62.866-348.562 50.286-79.433-8.558-160.585-29.696-225.134-79.433-30.28-23.443-30.28-63.415-35.986-97.134-20.005-117.138-42.862-234.277-57.161-352.585 6.839-51.42 64.585-73.728 107.447-89.71 57.16-21.138 118.272-30.866 178.87-36.571 129.134-12.58 261.157-8.01 386.304 28.562 44.581 13.13 92.563 31.415 122.844 69.705 13.714 17.7 9.143 40.01 6.29 60.014z"}));Tu.displayName="BitbucketIcon";const Su=()=>s(ie,{name:"source"},()=>s("path",{d:"M601.92 475.2c0 76.428-8.91 83.754-28.512 99.594-14.652 11.88-43.956 14.058-78.012 16.434-18.81 1.386-40.392 2.97-62.172 6.534-18.612 2.97-36.432 9.306-53.064 17.424V299.772c37.818-21.978 63.36-62.766 63.36-109.692 0-69.894-56.826-126.72-126.72-126.72S190.08 120.186 190.08 190.08c0 46.926 25.542 87.714 63.36 109.692v414.216c-37.818 21.978-63.36 62.766-63.36 109.692 0 69.894 56.826 126.72 126.72 126.72s126.72-56.826 126.72-126.72c0-31.086-11.286-59.598-29.7-81.576 13.266-9.504 27.522-17.226 39.996-19.206 16.038-2.574 32.868-3.762 50.688-5.148 48.312-3.366 103.158-7.326 148.896-44.55 61.182-49.698 74.25-103.158 75.24-187.902V475.2h-126.72zM316.8 126.72c34.848 0 63.36 28.512 63.36 63.36s-28.512 63.36-63.36 63.36-63.36-28.512-63.36-63.36 28.512-63.36 63.36-63.36zm0 760.32c-34.848 0-63.36-28.512-63.36-63.36s28.512-63.36 63.36-63.36 63.36 28.512 63.36 63.36-28.512 63.36-63.36 63.36zM823.68 158.4h-95.04V63.36h-126.72v95.04h-95.04v126.72h95.04v95.04h126.72v-95.04h95.04z"}));Su.displayName="SourceIcon";const a4=({link:e,type:t=Cl(e??"")})=>{if(!t)return null;const n=t.toLowerCase();return s(n==="bitbucket"?Tu:n==="github"?Cu:n==="gitlab"?"GitLab":n==="gitee"?ku:Su)};function o4(){const e=z(!1),t=ln();return t&&se(()=>{e.value=!0},t),e}function l4(e){return o4(),w(()=>!!e())}const s4=()=>l4(()=>typeof window<"u"&&window.navigator&&"userAgent"in window.navigator),i4=()=>{const e=s4();return w(()=>e.value&&/\b(?:Android|iPhone)/i.test(navigator.userAgent))},c4=e=>[/\((ipad);[-\w),; ]+apple/i,/applecoremedia\/[\w.]+ \((ipad)/i,/\b(ipad)\d\d?,\d\d?[;\]].+ios/i].some(t=>t.test(e)),u4=e=>[/ip[honead]{2,4}\b(?:.*os ([\w]+) like mac|; opera)/i,/cfnetwork\/.+darwin/i].some(t=>t.test(e)),d4=e=>[/(mac os x) ?([\w. ]*)/i,/(macintosh|mac_powerpc\b)(?!.+haiku)/i].some(t=>t.test(e)),f4=(e,t=0)=>{let n=3735928559^t,r=1103547991^t;for(let a=0,o;a<e.length;a++)o=e.charCodeAt(a),n=Math.imul(n^o,2654435761),r=Math.imul(r^o,1597334677);return n=Math.imul(n^n>>>16,2246822507),n^=Math.imul(r^r>>>13,3266489909),r=Math.imul(r^r>>>16,2246822507),r^=Math.imul(n^n>>>13,3266489909),4294967296*(2097151&r)+(n>>>0)},Ra=(e,t)=>f4(e)%t;let p4=class{constructor(){this.messageElements={};const t="message-container",n=document.getElementById(t);n?this.containerElement=n:(this.containerElement=document.createElement("div"),this.containerElement.id=t,document.body.appendChild(this.containerElement))}pop(t,n=2e3){const r=document.createElement("div"),a=Date.now();return r.className="message move-in",r.innerHTML=t,this.containerElement.appendChild(r),this.messageElements[a]=r,n>0&&setTimeout(()=>{this.close(a)},n),a}close(t){if(t){const n=this.messageElements[t];n.classList.remove("move-in"),n.classList.add("move-out"),n.addEventListener("animationend",()=>{n.remove(),delete this.messageElements[t]})}else n4(this.messageElements).forEach(n=>this.close(Number(n)))}destroy(){document.body.removeChild(this.containerElement)}};const xu=/#.*$/u,h4=e=>{const t=xu.exec(e);return t?t[0]:""},si=e=>decodeURI(e).replace(xu,"").replace(/\/index\.html$/iu,"/").replace(/\.html$/iu,"").replace(/(README|index)?\.md$/iu,""),Lu=(e,t)=>{if(!t4(t))return!1;const n=si(e.path),r=si(t),a=h4(t);return a?a===e.hash&&(!r||n===r):n===r};var m4=e=>Object.prototype.toString.call(e)==="[object Object]",Ar=e=>typeof e=="string";const Bu=Array.isArray,ii=e=>m4(e)&&Ar(e.name),Cr=(e,t=!1)=>e?Bu(e)?e.map(n=>Ar(n)?{name:n}:ii(n)?n:null).filter(n=>n!==null):Ar(e)?[{name:e}]:ii(e)?[e]:(console.error(`Expect "author" to be \`AuthorInfo[] | AuthorInfo | string[] | string ${t?"":"| false"} | undefined\`, but got`,e),[]):[],Iu=(e,t)=>{if(e){if(Bu(e)&&e.every(Ar))return e;if(Ar(e))return[e];console.error(`Expect ${t} to be \`string[] | string | undefined\`, but got`,e)}return[]},Pu=e=>Iu(e,"category"),Du=e=>Iu(e,"tag"),v4='<svg class="codepen-icon" viewBox="0 0 1024 1024" xmlns="http://www.w3.org/2000/svg"><path d="M123.429 668L468 897.714V692.571L277.143 565.143zM88 585.714L198.286 512 88 438.286v147.428zm468 312L900.571 668 746.857 565.143 556 692.57v205.143zM512 616l155.429-104L512 408 356.571 512zM277.143 458.857L468 331.43V126.286L123.429 356zM825.714 512L936 585.714V438.286zm-78.857-53.143L900.571 356 556 126.286v205.143zM1024 356v312q0 23.429-19.429 36.571l-468 312Q524.571 1024 512 1024t-24.571-7.429l-468-312Q0 691.43 0 668V356q0-23.429 19.429-36.571l468-312Q499.429 0 512 0t24.571 7.429l468 312Q1024 332.57 1024 356z"/></svg>',g4='<svg class="jsfiddle-icon" viewBox="0 0 1170 1024" xmlns="http://www.w3.org/2000/svg"><path d="M1028.571 441.143q63.429 26.286 102.572 83.143t39.143 126.571q0 93.714-67.429 160.286T940 877.714q-2.286 0-6.571-.285t-6-.286H232q-97.143-5.714-164.571-71.714T0 645.143q0-62.857 31.429-116t84-84q-6.858-22.286-6.858-46.857 0-65.715 46.858-112T269.143 240q54.286 0 98.286 33.143 42.857-88 127.142-141.714t186.572-53.715q94.857 0 174.857 46t126.571 124.857 46.572 172q0 3.429-.286 10.286t-.286 10.286zm-761.142 152q0 69.714 48 110.286T434.286 744q78.285 0 137.143-56.571-9.143-11.429-27.143-32.286t-24.857-28.857q-38.286 37.143-82.286 37.143-31.429 0-53.429-19.143t-22-50q0-30.286 22-49.715T436 525.143q25.143 0 48.286 12T526 568.57t37.143 42.858 39.428 46.857 44 42.857T702 732.57t69.429 12q69.142 0 116.857-40.857T936 594.857q0-69.143-48-109.714T769.714 444.57Q688 444.571 632 500l53.143 61.714q37.714-36.571 81.143-36.571 29.714 0 52.571 18.857t22.857 48q0 32.571-21.143 52.286T766.857 664q-24.571 0-47.143-12t-41.143-31.429-37.428-42.857-39.714-46.857T557.143 488 502 456.571t-67.714-12q-69.715 0-118.286 40.286t-48.571 108.286z"/></svg>';var y4={useBabel:!1,jsLib:[],cssLib:[],codepenLayout:"left",codepenEditors:"101",babel:"https://unpkg.com/@babel/standalone/babel.min.js",vue:"https://unpkg.com/vue/dist/vue.global.prod.js",react:"https://unpkg.com/react/umd/react.production.min.js",reactDOM:"https://unpkg.com/react-dom/umd/react-dom.production.min.js"};const lo=y4,ci={html:{types:["html","slim","haml","md","markdown","vue"],map:{html:"none",vue:"none",md:"markdown"}},js:{types:["js","javascript","coffee","coffeescript","ts","typescript","ls","livescript"],map:{js:"none",javascript:"none",coffee:"coffeescript",ls:"livescript",ts:"typescript"}},css:{types:["css","less","sass","scss","stylus","styl"],map:{css:"none",styl:"stylus"}}},b4=(e,t,n)=>{const r=document.createElement(e);return qn(t)&&wu(t).forEach(a=>{if(a.indexOf("data"))r[a]=t[a];else{const o=a.replace("data","");r.dataset[o]=t[a]}}),r},kl=e=>({...lo,...e,jsLib:Array.from(new Set([...lo.jsLib||[],...e.jsLib??[]])),cssLib:Array.from(new Set([...lo.cssLib||[],...e.cssLib??[]]))}),Rn=(e,t)=>{if(e4(e[t]))return e[t];const n=new Promise(r=>{var o;const a=document.createElement("script");a.src=t,(o=document.querySelector("body"))==null||o.appendChild(a),a.onload=()=>{r()}});return e[t]=n,n},E4=(e,t)=>{if(t.css&&Array.from(e.childNodes).every(n=>n.nodeName!=="STYLE")){const n=b4("style",{innerHTML:t.css});e.appendChild(n)}},_4=(e,t,n)=>{const r=n.getScript();if(r&&Array.from(t.childNodes).every(a=>a.nodeName!=="SCRIPT")){const a=document.createElement("script");a.appendChild(document.createTextNode(`{const document=window.document.querySelector('#${e} .vp-code-demo-display').shadowRoot;
 ${r}}`)),t.appendChild(a)}},w4=["html","js","css"],A4=e=>{const t=wu(e),n={html:[],js:[],css:[],isLegal:!1};return w4.forEach(r=>{const a=t.filter(o=>ci[r].types.includes(o));if(a.length){const o=a[0];n[r]=[e[o].replace(/^\n|\n$/g,""),ci[r].map[o]??o]}}),n.isLegal=(!n.html.length||n.html[1]==="none")&&(!n.js.length||n.js[1]==="none")&&(!n.css.length||n.css[1]==="none"),n},Ou=e=>e.replace(/<br \/>/g,"<br>").replace(/<((\S+)[^<]*?)\s+\/>/g,"<$1></$2>"),Mu=e=>`<div id="app">
 ${Ou(e)}
 </div>`,C4=e=>`${e.replace("export default ","const $reactApp = ").replace(/App\.__style__(\s*)=(\s*)`([\s\S]*)?`/,"")};
-ReactDOM.createRoot(document.getElementById("app")).render(React.createElement($reactApp))`,k4=e=>e.replace(/export\s+default\s*\{(\n*[\s\S]*)\n*\}\s*;?$/u,"Vue.createApp({$1}).mount('#app')").replace(/export\s+default\s*define(Async)?Component\s*\(\s*\{(\n*[\s\S]*)\n*\}\s*\)\s*;?$/u,"Vue.createApp({$1}).mount('#app')").trim(),Ru=e=>`(function(exports){var module={};module.exports=exports;${e};return module.exports.__esModule?module.exports.default:module.exports;})({})`,T4=(e,t)=>{const n=kl(t),r=e.js[0]??"";return{...n,html:Ou(e.html[0]??""),js:r,css:e.css[0]??"",isLegal:e.isLegal,getScript:()=>{var a;return n.useBabel?((a=window.Babel.transform(r,{presets:["es2015"]}))==null?void 0:a.code)??"":r}}},S4=/<template>([\s\S]+)<\/template>/u,x4=/<script(\s*lang=(['"])(.*?)\2)?>([\s\S]+)<\/script>/u,L4=/<style(\s*lang=(['"])(.*?)\2)?\s*(?:scoped)?>([\s\S]+)<\/style>/u,B4=(e,t)=>{const n=kl(t),r=e.html[0]??"",a=S4.exec(r),o=x4.exec(r),l=L4.exec(r),i=(a==null?void 0:a[1].replace(/^\n|\n$/g,""))??"",[c="",u=""]=o?[o[4].replace(/^\n|\n$/g,""),o[3]]:[],[d="",f=""]=l?[l[4].replace(/^\n|\n$/g,""),l[3]]:[],p=u===""&&(f===""||f==="css");return{...n,html:Mu(i),js:k4(c),css:d,isLegal:p,jsLib:[n.vue,...n.jsLib],getScript:()=>{var v,_;const h=t.useBabel?((_=(v=window.Babel)==null?void 0:v.transform(c,{presets:["es2015"]}))==null?void 0:_.code)??"":c.replace(/export\s+default/u,"return");return`const app=window.document.createElement('div');document.firstElementChild.appendChild(app);const appOptions=${Ru(h)};appOptions.template=\`${i.replace("`",'\\`"')}\`;window.Vue.createApp(appOptions).mount(app);`}}},I4=(e,t)=>{var a;const n=kl(t),r=e.js[0]??"";return{...n,html:Mu(""),js:C4(r),css:e.css[0]??((a=e.js[0])==null?void 0:a.replace(/App\.__style__(?:\s*)=(?:\s*)`([\s\S]*)?`/,"$1").trim())??"",isLegal:e.isLegal,jsLib:[n.react,n.reactDOM,...n.jsLib],jsx:!0,getScript:()=>{var l,i;const o=((i=(l=window.Babel)==null?void 0:l.transform(r,{presets:["es2015","react"]}))==null?void 0:i.code)??"";return`window.ReactDOM.createRoot(document.firstElementChild).render(window.React.createElement(${Ru(o)}))`}}},$n={},P4=e=>Promise.all([Rn($n,e.babel),Rn($n,e.react),Rn($n,e.reactDOM)]),D4=e=>{const t=[Rn($n,e.vue)];return e.useBabel&&t.push(Rn($n,e.babel)),Promise.all(t)},O4=e=>e.useBabel?Rn($n,e.babel):Promise.resolve();var M4=M({name:"CodeDemo",props:{id:{type:String,required:!0},type:{type:String,default:"normal"},title:{type:String,default:""},config:{type:String,default:""},code:{type:String,required:!0}},slots:Object,setup(e,{slots:t}){const[n,r]=wr(!1),a=xe(),o=xe(),l=z("0"),i=z(!1),c=w(()=>JSON.parse(e.config?ya(e.config):"{}")),u=w(()=>{const v=JSON.parse(ya(e.code));return A4(v)}),d=w(()=>e.type==="react"?I4(u.value,c.value):e.type==="vue"?B4(u.value,c.value):T4(u.value,c.value)),f=w(()=>d.value.isLegal),p=(v=!1)=>{const _=a.value.attachShadow({mode:"open"}),E=document.createElement("div");E.classList.add("code-demo-app"),_.appendChild(E),f.value?(v&&(E.innerHTML=d.value.html),E4(_,d.value),_4(e.id,_,d.value),l.value="0"):l.value="auto",i.value=!0},h=()=>{switch(e.type){case"react":return P4(d.value).then(()=>p());case"vue":return D4(d.value).then(()=>p());default:return O4(d.value).then(()=>p(!0))}};return Se("beforeprint",()=>{r(!0)}),se(()=>{setTimeout(()=>{h()},800)}),()=>{var v;return s("div",{class:"vp-code-demo",id:e.id},[s("div",{class:"vp-code-demo-header"},[d.value.isLegal?s("button",{type:"button",title:"toggle","aria-hidden":!0,class:["vp-code-demo-toggle-button",n.value?"down":"end"],onClick:()=>{l.value=n.value?"0":`${o.value.clientHeight+13.8}px`,r()}}):null,e.title?s("span",{class:"vp-code-demo-title"},decodeURIComponent(e.title)):null,d.value.isLegal&&d.value.jsfiddle!==!1?s("form",{class:"code-demo-jsfiddle",target:"_blank",action:"https://jsfiddle.net/api/post/library/pure/",method:"post"},[s("input",{type:"hidden",name:"html",value:d.value.html}),s("input",{type:"hidden",name:"js",value:d.value.js}),s("input",{type:"hidden",name:"css",value:d.value.css}),s("input",{type:"hidden",name:"wrap",value:"1"}),s("input",{type:"hidden",name:"panel_js",value:"3"}),s("input",{type:"hidden",name:"resources",value:[...d.value.cssLib,...d.value.jsLib].join(",")}),s("button",{type:"submit",class:"jsfiddle-button",innerHTML:g4,"aria-label":"JSFiddle","data-balloon-pos":"up"})]):null,!d.value.isLegal||d.value.codepen!==!1?s("form",{class:"code-demo-codepen",target:"_blank",action:"https://codepen.io/pen/define",method:"post"},[s("input",{type:"hidden",name:"data",value:JSON.stringify({html:d.value.html,js:d.value.js,css:d.value.css,js_external:d.value.jsLib.join(";"),css_external:d.value.cssLib.join(";"),layout:d.value.codepenLayout,html_pre_processor:u.value?u.value.html[1]:"none",js_pre_processor:u.value?u.value.js[1]:d.value.jsx?"babel":"none",css_pre_processor:u.value?u.value.css[1]:"none",editors:d.value.codepenEditors})}),s("button",{type:"submit",innerHTML:v4,class:"codepen-button","aria-label":"Codepen","data-balloon-pos":"up"})]):null]),i.value?null:s(Al,{class:"vp-code-demo-loading"}),s("div",{ref:a,class:"vp-code-demo-display",style:{display:f.value&&i.value?"block":"none"}}),s("div",{class:"vp-code-demo-code-wrapper",style:{height:l.value}},s("div",{ref:o,class:"vp-code-demo-codes"},(v=t.default)==null?void 0:v.call(t)))])}}}),R4=M({name:"MdDemo",props:{id:{type:String,required:!0},title:{type:String,default:""}},slots:Object,setup(e,{slots:t}){const[n,r]=wr(!1),a=xe(),o=z("0");return Se("beforeprint",()=>{r(!0)}),()=>{var l,i;return s("div",{class:"vp-md-demo",id:e.id},[s("div",{class:"vp-md-demo-header"},[s("button",{type:"button",title:"toggle","aria-hidden":!0,class:["vp-md-demo-toggle-button",n.value?"down":"end"],onClick:()=>{o.value=n.value?"0":`${a.value.clientHeight+13.8}px`,r()}}),e.title?decodeURIComponent(e.title):null]),s("div",{class:"vp-md-demo-display"},(l=t.default)==null?void 0:l.call(t)),s("div",{class:"vp-md-demo-code-wrapper",style:{height:o.value}},s("div",{ref:a,class:"vp-md-demo-codes"},(i=t.code)==null?void 0:i.call(t)))])}}});const $4=()=>{Se("beforeprint",()=>{document.querySelectorAll("details").forEach(e=>{e.open=!0})})};let F4={};const $u=Symbol(""),H4=()=>ve($u),N4=e=>{e.provide($u,F4)},ui=()=>{const e=document.documentElement;return e.classList.contains("dark")||e.getAttribute("data-theme")==="dark"},Tn={useMaxWidth:!1},V4=e=>({dark:e,background:e?"#1e1e1e":"#fff",primaryColor:e?"#389d70":"#4abf8a",primaryBorderColor:e?"#389d70":"#4abf8a",primaryTextColor:e?"#fff":"#000",secondaryColor:"#ffb500",secondaryBorderColor:e?"#fff":"#000",secondaryTextColor:e?"#ddd":"#333",tertiaryColor:e?"#282828":"#efeef4",tertiaryBorderColor:e?"#bbb":"#242424",tertiaryTextColor:e?"#ddd":"#333",noteBkgColor:e?"#f6d365":"#fff5ad",noteTextColor:"#242424",noteBorderColor:e?"#f6d365":"#333",lineColor:e?"#d3d3d3":"#333",textColor:e?"#fff":"#242424",mainBkg:e?"#389d70":"#4abf8a",errorBkgColor:"#eb4d5d",errorTextColor:"#fff",nodeBorder:e?"#389d70":"#4abf8a",nodeTextColor:e?"#fff":"#242424",signalTextColor:e?"#9e9e9e":"#242424",classText:"#fff",labelColor:"#fff",attributeBackgroundColorEven:e?"#0d1117":"#fff",attributeBackgroundColorOdd:e?"#161b22":"#f8f8f8",fillType0:e?"#cf1322":"#f1636e",fillType1:"#f39c12",fillType2:"#2ecc71",fillType3:"#fa541c",fillType4:"#25a55b",fillType5:"#13c2c2",fillType6:"#096dd9",fillType7:"#aa6fe9"});var j4=M({name:"Mermaid",props:{id:{type:String,required:!0},code:{type:String,required:!0},title:{type:String,default:""}},setup(e){const{themeVariables:t,...n}=H4(),r=xe(),a=w(()=>ya(e.code)),o=z(""),l=z(!1);let i=!1;const c=async()=>{const[{default:f}]=await Promise.all([T(()=>import("./mermaid.core-ChLYKTZm.js").then(p=>p.b8),[]),i?Promise.resolve():(i=!0,new Promise(p=>setTimeout(p,800)))]);f.initialize({theme:"base",themeVariables:{...V4(l.value),...$d(t)?t(l.value):t},flowchart:Tn,sequence:Tn,journey:Tn,gantt:Tn,er:Tn,pie:Tn,...n,startOnLoad:!1}),o.value=(await f.render(e.id,a.value)).svg},u=()=>{const{body:f}=document,p=document.createElement("div");p.classList.add("mermaid-preview"),p.innerHTML=o.value,f.appendChild(p),p.addEventListener("click",()=>{f.removeChild(p)})},d=()=>{const f=`data:image/svg+xml;charset=utf8,${o.value.replace(/<br>/g,"<br />").replace(/%/g,"%25").replace(/"/g,"%22").replace(/'/g,"%27").replace(/&/g,"%26").replace(/#/g,"%23").replace(/{/g,"%7B").replace(/}/g,"%7D").replace(/</g,"%3C").replace(/>/g,"%3E")}`,p=document.createElement("a");p.setAttribute("href",f),p.setAttribute("download",`${e.title?ya(e.title):e.id}.svg`),p.click()};return se(()=>{l.value=ui(),c(),z3(document.documentElement,()=>{l.value=ui()},{attributeFilter:["class","data-theme"],attributes:!0}),ae(l,()=>c())}),()=>[s("div",{class:"mermaid-actions"},[s("button",{class:"preview-button",onClick:()=>u(),title:"preview",innerHTML:'<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 1316 1024" fill="currentColor"><path d="M658.286 0C415.89 0 0 297.106 0 512c0 214.82 415.89 512 658.286 512 242.322 0 658.285-294.839 658.285-512S900.608 0 658.286 0zm0 877.714c-161.573 0-512-221.769-512-365.714 0-144.018 350.427-365.714 512-365.714 161.572 0 512 217.16 512 365.714s-350.428 365.714-512 365.714z"/><path d="M658.286 292.571a219.429 219.429 0 1 0 0 438.858 219.429 219.429 0 0 0 0-438.858zm0 292.572a73.143 73.143 0 1 1 0-146.286 73.143 73.143 0 0 1 0 146.286z"/></svg>'}),s("button",{class:"download-button",onClick:()=>d(),title:"download",innerHTML:'<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 1024 1024" fill="currentColor"><path d="M828.976 894.125H190.189c-70.55 0-127.754-57.185-127.754-127.753V606.674c0-17.634 14.31-31.933 31.933-31.933h63.889c17.634 0 31.932 14.299 31.932 31.933v95.822c0 35.282 28.596 63.877 63.877 63.877h511.033c35.281 0 63.877-28.595 63.877-63.877v-95.822c0-17.634 14.298-31.933 31.943-31.933h63.878c17.635 0 31.933 14.299 31.933 31.933v159.7c0 70.566-57.191 127.751-127.754 127.751zM249.939 267.51c12.921-12.92 33.885-12.92 46.807 0l148.97 148.972V94.893c0-17.634 14.302-31.947 31.934-31.947h63.876c17.638 0 31.946 14.313 31.946 31.947v321.589l148.97-148.972c12.922-12.92 33.876-12.92 46.797 0l46.814 46.818c12.922 12.922 12.922 33.874 0 46.807L552.261 624.93c-1.14 1.138-21.664 13.684-42.315 13.693-20.877.01-41.88-12.542-43.021-13.693L203.122 361.135c-12.923-12.934-12.923-33.885 0-46.807l46.817-46.818z"/></svg>'})]),s("div",{ref:r,class:"mermaid-wrapper"},o.value?s("div",{class:"mermaid-content",innerHTML:o.value}):s(Al,{class:"mermaid-loading",height:96}))]}});const so=cn("VUEPRESS_TAB_STORE",{});var z4=M({name:"Tabs",props:{active:{type:Number,default:0},data:{type:Array,required:!0},id:{type:String,required:!0},tabId:{type:String,default:""}},slots:Object,setup(e,{slots:t}){const n=z(e.active),r=xe([]),a=()=>{e.tabId&&(so.value[e.tabId]=e.data[n.value].id)},o=(u=n.value)=>{n.value=u<r.value.length-1?u+1:0,r.value[n.value].focus()},l=(u=n.value)=>{n.value=u>0?u-1:r.value.length-1,r.value[n.value].focus()},i=(u,d)=>{u.key===" "||u.key==="Enter"?(u.preventDefault(),n.value=d):u.key==="ArrowRight"?(u.preventDefault(),o()):u.key==="ArrowLeft"&&(u.preventDefault(),l()),a()},c=()=>{if(e.tabId){const u=e.data.findIndex(({id:d})=>so.value[e.tabId]===d);if(u!==-1)return u}return e.active};return se(()=>{n.value=c(),ae(()=>so.value[e.tabId],(u,d)=>{if(e.tabId&&u!==d){const f=e.data.findIndex(({id:p})=>p===u);f!==-1&&(n.value=f)}})}),()=>e.data.length?s("div",{class:"vp-tabs"},[s("div",{class:"vp-tabs-nav",role:"tablist"},e.data.map(({id:u},d)=>{const f=d===n.value;return s("button",{type:"button",ref:p=>{p&&(r.value[d]=p)},class:["vp-tab-nav",{active:f}],role:"tab","aria-controls":`tab-${e.id}-${d}`,"aria-selected":f,onClick:()=>{n.value=d,a()},onKeydown:p=>i(p,d)},t[`title${d}`]({value:u,isActive:f}))})),e.data.map(({id:u},d)=>{const f=d===n.value;return s("div",{class:["vp-tab",{active:f}],id:`tab-${e.id}-${d}`,role:"tabpanel","aria-expanded":f},[s("div",{class:"vp-tab-title"},t[`title${d}`]({value:u,isActive:f})),t[`tab${d}`]({value:u,isActive:f})])})]):null}});const q4=Ze({enhance:({app:e})=>{e.component("CodeTabs",Xp),e.component("CodeDemo",M4),e.component("MdDemo",R4),N4(e),e.component("Mermaid",j4),e.component("Tabs",z4)},setup:()=>{$4()}});let G4={};const Fu=Symbol(""),U4=()=>ve(Fu),W4=e=>{e.provide(Fu,G4)},K4='<div class="photo-swipe-loading"><svg xmlns="http://www.w3.org/2000/svg" width="48" height="48" preserveAspectRatio="xMidYMid" viewBox="25 25 50 50"><animateTransform attributeName="transform" type="rotate" dur="2s" keyTimes="0;1" repeatCount="indefinite" values="0;360"></animateTransform><circle cx="50" cy="50" r="20" fill="none" stroke="currentColor" stroke-width="4" stroke-linecap="round"><animate attributeName="stroke-dasharray" dur="1.5s" keyTimes="0;0.5;1" repeatCount="indefinite" values="1,200;90,200;1,200"></animate><animate attributeName="stroke-dashoffset" dur="1.5s" keyTimes="0;0.5;1" repeatCount="indefinite" values="0;-35px;-125px"></animate></circle></svg></div>',J4=e=>we(e)?Array.from(document.querySelectorAll(e)):e.map(t=>Array.from(document.querySelectorAll(t))).flat(),Hu=e=>new Promise((t,n)=>{e.complete?t({type:"image",element:e,src:e.src,width:e.naturalWidth,height:e.naturalHeight,alt:e.alt,msrc:e.src}):(e.onload=()=>t(Hu(e)),e.onerror=r=>n(r))}),Q4=e=>{const{isSupported:t,toggle:n}=yl();e.on("uiRegister",()=>{t.value&&e.ui.registerElement({name:"fullscreen",order:7,isButton:!0,html:'<svg class="pswp__icn" viewBox="0 0 1024 1024" xmlns="http://www.w3.org/2000/svg"><path d="M249.5 270.833H437v-75H212a37.5 37.5 0 0 0-37.5 37.5v225h75v-187.5zm-37.5 600h225v-75H249.5v-187.5h-75v225a37.5 37.5 0 0 0 37.5 37.5zm637.5-37.5v-225h-75v187.5H587v75h225a37.5 37.5 0 0 0 37.5-37.5zM587 270.833h187.5v187.5h75v-225a37.5 37.5 0 0 0-37.5-37.5H587v75z"/></svg>',onClick:()=>{n()}}),e.ui.registerElement({name:"download",order:8,isButton:!0,tagName:"a",html:{isCustomSVG:!0,inner:'<path d="M20.5 14.3 17.1 18V10h-2.2v7.9l-3.4-3.6L10 16l6 6.1 6-6.1-1.5-1.6ZM23 23H9v2h14" id="pswp__icn-download"/>',outlineID:"pswp__icn-download"},onInit:(r,a)=>{r.setAttribute("download",""),r.setAttribute("target","_blank"),r.setAttribute("rel","noopener"),a.on("change",()=>{r.setAttribute("href",a.currSlide.data.src)})}}),e.ui.registerElement({name:"bulletsIndicator",className:"photo-swipe-bullets-indicator",appendTo:"wrapper",onInit:(r,a)=>{const o=[];let l=-1;for(let i=0;i<a.getNumItems();i++){const c=document.createElement("div");c.className="photo-swipe-bullet",c.onclick=u=>{a.goTo(o.indexOf(u.target))},o.push(c),r.appendChild(c)}a.on("change",()=>{l>=0&&o[l].classList.remove("active"),o[a.currIndex].classList.add("active"),l=a.currIndex})}})})},Y4=(e,t,n=!0)=>T(()=>import("./photoswipe.esm-SzV8tJDW.js"),[]).then(({default:r})=>{let a=null;const o=e.map(l=>({html:K4,element:l,msrc:l.src}));return e.forEach((l,i)=>{const c=()=>{a==null||a.destroy(),a=new r({preloaderDelay:0,showHideAnimationType:"zoom",...t,dataSource:o,index:i,...n?{closeOnVerticalDrag:!0,wheelToZoom:!1}:{}}),Q4(a),a.addFilter("thumbEl",()=>l),a.addFilter("placeholderSrc",()=>l.src),a.init()};l.getAttribute("photo-swipe")||(l.style.cursor="zoom-in",l.addEventListener("click",()=>{c()}),l.addEventListener("keypress",({key:u})=>{u==="Enter"&&c()}),l.setAttribute("photo-swipe","")),Hu(l).then(u=>{o.splice(i,1,u),a==null||a.refreshSlideContent(i)})}),n?Se("wheel",()=>{a==null||a.close()}):()=>{}}),Z4=({selector:e,locales:t,delay:n=500,scrollToClose:r=!0})=>{const a=U4(),o=El(t),l=ge(),i=he();let c=null;const u=()=>{const{photoSwipe:d}=i.value;d!==!1&&_t().then(()=>ip(n)).then(async()=>{const f=we(d)?d:e;c=await Y4(J4(f),{...a,...o.value},r)})};se(()=>{u(),ae(()=>l.value.path,()=>{c==null||c(),u()})}),Ft(()=>{c==null||c()})};var X4={"/":{closeTitle:"关闭",downloadTitle:"下载图片",fullscreenTitle:"切换全屏",zoomTitle:"缩放",arrowPrevTitle:"上一个 (左箭头)",arrowNextTitle:"下一个 (右箭头)"}};const e6=".theme-hope-content :not(a) > img:not([no-view])",t6=X4,n6=800,r6=!0,a6=Ze({enhance:({app:e})=>{W4(e)},setup:()=>{Z4({selector:e6,delay:n6,locales:t6,scrollToClose:r6})}}),Tl=e=>{const t=Ye();return w(()=>e[t.value]??{})},o6=(e,t)=>we(e)&&e.startsWith(t),l6=Object.values,s6=()=>s(ie,{name:"heading"},()=>s("path",{d:"M250.4 704.6H64V595.4h202.4l26.2-166.6H94V319.6h214.4L352 64h127.8l-43.6 255.4h211.2L691 64h126.2l-43.6 255.4H960v109.2H756.2l-24.6 166.6H930v109.2H717L672 960H545.8l43.6-255.4H376.6L333 960H206.8l43.6-255.4zm168.4-276L394 595.4h211.2l24.6-166.6h-211z"}));s6.displayName="HeadingIcon";const i6=()=>s(ie,{name:"heart"},()=>s("path",{d:"M1024 358.156C1024 195.698 892.3 64 729.844 64c-86.362 0-164.03 37.218-217.844 96.49C458.186 101.218 380.518 64 294.156 64 131.698 64 0 195.698 0 358.156 0 444.518 37.218 522.186 96.49 576H96l320 320c32 32 64 64 96 64s64-32 96-64l320-320h-.49c59.272-53.814 96.49-131.482 96.49-217.844zM841.468 481.232 517.49 805.49a2981.962 2981.962 0 0 1-5.49 5.48c-1.96-1.95-3.814-3.802-5.49-5.48L182.532 481.234C147.366 449.306 128 405.596 128 358.156 128 266.538 202.538 192 294.156 192c47.44 0 91.15 19.366 123.076 54.532L512 350.912l94.768-104.378C638.696 211.366 682.404 192 729.844 192 821.462 192 896 266.538 896 358.156c0 47.44-19.368 91.15-54.532 123.076z"}));i6.displayName="HeartIcon";const c6=()=>s(ie,{name:"history"},()=>s("path",{d:"M512 1024a512 512 0 1 1 512-512 512 512 0 0 1-512 512zm0-896a384 384 0 1 0 384 384 384 384 0 0 0-384-384zm192 448H512a64 64 0 0 1-64-64V320a64 64 0 0 1 128 0v128h128a64 64 0 0 1 0 128z"}));c6.displayName="HistoryIcon";const u6=()=>s(ie,{name:"title"},()=>s("path",{d:"M512 256c70.656 0 134.656 28.672 180.992 75.008A254.933 254.933 0 0 1 768 512c0 83.968-41.024 157.888-103.488 204.48C688.96 748.736 704 788.48 704 832c0 105.984-86.016 192-192 192-106.048 0-192-86.016-192-192h128a64 64 0 1 0 128 0 64 64 0 0 0-64-64 255.19 255.19 0 0 1-181.056-75.008A255.403 255.403 0 0 1 256 512c0-83.968 41.024-157.824 103.488-204.544C335.04 275.264 320 235.584 320 192A192 192 0 0 1 512 0c105.984 0 192 85.952 192 192H576a64.021 64.021 0 0 0-128 0c0 35.328 28.672 64 64 64zM384 512c0 70.656 57.344 128 128 128s128-57.344 128-128-57.344-128-128-128-128 57.344-128 128z"}));u6.displayName="TitleIcon";const Sl=()=>s(ie,{name:"search"},()=>s("path",{d:"M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"}));Sl.displayName="SearchIcon";const Nu=()=>s("svg",{xmlns:"http://www.w3.org/2000/svg",width:"32",height:"32",preserveAspectRatio:"xMidYMid",viewBox:"0 0 100 100"},[s("circle",{cx:"28",cy:"75",r:"11",fill:"currentColor"},s("animate",{attributeName:"fill-opacity",begin:"0s",dur:"1s",keyTimes:"0;0.2;1",repeatCount:"indefinite",values:"0;1;1"})),s("path",{fill:"none",stroke:"#88baf0","stroke-width":"10",d:"M28 47a28 28 0 0 1 28 28"},s("animate",{attributeName:"stroke-opacity",begin:"0.1s",dur:"1s",keyTimes:"0;0.2;1",repeatCount:"indefinite",values:"0;1;1"})),s("path",{fill:"none",stroke:"#88baf0","stroke-width":"10",d:"M28 25a50 50 0 0 1 50 50"},s("animate",{attributeName:"stroke-opacity",begin:"0.2s",dur:"1s",keyTimes:"0;0.2;1",repeatCount:"indefinite",values:"0;1;1"}))]);Nu.displayName="LoadingIcon";const Vu=({hint:e})=>s("div",{class:"search-pro-result-wrapper loading"},[s(Nu),e]);Vu.displayName="SearchLoading";const d6='<svg width="20" height="20" viewBox="0 0 20 20"><path d="M10 10l5.09-5.09L10 10l5.09 5.09L10 10zm0 0L4.91 4.91 10 10l-5.09 5.09L10 10z" stroke="currentColor" fill="none" fill-rule="evenodd" stroke-linecap="round" stroke-linejoin="round"></path></svg>';var f6={0:{"/":{0:"分",1:"类",2:":",3:" ",4:"$",5:"c",6:"o",7:"n",8:"t",9:"e",10:"n",11:"t"}},1:{"/":{0:"标",1:"签",2:":",3:" ",4:"$",5:"c",6:"o",7:"n",8:"t",9:"e",10:"n",11:"t"}}},p6={"/":{cancel:"取消",placeholder:"搜索",search:"搜索",searching:"搜索中",defaultTitle:"文档",select:"选择",navigate:"切换",autocomplete:"自动补全",exit:"关闭",queryHistory:"搜索历史",resultHistory:"历史结果",emptyHistory:"无搜索历史",emptyResult:"没有找到结果",loading:"正在加载搜索索引..."}},h6={searchDelay:150,suggestDelay:0,queryHistoryCount:5,resultHistoryCount:5,hotKeys:[{key:"k",ctrl:!0},{key:"/",ctrl:!0}],worker:"search-pro.worker.js"};const ba=h6,Y5=f6,ju=ba.hotKeys,xl=p6,io="Canceled because of new search request.",m6=()=>{const e=new Worker(`/${ba.worker}`,{}),t={suggest:null,search:null,all:null};return e.addEventListener("message",({data:n})=>{const[r,a,o]=n,l=t[r];(l==null?void 0:l.id)===a&&l.resolve(o)}),e.addEventListener("error",n=>{console.error("Search Worker error:",n)}),{suggest:(n,r,a)=>new Promise((o,l)=>{var c;(c=t.suggest)==null||c.reject(new Error(io));const i=Date.now();e.postMessage({type:"suggest",id:i,query:n,locale:r,options:a}),t.suggest={id:i,resolve:o,reject:l}}),search:(n,r,a)=>new Promise((o,l)=>{var c;(c=t.search)==null||c.reject(new Error(io));const i=Date.now();e.postMessage({type:"search",id:i,query:n,locale:r,options:a}),t.search={id:i,resolve:o,reject:l}}),all:(n,r,a)=>new Promise((o,l)=>{var c;(c=t.all)==null||c.reject(new Error(io));const i=Date.now();e.postMessage({type:"all",id:i,query:n,locale:r,options:a}),t.all={id:i,resolve:o,reject:l}}),terminate:()=>{e.terminate(),l6(t).forEach(n=>{n==null||n.reject(new Error("Worker has been terminated."))})}}};let v6={};const zu=Symbol(""),qu=()=>{const e=Ye(),{locales:t={},...n}=ve(zu);return w(()=>({...n,...t[e.value]||{}}))},g6=e=>{e.provide(zu,v6)},y6=(e,t=!1)=>{const n=z(0),r=w(()=>e.value[n.value]),a=()=>{n.value=n.value>0?n.value-1:e.value.length-1},o=()=>{n.value=n.value<e.value.length-1?n.value+1:0};return ae(e,()=>{t||(n.value=0)}),{index:n,item:r,prev:a,next:o}},b6=e=>e instanceof Element?document.activeElement===e&&(["TEXTAREA","SELECT","INPUT"].includes(e.tagName)||e.hasAttribute("contenteditable")):!1,E6=e=>ju.some(t=>{const{key:n,ctrl:r=!1,shift:a=!1,alt:o=!1,meta:l=!1}=t;return n===e.key&&r===e.ctrlKey&&a===e.shiftKey&&o===e.altKey&&l===e.metaKey}),_6='<svg width="15" height="15" aria-label="Enter key" role="img"><g fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="1.2"><path d="M12 3.53088v3c0 1-1 2-2 2H4M7 11.53088l-3-3 3-3"></path></g></svg>',w6='<svg width="15" height="15" aria-label="Arrow down" role="img"><g fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="1.2"><path d="M7.5 3.5v8M10.5 8.5l-3 3-3-3"></path></g></svg>',A6='<svg width="15" height="15" aria-label="Arrow up" role="img"><g fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="1.2"><path d="M7.5 11.5v-8M10.5 6.5l-3-3-3 3"></path></g></svg>',C6='<svg width="15" height="15" aria-label="Escape key" role="img"><g fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="1.2"><path d="M13.6167 8.936c-.1065.3583-.6883.962-1.4875.962-.7993 0-1.653-.9165-1.653-2.1258v-.5678c0-1.2548.7896-2.1016 1.653-2.1016.8634 0 1.3601.4778 1.4875 1.0724M9 6c-.1352-.4735-.7506-.9219-1.46-.8972-.7092.0246-1.344.57-1.344 1.2166s.4198.8812 1.3445.9805C8.465 7.3992 8.968 7.9337 9 8.5c.032.5663-.454 1.398-1.4595 1.398C6.6593 9.898 6 9 5.963 8.4851m-1.4748.5368c-.2635.5941-.8099.876-1.5443.876s-1.7073-.6248-1.7073-2.204v-.4603c0-1.0416.721-2.131 1.7073-2.131.9864 0 1.6425 1.031 1.5443 2.2492h-2.956"></path></g></svg>',Ll=Symbol(""),k6=()=>{const e=z(!1);ht(Ll,e)},T6=e=>{const t=z([]);{const n=qu(),r=ge(),a=Ye();se(()=>{const{suggest:o,terminate:l}=m6(),i=c=>{const u=c.join(" "),{searchFilter:d,splitWord:f,suggestionsFilter:p=v=>v,...h}=n.value;u?o(u,a.value,h).then(v=>p(v,u,a.value,r.value)).then(v=>{t.value=v.length?o6(v[0],u)&&!v[0].slice(u.length).includes(" ")?v:[u,...v]:[]}).catch(v=>{console.warn(v)}):t.value=[]};ae([e,a],([c])=>i(c),{immediate:!0}),Ft(()=>{l()})})}return{suggestions:t}},co=ju[0];var S6=M({name:"SearchBox",setup(){const e=Tl(xl),t=ve(Ll),n=z(!1),r=w(()=>co?[(n.value?["⌃","⇧","⌥","⌘"]:["Ctrl","Shift","Alt","Win"]).filter((a,o)=>co[["ctrl","shift","alt","meta"][o]]),co.key.toUpperCase()]:null);return Se("keydown",a=>{!t.value&&E6(a)&&!b6(a.target)&&(a.preventDefault(),t.value=!0)}),se(()=>{const{userAgent:a}=navigator;n.value=d4(a)||u4(a)||c4(a)}),()=>[s("button",{type:"button",class:"search-pro-button","aria-label":e.value.search,onClick:()=>{t.value=!0}},[s(Sl),s("div",{class:"search-pro-placeholder"},e.value.search),r.value?s("div",{class:"search-pro-key-hints"},r.value.map(a=>s("kbd",{class:"search-pro-key"},a))):null])]}});const x6=tc({loader:()=>T(()=>import("./SearchResult-DUP77o_D.js"),[]),loadingComponent:()=>{const e=Tl(xl);return s(Vu,{hint:e.value.loading})}});var L6=M({name:"SearchModal",setup(){const e=ve(Ll),t=Gn(),n=i4(),r=Tl(xl),a=qu(),o=z(""),l=z([]),{suggestions:i}=T6(l),c=z(!1),{index:u,prev:d,next:f}=y6(i),p=xe(),h=xe(),v=(E=u.value)=>{o.value=i.value[E],c.value=!1};Se("keydown",E=>{c.value?E.key==="ArrowUp"?d():E.key==="ArrowDown"?f():E.key==="Enter"?v():E.key==="Escape"&&(c.value=!1):E.key==="Escape"&&(e.value=!1)});const _=ru(()=>{var E,b;(((b=(E=a.value).splitWord)==null?void 0:b.call(E,o.value))??Promise.resolve(o.value.split(" "))).then(C=>{l.value=C})},Math.min(ba.searchDelay,ba.suggestDelay));return ae(o,_,{immediate:!0}),se(()=>{const E=bl(document.body);ae(e,async b=>{var C;E.value=b,b&&(await _t(),(C=p.value)==null||C.focus())}),lu(h,()=>{c.value=!1}),Ft(()=>{E.value=!1})}),()=>e.value?s("div",{class:"search-pro-modal-wrapper"},[s("div",{class:"search-pro-mask",onClick:()=>{e.value=!1,o.value=""}}),s("div",{class:"search-pro-modal"},[s("div",{class:"search-pro-box"},[s("form",[s("label",{for:"search-pro","aria-label":r.value.search},s(Sl)),s("input",{ref:p,type:"search",class:"search-pro-input",id:"search-pro",placeholder:r.value.placeholder,spellcheck:"false",autocapitalize:"off",autocomplete:"off",autocorrect:"off",name:`${t.value.title}-search`,value:o.value,"aria-controls":"search-pro-results",onKeydown:E=>{const{key:b}=E;i.value.length&&(b==="Tab"?(v(),E.preventDefault()):(b==="ArrowDown"||b==="ArrowUp"||b==="Escape")&&E.preventDefault())},onInput:({target:E})=>{o.value=E.value,c.value=!0,u.value=0}}),o.value?s("button",{type:"reset",class:"search-pro-clear-button",innerHTML:d6,onClick:()=>{o.value=""}}):null,c.value&&i.value.length?s("ul",{class:"search-pro-suggestions",ref:h},i.value.map((E,b)=>s("li",{class:["search-pro-suggestion",{active:b===u.value}],onClick:()=>{v(b)}},[s("kbd",{class:"search-pro-auto-complete",title:`Tab ${r.value.autocomplete}`},"Tab"),E]))):null]),s("button",{type:"button",class:"search-pro-close-button",onClick:()=>{e.value=!1,o.value=""}},r.value.cancel)]),s(x6,{queries:l.value,isFocusing:!c.value,onClose:()=>{e.value=!1},onUpdateQuery:E=>{o.value=E}}),n.value?null:s("div",{class:"search-pro-hints"},[s("span",{class:"search-pro-hint"},[s("kbd",{innerHTML:_6}),r.value.select]),s("span",{class:"search-pro-hint"},[s("kbd",{innerHTML:A6}),s("kbd",{innerHTML:w6}),r.value.navigate]),s("span",{class:"search-pro-hint"},[s("kbd",{innerHTML:C6}),r.value.exit])])])]):null}}),B6=Ze({enhance({app:e}){g6(e),e.component("SearchBox",S6)},setup(){k6()},rootComponents:[L6]});const Ve=e=>{const{icon:t="",color:n,size:r}=e,a=n||r?{}:null;return n&&(a.color=n),r&&(a.height=Number.isNaN(Number(r))?r:`${r}px`),sn(t)?s("img",{class:"icon",src:t,alt:"","no-view":"",style:a}):Rr(t)?s("img",{class:"icon",src:be(t),alt:"","aria-hidden":"","no-view":"",style:a}):s(pt("FontIcon"),e)};Ve.displayName="HopeIcon";const I6="http://.",An=()=>{const e=wn(),t=Ht();return n=>{if(n)if(Rr(n))t.path!==n&&e.push(n);else if(La(n))window&&window.open(n);else{const r=t.path.slice(0,t.path.lastIndexOf("/"));e.push(new URL(`${r}/${encodeURI(n)}`,I6).pathname)}}},Gu=()=>{const e=ge();return w(()=>e.value.readingTime??null)},Uu=(e,t)=>{const{minutes:n,words:r}=e,{less1Minute:a,word:o,time:l}=t;return{time:n<1?a:l.replace("$time",Math.round(n).toString()),words:o.replace("$word",r.toString())}};var di={"/":{word:"约 $word 字",less1Minute:"小于 1 分钟",time:"大约 $time 分钟"}};const fi={words:"",time:""},Do=typeof di>"u"?null:di,Wu=()=>Do?El(Do):w(()=>null),P6=()=>{if(typeof Do>"u")return w(()=>fi);const e=Gu(),t=Wu();return w(()=>e.value&&t.value?Uu(e.value,t.value):fi)},Nt=()=>gu(),ce=()=>Ip(),Ku=()=>{const e=ce(),t=he();return w(()=>{const{author:n}=t.value;return n?Cr(n):n===!1?[]:Cr(e.value.author,!1)})},D6=()=>{const e=he(),t=ve(Symbol.for("categoryMap"));return w(()=>Pu(e.value.category??e.value.categories).map(n=>{var r;return{name:n,path:((r=t==null?void 0:t.value.map[n])==null?void 0:r.path)??""}}))},O6=()=>{const e=he(),t=ve(Symbol.for("tagMap"));return w(()=>Du(e.value.tag??e.value.tags).map(n=>{var r;return{name:n,path:((r=t==null?void 0:t.value.map[n])==null?void 0:r.path)??""}}))},M6=()=>{const e=he(),t=ge();return w(()=>{const n=_l(e.value.date);if(n)return n;const{createdTime:r}=t.value.git??{};return r?new Date(r):null})},R6=()=>{const e=ce(),t=ge(),n=he(),r=Ku(),a=D6(),o=O6(),l=M6(),i=Gu(),c=P6(),u=w(()=>({author:r.value,category:a.value,date:l.value,localizedDate:t.value.localizedDate,tag:o.value,isOriginal:n.value.isOriginal??!1,readingTime:i.value,readingTimeLocale:c.value,pageview:"pageview"in n.value?n.value.pageview:!0})),d=w(()=>"pageInfo"in n.value?n.value.pageInfo:"pageInfo"in e.value?e.value.pageInfo:null);return{info:u,items:d}},Cn=()=>{const e=Nt();return w(()=>!!e.value.pure)},$6="719px",F6="1440px",H6="false",Ju={mobileBreakPoint:$6,pcBreakPoint:F6,enableThemeColor:H6},{mobileBreakPoint:N6,pcBreakPoint:V6}=Ju,pi=e=>e.endsWith("px")?Number(e.slice(0,-2)):null,$r=()=>{const e=z(!1),t=z(!1),n=()=>{e.value=window.innerWidth<=(pi(N6)??719),t.value=window.innerWidth>=(pi(V6)??1440)};return Se("resize",n,!1),Se("orientationchange",n,!1),se(()=>{n()}),{isMobile:e,isPC:t}},Qu=Symbol(""),Fr=()=>{const e=ve(Qu);if(!e)throw new Error("useDarkmode() is called without provider.");return e},j6=e=>{const t=Nt(),n=j3(),r=w(()=>t.value.darkmode??"switch"),a=cn("vuepress-theme-hope-scheme","auto"),o=w(()=>{const i=r.value;return i==="disable"?!1:i==="enable"?!0:i==="auto"?n.value:i==="toggle"?a.value==="dark":a.value==="dark"||a.value==="auto"&&n.value}),l=w(()=>{const i=r.value;return i==="switch"||i==="toggle"});e.provide(Qu,{canToggle:l,config:r,isDarkmode:o,status:a}),Object.defineProperties(e.config.globalProperties,{$isDarkmode:{get:()=>o.value}})},z6=()=>{const{config:e,isDarkmode:t,status:n}=Fr();Qi(()=>{e.value==="disable"?n.value="light":e.value==="enable"?n.value="dark":e.value==="toggle"&&n.value==="auto"&&(n.value="light")}),se(()=>{ae(t,r=>document.documentElement.setAttribute("data-theme",r?"dark":"light"),{immediate:!0})})},kr=(e,t,n=!1)=>"activeMatch"in t?new RegExp(t.activeMatch,"u").test(e.path):Lu(e,t.link)?!0:"children"in t&&!n?t.children.some(r=>kr(e,r)):!1,Yu=(e,t)=>t.type==="group"?t.children.some(n=>n.type==="group"?Yu(e,n):n.type==="page"&&kr(e,n,!0))||"prefix"in t&&Lu(e,t.prefix):!1,Bl={"/tech/":["docker","modint","「算术公理系统 1」自然数","android studio换源","cicd",{text:"Design ASimpile CCompiler",prefix:"designASimpileCCompiler/",collapsible:!0,children:["0","1","3","4","5","6","7","8","9","2"]},{text:"Design Patterns",prefix:"DesignPatterns/",collapsible:!0,children:["bridge","builder","chainOfResponsibility","command","composite","decorator","facade","factory_method","flyweight","interpreter","mediator","memento","observer","prototype","proxy","singleton","state","strategy","template_method","visitor","abstractFactory","end","index","DesignPrinciples","iterator","adapter"]},"/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html","steam模组开发","figure_bed","github 工作流","python_requrements","Qt6 Maintence tools不能安装Qt5","程序员的PPT","tensorflow踩坑","vsocde插件开发小记","使用capacitor和ionic将vue项目迁移到mobile端","协程","协程(asyncio)到底需不需要加锁","index","mailserver","闭包实现类","style"],"/essay/":[],"/tutorials/":["typora激活","index"],"/resources/":[{text:"Html2md",prefix:"html2md/",collapsible:!0,children:["index"]},"index"]},q6=(e,t)=>{const n=e.replace(t,"/").split("/"),r=[];let a=pl(t);return n.forEach((o,l)=>{l!==n.length-1?(a+=`${o}/`,r.push({link:a,name:o||"Home"})):o!==""&&(a+=o,r.push({link:a,name:o}))}),r},Oo=e=>!xa(e)&&!La(e);let uo=null,Zn=null;const Mo={wait:()=>uo,pending:()=>{uo=new Promise(e=>{Zn=e})},resolve:()=>{Zn==null||Zn(),uo=null,Zn=null}};var Ue;(function(e){e.title="t",e.shortTitle="s",e.icon="i",e.index="I",e.order="O",e.breadcrumbExclude="b"})(Ue||(Ue={}));var je;(function(e){e.type="y",e.author="a",e.date="d",e.localizedDate="l",e.category="c",e.tag="g",e.isEncrypted="n",e.isOriginal="o",e.readingTime="r",e.excerpt="e",e.sticky="u",e.cover="v"})(je||(je={}));var Ro;(function(e){e.article="a",e.home="h",e.slide="s",e.page="p"})(Ro||(Ro={}));const Il=(e,t=!1,n)=>{const{meta:r,path:a,notFound:o}=vp(e,n);return o?{text:a,link:a}:{text:!t&&r[Ue.shortTitle]?r[Ue.shortTitle]:r[Ue.title]||a,link:a,...r[Ue.icon]?{icon:r[Ue.icon]}:{}}},vn=(e="",t="")=>Rr(t)||La(t)?t:`${Pc(e)}${t}`,$o=({config:e,prefix:t=""})=>{const n=(r,a=t)=>{const o=we(r)?Il(vn(a,r)):r.link?{...r,...Oo(r.link)?{link:xt(vn(a,r.link)).path}:{}}:r;if("children"in o){const l=vn(a,o.prefix),i=o.children==="structure"?Bl[l]:o.children;return{type:"group",...o,prefix:l,children:i.map(c=>n(c,l))}}return{type:"page",...o}};return e.map(r=>n(r))},G6=({config:e,page:t,headerDepth:n})=>{const r=En(e).sort((a,o)=>o.length-a.length);for(const a of r)if(Oa(decodeURI(t.path),a)){const o=e[a];return o?$o({config:o==="structure"?Bl[a]:o,page:t,headerDepth:n,prefix:a}):[]}return console.warn(`${t.path} is missing sidebar config.`),[]},U6=({config:e,routeLocale:t,page:n,headerDepth:r})=>e==="structure"?$o({config:Bl[t],page:n,headerDepth:r,prefix:t}):Po(e)?$o({config:e,page:n,headerDepth:r}):qn(e)?G6({config:e,page:n,headerDepth:r}):[],Zu=Symbol(""),W6=()=>{const e=he(),t=ce(),n=ge(),r=Ye(),a=w(()=>e.value.home?!1:e.value.sidebar??t.value.sidebar??"structure"),o=w(()=>e.value.headerDepth??t.value.headerDepth??2),l=eu(()=>[a.value,o.value,n.value.path,null],()=>U6({config:a.value,routeLocale:r.value,page:n.value,headerDepth:o.value}));ht(Zu,l)},Pl=()=>{const e=ve(Zu);if(!e)throw new Error("useSidebarItems() is called without provider.");return e},K6=M({name:"PageFooter",setup(){const e=Nt(),t=ce(),n=he(),r=Ku(),a=w(()=>{const{copyright:u,footer:d}=n.value;return d!==!1&&!!(u||d||t.value.displayFooter)}),o=w(()=>{const{footer:u}=n.value;return u??t.value.footer}),l=w(()=>r.value.map(({name:u})=>u).join(", ")),i=u=>`Copyright © ${new Date().getFullYear()} ${l.value} ${u?`${u} Licensed`:""}`,c=w(()=>{const{copyright:u,license:d=""}=n.value,{license:f}=e.value,{copyright:p}=t.value;return u??(d?i(d):we(p)?p:l.value||f?i(f):!1)});return()=>a.value?s("footer",{class:"vp-footer-wrapper"},[o.value?s("div",{class:"vp-footer",innerHTML:o.value}):null,c.value?s("div",{class:"vp-copyright",innerHTML:c.value}):null]):null}}),ia=()=>null,Je=M({name:"AutoLink",inheritAttrs:!1,props:{config:{type:Object,required:!0},exact:Boolean,noExternalLinkIcon:Boolean},emits:["focusout"],slots:Object,setup(e,{attrs:t,emit:n,slots:r}){const a=Ht(),o=qc(),l=zn(e,"config"),i=w(()=>sn(l.value.link)),c=w(()=>!i.value&&La(l.value.link)),u=w(()=>l.value.target??(i.value?"_blank":void 0)),d=w(()=>u.value==="_blank"),f=w(()=>!i.value&&!c.value&&!d.value),p=w(()=>l.value.rel??(d.value?"noopener noreferrer":"")),h=w(()=>l.value.ariaLabel??l.value.text),v=w(()=>{if(e.exact)return!1;const E=En(o.value.locales);return E.length?E.every(b=>b!==l.value.link):l.value.link!=="/"}),_=w(()=>f.value?l.value.activeMatch?new RegExp(l.value.activeMatch,"u").test(a.path):v.value?Oa(a.path,l.value.link):a.path===l.value.link:!1);return()=>{const{before:E,after:b,default:C}=r,{text:y,icon:A,link:D}=l.value;return f.value?s(Ie,{to:D,"aria-label":h.value,...t,class:["nav-link",{active:_.value},t.class],onFocusout:()=>n("focusout")},()=>C?C():[E?E():s(Ve,{icon:A}),y,b==null?void 0:b()]):s("a",{href:D,rel:p.value,target:u.value,"aria-label":h.value,...t,class:["nav-link",t.class],onFocusout:()=>n("focusout")},C?C():[E?E():s(Ve,{icon:A}),y,e.noExternalLinkIcon?null:s(mu),b==null?void 0:b()])}}}),J6=M({name:"NavbarDropdownLink",props:{config:{type:Object,required:!0}},slots:Object,setup(e,{slots:t}){const n=ge(),r=zn(e,"config"),a=w(()=>r.value.ariaLabel??r.value.text),o=z(!1);ae(()=>n.value.path,()=>{o.value=!1});const l=i=>{i.detail===0&&(o.value=!o.value)};return()=>{var i;return s("div",{class:["dropdown-wrapper",{open:o.value}]},[s("button",{type:"button",class:"dropdown-title","aria-label":a.value,onClick:l},[((i=t.title)==null?void 0:i.call(t))||s("span",{class:"title"},[s(Ve,{icon:r.value.icon}),e.config.text]),s("span",{class:"arrow"}),s("ul",{class:"nav-dropdown"},r.value.children.map((c,u)=>{const d=u===r.value.children.length-1;return s("li",{class:"dropdown-item"},"children"in c?[s("h4",{class:"dropdown-subtitle"},c.link?s(Je,{config:c,onFocusout:()=>{c.children.length===0&&d&&(o.value=!1)}}):s("span",c.text)),s("ul",{class:"dropdown-subitem-wrapper"},c.children.map((f,p)=>s("li",{class:"dropdown-subitem"},s(Je,{config:f,onFocusout:()=>{p===c.children.length-1&&d&&(o.value=!1)}}))))]:s(Je,{config:c,onFocusout:()=>{d&&(o.value=!1)}}))}))])])}}}),Xu=(e,t="")=>we(e)?Il(vn(t,e)):"children"in e?{...e,...e.link&&Oo(e.link)?{link:xt(vn(t,e.link)).path}:{},children:e.children.map(n=>Xu(n,vn(t,e.prefix)))}:{...e,link:Oo(e.link)?xt(vn(t,e.link)).path:e.link},e1=()=>{const e=ce(),t=()=>(e.value.navbar||[]).map(r=>Xu(r));return eu(()=>e.value.navbar,()=>t())},Q6=()=>{const e=ce(),t=w(()=>e.value.repo),n=w(()=>t.value?r4(t.value):null),r=w(()=>t.value?Cl(t.value):null),a=w(()=>n.value?e.value.repoLabel??r.value??"Source":null);return w(()=>!n.value||!a.value||e.value.repoDisplay===!1?null:{type:r.value??"Source",label:a.value,link:n.value})},Y6=M({name:"NavScreenDropdown",props:{config:{type:Object,required:!0}},setup(e){const t=ge(),n=zn(e,"config"),r=w(()=>n.value.ariaLabel??n.value.text),a=z(!1);ae(()=>t.value.path,()=>{a.value=!1});const o=(l,i)=>i[i.length-1]===l;return()=>[s("button",{type:"button",class:["nav-screen-dropdown-title",{active:a.value}],"aria-label":r.value,onClick:()=>{a.value=!a.value}},[s("span",{class:"title"},[s(Ve,{icon:n.value.icon}),e.config.text]),s("span",{class:["arrow",a.value?"down":"end"]})]),s("ul",{class:["nav-screen-dropdown",{hide:!a.value}]},n.value.children.map(l=>s("li",{class:"dropdown-item"},"children"in l?[s("h4",{class:"dropdown-subtitle"},l.link?s(Je,{config:l,onFocusout:()=>{o(l,n.value.children)&&l.children.length===0&&(a.value=!1)}}):s("span",l.text)),s("ul",{class:"dropdown-subitem-wrapper"},l.children.map(i=>s("li",{class:"dropdown-subitem"},s(Je,{config:i,onFocusout:()=>{o(i,l.children)&&o(l,n.value.children)&&(a.value=!1)}}))))]:s(Je,{config:l,onFocusout:()=>{o(l,n.value.children)&&(a.value=!1)}}))))]}}),Z6=M({name:"NavScreenLinks",setup(){const e=e1();return()=>e.value.length?s("nav",{class:"nav-screen-links"},e.value.map(t=>s("div",{class:"navbar-links-item"},"children"in t?s(Y6,{config:t}):s(Je,{config:t})))):null}}),t1=()=>s(ie,{name:"dark"},()=>s("path",{d:"M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"}));t1.displayName="DarkIcon";const n1=()=>s(ie,{name:"light"},()=>s("path",{d:"M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"}));n1.displayName="LightIcon";const r1=()=>s(ie,{name:"auto"},()=>s("path",{d:"M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"}));r1.displayName="AutoIcon";const a1=()=>s(ie,{name:"enter-fullscreen"},()=>s("path",{d:"M762.773 90.24h-497.28c-96.106 0-174.4 78.293-174.4 174.4v497.28c0 96.107 78.294 174.4 174.4 174.4h497.28c96.107 0 175.04-78.293 174.4-174.4V264.64c0-96.213-78.186-174.4-174.4-174.4zm-387.2 761.173H215.04c-21.867 0-40.427-17.92-41.067-41.066V649.92c0-22.507 17.92-40.427 40.427-40.427 11.307 0 21.227 4.694 28.48 11.947 7.253 7.253 11.947 17.92 11.947 28.48v62.293l145.28-145.28c15.893-15.893 41.813-15.893 57.706 0 15.894 15.894 15.894 41.814 0 57.707l-145.28 145.28h62.294c22.506 0 40.426 17.92 40.426 40.427s-17.173 41.066-39.68 41.066zM650.24 165.76h160.427c21.866 0 40.426 17.92 41.066 41.067v160.426c0 22.507-17.92 40.427-40.426 40.427-11.307 0-21.227-4.693-28.48-11.947-7.254-7.253-11.947-17.92-11.947-28.48v-62.186L625.6 450.347c-15.893 15.893-41.813 15.893-57.707 0-15.893-15.894-15.893-41.814 0-57.707l145.28-145.28H650.88c-22.507 0-40.427-17.92-40.427-40.427s17.174-41.173 39.787-41.173z"}));a1.displayName="EnterFullScreenIcon";const o1=()=>s(ie,{name:"cancel-fullscreen"},()=>s("path",{d:"M778.468 78.62H247.922c-102.514 0-186.027 83.513-186.027 186.027V795.08c0 102.514 83.513 186.027 186.027 186.027h530.432c102.514 0 186.71-83.513 186.026-186.027V264.647C964.494 162.02 880.981 78.62 778.468 78.62zM250.88 574.35h171.122c23.324 0 43.122 19.115 43.804 43.805v171.121c0 24.008-19.114 43.122-43.122 43.122-12.06 0-22.641-5.006-30.378-12.743s-12.743-19.115-12.743-30.379V722.83L224.597 877.91c-16.953 16.952-44.6 16.952-61.553 0-16.953-16.954-16.953-44.602 0-61.554L318.009 661.39h-66.446c-24.007 0-43.122-19.114-43.122-43.122 0-24.12 18.432-43.918 42.439-43.918zm521.899-98.873H601.657c-23.325 0-43.122-19.114-43.805-43.804V260.55c0-24.007 19.115-43.122 43.122-43.122 12.06 0 22.642 5.007 30.379 12.743s12.743 19.115 12.743 30.38v66.445l154.965-154.965c16.953-16.953 44.601-16.953 61.554 0 16.953 16.953 16.953 44.6 0 61.554L705.536 388.55h66.446c24.007 0 43.122 19.115 43.122 43.122.114 24.007-18.318 43.804-42.325 43.804z"}));o1.displayName="CancelFullScreenIcon";const l1=()=>s(ie,{name:"outlook"},()=>[s("path",{d:"M224 800c0 9.6 3.2 44.8 6.4 54.4 6.4 48-48 76.8-48 76.8s80 41.6 147.2 0 134.4-134.4 38.4-195.2c-22.4-12.8-41.6-19.2-57.6-19.2C259.2 716.8 227.2 761.6 224 800zM560 675.2l-32 51.2c-51.2 51.2-83.2 32-83.2 32 25.6 67.2 0 112-12.8 128 25.6 6.4 51.2 9.6 80 9.6 54.4 0 102.4-9.6 150.4-32l0 0c3.2 0 3.2-3.2 3.2-3.2 22.4-16 12.8-35.2 6.4-44.8-9.6-12.8-12.8-25.6-12.8-41.6 0-54.4 60.8-99.2 137.6-99.2 6.4 0 12.8 0 22.4 0 12.8 0 38.4 9.6 48-25.6 0-3.2 0-3.2 3.2-6.4 0-3.2 3.2-6.4 3.2-6.4 6.4-16 6.4-16 6.4-19.2 9.6-35.2 16-73.6 16-115.2 0-105.6-41.6-198.4-108.8-268.8C704 396.8 560 675.2 560 675.2zM224 419.2c0-28.8 22.4-51.2 51.2-51.2 28.8 0 51.2 22.4 51.2 51.2 0 28.8-22.4 51.2-51.2 51.2C246.4 470.4 224 448 224 419.2zM320 284.8c0-22.4 19.2-41.6 41.6-41.6 22.4 0 41.6 19.2 41.6 41.6 0 22.4-19.2 41.6-41.6 41.6C339.2 326.4 320 307.2 320 284.8zM457.6 208c0-12.8 12.8-25.6 25.6-25.6 12.8 0 25.6 12.8 25.6 25.6 0 12.8-12.8 25.6-25.6 25.6C470.4 233.6 457.6 220.8 457.6 208zM128 505.6C128 592 153.6 672 201.6 736c28.8-60.8 112-60.8 124.8-60.8-16-51.2 16-99.2 16-99.2l316.8-422.4c-48-19.2-99.2-32-150.4-32C297.6 118.4 128 291.2 128 505.6zM764.8 86.4c-22.4 19.2-390.4 518.4-390.4 518.4-22.4 28.8-12.8 76.8 22.4 99.2l9.6 6.4c35.2 22.4 80 12.8 99.2-25.6 0 0 6.4-12.8 9.6-19.2 54.4-105.6 275.2-524.8 288-553.6 6.4-19.2-3.2-32-19.2-32C777.6 76.8 771.2 80 764.8 86.4z"})]);l1.displayName="OutlookIcon";const s1=M({name:"AppearanceSwitch",setup(){const{config:e,isDarkmode:t,status:n}=Fr(),r=Cn(),a=()=>{e.value==="switch"?n.value={light:"dark",dark:"auto",auto:"light"}[n.value]:n.value=n.value==="light"?"dark":"light"},o=async l=>{if(!(document.startViewTransition&&!window.matchMedia("(prefers-reduced-motion: reduce)").matches&&!r.value)||!l){a();return}const c=l.clientX,u=l.clientY,d=Math.hypot(Math.max(c,innerWidth-c),Math.max(u,innerHeight-u)),f=t.value;await document.startViewTransition(async()=>{a(),await _t()}).ready,t.value!==f&&document.documentElement.animate({clipPath:t.value?[`circle(${d}px at ${c}px ${u}px)`,`circle(0px at ${c}px ${u}px)`]:[`circle(0px at ${c}px ${u}px)`,`circle(${d}px at ${c}px ${u}px)`]},{duration:400,pseudoElement:t.value?"::view-transition-old(root)":"::view-transition-new(root)"})};return()=>s("button",{type:"button",id:"appearance-switch",onClick:o},[s(r1,{style:{display:n.value==="auto"?"block":"none"}}),s(t1,{style:{display:n.value==="dark"?"block":"none"}}),s(n1,{style:{display:n.value==="light"?"block":"none"}})])}}),X6=M({name:"AppearanceMode",setup(){const e=ce(),{canToggle:t}=Fr(),n=w(()=>e.value.outlookLocales.darkmode);return()=>t.value?s("div",{class:"appearance-wrapper"},[s("label",{class:"appearance-title",for:"appearance-switch"},n.value),s(s1)]):null}}),fo=Ju.enableThemeColor==="true",i1=M({name:"ToggleFullScreenButton",setup(){const e=ce(),{isSupported:t,isFullscreen:n,toggle:r}=yl(),a=w(()=>e.value.outlookLocales.fullscreen);return()=>t?s("div",{class:"full-screen-wrapper"},[s("label",{class:"full-screen-title",for:"full-screen-switch"},a.value),s("button",{type:"button",id:"full-screen-switch",class:"full-screen",ariaPressed:n.value,onClick:()=>r()},n.value?s(o1):s(a1))]):null}}),c1=M({name:"OutlookSettings",setup(){const e=Nt(),t=Cn(),n=w(()=>!t.value&&e.value.fullscreen);return()=>s(Or,()=>[null,s(X6),n.value?s(i1):null])}}),e8=M({name:"NavScreen",props:{show:Boolean},emits:["close"],slots:Object,setup(e,{emit:t,slots:n}){const r=ge(),{isMobile:a}=$r(),o=xe(),l=bl(o);return se(()=>{o.value=document.body,ae(a,i=>{!i&&e.show&&(l.value=!1,t("close"))}),ae(()=>r.value.path,()=>{l.value=!1,t("close")})}),Ft(()=>{l.value=!1}),()=>s(Rt,{name:"fade",onEnter:()=>{l.value=!0},onAfterLeave:()=>{l.value=!1}},()=>{var i,c;return e.show?s("div",{id:"nav-screen"},s("div",{class:"vp-nav-screen-container"},[(i=n.before)==null?void 0:i.call(n),s(Z6),s("div",{class:"vp-outlook-wrapper"},s(c1)),(c=n.after)==null?void 0:c.call(n)])):null})}}),t8=M({name:"NavbarBrand",setup(){const e=Ye(),t=Gn(),n=ce(),r=w(()=>n.value.home||e.value),a=w(()=>t.value.title),o=w(()=>n.value.navbarTitle??a.value),l=w(()=>n.value.logo?be(n.value.logo):null),i=w(()=>n.value.logoDark?be(n.value.logoDark):null);return()=>s(Ie,{to:r.value,class:"vp-brand"},()=>[l.value?s("img",{class:["vp-nav-logo",{light:!!i.value}],src:l.value,alt:""}):null,i.value?s("img",{class:["vp-nav-logo dark"],src:i.value,alt:""}):null,o.value?s("span",{class:["vp-site-name",{"hide-in-pad":l.value&&(n.value.hideSiteNameOnMobile??!0)}]},o.value):null])}}),n8=M({name:"NavbarLinks",setup(){const e=e1();return()=>e.value.length?s("nav",{class:"vp-nav-links"},e.value.map(t=>s("div",{class:"vp-nav-item hide-in-mobile"},"children"in t?s(J6,{config:t}):s(Je,{config:t})))):null}}),r8=M({name:"RepoLink",setup(){const e=Q6();return()=>e.value?s("div",{class:"vp-nav-item vp-action"},s("a",{class:"vp-action-link",href:e.value.link,target:"_blank",rel:"noopener noreferrer","aria-label":e.value.label},s(a4,{type:e.value.type,style:{width:"1.25rem",height:"1.25rem",verticalAlign:"middle"}}))):null}}),u1=({active:e=!1},{emit:t})=>s("button",{type:"button",class:["vp-toggle-navbar-button",{"is-active":e}],"aria-label":"Toggle Navbar","aria-expanded":e,"aria-controls":"nav-screen",onClick:()=>t("toggle")},s("span",[s("span",{class:"vp-top"}),s("span",{class:"vp-middle"}),s("span",{class:"vp-bottom"})]));u1.displayName="ToggleNavbarButton";const Dl=(e,{emit:t})=>s("button",{type:"button",class:"vp-toggle-sidebar-button",title:"Toggle Sidebar",onClick:()=>t("toggle")},s("span",{class:"icon"}));Dl.displayName="ToggleSidebarButton";Dl.emits=["toggle"];const a8=M({name:"OutlookButton",setup(){const{isSupported:e}=yl(),t=Nt(),n=Cn(),r=ge(),{canToggle:a}=Fr(),o=z(!1),l=w(()=>!n.value&&t.value.fullscreen&&e);return ae(()=>r.value.path,()=>{o.value=!1}),()=>a.value||l.value||fo?s("div",{class:"vp-nav-item hide-in-mobile"},a.value&&!l.value&&!fo?s(s1):l.value&&!a.value&&!fo?s(i1):s("button",{type:"button",class:["outlook-button",{open:o.value}],tabindex:"-1","aria-hidden":!0},[s(l1),s("div",{class:"outlook-dropdown"},s(c1))])):null}}),o8=M({name:"NavBar",emits:["toggleSidebar"],slots:Object,setup(e,{emit:t,slots:n}){const r=ce(),{isMobile:a}=$r(),o=z(!1),l=w(()=>{const{navbarAutoHide:d="mobile"}=r.value;return d!=="none"&&(d==="always"||a.value)}),i=w(()=>r.value.navbarLayout??{start:["Brand"],center:["Links"],end:["Language","Repo","Outlook","Search"]}),c={Brand:t8,Language:ia,Links:n8,Repo:r8,Outlook:a8,Search:Mn("Docsearch")?pt("Docsearch"):Mn("SearchBox")?pt("SearchBox"):ia},u=d=>c[d]??(Mn(d)?pt(d):ia);return()=>{var d,f,p,h,v,_,E,b,C;return[s("header",{key:"navbar",id:"navbar",class:["vp-navbar",{"auto-hide":l.value}]},[s("div",{class:"vp-navbar-start"},[s(Dl,{onToggle:()=>{o.value&&(o.value=!1),t("toggleSidebar")}}),(d=n.startBefore)==null?void 0:d.call(n),(f=i.value.start)==null?void 0:f.map(y=>s(u(y))),(p=n.startAfter)==null?void 0:p.call(n)]),s("div",{class:"vp-navbar-center"},[(h=n.centerBefore)==null?void 0:h.call(n),(v=i.value.center)==null?void 0:v.map(y=>s(u(y))),(_=n.centerAfter)==null?void 0:_.call(n)]),s("div",{class:"vp-navbar-end"},[(E=n.endBefore)==null?void 0:E.call(n),(b=i.value.end)==null?void 0:b.map(y=>s(u(y))),(C=n.endAfter)==null?void 0:C.call(n),s(u1,{active:o.value,onToggle:()=>{o.value=!o.value}})])]),s(e8,{show:o.value,onClose:()=>{o.value=!1}},{before:()=>{var y;return(y=n.screenTop)==null?void 0:y.call(n)},after:()=>{var y;return(y=n.screenBottom)==null?void 0:y.call(n)}})]}}}),l8=M({name:"SidebarChild",props:{config:{type:Object,required:!0}},setup(e){const t=Ht();return()=>we(e.config.link)?s(Je,{class:["vp-sidebar-link","vp-sidebar-page",{active:kr(t,e.config,!0)}],exact:!0,config:e.config}):s("p",e,[s(Ve,{icon:e.config.icon}),e.config.text])}}),s8=M({name:"SidebarGroup",props:{config:{type:Object,required:!0},open:{type:Boolean,required:!0}},emits:["toggle"],setup(e,{emit:t}){const n=Ht(),r=w(()=>kr(n,e.config)),a=w(()=>kr(n,e.config,!0));return()=>{const{collapsible:o,children:l=[],icon:i,prefix:c,link:u,text:d}=e.config;return s("section",{class:"vp-sidebar-group"},[s(o?"button":"p",{class:["vp-sidebar-header",{clickable:o||u,exact:a.value,active:r.value}],...o?{type:"button",onClick:()=>t("toggle"),onKeydown:f=>{f.key==="Enter"&&t("toggle")}}:{}},[s(Ve,{icon:i}),u?s(Je,{class:"vp-sidebar-title",config:{text:d,link:u},noExternalLinkIcon:!0}):s("span",{class:"vp-sidebar-title"},d),o?s("span",{class:["vp-arrow",e.open?"down":"end"]}):null]),e.open||!o?s(d1,{key:c,config:l}):null])}}}),d1=M({name:"SidebarLinks",props:{config:{type:Array,required:!0}},setup(e){const t=Ht(),n=z(-1),r=a=>{n.value=a===n.value?-1:a};return ae(()=>t.path,()=>{const a=e.config.findIndex(o=>Yu(t,o));n.value=a},{immediate:!0,flush:"post"}),()=>s("ul",{class:"vp-sidebar-links"},e.config.map((a,o)=>s("li",a.type==="group"?s(s8,{config:a,open:o===n.value,onToggle:()=>r(o)}):s(l8,{config:a}))))}}),i8=M({name:"SideBar",slots:Object,setup(e,{slots:t}){const n=Ht(),r=Pl(),a=xe();return se(()=>{ae(()=>n.hash,o=>{const l=document.querySelector(`.vp-sidebar a.vp-sidebar-link[href="${n.path}${o}"]`);if(!l)return;const{top:i,height:c}=a.value.getBoundingClientRect(),{top:u,height:d}=l.getBoundingClientRect();u<i?l.scrollIntoView(!0):u+d>i+c&&l.scrollIntoView(!1)},{immediate:!0})}),()=>{var o,l,i;return s("aside",{ref:a,key:"sidebar",id:"sidebar",class:"vp-sidebar"},[(o=t.top)==null?void 0:o.call(t),((l=t.default)==null?void 0:l.call(t))??s(d1,{config:r.value}),(i=t.bottom)==null?void 0:i.call(t)])}}}),Ol=M({name:"CommonWrapper",props:{containerClass:{type:String,default:""},noNavbar:Boolean,noSidebar:Boolean,noToc:Boolean},slots:Object,setup(e,{slots:t}){const n=wn(),r=he(),a=ce(),{isMobile:o,isPC:l}=$r(),[i,c]=wr(!1),[u,d]=wr(!1),f=Pl(),p=z(!1),h=w(()=>e.noNavbar||r.value.navbar===!1||a.value.navbar===!1?!1:!!(a.value.logo??a.value.repo??a.value.navbar)),v=w(()=>e.noSidebar?!1:r.value.sidebar!==!1&&f.value.length!==0&&!r.value.home),_=w(()=>!e.noToc&&!r.value.home&&(r.value.toc??a.value.toc??!0)),E={x:0,y:0},b=A=>{E.x=A.changedTouches[0].clientX,E.y=A.changedTouches[0].clientY},C=A=>{const D=A.changedTouches[0].clientX-E.x,P=A.changedTouches[0].clientY-E.y;Math.abs(D)>Math.abs(P)*1.5&&Math.abs(D)>40&&(D>0&&E.x<=80?c(!0):c(!1))};let y=0;return Se("scroll",x3(()=>{const A=window.scrollY;A<=58||A<y?p.value=!1:y+200<A&&!i.value&&(p.value=!0),y=A},300,!0)),ae(o,A=>{A||c(!1)}),se(()=>{const A=bl(document.body);ae(i,P=>{A.value=P});const D=n.afterEach(()=>{c(!1)});Ft(()=>{A.value=!1,D()})}),()=>s(Mn("GlobalEncrypt")?pt("GlobalEncrypt"):Au,()=>s("div",{class:["theme-container",{"no-navbar":!h.value,"no-sidebar":!v.value&&!t.sidebar&&!t.sidebarTop&&!t.sidebarBottom,"has-toc":_.value,"hide-navbar":p.value,"sidebar-collapsed":!o.value&&!l.value&&u.value,"sidebar-open":o.value&&i.value},e.containerClass,r.value.containerClass??""],onTouchStart:b,onTouchEnd:C},[h.value?s(o8,{onToggleSidebar:()=>c()},{startBefore:()=>{var A;return(A=t.navbarStartBefore)==null?void 0:A.call(t)},startAfter:()=>{var A;return(A=t.navbarStartAfter)==null?void 0:A.call(t)},centerBefore:()=>{var A;return(A=t.navbarCenterBefore)==null?void 0:A.call(t)},centerAfter:()=>{var A;return(A=t.navbarCenterAfter)==null?void 0:A.call(t)},endBefore:()=>{var A;return(A=t.navbarEndBefore)==null?void 0:A.call(t)},endAfter:()=>{var A;return(A=t.navbarEndAfter)==null?void 0:A.call(t)},screenTop:()=>{var A;return(A=t.navScreenTop)==null?void 0:A.call(t)},screenBottom:()=>{var A;return(A=t.navScreenBottom)==null?void 0:A.call(t)}}):null,s(Rt,{name:"fade"},()=>i.value?s("div",{class:"vp-sidebar-mask",onClick:()=>c(!1)}):null),s(Rt,{name:"fade"},()=>o.value?null:s("div",{class:"toggle-sidebar-wrapper",onClick:()=>d()},s("span",{class:["arrow",u.value?"end":"start"]}))),s(i8,{},{...t.sidebar?{default:()=>t.sidebar()}:{},top:()=>{var A;return(A=t.sidebarTop)==null?void 0:A.call(t)},bottom:()=>{var A;return(A=t.sidebarBottom)==null?void 0:A.call(t)}}),t.default(),s(K6)]))}}),Fo=(e,{slots:t})=>{var f,p;const{bgImage:n,bgImageDark:r,bgImageStyle:a,color:o,description:l,image:i,imageDark:c,header:u,features:d=[]}=e;return s("div",{class:"vp-feature-wrapper"},[n?s("div",{class:["vp-feature-bg",{light:r}],style:[{"background-image":`url(${n})`},a]}):null,r?s("div",{class:"vp-feature-bg dark",style:[{"background-image":`url(${r})`},a]}):null,s("div",{class:"vp-feature",style:o?{color:o}:{}},[((f=t.image)==null?void 0:f.call(t,e))??[i?s("img",{class:["vp-feature-image",{light:c}],src:be(i),alt:""}):null,c?s("img",{class:"vp-feature-image dark",src:be(c),alt:""}):null],((p=t.info)==null?void 0:p.call(t,e))??[u?s("h2",{class:"vp-feature-header"},u):null,l?s("p",{class:"vp-feature-description",innerHTML:l}):null],d.length?s("div",{class:"vp-features"},d.map(({icon:h,title:v,details:_,link:E})=>{const b=[s("h3",{class:"vp-feature-title"},[s(Ve,{icon:h}),s("span",{innerHTML:v})]),s("p",{class:"vp-feature-details",innerHTML:_})];return E?xa(E)?s("a",{class:"vp-feature-item link",href:E,"aria-label":v,target:"_blank"},b):s(Ie,{class:"vp-feature-item link",to:E,"aria-label":v},()=>b):s("div",{class:"vp-feature-item"},b)})):null])])};Fo.displayName="FeaturePanel";const oe=M({name:"DropTransition",props:{type:{type:String,default:"single"},delay:{type:Number,default:0},duration:{type:Number,default:.25},appear:Boolean},slots:Object,setup(e,{slots:t}){const n=a=>{a.style.transition=`transform ${e.duration}s ease-in-out ${e.delay}s, opacity ${e.duration}s ease-in-out ${e.delay}s`,a.style.transform="translateY(-20px)",a.style.opacity="0"},r=a=>{a.style.transform="translateY(0)",a.style.opacity="1"};return()=>{const a={name:"drop",appear:e.appear,onAppear:n,onAfterAppear:r,onEnter:n,onAfterEnter:r,onBeforeLeave:n},o=()=>t.default();return e.type==="group"?s(bd,a,o):s(Rt,a,o)}}}),Ml=(e,{slots:t})=>s(Rt,{name:"fade-slide-y",mode:"out-in",onBeforeEnter:Mo.resolve,onBeforeLeave:Mo.pending},()=>{var n;return(n=t.default)==null?void 0:n.call(t)});Ml.displayName="FadeSlideY";const c8=M({name:"HeroInfo",slots:Object,setup(e,{slots:t}){const n=he(),r=Gn(),a=w(()=>n.value.heroFullScreen??!1),o=w(()=>{const{heroText:u,tagline:d}=n.value;return{text:u??r.value.title??"Hello",tagline:d??r.value.description??"",isFullScreen:a.value}}),l=w(()=>{const{heroText:u,heroImage:d,heroImageDark:f,heroAlt:p,heroImageStyle:h}=n.value;return{image:d?be(d):null,imageDark:f?be(f):null,imageStyle:h,alt:p??u??"",isFullScreen:a.value}}),i=w(()=>{const{bgImage:u,bgImageDark:d,bgImageStyle:f}=n.value;return{image:we(u)?be(u):null,imageDark:we(d)?be(d):null,bgStyle:f,isFullScreen:a.value}}),c=w(()=>n.value.actions??[]);return()=>{var u,d,f;return s("header",{class:["vp-hero-info-wrapper",{fullscreen:a.value}]},[((u=t.bg)==null?void 0:u.call(t,i.value))??[i.value.image?s("div",{class:["vp-hero-mask",{light:i.value.imageDark}],style:[{"background-image":`url(${i.value.image})`},i.value.bgStyle]}):null,i.value.imageDark?s("div",{class:"vp-hero-mask dark",style:[{"background-image":`url(${i.value.imageDark})`},i.value.bgStyle]}):null],s("div",{class:"vp-hero-info"},[((d=t.logo)==null?void 0:d.call(t,l.value))??s(oe,{appear:!0,type:"group"},()=>{const{image:p,imageDark:h,imageStyle:v,alt:_}=l.value;return[p?s("img",{key:"light",class:["vp-hero-image",{light:h}],style:v,src:p,alt:_}):null,h?s("img",{key:"dark",class:"vp-hero-image dark",style:v,src:h,alt:_}):null]}),((f=t.info)==null?void 0:f.call(t,o.value))??s("div",{class:"vp-hero-infos"},[o.value.text?s(oe,{appear:!0,delay:.04},()=>s("h1",{id:"main-title"},o.value.text)):null,o.value.tagline?s(oe,{appear:!0,delay:.08},()=>s("p",{id:"main-description",innerHTML:o.value.tagline})):null,c.value.length?s(oe,{appear:!0,delay:.12},()=>s("p",{class:"vp-hero-actions"},c.value.map(p=>s(Je,{class:["vp-hero-action",p.type??"default"],config:p,noExternalLinkIcon:!0},p.icon?{before:()=>s(Ve,{icon:p.icon})}:{})))):null])])])}}}),f1=(e,{slots:t})=>{var p,h,v;const{bgImage:n,bgImageDark:r,bgImageStyle:a,color:o,description:l,image:i,imageDark:c,header:u,highlights:d=[],type:f="un-order"}=e;return s("div",{class:"vp-highlight-wrapper",style:o?{color:o}:{}},[n?s("div",{class:["vp-highlight-bg",{light:r}],style:[{"background-image":`url(${n})`},a]}):null,r?s("div",{class:"vp-highlight-bg dark",style:[{"background-image":`url(${r})`},a]}):null,s("div",{class:"vp-highlight"},[((p=t.image)==null?void 0:p.call(t,e))??[i?s("img",{class:["vp-highlight-image",{light:c}],src:be(i),alt:""}):null,c?s("img",{class:"vp-highlight-image dark",src:be(c),alt:""}):null],((h=t.info)==null?void 0:h.call(t,e))??[s("div",{class:"vp-highlight-info-wrapper"},s("div",{class:"vp-highlight-info"},[u?s("h2",{class:"vp-highlight-header",innerHTML:u}):null,l?s("p",{class:"vp-highlight-description",innerHTML:l}):null,((v=t.highlights)==null?void 0:v.call(t,d))??s(f==="order"?"ol":f==="no-order"?"dl":"ul",{class:"vp-highlights"},d.map(({icon:_,title:E,details:b,link:C})=>{const y=[s(f==="no-order"?"dt":"h3",{class:"vp-highlight-title"},[_?s(Ve,{class:"vp-highlight-icon",icon:_}):null,s("span",{innerHTML:E})]),b?s(f==="no-order"?"dd":"p",{class:"vp-highlight-details",innerHTML:b}):null];return s(f==="no-order"?"div":"li",{class:["vp-highlight-item-wrapper",{link:C}]},C?xa(C)?s("a",{class:"vp-highlight-item link",href:C,"aria-label":E,target:"_blank"},y):s(Ie,{class:"vp-highlight-item link",to:C,"aria-label":E},()=>y):s("div",{class:"vp-highlight-item"},y))}))]))]])])};f1.displayName="HighlightPanel";const Wn=({custom:e})=>s(Uc,{class:["theme-hope-content",{custom:e}]});Wn.displayName="MarkdownContent";Wn.props={custom:Boolean};const u8=M({name:"HomePage",slots:Object,setup(e,{slots:t}){const n=Cn(),r=he(),a=w(()=>{const{features:l}=r.value;return Po(l)?l:null}),o=w(()=>{const{highlights:l}=r.value;return Po(l)?l:null});return()=>{var l,i,c,u;return s("main",{id:"main-content",class:["vp-project-home ",{pure:n.value}],"aria-labelledby":r.value.heroText===null?"":"main-title"},[(l=t.top)==null?void 0:l.call(t),s(c8),((i=o.value)==null?void 0:i.map(d=>"features"in d?s(Fo,d):s(f1,d)))??(a.value?s(oe,{appear:!0,delay:.24},()=>s(Fo,{features:a.value})):null),(c=t.center)==null?void 0:c.call(t),s(oe,{appear:!0,delay:.32},()=>s(Wn)),(u=t.bottom)==null?void 0:u.call(t)])}}}),d8={category:{"/":{path:"/category/",map:{"build-tools":{path:"/category/build-tools/",indexes:[0]},"CI/CD":{path:"/category/cicd/",indexes:[1]},nginx:{path:"/category/nginx/",indexes:[2]},奇技淫巧:{path:"/category/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/",indexes:[3]},docker:{path:"/category/docker/",indexes:[3]},OI:{path:"/category/oi/",indexes:[4,5]},python:{path:"/category/python/",indexes:[6]},风格:{path:"/category/%E9%A3%8E%E6%A0%BC/",indexes:[7]},数学:{path:"/category/%E6%95%B0%E5%AD%A6/",indexes:[8]},设计模式:{path:"/category/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/",indexes:[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34]},编译原理:{path:"/category/%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86/",indexes:[35,36,37,38,39,40,41,42]}}}},tag:{"/":{path:"/tag/",map:{"CI/CD":{path:"/tag/cicd/",indexes:[1]},部署:{path:"/tag/%E9%83%A8%E7%BD%B2/",indexes:[2]},docker:{path:"/tag/docker/",indexes:[3]},MODInt:{path:"/tag/modint/",indexes:[4,5]},踩坑记录:{path:"/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/",indexes:[6]},风格:{path:"/tag/%E9%A3%8E%E6%A0%BC/",indexes:[7]},公理系统:{path:"/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/",indexes:[8]},mobile:{path:"/tag/mobile/",indexes:[43]},激活:{path:"/tag/%E6%BF%80%E6%B4%BB/",indexes:[44]},设计模式:{path:"/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/",indexes:[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34]},typescript:{path:"/tag/typescript/",indexes:[19,26,27,28,29,30,31,32,33,34]},生成实例:{path:"/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/",indexes:[19,26,27,33]},TypeScript:{path:"/tag/typescript/",indexes:[9,10,11,12,13,14,15,16,17,18,20,21,22,23,24,25]},分开考虑:{path:"/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/",indexes:[20,24]},推卸责任:{path:"/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/",indexes:[21]},用类实现:{path:"/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/",indexes:[9,11]},容器与内容的一致性:{path:"/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/",indexes:[22,23]},简单化:{path:"/tag/%E7%AE%80%E5%8D%95%E5%8C%96/",indexes:[16,17]},工厂方法:{path:"/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/",indexes:[30]},交给子类:{path:"/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/",indexes:[30,34]},避免浪费:{path:"/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/",indexes:[12,13]},管理状态:{path:"/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/",indexes:[14,15,18]},整体的替换算法:{path:"/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/",indexes:[24]},访问数据结构并处理数据:{path:"/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/",indexes:[25]},c:{path:"/tag/c/",indexes:[35,36,37,38,39,40,41,42]},编译器:{path:"/tag/%E7%BC%96%E8%AF%91%E5%99%A8/",indexes:[35,36,37,38,39,40,41,42]},解释器:{path:"/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/",indexes:[35,36,37,38,39,40,41,42]}}}}},p1=["/tech/android%20studio%E6%8D%A2%E6%BA%90.html","/tech/cicd.html","/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html","/tech/docker.html","/tech/modint.html","/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html","/tech/python_requrements.html","/tech/style.html","/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html","/tech/DesignPatterns/command.html","/tech/DesignPatterns/end.html","/tech/DesignPatterns/interpreter.html","/tech/DesignPatterns/proxy.html","/tech/DesignPatterns/flyweight.html","/tech/DesignPatterns/memento.html","/tech/DesignPatterns/state.html","/tech/DesignPatterns/facade.html","/tech/DesignPatterns/mediator.html","/tech/DesignPatterns/observer.html","/tech/DesignPatterns/abstractFactory.html","/tech/DesignPatterns/bridge.html","/tech/DesignPatterns/chainOfResponsibility.html","/tech/DesignPatterns/composite.html","/tech/DesignPatterns/decorator.html","/tech/DesignPatterns/strategy.html","/tech/DesignPatterns/visitor.html","/tech/DesignPatterns/builder.html","/tech/DesignPatterns/prototype.html","/tech/DesignPatterns/DesignPrinciples.html","/tech/DesignPatterns/adapter.html","/tech/DesignPatterns/factory_method.html","/tech/DesignPatterns/","/tech/DesignPatterns/iterator.html","/tech/DesignPatterns/singleton.html","/tech/DesignPatterns/template_method.html","/tech/designASimpileCCompiler/0.html","/tech/designASimpileCCompiler/3.html","/tech/designASimpileCCompiler/4.html","/tech/designASimpileCCompiler/5.html","/tech/designASimpileCCompiler/6.html","/tech/designASimpileCCompiler/7.html","/tech/designASimpileCCompiler/8.html","/tech/designASimpileCCompiler/9.html","/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html","/tutorials/typora%E6%BF%80%E6%B4%BB.html","/tech/figure_bed.html","/tech/mailserver.html","/tech/tensorflow%E8%B8%A9%E5%9D%91.html","/essays/%E5%91%BD%E9%87%8C%E6%9C%89%E6%97%B6%E7%BB%88%E9%A1%BB%E6%9C%89.html","/essays/","/projects/","/resources/","/tech/","/tutorials/","/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html","/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html","/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html","/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html","/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html","/tech/%E5%8D%8F%E7%A8%8B.html","/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html","/resources/html2md/","/tech/designASimpileCCompiler/1.html","/tech/designASimpileCCompiler/2.html"],Ho=xe(d8);on(Ho);const h1=e=>{const t=ge(),n=he(),r=Ye();return w(()=>{var i;const a=e??((i=n.value.blog)==null?void 0:i.key)??"";if(!a)return console.warn("useBlogCategory: key not found"),{path:"/",map:{}};if(!Ho.value[a])throw new Error(`useBlogCategory: key ${a} is invalid`);const o=Ho.value[a][r.value],l={path:o.path,map:{}};for(const c in o.map){const u=o.map[c];l.map[c]={path:u.path,items:[]};for(const d of u.indexes){const{path:f,meta:p}=xt(p1[d]);l.map[c].items.push({path:f,info:p})}t.value.path===u.path&&(l.currentItems=l.map[c].items)}return l})},f8={article:{"/":{path:"/article/",indexes:[45,46,47,48,6,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,44,28,29,30,31,32,33,34,49,50,51,52,53,2,3,54,55,7,0,1,4,5,8,56,57,43,58,59,60,61,35,62,63,36,37,38,39,40,41,42]}},star:{"/":{path:"/star/",indexes:[2]}},timeline:{"/":{path:"/timeline/",indexes:[45,46,47,48,6,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,44,28,29,30,31,32,33,34,49,50,51,52,53,2,3,54,55,7,0,1,4,5,8]}}},No=xe(f8);on(No);const $a=e=>{const t=he(),n=Ye();return w(()=>{var l;const r=e??((l=t.value.blog)==null?void 0:l.key)??"";if(!r)return console.warn("useBlogType: key not found"),{path:"/",items:[]};if(!No.value[r])throw new Error(`useBlogType: key ${e} is invalid`);const a=No.value[r][n.value],o={path:a.path,items:[]};for(const i of a.indexes){const{path:c,meta:u}=xt(p1[i]);o.items.push({path:c,info:u})}return o})},m1=Symbol(""),Rl=()=>{const e=ve(m1);if(!e)throw new Error("useTimeline() is called without provider.");return e},p8=()=>{const e=$a("timeline"),t=w(()=>{const n=[];return e.value.items.forEach(({info:r,path:a})=>{const o=_l(r[je.date]);if(o){const l=o.getFullYear(),i=o.getMonth()+1,c=o.getDate();(!n[0]||n[0].year!==l)&&n.unshift({year:l,items:[]}),n[0].items.push({date:`${i}/${c}`,info:r,path:a})}}),{...e.value,config:n.reverse()}});ht(m1,t)},v1=Symbol(""),Kn=()=>{const e=ve(v1);if(!e)throw new Error("useArticles() is called without provider.");return e},h8=()=>{const e=$a("article");ht(v1,e)},g1=Symbol.for("categoryMap"),Hr=()=>{const e=ve(g1);if(!e)throw new Error("useCategoryMap() is called without provider.");return e},m8=()=>{const e=h1("category");ht(g1,e)},y1=Symbol(""),$l=()=>{const e=ve(y1);if(!e)throw new Error("useStars() is called without provider.");return e},v8=()=>{const e=$a("star");ht(y1,e)},b1=Symbol.for("tagMap"),Nr=()=>{const e=ve(b1);if(!e)throw new Error("useTagMap() is called without provider.");return e},g8=()=>{const e=h1("tag");ht(b1,e)},y8=()=>{h8(),m8(),v8(),g8(),p8()},Vr=()=>{const e=Nt(),t=ce();return w(()=>({...e.value.blog,...t.value.blog}))},b8=e=>{const t=ce();return w(()=>{const{[je.author]:n}=e.value;return n?Cr(n):n===!1?[]:Cr(t.value.author,!1)})},E8=e=>{const t=Hr();return w(()=>Pu(e.value[je.category]).map(n=>({name:n,path:t.value.map[n].path})))},_8=e=>{const t=Nr();return w(()=>Du(e.value[je.tag]).map(n=>({name:n,path:t.value.map[n].path})))},w8=e=>w(()=>{const{[je.date]:t}=e.value;return _l(t)}),A8=e=>{const t=zn(e,"info"),n=Vr(),r=b8(t),a=E8(t),o=_8(t),l=w8(t),i=Wu(),c=w(()=>({author:r.value,category:a.value,date:l.value,localizedDate:t.value[je.localizedDate]??"",tag:o.value,isOriginal:t.value[je.isOriginal]??!1,readingTime:t.value[je.readingTime]??null,readingTimeLocale:t.value[je.readingTime]&&i.value?Uu(t.value[je.readingTime],i.value):null,pageview:e.path})),u=w(()=>n.value.articleInfo);return{info:c,items:u}},C8=()=>{const e=ce();return w(()=>e.value.author)},k8=M({__name:"HomePage",setup(e){return Kn(),(t,n)=>{const r=pt("CommentService");return cl(),ul(bt(u8),null,{bottom:pa(()=>[R0(" TODO: it's not work "),Te(r)]),_:1})}}}),Fl=(e,t)=>{const n=e.__vccOpts||e;for(const[r,a]of t)n[r]=a;return n},T8=Fl(k8,[["__file","HomePage.vue"]]),S8=M({name:"BreadCrumb",setup(){const e=ge(),t=Ye(),n=he(),r=ce(),a=xe([]),o=w(()=>(n.value.breadcrumb??r.value.breadcrumb??!0)&&a.value.length>1),l=w(()=>n.value.breadcrumbIcon??r.value.breadcrumbIcon??!0),i=()=>{const c=q6(e.value.path,t.value).map(({link:u,name:d})=>{const{path:f,meta:p,notFound:h}=xt(u);return h||p[Ue.breadcrumbExclude]?null:{title:p[Ue.shortTitle]||p[Ue.title]||d,icon:p[Ue.icon],path:f}}).filter(u=>u!==null);c.length>1&&(a.value=c)};return se(()=>{ae(()=>e.value.path,i,{immediate:!0})}),()=>s("nav",{class:["vp-breadcrumb",{disable:!o.value}]},o.value?s("ol",{vocab:"https://schema.org/",typeof:"BreadcrumbList"},a.value.map((c,u)=>s("li",{class:{"is-active":a.value.length-1===u},property:"itemListElement",typeof:"ListItem"},[s(Ie,{to:c.path,property:"item",typeof:"WebPage"},()=>[l.value?s(Ve,{icon:c.icon}):null,s("span",{property:"name"},c.title||"Unknown")]),s("meta",{property:"position",content:u+1})]))):[])}}),hi=(e,t)=>e===!1||qn(e)?e:we(e)?Il(e,!0,t):null,Vo=(e,t,n)=>{const r=e.findIndex(a=>a.link===t);if(r!==-1){const a=e[r+n];return a!=null&&a.link?a:null}for(const a of e)if("children"in a){const o=Vo(a.children,t,n);if(o)return o}return null},x8=M({name:"PageNav",setup(){const e=ce(),t=he(),n=Pl(),r=ge(),a=An(),o=Ht(),l=w(()=>{const c=hi(t.value.prev,o.path);return c===!1?null:c||(e.value.prevLink===!1?null:Vo(n.value,r.value.path,-1))}),i=w(()=>{const c=hi(t.value.next,o.path);return c===!1?null:c||(e.value.nextLink===!1?null:Vo(n.value,r.value.path,1))});return Se("keydown",c=>{c.altKey&&(c.key==="ArrowRight"?i.value&&(a(i.value.link),c.preventDefault()):c.key==="ArrowLeft"&&l.value&&(a(l.value.link),c.preventDefault()))}),()=>l.value||i.value?s("nav",{class:"vp-page-nav"},[l.value?s(Je,{class:"prev",config:l.value},()=>{var c,u;return[s("div",{class:"hint"},[s("span",{class:"arrow start"}),e.value.metaLocales.prev]),s("div",{class:"link"},[s(Ve,{icon:(c=l.value)==null?void 0:c.icon}),(u=l.value)==null?void 0:u.text])]}):null,i.value?s(Je,{class:"next",config:i.value},()=>{var c,u;return[s("div",{class:"hint"},[e.value.metaLocales.next,s("span",{class:"arrow end"})]),s("div",{class:"link"},[(c=i.value)==null?void 0:c.text,s(Ve,{icon:(u=i.value)==null?void 0:u.icon})])]}):null]):null}}),E1=()=>s(ie,{name:"author"},()=>s("path",{d:"M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"}));E1.displayName="AuthorIcon";const _1=()=>s(ie,{name:"calendar"},()=>s("path",{d:"M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"}));_1.displayName="CalendarIcon";const w1=()=>s(ie,{name:"category"},()=>s("path",{d:"M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"}));w1.displayName="CategoryIcon";const A1=()=>s(ie,{name:"print"},()=>s("path",{d:"M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"}));A1.displayName="PrintIcon";const C1=()=>s(ie,{name:"tag"},()=>s("path",{d:"M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"}));C1.displayName="TagIcon";const k1=()=>s(ie,{name:"timer"},()=>s("path",{d:"M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"}));k1.displayName="TimerIcon";const T1=()=>s(ie,{name:"word"},()=>[s("path",{d:"M518.217 432.64V73.143A73.143 73.143 0 01603.43 1.097a512 512 0 01419.474 419.474 73.143 73.143 0 01-72.046 85.212H591.36a73.143 73.143 0 01-73.143-73.143z"}),s("path",{d:"M493.714 566.857h340.297a73.143 73.143 0 0173.143 85.577A457.143 457.143 0 11371.566 117.76a73.143 73.143 0 0185.577 73.143v339.383a36.571 36.571 0 0036.571 36.571z"})]);T1.displayName="WordIcon";const L8=()=>{const e=ce(),t=ge(),n=he();return w(()=>{var a;return n.value.contributors??e.value.contributors??!0?((a=t.value.git)==null?void 0:a.contributors)??null:null})},B8={GitHub:":repo/edit/:branch/:path",GitLab:":repo/-/edit/:branch/:path",Gitee:":repo/edit/:branch/:path",Bitbucket:":repo/src/:branch/:path?mode=edit&spa=0&at=:branch&fileviewer=file-view-default"},I8=({docsRepo:e,docsBranch:t,docsDir:n,filePathRelative:r,editLinkPattern:a})=>{if(!r)return null;const o=Cl(e);let l;return a?l=a:o!==null&&(l=B8[o]),l?l.replace(/:repo/u,sn(e)?e:`https://github.com/${e}`).replace(/:branch/u,t).replace(/:path/u,Dc(`${pl(n)}/${r}`)):null},P8=()=>{const e=ce(),t=ge(),n=he();return w(()=>{const{repo:r,docsRepo:a=r,docsBranch:o="main",docsDir:l="",editLink:i,editLinkPattern:c=""}=e.value;if(!(n.value.editLink??i??!0)||!a)return null;const d=I8({docsRepo:a,docsBranch:o,docsDir:l,editLinkPattern:c,filePathRelative:t.value.filePathRelative});return d?{text:e.value.metaLocales.editLink,link:d}:null})},un=()=>{const e=ce();return w(()=>e.value.metaLocales)},D8=()=>{const e=Gn(),t=ce(),n=ge(),r=he();return w(()=>{var l,i;return!(r.value.lastUpdated??t.value.lastUpdated??!0)||!((l=n.value.git)!=null&&l.updatedTime)?null:new Date((i=n.value.git)==null?void 0:i.updatedTime).toLocaleString(e.value.lang)})},O8=M({name:"AuthorInfo",inheritAttrs:!1,props:{author:{type:Array,required:!0},pure:Boolean},setup(e){const t=un();return()=>e.author.length?s("span",{class:"page-author-info","aria-label":`${t.value.author}${e.pure?"":"🖊"}`,...e.pure?{}:{"data-balloon-pos":"up"}},[s(E1),s("span",e.author.map(n=>n.url?s("a",{class:"page-author-item",href:n.url,target:"_blank",rel:"noopener noreferrer"},n.name):s("span",{class:"page-author-item"},n.name))),s("span",{property:"author",content:e.author.map(n=>n.name).join(", ")})]):null}}),M8=M({name:"CategoryInfo",inheritAttrs:!1,props:{category:{type:Array,required:!0},pure:Boolean},setup(e){const t=un(),n=An();return()=>e.category.length?s("span",{class:"page-category-info","aria-label":`${t.value.category}${e.pure?"":"🌈"}`,...e.pure?{}:{"data-balloon-pos":"up"}},[s(w1),e.category.map(({name:r,path:a})=>s("span",{class:["page-category-item",{[`category${Ra(r,9)}`]:!e.pure,clickable:a}],role:a?"navigation":"",onClick:()=>{a&&n(a)}},r)),s("meta",{property:"articleSection",content:e.category.map(({name:r})=>r).join(",")})]):null}}),R8=M({name:"DateInfo",inheritAttrs:!1,props:{date:{type:Object,default:null},localizedDate:{type:String,default:""},pure:Boolean},setup(e){const t=Pa(),n=un();return()=>e.date?s("span",{class:"page-date-info","aria-label":`${n.value.date}${e.pure?"":"📅"}`,...e.pure?{}:{"data-balloon-pos":"up"}},[s(_1),s("span",s(Or,()=>e.localizedDate||e.date.toLocaleDateString(t.value))),s("meta",{property:"datePublished",content:e.date.toISOString()||""})]):null}}),$8=M({name:"OriginalInfo",inheritAttrs:!1,props:{isOriginal:Boolean},setup(e){const t=un();return()=>e.isOriginal?s("span",{class:"page-original-info"},t.value.origin):null}}),F8=M({name:"ReadingTimeInfo",inheritAttrs:!1,props:{readingTime:{type:Object,default:()=>null},readingTimeLocale:{type:Object,default:()=>null},pure:Boolean},setup(e){const t=un(),n=w(()=>{if(!e.readingTime)return null;const{minutes:r}=e.readingTime;return r<1?"PT1M":`PT${Math.round(r)}M`});return()=>{var r,a;return(r=e.readingTimeLocale)!=null&&r.time?s("span",{class:"page-reading-time-info","aria-label":`${t.value.readingTime}${e.pure?"":"⌛"}`,...e.pure?{}:{"data-balloon-pos":"up"}},[s(k1),s("span",(a=e.readingTimeLocale)==null?void 0:a.time),s("meta",{property:"timeRequired",content:n.value})]):null}}}),H8=M({name:"TagInfo",inheritAttrs:!1,props:{tag:{type:Array,default:()=>[]},pure:Boolean},setup(e){const t=un(),n=An();return()=>e.tag.length?s("span",{class:"page-tag-info","aria-label":`${t.value.tag}${e.pure?"":"🏷"}`,...e.pure?{}:{"data-balloon-pos":"up"}},[s(C1),e.tag.map(({name:r,path:a})=>s("span",{class:["page-tag-item",{[`tag${Ra(r,9)}`]:!e.pure,clickable:a}],role:a?"navigation":"",onClick:()=>{a&&n(a)}},r)),s("meta",{property:"keywords",content:e.tag.map(({name:r})=>r).join(",")})]):null}}),N8=M({name:"ReadTimeInfo",inheritAttrs:!1,props:{readingTime:{type:Object,default:()=>null},readingTimeLocale:{type:Object,default:()=>null},pure:Boolean},setup(e){const t=un();return()=>{var n,r,a;return(n=e.readingTimeLocale)!=null&&n.words?s("span",{class:"page-word-info","aria-label":`${t.value.words}${e.pure?"":"🔠"}`,...e.pure?{}:{"data-balloon-pos":"up"}},[s(T1),s("span",(r=e.readingTimeLocale)==null?void 0:r.words),s("meta",{property:"wordCount",content:(a=e.readingTime)==null?void 0:a.words})]):null}}}),S1=M({name:"PageInfo",components:{AuthorInfo:O8,CategoryInfo:M8,DateInfo:R8,OriginalInfo:$8,PageViewInfo:ia,ReadingTimeInfo:F8,TagInfo:H8,WordInfo:N8},props:{items:{type:[Array,Boolean],default:()=>["Author","Original","Date","PageView","ReadingTime","Category","Tag"]},info:{type:Object,required:!0}},setup(e){const t=Cn();return()=>e.items?s("div",{class:"page-info"},e.items.map(n=>s(pt(`${n}Info`),{...e.info,pure:t.value}))):null}}),V8=M({name:"PageTitle",setup(){const e=ge(),t=he(),n=ce(),{info:r,items:a}=R6();return()=>s("div",{class:"vp-page-title"},[s("h1",[n.value.titleIcon===!1?null:s(Ve,{icon:t.value.icon}),e.value.title]),s(S1,{info:r.value,...a.value===null?{}:{items:a.value}}),s("hr")])}}),x1=()=>s(ie,{name:"edit"},()=>[s("path",{d:"M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"}),s("path",{d:"M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"})]);x1.displayName="EditIcon";const j8=M({name:"PageMeta",setup(){const e=ce(),t=P8(),n=D8(),r=L8();return()=>{var o;const{metaLocales:a}=e.value;return s("footer",{class:"vp-page-meta"},[t.value?s("div",{class:"vp-meta-item edit-link"},s(Je,{class:"vp-meta-label",config:t.value},{before:()=>s(x1)})):null,s("div",{class:"vp-meta-item git-info"},[n.value?s("div",{class:"update-time"},[s("span",{class:"vp-meta-label"},`${a.lastUpdated}: `),s(Or,()=>s("span",{class:"vp-meta-info"},n.value))]):null,(o=r.value)!=null&&o.length?s("div",{class:"contributors"},[s("span",{class:"vp-meta-label"},`${a.contributors}: `),r.value.map(({email:l,name:i},c)=>[s("span",{class:"vp-meta-info",title:`email: ${l}`},i),c!==r.value.length-1?",":""])]):null])])}}}),z8=M({name:"PrintButton",setup(){const e=Nt(),t=ce();return()=>e.value.print===!1?null:s("button",{type:"button",class:"print-button",title:t.value.metaLocales.print,onClick:()=>{window.print()}},s(A1))}}),L1=M({name:"TOC",props:{items:{type:Array,default:()=>[]},headerDepth:{type:Number,default:2}},slots:Object,setup(e,{slots:t}){const n=Ht(),r=ge(),a=un(),[o,l]=wr(),i=xe(),c=z("-1.7rem"),u=f=>{var p;(p=i.value)==null||p.scrollTo({top:f,behavior:"smooth"})},d=()=>{if(i.value){const f=document.querySelector(".vp-toc-item.active");f?c.value=`${f.getBoundingClientRect().top-i.value.getBoundingClientRect().top+i.value.scrollTop}px`:c.value="-1.7rem"}else c.value="-1.7rem"};return se(()=>{ae(()=>n.hash,f=>{if(i.value){const p=document.querySelector(`#toc a.toc-link[href$="${f}"]`);if(!p)return;const{top:h,height:v}=i.value.getBoundingClientRect(),{top:_,height:E}=p.getBoundingClientRect();_<h?u(i.value.scrollTop+_-h):_+E>h+v&&u(i.value.scrollTop+_+E-h-v)}}),ae(()=>n.fullPath,d,{flush:"post",immediate:!0})}),()=>{var v,_;const f=({title:E,level:b,slug:C})=>s(Ie,{to:`#${C}`,class:["vp-toc-link",`level${b}`],onClick:()=>{l()}},()=>E),p=(E,b)=>E.length&&b>0?s("ul",{class:"vp-toc-list"},E.map(C=>{const y=p(C.children,b-1);return[s("li",{class:["vp-toc-item",{active:n.hash===`#${C.slug}`}]},f(C)),y?s("li",y):null]})):null,h=e.items.length?p(e.items,e.headerDepth):r.value.headers?p(r.value.headers,e.headerDepth):null;return h?s("div",{class:"vp-toc-placeholder"},[s("aside",{id:"toc"},[(v=t.before)==null?void 0:v.call(t),s("div",{class:"vp-toc-header",onClick:()=>{l()}},[a.value.toc,s(z8),s("div",{class:["arrow",o.value?"down":"end"]})]),s("div",{class:["vp-toc-wrapper",o.value?"open":""],ref:i},[h,s("div",{class:"vp-toc-marker",style:{top:c.value}})]),(_=t.after)==null?void 0:_.call(t)])]):null}}}),q8=M({name:"NormalPage",slots:Object,setup(e,{slots:t}){const n=he(),{isDarkmode:r}=Fr(),a=ce(),o=w(()=>n.value.toc??a.value.toc??!0);return()=>s("main",{id:"main-content",class:"vp-page"},s(Mn("LocalEncrypt")?pt("LocalEncrypt"):Au,()=>{var l,i,c,u;return[(l=t.top)==null?void 0:l.call(t),n.value.cover?s("div",{class:"page-cover"},s("img",{src:be(n.value.cover),alt:"","no-view":""})):null,s(S8),s(V8),o.value?s(L1,{headerDepth:n.value.headerDepth??a.value.headerDepth??2},{before:()=>{var d;return(d=t.tocBefore)==null?void 0:d.call(t)},after:()=>{var d;return(d=t.tocAfter)==null?void 0:d.call(t)}}):null,(i=t.contentBefore)==null?void 0:i.call(t),s(Wn),(c=t.contentAfter)==null?void 0:c.call(t),s(j8),s(x8),Mn("CommentService")?s(pt("CommentService"),{darkmode:r.value}):null,(u=t.bottom)==null?void 0:u.call(t)]}))}}),Hl=M({name:"SkipLink",props:{content:{type:String,default:"main-content"}},setup(e){const t=ge(),n=ce(),r=xe(),a=({target:o})=>{const l=document.querySelector(o.hash);if(l){const i=()=>{l.removeAttribute("tabindex"),l.removeEventListener("blur",i)};l.setAttribute("tabindex","-1"),l.addEventListener("blur",i),l.focus(),window.scrollTo(0,0)}};return se(()=>{ae(()=>t.value.path,()=>r.value.focus())}),()=>[s("span",{ref:r,tabindex:"-1"}),s("a",{href:`#${e.content}`,class:"vp-skip-link sr-only",onClick:a},n.value.routeLocales.skipToContent)]}}),G8=M({name:"Layout",slots:Object,setup(e,{slots:t}){const n=Nt(),r=ce(),a=ge(),o=he(),{isMobile:l}=$r(),i=w(()=>{var c,u;return((c=r.value.blog)==null?void 0:c.sidebarDisplay)??((u=n.value.blog)==null?void 0:u.sidebarDisplay)??"mobile"});return()=>[s(Hl),s(Ol,{},{default:()=>{var c;return((c=t.default)==null?void 0:c.call(t))??(o.value.home?s(T8):s(Ml,()=>s(q8,{key:a.value.path},{top:()=>{var u;return(u=t.top)==null?void 0:u.call(t)},bottom:()=>{var u;return(u=t.bottom)==null?void 0:u.call(t)},contentBefore:()=>{var u;return(u=t.contentBefore)==null?void 0:u.call(t)},contentAfter:()=>{var u;return(u=t.contentAfter)==null?void 0:u.call(t)},tocBefore:()=>{var u;return(u=t.tocBefore)==null?void 0:u.call(t)},tocAfter:()=>{var u;return(u=t.tocAfter)==null?void 0:u.call(t)}})))},...i.value==="none"?{}:{navScreenBottom:()=>s(pt("BloggerInfo"))},...!l.value&&i.value==="always"?{sidebar:()=>s(pt("BloggerInfo"))}:{}})]}}),U8=M({name:"NotFoundHint",setup(){const e=ce(),t=()=>{const n=e.value.routeLocales.notFoundMsg;return n[Math.floor(Math.random()*n.length)]};return()=>s("div",{class:"not-found-hint"},[s("p",{class:"error-code"},"404"),s("h1",{class:"error-title"},e.value.routeLocales.notFoundTitle),s("p",{class:"error-hint"},t())])}}),W8=M({name:"NotFound",slots:Object,setup(e,{slots:t}){const n=wn(),r=Ye(),a=ce();return()=>[s(Hl),s(Ol,{noSidebar:!0},()=>{var o;return s("main",{id:"main-content",class:"vp-page not-found"},((o=t.default)==null?void 0:o.call(t))??[s(U8),s("div",{class:"actions"},[s("button",{type:"button",class:"action-button",onClick:()=>{window.history.go(-1)}},a.value.routeLocales.back),s("button",{type:"button",class:"action-button",onClick:()=>{n.push(a.value.home??r.value)}},a.value.routeLocales.home)])])})]}}),K8={Email:'<svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg>',GitHub:'<svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg>',QQ:'<svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg>'},B1=M({name:"SocialMedia",setup(){const e=Vr(),t=Cn(),n=w(()=>Ma(e.value.medias??{}).map(([r,a])=>({name:r,icon:K8[r],url:a})));return()=>n.value.length?s("div",{class:"vp-social-medias"},n.value.map(({name:r,icon:a,url:o})=>s("a",{class:"vp-social-media",href:o,rel:"noopener noreferrer",target:"_blank","aria-label":r||"",...t.value?{}:{"data-balloon-pos":"up"},innerHTML:a}))):null}}),Nl=M({name:"BloggerInfo",setup(){const e=Vr(),t=Gn(),n=ce(),r=Kn(),a=Hr(),o=Nr(),l=Rl(),i=An(),c=w(()=>{var p;return e.value.name??((p=Cr(n.value.author)[0])==null?void 0:p.name)??t.value.title}),u=w(()=>e.value.avatar??n.value.logo),d=w(()=>n.value.blogLocales),f=w(()=>e.value.intro);return()=>{const{article:p,category:h,tag:v,timeline:_}=d.value,E=[[r.value.path,r.value.items.length,p],[a.value.path,En(a.value.map).length,h],[o.value.path,En(o.value.map).length,v],[l.value.path,l.value.items.length,_]];return s("div",{class:"vp-blogger-info",vocab:"https://schema.org/",typeof:"Person"},[s("div",{class:"vp-blogger",...f.value?{style:{cursor:"pointer"},"aria-label":d.value.intro,"data-balloon-pos":"down",role:"link",onClick:()=>i(f.value)}:{}},[u.value?s("img",{class:"vp-blogger-avatar",src:be(u.value),property:"image",alt:"Blogger Avatar",loading:"lazy"}):null,c.value?s("div",{class:"vp-blogger-name",property:"name"},c.value):null,e.value.description?s("div",{class:"vp-blogger-description",innerHTML:e.value.description}):null,f.value?s("meta",{property:"url",content:be(f.value)}):null]),s("div",{class:"vp-blog-counts"},E.map(([b,C,y])=>s(Ie,{class:"vp-blog-count",to:b},()=>[s("div",{class:"count"},C),s("div",y)]))),s(B1)])}}}),Vl=()=>s(ie,{name:"category"},()=>s("path",{d:"M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"}));Vl.displayName="CategoryIcon";const jl=()=>s(ie,{name:"tag"},()=>s("path",{d:"M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"}));jl.displayName="TagIcon";const zl=()=>s(ie,{name:"timeline"},()=>s("path",{d:"M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"}));zl.displayName="TimelineIcon";const I1=()=>s(ie,{name:"slides"},()=>s("path",{d:"M896 170.667v426.666a85.333 85.333 0 0 1-85.333 85.334h-256v61.184l192.597 115.584-43.861 73.13-148.736-89.173v95.275h-85.334v-95.318l-148.736 89.216-43.861-73.13 192.597-115.627v-61.141h-256A85.333 85.333 0 0 1 128 597.333V170.667H85.333V85.333h853.334v85.334H896zm-682.667 0v426.666h597.334V170.667H213.333zM426.667 512h-85.334V341.333h85.334V512zm128 0h-85.334V256h85.334v256zm128 0h-85.334V384h85.334v128z"}));I1.displayName="SlideIcon";const P1=()=>s(ie,{name:"sticky"},()=>[s("path",{d:"m381.3 733.8l-161.9 118c-5.9 4.5-13.2 6.6-20.1 6.6-8.7 0-17.7-3.4-24.3-10-12.2-12.2-13.9-31.3-3.5-45.2l144.5-195.5-113.6-112.9c-11.1-11.1-13.2-28.4-5.5-42 5.5-8.7 52.1-76.4 155.5-51 1.8 0.3 3.5 0.3 5.6 0.7 4.2 0.3 9 0.7 14.2 1.7 21.9 3.5 60.8-13.9 94.5-42.7 32.3-27.5 53.1-59.4 53.1-81.6 0-5.2 0-10.8-0.3-16-0.7-20.8-2.1-52.8 21.5-76.4 28.1-28.1 72.9-30.6 103.9-5.2 0.6 0.3 1 1 1.7 1.7 16.7 16.3 187.5 187.2 189.3 188.9 14.5 14.6 22.9 34.4 22.9 55.3 0 20.8-8 40.2-22.9 54.8-23.7 23.6-56 22.6-77.1 21.6-4.9 0-10.5-0.4-15.7-0.4-20.8 0-45.8 14.6-70.5 41.3-34.3 37.5-55.5 85.8-53.8 107.7 0.7 6.9 2.1 19.1 2.4 20.8 25 101.4-42.7 147.6-50.7 152.8-13.9 8.4-31.6 6.3-42.7-4.8l-112.1-112.2z"})]);P1.displayName="StickyIcon";const Fa=()=>s(ie,{name:"article"},()=>s("path",{d:"M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"}));Fa.displayName="ArticleIcon";const D1=()=>s(ie,{name:"book"},()=>s("path",{d:"M256 853.333h426.667A85.333 85.333 0 0 0 768 768V256a85.333 85.333 0 0 0-85.333-85.333H469.333a42.667 42.667 0 0 1 0-85.334h213.334A170.667 170.667 0 0 1 853.333 256v512a170.667 170.667 0 0 1-170.666 170.667H213.333A42.667 42.667 0 0 1 170.667 896V128a42.667 42.667 0 0 1 42.666-42.667h128A42.667 42.667 0 0 1 384 128v304.256l61.653-41.088a42.667 42.667 0 0 1 47.36 0l61.654 41.045V256A42.667 42.667 0 0 1 640 256v256a42.667 42.667 0 0 1-66.347 35.499l-104.32-69.547-104.32 69.547A42.667 42.667 0 0 1 298.667 512V170.667H256v682.666z"}));D1.displayName="BookIcon";const O1=()=>s(ie,{name:"link"},()=>s("path",{d:"M460.8 584.533c17.067 17.067 17.067 42.667 0 59.734-17.067 17.066-42.667 17.066-59.733 0-85.334-85.334-85.334-217.6 0-302.934L554.667 192C640 110.933 776.533 110.933 857.6 196.267c81.067 81.066 81.067 213.333 0 294.4l-68.267 64c0-34.134-4.266-68.267-17.066-102.4l21.333-21.334c51.2-46.933 55.467-128 4.267-179.2s-128-55.466-179.2-4.266c-4.267 0-4.267 4.266-4.267 4.266L465.067 401.067c-51.2 51.2-51.2 132.266-4.267 183.466m123.733-183.466C601.6 384 627.2 384 644.267 401.067c85.333 85.333 85.333 217.6 0 302.933l-153.6 149.333C405.333 934.4 268.8 934.4 187.733 849.067c-81.066-81.067-81.066-213.334 0-294.4l68.267-64c0 34.133 4.267 72.533 17.067 102.4L251.733 614.4C204.8 665.6 204.8 746.667 256 793.6c51.2 46.933 123.733 46.933 174.933 0l149.334-149.333c51.2-51.2 51.2-128 0-179.2-12.8-17.067-17.067-46.934 4.266-64z"}));O1.displayName="LinkIcon";const M1=()=>s(ie,{name:"project"},()=>s("path",{d:"M987.456 425.152H864V295.296a36.48 36.48 0 0 0-36.544-36.544h-360l-134.08-128.256A9.344 9.344 0 0 0 327.04 128H36.48A36.48 36.48 0 0 0 0 164.544v676.608a36.48 36.48 0 0 0 36.544 36.544h797.76a36.672 36.672 0 0 0 33.92-22.848L1021.44 475.52a36.48 36.48 0 0 0-33.92-50.304zM82.304 210.304h215.424l136.64 130.752h347.328v84.096H198.848A36.672 36.672 0 0 0 164.928 448L82.304 652.8V210.304zM808.32 795.456H108.544l118.08-292.608h699.904L808.32 795.52z"}));M1.displayName="ProjectIcon";const R1=()=>s(ie,{name:"friend"},()=>s("path",{d:"M860.16 213.333A268.373 268.373 0 0 0 512 186.027a267.52 267.52 0 0 0-348.16 404.48L428.8 855.893a118.613 118.613 0 0 0 166.4 0l264.96-265.386a267.52 267.52 0 0 0 0-377.174zM800 531.627l-264.96 264.96a32.427 32.427 0 0 1-46.08 0L224 530.347a183.04 183.04 0 0 1 0-256 182.187 182.187 0 0 1 256 0 42.667 42.667 0 0 0 60.587 0 182.187 182.187 0 0 1 256 0 183.04 183.04 0 0 1 3.413 256z"}));R1.displayName="FriendIcon";const jo=()=>s(ie,{name:"slide-down"},()=>s("path",{d:"M108.775 312.23c13.553 0 27.106 3.734 39.153 11.806l375.205 250.338 363.641-252.808c32.587-21.624 76.499-12.83 98.123 19.757 21.685 32.467 12.95 76.56-19.576 98.184l-402.854 278.89c-23.733 15.901-54.694 15.962-78.547.12L69.501 442.097c-32.647-21.685-41.441-65.777-19.817-98.304 13.734-20.54 36.201-31.563 59.09-31.563Z"}));jo.displayName="SlideDownIcon";const $1=()=>s("svg",{xmlns:"http://www.w3.org/2000/svg","xmlns:xlink":"http://www.w3.org/1999/xlink",class:"empty-icon",viewBox:"0 0 1024 1024",innerHTML:'<defs><linearGradient id="f" x1="512.342" y1="2266.13" x2="512.342" y2="666.063" gradientUnits="userSpaceOnUse"><stop offset=".919" stop-color="#e6e6e6" stop-opacity="0"/><stop offset="1" stop-color="#e6e6e6"/></linearGradient><linearGradient id="g" x1="528.912" y1="774" x2="388.088" y2="612" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#ccc"/><stop offset="1" stop-color="#e6e6e6" stop-opacity="0"/></linearGradient><linearGradient id="h" x1="213.219" y1="721.704" x2="251.313" y2="683.61" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#d7d7d7"/><stop offset=".485" stop-color="#fafafa"/><stop offset="1" stop-color="#fafafa"/></linearGradient><linearGradient id="i" x1="724.813" y1="821.718" x2="768.656" y2="777.876" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#ccc"/><stop offset="1" stop-color="#fafafa"/></linearGradient><linearGradient id="a" x1="513.493" y1="714.594" x2="471.007" y2="544.188" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#999"/><stop offset="1" stop-color="#ccc"/></linearGradient><linearGradient id="b" x1="440.156" y1="564.031" x2="508.594" y2="495.594" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#ccc"/><stop offset="1" stop-color="#f0f0f0"/></linearGradient><linearGradient id="l" x1="660.988" y1="754.156" x2="608.637" y2="544.188" xlink:href="#a"/><linearGradient id="m" x1="479.188" y1="774.219" x2="649.782" y2="603.625" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#b3b3b3"/><stop offset="1" stop-color="#e6e6e6"/></linearGradient><linearGradient id="n" x1="447.121" y1="774.219" x2="394.661" y2="563.813" xlink:href="#a"/><linearGradient id="o" x1="494" y1="597" x2="628" y2="463" xlink:href="#b"/><linearGradient id="d" x1="610.485" y1="604.938" x2="697.298" y2="518.125" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#ccc"/><stop offset="1" stop-color="#fff"/></linearGradient><linearGradient id="p" x1="457.438" y1="619.25" x2="353.469" y2="619.25" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#e6e6e6" stop-opacity="0"/><stop offset="1" stop-color="#e6e6e6"/></linearGradient><linearGradient id="q" x1="542.734" y1="674.25" x2="615.672" y2="601.313" xlink:href="#b"/><linearGradient id="c" x1="627.933" y1="358.938" x2="685.192" y2="422.531" gradientUnits="userSpaceOnUse"><stop offset=".4" stop-color="#e6e6e6" stop-opacity=".4"/><stop offset=".443" stop-color="#fff"/><stop offset=".6" stop-color="#ccc"/></linearGradient><linearGradient id="r" x1="618.547" y1="422.531" x2="681.547" y2="359.531" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#e6e6e6"/><stop offset=".761" stop-color="#fff"/><stop offset="1" stop-color="#f0f0f0"/></linearGradient><linearGradient id="s" x1="625" y1="441.5" x2="697" y2="369.5" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#ccc"/><stop offset=".761" stop-color="#fff"/><stop offset="1" stop-color="#f0f0f0"/></linearGradient><linearGradient id="t" x1="627.681" y1="361.438" x2="692.257" y2="433.156" xlink:href="#c"/><linearGradient id="u" x1="561.414" y1="735.438" x2="573.149" y2="688.375" xlink:href="#d"/><linearGradient id="v" x1="405" y1="485.875" x2="440" y2="450.875" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#ccc"/><stop offset="1" stop-color="#fff" stop-opacity=".702"/></linearGradient><linearGradient id="w" x1="404.61" y1="486.906" x2="441.86" y2="449.656" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#ccc"/><stop offset=".495" stop-color="#ccc" stop-opacity=".702"/><stop offset=".498" stop-color="#ccc"/><stop offset="1" stop-color="#fff" stop-opacity=".302"/></linearGradient><radialGradient id="e" cx="329.297" cy="647.578" r="8.172" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#fafafa"/><stop offset="1.2" stop-color="#e6e6e6"/></radialGradient><radialGradient id="j" cx="802.297" cy="673.578" r="8.172" xlink:href="#e"/><radialGradient id="k" cx="774.844" cy="642.75" r="5.531" xlink:href="#e"/></defs><path d="M512.33 666.07c441.828 0 800 358.18 800 800.03s-358.172 800.02-800 800.02-800-358.18-800-800.02 358.17-800.03 800-800.03z" style="fill:url(#f);fill-rule:evenodd"/><path d="m272 694 242-82 131 119-188 43z" style="fill:url(#g);fill-rule:evenodd"/><path fill="#b3b3b3" fill-rule="evenodd" d="M232.391 723.534a2.4 2.4 0 0 1 2.4 2.4v17.725a2.4 2.4 0 0 1-4.8 0v-17.725a2.4 2.4 0 0 1 2.4-2.4z"/><path d="M232.255 676.559c10.33 0 17.067 15.408 18.7 28.493 1.619 12.942-2.372 23.694-18.7 23.694-16.878 0-20.213-10.733-18.7-23.694 1.633-14.061 8.37-28.493 18.7-28.493z" style="fill:url(#h);fill-rule:evenodd"/><path fill="#b3b3b3" fill-rule="evenodd" d="M745.853 826h.938a2.4 2.4 0 0 1 2.4 2.4v22.238a2.4 2.4 0 0 1-2.4 2.4h-.938a2.4 2.4 0 0 1-2.4-2.4V828.4a2.4 2.4 0 0 1 2.4-2.4z"/><path d="M746.727 830.3c-19.438 0-23.278-9.326-21.541-20.59a34.467 34.467 0 0 1 3.289-10.369 16.628 16.628 0 0 1 0-9.112c2.889-12.327 12.059-20.911 18.356-20.911 6.56 0 15.468 9.1 18.356 20.911a14.589 14.589 0 0 1-.335 9.217 34.36 34.36 0 0 1 3.419 10.264c1.861 11.243-2.735 20.59-21.544 20.59z" style="fill:url(#i);fill-rule:evenodd"/><path fill="#ccc" fill-rule="evenodd" d="M328.841 654.562a6.571 6.571 0 0 0-5.2-5.027q-4.107-.952-.034-2.045a6.571 6.571 0 0 0 5.027-5.2q.952-4.109 2.045-.035a6.569 6.569 0 0 0 5.2 5.027q4.109.954.035 2.045a6.569 6.569 0 0 0-5.027 5.2q-.955 4.108-2.046.035z"/><path d="M328.383 653.73a6.567 6.567 0 0 0-5.2-5.027q-4.109-.954-.035-2.045a6.568 6.568 0 0 0 5.027-5.2q.954-4.107 2.046-.034a6.568 6.568 0 0 0 5.2 5.027q4.107.952.035 2.045a6.568 6.568 0 0 0-5.027 5.2q-.954 4.104-2.046.034z" style="fill:url(#e);fill-rule:evenodd"/><path fill="#ccc" fill-rule="evenodd" d="M801.841 680.562a6.571 6.571 0 0 0-5.2-5.027q-4.107-.952-.034-2.045a6.571 6.571 0 0 0 5.027-5.2q.952-4.109 2.045-.035a6.569 6.569 0 0 0 5.2 5.027q4.108.954.035 2.045a6.569 6.569 0 0 0-5.027 5.2q-.955 4.108-2.046.035z"/><path d="M801.383 679.73a6.567 6.567 0 0 0-5.2-5.027q-4.108-.954-.035-2.045a6.568 6.568 0 0 0 5.027-5.2q.954-4.107 2.046-.034a6.568 6.568 0 0 0 5.2 5.027q4.107.952.035 2.045a6.568 6.568 0 0 0-5.027 5.2q-.954 4.104-2.046.034z" style="fill:url(#j);fill-rule:evenodd"/><path d="M774.21 646.9a4.446 4.446 0 0 0-3.517-3.4q-2.778-.643-.023-1.383a4.443 4.443 0 0 0 3.4-3.517q.645-2.778 1.383-.023a4.443 4.443 0 0 0 3.517 3.4q2.778.645.023 1.383a4.446 4.446 0 0 0-3.4 3.517q-.645 2.78-1.383.023z" style="fill:url(#k);fill-rule:evenodd"/><path d="m385.6 714.6.158-150.658L598.9 544.174l-.158 150.658z" style="fill:url(#a);fill-rule:evenodd"/><path d="m385.474 564.031 214.763-19.383-36.171-49.067-215.559 17.634z" style="fill:url(#b);fill-rule:evenodd"/><path d="m598.744 694.832.156-150.658 71.975 59.319-.158 150.658z" style="fill:url(#l);fill-rule:evenodd"/><path d="m457.064 774.209.158-150.658 214.691-19.914-.158 150.663z" style="fill:url(#m);fill-rule:evenodd"/><path d="m384.566 714.459.158-150.659 72.5 59.75-.158 150.658z" style="fill:url(#n);fill-rule:evenodd"/><path d="M494 640s75.357-58.4 42-83-38.887 1.663-37 14 53.847 12.465 54-26c.2-49.979 75-125 75-125" style="fill:none;stroke-width:3px;stroke-dasharray:12 6;stroke:url(#o);fill-rule:evenodd"/><path d="m670.275 604.939-72.041-59.9 38.476-26.909 72.86 58.159z" style="fill:url(#d);fill-rule:evenodd"/><path d="m425.5 674.383-72.042-59.9 31.109-50.347 72.86 58.16z" style="fill:url(#p);fill-rule:evenodd"/><path d="m487.918 674.235 214.482-22.57-31.1-50.346-215.309 20.833z" style="fill:url(#q);fill-rule:evenodd"/><path style="fill:#fff;fill-rule:evenodd" d="m697.363 358.927-69.58 62.511-12.035 1.082z"/><path d="m697.363 358.927-69.58 62.511-12.035 1.082z" style="fill:url(#c);fill-rule:evenodd"/><path d="M615.748 422.52 604 413l92.089-53.46" style="fill:url(#r);fill-rule:evenodd"/><path d="m625 432 12 18 60-89" style="fill:url(#s);fill-rule:evenodd"/><path d="m626.98 421.335-2.471 11.828 70.918-71.735" style="fill:#fff;fill-rule:evenodd"/><path d="m626.98 421.335-2.471 11.828 70.918-71.735" style="fill:url(#t);fill-rule:evenodd"/><path d="m494.814 735.44 21.293-2.1v-6.613l-13.4 1.319v-6.965l10.977-1.08v-6.613l-10.977 1.08v-6.084l12.917-1.27v-6.525l-20.808 2.047v32.8zM521 732.863l7.054-.694v-11.241a106.361 106.361 0 0 0-1.014-11.274l.176-.017 2.645 7.586 4.453 11.553 4.32-.425 4.408-12.424 2.733-8.116.177-.018a111.811 111.811 0 0 0-1.014 11.474v11.241l7.185-.707V697l-8.552.841-5.025 14.646c-.618 1.956-1.147 4.08-1.808 6.173l-.22.022c-.617-1.968-1.146-3.987-1.808-5.818l-5.2-13.639-8.508.837v32.8zm37.213-3.661 7.891-.776v-10.889l3.835-.377c6.922-.681 12.961-4.714 12.961-12.517 0-8.111-5.951-10.082-13.181-9.371l-11.504 1.128v32.8zm7.891-17.881v-9.478l3.218-.316c3.792-.373 5.908.565 5.908 3.871 0 3.218-1.852 5.208-5.687 5.585zM594 725.682l7.891-.777v-26.274l8.905-.876v-6.524l-25.657 2.524v6.524l8.861-.871v26.274zm27.991-2.754 7.847-.772v-11.594l9.919-22.18-8.244.811-2.733 7.542c-.925 2.56-1.807 4.939-2.733 7.587l-.176.018c-.926-2.466-1.764-4.676-2.645-7.058l-2.734-7-8.375.824 9.874 20.233v11.594z" style="fill:url(#u);fill-rule:evenodd"/><path fill="#ccc" fill-rule="evenodd" d="M408.938 457.309a17.5 17.5 0 0 0 21.374 26.725 17.5 17.5 0 1 1-16.306-30.955 17.442 17.442 0 0 0-5.068 4.23z"/><circle cx="422.5" cy="468.375" r="17.5" style="fill:url(#v)"/><path fill="#ccc" fill-rule="evenodd" d="M391.76 451.5c-2.358 4.419 9.827 15.52 27.215 24.8 15.131 8.071 29.212 12.1 34.166 10.093-4.191 2.772-18.943-1.24-34.86-9.73-17.388-9.275-29.573-20.376-27.215-24.8a2.96 2.96 0 0 1 1.585-1.3 2.606 2.606 0 0 0-.891.937z"/><path d="M418.975 476.29c-17.388-9.275-29.573-20.376-27.215-24.8s18.363-.484 35.751 8.791 29.572 20.376 27.215 24.8-18.364.483-35.751-8.791zm31.634 5.732c1.824-3.42-8.789-12.642-23.7-20.6s-28.486-11.633-30.31-8.213 8.789 12.642 23.7 20.6 28.486 11.633 30.31 8.213zm-36.645-29.008-2.775 1.452.032 1.751 28.637 14.183.266-4.559z" style="fill:url(#w);fill-rule:evenodd"/><g class="people"><path style="fill:#f8cfad;fill-rule:evenodd" d="m612.131 676.5 1.362 3.532 3.255-2.324-1.361-3.532zM629.131 665.5l1.362 3.532 3.255-2.324-1.361-3.532z"/><path style="fill:#141a33;fill-rule:evenodd" d="m617.764 678.184-3.162-.078a11.028 11.028 0 0 0-1.034 3.454c-.258 2.006-1.177 5-.449 5.367 1.5 2.659 4.118-.215 4.118-.215s2.187-2.848 1.925-5.265c-.106-.973-1.181-1.869-1.398-3.263zM633.781 665.855l3.019.945a11.008 11.008 0 0 1-.137 3.6c-.4 1.981-.179 4.166-.986 4.277-2.283 2.03-3.827-1.533-3.827-1.533s-1.473-2.456-.444-4.659c.412-.88 1.718-1.385 2.375-2.63z"/><path style="fill:#f0c5a8;fill-rule:evenodd" d="M599.935 592.534s10.293 9.761 11.95 7.564 3.536-3.463-6.758-13.65z"/><path style="fill:#f8cfad;fill-rule:evenodd" d="M611.3 596.361c1.674-1.105 11.5 7.048 14.5 11.774s-12.705-4.36-14.632-6.776-1.54-3.893.132-4.998z"/><path style="fill:#f8cfad;fill-rule:evenodd" d="M621.815 607.988s1.809 2.549 2.433 1.756 2.475-1.064 2.449-1.138.1-.819 1.288-2.331-3.8-3.632-5.81-.494a2.556 2.556 0 0 0-.36 2.207z"/><path fill="#232c57" fill-rule="evenodd" d="M598 617s14.968-5.618 17 7a150.235 150.235 0 0 1 2 22s12.666 11.836 16 19c0 0-4.753-1.629-4 2 0 0-18.132-14.647-19-19s-9.148-18.716-12-31z"/><path d="M589 622s14.968-5.618 17 7a150.235 150.235 0 0 1 2 22s4.666 17.836 8 25c0 0-4.753-1.629-4 2 0 0-10.132-20.647-11-25s-9.148-18.716-12-31z" style="fill:#292966;fill-rule:evenodd"/><path style="fill:#f0c5a8;fill-rule:evenodd" d="M585.626 597.7s-10.292 9.761-11.95 7.563-3.536-3.463 6.758-13.65z"/><path style="fill:#f8cfad;fill-rule:evenodd" d="M574.259 601.529c-1.675-1.105-11.5 7.049-14.5 11.774s12.7-4.36 14.631-6.775 1.543-3.894-.131-4.999z"/><path style="fill:#f0c5a8;fill-rule:evenodd" d="M591.715 577.752s-.606 1.681 1.48 3.716-3.615 5.307-4.645 2.85-.48-2.716-.48-2.716z"/><path style="fill:#f8cfad;fill-rule:evenodd" d="M583.527 574.123c-.839 1.043.491 3.873 1.453 5.449s2.749 2.833 3.364 2.428 4.088-2.657 4-4-.228-3.4-.228-3.4 2.562-1.641 2.154-2.916-2.916-.154-2.916-.154a15.853 15.853 0 0 0-.227-2.224c-.189-.929-6.887-1.445-7.827 2.6s.558 1.805.227 2.217z"/><path fill="#232c57" fill-rule="evenodd" d="M584.227 567.758c2.1-.885 7.2-3.684 10.125.318s.842 4.385.989 5.294-1.894 5.69-1.341 6.63-3.865.8-4.657-1.179-2.844-.539-2.227-1.224-1.3-4.456-2.916-2.154a9.252 9.252 0 0 0 .309-1.38c-.115.192.259-3.257-.673-1.32s-2.1 1.037-3.069.762-1.8-1.118-1.071-1.689c.023-.016 2.436-3.172 4.531-4.058z"/><path d="M589 585c-2.584-.47-10.055.362-13 13 0 0 1.9 3.349 5 4s6 21 6 21 24.016 11.06 27-3c-.07-13.826-8-21-8-21s5.829-3.2 5-6-8.016-10.153-11-10-6 0-6 0-2.416 2.47-5 2z" style="fill:#f6bb07;fill-rule:evenodd"/><path style="fill:#f8cfad;fill-rule:evenodd" d="M563.284 612.581s-.986 2.965-1.814 2.389-2.678-.3-2.675-.374-.333-.755-1.912-1.854 2.577-4.583 5.414-2.167a2.551 2.551 0 0 1 .987 2.006z"/></g>'});$1.displayName="EmptyIcon";const ql=()=>s(ie,{name:"lock"},()=>s("path",{d:"M787.168 952.268H236.832c-30.395 0-55.033-24.638-55.033-55.033V429.45c0-30.395 24.638-55.034 55.033-55.034h82.55V264.35c0-106.38 86.238-192.618 192.618-192.618S704.618 157.97 704.618 264.35v110.066h82.55c30.395 0 55.033 24.639 55.033 55.034v467.785c0 30.395-24.639 55.033-55.033 55.033zM484.483 672.046v115.122h55.034V672.046c31.99-11.373 55.033-41.605 55.033-77.496 0-45.592-36.958-82.55-82.55-82.55s-82.55 36.958-82.55 82.55c0 35.89 23.042 66.123 55.033 77.496zM622.067 264.35c0-60.788-49.28-110.067-110.067-110.067s-110.067 49.28-110.067 110.067v110.066h220.135V264.35z"}));ql.displayName="LockIcon";const J8=M({name:"ArticleItem",props:{info:{type:Object,required:!0},path:{type:String,required:!0}},slots:Object,setup(e,{slots:t}){const n=zn(e,"info"),{info:r,items:a}=A8(e);return()=>{var p,h,v;const{[Ue.title]:o,[je.type]:l,[je.isEncrypted]:i=!1,[je.cover]:c,[je.excerpt]:u,[je.sticky]:d}=n.value,f=r.value;return s("div",{class:"vp-article-wrapper"},s("article",{class:"vp-article-item",vocab:"https://schema.org/",typeof:"Article"},[((p=t.cover)==null?void 0:p.call(t,{cover:c}))??(c?[s("img",{class:"vp-article-cover",src:be(c),alt:"",loading:"lazy"}),s("meta",{property:"image",content:be(c)})]:[]),d?s(P1):null,s(Ie,{to:e.path},()=>{var _;return((_=t.title)==null?void 0:_.call(t,{title:o,isEncrypted:i,type:l}))??s("header",{class:"vp-article-title"},[i?s(ql):null,l===Ro.slide?s(I1):null,s("span",{property:"headline"},o)])}),((h=t.excerpt)==null?void 0:h.call(t,{excerpt:u}))??(u?s("div",{class:"vp-article-excerpt",innerHTML:u}):null),s("hr",{class:"vp-article-hr"}),((v=t.info)==null?void 0:v.call(t,{info:f}))??s(S1,{info:f,...a.value?{items:a.value}:{}})]))}}}),Q8=M({name:"Pagination",props:{total:{type:Number,default:10},perPage:{type:Number,default:10},current:{type:Number,default:1}},emits:["updateCurrentPage"],setup(e,{emit:t}){let n;const r=ce(),a=z(""),o=w(()=>r.value.paginationLocales),l=w(()=>Math.ceil(e.total/e.perPage)),i=w(()=>!!l.value&&l.value!==1),c=w(()=>l.value<7?!1:e.current>4),u=w(()=>l.value<7?!1:e.current<l.value-3),d=w(()=>{const{current:h}=e;let v=1,_=l.value;const E=[];l.value>=7&&(h<=4&&h<l.value-3?(v=1,_=5):h>4&&h>=l.value-3?(_=l.value,v=l.value-4):l.value>7&&(v=h-2,_=h+2));for(let b=v;b<=_;b++)E.push(b);return E}),f=h=>t("updateCurrentPage",h),p=h=>{const v=parseInt(h,10);v<=l.value&&v>0?f(v):n.pop(`<svg viewBox="0 0 1024 1024" xmlns="http://www.w3.org/2000/svg" width="16" height="16"><path d="M64 512a448 448 0 1 0 896 0 448 448 0 1 0-896 0Z" fill="#FA5151"/><path d="m557.3 512 113.1-113.1c12.5-12.5 12.5-32.8 0-45.3s-32.8-12.5-45.3 0L512 466.7 398.9 353.6c-12.5-12.5-32.8-12.5-45.3 0s-12.5 32.8 0 45.3L466.7 512 353.6 625.1c-12.5 12.5-12.5 32.8 0 45.3 6.2 6.2 14.4 9.4 22.6 9.4s16.4-3.1 22.6-9.4L512 557.3l113.1 113.1c6.2 6.2 14.4 9.4 22.6 9.4s16.4-3.1 22.6-9.4c12.5-12.5 12.5-32.8 0-45.3L557.3 512z" fill="#FFF"/></svg>${o.value.errorText.replace(/\$page/gu,l.value.toString())}`)};return se(()=>{n=new p4}),()=>s("div",{class:"vp-pagination"},i.value?s("nav",{class:"vp-pagination-list"},[s("div",{class:"vp-pagination-number "},[e.current>1?s("div",{class:"prev",role:"navigation",unselectable:"on",onClick:()=>f(e.current-1)},o.value.prev):null,c.value?[s("div",{role:"navigation",onClick:()=>f(1)},1),s("div",{class:"ellipsis"},"...")]:null,d.value.map(h=>s("div",{key:h,class:{active:e.current===h},role:"navigation",onClick:()=>f(h)},h)),u.value?[s("div",{class:"ellipsis"},"..."),s("div",{role:"navigation",onClick:()=>f(l.value)},l.value)]:null,e.current<l.value?s("div",{class:"next",role:"navigation",unselectable:"on",onClick:()=>f(e.current+1)},o.value.next):null]),s("div",{class:"vp-pagination-nav"},[s("label",{for:"navigation-text"},`${o.value.navigate}: `),s("input",{id:"navigation-text",value:a.value,onInput:({target:h})=>{a.value=h.value},onKeydown:h=>{h.key==="Enter"&&(h.preventDefault(),p(a.value))}}),s("button",{class:"vp-pagination-button",type:"button",role:"navigation",title:o.value.action,onClick:()=>p(a.value)},o.value.action)])]):[])}}),Gl=M({name:"ArticleList",props:{items:{type:Array,default:()=>[]}},setup(e){const t=Ht(),n=wn(),r=Vr(),a=z(1),o=w(()=>r.value.articlePerPage??10),l=w(()=>e.items.slice((a.value-1)*o.value,a.value*o.value)),i=async c=>{a.value=c;const u={...t.query};!(u.page===c.toString()||c===1&&!u.page)&&(c===1?delete u.page:u.page=c.toString(),await n.push({path:t.path,query:u}))};return se(()=>{const{page:c}=t.query;i(c?Number(c):1),ae(a,()=>{const u=document.querySelector("#article-list").getBoundingClientRect().top+window.scrollY;setTimeout(()=>{window.scrollTo(0,u)},100)})}),()=>s("div",{id:"article-list",class:"vp-article-list",role:"feed"},l.value.length?[...l.value.map(({info:c,path:u},d)=>s(oe,{appear:!0,delay:d*.04},()=>s(J8,{key:u,info:c,path:u}))),s(Q8,{current:a.value,perPage:o.value,total:e.items.length,onUpdateCurrentPage:i})]:s($1))}}),F1=M({name:"CategoryList",setup(){const e=ge(),t=Hr();return()=>s("ul",{class:"vp-category-list"},Ma(t.value.map).sort(([,n],[,r])=>r.items.length-n.items.length).map(([n,{path:r,items:a}])=>s("li",{class:["vp-category",`vp-category${Ra(n,9)}`,{active:r===e.value.path}]},s(Ie,{to:r},()=>[n,s("span",{class:"count"},a.length)]))))}}),H1=M({name:"TagList",setup(){const e=he(),t=Nr(),n=r=>{var a;return r===((a=e.value.blog)==null?void 0:a.name)};return()=>s("ul",{class:"tag-list-wrapper"},Ma(t.value.map).sort(([,r],[,a])=>a.items.length-r.items.length).map(([r,{path:a,items:o}])=>s("li",{class:["tag",`tag${Ra(r,9)}`,{active:n(r)}]},s(Ie,{to:a},()=>[r,s("span",{class:"tag-num"},o.length)]))))}}),Y8=M({name:"TimelineList",setup(){const e=ce(),t=Rl(),n=An(),r=w(()=>e.value.blogLocales.timeline);return()=>s("div",{class:"timeline-list-wrapper"},[s("div",{class:"timeline-list-title",onClick:()=>n(t.value.path)},[s(zl),s("span",{class:"num"},t.value.items.length),r.value]),s("hr"),s("div",{class:"timeline-content"},s("ul",{class:"timeline-list"},t.value.config.map(({year:a,items:o},l)=>s(oe,{appear:!0,delay:.08*(l+1)},()=>s("li",[s("h3",{class:"timeline-year"},a),s("ul",{class:"timeline-year-wrapper"},o.map(({date:i,info:c,path:u})=>s("li",{class:"timeline-item"},[s("span",{class:"timeline-date"},i),s(Ie,{class:"timeline-title",to:u},()=>c[Ue.title])])))])))))])}}),Z8={article:Fa,category:Vl,tag:jl,timeline:zl},N1=M({name:"InfoList",setup(){const e=ce(),t=Kn(),n=Hr(),r=w(()=>En(n.value.map).length),a=$l(),o=Nr(),l=w(()=>En(o.value.map).length),i=An(),c=z("article"),u=w(()=>e.value.blogLocales);return()=>s("div",{class:"vp-blog-infos"},[s("div",{class:"vp-blog-type-switcher"},Ma(Z8).map(([d,f])=>s("button",{type:"button",class:"vp-blog-type-button",onClick:()=>{c.value=d}},s("div",{class:["icon-wrapper",{active:c.value===d}],"aria-label":u.value[d],"data-balloon-pos":"up"},s(f))))),s(oe,()=>c.value==="article"?s("div",{class:"vp-star-article-wrapper"},[s("div",{class:"title",onClick:()=>i(t.value.path)},[s(Fa),s("span",{class:"num"},t.value.items.length),u.value.article]),s("hr"),a.value.items.length?s("ul",{class:"vp-star-articles"},a.value.items.map(({info:d,path:f},p)=>s(oe,{appear:!0,delay:.08*(p+1)},()=>s("li",{class:"vp-star-article"},s(Ie,{to:f},()=>d[Ue.title]))))):s("div",{class:"vp-star-article-empty"},u.value.empty.replace("$text",u.value.star))]):c.value==="category"?s("div",{class:"vp-category-wrapper"},[r.value?[s("div",{class:"title",onClick:()=>i(n.value.path)},[s(Vl),s("span",{class:"num"},r.value),u.value.category]),s("hr"),s(oe,{delay:.04},()=>s(F1))]:s("div",{class:"vp-category-empty"},u.value.empty.replace("$text",u.value.category))]):c.value==="tag"?s("div",{class:"vp-tag-wrapper"},[l.value?[s("div",{class:"title",onClick:()=>i(o.value.path)},[s(jl),s("span",{class:"num"},l.value),u.value.tag]),s("hr"),s(oe,{delay:.04},()=>s(H1))]:s("div",{class:"vp-tag-empty"},u.value.empty.replace("$text",u.value.tag))]):s(oe,()=>s(Y8)))])}}),jr=M({name:"BlogWrapper",slots:Object,setup(e,{slots:t}){const{isMobile:n}=$r();return()=>[s(Hl),s(Ol,{noSidebar:!0,noToc:!0},{default:()=>t.default(),navScreenBottom:()=>s(Nl),...n.value?{sidebar:()=>s(N1)}:{}})]}}),zr=()=>s("aside",{class:"vp-blog-info-wrapper"},[s(oe,()=>s(Nl)),s(oe,{delay:.04},()=>s(N1))]);zr.displayName="InfoPanel";const X8=M({name:"BlogPage",setup(){const e=ge(),t=he(),n=Hr(),r=Nr();return()=>{const{key:a="",name:o=""}=t.value.blog||{},l=o?a==="category"?n.value.map[o].items:a==="tag"?r.value.map[o].items:[]:[];return s(jr,()=>s("div",{class:"vp-page vp-blog"},s("div",{class:"blog-page-wrapper"},[s("main",{id:"main-content",class:"vp-blog-main"},[s(oe,()=>a==="category"?s(F1):a==="tag"?s(H1):null),o?s(oe,{appear:!0,delay:.24},()=>s(Gl,{key:e.value.path,items:l})):null]),s(oe,{delay:.16},()=>s(zr,{key:"blog"}))])))}}}),e5="//theme-hope-assets.vuejs.press/hero/default.jpg",t5=M({name:"BlogHero",slots:Object,setup(e,{slots:t}){const n=he(),r=Gn(),a=xe(),o=w(()=>n.value.heroFullScreen??!1),l=w(()=>{const{heroText:c,heroImage:u,heroImageDark:d,heroAlt:f,heroImageStyle:p,tagline:h}=n.value;return{text:c??r.value.title??"Hello",tagline:h??"",image:u?be(u):null,imageDark:d?be(d):null,alt:f??c??"",imageStyle:p,isFullScreen:o.value}}),i=w(()=>{const{bgImage:c,bgImageDark:u,bgImageStyle:d}=n.value;return{image:we(c)?be(c):c===!1?null:e5,imageDark:we(u)?be(u):null,bgStyle:d,isFullScreen:o.value}});return()=>{var c,u;return n.value.hero===!1?null:s("div",{ref:a,class:["vp-blog-hero",{fullscreen:o.value,"no-bg":!i.value.image}]},[((c=t.bg)==null?void 0:c.call(t,i.value))??[i.value.image?s("div",{class:["vp-blog-mask",{light:i.value.imageDark}],style:[{background:`url(${i.value.image}) center/cover no-repeat`},i.value.bgStyle]}):null,i.value.imageDark?s("div",{class:"vp-blog-mask dark",style:[{background:`url(${i.value.imageDark}) center/cover no-repeat`},i.value.bgStyle]}):null],((u=t.info)==null?void 0:u.call(t,l.value))??[s(oe,{appear:!0,type:"group",delay:.04},()=>{const{image:d,imageDark:f,imageStyle:p,alt:h}=l.value;return[d?s("img",{key:"light",class:["vp-blog-hero-image",{light:f}],style:p,src:d,alt:h}):null,f?s("img",{key:"dark",class:"vp-blog-hero-image dark",style:p,src:f,alt:h}):null]}),s(oe,{appear:!0,delay:.08},()=>l.value.text?s("h1",{class:"vp-blog-hero-title"},l.value.text):null),s(oe,{appear:!0,delay:.12},()=>l.value.tagline?s("p",{class:"vp-blog-hero-description",innerHTML:l.value.tagline}):null)],l.value.isFullScreen?s("button",{type:"button",class:"slide-down-button",onClick:()=>{window.scrollTo({top:a.value.clientHeight,behavior:"smooth"})}},[s(jo),s(jo)]):null])}}}),Gt=cn("bing-image",{index:0,data:[]}),n5=M({name:"BingHeroBackground",setup(){const e=Pa(),t=xe(),n=z(!1),r=w(()=>{const i=Gt.value.data[Gt.value.index],c=e.value.toLowerCase().split("-").shift();if(i){const{url:u,wallpaper:d,downloadable:f,locales:p}=i;return{url:u,wallpaper:d,downloadable:f,...p[c]??p.en}}return null}),a=()=>fetch("https://bing-wallpaper.vuejs.press/api/wallpaper").then(i=>i.json()),o=()=>{Gt.value.index-=1},l=()=>{Gt.value.index+=1};return lu(t,()=>{n.value=!1}),se(()=>{a().then(i=>{Gt.value.data=i})}),()=>{const{title:i,headline:c,url:u,backstage:d,quickFact:f,copyright:p}=r.value??{};return s(Or,()=>u?[s("div",{class:"vp-blog-mask",style:{background:`url(${u}) center/cover no-repeat`}}),s("div",{class:"bing-switch",onClick:()=>{n.value=!0}},[s(Rt,{name:"fade"},()=>n.value?s("div",{class:"bing-info",ref:t},[s("a",{href:d,target:"_blank",class:"bing-info-header"},c),s("hr"),s("div",{class:"bing-info-body"},f),s("div",{class:"bing-info-copyright"},p)]):null),s("div",{class:"bing-location"},[s("span",{class:"bing-location-icon"}),i]),s("button",{class:"bing-switch-prev",title:"prev image",type:"button",disabled:Gt.value.index===0,onClick:()=>o()}),s("button",{class:"bing-switch-next",title:"next image",type:"button",disabled:Gt.value.index===Gt.value.data.length-1,onClick:()=>l()})])]:null)}}}),r5=M({name:"HitokotoBlogHero",inheritAttrs:!1,props:{text:{type:String,required:!0},image:{type:String,default:null},imageDark:{type:String,default:null},alt:{type:String,required:!0},imageStyle:{type:[String,Object],default:null}},setup(e){const t=z(""),n=z(""),r=z("");let a=!1;const o=()=>fetch("https://v1.hitokoto.cn").then(l=>l.json()).then(({from:l,hitokoto:i})=>{t.value=i,r.value=l});return se(()=>{a=!0,ae(t,()=>{n.value="";let l=0;const i=()=>(n.value+=t.value[l],l+=1,_t().then(()=>{l<t.value.length?setTimeout(()=>{i()},150):a&&setTimeout(()=>{o()},3e3)}));i()}),o()}),Ft(()=>{a=!1}),()=>[s(oe,{appear:!0,type:"group",delay:.04},()=>[e.image?s("img",{key:"light",class:["vp-blog-hero-image",{light:e.imageDark}],style:e.imageStyle,src:e.image,alt:e.alt}):null,e.imageDark?s("img",{key:"dark",class:"vp-blog-hero-image dark",style:e.imageStyle,src:e.imageDark,alt:e.alt}):null]),s(oe,{appear:!0,delay:.08},()=>e.text?s("h1",{class:"vp-blog-hero-title"},e.text):null),s("div",{class:"hitokoto"},[s("p",{class:"hitokoto-text"},s("span",n.value)),s("p",{class:"hitokoto-author",style:{opacity:n.value.length>4?1:0}},`——「${r.value}」`)])]}}),a5=M({__name:"BlogHero",setup(e){return(t,n)=>(cl(),ul(bt(t5),null,{bg:pa(()=>[Te(bt(n5))]),info:pa(r=>[Te(bt(r5),s2(_c(r)),null,16)]),_:1}))}}),o5=Fl(a5,[["__file","BlogHero.vue"]]),l5=["link","article","book","project","friend"],s5=M({name:"ProjectPanel",components:{ArticleIcon:Fa,BookIcon:D1,FriendIcon:R1,LinkIcon:O1,ProjectIcon:M1},props:{items:{type:Array,required:!0}},setup(e){const t=Cn(),n=An(),r=(a="",o="icon")=>l5.includes(a)?s(pt(`${a}-icon`)):sn(a)?s("img",{class:"vp-project-image",src:a,alt:o}):Rr(a)?s("img",{class:"vp-project-image",src:be(a),alt:o}):s(Ve,{icon:a});return()=>s("div",{class:"vp-project-panel"},e.items.map(({icon:a,link:o,name:l,desc:i,background:c},u)=>s("div",{class:["vp-project-card",{[`project${u%9}`]:!t.value&&!c}],...c?{style:c}:{},onClick:()=>n(o)},[r(a,l),s("div",{class:"vp-project-name"},l),s("div",{class:"vp-project-desc"},i)])))}}),i5=M({name:"BlogHomePage",setup(){const e=Kn(),t=he(),n=w(()=>t.value.projects??[]);return()=>s("div",{class:"vp-page vp-blog"},[s(o5),s("div",{class:"blog-page-wrapper"},[s("main",{id:"main-content",class:"vp-blog-main"},[n.value.length?s(oe,{appear:!0,delay:.16},()=>s(s5,{items:n.value})):null,s(oe,{appear:!0,delay:.24},()=>s(Gl,{items:e.value.items}))]),s(oe,{appear:!0,delay:.16},()=>s(zr,{key:"blog"}))]),s(oe,{appear:!0,delay:.28},()=>s(Wn))])}}),V1=()=>s(jr,()=>s(i5));V1.displayName="BlogHome";var c5=[];const u5=M({name:"ArticleType",setup(){const e=ge(),t=Ye(),n=ce(),r=Kn(),a=$l(),o=w(()=>{const l=n.value.blogLocales;return[{text:l.all,path:r.value.path},{text:l.star,path:a.value.path},...c5.map(({key:i,path:c})=>({text:l[i],path:c.replace(/^\//,t.value)}))]});return()=>s("ul",{class:"vp-article-type-wrapper"},o.value.map(l=>s("li",{class:["vp-article-type",{active:l.path===e.value.path}]},s(Ie,{to:l.path},()=>l.text))))}}),d5=M({name:"BlogPage",setup(){const e=$a(),t=he(),n=ge(),r=Kn(),a=$l(),o=w(()=>{const{key:l="",type:i}=t.value.blog||{};return l==="star"?a.value.items:i==="type"&&l?e.value.items:r.value.items});return()=>s(jr,()=>s("div",{class:"vp-page vp-blog"},s("div",{class:"blog-page-wrapper"},[s("main",{id:"main-content",class:"vp-blog-main"},[s(oe,()=>s(u5)),s(oe,{appear:!0,delay:.24},()=>s(Gl,{key:n.value.path,items:o.value}))]),s(oe,{delay:.16},()=>s(zr,{key:"blog"}))])))}}),f5=M({name:"PortfolioHero",slots:Object,setup(e,{slots:t}){const n=C8(),r=he(),a=z(0),o=w(()=>{var p;return((p=r.value.titles)==null?void 0:p[a.value])??""}),l=z(""),i=w(()=>{const{name:p,avatar:h,avatarDark:v,avatarAlt:_,avatarStyle:E}=r.value;return{name:p??n.value.name,avatar:h?be(h):null,avatarDark:v?be(v):null,avatarStyle:E,alt:_||p||""}}),c=w(()=>{const{bgImage:p,bgImageDark:h,bgImageStyle:v}=r.value;return{image:we(p)?be(p):null,imageDark:we(h)?be(h):null,bgStyle:v}}),u=w(()=>{const{welcome:p,name:h,titles:v,medias:_}=r.value;return{name:h??n.value.name,welcome:p??"👋 Hi There, I'm",title:l.value,titles:v??[],medias:_??[]}}),d=()=>{l.value="";let p=0,h=!1;const v=async()=>{if(!h)if(l.value+=o.value[p],p+=1,await _t(),p<o.value.length)setTimeout(()=>{v()},150);else{const _=u.value.titles.length;setTimeout(()=>{a.value=_<=1||a.value===u.value.titles.length-1?0:a.value+1},1e3)}};return v(),()=>{h=!0}};let f;return se(()=>{ae(o,()=>{f==null||f(),f=d()},{immediate:!0})}),()=>{var p,h,v;return s("section",{id:"portfolio",class:["vp-portfolio-wrapper",{bg:c.value.image}]},[((p=t.bg)==null?void 0:p.call(t,c.value))??[c.value.image?s("div",{class:["vp-portfolio-mask",{light:c.value.imageDark}],style:[{background:`url(${c.value.image}) center/cover no-repeat`},c.value.bgStyle]}):null,c.value.imageDark?s("div",{class:"vp-portfolio-mask dark",style:[{background:`url(${c.value.imageDark}) center/cover no-repeat`},c.value.bgStyle]}):null],((h=t.avatar)==null?void 0:h.call(t,i.value))??s("div",{class:"vp-portfolio-avatar"},[s(oe,{delay:.04},()=>{const{avatarDark:_,name:E,alt:b,avatarStyle:C}=i.value;return[s("img",{key:"light",class:{light:_},src:i.value.avatar,title:E,alt:b,style:C}),_?s("img",{key:"dark",class:"dark",src:_,title:E,alt:b,style:C}):null]})]),s("div",{class:"vp-portfolio-container"},((v=t.info)==null?void 0:v.call(t,u.value))??s("div",{class:"vp-portfolio-info"},[s(oe,{appear:!0,delay:.08},()=>s("h6",{class:"vp-portfolio-welcome"},u.value.welcome)),s(oe,{appear:!0,delay:.12},()=>s("h1",{class:"vp-portfolio-name"},u.value.name)),s(oe,{appear:!0,delay:.16},()=>s("h2",{class:"vp-portfolio-title"},l.value)),s(oe,{appear:!0,delay:.2},()=>u.value.medias.length?s("div",{class:"vp-portfolio-medias"},u.value.medias.map(({name:_,url:E,icon:b})=>s("a",{class:"vp-portfolio-media",href:E,rel:"noopener noreferrer",target:"_blank",..._?{"aria-label":_,"data-balloon-pos":"up"}:{}},s(Ve,{icon:b})))):s(B1))]))])}}}),j1=()=>s(jr,()=>[s(f5),s("div",{class:"vp-page vp-portfolio"},s(oe,{appear:!0,delay:.24},()=>s(Wn)))]);j1.displayName="PortfolioHome";const p5=M({name:"TimelineItems",setup(){const e=Vr(),t=ce(),n=Rl(),r=w(()=>e.value.timeline??t.value.blogLocales.timelineTitle),a=w(()=>n.value.config.map(({year:o})=>({title:o.toString(),level:2,slug:o.toString(),children:[]})));return()=>s("div",{class:"timeline-wrapper"},s("ul",{class:"timeline-content"},[s(oe,()=>s("li",{class:"motto"},r.value)),s(L1,{items:a.value}),n.value.config.map(({year:o,items:l},i)=>s(oe,{appear:!0,delay:.08*(i+1),type:"group"},()=>[s("h3",{key:"title",id:o,class:"timeline-year-title"},s("span",o)),s("li",{key:"content",class:"timeline-year-list"},[s("ul",{class:"timeline-year-wrapper"},l.map(({date:c,info:u,path:d})=>s("li",{class:"timeline-item"},[s("span",{class:"timeline-date"},c),s(Ie,{class:"timeline-title",to:d},()=>u[Ue.title])])))])]))]))}}),z1=()=>s(jr,()=>s("div",{class:"vp-page vp-blog"},s("div",{class:"blog-page-wrapper"},[s("main",{id:"main-content",class:"vp-blog-main"},[s(oe,{appear:!0,delay:.24},()=>s(p5))]),s(oe,{delay:.16},()=>s(zr,{key:"blog"}))])));z1.displayName="Timeline";const q1=M({name:"PasswordModal",props:{full:Boolean},emits:["verify"],setup(e,{emit:t}){const n=he(),r=ce(),a=z(""),o=z(!1),l=z(!1),i=w(()=>r.value.encryptLocales);let c=null;const u=()=>{c&&clearTimeout(c),o.value=!1,t("verify",a.value,l.value),_t().then(()=>{o.value=!0,c=setTimeout(()=>{o.value=!1},1e3)})};return()=>s("div",{class:["vp-decrypt-layer",{expand:e.full||n.value.home}]},s("div",{class:"vp-decrypt-modal"},[s("div",{class:["vp-decrypt-hint",{tried:o.value}]},o.value?i.value.errorHint:s(ql,{"aria-label":i.value.iconLabel})),s("div",{class:"vp-decrypt-input"},[s("input",{type:"password",value:a.value,placeholder:i.value.placeholder,onInput:({target:d})=>{a.value=d.value},onKeydown:({key:d})=>{d==="Enter"&&u()}})]),s("div",{class:"vp-remember-password"},[s("input",{type:"checkbox",value:l.value,onChange:()=>l.value=!l.value}),i.value.remember]),s("button",{type:"button",class:"vp-decrypt-submit",onClick:()=>u()},"OK")]))}}),G1=()=>{const e=Nt();return w(()=>e.value.encrypt||{})};var h5={};const Sn="./ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789".split(""),po=Array.from({length:64},(e,t)=>t),aa=e=>Array(e).fill(-1),Ut=[...aa(46),0,1,...po.slice(54,64),...aa(7),...po.slice(2,28),...aa(6),...po.slice(28,54),...aa(5)],mi=[608135816,2242054355,320440878,57701188,2752067618,698298832,137296536,3964562569,1160258022,953160567,3193202383,887688300,3232508343,3380367581,1065670069,3041331479,2450970073,2306472731],vi=[3509652390,2564797868,805139163,3491422135,3101798381,1780907670,3128725573,4046225305,614570311,3012652279,134345442,2240740374,1667834072,1901547113,2757295779,4103290238,227898511,1921955416,1904987480,2182433518,2069144605,3260701109,2620446009,720527379,3318853667,677414384,3393288472,3101374703,2390351024,1614419982,1822297739,2954791486,3608508353,3174124327,2024746970,1432378464,3864339955,2857741204,1464375394,1676153920,1439316330,715854006,3033291828,289532110,2706671279,2087905683,3018724369,1668267050,732546397,1947742710,3462151702,2609353502,2950085171,1814351708,2050118529,680887927,999245976,1800124847,3300911131,1713906067,1641548236,4213287313,1216130144,1575780402,4018429277,3917837745,3693486850,3949271944,596196993,3549867205,258830323,2213823033,772490370,2760122372,1774776394,2652871518,566650946,4142492826,1728879713,2882767088,1783734482,3629395816,2517608232,2874225571,1861159788,326777828,3124490320,2130389656,2716951837,967770486,1724537150,2185432712,2364442137,1164943284,2105845187,998989502,3765401048,2244026483,1075463327,1455516326,1322494562,910128902,469688178,1117454909,936433444,3490320968,3675253459,1240580251,122909385,2157517691,634681816,4142456567,3825094682,3061402683,2540495037,79693498,3249098678,1084186820,1583128258,426386531,1761308591,1047286709,322548459,995290223,1845252383,2603652396,3431023940,2942221577,3202600964,3727903485,1712269319,422464435,3234572375,1170764815,3523960633,3117677531,1434042557,442511882,3600875718,1076654713,1738483198,4213154764,2393238008,3677496056,1014306527,4251020053,793779912,2902807211,842905082,4246964064,1395751752,1040244610,2656851899,3396308128,445077038,3742853595,3577915638,679411651,2892444358,2354009459,1767581616,3150600392,3791627101,3102740896,284835224,4246832056,1258075500,768725851,2589189241,3069724005,3532540348,1274779536,3789419226,2764799539,1660621633,3471099624,4011903706,913787905,3497959166,737222580,2514213453,2928710040,3937242737,1804850592,3499020752,2949064160,2386320175,2390070455,2415321851,4061277028,2290661394,2416832540,1336762016,1754252060,3520065937,3014181293,791618072,3188594551,3933548030,2332172193,3852520463,3043980520,413987798,3465142937,3030929376,4245938359,2093235073,3534596313,375366246,2157278981,2479649556,555357303,3870105701,2008414854,3344188149,4221384143,3956125452,2067696032,3594591187,2921233993,2428461,544322398,577241275,1471733935,610547355,4027169054,1432588573,1507829418,2025931657,3646575487,545086370,48609733,2200306550,1653985193,298326376,1316178497,3007786442,2064951626,458293330,2589141269,3591329599,3164325604,727753846,2179363840,146436021,1461446943,4069977195,705550613,3059967265,3887724982,4281599278,3313849956,1404054877,2845806497,146425753,1854211946,1266315497,3048417604,3681880366,3289982499,290971e4,1235738493,2632868024,2414719590,3970600049,1771706367,1449415276,3266420449,422970021,1963543593,2690192192,3826793022,1062508698,1531092325,1804592342,2583117782,2714934279,4024971509,1294809318,4028980673,1289560198,2221992742,1669523910,35572830,157838143,1052438473,1016535060,1802137761,1753167236,1386275462,3080475397,2857371447,1040679964,2145300060,2390574316,1461121720,2956646967,4031777805,4028374788,33600511,2920084762,1018524850,629373528,3691585981,3515945977,2091462646,2486323059,586499841,988145025,935516892,3367335476,2599673255,2839830854,265290510,3972581182,2759138881,3795373465,1005194799,847297441,406762289,1314163512,1332590856,1866599683,4127851711,750260880,613907577,1450815602,3165620655,3734664991,3650291728,3012275730,3704569646,1427272223,778793252,1343938022,2676280711,2052605720,1946737175,3164576444,3914038668,3967478842,3682934266,1661551462,3294938066,4011595847,840292616,3712170807,616741398,312560963,711312465,1351876610,322626781,1910503582,271666773,2175563734,1594956187,70604529,3617834859,1007753275,1495573769,4069517037,2549218298,2663038764,504708206,2263041392,3941167025,2249088522,1514023603,1998579484,1312622330,694541497,2582060303,2151582166,1382467621,776784248,2618340202,3323268794,2497899128,2784771155,503983604,4076293799,907881277,423175695,432175456,1378068232,4145222326,3954048622,3938656102,3820766613,2793130115,2977904593,26017576,3274890735,3194772133,1700274565,1756076034,4006520079,3677328699,720338349,1533947780,354530856,688349552,3973924725,1637815568,332179504,3949051286,53804574,2852348879,3044236432,1282449977,3583942155,3416972820,4006381244,1617046695,2628476075,3002303598,1686838959,431878346,2686675385,1700445008,1080580658,1009431731,832498133,3223435511,2605976345,2271191193,2516031870,1648197032,4164389018,2548247927,300782431,375919233,238389289,3353747414,2531188641,2019080857,1475708069,455242339,2609103871,448939670,3451063019,1395535956,2413381860,1841049896,1491858159,885456874,4264095073,4001119347,1565136089,3898914787,1108368660,540939232,1173283510,2745871338,3681308437,4207628240,3343053890,4016749493,1699691293,1103962373,3625875870,2256883143,3830138730,1031889488,3479347698,1535977030,4236805024,3251091107,2132092099,1774941330,1199868427,1452454533,157007616,2904115357,342012276,595725824,1480756522,206960106,497939518,591360097,863170706,2375253569,3596610801,1814182875,2094937945,3421402208,1082520231,3463918190,2785509508,435703966,3908032597,1641649973,2842273706,3305899714,1510255612,2148256476,2655287854,3276092548,4258621189,236887753,3681803219,274041037,1734335097,3815195456,3317970021,1899903192,1026095262,4050517792,356393447,2410691914,3873677099,3682840055,3913112168,2491498743,4132185628,2489919796,1091903735,1979897079,3170134830,3567386728,3557303409,857797738,1136121015,1342202287,507115054,2535736646,337727348,3213592640,1301675037,2528481711,1895095763,1721773893,3216771564,62756741,2142006736,835421444,2531993523,1442658625,3659876326,2882144922,676362277,1392781812,170690266,3921047035,1759253602,3611846912,1745797284,664899054,1329594018,3901205900,3045908486,2062866102,2865634940,3543621612,3464012697,1080764994,553557557,3656615353,3996768171,991055499,499776247,1265440854,648242737,3940784050,980351604,3713745714,1749149687,3396870395,4211799374,3640570775,1161844396,3125318951,1431517754,545492359,4268468663,3499529547,1437099964,2702547544,3433638243,2581715763,2787789398,1060185593,1593081372,2418618748,4260947970,69676912,2159744348,86519011,2512459080,3838209314,1220612927,3339683548,133810670,1090789135,1078426020,1569222167,845107691,3583754449,4072456591,1091646820,628848692,1613405280,3757631651,526609435,236106946,48312990,2942717905,3402727701,1797494240,859738849,992217954,4005476642,2243076622,3870952857,3732016268,765654824,3490871365,2511836413,1685915746,3888969200,1414112111,2273134842,3281911079,4080962846,172450625,2569994100,980381355,4109958455,2819808352,2716589560,2568741196,3681446669,3329971472,1835478071,660984891,3704678404,4045999559,3422617507,3040415634,1762651403,1719377915,3470491036,2693910283,3642056355,3138596744,1364962596,2073328063,1983633131,926494387,3423689081,2150032023,4096667949,1749200295,3328846651,309677260,2016342300,1779581495,3079819751,111262694,1274766160,443224088,298511866,1025883608,3806446537,1145181785,168956806,3641502830,3584813610,1689216846,3666258015,3200248200,1692713982,2646376535,4042768518,1618508792,1610833997,3523052358,4130873264,2001055236,3610705100,2202168115,4028541809,2961195399,1006657119,2006996926,3186142756,1430667929,3210227297,1314452623,4074634658,4101304120,2273951170,1399257539,3367210612,3027628629,1190975929,2062231137,2333990788,2221543033,2438960610,1181637006,548689776,2362791313,3372408396,3104550113,3145860560,296247880,1970579870,3078560182,3769228297,1714227617,3291629107,3898220290,166772364,1251581989,493813264,448347421,195405023,2709975567,677966185,3703036547,1463355134,2715995803,1338867538,1343315457,2802222074,2684532164,233230375,2599980071,2000651841,3277868038,1638401717,4028070440,3237316320,6314154,819756386,300326615,590932579,1405279636,3267499572,3150704214,2428286686,3959192993,3461946742,1862657033,1266418056,963775037,2089974820,2263052895,1917689273,448879540,3550394620,3981727096,150775221,3627908307,1303187396,508620638,2975983352,2726630617,1817252668,1876281319,1457606340,908771278,3720792119,3617206836,2455994898,1729034894,1080033504,976866871,3556439503,2881648439,1522871579,1555064734,1336096578,3548522304,2579274686,3574697629,3205460757,3593280638,3338716283,3079412587,564236357,2993598910,1781952180,1464380207,3163844217,3332601554,1699332808,1393555694,1183702653,3581086237,1288719814,691649499,2847557200,2895455976,3193889540,2717570544,1781354906,1676643554,2592534050,3230253752,1126444790,2770207658,2633158820,2210423226,2615765581,2414155088,3127139286,673620729,2805611233,1269405062,4015350505,3341807571,4149409754,1057255273,2012875353,2162469141,2276492801,2601117357,993977747,3918593370,2654263191,753973209,36408145,2530585658,25011837,3520020182,2088578344,530523599,2918365339,1524020338,1518925132,3760827505,3759777254,1202760957,3985898139,3906192525,674977740,4174734889,2031300136,2019492241,3983892565,4153806404,3822280332,352677332,2297720250,60907813,90501309,3286998549,1016092578,2535922412,2839152426,457141659,509813237,4120667899,652014361,1966332200,2975202805,55981186,2327461051,676427537,3255491064,2882294119,3433927263,1307055953,942726286,933058658,2468411793,3933900994,4215176142,1361170020,2001714738,2830558078,3274259782,1222529897,1679025792,2729314320,3714953764,1770335741,151462246,3013232138,1682292957,1483529935,471910574,1539241949,458788160,3436315007,1807016891,3718408830,978976581,1043663428,3165965781,1927990952,4200891579,2372276910,3208408903,3533431907,1412390302,2931980059,4132332400,1947078029,3881505623,4168226417,2941484381,1077988104,1320477388,886195818,18198404,3786409e3,2509781533,112762804,3463356488,1866414978,891333506,18488651,661792760,1628790961,3885187036,3141171499,876946877,2693282273,1372485963,791857591,2686433993,3759982718,3167212022,3472953795,2716379847,445679433,3561995674,3504004811,3574258232,54117162,3331405415,2381918588,3769707343,4154350007,1140177722,4074052095,668550556,3214352940,367459370,261225585,2610173221,4209349473,3468074219,3265815641,314222801,3066103646,3808782860,282218597,3406013506,3773591054,379116347,1285071038,846784868,2669647154,3771962079,3550491691,2305946142,453669953,1268987020,3317592352,3279303384,3744833421,2610507566,3859509063,266596637,3847019092,517658769,3462560207,3443424879,370717030,4247526661,2224018117,4143653529,4112773975,2788324899,2477274417,1456262402,2901442914,1517677493,1846949527,2295493580,3734397586,2176403920,1280348187,1908823572,3871786941,846861322,1172426758,3287448474,3383383037,1655181056,3139813346,901632758,1897031941,2986607138,3066810236,3447102507,1393639104,373351379,950779232,625454576,3124240540,4148612726,2007998917,544563296,2244738638,2330496472,2058025392,1291430526,424198748,50039436,29584100,3605783033,2429876329,2791104160,1057563949,3255363231,3075367218,3463963227,1469046755,985887462],U1=[1332899944,1700884034,1701343084,1684370003,1668446532,1869963892],zo=(e,t)=>{if(t<=0||t>e.length)throw Error(`Illegal len: ${t}`);let n=0,r,a;const o=[];for(;n<t;){if(r=e[n++]&255,o.push(Sn[r>>2&63]),r=(r&3)<<4,n>=t){o.push(Sn[r&63]);break}if(a=e[n++]&255,r|=a>>4&15,o.push(Sn[r&63]),r=(a&15)<<2,n>=t){o.push(Sn[r&63]);break}a=e[n++]&255,r|=a>>6&3,o.push(Sn[r&63]),o.push(Sn[a&63])}return o.join("")},m5=(e,t)=>{const n=e.length;let r=0,a=0,o,l,i,c,u,d;const f=[];for(;r<n-1&&a<t&&(d=e.charCodeAt(r++),o=d<Ut.length?Ut[d]:-1,d=e.charCodeAt(r++),l=d<Ut.length?Ut[d]:-1,!(o==-1||l==-1||(u=o<<2>>>0,u|=(l&48)>>4,f.push(String.fromCharCode(u)),++a>=t||r>=n)||(d=e.charCodeAt(r++),i=d<Ut.length?Ut[d]:-1,i==-1)||(u=(l&15)<<4>>>0,u|=(i&60)>>2,f.push(String.fromCharCode(u)),++a>=t||r>=n)));)d=e.charCodeAt(r++),c=d<Ut.length?Ut[d]:-1,u=(i&3)<<6>>>0,u|=c,f.push(String.fromCharCode(u)),++a;return f.map(p=>p.charCodeAt(0))},v5=(e,t)=>{let n=null;for(typeof e=="number"&&(n=e,e=()=>null);n!==null||(n=e())!==null;)n<128?t(n&127):n<2048?(t(n>>6&31|192),t(n&63|128)):n<65536?(t(n>>12&15|224),t(n>>6&63|128),t(n&63|128)):(t(n>>18&7|240),t(n>>12&63|128),t(n>>6&63|128),t(n&63|128)),n=null},g5=(e,t)=>{let n,r=null;for(;(n=r!==null?r:e())!==null;){if(n>=55296&&n<=57343&&(r=e())!==null&&r>=56320&&r<=57343){t((n-55296)*1024+r-56320+65536),r=null;continue}t(n)}r!==null&&t(r)},y5=(e,t)=>{g5(e,function(n){v5(n,t)})},b5=typeof process=="object"&&h5.NEXT_RUNTIME==="edge"?setTimeout:typeof setImmediate=="function"?setImmediate:typeof process=="object"&&typeof process.nextTick=="function"?process.nextTick:setTimeout,E5=e=>{const t=[];let n=0;return y5(()=>n>=e.length?null:e.charCodeAt(n++),r=>{t.push(r)}),t},Tr=(e,t,n,r)=>{let a,o=e[t],l=e[t+1];return o^=n[0],a=r[o>>>24],a+=r[256|o>>16&255],a^=r[512|o>>8&255],a+=r[768|o&255],l^=a^n[1],a=r[l>>>24],a+=r[256|l>>16&255],a^=r[512|l>>8&255],a+=r[768|l&255],o^=a^n[2],a=r[o>>>24],a+=r[256|o>>16&255],a^=r[512|o>>8&255],a+=r[768|o&255],l^=a^n[3],a=r[l>>>24],a+=r[256|l>>16&255],a^=r[512|l>>8&255],a+=r[768|l&255],o^=a^n[4],a=r[o>>>24],a+=r[256|o>>16&255],a^=r[512|o>>8&255],a+=r[768|o&255],l^=a^n[5],a=r[l>>>24],a+=r[256|l>>16&255],a^=r[512|l>>8&255],a+=r[768|l&255],o^=a^n[6],a=r[o>>>24],a+=r[256|o>>16&255],a^=r[512|o>>8&255],a+=r[768|o&255],l^=a^n[7],a=r[l>>>24],a+=r[256|l>>16&255],a^=r[512|l>>8&255],a+=r[768|l&255],o^=a^n[8],a=r[o>>>24],a+=r[256|o>>16&255],a^=r[512|o>>8&255],a+=r[768|o&255],l^=a^n[9],a=r[l>>>24],a+=r[256|l>>16&255],a^=r[512|l>>8&255],a+=r[768|l&255],o^=a^n[10],a=r[o>>>24],a+=r[256|o>>16&255],a^=r[512|o>>8&255],a+=r[768|o&255],l^=a^n[11],a=r[l>>>24],a+=r[256|l>>16&255],a^=r[512|l>>8&255],a+=r[768|l&255],o^=a^n[12],a=r[o>>>24],a+=r[256|o>>16&255],a^=r[512|o>>8&255],a+=r[768|o&255],l^=a^n[13],a=r[l>>>24],a+=r[256|l>>16&255],a^=r[512|l>>8&255],a+=r[768|l&255],o^=a^n[14],a=r[o>>>24],a+=r[256|o>>16&255],a^=r[512|o>>8&255],a+=r[768|o&255],l^=a^n[15],a=r[l>>>24],a+=r[256|l>>16&255],a^=r[512|l>>8&255],a+=r[768|l&255],o^=a^n[16],e[t]=l^n[17],e[t+1]=o,e},Ln=(e,t)=>{let n=0;for(let r=0;r<4;++r)n=n<<8|e[t]&255,t=(t+1)%e.length;return{key:n,offp:t}},gi=(e,t,n)=>{const r=t.length,a=n.length;let o=0,l=[0,0],i;for(let c=0;c<r;c++)i=Ln(e,o),o=i.offp,t[c]=t[c]^i.key;for(let c=0;c<r;c+=2)l=Tr(l,0,t,n),t[c]=l[0],t[c+1]=l[1];for(let c=0;c<a;c+=2)l=Tr(l,0,t,n),n[c]=l[0],n[c+1]=l[1]},_5=(e,t,n,r)=>{const a=n.length,o=r.length;let l=0,i=[0,0],c;for(let u=0;u<a;u++)c=Ln(t,l),l=c.offp,n[u]=n[u]^c.key;l=0;for(let u=0;u<a;u+=2)c=Ln(e,l),l=c.offp,i[0]^=c.key,c=Ln(e,l),l=c.offp,i[1]^=c.key,i=Tr(i,0,n,r),n[u]=i[0],n[u+1]=i[1];for(let u=0;u<o;u+=2)c=Ln(e,l),l=c.offp,i[0]^=c.key,c=Ln(e,l),l=c.offp,i[1]^=c.key,i=Tr(i,0,n,r),r[u]=i[0],r[u+1]=i[1]},yi=(e,t,n,r,a)=>{const o=U1.slice(),l=o.length;if(n<4||n>31){const p=new Error(`Illegal number of rounds (4-31): ${n}`);if(r===!1)return Promise.reject(p);throw p}if(t.length!==16){const p=new Error(`Illegal salt length: ${t.length} != 16`);if(r===!1)return Promise.reject(p);throw p}n=1<<n>>>0;let i,c,u=0,d;Int32Array?(i=new Int32Array(mi),c=new Int32Array(vi)):(i=mi.slice(),c=vi.slice()),_5(t,e,i,c);const f=()=>{if(u<n){const p=Date.now();for(;u<n&&(u=u+1,gi(e,i,c),gi(t,i,c),!(Date.now()-p>100)););}else{for(u=0;u<64;u++)for(d=0;d<l>>1;d++)Tr(o,d<<1,i,c);const p=[];for(u=0;u<l;u++)p.push((o[u]>>24&255)>>>0),p.push((o[u]>>16&255)>>>0),p.push((o[u]>>8&255)>>>0),p.push((o[u]&255)>>>0);return r===!1?Promise.resolve(p):p}if(r===!1)return new Promise(p=>b5(()=>{f().then(p)}))};if(r===!1)return f();{let p;for(;;)if(typeof(p=f())<"u")return p||[]}},w5=e=>{try{let t;typeof window<"u"?t=window.crypto??window.msCrypto:t=globalThis.crypto;const n=new Uint32Array(e);return t==null||t.getRandomValues(n),Array.from(n)}catch{throw Error("WebCryptoAPI is not available")}},A5=(e=10)=>{if(typeof e!="number")throw Error("Illegal arguments: "+typeof e);e<4?e=4:e>31&&(e=31);const t=[];return t.push("$2a$"),e<10&&t.push("0"),t.push(e.toString()),t.push("$"),t.push(zo(w5(16),16)),t.join("")};function C5(e,t,n,r){if(typeof e!="string"||typeof t!="string"){const h=new Error("Invalid string / salt: Not a string");if(n===!1)return Promise.reject(h);throw h}let a,o;if(t.charAt(0)!=="$"||t.charAt(1)!=="2"){const h=new Error("Invalid salt version: "+t.substring(0,2));if(n===!1)return Promise.reject(h);throw h}if(t.charAt(2)==="$")a="\0",o=3;else{if(a=t.charAt(2),a!=="a"&&a!=="b"&&a!=="y"||t.charAt(3)!=="$"){const h=Error("Invalid salt revision: "+t.substring(2,4));if(n===!1)return Promise.reject(h);throw h}o=4}if(t.charAt(o+2)>"$"){const h=new Error("Missing salt rounds");if(n===!1)return Promise.reject(h);throw h}const l=parseInt(t.substring(o,o+1),10)*10,i=parseInt(t.substring(o+1,o+2),10),c=l+i,u=t.substring(o+3,o+25);e+=a>="a"?"\0":"";const d=E5(e),f=m5(u,16),p=h=>{const v=[];return v.push("$2"),a>="a"&&v.push(a),v.push("$"),c<10&&v.push("0"),v.push(c.toString()),v.push("$"),v.push(zo(f,f.length)),v.push(zo(h,U1.length*4-1)),v.join("")};return n===!1?yi(d,f,c,!1).then(h=>p(h)):p(yi(d,f,c,!0))}const k5=(e,t=10)=>{if(typeof t=="number"&&(t=A5(t)),typeof e!="string"||typeof t!="string")throw Error("Illegal arguments: "+typeof e+", "+typeof t);return C5(e,t,!0)},qo=(e,t)=>{if(typeof e!="string"||typeof t!="string")throw Error("Illegal arguments: "+typeof e+", "+typeof t);return t.length!==60?!1:k5(e,t.substring(0,t.length-31))===t},bi="VUEPRESS_HOPE_GLOBAL_TOKEN",T5=()=>{const e=G1(),t=cn(bi,""),n=cu(bi,""),r=w(()=>{const{global:l=!1,admin:i=[]}=e.value;return l&&i.length>0}),a=w(()=>{if(r.value){if(t.value)return e.value.admin.some(l=>qo(t.value,l));if(n.value)return e.value.admin.some(l=>qo(n.value,l))}return!1});return{isEncrypted:r,isDecrypted:a,validate:(l,i=!1)=>{(i?t:n).value=l}}},ho=(e="",t)=>!!e&&qo(e,t),Ei="VUEPRESS_HOPE_PATH_TOKEN",S5=()=>{const e=ge(),t=G1(),n=cn(Ei,{}),r=cu(Ei,{}),a=c=>qn(t.value.config)?En(t.value.config).filter(u=>Oa(decodeURI(c),u)).sort((u,d)=>d.length-u.length):[],o=c=>{const u=a(c);if(u.length>0){const{config:d={}}=t.value;return{isEncrypted:!0,isDecrypted:u.some(f=>n.value[f]&&d[f].some(p=>ho(n.value[f],p))||r.value[f]&&d[f].some(p=>ho(r.value[f],p)))}}return{isDecrypted:!1,isEncrypted:!1}};return{status:w(()=>o(e.value.path)),getStatus:o,validate:(c,u=!1)=>{const{config:d={}}=t.value,f=a(e.value.path);for(const p of f)if(d[p].filter(h=>ho(c,h))){(u?n:r).value[p]=c;break}}}},x5=M({name:"GlobalEncrypt",slots:Object,setup(e,{slots:t}){const{isDecrypted:n,isEncrypted:r,validate:a}=T5(),o=z(!1);return se(()=>{o.value=!0}),()=>s(Ml,()=>r.value?o.value?n.value?t.default():s(q1,{full:!0,onVerify:a}):null:t.default())}}),L5=M({name:"LocalEncrypt",slots:Object,setup(e,{slots:t}){const{status:n,validate:r}=S5(),a=z(!1);return se(()=>{a.value=!0}),()=>{const{isEncrypted:o,isDecrypted:l}=n.value;return o?a.value?l?t.default():s(q1,{full:!0,onVerify:r}):null:t.default()}}});cp(e=>{const t=e.t,n=e.I!==!1,r=e.i;return n?{title:t,content:r?()=>[s(Ve,{icon:r}),t]:null,order:e.O,index:e.I}:null});const B5=Ze({enhance:({app:e,router:t})=>{const{scrollBehavior:n}=t.options;t.options.scrollBehavior=async(...r)=>(await Mo.wait(),n(...r)),j6(e),e.component("HopeIcon",Ve),e.component("BloggerInfo",Nl),e.component("GlobalEncrypt",x5),e.component("LocalEncrypt",L5)},setup:()=>{z6(),W6(),y8()},layouts:{Layout:G8,NotFound:W8,BlogCategory:X8,BlogHome:V1,BlogType:d5,PortfolioHome:j1,Timeline:z1}});var I5={models:[{path:"https://model.oml2d.com/HK416-1-normal/model.json",position:[0,60],scale:.08,stageStyle:{height:450}}]};const P5={setup:()=>{se(()=>{T(()=>import("./index-BNnYFWcz.js"),[]).then(({loadOml2d:e})=>e(I5))})}},D5=M({__name:"IndexLayout",setup(e){return(t,n)=>null}}),O5=Fl(D5,[["__file","IndexLayout.vue"]]),_i=1e3*60*60*24,M5=(e,t={"/":"Running time: :day days :hour hours :minute minutes :second seconds"},n=!1)=>{const r=(e instanceof Date?e:new Date(e)).getTime();let a="";const o=ge(),l=U3(),i=Ye(),c=w(()=>{const u=l.value.getTime()-r,d=new Date(u%_i);return{day:Math.floor(u/_i),hour:d.getHours(),minute:d.getMinutes(),second:d.getSeconds()}});se(()=>{ae(()=>[o.value.path,c.value],()=>{const u=document.querySelector(".vp-footer");if(u){const{day:d,hour:f,minute:p,second:h}=c.value,v=(t[i.value]||t["/"]).replace(":day",d.toString()).replace(":hour",f.toString()).replace(":minute",p.toString()).replace(":second",h.toString());u.innerHTML=`${n?`${u.innerHTML.replace(`<br>${a}`,"")}<br>`:""}${v}`,a=v}},{flush:"post",immediate:!0})})},R5=Ze({layouts:{IndexLayout:O5},setup(){M5(new Date("2024-05-08"),{"/":"Running time: :day days :hour hours :minute minutes :second seconds","/zh/":"已运行 :day 天 :hour 小时 :minute 分钟 :second 秒"},!0)}}),oa=[e3,Y3,rp,hp,Ep,Cp,xp,Dp,Vp,Zp,q4,a6,B6,B5,P5,R5],$5=JSON.parse('{"base":"/","lang":"zh-CN","title":"blog","description":"KSJ-blog","head":[],"locales":{}}');var er=xe($5),F5=bf,H5=()=>{const e=qf({history:F5(pl("/")),routes:[{name:"vuepress-route",path:"/:catchAll(.*)",components:{}}],scrollBehavior:(t,n,r)=>r||(t.hash?{el:t.hash}:{top:0})});return e.beforeResolve(async(t,n)=>{if(t.path!==n.path||n===Ot){const r=xt(t.path);if(r.path!==t.path)return r.path;const a=await r.loader();t.meta={...r.meta,_pageChunk:a}}else t.path===n.path&&(t.meta=n.meta)}),e},N5=e=>{e.component("ClientOnly",Or),e.component("Content",Uc),e.component("RouteLink",Ie)},V5=(e,t,n)=>{const r=w(()=>t.currentRoute.value.path),a=rl((E,b)=>({get(){return E(),t.currentRoute.value.meta._pageChunk},set(C){t.currentRoute.value.meta._pageChunk=C,b()}})),o=w(()=>pn.resolveLayouts(n)),l=w(()=>pn.resolveRouteLocale(er.value.locales,r.value)),i=w(()=>pn.resolveSiteLocaleData(er.value,l.value)),c=w(()=>a.value.comp),u=w(()=>a.value.data),d=w(()=>u.value.frontmatter),f=w(()=>pn.resolvePageHeadTitle(u.value,i.value)),p=w(()=>pn.resolvePageHead(f.value,d.value,i.value)),h=w(()=>pn.resolvePageLang(u.value,i.value)),v=w(()=>pn.resolvePageLayout(u.value,o.value)),_={layouts:o,pageData:u,pageComponent:c,pageFrontmatter:d,pageHead:p,pageHeadTitle:f,pageLang:h,pageLayout:v,redirects:xo,routeLocale:l,routePath:r,routes:_r,siteData:er,siteLocaleData:i};return e.provide(vl,_),Object.defineProperties(e.config.globalProperties,{$frontmatter:{get:()=>d.value},$head:{get:()=>p.value},$headTitle:{get:()=>f.value},$lang:{get:()=>h.value},$page:{get:()=>u.value},$routeLocale:{get:()=>l.value},$site:{get:()=>er.value},$siteLocale:{get:()=>i.value},$withBase:{get:()=>be}}),_},j5=()=>{const e=Wf(),t=Pa();let n=[];const r=()=>{e.value.forEach(l=>{const i=z5(l);i&&n.push(i)})},a=()=>{const l=[];return e.value.forEach(i=>{const c=q5(i);c&&l.push(c)}),l},o=()=>{document.documentElement.lang=t.value;const l=a();n.forEach((i,c)=>{const u=l.findIndex(d=>i.isEqualNode(d));u===-1?(i.remove(),delete n[c]):l.splice(u,1)}),l.forEach(i=>document.head.appendChild(i)),n=[...n.filter(i=>!!i),...l]};ht(Qf,o),se(()=>{r(),ae(e,o,{immediate:!1})})},z5=([e,t,n=""])=>{const r=Object.entries(t).map(([i,c])=>we(c)?`[${i}=${JSON.stringify(c)}]`:c===!0?`[${i}]`:"").join(""),a=`head > ${e}${r}`;return Array.from(document.querySelectorAll(a)).find(i=>i.innerText===n)||null},q5=([e,t,n])=>{if(!we(e))return null;const r=document.createElement(e);return qn(t)&&Object.entries(t).forEach(([a,o])=>{we(o)?r.setAttribute(a,o):o===!0&&r.setAttribute(a,"")}),we(n)&&r.appendChild(document.createTextNode(n)),r},G5=Td,U5=async()=>{var n;const e=G5({name:"Vuepress",setup(){var o;j5();for(const l of oa)(o=l.setup)==null||o.call(l);const r=oa.flatMap(({rootComponents:l=[]})=>l.map(i=>s(i))),a=Kf();return()=>[s(a.value),r]}}),t=H5();N5(e),V5(e,t,oa);for(const r of oa)await((n=r.enhance)==null?void 0:n.call(r,{app:e,router:t,siteData:er}));return e.use(t),{app:e,router:t}};U5().then(({app:e,router:t})=>{t.isReady().then(()=>{e.mount("#app")})});export{xe as A,se as B,qu as C,m6 as D,Ft as E,Y5 as F,qn as G,c6 as H,d6 as I,ru as J,ba as K,we as L,T as M,xl as P,Ie as R,Fl as _,R0 as a,Ec as b,W5 as c,U5 as createVueApp,Te as d,wc as e,K5 as f,M as g,wn as h,Ye as i,Tl as j,Lr as k,z as l,w as m,Se as n,cl as o,ae as p,s as q,pt as r,Vu as s,zn as t,J5 as u,u6 as v,pa as w,s6 as x,i6 as y,ge as z};
+ReactDOM.createRoot(document.getElementById("app")).render(React.createElement($reactApp))`,k4=e=>e.replace(/export\s+default\s*\{(\n*[\s\S]*)\n*\}\s*;?$/u,"Vue.createApp({$1}).mount('#app')").replace(/export\s+default\s*define(Async)?Component\s*\(\s*\{(\n*[\s\S]*)\n*\}\s*\)\s*;?$/u,"Vue.createApp({$1}).mount('#app')").trim(),Ru=e=>`(function(exports){var module={};module.exports=exports;${e};return module.exports.__esModule?module.exports.default:module.exports;})({})`,T4=(e,t)=>{const n=kl(t),r=e.js[0]??"";return{...n,html:Ou(e.html[0]??""),js:r,css:e.css[0]??"",isLegal:e.isLegal,getScript:()=>{var a;return n.useBabel?((a=window.Babel.transform(r,{presets:["es2015"]}))==null?void 0:a.code)??"":r}}},S4=/<template>([\s\S]+)<\/template>/u,x4=/<script(\s*lang=(['"])(.*?)\2)?>([\s\S]+)<\/script>/u,L4=/<style(\s*lang=(['"])(.*?)\2)?\s*(?:scoped)?>([\s\S]+)<\/style>/u,B4=(e,t)=>{const n=kl(t),r=e.html[0]??"",a=S4.exec(r),o=x4.exec(r),l=L4.exec(r),i=(a==null?void 0:a[1].replace(/^\n|\n$/g,""))??"",[c="",u=""]=o?[o[4].replace(/^\n|\n$/g,""),o[3]]:[],[d="",f=""]=l?[l[4].replace(/^\n|\n$/g,""),l[3]]:[],p=u===""&&(f===""||f==="css");return{...n,html:Mu(i),js:k4(c),css:d,isLegal:p,jsLib:[n.vue,...n.jsLib],getScript:()=>{var v,_;const h=t.useBabel?((_=(v=window.Babel)==null?void 0:v.transform(c,{presets:["es2015"]}))==null?void 0:_.code)??"":c.replace(/export\s+default/u,"return");return`const app=window.document.createElement('div');document.firstElementChild.appendChild(app);const appOptions=${Ru(h)};appOptions.template=\`${i.replace("`",'\\`"')}\`;window.Vue.createApp(appOptions).mount(app);`}}},I4=(e,t)=>{var a;const n=kl(t),r=e.js[0]??"";return{...n,html:Mu(""),js:C4(r),css:e.css[0]??((a=e.js[0])==null?void 0:a.replace(/App\.__style__(?:\s*)=(?:\s*)`([\s\S]*)?`/,"$1").trim())??"",isLegal:e.isLegal,jsLib:[n.react,n.reactDOM,...n.jsLib],jsx:!0,getScript:()=>{var l,i;const o=((i=(l=window.Babel)==null?void 0:l.transform(r,{presets:["es2015","react"]}))==null?void 0:i.code)??"";return`window.ReactDOM.createRoot(document.firstElementChild).render(window.React.createElement(${Ru(o)}))`}}},$n={},P4=e=>Promise.all([Rn($n,e.babel),Rn($n,e.react),Rn($n,e.reactDOM)]),D4=e=>{const t=[Rn($n,e.vue)];return e.useBabel&&t.push(Rn($n,e.babel)),Promise.all(t)},O4=e=>e.useBabel?Rn($n,e.babel):Promise.resolve();var M4=M({name:"CodeDemo",props:{id:{type:String,required:!0},type:{type:String,default:"normal"},title:{type:String,default:""},config:{type:String,default:""},code:{type:String,required:!0}},slots:Object,setup(e,{slots:t}){const[n,r]=wr(!1),a=xe(),o=xe(),l=z("0"),i=z(!1),c=w(()=>JSON.parse(e.config?ya(e.config):"{}")),u=w(()=>{const v=JSON.parse(ya(e.code));return A4(v)}),d=w(()=>e.type==="react"?I4(u.value,c.value):e.type==="vue"?B4(u.value,c.value):T4(u.value,c.value)),f=w(()=>d.value.isLegal),p=(v=!1)=>{const _=a.value.attachShadow({mode:"open"}),E=document.createElement("div");E.classList.add("code-demo-app"),_.appendChild(E),f.value?(v&&(E.innerHTML=d.value.html),E4(_,d.value),_4(e.id,_,d.value),l.value="0"):l.value="auto",i.value=!0},h=()=>{switch(e.type){case"react":return P4(d.value).then(()=>p());case"vue":return D4(d.value).then(()=>p());default:return O4(d.value).then(()=>p(!0))}};return Se("beforeprint",()=>{r(!0)}),se(()=>{setTimeout(()=>{h()},800)}),()=>{var v;return s("div",{class:"vp-code-demo",id:e.id},[s("div",{class:"vp-code-demo-header"},[d.value.isLegal?s("button",{type:"button",title:"toggle","aria-hidden":!0,class:["vp-code-demo-toggle-button",n.value?"down":"end"],onClick:()=>{l.value=n.value?"0":`${o.value.clientHeight+13.8}px`,r()}}):null,e.title?s("span",{class:"vp-code-demo-title"},decodeURIComponent(e.title)):null,d.value.isLegal&&d.value.jsfiddle!==!1?s("form",{class:"code-demo-jsfiddle",target:"_blank",action:"https://jsfiddle.net/api/post/library/pure/",method:"post"},[s("input",{type:"hidden",name:"html",value:d.value.html}),s("input",{type:"hidden",name:"js",value:d.value.js}),s("input",{type:"hidden",name:"css",value:d.value.css}),s("input",{type:"hidden",name:"wrap",value:"1"}),s("input",{type:"hidden",name:"panel_js",value:"3"}),s("input",{type:"hidden",name:"resources",value:[...d.value.cssLib,...d.value.jsLib].join(",")}),s("button",{type:"submit",class:"jsfiddle-button",innerHTML:g4,"aria-label":"JSFiddle","data-balloon-pos":"up"})]):null,!d.value.isLegal||d.value.codepen!==!1?s("form",{class:"code-demo-codepen",target:"_blank",action:"https://codepen.io/pen/define",method:"post"},[s("input",{type:"hidden",name:"data",value:JSON.stringify({html:d.value.html,js:d.value.js,css:d.value.css,js_external:d.value.jsLib.join(";"),css_external:d.value.cssLib.join(";"),layout:d.value.codepenLayout,html_pre_processor:u.value?u.value.html[1]:"none",js_pre_processor:u.value?u.value.js[1]:d.value.jsx?"babel":"none",css_pre_processor:u.value?u.value.css[1]:"none",editors:d.value.codepenEditors})}),s("button",{type:"submit",innerHTML:v4,class:"codepen-button","aria-label":"Codepen","data-balloon-pos":"up"})]):null]),i.value?null:s(Al,{class:"vp-code-demo-loading"}),s("div",{ref:a,class:"vp-code-demo-display",style:{display:f.value&&i.value?"block":"none"}}),s("div",{class:"vp-code-demo-code-wrapper",style:{height:l.value}},s("div",{ref:o,class:"vp-code-demo-codes"},(v=t.default)==null?void 0:v.call(t)))])}}}),R4=M({name:"MdDemo",props:{id:{type:String,required:!0},title:{type:String,default:""}},slots:Object,setup(e,{slots:t}){const[n,r]=wr(!1),a=xe(),o=z("0");return Se("beforeprint",()=>{r(!0)}),()=>{var l,i;return s("div",{class:"vp-md-demo",id:e.id},[s("div",{class:"vp-md-demo-header"},[s("button",{type:"button",title:"toggle","aria-hidden":!0,class:["vp-md-demo-toggle-button",n.value?"down":"end"],onClick:()=>{o.value=n.value?"0":`${a.value.clientHeight+13.8}px`,r()}}),e.title?decodeURIComponent(e.title):null]),s("div",{class:"vp-md-demo-display"},(l=t.default)==null?void 0:l.call(t)),s("div",{class:"vp-md-demo-code-wrapper",style:{height:o.value}},s("div",{ref:a,class:"vp-md-demo-codes"},(i=t.code)==null?void 0:i.call(t)))])}}});const $4=()=>{Se("beforeprint",()=>{document.querySelectorAll("details").forEach(e=>{e.open=!0})})};let F4={};const $u=Symbol(""),H4=()=>ve($u),N4=e=>{e.provide($u,F4)},ui=()=>{const e=document.documentElement;return e.classList.contains("dark")||e.getAttribute("data-theme")==="dark"},Tn={useMaxWidth:!1},V4=e=>({dark:e,background:e?"#1e1e1e":"#fff",primaryColor:e?"#389d70":"#4abf8a",primaryBorderColor:e?"#389d70":"#4abf8a",primaryTextColor:e?"#fff":"#000",secondaryColor:"#ffb500",secondaryBorderColor:e?"#fff":"#000",secondaryTextColor:e?"#ddd":"#333",tertiaryColor:e?"#282828":"#efeef4",tertiaryBorderColor:e?"#bbb":"#242424",tertiaryTextColor:e?"#ddd":"#333",noteBkgColor:e?"#f6d365":"#fff5ad",noteTextColor:"#242424",noteBorderColor:e?"#f6d365":"#333",lineColor:e?"#d3d3d3":"#333",textColor:e?"#fff":"#242424",mainBkg:e?"#389d70":"#4abf8a",errorBkgColor:"#eb4d5d",errorTextColor:"#fff",nodeBorder:e?"#389d70":"#4abf8a",nodeTextColor:e?"#fff":"#242424",signalTextColor:e?"#9e9e9e":"#242424",classText:"#fff",labelColor:"#fff",attributeBackgroundColorEven:e?"#0d1117":"#fff",attributeBackgroundColorOdd:e?"#161b22":"#f8f8f8",fillType0:e?"#cf1322":"#f1636e",fillType1:"#f39c12",fillType2:"#2ecc71",fillType3:"#fa541c",fillType4:"#25a55b",fillType5:"#13c2c2",fillType6:"#096dd9",fillType7:"#aa6fe9"});var j4=M({name:"Mermaid",props:{id:{type:String,required:!0},code:{type:String,required:!0},title:{type:String,default:""}},setup(e){const{themeVariables:t,...n}=H4(),r=xe(),a=w(()=>ya(e.code)),o=z(""),l=z(!1);let i=!1;const c=async()=>{const[{default:f}]=await Promise.all([T(()=>import("./mermaid.core-DNo_7Q2B.js").then(p=>p.b8),[]),i?Promise.resolve():(i=!0,new Promise(p=>setTimeout(p,800)))]);f.initialize({theme:"base",themeVariables:{...V4(l.value),...$d(t)?t(l.value):t},flowchart:Tn,sequence:Tn,journey:Tn,gantt:Tn,er:Tn,pie:Tn,...n,startOnLoad:!1}),o.value=(await f.render(e.id,a.value)).svg},u=()=>{const{body:f}=document,p=document.createElement("div");p.classList.add("mermaid-preview"),p.innerHTML=o.value,f.appendChild(p),p.addEventListener("click",()=>{f.removeChild(p)})},d=()=>{const f=`data:image/svg+xml;charset=utf8,${o.value.replace(/<br>/g,"<br />").replace(/%/g,"%25").replace(/"/g,"%22").replace(/'/g,"%27").replace(/&/g,"%26").replace(/#/g,"%23").replace(/{/g,"%7B").replace(/}/g,"%7D").replace(/</g,"%3C").replace(/>/g,"%3E")}`,p=document.createElement("a");p.setAttribute("href",f),p.setAttribute("download",`${e.title?ya(e.title):e.id}.svg`),p.click()};return se(()=>{l.value=ui(),c(),z3(document.documentElement,()=>{l.value=ui()},{attributeFilter:["class","data-theme"],attributes:!0}),ae(l,()=>c())}),()=>[s("div",{class:"mermaid-actions"},[s("button",{class:"preview-button",onClick:()=>u(),title:"preview",innerHTML:'<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 1316 1024" fill="currentColor"><path d="M658.286 0C415.89 0 0 297.106 0 512c0 214.82 415.89 512 658.286 512 242.322 0 658.285-294.839 658.285-512S900.608 0 658.286 0zm0 877.714c-161.573 0-512-221.769-512-365.714 0-144.018 350.427-365.714 512-365.714 161.572 0 512 217.16 512 365.714s-350.428 365.714-512 365.714z"/><path d="M658.286 292.571a219.429 219.429 0 1 0 0 438.858 219.429 219.429 0 0 0 0-438.858zm0 292.572a73.143 73.143 0 1 1 0-146.286 73.143 73.143 0 0 1 0 146.286z"/></svg>'}),s("button",{class:"download-button",onClick:()=>d(),title:"download",innerHTML:'<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 1024 1024" fill="currentColor"><path d="M828.976 894.125H190.189c-70.55 0-127.754-57.185-127.754-127.753V606.674c0-17.634 14.31-31.933 31.933-31.933h63.889c17.634 0 31.932 14.299 31.932 31.933v95.822c0 35.282 28.596 63.877 63.877 63.877h511.033c35.281 0 63.877-28.595 63.877-63.877v-95.822c0-17.634 14.298-31.933 31.943-31.933h63.878c17.635 0 31.933 14.299 31.933 31.933v159.7c0 70.566-57.191 127.751-127.754 127.751zM249.939 267.51c12.921-12.92 33.885-12.92 46.807 0l148.97 148.972V94.893c0-17.634 14.302-31.947 31.934-31.947h63.876c17.638 0 31.946 14.313 31.946 31.947v321.589l148.97-148.972c12.922-12.92 33.876-12.92 46.797 0l46.814 46.818c12.922 12.922 12.922 33.874 0 46.807L552.261 624.93c-1.14 1.138-21.664 13.684-42.315 13.693-20.877.01-41.88-12.542-43.021-13.693L203.122 361.135c-12.923-12.934-12.923-33.885 0-46.807l46.817-46.818z"/></svg>'})]),s("div",{ref:r,class:"mermaid-wrapper"},o.value?s("div",{class:"mermaid-content",innerHTML:o.value}):s(Al,{class:"mermaid-loading",height:96}))]}});const so=cn("VUEPRESS_TAB_STORE",{});var z4=M({name:"Tabs",props:{active:{type:Number,default:0},data:{type:Array,required:!0},id:{type:String,required:!0},tabId:{type:String,default:""}},slots:Object,setup(e,{slots:t}){const n=z(e.active),r=xe([]),a=()=>{e.tabId&&(so.value[e.tabId]=e.data[n.value].id)},o=(u=n.value)=>{n.value=u<r.value.length-1?u+1:0,r.value[n.value].focus()},l=(u=n.value)=>{n.value=u>0?u-1:r.value.length-1,r.value[n.value].focus()},i=(u,d)=>{u.key===" "||u.key==="Enter"?(u.preventDefault(),n.value=d):u.key==="ArrowRight"?(u.preventDefault(),o()):u.key==="ArrowLeft"&&(u.preventDefault(),l()),a()},c=()=>{if(e.tabId){const u=e.data.findIndex(({id:d})=>so.value[e.tabId]===d);if(u!==-1)return u}return e.active};return se(()=>{n.value=c(),ae(()=>so.value[e.tabId],(u,d)=>{if(e.tabId&&u!==d){const f=e.data.findIndex(({id:p})=>p===u);f!==-1&&(n.value=f)}})}),()=>e.data.length?s("div",{class:"vp-tabs"},[s("div",{class:"vp-tabs-nav",role:"tablist"},e.data.map(({id:u},d)=>{const f=d===n.value;return s("button",{type:"button",ref:p=>{p&&(r.value[d]=p)},class:["vp-tab-nav",{active:f}],role:"tab","aria-controls":`tab-${e.id}-${d}`,"aria-selected":f,onClick:()=>{n.value=d,a()},onKeydown:p=>i(p,d)},t[`title${d}`]({value:u,isActive:f}))})),e.data.map(({id:u},d)=>{const f=d===n.value;return s("div",{class:["vp-tab",{active:f}],id:`tab-${e.id}-${d}`,role:"tabpanel","aria-expanded":f},[s("div",{class:"vp-tab-title"},t[`title${d}`]({value:u,isActive:f})),t[`tab${d}`]({value:u,isActive:f})])})]):null}});const q4=Ze({enhance:({app:e})=>{e.component("CodeTabs",Xp),e.component("CodeDemo",M4),e.component("MdDemo",R4),N4(e),e.component("Mermaid",j4),e.component("Tabs",z4)},setup:()=>{$4()}});let G4={};const Fu=Symbol(""),U4=()=>ve(Fu),W4=e=>{e.provide(Fu,G4)},K4='<div class="photo-swipe-loading"><svg xmlns="http://www.w3.org/2000/svg" width="48" height="48" preserveAspectRatio="xMidYMid" viewBox="25 25 50 50"><animateTransform attributeName="transform" type="rotate" dur="2s" keyTimes="0;1" repeatCount="indefinite" values="0;360"></animateTransform><circle cx="50" cy="50" r="20" fill="none" stroke="currentColor" stroke-width="4" stroke-linecap="round"><animate attributeName="stroke-dasharray" dur="1.5s" keyTimes="0;0.5;1" repeatCount="indefinite" values="1,200;90,200;1,200"></animate><animate attributeName="stroke-dashoffset" dur="1.5s" keyTimes="0;0.5;1" repeatCount="indefinite" values="0;-35px;-125px"></animate></circle></svg></div>',J4=e=>we(e)?Array.from(document.querySelectorAll(e)):e.map(t=>Array.from(document.querySelectorAll(t))).flat(),Hu=e=>new Promise((t,n)=>{e.complete?t({type:"image",element:e,src:e.src,width:e.naturalWidth,height:e.naturalHeight,alt:e.alt,msrc:e.src}):(e.onload=()=>t(Hu(e)),e.onerror=r=>n(r))}),Q4=e=>{const{isSupported:t,toggle:n}=yl();e.on("uiRegister",()=>{t.value&&e.ui.registerElement({name:"fullscreen",order:7,isButton:!0,html:'<svg class="pswp__icn" viewBox="0 0 1024 1024" xmlns="http://www.w3.org/2000/svg"><path d="M249.5 270.833H437v-75H212a37.5 37.5 0 0 0-37.5 37.5v225h75v-187.5zm-37.5 600h225v-75H249.5v-187.5h-75v225a37.5 37.5 0 0 0 37.5 37.5zm637.5-37.5v-225h-75v187.5H587v75h225a37.5 37.5 0 0 0 37.5-37.5zM587 270.833h187.5v187.5h75v-225a37.5 37.5 0 0 0-37.5-37.5H587v75z"/></svg>',onClick:()=>{n()}}),e.ui.registerElement({name:"download",order:8,isButton:!0,tagName:"a",html:{isCustomSVG:!0,inner:'<path d="M20.5 14.3 17.1 18V10h-2.2v7.9l-3.4-3.6L10 16l6 6.1 6-6.1-1.5-1.6ZM23 23H9v2h14" id="pswp__icn-download"/>',outlineID:"pswp__icn-download"},onInit:(r,a)=>{r.setAttribute("download",""),r.setAttribute("target","_blank"),r.setAttribute("rel","noopener"),a.on("change",()=>{r.setAttribute("href",a.currSlide.data.src)})}}),e.ui.registerElement({name:"bulletsIndicator",className:"photo-swipe-bullets-indicator",appendTo:"wrapper",onInit:(r,a)=>{const o=[];let l=-1;for(let i=0;i<a.getNumItems();i++){const c=document.createElement("div");c.className="photo-swipe-bullet",c.onclick=u=>{a.goTo(o.indexOf(u.target))},o.push(c),r.appendChild(c)}a.on("change",()=>{l>=0&&o[l].classList.remove("active"),o[a.currIndex].classList.add("active"),l=a.currIndex})}})})},Y4=(e,t,n=!0)=>T(()=>import("./photoswipe.esm-SzV8tJDW.js"),[]).then(({default:r})=>{let a=null;const o=e.map(l=>({html:K4,element:l,msrc:l.src}));return e.forEach((l,i)=>{const c=()=>{a==null||a.destroy(),a=new r({preloaderDelay:0,showHideAnimationType:"zoom",...t,dataSource:o,index:i,...n?{closeOnVerticalDrag:!0,wheelToZoom:!1}:{}}),Q4(a),a.addFilter("thumbEl",()=>l),a.addFilter("placeholderSrc",()=>l.src),a.init()};l.getAttribute("photo-swipe")||(l.style.cursor="zoom-in",l.addEventListener("click",()=>{c()}),l.addEventListener("keypress",({key:u})=>{u==="Enter"&&c()}),l.setAttribute("photo-swipe","")),Hu(l).then(u=>{o.splice(i,1,u),a==null||a.refreshSlideContent(i)})}),n?Se("wheel",()=>{a==null||a.close()}):()=>{}}),Z4=({selector:e,locales:t,delay:n=500,scrollToClose:r=!0})=>{const a=U4(),o=El(t),l=ge(),i=he();let c=null;const u=()=>{const{photoSwipe:d}=i.value;d!==!1&&_t().then(()=>ip(n)).then(async()=>{const f=we(d)?d:e;c=await Y4(J4(f),{...a,...o.value},r)})};se(()=>{u(),ae(()=>l.value.path,()=>{c==null||c(),u()})}),Ft(()=>{c==null||c()})};var X4={"/":{closeTitle:"关闭",downloadTitle:"下载图片",fullscreenTitle:"切换全屏",zoomTitle:"缩放",arrowPrevTitle:"上一个 (左箭头)",arrowNextTitle:"下一个 (右箭头)"}};const e6=".theme-hope-content :not(a) > img:not([no-view])",t6=X4,n6=800,r6=!0,a6=Ze({enhance:({app:e})=>{W4(e)},setup:()=>{Z4({selector:e6,delay:n6,locales:t6,scrollToClose:r6})}}),Tl=e=>{const t=Ye();return w(()=>e[t.value]??{})},o6=(e,t)=>we(e)&&e.startsWith(t),l6=Object.values,s6=()=>s(ie,{name:"heading"},()=>s("path",{d:"M250.4 704.6H64V595.4h202.4l26.2-166.6H94V319.6h214.4L352 64h127.8l-43.6 255.4h211.2L691 64h126.2l-43.6 255.4H960v109.2H756.2l-24.6 166.6H930v109.2H717L672 960H545.8l43.6-255.4H376.6L333 960H206.8l43.6-255.4zm168.4-276L394 595.4h211.2l24.6-166.6h-211z"}));s6.displayName="HeadingIcon";const i6=()=>s(ie,{name:"heart"},()=>s("path",{d:"M1024 358.156C1024 195.698 892.3 64 729.844 64c-86.362 0-164.03 37.218-217.844 96.49C458.186 101.218 380.518 64 294.156 64 131.698 64 0 195.698 0 358.156 0 444.518 37.218 522.186 96.49 576H96l320 320c32 32 64 64 96 64s64-32 96-64l320-320h-.49c59.272-53.814 96.49-131.482 96.49-217.844zM841.468 481.232 517.49 805.49a2981.962 2981.962 0 0 1-5.49 5.48c-1.96-1.95-3.814-3.802-5.49-5.48L182.532 481.234C147.366 449.306 128 405.596 128 358.156 128 266.538 202.538 192 294.156 192c47.44 0 91.15 19.366 123.076 54.532L512 350.912l94.768-104.378C638.696 211.366 682.404 192 729.844 192 821.462 192 896 266.538 896 358.156c0 47.44-19.368 91.15-54.532 123.076z"}));i6.displayName="HeartIcon";const c6=()=>s(ie,{name:"history"},()=>s("path",{d:"M512 1024a512 512 0 1 1 512-512 512 512 0 0 1-512 512zm0-896a384 384 0 1 0 384 384 384 384 0 0 0-384-384zm192 448H512a64 64 0 0 1-64-64V320a64 64 0 0 1 128 0v128h128a64 64 0 0 1 0 128z"}));c6.displayName="HistoryIcon";const u6=()=>s(ie,{name:"title"},()=>s("path",{d:"M512 256c70.656 0 134.656 28.672 180.992 75.008A254.933 254.933 0 0 1 768 512c0 83.968-41.024 157.888-103.488 204.48C688.96 748.736 704 788.48 704 832c0 105.984-86.016 192-192 192-106.048 0-192-86.016-192-192h128a64 64 0 1 0 128 0 64 64 0 0 0-64-64 255.19 255.19 0 0 1-181.056-75.008A255.403 255.403 0 0 1 256 512c0-83.968 41.024-157.824 103.488-204.544C335.04 275.264 320 235.584 320 192A192 192 0 0 1 512 0c105.984 0 192 85.952 192 192H576a64.021 64.021 0 0 0-128 0c0 35.328 28.672 64 64 64zM384 512c0 70.656 57.344 128 128 128s128-57.344 128-128-57.344-128-128-128-128 57.344-128 128z"}));u6.displayName="TitleIcon";const Sl=()=>s(ie,{name:"search"},()=>s("path",{d:"M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"}));Sl.displayName="SearchIcon";const Nu=()=>s("svg",{xmlns:"http://www.w3.org/2000/svg",width:"32",height:"32",preserveAspectRatio:"xMidYMid",viewBox:"0 0 100 100"},[s("circle",{cx:"28",cy:"75",r:"11",fill:"currentColor"},s("animate",{attributeName:"fill-opacity",begin:"0s",dur:"1s",keyTimes:"0;0.2;1",repeatCount:"indefinite",values:"0;1;1"})),s("path",{fill:"none",stroke:"#88baf0","stroke-width":"10",d:"M28 47a28 28 0 0 1 28 28"},s("animate",{attributeName:"stroke-opacity",begin:"0.1s",dur:"1s",keyTimes:"0;0.2;1",repeatCount:"indefinite",values:"0;1;1"})),s("path",{fill:"none",stroke:"#88baf0","stroke-width":"10",d:"M28 25a50 50 0 0 1 50 50"},s("animate",{attributeName:"stroke-opacity",begin:"0.2s",dur:"1s",keyTimes:"0;0.2;1",repeatCount:"indefinite",values:"0;1;1"}))]);Nu.displayName="LoadingIcon";const Vu=({hint:e})=>s("div",{class:"search-pro-result-wrapper loading"},[s(Nu),e]);Vu.displayName="SearchLoading";const d6='<svg width="20" height="20" viewBox="0 0 20 20"><path d="M10 10l5.09-5.09L10 10l5.09 5.09L10 10zm0 0L4.91 4.91 10 10l-5.09 5.09L10 10z" stroke="currentColor" fill="none" fill-rule="evenodd" stroke-linecap="round" stroke-linejoin="round"></path></svg>';var f6={0:{"/":{0:"分",1:"类",2:":",3:" ",4:"$",5:"c",6:"o",7:"n",8:"t",9:"e",10:"n",11:"t"}},1:{"/":{0:"标",1:"签",2:":",3:" ",4:"$",5:"c",6:"o",7:"n",8:"t",9:"e",10:"n",11:"t"}}},p6={"/":{cancel:"取消",placeholder:"搜索",search:"搜索",searching:"搜索中",defaultTitle:"文档",select:"选择",navigate:"切换",autocomplete:"自动补全",exit:"关闭",queryHistory:"搜索历史",resultHistory:"历史结果",emptyHistory:"无搜索历史",emptyResult:"没有找到结果",loading:"正在加载搜索索引..."}},h6={searchDelay:150,suggestDelay:0,queryHistoryCount:5,resultHistoryCount:5,hotKeys:[{key:"k",ctrl:!0},{key:"/",ctrl:!0}],worker:"search-pro.worker.js"};const ba=h6,Y5=f6,ju=ba.hotKeys,xl=p6,io="Canceled because of new search request.",m6=()=>{const e=new Worker(`/${ba.worker}`,{}),t={suggest:null,search:null,all:null};return e.addEventListener("message",({data:n})=>{const[r,a,o]=n,l=t[r];(l==null?void 0:l.id)===a&&l.resolve(o)}),e.addEventListener("error",n=>{console.error("Search Worker error:",n)}),{suggest:(n,r,a)=>new Promise((o,l)=>{var c;(c=t.suggest)==null||c.reject(new Error(io));const i=Date.now();e.postMessage({type:"suggest",id:i,query:n,locale:r,options:a}),t.suggest={id:i,resolve:o,reject:l}}),search:(n,r,a)=>new Promise((o,l)=>{var c;(c=t.search)==null||c.reject(new Error(io));const i=Date.now();e.postMessage({type:"search",id:i,query:n,locale:r,options:a}),t.search={id:i,resolve:o,reject:l}}),all:(n,r,a)=>new Promise((o,l)=>{var c;(c=t.all)==null||c.reject(new Error(io));const i=Date.now();e.postMessage({type:"all",id:i,query:n,locale:r,options:a}),t.all={id:i,resolve:o,reject:l}}),terminate:()=>{e.terminate(),l6(t).forEach(n=>{n==null||n.reject(new Error("Worker has been terminated."))})}}};let v6={};const zu=Symbol(""),qu=()=>{const e=Ye(),{locales:t={},...n}=ve(zu);return w(()=>({...n,...t[e.value]||{}}))},g6=e=>{e.provide(zu,v6)},y6=(e,t=!1)=>{const n=z(0),r=w(()=>e.value[n.value]),a=()=>{n.value=n.value>0?n.value-1:e.value.length-1},o=()=>{n.value=n.value<e.value.length-1?n.value+1:0};return ae(e,()=>{t||(n.value=0)}),{index:n,item:r,prev:a,next:o}},b6=e=>e instanceof Element?document.activeElement===e&&(["TEXTAREA","SELECT","INPUT"].includes(e.tagName)||e.hasAttribute("contenteditable")):!1,E6=e=>ju.some(t=>{const{key:n,ctrl:r=!1,shift:a=!1,alt:o=!1,meta:l=!1}=t;return n===e.key&&r===e.ctrlKey&&a===e.shiftKey&&o===e.altKey&&l===e.metaKey}),_6='<svg width="15" height="15" aria-label="Enter key" role="img"><g fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="1.2"><path d="M12 3.53088v3c0 1-1 2-2 2H4M7 11.53088l-3-3 3-3"></path></g></svg>',w6='<svg width="15" height="15" aria-label="Arrow down" role="img"><g fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="1.2"><path d="M7.5 3.5v8M10.5 8.5l-3 3-3-3"></path></g></svg>',A6='<svg width="15" height="15" aria-label="Arrow up" role="img"><g fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="1.2"><path d="M7.5 11.5v-8M10.5 6.5l-3-3-3 3"></path></g></svg>',C6='<svg width="15" height="15" aria-label="Escape key" role="img"><g fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="1.2"><path d="M13.6167 8.936c-.1065.3583-.6883.962-1.4875.962-.7993 0-1.653-.9165-1.653-2.1258v-.5678c0-1.2548.7896-2.1016 1.653-2.1016.8634 0 1.3601.4778 1.4875 1.0724M9 6c-.1352-.4735-.7506-.9219-1.46-.8972-.7092.0246-1.344.57-1.344 1.2166s.4198.8812 1.3445.9805C8.465 7.3992 8.968 7.9337 9 8.5c.032.5663-.454 1.398-1.4595 1.398C6.6593 9.898 6 9 5.963 8.4851m-1.4748.5368c-.2635.5941-.8099.876-1.5443.876s-1.7073-.6248-1.7073-2.204v-.4603c0-1.0416.721-2.131 1.7073-2.131.9864 0 1.6425 1.031 1.5443 2.2492h-2.956"></path></g></svg>',Ll=Symbol(""),k6=()=>{const e=z(!1);ht(Ll,e)},T6=e=>{const t=z([]);{const n=qu(),r=ge(),a=Ye();se(()=>{const{suggest:o,terminate:l}=m6(),i=c=>{const u=c.join(" "),{searchFilter:d,splitWord:f,suggestionsFilter:p=v=>v,...h}=n.value;u?o(u,a.value,h).then(v=>p(v,u,a.value,r.value)).then(v=>{t.value=v.length?o6(v[0],u)&&!v[0].slice(u.length).includes(" ")?v:[u,...v]:[]}).catch(v=>{console.warn(v)}):t.value=[]};ae([e,a],([c])=>i(c),{immediate:!0}),Ft(()=>{l()})})}return{suggestions:t}},co=ju[0];var S6=M({name:"SearchBox",setup(){const e=Tl(xl),t=ve(Ll),n=z(!1),r=w(()=>co?[(n.value?["⌃","⇧","⌥","⌘"]:["Ctrl","Shift","Alt","Win"]).filter((a,o)=>co[["ctrl","shift","alt","meta"][o]]),co.key.toUpperCase()]:null);return Se("keydown",a=>{!t.value&&E6(a)&&!b6(a.target)&&(a.preventDefault(),t.value=!0)}),se(()=>{const{userAgent:a}=navigator;n.value=d4(a)||u4(a)||c4(a)}),()=>[s("button",{type:"button",class:"search-pro-button","aria-label":e.value.search,onClick:()=>{t.value=!0}},[s(Sl),s("div",{class:"search-pro-placeholder"},e.value.search),r.value?s("div",{class:"search-pro-key-hints"},r.value.map(a=>s("kbd",{class:"search-pro-key"},a))):null])]}});const x6=tc({loader:()=>T(()=>import("./SearchResult-DAas8KH8.js"),[]),loadingComponent:()=>{const e=Tl(xl);return s(Vu,{hint:e.value.loading})}});var L6=M({name:"SearchModal",setup(){const e=ve(Ll),t=Gn(),n=i4(),r=Tl(xl),a=qu(),o=z(""),l=z([]),{suggestions:i}=T6(l),c=z(!1),{index:u,prev:d,next:f}=y6(i),p=xe(),h=xe(),v=(E=u.value)=>{o.value=i.value[E],c.value=!1};Se("keydown",E=>{c.value?E.key==="ArrowUp"?d():E.key==="ArrowDown"?f():E.key==="Enter"?v():E.key==="Escape"&&(c.value=!1):E.key==="Escape"&&(e.value=!1)});const _=ru(()=>{var E,b;(((b=(E=a.value).splitWord)==null?void 0:b.call(E,o.value))??Promise.resolve(o.value.split(" "))).then(C=>{l.value=C})},Math.min(ba.searchDelay,ba.suggestDelay));return ae(o,_,{immediate:!0}),se(()=>{const E=bl(document.body);ae(e,async b=>{var C;E.value=b,b&&(await _t(),(C=p.value)==null||C.focus())}),lu(h,()=>{c.value=!1}),Ft(()=>{E.value=!1})}),()=>e.value?s("div",{class:"search-pro-modal-wrapper"},[s("div",{class:"search-pro-mask",onClick:()=>{e.value=!1,o.value=""}}),s("div",{class:"search-pro-modal"},[s("div",{class:"search-pro-box"},[s("form",[s("label",{for:"search-pro","aria-label":r.value.search},s(Sl)),s("input",{ref:p,type:"search",class:"search-pro-input",id:"search-pro",placeholder:r.value.placeholder,spellcheck:"false",autocapitalize:"off",autocomplete:"off",autocorrect:"off",name:`${t.value.title}-search`,value:o.value,"aria-controls":"search-pro-results",onKeydown:E=>{const{key:b}=E;i.value.length&&(b==="Tab"?(v(),E.preventDefault()):(b==="ArrowDown"||b==="ArrowUp"||b==="Escape")&&E.preventDefault())},onInput:({target:E})=>{o.value=E.value,c.value=!0,u.value=0}}),o.value?s("button",{type:"reset",class:"search-pro-clear-button",innerHTML:d6,onClick:()=>{o.value=""}}):null,c.value&&i.value.length?s("ul",{class:"search-pro-suggestions",ref:h},i.value.map((E,b)=>s("li",{class:["search-pro-suggestion",{active:b===u.value}],onClick:()=>{v(b)}},[s("kbd",{class:"search-pro-auto-complete",title:`Tab ${r.value.autocomplete}`},"Tab"),E]))):null]),s("button",{type:"button",class:"search-pro-close-button",onClick:()=>{e.value=!1,o.value=""}},r.value.cancel)]),s(x6,{queries:l.value,isFocusing:!c.value,onClose:()=>{e.value=!1},onUpdateQuery:E=>{o.value=E}}),n.value?null:s("div",{class:"search-pro-hints"},[s("span",{class:"search-pro-hint"},[s("kbd",{innerHTML:_6}),r.value.select]),s("span",{class:"search-pro-hint"},[s("kbd",{innerHTML:A6}),s("kbd",{innerHTML:w6}),r.value.navigate]),s("span",{class:"search-pro-hint"},[s("kbd",{innerHTML:C6}),r.value.exit])])])]):null}}),B6=Ze({enhance({app:e}){g6(e),e.component("SearchBox",S6)},setup(){k6()},rootComponents:[L6]});const Ve=e=>{const{icon:t="",color:n,size:r}=e,a=n||r?{}:null;return n&&(a.color=n),r&&(a.height=Number.isNaN(Number(r))?r:`${r}px`),sn(t)?s("img",{class:"icon",src:t,alt:"","no-view":"",style:a}):Rr(t)?s("img",{class:"icon",src:be(t),alt:"","aria-hidden":"","no-view":"",style:a}):s(pt("FontIcon"),e)};Ve.displayName="HopeIcon";const I6="http://.",An=()=>{const e=wn(),t=Ht();return n=>{if(n)if(Rr(n))t.path!==n&&e.push(n);else if(La(n))window&&window.open(n);else{const r=t.path.slice(0,t.path.lastIndexOf("/"));e.push(new URL(`${r}/${encodeURI(n)}`,I6).pathname)}}},Gu=()=>{const e=ge();return w(()=>e.value.readingTime??null)},Uu=(e,t)=>{const{minutes:n,words:r}=e,{less1Minute:a,word:o,time:l}=t;return{time:n<1?a:l.replace("$time",Math.round(n).toString()),words:o.replace("$word",r.toString())}};var di={"/":{word:"约 $word 字",less1Minute:"小于 1 分钟",time:"大约 $time 分钟"}};const fi={words:"",time:""},Do=typeof di>"u"?null:di,Wu=()=>Do?El(Do):w(()=>null),P6=()=>{if(typeof Do>"u")return w(()=>fi);const e=Gu(),t=Wu();return w(()=>e.value&&t.value?Uu(e.value,t.value):fi)},Nt=()=>gu(),ce=()=>Ip(),Ku=()=>{const e=ce(),t=he();return w(()=>{const{author:n}=t.value;return n?Cr(n):n===!1?[]:Cr(e.value.author,!1)})},D6=()=>{const e=he(),t=ve(Symbol.for("categoryMap"));return w(()=>Pu(e.value.category??e.value.categories).map(n=>{var r;return{name:n,path:((r=t==null?void 0:t.value.map[n])==null?void 0:r.path)??""}}))},O6=()=>{const e=he(),t=ve(Symbol.for("tagMap"));return w(()=>Du(e.value.tag??e.value.tags).map(n=>{var r;return{name:n,path:((r=t==null?void 0:t.value.map[n])==null?void 0:r.path)??""}}))},M6=()=>{const e=he(),t=ge();return w(()=>{const n=_l(e.value.date);if(n)return n;const{createdTime:r}=t.value.git??{};return r?new Date(r):null})},R6=()=>{const e=ce(),t=ge(),n=he(),r=Ku(),a=D6(),o=O6(),l=M6(),i=Gu(),c=P6(),u=w(()=>({author:r.value,category:a.value,date:l.value,localizedDate:t.value.localizedDate,tag:o.value,isOriginal:n.value.isOriginal??!1,readingTime:i.value,readingTimeLocale:c.value,pageview:"pageview"in n.value?n.value.pageview:!0})),d=w(()=>"pageInfo"in n.value?n.value.pageInfo:"pageInfo"in e.value?e.value.pageInfo:null);return{info:u,items:d}},Cn=()=>{const e=Nt();return w(()=>!!e.value.pure)},$6="719px",F6="1440px",H6="false",Ju={mobileBreakPoint:$6,pcBreakPoint:F6,enableThemeColor:H6},{mobileBreakPoint:N6,pcBreakPoint:V6}=Ju,pi=e=>e.endsWith("px")?Number(e.slice(0,-2)):null,$r=()=>{const e=z(!1),t=z(!1),n=()=>{e.value=window.innerWidth<=(pi(N6)??719),t.value=window.innerWidth>=(pi(V6)??1440)};return Se("resize",n,!1),Se("orientationchange",n,!1),se(()=>{n()}),{isMobile:e,isPC:t}},Qu=Symbol(""),Fr=()=>{const e=ve(Qu);if(!e)throw new Error("useDarkmode() is called without provider.");return e},j6=e=>{const t=Nt(),n=j3(),r=w(()=>t.value.darkmode??"switch"),a=cn("vuepress-theme-hope-scheme","auto"),o=w(()=>{const i=r.value;return i==="disable"?!1:i==="enable"?!0:i==="auto"?n.value:i==="toggle"?a.value==="dark":a.value==="dark"||a.value==="auto"&&n.value}),l=w(()=>{const i=r.value;return i==="switch"||i==="toggle"});e.provide(Qu,{canToggle:l,config:r,isDarkmode:o,status:a}),Object.defineProperties(e.config.globalProperties,{$isDarkmode:{get:()=>o.value}})},z6=()=>{const{config:e,isDarkmode:t,status:n}=Fr();Qi(()=>{e.value==="disable"?n.value="light":e.value==="enable"?n.value="dark":e.value==="toggle"&&n.value==="auto"&&(n.value="light")}),se(()=>{ae(t,r=>document.documentElement.setAttribute("data-theme",r?"dark":"light"),{immediate:!0})})},kr=(e,t,n=!1)=>"activeMatch"in t?new RegExp(t.activeMatch,"u").test(e.path):Lu(e,t.link)?!0:"children"in t&&!n?t.children.some(r=>kr(e,r)):!1,Yu=(e,t)=>t.type==="group"?t.children.some(n=>n.type==="group"?Yu(e,n):n.type==="page"&&kr(e,n,!0))||"prefix"in t&&Lu(e,t.prefix):!1,Bl={"/tech/":["docker","modint","「算术公理系统 1」自然数","android studio换源","cicd",{text:"Design ASimpile CCompiler",prefix:"designASimpileCCompiler/",collapsible:!0,children:["0","1","3","4","5","6","7","8","9","2"]},{text:"Design Patterns",prefix:"DesignPatterns/",collapsible:!0,children:["bridge","builder","chainOfResponsibility","command","composite","decorator","facade","factory_method","flyweight","interpreter","mediator","memento","observer","prototype","proxy","singleton","state","strategy","template_method","visitor","abstractFactory","end","index","DesignPrinciples","iterator","adapter"]},"/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html","steam模组开发","figure_bed","github 工作流","python_requrements","Qt6 Maintence tools不能安装Qt5","程序员的PPT","tensorflow踩坑","vsocde插件开发小记","使用capacitor和ionic将vue项目迁移到mobile端","协程","协程(asyncio)到底需不需要加锁","index","mailserver","闭包实现类","style"],"/essay/":[],"/tutorials/":["typora激活","index"],"/resources/":[{text:"Compile",prefix:"compile/",collapsible:!0,children:["index"]},{text:"Html2md",prefix:"html2md/",collapsible:!0,children:["index"]},"index"]},q6=(e,t)=>{const n=e.replace(t,"/").split("/"),r=[];let a=pl(t);return n.forEach((o,l)=>{l!==n.length-1?(a+=`${o}/`,r.push({link:a,name:o||"Home"})):o!==""&&(a+=o,r.push({link:a,name:o}))}),r},Oo=e=>!xa(e)&&!La(e);let uo=null,Zn=null;const Mo={wait:()=>uo,pending:()=>{uo=new Promise(e=>{Zn=e})},resolve:()=>{Zn==null||Zn(),uo=null,Zn=null}};var Ue;(function(e){e.title="t",e.shortTitle="s",e.icon="i",e.index="I",e.order="O",e.breadcrumbExclude="b"})(Ue||(Ue={}));var je;(function(e){e.type="y",e.author="a",e.date="d",e.localizedDate="l",e.category="c",e.tag="g",e.isEncrypted="n",e.isOriginal="o",e.readingTime="r",e.excerpt="e",e.sticky="u",e.cover="v"})(je||(je={}));var Ro;(function(e){e.article="a",e.home="h",e.slide="s",e.page="p"})(Ro||(Ro={}));const Il=(e,t=!1,n)=>{const{meta:r,path:a,notFound:o}=vp(e,n);return o?{text:a,link:a}:{text:!t&&r[Ue.shortTitle]?r[Ue.shortTitle]:r[Ue.title]||a,link:a,...r[Ue.icon]?{icon:r[Ue.icon]}:{}}},vn=(e="",t="")=>Rr(t)||La(t)?t:`${Pc(e)}${t}`,$o=({config:e,prefix:t=""})=>{const n=(r,a=t)=>{const o=we(r)?Il(vn(a,r)):r.link?{...r,...Oo(r.link)?{link:xt(vn(a,r.link)).path}:{}}:r;if("children"in o){const l=vn(a,o.prefix),i=o.children==="structure"?Bl[l]:o.children;return{type:"group",...o,prefix:l,children:i.map(c=>n(c,l))}}return{type:"page",...o}};return e.map(r=>n(r))},G6=({config:e,page:t,headerDepth:n})=>{const r=En(e).sort((a,o)=>o.length-a.length);for(const a of r)if(Oa(decodeURI(t.path),a)){const o=e[a];return o?$o({config:o==="structure"?Bl[a]:o,page:t,headerDepth:n,prefix:a}):[]}return console.warn(`${t.path} is missing sidebar config.`),[]},U6=({config:e,routeLocale:t,page:n,headerDepth:r})=>e==="structure"?$o({config:Bl[t],page:n,headerDepth:r,prefix:t}):Po(e)?$o({config:e,page:n,headerDepth:r}):qn(e)?G6({config:e,page:n,headerDepth:r}):[],Zu=Symbol(""),W6=()=>{const e=he(),t=ce(),n=ge(),r=Ye(),a=w(()=>e.value.home?!1:e.value.sidebar??t.value.sidebar??"structure"),o=w(()=>e.value.headerDepth??t.value.headerDepth??2),l=eu(()=>[a.value,o.value,n.value.path,null],()=>U6({config:a.value,routeLocale:r.value,page:n.value,headerDepth:o.value}));ht(Zu,l)},Pl=()=>{const e=ve(Zu);if(!e)throw new Error("useSidebarItems() is called without provider.");return e},K6=M({name:"PageFooter",setup(){const e=Nt(),t=ce(),n=he(),r=Ku(),a=w(()=>{const{copyright:u,footer:d}=n.value;return d!==!1&&!!(u||d||t.value.displayFooter)}),o=w(()=>{const{footer:u}=n.value;return u??t.value.footer}),l=w(()=>r.value.map(({name:u})=>u).join(", ")),i=u=>`Copyright © ${new Date().getFullYear()} ${l.value} ${u?`${u} Licensed`:""}`,c=w(()=>{const{copyright:u,license:d=""}=n.value,{license:f}=e.value,{copyright:p}=t.value;return u??(d?i(d):we(p)?p:l.value||f?i(f):!1)});return()=>a.value?s("footer",{class:"vp-footer-wrapper"},[o.value?s("div",{class:"vp-footer",innerHTML:o.value}):null,c.value?s("div",{class:"vp-copyright",innerHTML:c.value}):null]):null}}),ia=()=>null,Je=M({name:"AutoLink",inheritAttrs:!1,props:{config:{type:Object,required:!0},exact:Boolean,noExternalLinkIcon:Boolean},emits:["focusout"],slots:Object,setup(e,{attrs:t,emit:n,slots:r}){const a=Ht(),o=qc(),l=zn(e,"config"),i=w(()=>sn(l.value.link)),c=w(()=>!i.value&&La(l.value.link)),u=w(()=>l.value.target??(i.value?"_blank":void 0)),d=w(()=>u.value==="_blank"),f=w(()=>!i.value&&!c.value&&!d.value),p=w(()=>l.value.rel??(d.value?"noopener noreferrer":"")),h=w(()=>l.value.ariaLabel??l.value.text),v=w(()=>{if(e.exact)return!1;const E=En(o.value.locales);return E.length?E.every(b=>b!==l.value.link):l.value.link!=="/"}),_=w(()=>f.value?l.value.activeMatch?new RegExp(l.value.activeMatch,"u").test(a.path):v.value?Oa(a.path,l.value.link):a.path===l.value.link:!1);return()=>{const{before:E,after:b,default:C}=r,{text:y,icon:A,link:D}=l.value;return f.value?s(Ie,{to:D,"aria-label":h.value,...t,class:["nav-link",{active:_.value},t.class],onFocusout:()=>n("focusout")},()=>C?C():[E?E():s(Ve,{icon:A}),y,b==null?void 0:b()]):s("a",{href:D,rel:p.value,target:u.value,"aria-label":h.value,...t,class:["nav-link",t.class],onFocusout:()=>n("focusout")},C?C():[E?E():s(Ve,{icon:A}),y,e.noExternalLinkIcon?null:s(mu),b==null?void 0:b()])}}}),J6=M({name:"NavbarDropdownLink",props:{config:{type:Object,required:!0}},slots:Object,setup(e,{slots:t}){const n=ge(),r=zn(e,"config"),a=w(()=>r.value.ariaLabel??r.value.text),o=z(!1);ae(()=>n.value.path,()=>{o.value=!1});const l=i=>{i.detail===0&&(o.value=!o.value)};return()=>{var i;return s("div",{class:["dropdown-wrapper",{open:o.value}]},[s("button",{type:"button",class:"dropdown-title","aria-label":a.value,onClick:l},[((i=t.title)==null?void 0:i.call(t))||s("span",{class:"title"},[s(Ve,{icon:r.value.icon}),e.config.text]),s("span",{class:"arrow"}),s("ul",{class:"nav-dropdown"},r.value.children.map((c,u)=>{const d=u===r.value.children.length-1;return s("li",{class:"dropdown-item"},"children"in c?[s("h4",{class:"dropdown-subtitle"},c.link?s(Je,{config:c,onFocusout:()=>{c.children.length===0&&d&&(o.value=!1)}}):s("span",c.text)),s("ul",{class:"dropdown-subitem-wrapper"},c.children.map((f,p)=>s("li",{class:"dropdown-subitem"},s(Je,{config:f,onFocusout:()=>{p===c.children.length-1&&d&&(o.value=!1)}}))))]:s(Je,{config:c,onFocusout:()=>{d&&(o.value=!1)}}))}))])])}}}),Xu=(e,t="")=>we(e)?Il(vn(t,e)):"children"in e?{...e,...e.link&&Oo(e.link)?{link:xt(vn(t,e.link)).path}:{},children:e.children.map(n=>Xu(n,vn(t,e.prefix)))}:{...e,link:Oo(e.link)?xt(vn(t,e.link)).path:e.link},e1=()=>{const e=ce(),t=()=>(e.value.navbar||[]).map(r=>Xu(r));return eu(()=>e.value.navbar,()=>t())},Q6=()=>{const e=ce(),t=w(()=>e.value.repo),n=w(()=>t.value?r4(t.value):null),r=w(()=>t.value?Cl(t.value):null),a=w(()=>n.value?e.value.repoLabel??r.value??"Source":null);return w(()=>!n.value||!a.value||e.value.repoDisplay===!1?null:{type:r.value??"Source",label:a.value,link:n.value})},Y6=M({name:"NavScreenDropdown",props:{config:{type:Object,required:!0}},setup(e){const t=ge(),n=zn(e,"config"),r=w(()=>n.value.ariaLabel??n.value.text),a=z(!1);ae(()=>t.value.path,()=>{a.value=!1});const o=(l,i)=>i[i.length-1]===l;return()=>[s("button",{type:"button",class:["nav-screen-dropdown-title",{active:a.value}],"aria-label":r.value,onClick:()=>{a.value=!a.value}},[s("span",{class:"title"},[s(Ve,{icon:n.value.icon}),e.config.text]),s("span",{class:["arrow",a.value?"down":"end"]})]),s("ul",{class:["nav-screen-dropdown",{hide:!a.value}]},n.value.children.map(l=>s("li",{class:"dropdown-item"},"children"in l?[s("h4",{class:"dropdown-subtitle"},l.link?s(Je,{config:l,onFocusout:()=>{o(l,n.value.children)&&l.children.length===0&&(a.value=!1)}}):s("span",l.text)),s("ul",{class:"dropdown-subitem-wrapper"},l.children.map(i=>s("li",{class:"dropdown-subitem"},s(Je,{config:i,onFocusout:()=>{o(i,l.children)&&o(l,n.value.children)&&(a.value=!1)}}))))]:s(Je,{config:l,onFocusout:()=>{o(l,n.value.children)&&(a.value=!1)}}))))]}}),Z6=M({name:"NavScreenLinks",setup(){const e=e1();return()=>e.value.length?s("nav",{class:"nav-screen-links"},e.value.map(t=>s("div",{class:"navbar-links-item"},"children"in t?s(Y6,{config:t}):s(Je,{config:t})))):null}}),t1=()=>s(ie,{name:"dark"},()=>s("path",{d:"M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"}));t1.displayName="DarkIcon";const n1=()=>s(ie,{name:"light"},()=>s("path",{d:"M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"}));n1.displayName="LightIcon";const r1=()=>s(ie,{name:"auto"},()=>s("path",{d:"M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"}));r1.displayName="AutoIcon";const a1=()=>s(ie,{name:"enter-fullscreen"},()=>s("path",{d:"M762.773 90.24h-497.28c-96.106 0-174.4 78.293-174.4 174.4v497.28c0 96.107 78.294 174.4 174.4 174.4h497.28c96.107 0 175.04-78.293 174.4-174.4V264.64c0-96.213-78.186-174.4-174.4-174.4zm-387.2 761.173H215.04c-21.867 0-40.427-17.92-41.067-41.066V649.92c0-22.507 17.92-40.427 40.427-40.427 11.307 0 21.227 4.694 28.48 11.947 7.253 7.253 11.947 17.92 11.947 28.48v62.293l145.28-145.28c15.893-15.893 41.813-15.893 57.706 0 15.894 15.894 15.894 41.814 0 57.707l-145.28 145.28h62.294c22.506 0 40.426 17.92 40.426 40.427s-17.173 41.066-39.68 41.066zM650.24 165.76h160.427c21.866 0 40.426 17.92 41.066 41.067v160.426c0 22.507-17.92 40.427-40.426 40.427-11.307 0-21.227-4.693-28.48-11.947-7.254-7.253-11.947-17.92-11.947-28.48v-62.186L625.6 450.347c-15.893 15.893-41.813 15.893-57.707 0-15.893-15.894-15.893-41.814 0-57.707l145.28-145.28H650.88c-22.507 0-40.427-17.92-40.427-40.427s17.174-41.173 39.787-41.173z"}));a1.displayName="EnterFullScreenIcon";const o1=()=>s(ie,{name:"cancel-fullscreen"},()=>s("path",{d:"M778.468 78.62H247.922c-102.514 0-186.027 83.513-186.027 186.027V795.08c0 102.514 83.513 186.027 186.027 186.027h530.432c102.514 0 186.71-83.513 186.026-186.027V264.647C964.494 162.02 880.981 78.62 778.468 78.62zM250.88 574.35h171.122c23.324 0 43.122 19.115 43.804 43.805v171.121c0 24.008-19.114 43.122-43.122 43.122-12.06 0-22.641-5.006-30.378-12.743s-12.743-19.115-12.743-30.379V722.83L224.597 877.91c-16.953 16.952-44.6 16.952-61.553 0-16.953-16.954-16.953-44.602 0-61.554L318.009 661.39h-66.446c-24.007 0-43.122-19.114-43.122-43.122 0-24.12 18.432-43.918 42.439-43.918zm521.899-98.873H601.657c-23.325 0-43.122-19.114-43.805-43.804V260.55c0-24.007 19.115-43.122 43.122-43.122 12.06 0 22.642 5.007 30.379 12.743s12.743 19.115 12.743 30.38v66.445l154.965-154.965c16.953-16.953 44.601-16.953 61.554 0 16.953 16.953 16.953 44.6 0 61.554L705.536 388.55h66.446c24.007 0 43.122 19.115 43.122 43.122.114 24.007-18.318 43.804-42.325 43.804z"}));o1.displayName="CancelFullScreenIcon";const l1=()=>s(ie,{name:"outlook"},()=>[s("path",{d:"M224 800c0 9.6 3.2 44.8 6.4 54.4 6.4 48-48 76.8-48 76.8s80 41.6 147.2 0 134.4-134.4 38.4-195.2c-22.4-12.8-41.6-19.2-57.6-19.2C259.2 716.8 227.2 761.6 224 800zM560 675.2l-32 51.2c-51.2 51.2-83.2 32-83.2 32 25.6 67.2 0 112-12.8 128 25.6 6.4 51.2 9.6 80 9.6 54.4 0 102.4-9.6 150.4-32l0 0c3.2 0 3.2-3.2 3.2-3.2 22.4-16 12.8-35.2 6.4-44.8-9.6-12.8-12.8-25.6-12.8-41.6 0-54.4 60.8-99.2 137.6-99.2 6.4 0 12.8 0 22.4 0 12.8 0 38.4 9.6 48-25.6 0-3.2 0-3.2 3.2-6.4 0-3.2 3.2-6.4 3.2-6.4 6.4-16 6.4-16 6.4-19.2 9.6-35.2 16-73.6 16-115.2 0-105.6-41.6-198.4-108.8-268.8C704 396.8 560 675.2 560 675.2zM224 419.2c0-28.8 22.4-51.2 51.2-51.2 28.8 0 51.2 22.4 51.2 51.2 0 28.8-22.4 51.2-51.2 51.2C246.4 470.4 224 448 224 419.2zM320 284.8c0-22.4 19.2-41.6 41.6-41.6 22.4 0 41.6 19.2 41.6 41.6 0 22.4-19.2 41.6-41.6 41.6C339.2 326.4 320 307.2 320 284.8zM457.6 208c0-12.8 12.8-25.6 25.6-25.6 12.8 0 25.6 12.8 25.6 25.6 0 12.8-12.8 25.6-25.6 25.6C470.4 233.6 457.6 220.8 457.6 208zM128 505.6C128 592 153.6 672 201.6 736c28.8-60.8 112-60.8 124.8-60.8-16-51.2 16-99.2 16-99.2l316.8-422.4c-48-19.2-99.2-32-150.4-32C297.6 118.4 128 291.2 128 505.6zM764.8 86.4c-22.4 19.2-390.4 518.4-390.4 518.4-22.4 28.8-12.8 76.8 22.4 99.2l9.6 6.4c35.2 22.4 80 12.8 99.2-25.6 0 0 6.4-12.8 9.6-19.2 54.4-105.6 275.2-524.8 288-553.6 6.4-19.2-3.2-32-19.2-32C777.6 76.8 771.2 80 764.8 86.4z"})]);l1.displayName="OutlookIcon";const s1=M({name:"AppearanceSwitch",setup(){const{config:e,isDarkmode:t,status:n}=Fr(),r=Cn(),a=()=>{e.value==="switch"?n.value={light:"dark",dark:"auto",auto:"light"}[n.value]:n.value=n.value==="light"?"dark":"light"},o=async l=>{if(!(document.startViewTransition&&!window.matchMedia("(prefers-reduced-motion: reduce)").matches&&!r.value)||!l){a();return}const c=l.clientX,u=l.clientY,d=Math.hypot(Math.max(c,innerWidth-c),Math.max(u,innerHeight-u)),f=t.value;await document.startViewTransition(async()=>{a(),await _t()}).ready,t.value!==f&&document.documentElement.animate({clipPath:t.value?[`circle(${d}px at ${c}px ${u}px)`,`circle(0px at ${c}px ${u}px)`]:[`circle(0px at ${c}px ${u}px)`,`circle(${d}px at ${c}px ${u}px)`]},{duration:400,pseudoElement:t.value?"::view-transition-old(root)":"::view-transition-new(root)"})};return()=>s("button",{type:"button",id:"appearance-switch",onClick:o},[s(r1,{style:{display:n.value==="auto"?"block":"none"}}),s(t1,{style:{display:n.value==="dark"?"block":"none"}}),s(n1,{style:{display:n.value==="light"?"block":"none"}})])}}),X6=M({name:"AppearanceMode",setup(){const e=ce(),{canToggle:t}=Fr(),n=w(()=>e.value.outlookLocales.darkmode);return()=>t.value?s("div",{class:"appearance-wrapper"},[s("label",{class:"appearance-title",for:"appearance-switch"},n.value),s(s1)]):null}}),fo=Ju.enableThemeColor==="true",i1=M({name:"ToggleFullScreenButton",setup(){const e=ce(),{isSupported:t,isFullscreen:n,toggle:r}=yl(),a=w(()=>e.value.outlookLocales.fullscreen);return()=>t?s("div",{class:"full-screen-wrapper"},[s("label",{class:"full-screen-title",for:"full-screen-switch"},a.value),s("button",{type:"button",id:"full-screen-switch",class:"full-screen",ariaPressed:n.value,onClick:()=>r()},n.value?s(o1):s(a1))]):null}}),c1=M({name:"OutlookSettings",setup(){const e=Nt(),t=Cn(),n=w(()=>!t.value&&e.value.fullscreen);return()=>s(Or,()=>[null,s(X6),n.value?s(i1):null])}}),e8=M({name:"NavScreen",props:{show:Boolean},emits:["close"],slots:Object,setup(e,{emit:t,slots:n}){const r=ge(),{isMobile:a}=$r(),o=xe(),l=bl(o);return se(()=>{o.value=document.body,ae(a,i=>{!i&&e.show&&(l.value=!1,t("close"))}),ae(()=>r.value.path,()=>{l.value=!1,t("close")})}),Ft(()=>{l.value=!1}),()=>s(Rt,{name:"fade",onEnter:()=>{l.value=!0},onAfterLeave:()=>{l.value=!1}},()=>{var i,c;return e.show?s("div",{id:"nav-screen"},s("div",{class:"vp-nav-screen-container"},[(i=n.before)==null?void 0:i.call(n),s(Z6),s("div",{class:"vp-outlook-wrapper"},s(c1)),(c=n.after)==null?void 0:c.call(n)])):null})}}),t8=M({name:"NavbarBrand",setup(){const e=Ye(),t=Gn(),n=ce(),r=w(()=>n.value.home||e.value),a=w(()=>t.value.title),o=w(()=>n.value.navbarTitle??a.value),l=w(()=>n.value.logo?be(n.value.logo):null),i=w(()=>n.value.logoDark?be(n.value.logoDark):null);return()=>s(Ie,{to:r.value,class:"vp-brand"},()=>[l.value?s("img",{class:["vp-nav-logo",{light:!!i.value}],src:l.value,alt:""}):null,i.value?s("img",{class:["vp-nav-logo dark"],src:i.value,alt:""}):null,o.value?s("span",{class:["vp-site-name",{"hide-in-pad":l.value&&(n.value.hideSiteNameOnMobile??!0)}]},o.value):null])}}),n8=M({name:"NavbarLinks",setup(){const e=e1();return()=>e.value.length?s("nav",{class:"vp-nav-links"},e.value.map(t=>s("div",{class:"vp-nav-item hide-in-mobile"},"children"in t?s(J6,{config:t}):s(Je,{config:t})))):null}}),r8=M({name:"RepoLink",setup(){const e=Q6();return()=>e.value?s("div",{class:"vp-nav-item vp-action"},s("a",{class:"vp-action-link",href:e.value.link,target:"_blank",rel:"noopener noreferrer","aria-label":e.value.label},s(a4,{type:e.value.type,style:{width:"1.25rem",height:"1.25rem",verticalAlign:"middle"}}))):null}}),u1=({active:e=!1},{emit:t})=>s("button",{type:"button",class:["vp-toggle-navbar-button",{"is-active":e}],"aria-label":"Toggle Navbar","aria-expanded":e,"aria-controls":"nav-screen",onClick:()=>t("toggle")},s("span",[s("span",{class:"vp-top"}),s("span",{class:"vp-middle"}),s("span",{class:"vp-bottom"})]));u1.displayName="ToggleNavbarButton";const Dl=(e,{emit:t})=>s("button",{type:"button",class:"vp-toggle-sidebar-button",title:"Toggle Sidebar",onClick:()=>t("toggle")},s("span",{class:"icon"}));Dl.displayName="ToggleSidebarButton";Dl.emits=["toggle"];const a8=M({name:"OutlookButton",setup(){const{isSupported:e}=yl(),t=Nt(),n=Cn(),r=ge(),{canToggle:a}=Fr(),o=z(!1),l=w(()=>!n.value&&t.value.fullscreen&&e);return ae(()=>r.value.path,()=>{o.value=!1}),()=>a.value||l.value||fo?s("div",{class:"vp-nav-item hide-in-mobile"},a.value&&!l.value&&!fo?s(s1):l.value&&!a.value&&!fo?s(i1):s("button",{type:"button",class:["outlook-button",{open:o.value}],tabindex:"-1","aria-hidden":!0},[s(l1),s("div",{class:"outlook-dropdown"},s(c1))])):null}}),o8=M({name:"NavBar",emits:["toggleSidebar"],slots:Object,setup(e,{emit:t,slots:n}){const r=ce(),{isMobile:a}=$r(),o=z(!1),l=w(()=>{const{navbarAutoHide:d="mobile"}=r.value;return d!=="none"&&(d==="always"||a.value)}),i=w(()=>r.value.navbarLayout??{start:["Brand"],center:["Links"],end:["Language","Repo","Outlook","Search"]}),c={Brand:t8,Language:ia,Links:n8,Repo:r8,Outlook:a8,Search:Mn("Docsearch")?pt("Docsearch"):Mn("SearchBox")?pt("SearchBox"):ia},u=d=>c[d]??(Mn(d)?pt(d):ia);return()=>{var d,f,p,h,v,_,E,b,C;return[s("header",{key:"navbar",id:"navbar",class:["vp-navbar",{"auto-hide":l.value}]},[s("div",{class:"vp-navbar-start"},[s(Dl,{onToggle:()=>{o.value&&(o.value=!1),t("toggleSidebar")}}),(d=n.startBefore)==null?void 0:d.call(n),(f=i.value.start)==null?void 0:f.map(y=>s(u(y))),(p=n.startAfter)==null?void 0:p.call(n)]),s("div",{class:"vp-navbar-center"},[(h=n.centerBefore)==null?void 0:h.call(n),(v=i.value.center)==null?void 0:v.map(y=>s(u(y))),(_=n.centerAfter)==null?void 0:_.call(n)]),s("div",{class:"vp-navbar-end"},[(E=n.endBefore)==null?void 0:E.call(n),(b=i.value.end)==null?void 0:b.map(y=>s(u(y))),(C=n.endAfter)==null?void 0:C.call(n),s(u1,{active:o.value,onToggle:()=>{o.value=!o.value}})])]),s(e8,{show:o.value,onClose:()=>{o.value=!1}},{before:()=>{var y;return(y=n.screenTop)==null?void 0:y.call(n)},after:()=>{var y;return(y=n.screenBottom)==null?void 0:y.call(n)}})]}}}),l8=M({name:"SidebarChild",props:{config:{type:Object,required:!0}},setup(e){const t=Ht();return()=>we(e.config.link)?s(Je,{class:["vp-sidebar-link","vp-sidebar-page",{active:kr(t,e.config,!0)}],exact:!0,config:e.config}):s("p",e,[s(Ve,{icon:e.config.icon}),e.config.text])}}),s8=M({name:"SidebarGroup",props:{config:{type:Object,required:!0},open:{type:Boolean,required:!0}},emits:["toggle"],setup(e,{emit:t}){const n=Ht(),r=w(()=>kr(n,e.config)),a=w(()=>kr(n,e.config,!0));return()=>{const{collapsible:o,children:l=[],icon:i,prefix:c,link:u,text:d}=e.config;return s("section",{class:"vp-sidebar-group"},[s(o?"button":"p",{class:["vp-sidebar-header",{clickable:o||u,exact:a.value,active:r.value}],...o?{type:"button",onClick:()=>t("toggle"),onKeydown:f=>{f.key==="Enter"&&t("toggle")}}:{}},[s(Ve,{icon:i}),u?s(Je,{class:"vp-sidebar-title",config:{text:d,link:u},noExternalLinkIcon:!0}):s("span",{class:"vp-sidebar-title"},d),o?s("span",{class:["vp-arrow",e.open?"down":"end"]}):null]),e.open||!o?s(d1,{key:c,config:l}):null])}}}),d1=M({name:"SidebarLinks",props:{config:{type:Array,required:!0}},setup(e){const t=Ht(),n=z(-1),r=a=>{n.value=a===n.value?-1:a};return ae(()=>t.path,()=>{const a=e.config.findIndex(o=>Yu(t,o));n.value=a},{immediate:!0,flush:"post"}),()=>s("ul",{class:"vp-sidebar-links"},e.config.map((a,o)=>s("li",a.type==="group"?s(s8,{config:a,open:o===n.value,onToggle:()=>r(o)}):s(l8,{config:a}))))}}),i8=M({name:"SideBar",slots:Object,setup(e,{slots:t}){const n=Ht(),r=Pl(),a=xe();return se(()=>{ae(()=>n.hash,o=>{const l=document.querySelector(`.vp-sidebar a.vp-sidebar-link[href="${n.path}${o}"]`);if(!l)return;const{top:i,height:c}=a.value.getBoundingClientRect(),{top:u,height:d}=l.getBoundingClientRect();u<i?l.scrollIntoView(!0):u+d>i+c&&l.scrollIntoView(!1)},{immediate:!0})}),()=>{var o,l,i;return s("aside",{ref:a,key:"sidebar",id:"sidebar",class:"vp-sidebar"},[(o=t.top)==null?void 0:o.call(t),((l=t.default)==null?void 0:l.call(t))??s(d1,{config:r.value}),(i=t.bottom)==null?void 0:i.call(t)])}}}),Ol=M({name:"CommonWrapper",props:{containerClass:{type:String,default:""},noNavbar:Boolean,noSidebar:Boolean,noToc:Boolean},slots:Object,setup(e,{slots:t}){const n=wn(),r=he(),a=ce(),{isMobile:o,isPC:l}=$r(),[i,c]=wr(!1),[u,d]=wr(!1),f=Pl(),p=z(!1),h=w(()=>e.noNavbar||r.value.navbar===!1||a.value.navbar===!1?!1:!!(a.value.logo??a.value.repo??a.value.navbar)),v=w(()=>e.noSidebar?!1:r.value.sidebar!==!1&&f.value.length!==0&&!r.value.home),_=w(()=>!e.noToc&&!r.value.home&&(r.value.toc??a.value.toc??!0)),E={x:0,y:0},b=A=>{E.x=A.changedTouches[0].clientX,E.y=A.changedTouches[0].clientY},C=A=>{const D=A.changedTouches[0].clientX-E.x,P=A.changedTouches[0].clientY-E.y;Math.abs(D)>Math.abs(P)*1.5&&Math.abs(D)>40&&(D>0&&E.x<=80?c(!0):c(!1))};let y=0;return Se("scroll",x3(()=>{const A=window.scrollY;A<=58||A<y?p.value=!1:y+200<A&&!i.value&&(p.value=!0),y=A},300,!0)),ae(o,A=>{A||c(!1)}),se(()=>{const A=bl(document.body);ae(i,P=>{A.value=P});const D=n.afterEach(()=>{c(!1)});Ft(()=>{A.value=!1,D()})}),()=>s(Mn("GlobalEncrypt")?pt("GlobalEncrypt"):Au,()=>s("div",{class:["theme-container",{"no-navbar":!h.value,"no-sidebar":!v.value&&!t.sidebar&&!t.sidebarTop&&!t.sidebarBottom,"has-toc":_.value,"hide-navbar":p.value,"sidebar-collapsed":!o.value&&!l.value&&u.value,"sidebar-open":o.value&&i.value},e.containerClass,r.value.containerClass??""],onTouchStart:b,onTouchEnd:C},[h.value?s(o8,{onToggleSidebar:()=>c()},{startBefore:()=>{var A;return(A=t.navbarStartBefore)==null?void 0:A.call(t)},startAfter:()=>{var A;return(A=t.navbarStartAfter)==null?void 0:A.call(t)},centerBefore:()=>{var A;return(A=t.navbarCenterBefore)==null?void 0:A.call(t)},centerAfter:()=>{var A;return(A=t.navbarCenterAfter)==null?void 0:A.call(t)},endBefore:()=>{var A;return(A=t.navbarEndBefore)==null?void 0:A.call(t)},endAfter:()=>{var A;return(A=t.navbarEndAfter)==null?void 0:A.call(t)},screenTop:()=>{var A;return(A=t.navScreenTop)==null?void 0:A.call(t)},screenBottom:()=>{var A;return(A=t.navScreenBottom)==null?void 0:A.call(t)}}):null,s(Rt,{name:"fade"},()=>i.value?s("div",{class:"vp-sidebar-mask",onClick:()=>c(!1)}):null),s(Rt,{name:"fade"},()=>o.value?null:s("div",{class:"toggle-sidebar-wrapper",onClick:()=>d()},s("span",{class:["arrow",u.value?"end":"start"]}))),s(i8,{},{...t.sidebar?{default:()=>t.sidebar()}:{},top:()=>{var A;return(A=t.sidebarTop)==null?void 0:A.call(t)},bottom:()=>{var A;return(A=t.sidebarBottom)==null?void 0:A.call(t)}}),t.default(),s(K6)]))}}),Fo=(e,{slots:t})=>{var f,p;const{bgImage:n,bgImageDark:r,bgImageStyle:a,color:o,description:l,image:i,imageDark:c,header:u,features:d=[]}=e;return s("div",{class:"vp-feature-wrapper"},[n?s("div",{class:["vp-feature-bg",{light:r}],style:[{"background-image":`url(${n})`},a]}):null,r?s("div",{class:"vp-feature-bg dark",style:[{"background-image":`url(${r})`},a]}):null,s("div",{class:"vp-feature",style:o?{color:o}:{}},[((f=t.image)==null?void 0:f.call(t,e))??[i?s("img",{class:["vp-feature-image",{light:c}],src:be(i),alt:""}):null,c?s("img",{class:"vp-feature-image dark",src:be(c),alt:""}):null],((p=t.info)==null?void 0:p.call(t,e))??[u?s("h2",{class:"vp-feature-header"},u):null,l?s("p",{class:"vp-feature-description",innerHTML:l}):null],d.length?s("div",{class:"vp-features"},d.map(({icon:h,title:v,details:_,link:E})=>{const b=[s("h3",{class:"vp-feature-title"},[s(Ve,{icon:h}),s("span",{innerHTML:v})]),s("p",{class:"vp-feature-details",innerHTML:_})];return E?xa(E)?s("a",{class:"vp-feature-item link",href:E,"aria-label":v,target:"_blank"},b):s(Ie,{class:"vp-feature-item link",to:E,"aria-label":v},()=>b):s("div",{class:"vp-feature-item"},b)})):null])])};Fo.displayName="FeaturePanel";const oe=M({name:"DropTransition",props:{type:{type:String,default:"single"},delay:{type:Number,default:0},duration:{type:Number,default:.25},appear:Boolean},slots:Object,setup(e,{slots:t}){const n=a=>{a.style.transition=`transform ${e.duration}s ease-in-out ${e.delay}s, opacity ${e.duration}s ease-in-out ${e.delay}s`,a.style.transform="translateY(-20px)",a.style.opacity="0"},r=a=>{a.style.transform="translateY(0)",a.style.opacity="1"};return()=>{const a={name:"drop",appear:e.appear,onAppear:n,onAfterAppear:r,onEnter:n,onAfterEnter:r,onBeforeLeave:n},o=()=>t.default();return e.type==="group"?s(bd,a,o):s(Rt,a,o)}}}),Ml=(e,{slots:t})=>s(Rt,{name:"fade-slide-y",mode:"out-in",onBeforeEnter:Mo.resolve,onBeforeLeave:Mo.pending},()=>{var n;return(n=t.default)==null?void 0:n.call(t)});Ml.displayName="FadeSlideY";const c8=M({name:"HeroInfo",slots:Object,setup(e,{slots:t}){const n=he(),r=Gn(),a=w(()=>n.value.heroFullScreen??!1),o=w(()=>{const{heroText:u,tagline:d}=n.value;return{text:u??r.value.title??"Hello",tagline:d??r.value.description??"",isFullScreen:a.value}}),l=w(()=>{const{heroText:u,heroImage:d,heroImageDark:f,heroAlt:p,heroImageStyle:h}=n.value;return{image:d?be(d):null,imageDark:f?be(f):null,imageStyle:h,alt:p??u??"",isFullScreen:a.value}}),i=w(()=>{const{bgImage:u,bgImageDark:d,bgImageStyle:f}=n.value;return{image:we(u)?be(u):null,imageDark:we(d)?be(d):null,bgStyle:f,isFullScreen:a.value}}),c=w(()=>n.value.actions??[]);return()=>{var u,d,f;return s("header",{class:["vp-hero-info-wrapper",{fullscreen:a.value}]},[((u=t.bg)==null?void 0:u.call(t,i.value))??[i.value.image?s("div",{class:["vp-hero-mask",{light:i.value.imageDark}],style:[{"background-image":`url(${i.value.image})`},i.value.bgStyle]}):null,i.value.imageDark?s("div",{class:"vp-hero-mask dark",style:[{"background-image":`url(${i.value.imageDark})`},i.value.bgStyle]}):null],s("div",{class:"vp-hero-info"},[((d=t.logo)==null?void 0:d.call(t,l.value))??s(oe,{appear:!0,type:"group"},()=>{const{image:p,imageDark:h,imageStyle:v,alt:_}=l.value;return[p?s("img",{key:"light",class:["vp-hero-image",{light:h}],style:v,src:p,alt:_}):null,h?s("img",{key:"dark",class:"vp-hero-image dark",style:v,src:h,alt:_}):null]}),((f=t.info)==null?void 0:f.call(t,o.value))??s("div",{class:"vp-hero-infos"},[o.value.text?s(oe,{appear:!0,delay:.04},()=>s("h1",{id:"main-title"},o.value.text)):null,o.value.tagline?s(oe,{appear:!0,delay:.08},()=>s("p",{id:"main-description",innerHTML:o.value.tagline})):null,c.value.length?s(oe,{appear:!0,delay:.12},()=>s("p",{class:"vp-hero-actions"},c.value.map(p=>s(Je,{class:["vp-hero-action",p.type??"default"],config:p,noExternalLinkIcon:!0},p.icon?{before:()=>s(Ve,{icon:p.icon})}:{})))):null])])])}}}),f1=(e,{slots:t})=>{var p,h,v;const{bgImage:n,bgImageDark:r,bgImageStyle:a,color:o,description:l,image:i,imageDark:c,header:u,highlights:d=[],type:f="un-order"}=e;return s("div",{class:"vp-highlight-wrapper",style:o?{color:o}:{}},[n?s("div",{class:["vp-highlight-bg",{light:r}],style:[{"background-image":`url(${n})`},a]}):null,r?s("div",{class:"vp-highlight-bg dark",style:[{"background-image":`url(${r})`},a]}):null,s("div",{class:"vp-highlight"},[((p=t.image)==null?void 0:p.call(t,e))??[i?s("img",{class:["vp-highlight-image",{light:c}],src:be(i),alt:""}):null,c?s("img",{class:"vp-highlight-image dark",src:be(c),alt:""}):null],((h=t.info)==null?void 0:h.call(t,e))??[s("div",{class:"vp-highlight-info-wrapper"},s("div",{class:"vp-highlight-info"},[u?s("h2",{class:"vp-highlight-header",innerHTML:u}):null,l?s("p",{class:"vp-highlight-description",innerHTML:l}):null,((v=t.highlights)==null?void 0:v.call(t,d))??s(f==="order"?"ol":f==="no-order"?"dl":"ul",{class:"vp-highlights"},d.map(({icon:_,title:E,details:b,link:C})=>{const y=[s(f==="no-order"?"dt":"h3",{class:"vp-highlight-title"},[_?s(Ve,{class:"vp-highlight-icon",icon:_}):null,s("span",{innerHTML:E})]),b?s(f==="no-order"?"dd":"p",{class:"vp-highlight-details",innerHTML:b}):null];return s(f==="no-order"?"div":"li",{class:["vp-highlight-item-wrapper",{link:C}]},C?xa(C)?s("a",{class:"vp-highlight-item link",href:C,"aria-label":E,target:"_blank"},y):s(Ie,{class:"vp-highlight-item link",to:C,"aria-label":E},()=>y):s("div",{class:"vp-highlight-item"},y))}))]))]])])};f1.displayName="HighlightPanel";const Wn=({custom:e})=>s(Uc,{class:["theme-hope-content",{custom:e}]});Wn.displayName="MarkdownContent";Wn.props={custom:Boolean};const u8=M({name:"HomePage",slots:Object,setup(e,{slots:t}){const n=Cn(),r=he(),a=w(()=>{const{features:l}=r.value;return Po(l)?l:null}),o=w(()=>{const{highlights:l}=r.value;return Po(l)?l:null});return()=>{var l,i,c,u;return s("main",{id:"main-content",class:["vp-project-home ",{pure:n.value}],"aria-labelledby":r.value.heroText===null?"":"main-title"},[(l=t.top)==null?void 0:l.call(t),s(c8),((i=o.value)==null?void 0:i.map(d=>"features"in d?s(Fo,d):s(f1,d)))??(a.value?s(oe,{appear:!0,delay:.24},()=>s(Fo,{features:a.value})):null),(c=t.center)==null?void 0:c.call(t),s(oe,{appear:!0,delay:.32},()=>s(Wn)),(u=t.bottom)==null?void 0:u.call(t)])}}}),d8={category:{"/":{path:"/category/",map:{"build-tools":{path:"/category/build-tools/",indexes:[0]},"CI/CD":{path:"/category/cicd/",indexes:[1]},nginx:{path:"/category/nginx/",indexes:[2]},奇技淫巧:{path:"/category/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/",indexes:[3]},docker:{path:"/category/docker/",indexes:[3]},OI:{path:"/category/oi/",indexes:[4,5]},python:{path:"/category/python/",indexes:[6]},风格:{path:"/category/%E9%A3%8E%E6%A0%BC/",indexes:[7]},数学:{path:"/category/%E6%95%B0%E5%AD%A6/",indexes:[8]},设计模式:{path:"/category/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/",indexes:[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34]},编译原理:{path:"/category/%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86/",indexes:[35,36,37,38,39,40,41,42]}}}},tag:{"/":{path:"/tag/",map:{"CI/CD":{path:"/tag/cicd/",indexes:[1]},部署:{path:"/tag/%E9%83%A8%E7%BD%B2/",indexes:[2]},docker:{path:"/tag/docker/",indexes:[3]},MODInt:{path:"/tag/modint/",indexes:[4,5]},踩坑记录:{path:"/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/",indexes:[6]},风格:{path:"/tag/%E9%A3%8E%E6%A0%BC/",indexes:[7]},公理系统:{path:"/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/",indexes:[8]},mobile:{path:"/tag/mobile/",indexes:[43]},激活:{path:"/tag/%E6%BF%80%E6%B4%BB/",indexes:[44]},设计模式:{path:"/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/",indexes:[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34]},typescript:{path:"/tag/typescript/",indexes:[19,26,27,28,29,30,31,32,33,34]},生成实例:{path:"/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/",indexes:[19,26,27,33]},TypeScript:{path:"/tag/typescript/",indexes:[9,10,11,12,13,14,15,16,17,18,20,21,22,23,24,25]},分开考虑:{path:"/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/",indexes:[20,24]},推卸责任:{path:"/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/",indexes:[21]},用类实现:{path:"/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/",indexes:[9,11]},容器与内容的一致性:{path:"/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/",indexes:[22,23]},简单化:{path:"/tag/%E7%AE%80%E5%8D%95%E5%8C%96/",indexes:[16,17]},工厂方法:{path:"/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/",indexes:[30]},交给子类:{path:"/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/",indexes:[30,34]},避免浪费:{path:"/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/",indexes:[12,13]},管理状态:{path:"/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/",indexes:[14,15,18]},整体的替换算法:{path:"/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/",indexes:[24]},访问数据结构并处理数据:{path:"/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/",indexes:[25]},c:{path:"/tag/c/",indexes:[35,36,37,38,39,40,41,42]},编译器:{path:"/tag/%E7%BC%96%E8%AF%91%E5%99%A8/",indexes:[35,36,37,38,39,40,41,42]},解释器:{path:"/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/",indexes:[35,36,37,38,39,40,41,42]}}}}},p1=["/tech/android%20studio%E6%8D%A2%E6%BA%90.html","/tech/cicd.html","/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html","/tech/docker.html","/tech/modint.html","/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html","/tech/python_requrements.html","/tech/style.html","/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html","/tech/DesignPatterns/command.html","/tech/DesignPatterns/end.html","/tech/DesignPatterns/interpreter.html","/tech/DesignPatterns/proxy.html","/tech/DesignPatterns/flyweight.html","/tech/DesignPatterns/memento.html","/tech/DesignPatterns/state.html","/tech/DesignPatterns/facade.html","/tech/DesignPatterns/mediator.html","/tech/DesignPatterns/observer.html","/tech/DesignPatterns/abstractFactory.html","/tech/DesignPatterns/bridge.html","/tech/DesignPatterns/chainOfResponsibility.html","/tech/DesignPatterns/composite.html","/tech/DesignPatterns/decorator.html","/tech/DesignPatterns/strategy.html","/tech/DesignPatterns/visitor.html","/tech/DesignPatterns/builder.html","/tech/DesignPatterns/prototype.html","/tech/DesignPatterns/DesignPrinciples.html","/tech/DesignPatterns/adapter.html","/tech/DesignPatterns/factory_method.html","/tech/DesignPatterns/","/tech/DesignPatterns/iterator.html","/tech/DesignPatterns/singleton.html","/tech/DesignPatterns/template_method.html","/tech/designASimpileCCompiler/0.html","/tech/designASimpileCCompiler/3.html","/tech/designASimpileCCompiler/4.html","/tech/designASimpileCCompiler/5.html","/tech/designASimpileCCompiler/6.html","/tech/designASimpileCCompiler/7.html","/tech/designASimpileCCompiler/8.html","/tech/designASimpileCCompiler/9.html","/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html","/tutorials/typora%E6%BF%80%E6%B4%BB.html","/projects/carrobot.html","/resources/compile/","/tech/figure_bed.html","/tech/mailserver.html","/tech/tensorflow%E8%B8%A9%E5%9D%91.html","/essays/%E5%91%BD%E9%87%8C%E6%9C%89%E6%97%B6%E7%BB%88%E9%A1%BB%E6%9C%89.html","/essays/","/projects/","/resources/","/tech/","/tutorials/","/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html","/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html","/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html","/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html","/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html","/tech/%E5%8D%8F%E7%A8%8B.html","/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html","/resources/html2md/","/tech/designASimpileCCompiler/1.html","/tech/designASimpileCCompiler/2.html"],Ho=xe(d8);on(Ho);const h1=e=>{const t=ge(),n=he(),r=Ye();return w(()=>{var i;const a=e??((i=n.value.blog)==null?void 0:i.key)??"";if(!a)return console.warn("useBlogCategory: key not found"),{path:"/",map:{}};if(!Ho.value[a])throw new Error(`useBlogCategory: key ${a} is invalid`);const o=Ho.value[a][r.value],l={path:o.path,map:{}};for(const c in o.map){const u=o.map[c];l.map[c]={path:u.path,items:[]};for(const d of u.indexes){const{path:f,meta:p}=xt(p1[d]);l.map[c].items.push({path:f,info:p})}t.value.path===u.path&&(l.currentItems=l.map[c].items)}return l})},f8={article:{"/":{path:"/article/",indexes:[45,46,47,48,49,50,6,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,44,28,29,30,31,32,33,34,51,52,53,54,55,2,3,56,57,7,0,1,4,5,8,58,59,43,60,61,62,63,35,64,65,36,37,38,39,40,41,42]}},star:{"/":{path:"/star/",indexes:[2]}},timeline:{"/":{path:"/timeline/",indexes:[45,46,47,48,49,50,6,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,44,28,29,30,31,32,33,34,51,52,53,54,55,2,3,56,57,7,0,1,4,5,8]}}},No=xe(f8);on(No);const $a=e=>{const t=he(),n=Ye();return w(()=>{var l;const r=e??((l=t.value.blog)==null?void 0:l.key)??"";if(!r)return console.warn("useBlogType: key not found"),{path:"/",items:[]};if(!No.value[r])throw new Error(`useBlogType: key ${e} is invalid`);const a=No.value[r][n.value],o={path:a.path,items:[]};for(const i of a.indexes){const{path:c,meta:u}=xt(p1[i]);o.items.push({path:c,info:u})}return o})},m1=Symbol(""),Rl=()=>{const e=ve(m1);if(!e)throw new Error("useTimeline() is called without provider.");return e},p8=()=>{const e=$a("timeline"),t=w(()=>{const n=[];return e.value.items.forEach(({info:r,path:a})=>{const o=_l(r[je.date]);if(o){const l=o.getFullYear(),i=o.getMonth()+1,c=o.getDate();(!n[0]||n[0].year!==l)&&n.unshift({year:l,items:[]}),n[0].items.push({date:`${i}/${c}`,info:r,path:a})}}),{...e.value,config:n.reverse()}});ht(m1,t)},v1=Symbol(""),Kn=()=>{const e=ve(v1);if(!e)throw new Error("useArticles() is called without provider.");return e},h8=()=>{const e=$a("article");ht(v1,e)},g1=Symbol.for("categoryMap"),Hr=()=>{const e=ve(g1);if(!e)throw new Error("useCategoryMap() is called without provider.");return e},m8=()=>{const e=h1("category");ht(g1,e)},y1=Symbol(""),$l=()=>{const e=ve(y1);if(!e)throw new Error("useStars() is called without provider.");return e},v8=()=>{const e=$a("star");ht(y1,e)},b1=Symbol.for("tagMap"),Nr=()=>{const e=ve(b1);if(!e)throw new Error("useTagMap() is called without provider.");return e},g8=()=>{const e=h1("tag");ht(b1,e)},y8=()=>{h8(),m8(),v8(),g8(),p8()},Vr=()=>{const e=Nt(),t=ce();return w(()=>({...e.value.blog,...t.value.blog}))},b8=e=>{const t=ce();return w(()=>{const{[je.author]:n}=e.value;return n?Cr(n):n===!1?[]:Cr(t.value.author,!1)})},E8=e=>{const t=Hr();return w(()=>Pu(e.value[je.category]).map(n=>({name:n,path:t.value.map[n].path})))},_8=e=>{const t=Nr();return w(()=>Du(e.value[je.tag]).map(n=>({name:n,path:t.value.map[n].path})))},w8=e=>w(()=>{const{[je.date]:t}=e.value;return _l(t)}),A8=e=>{const t=zn(e,"info"),n=Vr(),r=b8(t),a=E8(t),o=_8(t),l=w8(t),i=Wu(),c=w(()=>({author:r.value,category:a.value,date:l.value,localizedDate:t.value[je.localizedDate]??"",tag:o.value,isOriginal:t.value[je.isOriginal]??!1,readingTime:t.value[je.readingTime]??null,readingTimeLocale:t.value[je.readingTime]&&i.value?Uu(t.value[je.readingTime],i.value):null,pageview:e.path})),u=w(()=>n.value.articleInfo);return{info:c,items:u}},C8=()=>{const e=ce();return w(()=>e.value.author)},k8=M({__name:"HomePage",setup(e){return Kn(),(t,n)=>{const r=pt("CommentService");return cl(),ul(bt(u8),null,{bottom:pa(()=>[R0(" TODO: it's not work "),Te(r)]),_:1})}}}),Fl=(e,t)=>{const n=e.__vccOpts||e;for(const[r,a]of t)n[r]=a;return n},T8=Fl(k8,[["__file","HomePage.vue"]]),S8=M({name:"BreadCrumb",setup(){const e=ge(),t=Ye(),n=he(),r=ce(),a=xe([]),o=w(()=>(n.value.breadcrumb??r.value.breadcrumb??!0)&&a.value.length>1),l=w(()=>n.value.breadcrumbIcon??r.value.breadcrumbIcon??!0),i=()=>{const c=q6(e.value.path,t.value).map(({link:u,name:d})=>{const{path:f,meta:p,notFound:h}=xt(u);return h||p[Ue.breadcrumbExclude]?null:{title:p[Ue.shortTitle]||p[Ue.title]||d,icon:p[Ue.icon],path:f}}).filter(u=>u!==null);c.length>1&&(a.value=c)};return se(()=>{ae(()=>e.value.path,i,{immediate:!0})}),()=>s("nav",{class:["vp-breadcrumb",{disable:!o.value}]},o.value?s("ol",{vocab:"https://schema.org/",typeof:"BreadcrumbList"},a.value.map((c,u)=>s("li",{class:{"is-active":a.value.length-1===u},property:"itemListElement",typeof:"ListItem"},[s(Ie,{to:c.path,property:"item",typeof:"WebPage"},()=>[l.value?s(Ve,{icon:c.icon}):null,s("span",{property:"name"},c.title||"Unknown")]),s("meta",{property:"position",content:u+1})]))):[])}}),hi=(e,t)=>e===!1||qn(e)?e:we(e)?Il(e,!0,t):null,Vo=(e,t,n)=>{const r=e.findIndex(a=>a.link===t);if(r!==-1){const a=e[r+n];return a!=null&&a.link?a:null}for(const a of e)if("children"in a){const o=Vo(a.children,t,n);if(o)return o}return null},x8=M({name:"PageNav",setup(){const e=ce(),t=he(),n=Pl(),r=ge(),a=An(),o=Ht(),l=w(()=>{const c=hi(t.value.prev,o.path);return c===!1?null:c||(e.value.prevLink===!1?null:Vo(n.value,r.value.path,-1))}),i=w(()=>{const c=hi(t.value.next,o.path);return c===!1?null:c||(e.value.nextLink===!1?null:Vo(n.value,r.value.path,1))});return Se("keydown",c=>{c.altKey&&(c.key==="ArrowRight"?i.value&&(a(i.value.link),c.preventDefault()):c.key==="ArrowLeft"&&l.value&&(a(l.value.link),c.preventDefault()))}),()=>l.value||i.value?s("nav",{class:"vp-page-nav"},[l.value?s(Je,{class:"prev",config:l.value},()=>{var c,u;return[s("div",{class:"hint"},[s("span",{class:"arrow start"}),e.value.metaLocales.prev]),s("div",{class:"link"},[s(Ve,{icon:(c=l.value)==null?void 0:c.icon}),(u=l.value)==null?void 0:u.text])]}):null,i.value?s(Je,{class:"next",config:i.value},()=>{var c,u;return[s("div",{class:"hint"},[e.value.metaLocales.next,s("span",{class:"arrow end"})]),s("div",{class:"link"},[(c=i.value)==null?void 0:c.text,s(Ve,{icon:(u=i.value)==null?void 0:u.icon})])]}):null]):null}}),E1=()=>s(ie,{name:"author"},()=>s("path",{d:"M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"}));E1.displayName="AuthorIcon";const _1=()=>s(ie,{name:"calendar"},()=>s("path",{d:"M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"}));_1.displayName="CalendarIcon";const w1=()=>s(ie,{name:"category"},()=>s("path",{d:"M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"}));w1.displayName="CategoryIcon";const A1=()=>s(ie,{name:"print"},()=>s("path",{d:"M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"}));A1.displayName="PrintIcon";const C1=()=>s(ie,{name:"tag"},()=>s("path",{d:"M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"}));C1.displayName="TagIcon";const k1=()=>s(ie,{name:"timer"},()=>s("path",{d:"M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"}));k1.displayName="TimerIcon";const T1=()=>s(ie,{name:"word"},()=>[s("path",{d:"M518.217 432.64V73.143A73.143 73.143 0 01603.43 1.097a512 512 0 01419.474 419.474 73.143 73.143 0 01-72.046 85.212H591.36a73.143 73.143 0 01-73.143-73.143z"}),s("path",{d:"M493.714 566.857h340.297a73.143 73.143 0 0173.143 85.577A457.143 457.143 0 11371.566 117.76a73.143 73.143 0 0185.577 73.143v339.383a36.571 36.571 0 0036.571 36.571z"})]);T1.displayName="WordIcon";const L8=()=>{const e=ce(),t=ge(),n=he();return w(()=>{var a;return n.value.contributors??e.value.contributors??!0?((a=t.value.git)==null?void 0:a.contributors)??null:null})},B8={GitHub:":repo/edit/:branch/:path",GitLab:":repo/-/edit/:branch/:path",Gitee:":repo/edit/:branch/:path",Bitbucket:":repo/src/:branch/:path?mode=edit&spa=0&at=:branch&fileviewer=file-view-default"},I8=({docsRepo:e,docsBranch:t,docsDir:n,filePathRelative:r,editLinkPattern:a})=>{if(!r)return null;const o=Cl(e);let l;return a?l=a:o!==null&&(l=B8[o]),l?l.replace(/:repo/u,sn(e)?e:`https://github.com/${e}`).replace(/:branch/u,t).replace(/:path/u,Dc(`${pl(n)}/${r}`)):null},P8=()=>{const e=ce(),t=ge(),n=he();return w(()=>{const{repo:r,docsRepo:a=r,docsBranch:o="main",docsDir:l="",editLink:i,editLinkPattern:c=""}=e.value;if(!(n.value.editLink??i??!0)||!a)return null;const d=I8({docsRepo:a,docsBranch:o,docsDir:l,editLinkPattern:c,filePathRelative:t.value.filePathRelative});return d?{text:e.value.metaLocales.editLink,link:d}:null})},un=()=>{const e=ce();return w(()=>e.value.metaLocales)},D8=()=>{const e=Gn(),t=ce(),n=ge(),r=he();return w(()=>{var l,i;return!(r.value.lastUpdated??t.value.lastUpdated??!0)||!((l=n.value.git)!=null&&l.updatedTime)?null:new Date((i=n.value.git)==null?void 0:i.updatedTime).toLocaleString(e.value.lang)})},O8=M({name:"AuthorInfo",inheritAttrs:!1,props:{author:{type:Array,required:!0},pure:Boolean},setup(e){const t=un();return()=>e.author.length?s("span",{class:"page-author-info","aria-label":`${t.value.author}${e.pure?"":"🖊"}`,...e.pure?{}:{"data-balloon-pos":"up"}},[s(E1),s("span",e.author.map(n=>n.url?s("a",{class:"page-author-item",href:n.url,target:"_blank",rel:"noopener noreferrer"},n.name):s("span",{class:"page-author-item"},n.name))),s("span",{property:"author",content:e.author.map(n=>n.name).join(", ")})]):null}}),M8=M({name:"CategoryInfo",inheritAttrs:!1,props:{category:{type:Array,required:!0},pure:Boolean},setup(e){const t=un(),n=An();return()=>e.category.length?s("span",{class:"page-category-info","aria-label":`${t.value.category}${e.pure?"":"🌈"}`,...e.pure?{}:{"data-balloon-pos":"up"}},[s(w1),e.category.map(({name:r,path:a})=>s("span",{class:["page-category-item",{[`category${Ra(r,9)}`]:!e.pure,clickable:a}],role:a?"navigation":"",onClick:()=>{a&&n(a)}},r)),s("meta",{property:"articleSection",content:e.category.map(({name:r})=>r).join(",")})]):null}}),R8=M({name:"DateInfo",inheritAttrs:!1,props:{date:{type:Object,default:null},localizedDate:{type:String,default:""},pure:Boolean},setup(e){const t=Pa(),n=un();return()=>e.date?s("span",{class:"page-date-info","aria-label":`${n.value.date}${e.pure?"":"📅"}`,...e.pure?{}:{"data-balloon-pos":"up"}},[s(_1),s("span",s(Or,()=>e.localizedDate||e.date.toLocaleDateString(t.value))),s("meta",{property:"datePublished",content:e.date.toISOString()||""})]):null}}),$8=M({name:"OriginalInfo",inheritAttrs:!1,props:{isOriginal:Boolean},setup(e){const t=un();return()=>e.isOriginal?s("span",{class:"page-original-info"},t.value.origin):null}}),F8=M({name:"ReadingTimeInfo",inheritAttrs:!1,props:{readingTime:{type:Object,default:()=>null},readingTimeLocale:{type:Object,default:()=>null},pure:Boolean},setup(e){const t=un(),n=w(()=>{if(!e.readingTime)return null;const{minutes:r}=e.readingTime;return r<1?"PT1M":`PT${Math.round(r)}M`});return()=>{var r,a;return(r=e.readingTimeLocale)!=null&&r.time?s("span",{class:"page-reading-time-info","aria-label":`${t.value.readingTime}${e.pure?"":"⌛"}`,...e.pure?{}:{"data-balloon-pos":"up"}},[s(k1),s("span",(a=e.readingTimeLocale)==null?void 0:a.time),s("meta",{property:"timeRequired",content:n.value})]):null}}}),H8=M({name:"TagInfo",inheritAttrs:!1,props:{tag:{type:Array,default:()=>[]},pure:Boolean},setup(e){const t=un(),n=An();return()=>e.tag.length?s("span",{class:"page-tag-info","aria-label":`${t.value.tag}${e.pure?"":"🏷"}`,...e.pure?{}:{"data-balloon-pos":"up"}},[s(C1),e.tag.map(({name:r,path:a})=>s("span",{class:["page-tag-item",{[`tag${Ra(r,9)}`]:!e.pure,clickable:a}],role:a?"navigation":"",onClick:()=>{a&&n(a)}},r)),s("meta",{property:"keywords",content:e.tag.map(({name:r})=>r).join(",")})]):null}}),N8=M({name:"ReadTimeInfo",inheritAttrs:!1,props:{readingTime:{type:Object,default:()=>null},readingTimeLocale:{type:Object,default:()=>null},pure:Boolean},setup(e){const t=un();return()=>{var n,r,a;return(n=e.readingTimeLocale)!=null&&n.words?s("span",{class:"page-word-info","aria-label":`${t.value.words}${e.pure?"":"🔠"}`,...e.pure?{}:{"data-balloon-pos":"up"}},[s(T1),s("span",(r=e.readingTimeLocale)==null?void 0:r.words),s("meta",{property:"wordCount",content:(a=e.readingTime)==null?void 0:a.words})]):null}}}),S1=M({name:"PageInfo",components:{AuthorInfo:O8,CategoryInfo:M8,DateInfo:R8,OriginalInfo:$8,PageViewInfo:ia,ReadingTimeInfo:F8,TagInfo:H8,WordInfo:N8},props:{items:{type:[Array,Boolean],default:()=>["Author","Original","Date","PageView","ReadingTime","Category","Tag"]},info:{type:Object,required:!0}},setup(e){const t=Cn();return()=>e.items?s("div",{class:"page-info"},e.items.map(n=>s(pt(`${n}Info`),{...e.info,pure:t.value}))):null}}),V8=M({name:"PageTitle",setup(){const e=ge(),t=he(),n=ce(),{info:r,items:a}=R6();return()=>s("div",{class:"vp-page-title"},[s("h1",[n.value.titleIcon===!1?null:s(Ve,{icon:t.value.icon}),e.value.title]),s(S1,{info:r.value,...a.value===null?{}:{items:a.value}}),s("hr")])}}),x1=()=>s(ie,{name:"edit"},()=>[s("path",{d:"M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"}),s("path",{d:"M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"})]);x1.displayName="EditIcon";const j8=M({name:"PageMeta",setup(){const e=ce(),t=P8(),n=D8(),r=L8();return()=>{var o;const{metaLocales:a}=e.value;return s("footer",{class:"vp-page-meta"},[t.value?s("div",{class:"vp-meta-item edit-link"},s(Je,{class:"vp-meta-label",config:t.value},{before:()=>s(x1)})):null,s("div",{class:"vp-meta-item git-info"},[n.value?s("div",{class:"update-time"},[s("span",{class:"vp-meta-label"},`${a.lastUpdated}: `),s(Or,()=>s("span",{class:"vp-meta-info"},n.value))]):null,(o=r.value)!=null&&o.length?s("div",{class:"contributors"},[s("span",{class:"vp-meta-label"},`${a.contributors}: `),r.value.map(({email:l,name:i},c)=>[s("span",{class:"vp-meta-info",title:`email: ${l}`},i),c!==r.value.length-1?",":""])]):null])])}}}),z8=M({name:"PrintButton",setup(){const e=Nt(),t=ce();return()=>e.value.print===!1?null:s("button",{type:"button",class:"print-button",title:t.value.metaLocales.print,onClick:()=>{window.print()}},s(A1))}}),L1=M({name:"TOC",props:{items:{type:Array,default:()=>[]},headerDepth:{type:Number,default:2}},slots:Object,setup(e,{slots:t}){const n=Ht(),r=ge(),a=un(),[o,l]=wr(),i=xe(),c=z("-1.7rem"),u=f=>{var p;(p=i.value)==null||p.scrollTo({top:f,behavior:"smooth"})},d=()=>{if(i.value){const f=document.querySelector(".vp-toc-item.active");f?c.value=`${f.getBoundingClientRect().top-i.value.getBoundingClientRect().top+i.value.scrollTop}px`:c.value="-1.7rem"}else c.value="-1.7rem"};return se(()=>{ae(()=>n.hash,f=>{if(i.value){const p=document.querySelector(`#toc a.toc-link[href$="${f}"]`);if(!p)return;const{top:h,height:v}=i.value.getBoundingClientRect(),{top:_,height:E}=p.getBoundingClientRect();_<h?u(i.value.scrollTop+_-h):_+E>h+v&&u(i.value.scrollTop+_+E-h-v)}}),ae(()=>n.fullPath,d,{flush:"post",immediate:!0})}),()=>{var v,_;const f=({title:E,level:b,slug:C})=>s(Ie,{to:`#${C}`,class:["vp-toc-link",`level${b}`],onClick:()=>{l()}},()=>E),p=(E,b)=>E.length&&b>0?s("ul",{class:"vp-toc-list"},E.map(C=>{const y=p(C.children,b-1);return[s("li",{class:["vp-toc-item",{active:n.hash===`#${C.slug}`}]},f(C)),y?s("li",y):null]})):null,h=e.items.length?p(e.items,e.headerDepth):r.value.headers?p(r.value.headers,e.headerDepth):null;return h?s("div",{class:"vp-toc-placeholder"},[s("aside",{id:"toc"},[(v=t.before)==null?void 0:v.call(t),s("div",{class:"vp-toc-header",onClick:()=>{l()}},[a.value.toc,s(z8),s("div",{class:["arrow",o.value?"down":"end"]})]),s("div",{class:["vp-toc-wrapper",o.value?"open":""],ref:i},[h,s("div",{class:"vp-toc-marker",style:{top:c.value}})]),(_=t.after)==null?void 0:_.call(t)])]):null}}}),q8=M({name:"NormalPage",slots:Object,setup(e,{slots:t}){const n=he(),{isDarkmode:r}=Fr(),a=ce(),o=w(()=>n.value.toc??a.value.toc??!0);return()=>s("main",{id:"main-content",class:"vp-page"},s(Mn("LocalEncrypt")?pt("LocalEncrypt"):Au,()=>{var l,i,c,u;return[(l=t.top)==null?void 0:l.call(t),n.value.cover?s("div",{class:"page-cover"},s("img",{src:be(n.value.cover),alt:"","no-view":""})):null,s(S8),s(V8),o.value?s(L1,{headerDepth:n.value.headerDepth??a.value.headerDepth??2},{before:()=>{var d;return(d=t.tocBefore)==null?void 0:d.call(t)},after:()=>{var d;return(d=t.tocAfter)==null?void 0:d.call(t)}}):null,(i=t.contentBefore)==null?void 0:i.call(t),s(Wn),(c=t.contentAfter)==null?void 0:c.call(t),s(j8),s(x8),Mn("CommentService")?s(pt("CommentService"),{darkmode:r.value}):null,(u=t.bottom)==null?void 0:u.call(t)]}))}}),Hl=M({name:"SkipLink",props:{content:{type:String,default:"main-content"}},setup(e){const t=ge(),n=ce(),r=xe(),a=({target:o})=>{const l=document.querySelector(o.hash);if(l){const i=()=>{l.removeAttribute("tabindex"),l.removeEventListener("blur",i)};l.setAttribute("tabindex","-1"),l.addEventListener("blur",i),l.focus(),window.scrollTo(0,0)}};return se(()=>{ae(()=>t.value.path,()=>r.value.focus())}),()=>[s("span",{ref:r,tabindex:"-1"}),s("a",{href:`#${e.content}`,class:"vp-skip-link sr-only",onClick:a},n.value.routeLocales.skipToContent)]}}),G8=M({name:"Layout",slots:Object,setup(e,{slots:t}){const n=Nt(),r=ce(),a=ge(),o=he(),{isMobile:l}=$r(),i=w(()=>{var c,u;return((c=r.value.blog)==null?void 0:c.sidebarDisplay)??((u=n.value.blog)==null?void 0:u.sidebarDisplay)??"mobile"});return()=>[s(Hl),s(Ol,{},{default:()=>{var c;return((c=t.default)==null?void 0:c.call(t))??(o.value.home?s(T8):s(Ml,()=>s(q8,{key:a.value.path},{top:()=>{var u;return(u=t.top)==null?void 0:u.call(t)},bottom:()=>{var u;return(u=t.bottom)==null?void 0:u.call(t)},contentBefore:()=>{var u;return(u=t.contentBefore)==null?void 0:u.call(t)},contentAfter:()=>{var u;return(u=t.contentAfter)==null?void 0:u.call(t)},tocBefore:()=>{var u;return(u=t.tocBefore)==null?void 0:u.call(t)},tocAfter:()=>{var u;return(u=t.tocAfter)==null?void 0:u.call(t)}})))},...i.value==="none"?{}:{navScreenBottom:()=>s(pt("BloggerInfo"))},...!l.value&&i.value==="always"?{sidebar:()=>s(pt("BloggerInfo"))}:{}})]}}),U8=M({name:"NotFoundHint",setup(){const e=ce(),t=()=>{const n=e.value.routeLocales.notFoundMsg;return n[Math.floor(Math.random()*n.length)]};return()=>s("div",{class:"not-found-hint"},[s("p",{class:"error-code"},"404"),s("h1",{class:"error-title"},e.value.routeLocales.notFoundTitle),s("p",{class:"error-hint"},t())])}}),W8=M({name:"NotFound",slots:Object,setup(e,{slots:t}){const n=wn(),r=Ye(),a=ce();return()=>[s(Hl),s(Ol,{noSidebar:!0},()=>{var o;return s("main",{id:"main-content",class:"vp-page not-found"},((o=t.default)==null?void 0:o.call(t))??[s(U8),s("div",{class:"actions"},[s("button",{type:"button",class:"action-button",onClick:()=>{window.history.go(-1)}},a.value.routeLocales.back),s("button",{type:"button",class:"action-button",onClick:()=>{n.push(a.value.home??r.value)}},a.value.routeLocales.home)])])})]}}),K8={Email:'<svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg>',GitHub:'<svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg>',QQ:'<svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg>'},B1=M({name:"SocialMedia",setup(){const e=Vr(),t=Cn(),n=w(()=>Ma(e.value.medias??{}).map(([r,a])=>({name:r,icon:K8[r],url:a})));return()=>n.value.length?s("div",{class:"vp-social-medias"},n.value.map(({name:r,icon:a,url:o})=>s("a",{class:"vp-social-media",href:o,rel:"noopener noreferrer",target:"_blank","aria-label":r||"",...t.value?{}:{"data-balloon-pos":"up"},innerHTML:a}))):null}}),Nl=M({name:"BloggerInfo",setup(){const e=Vr(),t=Gn(),n=ce(),r=Kn(),a=Hr(),o=Nr(),l=Rl(),i=An(),c=w(()=>{var p;return e.value.name??((p=Cr(n.value.author)[0])==null?void 0:p.name)??t.value.title}),u=w(()=>e.value.avatar??n.value.logo),d=w(()=>n.value.blogLocales),f=w(()=>e.value.intro);return()=>{const{article:p,category:h,tag:v,timeline:_}=d.value,E=[[r.value.path,r.value.items.length,p],[a.value.path,En(a.value.map).length,h],[o.value.path,En(o.value.map).length,v],[l.value.path,l.value.items.length,_]];return s("div",{class:"vp-blogger-info",vocab:"https://schema.org/",typeof:"Person"},[s("div",{class:"vp-blogger",...f.value?{style:{cursor:"pointer"},"aria-label":d.value.intro,"data-balloon-pos":"down",role:"link",onClick:()=>i(f.value)}:{}},[u.value?s("img",{class:"vp-blogger-avatar",src:be(u.value),property:"image",alt:"Blogger Avatar",loading:"lazy"}):null,c.value?s("div",{class:"vp-blogger-name",property:"name"},c.value):null,e.value.description?s("div",{class:"vp-blogger-description",innerHTML:e.value.description}):null,f.value?s("meta",{property:"url",content:be(f.value)}):null]),s("div",{class:"vp-blog-counts"},E.map(([b,C,y])=>s(Ie,{class:"vp-blog-count",to:b},()=>[s("div",{class:"count"},C),s("div",y)]))),s(B1)])}}}),Vl=()=>s(ie,{name:"category"},()=>s("path",{d:"M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"}));Vl.displayName="CategoryIcon";const jl=()=>s(ie,{name:"tag"},()=>s("path",{d:"M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"}));jl.displayName="TagIcon";const zl=()=>s(ie,{name:"timeline"},()=>s("path",{d:"M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"}));zl.displayName="TimelineIcon";const I1=()=>s(ie,{name:"slides"},()=>s("path",{d:"M896 170.667v426.666a85.333 85.333 0 0 1-85.333 85.334h-256v61.184l192.597 115.584-43.861 73.13-148.736-89.173v95.275h-85.334v-95.318l-148.736 89.216-43.861-73.13 192.597-115.627v-61.141h-256A85.333 85.333 0 0 1 128 597.333V170.667H85.333V85.333h853.334v85.334H896zm-682.667 0v426.666h597.334V170.667H213.333zM426.667 512h-85.334V341.333h85.334V512zm128 0h-85.334V256h85.334v256zm128 0h-85.334V384h85.334v128z"}));I1.displayName="SlideIcon";const P1=()=>s(ie,{name:"sticky"},()=>[s("path",{d:"m381.3 733.8l-161.9 118c-5.9 4.5-13.2 6.6-20.1 6.6-8.7 0-17.7-3.4-24.3-10-12.2-12.2-13.9-31.3-3.5-45.2l144.5-195.5-113.6-112.9c-11.1-11.1-13.2-28.4-5.5-42 5.5-8.7 52.1-76.4 155.5-51 1.8 0.3 3.5 0.3 5.6 0.7 4.2 0.3 9 0.7 14.2 1.7 21.9 3.5 60.8-13.9 94.5-42.7 32.3-27.5 53.1-59.4 53.1-81.6 0-5.2 0-10.8-0.3-16-0.7-20.8-2.1-52.8 21.5-76.4 28.1-28.1 72.9-30.6 103.9-5.2 0.6 0.3 1 1 1.7 1.7 16.7 16.3 187.5 187.2 189.3 188.9 14.5 14.6 22.9 34.4 22.9 55.3 0 20.8-8 40.2-22.9 54.8-23.7 23.6-56 22.6-77.1 21.6-4.9 0-10.5-0.4-15.7-0.4-20.8 0-45.8 14.6-70.5 41.3-34.3 37.5-55.5 85.8-53.8 107.7 0.7 6.9 2.1 19.1 2.4 20.8 25 101.4-42.7 147.6-50.7 152.8-13.9 8.4-31.6 6.3-42.7-4.8l-112.1-112.2z"})]);P1.displayName="StickyIcon";const Fa=()=>s(ie,{name:"article"},()=>s("path",{d:"M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"}));Fa.displayName="ArticleIcon";const D1=()=>s(ie,{name:"book"},()=>s("path",{d:"M256 853.333h426.667A85.333 85.333 0 0 0 768 768V256a85.333 85.333 0 0 0-85.333-85.333H469.333a42.667 42.667 0 0 1 0-85.334h213.334A170.667 170.667 0 0 1 853.333 256v512a170.667 170.667 0 0 1-170.666 170.667H213.333A42.667 42.667 0 0 1 170.667 896V128a42.667 42.667 0 0 1 42.666-42.667h128A42.667 42.667 0 0 1 384 128v304.256l61.653-41.088a42.667 42.667 0 0 1 47.36 0l61.654 41.045V256A42.667 42.667 0 0 1 640 256v256a42.667 42.667 0 0 1-66.347 35.499l-104.32-69.547-104.32 69.547A42.667 42.667 0 0 1 298.667 512V170.667H256v682.666z"}));D1.displayName="BookIcon";const O1=()=>s(ie,{name:"link"},()=>s("path",{d:"M460.8 584.533c17.067 17.067 17.067 42.667 0 59.734-17.067 17.066-42.667 17.066-59.733 0-85.334-85.334-85.334-217.6 0-302.934L554.667 192C640 110.933 776.533 110.933 857.6 196.267c81.067 81.066 81.067 213.333 0 294.4l-68.267 64c0-34.134-4.266-68.267-17.066-102.4l21.333-21.334c51.2-46.933 55.467-128 4.267-179.2s-128-55.466-179.2-4.266c-4.267 0-4.267 4.266-4.267 4.266L465.067 401.067c-51.2 51.2-51.2 132.266-4.267 183.466m123.733-183.466C601.6 384 627.2 384 644.267 401.067c85.333 85.333 85.333 217.6 0 302.933l-153.6 149.333C405.333 934.4 268.8 934.4 187.733 849.067c-81.066-81.067-81.066-213.334 0-294.4l68.267-64c0 34.133 4.267 72.533 17.067 102.4L251.733 614.4C204.8 665.6 204.8 746.667 256 793.6c51.2 46.933 123.733 46.933 174.933 0l149.334-149.333c51.2-51.2 51.2-128 0-179.2-12.8-17.067-17.067-46.934 4.266-64z"}));O1.displayName="LinkIcon";const M1=()=>s(ie,{name:"project"},()=>s("path",{d:"M987.456 425.152H864V295.296a36.48 36.48 0 0 0-36.544-36.544h-360l-134.08-128.256A9.344 9.344 0 0 0 327.04 128H36.48A36.48 36.48 0 0 0 0 164.544v676.608a36.48 36.48 0 0 0 36.544 36.544h797.76a36.672 36.672 0 0 0 33.92-22.848L1021.44 475.52a36.48 36.48 0 0 0-33.92-50.304zM82.304 210.304h215.424l136.64 130.752h347.328v84.096H198.848A36.672 36.672 0 0 0 164.928 448L82.304 652.8V210.304zM808.32 795.456H108.544l118.08-292.608h699.904L808.32 795.52z"}));M1.displayName="ProjectIcon";const R1=()=>s(ie,{name:"friend"},()=>s("path",{d:"M860.16 213.333A268.373 268.373 0 0 0 512 186.027a267.52 267.52 0 0 0-348.16 404.48L428.8 855.893a118.613 118.613 0 0 0 166.4 0l264.96-265.386a267.52 267.52 0 0 0 0-377.174zM800 531.627l-264.96 264.96a32.427 32.427 0 0 1-46.08 0L224 530.347a183.04 183.04 0 0 1 0-256 182.187 182.187 0 0 1 256 0 42.667 42.667 0 0 0 60.587 0 182.187 182.187 0 0 1 256 0 183.04 183.04 0 0 1 3.413 256z"}));R1.displayName="FriendIcon";const jo=()=>s(ie,{name:"slide-down"},()=>s("path",{d:"M108.775 312.23c13.553 0 27.106 3.734 39.153 11.806l375.205 250.338 363.641-252.808c32.587-21.624 76.499-12.83 98.123 19.757 21.685 32.467 12.95 76.56-19.576 98.184l-402.854 278.89c-23.733 15.901-54.694 15.962-78.547.12L69.501 442.097c-32.647-21.685-41.441-65.777-19.817-98.304 13.734-20.54 36.201-31.563 59.09-31.563Z"}));jo.displayName="SlideDownIcon";const $1=()=>s("svg",{xmlns:"http://www.w3.org/2000/svg","xmlns:xlink":"http://www.w3.org/1999/xlink",class:"empty-icon",viewBox:"0 0 1024 1024",innerHTML:'<defs><linearGradient id="f" x1="512.342" y1="2266.13" x2="512.342" y2="666.063" gradientUnits="userSpaceOnUse"><stop offset=".919" stop-color="#e6e6e6" stop-opacity="0"/><stop offset="1" stop-color="#e6e6e6"/></linearGradient><linearGradient id="g" x1="528.912" y1="774" x2="388.088" y2="612" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#ccc"/><stop offset="1" stop-color="#e6e6e6" stop-opacity="0"/></linearGradient><linearGradient id="h" x1="213.219" y1="721.704" x2="251.313" y2="683.61" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#d7d7d7"/><stop offset=".485" stop-color="#fafafa"/><stop offset="1" stop-color="#fafafa"/></linearGradient><linearGradient id="i" x1="724.813" y1="821.718" x2="768.656" y2="777.876" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#ccc"/><stop offset="1" stop-color="#fafafa"/></linearGradient><linearGradient id="a" x1="513.493" y1="714.594" x2="471.007" y2="544.188" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#999"/><stop offset="1" stop-color="#ccc"/></linearGradient><linearGradient id="b" x1="440.156" y1="564.031" x2="508.594" y2="495.594" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#ccc"/><stop offset="1" stop-color="#f0f0f0"/></linearGradient><linearGradient id="l" x1="660.988" y1="754.156" x2="608.637" y2="544.188" xlink:href="#a"/><linearGradient id="m" x1="479.188" y1="774.219" x2="649.782" y2="603.625" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#b3b3b3"/><stop offset="1" stop-color="#e6e6e6"/></linearGradient><linearGradient id="n" x1="447.121" y1="774.219" x2="394.661" y2="563.813" xlink:href="#a"/><linearGradient id="o" x1="494" y1="597" x2="628" y2="463" xlink:href="#b"/><linearGradient id="d" x1="610.485" y1="604.938" x2="697.298" y2="518.125" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#ccc"/><stop offset="1" stop-color="#fff"/></linearGradient><linearGradient id="p" x1="457.438" y1="619.25" x2="353.469" y2="619.25" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#e6e6e6" stop-opacity="0"/><stop offset="1" stop-color="#e6e6e6"/></linearGradient><linearGradient id="q" x1="542.734" y1="674.25" x2="615.672" y2="601.313" xlink:href="#b"/><linearGradient id="c" x1="627.933" y1="358.938" x2="685.192" y2="422.531" gradientUnits="userSpaceOnUse"><stop offset=".4" stop-color="#e6e6e6" stop-opacity=".4"/><stop offset=".443" stop-color="#fff"/><stop offset=".6" stop-color="#ccc"/></linearGradient><linearGradient id="r" x1="618.547" y1="422.531" x2="681.547" y2="359.531" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#e6e6e6"/><stop offset=".761" stop-color="#fff"/><stop offset="1" stop-color="#f0f0f0"/></linearGradient><linearGradient id="s" x1="625" y1="441.5" x2="697" y2="369.5" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#ccc"/><stop offset=".761" stop-color="#fff"/><stop offset="1" stop-color="#f0f0f0"/></linearGradient><linearGradient id="t" x1="627.681" y1="361.438" x2="692.257" y2="433.156" xlink:href="#c"/><linearGradient id="u" x1="561.414" y1="735.438" x2="573.149" y2="688.375" xlink:href="#d"/><linearGradient id="v" x1="405" y1="485.875" x2="440" y2="450.875" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#ccc"/><stop offset="1" stop-color="#fff" stop-opacity=".702"/></linearGradient><linearGradient id="w" x1="404.61" y1="486.906" x2="441.86" y2="449.656" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#ccc"/><stop offset=".495" stop-color="#ccc" stop-opacity=".702"/><stop offset=".498" stop-color="#ccc"/><stop offset="1" stop-color="#fff" stop-opacity=".302"/></linearGradient><radialGradient id="e" cx="329.297" cy="647.578" r="8.172" gradientUnits="userSpaceOnUse"><stop offset="0" stop-color="#fafafa"/><stop offset="1.2" stop-color="#e6e6e6"/></radialGradient><radialGradient id="j" cx="802.297" cy="673.578" r="8.172" xlink:href="#e"/><radialGradient id="k" cx="774.844" cy="642.75" r="5.531" xlink:href="#e"/></defs><path d="M512.33 666.07c441.828 0 800 358.18 800 800.03s-358.172 800.02-800 800.02-800-358.18-800-800.02 358.17-800.03 800-800.03z" style="fill:url(#f);fill-rule:evenodd"/><path d="m272 694 242-82 131 119-188 43z" style="fill:url(#g);fill-rule:evenodd"/><path fill="#b3b3b3" fill-rule="evenodd" d="M232.391 723.534a2.4 2.4 0 0 1 2.4 2.4v17.725a2.4 2.4 0 0 1-4.8 0v-17.725a2.4 2.4 0 0 1 2.4-2.4z"/><path d="M232.255 676.559c10.33 0 17.067 15.408 18.7 28.493 1.619 12.942-2.372 23.694-18.7 23.694-16.878 0-20.213-10.733-18.7-23.694 1.633-14.061 8.37-28.493 18.7-28.493z" style="fill:url(#h);fill-rule:evenodd"/><path fill="#b3b3b3" fill-rule="evenodd" d="M745.853 826h.938a2.4 2.4 0 0 1 2.4 2.4v22.238a2.4 2.4 0 0 1-2.4 2.4h-.938a2.4 2.4 0 0 1-2.4-2.4V828.4a2.4 2.4 0 0 1 2.4-2.4z"/><path d="M746.727 830.3c-19.438 0-23.278-9.326-21.541-20.59a34.467 34.467 0 0 1 3.289-10.369 16.628 16.628 0 0 1 0-9.112c2.889-12.327 12.059-20.911 18.356-20.911 6.56 0 15.468 9.1 18.356 20.911a14.589 14.589 0 0 1-.335 9.217 34.36 34.36 0 0 1 3.419 10.264c1.861 11.243-2.735 20.59-21.544 20.59z" style="fill:url(#i);fill-rule:evenodd"/><path fill="#ccc" fill-rule="evenodd" d="M328.841 654.562a6.571 6.571 0 0 0-5.2-5.027q-4.107-.952-.034-2.045a6.571 6.571 0 0 0 5.027-5.2q.952-4.109 2.045-.035a6.569 6.569 0 0 0 5.2 5.027q4.109.954.035 2.045a6.569 6.569 0 0 0-5.027 5.2q-.955 4.108-2.046.035z"/><path d="M328.383 653.73a6.567 6.567 0 0 0-5.2-5.027q-4.109-.954-.035-2.045a6.568 6.568 0 0 0 5.027-5.2q.954-4.107 2.046-.034a6.568 6.568 0 0 0 5.2 5.027q4.107.952.035 2.045a6.568 6.568 0 0 0-5.027 5.2q-.954 4.104-2.046.034z" style="fill:url(#e);fill-rule:evenodd"/><path fill="#ccc" fill-rule="evenodd" d="M801.841 680.562a6.571 6.571 0 0 0-5.2-5.027q-4.107-.952-.034-2.045a6.571 6.571 0 0 0 5.027-5.2q.952-4.109 2.045-.035a6.569 6.569 0 0 0 5.2 5.027q4.108.954.035 2.045a6.569 6.569 0 0 0-5.027 5.2q-.955 4.108-2.046.035z"/><path d="M801.383 679.73a6.567 6.567 0 0 0-5.2-5.027q-4.108-.954-.035-2.045a6.568 6.568 0 0 0 5.027-5.2q.954-4.107 2.046-.034a6.568 6.568 0 0 0 5.2 5.027q4.107.952.035 2.045a6.568 6.568 0 0 0-5.027 5.2q-.954 4.104-2.046.034z" style="fill:url(#j);fill-rule:evenodd"/><path d="M774.21 646.9a4.446 4.446 0 0 0-3.517-3.4q-2.778-.643-.023-1.383a4.443 4.443 0 0 0 3.4-3.517q.645-2.778 1.383-.023a4.443 4.443 0 0 0 3.517 3.4q2.778.645.023 1.383a4.446 4.446 0 0 0-3.4 3.517q-.645 2.78-1.383.023z" style="fill:url(#k);fill-rule:evenodd"/><path d="m385.6 714.6.158-150.658L598.9 544.174l-.158 150.658z" style="fill:url(#a);fill-rule:evenodd"/><path d="m385.474 564.031 214.763-19.383-36.171-49.067-215.559 17.634z" style="fill:url(#b);fill-rule:evenodd"/><path d="m598.744 694.832.156-150.658 71.975 59.319-.158 150.658z" style="fill:url(#l);fill-rule:evenodd"/><path d="m457.064 774.209.158-150.658 214.691-19.914-.158 150.663z" style="fill:url(#m);fill-rule:evenodd"/><path d="m384.566 714.459.158-150.659 72.5 59.75-.158 150.658z" style="fill:url(#n);fill-rule:evenodd"/><path d="M494 640s75.357-58.4 42-83-38.887 1.663-37 14 53.847 12.465 54-26c.2-49.979 75-125 75-125" style="fill:none;stroke-width:3px;stroke-dasharray:12 6;stroke:url(#o);fill-rule:evenodd"/><path d="m670.275 604.939-72.041-59.9 38.476-26.909 72.86 58.159z" style="fill:url(#d);fill-rule:evenodd"/><path d="m425.5 674.383-72.042-59.9 31.109-50.347 72.86 58.16z" style="fill:url(#p);fill-rule:evenodd"/><path d="m487.918 674.235 214.482-22.57-31.1-50.346-215.309 20.833z" style="fill:url(#q);fill-rule:evenodd"/><path style="fill:#fff;fill-rule:evenodd" d="m697.363 358.927-69.58 62.511-12.035 1.082z"/><path d="m697.363 358.927-69.58 62.511-12.035 1.082z" style="fill:url(#c);fill-rule:evenodd"/><path d="M615.748 422.52 604 413l92.089-53.46" style="fill:url(#r);fill-rule:evenodd"/><path d="m625 432 12 18 60-89" style="fill:url(#s);fill-rule:evenodd"/><path d="m626.98 421.335-2.471 11.828 70.918-71.735" style="fill:#fff;fill-rule:evenodd"/><path d="m626.98 421.335-2.471 11.828 70.918-71.735" style="fill:url(#t);fill-rule:evenodd"/><path d="m494.814 735.44 21.293-2.1v-6.613l-13.4 1.319v-6.965l10.977-1.08v-6.613l-10.977 1.08v-6.084l12.917-1.27v-6.525l-20.808 2.047v32.8zM521 732.863l7.054-.694v-11.241a106.361 106.361 0 0 0-1.014-11.274l.176-.017 2.645 7.586 4.453 11.553 4.32-.425 4.408-12.424 2.733-8.116.177-.018a111.811 111.811 0 0 0-1.014 11.474v11.241l7.185-.707V697l-8.552.841-5.025 14.646c-.618 1.956-1.147 4.08-1.808 6.173l-.22.022c-.617-1.968-1.146-3.987-1.808-5.818l-5.2-13.639-8.508.837v32.8zm37.213-3.661 7.891-.776v-10.889l3.835-.377c6.922-.681 12.961-4.714 12.961-12.517 0-8.111-5.951-10.082-13.181-9.371l-11.504 1.128v32.8zm7.891-17.881v-9.478l3.218-.316c3.792-.373 5.908.565 5.908 3.871 0 3.218-1.852 5.208-5.687 5.585zM594 725.682l7.891-.777v-26.274l8.905-.876v-6.524l-25.657 2.524v6.524l8.861-.871v26.274zm27.991-2.754 7.847-.772v-11.594l9.919-22.18-8.244.811-2.733 7.542c-.925 2.56-1.807 4.939-2.733 7.587l-.176.018c-.926-2.466-1.764-4.676-2.645-7.058l-2.734-7-8.375.824 9.874 20.233v11.594z" style="fill:url(#u);fill-rule:evenodd"/><path fill="#ccc" fill-rule="evenodd" d="M408.938 457.309a17.5 17.5 0 0 0 21.374 26.725 17.5 17.5 0 1 1-16.306-30.955 17.442 17.442 0 0 0-5.068 4.23z"/><circle cx="422.5" cy="468.375" r="17.5" style="fill:url(#v)"/><path fill="#ccc" fill-rule="evenodd" d="M391.76 451.5c-2.358 4.419 9.827 15.52 27.215 24.8 15.131 8.071 29.212 12.1 34.166 10.093-4.191 2.772-18.943-1.24-34.86-9.73-17.388-9.275-29.573-20.376-27.215-24.8a2.96 2.96 0 0 1 1.585-1.3 2.606 2.606 0 0 0-.891.937z"/><path d="M418.975 476.29c-17.388-9.275-29.573-20.376-27.215-24.8s18.363-.484 35.751 8.791 29.572 20.376 27.215 24.8-18.364.483-35.751-8.791zm31.634 5.732c1.824-3.42-8.789-12.642-23.7-20.6s-28.486-11.633-30.31-8.213 8.789 12.642 23.7 20.6 28.486 11.633 30.31 8.213zm-36.645-29.008-2.775 1.452.032 1.751 28.637 14.183.266-4.559z" style="fill:url(#w);fill-rule:evenodd"/><g class="people"><path style="fill:#f8cfad;fill-rule:evenodd" d="m612.131 676.5 1.362 3.532 3.255-2.324-1.361-3.532zM629.131 665.5l1.362 3.532 3.255-2.324-1.361-3.532z"/><path style="fill:#141a33;fill-rule:evenodd" d="m617.764 678.184-3.162-.078a11.028 11.028 0 0 0-1.034 3.454c-.258 2.006-1.177 5-.449 5.367 1.5 2.659 4.118-.215 4.118-.215s2.187-2.848 1.925-5.265c-.106-.973-1.181-1.869-1.398-3.263zM633.781 665.855l3.019.945a11.008 11.008 0 0 1-.137 3.6c-.4 1.981-.179 4.166-.986 4.277-2.283 2.03-3.827-1.533-3.827-1.533s-1.473-2.456-.444-4.659c.412-.88 1.718-1.385 2.375-2.63z"/><path style="fill:#f0c5a8;fill-rule:evenodd" d="M599.935 592.534s10.293 9.761 11.95 7.564 3.536-3.463-6.758-13.65z"/><path style="fill:#f8cfad;fill-rule:evenodd" d="M611.3 596.361c1.674-1.105 11.5 7.048 14.5 11.774s-12.705-4.36-14.632-6.776-1.54-3.893.132-4.998z"/><path style="fill:#f8cfad;fill-rule:evenodd" d="M621.815 607.988s1.809 2.549 2.433 1.756 2.475-1.064 2.449-1.138.1-.819 1.288-2.331-3.8-3.632-5.81-.494a2.556 2.556 0 0 0-.36 2.207z"/><path fill="#232c57" fill-rule="evenodd" d="M598 617s14.968-5.618 17 7a150.235 150.235 0 0 1 2 22s12.666 11.836 16 19c0 0-4.753-1.629-4 2 0 0-18.132-14.647-19-19s-9.148-18.716-12-31z"/><path d="M589 622s14.968-5.618 17 7a150.235 150.235 0 0 1 2 22s4.666 17.836 8 25c0 0-4.753-1.629-4 2 0 0-10.132-20.647-11-25s-9.148-18.716-12-31z" style="fill:#292966;fill-rule:evenodd"/><path style="fill:#f0c5a8;fill-rule:evenodd" d="M585.626 597.7s-10.292 9.761-11.95 7.563-3.536-3.463 6.758-13.65z"/><path style="fill:#f8cfad;fill-rule:evenodd" d="M574.259 601.529c-1.675-1.105-11.5 7.049-14.5 11.774s12.7-4.36 14.631-6.775 1.543-3.894-.131-4.999z"/><path style="fill:#f0c5a8;fill-rule:evenodd" d="M591.715 577.752s-.606 1.681 1.48 3.716-3.615 5.307-4.645 2.85-.48-2.716-.48-2.716z"/><path style="fill:#f8cfad;fill-rule:evenodd" d="M583.527 574.123c-.839 1.043.491 3.873 1.453 5.449s2.749 2.833 3.364 2.428 4.088-2.657 4-4-.228-3.4-.228-3.4 2.562-1.641 2.154-2.916-2.916-.154-2.916-.154a15.853 15.853 0 0 0-.227-2.224c-.189-.929-6.887-1.445-7.827 2.6s.558 1.805.227 2.217z"/><path fill="#232c57" fill-rule="evenodd" d="M584.227 567.758c2.1-.885 7.2-3.684 10.125.318s.842 4.385.989 5.294-1.894 5.69-1.341 6.63-3.865.8-4.657-1.179-2.844-.539-2.227-1.224-1.3-4.456-2.916-2.154a9.252 9.252 0 0 0 .309-1.38c-.115.192.259-3.257-.673-1.32s-2.1 1.037-3.069.762-1.8-1.118-1.071-1.689c.023-.016 2.436-3.172 4.531-4.058z"/><path d="M589 585c-2.584-.47-10.055.362-13 13 0 0 1.9 3.349 5 4s6 21 6 21 24.016 11.06 27-3c-.07-13.826-8-21-8-21s5.829-3.2 5-6-8.016-10.153-11-10-6 0-6 0-2.416 2.47-5 2z" style="fill:#f6bb07;fill-rule:evenodd"/><path style="fill:#f8cfad;fill-rule:evenodd" d="M563.284 612.581s-.986 2.965-1.814 2.389-2.678-.3-2.675-.374-.333-.755-1.912-1.854 2.577-4.583 5.414-2.167a2.551 2.551 0 0 1 .987 2.006z"/></g>'});$1.displayName="EmptyIcon";const ql=()=>s(ie,{name:"lock"},()=>s("path",{d:"M787.168 952.268H236.832c-30.395 0-55.033-24.638-55.033-55.033V429.45c0-30.395 24.638-55.034 55.033-55.034h82.55V264.35c0-106.38 86.238-192.618 192.618-192.618S704.618 157.97 704.618 264.35v110.066h82.55c30.395 0 55.033 24.639 55.033 55.034v467.785c0 30.395-24.639 55.033-55.033 55.033zM484.483 672.046v115.122h55.034V672.046c31.99-11.373 55.033-41.605 55.033-77.496 0-45.592-36.958-82.55-82.55-82.55s-82.55 36.958-82.55 82.55c0 35.89 23.042 66.123 55.033 77.496zM622.067 264.35c0-60.788-49.28-110.067-110.067-110.067s-110.067 49.28-110.067 110.067v110.066h220.135V264.35z"}));ql.displayName="LockIcon";const J8=M({name:"ArticleItem",props:{info:{type:Object,required:!0},path:{type:String,required:!0}},slots:Object,setup(e,{slots:t}){const n=zn(e,"info"),{info:r,items:a}=A8(e);return()=>{var p,h,v;const{[Ue.title]:o,[je.type]:l,[je.isEncrypted]:i=!1,[je.cover]:c,[je.excerpt]:u,[je.sticky]:d}=n.value,f=r.value;return s("div",{class:"vp-article-wrapper"},s("article",{class:"vp-article-item",vocab:"https://schema.org/",typeof:"Article"},[((p=t.cover)==null?void 0:p.call(t,{cover:c}))??(c?[s("img",{class:"vp-article-cover",src:be(c),alt:"",loading:"lazy"}),s("meta",{property:"image",content:be(c)})]:[]),d?s(P1):null,s(Ie,{to:e.path},()=>{var _;return((_=t.title)==null?void 0:_.call(t,{title:o,isEncrypted:i,type:l}))??s("header",{class:"vp-article-title"},[i?s(ql):null,l===Ro.slide?s(I1):null,s("span",{property:"headline"},o)])}),((h=t.excerpt)==null?void 0:h.call(t,{excerpt:u}))??(u?s("div",{class:"vp-article-excerpt",innerHTML:u}):null),s("hr",{class:"vp-article-hr"}),((v=t.info)==null?void 0:v.call(t,{info:f}))??s(S1,{info:f,...a.value?{items:a.value}:{}})]))}}}),Q8=M({name:"Pagination",props:{total:{type:Number,default:10},perPage:{type:Number,default:10},current:{type:Number,default:1}},emits:["updateCurrentPage"],setup(e,{emit:t}){let n;const r=ce(),a=z(""),o=w(()=>r.value.paginationLocales),l=w(()=>Math.ceil(e.total/e.perPage)),i=w(()=>!!l.value&&l.value!==1),c=w(()=>l.value<7?!1:e.current>4),u=w(()=>l.value<7?!1:e.current<l.value-3),d=w(()=>{const{current:h}=e;let v=1,_=l.value;const E=[];l.value>=7&&(h<=4&&h<l.value-3?(v=1,_=5):h>4&&h>=l.value-3?(_=l.value,v=l.value-4):l.value>7&&(v=h-2,_=h+2));for(let b=v;b<=_;b++)E.push(b);return E}),f=h=>t("updateCurrentPage",h),p=h=>{const v=parseInt(h,10);v<=l.value&&v>0?f(v):n.pop(`<svg viewBox="0 0 1024 1024" xmlns="http://www.w3.org/2000/svg" width="16" height="16"><path d="M64 512a448 448 0 1 0 896 0 448 448 0 1 0-896 0Z" fill="#FA5151"/><path d="m557.3 512 113.1-113.1c12.5-12.5 12.5-32.8 0-45.3s-32.8-12.5-45.3 0L512 466.7 398.9 353.6c-12.5-12.5-32.8-12.5-45.3 0s-12.5 32.8 0 45.3L466.7 512 353.6 625.1c-12.5 12.5-12.5 32.8 0 45.3 6.2 6.2 14.4 9.4 22.6 9.4s16.4-3.1 22.6-9.4L512 557.3l113.1 113.1c6.2 6.2 14.4 9.4 22.6 9.4s16.4-3.1 22.6-9.4c12.5-12.5 12.5-32.8 0-45.3L557.3 512z" fill="#FFF"/></svg>${o.value.errorText.replace(/\$page/gu,l.value.toString())}`)};return se(()=>{n=new p4}),()=>s("div",{class:"vp-pagination"},i.value?s("nav",{class:"vp-pagination-list"},[s("div",{class:"vp-pagination-number "},[e.current>1?s("div",{class:"prev",role:"navigation",unselectable:"on",onClick:()=>f(e.current-1)},o.value.prev):null,c.value?[s("div",{role:"navigation",onClick:()=>f(1)},1),s("div",{class:"ellipsis"},"...")]:null,d.value.map(h=>s("div",{key:h,class:{active:e.current===h},role:"navigation",onClick:()=>f(h)},h)),u.value?[s("div",{class:"ellipsis"},"..."),s("div",{role:"navigation",onClick:()=>f(l.value)},l.value)]:null,e.current<l.value?s("div",{class:"next",role:"navigation",unselectable:"on",onClick:()=>f(e.current+1)},o.value.next):null]),s("div",{class:"vp-pagination-nav"},[s("label",{for:"navigation-text"},`${o.value.navigate}: `),s("input",{id:"navigation-text",value:a.value,onInput:({target:h})=>{a.value=h.value},onKeydown:h=>{h.key==="Enter"&&(h.preventDefault(),p(a.value))}}),s("button",{class:"vp-pagination-button",type:"button",role:"navigation",title:o.value.action,onClick:()=>p(a.value)},o.value.action)])]):[])}}),Gl=M({name:"ArticleList",props:{items:{type:Array,default:()=>[]}},setup(e){const t=Ht(),n=wn(),r=Vr(),a=z(1),o=w(()=>r.value.articlePerPage??10),l=w(()=>e.items.slice((a.value-1)*o.value,a.value*o.value)),i=async c=>{a.value=c;const u={...t.query};!(u.page===c.toString()||c===1&&!u.page)&&(c===1?delete u.page:u.page=c.toString(),await n.push({path:t.path,query:u}))};return se(()=>{const{page:c}=t.query;i(c?Number(c):1),ae(a,()=>{const u=document.querySelector("#article-list").getBoundingClientRect().top+window.scrollY;setTimeout(()=>{window.scrollTo(0,u)},100)})}),()=>s("div",{id:"article-list",class:"vp-article-list",role:"feed"},l.value.length?[...l.value.map(({info:c,path:u},d)=>s(oe,{appear:!0,delay:d*.04},()=>s(J8,{key:u,info:c,path:u}))),s(Q8,{current:a.value,perPage:o.value,total:e.items.length,onUpdateCurrentPage:i})]:s($1))}}),F1=M({name:"CategoryList",setup(){const e=ge(),t=Hr();return()=>s("ul",{class:"vp-category-list"},Ma(t.value.map).sort(([,n],[,r])=>r.items.length-n.items.length).map(([n,{path:r,items:a}])=>s("li",{class:["vp-category",`vp-category${Ra(n,9)}`,{active:r===e.value.path}]},s(Ie,{to:r},()=>[n,s("span",{class:"count"},a.length)]))))}}),H1=M({name:"TagList",setup(){const e=he(),t=Nr(),n=r=>{var a;return r===((a=e.value.blog)==null?void 0:a.name)};return()=>s("ul",{class:"tag-list-wrapper"},Ma(t.value.map).sort(([,r],[,a])=>a.items.length-r.items.length).map(([r,{path:a,items:o}])=>s("li",{class:["tag",`tag${Ra(r,9)}`,{active:n(r)}]},s(Ie,{to:a},()=>[r,s("span",{class:"tag-num"},o.length)]))))}}),Y8=M({name:"TimelineList",setup(){const e=ce(),t=Rl(),n=An(),r=w(()=>e.value.blogLocales.timeline);return()=>s("div",{class:"timeline-list-wrapper"},[s("div",{class:"timeline-list-title",onClick:()=>n(t.value.path)},[s(zl),s("span",{class:"num"},t.value.items.length),r.value]),s("hr"),s("div",{class:"timeline-content"},s("ul",{class:"timeline-list"},t.value.config.map(({year:a,items:o},l)=>s(oe,{appear:!0,delay:.08*(l+1)},()=>s("li",[s("h3",{class:"timeline-year"},a),s("ul",{class:"timeline-year-wrapper"},o.map(({date:i,info:c,path:u})=>s("li",{class:"timeline-item"},[s("span",{class:"timeline-date"},i),s(Ie,{class:"timeline-title",to:u},()=>c[Ue.title])])))])))))])}}),Z8={article:Fa,category:Vl,tag:jl,timeline:zl},N1=M({name:"InfoList",setup(){const e=ce(),t=Kn(),n=Hr(),r=w(()=>En(n.value.map).length),a=$l(),o=Nr(),l=w(()=>En(o.value.map).length),i=An(),c=z("article"),u=w(()=>e.value.blogLocales);return()=>s("div",{class:"vp-blog-infos"},[s("div",{class:"vp-blog-type-switcher"},Ma(Z8).map(([d,f])=>s("button",{type:"button",class:"vp-blog-type-button",onClick:()=>{c.value=d}},s("div",{class:["icon-wrapper",{active:c.value===d}],"aria-label":u.value[d],"data-balloon-pos":"up"},s(f))))),s(oe,()=>c.value==="article"?s("div",{class:"vp-star-article-wrapper"},[s("div",{class:"title",onClick:()=>i(t.value.path)},[s(Fa),s("span",{class:"num"},t.value.items.length),u.value.article]),s("hr"),a.value.items.length?s("ul",{class:"vp-star-articles"},a.value.items.map(({info:d,path:f},p)=>s(oe,{appear:!0,delay:.08*(p+1)},()=>s("li",{class:"vp-star-article"},s(Ie,{to:f},()=>d[Ue.title]))))):s("div",{class:"vp-star-article-empty"},u.value.empty.replace("$text",u.value.star))]):c.value==="category"?s("div",{class:"vp-category-wrapper"},[r.value?[s("div",{class:"title",onClick:()=>i(n.value.path)},[s(Vl),s("span",{class:"num"},r.value),u.value.category]),s("hr"),s(oe,{delay:.04},()=>s(F1))]:s("div",{class:"vp-category-empty"},u.value.empty.replace("$text",u.value.category))]):c.value==="tag"?s("div",{class:"vp-tag-wrapper"},[l.value?[s("div",{class:"title",onClick:()=>i(o.value.path)},[s(jl),s("span",{class:"num"},l.value),u.value.tag]),s("hr"),s(oe,{delay:.04},()=>s(H1))]:s("div",{class:"vp-tag-empty"},u.value.empty.replace("$text",u.value.tag))]):s(oe,()=>s(Y8)))])}}),jr=M({name:"BlogWrapper",slots:Object,setup(e,{slots:t}){const{isMobile:n}=$r();return()=>[s(Hl),s(Ol,{noSidebar:!0,noToc:!0},{default:()=>t.default(),navScreenBottom:()=>s(Nl),...n.value?{sidebar:()=>s(N1)}:{}})]}}),zr=()=>s("aside",{class:"vp-blog-info-wrapper"},[s(oe,()=>s(Nl)),s(oe,{delay:.04},()=>s(N1))]);zr.displayName="InfoPanel";const X8=M({name:"BlogPage",setup(){const e=ge(),t=he(),n=Hr(),r=Nr();return()=>{const{key:a="",name:o=""}=t.value.blog||{},l=o?a==="category"?n.value.map[o].items:a==="tag"?r.value.map[o].items:[]:[];return s(jr,()=>s("div",{class:"vp-page vp-blog"},s("div",{class:"blog-page-wrapper"},[s("main",{id:"main-content",class:"vp-blog-main"},[s(oe,()=>a==="category"?s(F1):a==="tag"?s(H1):null),o?s(oe,{appear:!0,delay:.24},()=>s(Gl,{key:e.value.path,items:l})):null]),s(oe,{delay:.16},()=>s(zr,{key:"blog"}))])))}}}),e5="//theme-hope-assets.vuejs.press/hero/default.jpg",t5=M({name:"BlogHero",slots:Object,setup(e,{slots:t}){const n=he(),r=Gn(),a=xe(),o=w(()=>n.value.heroFullScreen??!1),l=w(()=>{const{heroText:c,heroImage:u,heroImageDark:d,heroAlt:f,heroImageStyle:p,tagline:h}=n.value;return{text:c??r.value.title??"Hello",tagline:h??"",image:u?be(u):null,imageDark:d?be(d):null,alt:f??c??"",imageStyle:p,isFullScreen:o.value}}),i=w(()=>{const{bgImage:c,bgImageDark:u,bgImageStyle:d}=n.value;return{image:we(c)?be(c):c===!1?null:e5,imageDark:we(u)?be(u):null,bgStyle:d,isFullScreen:o.value}});return()=>{var c,u;return n.value.hero===!1?null:s("div",{ref:a,class:["vp-blog-hero",{fullscreen:o.value,"no-bg":!i.value.image}]},[((c=t.bg)==null?void 0:c.call(t,i.value))??[i.value.image?s("div",{class:["vp-blog-mask",{light:i.value.imageDark}],style:[{background:`url(${i.value.image}) center/cover no-repeat`},i.value.bgStyle]}):null,i.value.imageDark?s("div",{class:"vp-blog-mask dark",style:[{background:`url(${i.value.imageDark}) center/cover no-repeat`},i.value.bgStyle]}):null],((u=t.info)==null?void 0:u.call(t,l.value))??[s(oe,{appear:!0,type:"group",delay:.04},()=>{const{image:d,imageDark:f,imageStyle:p,alt:h}=l.value;return[d?s("img",{key:"light",class:["vp-blog-hero-image",{light:f}],style:p,src:d,alt:h}):null,f?s("img",{key:"dark",class:"vp-blog-hero-image dark",style:p,src:f,alt:h}):null]}),s(oe,{appear:!0,delay:.08},()=>l.value.text?s("h1",{class:"vp-blog-hero-title"},l.value.text):null),s(oe,{appear:!0,delay:.12},()=>l.value.tagline?s("p",{class:"vp-blog-hero-description",innerHTML:l.value.tagline}):null)],l.value.isFullScreen?s("button",{type:"button",class:"slide-down-button",onClick:()=>{window.scrollTo({top:a.value.clientHeight,behavior:"smooth"})}},[s(jo),s(jo)]):null])}}}),Gt=cn("bing-image",{index:0,data:[]}),n5=M({name:"BingHeroBackground",setup(){const e=Pa(),t=xe(),n=z(!1),r=w(()=>{const i=Gt.value.data[Gt.value.index],c=e.value.toLowerCase().split("-").shift();if(i){const{url:u,wallpaper:d,downloadable:f,locales:p}=i;return{url:u,wallpaper:d,downloadable:f,...p[c]??p.en}}return null}),a=()=>fetch("https://bing-wallpaper.vuejs.press/api/wallpaper").then(i=>i.json()),o=()=>{Gt.value.index-=1},l=()=>{Gt.value.index+=1};return lu(t,()=>{n.value=!1}),se(()=>{a().then(i=>{Gt.value.data=i})}),()=>{const{title:i,headline:c,url:u,backstage:d,quickFact:f,copyright:p}=r.value??{};return s(Or,()=>u?[s("div",{class:"vp-blog-mask",style:{background:`url(${u}) center/cover no-repeat`}}),s("div",{class:"bing-switch",onClick:()=>{n.value=!0}},[s(Rt,{name:"fade"},()=>n.value?s("div",{class:"bing-info",ref:t},[s("a",{href:d,target:"_blank",class:"bing-info-header"},c),s("hr"),s("div",{class:"bing-info-body"},f),s("div",{class:"bing-info-copyright"},p)]):null),s("div",{class:"bing-location"},[s("span",{class:"bing-location-icon"}),i]),s("button",{class:"bing-switch-prev",title:"prev image",type:"button",disabled:Gt.value.index===0,onClick:()=>o()}),s("button",{class:"bing-switch-next",title:"next image",type:"button",disabled:Gt.value.index===Gt.value.data.length-1,onClick:()=>l()})])]:null)}}}),r5=M({name:"HitokotoBlogHero",inheritAttrs:!1,props:{text:{type:String,required:!0},image:{type:String,default:null},imageDark:{type:String,default:null},alt:{type:String,required:!0},imageStyle:{type:[String,Object],default:null}},setup(e){const t=z(""),n=z(""),r=z("");let a=!1;const o=()=>fetch("https://v1.hitokoto.cn").then(l=>l.json()).then(({from:l,hitokoto:i})=>{t.value=i,r.value=l});return se(()=>{a=!0,ae(t,()=>{n.value="";let l=0;const i=()=>(n.value+=t.value[l],l+=1,_t().then(()=>{l<t.value.length?setTimeout(()=>{i()},150):a&&setTimeout(()=>{o()},3e3)}));i()}),o()}),Ft(()=>{a=!1}),()=>[s(oe,{appear:!0,type:"group",delay:.04},()=>[e.image?s("img",{key:"light",class:["vp-blog-hero-image",{light:e.imageDark}],style:e.imageStyle,src:e.image,alt:e.alt}):null,e.imageDark?s("img",{key:"dark",class:"vp-blog-hero-image dark",style:e.imageStyle,src:e.imageDark,alt:e.alt}):null]),s(oe,{appear:!0,delay:.08},()=>e.text?s("h1",{class:"vp-blog-hero-title"},e.text):null),s("div",{class:"hitokoto"},[s("p",{class:"hitokoto-text"},s("span",n.value)),s("p",{class:"hitokoto-author",style:{opacity:n.value.length>4?1:0}},`——「${r.value}」`)])]}}),a5=M({__name:"BlogHero",setup(e){return(t,n)=>(cl(),ul(bt(t5),null,{bg:pa(()=>[Te(bt(n5))]),info:pa(r=>[Te(bt(r5),s2(_c(r)),null,16)]),_:1}))}}),o5=Fl(a5,[["__file","BlogHero.vue"]]),l5=["link","article","book","project","friend"],s5=M({name:"ProjectPanel",components:{ArticleIcon:Fa,BookIcon:D1,FriendIcon:R1,LinkIcon:O1,ProjectIcon:M1},props:{items:{type:Array,required:!0}},setup(e){const t=Cn(),n=An(),r=(a="",o="icon")=>l5.includes(a)?s(pt(`${a}-icon`)):sn(a)?s("img",{class:"vp-project-image",src:a,alt:o}):Rr(a)?s("img",{class:"vp-project-image",src:be(a),alt:o}):s(Ve,{icon:a});return()=>s("div",{class:"vp-project-panel"},e.items.map(({icon:a,link:o,name:l,desc:i,background:c},u)=>s("div",{class:["vp-project-card",{[`project${u%9}`]:!t.value&&!c}],...c?{style:c}:{},onClick:()=>n(o)},[r(a,l),s("div",{class:"vp-project-name"},l),s("div",{class:"vp-project-desc"},i)])))}}),i5=M({name:"BlogHomePage",setup(){const e=Kn(),t=he(),n=w(()=>t.value.projects??[]);return()=>s("div",{class:"vp-page vp-blog"},[s(o5),s("div",{class:"blog-page-wrapper"},[s("main",{id:"main-content",class:"vp-blog-main"},[n.value.length?s(oe,{appear:!0,delay:.16},()=>s(s5,{items:n.value})):null,s(oe,{appear:!0,delay:.24},()=>s(Gl,{items:e.value.items}))]),s(oe,{appear:!0,delay:.16},()=>s(zr,{key:"blog"}))]),s(oe,{appear:!0,delay:.28},()=>s(Wn))])}}),V1=()=>s(jr,()=>s(i5));V1.displayName="BlogHome";var c5=[];const u5=M({name:"ArticleType",setup(){const e=ge(),t=Ye(),n=ce(),r=Kn(),a=$l(),o=w(()=>{const l=n.value.blogLocales;return[{text:l.all,path:r.value.path},{text:l.star,path:a.value.path},...c5.map(({key:i,path:c})=>({text:l[i],path:c.replace(/^\//,t.value)}))]});return()=>s("ul",{class:"vp-article-type-wrapper"},o.value.map(l=>s("li",{class:["vp-article-type",{active:l.path===e.value.path}]},s(Ie,{to:l.path},()=>l.text))))}}),d5=M({name:"BlogPage",setup(){const e=$a(),t=he(),n=ge(),r=Kn(),a=$l(),o=w(()=>{const{key:l="",type:i}=t.value.blog||{};return l==="star"?a.value.items:i==="type"&&l?e.value.items:r.value.items});return()=>s(jr,()=>s("div",{class:"vp-page vp-blog"},s("div",{class:"blog-page-wrapper"},[s("main",{id:"main-content",class:"vp-blog-main"},[s(oe,()=>s(u5)),s(oe,{appear:!0,delay:.24},()=>s(Gl,{key:n.value.path,items:o.value}))]),s(oe,{delay:.16},()=>s(zr,{key:"blog"}))])))}}),f5=M({name:"PortfolioHero",slots:Object,setup(e,{slots:t}){const n=C8(),r=he(),a=z(0),o=w(()=>{var p;return((p=r.value.titles)==null?void 0:p[a.value])??""}),l=z(""),i=w(()=>{const{name:p,avatar:h,avatarDark:v,avatarAlt:_,avatarStyle:E}=r.value;return{name:p??n.value.name,avatar:h?be(h):null,avatarDark:v?be(v):null,avatarStyle:E,alt:_||p||""}}),c=w(()=>{const{bgImage:p,bgImageDark:h,bgImageStyle:v}=r.value;return{image:we(p)?be(p):null,imageDark:we(h)?be(h):null,bgStyle:v}}),u=w(()=>{const{welcome:p,name:h,titles:v,medias:_}=r.value;return{name:h??n.value.name,welcome:p??"👋 Hi There, I'm",title:l.value,titles:v??[],medias:_??[]}}),d=()=>{l.value="";let p=0,h=!1;const v=async()=>{if(!h)if(l.value+=o.value[p],p+=1,await _t(),p<o.value.length)setTimeout(()=>{v()},150);else{const _=u.value.titles.length;setTimeout(()=>{a.value=_<=1||a.value===u.value.titles.length-1?0:a.value+1},1e3)}};return v(),()=>{h=!0}};let f;return se(()=>{ae(o,()=>{f==null||f(),f=d()},{immediate:!0})}),()=>{var p,h,v;return s("section",{id:"portfolio",class:["vp-portfolio-wrapper",{bg:c.value.image}]},[((p=t.bg)==null?void 0:p.call(t,c.value))??[c.value.image?s("div",{class:["vp-portfolio-mask",{light:c.value.imageDark}],style:[{background:`url(${c.value.image}) center/cover no-repeat`},c.value.bgStyle]}):null,c.value.imageDark?s("div",{class:"vp-portfolio-mask dark",style:[{background:`url(${c.value.imageDark}) center/cover no-repeat`},c.value.bgStyle]}):null],((h=t.avatar)==null?void 0:h.call(t,i.value))??s("div",{class:"vp-portfolio-avatar"},[s(oe,{delay:.04},()=>{const{avatarDark:_,name:E,alt:b,avatarStyle:C}=i.value;return[s("img",{key:"light",class:{light:_},src:i.value.avatar,title:E,alt:b,style:C}),_?s("img",{key:"dark",class:"dark",src:_,title:E,alt:b,style:C}):null]})]),s("div",{class:"vp-portfolio-container"},((v=t.info)==null?void 0:v.call(t,u.value))??s("div",{class:"vp-portfolio-info"},[s(oe,{appear:!0,delay:.08},()=>s("h6",{class:"vp-portfolio-welcome"},u.value.welcome)),s(oe,{appear:!0,delay:.12},()=>s("h1",{class:"vp-portfolio-name"},u.value.name)),s(oe,{appear:!0,delay:.16},()=>s("h2",{class:"vp-portfolio-title"},l.value)),s(oe,{appear:!0,delay:.2},()=>u.value.medias.length?s("div",{class:"vp-portfolio-medias"},u.value.medias.map(({name:_,url:E,icon:b})=>s("a",{class:"vp-portfolio-media",href:E,rel:"noopener noreferrer",target:"_blank",..._?{"aria-label":_,"data-balloon-pos":"up"}:{}},s(Ve,{icon:b})))):s(B1))]))])}}}),j1=()=>s(jr,()=>[s(f5),s("div",{class:"vp-page vp-portfolio"},s(oe,{appear:!0,delay:.24},()=>s(Wn)))]);j1.displayName="PortfolioHome";const p5=M({name:"TimelineItems",setup(){const e=Vr(),t=ce(),n=Rl(),r=w(()=>e.value.timeline??t.value.blogLocales.timelineTitle),a=w(()=>n.value.config.map(({year:o})=>({title:o.toString(),level:2,slug:o.toString(),children:[]})));return()=>s("div",{class:"timeline-wrapper"},s("ul",{class:"timeline-content"},[s(oe,()=>s("li",{class:"motto"},r.value)),s(L1,{items:a.value}),n.value.config.map(({year:o,items:l},i)=>s(oe,{appear:!0,delay:.08*(i+1),type:"group"},()=>[s("h3",{key:"title",id:o,class:"timeline-year-title"},s("span",o)),s("li",{key:"content",class:"timeline-year-list"},[s("ul",{class:"timeline-year-wrapper"},l.map(({date:c,info:u,path:d})=>s("li",{class:"timeline-item"},[s("span",{class:"timeline-date"},c),s(Ie,{class:"timeline-title",to:d},()=>u[Ue.title])])))])]))]))}}),z1=()=>s(jr,()=>s("div",{class:"vp-page vp-blog"},s("div",{class:"blog-page-wrapper"},[s("main",{id:"main-content",class:"vp-blog-main"},[s(oe,{appear:!0,delay:.24},()=>s(p5))]),s(oe,{delay:.16},()=>s(zr,{key:"blog"}))])));z1.displayName="Timeline";const q1=M({name:"PasswordModal",props:{full:Boolean},emits:["verify"],setup(e,{emit:t}){const n=he(),r=ce(),a=z(""),o=z(!1),l=z(!1),i=w(()=>r.value.encryptLocales);let c=null;const u=()=>{c&&clearTimeout(c),o.value=!1,t("verify",a.value,l.value),_t().then(()=>{o.value=!0,c=setTimeout(()=>{o.value=!1},1e3)})};return()=>s("div",{class:["vp-decrypt-layer",{expand:e.full||n.value.home}]},s("div",{class:"vp-decrypt-modal"},[s("div",{class:["vp-decrypt-hint",{tried:o.value}]},o.value?i.value.errorHint:s(ql,{"aria-label":i.value.iconLabel})),s("div",{class:"vp-decrypt-input"},[s("input",{type:"password",value:a.value,placeholder:i.value.placeholder,onInput:({target:d})=>{a.value=d.value},onKeydown:({key:d})=>{d==="Enter"&&u()}})]),s("div",{class:"vp-remember-password"},[s("input",{type:"checkbox",value:l.value,onChange:()=>l.value=!l.value}),i.value.remember]),s("button",{type:"button",class:"vp-decrypt-submit",onClick:()=>u()},"OK")]))}}),G1=()=>{const e=Nt();return w(()=>e.value.encrypt||{})};var h5={};const Sn="./ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789".split(""),po=Array.from({length:64},(e,t)=>t),aa=e=>Array(e).fill(-1),Ut=[...aa(46),0,1,...po.slice(54,64),...aa(7),...po.slice(2,28),...aa(6),...po.slice(28,54),...aa(5)],mi=[608135816,2242054355,320440878,57701188,2752067618,698298832,137296536,3964562569,1160258022,953160567,3193202383,887688300,3232508343,3380367581,1065670069,3041331479,2450970073,2306472731],vi=[3509652390,2564797868,805139163,3491422135,3101798381,1780907670,3128725573,4046225305,614570311,3012652279,134345442,2240740374,1667834072,1901547113,2757295779,4103290238,227898511,1921955416,1904987480,2182433518,2069144605,3260701109,2620446009,720527379,3318853667,677414384,3393288472,3101374703,2390351024,1614419982,1822297739,2954791486,3608508353,3174124327,2024746970,1432378464,3864339955,2857741204,1464375394,1676153920,1439316330,715854006,3033291828,289532110,2706671279,2087905683,3018724369,1668267050,732546397,1947742710,3462151702,2609353502,2950085171,1814351708,2050118529,680887927,999245976,1800124847,3300911131,1713906067,1641548236,4213287313,1216130144,1575780402,4018429277,3917837745,3693486850,3949271944,596196993,3549867205,258830323,2213823033,772490370,2760122372,1774776394,2652871518,566650946,4142492826,1728879713,2882767088,1783734482,3629395816,2517608232,2874225571,1861159788,326777828,3124490320,2130389656,2716951837,967770486,1724537150,2185432712,2364442137,1164943284,2105845187,998989502,3765401048,2244026483,1075463327,1455516326,1322494562,910128902,469688178,1117454909,936433444,3490320968,3675253459,1240580251,122909385,2157517691,634681816,4142456567,3825094682,3061402683,2540495037,79693498,3249098678,1084186820,1583128258,426386531,1761308591,1047286709,322548459,995290223,1845252383,2603652396,3431023940,2942221577,3202600964,3727903485,1712269319,422464435,3234572375,1170764815,3523960633,3117677531,1434042557,442511882,3600875718,1076654713,1738483198,4213154764,2393238008,3677496056,1014306527,4251020053,793779912,2902807211,842905082,4246964064,1395751752,1040244610,2656851899,3396308128,445077038,3742853595,3577915638,679411651,2892444358,2354009459,1767581616,3150600392,3791627101,3102740896,284835224,4246832056,1258075500,768725851,2589189241,3069724005,3532540348,1274779536,3789419226,2764799539,1660621633,3471099624,4011903706,913787905,3497959166,737222580,2514213453,2928710040,3937242737,1804850592,3499020752,2949064160,2386320175,2390070455,2415321851,4061277028,2290661394,2416832540,1336762016,1754252060,3520065937,3014181293,791618072,3188594551,3933548030,2332172193,3852520463,3043980520,413987798,3465142937,3030929376,4245938359,2093235073,3534596313,375366246,2157278981,2479649556,555357303,3870105701,2008414854,3344188149,4221384143,3956125452,2067696032,3594591187,2921233993,2428461,544322398,577241275,1471733935,610547355,4027169054,1432588573,1507829418,2025931657,3646575487,545086370,48609733,2200306550,1653985193,298326376,1316178497,3007786442,2064951626,458293330,2589141269,3591329599,3164325604,727753846,2179363840,146436021,1461446943,4069977195,705550613,3059967265,3887724982,4281599278,3313849956,1404054877,2845806497,146425753,1854211946,1266315497,3048417604,3681880366,3289982499,290971e4,1235738493,2632868024,2414719590,3970600049,1771706367,1449415276,3266420449,422970021,1963543593,2690192192,3826793022,1062508698,1531092325,1804592342,2583117782,2714934279,4024971509,1294809318,4028980673,1289560198,2221992742,1669523910,35572830,157838143,1052438473,1016535060,1802137761,1753167236,1386275462,3080475397,2857371447,1040679964,2145300060,2390574316,1461121720,2956646967,4031777805,4028374788,33600511,2920084762,1018524850,629373528,3691585981,3515945977,2091462646,2486323059,586499841,988145025,935516892,3367335476,2599673255,2839830854,265290510,3972581182,2759138881,3795373465,1005194799,847297441,406762289,1314163512,1332590856,1866599683,4127851711,750260880,613907577,1450815602,3165620655,3734664991,3650291728,3012275730,3704569646,1427272223,778793252,1343938022,2676280711,2052605720,1946737175,3164576444,3914038668,3967478842,3682934266,1661551462,3294938066,4011595847,840292616,3712170807,616741398,312560963,711312465,1351876610,322626781,1910503582,271666773,2175563734,1594956187,70604529,3617834859,1007753275,1495573769,4069517037,2549218298,2663038764,504708206,2263041392,3941167025,2249088522,1514023603,1998579484,1312622330,694541497,2582060303,2151582166,1382467621,776784248,2618340202,3323268794,2497899128,2784771155,503983604,4076293799,907881277,423175695,432175456,1378068232,4145222326,3954048622,3938656102,3820766613,2793130115,2977904593,26017576,3274890735,3194772133,1700274565,1756076034,4006520079,3677328699,720338349,1533947780,354530856,688349552,3973924725,1637815568,332179504,3949051286,53804574,2852348879,3044236432,1282449977,3583942155,3416972820,4006381244,1617046695,2628476075,3002303598,1686838959,431878346,2686675385,1700445008,1080580658,1009431731,832498133,3223435511,2605976345,2271191193,2516031870,1648197032,4164389018,2548247927,300782431,375919233,238389289,3353747414,2531188641,2019080857,1475708069,455242339,2609103871,448939670,3451063019,1395535956,2413381860,1841049896,1491858159,885456874,4264095073,4001119347,1565136089,3898914787,1108368660,540939232,1173283510,2745871338,3681308437,4207628240,3343053890,4016749493,1699691293,1103962373,3625875870,2256883143,3830138730,1031889488,3479347698,1535977030,4236805024,3251091107,2132092099,1774941330,1199868427,1452454533,157007616,2904115357,342012276,595725824,1480756522,206960106,497939518,591360097,863170706,2375253569,3596610801,1814182875,2094937945,3421402208,1082520231,3463918190,2785509508,435703966,3908032597,1641649973,2842273706,3305899714,1510255612,2148256476,2655287854,3276092548,4258621189,236887753,3681803219,274041037,1734335097,3815195456,3317970021,1899903192,1026095262,4050517792,356393447,2410691914,3873677099,3682840055,3913112168,2491498743,4132185628,2489919796,1091903735,1979897079,3170134830,3567386728,3557303409,857797738,1136121015,1342202287,507115054,2535736646,337727348,3213592640,1301675037,2528481711,1895095763,1721773893,3216771564,62756741,2142006736,835421444,2531993523,1442658625,3659876326,2882144922,676362277,1392781812,170690266,3921047035,1759253602,3611846912,1745797284,664899054,1329594018,3901205900,3045908486,2062866102,2865634940,3543621612,3464012697,1080764994,553557557,3656615353,3996768171,991055499,499776247,1265440854,648242737,3940784050,980351604,3713745714,1749149687,3396870395,4211799374,3640570775,1161844396,3125318951,1431517754,545492359,4268468663,3499529547,1437099964,2702547544,3433638243,2581715763,2787789398,1060185593,1593081372,2418618748,4260947970,69676912,2159744348,86519011,2512459080,3838209314,1220612927,3339683548,133810670,1090789135,1078426020,1569222167,845107691,3583754449,4072456591,1091646820,628848692,1613405280,3757631651,526609435,236106946,48312990,2942717905,3402727701,1797494240,859738849,992217954,4005476642,2243076622,3870952857,3732016268,765654824,3490871365,2511836413,1685915746,3888969200,1414112111,2273134842,3281911079,4080962846,172450625,2569994100,980381355,4109958455,2819808352,2716589560,2568741196,3681446669,3329971472,1835478071,660984891,3704678404,4045999559,3422617507,3040415634,1762651403,1719377915,3470491036,2693910283,3642056355,3138596744,1364962596,2073328063,1983633131,926494387,3423689081,2150032023,4096667949,1749200295,3328846651,309677260,2016342300,1779581495,3079819751,111262694,1274766160,443224088,298511866,1025883608,3806446537,1145181785,168956806,3641502830,3584813610,1689216846,3666258015,3200248200,1692713982,2646376535,4042768518,1618508792,1610833997,3523052358,4130873264,2001055236,3610705100,2202168115,4028541809,2961195399,1006657119,2006996926,3186142756,1430667929,3210227297,1314452623,4074634658,4101304120,2273951170,1399257539,3367210612,3027628629,1190975929,2062231137,2333990788,2221543033,2438960610,1181637006,548689776,2362791313,3372408396,3104550113,3145860560,296247880,1970579870,3078560182,3769228297,1714227617,3291629107,3898220290,166772364,1251581989,493813264,448347421,195405023,2709975567,677966185,3703036547,1463355134,2715995803,1338867538,1343315457,2802222074,2684532164,233230375,2599980071,2000651841,3277868038,1638401717,4028070440,3237316320,6314154,819756386,300326615,590932579,1405279636,3267499572,3150704214,2428286686,3959192993,3461946742,1862657033,1266418056,963775037,2089974820,2263052895,1917689273,448879540,3550394620,3981727096,150775221,3627908307,1303187396,508620638,2975983352,2726630617,1817252668,1876281319,1457606340,908771278,3720792119,3617206836,2455994898,1729034894,1080033504,976866871,3556439503,2881648439,1522871579,1555064734,1336096578,3548522304,2579274686,3574697629,3205460757,3593280638,3338716283,3079412587,564236357,2993598910,1781952180,1464380207,3163844217,3332601554,1699332808,1393555694,1183702653,3581086237,1288719814,691649499,2847557200,2895455976,3193889540,2717570544,1781354906,1676643554,2592534050,3230253752,1126444790,2770207658,2633158820,2210423226,2615765581,2414155088,3127139286,673620729,2805611233,1269405062,4015350505,3341807571,4149409754,1057255273,2012875353,2162469141,2276492801,2601117357,993977747,3918593370,2654263191,753973209,36408145,2530585658,25011837,3520020182,2088578344,530523599,2918365339,1524020338,1518925132,3760827505,3759777254,1202760957,3985898139,3906192525,674977740,4174734889,2031300136,2019492241,3983892565,4153806404,3822280332,352677332,2297720250,60907813,90501309,3286998549,1016092578,2535922412,2839152426,457141659,509813237,4120667899,652014361,1966332200,2975202805,55981186,2327461051,676427537,3255491064,2882294119,3433927263,1307055953,942726286,933058658,2468411793,3933900994,4215176142,1361170020,2001714738,2830558078,3274259782,1222529897,1679025792,2729314320,3714953764,1770335741,151462246,3013232138,1682292957,1483529935,471910574,1539241949,458788160,3436315007,1807016891,3718408830,978976581,1043663428,3165965781,1927990952,4200891579,2372276910,3208408903,3533431907,1412390302,2931980059,4132332400,1947078029,3881505623,4168226417,2941484381,1077988104,1320477388,886195818,18198404,3786409e3,2509781533,112762804,3463356488,1866414978,891333506,18488651,661792760,1628790961,3885187036,3141171499,876946877,2693282273,1372485963,791857591,2686433993,3759982718,3167212022,3472953795,2716379847,445679433,3561995674,3504004811,3574258232,54117162,3331405415,2381918588,3769707343,4154350007,1140177722,4074052095,668550556,3214352940,367459370,261225585,2610173221,4209349473,3468074219,3265815641,314222801,3066103646,3808782860,282218597,3406013506,3773591054,379116347,1285071038,846784868,2669647154,3771962079,3550491691,2305946142,453669953,1268987020,3317592352,3279303384,3744833421,2610507566,3859509063,266596637,3847019092,517658769,3462560207,3443424879,370717030,4247526661,2224018117,4143653529,4112773975,2788324899,2477274417,1456262402,2901442914,1517677493,1846949527,2295493580,3734397586,2176403920,1280348187,1908823572,3871786941,846861322,1172426758,3287448474,3383383037,1655181056,3139813346,901632758,1897031941,2986607138,3066810236,3447102507,1393639104,373351379,950779232,625454576,3124240540,4148612726,2007998917,544563296,2244738638,2330496472,2058025392,1291430526,424198748,50039436,29584100,3605783033,2429876329,2791104160,1057563949,3255363231,3075367218,3463963227,1469046755,985887462],U1=[1332899944,1700884034,1701343084,1684370003,1668446532,1869963892],zo=(e,t)=>{if(t<=0||t>e.length)throw Error(`Illegal len: ${t}`);let n=0,r,a;const o=[];for(;n<t;){if(r=e[n++]&255,o.push(Sn[r>>2&63]),r=(r&3)<<4,n>=t){o.push(Sn[r&63]);break}if(a=e[n++]&255,r|=a>>4&15,o.push(Sn[r&63]),r=(a&15)<<2,n>=t){o.push(Sn[r&63]);break}a=e[n++]&255,r|=a>>6&3,o.push(Sn[r&63]),o.push(Sn[a&63])}return o.join("")},m5=(e,t)=>{const n=e.length;let r=0,a=0,o,l,i,c,u,d;const f=[];for(;r<n-1&&a<t&&(d=e.charCodeAt(r++),o=d<Ut.length?Ut[d]:-1,d=e.charCodeAt(r++),l=d<Ut.length?Ut[d]:-1,!(o==-1||l==-1||(u=o<<2>>>0,u|=(l&48)>>4,f.push(String.fromCharCode(u)),++a>=t||r>=n)||(d=e.charCodeAt(r++),i=d<Ut.length?Ut[d]:-1,i==-1)||(u=(l&15)<<4>>>0,u|=(i&60)>>2,f.push(String.fromCharCode(u)),++a>=t||r>=n)));)d=e.charCodeAt(r++),c=d<Ut.length?Ut[d]:-1,u=(i&3)<<6>>>0,u|=c,f.push(String.fromCharCode(u)),++a;return f.map(p=>p.charCodeAt(0))},v5=(e,t)=>{let n=null;for(typeof e=="number"&&(n=e,e=()=>null);n!==null||(n=e())!==null;)n<128?t(n&127):n<2048?(t(n>>6&31|192),t(n&63|128)):n<65536?(t(n>>12&15|224),t(n>>6&63|128),t(n&63|128)):(t(n>>18&7|240),t(n>>12&63|128),t(n>>6&63|128),t(n&63|128)),n=null},g5=(e,t)=>{let n,r=null;for(;(n=r!==null?r:e())!==null;){if(n>=55296&&n<=57343&&(r=e())!==null&&r>=56320&&r<=57343){t((n-55296)*1024+r-56320+65536),r=null;continue}t(n)}r!==null&&t(r)},y5=(e,t)=>{g5(e,function(n){v5(n,t)})},b5=typeof process=="object"&&h5.NEXT_RUNTIME==="edge"?setTimeout:typeof setImmediate=="function"?setImmediate:typeof process=="object"&&typeof process.nextTick=="function"?process.nextTick:setTimeout,E5=e=>{const t=[];let n=0;return y5(()=>n>=e.length?null:e.charCodeAt(n++),r=>{t.push(r)}),t},Tr=(e,t,n,r)=>{let a,o=e[t],l=e[t+1];return o^=n[0],a=r[o>>>24],a+=r[256|o>>16&255],a^=r[512|o>>8&255],a+=r[768|o&255],l^=a^n[1],a=r[l>>>24],a+=r[256|l>>16&255],a^=r[512|l>>8&255],a+=r[768|l&255],o^=a^n[2],a=r[o>>>24],a+=r[256|o>>16&255],a^=r[512|o>>8&255],a+=r[768|o&255],l^=a^n[3],a=r[l>>>24],a+=r[256|l>>16&255],a^=r[512|l>>8&255],a+=r[768|l&255],o^=a^n[4],a=r[o>>>24],a+=r[256|o>>16&255],a^=r[512|o>>8&255],a+=r[768|o&255],l^=a^n[5],a=r[l>>>24],a+=r[256|l>>16&255],a^=r[512|l>>8&255],a+=r[768|l&255],o^=a^n[6],a=r[o>>>24],a+=r[256|o>>16&255],a^=r[512|o>>8&255],a+=r[768|o&255],l^=a^n[7],a=r[l>>>24],a+=r[256|l>>16&255],a^=r[512|l>>8&255],a+=r[768|l&255],o^=a^n[8],a=r[o>>>24],a+=r[256|o>>16&255],a^=r[512|o>>8&255],a+=r[768|o&255],l^=a^n[9],a=r[l>>>24],a+=r[256|l>>16&255],a^=r[512|l>>8&255],a+=r[768|l&255],o^=a^n[10],a=r[o>>>24],a+=r[256|o>>16&255],a^=r[512|o>>8&255],a+=r[768|o&255],l^=a^n[11],a=r[l>>>24],a+=r[256|l>>16&255],a^=r[512|l>>8&255],a+=r[768|l&255],o^=a^n[12],a=r[o>>>24],a+=r[256|o>>16&255],a^=r[512|o>>8&255],a+=r[768|o&255],l^=a^n[13],a=r[l>>>24],a+=r[256|l>>16&255],a^=r[512|l>>8&255],a+=r[768|l&255],o^=a^n[14],a=r[o>>>24],a+=r[256|o>>16&255],a^=r[512|o>>8&255],a+=r[768|o&255],l^=a^n[15],a=r[l>>>24],a+=r[256|l>>16&255],a^=r[512|l>>8&255],a+=r[768|l&255],o^=a^n[16],e[t]=l^n[17],e[t+1]=o,e},Ln=(e,t)=>{let n=0;for(let r=0;r<4;++r)n=n<<8|e[t]&255,t=(t+1)%e.length;return{key:n,offp:t}},gi=(e,t,n)=>{const r=t.length,a=n.length;let o=0,l=[0,0],i;for(let c=0;c<r;c++)i=Ln(e,o),o=i.offp,t[c]=t[c]^i.key;for(let c=0;c<r;c+=2)l=Tr(l,0,t,n),t[c]=l[0],t[c+1]=l[1];for(let c=0;c<a;c+=2)l=Tr(l,0,t,n),n[c]=l[0],n[c+1]=l[1]},_5=(e,t,n,r)=>{const a=n.length,o=r.length;let l=0,i=[0,0],c;for(let u=0;u<a;u++)c=Ln(t,l),l=c.offp,n[u]=n[u]^c.key;l=0;for(let u=0;u<a;u+=2)c=Ln(e,l),l=c.offp,i[0]^=c.key,c=Ln(e,l),l=c.offp,i[1]^=c.key,i=Tr(i,0,n,r),n[u]=i[0],n[u+1]=i[1];for(let u=0;u<o;u+=2)c=Ln(e,l),l=c.offp,i[0]^=c.key,c=Ln(e,l),l=c.offp,i[1]^=c.key,i=Tr(i,0,n,r),r[u]=i[0],r[u+1]=i[1]},yi=(e,t,n,r,a)=>{const o=U1.slice(),l=o.length;if(n<4||n>31){const p=new Error(`Illegal number of rounds (4-31): ${n}`);if(r===!1)return Promise.reject(p);throw p}if(t.length!==16){const p=new Error(`Illegal salt length: ${t.length} != 16`);if(r===!1)return Promise.reject(p);throw p}n=1<<n>>>0;let i,c,u=0,d;Int32Array?(i=new Int32Array(mi),c=new Int32Array(vi)):(i=mi.slice(),c=vi.slice()),_5(t,e,i,c);const f=()=>{if(u<n){const p=Date.now();for(;u<n&&(u=u+1,gi(e,i,c),gi(t,i,c),!(Date.now()-p>100)););}else{for(u=0;u<64;u++)for(d=0;d<l>>1;d++)Tr(o,d<<1,i,c);const p=[];for(u=0;u<l;u++)p.push((o[u]>>24&255)>>>0),p.push((o[u]>>16&255)>>>0),p.push((o[u]>>8&255)>>>0),p.push((o[u]&255)>>>0);return r===!1?Promise.resolve(p):p}if(r===!1)return new Promise(p=>b5(()=>{f().then(p)}))};if(r===!1)return f();{let p;for(;;)if(typeof(p=f())<"u")return p||[]}},w5=e=>{try{let t;typeof window<"u"?t=window.crypto??window.msCrypto:t=globalThis.crypto;const n=new Uint32Array(e);return t==null||t.getRandomValues(n),Array.from(n)}catch{throw Error("WebCryptoAPI is not available")}},A5=(e=10)=>{if(typeof e!="number")throw Error("Illegal arguments: "+typeof e);e<4?e=4:e>31&&(e=31);const t=[];return t.push("$2a$"),e<10&&t.push("0"),t.push(e.toString()),t.push("$"),t.push(zo(w5(16),16)),t.join("")};function C5(e,t,n,r){if(typeof e!="string"||typeof t!="string"){const h=new Error("Invalid string / salt: Not a string");if(n===!1)return Promise.reject(h);throw h}let a,o;if(t.charAt(0)!=="$"||t.charAt(1)!=="2"){const h=new Error("Invalid salt version: "+t.substring(0,2));if(n===!1)return Promise.reject(h);throw h}if(t.charAt(2)==="$")a="\0",o=3;else{if(a=t.charAt(2),a!=="a"&&a!=="b"&&a!=="y"||t.charAt(3)!=="$"){const h=Error("Invalid salt revision: "+t.substring(2,4));if(n===!1)return Promise.reject(h);throw h}o=4}if(t.charAt(o+2)>"$"){const h=new Error("Missing salt rounds");if(n===!1)return Promise.reject(h);throw h}const l=parseInt(t.substring(o,o+1),10)*10,i=parseInt(t.substring(o+1,o+2),10),c=l+i,u=t.substring(o+3,o+25);e+=a>="a"?"\0":"";const d=E5(e),f=m5(u,16),p=h=>{const v=[];return v.push("$2"),a>="a"&&v.push(a),v.push("$"),c<10&&v.push("0"),v.push(c.toString()),v.push("$"),v.push(zo(f,f.length)),v.push(zo(h,U1.length*4-1)),v.join("")};return n===!1?yi(d,f,c,!1).then(h=>p(h)):p(yi(d,f,c,!0))}const k5=(e,t=10)=>{if(typeof t=="number"&&(t=A5(t)),typeof e!="string"||typeof t!="string")throw Error("Illegal arguments: "+typeof e+", "+typeof t);return C5(e,t,!0)},qo=(e,t)=>{if(typeof e!="string"||typeof t!="string")throw Error("Illegal arguments: "+typeof e+", "+typeof t);return t.length!==60?!1:k5(e,t.substring(0,t.length-31))===t},bi="VUEPRESS_HOPE_GLOBAL_TOKEN",T5=()=>{const e=G1(),t=cn(bi,""),n=cu(bi,""),r=w(()=>{const{global:l=!1,admin:i=[]}=e.value;return l&&i.length>0}),a=w(()=>{if(r.value){if(t.value)return e.value.admin.some(l=>qo(t.value,l));if(n.value)return e.value.admin.some(l=>qo(n.value,l))}return!1});return{isEncrypted:r,isDecrypted:a,validate:(l,i=!1)=>{(i?t:n).value=l}}},ho=(e="",t)=>!!e&&qo(e,t),Ei="VUEPRESS_HOPE_PATH_TOKEN",S5=()=>{const e=ge(),t=G1(),n=cn(Ei,{}),r=cu(Ei,{}),a=c=>qn(t.value.config)?En(t.value.config).filter(u=>Oa(decodeURI(c),u)).sort((u,d)=>d.length-u.length):[],o=c=>{const u=a(c);if(u.length>0){const{config:d={}}=t.value;return{isEncrypted:!0,isDecrypted:u.some(f=>n.value[f]&&d[f].some(p=>ho(n.value[f],p))||r.value[f]&&d[f].some(p=>ho(r.value[f],p)))}}return{isDecrypted:!1,isEncrypted:!1}};return{status:w(()=>o(e.value.path)),getStatus:o,validate:(c,u=!1)=>{const{config:d={}}=t.value,f=a(e.value.path);for(const p of f)if(d[p].filter(h=>ho(c,h))){(u?n:r).value[p]=c;break}}}},x5=M({name:"GlobalEncrypt",slots:Object,setup(e,{slots:t}){const{isDecrypted:n,isEncrypted:r,validate:a}=T5(),o=z(!1);return se(()=>{o.value=!0}),()=>s(Ml,()=>r.value?o.value?n.value?t.default():s(q1,{full:!0,onVerify:a}):null:t.default())}}),L5=M({name:"LocalEncrypt",slots:Object,setup(e,{slots:t}){const{status:n,validate:r}=S5(),a=z(!1);return se(()=>{a.value=!0}),()=>{const{isEncrypted:o,isDecrypted:l}=n.value;return o?a.value?l?t.default():s(q1,{full:!0,onVerify:r}):null:t.default()}}});cp(e=>{const t=e.t,n=e.I!==!1,r=e.i;return n?{title:t,content:r?()=>[s(Ve,{icon:r}),t]:null,order:e.O,index:e.I}:null});const B5=Ze({enhance:({app:e,router:t})=>{const{scrollBehavior:n}=t.options;t.options.scrollBehavior=async(...r)=>(await Mo.wait(),n(...r)),j6(e),e.component("HopeIcon",Ve),e.component("BloggerInfo",Nl),e.component("GlobalEncrypt",x5),e.component("LocalEncrypt",L5)},setup:()=>{z6(),W6(),y8()},layouts:{Layout:G8,NotFound:W8,BlogCategory:X8,BlogHome:V1,BlogType:d5,PortfolioHome:j1,Timeline:z1}});var I5={models:[{path:"https://model.oml2d.com/HK416-1-normal/model.json",position:[0,60],scale:.08,stageStyle:{height:450}}]};const P5={setup:()=>{se(()=>{T(()=>import("./index-BNnYFWcz.js"),[]).then(({loadOml2d:e})=>e(I5))})}},D5=M({__name:"IndexLayout",setup(e){return(t,n)=>null}}),O5=Fl(D5,[["__file","IndexLayout.vue"]]),_i=1e3*60*60*24,M5=(e,t={"/":"Running time: :day days :hour hours :minute minutes :second seconds"},n=!1)=>{const r=(e instanceof Date?e:new Date(e)).getTime();let a="";const o=ge(),l=U3(),i=Ye(),c=w(()=>{const u=l.value.getTime()-r,d=new Date(u%_i);return{day:Math.floor(u/_i),hour:d.getHours(),minute:d.getMinutes(),second:d.getSeconds()}});se(()=>{ae(()=>[o.value.path,c.value],()=>{const u=document.querySelector(".vp-footer");if(u){const{day:d,hour:f,minute:p,second:h}=c.value,v=(t[i.value]||t["/"]).replace(":day",d.toString()).replace(":hour",f.toString()).replace(":minute",p.toString()).replace(":second",h.toString());u.innerHTML=`${n?`${u.innerHTML.replace(`<br>${a}`,"")}<br>`:""}${v}`,a=v}},{flush:"post",immediate:!0})})},R5=Ze({layouts:{IndexLayout:O5},setup(){M5(new Date("2024-05-08"),{"/":"Running time: :day days :hour hours :minute minutes :second seconds","/zh/":"已运行 :day 天 :hour 小时 :minute 分钟 :second 秒"},!0)}}),oa=[e3,Y3,rp,hp,Ep,Cp,xp,Dp,Vp,Zp,q4,a6,B6,B5,P5,R5],$5=JSON.parse('{"base":"/","lang":"zh-CN","title":"blog","description":"KSJ-blog","head":[],"locales":{}}');var er=xe($5),F5=bf,H5=()=>{const e=qf({history:F5(pl("/")),routes:[{name:"vuepress-route",path:"/:catchAll(.*)",components:{}}],scrollBehavior:(t,n,r)=>r||(t.hash?{el:t.hash}:{top:0})});return e.beforeResolve(async(t,n)=>{if(t.path!==n.path||n===Ot){const r=xt(t.path);if(r.path!==t.path)return r.path;const a=await r.loader();t.meta={...r.meta,_pageChunk:a}}else t.path===n.path&&(t.meta=n.meta)}),e},N5=e=>{e.component("ClientOnly",Or),e.component("Content",Uc),e.component("RouteLink",Ie)},V5=(e,t,n)=>{const r=w(()=>t.currentRoute.value.path),a=rl((E,b)=>({get(){return E(),t.currentRoute.value.meta._pageChunk},set(C){t.currentRoute.value.meta._pageChunk=C,b()}})),o=w(()=>pn.resolveLayouts(n)),l=w(()=>pn.resolveRouteLocale(er.value.locales,r.value)),i=w(()=>pn.resolveSiteLocaleData(er.value,l.value)),c=w(()=>a.value.comp),u=w(()=>a.value.data),d=w(()=>u.value.frontmatter),f=w(()=>pn.resolvePageHeadTitle(u.value,i.value)),p=w(()=>pn.resolvePageHead(f.value,d.value,i.value)),h=w(()=>pn.resolvePageLang(u.value,i.value)),v=w(()=>pn.resolvePageLayout(u.value,o.value)),_={layouts:o,pageData:u,pageComponent:c,pageFrontmatter:d,pageHead:p,pageHeadTitle:f,pageLang:h,pageLayout:v,redirects:xo,routeLocale:l,routePath:r,routes:_r,siteData:er,siteLocaleData:i};return e.provide(vl,_),Object.defineProperties(e.config.globalProperties,{$frontmatter:{get:()=>d.value},$head:{get:()=>p.value},$headTitle:{get:()=>f.value},$lang:{get:()=>h.value},$page:{get:()=>u.value},$routeLocale:{get:()=>l.value},$site:{get:()=>er.value},$siteLocale:{get:()=>i.value},$withBase:{get:()=>be}}),_},j5=()=>{const e=Wf(),t=Pa();let n=[];const r=()=>{e.value.forEach(l=>{const i=z5(l);i&&n.push(i)})},a=()=>{const l=[];return e.value.forEach(i=>{const c=q5(i);c&&l.push(c)}),l},o=()=>{document.documentElement.lang=t.value;const l=a();n.forEach((i,c)=>{const u=l.findIndex(d=>i.isEqualNode(d));u===-1?(i.remove(),delete n[c]):l.splice(u,1)}),l.forEach(i=>document.head.appendChild(i)),n=[...n.filter(i=>!!i),...l]};ht(Qf,o),se(()=>{r(),ae(e,o,{immediate:!1})})},z5=([e,t,n=""])=>{const r=Object.entries(t).map(([i,c])=>we(c)?`[${i}=${JSON.stringify(c)}]`:c===!0?`[${i}]`:"").join(""),a=`head > ${e}${r}`;return Array.from(document.querySelectorAll(a)).find(i=>i.innerText===n)||null},q5=([e,t,n])=>{if(!we(e))return null;const r=document.createElement(e);return qn(t)&&Object.entries(t).forEach(([a,o])=>{we(o)?r.setAttribute(a,o):o===!0&&r.setAttribute(a,"")}),we(n)&&r.appendChild(document.createTextNode(n)),r},G5=Td,U5=async()=>{var n;const e=G5({name:"Vuepress",setup(){var o;j5();for(const l of oa)(o=l.setup)==null||o.call(l);const r=oa.flatMap(({rootComponents:l=[]})=>l.map(i=>s(i))),a=Kf();return()=>[s(a.value),r]}}),t=H5();N5(e),V5(e,t,oa);for(const r of oa)await((n=r.enhance)==null?void 0:n.call(r,{app:e,router:t,siteData:er}));return e.use(t),{app:e,router:t}};U5().then(({app:e,router:t})=>{t.isReady().then(()=>{e.mount("#app")})});export{xe as A,se as B,qu as C,m6 as D,Ft as E,Y5 as F,qn as G,c6 as H,d6 as I,ru as J,ba as K,we as L,T as M,xl as P,Ie as R,Fl as _,R0 as a,Ec as b,W5 as c,U5 as createVueApp,Te as d,wc as e,K5 as f,M as g,wn as h,Ye as i,Tl as j,Lr as k,z as l,w as m,Se as n,cl as o,ae as p,s as q,pt as r,Vu as s,zn as t,J5 as u,u6 as v,pa as w,s6 as x,i6 as y,ge as z};
diff --git a/assets/arc-BCmLGSVu.js b/assets/arc-DWlpCdAw.js
similarity index 96%
rename from assets/arc-BCmLGSVu.js
rename to assets/arc-DWlpCdAw.js
index 853582f..2c37815 100644
--- a/assets/arc-BCmLGSVu.js
+++ b/assets/arc-DWlpCdAw.js
@@ -1 +1 @@
-import{w as ln,c as U}from"./path-CbwjOpE9.js";import{aO as an,aP as Y,aQ as O,aR as rn,aS as y,aK as on,aT as z,aU as _,aV as un,aW as t,aX as sn,aY as tn,aZ as fn}from"./mermaid.core-ChLYKTZm.js";function cn(l){return l.innerRadius}function yn(l){return l.outerRadius}function gn(l){return l.startAngle}function mn(l){return l.endAngle}function pn(l){return l&&l.padAngle}function dn(l,h,D,S,v,R,V,a){var E=D-l,i=S-h,n=V-v,m=a-R,r=m*E-n*i;if(!(r*r<y))return r=(n*(h-R)-m*(l-v))/r,[l+r*E,h+r*i]}function J(l,h,D,S,v,R,V){var a=l-D,E=h-S,i=(V?R:-R)/z(a*a+E*E),n=i*E,m=-i*a,r=l+n,s=h+m,f=D+n,c=S+m,W=(r+f)/2,o=(s+c)/2,p=f-r,g=c-s,A=p*p+g*g,T=v-R,P=r*c-f*s,I=(g<0?-1:1)*z(fn(0,T*T*A-P*P)),K=(P*g-p*I)/A,Q=(-P*p-g*I)/A,w=(P*g+p*I)/A,d=(-P*p+g*I)/A,x=K-W,e=Q-o,u=w-W,X=d-o;return x*x+e*e>u*u+X*X&&(K=w,Q=d),{cx:K,cy:Q,x01:-n,y01:-m,x11:K*(v/T-1),y11:Q*(v/T-1)}}function vn(){var l=cn,h=yn,D=U(0),S=null,v=gn,R=mn,V=pn,a=null,E=ln(i);function i(){var n,m,r=+l.apply(this,arguments),s=+h.apply(this,arguments),f=v.apply(this,arguments)-rn,c=R.apply(this,arguments)-rn,W=un(c-f),o=c>f;if(a||(a=n=E()),s<r&&(m=s,s=r,r=m),!(s>y))a.moveTo(0,0);else if(W>on-y)a.moveTo(s*Y(f),s*O(f)),a.arc(0,0,s,f,c,!o),r>y&&(a.moveTo(r*Y(c),r*O(c)),a.arc(0,0,r,c,f,o));else{var p=f,g=c,A=f,T=c,P=W,I=W,K=V.apply(this,arguments)/2,Q=K>y&&(S?+S.apply(this,arguments):z(r*r+s*s)),w=_(un(s-r)/2,+D.apply(this,arguments)),d=w,x=w,e,u;if(Q>y){var X=sn(Q/r*O(K)),B=sn(Q/s*O(K));(P-=X*2)>y?(X*=o?1:-1,A+=X,T-=X):(P=0,A=T=(f+c)/2),(I-=B*2)>y?(B*=o?1:-1,p+=B,g-=B):(I=0,p=g=(f+c)/2)}var Z=s*Y(p),j=s*O(p),C=r*Y(T),F=r*O(T);if(w>y){var G=s*Y(g),H=s*O(g),L=r*Y(A),M=r*O(A),q;if(W<an)if(q=dn(Z,j,L,M,G,H,C,F)){var N=Z-q[0],$=j-q[1],k=G-q[0],b=H-q[1],nn=1/O(tn((N*k+$*b)/(z(N*N+$*$)*z(k*k+b*b)))/2),en=z(q[0]*q[0]+q[1]*q[1]);d=_(w,(r-en)/(nn-1)),x=_(w,(s-en)/(nn+1))}else d=x=0}I>y?x>y?(e=J(L,M,Z,j,s,x,o),u=J(G,H,C,F,s,x,o),a.moveTo(e.cx+e.x01,e.cy+e.y01),x<w?a.arc(e.cx,e.cy,x,t(e.y01,e.x01),t(u.y01,u.x01),!o):(a.arc(e.cx,e.cy,x,t(e.y01,e.x01),t(e.y11,e.x11),!o),a.arc(0,0,s,t(e.cy+e.y11,e.cx+e.x11),t(u.cy+u.y11,u.cx+u.x11),!o),a.arc(u.cx,u.cy,x,t(u.y11,u.x11),t(u.y01,u.x01),!o))):(a.moveTo(Z,j),a.arc(0,0,s,p,g,!o)):a.moveTo(Z,j),!(r>y)||!(P>y)?a.lineTo(C,F):d>y?(e=J(C,F,G,H,r,-d,o),u=J(Z,j,L,M,r,-d,o),a.lineTo(e.cx+e.x01,e.cy+e.y01),d<w?a.arc(e.cx,e.cy,d,t(e.y01,e.x01),t(u.y01,u.x01),!o):(a.arc(e.cx,e.cy,d,t(e.y01,e.x01),t(e.y11,e.x11),!o),a.arc(0,0,r,t(e.cy+e.y11,e.cx+e.x11),t(u.cy+u.y11,u.cx+u.x11),o),a.arc(u.cx,u.cy,d,t(u.y11,u.x11),t(u.y01,u.x01),!o))):a.arc(0,0,r,T,A,o)}if(a.closePath(),n)return a=null,n+""||null}return i.centroid=function(){var n=(+l.apply(this,arguments)+ +h.apply(this,arguments))/2,m=(+v.apply(this,arguments)+ +R.apply(this,arguments))/2-an/2;return[Y(m)*n,O(m)*n]},i.innerRadius=function(n){return arguments.length?(l=typeof n=="function"?n:U(+n),i):l},i.outerRadius=function(n){return arguments.length?(h=typeof n=="function"?n:U(+n),i):h},i.cornerRadius=function(n){return arguments.length?(D=typeof n=="function"?n:U(+n),i):D},i.padRadius=function(n){return arguments.length?(S=n==null?null:typeof n=="function"?n:U(+n),i):S},i.startAngle=function(n){return arguments.length?(v=typeof n=="function"?n:U(+n),i):v},i.endAngle=function(n){return arguments.length?(R=typeof n=="function"?n:U(+n),i):R},i.padAngle=function(n){return arguments.length?(V=typeof n=="function"?n:U(+n),i):V},i.context=function(n){return arguments.length?(a=n??null,i):a},i}export{vn as a};
+import{w as ln,c as U}from"./path-CbwjOpE9.js";import{aO as an,aP as Y,aQ as O,aR as rn,aS as y,aK as on,aT as z,aU as _,aV as un,aW as t,aX as sn,aY as tn,aZ as fn}from"./mermaid.core-DNo_7Q2B.js";function cn(l){return l.innerRadius}function yn(l){return l.outerRadius}function gn(l){return l.startAngle}function mn(l){return l.endAngle}function pn(l){return l&&l.padAngle}function dn(l,h,D,S,v,R,V,a){var E=D-l,i=S-h,n=V-v,m=a-R,r=m*E-n*i;if(!(r*r<y))return r=(n*(h-R)-m*(l-v))/r,[l+r*E,h+r*i]}function J(l,h,D,S,v,R,V){var a=l-D,E=h-S,i=(V?R:-R)/z(a*a+E*E),n=i*E,m=-i*a,r=l+n,s=h+m,f=D+n,c=S+m,W=(r+f)/2,o=(s+c)/2,p=f-r,g=c-s,A=p*p+g*g,T=v-R,P=r*c-f*s,I=(g<0?-1:1)*z(fn(0,T*T*A-P*P)),K=(P*g-p*I)/A,Q=(-P*p-g*I)/A,w=(P*g+p*I)/A,d=(-P*p+g*I)/A,x=K-W,e=Q-o,u=w-W,X=d-o;return x*x+e*e>u*u+X*X&&(K=w,Q=d),{cx:K,cy:Q,x01:-n,y01:-m,x11:K*(v/T-1),y11:Q*(v/T-1)}}function vn(){var l=cn,h=yn,D=U(0),S=null,v=gn,R=mn,V=pn,a=null,E=ln(i);function i(){var n,m,r=+l.apply(this,arguments),s=+h.apply(this,arguments),f=v.apply(this,arguments)-rn,c=R.apply(this,arguments)-rn,W=un(c-f),o=c>f;if(a||(a=n=E()),s<r&&(m=s,s=r,r=m),!(s>y))a.moveTo(0,0);else if(W>on-y)a.moveTo(s*Y(f),s*O(f)),a.arc(0,0,s,f,c,!o),r>y&&(a.moveTo(r*Y(c),r*O(c)),a.arc(0,0,r,c,f,o));else{var p=f,g=c,A=f,T=c,P=W,I=W,K=V.apply(this,arguments)/2,Q=K>y&&(S?+S.apply(this,arguments):z(r*r+s*s)),w=_(un(s-r)/2,+D.apply(this,arguments)),d=w,x=w,e,u;if(Q>y){var X=sn(Q/r*O(K)),B=sn(Q/s*O(K));(P-=X*2)>y?(X*=o?1:-1,A+=X,T-=X):(P=0,A=T=(f+c)/2),(I-=B*2)>y?(B*=o?1:-1,p+=B,g-=B):(I=0,p=g=(f+c)/2)}var Z=s*Y(p),j=s*O(p),C=r*Y(T),F=r*O(T);if(w>y){var G=s*Y(g),H=s*O(g),L=r*Y(A),M=r*O(A),q;if(W<an)if(q=dn(Z,j,L,M,G,H,C,F)){var N=Z-q[0],$=j-q[1],k=G-q[0],b=H-q[1],nn=1/O(tn((N*k+$*b)/(z(N*N+$*$)*z(k*k+b*b)))/2),en=z(q[0]*q[0]+q[1]*q[1]);d=_(w,(r-en)/(nn-1)),x=_(w,(s-en)/(nn+1))}else d=x=0}I>y?x>y?(e=J(L,M,Z,j,s,x,o),u=J(G,H,C,F,s,x,o),a.moveTo(e.cx+e.x01,e.cy+e.y01),x<w?a.arc(e.cx,e.cy,x,t(e.y01,e.x01),t(u.y01,u.x01),!o):(a.arc(e.cx,e.cy,x,t(e.y01,e.x01),t(e.y11,e.x11),!o),a.arc(0,0,s,t(e.cy+e.y11,e.cx+e.x11),t(u.cy+u.y11,u.cx+u.x11),!o),a.arc(u.cx,u.cy,x,t(u.y11,u.x11),t(u.y01,u.x01),!o))):(a.moveTo(Z,j),a.arc(0,0,s,p,g,!o)):a.moveTo(Z,j),!(r>y)||!(P>y)?a.lineTo(C,F):d>y?(e=J(C,F,G,H,r,-d,o),u=J(Z,j,L,M,r,-d,o),a.lineTo(e.cx+e.x01,e.cy+e.y01),d<w?a.arc(e.cx,e.cy,d,t(e.y01,e.x01),t(u.y01,u.x01),!o):(a.arc(e.cx,e.cy,d,t(e.y01,e.x01),t(e.y11,e.x11),!o),a.arc(0,0,r,t(e.cy+e.y11,e.cx+e.x11),t(u.cy+u.y11,u.cx+u.x11),o),a.arc(u.cx,u.cy,d,t(u.y11,u.x11),t(u.y01,u.x01),!o))):a.arc(0,0,r,T,A,o)}if(a.closePath(),n)return a=null,n+""||null}return i.centroid=function(){var n=(+l.apply(this,arguments)+ +h.apply(this,arguments))/2,m=(+v.apply(this,arguments)+ +R.apply(this,arguments))/2-an/2;return[Y(m)*n,O(m)*n]},i.innerRadius=function(n){return arguments.length?(l=typeof n=="function"?n:U(+n),i):l},i.outerRadius=function(n){return arguments.length?(h=typeof n=="function"?n:U(+n),i):h},i.cornerRadius=function(n){return arguments.length?(D=typeof n=="function"?n:U(+n),i):D},i.padRadius=function(n){return arguments.length?(S=n==null?null:typeof n=="function"?n:U(+n),i):S},i.startAngle=function(n){return arguments.length?(v=typeof n=="function"?n:U(+n),i):v},i.endAngle=function(n){return arguments.length?(R=typeof n=="function"?n:U(+n),i):R},i.padAngle=function(n){return arguments.length?(V=typeof n=="function"?n:U(+n),i):V},i.context=function(n){return arguments.length?(a=n??null,i):a},i}export{vn as a};
diff --git a/assets/blockDiagram-a8a0820c-1CGnBiz2.js b/assets/blockDiagram-a8a0820c-DvOSxzpN.js
similarity index 98%
rename from assets/blockDiagram-a8a0820c-1CGnBiz2.js
rename to assets/blockDiagram-a8a0820c-DvOSxzpN.js
index d0e29eb..8bf416c 100644
--- a/assets/blockDiagram-a8a0820c-1CGnBiz2.js
+++ b/assets/blockDiagram-a8a0820c-DvOSxzpN.js
@@ -1,4 +1,4 @@
-import{c as he,a$ as se,h as H,i as ye,l as S,A as Ee,af as we,j as De,p as ve}from"./mermaid.core-ChLYKTZm.js";import{c as Ne}from"./clone-CI3kFeqi.js";import{i as ke,c as Ie,b as Oe,d as Te,a as ge,p as ze}from"./edges-5962ec63-B19hLEst.js";import{G as Ce}from"./graph-T5JS4vfK.js";import{o as Ae}from"./ordinal-Cboi1Yqb.js";import{c as Re}from"./channel-DJsAcM5I.js";import{s as Be}from"./Tableau10-B-NsZVaP.js";import"./app-B69Gl_S-.js";import"./createText-4a4f35c9-BuT3nXUz.js";import"./line-D0jG_HZ-.js";import"./array-BKyUJesY.js";import"./path-CbwjOpE9.js";import"./init-Gi6I4Gst.js";var le,oe,ee=function(){var e=function(D,o,s,i){for(s=s||{},i=D.length;i--;s[D[i]]=o);return s},a=[1,7],d=[1,13],c=[1,14],n=[1,15],g=[1,19],l=[1,16],f=[1,17],b=[1,18],p=[8,30],x=[8,21,28,29,30,31,32,40,44,47],y=[1,23],T=[1,24],v=[8,15,16,21,28,29,30,31,32,40,44,47],N=[8,15,16,21,27,28,29,30,31,32,40,44,47],E=[1,49],L={trace:function(){},yy:{},symbols_:{error:2,spaceLines:3,SPACELINE:4,NL:5,separator:6,SPACE:7,EOF:8,start:9,BLOCK_DIAGRAM_KEY:10,document:11,stop:12,statement:13,link:14,LINK:15,START_LINK:16,LINK_LABEL:17,STR:18,nodeStatement:19,columnsStatement:20,SPACE_BLOCK:21,blockStatement:22,classDefStatement:23,cssClassStatement:24,styleStatement:25,node:26,SIZE:27,COLUMNS:28,"id-block":29,end:30,block:31,NODE_ID:32,nodeShapeNLabel:33,dirList:34,DIR:35,NODE_DSTART:36,NODE_DEND:37,BLOCK_ARROW_START:38,BLOCK_ARROW_END:39,classDef:40,CLASSDEF_ID:41,CLASSDEF_STYLEOPTS:42,DEFAULT:43,class:44,CLASSENTITY_IDS:45,STYLECLASS:46,style:47,STYLE_ENTITY_IDS:48,STYLE_DEFINITION_DATA:49,$accept:0,$end:1},terminals_:{2:"error",4:"SPACELINE",5:"NL",7:"SPACE",8:"EOF",10:"BLOCK_DIAGRAM_KEY",15:"LINK",16:"START_LINK",17:"LINK_LABEL",18:"STR",21:"SPACE_BLOCK",27:"SIZE",28:"COLUMNS",29:"id-block",30:"end",31:"block",32:"NODE_ID",35:"DIR",36:"NODE_DSTART",37:"NODE_DEND",38:"BLOCK_ARROW_START",39:"BLOCK_ARROW_END",40:"classDef",41:"CLASSDEF_ID",42:"CLASSDEF_STYLEOPTS",43:"DEFAULT",44:"class",45:"CLASSENTITY_IDS",46:"STYLECLASS",47:"style",48:"STYLE_ENTITY_IDS",49:"STYLE_DEFINITION_DATA"},productions_:[0,[3,1],[3,2],[3,2],[6,1],[6,1],[6,1],[9,3],[12,1],[12,1],[12,2],[12,2],[11,1],[11,2],[14,1],[14,4],[13,1],[13,1],[13,1],[13,1],[13,1],[13,1],[13,1],[19,3],[19,2],[19,1],[20,1],[22,4],[22,3],[26,1],[26,2],[34,1],[34,2],[33,3],[33,4],[23,3],[23,3],[24,3],[25,3]],performAction:function(o,s,i,u,h,t,m){var r=t.length-1;switch(h){case 4:u.getLogger().debug("Rule: separator (NL) ");break;case 5:u.getLogger().debug("Rule: separator (Space) ");break;case 6:u.getLogger().debug("Rule: separator (EOF) ");break;case 7:u.getLogger().debug("Rule: hierarchy: ",t[r-1]),u.setHierarchy(t[r-1]);break;case 8:u.getLogger().debug("Stop NL ");break;case 9:u.getLogger().debug("Stop EOF ");break;case 10:u.getLogger().debug("Stop NL2 ");break;case 11:u.getLogger().debug("Stop EOF2 ");break;case 12:u.getLogger().debug("Rule: statement: ",t[r]),typeof t[r].length=="number"?this.$=t[r]:this.$=[t[r]];break;case 13:u.getLogger().debug("Rule: statement #2: ",t[r-1]),this.$=[t[r-1]].concat(t[r]);break;case 14:u.getLogger().debug("Rule: link: ",t[r],o),this.$={edgeTypeStr:t[r],label:""};break;case 15:u.getLogger().debug("Rule: LABEL link: ",t[r-3],t[r-1],t[r]),this.$={edgeTypeStr:t[r],label:t[r-1]};break;case 18:const R=parseInt(t[r]),Y=u.generateId();this.$={id:Y,type:"space",label:"",width:R,children:[]};break;case 23:u.getLogger().debug("Rule: (nodeStatement link node) ",t[r-2],t[r-1],t[r]," typestr: ",t[r-1].edgeTypeStr);const F=u.edgeStrToEdgeData(t[r-1].edgeTypeStr);this.$=[{id:t[r-2].id,label:t[r-2].label,type:t[r-2].type,directions:t[r-2].directions},{id:t[r-2].id+"-"+t[r].id,start:t[r-2].id,end:t[r].id,label:t[r-1].label,type:"edge",directions:t[r].directions,arrowTypeEnd:F,arrowTypeStart:"arrow_open"},{id:t[r].id,label:t[r].label,type:u.typeStr2Type(t[r].typeStr),directions:t[r].directions}];break;case 24:u.getLogger().debug("Rule: nodeStatement (abc88 node size) ",t[r-1],t[r]),this.$={id:t[r-1].id,label:t[r-1].label,type:u.typeStr2Type(t[r-1].typeStr),directions:t[r-1].directions,widthInColumns:parseInt(t[r],10)};break;case 25:u.getLogger().debug("Rule: nodeStatement (node) ",t[r]),this.$={id:t[r].id,label:t[r].label,type:u.typeStr2Type(t[r].typeStr),directions:t[r].directions,widthInColumns:1};break;case 26:u.getLogger().debug("APA123",this?this:"na"),u.getLogger().debug("COLUMNS: ",t[r]),this.$={type:"column-setting",columns:t[r]==="auto"?-1:parseInt(t[r])};break;case 27:u.getLogger().debug("Rule: id-block statement : ",t[r-2],t[r-1]),u.generateId(),this.$={...t[r-2],type:"composite",children:t[r-1]};break;case 28:u.getLogger().debug("Rule: blockStatement : ",t[r-2],t[r-1],t[r]);const C=u.generateId();this.$={id:C,type:"composite",label:"",children:t[r-1]};break;case 29:u.getLogger().debug("Rule: node (NODE_ID separator): ",t[r]),this.$={id:t[r]};break;case 30:u.getLogger().debug("Rule: node (NODE_ID nodeShapeNLabel separator): ",t[r-1],t[r]),this.$={id:t[r-1],label:t[r].label,typeStr:t[r].typeStr,directions:t[r].directions};break;case 31:u.getLogger().debug("Rule: dirList: ",t[r]),this.$=[t[r]];break;case 32:u.getLogger().debug("Rule: dirList: ",t[r-1],t[r]),this.$=[t[r-1]].concat(t[r]);break;case 33:u.getLogger().debug("Rule: nodeShapeNLabel: ",t[r-2],t[r-1],t[r]),this.$={typeStr:t[r-2]+t[r],label:t[r-1]};break;case 34:u.getLogger().debug("Rule: BLOCK_ARROW nodeShapeNLabel: ",t[r-3],t[r-2]," #3:",t[r-1],t[r]),this.$={typeStr:t[r-3]+t[r],label:t[r-2],directions:t[r-1]};break;case 35:case 36:this.$={type:"classDef",id:t[r-1].trim(),css:t[r].trim()};break;case 37:this.$={type:"applyClass",id:t[r-1].trim(),styleClass:t[r].trim()};break;case 38:this.$={type:"applyStyles",id:t[r-1].trim(),stylesStr:t[r].trim()};break}},table:[{9:1,10:[1,2]},{1:[3]},{11:3,13:4,19:5,20:6,21:a,22:8,23:9,24:10,25:11,26:12,28:d,29:c,31:n,32:g,40:l,44:f,47:b},{8:[1,20]},e(p,[2,12],{13:4,19:5,20:6,22:8,23:9,24:10,25:11,26:12,11:21,21:a,28:d,29:c,31:n,32:g,40:l,44:f,47:b}),e(x,[2,16],{14:22,15:y,16:T}),e(x,[2,17]),e(x,[2,18]),e(x,[2,19]),e(x,[2,20]),e(x,[2,21]),e(x,[2,22]),e(v,[2,25],{27:[1,25]}),e(x,[2,26]),{19:26,26:12,32:g},{11:27,13:4,19:5,20:6,21:a,22:8,23:9,24:10,25:11,26:12,28:d,29:c,31:n,32:g,40:l,44:f,47:b},{41:[1,28],43:[1,29]},{45:[1,30]},{48:[1,31]},e(N,[2,29],{33:32,36:[1,33],38:[1,34]}),{1:[2,7]},e(p,[2,13]),{26:35,32:g},{32:[2,14]},{17:[1,36]},e(v,[2,24]),{11:37,13:4,14:22,15:y,16:T,19:5,20:6,21:a,22:8,23:9,24:10,25:11,26:12,28:d,29:c,31:n,32:g,40:l,44:f,47:b},{30:[1,38]},{42:[1,39]},{42:[1,40]},{46:[1,41]},{49:[1,42]},e(N,[2,30]),{18:[1,43]},{18:[1,44]},e(v,[2,23]),{18:[1,45]},{30:[1,46]},e(x,[2,28]),e(x,[2,35]),e(x,[2,36]),e(x,[2,37]),e(x,[2,38]),{37:[1,47]},{34:48,35:E},{15:[1,50]},e(x,[2,27]),e(N,[2,33]),{39:[1,51]},{34:52,35:E,39:[2,31]},{32:[2,15]},e(N,[2,34]),{39:[2,32]}],defaultActions:{20:[2,7],23:[2,14],50:[2,15],52:[2,32]},parseError:function(o,s){if(s.recoverable)this.trace(o);else{var i=new Error(o);throw i.hash=s,i}},parse:function(o){var s=this,i=[0],u=[],h=[null],t=[],m=this.table,r="",R=0,Y=0,F=2,C=1,Le=t.slice.call(arguments,1),w=Object.create(this.lexer),K={yy:{}};for(var Z in this.yy)Object.prototype.hasOwnProperty.call(this.yy,Z)&&(K.yy[Z]=this.yy[Z]);w.setInput(o,K.yy),K.yy.lexer=w,K.yy.parser=this,typeof w.yylloc>"u"&&(w.yylloc={});var J=w.yylloc;t.push(J);var me=w.options&&w.options.ranges;typeof K.yy.parseError=="function"?this.parseError=K.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function _e(){var P;return P=u.pop()||w.lex()||C,typeof P!="number"&&(P instanceof Array&&(u=P,P=u.pop()),P=s.symbols_[P]||P),P}for(var I,M,z,Q,W={},X,B,ae,G;;){if(M=i[i.length-1],this.defaultActions[M]?z=this.defaultActions[M]:((I===null||typeof I>"u")&&(I=_e()),z=m[M]&&m[M][I]),typeof z>"u"||!z.length||!z[0]){var $="";G=[];for(X in m[M])this.terminals_[X]&&X>F&&G.push("'"+this.terminals_[X]+"'");w.showPosition?$="Parse error on line "+(R+1)+`:
+import{c as he,a$ as se,h as H,i as ye,l as S,A as Ee,af as we,j as De,p as ve}from"./mermaid.core-DNo_7Q2B.js";import{c as Ne}from"./clone-C3EvpqoY.js";import{i as ke,c as Ie,b as Oe,d as Te,a as ge,p as ze}from"./edges-5962ec63-ApWhby2b.js";import{G as Ce}from"./graph-B1296pfd.js";import{o as Ae}from"./ordinal-Cboi1Yqb.js";import{c as Re}from"./channel-yU22lAlC.js";import{s as Be}from"./Tableau10-B-NsZVaP.js";import"./app-B4LGNJZ0.js";import"./createText-4a4f35c9-CISzj231.js";import"./line-BqHmcuby.js";import"./array-BKyUJesY.js";import"./path-CbwjOpE9.js";import"./init-Gi6I4Gst.js";var le,oe,ee=function(){var e=function(D,o,s,i){for(s=s||{},i=D.length;i--;s[D[i]]=o);return s},a=[1,7],d=[1,13],c=[1,14],n=[1,15],g=[1,19],l=[1,16],f=[1,17],b=[1,18],p=[8,30],x=[8,21,28,29,30,31,32,40,44,47],y=[1,23],T=[1,24],v=[8,15,16,21,28,29,30,31,32,40,44,47],N=[8,15,16,21,27,28,29,30,31,32,40,44,47],E=[1,49],L={trace:function(){},yy:{},symbols_:{error:2,spaceLines:3,SPACELINE:4,NL:5,separator:6,SPACE:7,EOF:8,start:9,BLOCK_DIAGRAM_KEY:10,document:11,stop:12,statement:13,link:14,LINK:15,START_LINK:16,LINK_LABEL:17,STR:18,nodeStatement:19,columnsStatement:20,SPACE_BLOCK:21,blockStatement:22,classDefStatement:23,cssClassStatement:24,styleStatement:25,node:26,SIZE:27,COLUMNS:28,"id-block":29,end:30,block:31,NODE_ID:32,nodeShapeNLabel:33,dirList:34,DIR:35,NODE_DSTART:36,NODE_DEND:37,BLOCK_ARROW_START:38,BLOCK_ARROW_END:39,classDef:40,CLASSDEF_ID:41,CLASSDEF_STYLEOPTS:42,DEFAULT:43,class:44,CLASSENTITY_IDS:45,STYLECLASS:46,style:47,STYLE_ENTITY_IDS:48,STYLE_DEFINITION_DATA:49,$accept:0,$end:1},terminals_:{2:"error",4:"SPACELINE",5:"NL",7:"SPACE",8:"EOF",10:"BLOCK_DIAGRAM_KEY",15:"LINK",16:"START_LINK",17:"LINK_LABEL",18:"STR",21:"SPACE_BLOCK",27:"SIZE",28:"COLUMNS",29:"id-block",30:"end",31:"block",32:"NODE_ID",35:"DIR",36:"NODE_DSTART",37:"NODE_DEND",38:"BLOCK_ARROW_START",39:"BLOCK_ARROW_END",40:"classDef",41:"CLASSDEF_ID",42:"CLASSDEF_STYLEOPTS",43:"DEFAULT",44:"class",45:"CLASSENTITY_IDS",46:"STYLECLASS",47:"style",48:"STYLE_ENTITY_IDS",49:"STYLE_DEFINITION_DATA"},productions_:[0,[3,1],[3,2],[3,2],[6,1],[6,1],[6,1],[9,3],[12,1],[12,1],[12,2],[12,2],[11,1],[11,2],[14,1],[14,4],[13,1],[13,1],[13,1],[13,1],[13,1],[13,1],[13,1],[19,3],[19,2],[19,1],[20,1],[22,4],[22,3],[26,1],[26,2],[34,1],[34,2],[33,3],[33,4],[23,3],[23,3],[24,3],[25,3]],performAction:function(o,s,i,u,h,t,m){var r=t.length-1;switch(h){case 4:u.getLogger().debug("Rule: separator (NL) ");break;case 5:u.getLogger().debug("Rule: separator (Space) ");break;case 6:u.getLogger().debug("Rule: separator (EOF) ");break;case 7:u.getLogger().debug("Rule: hierarchy: ",t[r-1]),u.setHierarchy(t[r-1]);break;case 8:u.getLogger().debug("Stop NL ");break;case 9:u.getLogger().debug("Stop EOF ");break;case 10:u.getLogger().debug("Stop NL2 ");break;case 11:u.getLogger().debug("Stop EOF2 ");break;case 12:u.getLogger().debug("Rule: statement: ",t[r]),typeof t[r].length=="number"?this.$=t[r]:this.$=[t[r]];break;case 13:u.getLogger().debug("Rule: statement #2: ",t[r-1]),this.$=[t[r-1]].concat(t[r]);break;case 14:u.getLogger().debug("Rule: link: ",t[r],o),this.$={edgeTypeStr:t[r],label:""};break;case 15:u.getLogger().debug("Rule: LABEL link: ",t[r-3],t[r-1],t[r]),this.$={edgeTypeStr:t[r],label:t[r-1]};break;case 18:const R=parseInt(t[r]),Y=u.generateId();this.$={id:Y,type:"space",label:"",width:R,children:[]};break;case 23:u.getLogger().debug("Rule: (nodeStatement link node) ",t[r-2],t[r-1],t[r]," typestr: ",t[r-1].edgeTypeStr);const F=u.edgeStrToEdgeData(t[r-1].edgeTypeStr);this.$=[{id:t[r-2].id,label:t[r-2].label,type:t[r-2].type,directions:t[r-2].directions},{id:t[r-2].id+"-"+t[r].id,start:t[r-2].id,end:t[r].id,label:t[r-1].label,type:"edge",directions:t[r].directions,arrowTypeEnd:F,arrowTypeStart:"arrow_open"},{id:t[r].id,label:t[r].label,type:u.typeStr2Type(t[r].typeStr),directions:t[r].directions}];break;case 24:u.getLogger().debug("Rule: nodeStatement (abc88 node size) ",t[r-1],t[r]),this.$={id:t[r-1].id,label:t[r-1].label,type:u.typeStr2Type(t[r-1].typeStr),directions:t[r-1].directions,widthInColumns:parseInt(t[r],10)};break;case 25:u.getLogger().debug("Rule: nodeStatement (node) ",t[r]),this.$={id:t[r].id,label:t[r].label,type:u.typeStr2Type(t[r].typeStr),directions:t[r].directions,widthInColumns:1};break;case 26:u.getLogger().debug("APA123",this?this:"na"),u.getLogger().debug("COLUMNS: ",t[r]),this.$={type:"column-setting",columns:t[r]==="auto"?-1:parseInt(t[r])};break;case 27:u.getLogger().debug("Rule: id-block statement : ",t[r-2],t[r-1]),u.generateId(),this.$={...t[r-2],type:"composite",children:t[r-1]};break;case 28:u.getLogger().debug("Rule: blockStatement : ",t[r-2],t[r-1],t[r]);const C=u.generateId();this.$={id:C,type:"composite",label:"",children:t[r-1]};break;case 29:u.getLogger().debug("Rule: node (NODE_ID separator): ",t[r]),this.$={id:t[r]};break;case 30:u.getLogger().debug("Rule: node (NODE_ID nodeShapeNLabel separator): ",t[r-1],t[r]),this.$={id:t[r-1],label:t[r].label,typeStr:t[r].typeStr,directions:t[r].directions};break;case 31:u.getLogger().debug("Rule: dirList: ",t[r]),this.$=[t[r]];break;case 32:u.getLogger().debug("Rule: dirList: ",t[r-1],t[r]),this.$=[t[r-1]].concat(t[r]);break;case 33:u.getLogger().debug("Rule: nodeShapeNLabel: ",t[r-2],t[r-1],t[r]),this.$={typeStr:t[r-2]+t[r],label:t[r-1]};break;case 34:u.getLogger().debug("Rule: BLOCK_ARROW nodeShapeNLabel: ",t[r-3],t[r-2]," #3:",t[r-1],t[r]),this.$={typeStr:t[r-3]+t[r],label:t[r-2],directions:t[r-1]};break;case 35:case 36:this.$={type:"classDef",id:t[r-1].trim(),css:t[r].trim()};break;case 37:this.$={type:"applyClass",id:t[r-1].trim(),styleClass:t[r].trim()};break;case 38:this.$={type:"applyStyles",id:t[r-1].trim(),stylesStr:t[r].trim()};break}},table:[{9:1,10:[1,2]},{1:[3]},{11:3,13:4,19:5,20:6,21:a,22:8,23:9,24:10,25:11,26:12,28:d,29:c,31:n,32:g,40:l,44:f,47:b},{8:[1,20]},e(p,[2,12],{13:4,19:5,20:6,22:8,23:9,24:10,25:11,26:12,11:21,21:a,28:d,29:c,31:n,32:g,40:l,44:f,47:b}),e(x,[2,16],{14:22,15:y,16:T}),e(x,[2,17]),e(x,[2,18]),e(x,[2,19]),e(x,[2,20]),e(x,[2,21]),e(x,[2,22]),e(v,[2,25],{27:[1,25]}),e(x,[2,26]),{19:26,26:12,32:g},{11:27,13:4,19:5,20:6,21:a,22:8,23:9,24:10,25:11,26:12,28:d,29:c,31:n,32:g,40:l,44:f,47:b},{41:[1,28],43:[1,29]},{45:[1,30]},{48:[1,31]},e(N,[2,29],{33:32,36:[1,33],38:[1,34]}),{1:[2,7]},e(p,[2,13]),{26:35,32:g},{32:[2,14]},{17:[1,36]},e(v,[2,24]),{11:37,13:4,14:22,15:y,16:T,19:5,20:6,21:a,22:8,23:9,24:10,25:11,26:12,28:d,29:c,31:n,32:g,40:l,44:f,47:b},{30:[1,38]},{42:[1,39]},{42:[1,40]},{46:[1,41]},{49:[1,42]},e(N,[2,30]),{18:[1,43]},{18:[1,44]},e(v,[2,23]),{18:[1,45]},{30:[1,46]},e(x,[2,28]),e(x,[2,35]),e(x,[2,36]),e(x,[2,37]),e(x,[2,38]),{37:[1,47]},{34:48,35:E},{15:[1,50]},e(x,[2,27]),e(N,[2,33]),{39:[1,51]},{34:52,35:E,39:[2,31]},{32:[2,15]},e(N,[2,34]),{39:[2,32]}],defaultActions:{20:[2,7],23:[2,14],50:[2,15],52:[2,32]},parseError:function(o,s){if(s.recoverable)this.trace(o);else{var i=new Error(o);throw i.hash=s,i}},parse:function(o){var s=this,i=[0],u=[],h=[null],t=[],m=this.table,r="",R=0,Y=0,F=2,C=1,Le=t.slice.call(arguments,1),w=Object.create(this.lexer),K={yy:{}};for(var Z in this.yy)Object.prototype.hasOwnProperty.call(this.yy,Z)&&(K.yy[Z]=this.yy[Z]);w.setInput(o,K.yy),K.yy.lexer=w,K.yy.parser=this,typeof w.yylloc>"u"&&(w.yylloc={});var J=w.yylloc;t.push(J);var me=w.options&&w.options.ranges;typeof K.yy.parseError=="function"?this.parseError=K.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function _e(){var P;return P=u.pop()||w.lex()||C,typeof P!="number"&&(P instanceof Array&&(u=P,P=u.pop()),P=s.symbols_[P]||P),P}for(var I,M,z,Q,W={},X,B,ae,G;;){if(M=i[i.length-1],this.defaultActions[M]?z=this.defaultActions[M]:((I===null||typeof I>"u")&&(I=_e()),z=m[M]&&m[M][I]),typeof z>"u"||!z.length||!z[0]){var $="";G=[];for(X in m[M])this.terminals_[X]&&X>F&&G.push("'"+this.terminals_[X]+"'");w.showPosition?$="Parse error on line "+(R+1)+`:
 `+w.showPosition()+`
 Expecting `+G.join(", ")+", got '"+(this.terminals_[I]||I)+"'":$="Parse error on line "+(R+1)+": Unexpected "+(I==C?"end of input":"'"+(this.terminals_[I]||I)+"'"),this.parseError($,{text:w.match,token:this.terminals_[I]||I,line:w.yylineno,loc:J,expected:G})}if(z[0]instanceof Array&&z.length>1)throw new Error("Parse Error: multiple actions possible at state: "+M+", token: "+I);switch(z[0]){case 1:i.push(I),h.push(w.yytext),t.push(w.yylloc),i.push(z[1]),I=null,Y=w.yyleng,r=w.yytext,R=w.yylineno,J=w.yylloc;break;case 2:if(B=this.productions_[z[1]][1],W.$=h[h.length-B],W._$={first_line:t[t.length-(B||1)].first_line,last_line:t[t.length-1].last_line,first_column:t[t.length-(B||1)].first_column,last_column:t[t.length-1].last_column},me&&(W._$.range=[t[t.length-(B||1)].range[0],t[t.length-1].range[1]]),Q=this.performAction.apply(W,[r,Y,R,K.yy,z[1],h,t].concat(Le)),typeof Q<"u")return Q;B&&(i=i.slice(0,-1*B*2),h=h.slice(0,-1*B),t=t.slice(0,-1*B)),i.push(this.productions_[z[1]][0]),h.push(W.$),t.push(W._$),ae=m[i[i.length-2]][i[i.length-1]],i.push(ae);break;case 3:return!0}}return!0}},A=function(){var D={EOF:1,parseError:function(s,i){if(this.yy.parser)this.yy.parser.parseError(s,i);else throw new Error(s)},setInput:function(o,s){return this.yy=s||this.yy||{},this._input=o,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var o=this._input[0];this.yytext+=o,this.yyleng++,this.offset++,this.match+=o,this.matched+=o;var s=o.match(/(?:\r\n?|\n).*/g);return s?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),o},unput:function(o){var s=o.length,i=o.split(/(?:\r\n?|\n)/g);this._input=o+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-s),this.offset-=s;var u=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),i.length-1&&(this.yylineno-=i.length-1);var h=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:i?(i.length===u.length?this.yylloc.first_column:0)+u[u.length-i.length].length-i[0].length:this.yylloc.first_column-s},this.options.ranges&&(this.yylloc.range=[h[0],h[0]+this.yyleng-s]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){if(this.options.backtrack_lexer)this._backtrack=!0;else return this.parseError("Lexical error on line "+(this.yylineno+1)+`. You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).
 `+this.showPosition(),{text:"",token:null,line:this.yylineno});return this},less:function(o){this.unput(this.match.slice(o))},pastInput:function(){var o=this.matched.substr(0,this.matched.length-this.match.length);return(o.length>20?"...":"")+o.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var o=this.match;return o.length<20&&(o+=this._input.substr(0,20-o.length)),(o.substr(0,20)+(o.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var o=this.pastInput(),s=new Array(o.length+1).join("-");return o+this.upcomingInput()+`
diff --git a/assets/bridge.html-LTDknqB7.js b/assets/bridge.html-DzkNbynT.js
similarity index 99%
rename from assets/bridge.html-LTDknqB7.js
rename to assets/bridge.html-DzkNbynT.js
index 279c178..99f8c29 100644
--- a/assets/bridge.html-LTDknqB7.js
+++ b/assets/bridge.html-DzkNbynT.js
@@ -1,4 +1,4 @@
-import{_ as n,o as s,c as a,a as t,b as p,f as e}from"./app-B69Gl_S-.js";const o={},i=p("p",null,"Bridge 模式在“类的功能层次结构”和“类的实现层次结构”之间搭建桥梁。",-1),l=e(`<h2 id="使用此设计模式的理由" tabindex="-1"><a class="header-anchor" href="#使用此设计模式的理由"><span>使用此设计模式的理由</span></a></h2><p>Bridge 模式的主要目的是将抽象部分与实现部分分离，使它们可以独立变化。这种模式通过组合而不是继承来实现功能的扩展，减少了类之间的耦合度，提高了系统的可扩展性和可维护性。</p><h2 id="类的层次结构的两个作用" tabindex="-1"><a class="header-anchor" href="#类的层次结构的两个作用"><span>类的层次结构的两个作用</span></a></h2><h3 id="增加新功能时" tabindex="-1"><a class="header-anchor" href="#增加新功能时"><span>增加新功能时</span></a></h3><p>假设现在有一个类 <code>Something</code>，当我们想在 <code>Something</code> 中增加新功能时（例如增加一个具体方法），会编写一个 <code>Something</code> 类的子类（派生类），即 <code>SomethingGood</code> 类。这样就构成了一个小小的类层次结构。这就是为了增加新功能而产生的层次结构。</p><p>SomeThing</p><p>----\\ SomeThingGood</p><h3 id="增加新的实现时" tabindex="-1"><a class="header-anchor" href="#增加新的实现时"><span>增加新的实现时</span></a></h3><p>在 Template Method 模式（第 3 章）中，我们学习了抽象类的作用。抽象类声明了一些抽象方法，定义了接口 (API)，然后子类负责实现这些抽象方法。父类的任务是通过声明抽象方法的方式定义接口 (API)，而子类的任务是实现抽象方法。正是由于父类和子类的这种任务分担，我们才可以编写出具有高可替换性的类。</p><p>这里其实也存在层次结构。例如，当子类实现了父类 <code>AbstractClass</code> 类的抽象方法时，它们之间就构成了一个小小的层次结构。</p><p>AbstractClass</p><p>----\\ ConcreteClass</p><p>但是，这里的类的层次结构并非用于增加功能，也就是说，这种层次结构并非用于方便我们增加新的方法。它的真正作用是帮助我们实现任务分担。</p><h3 id="类的层次结构的混杂和分离" tabindex="-1"><a class="header-anchor" href="#类的层次结构的混杂和分离"><span>类的层次结构的混杂和分离</span></a></h3><p>当我们想要编写子类时，就需要先确认自己的意图：“我是要增加功能呢？还是要增加实现呢？”</p><p>当类的层次结构只有一层时，功能层次结构与实现层次结构是混杂在一个层次结构中的。这样很容易使类的层次结构变得复杂，也难以透彻地理解类的层次结构。因为自己难以确定究竟应该在类的哪一个层次结构中去增加子类。</p><p>因此，我们需要将“类的功能层次结构&quot;与“类的实现层次结构&quot;分离为两个独立的类层次结构。当然，如果只是简单地将它们分开，两者之间必然会缺少联系。所以我们还需要在它们之间搭建一座桥梁。本章中要学习的 Bridge 模式的作用就是搭建这座桥梁。</p><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><h3 id="类的一览表" tabindex="-1"><a class="header-anchor" href="#类的一览表"><span>类的一览表</span></a></h3><table><thead><tr><th>在桥的哪一侧</th><th>名字</th><th>说明</th></tr></thead><tbody><tr><td>类的功能层次结构</td><td>Display</td><td>负责“显示”的类</td></tr><tr><td>类的功能层次结构</td><td>CountDisplay</td><td>增加了“只显示规定次数”这一功能的类</td></tr><tr><td>类的实现层次结构</td><td>DisplayImpl</td><td>负责“显示”的类</td></tr><tr><td>类的实现层次结构</td><td>StringDisplayImpl</td><td>“用字符串显示”的类</td></tr><tr><td>主程序</td><td>Main</td><td>试程序行为的类</td></tr></tbody></table><p>Display 类（代码清单 9 · 1 ）的功能是抽象的，负责“显示一些东西&quot;。该类位于“类的功能层次结构&quot;的最上层。在 impl 字段中保存的是实现了 Display 类的具体功能的实例（ impl 是 implementation （实现）的缩写）。该实例通过 Display 类的构造函数被传递给 Display 类，然后保存在字段中，以供后面的处理使用（ impl 字段即是类的两个层次结构的“桥梁&quot;）。</p><p>CountDisplay 类继承了 Display 类的 open、print、close 方法，并使用它们来增加这个新功能。这就是“类的功能层次结构&quot;。</p><img src="https://www.plantuml.com/plantuml/svg/fPBF2i8m3CRlUueSDsGlq9CmBuAWu1FKhMYXVqQREcNuxcRLokhmvAMGNzBa-zAkFNA7GQkYLTnxs4ZVAtw7iG2eGUfUiSIs511TfRXSPAkOjhqmPSNWQcKNGU-amOoqodgHaUxTCx57yHRKs60mgH8t5ARxg1pZrNd5BqqwA9If1gKMde49-YJSR20_UNIyHSXMCJM1roJ7X_stEMA7XJ-2JMRnO-U8L7oUj_xoDB7NyaaCcmwgZ_4WExmasN7CebavkrFzANaQ6Lzk9qrc93r6NTjiHmo25yMQpD1tUW80" alt=""><h3 id="countdisplay-ts" tabindex="-1"><a class="header-anchor" href="#countdisplay-ts"><span>countDisplay.ts</span></a></h3><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token keyword">import</span> <span class="token punctuation">{</span> Display <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&#39;./display&#39;</span><span class="token punctuation">;</span>
+import{_ as n,o as s,c as a,a as t,b as p,f as e}from"./app-B4LGNJZ0.js";const o={},i=p("p",null,"Bridge 模式在“类的功能层次结构”和“类的实现层次结构”之间搭建桥梁。",-1),l=e(`<h2 id="使用此设计模式的理由" tabindex="-1"><a class="header-anchor" href="#使用此设计模式的理由"><span>使用此设计模式的理由</span></a></h2><p>Bridge 模式的主要目的是将抽象部分与实现部分分离，使它们可以独立变化。这种模式通过组合而不是继承来实现功能的扩展，减少了类之间的耦合度，提高了系统的可扩展性和可维护性。</p><h2 id="类的层次结构的两个作用" tabindex="-1"><a class="header-anchor" href="#类的层次结构的两个作用"><span>类的层次结构的两个作用</span></a></h2><h3 id="增加新功能时" tabindex="-1"><a class="header-anchor" href="#增加新功能时"><span>增加新功能时</span></a></h3><p>假设现在有一个类 <code>Something</code>，当我们想在 <code>Something</code> 中增加新功能时（例如增加一个具体方法），会编写一个 <code>Something</code> 类的子类（派生类），即 <code>SomethingGood</code> 类。这样就构成了一个小小的类层次结构。这就是为了增加新功能而产生的层次结构。</p><p>SomeThing</p><p>----\\ SomeThingGood</p><h3 id="增加新的实现时" tabindex="-1"><a class="header-anchor" href="#增加新的实现时"><span>增加新的实现时</span></a></h3><p>在 Template Method 模式（第 3 章）中，我们学习了抽象类的作用。抽象类声明了一些抽象方法，定义了接口 (API)，然后子类负责实现这些抽象方法。父类的任务是通过声明抽象方法的方式定义接口 (API)，而子类的任务是实现抽象方法。正是由于父类和子类的这种任务分担，我们才可以编写出具有高可替换性的类。</p><p>这里其实也存在层次结构。例如，当子类实现了父类 <code>AbstractClass</code> 类的抽象方法时，它们之间就构成了一个小小的层次结构。</p><p>AbstractClass</p><p>----\\ ConcreteClass</p><p>但是，这里的类的层次结构并非用于增加功能，也就是说，这种层次结构并非用于方便我们增加新的方法。它的真正作用是帮助我们实现任务分担。</p><h3 id="类的层次结构的混杂和分离" tabindex="-1"><a class="header-anchor" href="#类的层次结构的混杂和分离"><span>类的层次结构的混杂和分离</span></a></h3><p>当我们想要编写子类时，就需要先确认自己的意图：“我是要增加功能呢？还是要增加实现呢？”</p><p>当类的层次结构只有一层时，功能层次结构与实现层次结构是混杂在一个层次结构中的。这样很容易使类的层次结构变得复杂，也难以透彻地理解类的层次结构。因为自己难以确定究竟应该在类的哪一个层次结构中去增加子类。</p><p>因此，我们需要将“类的功能层次结构&quot;与“类的实现层次结构&quot;分离为两个独立的类层次结构。当然，如果只是简单地将它们分开，两者之间必然会缺少联系。所以我们还需要在它们之间搭建一座桥梁。本章中要学习的 Bridge 模式的作用就是搭建这座桥梁。</p><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><h3 id="类的一览表" tabindex="-1"><a class="header-anchor" href="#类的一览表"><span>类的一览表</span></a></h3><table><thead><tr><th>在桥的哪一侧</th><th>名字</th><th>说明</th></tr></thead><tbody><tr><td>类的功能层次结构</td><td>Display</td><td>负责“显示”的类</td></tr><tr><td>类的功能层次结构</td><td>CountDisplay</td><td>增加了“只显示规定次数”这一功能的类</td></tr><tr><td>类的实现层次结构</td><td>DisplayImpl</td><td>负责“显示”的类</td></tr><tr><td>类的实现层次结构</td><td>StringDisplayImpl</td><td>“用字符串显示”的类</td></tr><tr><td>主程序</td><td>Main</td><td>试程序行为的类</td></tr></tbody></table><p>Display 类（代码清单 9 · 1 ）的功能是抽象的，负责“显示一些东西&quot;。该类位于“类的功能层次结构&quot;的最上层。在 impl 字段中保存的是实现了 Display 类的具体功能的实例（ impl 是 implementation （实现）的缩写）。该实例通过 Display 类的构造函数被传递给 Display 类，然后保存在字段中，以供后面的处理使用（ impl 字段即是类的两个层次结构的“桥梁&quot;）。</p><p>CountDisplay 类继承了 Display 类的 open、print、close 方法，并使用它们来增加这个新功能。这就是“类的功能层次结构&quot;。</p><img src="https://www.plantuml.com/plantuml/svg/fPBF2i8m3CRlUueSDsGlq9CmBuAWu1FKhMYXVqQREcNuxcRLokhmvAMGNzBa-zAkFNA7GQkYLTnxs4ZVAtw7iG2eGUfUiSIs511TfRXSPAkOjhqmPSNWQcKNGU-amOoqodgHaUxTCx57yHRKs60mgH8t5ARxg1pZrNd5BqqwA9If1gKMde49-YJSR20_UNIyHSXMCJM1roJ7X_stEMA7XJ-2JMRnO-U8L7oUj_xoDB7NyaaCcmwgZ_4WExmasN7CebavkrFzANaQ6Lzk9qrc93r6NTjiHmo25yMQpD1tUW80" alt=""><h3 id="countdisplay-ts" tabindex="-1"><a class="header-anchor" href="#countdisplay-ts"><span>countDisplay.ts</span></a></h3><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token keyword">import</span> <span class="token punctuation">{</span> Display <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&#39;./display&#39;</span><span class="token punctuation">;</span>
 <span class="token keyword">import</span> <span class="token punctuation">{</span> DisplayImpl <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&#39;./displayImpl&#39;</span><span class="token punctuation">;</span>
 
 <span class="token keyword">export</span> <span class="token keyword">class</span> <span class="token class-name">CountDisplay</span> <span class="token keyword">extends</span> <span class="token class-name">Display</span> <span class="token punctuation">{</span>
diff --git a/assets/builder.html-Ba33pTyP.js b/assets/builder.html-B7MALN7e.js
similarity index 99%
rename from assets/builder.html-Ba33pTyP.js
rename to assets/builder.html-B7MALN7e.js
index cf1e368..6c4a064 100644
--- a/assets/builder.html-Ba33pTyP.js
+++ b/assets/builder.html-B7MALN7e.js
@@ -1,4 +1,4 @@
-import{_ as n,o as s,c as a,f as t}from"./app-B69Gl_S-.js";const p={},e=t(`<h2 id="为什么要使用-builder-模式" tabindex="-1"><a class="header-anchor" href="#为什么要使用-builder-模式"><span>为什么要使用 Builder 模式</span></a></h2><p>Builder 模式通过将对象的构建过程与其表示分离，使得同样的构建过程可以创建不同的表示。它主要用于以下情况：</p><ol><li><strong>复杂对象的创建</strong>：当一个对象的构建过程非常复杂时，Builder 模式可以将构建过程分解为多个步骤，使代码更易于维护和理解。</li><li><strong>不同的表示</strong>：当需要创建不同表示的对象时，Builder 模式允许使用相同的构建过程来生成不同的对象表示。</li><li><strong>代码复用</strong>：通过将构建过程封装在 Director 类中，可以在不同的上下文中重用相同的构建逻辑。</li></ol><h2 id="代码示例" tabindex="-1"><a class="header-anchor" href="#代码示例"><span>代码示例</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/pPA_2i8m4CRtFaN65CaB594Y3WgwQ3TngEcr1DCMaei8whkR_ab85MTTRlZko-Nt9PTgp1MQMaPSvbgJfH6o04Nk4I6pEhz09b02nQucHACIJHKdvDgAmZaElKXjxujXWr1hAhhg7CTJuE6orK2Ty8n6b9LGmB4TMDXv04iSONVGEUXxC-x7jeszp73y7BtETjimAIk5X2QlVSJXnh845IY_UGyhL81xq4RsIKOSdoM36qwo_3stevq_60k_Oje8SaL-5HXR-0L8eIdiuhu0" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// builder.ts</span>
+import{_ as n,o as s,c as a,f as t}from"./app-B4LGNJZ0.js";const p={},e=t(`<h2 id="为什么要使用-builder-模式" tabindex="-1"><a class="header-anchor" href="#为什么要使用-builder-模式"><span>为什么要使用 Builder 模式</span></a></h2><p>Builder 模式通过将对象的构建过程与其表示分离，使得同样的构建过程可以创建不同的表示。它主要用于以下情况：</p><ol><li><strong>复杂对象的创建</strong>：当一个对象的构建过程非常复杂时，Builder 模式可以将构建过程分解为多个步骤，使代码更易于维护和理解。</li><li><strong>不同的表示</strong>：当需要创建不同表示的对象时，Builder 模式允许使用相同的构建过程来生成不同的对象表示。</li><li><strong>代码复用</strong>：通过将构建过程封装在 Director 类中，可以在不同的上下文中重用相同的构建逻辑。</li></ol><h2 id="代码示例" tabindex="-1"><a class="header-anchor" href="#代码示例"><span>代码示例</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/pPA_2i8m4CRtFaN65CaB594Y3WgwQ3TngEcr1DCMaei8whkR_ab85MTTRlZko-Nt9PTgp1MQMaPSvbgJfH6o04Nk4I6pEhz09b02nQucHACIJHKdvDgAmZaElKXjxujXWr1hAhhg7CTJuE6orK2Ty8n6b9LGmB4TMDXv04iSONVGEUXxC-x7jeszp73y7BtETjimAIk5X2QlVSJXnh845IY_UGyhL81xq4RsIKOSdoM36qwo_3stevq_60k_Oje8SaL-5HXR-0L8eIdiuhu0" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// builder.ts</span>
 <span class="token keyword">export</span> <span class="token keyword">abstract</span> <span class="token keyword">class</span> <span class="token class-name">Builder</span> <span class="token punctuation">{</span>
   <span class="token keyword">public</span> <span class="token keyword">abstract</span> <span class="token function">makeTitle</span><span class="token punctuation">(</span>title<span class="token operator">:</span> <span class="token builtin">string</span><span class="token punctuation">)</span><span class="token operator">:</span> <span class="token keyword">void</span><span class="token punctuation">;</span>
   <span class="token keyword">public</span> <span class="token keyword">abstract</span> <span class="token function">makeString</span><span class="token punctuation">(</span>str<span class="token operator">:</span> <span class="token builtin">string</span><span class="token punctuation">)</span><span class="token operator">:</span> <span class="token keyword">void</span><span class="token punctuation">;</span>
diff --git a/assets/c4Diagram-dc8f04df-CiA8sQW3.js b/assets/c4Diagram-dc8f04df-DWstOjwk.js
similarity index 99%
rename from assets/c4Diagram-dc8f04df-CiA8sQW3.js
rename to assets/c4Diagram-dc8f04df-DWstOjwk.js
index 8ddc20e..20703d1 100644
--- a/assets/c4Diagram-dc8f04df-CiA8sQW3.js
+++ b/assets/c4Diagram-dc8f04df-DWstOjwk.js
@@ -1,4 +1,4 @@
-import{s as we,g as Oe,a as Te,b as Re,c as Dt,d as ue,e as De,f as wt,h as Nt,l as le,i as Se,w as Pe,j as Kt,k as oe,m as Me}from"./mermaid.core-ChLYKTZm.js";import{d as Le,g as Ne}from"./svgDrawCommon-9d162435-DXbPg0E8.js";import"./app-B69Gl_S-.js";var Yt=function(){var e=function(bt,_,x,m){for(x=x||{},m=bt.length;m--;x[bt[m]]=_);return x},t=[1,24],a=[1,25],o=[1,26],l=[1,27],i=[1,28],s=[1,63],r=[1,64],n=[1,65],h=[1,66],f=[1,67],d=[1,68],p=[1,69],E=[1,29],O=[1,30],R=[1,31],S=[1,32],L=[1,33],Y=[1,34],Q=[1,35],H=[1,36],q=[1,37],G=[1,38],K=[1,39],J=[1,40],Z=[1,41],$=[1,42],tt=[1,43],et=[1,44],it=[1,45],nt=[1,46],st=[1,47],at=[1,48],rt=[1,50],lt=[1,51],ot=[1,52],ct=[1,53],ht=[1,54],ut=[1,55],dt=[1,56],ft=[1,57],pt=[1,58],yt=[1,59],gt=[1,60],At=[14,42],Vt=[14,34,36,37,38,39,40,41,42,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74],Ot=[12,14,34,36,37,38,39,40,41,42,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74],v=[1,82],k=[1,83],A=[1,84],C=[1,85],w=[12,14,42],ne=[12,14,33,42],Pt=[12,14,33,42,76,77,79,80],mt=[12,33],zt=[34,36,37,38,39,40,41,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74],Xt={trace:function(){},yy:{},symbols_:{error:2,start:3,mermaidDoc:4,direction:5,direction_tb:6,direction_bt:7,direction_rl:8,direction_lr:9,graphConfig:10,C4_CONTEXT:11,NEWLINE:12,statements:13,EOF:14,C4_CONTAINER:15,C4_COMPONENT:16,C4_DYNAMIC:17,C4_DEPLOYMENT:18,otherStatements:19,diagramStatements:20,otherStatement:21,title:22,accDescription:23,acc_title:24,acc_title_value:25,acc_descr:26,acc_descr_value:27,acc_descr_multiline_value:28,boundaryStatement:29,boundaryStartStatement:30,boundaryStopStatement:31,boundaryStart:32,LBRACE:33,ENTERPRISE_BOUNDARY:34,attributes:35,SYSTEM_BOUNDARY:36,BOUNDARY:37,CONTAINER_BOUNDARY:38,NODE:39,NODE_L:40,NODE_R:41,RBRACE:42,diagramStatement:43,PERSON:44,PERSON_EXT:45,SYSTEM:46,SYSTEM_DB:47,SYSTEM_QUEUE:48,SYSTEM_EXT:49,SYSTEM_EXT_DB:50,SYSTEM_EXT_QUEUE:51,CONTAINER:52,CONTAINER_DB:53,CONTAINER_QUEUE:54,CONTAINER_EXT:55,CONTAINER_EXT_DB:56,CONTAINER_EXT_QUEUE:57,COMPONENT:58,COMPONENT_DB:59,COMPONENT_QUEUE:60,COMPONENT_EXT:61,COMPONENT_EXT_DB:62,COMPONENT_EXT_QUEUE:63,REL:64,BIREL:65,REL_U:66,REL_D:67,REL_L:68,REL_R:69,REL_B:70,REL_INDEX:71,UPDATE_EL_STYLE:72,UPDATE_REL_STYLE:73,UPDATE_LAYOUT_CONFIG:74,attribute:75,STR:76,STR_KEY:77,STR_VALUE:78,ATTRIBUTE:79,ATTRIBUTE_EMPTY:80,$accept:0,$end:1},terminals_:{2:"error",6:"direction_tb",7:"direction_bt",8:"direction_rl",9:"direction_lr",11:"C4_CONTEXT",12:"NEWLINE",14:"EOF",15:"C4_CONTAINER",16:"C4_COMPONENT",17:"C4_DYNAMIC",18:"C4_DEPLOYMENT",22:"title",23:"accDescription",24:"acc_title",25:"acc_title_value",26:"acc_descr",27:"acc_descr_value",28:"acc_descr_multiline_value",33:"LBRACE",34:"ENTERPRISE_BOUNDARY",36:"SYSTEM_BOUNDARY",37:"BOUNDARY",38:"CONTAINER_BOUNDARY",39:"NODE",40:"NODE_L",41:"NODE_R",42:"RBRACE",44:"PERSON",45:"PERSON_EXT",46:"SYSTEM",47:"SYSTEM_DB",48:"SYSTEM_QUEUE",49:"SYSTEM_EXT",50:"SYSTEM_EXT_DB",51:"SYSTEM_EXT_QUEUE",52:"CONTAINER",53:"CONTAINER_DB",54:"CONTAINER_QUEUE",55:"CONTAINER_EXT",56:"CONTAINER_EXT_DB",57:"CONTAINER_EXT_QUEUE",58:"COMPONENT",59:"COMPONENT_DB",60:"COMPONENT_QUEUE",61:"COMPONENT_EXT",62:"COMPONENT_EXT_DB",63:"COMPONENT_EXT_QUEUE",64:"REL",65:"BIREL",66:"REL_U",67:"REL_D",68:"REL_L",69:"REL_R",70:"REL_B",71:"REL_INDEX",72:"UPDATE_EL_STYLE",73:"UPDATE_REL_STYLE",74:"UPDATE_LAYOUT_CONFIG",76:"STR",77:"STR_KEY",78:"STR_VALUE",79:"ATTRIBUTE",80:"ATTRIBUTE_EMPTY"},productions_:[0,[3,1],[3,1],[5,1],[5,1],[5,1],[5,1],[4,1],[10,4],[10,4],[10,4],[10,4],[10,4],[13,1],[13,1],[13,2],[19,1],[19,2],[19,3],[21,1],[21,1],[21,2],[21,2],[21,1],[29,3],[30,3],[30,3],[30,4],[32,2],[32,2],[32,2],[32,2],[32,2],[32,2],[32,2],[31,1],[20,1],[20,2],[20,3],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,1],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[35,1],[35,2],[75,1],[75,2],[75,1],[75,1]],performAction:function(_,x,m,g,T,u,Tt){var y=u.length-1;switch(T){case 3:g.setDirection("TB");break;case 4:g.setDirection("BT");break;case 5:g.setDirection("RL");break;case 6:g.setDirection("LR");break;case 8:case 9:case 10:case 11:case 12:g.setC4Type(u[y-3]);break;case 19:g.setTitle(u[y].substring(6)),this.$=u[y].substring(6);break;case 20:g.setAccDescription(u[y].substring(15)),this.$=u[y].substring(15);break;case 21:this.$=u[y].trim(),g.setTitle(this.$);break;case 22:case 23:this.$=u[y].trim(),g.setAccDescription(this.$);break;case 28:case 29:u[y].splice(2,0,"ENTERPRISE"),g.addPersonOrSystemBoundary(...u[y]),this.$=u[y];break;case 30:g.addPersonOrSystemBoundary(...u[y]),this.$=u[y];break;case 31:u[y].splice(2,0,"CONTAINER"),g.addContainerBoundary(...u[y]),this.$=u[y];break;case 32:g.addDeploymentNode("node",...u[y]),this.$=u[y];break;case 33:g.addDeploymentNode("nodeL",...u[y]),this.$=u[y];break;case 34:g.addDeploymentNode("nodeR",...u[y]),this.$=u[y];break;case 35:g.popBoundaryParseStack();break;case 39:g.addPersonOrSystem("person",...u[y]),this.$=u[y];break;case 40:g.addPersonOrSystem("external_person",...u[y]),this.$=u[y];break;case 41:g.addPersonOrSystem("system",...u[y]),this.$=u[y];break;case 42:g.addPersonOrSystem("system_db",...u[y]),this.$=u[y];break;case 43:g.addPersonOrSystem("system_queue",...u[y]),this.$=u[y];break;case 44:g.addPersonOrSystem("external_system",...u[y]),this.$=u[y];break;case 45:g.addPersonOrSystem("external_system_db",...u[y]),this.$=u[y];break;case 46:g.addPersonOrSystem("external_system_queue",...u[y]),this.$=u[y];break;case 47:g.addContainer("container",...u[y]),this.$=u[y];break;case 48:g.addContainer("container_db",...u[y]),this.$=u[y];break;case 49:g.addContainer("container_queue",...u[y]),this.$=u[y];break;case 50:g.addContainer("external_container",...u[y]),this.$=u[y];break;case 51:g.addContainer("external_container_db",...u[y]),this.$=u[y];break;case 52:g.addContainer("external_container_queue",...u[y]),this.$=u[y];break;case 53:g.addComponent("component",...u[y]),this.$=u[y];break;case 54:g.addComponent("component_db",...u[y]),this.$=u[y];break;case 55:g.addComponent("component_queue",...u[y]),this.$=u[y];break;case 56:g.addComponent("external_component",...u[y]),this.$=u[y];break;case 57:g.addComponent("external_component_db",...u[y]),this.$=u[y];break;case 58:g.addComponent("external_component_queue",...u[y]),this.$=u[y];break;case 60:g.addRel("rel",...u[y]),this.$=u[y];break;case 61:g.addRel("birel",...u[y]),this.$=u[y];break;case 62:g.addRel("rel_u",...u[y]),this.$=u[y];break;case 63:g.addRel("rel_d",...u[y]),this.$=u[y];break;case 64:g.addRel("rel_l",...u[y]),this.$=u[y];break;case 65:g.addRel("rel_r",...u[y]),this.$=u[y];break;case 66:g.addRel("rel_b",...u[y]),this.$=u[y];break;case 67:u[y].splice(0,1),g.addRel("rel",...u[y]),this.$=u[y];break;case 68:g.updateElStyle("update_el_style",...u[y]),this.$=u[y];break;case 69:g.updateRelStyle("update_rel_style",...u[y]),this.$=u[y];break;case 70:g.updateLayoutConfig("update_layout_config",...u[y]),this.$=u[y];break;case 71:this.$=[u[y]];break;case 72:u[y].unshift(u[y-1]),this.$=u[y];break;case 73:case 75:this.$=u[y].trim();break;case 74:let Et={};Et[u[y-1].trim()]=u[y].trim(),this.$=Et;break;case 76:this.$="";break}},table:[{3:1,4:2,5:3,6:[1,5],7:[1,6],8:[1,7],9:[1,8],10:4,11:[1,9],15:[1,10],16:[1,11],17:[1,12],18:[1,13]},{1:[3]},{1:[2,1]},{1:[2,2]},{1:[2,7]},{1:[2,3]},{1:[2,4]},{1:[2,5]},{1:[2,6]},{12:[1,14]},{12:[1,15]},{12:[1,16]},{12:[1,17]},{12:[1,18]},{13:19,19:20,20:21,21:22,22:t,23:a,24:o,26:l,28:i,29:49,30:61,32:62,34:s,36:r,37:n,38:h,39:f,40:d,41:p,43:23,44:E,45:O,46:R,47:S,48:L,49:Y,50:Q,51:H,52:q,53:G,54:K,55:J,56:Z,57:$,58:tt,59:et,60:it,61:nt,62:st,63:at,64:rt,65:lt,66:ot,67:ct,68:ht,69:ut,70:dt,71:ft,72:pt,73:yt,74:gt},{13:70,19:20,20:21,21:22,22:t,23:a,24:o,26:l,28:i,29:49,30:61,32:62,34:s,36:r,37:n,38:h,39:f,40:d,41:p,43:23,44:E,45:O,46:R,47:S,48:L,49:Y,50:Q,51:H,52:q,53:G,54:K,55:J,56:Z,57:$,58:tt,59:et,60:it,61:nt,62:st,63:at,64:rt,65:lt,66:ot,67:ct,68:ht,69:ut,70:dt,71:ft,72:pt,73:yt,74:gt},{13:71,19:20,20:21,21:22,22:t,23:a,24:o,26:l,28:i,29:49,30:61,32:62,34:s,36:r,37:n,38:h,39:f,40:d,41:p,43:23,44:E,45:O,46:R,47:S,48:L,49:Y,50:Q,51:H,52:q,53:G,54:K,55:J,56:Z,57:$,58:tt,59:et,60:it,61:nt,62:st,63:at,64:rt,65:lt,66:ot,67:ct,68:ht,69:ut,70:dt,71:ft,72:pt,73:yt,74:gt},{13:72,19:20,20:21,21:22,22:t,23:a,24:o,26:l,28:i,29:49,30:61,32:62,34:s,36:r,37:n,38:h,39:f,40:d,41:p,43:23,44:E,45:O,46:R,47:S,48:L,49:Y,50:Q,51:H,52:q,53:G,54:K,55:J,56:Z,57:$,58:tt,59:et,60:it,61:nt,62:st,63:at,64:rt,65:lt,66:ot,67:ct,68:ht,69:ut,70:dt,71:ft,72:pt,73:yt,74:gt},{13:73,19:20,20:21,21:22,22:t,23:a,24:o,26:l,28:i,29:49,30:61,32:62,34:s,36:r,37:n,38:h,39:f,40:d,41:p,43:23,44:E,45:O,46:R,47:S,48:L,49:Y,50:Q,51:H,52:q,53:G,54:K,55:J,56:Z,57:$,58:tt,59:et,60:it,61:nt,62:st,63:at,64:rt,65:lt,66:ot,67:ct,68:ht,69:ut,70:dt,71:ft,72:pt,73:yt,74:gt},{14:[1,74]},e(At,[2,13],{43:23,29:49,30:61,32:62,20:75,34:s,36:r,37:n,38:h,39:f,40:d,41:p,44:E,45:O,46:R,47:S,48:L,49:Y,50:Q,51:H,52:q,53:G,54:K,55:J,56:Z,57:$,58:tt,59:et,60:it,61:nt,62:st,63:at,64:rt,65:lt,66:ot,67:ct,68:ht,69:ut,70:dt,71:ft,72:pt,73:yt,74:gt}),e(At,[2,14]),e(Vt,[2,16],{12:[1,76]}),e(At,[2,36],{12:[1,77]}),e(Ot,[2,19]),e(Ot,[2,20]),{25:[1,78]},{27:[1,79]},e(Ot,[2,23]),{35:80,75:81,76:v,77:k,79:A,80:C},{35:86,75:81,76:v,77:k,79:A,80:C},{35:87,75:81,76:v,77:k,79:A,80:C},{35:88,75:81,76:v,77:k,79:A,80:C},{35:89,75:81,76:v,77:k,79:A,80:C},{35:90,75:81,76:v,77:k,79:A,80:C},{35:91,75:81,76:v,77:k,79:A,80:C},{35:92,75:81,76:v,77:k,79:A,80:C},{35:93,75:81,76:v,77:k,79:A,80:C},{35:94,75:81,76:v,77:k,79:A,80:C},{35:95,75:81,76:v,77:k,79:A,80:C},{35:96,75:81,76:v,77:k,79:A,80:C},{35:97,75:81,76:v,77:k,79:A,80:C},{35:98,75:81,76:v,77:k,79:A,80:C},{35:99,75:81,76:v,77:k,79:A,80:C},{35:100,75:81,76:v,77:k,79:A,80:C},{35:101,75:81,76:v,77:k,79:A,80:C},{35:102,75:81,76:v,77:k,79:A,80:C},{35:103,75:81,76:v,77:k,79:A,80:C},{35:104,75:81,76:v,77:k,79:A,80:C},e(w,[2,59]),{35:105,75:81,76:v,77:k,79:A,80:C},{35:106,75:81,76:v,77:k,79:A,80:C},{35:107,75:81,76:v,77:k,79:A,80:C},{35:108,75:81,76:v,77:k,79:A,80:C},{35:109,75:81,76:v,77:k,79:A,80:C},{35:110,75:81,76:v,77:k,79:A,80:C},{35:111,75:81,76:v,77:k,79:A,80:C},{35:112,75:81,76:v,77:k,79:A,80:C},{35:113,75:81,76:v,77:k,79:A,80:C},{35:114,75:81,76:v,77:k,79:A,80:C},{35:115,75:81,76:v,77:k,79:A,80:C},{20:116,29:49,30:61,32:62,34:s,36:r,37:n,38:h,39:f,40:d,41:p,43:23,44:E,45:O,46:R,47:S,48:L,49:Y,50:Q,51:H,52:q,53:G,54:K,55:J,56:Z,57:$,58:tt,59:et,60:it,61:nt,62:st,63:at,64:rt,65:lt,66:ot,67:ct,68:ht,69:ut,70:dt,71:ft,72:pt,73:yt,74:gt},{12:[1,118],33:[1,117]},{35:119,75:81,76:v,77:k,79:A,80:C},{35:120,75:81,76:v,77:k,79:A,80:C},{35:121,75:81,76:v,77:k,79:A,80:C},{35:122,75:81,76:v,77:k,79:A,80:C},{35:123,75:81,76:v,77:k,79:A,80:C},{35:124,75:81,76:v,77:k,79:A,80:C},{35:125,75:81,76:v,77:k,79:A,80:C},{14:[1,126]},{14:[1,127]},{14:[1,128]},{14:[1,129]},{1:[2,8]},e(At,[2,15]),e(Vt,[2,17],{21:22,19:130,22:t,23:a,24:o,26:l,28:i}),e(At,[2,37],{19:20,20:21,21:22,43:23,29:49,30:61,32:62,13:131,22:t,23:a,24:o,26:l,28:i,34:s,36:r,37:n,38:h,39:f,40:d,41:p,44:E,45:O,46:R,47:S,48:L,49:Y,50:Q,51:H,52:q,53:G,54:K,55:J,56:Z,57:$,58:tt,59:et,60:it,61:nt,62:st,63:at,64:rt,65:lt,66:ot,67:ct,68:ht,69:ut,70:dt,71:ft,72:pt,73:yt,74:gt}),e(Ot,[2,21]),e(Ot,[2,22]),e(w,[2,39]),e(ne,[2,71],{75:81,35:132,76:v,77:k,79:A,80:C}),e(Pt,[2,73]),{78:[1,133]},e(Pt,[2,75]),e(Pt,[2,76]),e(w,[2,40]),e(w,[2,41]),e(w,[2,42]),e(w,[2,43]),e(w,[2,44]),e(w,[2,45]),e(w,[2,46]),e(w,[2,47]),e(w,[2,48]),e(w,[2,49]),e(w,[2,50]),e(w,[2,51]),e(w,[2,52]),e(w,[2,53]),e(w,[2,54]),e(w,[2,55]),e(w,[2,56]),e(w,[2,57]),e(w,[2,58]),e(w,[2,60]),e(w,[2,61]),e(w,[2,62]),e(w,[2,63]),e(w,[2,64]),e(w,[2,65]),e(w,[2,66]),e(w,[2,67]),e(w,[2,68]),e(w,[2,69]),e(w,[2,70]),{31:134,42:[1,135]},{12:[1,136]},{33:[1,137]},e(mt,[2,28]),e(mt,[2,29]),e(mt,[2,30]),e(mt,[2,31]),e(mt,[2,32]),e(mt,[2,33]),e(mt,[2,34]),{1:[2,9]},{1:[2,10]},{1:[2,11]},{1:[2,12]},e(Vt,[2,18]),e(At,[2,38]),e(ne,[2,72]),e(Pt,[2,74]),e(w,[2,24]),e(w,[2,35]),e(zt,[2,25]),e(zt,[2,26],{12:[1,138]}),e(zt,[2,27])],defaultActions:{2:[2,1],3:[2,2],4:[2,7],5:[2,3],6:[2,4],7:[2,5],8:[2,6],74:[2,8],126:[2,9],127:[2,10],128:[2,11],129:[2,12]},parseError:function(_,x){if(x.recoverable)this.trace(_);else{var m=new Error(_);throw m.hash=x,m}},parse:function(_){var x=this,m=[0],g=[],T=[null],u=[],Tt=this.table,y="",Et=0,se=0,ve=2,ae=1,ke=u.slice.call(arguments,1),D=Object.create(this.lexer),vt={yy:{}};for(var Qt in this.yy)Object.prototype.hasOwnProperty.call(this.yy,Qt)&&(vt.yy[Qt]=this.yy[Qt]);D.setInput(_,vt.yy),vt.yy.lexer=D,vt.yy.parser=this,typeof D.yylloc>"u"&&(D.yylloc={});var Ht=D.yylloc;u.push(Ht);var Ae=D.options&&D.options.ranges;typeof vt.yy.parseError=="function"?this.parseError=vt.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function Ce(){var X;return X=g.pop()||D.lex()||ae,typeof X!="number"&&(X instanceof Array&&(g=X,X=g.pop()),X=x.symbols_[X]||X),X}for(var M,kt,N,qt,Ct={},Mt,z,re,Lt;;){if(kt=m[m.length-1],this.defaultActions[kt]?N=this.defaultActions[kt]:((M===null||typeof M>"u")&&(M=Ce()),N=Tt[kt]&&Tt[kt][M]),typeof N>"u"||!N.length||!N[0]){var Gt="";Lt=[];for(Mt in Tt[kt])this.terminals_[Mt]&&Mt>ve&&Lt.push("'"+this.terminals_[Mt]+"'");D.showPosition?Gt="Parse error on line "+(Et+1)+`:
+import{s as we,g as Oe,a as Te,b as Re,c as Dt,d as ue,e as De,f as wt,h as Nt,l as le,i as Se,w as Pe,j as Kt,k as oe,m as Me}from"./mermaid.core-DNo_7Q2B.js";import{d as Le,g as Ne}from"./svgDrawCommon-9d162435-DBc9TLjw.js";import"./app-B4LGNJZ0.js";var Yt=function(){var e=function(bt,_,x,m){for(x=x||{},m=bt.length;m--;x[bt[m]]=_);return x},t=[1,24],a=[1,25],o=[1,26],l=[1,27],i=[1,28],s=[1,63],r=[1,64],n=[1,65],h=[1,66],f=[1,67],d=[1,68],p=[1,69],E=[1,29],O=[1,30],R=[1,31],S=[1,32],L=[1,33],Y=[1,34],Q=[1,35],H=[1,36],q=[1,37],G=[1,38],K=[1,39],J=[1,40],Z=[1,41],$=[1,42],tt=[1,43],et=[1,44],it=[1,45],nt=[1,46],st=[1,47],at=[1,48],rt=[1,50],lt=[1,51],ot=[1,52],ct=[1,53],ht=[1,54],ut=[1,55],dt=[1,56],ft=[1,57],pt=[1,58],yt=[1,59],gt=[1,60],At=[14,42],Vt=[14,34,36,37,38,39,40,41,42,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74],Ot=[12,14,34,36,37,38,39,40,41,42,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74],v=[1,82],k=[1,83],A=[1,84],C=[1,85],w=[12,14,42],ne=[12,14,33,42],Pt=[12,14,33,42,76,77,79,80],mt=[12,33],zt=[34,36,37,38,39,40,41,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74],Xt={trace:function(){},yy:{},symbols_:{error:2,start:3,mermaidDoc:4,direction:5,direction_tb:6,direction_bt:7,direction_rl:8,direction_lr:9,graphConfig:10,C4_CONTEXT:11,NEWLINE:12,statements:13,EOF:14,C4_CONTAINER:15,C4_COMPONENT:16,C4_DYNAMIC:17,C4_DEPLOYMENT:18,otherStatements:19,diagramStatements:20,otherStatement:21,title:22,accDescription:23,acc_title:24,acc_title_value:25,acc_descr:26,acc_descr_value:27,acc_descr_multiline_value:28,boundaryStatement:29,boundaryStartStatement:30,boundaryStopStatement:31,boundaryStart:32,LBRACE:33,ENTERPRISE_BOUNDARY:34,attributes:35,SYSTEM_BOUNDARY:36,BOUNDARY:37,CONTAINER_BOUNDARY:38,NODE:39,NODE_L:40,NODE_R:41,RBRACE:42,diagramStatement:43,PERSON:44,PERSON_EXT:45,SYSTEM:46,SYSTEM_DB:47,SYSTEM_QUEUE:48,SYSTEM_EXT:49,SYSTEM_EXT_DB:50,SYSTEM_EXT_QUEUE:51,CONTAINER:52,CONTAINER_DB:53,CONTAINER_QUEUE:54,CONTAINER_EXT:55,CONTAINER_EXT_DB:56,CONTAINER_EXT_QUEUE:57,COMPONENT:58,COMPONENT_DB:59,COMPONENT_QUEUE:60,COMPONENT_EXT:61,COMPONENT_EXT_DB:62,COMPONENT_EXT_QUEUE:63,REL:64,BIREL:65,REL_U:66,REL_D:67,REL_L:68,REL_R:69,REL_B:70,REL_INDEX:71,UPDATE_EL_STYLE:72,UPDATE_REL_STYLE:73,UPDATE_LAYOUT_CONFIG:74,attribute:75,STR:76,STR_KEY:77,STR_VALUE:78,ATTRIBUTE:79,ATTRIBUTE_EMPTY:80,$accept:0,$end:1},terminals_:{2:"error",6:"direction_tb",7:"direction_bt",8:"direction_rl",9:"direction_lr",11:"C4_CONTEXT",12:"NEWLINE",14:"EOF",15:"C4_CONTAINER",16:"C4_COMPONENT",17:"C4_DYNAMIC",18:"C4_DEPLOYMENT",22:"title",23:"accDescription",24:"acc_title",25:"acc_title_value",26:"acc_descr",27:"acc_descr_value",28:"acc_descr_multiline_value",33:"LBRACE",34:"ENTERPRISE_BOUNDARY",36:"SYSTEM_BOUNDARY",37:"BOUNDARY",38:"CONTAINER_BOUNDARY",39:"NODE",40:"NODE_L",41:"NODE_R",42:"RBRACE",44:"PERSON",45:"PERSON_EXT",46:"SYSTEM",47:"SYSTEM_DB",48:"SYSTEM_QUEUE",49:"SYSTEM_EXT",50:"SYSTEM_EXT_DB",51:"SYSTEM_EXT_QUEUE",52:"CONTAINER",53:"CONTAINER_DB",54:"CONTAINER_QUEUE",55:"CONTAINER_EXT",56:"CONTAINER_EXT_DB",57:"CONTAINER_EXT_QUEUE",58:"COMPONENT",59:"COMPONENT_DB",60:"COMPONENT_QUEUE",61:"COMPONENT_EXT",62:"COMPONENT_EXT_DB",63:"COMPONENT_EXT_QUEUE",64:"REL",65:"BIREL",66:"REL_U",67:"REL_D",68:"REL_L",69:"REL_R",70:"REL_B",71:"REL_INDEX",72:"UPDATE_EL_STYLE",73:"UPDATE_REL_STYLE",74:"UPDATE_LAYOUT_CONFIG",76:"STR",77:"STR_KEY",78:"STR_VALUE",79:"ATTRIBUTE",80:"ATTRIBUTE_EMPTY"},productions_:[0,[3,1],[3,1],[5,1],[5,1],[5,1],[5,1],[4,1],[10,4],[10,4],[10,4],[10,4],[10,4],[13,1],[13,1],[13,2],[19,1],[19,2],[19,3],[21,1],[21,1],[21,2],[21,2],[21,1],[29,3],[30,3],[30,3],[30,4],[32,2],[32,2],[32,2],[32,2],[32,2],[32,2],[32,2],[31,1],[20,1],[20,2],[20,3],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,1],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[43,2],[35,1],[35,2],[75,1],[75,2],[75,1],[75,1]],performAction:function(_,x,m,g,T,u,Tt){var y=u.length-1;switch(T){case 3:g.setDirection("TB");break;case 4:g.setDirection("BT");break;case 5:g.setDirection("RL");break;case 6:g.setDirection("LR");break;case 8:case 9:case 10:case 11:case 12:g.setC4Type(u[y-3]);break;case 19:g.setTitle(u[y].substring(6)),this.$=u[y].substring(6);break;case 20:g.setAccDescription(u[y].substring(15)),this.$=u[y].substring(15);break;case 21:this.$=u[y].trim(),g.setTitle(this.$);break;case 22:case 23:this.$=u[y].trim(),g.setAccDescription(this.$);break;case 28:case 29:u[y].splice(2,0,"ENTERPRISE"),g.addPersonOrSystemBoundary(...u[y]),this.$=u[y];break;case 30:g.addPersonOrSystemBoundary(...u[y]),this.$=u[y];break;case 31:u[y].splice(2,0,"CONTAINER"),g.addContainerBoundary(...u[y]),this.$=u[y];break;case 32:g.addDeploymentNode("node",...u[y]),this.$=u[y];break;case 33:g.addDeploymentNode("nodeL",...u[y]),this.$=u[y];break;case 34:g.addDeploymentNode("nodeR",...u[y]),this.$=u[y];break;case 35:g.popBoundaryParseStack();break;case 39:g.addPersonOrSystem("person",...u[y]),this.$=u[y];break;case 40:g.addPersonOrSystem("external_person",...u[y]),this.$=u[y];break;case 41:g.addPersonOrSystem("system",...u[y]),this.$=u[y];break;case 42:g.addPersonOrSystem("system_db",...u[y]),this.$=u[y];break;case 43:g.addPersonOrSystem("system_queue",...u[y]),this.$=u[y];break;case 44:g.addPersonOrSystem("external_system",...u[y]),this.$=u[y];break;case 45:g.addPersonOrSystem("external_system_db",...u[y]),this.$=u[y];break;case 46:g.addPersonOrSystem("external_system_queue",...u[y]),this.$=u[y];break;case 47:g.addContainer("container",...u[y]),this.$=u[y];break;case 48:g.addContainer("container_db",...u[y]),this.$=u[y];break;case 49:g.addContainer("container_queue",...u[y]),this.$=u[y];break;case 50:g.addContainer("external_container",...u[y]),this.$=u[y];break;case 51:g.addContainer("external_container_db",...u[y]),this.$=u[y];break;case 52:g.addContainer("external_container_queue",...u[y]),this.$=u[y];break;case 53:g.addComponent("component",...u[y]),this.$=u[y];break;case 54:g.addComponent("component_db",...u[y]),this.$=u[y];break;case 55:g.addComponent("component_queue",...u[y]),this.$=u[y];break;case 56:g.addComponent("external_component",...u[y]),this.$=u[y];break;case 57:g.addComponent("external_component_db",...u[y]),this.$=u[y];break;case 58:g.addComponent("external_component_queue",...u[y]),this.$=u[y];break;case 60:g.addRel("rel",...u[y]),this.$=u[y];break;case 61:g.addRel("birel",...u[y]),this.$=u[y];break;case 62:g.addRel("rel_u",...u[y]),this.$=u[y];break;case 63:g.addRel("rel_d",...u[y]),this.$=u[y];break;case 64:g.addRel("rel_l",...u[y]),this.$=u[y];break;case 65:g.addRel("rel_r",...u[y]),this.$=u[y];break;case 66:g.addRel("rel_b",...u[y]),this.$=u[y];break;case 67:u[y].splice(0,1),g.addRel("rel",...u[y]),this.$=u[y];break;case 68:g.updateElStyle("update_el_style",...u[y]),this.$=u[y];break;case 69:g.updateRelStyle("update_rel_style",...u[y]),this.$=u[y];break;case 70:g.updateLayoutConfig("update_layout_config",...u[y]),this.$=u[y];break;case 71:this.$=[u[y]];break;case 72:u[y].unshift(u[y-1]),this.$=u[y];break;case 73:case 75:this.$=u[y].trim();break;case 74:let Et={};Et[u[y-1].trim()]=u[y].trim(),this.$=Et;break;case 76:this.$="";break}},table:[{3:1,4:2,5:3,6:[1,5],7:[1,6],8:[1,7],9:[1,8],10:4,11:[1,9],15:[1,10],16:[1,11],17:[1,12],18:[1,13]},{1:[3]},{1:[2,1]},{1:[2,2]},{1:[2,7]},{1:[2,3]},{1:[2,4]},{1:[2,5]},{1:[2,6]},{12:[1,14]},{12:[1,15]},{12:[1,16]},{12:[1,17]},{12:[1,18]},{13:19,19:20,20:21,21:22,22:t,23:a,24:o,26:l,28:i,29:49,30:61,32:62,34:s,36:r,37:n,38:h,39:f,40:d,41:p,43:23,44:E,45:O,46:R,47:S,48:L,49:Y,50:Q,51:H,52:q,53:G,54:K,55:J,56:Z,57:$,58:tt,59:et,60:it,61:nt,62:st,63:at,64:rt,65:lt,66:ot,67:ct,68:ht,69:ut,70:dt,71:ft,72:pt,73:yt,74:gt},{13:70,19:20,20:21,21:22,22:t,23:a,24:o,26:l,28:i,29:49,30:61,32:62,34:s,36:r,37:n,38:h,39:f,40:d,41:p,43:23,44:E,45:O,46:R,47:S,48:L,49:Y,50:Q,51:H,52:q,53:G,54:K,55:J,56:Z,57:$,58:tt,59:et,60:it,61:nt,62:st,63:at,64:rt,65:lt,66:ot,67:ct,68:ht,69:ut,70:dt,71:ft,72:pt,73:yt,74:gt},{13:71,19:20,20:21,21:22,22:t,23:a,24:o,26:l,28:i,29:49,30:61,32:62,34:s,36:r,37:n,38:h,39:f,40:d,41:p,43:23,44:E,45:O,46:R,47:S,48:L,49:Y,50:Q,51:H,52:q,53:G,54:K,55:J,56:Z,57:$,58:tt,59:et,60:it,61:nt,62:st,63:at,64:rt,65:lt,66:ot,67:ct,68:ht,69:ut,70:dt,71:ft,72:pt,73:yt,74:gt},{13:72,19:20,20:21,21:22,22:t,23:a,24:o,26:l,28:i,29:49,30:61,32:62,34:s,36:r,37:n,38:h,39:f,40:d,41:p,43:23,44:E,45:O,46:R,47:S,48:L,49:Y,50:Q,51:H,52:q,53:G,54:K,55:J,56:Z,57:$,58:tt,59:et,60:it,61:nt,62:st,63:at,64:rt,65:lt,66:ot,67:ct,68:ht,69:ut,70:dt,71:ft,72:pt,73:yt,74:gt},{13:73,19:20,20:21,21:22,22:t,23:a,24:o,26:l,28:i,29:49,30:61,32:62,34:s,36:r,37:n,38:h,39:f,40:d,41:p,43:23,44:E,45:O,46:R,47:S,48:L,49:Y,50:Q,51:H,52:q,53:G,54:K,55:J,56:Z,57:$,58:tt,59:et,60:it,61:nt,62:st,63:at,64:rt,65:lt,66:ot,67:ct,68:ht,69:ut,70:dt,71:ft,72:pt,73:yt,74:gt},{14:[1,74]},e(At,[2,13],{43:23,29:49,30:61,32:62,20:75,34:s,36:r,37:n,38:h,39:f,40:d,41:p,44:E,45:O,46:R,47:S,48:L,49:Y,50:Q,51:H,52:q,53:G,54:K,55:J,56:Z,57:$,58:tt,59:et,60:it,61:nt,62:st,63:at,64:rt,65:lt,66:ot,67:ct,68:ht,69:ut,70:dt,71:ft,72:pt,73:yt,74:gt}),e(At,[2,14]),e(Vt,[2,16],{12:[1,76]}),e(At,[2,36],{12:[1,77]}),e(Ot,[2,19]),e(Ot,[2,20]),{25:[1,78]},{27:[1,79]},e(Ot,[2,23]),{35:80,75:81,76:v,77:k,79:A,80:C},{35:86,75:81,76:v,77:k,79:A,80:C},{35:87,75:81,76:v,77:k,79:A,80:C},{35:88,75:81,76:v,77:k,79:A,80:C},{35:89,75:81,76:v,77:k,79:A,80:C},{35:90,75:81,76:v,77:k,79:A,80:C},{35:91,75:81,76:v,77:k,79:A,80:C},{35:92,75:81,76:v,77:k,79:A,80:C},{35:93,75:81,76:v,77:k,79:A,80:C},{35:94,75:81,76:v,77:k,79:A,80:C},{35:95,75:81,76:v,77:k,79:A,80:C},{35:96,75:81,76:v,77:k,79:A,80:C},{35:97,75:81,76:v,77:k,79:A,80:C},{35:98,75:81,76:v,77:k,79:A,80:C},{35:99,75:81,76:v,77:k,79:A,80:C},{35:100,75:81,76:v,77:k,79:A,80:C},{35:101,75:81,76:v,77:k,79:A,80:C},{35:102,75:81,76:v,77:k,79:A,80:C},{35:103,75:81,76:v,77:k,79:A,80:C},{35:104,75:81,76:v,77:k,79:A,80:C},e(w,[2,59]),{35:105,75:81,76:v,77:k,79:A,80:C},{35:106,75:81,76:v,77:k,79:A,80:C},{35:107,75:81,76:v,77:k,79:A,80:C},{35:108,75:81,76:v,77:k,79:A,80:C},{35:109,75:81,76:v,77:k,79:A,80:C},{35:110,75:81,76:v,77:k,79:A,80:C},{35:111,75:81,76:v,77:k,79:A,80:C},{35:112,75:81,76:v,77:k,79:A,80:C},{35:113,75:81,76:v,77:k,79:A,80:C},{35:114,75:81,76:v,77:k,79:A,80:C},{35:115,75:81,76:v,77:k,79:A,80:C},{20:116,29:49,30:61,32:62,34:s,36:r,37:n,38:h,39:f,40:d,41:p,43:23,44:E,45:O,46:R,47:S,48:L,49:Y,50:Q,51:H,52:q,53:G,54:K,55:J,56:Z,57:$,58:tt,59:et,60:it,61:nt,62:st,63:at,64:rt,65:lt,66:ot,67:ct,68:ht,69:ut,70:dt,71:ft,72:pt,73:yt,74:gt},{12:[1,118],33:[1,117]},{35:119,75:81,76:v,77:k,79:A,80:C},{35:120,75:81,76:v,77:k,79:A,80:C},{35:121,75:81,76:v,77:k,79:A,80:C},{35:122,75:81,76:v,77:k,79:A,80:C},{35:123,75:81,76:v,77:k,79:A,80:C},{35:124,75:81,76:v,77:k,79:A,80:C},{35:125,75:81,76:v,77:k,79:A,80:C},{14:[1,126]},{14:[1,127]},{14:[1,128]},{14:[1,129]},{1:[2,8]},e(At,[2,15]),e(Vt,[2,17],{21:22,19:130,22:t,23:a,24:o,26:l,28:i}),e(At,[2,37],{19:20,20:21,21:22,43:23,29:49,30:61,32:62,13:131,22:t,23:a,24:o,26:l,28:i,34:s,36:r,37:n,38:h,39:f,40:d,41:p,44:E,45:O,46:R,47:S,48:L,49:Y,50:Q,51:H,52:q,53:G,54:K,55:J,56:Z,57:$,58:tt,59:et,60:it,61:nt,62:st,63:at,64:rt,65:lt,66:ot,67:ct,68:ht,69:ut,70:dt,71:ft,72:pt,73:yt,74:gt}),e(Ot,[2,21]),e(Ot,[2,22]),e(w,[2,39]),e(ne,[2,71],{75:81,35:132,76:v,77:k,79:A,80:C}),e(Pt,[2,73]),{78:[1,133]},e(Pt,[2,75]),e(Pt,[2,76]),e(w,[2,40]),e(w,[2,41]),e(w,[2,42]),e(w,[2,43]),e(w,[2,44]),e(w,[2,45]),e(w,[2,46]),e(w,[2,47]),e(w,[2,48]),e(w,[2,49]),e(w,[2,50]),e(w,[2,51]),e(w,[2,52]),e(w,[2,53]),e(w,[2,54]),e(w,[2,55]),e(w,[2,56]),e(w,[2,57]),e(w,[2,58]),e(w,[2,60]),e(w,[2,61]),e(w,[2,62]),e(w,[2,63]),e(w,[2,64]),e(w,[2,65]),e(w,[2,66]),e(w,[2,67]),e(w,[2,68]),e(w,[2,69]),e(w,[2,70]),{31:134,42:[1,135]},{12:[1,136]},{33:[1,137]},e(mt,[2,28]),e(mt,[2,29]),e(mt,[2,30]),e(mt,[2,31]),e(mt,[2,32]),e(mt,[2,33]),e(mt,[2,34]),{1:[2,9]},{1:[2,10]},{1:[2,11]},{1:[2,12]},e(Vt,[2,18]),e(At,[2,38]),e(ne,[2,72]),e(Pt,[2,74]),e(w,[2,24]),e(w,[2,35]),e(zt,[2,25]),e(zt,[2,26],{12:[1,138]}),e(zt,[2,27])],defaultActions:{2:[2,1],3:[2,2],4:[2,7],5:[2,3],6:[2,4],7:[2,5],8:[2,6],74:[2,8],126:[2,9],127:[2,10],128:[2,11],129:[2,12]},parseError:function(_,x){if(x.recoverable)this.trace(_);else{var m=new Error(_);throw m.hash=x,m}},parse:function(_){var x=this,m=[0],g=[],T=[null],u=[],Tt=this.table,y="",Et=0,se=0,ve=2,ae=1,ke=u.slice.call(arguments,1),D=Object.create(this.lexer),vt={yy:{}};for(var Qt in this.yy)Object.prototype.hasOwnProperty.call(this.yy,Qt)&&(vt.yy[Qt]=this.yy[Qt]);D.setInput(_,vt.yy),vt.yy.lexer=D,vt.yy.parser=this,typeof D.yylloc>"u"&&(D.yylloc={});var Ht=D.yylloc;u.push(Ht);var Ae=D.options&&D.options.ranges;typeof vt.yy.parseError=="function"?this.parseError=vt.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function Ce(){var X;return X=g.pop()||D.lex()||ae,typeof X!="number"&&(X instanceof Array&&(g=X,X=g.pop()),X=x.symbols_[X]||X),X}for(var M,kt,N,qt,Ct={},Mt,z,re,Lt;;){if(kt=m[m.length-1],this.defaultActions[kt]?N=this.defaultActions[kt]:((M===null||typeof M>"u")&&(M=Ce()),N=Tt[kt]&&Tt[kt][M]),typeof N>"u"||!N.length||!N[0]){var Gt="";Lt=[];for(Mt in Tt[kt])this.terminals_[Mt]&&Mt>ve&&Lt.push("'"+this.terminals_[Mt]+"'");D.showPosition?Gt="Parse error on line "+(Et+1)+`:
 `+D.showPosition()+`
 Expecting `+Lt.join(", ")+", got '"+(this.terminals_[M]||M)+"'":Gt="Parse error on line "+(Et+1)+": Unexpected "+(M==ae?"end of input":"'"+(this.terminals_[M]||M)+"'"),this.parseError(Gt,{text:D.match,token:this.terminals_[M]||M,line:D.yylineno,loc:Ht,expected:Lt})}if(N[0]instanceof Array&&N.length>1)throw new Error("Parse Error: multiple actions possible at state: "+kt+", token: "+M);switch(N[0]){case 1:m.push(M),T.push(D.yytext),u.push(D.yylloc),m.push(N[1]),M=null,se=D.yyleng,y=D.yytext,Et=D.yylineno,Ht=D.yylloc;break;case 2:if(z=this.productions_[N[1]][1],Ct.$=T[T.length-z],Ct._$={first_line:u[u.length-(z||1)].first_line,last_line:u[u.length-1].last_line,first_column:u[u.length-(z||1)].first_column,last_column:u[u.length-1].last_column},Ae&&(Ct._$.range=[u[u.length-(z||1)].range[0],u[u.length-1].range[1]]),qt=this.performAction.apply(Ct,[y,se,Et,vt.yy,N[1],T,u].concat(ke)),typeof qt<"u")return qt;z&&(m=m.slice(0,-1*z*2),T=T.slice(0,-1*z),u=u.slice(0,-1*z)),m.push(this.productions_[N[1]][0]),T.push(Ct.$),u.push(Ct._$),re=Tt[m[m.length-2]][m[m.length-1]],m.push(re);break;case 3:return!0}}return!0}},Ee=function(){var bt={EOF:1,parseError:function(x,m){if(this.yy.parser)this.yy.parser.parseError(x,m);else throw new Error(x)},setInput:function(_,x){return this.yy=x||this.yy||{},this._input=_,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var _=this._input[0];this.yytext+=_,this.yyleng++,this.offset++,this.match+=_,this.matched+=_;var x=_.match(/(?:\r\n?|\n).*/g);return x?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),_},unput:function(_){var x=_.length,m=_.split(/(?:\r\n?|\n)/g);this._input=_+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-x),this.offset-=x;var g=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),m.length-1&&(this.yylineno-=m.length-1);var T=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:m?(m.length===g.length?this.yylloc.first_column:0)+g[g.length-m.length].length-m[0].length:this.yylloc.first_column-x},this.options.ranges&&(this.yylloc.range=[T[0],T[0]+this.yyleng-x]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){if(this.options.backtrack_lexer)this._backtrack=!0;else return this.parseError("Lexical error on line "+(this.yylineno+1)+`. You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).
 `+this.showPosition(),{text:"",token:null,line:this.yylineno});return this},less:function(_){this.unput(this.match.slice(_))},pastInput:function(){var _=this.matched.substr(0,this.matched.length-this.match.length);return(_.length>20?"...":"")+_.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var _=this.match;return _.length<20&&(_+=this._input.substr(0,20-_.length)),(_.substr(0,20)+(_.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var _=this.pastInput(),x=new Array(_.length+1).join("-");return _+this.upcomingInput()+`
diff --git a/assets/carrobot.html-B7set7IG.js b/assets/carrobot.html-B7set7IG.js
new file mode 100644
index 0000000..b7ed6da
--- /dev/null
+++ b/assets/carrobot.html-B7set7IG.js
@@ -0,0 +1 @@
+import{_ as l,r as s,o as T,c as e,b as Q,e as a,d as r,a as o,f as t}from"./app-B4LGNJZ0.js";const d="/assets/image-Dc9IOqtq.png",i={},h={href:"https://github.com/king-sj/carrobot",target:"_blank",rel:"noopener noreferrer"},p=Q("p",null,[Q("s",null,"因为想要创新学分，所以选了创新创业智能车课程"),a("，项目要求完成智能车的循迹和避障。")],-1),m=Q("p",null,[a("由于笔者不喜欢使用VPL的图形化（"),Q("s",null,"报用qWq"),a("）, 故而使用手写代码的方式实现。")],-1),c=t('<h2 id="主要思路" tabindex="-1"><a class="header-anchor" href="#主要思路"><span>主要思路</span></a></h2><p>通过接发TCP包的方法与智能车进行交互， 创建两个<strong>并行</strong>任务，一个用于实时接收TCP报文来更新小车状态， 一个用于读取小车状态，作出决策并发送报文控制小车。</p><h2 id="编程语言的选择" tabindex="-1"><a class="header-anchor" href="#编程语言的选择"><span>编程语言的选择</span></a></h2><ul><li><code>python</code> 笔者的项目采用了该语言，主要原因是方便且能快速实现（<s>以及没考虑到GIL会影响介么大</s>），并采用asyncio作为“并行”库（实际上只能并发，笔者最初以为只有两个任务，用python也足够了，<s>虽然实际上也够，但是写起来没那么舒服了</s>，可能使用threads会好一点）</li><li><code>go</code> 后续又采用go重构了一遍（<s>虽然实际效果貌似变化不大，emmm...应该是硬件/小车的原因</s>）</li></ul><p>当然采用什么编程语言并不是重要（吗？，不许用rust 😠 ）</p><h2 id="通信协议" tabindex="-1"><a class="header-anchor" href="#通信协议"><span>通信协议</span></a></h2><figure><img src="'+d+'" alt="alt text" tabindex="0" loading="lazy"><figcaption>alt text</figcaption></figure><h2 id="初步思路" tabindex="-1"><a class="header-anchor" href="#初步思路"><span>初步思路</span></a></h2>',8),g=Q("s",null,"当然超声波传感器有大概的距离，本项目不考虑介么多，取较小距离为有障碍",-1),u={class:"MathJax",jax:"SVG",style:{position:"relative"}},f={style:{"vertical-align":"-0.651ex"},xmlns:"http://www.w3.org/2000/svg",width:"28.73ex",height:"2.538ex",role:"img",focusable:"false",viewBox:"0 -833.9 12698.8 1121.9","aria-hidden":"true"},H=t('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D456" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(734,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(1334,0)"><path data-c="1D445" d="M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z"></path></g><g data-mml-node="mi" transform="translate(2093,0)"><path data-c="1D45C" d="M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z"></path></g><g data-mml-node="mi" transform="translate(2578,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mi" transform="translate(3107,0)"><path data-c="1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path></g><g data-mml-node="mo" transform="translate(3627,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(4071.7,0)"><path data-c="210E" d="M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z"></path></g><g data-mml-node="mi" transform="translate(4647.7,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mi" transform="translate(5176.7,0)"><path data-c="1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path></g><g data-mml-node="mi" transform="translate(5661.7,0)"><path data-c="1D452" d="M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z"></path></g><g data-mml-node="mi" transform="translate(6127.7,0)"><path data-c="1D442" d="M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z"></path></g><g data-mml-node="mi" transform="translate(6890.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mi" transform="translate(7319.7,0)"><path data-c="1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path></g><g data-mml-node="mi" transform="translate(7788.7,0)"><path data-c="1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path></g><g data-mml-node="mi" transform="translate(8149.7,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mi" transform="translate(8678.7,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mi" transform="translate(9111.7,0)"><path data-c="1D459" d="M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z"></path></g><g data-mml-node="mi" transform="translate(9409.7,0)"><path data-c="1D452" d="M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z"></path></g><g data-mml-node="mo" transform="translate(9875.7,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(10542.4,0)"><path data-c="2208" d="M84 250Q84 372 166 450T360 539Q361 539 377 539T419 540T469 540H568Q583 532 583 520Q583 511 570 501L466 500Q355 499 329 494Q280 482 242 458T183 409T147 354T129 306T124 272V270H568Q583 262 583 250T568 230H124V228Q124 207 134 177T167 112T231 48T328 7Q355 1 466 0H570Q583 -10 583 -20Q583 -32 568 -40H471Q464 -40 446 -40T417 -41Q262 -41 172 45Q84 127 84 250Z"></path></g><g data-mml-node="msubsup" transform="translate(11487.2,0)"><g data-mml-node="mi"><path data-c="1D44D" d="M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z"></path></g><g data-mml-node="mn" transform="translate(808,363) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g><g data-mml-node="mn" transform="translate(716,-287.9) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g></g></g>',1),L=[H],M=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mo",{stretchy:"false"},"("),Q("mi",null,"i"),Q("mi",null,"n"),Q("mi",null,"R"),Q("mi",null,"o"),Q("mi",null,"a"),Q("mi",null,"d"),Q("mo",null,","),Q("mi",null,"h"),Q("mi",null,"a"),Q("mi",null,"v"),Q("mi",null,"e"),Q("mi",null,"O"),Q("mi",null,"b"),Q("mi",null,"s"),Q("mi",null,"t"),Q("mi",null,"a"),Q("mi",null,"c"),Q("mi",null,"l"),Q("mi",null,"e"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"∈"),Q("msubsup",null,[Q("mi",null,"Z"),Q("mn",null,"2"),Q("mn",null,"2")])])],-1),Z=Q("strong",null,"正确",-1),_=t('<h2 id="遇到的问题和改进方案" tabindex="-1"><a class="header-anchor" href="#遇到的问题和改进方案"><span>遇到的问题和改进方案</span></a></h2><h3 id="小车左右轮力矩不一致" tabindex="-1"><a class="header-anchor" href="#小车左右轮力矩不一致"><span>小车左右轮力矩不一致</span></a></h3><p>由于硬件限制，若设置两个轮的速度一致的话小车直行也会偏转， 而且小车并不能知道自己“偏航”了，故而采取手动测试的方式， 通过二分左右轮的速度来得到使得小车直行的左右轮速度。并且这个关系并非简单的倍速或差量的关系。</p><p>因此无奈之下只能选取一个固定的速度来测试（比如左轮设置为0.8, 然后不断二分得到直行时右轮的速度为 0.x ）, 整个系统都在该速度下运行。</p><div class="hint-container tip"><p class="hint-container-title">提示</p><p>各个小车有各个的体质， 因此挑选一辆&quot;正确&quot;的小车是很重要的事情。 以及测试完小车后保护小车也是很重要的，不要找不到了或者被人踢坏了， 否则得重新找车及测速。</p></div><h3 id="小车容易冲出轨道" tabindex="-1"><a class="header-anchor" href="#小车容易冲出轨道"><span>小车容易冲出轨道</span></a></h3><p>小车还未找到合适的“姿势”就前进，导致频繁冲出赛道，耗费时间。</p><p>基于此，采取速度渐进增长的形式，使得刚回到正确姿势时速度较慢，从而不会前进太多，便于更快的回到正确的姿势。</p><h3 id="小车总是左右左摆头太蠢了" tabindex="-1"><a class="header-anchor" href="#小车总是左右左摆头太蠢了"><span>小车总是左右左摆头太蠢了</span></a></h3><p>首先采取的改进方案是先左小幅度转弯，后右大幅度转弯，最后左大幅度转弯寻找正确姿势，但效果不理想，遂放弃。</p><p>考虑到小车路线是闭合的，且局部多为凸多边形， 故而每次转弯时优先考虑上一次转弯的方向， 这样子能减少摆头次数， 多数情况转弯的方向都是对的。（<s>有一些启发式的smell</s>）</p><h3 id="其它问题" tabindex="-1"><a class="header-anchor" href="#其它问题"><span>其它问题</span></a></h3><p><s>时间有点久搞忘了，记起来再补充</s></p><h2 id="设计方案参考" tabindex="-1"><a class="header-anchor" href="#设计方案参考"><span>设计方案参考</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/TP9DRiCW48Ntd09bbIwI0tXHHSgsNNQDHa08bGqM395o-mu_ZcsYBcnZtlERRmPV8aB0D8qC9Fh0Vw8ERAOjA-qC3latMCSXyiD4Y-F7OIT-UMEiCqMF6jCinhhJ6wyGYecUdU0T1ZyMKTQra12ET544opZyz5ae1Yv4XX3YF3yphdq0wYAnGac-1ZJmZcQrDmTRq4-lz6RcX76p9WMjcD9ltxrAKIj3lct3wNMlKvRJ4djF7iTQk9dszR9jpQgJATRTY3QnLM7BG1U2D2kI1HqpwZUCpXinW3NtZDjBe7vJn4ax5ChcdhUehVH_zBLBY4ydhJyRmBlk4iePNhHJz2F-0G00" alt=""><img src="https://www.plantuml.com/plantuml/svg/LP7FRiCW3CRlF0N7L6jUe9gcIjbVQQUgT-I0qp8vK1cp7RQz-w29ckM0i3y-sp-BVH9WoICfIv2Ixe3rjzBwpiOGq4gpgKc-E10qnIiuAGd5f0kYQmY7ETpfWIB8LhC_dTVQjSRvqY1OdBKg-M0uGd7rCL8Lpl299lR5Q0bd-LVDS8VOH-aO1hbX9c6eqoOgYbzchKZcO2hYlvINPt0VESc8GOppt9Ipqu-Uo-8-XgrscQ56jyrycghD2LFfLGWx88AUS5CnAzRzJzkkIPN2aCUbxvNy_UdvMAx3sylhiPQkTslRXyMlzXXS-Q8_" alt=""><h2 id="和机械臂联动" tabindex="-1"><a class="header-anchor" href="#和机械臂联动"><span>和机械臂联动</span></a></h2><p>emm... 本来想让机械臂识别“货物”并放在车上托运并最后卸货的，但是小车不好运货。遂放弃，转而实验机械臂放置障碍在赛道上。</p><h2 id="结语" tabindex="-1"><a class="header-anchor" href="#结语"><span>结语</span></a></h2><p>本次智能车实验不是很愉快， 特别是重调了3，4次速度（几次换车<s>其中一次车被踩烂了</s>）</p><p>如果没有熟悉的编程语言（例如c）且不了解 多线程/协程，网络I/O的话 还是采用VPL图形化吧 <s>不过我认为报用就是了</s>。</p><p>记得给我的仓库点Star欧~</p>',22);function b(x,y){const n=s("ExternalLinkIcon");return T(),e("div",null,[Q("p",null,[Q("a",h,[a("项目源码"),r(n)])]),p,m,o(" more "),c,Q("p",null,[a("由于硬件限制，只有一个红外传感器用于判断底部是否为黑色， 一个红外传感器+超声波传感器用于确定前方是否有障碍，信息量非常小（"),g,a("）， 为 "),Q("mjx-container",u,[(T(),e("svg",f,L)),M]),a("。 故而首先考虑的基本策略是偏航时左右摆头寻找"),Z,a("的角度前行。")]),_])}const v=l(i,[["render",b],["__file","carrobot.html.vue"]]),D=JSON.parse('{"path":"/projects/carrobot.html","title":"北京邮电大学创新创业智能车循迹python版","lang":"zh-CN","frontmatter":{"date":"2024-11-07T00:00:00.000Z","title":"北京邮电大学创新创业智能车循迹python版","description":"项目源码 ，项目要求完成智能车的循迹和避障。 由于笔者不喜欢使用VPL的图形化（）, 故而使用手写代码的方式实现。","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/projects/carrobot.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"北京邮电大学创新创业智能车循迹python版"}],["meta",{"property":"og:description","content":"项目源码 ，项目要求完成智能车的循迹和避障。 由于笔者不喜欢使用VPL的图形化（）, 故而使用手写代码的方式实现。"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:published_time","content":"2024-11-07T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"北京邮电大学创新创业智能车循迹python版\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-11-07T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"主要思路","slug":"主要思路","link":"#主要思路","children":[]},{"level":2,"title":"编程语言的选择","slug":"编程语言的选择","link":"#编程语言的选择","children":[]},{"level":2,"title":"通信协议","slug":"通信协议","link":"#通信协议","children":[]},{"level":2,"title":"初步思路","slug":"初步思路","link":"#初步思路","children":[]},{"level":2,"title":"遇到的问题和改进方案","slug":"遇到的问题和改进方案","link":"#遇到的问题和改进方案","children":[{"level":3,"title":"小车左右轮力矩不一致","slug":"小车左右轮力矩不一致","link":"#小车左右轮力矩不一致","children":[]},{"level":3,"title":"小车容易冲出轨道","slug":"小车容易冲出轨道","link":"#小车容易冲出轨道","children":[]},{"level":3,"title":"小车总是左右左摆头太蠢了","slug":"小车总是左右左摆头太蠢了","link":"#小车总是左右左摆头太蠢了","children":[]},{"level":3,"title":"其它问题","slug":"其它问题","link":"#其它问题","children":[]}]},{"level":2,"title":"设计方案参考","slug":"设计方案参考","link":"#设计方案参考","children":[]},{"level":2,"title":"和机械臂联动","slug":"和机械臂联动","link":"#和机械臂联动","children":[]},{"level":2,"title":"结语","slug":"结语","link":"#结语","children":[]}],"readingTime":{"minutes":4.03,"words":1210},"filePathRelative":"projects/carrobot.md","localizedDate":"2024年11月7日","excerpt":"<p><a href=\\"https://github.com/king-sj/carrobot\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">项目源码</a></p>\\n<p><s>因为想要创新学分，所以选了创新创业智能车课程</s>，项目要求完成智能车的循迹和避障。</p>\\n<p>由于笔者不喜欢使用VPL的图形化（<s>报用qWq</s>）, 故而使用手写代码的方式实现。</p>\\n","autoDesc":true}');export{v as comp,D as data};
diff --git a/assets/chainOfResponsibility.html-DhJtx4gW.js b/assets/chainOfResponsibility.html-CpbeYqOk.js
similarity index 99%
rename from assets/chainOfResponsibility.html-DhJtx4gW.js
rename to assets/chainOfResponsibility.html-CpbeYqOk.js
index e45a42b..78e6583 100644
--- a/assets/chainOfResponsibility.html-DhJtx4gW.js
+++ b/assets/chainOfResponsibility.html-CpbeYqOk.js
@@ -1,4 +1,4 @@
-import{_ as n,o as s,c as a,a as t,b as p,f as o}from"./app-B69Gl_S-.js";const e={},c=p("p",null,'“推卸责任"听起来有些贬义的意思，但是有时候也确实存在需要“推卸责任"的情况。例如，当外部请求程序进行某个处理，但程序暂时无法直接决定由哪个对象负责处理时，就需要推卸责任。这种情况下，我们可以考虑将多个对象组成一条职责链，然后按照它们在职责链上的顺序一个一个地找出到底应该谁来负责处理。',-1),l=o(`<p>当一个人被要求做什么事情时，如果他可以做就自己做，如果不能做就将“要求&quot;转给另外一个人。下一个人如果可以自己处理，就自己做；如果也不能自己处理，就再转给另外一个人““这就是 Chain Of Responsibility 模式。</p><h3 id="为什么使用此类" tabindex="-1"><a class="header-anchor" href="#为什么使用此类"><span>为什么使用此类</span></a></h3><p>使用 Chain of Responsibility 模式有以下几个优点：</p><ol><li><strong>解耦请求发送者和接收者</strong>：发送者无需知道哪个对象会处理请求。</li><li><strong>动态组合职责链</strong>：可以在运行时动态地改变职责链的结构。</li><li><strong>增加灵活性</strong>：可以很容易地添加新的处理者而不影响现有代码。</li></ol><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><p>在这个示例中，我们使用了 Chain of Responsibility 模式来处理一系列的请求。每个请求都会沿着职责链传递，直到有一个对象能够处理它。这样做的好处是请求的发送者和接收者解耦，发送者无需知道哪个对象会处理请求。</p><img src="https://www.plantuml.com/plantuml/svg/hP912i8m44NtESM0cuhq0btr058NzG9fCqeWpPHaAeBqxewD2eeM5NV9dyVd3KmPMGSUEgTq4pdebg5rEaQeXxwdm71I03butM410bY_Jm4UkRX1agmW8bSIPW-JvHEJtXa76XedZTlq4En0rWYpW82Ht05VCGsHG-qdp937sPwTjkujC2gLrgpejgXeepVtnK-Jy0SozwgrxIpFjENWBaG1VkWQ35_tRupvcslTOskrcxLDcZ_hNaVmjcml1pFzikL3pbHFTtQ9hnStgbByv4hF" alt=""><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuKfCBialKd3EoKpDA-62K0gwTWf--S6b1GNvHILM2iKGXaP9KNvfKawg9XTS3gJG9pCtimItMcHfaFBWWjJapCGSt1fG5O2q-AUa4AtSHXT9EQhbG2bKnKZ-0CeXguM50r0OheRB8JKl1HXW0000" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// limitSupport.ts</span>
+import{_ as n,o as s,c as a,a as t,b as p,f as o}from"./app-B4LGNJZ0.js";const e={},c=p("p",null,'“推卸责任"听起来有些贬义的意思，但是有时候也确实存在需要“推卸责任"的情况。例如，当外部请求程序进行某个处理，但程序暂时无法直接决定由哪个对象负责处理时，就需要推卸责任。这种情况下，我们可以考虑将多个对象组成一条职责链，然后按照它们在职责链上的顺序一个一个地找出到底应该谁来负责处理。',-1),l=o(`<p>当一个人被要求做什么事情时，如果他可以做就自己做，如果不能做就将“要求&quot;转给另外一个人。下一个人如果可以自己处理，就自己做；如果也不能自己处理，就再转给另外一个人““这就是 Chain Of Responsibility 模式。</p><h3 id="为什么使用此类" tabindex="-1"><a class="header-anchor" href="#为什么使用此类"><span>为什么使用此类</span></a></h3><p>使用 Chain of Responsibility 模式有以下几个优点：</p><ol><li><strong>解耦请求发送者和接收者</strong>：发送者无需知道哪个对象会处理请求。</li><li><strong>动态组合职责链</strong>：可以在运行时动态地改变职责链的结构。</li><li><strong>增加灵活性</strong>：可以很容易地添加新的处理者而不影响现有代码。</li></ol><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><p>在这个示例中，我们使用了 Chain of Responsibility 模式来处理一系列的请求。每个请求都会沿着职责链传递，直到有一个对象能够处理它。这样做的好处是请求的发送者和接收者解耦，发送者无需知道哪个对象会处理请求。</p><img src="https://www.plantuml.com/plantuml/svg/hP912i8m44NtESM0cuhq0btr058NzG9fCqeWpPHaAeBqxewD2eeM5NV9dyVd3KmPMGSUEgTq4pdebg5rEaQeXxwdm71I03butM410bY_Jm4UkRX1agmW8bSIPW-JvHEJtXa76XedZTlq4En0rWYpW82Ht05VCGsHG-qdp937sPwTjkujC2gLrgpejgXeepVtnK-Jy0SozwgrxIpFjENWBaG1VkWQ35_tRupvcslTOskrcxLDcZ_hNaVmjcml1pFzikL3pbHFTtQ9hnStgbByv4hF" alt=""><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuKfCBialKd3EoKpDA-62K0gwTWf--S6b1GNvHILM2iKGXaP9KNvfKawg9XTS3gJG9pCtimItMcHfaFBWWjJapCGSt1fG5O2q-AUa4AtSHXT9EQhbG2bKnKZ-0CeXguM50r0OheRB8JKl1HXW0000" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// limitSupport.ts</span>
 <span class="token keyword">import</span> <span class="token punctuation">{</span> Support <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&#39;./support&#39;</span><span class="token punctuation">;</span>
 <span class="token keyword">import</span> <span class="token punctuation">{</span> Trouble <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&#39;./trouble&#39;</span><span class="token punctuation">;</span>
 <span class="token keyword">export</span> <span class="token keyword">class</span> <span class="token class-name">LimitSupport</span> <span class="token keyword">extends</span> <span class="token class-name">Support</span> <span class="token punctuation">{</span>
diff --git a/assets/channel-DJsAcM5I.js b/assets/channel-DJsAcM5I.js
deleted file mode 100644
index d9c0f85..0000000
--- a/assets/channel-DJsAcM5I.js
+++ /dev/null
@@ -1 +0,0 @@
-import{al as o,am as n}from"./mermaid.core-ChLYKTZm.js";const l=(a,r)=>o.lang.round(n.parse(a)[r]);export{l as c};
diff --git a/assets/channel-yU22lAlC.js b/assets/channel-yU22lAlC.js
new file mode 100644
index 0000000..d16764e
--- /dev/null
+++ b/assets/channel-yU22lAlC.js
@@ -0,0 +1 @@
+import{al as o,am as n}from"./mermaid.core-DNo_7Q2B.js";const l=(a,r)=>o.lang.round(n.parse(a)[r]);export{l as c};
diff --git a/assets/cicd.html-CedraPRV.js b/assets/cicd.html-BxLHD3yn.js
similarity index 98%
rename from assets/cicd.html-CedraPRV.js
rename to assets/cicd.html-BxLHD3yn.js
index c5440aa..d7ee06d 100644
--- a/assets/cicd.html-CedraPRV.js
+++ b/assets/cicd.html-BxLHD3yn.js
@@ -1,2 +1,2 @@
-import{_ as n,r as s,o as c,c as o,b as t,e,d as r,a as i,f as p}from"./app-B69Gl_S-.js";const l={},d=t("h1",{id:"github-actions",tabindex:"-1"},[t("a",{class:"header-anchor",href:"#github-actions"},[t("span",null,"Github Actions")])],-1),u={href:"https://github.com/nektos/act",target:"_blank",rel:"noopener noreferrer"},h=t("p",null,"需要创建配置文件",-1),g=p(`<p>也可另外指定</p><div class="language-bash line-numbers-mode" data-ext="sh" data-title="sh"><pre class="language-bash"><code>act --var-file <span class="token string">&quot;./.act/.vars&quot;</span> --secret-file <span class="token string">&quot;./.act/.secrets&quot;</span> --env-file <span class="token string">&quot;./.act/.env&quot;</span> <span class="token punctuation">{</span><span class="token punctuation">{</span>other<span class="token punctuation">}</span><span class="token punctuation">}</span>
+import{_ as n,r as s,o as c,c as o,b as t,e,d as r,a as i,f as p}from"./app-B4LGNJZ0.js";const l={},d=t("h1",{id:"github-actions",tabindex:"-1"},[t("a",{class:"header-anchor",href:"#github-actions"},[t("span",null,"Github Actions")])],-1),u={href:"https://github.com/nektos/act",target:"_blank",rel:"noopener noreferrer"},h=t("p",null,"需要创建配置文件",-1),g=p(`<p>也可另外指定</p><div class="language-bash line-numbers-mode" data-ext="sh" data-title="sh"><pre class="language-bash"><code>act --var-file <span class="token string">&quot;./.act/.vars&quot;</span> --secret-file <span class="token string">&quot;./.act/.secrets&quot;</span> --env-file <span class="token string">&quot;./.act/.env&quot;</span> <span class="token punctuation">{</span><span class="token punctuation">{</span>other<span class="token punctuation">}</span><span class="token punctuation">}</span>
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div></div></div>`,2);function m(_,b){const a=s("ExternalLinkIcon");return c(),o("div",null,[d,t("p",null,[e("本地调试工具 "),t("a",u,[e("act"),r(a)])]),h,i(" TODO "),g])}const f=n(l,[["render",m],["__file","cicd.html.vue"]]),v=JSON.parse('{"path":"/tech/cicd.html","title":"CI/CD","lang":"zh-CN","frontmatter":{"title":"CI/CD","date":"2024-08-02T00:00:00.000Z","category":["CI/CD"],"tag":["CI/CD"],"description":"Github Actions 本地调试工具 act 需要创建配置文件 也可另外指定","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/cicd.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"CI/CD"}],["meta",{"property":"og:description","content":"Github Actions 本地调试工具 act 需要创建配置文件 也可另外指定"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"CI/CD"}],["meta",{"property":"article:published_time","content":"2024-08-02T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"CI/CD\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-08-02T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.16,"words":48},"filePathRelative":"tech/cicd.md","localizedDate":"2024年8月2日","excerpt":"\\n<p>本地调试工具 <a href=\\"https://github.com/nektos/act\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">act</a></p>\\n<p>需要创建配置文件</p>\\n<!-- TODO -->\\n<p>也可另外指定</p>\\n<div class=\\"language-bash\\" data-ext=\\"sh\\" data-title=\\"sh\\"><pre class=\\"language-bash\\"><code>act --var-file <span class=\\"token string\\">\\"./.act/.vars\\"</span> --secret-file <span class=\\"token string\\">\\"./.act/.secrets\\"</span> --env-file <span class=\\"token string\\">\\"./.act/.env\\"</span> <span class=\\"token punctuation\\">{</span><span class=\\"token punctuation\\">{</span>other<span class=\\"token punctuation\\">}</span><span class=\\"token punctuation\\">}</span>\\n</code></pre></div>","autoDesc":true}');export{f as comp,v as data};
diff --git a/assets/classDiagram-8298e144-w121JOWu.js b/assets/classDiagram-8298e144-DKojaSxZ.js
similarity index 97%
rename from assets/classDiagram-8298e144-w121JOWu.js
rename to assets/classDiagram-8298e144-DKojaSxZ.js
index 00e95bb..f1d904b 100644
--- a/assets/classDiagram-8298e144-w121JOWu.js
+++ b/assets/classDiagram-8298e144-DKojaSxZ.js
@@ -1,2 +1,2 @@
-import{p as A,d as S,s as G}from"./styles-e2b9d258-TYWOaoPC.js";import{c as v,l as y,h as B,i as W,ao as $,z as M,ar as I}from"./mermaid.core-ChLYKTZm.js";import{G as O}from"./graph-T5JS4vfK.js";import{l as P}from"./layout-DUYLy6Ue.js";import{l as X}from"./line-D0jG_HZ-.js";import"./app-B69Gl_S-.js";import"./array-BKyUJesY.js";import"./path-CbwjOpE9.js";let H=0;const Y=function(i,a,t,o,p){const g=function(e){switch(e){case p.db.relationType.AGGREGATION:return"aggregation";case p.db.relationType.EXTENSION:return"extension";case p.db.relationType.COMPOSITION:return"composition";case p.db.relationType.DEPENDENCY:return"dependency";case p.db.relationType.LOLLIPOP:return"lollipop"}};a.points=a.points.filter(e=>!Number.isNaN(e.y));const s=a.points,c=X().x(function(e){return e.x}).y(function(e){return e.y}).curve($),n=i.append("path").attr("d",c(s)).attr("id","edge"+H).attr("class","relation");let r="";o.arrowMarkerAbsolute&&(r=window.location.protocol+"//"+window.location.host+window.location.pathname+window.location.search,r=r.replace(/\(/g,"\\("),r=r.replace(/\)/g,"\\)")),t.relation.lineType==1&&n.attr("class","relation dashed-line"),t.relation.lineType==10&&n.attr("class","relation dotted-line"),t.relation.type1!=="none"&&n.attr("marker-start","url("+r+"#"+g(t.relation.type1)+"Start)"),t.relation.type2!=="none"&&n.attr("marker-end","url("+r+"#"+g(t.relation.type2)+"End)");let f,h;const x=a.points.length;let b=M.calcLabelPosition(a.points);f=b.x,h=b.y;let u,m,w,k;if(x%2!==0&&x>1){let e=M.calcCardinalityPosition(t.relation.type1!=="none",a.points,a.points[0]),d=M.calcCardinalityPosition(t.relation.type2!=="none",a.points,a.points[x-1]);y.debug("cardinality_1_point "+JSON.stringify(e)),y.debug("cardinality_2_point "+JSON.stringify(d)),u=e.x,m=e.y,w=d.x,k=d.y}if(t.title!==void 0){const e=i.append("g").attr("class","classLabel"),d=e.append("text").attr("class","label").attr("x",f).attr("y",h).attr("fill","red").attr("text-anchor","middle").text(t.title);window.label=d;const l=d.node().getBBox();e.insert("rect",":first-child").attr("class","box").attr("x",l.x-o.padding/2).attr("y",l.y-o.padding/2).attr("width",l.width+o.padding).attr("height",l.height+o.padding)}y.info("Rendering relation "+JSON.stringify(t)),t.relationTitle1!==void 0&&t.relationTitle1!=="none"&&i.append("g").attr("class","cardinality").append("text").attr("class","type1").attr("x",u).attr("y",m).attr("fill","black").attr("font-size","6").text(t.relationTitle1),t.relationTitle2!==void 0&&t.relationTitle2!=="none"&&i.append("g").attr("class","cardinality").append("text").attr("class","type2").attr("x",w).attr("y",k).attr("fill","black").attr("font-size","6").text(t.relationTitle2),H++},J=function(i,a,t,o){y.debug("Rendering class ",a,t);const p=a.id,g={id:p,label:a.id,width:0,height:0},s=i.append("g").attr("id",o.db.lookUpDomId(p)).attr("class","classGroup");let c;a.link?c=s.append("svg:a").attr("xlink:href",a.link).attr("target",a.linkTarget).append("text").attr("y",t.textHeight+t.padding).attr("x",0):c=s.append("text").attr("y",t.textHeight+t.padding).attr("x",0);let n=!0;a.annotations.forEach(function(d){const l=c.append("tspan").text("«"+d+"»");n||l.attr("dy",t.textHeight),n=!1});let r=C(a);const f=c.append("tspan").text(r).attr("class","title");n||f.attr("dy",t.textHeight);const h=c.node().getBBox().height;let x,b,u;if(a.members.length>0){x=s.append("line").attr("x1",0).attr("y1",t.padding+h+t.dividerMargin/2).attr("y2",t.padding+h+t.dividerMargin/2);const d=s.append("text").attr("x",t.padding).attr("y",h+t.dividerMargin+t.textHeight).attr("fill","white").attr("class","classText");n=!0,a.members.forEach(function(l){_(d,l,n,t),n=!1}),b=d.node().getBBox()}if(a.methods.length>0){u=s.append("line").attr("x1",0).attr("y1",t.padding+h+t.dividerMargin+b.height).attr("y2",t.padding+h+t.dividerMargin+b.height);const d=s.append("text").attr("x",t.padding).attr("y",h+2*t.dividerMargin+b.height+t.textHeight).attr("fill","white").attr("class","classText");n=!0,a.methods.forEach(function(l){_(d,l,n,t),n=!1})}const m=s.node().getBBox();var w=" ";a.cssClasses.length>0&&(w=w+a.cssClasses.join(" "));const e=s.insert("rect",":first-child").attr("x",0).attr("y",0).attr("width",m.width+2*t.padding).attr("height",m.height+t.padding+.5*t.dividerMargin).attr("class",w).node().getBBox().width;return c.node().childNodes.forEach(function(d){d.setAttribute("x",(e-d.getBBox().width)/2)}),a.tooltip&&c.insert("title").text(a.tooltip),x&&x.attr("x2",e),u&&u.attr("x2",e),g.width=e,g.height=m.height+t.padding+.5*t.dividerMargin,g},C=function(i){let a=i.id;return i.type&&(a+="<"+I(i.type)+">"),a},Z=function(i,a,t,o){y.debug("Rendering note ",a,t);const p=a.id,g={id:p,text:a.text,width:0,height:0},s=i.append("g").attr("id",p).attr("class","classGroup");let c=s.append("text").attr("y",t.textHeight+t.padding).attr("x",0);const n=JSON.parse(`"${a.text}"`).split(`
+import{p as A,d as S,s as G}from"./styles-e2b9d258-CoUUuHq5.js";import{c as v,l as y,h as B,i as W,ao as $,z as M,ar as I}from"./mermaid.core-DNo_7Q2B.js";import{G as O}from"./graph-B1296pfd.js";import{l as P}from"./layout-qMafh1ee.js";import{l as X}from"./line-BqHmcuby.js";import"./app-B4LGNJZ0.js";import"./array-BKyUJesY.js";import"./path-CbwjOpE9.js";let H=0;const Y=function(i,a,t,o,p){const g=function(e){switch(e){case p.db.relationType.AGGREGATION:return"aggregation";case p.db.relationType.EXTENSION:return"extension";case p.db.relationType.COMPOSITION:return"composition";case p.db.relationType.DEPENDENCY:return"dependency";case p.db.relationType.LOLLIPOP:return"lollipop"}};a.points=a.points.filter(e=>!Number.isNaN(e.y));const s=a.points,c=X().x(function(e){return e.x}).y(function(e){return e.y}).curve($),n=i.append("path").attr("d",c(s)).attr("id","edge"+H).attr("class","relation");let r="";o.arrowMarkerAbsolute&&(r=window.location.protocol+"//"+window.location.host+window.location.pathname+window.location.search,r=r.replace(/\(/g,"\\("),r=r.replace(/\)/g,"\\)")),t.relation.lineType==1&&n.attr("class","relation dashed-line"),t.relation.lineType==10&&n.attr("class","relation dotted-line"),t.relation.type1!=="none"&&n.attr("marker-start","url("+r+"#"+g(t.relation.type1)+"Start)"),t.relation.type2!=="none"&&n.attr("marker-end","url("+r+"#"+g(t.relation.type2)+"End)");let f,h;const x=a.points.length;let b=M.calcLabelPosition(a.points);f=b.x,h=b.y;let u,m,w,k;if(x%2!==0&&x>1){let e=M.calcCardinalityPosition(t.relation.type1!=="none",a.points,a.points[0]),d=M.calcCardinalityPosition(t.relation.type2!=="none",a.points,a.points[x-1]);y.debug("cardinality_1_point "+JSON.stringify(e)),y.debug("cardinality_2_point "+JSON.stringify(d)),u=e.x,m=e.y,w=d.x,k=d.y}if(t.title!==void 0){const e=i.append("g").attr("class","classLabel"),d=e.append("text").attr("class","label").attr("x",f).attr("y",h).attr("fill","red").attr("text-anchor","middle").text(t.title);window.label=d;const l=d.node().getBBox();e.insert("rect",":first-child").attr("class","box").attr("x",l.x-o.padding/2).attr("y",l.y-o.padding/2).attr("width",l.width+o.padding).attr("height",l.height+o.padding)}y.info("Rendering relation "+JSON.stringify(t)),t.relationTitle1!==void 0&&t.relationTitle1!=="none"&&i.append("g").attr("class","cardinality").append("text").attr("class","type1").attr("x",u).attr("y",m).attr("fill","black").attr("font-size","6").text(t.relationTitle1),t.relationTitle2!==void 0&&t.relationTitle2!=="none"&&i.append("g").attr("class","cardinality").append("text").attr("class","type2").attr("x",w).attr("y",k).attr("fill","black").attr("font-size","6").text(t.relationTitle2),H++},J=function(i,a,t,o){y.debug("Rendering class ",a,t);const p=a.id,g={id:p,label:a.id,width:0,height:0},s=i.append("g").attr("id",o.db.lookUpDomId(p)).attr("class","classGroup");let c;a.link?c=s.append("svg:a").attr("xlink:href",a.link).attr("target",a.linkTarget).append("text").attr("y",t.textHeight+t.padding).attr("x",0):c=s.append("text").attr("y",t.textHeight+t.padding).attr("x",0);let n=!0;a.annotations.forEach(function(d){const l=c.append("tspan").text("«"+d+"»");n||l.attr("dy",t.textHeight),n=!1});let r=C(a);const f=c.append("tspan").text(r).attr("class","title");n||f.attr("dy",t.textHeight);const h=c.node().getBBox().height;let x,b,u;if(a.members.length>0){x=s.append("line").attr("x1",0).attr("y1",t.padding+h+t.dividerMargin/2).attr("y2",t.padding+h+t.dividerMargin/2);const d=s.append("text").attr("x",t.padding).attr("y",h+t.dividerMargin+t.textHeight).attr("fill","white").attr("class","classText");n=!0,a.members.forEach(function(l){_(d,l,n,t),n=!1}),b=d.node().getBBox()}if(a.methods.length>0){u=s.append("line").attr("x1",0).attr("y1",t.padding+h+t.dividerMargin+b.height).attr("y2",t.padding+h+t.dividerMargin+b.height);const d=s.append("text").attr("x",t.padding).attr("y",h+2*t.dividerMargin+b.height+t.textHeight).attr("fill","white").attr("class","classText");n=!0,a.methods.forEach(function(l){_(d,l,n,t),n=!1})}const m=s.node().getBBox();var w=" ";a.cssClasses.length>0&&(w=w+a.cssClasses.join(" "));const e=s.insert("rect",":first-child").attr("x",0).attr("y",0).attr("width",m.width+2*t.padding).attr("height",m.height+t.padding+.5*t.dividerMargin).attr("class",w).node().getBBox().width;return c.node().childNodes.forEach(function(d){d.setAttribute("x",(e-d.getBBox().width)/2)}),a.tooltip&&c.insert("title").text(a.tooltip),x&&x.attr("x2",e),u&&u.attr("x2",e),g.width=e,g.height=m.height+t.padding+.5*t.dividerMargin,g},C=function(i){let a=i.id;return i.type&&(a+="<"+I(i.type)+">"),a},Z=function(i,a,t,o){y.debug("Rendering note ",a,t);const p=a.id,g={id:p,text:a.text,width:0,height:0},s=i.append("g").attr("id",p).attr("class","classGroup");let c=s.append("text").attr("y",t.textHeight+t.padding).attr("x",0);const n=JSON.parse(`"${a.text}"`).split(`
 `);n.forEach(function(x){y.debug(`Adding line: ${x}`),c.append("tspan").text(x).attr("class","title").attr("dy",t.textHeight)});const r=s.node().getBBox(),h=s.insert("rect",":first-child").attr("x",0).attr("y",0).attr("width",r.width+2*t.padding).attr("height",r.height+n.length*t.textHeight+t.padding+.5*t.dividerMargin).node().getBBox().width;return c.node().childNodes.forEach(function(x){x.setAttribute("x",(h-x.getBBox().width)/2)}),g.width=h,g.height=r.height+n.length*t.textHeight+t.padding+.5*t.dividerMargin,g},_=function(i,a,t,o){const{displayText:p,cssStyle:g}=a.getDisplayDetails(),s=i.append("tspan").attr("x",o.padding).text(p);g!==""&&s.attr("style",a.cssStyle),t||s.attr("dy",o.textHeight)},N={getClassTitleString:C,drawClass:J,drawEdge:Y,drawNote:Z};let T={};const E=20,L=function(i){const a=Object.entries(T).find(t=>t[1].label===i);if(a)return a[0]},R=function(i){i.append("defs").append("marker").attr("id","extensionStart").attr("class","extension").attr("refX",0).attr("refY",7).attr("markerWidth",190).attr("markerHeight",240).attr("orient","auto").append("path").attr("d","M 1,7 L18,13 V 1 Z"),i.append("defs").append("marker").attr("id","extensionEnd").attr("refX",19).attr("refY",7).attr("markerWidth",20).attr("markerHeight",28).attr("orient","auto").append("path").attr("d","M 1,1 V 13 L18,7 Z"),i.append("defs").append("marker").attr("id","compositionStart").attr("class","extension").attr("refX",0).attr("refY",7).attr("markerWidth",190).attr("markerHeight",240).attr("orient","auto").append("path").attr("d","M 18,7 L9,13 L1,7 L9,1 Z"),i.append("defs").append("marker").attr("id","compositionEnd").attr("refX",19).attr("refY",7).attr("markerWidth",20).attr("markerHeight",28).attr("orient","auto").append("path").attr("d","M 18,7 L9,13 L1,7 L9,1 Z"),i.append("defs").append("marker").attr("id","aggregationStart").attr("class","extension").attr("refX",0).attr("refY",7).attr("markerWidth",190).attr("markerHeight",240).attr("orient","auto").append("path").attr("d","M 18,7 L9,13 L1,7 L9,1 Z"),i.append("defs").append("marker").attr("id","aggregationEnd").attr("refX",19).attr("refY",7).attr("markerWidth",20).attr("markerHeight",28).attr("orient","auto").append("path").attr("d","M 18,7 L9,13 L1,7 L9,1 Z"),i.append("defs").append("marker").attr("id","dependencyStart").attr("class","extension").attr("refX",0).attr("refY",7).attr("markerWidth",190).attr("markerHeight",240).attr("orient","auto").append("path").attr("d","M 5,7 L9,13 L1,7 L9,1 Z"),i.append("defs").append("marker").attr("id","dependencyEnd").attr("refX",19).attr("refY",7).attr("markerWidth",20).attr("markerHeight",28).attr("orient","auto").append("path").attr("d","M 18,7 L9,13 L14,7 L9,1 Z")},z=function(i,a,t,o){const p=v().class;T={},y.info("Rendering diagram "+i);const g=v().securityLevel;let s;g==="sandbox"&&(s=B("#i"+a));const c=g==="sandbox"?B(s.nodes()[0].contentDocument.body):B("body"),n=c.select(`[id='${a}']`);R(n);const r=new O({multigraph:!0});r.setGraph({isMultiGraph:!0}),r.setDefaultEdgeLabel(function(){return{}});const f=o.db.getClasses(),h=Object.keys(f);for(const e of h){const d=f[e],l=N.drawClass(n,d,p,o);T[l.id]=l,r.setNode(l.id,l),y.info("Org height: "+l.height)}o.db.getRelations().forEach(function(e){y.info("tjoho"+L(e.id1)+L(e.id2)+JSON.stringify(e)),r.setEdge(L(e.id1),L(e.id2),{relation:e},e.title||"DEFAULT")}),o.db.getNotes().forEach(function(e){y.debug(`Adding note: ${JSON.stringify(e)}`);const d=N.drawNote(n,e,p,o);T[d.id]=d,r.setNode(d.id,d),e.class&&e.class in f&&r.setEdge(e.id,L(e.class),{relation:{id1:e.id,id2:e.class,relation:{type1:"none",type2:"none",lineType:10}}},"DEFAULT")}),P(r),r.nodes().forEach(function(e){e!==void 0&&r.node(e)!==void 0&&(y.debug("Node "+e+": "+JSON.stringify(r.node(e))),c.select("#"+(o.db.lookUpDomId(e)||e)).attr("transform","translate("+(r.node(e).x-r.node(e).width/2)+","+(r.node(e).y-r.node(e).height/2)+" )"))}),r.edges().forEach(function(e){e!==void 0&&r.edge(e)!==void 0&&(y.debug("Edge "+e.v+" -> "+e.w+": "+JSON.stringify(r.edge(e))),N.drawEdge(n,r.edge(e),r.edge(e).relation,p,o))});const u=n.node().getBBox(),m=u.width+E*2,w=u.height+E*2;W(n,w,m,p.useMaxWidth);const k=`${u.x-E} ${u.y-E} ${m} ${w}`;y.debug(`viewBox ${k}`),n.attr("viewBox",k)},F={draw:z},et={parser:A,db:S,renderer:F,styles:G,init:i=>{i.class||(i.class={}),i.class.arrowMarkerAbsolute=i.arrowMarkerAbsolute,S.clear()}};export{et as diagram};
diff --git a/assets/classDiagram-v2-296fb1cd-BmyNy9b3.js b/assets/classDiagram-v2-296fb1cd-DTrZkQpq.js
similarity index 92%
rename from assets/classDiagram-v2-296fb1cd-BmyNy9b3.js
rename to assets/classDiagram-v2-296fb1cd-DTrZkQpq.js
index 030bc84..560982c 100644
--- a/assets/classDiagram-v2-296fb1cd-BmyNy9b3.js
+++ b/assets/classDiagram-v2-296fb1cd-DTrZkQpq.js
@@ -1,2 +1,2 @@
-import{p as M,d as _,s as R}from"./styles-e2b9d258-TYWOaoPC.js";import{l as d,c,h as w,z as B,u as G,p as D,t as E,o as C,j as A}from"./mermaid.core-ChLYKTZm.js";import{G as z}from"./graph-T5JS4vfK.js";import{r as P}from"./index-9620d214-B8uh0R2i.js";import"./layout-DUYLy6Ue.js";import"./app-B69Gl_S-.js";import"./clone-CI3kFeqi.js";import"./edges-5962ec63-B19hLEst.js";import"./createText-4a4f35c9-BuT3nXUz.js";import"./line-D0jG_HZ-.js";import"./array-BKyUJesY.js";import"./path-CbwjOpE9.js";const S=s=>A.sanitizeText(s,c());let k={dividerMargin:10,padding:5,textHeight:10,curve:void 0};const q=function(s,t,y,a){const e=Object.keys(s);d.info("keys:",e),d.info(s),e.forEach(function(i){var o,r;const l=s[i],p={shape:"rect",id:l.id,domId:l.domId,labelText:S(l.id),labelStyle:"",style:"fill: none; stroke: black",padding:((o=c().flowchart)==null?void 0:o.padding)??((r=c().class)==null?void 0:r.padding)};t.setNode(l.id,p),$(l.classes,t,y,a,l.id),d.info("setNode",p)})},$=function(s,t,y,a,e){const i=Object.keys(s);d.info("keys:",i),d.info(s),i.filter(o=>s[o].parent==e).forEach(function(o){var r,l;const n=s[o],p=n.cssClasses.join(" "),f=D(n.styles),h=n.label??n.id,u=0,b={labelStyle:f.labelStyle,shape:"class_box",labelText:S(h),classData:n,rx:u,ry:u,class:p,style:f.style,id:n.id,domId:n.domId,tooltip:a.db.getTooltip(n.id,e)||"",haveCallback:n.haveCallback,link:n.link,width:n.type==="group"?500:void 0,type:n.type,padding:((r=c().flowchart)==null?void 0:r.padding)??((l=c().class)==null?void 0:l.padding)};t.setNode(n.id,b),e&&t.setParent(n.id,e),d.info("setNode",b)})},F=function(s,t,y,a){d.info(s),s.forEach(function(e,i){var o,r;const l=e,n="",p={labelStyle:"",style:""},f=l.text,h=0,m={labelStyle:p.labelStyle,shape:"note",labelText:S(f),noteData:l,rx:h,ry:h,class:n,style:p.style,id:l.id,domId:l.id,tooltip:"",type:"note",padding:((o=c().flowchart)==null?void 0:o.padding)??((r=c().class)==null?void 0:r.padding)};if(t.setNode(l.id,m),d.info("setNode",m),!l.class||!(l.class in a))return;const b=y+i,x={id:`edgeNote${b}`,classes:"relation",pattern:"dotted",arrowhead:"none",startLabelRight:"",endLabelLeft:"",arrowTypeStart:"none",arrowTypeEnd:"none",style:"fill:none",labelStyle:"",curve:E(k.curve,C)};t.setEdge(l.id,l.class,x,b)})},H=function(s,t){const y=c().flowchart;let a=0;s.forEach(function(e){var i;a++;const o={classes:"relation",pattern:e.relation.lineType==1?"dashed":"solid",id:`id_${e.id1}_${e.id2}_${a}`,arrowhead:e.type==="arrow_open"?"none":"normal",startLabelRight:e.relationTitle1==="none"?"":e.relationTitle1,endLabelLeft:e.relationTitle2==="none"?"":e.relationTitle2,arrowTypeStart:N(e.relation.type1),arrowTypeEnd:N(e.relation.type2),style:"fill:none",labelStyle:"",curve:E(y==null?void 0:y.curve,C)};if(d.info(o,e),e.style!==void 0){const r=D(e.style);o.style=r.style,o.labelStyle=r.labelStyle}e.text=e.title,e.text===void 0?e.style!==void 0&&(o.arrowheadStyle="fill: #333"):(o.arrowheadStyle="fill: #333",o.labelpos="c",((i=c().flowchart)==null?void 0:i.htmlLabels)??c().htmlLabels?(o.labelType="html",o.label='<span class="edgeLabel">'+e.text+"</span>"):(o.labelType="text",o.label=e.text.replace(A.lineBreakRegex,`
+import{p as M,d as _,s as R}from"./styles-e2b9d258-CoUUuHq5.js";import{l as d,c,h as w,z as B,u as G,p as D,t as E,o as C,j as A}from"./mermaid.core-DNo_7Q2B.js";import{G as z}from"./graph-B1296pfd.js";import{r as P}from"./index-9620d214-BlfbO5wW.js";import"./layout-qMafh1ee.js";import"./app-B4LGNJZ0.js";import"./clone-C3EvpqoY.js";import"./edges-5962ec63-ApWhby2b.js";import"./createText-4a4f35c9-CISzj231.js";import"./line-BqHmcuby.js";import"./array-BKyUJesY.js";import"./path-CbwjOpE9.js";const S=s=>A.sanitizeText(s,c());let k={dividerMargin:10,padding:5,textHeight:10,curve:void 0};const q=function(s,t,y,a){const e=Object.keys(s);d.info("keys:",e),d.info(s),e.forEach(function(i){var o,r;const l=s[i],p={shape:"rect",id:l.id,domId:l.domId,labelText:S(l.id),labelStyle:"",style:"fill: none; stroke: black",padding:((o=c().flowchart)==null?void 0:o.padding)??((r=c().class)==null?void 0:r.padding)};t.setNode(l.id,p),$(l.classes,t,y,a,l.id),d.info("setNode",p)})},$=function(s,t,y,a,e){const i=Object.keys(s);d.info("keys:",i),d.info(s),i.filter(o=>s[o].parent==e).forEach(function(o){var r,l;const n=s[o],p=n.cssClasses.join(" "),f=D(n.styles),h=n.label??n.id,u=0,b={labelStyle:f.labelStyle,shape:"class_box",labelText:S(h),classData:n,rx:u,ry:u,class:p,style:f.style,id:n.id,domId:n.domId,tooltip:a.db.getTooltip(n.id,e)||"",haveCallback:n.haveCallback,link:n.link,width:n.type==="group"?500:void 0,type:n.type,padding:((r=c().flowchart)==null?void 0:r.padding)??((l=c().class)==null?void 0:l.padding)};t.setNode(n.id,b),e&&t.setParent(n.id,e),d.info("setNode",b)})},F=function(s,t,y,a){d.info(s),s.forEach(function(e,i){var o,r;const l=e,n="",p={labelStyle:"",style:""},f=l.text,h=0,m={labelStyle:p.labelStyle,shape:"note",labelText:S(f),noteData:l,rx:h,ry:h,class:n,style:p.style,id:l.id,domId:l.id,tooltip:"",type:"note",padding:((o=c().flowchart)==null?void 0:o.padding)??((r=c().class)==null?void 0:r.padding)};if(t.setNode(l.id,m),d.info("setNode",m),!l.class||!(l.class in a))return;const b=y+i,x={id:`edgeNote${b}`,classes:"relation",pattern:"dotted",arrowhead:"none",startLabelRight:"",endLabelLeft:"",arrowTypeStart:"none",arrowTypeEnd:"none",style:"fill:none",labelStyle:"",curve:E(k.curve,C)};t.setEdge(l.id,l.class,x,b)})},H=function(s,t){const y=c().flowchart;let a=0;s.forEach(function(e){var i;a++;const o={classes:"relation",pattern:e.relation.lineType==1?"dashed":"solid",id:`id_${e.id1}_${e.id2}_${a}`,arrowhead:e.type==="arrow_open"?"none":"normal",startLabelRight:e.relationTitle1==="none"?"":e.relationTitle1,endLabelLeft:e.relationTitle2==="none"?"":e.relationTitle2,arrowTypeStart:N(e.relation.type1),arrowTypeEnd:N(e.relation.type2),style:"fill:none",labelStyle:"",curve:E(y==null?void 0:y.curve,C)};if(d.info(o,e),e.style!==void 0){const r=D(e.style);o.style=r.style,o.labelStyle=r.labelStyle}e.text=e.title,e.text===void 0?e.style!==void 0&&(o.arrowheadStyle="fill: #333"):(o.arrowheadStyle="fill: #333",o.labelpos="c",((i=c().flowchart)==null?void 0:i.htmlLabels)??c().htmlLabels?(o.labelType="html",o.label='<span class="edgeLabel">'+e.text+"</span>"):(o.labelType="text",o.label=e.text.replace(A.lineBreakRegex,`
 `),e.style===void 0&&(o.style=o.style||"stroke: #333; stroke-width: 1.5px;fill:none"),o.labelStyle=o.labelStyle.replace("color:","fill:"))),t.setEdge(e.id1,e.id2,o,a)})},V=function(s){k={...k,...s}},W=async function(s,t,y,a){d.info("Drawing class - ",t);const e=c().flowchart??c().class,i=c().securityLevel;d.info("config:",e);const o=(e==null?void 0:e.nodeSpacing)??50,r=(e==null?void 0:e.rankSpacing)??50,l=new z({multigraph:!0,compound:!0}).setGraph({rankdir:a.db.getDirection(),nodesep:o,ranksep:r,marginx:8,marginy:8}).setDefaultEdgeLabel(function(){return{}}),n=a.db.getNamespaces(),p=a.db.getClasses(),f=a.db.getRelations(),h=a.db.getNotes();d.info(f),q(n,l,t,a),$(p,l,t,a),H(f,l),F(h,l,f.length+1,p);let u;i==="sandbox"&&(u=w("#i"+t));const m=i==="sandbox"?w(u.nodes()[0].contentDocument.body):w("body"),b=m.select(`[id="${t}"]`),x=m.select("#"+t+" g");if(await P(x,l,["aggregation","extension","composition","dependency","lollipop"],"classDiagram",t),B.insertTitle(b,"classTitleText",(e==null?void 0:e.titleTopMargin)??5,a.db.getDiagramTitle()),G(l,b,e==null?void 0:e.diagramPadding,e==null?void 0:e.useMaxWidth),!(e!=null&&e.htmlLabels)){const T=i==="sandbox"?u.nodes()[0].contentDocument:document,I=T.querySelectorAll('[id="'+t+'"] .edgeLabel .label');for(const g of I){const L=g.getBBox(),v=T.createElementNS("http://www.w3.org/2000/svg","rect");v.setAttribute("rx",0),v.setAttribute("ry",0),v.setAttribute("width",L.width),v.setAttribute("height",L.height),g.insertBefore(v,g.firstChild)}}};function N(s){let t;switch(s){case 0:t="aggregation";break;case 1:t="extension";break;case 2:t="composition";break;case 3:t="dependency";break;case 4:t="lollipop";break;default:t="none"}return t}const J={setConf:V,draw:W},se={parser:M,db:_,renderer:J,styles:R,init:s=>{s.class||(s.class={}),s.class.arrowMarkerAbsolute=s.arrowMarkerAbsolute,_.clear()}};export{se as diagram};
diff --git a/assets/clone-C3EvpqoY.js b/assets/clone-C3EvpqoY.js
new file mode 100644
index 0000000..be40e14
--- /dev/null
+++ b/assets/clone-C3EvpqoY.js
@@ -0,0 +1 @@
+import{a as r}from"./graph-B1296pfd.js";var a=4;function n(o){return r(o,a)}export{n as c};
diff --git a/assets/clone-CI3kFeqi.js b/assets/clone-CI3kFeqi.js
deleted file mode 100644
index 3e6d9dd..0000000
--- a/assets/clone-CI3kFeqi.js
+++ /dev/null
@@ -1 +0,0 @@
-import{a as r}from"./graph-T5JS4vfK.js";var a=4;function n(o){return r(o,a)}export{n as c};
diff --git a/assets/command.html-d4IhdjVF.js b/assets/command.html-Bzqk5uGA.js
similarity index 99%
rename from assets/command.html-d4IhdjVF.js
rename to assets/command.html-Bzqk5uGA.js
index 6878f3b..61515b4 100644
--- a/assets/command.html-d4IhdjVF.js
+++ b/assets/command.html-Bzqk5uGA.js
@@ -1,4 +1,4 @@
-import{_ as n,o as s,c as a,f as t}from"./app-B69Gl_S-.js";const p={},e=t(`<h2 id="为什么使用此模式" tabindex="-1"><a class="header-anchor" href="#为什么使用此模式"><span>为什么使用此模式</span></a></h2><p>Command 模式将请求封装成对象，使得可以用不同的请求、队列或者日志来参数化其他对象。Command 模式也支持可撤销的操作。</p><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/bL992i8m5Dtt55bMj1VeGWfrwmd4nM_ofOKCag6sY7St7Va5kt2NzwStaC9vi3uecJJQetq0HrOQfK0BzauOEsA7F7XC3pbhJIEIJq8cBnPUK4cSHaL4QPSp7LI5ziJwvKbskGJdnhqIT0kEDUefKQ7sRdijgnldZOqthi2jcJKDD4-80bOz__FExWWnDPojXmRGKy2ZufnetubdegAgTxdu15o-b6_tqM5mTJhtrXOn7BGmD00k4Imj_5158i-oypPK6ilG91OBr2B-ZYy0" alt=""><img src="https://www.plantuml.com/plantuml/svg/RP512eGm34NtFKLmLS6vm2m6mTdE8K9RiA2nj75qRZ_51gpWBltvUVz3-yGOUPqdXOQN2CFa7R4AMVJ61oI6vXrn6v2-c1h01EOOhvOFchWCopmZsSCq-fHnlnjGPJ9bLggamkCby2UGs-3CrO9hAwT8nLhdwzeb4HLGJ2MeWxs3UsnOqwZblBrf6D0JvwpolfowtPcLNLwAT6boRaMggJPNrALJxyZcZ_a3" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// command.ts</span>
+import{_ as n,o as s,c as a,f as t}from"./app-B4LGNJZ0.js";const p={},e=t(`<h2 id="为什么使用此模式" tabindex="-1"><a class="header-anchor" href="#为什么使用此模式"><span>为什么使用此模式</span></a></h2><p>Command 模式将请求封装成对象，使得可以用不同的请求、队列或者日志来参数化其他对象。Command 模式也支持可撤销的操作。</p><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/bL992i8m5Dtt55bMj1VeGWfrwmd4nM_ofOKCag6sY7St7Va5kt2NzwStaC9vi3uecJJQetq0HrOQfK0BzauOEsA7F7XC3pbhJIEIJq8cBnPUK4cSHaL4QPSp7LI5ziJwvKbskGJdnhqIT0kEDUefKQ7sRdijgnldZOqthi2jcJKDD4-80bOz__FExWWnDPojXmRGKy2ZufnetubdegAgTxdu15o-b6_tqM5mTJhtrXOn7BGmD00k4Imj_5158i-oypPK6ilG91OBr2B-ZYy0" alt=""><img src="https://www.plantuml.com/plantuml/svg/RP512eGm34NtFKLmLS6vm2m6mTdE8K9RiA2nj75qRZ_51gpWBltvUVz3-yGOUPqdXOQN2CFa7R4AMVJ61oI6vXrn6v2-c1h01EOOhvOFchWCopmZsSCq-fHnlnjGPJ9bLggamkCby2UGs-3CrO9hAwT8nLhdwzeb4HLGJ2MeWxs3UsnOqwZblBrf6D0JvwpolfowtPcLNLwAT6boRaMggJPNrALJxyZcZ_a3" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// command.ts</span>
 <span class="token keyword">export</span> <span class="token keyword">interface</span> <span class="token class-name">Command</span> <span class="token punctuation">{</span>
   <span class="token function">execute</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">:</span> <span class="token keyword">void</span><span class="token punctuation">;</span>
 <span class="token punctuation">}</span>
diff --git a/assets/composite.html-DOBxYen3.js b/assets/composite.html-D89dw1yo.js
similarity index 99%
rename from assets/composite.html-DOBxYen3.js
rename to assets/composite.html-D89dw1yo.js
index 89c8a9e..f6aeefa 100644
--- a/assets/composite.html-DOBxYen3.js
+++ b/assets/composite.html-D89dw1yo.js
@@ -1,4 +1,4 @@
-import{_ as n,o as s,c as a,f as t}from"./app-B69Gl_S-.js";const p={},e=t(`<h2 id="使用此设计模式的理由" tabindex="-1"><a class="header-anchor" href="#使用此设计模式的理由"><span>使用此设计模式的理由</span></a></h2><p>Composite 模式允许你将对象组合成递归结构来表示“部分-整体”的层次结构。使用 Composite 模式，用户可以统一地对待单个对象和组合对象。例如，在文件系统中，目录和文件都可以被视为条目（Entry），目录可以包含其他目录和文件，而文件则是叶子节点。</p><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/hPAn3e8m48Ptdk8I5mZX1OW3WpePOyBWO1mAFR495D8U1ZM-kwM0A77GnEcI_-xQxsiQQMAAwY9tMA99iPGWpPdMi9IaBd1p07p8a3QiGDSBmSm8cGrfBAusbNMHeB8fuzp5TZViZl3wQfkLMQQrqDGkdKl1JJeRqvsWqrRXKJHkPSjmtpZj0vMnpLvexexJGI-4mfHA0uuDeUIzHciH01-QFT7-O6DfpAPU_x3znUifi18vVcAVG0QW3SiRoVVKlu6DJpeFWhAtYmoV-JCF" alt=""><h3 id="目录类-directory-ts" tabindex="-1"><a class="header-anchor" href="#目录类-directory-ts"><span>目录类 (directory.ts)</span></a></h3><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token keyword">import</span> <span class="token punctuation">{</span> Entry <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&#39;./entry&#39;</span><span class="token punctuation">;</span>
+import{_ as n,o as s,c as a,f as t}from"./app-B4LGNJZ0.js";const p={},e=t(`<h2 id="使用此设计模式的理由" tabindex="-1"><a class="header-anchor" href="#使用此设计模式的理由"><span>使用此设计模式的理由</span></a></h2><p>Composite 模式允许你将对象组合成递归结构来表示“部分-整体”的层次结构。使用 Composite 模式，用户可以统一地对待单个对象和组合对象。例如，在文件系统中，目录和文件都可以被视为条目（Entry），目录可以包含其他目录和文件，而文件则是叶子节点。</p><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/hPAn3e8m48Ptdk8I5mZX1OW3WpePOyBWO1mAFR495D8U1ZM-kwM0A77GnEcI_-xQxsiQQMAAwY9tMA99iPGWpPdMi9IaBd1p07p8a3QiGDSBmSm8cGrfBAusbNMHeB8fuzp5TZViZl3wQfkLMQQrqDGkdKl1JJeRqvsWqrRXKJHkPSjmtpZj0vMnpLvexexJGI-4mfHA0uuDeUIzHciH01-QFT7-O6DfpAPU_x3znUifi18vVcAVG0QW3SiRoVVKlu6DJpeFWhAtYmoV-JCF" alt=""><h3 id="目录类-directory-ts" tabindex="-1"><a class="header-anchor" href="#目录类-directory-ts"><span>目录类 (directory.ts)</span></a></h3><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token keyword">import</span> <span class="token punctuation">{</span> Entry <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&#39;./entry&#39;</span><span class="token punctuation">;</span>
 <span class="token keyword">export</span> <span class="token keyword">class</span> <span class="token class-name">Directory</span> <span class="token keyword">extends</span> <span class="token class-name">Entry</span> <span class="token punctuation">{</span>
   <span class="token keyword">private</span> directory<span class="token operator">:</span> Entry<span class="token punctuation">[</span><span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
   <span class="token function">constructor</span><span class="token punctuation">(</span><span class="token keyword">private</span> name<span class="token operator">:</span> <span class="token builtin">string</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
diff --git a/assets/createText-4a4f35c9-BuT3nXUz.js b/assets/createText-4a4f35c9-CISzj231.js
similarity index 99%
rename from assets/createText-4a4f35c9-BuT3nXUz.js
rename to assets/createText-4a4f35c9-CISzj231.js
index bd8c7ef..d57b997 100644
--- a/assets/createText-4a4f35c9-BuT3nXUz.js
+++ b/assets/createText-4a4f35c9-CISzj231.js
@@ -1,4 +1,4 @@
-import{l as At,an as zt,ap as It}from"./mermaid.core-ChLYKTZm.js";const Tt={};function Bt(n,r){const t=Tt,e=typeof t.includeImageAlt=="boolean"?t.includeImageAlt:!0,u=typeof t.includeHtml=="boolean"?t.includeHtml:!0;return et(n,e,u)}function et(n,r,t){if(Lt(n)){if("value"in n)return n.type==="html"&&!t?"":n.value;if(r&&"alt"in n&&n.alt)return n.alt;if("children"in n)return Vn(n.children,r,t)}return Array.isArray(n)?Vn(n,r,t):""}function Vn(n,r,t){const e=[];let u=-1;for(;++u<n.length;)e[u]=et(n[u],r,t);return e.join("")}function Lt(n){return!!(n&&typeof n=="object")}function tn(n,r,t,e){const u=n.length;let i=0,l;if(r<0?r=-r>u?0:u+r:r=r>u?u:r,t=t>0?t:0,e.length<1e4)l=Array.from(e),l.unshift(r,t),n.splice(...l);else for(t&&n.splice(r,t);i<e.length;)l=e.slice(i,i+1e4),l.unshift(r,0),n.splice(...l),i+=1e4,r+=1e4}function Y(n,r){return n.length>0?(tn(n,n.length,0,r),n):r}const Wn={}.hasOwnProperty;function Ot(n){const r={};let t=-1;for(;++t<n.length;)Dt(r,n[t]);return r}function Dt(n,r){let t;for(t in r){const u=(Wn.call(n,t)?n[t]:void 0)||(n[t]={}),i=r[t];let l;if(i)for(l in i){Wn.call(u,l)||(u[l]=[]);const a=i[l];Pt(u[l],Array.isArray(a)?a:a?[a]:[])}}}function Pt(n,r){let t=-1;const e=[];for(;++t<r.length;)(r[t].add==="after"?n:e).push(r[t]);tn(n,0,0,e)}const _t=/[!-\/:-@\[-`\{-~\xA1\xA7\xAB\xB6\xB7\xBB\xBF\u037E\u0387\u055A-\u055F\u0589\u058A\u05BE\u05C0\u05C3\u05C6\u05F3\u05F4\u0609\u060A\u060C\u060D\u061B\u061D-\u061F\u066A-\u066D\u06D4\u0700-\u070D\u07F7-\u07F9\u0830-\u083E\u085E\u0964\u0965\u0970\u09FD\u0A76\u0AF0\u0C77\u0C84\u0DF4\u0E4F\u0E5A\u0E5B\u0F04-\u0F12\u0F14\u0F3A-\u0F3D\u0F85\u0FD0-\u0FD4\u0FD9\u0FDA\u104A-\u104F\u10FB\u1360-\u1368\u1400\u166E\u169B\u169C\u16EB-\u16ED\u1735\u1736\u17D4-\u17D6\u17D8-\u17DA\u1800-\u180A\u1944\u1945\u1A1E\u1A1F\u1AA0-\u1AA6\u1AA8-\u1AAD\u1B5A-\u1B60\u1B7D\u1B7E\u1BFC-\u1BFF\u1C3B-\u1C3F\u1C7E\u1C7F\u1CC0-\u1CC7\u1CD3\u2010-\u2027\u2030-\u2043\u2045-\u2051\u2053-\u205E\u207D\u207E\u208D\u208E\u2308-\u230B\u2329\u232A\u2768-\u2775\u27C5\u27C6\u27E6-\u27EF\u2983-\u2998\u29D8-\u29DB\u29FC\u29FD\u2CF9-\u2CFC\u2CFE\u2CFF\u2D70\u2E00-\u2E2E\u2E30-\u2E4F\u2E52-\u2E5D\u3001-\u3003\u3008-\u3011\u3014-\u301F\u3030\u303D\u30A0\u30FB\uA4FE\uA4FF\uA60D-\uA60F\uA673\uA67E\uA6F2-\uA6F7\uA874-\uA877\uA8CE\uA8CF\uA8F8-\uA8FA\uA8FC\uA92E\uA92F\uA95F\uA9C1-\uA9CD\uA9DE\uA9DF\uAA5C-\uAA5F\uAADE\uAADF\uAAF0\uAAF1\uABEB\uFD3E\uFD3F\uFE10-\uFE19\uFE30-\uFE52\uFE54-\uFE61\uFE63\uFE68\uFE6A\uFE6B\uFF01-\uFF03\uFF05-\uFF0A\uFF0C-\uFF0F\uFF1A\uFF1B\uFF1F\uFF20\uFF3B-\uFF3D\uFF3F\uFF5B\uFF5D\uFF5F-\uFF65]/,nn=cn(/[A-Za-z]/),v=cn(/[\dA-Za-z]/),Mt=cn(/[#-'*+\--9=?A-Z^-~]/);function An(n){return n!==null&&(n<32||n===127)}const zn=cn(/\d/),jt=cn(/[\dA-Fa-f]/),Rt=cn(/[!-/:-@[-`{-~]/);function C(n){return n!==null&&n<-2}function Z(n){return n!==null&&(n<0||n===32)}function z(n){return n===-2||n===-1||n===32}const qt=cn(_t),Ht=cn(/\s/);function cn(n){return r;function r(t){return t!==null&&n.test(String.fromCharCode(t))}}function O(n,r,t,e){const u=e?e-1:Number.POSITIVE_INFINITY;let i=0;return l;function l(m){return z(m)?(n.enter(t),a(m)):r(m)}function a(m){return z(m)&&i++<u?(n.consume(m),a):(n.exit(t),r(m))}}const Nt={tokenize:Vt};function Vt(n){const r=n.attempt(this.parser.constructs.contentInitial,e,u);let t;return r;function e(a){if(a===null){n.consume(a);return}return n.enter("lineEnding"),n.consume(a),n.exit("lineEnding"),O(n,r,"linePrefix")}function u(a){return n.enter("paragraph"),i(a)}function i(a){const m=n.enter("chunkText",{contentType:"text",previous:t});return t&&(t.next=m),t=m,l(a)}function l(a){if(a===null){n.exit("chunkText"),n.exit("paragraph"),n.consume(a);return}return C(a)?(n.consume(a),n.exit("chunkText"),i):(n.consume(a),l)}}const Wt={tokenize:Qt},Qn={tokenize:Ut};function Qt(n){const r=this,t=[];let e=0,u,i,l;return a;function a(F){if(e<t.length){const D=t[e];return r.containerState=D[1],n.attempt(D[0].continuation,m,c)(F)}return c(F)}function m(F){if(e++,r.containerState._closeFlow){r.containerState._closeFlow=void 0,u&&j();const D=r.events.length;let _=D,k;for(;_--;)if(r.events[_][0]==="exit"&&r.events[_][1].type==="chunkFlow"){k=r.events[_][1].end;break}b(e);let T=D;for(;T<r.events.length;)r.events[T][1].end=Object.assign({},k),T++;return tn(r.events,_+1,0,r.events.slice(D)),r.events.length=T,c(F)}return a(F)}function c(F){if(e===t.length){if(!u)return x(F);if(u.currentConstruct&&u.currentConstruct.concrete)return A(F);r.interrupt=!!(u.currentConstruct&&!u._gfmTableDynamicInterruptHack)}return r.containerState={},n.check(Qn,p,f)(F)}function p(F){return u&&j(),b(e),x(F)}function f(F){return r.parser.lazy[r.now().line]=e!==t.length,l=r.now().offset,A(F)}function x(F){return r.containerState={},n.attempt(Qn,h,A)(F)}function h(F){return e++,t.push([r.currentConstruct,r.containerState]),x(F)}function A(F){if(F===null){u&&j(),b(0),n.consume(F);return}return u=u||r.parser.flow(r.now()),n.enter("chunkFlow",{contentType:"flow",previous:i,_tokenizer:u}),I(F)}function I(F){if(F===null){M(n.exit("chunkFlow"),!0),b(0),n.consume(F);return}return C(F)?(n.consume(F),M(n.exit("chunkFlow")),e=0,r.interrupt=void 0,a):(n.consume(F),I)}function M(F,D){const _=r.sliceStream(F);if(D&&_.push(null),F.previous=i,i&&(i.next=F),i=F,u.defineSkip(F.start),u.write(_),r.parser.lazy[F.start.line]){let k=u.events.length;for(;k--;)if(u.events[k][1].start.offset<l&&(!u.events[k][1].end||u.events[k][1].end.offset>l))return;const T=r.events.length;let H=T,N,V;for(;H--;)if(r.events[H][0]==="exit"&&r.events[H][1].type==="chunkFlow"){if(N){V=r.events[H][1].end;break}N=!0}for(b(e),k=T;k<r.events.length;)r.events[k][1].end=Object.assign({},V),k++;tn(r.events,H+1,0,r.events.slice(T)),r.events.length=k}}function b(F){let D=t.length;for(;D-- >F;){const _=t[D];r.containerState=_[1],_[0].exit.call(r,n)}t.length=F}function j(){u.write([null]),i=void 0,u=void 0,r.containerState._closeFlow=void 0}}function Ut(n,r,t){return O(n,n.attempt(this.parser.constructs.document,r,t),"linePrefix",this.parser.constructs.disable.null.includes("codeIndented")?void 0:4)}function Un(n){if(n===null||Z(n)||Ht(n))return 1;if(qt(n))return 2}function Ln(n,r,t){const e=[];let u=-1;for(;++u<n.length;){const i=n[u].resolveAll;i&&!e.includes(i)&&(r=i(r,t),e.push(i))}return r}const In={name:"attention",tokenize:Zt,resolveAll:$t};function $t(n,r){let t=-1,e,u,i,l,a,m,c,p;for(;++t<n.length;)if(n[t][0]==="enter"&&n[t][1].type==="attentionSequence"&&n[t][1]._close){for(e=t;e--;)if(n[e][0]==="exit"&&n[e][1].type==="attentionSequence"&&n[e][1]._open&&r.sliceSerialize(n[e][1]).charCodeAt(0)===r.sliceSerialize(n[t][1]).charCodeAt(0)){if((n[e][1]._close||n[t][1]._open)&&(n[t][1].end.offset-n[t][1].start.offset)%3&&!((n[e][1].end.offset-n[e][1].start.offset+n[t][1].end.offset-n[t][1].start.offset)%3))continue;m=n[e][1].end.offset-n[e][1].start.offset>1&&n[t][1].end.offset-n[t][1].start.offset>1?2:1;const f=Object.assign({},n[e][1].end),x=Object.assign({},n[t][1].start);$n(f,-m),$n(x,m),l={type:m>1?"strongSequence":"emphasisSequence",start:f,end:Object.assign({},n[e][1].end)},a={type:m>1?"strongSequence":"emphasisSequence",start:Object.assign({},n[t][1].start),end:x},i={type:m>1?"strongText":"emphasisText",start:Object.assign({},n[e][1].end),end:Object.assign({},n[t][1].start)},u={type:m>1?"strong":"emphasis",start:Object.assign({},l.start),end:Object.assign({},a.end)},n[e][1].end=Object.assign({},l.start),n[t][1].start=Object.assign({},a.end),c=[],n[e][1].end.offset-n[e][1].start.offset&&(c=Y(c,[["enter",n[e][1],r],["exit",n[e][1],r]])),c=Y(c,[["enter",u,r],["enter",l,r],["exit",l,r],["enter",i,r]]),c=Y(c,Ln(r.parser.constructs.insideSpan.null,n.slice(e+1,t),r)),c=Y(c,[["exit",i,r],["enter",a,r],["exit",a,r],["exit",u,r]]),n[t][1].end.offset-n[t][1].start.offset?(p=2,c=Y(c,[["enter",n[t][1],r],["exit",n[t][1],r]])):p=0,tn(n,e-1,t-e+3,c),t=e+c.length-p-2;break}}for(t=-1;++t<n.length;)n[t][1].type==="attentionSequence"&&(n[t][1].type="data");return n}function Zt(n,r){const t=this.parser.constructs.attentionMarkers.null,e=this.previous,u=Un(e);let i;return l;function l(m){return i=m,n.enter("attentionSequence"),a(m)}function a(m){if(m===i)return n.consume(m),a;const c=n.exit("attentionSequence"),p=Un(m),f=!p||p===2&&u||t.includes(m),x=!u||u===2&&p||t.includes(e);return c._open=!!(i===42?f:f&&(u||!x)),c._close=!!(i===42?x:x&&(p||!f)),r(m)}}function $n(n,r){n.column+=r,n.offset+=r,n._bufferIndex+=r}const Yt={name:"autolink",tokenize:Gt};function Gt(n,r,t){let e=0;return u;function u(h){return n.enter("autolink"),n.enter("autolinkMarker"),n.consume(h),n.exit("autolinkMarker"),n.enter("autolinkProtocol"),i}function i(h){return nn(h)?(n.consume(h),l):c(h)}function l(h){return h===43||h===45||h===46||v(h)?(e=1,a(h)):c(h)}function a(h){return h===58?(n.consume(h),e=0,m):(h===43||h===45||h===46||v(h))&&e++<32?(n.consume(h),a):(e=0,c(h))}function m(h){return h===62?(n.exit("autolinkProtocol"),n.enter("autolinkMarker"),n.consume(h),n.exit("autolinkMarker"),n.exit("autolink"),r):h===null||h===32||h===60||An(h)?t(h):(n.consume(h),m)}function c(h){return h===64?(n.consume(h),p):Mt(h)?(n.consume(h),c):t(h)}function p(h){return v(h)?f(h):t(h)}function f(h){return h===46?(n.consume(h),e=0,p):h===62?(n.exit("autolinkProtocol").type="autolinkEmail",n.enter("autolinkMarker"),n.consume(h),n.exit("autolinkMarker"),n.exit("autolink"),r):x(h)}function x(h){if((h===45||v(h))&&e++<63){const A=h===45?x:f;return n.consume(h),A}return t(h)}}const Sn={tokenize:Jt,partial:!0};function Jt(n,r,t){return e;function e(i){return z(i)?O(n,u,"linePrefix")(i):u(i)}function u(i){return i===null||C(i)?r(i):t(i)}}const rt={name:"blockQuote",tokenize:Kt,continuation:{tokenize:Xt},exit:vt};function Kt(n,r,t){const e=this;return u;function u(l){if(l===62){const a=e.containerState;return a.open||(n.enter("blockQuote",{_container:!0}),a.open=!0),n.enter("blockQuotePrefix"),n.enter("blockQuoteMarker"),n.consume(l),n.exit("blockQuoteMarker"),i}return t(l)}function i(l){return z(l)?(n.enter("blockQuotePrefixWhitespace"),n.consume(l),n.exit("blockQuotePrefixWhitespace"),n.exit("blockQuotePrefix"),r):(n.exit("blockQuotePrefix"),r(l))}}function Xt(n,r,t){const e=this;return u;function u(l){return z(l)?O(n,i,"linePrefix",e.parser.constructs.disable.null.includes("codeIndented")?void 0:4)(l):i(l)}function i(l){return n.attempt(rt,r,t)(l)}}function vt(n){n.exit("blockQuote")}const it={name:"characterEscape",tokenize:ne};function ne(n,r,t){return e;function e(i){return n.enter("characterEscape"),n.enter("escapeMarker"),n.consume(i),n.exit("escapeMarker"),u}function u(i){return Rt(i)?(n.enter("characterEscapeValue"),n.consume(i),n.exit("characterEscapeValue"),n.exit("characterEscape"),r):t(i)}}const Zn=document.createElement("i");function On(n){const r="&"+n+";";Zn.innerHTML=r;const t=Zn.textContent;return t.charCodeAt(t.length-1)===59&&n!=="semi"||t===r?!1:t}const ut={name:"characterReference",tokenize:te};function te(n,r,t){const e=this;let u=0,i,l;return a;function a(f){return n.enter("characterReference"),n.enter("characterReferenceMarker"),n.consume(f),n.exit("characterReferenceMarker"),m}function m(f){return f===35?(n.enter("characterReferenceMarkerNumeric"),n.consume(f),n.exit("characterReferenceMarkerNumeric"),c):(n.enter("characterReferenceValue"),i=31,l=v,p(f))}function c(f){return f===88||f===120?(n.enter("characterReferenceMarkerHexadecimal"),n.consume(f),n.exit("characterReferenceMarkerHexadecimal"),n.enter("characterReferenceValue"),i=6,l=jt,p):(n.enter("characterReferenceValue"),i=7,l=zn,p(f))}function p(f){if(f===59&&u){const x=n.exit("characterReferenceValue");return l===v&&!On(e.sliceSerialize(x))?t(f):(n.enter("characterReferenceMarker"),n.consume(f),n.exit("characterReferenceMarker"),n.exit("characterReference"),r)}return l(f)&&u++<i?(n.consume(f),p):t(f)}}const Yn={tokenize:re,partial:!0},Gn={name:"codeFenced",tokenize:ee,concrete:!0};function ee(n,r,t){const e=this,u={tokenize:_,partial:!0};let i=0,l=0,a;return m;function m(k){return c(k)}function c(k){const T=e.events[e.events.length-1];return i=T&&T[1].type==="linePrefix"?T[2].sliceSerialize(T[1],!0).length:0,a=k,n.enter("codeFenced"),n.enter("codeFencedFence"),n.enter("codeFencedFenceSequence"),p(k)}function p(k){return k===a?(l++,n.consume(k),p):l<3?t(k):(n.exit("codeFencedFenceSequence"),z(k)?O(n,f,"whitespace")(k):f(k))}function f(k){return k===null||C(k)?(n.exit("codeFencedFence"),e.interrupt?r(k):n.check(Yn,I,D)(k)):(n.enter("codeFencedFenceInfo"),n.enter("chunkString",{contentType:"string"}),x(k))}function x(k){return k===null||C(k)?(n.exit("chunkString"),n.exit("codeFencedFenceInfo"),f(k)):z(k)?(n.exit("chunkString"),n.exit("codeFencedFenceInfo"),O(n,h,"whitespace")(k)):k===96&&k===a?t(k):(n.consume(k),x)}function h(k){return k===null||C(k)?f(k):(n.enter("codeFencedFenceMeta"),n.enter("chunkString",{contentType:"string"}),A(k))}function A(k){return k===null||C(k)?(n.exit("chunkString"),n.exit("codeFencedFenceMeta"),f(k)):k===96&&k===a?t(k):(n.consume(k),A)}function I(k){return n.attempt(u,D,M)(k)}function M(k){return n.enter("lineEnding"),n.consume(k),n.exit("lineEnding"),b}function b(k){return i>0&&z(k)?O(n,j,"linePrefix",i+1)(k):j(k)}function j(k){return k===null||C(k)?n.check(Yn,I,D)(k):(n.enter("codeFlowValue"),F(k))}function F(k){return k===null||C(k)?(n.exit("codeFlowValue"),j(k)):(n.consume(k),F)}function D(k){return n.exit("codeFenced"),r(k)}function _(k,T,H){let N=0;return V;function V(w){return k.enter("lineEnding"),k.consume(w),k.exit("lineEnding"),y}function y(w){return k.enter("codeFencedFence"),z(w)?O(k,S,"linePrefix",e.parser.constructs.disable.null.includes("codeIndented")?void 0:4)(w):S(w)}function S(w){return w===a?(k.enter("codeFencedFenceSequence"),P(w)):H(w)}function P(w){return w===a?(N++,k.consume(w),P):N>=l?(k.exit("codeFencedFenceSequence"),z(w)?O(k,R,"whitespace")(w):R(w)):H(w)}function R(w){return w===null||C(w)?(k.exit("codeFencedFence"),T(w)):H(w)}}}function re(n,r,t){const e=this;return u;function u(l){return l===null?t(l):(n.enter("lineEnding"),n.consume(l),n.exit("lineEnding"),i)}function i(l){return e.parser.lazy[e.now().line]?t(l):r(l)}}const Cn={name:"codeIndented",tokenize:ue},ie={tokenize:le,partial:!0};function ue(n,r,t){const e=this;return u;function u(c){return n.enter("codeIndented"),O(n,i,"linePrefix",5)(c)}function i(c){const p=e.events[e.events.length-1];return p&&p[1].type==="linePrefix"&&p[2].sliceSerialize(p[1],!0).length>=4?l(c):t(c)}function l(c){return c===null?m(c):C(c)?n.attempt(ie,l,m)(c):(n.enter("codeFlowValue"),a(c))}function a(c){return c===null||C(c)?(n.exit("codeFlowValue"),l(c)):(n.consume(c),a)}function m(c){return n.exit("codeIndented"),r(c)}}function le(n,r,t){const e=this;return u;function u(l){return e.parser.lazy[e.now().line]?t(l):C(l)?(n.enter("lineEnding"),n.consume(l),n.exit("lineEnding"),u):O(n,i,"linePrefix",5)(l)}function i(l){const a=e.events[e.events.length-1];return a&&a[1].type==="linePrefix"&&a[2].sliceSerialize(a[1],!0).length>=4?r(l):C(l)?u(l):t(l)}}const ae={name:"codeText",tokenize:ce,resolve:oe,previous:se};function oe(n){let r=n.length-4,t=3,e,u;if((n[t][1].type==="lineEnding"||n[t][1].type==="space")&&(n[r][1].type==="lineEnding"||n[r][1].type==="space")){for(e=t;++e<r;)if(n[e][1].type==="codeTextData"){n[t][1].type="codeTextPadding",n[r][1].type="codeTextPadding",t+=2,r-=2;break}}for(e=t-1,r++;++e<=r;)u===void 0?e!==r&&n[e][1].type!=="lineEnding"&&(u=e):(e===r||n[e][1].type==="lineEnding")&&(n[u][1].type="codeTextData",e!==u+2&&(n[u][1].end=n[e-1][1].end,n.splice(u+2,e-u-2),r-=e-u-2,e=u+2),u=void 0);return n}function se(n){return n!==96||this.events[this.events.length-1][1].type==="characterEscape"}function ce(n,r,t){let e=0,u,i;return l;function l(f){return n.enter("codeText"),n.enter("codeTextSequence"),a(f)}function a(f){return f===96?(n.consume(f),e++,a):(n.exit("codeTextSequence"),m(f))}function m(f){return f===null?t(f):f===32?(n.enter("space"),n.consume(f),n.exit("space"),m):f===96?(i=n.enter("codeTextSequence"),u=0,p(f)):C(f)?(n.enter("lineEnding"),n.consume(f),n.exit("lineEnding"),m):(n.enter("codeTextData"),c(f))}function c(f){return f===null||f===32||f===96||C(f)?(n.exit("codeTextData"),m(f)):(n.consume(f),c)}function p(f){return f===96?(n.consume(f),u++,p):u===e?(n.exit("codeTextSequence"),n.exit("codeText"),r(f)):(i.type="codeTextData",c(f))}}function lt(n){const r={};let t=-1,e,u,i,l,a,m,c;for(;++t<n.length;){for(;t in r;)t=r[t];if(e=n[t],t&&e[1].type==="chunkFlow"&&n[t-1][1].type==="listItemPrefix"&&(m=e[1]._tokenizer.events,i=0,i<m.length&&m[i][1].type==="lineEndingBlank"&&(i+=2),i<m.length&&m[i][1].type==="content"))for(;++i<m.length&&m[i][1].type!=="content";)m[i][1].type==="chunkText"&&(m[i][1]._isInFirstContentOfListItem=!0,i++);if(e[0]==="enter")e[1].contentType&&(Object.assign(r,he(n,t)),t=r[t],c=!0);else if(e[1]._container){for(i=t,u=void 0;i--&&(l=n[i],l[1].type==="lineEnding"||l[1].type==="lineEndingBlank");)l[0]==="enter"&&(u&&(n[u][1].type="lineEndingBlank"),l[1].type="lineEnding",u=i);u&&(e[1].end=Object.assign({},n[u][1].start),a=n.slice(u,t),a.unshift(e),tn(n,u,t-u+1,a))}}return!c}function he(n,r){const t=n[r][1],e=n[r][2];let u=r-1;const i=[],l=t._tokenizer||e.parser[t.contentType](t.start),a=l.events,m=[],c={};let p,f,x=-1,h=t,A=0,I=0;const M=[I];for(;h;){for(;n[++u][1]!==h;);i.push(u),h._tokenizer||(p=e.sliceStream(h),h.next||p.push(null),f&&l.defineSkip(h.start),h._isInFirstContentOfListItem&&(l._gfmTasklistFirstContentOfListItem=!0),l.write(p),h._isInFirstContentOfListItem&&(l._gfmTasklistFirstContentOfListItem=void 0)),f=h,h=h.next}for(h=t;++x<a.length;)a[x][0]==="exit"&&a[x-1][0]==="enter"&&a[x][1].type===a[x-1][1].type&&a[x][1].start.line!==a[x][1].end.line&&(I=x+1,M.push(I),h._tokenizer=void 0,h.previous=void 0,h=h.next);for(l.events=[],h?(h._tokenizer=void 0,h.previous=void 0):M.pop(),x=M.length;x--;){const b=a.slice(M[x],M[x+1]),j=i.pop();m.unshift([j,j+b.length-1]),tn(n,j,2,b)}for(x=-1;++x<m.length;)c[A+m[x][0]]=A+m[x][1],A+=m[x][1]-m[x][0]-1;return c}const pe={tokenize:xe,resolve:me},fe={tokenize:ge,partial:!0};function me(n){return lt(n),n}function xe(n,r){let t;return e;function e(a){return n.enter("content"),t=n.enter("chunkContent",{contentType:"content"}),u(a)}function u(a){return a===null?i(a):C(a)?n.check(fe,l,i)(a):(n.consume(a),u)}function i(a){return n.exit("chunkContent"),n.exit("content"),r(a)}function l(a){return n.consume(a),n.exit("chunkContent"),t.next=n.enter("chunkContent",{contentType:"content",previous:t}),t=t.next,u}}function ge(n,r,t){const e=this;return u;function u(l){return n.exit("chunkContent"),n.enter("lineEnding"),n.consume(l),n.exit("lineEnding"),O(n,i,"linePrefix")}function i(l){if(l===null||C(l))return t(l);const a=e.events[e.events.length-1];return!e.parser.constructs.disable.null.includes("codeIndented")&&a&&a[1].type==="linePrefix"&&a[2].sliceSerialize(a[1],!0).length>=4?r(l):n.interrupt(e.parser.constructs.flow,t,r)(l)}}function at(n,r,t,e,u,i,l,a,m){const c=m||Number.POSITIVE_INFINITY;let p=0;return f;function f(b){return b===60?(n.enter(e),n.enter(u),n.enter(i),n.consume(b),n.exit(i),x):b===null||b===32||b===41||An(b)?t(b):(n.enter(e),n.enter(l),n.enter(a),n.enter("chunkString",{contentType:"string"}),I(b))}function x(b){return b===62?(n.enter(i),n.consume(b),n.exit(i),n.exit(u),n.exit(e),r):(n.enter(a),n.enter("chunkString",{contentType:"string"}),h(b))}function h(b){return b===62?(n.exit("chunkString"),n.exit(a),x(b)):b===null||b===60||C(b)?t(b):(n.consume(b),b===92?A:h)}function A(b){return b===60||b===62||b===92?(n.consume(b),h):h(b)}function I(b){return!p&&(b===null||b===41||Z(b))?(n.exit("chunkString"),n.exit(a),n.exit(l),n.exit(e),r(b)):p<c&&b===40?(n.consume(b),p++,I):b===41?(n.consume(b),p--,I):b===null||b===32||b===40||An(b)?t(b):(n.consume(b),b===92?M:I)}function M(b){return b===40||b===41||b===92?(n.consume(b),I):I(b)}}function ot(n,r,t,e,u,i){const l=this;let a=0,m;return c;function c(h){return n.enter(e),n.enter(u),n.consume(h),n.exit(u),n.enter(i),p}function p(h){return a>999||h===null||h===91||h===93&&!m||h===94&&!a&&"_hiddenFootnoteSupport"in l.parser.constructs?t(h):h===93?(n.exit(i),n.enter(u),n.consume(h),n.exit(u),n.exit(e),r):C(h)?(n.enter("lineEnding"),n.consume(h),n.exit("lineEnding"),p):(n.enter("chunkString",{contentType:"string"}),f(h))}function f(h){return h===null||h===91||h===93||C(h)||a++>999?(n.exit("chunkString"),p(h)):(n.consume(h),m||(m=!z(h)),h===92?x:f)}function x(h){return h===91||h===92||h===93?(n.consume(h),a++,f):f(h)}}function st(n,r,t,e,u,i){let l;return a;function a(x){return x===34||x===39||x===40?(n.enter(e),n.enter(u),n.consume(x),n.exit(u),l=x===40?41:x,m):t(x)}function m(x){return x===l?(n.enter(u),n.consume(x),n.exit(u),n.exit(e),r):(n.enter(i),c(x))}function c(x){return x===l?(n.exit(i),m(l)):x===null?t(x):C(x)?(n.enter("lineEnding"),n.consume(x),n.exit("lineEnding"),O(n,c,"linePrefix")):(n.enter("chunkString",{contentType:"string"}),p(x))}function p(x){return x===l||x===null||C(x)?(n.exit("chunkString"),c(x)):(n.consume(x),x===92?f:p)}function f(x){return x===l||x===92?(n.consume(x),p):p(x)}}function dn(n,r){let t;return e;function e(u){return C(u)?(n.enter("lineEnding"),n.consume(u),n.exit("lineEnding"),t=!0,e):z(u)?O(n,e,t?"linePrefix":"lineSuffix")(u):r(u)}}function xn(n){return n.replace(/[\t\n\r ]+/g," ").replace(/^ | $/g,"").toLowerCase().toUpperCase()}const ke={name:"definition",tokenize:be},de={tokenize:ye,partial:!0};function be(n,r,t){const e=this;let u;return i;function i(h){return n.enter("definition"),l(h)}function l(h){return ot.call(e,n,a,t,"definitionLabel","definitionLabelMarker","definitionLabelString")(h)}function a(h){return u=xn(e.sliceSerialize(e.events[e.events.length-1][1]).slice(1,-1)),h===58?(n.enter("definitionMarker"),n.consume(h),n.exit("definitionMarker"),m):t(h)}function m(h){return Z(h)?dn(n,c)(h):c(h)}function c(h){return at(n,p,t,"definitionDestination","definitionDestinationLiteral","definitionDestinationLiteralMarker","definitionDestinationRaw","definitionDestinationString")(h)}function p(h){return n.attempt(de,f,f)(h)}function f(h){return z(h)?O(n,x,"whitespace")(h):x(h)}function x(h){return h===null||C(h)?(n.exit("definition"),e.parser.defined.push(u),r(h)):t(h)}}function ye(n,r,t){return e;function e(a){return Z(a)?dn(n,u)(a):t(a)}function u(a){return st(n,i,t,"definitionTitle","definitionTitleMarker","definitionTitleString")(a)}function i(a){return z(a)?O(n,l,"whitespace")(a):l(a)}function l(a){return a===null||C(a)?r(a):t(a)}}const Se={name:"hardBreakEscape",tokenize:Fe};function Fe(n,r,t){return e;function e(i){return n.enter("hardBreakEscape"),n.consume(i),u}function u(i){return C(i)?(n.exit("hardBreakEscape"),r(i)):t(i)}}const Ee={name:"headingAtx",tokenize:we,resolve:Ce};function Ce(n,r){let t=n.length-2,e=3,u,i;return n[e][1].type==="whitespace"&&(e+=2),t-2>e&&n[t][1].type==="whitespace"&&(t-=2),n[t][1].type==="atxHeadingSequence"&&(e===t-1||t-4>e&&n[t-2][1].type==="whitespace")&&(t-=e+1===t?2:4),t>e&&(u={type:"atxHeadingText",start:n[e][1].start,end:n[t][1].end},i={type:"chunkText",start:n[e][1].start,end:n[t][1].end,contentType:"text"},tn(n,e,t-e+1,[["enter",u,r],["enter",i,r],["exit",i,r],["exit",u,r]])),n}function we(n,r,t){let e=0;return u;function u(p){return n.enter("atxHeading"),i(p)}function i(p){return n.enter("atxHeadingSequence"),l(p)}function l(p){return p===35&&e++<6?(n.consume(p),l):p===null||Z(p)?(n.exit("atxHeadingSequence"),a(p)):t(p)}function a(p){return p===35?(n.enter("atxHeadingSequence"),m(p)):p===null||C(p)?(n.exit("atxHeading"),r(p)):z(p)?O(n,a,"whitespace")(p):(n.enter("atxHeadingText"),c(p))}function m(p){return p===35?(n.consume(p),m):(n.exit("atxHeadingSequence"),a(p))}function c(p){return p===null||p===35||Z(p)?(n.exit("atxHeadingText"),a(p)):(n.consume(p),c)}}const Ae=["address","article","aside","base","basefont","blockquote","body","caption","center","col","colgroup","dd","details","dialog","dir","div","dl","dt","fieldset","figcaption","figure","footer","form","frame","frameset","h1","h2","h3","h4","h5","h6","head","header","hr","html","iframe","legend","li","link","main","menu","menuitem","nav","noframes","ol","optgroup","option","p","param","search","section","summary","table","tbody","td","tfoot","th","thead","title","tr","track","ul"],Jn=["pre","script","style","textarea"],ze={name:"htmlFlow",tokenize:Le,resolveTo:Be,concrete:!0},Ie={tokenize:De,partial:!0},Te={tokenize:Oe,partial:!0};function Be(n){let r=n.length;for(;r--&&!(n[r][0]==="enter"&&n[r][1].type==="htmlFlow"););return r>1&&n[r-2][1].type==="linePrefix"&&(n[r][1].start=n[r-2][1].start,n[r+1][1].start=n[r-2][1].start,n.splice(r-2,2)),n}function Le(n,r,t){const e=this;let u,i,l,a,m;return c;function c(s){return p(s)}function p(s){return n.enter("htmlFlow"),n.enter("htmlFlowData"),n.consume(s),f}function f(s){return s===33?(n.consume(s),x):s===47?(n.consume(s),i=!0,I):s===63?(n.consume(s),u=3,e.interrupt?r:o):nn(s)?(n.consume(s),l=String.fromCharCode(s),M):t(s)}function x(s){return s===45?(n.consume(s),u=2,h):s===91?(n.consume(s),u=5,a=0,A):nn(s)?(n.consume(s),u=4,e.interrupt?r:o):t(s)}function h(s){return s===45?(n.consume(s),e.interrupt?r:o):t(s)}function A(s){const K="CDATA[";return s===K.charCodeAt(a++)?(n.consume(s),a===K.length?e.interrupt?r:S:A):t(s)}function I(s){return nn(s)?(n.consume(s),l=String.fromCharCode(s),M):t(s)}function M(s){if(s===null||s===47||s===62||Z(s)){const K=s===47,hn=l.toLowerCase();return!K&&!i&&Jn.includes(hn)?(u=1,e.interrupt?r(s):S(s)):Ae.includes(l.toLowerCase())?(u=6,K?(n.consume(s),b):e.interrupt?r(s):S(s)):(u=7,e.interrupt&&!e.parser.lazy[e.now().line]?t(s):i?j(s):F(s))}return s===45||v(s)?(n.consume(s),l+=String.fromCharCode(s),M):t(s)}function b(s){return s===62?(n.consume(s),e.interrupt?r:S):t(s)}function j(s){return z(s)?(n.consume(s),j):V(s)}function F(s){return s===47?(n.consume(s),V):s===58||s===95||nn(s)?(n.consume(s),D):z(s)?(n.consume(s),F):V(s)}function D(s){return s===45||s===46||s===58||s===95||v(s)?(n.consume(s),D):_(s)}function _(s){return s===61?(n.consume(s),k):z(s)?(n.consume(s),_):F(s)}function k(s){return s===null||s===60||s===61||s===62||s===96?t(s):s===34||s===39?(n.consume(s),m=s,T):z(s)?(n.consume(s),k):H(s)}function T(s){return s===m?(n.consume(s),m=null,N):s===null||C(s)?t(s):(n.consume(s),T)}function H(s){return s===null||s===34||s===39||s===47||s===60||s===61||s===62||s===96||Z(s)?_(s):(n.consume(s),H)}function N(s){return s===47||s===62||z(s)?F(s):t(s)}function V(s){return s===62?(n.consume(s),y):t(s)}function y(s){return s===null||C(s)?S(s):z(s)?(n.consume(s),y):t(s)}function S(s){return s===45&&u===2?(n.consume(s),U):s===60&&u===1?(n.consume(s),W):s===62&&u===4?(n.consume(s),J):s===63&&u===3?(n.consume(s),o):s===93&&u===5?(n.consume(s),en):C(s)&&(u===6||u===7)?(n.exit("htmlFlowData"),n.check(Ie,rn,P)(s)):s===null||C(s)?(n.exit("htmlFlowData"),P(s)):(n.consume(s),S)}function P(s){return n.check(Te,R,rn)(s)}function R(s){return n.enter("lineEnding"),n.consume(s),n.exit("lineEnding"),w}function w(s){return s===null||C(s)?P(s):(n.enter("htmlFlowData"),S(s))}function U(s){return s===45?(n.consume(s),o):S(s)}function W(s){return s===47?(n.consume(s),l="",G):S(s)}function G(s){if(s===62){const K=l.toLowerCase();return Jn.includes(K)?(n.consume(s),J):S(s)}return nn(s)&&l.length<8?(n.consume(s),l+=String.fromCharCode(s),G):S(s)}function en(s){return s===93?(n.consume(s),o):S(s)}function o(s){return s===62?(n.consume(s),J):s===45&&u===2?(n.consume(s),o):S(s)}function J(s){return s===null||C(s)?(n.exit("htmlFlowData"),rn(s)):(n.consume(s),J)}function rn(s){return n.exit("htmlFlow"),r(s)}}function Oe(n,r,t){const e=this;return u;function u(l){return C(l)?(n.enter("lineEnding"),n.consume(l),n.exit("lineEnding"),i):t(l)}function i(l){return e.parser.lazy[e.now().line]?t(l):r(l)}}function De(n,r,t){return e;function e(u){return n.enter("lineEnding"),n.consume(u),n.exit("lineEnding"),n.attempt(Sn,r,t)}}const Pe={name:"htmlText",tokenize:_e};function _e(n,r,t){const e=this;let u,i,l;return a;function a(o){return n.enter("htmlText"),n.enter("htmlTextData"),n.consume(o),m}function m(o){return o===33?(n.consume(o),c):o===47?(n.consume(o),_):o===63?(n.consume(o),F):nn(o)?(n.consume(o),H):t(o)}function c(o){return o===45?(n.consume(o),p):o===91?(n.consume(o),i=0,A):nn(o)?(n.consume(o),j):t(o)}function p(o){return o===45?(n.consume(o),h):t(o)}function f(o){return o===null?t(o):o===45?(n.consume(o),x):C(o)?(l=f,W(o)):(n.consume(o),f)}function x(o){return o===45?(n.consume(o),h):f(o)}function h(o){return o===62?U(o):o===45?x(o):f(o)}function A(o){const J="CDATA[";return o===J.charCodeAt(i++)?(n.consume(o),i===J.length?I:A):t(o)}function I(o){return o===null?t(o):o===93?(n.consume(o),M):C(o)?(l=I,W(o)):(n.consume(o),I)}function M(o){return o===93?(n.consume(o),b):I(o)}function b(o){return o===62?U(o):o===93?(n.consume(o),b):I(o)}function j(o){return o===null||o===62?U(o):C(o)?(l=j,W(o)):(n.consume(o),j)}function F(o){return o===null?t(o):o===63?(n.consume(o),D):C(o)?(l=F,W(o)):(n.consume(o),F)}function D(o){return o===62?U(o):F(o)}function _(o){return nn(o)?(n.consume(o),k):t(o)}function k(o){return o===45||v(o)?(n.consume(o),k):T(o)}function T(o){return C(o)?(l=T,W(o)):z(o)?(n.consume(o),T):U(o)}function H(o){return o===45||v(o)?(n.consume(o),H):o===47||o===62||Z(o)?N(o):t(o)}function N(o){return o===47?(n.consume(o),U):o===58||o===95||nn(o)?(n.consume(o),V):C(o)?(l=N,W(o)):z(o)?(n.consume(o),N):U(o)}function V(o){return o===45||o===46||o===58||o===95||v(o)?(n.consume(o),V):y(o)}function y(o){return o===61?(n.consume(o),S):C(o)?(l=y,W(o)):z(o)?(n.consume(o),y):N(o)}function S(o){return o===null||o===60||o===61||o===62||o===96?t(o):o===34||o===39?(n.consume(o),u=o,P):C(o)?(l=S,W(o)):z(o)?(n.consume(o),S):(n.consume(o),R)}function P(o){return o===u?(n.consume(o),u=void 0,w):o===null?t(o):C(o)?(l=P,W(o)):(n.consume(o),P)}function R(o){return o===null||o===34||o===39||o===60||o===61||o===96?t(o):o===47||o===62||Z(o)?N(o):(n.consume(o),R)}function w(o){return o===47||o===62||Z(o)?N(o):t(o)}function U(o){return o===62?(n.consume(o),n.exit("htmlTextData"),n.exit("htmlText"),r):t(o)}function W(o){return n.exit("htmlTextData"),n.enter("lineEnding"),n.consume(o),n.exit("lineEnding"),G}function G(o){return z(o)?O(n,en,"linePrefix",e.parser.constructs.disable.null.includes("codeIndented")?void 0:4)(o):en(o)}function en(o){return n.enter("htmlTextData"),l(o)}}const Dn={name:"labelEnd",tokenize:Ne,resolveTo:He,resolveAll:qe},Me={tokenize:Ve},je={tokenize:We},Re={tokenize:Qe};function qe(n){let r=-1;for(;++r<n.length;){const t=n[r][1];(t.type==="labelImage"||t.type==="labelLink"||t.type==="labelEnd")&&(n.splice(r+1,t.type==="labelImage"?4:2),t.type="data",r++)}return n}function He(n,r){let t=n.length,e=0,u,i,l,a;for(;t--;)if(u=n[t][1],i){if(u.type==="link"||u.type==="labelLink"&&u._inactive)break;n[t][0]==="enter"&&u.type==="labelLink"&&(u._inactive=!0)}else if(l){if(n[t][0]==="enter"&&(u.type==="labelImage"||u.type==="labelLink")&&!u._balanced&&(i=t,u.type!=="labelLink")){e=2;break}}else u.type==="labelEnd"&&(l=t);const m={type:n[i][1].type==="labelLink"?"link":"image",start:Object.assign({},n[i][1].start),end:Object.assign({},n[n.length-1][1].end)},c={type:"label",start:Object.assign({},n[i][1].start),end:Object.assign({},n[l][1].end)},p={type:"labelText",start:Object.assign({},n[i+e+2][1].end),end:Object.assign({},n[l-2][1].start)};return a=[["enter",m,r],["enter",c,r]],a=Y(a,n.slice(i+1,i+e+3)),a=Y(a,[["enter",p,r]]),a=Y(a,Ln(r.parser.constructs.insideSpan.null,n.slice(i+e+4,l-3),r)),a=Y(a,[["exit",p,r],n[l-2],n[l-1],["exit",c,r]]),a=Y(a,n.slice(l+1)),a=Y(a,[["exit",m,r]]),tn(n,i,n.length,a),n}function Ne(n,r,t){const e=this;let u=e.events.length,i,l;for(;u--;)if((e.events[u][1].type==="labelImage"||e.events[u][1].type==="labelLink")&&!e.events[u][1]._balanced){i=e.events[u][1];break}return a;function a(x){return i?i._inactive?f(x):(l=e.parser.defined.includes(xn(e.sliceSerialize({start:i.end,end:e.now()}))),n.enter("labelEnd"),n.enter("labelMarker"),n.consume(x),n.exit("labelMarker"),n.exit("labelEnd"),m):t(x)}function m(x){return x===40?n.attempt(Me,p,l?p:f)(x):x===91?n.attempt(je,p,l?c:f)(x):l?p(x):f(x)}function c(x){return n.attempt(Re,p,f)(x)}function p(x){return r(x)}function f(x){return i._balanced=!0,t(x)}}function Ve(n,r,t){return e;function e(f){return n.enter("resource"),n.enter("resourceMarker"),n.consume(f),n.exit("resourceMarker"),u}function u(f){return Z(f)?dn(n,i)(f):i(f)}function i(f){return f===41?p(f):at(n,l,a,"resourceDestination","resourceDestinationLiteral","resourceDestinationLiteralMarker","resourceDestinationRaw","resourceDestinationString",32)(f)}function l(f){return Z(f)?dn(n,m)(f):p(f)}function a(f){return t(f)}function m(f){return f===34||f===39||f===40?st(n,c,t,"resourceTitle","resourceTitleMarker","resourceTitleString")(f):p(f)}function c(f){return Z(f)?dn(n,p)(f):p(f)}function p(f){return f===41?(n.enter("resourceMarker"),n.consume(f),n.exit("resourceMarker"),n.exit("resource"),r):t(f)}}function We(n,r,t){const e=this;return u;function u(a){return ot.call(e,n,i,l,"reference","referenceMarker","referenceString")(a)}function i(a){return e.parser.defined.includes(xn(e.sliceSerialize(e.events[e.events.length-1][1]).slice(1,-1)))?r(a):t(a)}function l(a){return t(a)}}function Qe(n,r,t){return e;function e(i){return n.enter("reference"),n.enter("referenceMarker"),n.consume(i),n.exit("referenceMarker"),u}function u(i){return i===93?(n.enter("referenceMarker"),n.consume(i),n.exit("referenceMarker"),n.exit("reference"),r):t(i)}}const Ue={name:"labelStartImage",tokenize:$e,resolveAll:Dn.resolveAll};function $e(n,r,t){const e=this;return u;function u(a){return n.enter("labelImage"),n.enter("labelImageMarker"),n.consume(a),n.exit("labelImageMarker"),i}function i(a){return a===91?(n.enter("labelMarker"),n.consume(a),n.exit("labelMarker"),n.exit("labelImage"),l):t(a)}function l(a){return a===94&&"_hiddenFootnoteSupport"in e.parser.constructs?t(a):r(a)}}const Ze={name:"labelStartLink",tokenize:Ye,resolveAll:Dn.resolveAll};function Ye(n,r,t){const e=this;return u;function u(l){return n.enter("labelLink"),n.enter("labelMarker"),n.consume(l),n.exit("labelMarker"),n.exit("labelLink"),i}function i(l){return l===94&&"_hiddenFootnoteSupport"in e.parser.constructs?t(l):r(l)}}const wn={name:"lineEnding",tokenize:Ge};function Ge(n,r){return t;function t(e){return n.enter("lineEnding"),n.consume(e),n.exit("lineEnding"),O(n,r,"linePrefix")}}const bn={name:"thematicBreak",tokenize:Je};function Je(n,r,t){let e=0,u;return i;function i(c){return n.enter("thematicBreak"),l(c)}function l(c){return u=c,a(c)}function a(c){return c===u?(n.enter("thematicBreakSequence"),m(c)):e>=3&&(c===null||C(c))?(n.exit("thematicBreak"),r(c)):t(c)}function m(c){return c===u?(n.consume(c),e++,m):(n.exit("thematicBreakSequence"),z(c)?O(n,a,"whitespace")(c):a(c))}}const $={name:"list",tokenize:ve,continuation:{tokenize:nr},exit:er},Ke={tokenize:rr,partial:!0},Xe={tokenize:tr,partial:!0};function ve(n,r,t){const e=this,u=e.events[e.events.length-1];let i=u&&u[1].type==="linePrefix"?u[2].sliceSerialize(u[1],!0).length:0,l=0;return a;function a(h){const A=e.containerState.type||(h===42||h===43||h===45?"listUnordered":"listOrdered");if(A==="listUnordered"?!e.containerState.marker||h===e.containerState.marker:zn(h)){if(e.containerState.type||(e.containerState.type=A,n.enter(A,{_container:!0})),A==="listUnordered")return n.enter("listItemPrefix"),h===42||h===45?n.check(bn,t,c)(h):c(h);if(!e.interrupt||h===49)return n.enter("listItemPrefix"),n.enter("listItemValue"),m(h)}return t(h)}function m(h){return zn(h)&&++l<10?(n.consume(h),m):(!e.interrupt||l<2)&&(e.containerState.marker?h===e.containerState.marker:h===41||h===46)?(n.exit("listItemValue"),c(h)):t(h)}function c(h){return n.enter("listItemMarker"),n.consume(h),n.exit("listItemMarker"),e.containerState.marker=e.containerState.marker||h,n.check(Sn,e.interrupt?t:p,n.attempt(Ke,x,f))}function p(h){return e.containerState.initialBlankLine=!0,i++,x(h)}function f(h){return z(h)?(n.enter("listItemPrefixWhitespace"),n.consume(h),n.exit("listItemPrefixWhitespace"),x):t(h)}function x(h){return e.containerState.size=i+e.sliceSerialize(n.exit("listItemPrefix"),!0).length,r(h)}}function nr(n,r,t){const e=this;return e.containerState._closeFlow=void 0,n.check(Sn,u,i);function u(a){return e.containerState.furtherBlankLines=e.containerState.furtherBlankLines||e.containerState.initialBlankLine,O(n,r,"listItemIndent",e.containerState.size+1)(a)}function i(a){return e.containerState.furtherBlankLines||!z(a)?(e.containerState.furtherBlankLines=void 0,e.containerState.initialBlankLine=void 0,l(a)):(e.containerState.furtherBlankLines=void 0,e.containerState.initialBlankLine=void 0,n.attempt(Xe,r,l)(a))}function l(a){return e.containerState._closeFlow=!0,e.interrupt=void 0,O(n,n.attempt($,r,t),"linePrefix",e.parser.constructs.disable.null.includes("codeIndented")?void 0:4)(a)}}function tr(n,r,t){const e=this;return O(n,u,"listItemIndent",e.containerState.size+1);function u(i){const l=e.events[e.events.length-1];return l&&l[1].type==="listItemIndent"&&l[2].sliceSerialize(l[1],!0).length===e.containerState.size?r(i):t(i)}}function er(n){n.exit(this.containerState.type)}function rr(n,r,t){const e=this;return O(n,u,"listItemPrefixWhitespace",e.parser.constructs.disable.null.includes("codeIndented")?void 0:5);function u(i){const l=e.events[e.events.length-1];return!z(i)&&l&&l[1].type==="listItemPrefixWhitespace"?r(i):t(i)}}const Kn={name:"setextUnderline",tokenize:ur,resolveTo:ir};function ir(n,r){let t=n.length,e,u,i;for(;t--;)if(n[t][0]==="enter"){if(n[t][1].type==="content"){e=t;break}n[t][1].type==="paragraph"&&(u=t)}else n[t][1].type==="content"&&n.splice(t,1),!i&&n[t][1].type==="definition"&&(i=t);const l={type:"setextHeading",start:Object.assign({},n[u][1].start),end:Object.assign({},n[n.length-1][1].end)};return n[u][1].type="setextHeadingText",i?(n.splice(u,0,["enter",l,r]),n.splice(i+1,0,["exit",n[e][1],r]),n[e][1].end=Object.assign({},n[i][1].end)):n[e][1]=l,n.push(["exit",l,r]),n}function ur(n,r,t){const e=this;let u;return i;function i(c){let p=e.events.length,f;for(;p--;)if(e.events[p][1].type!=="lineEnding"&&e.events[p][1].type!=="linePrefix"&&e.events[p][1].type!=="content"){f=e.events[p][1].type==="paragraph";break}return!e.parser.lazy[e.now().line]&&(e.interrupt||f)?(n.enter("setextHeadingLine"),u=c,l(c)):t(c)}function l(c){return n.enter("setextHeadingLineSequence"),a(c)}function a(c){return c===u?(n.consume(c),a):(n.exit("setextHeadingLineSequence"),z(c)?O(n,m,"lineSuffix")(c):m(c))}function m(c){return c===null||C(c)?(n.exit("setextHeadingLine"),r(c)):t(c)}}const lr={tokenize:ar};function ar(n){const r=this,t=n.attempt(Sn,e,n.attempt(this.parser.constructs.flowInitial,u,O(n,n.attempt(this.parser.constructs.flow,u,n.attempt(pe,u)),"linePrefix")));return t;function e(i){if(i===null){n.consume(i);return}return n.enter("lineEndingBlank"),n.consume(i),n.exit("lineEndingBlank"),r.currentConstruct=void 0,t}function u(i){if(i===null){n.consume(i);return}return n.enter("lineEnding"),n.consume(i),n.exit("lineEnding"),r.currentConstruct=void 0,t}}const or={resolveAll:ht()},sr=ct("string"),cr=ct("text");function ct(n){return{tokenize:r,resolveAll:ht(n==="text"?hr:void 0)};function r(t){const e=this,u=this.parser.constructs[n],i=t.attempt(u,l,a);return l;function l(p){return c(p)?i(p):a(p)}function a(p){if(p===null){t.consume(p);return}return t.enter("data"),t.consume(p),m}function m(p){return c(p)?(t.exit("data"),i(p)):(t.consume(p),m)}function c(p){if(p===null)return!0;const f=u[p];let x=-1;if(f)for(;++x<f.length;){const h=f[x];if(!h.previous||h.previous.call(e,e.previous))return!0}return!1}}}function ht(n){return r;function r(t,e){let u=-1,i;for(;++u<=t.length;)i===void 0?t[u]&&t[u][1].type==="data"&&(i=u,u++):(!t[u]||t[u][1].type!=="data")&&(u!==i+2&&(t[i][1].end=t[u-1][1].end,t.splice(i+2,u-i-2),u=i+2),i=void 0);return n?n(t,e):t}}function hr(n,r){let t=0;for(;++t<=n.length;)if((t===n.length||n[t][1].type==="lineEnding")&&n[t-1][1].type==="data"){const e=n[t-1][1],u=r.sliceStream(e);let i=u.length,l=-1,a=0,m;for(;i--;){const c=u[i];if(typeof c=="string"){for(l=c.length;c.charCodeAt(l-1)===32;)a++,l--;if(l)break;l=-1}else if(c===-2)m=!0,a++;else if(c!==-1){i++;break}}if(a){const c={type:t===n.length||m||a<2?"lineSuffix":"hardBreakTrailing",start:{line:e.end.line,column:e.end.column-a,offset:e.end.offset-a,_index:e.start._index+i,_bufferIndex:i?l:e.start._bufferIndex+l},end:Object.assign({},e.end)};e.end=Object.assign({},c.start),e.start.offset===e.end.offset?Object.assign(e,c):(n.splice(t,0,["enter",c,r],["exit",c,r]),t+=2)}t++}return n}function pr(n,r,t){let e=Object.assign(t?Object.assign({},t):{line:1,column:1,offset:0},{_index:0,_bufferIndex:-1});const u={},i=[];let l=[],a=[];const m={consume:j,enter:F,exit:D,attempt:T(_),check:T(k),interrupt:T(k,{interrupt:!0})},c={previous:null,code:null,containerState:{},events:[],parser:n,sliceStream:h,sliceSerialize:x,now:A,defineSkip:I,write:f};let p=r.tokenize.call(c,m);return r.resolveAll&&i.push(r),c;function f(y){return l=Y(l,y),M(),l[l.length-1]!==null?[]:(H(r,0),c.events=Ln(i,c.events,c),c.events)}function x(y,S){return mr(h(y),S)}function h(y){return fr(l,y)}function A(){const{line:y,column:S,offset:P,_index:R,_bufferIndex:w}=e;return{line:y,column:S,offset:P,_index:R,_bufferIndex:w}}function I(y){u[y.line]=y.column,V()}function M(){let y;for(;e._index<l.length;){const S=l[e._index];if(typeof S=="string")for(y=e._index,e._bufferIndex<0&&(e._bufferIndex=0);e._index===y&&e._bufferIndex<S.length;)b(S.charCodeAt(e._bufferIndex));else b(S)}}function b(y){p=p(y)}function j(y){C(y)?(e.line++,e.column=1,e.offset+=y===-3?2:1,V()):y!==-1&&(e.column++,e.offset++),e._bufferIndex<0?e._index++:(e._bufferIndex++,e._bufferIndex===l[e._index].length&&(e._bufferIndex=-1,e._index++)),c.previous=y}function F(y,S){const P=S||{};return P.type=y,P.start=A(),c.events.push(["enter",P,c]),a.push(P),P}function D(y){const S=a.pop();return S.end=A(),c.events.push(["exit",S,c]),S}function _(y,S){H(y,S.from)}function k(y,S){S.restore()}function T(y,S){return P;function P(R,w,U){let W,G,en,o;return Array.isArray(R)?rn(R):"tokenize"in R?rn([R]):J(R);function J(Q){return pn;function pn(an){const fn=an!==null&&Q[an],mn=an!==null&&Q.null,Fn=[...Array.isArray(fn)?fn:fn?[fn]:[],...Array.isArray(mn)?mn:mn?[mn]:[]];return rn(Fn)(an)}}function rn(Q){return W=Q,G=0,Q.length===0?U:s(Q[G])}function s(Q){return pn;function pn(an){return o=N(),en=Q,Q.partial||(c.currentConstruct=Q),Q.name&&c.parser.constructs.disable.null.includes(Q.name)?hn():Q.tokenize.call(S?Object.assign(Object.create(c),S):c,m,K,hn)(an)}}function K(Q){return y(en,o),w}function hn(Q){return o.restore(),++G<W.length?s(W[G]):U}}}function H(y,S){y.resolveAll&&!i.includes(y)&&i.push(y),y.resolve&&tn(c.events,S,c.events.length-S,y.resolve(c.events.slice(S),c)),y.resolveTo&&(c.events=y.resolveTo(c.events,c))}function N(){const y=A(),S=c.previous,P=c.currentConstruct,R=c.events.length,w=Array.from(a);return{restore:U,from:R};function U(){e=y,c.previous=S,c.currentConstruct=P,c.events.length=R,a=w,V()}}function V(){e.line in u&&e.column<2&&(e.column=u[e.line],e.offset+=u[e.line]-1)}}function fr(n,r){const t=r.start._index,e=r.start._bufferIndex,u=r.end._index,i=r.end._bufferIndex;let l;if(t===u)l=[n[t].slice(e,i)];else{if(l=n.slice(t,u),e>-1){const a=l[0];typeof a=="string"?l[0]=a.slice(e):l.shift()}i>0&&l.push(n[u].slice(0,i))}return l}function mr(n,r){let t=-1;const e=[];let u;for(;++t<n.length;){const i=n[t];let l;if(typeof i=="string")l=i;else switch(i){case-5:{l="\r";break}case-4:{l=`
+import{l as At,an as zt,ap as It}from"./mermaid.core-DNo_7Q2B.js";const Tt={};function Bt(n,r){const t=Tt,e=typeof t.includeImageAlt=="boolean"?t.includeImageAlt:!0,u=typeof t.includeHtml=="boolean"?t.includeHtml:!0;return et(n,e,u)}function et(n,r,t){if(Lt(n)){if("value"in n)return n.type==="html"&&!t?"":n.value;if(r&&"alt"in n&&n.alt)return n.alt;if("children"in n)return Vn(n.children,r,t)}return Array.isArray(n)?Vn(n,r,t):""}function Vn(n,r,t){const e=[];let u=-1;for(;++u<n.length;)e[u]=et(n[u],r,t);return e.join("")}function Lt(n){return!!(n&&typeof n=="object")}function tn(n,r,t,e){const u=n.length;let i=0,l;if(r<0?r=-r>u?0:u+r:r=r>u?u:r,t=t>0?t:0,e.length<1e4)l=Array.from(e),l.unshift(r,t),n.splice(...l);else for(t&&n.splice(r,t);i<e.length;)l=e.slice(i,i+1e4),l.unshift(r,0),n.splice(...l),i+=1e4,r+=1e4}function Y(n,r){return n.length>0?(tn(n,n.length,0,r),n):r}const Wn={}.hasOwnProperty;function Ot(n){const r={};let t=-1;for(;++t<n.length;)Dt(r,n[t]);return r}function Dt(n,r){let t;for(t in r){const u=(Wn.call(n,t)?n[t]:void 0)||(n[t]={}),i=r[t];let l;if(i)for(l in i){Wn.call(u,l)||(u[l]=[]);const a=i[l];Pt(u[l],Array.isArray(a)?a:a?[a]:[])}}}function Pt(n,r){let t=-1;const e=[];for(;++t<r.length;)(r[t].add==="after"?n:e).push(r[t]);tn(n,0,0,e)}const _t=/[!-\/:-@\[-`\{-~\xA1\xA7\xAB\xB6\xB7\xBB\xBF\u037E\u0387\u055A-\u055F\u0589\u058A\u05BE\u05C0\u05C3\u05C6\u05F3\u05F4\u0609\u060A\u060C\u060D\u061B\u061D-\u061F\u066A-\u066D\u06D4\u0700-\u070D\u07F7-\u07F9\u0830-\u083E\u085E\u0964\u0965\u0970\u09FD\u0A76\u0AF0\u0C77\u0C84\u0DF4\u0E4F\u0E5A\u0E5B\u0F04-\u0F12\u0F14\u0F3A-\u0F3D\u0F85\u0FD0-\u0FD4\u0FD9\u0FDA\u104A-\u104F\u10FB\u1360-\u1368\u1400\u166E\u169B\u169C\u16EB-\u16ED\u1735\u1736\u17D4-\u17D6\u17D8-\u17DA\u1800-\u180A\u1944\u1945\u1A1E\u1A1F\u1AA0-\u1AA6\u1AA8-\u1AAD\u1B5A-\u1B60\u1B7D\u1B7E\u1BFC-\u1BFF\u1C3B-\u1C3F\u1C7E\u1C7F\u1CC0-\u1CC7\u1CD3\u2010-\u2027\u2030-\u2043\u2045-\u2051\u2053-\u205E\u207D\u207E\u208D\u208E\u2308-\u230B\u2329\u232A\u2768-\u2775\u27C5\u27C6\u27E6-\u27EF\u2983-\u2998\u29D8-\u29DB\u29FC\u29FD\u2CF9-\u2CFC\u2CFE\u2CFF\u2D70\u2E00-\u2E2E\u2E30-\u2E4F\u2E52-\u2E5D\u3001-\u3003\u3008-\u3011\u3014-\u301F\u3030\u303D\u30A0\u30FB\uA4FE\uA4FF\uA60D-\uA60F\uA673\uA67E\uA6F2-\uA6F7\uA874-\uA877\uA8CE\uA8CF\uA8F8-\uA8FA\uA8FC\uA92E\uA92F\uA95F\uA9C1-\uA9CD\uA9DE\uA9DF\uAA5C-\uAA5F\uAADE\uAADF\uAAF0\uAAF1\uABEB\uFD3E\uFD3F\uFE10-\uFE19\uFE30-\uFE52\uFE54-\uFE61\uFE63\uFE68\uFE6A\uFE6B\uFF01-\uFF03\uFF05-\uFF0A\uFF0C-\uFF0F\uFF1A\uFF1B\uFF1F\uFF20\uFF3B-\uFF3D\uFF3F\uFF5B\uFF5D\uFF5F-\uFF65]/,nn=cn(/[A-Za-z]/),v=cn(/[\dA-Za-z]/),Mt=cn(/[#-'*+\--9=?A-Z^-~]/);function An(n){return n!==null&&(n<32||n===127)}const zn=cn(/\d/),jt=cn(/[\dA-Fa-f]/),Rt=cn(/[!-/:-@[-`{-~]/);function C(n){return n!==null&&n<-2}function Z(n){return n!==null&&(n<0||n===32)}function z(n){return n===-2||n===-1||n===32}const qt=cn(_t),Ht=cn(/\s/);function cn(n){return r;function r(t){return t!==null&&n.test(String.fromCharCode(t))}}function O(n,r,t,e){const u=e?e-1:Number.POSITIVE_INFINITY;let i=0;return l;function l(m){return z(m)?(n.enter(t),a(m)):r(m)}function a(m){return z(m)&&i++<u?(n.consume(m),a):(n.exit(t),r(m))}}const Nt={tokenize:Vt};function Vt(n){const r=n.attempt(this.parser.constructs.contentInitial,e,u);let t;return r;function e(a){if(a===null){n.consume(a);return}return n.enter("lineEnding"),n.consume(a),n.exit("lineEnding"),O(n,r,"linePrefix")}function u(a){return n.enter("paragraph"),i(a)}function i(a){const m=n.enter("chunkText",{contentType:"text",previous:t});return t&&(t.next=m),t=m,l(a)}function l(a){if(a===null){n.exit("chunkText"),n.exit("paragraph"),n.consume(a);return}return C(a)?(n.consume(a),n.exit("chunkText"),i):(n.consume(a),l)}}const Wt={tokenize:Qt},Qn={tokenize:Ut};function Qt(n){const r=this,t=[];let e=0,u,i,l;return a;function a(F){if(e<t.length){const D=t[e];return r.containerState=D[1],n.attempt(D[0].continuation,m,c)(F)}return c(F)}function m(F){if(e++,r.containerState._closeFlow){r.containerState._closeFlow=void 0,u&&j();const D=r.events.length;let _=D,k;for(;_--;)if(r.events[_][0]==="exit"&&r.events[_][1].type==="chunkFlow"){k=r.events[_][1].end;break}b(e);let T=D;for(;T<r.events.length;)r.events[T][1].end=Object.assign({},k),T++;return tn(r.events,_+1,0,r.events.slice(D)),r.events.length=T,c(F)}return a(F)}function c(F){if(e===t.length){if(!u)return x(F);if(u.currentConstruct&&u.currentConstruct.concrete)return A(F);r.interrupt=!!(u.currentConstruct&&!u._gfmTableDynamicInterruptHack)}return r.containerState={},n.check(Qn,p,f)(F)}function p(F){return u&&j(),b(e),x(F)}function f(F){return r.parser.lazy[r.now().line]=e!==t.length,l=r.now().offset,A(F)}function x(F){return r.containerState={},n.attempt(Qn,h,A)(F)}function h(F){return e++,t.push([r.currentConstruct,r.containerState]),x(F)}function A(F){if(F===null){u&&j(),b(0),n.consume(F);return}return u=u||r.parser.flow(r.now()),n.enter("chunkFlow",{contentType:"flow",previous:i,_tokenizer:u}),I(F)}function I(F){if(F===null){M(n.exit("chunkFlow"),!0),b(0),n.consume(F);return}return C(F)?(n.consume(F),M(n.exit("chunkFlow")),e=0,r.interrupt=void 0,a):(n.consume(F),I)}function M(F,D){const _=r.sliceStream(F);if(D&&_.push(null),F.previous=i,i&&(i.next=F),i=F,u.defineSkip(F.start),u.write(_),r.parser.lazy[F.start.line]){let k=u.events.length;for(;k--;)if(u.events[k][1].start.offset<l&&(!u.events[k][1].end||u.events[k][1].end.offset>l))return;const T=r.events.length;let H=T,N,V;for(;H--;)if(r.events[H][0]==="exit"&&r.events[H][1].type==="chunkFlow"){if(N){V=r.events[H][1].end;break}N=!0}for(b(e),k=T;k<r.events.length;)r.events[k][1].end=Object.assign({},V),k++;tn(r.events,H+1,0,r.events.slice(T)),r.events.length=k}}function b(F){let D=t.length;for(;D-- >F;){const _=t[D];r.containerState=_[1],_[0].exit.call(r,n)}t.length=F}function j(){u.write([null]),i=void 0,u=void 0,r.containerState._closeFlow=void 0}}function Ut(n,r,t){return O(n,n.attempt(this.parser.constructs.document,r,t),"linePrefix",this.parser.constructs.disable.null.includes("codeIndented")?void 0:4)}function Un(n){if(n===null||Z(n)||Ht(n))return 1;if(qt(n))return 2}function Ln(n,r,t){const e=[];let u=-1;for(;++u<n.length;){const i=n[u].resolveAll;i&&!e.includes(i)&&(r=i(r,t),e.push(i))}return r}const In={name:"attention",tokenize:Zt,resolveAll:$t};function $t(n,r){let t=-1,e,u,i,l,a,m,c,p;for(;++t<n.length;)if(n[t][0]==="enter"&&n[t][1].type==="attentionSequence"&&n[t][1]._close){for(e=t;e--;)if(n[e][0]==="exit"&&n[e][1].type==="attentionSequence"&&n[e][1]._open&&r.sliceSerialize(n[e][1]).charCodeAt(0)===r.sliceSerialize(n[t][1]).charCodeAt(0)){if((n[e][1]._close||n[t][1]._open)&&(n[t][1].end.offset-n[t][1].start.offset)%3&&!((n[e][1].end.offset-n[e][1].start.offset+n[t][1].end.offset-n[t][1].start.offset)%3))continue;m=n[e][1].end.offset-n[e][1].start.offset>1&&n[t][1].end.offset-n[t][1].start.offset>1?2:1;const f=Object.assign({},n[e][1].end),x=Object.assign({},n[t][1].start);$n(f,-m),$n(x,m),l={type:m>1?"strongSequence":"emphasisSequence",start:f,end:Object.assign({},n[e][1].end)},a={type:m>1?"strongSequence":"emphasisSequence",start:Object.assign({},n[t][1].start),end:x},i={type:m>1?"strongText":"emphasisText",start:Object.assign({},n[e][1].end),end:Object.assign({},n[t][1].start)},u={type:m>1?"strong":"emphasis",start:Object.assign({},l.start),end:Object.assign({},a.end)},n[e][1].end=Object.assign({},l.start),n[t][1].start=Object.assign({},a.end),c=[],n[e][1].end.offset-n[e][1].start.offset&&(c=Y(c,[["enter",n[e][1],r],["exit",n[e][1],r]])),c=Y(c,[["enter",u,r],["enter",l,r],["exit",l,r],["enter",i,r]]),c=Y(c,Ln(r.parser.constructs.insideSpan.null,n.slice(e+1,t),r)),c=Y(c,[["exit",i,r],["enter",a,r],["exit",a,r],["exit",u,r]]),n[t][1].end.offset-n[t][1].start.offset?(p=2,c=Y(c,[["enter",n[t][1],r],["exit",n[t][1],r]])):p=0,tn(n,e-1,t-e+3,c),t=e+c.length-p-2;break}}for(t=-1;++t<n.length;)n[t][1].type==="attentionSequence"&&(n[t][1].type="data");return n}function Zt(n,r){const t=this.parser.constructs.attentionMarkers.null,e=this.previous,u=Un(e);let i;return l;function l(m){return i=m,n.enter("attentionSequence"),a(m)}function a(m){if(m===i)return n.consume(m),a;const c=n.exit("attentionSequence"),p=Un(m),f=!p||p===2&&u||t.includes(m),x=!u||u===2&&p||t.includes(e);return c._open=!!(i===42?f:f&&(u||!x)),c._close=!!(i===42?x:x&&(p||!f)),r(m)}}function $n(n,r){n.column+=r,n.offset+=r,n._bufferIndex+=r}const Yt={name:"autolink",tokenize:Gt};function Gt(n,r,t){let e=0;return u;function u(h){return n.enter("autolink"),n.enter("autolinkMarker"),n.consume(h),n.exit("autolinkMarker"),n.enter("autolinkProtocol"),i}function i(h){return nn(h)?(n.consume(h),l):c(h)}function l(h){return h===43||h===45||h===46||v(h)?(e=1,a(h)):c(h)}function a(h){return h===58?(n.consume(h),e=0,m):(h===43||h===45||h===46||v(h))&&e++<32?(n.consume(h),a):(e=0,c(h))}function m(h){return h===62?(n.exit("autolinkProtocol"),n.enter("autolinkMarker"),n.consume(h),n.exit("autolinkMarker"),n.exit("autolink"),r):h===null||h===32||h===60||An(h)?t(h):(n.consume(h),m)}function c(h){return h===64?(n.consume(h),p):Mt(h)?(n.consume(h),c):t(h)}function p(h){return v(h)?f(h):t(h)}function f(h){return h===46?(n.consume(h),e=0,p):h===62?(n.exit("autolinkProtocol").type="autolinkEmail",n.enter("autolinkMarker"),n.consume(h),n.exit("autolinkMarker"),n.exit("autolink"),r):x(h)}function x(h){if((h===45||v(h))&&e++<63){const A=h===45?x:f;return n.consume(h),A}return t(h)}}const Sn={tokenize:Jt,partial:!0};function Jt(n,r,t){return e;function e(i){return z(i)?O(n,u,"linePrefix")(i):u(i)}function u(i){return i===null||C(i)?r(i):t(i)}}const rt={name:"blockQuote",tokenize:Kt,continuation:{tokenize:Xt},exit:vt};function Kt(n,r,t){const e=this;return u;function u(l){if(l===62){const a=e.containerState;return a.open||(n.enter("blockQuote",{_container:!0}),a.open=!0),n.enter("blockQuotePrefix"),n.enter("blockQuoteMarker"),n.consume(l),n.exit("blockQuoteMarker"),i}return t(l)}function i(l){return z(l)?(n.enter("blockQuotePrefixWhitespace"),n.consume(l),n.exit("blockQuotePrefixWhitespace"),n.exit("blockQuotePrefix"),r):(n.exit("blockQuotePrefix"),r(l))}}function Xt(n,r,t){const e=this;return u;function u(l){return z(l)?O(n,i,"linePrefix",e.parser.constructs.disable.null.includes("codeIndented")?void 0:4)(l):i(l)}function i(l){return n.attempt(rt,r,t)(l)}}function vt(n){n.exit("blockQuote")}const it={name:"characterEscape",tokenize:ne};function ne(n,r,t){return e;function e(i){return n.enter("characterEscape"),n.enter("escapeMarker"),n.consume(i),n.exit("escapeMarker"),u}function u(i){return Rt(i)?(n.enter("characterEscapeValue"),n.consume(i),n.exit("characterEscapeValue"),n.exit("characterEscape"),r):t(i)}}const Zn=document.createElement("i");function On(n){const r="&"+n+";";Zn.innerHTML=r;const t=Zn.textContent;return t.charCodeAt(t.length-1)===59&&n!=="semi"||t===r?!1:t}const ut={name:"characterReference",tokenize:te};function te(n,r,t){const e=this;let u=0,i,l;return a;function a(f){return n.enter("characterReference"),n.enter("characterReferenceMarker"),n.consume(f),n.exit("characterReferenceMarker"),m}function m(f){return f===35?(n.enter("characterReferenceMarkerNumeric"),n.consume(f),n.exit("characterReferenceMarkerNumeric"),c):(n.enter("characterReferenceValue"),i=31,l=v,p(f))}function c(f){return f===88||f===120?(n.enter("characterReferenceMarkerHexadecimal"),n.consume(f),n.exit("characterReferenceMarkerHexadecimal"),n.enter("characterReferenceValue"),i=6,l=jt,p):(n.enter("characterReferenceValue"),i=7,l=zn,p(f))}function p(f){if(f===59&&u){const x=n.exit("characterReferenceValue");return l===v&&!On(e.sliceSerialize(x))?t(f):(n.enter("characterReferenceMarker"),n.consume(f),n.exit("characterReferenceMarker"),n.exit("characterReference"),r)}return l(f)&&u++<i?(n.consume(f),p):t(f)}}const Yn={tokenize:re,partial:!0},Gn={name:"codeFenced",tokenize:ee,concrete:!0};function ee(n,r,t){const e=this,u={tokenize:_,partial:!0};let i=0,l=0,a;return m;function m(k){return c(k)}function c(k){const T=e.events[e.events.length-1];return i=T&&T[1].type==="linePrefix"?T[2].sliceSerialize(T[1],!0).length:0,a=k,n.enter("codeFenced"),n.enter("codeFencedFence"),n.enter("codeFencedFenceSequence"),p(k)}function p(k){return k===a?(l++,n.consume(k),p):l<3?t(k):(n.exit("codeFencedFenceSequence"),z(k)?O(n,f,"whitespace")(k):f(k))}function f(k){return k===null||C(k)?(n.exit("codeFencedFence"),e.interrupt?r(k):n.check(Yn,I,D)(k)):(n.enter("codeFencedFenceInfo"),n.enter("chunkString",{contentType:"string"}),x(k))}function x(k){return k===null||C(k)?(n.exit("chunkString"),n.exit("codeFencedFenceInfo"),f(k)):z(k)?(n.exit("chunkString"),n.exit("codeFencedFenceInfo"),O(n,h,"whitespace")(k)):k===96&&k===a?t(k):(n.consume(k),x)}function h(k){return k===null||C(k)?f(k):(n.enter("codeFencedFenceMeta"),n.enter("chunkString",{contentType:"string"}),A(k))}function A(k){return k===null||C(k)?(n.exit("chunkString"),n.exit("codeFencedFenceMeta"),f(k)):k===96&&k===a?t(k):(n.consume(k),A)}function I(k){return n.attempt(u,D,M)(k)}function M(k){return n.enter("lineEnding"),n.consume(k),n.exit("lineEnding"),b}function b(k){return i>0&&z(k)?O(n,j,"linePrefix",i+1)(k):j(k)}function j(k){return k===null||C(k)?n.check(Yn,I,D)(k):(n.enter("codeFlowValue"),F(k))}function F(k){return k===null||C(k)?(n.exit("codeFlowValue"),j(k)):(n.consume(k),F)}function D(k){return n.exit("codeFenced"),r(k)}function _(k,T,H){let N=0;return V;function V(w){return k.enter("lineEnding"),k.consume(w),k.exit("lineEnding"),y}function y(w){return k.enter("codeFencedFence"),z(w)?O(k,S,"linePrefix",e.parser.constructs.disable.null.includes("codeIndented")?void 0:4)(w):S(w)}function S(w){return w===a?(k.enter("codeFencedFenceSequence"),P(w)):H(w)}function P(w){return w===a?(N++,k.consume(w),P):N>=l?(k.exit("codeFencedFenceSequence"),z(w)?O(k,R,"whitespace")(w):R(w)):H(w)}function R(w){return w===null||C(w)?(k.exit("codeFencedFence"),T(w)):H(w)}}}function re(n,r,t){const e=this;return u;function u(l){return l===null?t(l):(n.enter("lineEnding"),n.consume(l),n.exit("lineEnding"),i)}function i(l){return e.parser.lazy[e.now().line]?t(l):r(l)}}const Cn={name:"codeIndented",tokenize:ue},ie={tokenize:le,partial:!0};function ue(n,r,t){const e=this;return u;function u(c){return n.enter("codeIndented"),O(n,i,"linePrefix",5)(c)}function i(c){const p=e.events[e.events.length-1];return p&&p[1].type==="linePrefix"&&p[2].sliceSerialize(p[1],!0).length>=4?l(c):t(c)}function l(c){return c===null?m(c):C(c)?n.attempt(ie,l,m)(c):(n.enter("codeFlowValue"),a(c))}function a(c){return c===null||C(c)?(n.exit("codeFlowValue"),l(c)):(n.consume(c),a)}function m(c){return n.exit("codeIndented"),r(c)}}function le(n,r,t){const e=this;return u;function u(l){return e.parser.lazy[e.now().line]?t(l):C(l)?(n.enter("lineEnding"),n.consume(l),n.exit("lineEnding"),u):O(n,i,"linePrefix",5)(l)}function i(l){const a=e.events[e.events.length-1];return a&&a[1].type==="linePrefix"&&a[2].sliceSerialize(a[1],!0).length>=4?r(l):C(l)?u(l):t(l)}}const ae={name:"codeText",tokenize:ce,resolve:oe,previous:se};function oe(n){let r=n.length-4,t=3,e,u;if((n[t][1].type==="lineEnding"||n[t][1].type==="space")&&(n[r][1].type==="lineEnding"||n[r][1].type==="space")){for(e=t;++e<r;)if(n[e][1].type==="codeTextData"){n[t][1].type="codeTextPadding",n[r][1].type="codeTextPadding",t+=2,r-=2;break}}for(e=t-1,r++;++e<=r;)u===void 0?e!==r&&n[e][1].type!=="lineEnding"&&(u=e):(e===r||n[e][1].type==="lineEnding")&&(n[u][1].type="codeTextData",e!==u+2&&(n[u][1].end=n[e-1][1].end,n.splice(u+2,e-u-2),r-=e-u-2,e=u+2),u=void 0);return n}function se(n){return n!==96||this.events[this.events.length-1][1].type==="characterEscape"}function ce(n,r,t){let e=0,u,i;return l;function l(f){return n.enter("codeText"),n.enter("codeTextSequence"),a(f)}function a(f){return f===96?(n.consume(f),e++,a):(n.exit("codeTextSequence"),m(f))}function m(f){return f===null?t(f):f===32?(n.enter("space"),n.consume(f),n.exit("space"),m):f===96?(i=n.enter("codeTextSequence"),u=0,p(f)):C(f)?(n.enter("lineEnding"),n.consume(f),n.exit("lineEnding"),m):(n.enter("codeTextData"),c(f))}function c(f){return f===null||f===32||f===96||C(f)?(n.exit("codeTextData"),m(f)):(n.consume(f),c)}function p(f){return f===96?(n.consume(f),u++,p):u===e?(n.exit("codeTextSequence"),n.exit("codeText"),r(f)):(i.type="codeTextData",c(f))}}function lt(n){const r={};let t=-1,e,u,i,l,a,m,c;for(;++t<n.length;){for(;t in r;)t=r[t];if(e=n[t],t&&e[1].type==="chunkFlow"&&n[t-1][1].type==="listItemPrefix"&&(m=e[1]._tokenizer.events,i=0,i<m.length&&m[i][1].type==="lineEndingBlank"&&(i+=2),i<m.length&&m[i][1].type==="content"))for(;++i<m.length&&m[i][1].type!=="content";)m[i][1].type==="chunkText"&&(m[i][1]._isInFirstContentOfListItem=!0,i++);if(e[0]==="enter")e[1].contentType&&(Object.assign(r,he(n,t)),t=r[t],c=!0);else if(e[1]._container){for(i=t,u=void 0;i--&&(l=n[i],l[1].type==="lineEnding"||l[1].type==="lineEndingBlank");)l[0]==="enter"&&(u&&(n[u][1].type="lineEndingBlank"),l[1].type="lineEnding",u=i);u&&(e[1].end=Object.assign({},n[u][1].start),a=n.slice(u,t),a.unshift(e),tn(n,u,t-u+1,a))}}return!c}function he(n,r){const t=n[r][1],e=n[r][2];let u=r-1;const i=[],l=t._tokenizer||e.parser[t.contentType](t.start),a=l.events,m=[],c={};let p,f,x=-1,h=t,A=0,I=0;const M=[I];for(;h;){for(;n[++u][1]!==h;);i.push(u),h._tokenizer||(p=e.sliceStream(h),h.next||p.push(null),f&&l.defineSkip(h.start),h._isInFirstContentOfListItem&&(l._gfmTasklistFirstContentOfListItem=!0),l.write(p),h._isInFirstContentOfListItem&&(l._gfmTasklistFirstContentOfListItem=void 0)),f=h,h=h.next}for(h=t;++x<a.length;)a[x][0]==="exit"&&a[x-1][0]==="enter"&&a[x][1].type===a[x-1][1].type&&a[x][1].start.line!==a[x][1].end.line&&(I=x+1,M.push(I),h._tokenizer=void 0,h.previous=void 0,h=h.next);for(l.events=[],h?(h._tokenizer=void 0,h.previous=void 0):M.pop(),x=M.length;x--;){const b=a.slice(M[x],M[x+1]),j=i.pop();m.unshift([j,j+b.length-1]),tn(n,j,2,b)}for(x=-1;++x<m.length;)c[A+m[x][0]]=A+m[x][1],A+=m[x][1]-m[x][0]-1;return c}const pe={tokenize:xe,resolve:me},fe={tokenize:ge,partial:!0};function me(n){return lt(n),n}function xe(n,r){let t;return e;function e(a){return n.enter("content"),t=n.enter("chunkContent",{contentType:"content"}),u(a)}function u(a){return a===null?i(a):C(a)?n.check(fe,l,i)(a):(n.consume(a),u)}function i(a){return n.exit("chunkContent"),n.exit("content"),r(a)}function l(a){return n.consume(a),n.exit("chunkContent"),t.next=n.enter("chunkContent",{contentType:"content",previous:t}),t=t.next,u}}function ge(n,r,t){const e=this;return u;function u(l){return n.exit("chunkContent"),n.enter("lineEnding"),n.consume(l),n.exit("lineEnding"),O(n,i,"linePrefix")}function i(l){if(l===null||C(l))return t(l);const a=e.events[e.events.length-1];return!e.parser.constructs.disable.null.includes("codeIndented")&&a&&a[1].type==="linePrefix"&&a[2].sliceSerialize(a[1],!0).length>=4?r(l):n.interrupt(e.parser.constructs.flow,t,r)(l)}}function at(n,r,t,e,u,i,l,a,m){const c=m||Number.POSITIVE_INFINITY;let p=0;return f;function f(b){return b===60?(n.enter(e),n.enter(u),n.enter(i),n.consume(b),n.exit(i),x):b===null||b===32||b===41||An(b)?t(b):(n.enter(e),n.enter(l),n.enter(a),n.enter("chunkString",{contentType:"string"}),I(b))}function x(b){return b===62?(n.enter(i),n.consume(b),n.exit(i),n.exit(u),n.exit(e),r):(n.enter(a),n.enter("chunkString",{contentType:"string"}),h(b))}function h(b){return b===62?(n.exit("chunkString"),n.exit(a),x(b)):b===null||b===60||C(b)?t(b):(n.consume(b),b===92?A:h)}function A(b){return b===60||b===62||b===92?(n.consume(b),h):h(b)}function I(b){return!p&&(b===null||b===41||Z(b))?(n.exit("chunkString"),n.exit(a),n.exit(l),n.exit(e),r(b)):p<c&&b===40?(n.consume(b),p++,I):b===41?(n.consume(b),p--,I):b===null||b===32||b===40||An(b)?t(b):(n.consume(b),b===92?M:I)}function M(b){return b===40||b===41||b===92?(n.consume(b),I):I(b)}}function ot(n,r,t,e,u,i){const l=this;let a=0,m;return c;function c(h){return n.enter(e),n.enter(u),n.consume(h),n.exit(u),n.enter(i),p}function p(h){return a>999||h===null||h===91||h===93&&!m||h===94&&!a&&"_hiddenFootnoteSupport"in l.parser.constructs?t(h):h===93?(n.exit(i),n.enter(u),n.consume(h),n.exit(u),n.exit(e),r):C(h)?(n.enter("lineEnding"),n.consume(h),n.exit("lineEnding"),p):(n.enter("chunkString",{contentType:"string"}),f(h))}function f(h){return h===null||h===91||h===93||C(h)||a++>999?(n.exit("chunkString"),p(h)):(n.consume(h),m||(m=!z(h)),h===92?x:f)}function x(h){return h===91||h===92||h===93?(n.consume(h),a++,f):f(h)}}function st(n,r,t,e,u,i){let l;return a;function a(x){return x===34||x===39||x===40?(n.enter(e),n.enter(u),n.consume(x),n.exit(u),l=x===40?41:x,m):t(x)}function m(x){return x===l?(n.enter(u),n.consume(x),n.exit(u),n.exit(e),r):(n.enter(i),c(x))}function c(x){return x===l?(n.exit(i),m(l)):x===null?t(x):C(x)?(n.enter("lineEnding"),n.consume(x),n.exit("lineEnding"),O(n,c,"linePrefix")):(n.enter("chunkString",{contentType:"string"}),p(x))}function p(x){return x===l||x===null||C(x)?(n.exit("chunkString"),c(x)):(n.consume(x),x===92?f:p)}function f(x){return x===l||x===92?(n.consume(x),p):p(x)}}function dn(n,r){let t;return e;function e(u){return C(u)?(n.enter("lineEnding"),n.consume(u),n.exit("lineEnding"),t=!0,e):z(u)?O(n,e,t?"linePrefix":"lineSuffix")(u):r(u)}}function xn(n){return n.replace(/[\t\n\r ]+/g," ").replace(/^ | $/g,"").toLowerCase().toUpperCase()}const ke={name:"definition",tokenize:be},de={tokenize:ye,partial:!0};function be(n,r,t){const e=this;let u;return i;function i(h){return n.enter("definition"),l(h)}function l(h){return ot.call(e,n,a,t,"definitionLabel","definitionLabelMarker","definitionLabelString")(h)}function a(h){return u=xn(e.sliceSerialize(e.events[e.events.length-1][1]).slice(1,-1)),h===58?(n.enter("definitionMarker"),n.consume(h),n.exit("definitionMarker"),m):t(h)}function m(h){return Z(h)?dn(n,c)(h):c(h)}function c(h){return at(n,p,t,"definitionDestination","definitionDestinationLiteral","definitionDestinationLiteralMarker","definitionDestinationRaw","definitionDestinationString")(h)}function p(h){return n.attempt(de,f,f)(h)}function f(h){return z(h)?O(n,x,"whitespace")(h):x(h)}function x(h){return h===null||C(h)?(n.exit("definition"),e.parser.defined.push(u),r(h)):t(h)}}function ye(n,r,t){return e;function e(a){return Z(a)?dn(n,u)(a):t(a)}function u(a){return st(n,i,t,"definitionTitle","definitionTitleMarker","definitionTitleString")(a)}function i(a){return z(a)?O(n,l,"whitespace")(a):l(a)}function l(a){return a===null||C(a)?r(a):t(a)}}const Se={name:"hardBreakEscape",tokenize:Fe};function Fe(n,r,t){return e;function e(i){return n.enter("hardBreakEscape"),n.consume(i),u}function u(i){return C(i)?(n.exit("hardBreakEscape"),r(i)):t(i)}}const Ee={name:"headingAtx",tokenize:we,resolve:Ce};function Ce(n,r){let t=n.length-2,e=3,u,i;return n[e][1].type==="whitespace"&&(e+=2),t-2>e&&n[t][1].type==="whitespace"&&(t-=2),n[t][1].type==="atxHeadingSequence"&&(e===t-1||t-4>e&&n[t-2][1].type==="whitespace")&&(t-=e+1===t?2:4),t>e&&(u={type:"atxHeadingText",start:n[e][1].start,end:n[t][1].end},i={type:"chunkText",start:n[e][1].start,end:n[t][1].end,contentType:"text"},tn(n,e,t-e+1,[["enter",u,r],["enter",i,r],["exit",i,r],["exit",u,r]])),n}function we(n,r,t){let e=0;return u;function u(p){return n.enter("atxHeading"),i(p)}function i(p){return n.enter("atxHeadingSequence"),l(p)}function l(p){return p===35&&e++<6?(n.consume(p),l):p===null||Z(p)?(n.exit("atxHeadingSequence"),a(p)):t(p)}function a(p){return p===35?(n.enter("atxHeadingSequence"),m(p)):p===null||C(p)?(n.exit("atxHeading"),r(p)):z(p)?O(n,a,"whitespace")(p):(n.enter("atxHeadingText"),c(p))}function m(p){return p===35?(n.consume(p),m):(n.exit("atxHeadingSequence"),a(p))}function c(p){return p===null||p===35||Z(p)?(n.exit("atxHeadingText"),a(p)):(n.consume(p),c)}}const Ae=["address","article","aside","base","basefont","blockquote","body","caption","center","col","colgroup","dd","details","dialog","dir","div","dl","dt","fieldset","figcaption","figure","footer","form","frame","frameset","h1","h2","h3","h4","h5","h6","head","header","hr","html","iframe","legend","li","link","main","menu","menuitem","nav","noframes","ol","optgroup","option","p","param","search","section","summary","table","tbody","td","tfoot","th","thead","title","tr","track","ul"],Jn=["pre","script","style","textarea"],ze={name:"htmlFlow",tokenize:Le,resolveTo:Be,concrete:!0},Ie={tokenize:De,partial:!0},Te={tokenize:Oe,partial:!0};function Be(n){let r=n.length;for(;r--&&!(n[r][0]==="enter"&&n[r][1].type==="htmlFlow"););return r>1&&n[r-2][1].type==="linePrefix"&&(n[r][1].start=n[r-2][1].start,n[r+1][1].start=n[r-2][1].start,n.splice(r-2,2)),n}function Le(n,r,t){const e=this;let u,i,l,a,m;return c;function c(s){return p(s)}function p(s){return n.enter("htmlFlow"),n.enter("htmlFlowData"),n.consume(s),f}function f(s){return s===33?(n.consume(s),x):s===47?(n.consume(s),i=!0,I):s===63?(n.consume(s),u=3,e.interrupt?r:o):nn(s)?(n.consume(s),l=String.fromCharCode(s),M):t(s)}function x(s){return s===45?(n.consume(s),u=2,h):s===91?(n.consume(s),u=5,a=0,A):nn(s)?(n.consume(s),u=4,e.interrupt?r:o):t(s)}function h(s){return s===45?(n.consume(s),e.interrupt?r:o):t(s)}function A(s){const K="CDATA[";return s===K.charCodeAt(a++)?(n.consume(s),a===K.length?e.interrupt?r:S:A):t(s)}function I(s){return nn(s)?(n.consume(s),l=String.fromCharCode(s),M):t(s)}function M(s){if(s===null||s===47||s===62||Z(s)){const K=s===47,hn=l.toLowerCase();return!K&&!i&&Jn.includes(hn)?(u=1,e.interrupt?r(s):S(s)):Ae.includes(l.toLowerCase())?(u=6,K?(n.consume(s),b):e.interrupt?r(s):S(s)):(u=7,e.interrupt&&!e.parser.lazy[e.now().line]?t(s):i?j(s):F(s))}return s===45||v(s)?(n.consume(s),l+=String.fromCharCode(s),M):t(s)}function b(s){return s===62?(n.consume(s),e.interrupt?r:S):t(s)}function j(s){return z(s)?(n.consume(s),j):V(s)}function F(s){return s===47?(n.consume(s),V):s===58||s===95||nn(s)?(n.consume(s),D):z(s)?(n.consume(s),F):V(s)}function D(s){return s===45||s===46||s===58||s===95||v(s)?(n.consume(s),D):_(s)}function _(s){return s===61?(n.consume(s),k):z(s)?(n.consume(s),_):F(s)}function k(s){return s===null||s===60||s===61||s===62||s===96?t(s):s===34||s===39?(n.consume(s),m=s,T):z(s)?(n.consume(s),k):H(s)}function T(s){return s===m?(n.consume(s),m=null,N):s===null||C(s)?t(s):(n.consume(s),T)}function H(s){return s===null||s===34||s===39||s===47||s===60||s===61||s===62||s===96||Z(s)?_(s):(n.consume(s),H)}function N(s){return s===47||s===62||z(s)?F(s):t(s)}function V(s){return s===62?(n.consume(s),y):t(s)}function y(s){return s===null||C(s)?S(s):z(s)?(n.consume(s),y):t(s)}function S(s){return s===45&&u===2?(n.consume(s),U):s===60&&u===1?(n.consume(s),W):s===62&&u===4?(n.consume(s),J):s===63&&u===3?(n.consume(s),o):s===93&&u===5?(n.consume(s),en):C(s)&&(u===6||u===7)?(n.exit("htmlFlowData"),n.check(Ie,rn,P)(s)):s===null||C(s)?(n.exit("htmlFlowData"),P(s)):(n.consume(s),S)}function P(s){return n.check(Te,R,rn)(s)}function R(s){return n.enter("lineEnding"),n.consume(s),n.exit("lineEnding"),w}function w(s){return s===null||C(s)?P(s):(n.enter("htmlFlowData"),S(s))}function U(s){return s===45?(n.consume(s),o):S(s)}function W(s){return s===47?(n.consume(s),l="",G):S(s)}function G(s){if(s===62){const K=l.toLowerCase();return Jn.includes(K)?(n.consume(s),J):S(s)}return nn(s)&&l.length<8?(n.consume(s),l+=String.fromCharCode(s),G):S(s)}function en(s){return s===93?(n.consume(s),o):S(s)}function o(s){return s===62?(n.consume(s),J):s===45&&u===2?(n.consume(s),o):S(s)}function J(s){return s===null||C(s)?(n.exit("htmlFlowData"),rn(s)):(n.consume(s),J)}function rn(s){return n.exit("htmlFlow"),r(s)}}function Oe(n,r,t){const e=this;return u;function u(l){return C(l)?(n.enter("lineEnding"),n.consume(l),n.exit("lineEnding"),i):t(l)}function i(l){return e.parser.lazy[e.now().line]?t(l):r(l)}}function De(n,r,t){return e;function e(u){return n.enter("lineEnding"),n.consume(u),n.exit("lineEnding"),n.attempt(Sn,r,t)}}const Pe={name:"htmlText",tokenize:_e};function _e(n,r,t){const e=this;let u,i,l;return a;function a(o){return n.enter("htmlText"),n.enter("htmlTextData"),n.consume(o),m}function m(o){return o===33?(n.consume(o),c):o===47?(n.consume(o),_):o===63?(n.consume(o),F):nn(o)?(n.consume(o),H):t(o)}function c(o){return o===45?(n.consume(o),p):o===91?(n.consume(o),i=0,A):nn(o)?(n.consume(o),j):t(o)}function p(o){return o===45?(n.consume(o),h):t(o)}function f(o){return o===null?t(o):o===45?(n.consume(o),x):C(o)?(l=f,W(o)):(n.consume(o),f)}function x(o){return o===45?(n.consume(o),h):f(o)}function h(o){return o===62?U(o):o===45?x(o):f(o)}function A(o){const J="CDATA[";return o===J.charCodeAt(i++)?(n.consume(o),i===J.length?I:A):t(o)}function I(o){return o===null?t(o):o===93?(n.consume(o),M):C(o)?(l=I,W(o)):(n.consume(o),I)}function M(o){return o===93?(n.consume(o),b):I(o)}function b(o){return o===62?U(o):o===93?(n.consume(o),b):I(o)}function j(o){return o===null||o===62?U(o):C(o)?(l=j,W(o)):(n.consume(o),j)}function F(o){return o===null?t(o):o===63?(n.consume(o),D):C(o)?(l=F,W(o)):(n.consume(o),F)}function D(o){return o===62?U(o):F(o)}function _(o){return nn(o)?(n.consume(o),k):t(o)}function k(o){return o===45||v(o)?(n.consume(o),k):T(o)}function T(o){return C(o)?(l=T,W(o)):z(o)?(n.consume(o),T):U(o)}function H(o){return o===45||v(o)?(n.consume(o),H):o===47||o===62||Z(o)?N(o):t(o)}function N(o){return o===47?(n.consume(o),U):o===58||o===95||nn(o)?(n.consume(o),V):C(o)?(l=N,W(o)):z(o)?(n.consume(o),N):U(o)}function V(o){return o===45||o===46||o===58||o===95||v(o)?(n.consume(o),V):y(o)}function y(o){return o===61?(n.consume(o),S):C(o)?(l=y,W(o)):z(o)?(n.consume(o),y):N(o)}function S(o){return o===null||o===60||o===61||o===62||o===96?t(o):o===34||o===39?(n.consume(o),u=o,P):C(o)?(l=S,W(o)):z(o)?(n.consume(o),S):(n.consume(o),R)}function P(o){return o===u?(n.consume(o),u=void 0,w):o===null?t(o):C(o)?(l=P,W(o)):(n.consume(o),P)}function R(o){return o===null||o===34||o===39||o===60||o===61||o===96?t(o):o===47||o===62||Z(o)?N(o):(n.consume(o),R)}function w(o){return o===47||o===62||Z(o)?N(o):t(o)}function U(o){return o===62?(n.consume(o),n.exit("htmlTextData"),n.exit("htmlText"),r):t(o)}function W(o){return n.exit("htmlTextData"),n.enter("lineEnding"),n.consume(o),n.exit("lineEnding"),G}function G(o){return z(o)?O(n,en,"linePrefix",e.parser.constructs.disable.null.includes("codeIndented")?void 0:4)(o):en(o)}function en(o){return n.enter("htmlTextData"),l(o)}}const Dn={name:"labelEnd",tokenize:Ne,resolveTo:He,resolveAll:qe},Me={tokenize:Ve},je={tokenize:We},Re={tokenize:Qe};function qe(n){let r=-1;for(;++r<n.length;){const t=n[r][1];(t.type==="labelImage"||t.type==="labelLink"||t.type==="labelEnd")&&(n.splice(r+1,t.type==="labelImage"?4:2),t.type="data",r++)}return n}function He(n,r){let t=n.length,e=0,u,i,l,a;for(;t--;)if(u=n[t][1],i){if(u.type==="link"||u.type==="labelLink"&&u._inactive)break;n[t][0]==="enter"&&u.type==="labelLink"&&(u._inactive=!0)}else if(l){if(n[t][0]==="enter"&&(u.type==="labelImage"||u.type==="labelLink")&&!u._balanced&&(i=t,u.type!=="labelLink")){e=2;break}}else u.type==="labelEnd"&&(l=t);const m={type:n[i][1].type==="labelLink"?"link":"image",start:Object.assign({},n[i][1].start),end:Object.assign({},n[n.length-1][1].end)},c={type:"label",start:Object.assign({},n[i][1].start),end:Object.assign({},n[l][1].end)},p={type:"labelText",start:Object.assign({},n[i+e+2][1].end),end:Object.assign({},n[l-2][1].start)};return a=[["enter",m,r],["enter",c,r]],a=Y(a,n.slice(i+1,i+e+3)),a=Y(a,[["enter",p,r]]),a=Y(a,Ln(r.parser.constructs.insideSpan.null,n.slice(i+e+4,l-3),r)),a=Y(a,[["exit",p,r],n[l-2],n[l-1],["exit",c,r]]),a=Y(a,n.slice(l+1)),a=Y(a,[["exit",m,r]]),tn(n,i,n.length,a),n}function Ne(n,r,t){const e=this;let u=e.events.length,i,l;for(;u--;)if((e.events[u][1].type==="labelImage"||e.events[u][1].type==="labelLink")&&!e.events[u][1]._balanced){i=e.events[u][1];break}return a;function a(x){return i?i._inactive?f(x):(l=e.parser.defined.includes(xn(e.sliceSerialize({start:i.end,end:e.now()}))),n.enter("labelEnd"),n.enter("labelMarker"),n.consume(x),n.exit("labelMarker"),n.exit("labelEnd"),m):t(x)}function m(x){return x===40?n.attempt(Me,p,l?p:f)(x):x===91?n.attempt(je,p,l?c:f)(x):l?p(x):f(x)}function c(x){return n.attempt(Re,p,f)(x)}function p(x){return r(x)}function f(x){return i._balanced=!0,t(x)}}function Ve(n,r,t){return e;function e(f){return n.enter("resource"),n.enter("resourceMarker"),n.consume(f),n.exit("resourceMarker"),u}function u(f){return Z(f)?dn(n,i)(f):i(f)}function i(f){return f===41?p(f):at(n,l,a,"resourceDestination","resourceDestinationLiteral","resourceDestinationLiteralMarker","resourceDestinationRaw","resourceDestinationString",32)(f)}function l(f){return Z(f)?dn(n,m)(f):p(f)}function a(f){return t(f)}function m(f){return f===34||f===39||f===40?st(n,c,t,"resourceTitle","resourceTitleMarker","resourceTitleString")(f):p(f)}function c(f){return Z(f)?dn(n,p)(f):p(f)}function p(f){return f===41?(n.enter("resourceMarker"),n.consume(f),n.exit("resourceMarker"),n.exit("resource"),r):t(f)}}function We(n,r,t){const e=this;return u;function u(a){return ot.call(e,n,i,l,"reference","referenceMarker","referenceString")(a)}function i(a){return e.parser.defined.includes(xn(e.sliceSerialize(e.events[e.events.length-1][1]).slice(1,-1)))?r(a):t(a)}function l(a){return t(a)}}function Qe(n,r,t){return e;function e(i){return n.enter("reference"),n.enter("referenceMarker"),n.consume(i),n.exit("referenceMarker"),u}function u(i){return i===93?(n.enter("referenceMarker"),n.consume(i),n.exit("referenceMarker"),n.exit("reference"),r):t(i)}}const Ue={name:"labelStartImage",tokenize:$e,resolveAll:Dn.resolveAll};function $e(n,r,t){const e=this;return u;function u(a){return n.enter("labelImage"),n.enter("labelImageMarker"),n.consume(a),n.exit("labelImageMarker"),i}function i(a){return a===91?(n.enter("labelMarker"),n.consume(a),n.exit("labelMarker"),n.exit("labelImage"),l):t(a)}function l(a){return a===94&&"_hiddenFootnoteSupport"in e.parser.constructs?t(a):r(a)}}const Ze={name:"labelStartLink",tokenize:Ye,resolveAll:Dn.resolveAll};function Ye(n,r,t){const e=this;return u;function u(l){return n.enter("labelLink"),n.enter("labelMarker"),n.consume(l),n.exit("labelMarker"),n.exit("labelLink"),i}function i(l){return l===94&&"_hiddenFootnoteSupport"in e.parser.constructs?t(l):r(l)}}const wn={name:"lineEnding",tokenize:Ge};function Ge(n,r){return t;function t(e){return n.enter("lineEnding"),n.consume(e),n.exit("lineEnding"),O(n,r,"linePrefix")}}const bn={name:"thematicBreak",tokenize:Je};function Je(n,r,t){let e=0,u;return i;function i(c){return n.enter("thematicBreak"),l(c)}function l(c){return u=c,a(c)}function a(c){return c===u?(n.enter("thematicBreakSequence"),m(c)):e>=3&&(c===null||C(c))?(n.exit("thematicBreak"),r(c)):t(c)}function m(c){return c===u?(n.consume(c),e++,m):(n.exit("thematicBreakSequence"),z(c)?O(n,a,"whitespace")(c):a(c))}}const $={name:"list",tokenize:ve,continuation:{tokenize:nr},exit:er},Ke={tokenize:rr,partial:!0},Xe={tokenize:tr,partial:!0};function ve(n,r,t){const e=this,u=e.events[e.events.length-1];let i=u&&u[1].type==="linePrefix"?u[2].sliceSerialize(u[1],!0).length:0,l=0;return a;function a(h){const A=e.containerState.type||(h===42||h===43||h===45?"listUnordered":"listOrdered");if(A==="listUnordered"?!e.containerState.marker||h===e.containerState.marker:zn(h)){if(e.containerState.type||(e.containerState.type=A,n.enter(A,{_container:!0})),A==="listUnordered")return n.enter("listItemPrefix"),h===42||h===45?n.check(bn,t,c)(h):c(h);if(!e.interrupt||h===49)return n.enter("listItemPrefix"),n.enter("listItemValue"),m(h)}return t(h)}function m(h){return zn(h)&&++l<10?(n.consume(h),m):(!e.interrupt||l<2)&&(e.containerState.marker?h===e.containerState.marker:h===41||h===46)?(n.exit("listItemValue"),c(h)):t(h)}function c(h){return n.enter("listItemMarker"),n.consume(h),n.exit("listItemMarker"),e.containerState.marker=e.containerState.marker||h,n.check(Sn,e.interrupt?t:p,n.attempt(Ke,x,f))}function p(h){return e.containerState.initialBlankLine=!0,i++,x(h)}function f(h){return z(h)?(n.enter("listItemPrefixWhitespace"),n.consume(h),n.exit("listItemPrefixWhitespace"),x):t(h)}function x(h){return e.containerState.size=i+e.sliceSerialize(n.exit("listItemPrefix"),!0).length,r(h)}}function nr(n,r,t){const e=this;return e.containerState._closeFlow=void 0,n.check(Sn,u,i);function u(a){return e.containerState.furtherBlankLines=e.containerState.furtherBlankLines||e.containerState.initialBlankLine,O(n,r,"listItemIndent",e.containerState.size+1)(a)}function i(a){return e.containerState.furtherBlankLines||!z(a)?(e.containerState.furtherBlankLines=void 0,e.containerState.initialBlankLine=void 0,l(a)):(e.containerState.furtherBlankLines=void 0,e.containerState.initialBlankLine=void 0,n.attempt(Xe,r,l)(a))}function l(a){return e.containerState._closeFlow=!0,e.interrupt=void 0,O(n,n.attempt($,r,t),"linePrefix",e.parser.constructs.disable.null.includes("codeIndented")?void 0:4)(a)}}function tr(n,r,t){const e=this;return O(n,u,"listItemIndent",e.containerState.size+1);function u(i){const l=e.events[e.events.length-1];return l&&l[1].type==="listItemIndent"&&l[2].sliceSerialize(l[1],!0).length===e.containerState.size?r(i):t(i)}}function er(n){n.exit(this.containerState.type)}function rr(n,r,t){const e=this;return O(n,u,"listItemPrefixWhitespace",e.parser.constructs.disable.null.includes("codeIndented")?void 0:5);function u(i){const l=e.events[e.events.length-1];return!z(i)&&l&&l[1].type==="listItemPrefixWhitespace"?r(i):t(i)}}const Kn={name:"setextUnderline",tokenize:ur,resolveTo:ir};function ir(n,r){let t=n.length,e,u,i;for(;t--;)if(n[t][0]==="enter"){if(n[t][1].type==="content"){e=t;break}n[t][1].type==="paragraph"&&(u=t)}else n[t][1].type==="content"&&n.splice(t,1),!i&&n[t][1].type==="definition"&&(i=t);const l={type:"setextHeading",start:Object.assign({},n[u][1].start),end:Object.assign({},n[n.length-1][1].end)};return n[u][1].type="setextHeadingText",i?(n.splice(u,0,["enter",l,r]),n.splice(i+1,0,["exit",n[e][1],r]),n[e][1].end=Object.assign({},n[i][1].end)):n[e][1]=l,n.push(["exit",l,r]),n}function ur(n,r,t){const e=this;let u;return i;function i(c){let p=e.events.length,f;for(;p--;)if(e.events[p][1].type!=="lineEnding"&&e.events[p][1].type!=="linePrefix"&&e.events[p][1].type!=="content"){f=e.events[p][1].type==="paragraph";break}return!e.parser.lazy[e.now().line]&&(e.interrupt||f)?(n.enter("setextHeadingLine"),u=c,l(c)):t(c)}function l(c){return n.enter("setextHeadingLineSequence"),a(c)}function a(c){return c===u?(n.consume(c),a):(n.exit("setextHeadingLineSequence"),z(c)?O(n,m,"lineSuffix")(c):m(c))}function m(c){return c===null||C(c)?(n.exit("setextHeadingLine"),r(c)):t(c)}}const lr={tokenize:ar};function ar(n){const r=this,t=n.attempt(Sn,e,n.attempt(this.parser.constructs.flowInitial,u,O(n,n.attempt(this.parser.constructs.flow,u,n.attempt(pe,u)),"linePrefix")));return t;function e(i){if(i===null){n.consume(i);return}return n.enter("lineEndingBlank"),n.consume(i),n.exit("lineEndingBlank"),r.currentConstruct=void 0,t}function u(i){if(i===null){n.consume(i);return}return n.enter("lineEnding"),n.consume(i),n.exit("lineEnding"),r.currentConstruct=void 0,t}}const or={resolveAll:ht()},sr=ct("string"),cr=ct("text");function ct(n){return{tokenize:r,resolveAll:ht(n==="text"?hr:void 0)};function r(t){const e=this,u=this.parser.constructs[n],i=t.attempt(u,l,a);return l;function l(p){return c(p)?i(p):a(p)}function a(p){if(p===null){t.consume(p);return}return t.enter("data"),t.consume(p),m}function m(p){return c(p)?(t.exit("data"),i(p)):(t.consume(p),m)}function c(p){if(p===null)return!0;const f=u[p];let x=-1;if(f)for(;++x<f.length;){const h=f[x];if(!h.previous||h.previous.call(e,e.previous))return!0}return!1}}}function ht(n){return r;function r(t,e){let u=-1,i;for(;++u<=t.length;)i===void 0?t[u]&&t[u][1].type==="data"&&(i=u,u++):(!t[u]||t[u][1].type!=="data")&&(u!==i+2&&(t[i][1].end=t[u-1][1].end,t.splice(i+2,u-i-2),u=i+2),i=void 0);return n?n(t,e):t}}function hr(n,r){let t=0;for(;++t<=n.length;)if((t===n.length||n[t][1].type==="lineEnding")&&n[t-1][1].type==="data"){const e=n[t-1][1],u=r.sliceStream(e);let i=u.length,l=-1,a=0,m;for(;i--;){const c=u[i];if(typeof c=="string"){for(l=c.length;c.charCodeAt(l-1)===32;)a++,l--;if(l)break;l=-1}else if(c===-2)m=!0,a++;else if(c!==-1){i++;break}}if(a){const c={type:t===n.length||m||a<2?"lineSuffix":"hardBreakTrailing",start:{line:e.end.line,column:e.end.column-a,offset:e.end.offset-a,_index:e.start._index+i,_bufferIndex:i?l:e.start._bufferIndex+l},end:Object.assign({},e.end)};e.end=Object.assign({},c.start),e.start.offset===e.end.offset?Object.assign(e,c):(n.splice(t,0,["enter",c,r],["exit",c,r]),t+=2)}t++}return n}function pr(n,r,t){let e=Object.assign(t?Object.assign({},t):{line:1,column:1,offset:0},{_index:0,_bufferIndex:-1});const u={},i=[];let l=[],a=[];const m={consume:j,enter:F,exit:D,attempt:T(_),check:T(k),interrupt:T(k,{interrupt:!0})},c={previous:null,code:null,containerState:{},events:[],parser:n,sliceStream:h,sliceSerialize:x,now:A,defineSkip:I,write:f};let p=r.tokenize.call(c,m);return r.resolveAll&&i.push(r),c;function f(y){return l=Y(l,y),M(),l[l.length-1]!==null?[]:(H(r,0),c.events=Ln(i,c.events,c),c.events)}function x(y,S){return mr(h(y),S)}function h(y){return fr(l,y)}function A(){const{line:y,column:S,offset:P,_index:R,_bufferIndex:w}=e;return{line:y,column:S,offset:P,_index:R,_bufferIndex:w}}function I(y){u[y.line]=y.column,V()}function M(){let y;for(;e._index<l.length;){const S=l[e._index];if(typeof S=="string")for(y=e._index,e._bufferIndex<0&&(e._bufferIndex=0);e._index===y&&e._bufferIndex<S.length;)b(S.charCodeAt(e._bufferIndex));else b(S)}}function b(y){p=p(y)}function j(y){C(y)?(e.line++,e.column=1,e.offset+=y===-3?2:1,V()):y!==-1&&(e.column++,e.offset++),e._bufferIndex<0?e._index++:(e._bufferIndex++,e._bufferIndex===l[e._index].length&&(e._bufferIndex=-1,e._index++)),c.previous=y}function F(y,S){const P=S||{};return P.type=y,P.start=A(),c.events.push(["enter",P,c]),a.push(P),P}function D(y){const S=a.pop();return S.end=A(),c.events.push(["exit",S,c]),S}function _(y,S){H(y,S.from)}function k(y,S){S.restore()}function T(y,S){return P;function P(R,w,U){let W,G,en,o;return Array.isArray(R)?rn(R):"tokenize"in R?rn([R]):J(R);function J(Q){return pn;function pn(an){const fn=an!==null&&Q[an],mn=an!==null&&Q.null,Fn=[...Array.isArray(fn)?fn:fn?[fn]:[],...Array.isArray(mn)?mn:mn?[mn]:[]];return rn(Fn)(an)}}function rn(Q){return W=Q,G=0,Q.length===0?U:s(Q[G])}function s(Q){return pn;function pn(an){return o=N(),en=Q,Q.partial||(c.currentConstruct=Q),Q.name&&c.parser.constructs.disable.null.includes(Q.name)?hn():Q.tokenize.call(S?Object.assign(Object.create(c),S):c,m,K,hn)(an)}}function K(Q){return y(en,o),w}function hn(Q){return o.restore(),++G<W.length?s(W[G]):U}}}function H(y,S){y.resolveAll&&!i.includes(y)&&i.push(y),y.resolve&&tn(c.events,S,c.events.length-S,y.resolve(c.events.slice(S),c)),y.resolveTo&&(c.events=y.resolveTo(c.events,c))}function N(){const y=A(),S=c.previous,P=c.currentConstruct,R=c.events.length,w=Array.from(a);return{restore:U,from:R};function U(){e=y,c.previous=S,c.currentConstruct=P,c.events.length=R,a=w,V()}}function V(){e.line in u&&e.column<2&&(e.column=u[e.line],e.offset+=u[e.line]-1)}}function fr(n,r){const t=r.start._index,e=r.start._bufferIndex,u=r.end._index,i=r.end._bufferIndex;let l;if(t===u)l=[n[t].slice(e,i)];else{if(l=n.slice(t,u),e>-1){const a=l[0];typeof a=="string"?l[0]=a.slice(e):l.shift()}i>0&&l.push(n[u].slice(0,i))}return l}function mr(n,r){let t=-1;const e=[];let u;for(;++t<n.length;){const i=n[t];let l;if(typeof i=="string")l=i;else switch(i){case-5:{l="\r";break}case-4:{l=`
 `;break}case-3:{l=`\r
 `;break}case-2:{l=r?" ":"	";break}case-1:{if(!r&&u)continue;l=" ";break}default:l=String.fromCharCode(i)}u=i===-2,e.push(l)}return e.join("")}const xr={42:$,43:$,45:$,48:$,49:$,50:$,51:$,52:$,53:$,54:$,55:$,56:$,57:$,62:rt},gr={91:ke},kr={[-2]:Cn,[-1]:Cn,32:Cn},dr={35:Ee,42:bn,45:[Kn,bn],60:ze,61:Kn,95:bn,96:Gn,126:Gn},br={38:ut,92:it},yr={[-5]:wn,[-4]:wn,[-3]:wn,33:Ue,38:ut,42:In,60:[Yt,Pe],91:Ze,92:[Se,it],93:Dn,95:In,96:ae},Sr={null:[In,or]},Fr={null:[42,95]},Er={null:[]},Cr=Object.freeze(Object.defineProperty({__proto__:null,attentionMarkers:Fr,contentInitial:gr,disable:Er,document:xr,flow:dr,flowInitial:kr,insideSpan:Sr,string:br,text:yr},Symbol.toStringTag,{value:"Module"}));function wr(n){const t=Ot([Cr,...(n||{}).extensions||[]]),e={defined:[],lazy:{},constructs:t,content:u(Nt),document:u(Wt),flow:u(lr),string:u(sr),text:u(cr)};return e;function u(i){return l;function l(a){return pr(e,i,a)}}}const Xn=/[\0\t\n\r]/g;function Ar(){let n=1,r="",t=!0,e;return u;function u(i,l,a){const m=[];let c,p,f,x,h;for(i=r+i.toString(l),f=0,r="",t&&(i.charCodeAt(0)===65279&&f++,t=void 0);f<i.length;){if(Xn.lastIndex=f,c=Xn.exec(i),x=c&&c.index!==void 0?c.index:i.length,h=i.charCodeAt(x),!c){r=i.slice(f);break}if(h===10&&f===x&&e)m.push(-3),e=void 0;else switch(e&&(m.push(-5),e=void 0),f<x&&(m.push(i.slice(f,x)),n+=x-f),h){case 0:{m.push(65533),n++;break}case 9:{for(p=Math.ceil(n/4)*4,m.push(-2);n++<p;)m.push(-1);break}case 10:{m.push(-4),n=1;break}default:e=!0,n=1}f=x+1}return a&&(e&&m.push(-5),r&&m.push(r),m.push(null)),m}}function zr(n){for(;!lt(n););return n}function pt(n,r){const t=Number.parseInt(n,r);return t<9||t===11||t>13&&t<32||t>126&&t<160||t>55295&&t<57344||t>64975&&t<65008||(t&65535)===65535||(t&65535)===65534||t>1114111?"�":String.fromCharCode(t)}const Ir=/\\([!-/:-@[-`{-~])|&(#(?:\d{1,7}|x[\da-f]{1,6})|[\da-z]{1,31});/gi;function Tr(n){return n.replace(Ir,Br)}function Br(n,r,t){if(r)return r;if(t.charCodeAt(0)===35){const u=t.charCodeAt(1),i=u===120||u===88;return pt(t.slice(i?2:1),i?16:10)}return On(t)||n}function yn(n){return!n||typeof n!="object"?"":"position"in n||"type"in n?vn(n.position):"start"in n||"end"in n?vn(n):"line"in n||"column"in n?Tn(n):""}function Tn(n){return nt(n&&n.line)+":"+nt(n&&n.column)}function vn(n){return Tn(n&&n.start)+"-"+Tn(n&&n.end)}function nt(n){return n&&typeof n=="number"?n:1}const ft={}.hasOwnProperty,mt=function(n,r,t){return typeof r!="string"&&(t=r,r=void 0),Lr(t)(zr(wr(t).document().write(Ar()(n,r,!0))))};function Lr(n){const r={transforms:[],canContainEols:["emphasis","fragment","heading","paragraph","strong"],enter:{autolink:a(Hn),autolinkProtocol:y,autolinkEmail:y,atxHeading:a(jn),blockQuote:a(Fn),characterEscape:y,characterReference:y,codeFenced:a(Mn),codeFencedFenceInfo:m,codeFencedFenceMeta:m,codeIndented:a(Mn,m),codeText:a(kt,m),codeTextData:y,data:y,codeFlowValue:y,definition:a(dt),definitionDestinationString:m,definitionLabelString:m,definitionTitleString:m,emphasis:a(bt),hardBreakEscape:a(Rn),hardBreakTrailing:a(Rn),htmlFlow:a(qn,m),htmlFlowData:y,htmlText:a(qn,m),htmlTextData:y,image:a(yt),label:m,link:a(Hn),listItem:a(St),listItemValue:A,listOrdered:a(Nn,h),listUnordered:a(Nn),paragraph:a(Ft),reference:hn,referenceString:m,resourceDestinationString:m,resourceTitleString:m,setextHeading:a(jn),strong:a(Et),thematicBreak:a(wt)},exit:{atxHeading:p(),atxHeadingSequence:T,autolink:p(),autolinkEmail:mn,autolinkProtocol:fn,blockQuote:p(),characterEscapeValue:S,characterReferenceMarkerHexadecimal:pn,characterReferenceMarkerNumeric:pn,characterReferenceValue:an,codeFenced:p(j),codeFencedFence:b,codeFencedFenceInfo:I,codeFencedFenceMeta:M,codeFlowValue:S,codeIndented:p(F),codeText:p(W),codeTextData:S,data:S,definition:p(),definitionDestinationString:k,definitionLabelString:D,definitionTitleString:_,emphasis:p(),hardBreakEscape:p(R),hardBreakTrailing:p(R),htmlFlow:p(w),htmlFlowData:S,htmlText:p(U),htmlTextData:S,image:p(en),label:J,labelText:o,lineEnding:P,link:p(G),listItem:p(),listOrdered:p(),listUnordered:p(),paragraph:p(),referenceString:Q,resourceDestinationString:rn,resourceTitleString:s,resource:K,setextHeading:p(V),setextHeadingLineSequence:N,setextHeadingText:H,strong:p(),thematicBreak:p()}};xt(r,(n||{}).mdastExtensions||[]);const t={};return e;function e(g){let d={type:"root",children:[]};const E={stack:[d],tokenStack:[],config:r,enter:c,exit:f,buffer:m,resume:x,setData:i,getData:l},B=[];let L=-1;for(;++L<g.length;)if(g[L][1].type==="listOrdered"||g[L][1].type==="listUnordered")if(g[L][0]==="enter")B.push(L);else{const X=B.pop();L=u(g,X,L)}for(L=-1;++L<g.length;){const X=r[g[L][0]];ft.call(X,g[L][1].type)&&X[g[L][1].type].call(Object.assign({sliceSerialize:g[L][2].sliceSerialize},E),g[L][1])}if(E.tokenStack.length>0){const X=E.tokenStack[E.tokenStack.length-1];(X[1]||tt).call(E,void 0,X[0])}for(d.position={start:sn(g.length>0?g[0][1].start:{line:1,column:1,offset:0}),end:sn(g.length>0?g[g.length-2][1].end:{line:1,column:1,offset:0})},L=-1;++L<r.transforms.length;)d=r.transforms[L](d)||d;return d}function u(g,d,E){let B=d-1,L=-1,X=!1,on,un,gn,kn;for(;++B<=E;){const q=g[B];if(q[1].type==="listUnordered"||q[1].type==="listOrdered"||q[1].type==="blockQuote"?(q[0]==="enter"?L++:L--,kn=void 0):q[1].type==="lineEndingBlank"?q[0]==="enter"&&(on&&!kn&&!L&&!gn&&(gn=B),kn=void 0):q[1].type==="linePrefix"||q[1].type==="listItemValue"||q[1].type==="listItemMarker"||q[1].type==="listItemPrefix"||q[1].type==="listItemPrefixWhitespace"||(kn=void 0),!L&&q[0]==="enter"&&q[1].type==="listItemPrefix"||L===-1&&q[0]==="exit"&&(q[1].type==="listUnordered"||q[1].type==="listOrdered")){if(on){let En=B;for(un=void 0;En--;){const ln=g[En];if(ln[1].type==="lineEnding"||ln[1].type==="lineEndingBlank"){if(ln[0]==="exit")continue;un&&(g[un][1].type="lineEndingBlank",X=!0),ln[1].type="lineEnding",un=En}else if(!(ln[1].type==="linePrefix"||ln[1].type==="blockQuotePrefix"||ln[1].type==="blockQuotePrefixWhitespace"||ln[1].type==="blockQuoteMarker"||ln[1].type==="listItemIndent"))break}gn&&(!un||gn<un)&&(on._spread=!0),on.end=Object.assign({},un?g[un][1].start:q[1].end),g.splice(un||B,0,["exit",on,q[2]]),B++,E++}q[1].type==="listItemPrefix"&&(on={type:"listItem",_spread:!1,start:Object.assign({},q[1].start),end:void 0},g.splice(B,0,["enter",on,q[2]]),B++,E++,gn=void 0,kn=!0)}}return g[d][1]._spread=X,E}function i(g,d){t[g]=d}function l(g){return t[g]}function a(g,d){return E;function E(B){c.call(this,g(B),B),d&&d.call(this,B)}}function m(){this.stack.push({type:"fragment",children:[]})}function c(g,d,E){return this.stack[this.stack.length-1].children.push(g),this.stack.push(g),this.tokenStack.push([d,E]),g.position={start:sn(d.start)},g}function p(g){return d;function d(E){g&&g.call(this,E),f.call(this,E)}}function f(g,d){const E=this.stack.pop(),B=this.tokenStack.pop();if(B)B[0].type!==g.type&&(d?d.call(this,g,B[0]):(B[1]||tt).call(this,g,B[0]));else throw new Error("Cannot close `"+g.type+"` ("+yn({start:g.start,end:g.end})+"): it’s not open");return E.position.end=sn(g.end),E}function x(){return Bt(this.stack.pop())}function h(){i("expectingFirstListItemValue",!0)}function A(g){if(l("expectingFirstListItemValue")){const d=this.stack[this.stack.length-2];d.start=Number.parseInt(this.sliceSerialize(g),10),i("expectingFirstListItemValue")}}function I(){const g=this.resume(),d=this.stack[this.stack.length-1];d.lang=g}function M(){const g=this.resume(),d=this.stack[this.stack.length-1];d.meta=g}function b(){l("flowCodeInside")||(this.buffer(),i("flowCodeInside",!0))}function j(){const g=this.resume(),d=this.stack[this.stack.length-1];d.value=g.replace(/^(\r?\n|\r)|(\r?\n|\r)$/g,""),i("flowCodeInside")}function F(){const g=this.resume(),d=this.stack[this.stack.length-1];d.value=g.replace(/(\r?\n|\r)$/g,"")}function D(g){const d=this.resume(),E=this.stack[this.stack.length-1];E.label=d,E.identifier=xn(this.sliceSerialize(g)).toLowerCase()}function _(){const g=this.resume(),d=this.stack[this.stack.length-1];d.title=g}function k(){const g=this.resume(),d=this.stack[this.stack.length-1];d.url=g}function T(g){const d=this.stack[this.stack.length-1];if(!d.depth){const E=this.sliceSerialize(g).length;d.depth=E}}function H(){i("setextHeadingSlurpLineEnding",!0)}function N(g){const d=this.stack[this.stack.length-1];d.depth=this.sliceSerialize(g).charCodeAt(0)===61?1:2}function V(){i("setextHeadingSlurpLineEnding")}function y(g){const d=this.stack[this.stack.length-1];let E=d.children[d.children.length-1];(!E||E.type!=="text")&&(E=Ct(),E.position={start:sn(g.start)},d.children.push(E)),this.stack.push(E)}function S(g){const d=this.stack.pop();d.value+=this.sliceSerialize(g),d.position.end=sn(g.end)}function P(g){const d=this.stack[this.stack.length-1];if(l("atHardBreak")){const E=d.children[d.children.length-1];E.position.end=sn(g.end),i("atHardBreak");return}!l("setextHeadingSlurpLineEnding")&&r.canContainEols.includes(d.type)&&(y.call(this,g),S.call(this,g))}function R(){i("atHardBreak",!0)}function w(){const g=this.resume(),d=this.stack[this.stack.length-1];d.value=g}function U(){const g=this.resume(),d=this.stack[this.stack.length-1];d.value=g}function W(){const g=this.resume(),d=this.stack[this.stack.length-1];d.value=g}function G(){const g=this.stack[this.stack.length-1];if(l("inReference")){const d=l("referenceType")||"shortcut";g.type+="Reference",g.referenceType=d,delete g.url,delete g.title}else delete g.identifier,delete g.label;i("referenceType")}function en(){const g=this.stack[this.stack.length-1];if(l("inReference")){const d=l("referenceType")||"shortcut";g.type+="Reference",g.referenceType=d,delete g.url,delete g.title}else delete g.identifier,delete g.label;i("referenceType")}function o(g){const d=this.sliceSerialize(g),E=this.stack[this.stack.length-2];E.label=Tr(d),E.identifier=xn(d).toLowerCase()}function J(){const g=this.stack[this.stack.length-1],d=this.resume(),E=this.stack[this.stack.length-1];if(i("inReference",!0),E.type==="link"){const B=g.children;E.children=B}else E.alt=d}function rn(){const g=this.resume(),d=this.stack[this.stack.length-1];d.url=g}function s(){const g=this.resume(),d=this.stack[this.stack.length-1];d.title=g}function K(){i("inReference")}function hn(){i("referenceType","collapsed")}function Q(g){const d=this.resume(),E=this.stack[this.stack.length-1];E.label=d,E.identifier=xn(this.sliceSerialize(g)).toLowerCase(),i("referenceType","full")}function pn(g){i("characterReferenceType",g.type)}function an(g){const d=this.sliceSerialize(g),E=l("characterReferenceType");let B;E?(B=pt(d,E==="characterReferenceMarkerNumeric"?10:16),i("characterReferenceType")):B=On(d);const L=this.stack.pop();L.value+=B,L.position.end=sn(g.end)}function fn(g){S.call(this,g);const d=this.stack[this.stack.length-1];d.url=this.sliceSerialize(g)}function mn(g){S.call(this,g);const d=this.stack[this.stack.length-1];d.url="mailto:"+this.sliceSerialize(g)}function Fn(){return{type:"blockquote",children:[]}}function Mn(){return{type:"code",lang:null,meta:null,value:""}}function kt(){return{type:"inlineCode",value:""}}function dt(){return{type:"definition",identifier:"",label:null,title:null,url:""}}function bt(){return{type:"emphasis",children:[]}}function jn(){return{type:"heading",depth:void 0,children:[]}}function Rn(){return{type:"break"}}function qn(){return{type:"html",value:""}}function yt(){return{type:"image",title:null,url:"",alt:null}}function Hn(){return{type:"link",title:null,url:"",children:[]}}function Nn(g){return{type:"list",ordered:g.type==="listOrdered",start:null,spread:g._spread,children:[]}}function St(g){return{type:"listItem",spread:g._spread,checked:null,children:[]}}function Ft(){return{type:"paragraph",children:[]}}function Et(){return{type:"strong",children:[]}}function Ct(){return{type:"text",value:""}}function wt(){return{type:"thematicBreak"}}}function sn(n){return{line:n.line,column:n.column,offset:n.offset}}function xt(n,r){let t=-1;for(;++t<r.length;){const e=r[t];Array.isArray(e)?xt(n,e):Or(n,e)}}function Or(n,r){let t;for(t in r)if(ft.call(r,t)){if(t==="canContainEols"){const e=r[t];e&&n[t].push(...e)}else if(t==="transforms"){const e=r[t];e&&n[t].push(...e)}else if(t==="enter"||t==="exit"){const e=r[t];e&&Object.assign(n[t],e)}}}function tt(n,r){throw n?new Error("Cannot close `"+n.type+"` ("+yn({start:n.start,end:n.end})+"): a different token (`"+r.type+"`, "+yn({start:r.start,end:r.end})+") is open"):new Error("Cannot close document, a token (`"+r.type+"`, "+yn({start:r.start,end:r.end})+") is still open")}function Dr(n){const r=n.replace(/\n{2,}/g,`
 `);return It(r)}function Pr(n){const r=Dr(n),{children:t}=mt(r),e=[[]];let u=0;function i(l,a="normal"){l.type==="text"?l.value.split(`
diff --git a/assets/decorator.html-FfT8RlFX.js b/assets/decorator.html-0jwtowLH.js
similarity index 99%
rename from assets/decorator.html-FfT8RlFX.js
rename to assets/decorator.html-0jwtowLH.js
index 644f550..79ec89b 100644
--- a/assets/decorator.html-FfT8RlFX.js
+++ b/assets/decorator.html-0jwtowLH.js
@@ -1,4 +1,4 @@
-import{_ as n,o as s,c as a,a as t,b as p,f as e}from"./app-B69Gl_S-.js";const o={},c=p("p",null,"在这个示例中，我们使用装饰器模式来动态地给对象添加职责。装饰器模式允许我们通过将对象放入包含行为的特殊封装对象中来扩展对象的功能，而无需修改原始类的代码。",-1),l=e(`<h2 id="为什么使用装饰器模式" tabindex="-1"><a class="header-anchor" href="#为什么使用装饰器模式"><span>为什么使用装饰器模式？</span></a></h2><ol><li><strong>职责扩展</strong>：装饰器模式允许我们在不修改现有代码的情况下扩展对象的功能。</li><li><strong>灵活性</strong>：可以根据需要动态地添加或删除职责。</li><li><strong>遵循开闭原则</strong>：通过使用装饰器模式，我们可以在不修改现有类的情况下添加新功能，从而遵循开闭原则。</li></ol><h2 id="代码示例" tabindex="-1"><a class="header-anchor" href="#代码示例"><span>代码示例</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/lLDB3i8W4DrpYbdIQ2zWN1Wrhbof5w25M285myTgZ7UN5b6fTQdBcJVpvirZc1bBj7MrGAGmLfFIGYc8CR3avYZ81Qu8O0HxPXTAk5eQd4r0khfWEW8RrGndT-niiLPDX7oD7y7blginbMhQjfFY5DrGV_vSQSeqU0ecQIed1ngYIKntXA43zx6i9G-Sssvwf1gc3WeJfKaRJWkoNzZp4imfwndn28FOeWiM5T6fu6VRXnjZAAl_Q5yv8Rvh7xtX0q_savlBeIO7jkQIuPS9tX3bf1rSvA4tprLw0oYUpBI5GXMQ-HNzFxe3" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// border.ts</span>
+import{_ as n,o as s,c as a,a as t,b as p,f as e}from"./app-B4LGNJZ0.js";const o={},c=p("p",null,"在这个示例中，我们使用装饰器模式来动态地给对象添加职责。装饰器模式允许我们通过将对象放入包含行为的特殊封装对象中来扩展对象的功能，而无需修改原始类的代码。",-1),l=e(`<h2 id="为什么使用装饰器模式" tabindex="-1"><a class="header-anchor" href="#为什么使用装饰器模式"><span>为什么使用装饰器模式？</span></a></h2><ol><li><strong>职责扩展</strong>：装饰器模式允许我们在不修改现有代码的情况下扩展对象的功能。</li><li><strong>灵活性</strong>：可以根据需要动态地添加或删除职责。</li><li><strong>遵循开闭原则</strong>：通过使用装饰器模式，我们可以在不修改现有类的情况下添加新功能，从而遵循开闭原则。</li></ol><h2 id="代码示例" tabindex="-1"><a class="header-anchor" href="#代码示例"><span>代码示例</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/lLDB3i8W4DrpYbdIQ2zWN1Wrhbof5w25M285myTgZ7UN5b6fTQdBcJVpvirZc1bBj7MrGAGmLfFIGYc8CR3avYZ81Qu8O0HxPXTAk5eQd4r0khfWEW8RrGndT-niiLPDX7oD7y7blginbMhQjfFY5DrGV_vSQSeqU0ecQIed1ngYIKntXA43zx6i9G-Sssvwf1gc3WeJfKaRJWkoNzZp4imfwndn28FOeWiM5T6fu6VRXnjZAAl_Q5yv8Rvh7xtX0q_savlBeIO7jkQIuPS9tX3bf1rSvA4tprLw0oYUpBI5GXMQ-HNzFxe3" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// border.ts</span>
 <span class="token keyword">import</span> <span class="token punctuation">{</span> Display <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&quot;./display&quot;</span><span class="token punctuation">;</span>
 <span class="token keyword">export</span> <span class="token keyword">abstract</span> <span class="token keyword">class</span> <span class="token class-name">Border</span> <span class="token keyword">extends</span> <span class="token class-name">Display</span> <span class="token punctuation">{</span>
   <span class="token keyword">protected</span> display<span class="token operator">:</span> Display<span class="token punctuation">;</span>
diff --git a/assets/docker.html-B-hYGcsZ.js b/assets/docker.html-DtdutZB7.js
similarity index 99%
rename from assets/docker.html-B-hYGcsZ.js
rename to assets/docker.html-DtdutZB7.js
index c35fddb..c174bd0 100644
--- a/assets/docker.html-B-hYGcsZ.js
+++ b/assets/docker.html-DtdutZB7.js
@@ -1,4 +1,4 @@
-import{_ as e,o as t,c as i,f as n}from"./app-B69Gl_S-.js";const a={},s=n(`<h2 id="github-container-registry-加速" tabindex="-1"><a class="header-anchor" href="#github-container-registry-加速"><span>GitHub Container Registry 加速</span></a></h2><h3 id="ghcr-io简介" tabindex="-1"><a class="header-anchor" href="#ghcr-io简介"><span>ghcr.io简介</span></a></h3><ul><li>ghcr.io 是 GitHub Container Registry 的域名。GitHub Container Registry 是 GitHub 提供的容器镜像注册表服务，允许开发者在 GitHub 上存储、管理和分享 Docker 镜像。它与 GitHub 代码仓库紧密集成，可以使用相同的权限管理、团队协作和版本控制工具来管理容器镜像。</li><li>通过 GitHub Container Registry，开发者可以方便地将他们的容器镜像与代码仓库关联起来，这样就可以在同一个平台上管理代码和镜像。这种集成性使得持续集成/持续交付 (CI/CD) 流程更加简化和统一，开发团队可以更容易地构建、测试和部署应用程序。</li><li>对于使用 GitHub 作为代码托管平台的开发者来说，GitHub Container Registry 提供一个便捷且强大的容器镜像管理解决方案。通过该服务，可以更轻松地构建和部署容器化的应用程序，从而加速开发和交付周期。</li></ul><h3 id="镜像地址" tabindex="-1"><a class="header-anchor" href="#镜像地址"><span>镜像地址</span></a></h3><p>https://ghcr.nju.edu.cn</p><h3 id="配置方法" tabindex="-1"><a class="header-anchor" href="#配置方法"><span>配置方法</span></a></h3><div class="language-bash line-numbers-mode" data-ext="sh" data-title="sh"><pre class="language-bash"><code><span class="token function">sudo</span> <span class="token function">vim</span> /etc/docker/daemon.json
+import{_ as e,o as t,c as i,f as n}from"./app-B4LGNJZ0.js";const a={},s=n(`<h2 id="github-container-registry-加速" tabindex="-1"><a class="header-anchor" href="#github-container-registry-加速"><span>GitHub Container Registry 加速</span></a></h2><h3 id="ghcr-io简介" tabindex="-1"><a class="header-anchor" href="#ghcr-io简介"><span>ghcr.io简介</span></a></h3><ul><li>ghcr.io 是 GitHub Container Registry 的域名。GitHub Container Registry 是 GitHub 提供的容器镜像注册表服务，允许开发者在 GitHub 上存储、管理和分享 Docker 镜像。它与 GitHub 代码仓库紧密集成，可以使用相同的权限管理、团队协作和版本控制工具来管理容器镜像。</li><li>通过 GitHub Container Registry，开发者可以方便地将他们的容器镜像与代码仓库关联起来，这样就可以在同一个平台上管理代码和镜像。这种集成性使得持续集成/持续交付 (CI/CD) 流程更加简化和统一，开发团队可以更容易地构建、测试和部署应用程序。</li><li>对于使用 GitHub 作为代码托管平台的开发者来说，GitHub Container Registry 提供一个便捷且强大的容器镜像管理解决方案。通过该服务，可以更轻松地构建和部署容器化的应用程序，从而加速开发和交付周期。</li></ul><h3 id="镜像地址" tabindex="-1"><a class="header-anchor" href="#镜像地址"><span>镜像地址</span></a></h3><p>https://ghcr.nju.edu.cn</p><h3 id="配置方法" tabindex="-1"><a class="header-anchor" href="#配置方法"><span>配置方法</span></a></h3><div class="language-bash line-numbers-mode" data-ext="sh" data-title="sh"><pre class="language-bash"><code><span class="token function">sudo</span> <span class="token function">vim</span> /etc/docker/daemon.json
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div></div></div><div class="language-json line-numbers-mode" data-ext="json" data-title="json"><pre class="language-json"><code><span class="token punctuation">{</span>
   <span class="token property">&quot;registry-mirrors&quot;</span><span class="token operator">:</span> <span class="token punctuation">[</span><span class="token string">&quot;https://ghcr.nju.edu.cn&quot;</span><span class="token punctuation">]</span>
 <span class="token punctuation">}</span>
diff --git "a/assets/docker_nginx\351\203\250\347\275\262web\351\241\271\347\233\256.html-4IxhKq9E.js" "b/assets/docker_nginx\351\203\250\347\275\262web\351\241\271\347\233\256.html-CZONKQdf.js"
similarity index 99%
rename from "assets/docker_nginx\351\203\250\347\275\262web\351\241\271\347\233\256.html-4IxhKq9E.js"
rename to "assets/docker_nginx\351\203\250\347\275\262web\351\241\271\347\233\256.html-CZONKQdf.js"
index 792397d..0460d30 100644
--- "a/assets/docker_nginx\351\203\250\347\275\262web\351\241\271\347\233\256.html-4IxhKq9E.js"
+++ "b/assets/docker_nginx\351\203\250\347\275\262web\351\241\271\347\233\256.html-CZONKQdf.js"
@@ -1,4 +1,4 @@
-import{_ as i,r as l,o as t,c as r,a as o,b as n,e as s,d as a,f as c}from"./app-B69Gl_S-.js";const d={},u=n("h1",{id:"docker-nginx-acme-sh-部署-vue-flask-项目",tabindex:"-1"},[n("a",{class:"header-anchor",href:"#docker-nginx-acme-sh-部署-vue-flask-项目"},[n("span",null,"docker + nginx + acme.sh 部署 vue/flask 项目")])],-1),p=n("p",null,"本文将介绍如何使用 Docker、Nginx 和 acme.sh 部署一个 Vue 和 Flask 项目。我们将详细讲解环境配置、项目结构、Nginx 配置、Docker 配置以及如何升级到 HTTPS。",-1),v=c(`<div class="hint-container tip"><p class="hint-container-title">提示</p><p>需要先申请一个域名，本文是 bupt.online</p></div><h2 id="环境" tabindex="-1"><a class="header-anchor" href="#环境"><span>环境</span></a></h2><ul><li>Ubuntu</li><li>Docker</li><li>Docker-Compose</li><li>acme.sh</li><li>(python)</li><li>nginx</li></ul><h2 id="项目结构" tabindex="-1"><a class="header-anchor" href="#项目结构"><span>项目结构</span></a></h2><div class="language-tree line-numbers-mode" data-ext="tree" data-title="tree"><pre class="language-tree"><code>./nginx
+import{_ as i,r as l,o as t,c as r,a as o,b as n,e as s,d as a,f as c}from"./app-B4LGNJZ0.js";const d={},u=n("h1",{id:"docker-nginx-acme-sh-部署-vue-flask-项目",tabindex:"-1"},[n("a",{class:"header-anchor",href:"#docker-nginx-acme-sh-部署-vue-flask-项目"},[n("span",null,"docker + nginx + acme.sh 部署 vue/flask 项目")])],-1),p=n("p",null,"本文将介绍如何使用 Docker、Nginx 和 acme.sh 部署一个 Vue 和 Flask 项目。我们将详细讲解环境配置、项目结构、Nginx 配置、Docker 配置以及如何升级到 HTTPS。",-1),v=c(`<div class="hint-container tip"><p class="hint-container-title">提示</p><p>需要先申请一个域名，本文是 bupt.online</p></div><h2 id="环境" tabindex="-1"><a class="header-anchor" href="#环境"><span>环境</span></a></h2><ul><li>Ubuntu</li><li>Docker</li><li>Docker-Compose</li><li>acme.sh</li><li>(python)</li><li>nginx</li></ul><h2 id="项目结构" tabindex="-1"><a class="header-anchor" href="#项目结构"><span>项目结构</span></a></h2><div class="language-tree line-numbers-mode" data-ext="tree" data-title="tree"><pre class="language-tree"><code>./nginx
 ├── acme  # 存放SSL证书
 ├── conf.d
 │   ├── Automaton.conf
diff --git a/assets/edges-5962ec63-B19hLEst.js b/assets/edges-5962ec63-ApWhby2b.js
similarity index 99%
rename from assets/edges-5962ec63-B19hLEst.js
rename to assets/edges-5962ec63-ApWhby2b.js
index 42ff880..2155e91 100644
--- a/assets/edges-5962ec63-B19hLEst.js
+++ b/assets/edges-5962ec63-ApWhby2b.js
@@ -1,4 +1,4 @@
-import{q as H,c as b,d as V,an as q,h as E,l as g,z as j,ao as lt}from"./mermaid.core-ChLYKTZm.js";import{c as st}from"./createText-4a4f35c9-BuT3nXUz.js";import{l as ct}from"./line-D0jG_HZ-.js";const ht=(e,t,a,i)=>{t.forEach(l=>{wt[l](e,a,i)})},ot=(e,t,a)=>{g.trace("Making markers for ",a),e.append("defs").append("marker").attr("id",a+"_"+t+"-extensionStart").attr("class","marker extension "+t).attr("refX",18).attr("refY",7).attr("markerWidth",190).attr("markerHeight",240).attr("orient","auto").append("path").attr("d","M 1,7 L18,13 V 1 Z"),e.append("defs").append("marker").attr("id",a+"_"+t+"-extensionEnd").attr("class","marker extension "+t).attr("refX",1).attr("refY",7).attr("markerWidth",20).attr("markerHeight",28).attr("orient","auto").append("path").attr("d","M 1,1 V 13 L18,7 Z")},yt=(e,t,a)=>{e.append("defs").append("marker").attr("id",a+"_"+t+"-compositionStart").attr("class","marker composition "+t).attr("refX",18).attr("refY",7).attr("markerWidth",190).attr("markerHeight",240).attr("orient","auto").append("path").attr("d","M 18,7 L9,13 L1,7 L9,1 Z"),e.append("defs").append("marker").attr("id",a+"_"+t+"-compositionEnd").attr("class","marker composition "+t).attr("refX",1).attr("refY",7).attr("markerWidth",20).attr("markerHeight",28).attr("orient","auto").append("path").attr("d","M 18,7 L9,13 L1,7 L9,1 Z")},pt=(e,t,a)=>{e.append("defs").append("marker").attr("id",a+"_"+t+"-aggregationStart").attr("class","marker aggregation "+t).attr("refX",18).attr("refY",7).attr("markerWidth",190).attr("markerHeight",240).attr("orient","auto").append("path").attr("d","M 18,7 L9,13 L1,7 L9,1 Z"),e.append("defs").append("marker").attr("id",a+"_"+t+"-aggregationEnd").attr("class","marker aggregation "+t).attr("refX",1).attr("refY",7).attr("markerWidth",20).attr("markerHeight",28).attr("orient","auto").append("path").attr("d","M 18,7 L9,13 L1,7 L9,1 Z")},ft=(e,t,a)=>{e.append("defs").append("marker").attr("id",a+"_"+t+"-dependencyStart").attr("class","marker dependency "+t).attr("refX",6).attr("refY",7).attr("markerWidth",190).attr("markerHeight",240).attr("orient","auto").append("path").attr("d","M 5,7 L9,13 L1,7 L9,1 Z"),e.append("defs").append("marker").attr("id",a+"_"+t+"-dependencyEnd").attr("class","marker dependency "+t).attr("refX",13).attr("refY",7).attr("markerWidth",20).attr("markerHeight",28).attr("orient","auto").append("path").attr("d","M 18,7 L9,13 L14,7 L9,1 Z")},xt=(e,t,a)=>{e.append("defs").append("marker").attr("id",a+"_"+t+"-lollipopStart").attr("class","marker lollipop "+t).attr("refX",13).attr("refY",7).attr("markerWidth",190).attr("markerHeight",240).attr("orient","auto").append("circle").attr("stroke","black").attr("fill","transparent").attr("cx",7).attr("cy",7).attr("r",6),e.append("defs").append("marker").attr("id",a+"_"+t+"-lollipopEnd").attr("class","marker lollipop "+t).attr("refX",1).attr("refY",7).attr("markerWidth",190).attr("markerHeight",240).attr("orient","auto").append("circle").attr("stroke","black").attr("fill","transparent").attr("cx",7).attr("cy",7).attr("r",6)},dt=(e,t,a)=>{e.append("marker").attr("id",a+"_"+t+"-pointEnd").attr("class","marker "+t).attr("viewBox","0 0 10 10").attr("refX",6).attr("refY",5).attr("markerUnits","userSpaceOnUse").attr("markerWidth",12).attr("markerHeight",12).attr("orient","auto").append("path").attr("d","M 0 0 L 10 5 L 0 10 z").attr("class","arrowMarkerPath").style("stroke-width",1).style("stroke-dasharray","1,0"),e.append("marker").attr("id",a+"_"+t+"-pointStart").attr("class","marker "+t).attr("viewBox","0 0 10 10").attr("refX",4.5).attr("refY",5).attr("markerUnits","userSpaceOnUse").attr("markerWidth",12).attr("markerHeight",12).attr("orient","auto").append("path").attr("d","M 0 5 L 10 10 L 10 0 z").attr("class","arrowMarkerPath").style("stroke-width",1).style("stroke-dasharray","1,0")},gt=(e,t,a)=>{e.append("marker").attr("id",a+"_"+t+"-circleEnd").attr("class","marker "+t).attr("viewBox","0 0 10 10").attr("refX",11).attr("refY",5).attr("markerUnits","userSpaceOnUse").attr("markerWidth",11).attr("markerHeight",11).attr("orient","auto").append("circle").attr("cx","5").attr("cy","5").attr("r","5").attr("class","arrowMarkerPath").style("stroke-width",1).style("stroke-dasharray","1,0"),e.append("marker").attr("id",a+"_"+t+"-circleStart").attr("class","marker "+t).attr("viewBox","0 0 10 10").attr("refX",-1).attr("refY",5).attr("markerUnits","userSpaceOnUse").attr("markerWidth",11).attr("markerHeight",11).attr("orient","auto").append("circle").attr("cx","5").attr("cy","5").attr("r","5").attr("class","arrowMarkerPath").style("stroke-width",1).style("stroke-dasharray","1,0")},ut=(e,t,a)=>{e.append("marker").attr("id",a+"_"+t+"-crossEnd").attr("class","marker cross "+t).attr("viewBox","0 0 11 11").attr("refX",12).attr("refY",5.2).attr("markerUnits","userSpaceOnUse").attr("markerWidth",11).attr("markerHeight",11).attr("orient","auto").append("path").attr("d","M 1,1 l 9,9 M 10,1 l -9,9").attr("class","arrowMarkerPath").style("stroke-width",2).style("stroke-dasharray","1,0"),e.append("marker").attr("id",a+"_"+t+"-crossStart").attr("class","marker cross "+t).attr("viewBox","0 0 11 11").attr("refX",-1).attr("refY",5.2).attr("markerUnits","userSpaceOnUse").attr("markerWidth",11).attr("markerHeight",11).attr("orient","auto").append("path").attr("d","M 1,1 l 9,9 M 10,1 l -9,9").attr("class","arrowMarkerPath").style("stroke-width",2).style("stroke-dasharray","1,0")},bt=(e,t,a)=>{e.append("defs").append("marker").attr("id",a+"_"+t+"-barbEnd").attr("refX",19).attr("refY",7).attr("markerWidth",20).attr("markerHeight",14).attr("markerUnits","strokeWidth").attr("orient","auto").append("path").attr("d","M 19,7 L9,13 L14,7 L9,1 Z")},wt={extension:ot,composition:yt,aggregation:pt,dependency:ft,lollipop:xt,point:dt,circle:gt,cross:ut,barb:bt},hr=ht;function mt(e,t){t&&e.attr("style",t)}function kt(e){const t=E(document.createElementNS("http://www.w3.org/2000/svg","foreignObject")),a=t.append("xhtml:div"),i=e.label,l=e.isNode?"nodeLabel":"edgeLabel";return a.html('<span class="'+l+'" '+(e.labelStyle?'style="'+e.labelStyle+'"':"")+">"+i+"</span>"),mt(a,e.labelStyle),a.style("display","inline-block"),a.style("white-space","nowrap"),a.attr("xmlns","http://www.w3.org/1999/xhtml"),t.node()}const vt=(e,t,a,i)=>{let l=e||"";if(typeof l=="object"&&(l=l[0]),H(b().flowchart.htmlLabels)){l=l.replace(/\\n|\n/g,"<br />"),g.debug("vertexText"+l);const r={isNode:i,label:q(l).replace(/fa[blrs]?:fa-[\w-]+/g,n=>`<i class='${n.replace(":"," ")}'></i>`),labelStyle:t.replace("fill:","color:")};return kt(r)}else{const r=document.createElementNS("http://www.w3.org/2000/svg","text");r.setAttribute("style",t.replace("color:","fill:"));let s=[];typeof l=="string"?s=l.split(/\\n|\n|<br\s*\/?>/gi):Array.isArray(l)?s=l:s=[];for(const n of s){const c=document.createElementNS("http://www.w3.org/2000/svg","tspan");c.setAttributeNS("http://www.w3.org/XML/1998/namespace","xml:space","preserve"),c.setAttribute("dy","1em"),c.setAttribute("x","0"),a?c.setAttribute("class","title-row"):c.setAttribute("class","row"),c.textContent=n.trim(),r.appendChild(c)}return r}},R=vt,M=async(e,t,a,i)=>{let l;const r=t.useHtmlLabels||H(b().flowchart.htmlLabels);a?l=a:l="node default";const s=e.insert("g").attr("class",l).attr("id",t.domId||t.id),n=s.insert("g").attr("class","label").attr("style",t.labelStyle);let c;t.labelText===void 0?c="":c=typeof t.labelText=="string"?t.labelText:t.labelText[0];const o=n.node();let h;t.labelType==="markdown"?h=st(n,V(q(c),b()),{useHtmlLabels:r,width:t.width||b().flowchart.wrappingWidth,classes:"markdown-node-label"}):h=o.appendChild(R(V(q(c),b()),t.labelStyle,!1,i));let y=h.getBBox();const f=t.padding/2;if(H(b().flowchart.htmlLabels)){const p=h.children[0],d=E(h),k=p.getElementsByTagName("img");if(k){const x=c.replace(/<img[^>]*>/g,"").trim()==="";await Promise.all([...k].map(u=>new Promise(S=>{function B(){if(u.style.display="flex",u.style.flexDirection="column",x){const C=b().fontSize?b().fontSize:window.getComputedStyle(document.body).fontSize,D=parseInt(C,10)*5+"px";u.style.minWidth=D,u.style.maxWidth=D}else u.style.width="100%";S(u)}setTimeout(()=>{u.complete&&B()}),u.addEventListener("error",B),u.addEventListener("load",B)})))}y=p.getBoundingClientRect(),d.attr("width",y.width),d.attr("height",y.height)}return r?n.attr("transform","translate("+-y.width/2+", "+-y.height/2+")"):n.attr("transform","translate(0, "+-y.height/2+")"),t.centerLabel&&n.attr("transform","translate("+-y.width/2+", "+-y.height/2+")"),n.insert("rect",":first-child"),{shapeSvg:s,bbox:y,halfPadding:f,label:n}},m=(e,t)=>{const a=t.node().getBBox();e.width=a.width,e.height=a.height};function I(e,t,a,i){return e.insert("polygon",":first-child").attr("points",i.map(function(l){return l.x+","+l.y}).join(" ")).attr("class","label-container").attr("transform","translate("+-t/2+","+a/2+")")}function Lt(e,t){return e.intersect(t)}function it(e,t,a,i){var l=e.x,r=e.y,s=l-i.x,n=r-i.y,c=Math.sqrt(t*t*n*n+a*a*s*s),o=Math.abs(t*a*s/c);i.x<l&&(o=-o);var h=Math.abs(t*a*n/c);return i.y<r&&(h=-h),{x:l+o,y:r+h}}function St(e,t,a){return it(e,t,t,a)}function Mt(e,t,a,i){var l,r,s,n,c,o,h,y,f,p,d,k,x,u,S;if(l=t.y-e.y,s=e.x-t.x,c=t.x*e.y-e.x*t.y,f=l*a.x+s*a.y+c,p=l*i.x+s*i.y+c,!(f!==0&&p!==0&&J(f,p))&&(r=i.y-a.y,n=a.x-i.x,o=i.x*a.y-a.x*i.y,h=r*e.x+n*e.y+o,y=r*t.x+n*t.y+o,!(h!==0&&y!==0&&J(h,y))&&(d=l*n-r*s,d!==0)))return k=Math.abs(d/2),x=s*o-n*c,u=x<0?(x-k)/d:(x+k)/d,x=r*c-l*o,S=x<0?(x-k)/d:(x+k)/d,{x:u,y:S}}function J(e,t){return e*t>0}function Tt(e,t,a){var i=e.x,l=e.y,r=[],s=Number.POSITIVE_INFINITY,n=Number.POSITIVE_INFINITY;typeof t.forEach=="function"?t.forEach(function(d){s=Math.min(s,d.x),n=Math.min(n,d.y)}):(s=Math.min(s,t.x),n=Math.min(n,t.y));for(var c=i-e.width/2-s,o=l-e.height/2-n,h=0;h<t.length;h++){var y=t[h],f=t[h<t.length-1?h+1:0],p=Mt(e,a,{x:c+y.x,y:o+y.y},{x:c+f.x,y:o+f.y});p&&r.push(p)}return r.length?(r.length>1&&r.sort(function(d,k){var x=d.x-a.x,u=d.y-a.y,S=Math.sqrt(x*x+u*u),B=k.x-a.x,C=k.y-a.y,X=Math.sqrt(B*B+C*C);return S<X?-1:S===X?0:1}),r[0]):e}const Bt=(e,t)=>{var a=e.x,i=e.y,l=t.x-a,r=t.y-i,s=e.width/2,n=e.height/2,c,o;return Math.abs(r)*s>Math.abs(l)*n?(r<0&&(n=-n),c=r===0?0:n*l/r,o=n):(l<0&&(s=-s),c=s,o=l===0?0:s*r/l),{x:a+c,y:i+o}},Et=Bt,w={node:Lt,circle:St,ellipse:it,polygon:Tt,rect:Et},Ct=async(e,t)=>{t.useHtmlLabels||b().flowchart.htmlLabels||(t.centerLabel=!0);const{shapeSvg:i,bbox:l,halfPadding:r}=await M(e,t,"node "+t.classes,!0);g.info("Classes = ",t.classes);const s=i.insert("rect",":first-child");return s.attr("rx",t.rx).attr("ry",t.ry).attr("x",-l.width/2-r).attr("y",-l.height/2-r).attr("width",l.width+t.padding).attr("height",l.height+t.padding),m(t,s),t.intersect=function(n){return w.rect(t,n)},i},$t=Ct,_t=e=>{const t=new Set;for(const a of e)switch(a){case"x":t.add("right"),t.add("left");break;case"y":t.add("up"),t.add("down");break;default:t.add(a);break}return t},Rt=(e,t,a)=>{const i=_t(e),l=2,r=t.height+2*a.padding,s=r/l,n=t.width+2*s+a.padding,c=a.padding/2;return i.has("right")&&i.has("left")&&i.has("up")&&i.has("down")?[{x:0,y:0},{x:s,y:0},{x:n/2,y:2*c},{x:n-s,y:0},{x:n,y:0},{x:n,y:-r/3},{x:n+2*c,y:-r/2},{x:n,y:-2*r/3},{x:n,y:-r},{x:n-s,y:-r},{x:n/2,y:-r-2*c},{x:s,y:-r},{x:0,y:-r},{x:0,y:-2*r/3},{x:-2*c,y:-r/2},{x:0,y:-r/3}]:i.has("right")&&i.has("left")&&i.has("up")?[{x:s,y:0},{x:n-s,y:0},{x:n,y:-r/2},{x:n-s,y:-r},{x:s,y:-r},{x:0,y:-r/2}]:i.has("right")&&i.has("left")&&i.has("down")?[{x:0,y:0},{x:s,y:-r},{x:n-s,y:-r},{x:n,y:0}]:i.has("right")&&i.has("up")&&i.has("down")?[{x:0,y:0},{x:n,y:-s},{x:n,y:-r+s},{x:0,y:-r}]:i.has("left")&&i.has("up")&&i.has("down")?[{x:n,y:0},{x:0,y:-s},{x:0,y:-r+s},{x:n,y:-r}]:i.has("right")&&i.has("left")?[{x:s,y:0},{x:s,y:-c},{x:n-s,y:-c},{x:n-s,y:0},{x:n,y:-r/2},{x:n-s,y:-r},{x:n-s,y:-r+c},{x:s,y:-r+c},{x:s,y:-r},{x:0,y:-r/2}]:i.has("up")&&i.has("down")?[{x:n/2,y:0},{x:0,y:-c},{x:s,y:-c},{x:s,y:-r+c},{x:0,y:-r+c},{x:n/2,y:-r},{x:n,y:-r+c},{x:n-s,y:-r+c},{x:n-s,y:-c},{x:n,y:-c}]:i.has("right")&&i.has("up")?[{x:0,y:0},{x:n,y:-s},{x:0,y:-r}]:i.has("right")&&i.has("down")?[{x:0,y:0},{x:n,y:0},{x:0,y:-r}]:i.has("left")&&i.has("up")?[{x:n,y:0},{x:0,y:-s},{x:n,y:-r}]:i.has("left")&&i.has("down")?[{x:n,y:0},{x:0,y:0},{x:n,y:-r}]:i.has("right")?[{x:s,y:-c},{x:s,y:-c},{x:n-s,y:-c},{x:n-s,y:0},{x:n,y:-r/2},{x:n-s,y:-r},{x:n-s,y:-r+c},{x:s,y:-r+c},{x:s,y:-r+c}]:i.has("left")?[{x:s,y:0},{x:s,y:-c},{x:n-s,y:-c},{x:n-s,y:-r+c},{x:s,y:-r+c},{x:s,y:-r},{x:0,y:-r/2}]:i.has("up")?[{x:s,y:-c},{x:s,y:-r+c},{x:0,y:-r+c},{x:n/2,y:-r},{x:n,y:-r+c},{x:n-s,y:-r+c},{x:n-s,y:-c}]:i.has("down")?[{x:n/2,y:0},{x:0,y:-c},{x:s,y:-c},{x:s,y:-r+c},{x:n-s,y:-r+c},{x:n-s,y:-c},{x:n,y:-c}]:[{x:0,y:0}]},K=e=>e?" "+e:"",_=(e,t)=>`node default${K(e.classes)} ${K(e.class)}`,P=async(e,t)=>{const{shapeSvg:a,bbox:i}=await M(e,t,_(t),!0),l=i.width+t.padding,r=i.height+t.padding,s=l+r,n=[{x:s/2,y:0},{x:s,y:-s/2},{x:s/2,y:-s},{x:0,y:-s/2}];g.info("Question main (Circle)");const c=I(a,s,s,n);return c.attr("style",t.style),m(t,c),t.intersect=function(o){return g.warn("Intersect called"),w.polygon(t,n,o)},a},Ht=(e,t)=>{const a=e.insert("g").attr("class","node default").attr("id",t.domId||t.id),i=28,l=[{x:0,y:i/2},{x:i/2,y:0},{x:0,y:-i/2},{x:-i/2,y:0}];return a.insert("polygon",":first-child").attr("points",l.map(function(s){return s.x+","+s.y}).join(" ")).attr("class","state-start").attr("r",7).attr("width",28).attr("height",28),t.width=28,t.height=28,t.intersect=function(s){return w.circle(t,14,s)},a},It=async(e,t)=>{const{shapeSvg:a,bbox:i}=await M(e,t,_(t),!0),l=4,r=i.height+t.padding,s=r/l,n=i.width+2*s+t.padding,c=[{x:s,y:0},{x:n-s,y:0},{x:n,y:-r/2},{x:n-s,y:-r},{x:s,y:-r},{x:0,y:-r/2}],o=I(a,n,r,c);return o.attr("style",t.style),m(t,o),t.intersect=function(h){return w.polygon(t,c,h)},a},Nt=async(e,t)=>{const{shapeSvg:a,bbox:i}=await M(e,t,void 0,!0),l=2,r=i.height+2*t.padding,s=r/l,n=i.width+2*s+t.padding,c=Rt(t.directions,i,t),o=I(a,n,r,c);return o.attr("style",t.style),m(t,o),t.intersect=function(h){return w.polygon(t,c,h)},a},Ot=async(e,t)=>{const{shapeSvg:a,bbox:i}=await M(e,t,_(t),!0),l=i.width+t.padding,r=i.height+t.padding,s=[{x:-r/2,y:0},{x:l,y:0},{x:l,y:-r},{x:-r/2,y:-r},{x:0,y:-r/2}];return I(a,l,r,s).attr("style",t.style),t.width=l+r,t.height=r,t.intersect=function(c){return w.polygon(t,s,c)},a},Wt=async(e,t)=>{const{shapeSvg:a,bbox:i}=await M(e,t,_(t),!0),l=i.width+t.padding,r=i.height+t.padding,s=[{x:-2*r/6,y:0},{x:l-r/6,y:0},{x:l+2*r/6,y:-r},{x:r/6,y:-r}],n=I(a,l,r,s);return n.attr("style",t.style),m(t,n),t.intersect=function(c){return w.polygon(t,s,c)},a},Xt=async(e,t)=>{const{shapeSvg:a,bbox:i}=await M(e,t,_(t),!0),l=i.width+t.padding,r=i.height+t.padding,s=[{x:2*r/6,y:0},{x:l+r/6,y:0},{x:l-2*r/6,y:-r},{x:-r/6,y:-r}],n=I(a,l,r,s);return n.attr("style",t.style),m(t,n),t.intersect=function(c){return w.polygon(t,s,c)},a},Yt=async(e,t)=>{const{shapeSvg:a,bbox:i}=await M(e,t,_(t),!0),l=i.width+t.padding,r=i.height+t.padding,s=[{x:-2*r/6,y:0},{x:l+2*r/6,y:0},{x:l-r/6,y:-r},{x:r/6,y:-r}],n=I(a,l,r,s);return n.attr("style",t.style),m(t,n),t.intersect=function(c){return w.polygon(t,s,c)},a},Dt=async(e,t)=>{const{shapeSvg:a,bbox:i}=await M(e,t,_(t),!0),l=i.width+t.padding,r=i.height+t.padding,s=[{x:r/6,y:0},{x:l-r/6,y:0},{x:l+2*r/6,y:-r},{x:-2*r/6,y:-r}],n=I(a,l,r,s);return n.attr("style",t.style),m(t,n),t.intersect=function(c){return w.polygon(t,s,c)},a},At=async(e,t)=>{const{shapeSvg:a,bbox:i}=await M(e,t,_(t),!0),l=i.width+t.padding,r=i.height+t.padding,s=[{x:0,y:0},{x:l+r/2,y:0},{x:l,y:-r/2},{x:l+r/2,y:-r},{x:0,y:-r}],n=I(a,l,r,s);return n.attr("style",t.style),m(t,n),t.intersect=function(c){return w.polygon(t,s,c)},a},jt=async(e,t)=>{const{shapeSvg:a,bbox:i}=await M(e,t,_(t),!0),l=i.width+t.padding,r=l/2,s=r/(2.5+l/50),n=i.height+s+t.padding,c="M 0,"+s+" a "+r+","+s+" 0,0,0 "+l+" 0 a "+r+","+s+" 0,0,0 "+-l+" 0 l 0,"+n+" a "+r+","+s+" 0,0,0 "+l+" 0 l 0,"+-n,o=a.attr("label-offset-y",s).insert("path",":first-child").attr("style",t.style).attr("d",c).attr("transform","translate("+-l/2+","+-(n/2+s)+")");return m(t,o),t.intersect=function(h){const y=w.rect(t,h),f=y.x-t.x;if(r!=0&&(Math.abs(f)<t.width/2||Math.abs(f)==t.width/2&&Math.abs(y.y-t.y)>t.height/2-s)){let p=s*s*(1-f*f/(r*r));p!=0&&(p=Math.sqrt(p)),p=s-p,h.y-t.y>0&&(p=-p),y.y+=p}return y},a},Ut=async(e,t)=>{const{shapeSvg:a,bbox:i,halfPadding:l}=await M(e,t,"node "+t.classes+" "+t.class,!0),r=a.insert("rect",":first-child"),s=t.positioned?t.width:i.width+t.padding,n=t.positioned?t.height:i.height+t.padding,c=t.positioned?-s/2:-i.width/2-l,o=t.positioned?-n/2:-i.height/2-l;if(r.attr("class","basic label-container").attr("style",t.style).attr("rx",t.rx).attr("ry",t.ry).attr("x",c).attr("y",o).attr("width",s).attr("height",n),t.props){const h=new Set(Object.keys(t.props));t.props.borders&&(Q(r,t.props.borders,s,n),h.delete("borders")),h.forEach(y=>{g.warn(`Unknown node property ${y}`)})}return m(t,r),t.intersect=function(h){return w.rect(t,h)},a},zt=async(e,t)=>{const{shapeSvg:a,bbox:i,halfPadding:l}=await M(e,t,"node "+t.classes,!0),r=a.insert("rect",":first-child"),s=t.positioned?t.width:i.width+t.padding,n=t.positioned?t.height:i.height+t.padding,c=t.positioned?-s/2:-i.width/2-l,o=t.positioned?-n/2:-i.height/2-l;if(r.attr("class","basic cluster composite label-container").attr("style",t.style).attr("rx",t.rx).attr("ry",t.ry).attr("x",c).attr("y",o).attr("width",s).attr("height",n),t.props){const h=new Set(Object.keys(t.props));t.props.borders&&(Q(r,t.props.borders,s,n),h.delete("borders")),h.forEach(y=>{g.warn(`Unknown node property ${y}`)})}return m(t,r),t.intersect=function(h){return w.rect(t,h)},a},Zt=async(e,t)=>{const{shapeSvg:a}=await M(e,t,"label",!0);g.trace("Classes = ",t.class);const i=a.insert("rect",":first-child"),l=0,r=0;if(i.attr("width",l).attr("height",r),a.attr("class","label edgeLabel"),t.props){const s=new Set(Object.keys(t.props));t.props.borders&&(Q(i,t.props.borders,l,r),s.delete("borders")),s.forEach(n=>{g.warn(`Unknown node property ${n}`)})}return m(t,i),t.intersect=function(s){return w.rect(t,s)},a};function Q(e,t,a,i){const l=[],r=n=>{l.push(n,0)},s=n=>{l.push(0,n)};t.includes("t")?(g.debug("add top border"),r(a)):s(a),t.includes("r")?(g.debug("add right border"),r(i)):s(i),t.includes("b")?(g.debug("add bottom border"),r(a)):s(a),t.includes("l")?(g.debug("add left border"),r(i)):s(i),e.attr("stroke-dasharray",l.join(" "))}const Gt=(e,t)=>{let a;t.classes?a="node "+t.classes:a="node default";const i=e.insert("g").attr("class",a).attr("id",t.domId||t.id),l=i.insert("rect",":first-child"),r=i.insert("line"),s=i.insert("g").attr("class","label"),n=t.labelText.flat?t.labelText.flat():t.labelText;let c="";typeof n=="object"?c=n[0]:c=n,g.info("Label text abc79",c,n,typeof n=="object");const o=s.node().appendChild(R(c,t.labelStyle,!0,!0));let h={width:0,height:0};if(H(b().flowchart.htmlLabels)){const k=o.children[0],x=E(o);h=k.getBoundingClientRect(),x.attr("width",h.width),x.attr("height",h.height)}g.info("Text 2",n);const y=n.slice(1,n.length);let f=o.getBBox();const p=s.node().appendChild(R(y.join?y.join("<br/>"):y,t.labelStyle,!0,!0));if(H(b().flowchart.htmlLabels)){const k=p.children[0],x=E(p);h=k.getBoundingClientRect(),x.attr("width",h.width),x.attr("height",h.height)}const d=t.padding/2;return E(p).attr("transform","translate( "+(h.width>f.width?0:(f.width-h.width)/2)+", "+(f.height+d+5)+")"),E(o).attr("transform","translate( "+(h.width<f.width?0:-(f.width-h.width)/2)+", 0)"),h=s.node().getBBox(),s.attr("transform","translate("+-h.width/2+", "+(-h.height/2-d+3)+")"),l.attr("class","outer title-state").attr("x",-h.width/2-d).attr("y",-h.height/2-d).attr("width",h.width+t.padding).attr("height",h.height+t.padding),r.attr("class","divider").attr("x1",-h.width/2-d).attr("x2",h.width/2+d).attr("y1",-h.height/2-d+f.height+d).attr("y2",-h.height/2-d+f.height+d),m(t,l),t.intersect=function(k){return w.rect(t,k)},i},Ft=async(e,t)=>{const{shapeSvg:a,bbox:i}=await M(e,t,_(t),!0),l=i.height+t.padding,r=i.width+l/4+t.padding,s=a.insert("rect",":first-child").attr("style",t.style).attr("rx",l/2).attr("ry",l/2).attr("x",-r/2).attr("y",-l/2).attr("width",r).attr("height",l);return m(t,s),t.intersect=function(n){return w.rect(t,n)},a},qt=async(e,t)=>{const{shapeSvg:a,bbox:i,halfPadding:l}=await M(e,t,_(t),!0),r=a.insert("circle",":first-child");return r.attr("style",t.style).attr("rx",t.rx).attr("ry",t.ry).attr("r",i.width/2+l).attr("width",i.width+t.padding).attr("height",i.height+t.padding),g.info("Circle main"),m(t,r),t.intersect=function(s){return g.info("Circle intersect",t,i.width/2+l,s),w.circle(t,i.width/2+l,s)},a},Qt=async(e,t)=>{const{shapeSvg:a,bbox:i,halfPadding:l}=await M(e,t,_(t),!0),r=5,s=a.insert("g",":first-child"),n=s.insert("circle"),c=s.insert("circle");return s.attr("class",t.class),n.attr("style",t.style).attr("rx",t.rx).attr("ry",t.ry).attr("r",i.width/2+l+r).attr("width",i.width+t.padding+r*2).attr("height",i.height+t.padding+r*2),c.attr("style",t.style).attr("rx",t.rx).attr("ry",t.ry).attr("r",i.width/2+l).attr("width",i.width+t.padding).attr("height",i.height+t.padding),g.info("DoubleCircle main"),m(t,n),t.intersect=function(o){return g.info("DoubleCircle intersect",t,i.width/2+l+r,o),w.circle(t,i.width/2+l+r,o)},a},Vt=async(e,t)=>{const{shapeSvg:a,bbox:i}=await M(e,t,_(t),!0),l=i.width+t.padding,r=i.height+t.padding,s=[{x:0,y:0},{x:l,y:0},{x:l,y:-r},{x:0,y:-r},{x:0,y:0},{x:-8,y:0},{x:l+8,y:0},{x:l+8,y:-r},{x:-8,y:-r},{x:-8,y:0}],n=I(a,l,r,s);return n.attr("style",t.style),m(t,n),t.intersect=function(c){return w.polygon(t,s,c)},a},Jt=(e,t)=>{const a=e.insert("g").attr("class","node default").attr("id",t.domId||t.id),i=a.insert("circle",":first-child");return i.attr("class","state-start").attr("r",7).attr("width",14).attr("height",14),m(t,i),t.intersect=function(l){return w.circle(t,7,l)},a},tt=(e,t,a)=>{const i=e.insert("g").attr("class","node default").attr("id",t.domId||t.id);let l=70,r=10;a==="LR"&&(l=10,r=70);const s=i.append("rect").attr("x",-1*l/2).attr("y",-1*r/2).attr("width",l).attr("height",r).attr("class","fork-join");return m(t,s),t.height=t.height+t.padding/2,t.width=t.width+t.padding/2,t.intersect=function(n){return w.rect(t,n)},i},Kt=(e,t)=>{const a=e.insert("g").attr("class","node default").attr("id",t.domId||t.id),i=a.insert("circle",":first-child"),l=a.insert("circle",":first-child");return l.attr("class","state-start").attr("r",7).attr("width",14).attr("height",14),i.attr("class","state-end").attr("r",5).attr("width",10).attr("height",10),m(t,l),t.intersect=function(r){return w.circle(t,7,r)},a},Pt=(e,t)=>{const a=t.padding/2,i=4,l=8;let r;t.classes?r="node "+t.classes:r="node default";const s=e.insert("g").attr("class",r).attr("id",t.domId||t.id),n=s.insert("rect",":first-child"),c=s.insert("line"),o=s.insert("line");let h=0,y=i;const f=s.insert("g").attr("class","label");let p=0;const d=t.classData.annotations&&t.classData.annotations[0],k=t.classData.annotations[0]?"«"+t.classData.annotations[0]+"»":"",x=f.node().appendChild(R(k,t.labelStyle,!0,!0));let u=x.getBBox();if(H(b().flowchart.htmlLabels)){const v=x.children[0],L=E(x);u=v.getBoundingClientRect(),L.attr("width",u.width),L.attr("height",u.height)}t.classData.annotations[0]&&(y+=u.height+i,h+=u.width);let S=t.classData.label;t.classData.type!==void 0&&t.classData.type!==""&&(b().flowchart.htmlLabels?S+="&lt;"+t.classData.type+"&gt;":S+="<"+t.classData.type+">");const B=f.node().appendChild(R(S,t.labelStyle,!0,!0));E(B).attr("class","classTitle");let C=B.getBBox();if(H(b().flowchart.htmlLabels)){const v=B.children[0],L=E(B);C=v.getBoundingClientRect(),L.attr("width",C.width),L.attr("height",C.height)}y+=C.height+i,C.width>h&&(h=C.width);const X=[];t.classData.members.forEach(v=>{const L=v.getDisplayDetails();let W=L.displayText;b().flowchart.htmlLabels&&(W=W.replace(/</g,"&lt;").replace(/>/g,"&gt;"));const N=f.node().appendChild(R(W,L.cssStyle?L.cssStyle:t.labelStyle,!0,!0));let $=N.getBBox();if(H(b().flowchart.htmlLabels)){const F=N.children[0],A=E(N);$=F.getBoundingClientRect(),A.attr("width",$.width),A.attr("height",$.height)}$.width>h&&(h=$.width),y+=$.height+i,X.push(N)}),y+=l;const D=[];if(t.classData.methods.forEach(v=>{const L=v.getDisplayDetails();let W=L.displayText;b().flowchart.htmlLabels&&(W=W.replace(/</g,"&lt;").replace(/>/g,"&gt;"));const N=f.node().appendChild(R(W,L.cssStyle?L.cssStyle:t.labelStyle,!0,!0));let $=N.getBBox();if(H(b().flowchart.htmlLabels)){const F=N.children[0],A=E(N);$=F.getBoundingClientRect(),A.attr("width",$.width),A.attr("height",$.height)}$.width>h&&(h=$.width),y+=$.height+i,D.push(N)}),y+=l,d){let v=(h-u.width)/2;E(x).attr("transform","translate( "+(-1*h/2+v)+", "+-1*y/2+")"),p=u.height+i}let nt=(h-C.width)/2;return E(B).attr("transform","translate( "+(-1*h/2+nt)+", "+(-1*y/2+p)+")"),p+=C.height+i,c.attr("class","divider").attr("x1",-h/2-a).attr("x2",h/2+a).attr("y1",-y/2-a+l+p).attr("y2",-y/2-a+l+p),p+=l,X.forEach(v=>{E(v).attr("transform","translate( "+-h/2+", "+(-1*y/2+p+l/2)+")");const L=v==null?void 0:v.getBBox();p+=((L==null?void 0:L.height)??0)+i}),p+=l,o.attr("class","divider").attr("x1",-h/2-a).attr("x2",h/2+a).attr("y1",-y/2-a+l+p).attr("y2",-y/2-a+l+p),p+=l,D.forEach(v=>{E(v).attr("transform","translate( "+-h/2+", "+(-1*y/2+p)+")");const L=v==null?void 0:v.getBBox();p+=((L==null?void 0:L.height)??0)+i}),n.attr("style",t.style).attr("class","outer title-state").attr("x",-h/2-a).attr("y",-(y/2)-a).attr("width",h+t.padding).attr("height",y+t.padding),m(t,n),t.intersect=function(v){return w.rect(t,v)},s},rt={rhombus:P,composite:zt,question:P,rect:Ut,labelRect:Zt,rectWithTitle:Gt,choice:Ht,circle:qt,doublecircle:Qt,stadium:Ft,hexagon:It,block_arrow:Nt,rect_left_inv_arrow:Ot,lean_right:Wt,lean_left:Xt,trapezoid:Yt,inv_trapezoid:Dt,rect_right_inv_arrow:At,cylinder:jt,start:Jt,end:Kt,note:$t,subroutine:Vt,fork:tt,join:tt,class_box:Pt};let Y={};const or=async(e,t,a)=>{let i,l;if(t.link){let r;b().securityLevel==="sandbox"?r="_top":t.linkTarget&&(r=t.linkTarget||"_blank"),i=e.insert("svg:a").attr("xlink:href",t.link).attr("target",r),l=await rt[t.shape](i,t,a)}else l=await rt[t.shape](e,t,a),i=l;return t.tooltip&&l.attr("title",t.tooltip),t.class&&l.attr("class","node default "+t.class),i.attr("data-node","true"),i.attr("data-id",t.id),Y[t.id]=i,t.haveCallback&&Y[t.id].attr("class",Y[t.id].attr("class")+" clickable"),i},yr=(e,t)=>{Y[t.id]=e},pr=()=>{Y={}},fr=e=>{const t=Y[e.id];g.trace("Transforming node",e.diff,e,"translate("+(e.x-e.width/2-5)+", "+e.width/2+")");const a=8,i=e.diff||0;return e.clusterNode?t.attr("transform","translate("+(e.x+i-e.width/2)+", "+(e.y-e.height/2-a)+")"):t.attr("transform","translate("+e.x+", "+e.y+")"),i},tr=({flowchart:e})=>{var t,a;const i=((t=e==null?void 0:e.subGraphTitleMargin)==null?void 0:t.top)??0,l=((a=e==null?void 0:e.subGraphTitleMargin)==null?void 0:a.bottom)??0,r=i+l;return{subGraphTitleTopMargin:i,subGraphTitleBottomMargin:l,subGraphTitleTotalMargin:r}},O={aggregation:18,extension:18,composition:18,dependency:6,lollipop:13.5,arrow_point:5.3};function U(e,t){if(e===void 0||t===void 0)return{angle:0,deltaX:0,deltaY:0};e=Z(e),t=Z(t);const[a,i]=[e.x,e.y],[l,r]=[t.x,t.y],s=l-a,n=r-i;return{angle:Math.atan(n/s),deltaX:s,deltaY:n}}const Z=e=>Array.isArray(e)?{x:e[0],y:e[1]}:e,rr=e=>({x:function(t,a,i){let l=0;if(a===0&&Object.hasOwn(O,e.arrowTypeStart)){const{angle:r,deltaX:s}=U(i[0],i[1]);l=O[e.arrowTypeStart]*Math.cos(r)*(s>=0?1:-1)}else if(a===i.length-1&&Object.hasOwn(O,e.arrowTypeEnd)){const{angle:r,deltaX:s}=U(i[i.length-1],i[i.length-2]);l=O[e.arrowTypeEnd]*Math.cos(r)*(s>=0?1:-1)}return Z(t).x+l},y:function(t,a,i){let l=0;if(a===0&&Object.hasOwn(O,e.arrowTypeStart)){const{angle:r,deltaY:s}=U(i[0],i[1]);l=O[e.arrowTypeStart]*Math.abs(Math.sin(r))*(s>=0?1:-1)}else if(a===i.length-1&&Object.hasOwn(O,e.arrowTypeEnd)){const{angle:r,deltaY:s}=U(i[i.length-1],i[i.length-2]);l=O[e.arrowTypeEnd]*Math.abs(Math.sin(r))*(s>=0?1:-1)}return Z(t).y+l}}),ar=(e,t,a,i,l)=>{t.arrowTypeStart&&at(e,"start",t.arrowTypeStart,a,i,l),t.arrowTypeEnd&&at(e,"end",t.arrowTypeEnd,a,i,l)},er={arrow_cross:"cross",arrow_point:"point",arrow_barb:"barb",arrow_circle:"circle",aggregation:"aggregation",extension:"extension",composition:"composition",dependency:"dependency",lollipop:"lollipop"},at=(e,t,a,i,l,r)=>{const s=er[a];if(!s){g.warn(`Unknown arrow type: ${a}`);return}const n=t==="start"?"Start":"End";e.attr(`marker-${t}`,`url(${i}#${l}_${r}-${s}${n})`)};let G={},T={};const xr=()=>{G={},T={}},dr=(e,t)=>{const a=H(b().flowchart.htmlLabels),i=t.labelType==="markdown"?st(e,t.label,{style:t.labelStyle,useHtmlLabels:a,addSvgBackground:!0}):R(t.label,t.labelStyle),l=e.insert("g").attr("class","edgeLabel"),r=l.insert("g").attr("class","label");r.node().appendChild(i);let s=i.getBBox();if(a){const c=i.children[0],o=E(i);s=c.getBoundingClientRect(),o.attr("width",s.width),o.attr("height",s.height)}r.attr("transform","translate("+-s.width/2+", "+-s.height/2+")"),G[t.id]=l,t.width=s.width,t.height=s.height;let n;if(t.startLabelLeft){const c=R(t.startLabelLeft,t.labelStyle),o=e.insert("g").attr("class","edgeTerminals"),h=o.insert("g").attr("class","inner");n=h.node().appendChild(c);const y=c.getBBox();h.attr("transform","translate("+-y.width/2+", "+-y.height/2+")"),T[t.id]||(T[t.id]={}),T[t.id].startLeft=o,z(n,t.startLabelLeft)}if(t.startLabelRight){const c=R(t.startLabelRight,t.labelStyle),o=e.insert("g").attr("class","edgeTerminals"),h=o.insert("g").attr("class","inner");n=o.node().appendChild(c),h.node().appendChild(c);const y=c.getBBox();h.attr("transform","translate("+-y.width/2+", "+-y.height/2+")"),T[t.id]||(T[t.id]={}),T[t.id].startRight=o,z(n,t.startLabelRight)}if(t.endLabelLeft){const c=R(t.endLabelLeft,t.labelStyle),o=e.insert("g").attr("class","edgeTerminals"),h=o.insert("g").attr("class","inner");n=h.node().appendChild(c);const y=c.getBBox();h.attr("transform","translate("+-y.width/2+", "+-y.height/2+")"),o.node().appendChild(c),T[t.id]||(T[t.id]={}),T[t.id].endLeft=o,z(n,t.endLabelLeft)}if(t.endLabelRight){const c=R(t.endLabelRight,t.labelStyle),o=e.insert("g").attr("class","edgeTerminals"),h=o.insert("g").attr("class","inner");n=h.node().appendChild(c);const y=c.getBBox();h.attr("transform","translate("+-y.width/2+", "+-y.height/2+")"),o.node().appendChild(c),T[t.id]||(T[t.id]={}),T[t.id].endRight=o,z(n,t.endLabelRight)}return i};function z(e,t){b().flowchart.htmlLabels&&e&&(e.style.width=t.length*9+"px",e.style.height="12px")}const gr=(e,t)=>{g.debug("Moving label abc88 ",e.id,e.label,G[e.id],t);let a=t.updatedPath?t.updatedPath:t.originalPath;const i=b(),{subGraphTitleTotalMargin:l}=tr(i);if(e.label){const r=G[e.id];let s=e.x,n=e.y;if(a){const c=j.calcLabelPosition(a);g.debug("Moving label "+e.label+" from (",s,",",n,") to (",c.x,",",c.y,") abc88"),t.updatedPath&&(s=c.x,n=c.y)}r.attr("transform",`translate(${s}, ${n+l/2})`)}if(e.startLabelLeft){const r=T[e.id].startLeft;let s=e.x,n=e.y;if(a){const c=j.calcTerminalLabelPosition(e.arrowTypeStart?10:0,"start_left",a);s=c.x,n=c.y}r.attr("transform",`translate(${s}, ${n})`)}if(e.startLabelRight){const r=T[e.id].startRight;let s=e.x,n=e.y;if(a){const c=j.calcTerminalLabelPosition(e.arrowTypeStart?10:0,"start_right",a);s=c.x,n=c.y}r.attr("transform",`translate(${s}, ${n})`)}if(e.endLabelLeft){const r=T[e.id].endLeft;let s=e.x,n=e.y;if(a){const c=j.calcTerminalLabelPosition(e.arrowTypeEnd?10:0,"end_left",a);s=c.x,n=c.y}r.attr("transform",`translate(${s}, ${n})`)}if(e.endLabelRight){const r=T[e.id].endRight;let s=e.x,n=e.y;if(a){const c=j.calcTerminalLabelPosition(e.arrowTypeEnd?10:0,"end_right",a);s=c.x,n=c.y}r.attr("transform",`translate(${s}, ${n})`)}},sr=(e,t)=>{const a=e.x,i=e.y,l=Math.abs(t.x-a),r=Math.abs(t.y-i),s=e.width/2,n=e.height/2;return l>=s||r>=n},ir=(e,t,a)=>{g.debug(`intersection calc abc89:
+import{q as H,c as b,d as V,an as q,h as E,l as g,z as j,ao as lt}from"./mermaid.core-DNo_7Q2B.js";import{c as st}from"./createText-4a4f35c9-CISzj231.js";import{l as ct}from"./line-BqHmcuby.js";const ht=(e,t,a,i)=>{t.forEach(l=>{wt[l](e,a,i)})},ot=(e,t,a)=>{g.trace("Making markers for ",a),e.append("defs").append("marker").attr("id",a+"_"+t+"-extensionStart").attr("class","marker extension "+t).attr("refX",18).attr("refY",7).attr("markerWidth",190).attr("markerHeight",240).attr("orient","auto").append("path").attr("d","M 1,7 L18,13 V 1 Z"),e.append("defs").append("marker").attr("id",a+"_"+t+"-extensionEnd").attr("class","marker extension "+t).attr("refX",1).attr("refY",7).attr("markerWidth",20).attr("markerHeight",28).attr("orient","auto").append("path").attr("d","M 1,1 V 13 L18,7 Z")},yt=(e,t,a)=>{e.append("defs").append("marker").attr("id",a+"_"+t+"-compositionStart").attr("class","marker composition "+t).attr("refX",18).attr("refY",7).attr("markerWidth",190).attr("markerHeight",240).attr("orient","auto").append("path").attr("d","M 18,7 L9,13 L1,7 L9,1 Z"),e.append("defs").append("marker").attr("id",a+"_"+t+"-compositionEnd").attr("class","marker composition "+t).attr("refX",1).attr("refY",7).attr("markerWidth",20).attr("markerHeight",28).attr("orient","auto").append("path").attr("d","M 18,7 L9,13 L1,7 L9,1 Z")},pt=(e,t,a)=>{e.append("defs").append("marker").attr("id",a+"_"+t+"-aggregationStart").attr("class","marker aggregation "+t).attr("refX",18).attr("refY",7).attr("markerWidth",190).attr("markerHeight",240).attr("orient","auto").append("path").attr("d","M 18,7 L9,13 L1,7 L9,1 Z"),e.append("defs").append("marker").attr("id",a+"_"+t+"-aggregationEnd").attr("class","marker aggregation "+t).attr("refX",1).attr("refY",7).attr("markerWidth",20).attr("markerHeight",28).attr("orient","auto").append("path").attr("d","M 18,7 L9,13 L1,7 L9,1 Z")},ft=(e,t,a)=>{e.append("defs").append("marker").attr("id",a+"_"+t+"-dependencyStart").attr("class","marker dependency "+t).attr("refX",6).attr("refY",7).attr("markerWidth",190).attr("markerHeight",240).attr("orient","auto").append("path").attr("d","M 5,7 L9,13 L1,7 L9,1 Z"),e.append("defs").append("marker").attr("id",a+"_"+t+"-dependencyEnd").attr("class","marker dependency "+t).attr("refX",13).attr("refY",7).attr("markerWidth",20).attr("markerHeight",28).attr("orient","auto").append("path").attr("d","M 18,7 L9,13 L14,7 L9,1 Z")},xt=(e,t,a)=>{e.append("defs").append("marker").attr("id",a+"_"+t+"-lollipopStart").attr("class","marker lollipop "+t).attr("refX",13).attr("refY",7).attr("markerWidth",190).attr("markerHeight",240).attr("orient","auto").append("circle").attr("stroke","black").attr("fill","transparent").attr("cx",7).attr("cy",7).attr("r",6),e.append("defs").append("marker").attr("id",a+"_"+t+"-lollipopEnd").attr("class","marker lollipop "+t).attr("refX",1).attr("refY",7).attr("markerWidth",190).attr("markerHeight",240).attr("orient","auto").append("circle").attr("stroke","black").attr("fill","transparent").attr("cx",7).attr("cy",7).attr("r",6)},dt=(e,t,a)=>{e.append("marker").attr("id",a+"_"+t+"-pointEnd").attr("class","marker "+t).attr("viewBox","0 0 10 10").attr("refX",6).attr("refY",5).attr("markerUnits","userSpaceOnUse").attr("markerWidth",12).attr("markerHeight",12).attr("orient","auto").append("path").attr("d","M 0 0 L 10 5 L 0 10 z").attr("class","arrowMarkerPath").style("stroke-width",1).style("stroke-dasharray","1,0"),e.append("marker").attr("id",a+"_"+t+"-pointStart").attr("class","marker "+t).attr("viewBox","0 0 10 10").attr("refX",4.5).attr("refY",5).attr("markerUnits","userSpaceOnUse").attr("markerWidth",12).attr("markerHeight",12).attr("orient","auto").append("path").attr("d","M 0 5 L 10 10 L 10 0 z").attr("class","arrowMarkerPath").style("stroke-width",1).style("stroke-dasharray","1,0")},gt=(e,t,a)=>{e.append("marker").attr("id",a+"_"+t+"-circleEnd").attr("class","marker "+t).attr("viewBox","0 0 10 10").attr("refX",11).attr("refY",5).attr("markerUnits","userSpaceOnUse").attr("markerWidth",11).attr("markerHeight",11).attr("orient","auto").append("circle").attr("cx","5").attr("cy","5").attr("r","5").attr("class","arrowMarkerPath").style("stroke-width",1).style("stroke-dasharray","1,0"),e.append("marker").attr("id",a+"_"+t+"-circleStart").attr("class","marker "+t).attr("viewBox","0 0 10 10").attr("refX",-1).attr("refY",5).attr("markerUnits","userSpaceOnUse").attr("markerWidth",11).attr("markerHeight",11).attr("orient","auto").append("circle").attr("cx","5").attr("cy","5").attr("r","5").attr("class","arrowMarkerPath").style("stroke-width",1).style("stroke-dasharray","1,0")},ut=(e,t,a)=>{e.append("marker").attr("id",a+"_"+t+"-crossEnd").attr("class","marker cross "+t).attr("viewBox","0 0 11 11").attr("refX",12).attr("refY",5.2).attr("markerUnits","userSpaceOnUse").attr("markerWidth",11).attr("markerHeight",11).attr("orient","auto").append("path").attr("d","M 1,1 l 9,9 M 10,1 l -9,9").attr("class","arrowMarkerPath").style("stroke-width",2).style("stroke-dasharray","1,0"),e.append("marker").attr("id",a+"_"+t+"-crossStart").attr("class","marker cross "+t).attr("viewBox","0 0 11 11").attr("refX",-1).attr("refY",5.2).attr("markerUnits","userSpaceOnUse").attr("markerWidth",11).attr("markerHeight",11).attr("orient","auto").append("path").attr("d","M 1,1 l 9,9 M 10,1 l -9,9").attr("class","arrowMarkerPath").style("stroke-width",2).style("stroke-dasharray","1,0")},bt=(e,t,a)=>{e.append("defs").append("marker").attr("id",a+"_"+t+"-barbEnd").attr("refX",19).attr("refY",7).attr("markerWidth",20).attr("markerHeight",14).attr("markerUnits","strokeWidth").attr("orient","auto").append("path").attr("d","M 19,7 L9,13 L14,7 L9,1 Z")},wt={extension:ot,composition:yt,aggregation:pt,dependency:ft,lollipop:xt,point:dt,circle:gt,cross:ut,barb:bt},hr=ht;function mt(e,t){t&&e.attr("style",t)}function kt(e){const t=E(document.createElementNS("http://www.w3.org/2000/svg","foreignObject")),a=t.append("xhtml:div"),i=e.label,l=e.isNode?"nodeLabel":"edgeLabel";return a.html('<span class="'+l+'" '+(e.labelStyle?'style="'+e.labelStyle+'"':"")+">"+i+"</span>"),mt(a,e.labelStyle),a.style("display","inline-block"),a.style("white-space","nowrap"),a.attr("xmlns","http://www.w3.org/1999/xhtml"),t.node()}const vt=(e,t,a,i)=>{let l=e||"";if(typeof l=="object"&&(l=l[0]),H(b().flowchart.htmlLabels)){l=l.replace(/\\n|\n/g,"<br />"),g.debug("vertexText"+l);const r={isNode:i,label:q(l).replace(/fa[blrs]?:fa-[\w-]+/g,n=>`<i class='${n.replace(":"," ")}'></i>`),labelStyle:t.replace("fill:","color:")};return kt(r)}else{const r=document.createElementNS("http://www.w3.org/2000/svg","text");r.setAttribute("style",t.replace("color:","fill:"));let s=[];typeof l=="string"?s=l.split(/\\n|\n|<br\s*\/?>/gi):Array.isArray(l)?s=l:s=[];for(const n of s){const c=document.createElementNS("http://www.w3.org/2000/svg","tspan");c.setAttributeNS("http://www.w3.org/XML/1998/namespace","xml:space","preserve"),c.setAttribute("dy","1em"),c.setAttribute("x","0"),a?c.setAttribute("class","title-row"):c.setAttribute("class","row"),c.textContent=n.trim(),r.appendChild(c)}return r}},R=vt,M=async(e,t,a,i)=>{let l;const r=t.useHtmlLabels||H(b().flowchart.htmlLabels);a?l=a:l="node default";const s=e.insert("g").attr("class",l).attr("id",t.domId||t.id),n=s.insert("g").attr("class","label").attr("style",t.labelStyle);let c;t.labelText===void 0?c="":c=typeof t.labelText=="string"?t.labelText:t.labelText[0];const o=n.node();let h;t.labelType==="markdown"?h=st(n,V(q(c),b()),{useHtmlLabels:r,width:t.width||b().flowchart.wrappingWidth,classes:"markdown-node-label"}):h=o.appendChild(R(V(q(c),b()),t.labelStyle,!1,i));let y=h.getBBox();const f=t.padding/2;if(H(b().flowchart.htmlLabels)){const p=h.children[0],d=E(h),k=p.getElementsByTagName("img");if(k){const x=c.replace(/<img[^>]*>/g,"").trim()==="";await Promise.all([...k].map(u=>new Promise(S=>{function B(){if(u.style.display="flex",u.style.flexDirection="column",x){const C=b().fontSize?b().fontSize:window.getComputedStyle(document.body).fontSize,D=parseInt(C,10)*5+"px";u.style.minWidth=D,u.style.maxWidth=D}else u.style.width="100%";S(u)}setTimeout(()=>{u.complete&&B()}),u.addEventListener("error",B),u.addEventListener("load",B)})))}y=p.getBoundingClientRect(),d.attr("width",y.width),d.attr("height",y.height)}return r?n.attr("transform","translate("+-y.width/2+", "+-y.height/2+")"):n.attr("transform","translate(0, "+-y.height/2+")"),t.centerLabel&&n.attr("transform","translate("+-y.width/2+", "+-y.height/2+")"),n.insert("rect",":first-child"),{shapeSvg:s,bbox:y,halfPadding:f,label:n}},m=(e,t)=>{const a=t.node().getBBox();e.width=a.width,e.height=a.height};function I(e,t,a,i){return e.insert("polygon",":first-child").attr("points",i.map(function(l){return l.x+","+l.y}).join(" ")).attr("class","label-container").attr("transform","translate("+-t/2+","+a/2+")")}function Lt(e,t){return e.intersect(t)}function it(e,t,a,i){var l=e.x,r=e.y,s=l-i.x,n=r-i.y,c=Math.sqrt(t*t*n*n+a*a*s*s),o=Math.abs(t*a*s/c);i.x<l&&(o=-o);var h=Math.abs(t*a*n/c);return i.y<r&&(h=-h),{x:l+o,y:r+h}}function St(e,t,a){return it(e,t,t,a)}function Mt(e,t,a,i){var l,r,s,n,c,o,h,y,f,p,d,k,x,u,S;if(l=t.y-e.y,s=e.x-t.x,c=t.x*e.y-e.x*t.y,f=l*a.x+s*a.y+c,p=l*i.x+s*i.y+c,!(f!==0&&p!==0&&J(f,p))&&(r=i.y-a.y,n=a.x-i.x,o=i.x*a.y-a.x*i.y,h=r*e.x+n*e.y+o,y=r*t.x+n*t.y+o,!(h!==0&&y!==0&&J(h,y))&&(d=l*n-r*s,d!==0)))return k=Math.abs(d/2),x=s*o-n*c,u=x<0?(x-k)/d:(x+k)/d,x=r*c-l*o,S=x<0?(x-k)/d:(x+k)/d,{x:u,y:S}}function J(e,t){return e*t>0}function Tt(e,t,a){var i=e.x,l=e.y,r=[],s=Number.POSITIVE_INFINITY,n=Number.POSITIVE_INFINITY;typeof t.forEach=="function"?t.forEach(function(d){s=Math.min(s,d.x),n=Math.min(n,d.y)}):(s=Math.min(s,t.x),n=Math.min(n,t.y));for(var c=i-e.width/2-s,o=l-e.height/2-n,h=0;h<t.length;h++){var y=t[h],f=t[h<t.length-1?h+1:0],p=Mt(e,a,{x:c+y.x,y:o+y.y},{x:c+f.x,y:o+f.y});p&&r.push(p)}return r.length?(r.length>1&&r.sort(function(d,k){var x=d.x-a.x,u=d.y-a.y,S=Math.sqrt(x*x+u*u),B=k.x-a.x,C=k.y-a.y,X=Math.sqrt(B*B+C*C);return S<X?-1:S===X?0:1}),r[0]):e}const Bt=(e,t)=>{var a=e.x,i=e.y,l=t.x-a,r=t.y-i,s=e.width/2,n=e.height/2,c,o;return Math.abs(r)*s>Math.abs(l)*n?(r<0&&(n=-n),c=r===0?0:n*l/r,o=n):(l<0&&(s=-s),c=s,o=l===0?0:s*r/l),{x:a+c,y:i+o}},Et=Bt,w={node:Lt,circle:St,ellipse:it,polygon:Tt,rect:Et},Ct=async(e,t)=>{t.useHtmlLabels||b().flowchart.htmlLabels||(t.centerLabel=!0);const{shapeSvg:i,bbox:l,halfPadding:r}=await M(e,t,"node "+t.classes,!0);g.info("Classes = ",t.classes);const s=i.insert("rect",":first-child");return s.attr("rx",t.rx).attr("ry",t.ry).attr("x",-l.width/2-r).attr("y",-l.height/2-r).attr("width",l.width+t.padding).attr("height",l.height+t.padding),m(t,s),t.intersect=function(n){return w.rect(t,n)},i},$t=Ct,_t=e=>{const t=new Set;for(const a of e)switch(a){case"x":t.add("right"),t.add("left");break;case"y":t.add("up"),t.add("down");break;default:t.add(a);break}return t},Rt=(e,t,a)=>{const i=_t(e),l=2,r=t.height+2*a.padding,s=r/l,n=t.width+2*s+a.padding,c=a.padding/2;return i.has("right")&&i.has("left")&&i.has("up")&&i.has("down")?[{x:0,y:0},{x:s,y:0},{x:n/2,y:2*c},{x:n-s,y:0},{x:n,y:0},{x:n,y:-r/3},{x:n+2*c,y:-r/2},{x:n,y:-2*r/3},{x:n,y:-r},{x:n-s,y:-r},{x:n/2,y:-r-2*c},{x:s,y:-r},{x:0,y:-r},{x:0,y:-2*r/3},{x:-2*c,y:-r/2},{x:0,y:-r/3}]:i.has("right")&&i.has("left")&&i.has("up")?[{x:s,y:0},{x:n-s,y:0},{x:n,y:-r/2},{x:n-s,y:-r},{x:s,y:-r},{x:0,y:-r/2}]:i.has("right")&&i.has("left")&&i.has("down")?[{x:0,y:0},{x:s,y:-r},{x:n-s,y:-r},{x:n,y:0}]:i.has("right")&&i.has("up")&&i.has("down")?[{x:0,y:0},{x:n,y:-s},{x:n,y:-r+s},{x:0,y:-r}]:i.has("left")&&i.has("up")&&i.has("down")?[{x:n,y:0},{x:0,y:-s},{x:0,y:-r+s},{x:n,y:-r}]:i.has("right")&&i.has("left")?[{x:s,y:0},{x:s,y:-c},{x:n-s,y:-c},{x:n-s,y:0},{x:n,y:-r/2},{x:n-s,y:-r},{x:n-s,y:-r+c},{x:s,y:-r+c},{x:s,y:-r},{x:0,y:-r/2}]:i.has("up")&&i.has("down")?[{x:n/2,y:0},{x:0,y:-c},{x:s,y:-c},{x:s,y:-r+c},{x:0,y:-r+c},{x:n/2,y:-r},{x:n,y:-r+c},{x:n-s,y:-r+c},{x:n-s,y:-c},{x:n,y:-c}]:i.has("right")&&i.has("up")?[{x:0,y:0},{x:n,y:-s},{x:0,y:-r}]:i.has("right")&&i.has("down")?[{x:0,y:0},{x:n,y:0},{x:0,y:-r}]:i.has("left")&&i.has("up")?[{x:n,y:0},{x:0,y:-s},{x:n,y:-r}]:i.has("left")&&i.has("down")?[{x:n,y:0},{x:0,y:0},{x:n,y:-r}]:i.has("right")?[{x:s,y:-c},{x:s,y:-c},{x:n-s,y:-c},{x:n-s,y:0},{x:n,y:-r/2},{x:n-s,y:-r},{x:n-s,y:-r+c},{x:s,y:-r+c},{x:s,y:-r+c}]:i.has("left")?[{x:s,y:0},{x:s,y:-c},{x:n-s,y:-c},{x:n-s,y:-r+c},{x:s,y:-r+c},{x:s,y:-r},{x:0,y:-r/2}]:i.has("up")?[{x:s,y:-c},{x:s,y:-r+c},{x:0,y:-r+c},{x:n/2,y:-r},{x:n,y:-r+c},{x:n-s,y:-r+c},{x:n-s,y:-c}]:i.has("down")?[{x:n/2,y:0},{x:0,y:-c},{x:s,y:-c},{x:s,y:-r+c},{x:n-s,y:-r+c},{x:n-s,y:-c},{x:n,y:-c}]:[{x:0,y:0}]},K=e=>e?" "+e:"",_=(e,t)=>`node default${K(e.classes)} ${K(e.class)}`,P=async(e,t)=>{const{shapeSvg:a,bbox:i}=await M(e,t,_(t),!0),l=i.width+t.padding,r=i.height+t.padding,s=l+r,n=[{x:s/2,y:0},{x:s,y:-s/2},{x:s/2,y:-s},{x:0,y:-s/2}];g.info("Question main (Circle)");const c=I(a,s,s,n);return c.attr("style",t.style),m(t,c),t.intersect=function(o){return g.warn("Intersect called"),w.polygon(t,n,o)},a},Ht=(e,t)=>{const a=e.insert("g").attr("class","node default").attr("id",t.domId||t.id),i=28,l=[{x:0,y:i/2},{x:i/2,y:0},{x:0,y:-i/2},{x:-i/2,y:0}];return a.insert("polygon",":first-child").attr("points",l.map(function(s){return s.x+","+s.y}).join(" ")).attr("class","state-start").attr("r",7).attr("width",28).attr("height",28),t.width=28,t.height=28,t.intersect=function(s){return w.circle(t,14,s)},a},It=async(e,t)=>{const{shapeSvg:a,bbox:i}=await M(e,t,_(t),!0),l=4,r=i.height+t.padding,s=r/l,n=i.width+2*s+t.padding,c=[{x:s,y:0},{x:n-s,y:0},{x:n,y:-r/2},{x:n-s,y:-r},{x:s,y:-r},{x:0,y:-r/2}],o=I(a,n,r,c);return o.attr("style",t.style),m(t,o),t.intersect=function(h){return w.polygon(t,c,h)},a},Nt=async(e,t)=>{const{shapeSvg:a,bbox:i}=await M(e,t,void 0,!0),l=2,r=i.height+2*t.padding,s=r/l,n=i.width+2*s+t.padding,c=Rt(t.directions,i,t),o=I(a,n,r,c);return o.attr("style",t.style),m(t,o),t.intersect=function(h){return w.polygon(t,c,h)},a},Ot=async(e,t)=>{const{shapeSvg:a,bbox:i}=await M(e,t,_(t),!0),l=i.width+t.padding,r=i.height+t.padding,s=[{x:-r/2,y:0},{x:l,y:0},{x:l,y:-r},{x:-r/2,y:-r},{x:0,y:-r/2}];return I(a,l,r,s).attr("style",t.style),t.width=l+r,t.height=r,t.intersect=function(c){return w.polygon(t,s,c)},a},Wt=async(e,t)=>{const{shapeSvg:a,bbox:i}=await M(e,t,_(t),!0),l=i.width+t.padding,r=i.height+t.padding,s=[{x:-2*r/6,y:0},{x:l-r/6,y:0},{x:l+2*r/6,y:-r},{x:r/6,y:-r}],n=I(a,l,r,s);return n.attr("style",t.style),m(t,n),t.intersect=function(c){return w.polygon(t,s,c)},a},Xt=async(e,t)=>{const{shapeSvg:a,bbox:i}=await M(e,t,_(t),!0),l=i.width+t.padding,r=i.height+t.padding,s=[{x:2*r/6,y:0},{x:l+r/6,y:0},{x:l-2*r/6,y:-r},{x:-r/6,y:-r}],n=I(a,l,r,s);return n.attr("style",t.style),m(t,n),t.intersect=function(c){return w.polygon(t,s,c)},a},Yt=async(e,t)=>{const{shapeSvg:a,bbox:i}=await M(e,t,_(t),!0),l=i.width+t.padding,r=i.height+t.padding,s=[{x:-2*r/6,y:0},{x:l+2*r/6,y:0},{x:l-r/6,y:-r},{x:r/6,y:-r}],n=I(a,l,r,s);return n.attr("style",t.style),m(t,n),t.intersect=function(c){return w.polygon(t,s,c)},a},Dt=async(e,t)=>{const{shapeSvg:a,bbox:i}=await M(e,t,_(t),!0),l=i.width+t.padding,r=i.height+t.padding,s=[{x:r/6,y:0},{x:l-r/6,y:0},{x:l+2*r/6,y:-r},{x:-2*r/6,y:-r}],n=I(a,l,r,s);return n.attr("style",t.style),m(t,n),t.intersect=function(c){return w.polygon(t,s,c)},a},At=async(e,t)=>{const{shapeSvg:a,bbox:i}=await M(e,t,_(t),!0),l=i.width+t.padding,r=i.height+t.padding,s=[{x:0,y:0},{x:l+r/2,y:0},{x:l,y:-r/2},{x:l+r/2,y:-r},{x:0,y:-r}],n=I(a,l,r,s);return n.attr("style",t.style),m(t,n),t.intersect=function(c){return w.polygon(t,s,c)},a},jt=async(e,t)=>{const{shapeSvg:a,bbox:i}=await M(e,t,_(t),!0),l=i.width+t.padding,r=l/2,s=r/(2.5+l/50),n=i.height+s+t.padding,c="M 0,"+s+" a "+r+","+s+" 0,0,0 "+l+" 0 a "+r+","+s+" 0,0,0 "+-l+" 0 l 0,"+n+" a "+r+","+s+" 0,0,0 "+l+" 0 l 0,"+-n,o=a.attr("label-offset-y",s).insert("path",":first-child").attr("style",t.style).attr("d",c).attr("transform","translate("+-l/2+","+-(n/2+s)+")");return m(t,o),t.intersect=function(h){const y=w.rect(t,h),f=y.x-t.x;if(r!=0&&(Math.abs(f)<t.width/2||Math.abs(f)==t.width/2&&Math.abs(y.y-t.y)>t.height/2-s)){let p=s*s*(1-f*f/(r*r));p!=0&&(p=Math.sqrt(p)),p=s-p,h.y-t.y>0&&(p=-p),y.y+=p}return y},a},Ut=async(e,t)=>{const{shapeSvg:a,bbox:i,halfPadding:l}=await M(e,t,"node "+t.classes+" "+t.class,!0),r=a.insert("rect",":first-child"),s=t.positioned?t.width:i.width+t.padding,n=t.positioned?t.height:i.height+t.padding,c=t.positioned?-s/2:-i.width/2-l,o=t.positioned?-n/2:-i.height/2-l;if(r.attr("class","basic label-container").attr("style",t.style).attr("rx",t.rx).attr("ry",t.ry).attr("x",c).attr("y",o).attr("width",s).attr("height",n),t.props){const h=new Set(Object.keys(t.props));t.props.borders&&(Q(r,t.props.borders,s,n),h.delete("borders")),h.forEach(y=>{g.warn(`Unknown node property ${y}`)})}return m(t,r),t.intersect=function(h){return w.rect(t,h)},a},zt=async(e,t)=>{const{shapeSvg:a,bbox:i,halfPadding:l}=await M(e,t,"node "+t.classes,!0),r=a.insert("rect",":first-child"),s=t.positioned?t.width:i.width+t.padding,n=t.positioned?t.height:i.height+t.padding,c=t.positioned?-s/2:-i.width/2-l,o=t.positioned?-n/2:-i.height/2-l;if(r.attr("class","basic cluster composite label-container").attr("style",t.style).attr("rx",t.rx).attr("ry",t.ry).attr("x",c).attr("y",o).attr("width",s).attr("height",n),t.props){const h=new Set(Object.keys(t.props));t.props.borders&&(Q(r,t.props.borders,s,n),h.delete("borders")),h.forEach(y=>{g.warn(`Unknown node property ${y}`)})}return m(t,r),t.intersect=function(h){return w.rect(t,h)},a},Zt=async(e,t)=>{const{shapeSvg:a}=await M(e,t,"label",!0);g.trace("Classes = ",t.class);const i=a.insert("rect",":first-child"),l=0,r=0;if(i.attr("width",l).attr("height",r),a.attr("class","label edgeLabel"),t.props){const s=new Set(Object.keys(t.props));t.props.borders&&(Q(i,t.props.borders,l,r),s.delete("borders")),s.forEach(n=>{g.warn(`Unknown node property ${n}`)})}return m(t,i),t.intersect=function(s){return w.rect(t,s)},a};function Q(e,t,a,i){const l=[],r=n=>{l.push(n,0)},s=n=>{l.push(0,n)};t.includes("t")?(g.debug("add top border"),r(a)):s(a),t.includes("r")?(g.debug("add right border"),r(i)):s(i),t.includes("b")?(g.debug("add bottom border"),r(a)):s(a),t.includes("l")?(g.debug("add left border"),r(i)):s(i),e.attr("stroke-dasharray",l.join(" "))}const Gt=(e,t)=>{let a;t.classes?a="node "+t.classes:a="node default";const i=e.insert("g").attr("class",a).attr("id",t.domId||t.id),l=i.insert("rect",":first-child"),r=i.insert("line"),s=i.insert("g").attr("class","label"),n=t.labelText.flat?t.labelText.flat():t.labelText;let c="";typeof n=="object"?c=n[0]:c=n,g.info("Label text abc79",c,n,typeof n=="object");const o=s.node().appendChild(R(c,t.labelStyle,!0,!0));let h={width:0,height:0};if(H(b().flowchart.htmlLabels)){const k=o.children[0],x=E(o);h=k.getBoundingClientRect(),x.attr("width",h.width),x.attr("height",h.height)}g.info("Text 2",n);const y=n.slice(1,n.length);let f=o.getBBox();const p=s.node().appendChild(R(y.join?y.join("<br/>"):y,t.labelStyle,!0,!0));if(H(b().flowchart.htmlLabels)){const k=p.children[0],x=E(p);h=k.getBoundingClientRect(),x.attr("width",h.width),x.attr("height",h.height)}const d=t.padding/2;return E(p).attr("transform","translate( "+(h.width>f.width?0:(f.width-h.width)/2)+", "+(f.height+d+5)+")"),E(o).attr("transform","translate( "+(h.width<f.width?0:-(f.width-h.width)/2)+", 0)"),h=s.node().getBBox(),s.attr("transform","translate("+-h.width/2+", "+(-h.height/2-d+3)+")"),l.attr("class","outer title-state").attr("x",-h.width/2-d).attr("y",-h.height/2-d).attr("width",h.width+t.padding).attr("height",h.height+t.padding),r.attr("class","divider").attr("x1",-h.width/2-d).attr("x2",h.width/2+d).attr("y1",-h.height/2-d+f.height+d).attr("y2",-h.height/2-d+f.height+d),m(t,l),t.intersect=function(k){return w.rect(t,k)},i},Ft=async(e,t)=>{const{shapeSvg:a,bbox:i}=await M(e,t,_(t),!0),l=i.height+t.padding,r=i.width+l/4+t.padding,s=a.insert("rect",":first-child").attr("style",t.style).attr("rx",l/2).attr("ry",l/2).attr("x",-r/2).attr("y",-l/2).attr("width",r).attr("height",l);return m(t,s),t.intersect=function(n){return w.rect(t,n)},a},qt=async(e,t)=>{const{shapeSvg:a,bbox:i,halfPadding:l}=await M(e,t,_(t),!0),r=a.insert("circle",":first-child");return r.attr("style",t.style).attr("rx",t.rx).attr("ry",t.ry).attr("r",i.width/2+l).attr("width",i.width+t.padding).attr("height",i.height+t.padding),g.info("Circle main"),m(t,r),t.intersect=function(s){return g.info("Circle intersect",t,i.width/2+l,s),w.circle(t,i.width/2+l,s)},a},Qt=async(e,t)=>{const{shapeSvg:a,bbox:i,halfPadding:l}=await M(e,t,_(t),!0),r=5,s=a.insert("g",":first-child"),n=s.insert("circle"),c=s.insert("circle");return s.attr("class",t.class),n.attr("style",t.style).attr("rx",t.rx).attr("ry",t.ry).attr("r",i.width/2+l+r).attr("width",i.width+t.padding+r*2).attr("height",i.height+t.padding+r*2),c.attr("style",t.style).attr("rx",t.rx).attr("ry",t.ry).attr("r",i.width/2+l).attr("width",i.width+t.padding).attr("height",i.height+t.padding),g.info("DoubleCircle main"),m(t,n),t.intersect=function(o){return g.info("DoubleCircle intersect",t,i.width/2+l+r,o),w.circle(t,i.width/2+l+r,o)},a},Vt=async(e,t)=>{const{shapeSvg:a,bbox:i}=await M(e,t,_(t),!0),l=i.width+t.padding,r=i.height+t.padding,s=[{x:0,y:0},{x:l,y:0},{x:l,y:-r},{x:0,y:-r},{x:0,y:0},{x:-8,y:0},{x:l+8,y:0},{x:l+8,y:-r},{x:-8,y:-r},{x:-8,y:0}],n=I(a,l,r,s);return n.attr("style",t.style),m(t,n),t.intersect=function(c){return w.polygon(t,s,c)},a},Jt=(e,t)=>{const a=e.insert("g").attr("class","node default").attr("id",t.domId||t.id),i=a.insert("circle",":first-child");return i.attr("class","state-start").attr("r",7).attr("width",14).attr("height",14),m(t,i),t.intersect=function(l){return w.circle(t,7,l)},a},tt=(e,t,a)=>{const i=e.insert("g").attr("class","node default").attr("id",t.domId||t.id);let l=70,r=10;a==="LR"&&(l=10,r=70);const s=i.append("rect").attr("x",-1*l/2).attr("y",-1*r/2).attr("width",l).attr("height",r).attr("class","fork-join");return m(t,s),t.height=t.height+t.padding/2,t.width=t.width+t.padding/2,t.intersect=function(n){return w.rect(t,n)},i},Kt=(e,t)=>{const a=e.insert("g").attr("class","node default").attr("id",t.domId||t.id),i=a.insert("circle",":first-child"),l=a.insert("circle",":first-child");return l.attr("class","state-start").attr("r",7).attr("width",14).attr("height",14),i.attr("class","state-end").attr("r",5).attr("width",10).attr("height",10),m(t,l),t.intersect=function(r){return w.circle(t,7,r)},a},Pt=(e,t)=>{const a=t.padding/2,i=4,l=8;let r;t.classes?r="node "+t.classes:r="node default";const s=e.insert("g").attr("class",r).attr("id",t.domId||t.id),n=s.insert("rect",":first-child"),c=s.insert("line"),o=s.insert("line");let h=0,y=i;const f=s.insert("g").attr("class","label");let p=0;const d=t.classData.annotations&&t.classData.annotations[0],k=t.classData.annotations[0]?"«"+t.classData.annotations[0]+"»":"",x=f.node().appendChild(R(k,t.labelStyle,!0,!0));let u=x.getBBox();if(H(b().flowchart.htmlLabels)){const v=x.children[0],L=E(x);u=v.getBoundingClientRect(),L.attr("width",u.width),L.attr("height",u.height)}t.classData.annotations[0]&&(y+=u.height+i,h+=u.width);let S=t.classData.label;t.classData.type!==void 0&&t.classData.type!==""&&(b().flowchart.htmlLabels?S+="&lt;"+t.classData.type+"&gt;":S+="<"+t.classData.type+">");const B=f.node().appendChild(R(S,t.labelStyle,!0,!0));E(B).attr("class","classTitle");let C=B.getBBox();if(H(b().flowchart.htmlLabels)){const v=B.children[0],L=E(B);C=v.getBoundingClientRect(),L.attr("width",C.width),L.attr("height",C.height)}y+=C.height+i,C.width>h&&(h=C.width);const X=[];t.classData.members.forEach(v=>{const L=v.getDisplayDetails();let W=L.displayText;b().flowchart.htmlLabels&&(W=W.replace(/</g,"&lt;").replace(/>/g,"&gt;"));const N=f.node().appendChild(R(W,L.cssStyle?L.cssStyle:t.labelStyle,!0,!0));let $=N.getBBox();if(H(b().flowchart.htmlLabels)){const F=N.children[0],A=E(N);$=F.getBoundingClientRect(),A.attr("width",$.width),A.attr("height",$.height)}$.width>h&&(h=$.width),y+=$.height+i,X.push(N)}),y+=l;const D=[];if(t.classData.methods.forEach(v=>{const L=v.getDisplayDetails();let W=L.displayText;b().flowchart.htmlLabels&&(W=W.replace(/</g,"&lt;").replace(/>/g,"&gt;"));const N=f.node().appendChild(R(W,L.cssStyle?L.cssStyle:t.labelStyle,!0,!0));let $=N.getBBox();if(H(b().flowchart.htmlLabels)){const F=N.children[0],A=E(N);$=F.getBoundingClientRect(),A.attr("width",$.width),A.attr("height",$.height)}$.width>h&&(h=$.width),y+=$.height+i,D.push(N)}),y+=l,d){let v=(h-u.width)/2;E(x).attr("transform","translate( "+(-1*h/2+v)+", "+-1*y/2+")"),p=u.height+i}let nt=(h-C.width)/2;return E(B).attr("transform","translate( "+(-1*h/2+nt)+", "+(-1*y/2+p)+")"),p+=C.height+i,c.attr("class","divider").attr("x1",-h/2-a).attr("x2",h/2+a).attr("y1",-y/2-a+l+p).attr("y2",-y/2-a+l+p),p+=l,X.forEach(v=>{E(v).attr("transform","translate( "+-h/2+", "+(-1*y/2+p+l/2)+")");const L=v==null?void 0:v.getBBox();p+=((L==null?void 0:L.height)??0)+i}),p+=l,o.attr("class","divider").attr("x1",-h/2-a).attr("x2",h/2+a).attr("y1",-y/2-a+l+p).attr("y2",-y/2-a+l+p),p+=l,D.forEach(v=>{E(v).attr("transform","translate( "+-h/2+", "+(-1*y/2+p)+")");const L=v==null?void 0:v.getBBox();p+=((L==null?void 0:L.height)??0)+i}),n.attr("style",t.style).attr("class","outer title-state").attr("x",-h/2-a).attr("y",-(y/2)-a).attr("width",h+t.padding).attr("height",y+t.padding),m(t,n),t.intersect=function(v){return w.rect(t,v)},s},rt={rhombus:P,composite:zt,question:P,rect:Ut,labelRect:Zt,rectWithTitle:Gt,choice:Ht,circle:qt,doublecircle:Qt,stadium:Ft,hexagon:It,block_arrow:Nt,rect_left_inv_arrow:Ot,lean_right:Wt,lean_left:Xt,trapezoid:Yt,inv_trapezoid:Dt,rect_right_inv_arrow:At,cylinder:jt,start:Jt,end:Kt,note:$t,subroutine:Vt,fork:tt,join:tt,class_box:Pt};let Y={};const or=async(e,t,a)=>{let i,l;if(t.link){let r;b().securityLevel==="sandbox"?r="_top":t.linkTarget&&(r=t.linkTarget||"_blank"),i=e.insert("svg:a").attr("xlink:href",t.link).attr("target",r),l=await rt[t.shape](i,t,a)}else l=await rt[t.shape](e,t,a),i=l;return t.tooltip&&l.attr("title",t.tooltip),t.class&&l.attr("class","node default "+t.class),i.attr("data-node","true"),i.attr("data-id",t.id),Y[t.id]=i,t.haveCallback&&Y[t.id].attr("class",Y[t.id].attr("class")+" clickable"),i},yr=(e,t)=>{Y[t.id]=e},pr=()=>{Y={}},fr=e=>{const t=Y[e.id];g.trace("Transforming node",e.diff,e,"translate("+(e.x-e.width/2-5)+", "+e.width/2+")");const a=8,i=e.diff||0;return e.clusterNode?t.attr("transform","translate("+(e.x+i-e.width/2)+", "+(e.y-e.height/2-a)+")"):t.attr("transform","translate("+e.x+", "+e.y+")"),i},tr=({flowchart:e})=>{var t,a;const i=((t=e==null?void 0:e.subGraphTitleMargin)==null?void 0:t.top)??0,l=((a=e==null?void 0:e.subGraphTitleMargin)==null?void 0:a.bottom)??0,r=i+l;return{subGraphTitleTopMargin:i,subGraphTitleBottomMargin:l,subGraphTitleTotalMargin:r}},O={aggregation:18,extension:18,composition:18,dependency:6,lollipop:13.5,arrow_point:5.3};function U(e,t){if(e===void 0||t===void 0)return{angle:0,deltaX:0,deltaY:0};e=Z(e),t=Z(t);const[a,i]=[e.x,e.y],[l,r]=[t.x,t.y],s=l-a,n=r-i;return{angle:Math.atan(n/s),deltaX:s,deltaY:n}}const Z=e=>Array.isArray(e)?{x:e[0],y:e[1]}:e,rr=e=>({x:function(t,a,i){let l=0;if(a===0&&Object.hasOwn(O,e.arrowTypeStart)){const{angle:r,deltaX:s}=U(i[0],i[1]);l=O[e.arrowTypeStart]*Math.cos(r)*(s>=0?1:-1)}else if(a===i.length-1&&Object.hasOwn(O,e.arrowTypeEnd)){const{angle:r,deltaX:s}=U(i[i.length-1],i[i.length-2]);l=O[e.arrowTypeEnd]*Math.cos(r)*(s>=0?1:-1)}return Z(t).x+l},y:function(t,a,i){let l=0;if(a===0&&Object.hasOwn(O,e.arrowTypeStart)){const{angle:r,deltaY:s}=U(i[0],i[1]);l=O[e.arrowTypeStart]*Math.abs(Math.sin(r))*(s>=0?1:-1)}else if(a===i.length-1&&Object.hasOwn(O,e.arrowTypeEnd)){const{angle:r,deltaY:s}=U(i[i.length-1],i[i.length-2]);l=O[e.arrowTypeEnd]*Math.abs(Math.sin(r))*(s>=0?1:-1)}return Z(t).y+l}}),ar=(e,t,a,i,l)=>{t.arrowTypeStart&&at(e,"start",t.arrowTypeStart,a,i,l),t.arrowTypeEnd&&at(e,"end",t.arrowTypeEnd,a,i,l)},er={arrow_cross:"cross",arrow_point:"point",arrow_barb:"barb",arrow_circle:"circle",aggregation:"aggregation",extension:"extension",composition:"composition",dependency:"dependency",lollipop:"lollipop"},at=(e,t,a,i,l,r)=>{const s=er[a];if(!s){g.warn(`Unknown arrow type: ${a}`);return}const n=t==="start"?"Start":"End";e.attr(`marker-${t}`,`url(${i}#${l}_${r}-${s}${n})`)};let G={},T={};const xr=()=>{G={},T={}},dr=(e,t)=>{const a=H(b().flowchart.htmlLabels),i=t.labelType==="markdown"?st(e,t.label,{style:t.labelStyle,useHtmlLabels:a,addSvgBackground:!0}):R(t.label,t.labelStyle),l=e.insert("g").attr("class","edgeLabel"),r=l.insert("g").attr("class","label");r.node().appendChild(i);let s=i.getBBox();if(a){const c=i.children[0],o=E(i);s=c.getBoundingClientRect(),o.attr("width",s.width),o.attr("height",s.height)}r.attr("transform","translate("+-s.width/2+", "+-s.height/2+")"),G[t.id]=l,t.width=s.width,t.height=s.height;let n;if(t.startLabelLeft){const c=R(t.startLabelLeft,t.labelStyle),o=e.insert("g").attr("class","edgeTerminals"),h=o.insert("g").attr("class","inner");n=h.node().appendChild(c);const y=c.getBBox();h.attr("transform","translate("+-y.width/2+", "+-y.height/2+")"),T[t.id]||(T[t.id]={}),T[t.id].startLeft=o,z(n,t.startLabelLeft)}if(t.startLabelRight){const c=R(t.startLabelRight,t.labelStyle),o=e.insert("g").attr("class","edgeTerminals"),h=o.insert("g").attr("class","inner");n=o.node().appendChild(c),h.node().appendChild(c);const y=c.getBBox();h.attr("transform","translate("+-y.width/2+", "+-y.height/2+")"),T[t.id]||(T[t.id]={}),T[t.id].startRight=o,z(n,t.startLabelRight)}if(t.endLabelLeft){const c=R(t.endLabelLeft,t.labelStyle),o=e.insert("g").attr("class","edgeTerminals"),h=o.insert("g").attr("class","inner");n=h.node().appendChild(c);const y=c.getBBox();h.attr("transform","translate("+-y.width/2+", "+-y.height/2+")"),o.node().appendChild(c),T[t.id]||(T[t.id]={}),T[t.id].endLeft=o,z(n,t.endLabelLeft)}if(t.endLabelRight){const c=R(t.endLabelRight,t.labelStyle),o=e.insert("g").attr("class","edgeTerminals"),h=o.insert("g").attr("class","inner");n=h.node().appendChild(c);const y=c.getBBox();h.attr("transform","translate("+-y.width/2+", "+-y.height/2+")"),o.node().appendChild(c),T[t.id]||(T[t.id]={}),T[t.id].endRight=o,z(n,t.endLabelRight)}return i};function z(e,t){b().flowchart.htmlLabels&&e&&(e.style.width=t.length*9+"px",e.style.height="12px")}const gr=(e,t)=>{g.debug("Moving label abc88 ",e.id,e.label,G[e.id],t);let a=t.updatedPath?t.updatedPath:t.originalPath;const i=b(),{subGraphTitleTotalMargin:l}=tr(i);if(e.label){const r=G[e.id];let s=e.x,n=e.y;if(a){const c=j.calcLabelPosition(a);g.debug("Moving label "+e.label+" from (",s,",",n,") to (",c.x,",",c.y,") abc88"),t.updatedPath&&(s=c.x,n=c.y)}r.attr("transform",`translate(${s}, ${n+l/2})`)}if(e.startLabelLeft){const r=T[e.id].startLeft;let s=e.x,n=e.y;if(a){const c=j.calcTerminalLabelPosition(e.arrowTypeStart?10:0,"start_left",a);s=c.x,n=c.y}r.attr("transform",`translate(${s}, ${n})`)}if(e.startLabelRight){const r=T[e.id].startRight;let s=e.x,n=e.y;if(a){const c=j.calcTerminalLabelPosition(e.arrowTypeStart?10:0,"start_right",a);s=c.x,n=c.y}r.attr("transform",`translate(${s}, ${n})`)}if(e.endLabelLeft){const r=T[e.id].endLeft;let s=e.x,n=e.y;if(a){const c=j.calcTerminalLabelPosition(e.arrowTypeEnd?10:0,"end_left",a);s=c.x,n=c.y}r.attr("transform",`translate(${s}, ${n})`)}if(e.endLabelRight){const r=T[e.id].endRight;let s=e.x,n=e.y;if(a){const c=j.calcTerminalLabelPosition(e.arrowTypeEnd?10:0,"end_right",a);s=c.x,n=c.y}r.attr("transform",`translate(${s}, ${n})`)}},sr=(e,t)=>{const a=e.x,i=e.y,l=Math.abs(t.x-a),r=Math.abs(t.y-i),s=e.width/2,n=e.height/2;return l>=s||r>=n},ir=(e,t,a)=>{g.debug(`intersection calc abc89:
   outsidePoint: ${JSON.stringify(t)}
   insidePoint : ${JSON.stringify(a)}
   node        : x:${e.x} y:${e.y} w:${e.width} h:${e.height}`);const i=e.x,l=e.y,r=Math.abs(i-a.x),s=e.width/2;let n=a.x<t.x?s-r:s+r;const c=e.height/2,o=Math.abs(t.y-a.y),h=Math.abs(t.x-a.x);if(Math.abs(l-t.y)*s>Math.abs(i-t.x)*c){let y=a.y<t.y?t.y-c-l:l-c-t.y;n=h*y/o;const f={x:a.x<t.x?a.x+n:a.x-h+n,y:a.y<t.y?a.y+o-y:a.y-o+y};return n===0&&(f.x=t.x,f.y=t.y),h===0&&(f.x=t.x),o===0&&(f.y=t.y),g.debug(`abc89 topp/bott calc, Q ${o}, q ${y}, R ${h}, r ${n}`,f),f}else{a.x<t.x?n=t.x-s-i:n=i-s-t.x;let y=o*n/h,f=a.x<t.x?a.x+h-n:a.x-h+n,p=a.y<t.y?a.y+y:a.y-y;return g.debug(`sides calc abc89, Q ${o}, q ${y}, R ${h}, r ${n}`,{_x:f,_y:p}),n===0&&(f=t.x,p=t.y),h===0&&(f=t.x),o===0&&(p=t.y),{x:f,y:p}}},et=(e,t)=>{g.debug("abc88 cutPathAtIntersect",e,t);let a=[],i=e[0],l=!1;return e.forEach(r=>{if(!sr(t,r)&&!l){const s=ir(t,i,r);let n=!1;a.forEach(c=>{n=n||c.x===s.x&&c.y===s.y}),a.some(c=>c.x===s.x&&c.y===s.y)||a.push(s),l=!0}else i=r,l||a.push(r)}),a},ur=function(e,t,a,i,l,r,s){let n=a.points;g.debug("abc88 InsertEdge: edge=",a,"e=",t);let c=!1;const o=r.node(t.v);var h=r.node(t.w);h!=null&&h.intersect&&(o!=null&&o.intersect)&&(n=n.slice(1,a.points.length-1),n.unshift(o.intersect(n[0])),n.push(h.intersect(n[n.length-1]))),a.toCluster&&(g.debug("to cluster abc88",i[a.toCluster]),n=et(a.points,i[a.toCluster].node),c=!0),a.fromCluster&&(g.debug("from cluster abc88",i[a.fromCluster]),n=et(n.reverse(),i[a.fromCluster].node).reverse(),c=!0);const y=n.filter(C=>!Number.isNaN(C.y));let f=lt;a.curve&&(l==="graph"||l==="flowchart")&&(f=a.curve);const{x:p,y:d}=rr(a),k=ct().x(p).y(d).curve(f);let x;switch(a.thickness){case"normal":x="edge-thickness-normal";break;case"thick":x="edge-thickness-thick";break;case"invisible":x="edge-thickness-thick";break;default:x=""}switch(a.pattern){case"solid":x+=" edge-pattern-solid";break;case"dotted":x+=" edge-pattern-dotted";break;case"dashed":x+=" edge-pattern-dashed";break}const u=e.append("path").attr("d",k(y)).attr("id",a.id).attr("class"," "+x+(a.classes?" "+a.classes:"")).attr("style",a.style);let S="";(b().flowchart.arrowMarkerAbsolute||b().state.arrowMarkerAbsolute)&&(S=window.location.protocol+"//"+window.location.host+window.location.pathname+window.location.search,S=S.replace(/\(/g,"\\("),S=S.replace(/\)/g,"\\)")),ar(u,a,S,s,l);let B={};return c&&(B.updatedPath=n),B.originalPath=a.points,B};export{or as a,dr as b,ur as c,gr as d,pr as e,xr as f,tr as g,R as h,hr as i,Et as j,rr as k,M as l,ar as m,fr as p,yr as s,m as u};
diff --git a/assets/end.html-De4ifiEs.js b/assets/end.html-CkqhlgwJ.js
similarity index 97%
rename from assets/end.html-De4ifiEs.js
rename to assets/end.html-CkqhlgwJ.js
index 2fc8ee9..4f88650 100644
--- a/assets/end.html-De4ifiEs.js
+++ b/assets/end.html-CkqhlgwJ.js
@@ -1 +1 @@
-import{_ as n,r,o,c as a,b as e,e as c,d as p}from"./app-B69Gl_S-.js";const s={},i={href:"https://github.com/King-sj/DesignPatterns",target:"_blank",rel:"noopener noreferrer"},l=e("p",null,"使用设计模式的目的是重用代码，并在增加需求时尽量不修改已有的类。我们不应死记硬背这些设计模式，而应理解其背后的核心思想。设计模式的使用不是最终目的，而是为了更好地解决问题和优化代码结构。同时，我们也要避免过早地进行“工程化”，应根据实际需求灵活应用设计模式。",-1),d=e("p",null,"设计模式提供了一种通用的解决方案，可以帮助我们应对软件开发中的常见问题。通过学习和应用设计模式，我们可以提高代码的可读性、可维护性和可扩展性。然而，设计模式并不是万能的，它们也有其局限性和适用范围。在实际开发中，我们需要根据具体情况选择合适的设计模式，而不是盲目地套用。",-1),h=e("p",null,"此外，设计模式的学习和应用需要不断的实践和积累。只有在实际项目中多次使用，才能真正理解和掌握这些模式。我们还应关注设计模式的演变和新模式的出现，以保持我们的知识体系与时俱进。",-1),m=e("p",null,"总之，设计模式是软件开发中的一把利器，但它需要我们在理解其核心思想的基础上，灵活应用于实际项目中。希望通过本章的学习，您能够掌握这些设计模式，并在实际项目中灵活运用它们，编写出更加健壮和优雅的代码。",-1);function g(_,u){const t=r("ExternalLinkIcon");return o(),a("div",null,[e("p",null,[e("a",i,[c("教程源码示例"),p(t)])]),l,d,h,m])}const f=n(s,[["render",g],["__file","end.html.vue"]]),b=JSON.parse('{"path":"/tech/DesignPatterns/end.html","title":"结语","lang":"zh-CN","frontmatter":{"title":"结语","date":"2024-10-29T00:00:00.000Z","category":["设计模式"],"tag":["设计模式","TypeScript"],"prev":"./interpreter","next":false,"description":"教程源码示例 使用设计模式的目的是重用代码，并在增加需求时尽量不修改已有的类。我们不应死记硬背这些设计模式，而应理解其背后的核心思想。设计模式的使用不是最终目的，而是为了更好地解决问题和优化代码结构。同时，我们也要避免过早地进行“工程化”，应根据实际需求灵活应用设计模式。 设计模式提供了一种通用的解决方案，可以帮助我们应对软件开发中的常见问题。通过学习...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/DesignPatterns/end.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"结语"}],["meta",{"property":"og:description","content":"教程源码示例 使用设计模式的目的是重用代码，并在增加需求时尽量不修改已有的类。我们不应死记硬背这些设计模式，而应理解其背后的核心思想。设计模式的使用不是最终目的，而是为了更好地解决问题和优化代码结构。同时，我们也要避免过早地进行“工程化”，应根据实际需求灵活应用设计模式。 设计模式提供了一种通用的解决方案，可以帮助我们应对软件开发中的常见问题。通过学习..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"设计模式"}],["meta",{"property":"article:tag","content":"TypeScript"}],["meta",{"property":"article:published_time","content":"2024-10-29T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"结语\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-10-29T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":1.48,"words":445},"filePathRelative":"tech/DesignPatterns/end.md","localizedDate":"2024年10月29日","excerpt":"<p><a href=\\"https://github.com/King-sj/DesignPatterns\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">教程源码示例</a></p>\\n<p>使用设计模式的目的是重用代码，并在增加需求时尽量不修改已有的类。我们不应死记硬背这些设计模式，而应理解其背后的核心思想。设计模式的使用不是最终目的，而是为了更好地解决问题和优化代码结构。同时，我们也要避免过早地进行“工程化”，应根据实际需求灵活应用设计模式。</p>\\n<p>设计模式提供了一种通用的解决方案，可以帮助我们应对软件开发中的常见问题。通过学习和应用设计模式，我们可以提高代码的可读性、可维护性和可扩展性。然而，设计模式并不是万能的，它们也有其局限性和适用范围。在实际开发中，我们需要根据具体情况选择合适的设计模式，而不是盲目地套用。</p>","autoDesc":true}');export{f as comp,b as data};
+import{_ as n,r,o,c as a,b as e,e as c,d as p}from"./app-B4LGNJZ0.js";const s={},i={href:"https://github.com/King-sj/DesignPatterns",target:"_blank",rel:"noopener noreferrer"},l=e("p",null,"使用设计模式的目的是重用代码，并在增加需求时尽量不修改已有的类。我们不应死记硬背这些设计模式，而应理解其背后的核心思想。设计模式的使用不是最终目的，而是为了更好地解决问题和优化代码结构。同时，我们也要避免过早地进行“工程化”，应根据实际需求灵活应用设计模式。",-1),d=e("p",null,"设计模式提供了一种通用的解决方案，可以帮助我们应对软件开发中的常见问题。通过学习和应用设计模式，我们可以提高代码的可读性、可维护性和可扩展性。然而，设计模式并不是万能的，它们也有其局限性和适用范围。在实际开发中，我们需要根据具体情况选择合适的设计模式，而不是盲目地套用。",-1),h=e("p",null,"此外，设计模式的学习和应用需要不断的实践和积累。只有在实际项目中多次使用，才能真正理解和掌握这些模式。我们还应关注设计模式的演变和新模式的出现，以保持我们的知识体系与时俱进。",-1),m=e("p",null,"总之，设计模式是软件开发中的一把利器，但它需要我们在理解其核心思想的基础上，灵活应用于实际项目中。希望通过本章的学习，您能够掌握这些设计模式，并在实际项目中灵活运用它们，编写出更加健壮和优雅的代码。",-1);function g(_,u){const t=r("ExternalLinkIcon");return o(),a("div",null,[e("p",null,[e("a",i,[c("教程源码示例"),p(t)])]),l,d,h,m])}const f=n(s,[["render",g],["__file","end.html.vue"]]),b=JSON.parse('{"path":"/tech/DesignPatterns/end.html","title":"结语","lang":"zh-CN","frontmatter":{"title":"结语","date":"2024-10-29T00:00:00.000Z","category":["设计模式"],"tag":["设计模式","TypeScript"],"prev":"./interpreter","next":false,"description":"教程源码示例 使用设计模式的目的是重用代码，并在增加需求时尽量不修改已有的类。我们不应死记硬背这些设计模式，而应理解其背后的核心思想。设计模式的使用不是最终目的，而是为了更好地解决问题和优化代码结构。同时，我们也要避免过早地进行“工程化”，应根据实际需求灵活应用设计模式。 设计模式提供了一种通用的解决方案，可以帮助我们应对软件开发中的常见问题。通过学习...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/DesignPatterns/end.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"结语"}],["meta",{"property":"og:description","content":"教程源码示例 使用设计模式的目的是重用代码，并在增加需求时尽量不修改已有的类。我们不应死记硬背这些设计模式，而应理解其背后的核心思想。设计模式的使用不是最终目的，而是为了更好地解决问题和优化代码结构。同时，我们也要避免过早地进行“工程化”，应根据实际需求灵活应用设计模式。 设计模式提供了一种通用的解决方案，可以帮助我们应对软件开发中的常见问题。通过学习..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"设计模式"}],["meta",{"property":"article:tag","content":"TypeScript"}],["meta",{"property":"article:published_time","content":"2024-10-29T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"结语\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-10-29T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":1.48,"words":445},"filePathRelative":"tech/DesignPatterns/end.md","localizedDate":"2024年10月29日","excerpt":"<p><a href=\\"https://github.com/King-sj/DesignPatterns\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">教程源码示例</a></p>\\n<p>使用设计模式的目的是重用代码，并在增加需求时尽量不修改已有的类。我们不应死记硬背这些设计模式，而应理解其背后的核心思想。设计模式的使用不是最终目的，而是为了更好地解决问题和优化代码结构。同时，我们也要避免过早地进行“工程化”，应根据实际需求灵活应用设计模式。</p>\\n<p>设计模式提供了一种通用的解决方案，可以帮助我们应对软件开发中的常见问题。通过学习和应用设计模式，我们可以提高代码的可读性、可维护性和可扩展性。然而，设计模式并不是万能的，它们也有其局限性和适用范围。在实际开发中，我们需要根据具体情况选择合适的设计模式，而不是盲目地套用。</p>","autoDesc":true}');export{f as comp,b as data};
diff --git a/assets/erDiagram-51d2b61e-BxYe-GEp.js b/assets/erDiagram-51d2b61e-D5StoYmd.js
similarity index 99%
rename from assets/erDiagram-51d2b61e-BxYe-GEp.js
rename to assets/erDiagram-51d2b61e-D5StoYmd.js
index f94dfea..e1a001f 100644
--- a/assets/erDiagram-51d2b61e-BxYe-GEp.js
+++ b/assets/erDiagram-51d2b61e-D5StoYmd.js
@@ -1,4 +1,4 @@
-import{c as Z,s as Et,g as mt,b as gt,a as kt,x as xt,y as Rt,l as V,A as Ot,h as rt,z as bt,i as Nt,ao as Tt,ar as At}from"./mermaid.core-ChLYKTZm.js";import{G as Mt}from"./graph-T5JS4vfK.js";import{l as St}from"./layout-DUYLy6Ue.js";import{l as wt}from"./line-D0jG_HZ-.js";import"./app-B69Gl_S-.js";import"./array-BKyUJesY.js";import"./path-CbwjOpE9.js";const It=/^(?:[0-9a-f]{8}-[0-9a-f]{4}-[1-5][0-9a-f]{3}-[89ab][0-9a-f]{3}-[0-9a-f]{12}|00000000-0000-0000-0000-000000000000)$/i;function Dt(t){return typeof t=="string"&&It.test(t)}const A=[];for(let t=0;t<256;++t)A.push((t+256).toString(16).slice(1));function vt(t,e=0){return A[t[e+0]]+A[t[e+1]]+A[t[e+2]]+A[t[e+3]]+"-"+A[t[e+4]]+A[t[e+5]]+"-"+A[t[e+6]]+A[t[e+7]]+"-"+A[t[e+8]]+A[t[e+9]]+"-"+A[t[e+10]]+A[t[e+11]]+A[t[e+12]]+A[t[e+13]]+A[t[e+14]]+A[t[e+15]]}function Lt(t){if(!Dt(t))throw TypeError("Invalid UUID");let e;const r=new Uint8Array(16);return r[0]=(e=parseInt(t.slice(0,8),16))>>>24,r[1]=e>>>16&255,r[2]=e>>>8&255,r[3]=e&255,r[4]=(e=parseInt(t.slice(9,13),16))>>>8,r[5]=e&255,r[6]=(e=parseInt(t.slice(14,18),16))>>>8,r[7]=e&255,r[8]=(e=parseInt(t.slice(19,23),16))>>>8,r[9]=e&255,r[10]=(e=parseInt(t.slice(24,36),16))/1099511627776&255,r[11]=e/4294967296&255,r[12]=e>>>24&255,r[13]=e>>>16&255,r[14]=e>>>8&255,r[15]=e&255,r}function Bt(t){t=unescape(encodeURIComponent(t));const e=[];for(let r=0;r<t.length;++r)e.push(t.charCodeAt(r));return e}const Ct="6ba7b810-9dad-11d1-80b4-00c04fd430c8",Pt="6ba7b811-9dad-11d1-80b4-00c04fd430c8";function Yt(t,e,r){function u(l,p,f,o){var h;if(typeof l=="string"&&(l=Bt(l)),typeof p=="string"&&(p=Lt(p)),((h=p)===null||h===void 0?void 0:h.length)!==16)throw TypeError("Namespace must be array-like (16 iterable integer values, 0-255)");let _=new Uint8Array(16+l.length);if(_.set(p),_.set(l,p.length),_=r(_),_[6]=_[6]&15|e,_[8]=_[8]&63|128,f){o=o||0;for(let m=0;m<16;++m)f[o+m]=_[m];return f}return vt(_)}try{u.name=t}catch{}return u.DNS=Ct,u.URL=Pt,u}function Zt(t,e,r,u){switch(t){case 0:return e&r^~e&u;case 1:return e^r^u;case 2:return e&r^e&u^r&u;case 3:return e^r^u}}function it(t,e){return t<<e|t>>>32-e}function Ft(t){const e=[1518500249,1859775393,2400959708,3395469782],r=[1732584193,4023233417,2562383102,271733878,3285377520];if(typeof t=="string"){const f=unescape(encodeURIComponent(t));t=[];for(let o=0;o<f.length;++o)t.push(f.charCodeAt(o))}else Array.isArray(t)||(t=Array.prototype.slice.call(t));t.push(128);const u=t.length/4+2,l=Math.ceil(u/16),p=new Array(l);for(let f=0;f<l;++f){const o=new Uint32Array(16);for(let h=0;h<16;++h)o[h]=t[f*64+h*4]<<24|t[f*64+h*4+1]<<16|t[f*64+h*4+2]<<8|t[f*64+h*4+3];p[f]=o}p[l-1][14]=(t.length-1)*8/Math.pow(2,32),p[l-1][14]=Math.floor(p[l-1][14]),p[l-1][15]=(t.length-1)*8&4294967295;for(let f=0;f<l;++f){const o=new Uint32Array(80);for(let y=0;y<16;++y)o[y]=p[f][y];for(let y=16;y<80;++y)o[y]=it(o[y-3]^o[y-8]^o[y-14]^o[y-16],1);let h=r[0],_=r[1],m=r[2],g=r[3],x=r[4];for(let y=0;y<80;++y){const N=Math.floor(y/20),I=it(h,5)+Zt(N,_,m,g)+x+e[N]+o[y]>>>0;x=g,g=m,m=it(_,30)>>>0,_=h,h=I}r[0]=r[0]+h>>>0,r[1]=r[1]+_>>>0,r[2]=r[2]+m>>>0,r[3]=r[3]+g>>>0,r[4]=r[4]+x>>>0}return[r[0]>>24&255,r[0]>>16&255,r[0]>>8&255,r[0]&255,r[1]>>24&255,r[1]>>16&255,r[1]>>8&255,r[1]&255,r[2]>>24&255,r[2]>>16&255,r[2]>>8&255,r[2]&255,r[3]>>24&255,r[3]>>16&255,r[3]>>8&255,r[3]&255,r[4]>>24&255,r[4]>>16&255,r[4]>>8&255,r[4]&255]}const Wt=Yt("v5",80,Ft);var at=function(){var t=function(S,a,n,c){for(n=n||{},c=S.length;c--;n[S[c]]=a);return n},e=[6,8,10,20,22,24,26,27,28],r=[1,10],u=[1,11],l=[1,12],p=[1,13],f=[1,14],o=[1,15],h=[1,21],_=[1,22],m=[1,23],g=[1,24],x=[1,25],y=[6,8,10,13,15,18,19,20,22,24,26,27,28,41,42,43,44,45],N=[1,34],I=[27,28,46,47],F=[41,42,43,44,45],W=[17,34],C=[1,54],T=[1,53],M=[17,34,36,38],R={trace:function(){},yy:{},symbols_:{error:2,start:3,ER_DIAGRAM:4,document:5,EOF:6,line:7,SPACE:8,statement:9,NEWLINE:10,entityName:11,relSpec:12,":":13,role:14,BLOCK_START:15,attributes:16,BLOCK_STOP:17,SQS:18,SQE:19,title:20,title_value:21,acc_title:22,acc_title_value:23,acc_descr:24,acc_descr_value:25,acc_descr_multiline_value:26,ALPHANUM:27,ENTITY_NAME:28,attribute:29,attributeType:30,attributeName:31,attributeKeyTypeList:32,attributeComment:33,ATTRIBUTE_WORD:34,attributeKeyType:35,COMMA:36,ATTRIBUTE_KEY:37,COMMENT:38,cardinality:39,relType:40,ZERO_OR_ONE:41,ZERO_OR_MORE:42,ONE_OR_MORE:43,ONLY_ONE:44,MD_PARENT:45,NON_IDENTIFYING:46,IDENTIFYING:47,WORD:48,$accept:0,$end:1},terminals_:{2:"error",4:"ER_DIAGRAM",6:"EOF",8:"SPACE",10:"NEWLINE",13:":",15:"BLOCK_START",17:"BLOCK_STOP",18:"SQS",19:"SQE",20:"title",21:"title_value",22:"acc_title",23:"acc_title_value",24:"acc_descr",25:"acc_descr_value",26:"acc_descr_multiline_value",27:"ALPHANUM",28:"ENTITY_NAME",34:"ATTRIBUTE_WORD",36:"COMMA",37:"ATTRIBUTE_KEY",38:"COMMENT",41:"ZERO_OR_ONE",42:"ZERO_OR_MORE",43:"ONE_OR_MORE",44:"ONLY_ONE",45:"MD_PARENT",46:"NON_IDENTIFYING",47:"IDENTIFYING",48:"WORD"},productions_:[0,[3,3],[5,0],[5,2],[7,2],[7,1],[7,1],[7,1],[9,5],[9,4],[9,3],[9,1],[9,7],[9,6],[9,4],[9,2],[9,2],[9,2],[9,1],[11,1],[11,1],[16,1],[16,2],[29,2],[29,3],[29,3],[29,4],[30,1],[31,1],[32,1],[32,3],[35,1],[33,1],[12,3],[39,1],[39,1],[39,1],[39,1],[39,1],[40,1],[40,1],[14,1],[14,1],[14,1]],performAction:function(a,n,c,d,E,i,K){var s=i.length-1;switch(E){case 1:break;case 2:this.$=[];break;case 3:i[s-1].push(i[s]),this.$=i[s-1];break;case 4:case 5:this.$=i[s];break;case 6:case 7:this.$=[];break;case 8:d.addEntity(i[s-4]),d.addEntity(i[s-2]),d.addRelationship(i[s-4],i[s],i[s-2],i[s-3]);break;case 9:d.addEntity(i[s-3]),d.addAttributes(i[s-3],i[s-1]);break;case 10:d.addEntity(i[s-2]);break;case 11:d.addEntity(i[s]);break;case 12:d.addEntity(i[s-6],i[s-4]),d.addAttributes(i[s-6],i[s-1]);break;case 13:d.addEntity(i[s-5],i[s-3]);break;case 14:d.addEntity(i[s-3],i[s-1]);break;case 15:case 16:this.$=i[s].trim(),d.setAccTitle(this.$);break;case 17:case 18:this.$=i[s].trim(),d.setAccDescription(this.$);break;case 19:case 43:this.$=i[s];break;case 20:case 41:case 42:this.$=i[s].replace(/"/g,"");break;case 21:case 29:this.$=[i[s]];break;case 22:i[s].push(i[s-1]),this.$=i[s];break;case 23:this.$={attributeType:i[s-1],attributeName:i[s]};break;case 24:this.$={attributeType:i[s-2],attributeName:i[s-1],attributeKeyTypeList:i[s]};break;case 25:this.$={attributeType:i[s-2],attributeName:i[s-1],attributeComment:i[s]};break;case 26:this.$={attributeType:i[s-3],attributeName:i[s-2],attributeKeyTypeList:i[s-1],attributeComment:i[s]};break;case 27:case 28:case 31:this.$=i[s];break;case 30:i[s-2].push(i[s]),this.$=i[s-2];break;case 32:this.$=i[s].replace(/"/g,"");break;case 33:this.$={cardA:i[s],relType:i[s-1],cardB:i[s-2]};break;case 34:this.$=d.Cardinality.ZERO_OR_ONE;break;case 35:this.$=d.Cardinality.ZERO_OR_MORE;break;case 36:this.$=d.Cardinality.ONE_OR_MORE;break;case 37:this.$=d.Cardinality.ONLY_ONE;break;case 38:this.$=d.Cardinality.MD_PARENT;break;case 39:this.$=d.Identification.NON_IDENTIFYING;break;case 40:this.$=d.Identification.IDENTIFYING;break}},table:[{3:1,4:[1,2]},{1:[3]},t(e,[2,2],{5:3}),{6:[1,4],7:5,8:[1,6],9:7,10:[1,8],11:9,20:r,22:u,24:l,26:p,27:f,28:o},t(e,[2,7],{1:[2,1]}),t(e,[2,3]),{9:16,11:9,20:r,22:u,24:l,26:p,27:f,28:o},t(e,[2,5]),t(e,[2,6]),t(e,[2,11],{12:17,39:20,15:[1,18],18:[1,19],41:h,42:_,43:m,44:g,45:x}),{21:[1,26]},{23:[1,27]},{25:[1,28]},t(e,[2,18]),t(y,[2,19]),t(y,[2,20]),t(e,[2,4]),{11:29,27:f,28:o},{16:30,17:[1,31],29:32,30:33,34:N},{11:35,27:f,28:o},{40:36,46:[1,37],47:[1,38]},t(I,[2,34]),t(I,[2,35]),t(I,[2,36]),t(I,[2,37]),t(I,[2,38]),t(e,[2,15]),t(e,[2,16]),t(e,[2,17]),{13:[1,39]},{17:[1,40]},t(e,[2,10]),{16:41,17:[2,21],29:32,30:33,34:N},{31:42,34:[1,43]},{34:[2,27]},{19:[1,44]},{39:45,41:h,42:_,43:m,44:g,45:x},t(F,[2,39]),t(F,[2,40]),{14:46,27:[1,49],28:[1,48],48:[1,47]},t(e,[2,9]),{17:[2,22]},t(W,[2,23],{32:50,33:51,35:52,37:C,38:T}),t([17,34,37,38],[2,28]),t(e,[2,14],{15:[1,55]}),t([27,28],[2,33]),t(e,[2,8]),t(e,[2,41]),t(e,[2,42]),t(e,[2,43]),t(W,[2,24],{33:56,36:[1,57],38:T}),t(W,[2,25]),t(M,[2,29]),t(W,[2,32]),t(M,[2,31]),{16:58,17:[1,59],29:32,30:33,34:N},t(W,[2,26]),{35:60,37:C},{17:[1,61]},t(e,[2,13]),t(M,[2,30]),t(e,[2,12])],defaultActions:{34:[2,27],41:[2,22]},parseError:function(a,n){if(n.recoverable)this.trace(a);else{var c=new Error(a);throw c.hash=n,c}},parse:function(a){var n=this,c=[0],d=[],E=[null],i=[],K=this.table,s="",Q=0,st=0,ft=2,ot=1,yt=i.slice.call(arguments,1),b=Object.create(this.lexer),z={yy:{}};for(var J in this.yy)Object.prototype.hasOwnProperty.call(this.yy,J)&&(z.yy[J]=this.yy[J]);b.setInput(a,z.yy),z.yy.lexer=b,z.yy.parser=this,typeof b.yylloc>"u"&&(b.yylloc={});var $=b.yylloc;i.push($);var pt=b.options&&b.options.ranges;typeof z.yy.parseError=="function"?this.parseError=z.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function _t(){var Y;return Y=d.pop()||b.lex()||ot,typeof Y!="number"&&(Y instanceof Array&&(d=Y,Y=d.pop()),Y=n.symbols_[Y]||Y),Y}for(var w,H,D,tt,G={},j,P,lt,q;;){if(H=c[c.length-1],this.defaultActions[H]?D=this.defaultActions[H]:((w===null||typeof w>"u")&&(w=_t()),D=K[H]&&K[H][w]),typeof D>"u"||!D.length||!D[0]){var et="";q=[];for(j in K[H])this.terminals_[j]&&j>ft&&q.push("'"+this.terminals_[j]+"'");b.showPosition?et="Parse error on line "+(Q+1)+`:
+import{c as Z,s as Et,g as mt,b as gt,a as kt,x as xt,y as Rt,l as V,A as Ot,h as rt,z as bt,i as Nt,ao as Tt,ar as At}from"./mermaid.core-DNo_7Q2B.js";import{G as Mt}from"./graph-B1296pfd.js";import{l as St}from"./layout-qMafh1ee.js";import{l as wt}from"./line-BqHmcuby.js";import"./app-B4LGNJZ0.js";import"./array-BKyUJesY.js";import"./path-CbwjOpE9.js";const It=/^(?:[0-9a-f]{8}-[0-9a-f]{4}-[1-5][0-9a-f]{3}-[89ab][0-9a-f]{3}-[0-9a-f]{12}|00000000-0000-0000-0000-000000000000)$/i;function Dt(t){return typeof t=="string"&&It.test(t)}const A=[];for(let t=0;t<256;++t)A.push((t+256).toString(16).slice(1));function vt(t,e=0){return A[t[e+0]]+A[t[e+1]]+A[t[e+2]]+A[t[e+3]]+"-"+A[t[e+4]]+A[t[e+5]]+"-"+A[t[e+6]]+A[t[e+7]]+"-"+A[t[e+8]]+A[t[e+9]]+"-"+A[t[e+10]]+A[t[e+11]]+A[t[e+12]]+A[t[e+13]]+A[t[e+14]]+A[t[e+15]]}function Lt(t){if(!Dt(t))throw TypeError("Invalid UUID");let e;const r=new Uint8Array(16);return r[0]=(e=parseInt(t.slice(0,8),16))>>>24,r[1]=e>>>16&255,r[2]=e>>>8&255,r[3]=e&255,r[4]=(e=parseInt(t.slice(9,13),16))>>>8,r[5]=e&255,r[6]=(e=parseInt(t.slice(14,18),16))>>>8,r[7]=e&255,r[8]=(e=parseInt(t.slice(19,23),16))>>>8,r[9]=e&255,r[10]=(e=parseInt(t.slice(24,36),16))/1099511627776&255,r[11]=e/4294967296&255,r[12]=e>>>24&255,r[13]=e>>>16&255,r[14]=e>>>8&255,r[15]=e&255,r}function Bt(t){t=unescape(encodeURIComponent(t));const e=[];for(let r=0;r<t.length;++r)e.push(t.charCodeAt(r));return e}const Ct="6ba7b810-9dad-11d1-80b4-00c04fd430c8",Pt="6ba7b811-9dad-11d1-80b4-00c04fd430c8";function Yt(t,e,r){function u(l,p,f,o){var h;if(typeof l=="string"&&(l=Bt(l)),typeof p=="string"&&(p=Lt(p)),((h=p)===null||h===void 0?void 0:h.length)!==16)throw TypeError("Namespace must be array-like (16 iterable integer values, 0-255)");let _=new Uint8Array(16+l.length);if(_.set(p),_.set(l,p.length),_=r(_),_[6]=_[6]&15|e,_[8]=_[8]&63|128,f){o=o||0;for(let m=0;m<16;++m)f[o+m]=_[m];return f}return vt(_)}try{u.name=t}catch{}return u.DNS=Ct,u.URL=Pt,u}function Zt(t,e,r,u){switch(t){case 0:return e&r^~e&u;case 1:return e^r^u;case 2:return e&r^e&u^r&u;case 3:return e^r^u}}function it(t,e){return t<<e|t>>>32-e}function Ft(t){const e=[1518500249,1859775393,2400959708,3395469782],r=[1732584193,4023233417,2562383102,271733878,3285377520];if(typeof t=="string"){const f=unescape(encodeURIComponent(t));t=[];for(let o=0;o<f.length;++o)t.push(f.charCodeAt(o))}else Array.isArray(t)||(t=Array.prototype.slice.call(t));t.push(128);const u=t.length/4+2,l=Math.ceil(u/16),p=new Array(l);for(let f=0;f<l;++f){const o=new Uint32Array(16);for(let h=0;h<16;++h)o[h]=t[f*64+h*4]<<24|t[f*64+h*4+1]<<16|t[f*64+h*4+2]<<8|t[f*64+h*4+3];p[f]=o}p[l-1][14]=(t.length-1)*8/Math.pow(2,32),p[l-1][14]=Math.floor(p[l-1][14]),p[l-1][15]=(t.length-1)*8&4294967295;for(let f=0;f<l;++f){const o=new Uint32Array(80);for(let y=0;y<16;++y)o[y]=p[f][y];for(let y=16;y<80;++y)o[y]=it(o[y-3]^o[y-8]^o[y-14]^o[y-16],1);let h=r[0],_=r[1],m=r[2],g=r[3],x=r[4];for(let y=0;y<80;++y){const N=Math.floor(y/20),I=it(h,5)+Zt(N,_,m,g)+x+e[N]+o[y]>>>0;x=g,g=m,m=it(_,30)>>>0,_=h,h=I}r[0]=r[0]+h>>>0,r[1]=r[1]+_>>>0,r[2]=r[2]+m>>>0,r[3]=r[3]+g>>>0,r[4]=r[4]+x>>>0}return[r[0]>>24&255,r[0]>>16&255,r[0]>>8&255,r[0]&255,r[1]>>24&255,r[1]>>16&255,r[1]>>8&255,r[1]&255,r[2]>>24&255,r[2]>>16&255,r[2]>>8&255,r[2]&255,r[3]>>24&255,r[3]>>16&255,r[3]>>8&255,r[3]&255,r[4]>>24&255,r[4]>>16&255,r[4]>>8&255,r[4]&255]}const Wt=Yt("v5",80,Ft);var at=function(){var t=function(S,a,n,c){for(n=n||{},c=S.length;c--;n[S[c]]=a);return n},e=[6,8,10,20,22,24,26,27,28],r=[1,10],u=[1,11],l=[1,12],p=[1,13],f=[1,14],o=[1,15],h=[1,21],_=[1,22],m=[1,23],g=[1,24],x=[1,25],y=[6,8,10,13,15,18,19,20,22,24,26,27,28,41,42,43,44,45],N=[1,34],I=[27,28,46,47],F=[41,42,43,44,45],W=[17,34],C=[1,54],T=[1,53],M=[17,34,36,38],R={trace:function(){},yy:{},symbols_:{error:2,start:3,ER_DIAGRAM:4,document:5,EOF:6,line:7,SPACE:8,statement:9,NEWLINE:10,entityName:11,relSpec:12,":":13,role:14,BLOCK_START:15,attributes:16,BLOCK_STOP:17,SQS:18,SQE:19,title:20,title_value:21,acc_title:22,acc_title_value:23,acc_descr:24,acc_descr_value:25,acc_descr_multiline_value:26,ALPHANUM:27,ENTITY_NAME:28,attribute:29,attributeType:30,attributeName:31,attributeKeyTypeList:32,attributeComment:33,ATTRIBUTE_WORD:34,attributeKeyType:35,COMMA:36,ATTRIBUTE_KEY:37,COMMENT:38,cardinality:39,relType:40,ZERO_OR_ONE:41,ZERO_OR_MORE:42,ONE_OR_MORE:43,ONLY_ONE:44,MD_PARENT:45,NON_IDENTIFYING:46,IDENTIFYING:47,WORD:48,$accept:0,$end:1},terminals_:{2:"error",4:"ER_DIAGRAM",6:"EOF",8:"SPACE",10:"NEWLINE",13:":",15:"BLOCK_START",17:"BLOCK_STOP",18:"SQS",19:"SQE",20:"title",21:"title_value",22:"acc_title",23:"acc_title_value",24:"acc_descr",25:"acc_descr_value",26:"acc_descr_multiline_value",27:"ALPHANUM",28:"ENTITY_NAME",34:"ATTRIBUTE_WORD",36:"COMMA",37:"ATTRIBUTE_KEY",38:"COMMENT",41:"ZERO_OR_ONE",42:"ZERO_OR_MORE",43:"ONE_OR_MORE",44:"ONLY_ONE",45:"MD_PARENT",46:"NON_IDENTIFYING",47:"IDENTIFYING",48:"WORD"},productions_:[0,[3,3],[5,0],[5,2],[7,2],[7,1],[7,1],[7,1],[9,5],[9,4],[9,3],[9,1],[9,7],[9,6],[9,4],[9,2],[9,2],[9,2],[9,1],[11,1],[11,1],[16,1],[16,2],[29,2],[29,3],[29,3],[29,4],[30,1],[31,1],[32,1],[32,3],[35,1],[33,1],[12,3],[39,1],[39,1],[39,1],[39,1],[39,1],[40,1],[40,1],[14,1],[14,1],[14,1]],performAction:function(a,n,c,d,E,i,K){var s=i.length-1;switch(E){case 1:break;case 2:this.$=[];break;case 3:i[s-1].push(i[s]),this.$=i[s-1];break;case 4:case 5:this.$=i[s];break;case 6:case 7:this.$=[];break;case 8:d.addEntity(i[s-4]),d.addEntity(i[s-2]),d.addRelationship(i[s-4],i[s],i[s-2],i[s-3]);break;case 9:d.addEntity(i[s-3]),d.addAttributes(i[s-3],i[s-1]);break;case 10:d.addEntity(i[s-2]);break;case 11:d.addEntity(i[s]);break;case 12:d.addEntity(i[s-6],i[s-4]),d.addAttributes(i[s-6],i[s-1]);break;case 13:d.addEntity(i[s-5],i[s-3]);break;case 14:d.addEntity(i[s-3],i[s-1]);break;case 15:case 16:this.$=i[s].trim(),d.setAccTitle(this.$);break;case 17:case 18:this.$=i[s].trim(),d.setAccDescription(this.$);break;case 19:case 43:this.$=i[s];break;case 20:case 41:case 42:this.$=i[s].replace(/"/g,"");break;case 21:case 29:this.$=[i[s]];break;case 22:i[s].push(i[s-1]),this.$=i[s];break;case 23:this.$={attributeType:i[s-1],attributeName:i[s]};break;case 24:this.$={attributeType:i[s-2],attributeName:i[s-1],attributeKeyTypeList:i[s]};break;case 25:this.$={attributeType:i[s-2],attributeName:i[s-1],attributeComment:i[s]};break;case 26:this.$={attributeType:i[s-3],attributeName:i[s-2],attributeKeyTypeList:i[s-1],attributeComment:i[s]};break;case 27:case 28:case 31:this.$=i[s];break;case 30:i[s-2].push(i[s]),this.$=i[s-2];break;case 32:this.$=i[s].replace(/"/g,"");break;case 33:this.$={cardA:i[s],relType:i[s-1],cardB:i[s-2]};break;case 34:this.$=d.Cardinality.ZERO_OR_ONE;break;case 35:this.$=d.Cardinality.ZERO_OR_MORE;break;case 36:this.$=d.Cardinality.ONE_OR_MORE;break;case 37:this.$=d.Cardinality.ONLY_ONE;break;case 38:this.$=d.Cardinality.MD_PARENT;break;case 39:this.$=d.Identification.NON_IDENTIFYING;break;case 40:this.$=d.Identification.IDENTIFYING;break}},table:[{3:1,4:[1,2]},{1:[3]},t(e,[2,2],{5:3}),{6:[1,4],7:5,8:[1,6],9:7,10:[1,8],11:9,20:r,22:u,24:l,26:p,27:f,28:o},t(e,[2,7],{1:[2,1]}),t(e,[2,3]),{9:16,11:9,20:r,22:u,24:l,26:p,27:f,28:o},t(e,[2,5]),t(e,[2,6]),t(e,[2,11],{12:17,39:20,15:[1,18],18:[1,19],41:h,42:_,43:m,44:g,45:x}),{21:[1,26]},{23:[1,27]},{25:[1,28]},t(e,[2,18]),t(y,[2,19]),t(y,[2,20]),t(e,[2,4]),{11:29,27:f,28:o},{16:30,17:[1,31],29:32,30:33,34:N},{11:35,27:f,28:o},{40:36,46:[1,37],47:[1,38]},t(I,[2,34]),t(I,[2,35]),t(I,[2,36]),t(I,[2,37]),t(I,[2,38]),t(e,[2,15]),t(e,[2,16]),t(e,[2,17]),{13:[1,39]},{17:[1,40]},t(e,[2,10]),{16:41,17:[2,21],29:32,30:33,34:N},{31:42,34:[1,43]},{34:[2,27]},{19:[1,44]},{39:45,41:h,42:_,43:m,44:g,45:x},t(F,[2,39]),t(F,[2,40]),{14:46,27:[1,49],28:[1,48],48:[1,47]},t(e,[2,9]),{17:[2,22]},t(W,[2,23],{32:50,33:51,35:52,37:C,38:T}),t([17,34,37,38],[2,28]),t(e,[2,14],{15:[1,55]}),t([27,28],[2,33]),t(e,[2,8]),t(e,[2,41]),t(e,[2,42]),t(e,[2,43]),t(W,[2,24],{33:56,36:[1,57],38:T}),t(W,[2,25]),t(M,[2,29]),t(W,[2,32]),t(M,[2,31]),{16:58,17:[1,59],29:32,30:33,34:N},t(W,[2,26]),{35:60,37:C},{17:[1,61]},t(e,[2,13]),t(M,[2,30]),t(e,[2,12])],defaultActions:{34:[2,27],41:[2,22]},parseError:function(a,n){if(n.recoverable)this.trace(a);else{var c=new Error(a);throw c.hash=n,c}},parse:function(a){var n=this,c=[0],d=[],E=[null],i=[],K=this.table,s="",Q=0,st=0,ft=2,ot=1,yt=i.slice.call(arguments,1),b=Object.create(this.lexer),z={yy:{}};for(var J in this.yy)Object.prototype.hasOwnProperty.call(this.yy,J)&&(z.yy[J]=this.yy[J]);b.setInput(a,z.yy),z.yy.lexer=b,z.yy.parser=this,typeof b.yylloc>"u"&&(b.yylloc={});var $=b.yylloc;i.push($);var pt=b.options&&b.options.ranges;typeof z.yy.parseError=="function"?this.parseError=z.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function _t(){var Y;return Y=d.pop()||b.lex()||ot,typeof Y!="number"&&(Y instanceof Array&&(d=Y,Y=d.pop()),Y=n.symbols_[Y]||Y),Y}for(var w,H,D,tt,G={},j,P,lt,q;;){if(H=c[c.length-1],this.defaultActions[H]?D=this.defaultActions[H]:((w===null||typeof w>"u")&&(w=_t()),D=K[H]&&K[H][w]),typeof D>"u"||!D.length||!D[0]){var et="";q=[];for(j in K[H])this.terminals_[j]&&j>ft&&q.push("'"+this.terminals_[j]+"'");b.showPosition?et="Parse error on line "+(Q+1)+`:
 `+b.showPosition()+`
 Expecting `+q.join(", ")+", got '"+(this.terminals_[w]||w)+"'":et="Parse error on line "+(Q+1)+": Unexpected "+(w==ot?"end of input":"'"+(this.terminals_[w]||w)+"'"),this.parseError(et,{text:b.match,token:this.terminals_[w]||w,line:b.yylineno,loc:$,expected:q})}if(D[0]instanceof Array&&D.length>1)throw new Error("Parse Error: multiple actions possible at state: "+H+", token: "+w);switch(D[0]){case 1:c.push(w),E.push(b.yytext),i.push(b.yylloc),c.push(D[1]),w=null,st=b.yyleng,s=b.yytext,Q=b.yylineno,$=b.yylloc;break;case 2:if(P=this.productions_[D[1]][1],G.$=E[E.length-P],G._$={first_line:i[i.length-(P||1)].first_line,last_line:i[i.length-1].last_line,first_column:i[i.length-(P||1)].first_column,last_column:i[i.length-1].last_column},pt&&(G._$.range=[i[i.length-(P||1)].range[0],i[i.length-1].range[1]]),tt=this.performAction.apply(G,[s,st,Q,z.yy,D[1],E,i].concat(yt)),typeof tt<"u")return tt;P&&(c=c.slice(0,-1*P*2),E=E.slice(0,-1*P),i=i.slice(0,-1*P)),c.push(this.productions_[D[1]][0]),E.push(G.$),i.push(G._$),lt=K[c[c.length-2]][c[c.length-1]],c.push(lt);break;case 3:return!0}}return!0}},O=function(){var S={EOF:1,parseError:function(n,c){if(this.yy.parser)this.yy.parser.parseError(n,c);else throw new Error(n)},setInput:function(a,n){return this.yy=n||this.yy||{},this._input=a,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var a=this._input[0];this.yytext+=a,this.yyleng++,this.offset++,this.match+=a,this.matched+=a;var n=a.match(/(?:\r\n?|\n).*/g);return n?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),a},unput:function(a){var n=a.length,c=a.split(/(?:\r\n?|\n)/g);this._input=a+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-n),this.offset-=n;var d=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),c.length-1&&(this.yylineno-=c.length-1);var E=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:c?(c.length===d.length?this.yylloc.first_column:0)+d[d.length-c.length].length-c[0].length:this.yylloc.first_column-n},this.options.ranges&&(this.yylloc.range=[E[0],E[0]+this.yyleng-n]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){if(this.options.backtrack_lexer)this._backtrack=!0;else return this.parseError("Lexical error on line "+(this.yylineno+1)+`. You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).
 `+this.showPosition(),{text:"",token:null,line:this.yylineno});return this},less:function(a){this.unput(this.match.slice(a))},pastInput:function(){var a=this.matched.substr(0,this.matched.length-this.match.length);return(a.length>20?"...":"")+a.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var a=this.match;return a.length<20&&(a+=this._input.substr(0,20-a.length)),(a.substr(0,20)+(a.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var a=this.pastInput(),n=new Array(a.length+1).join("-");return a+this.upcomingInput()+`
diff --git a/assets/facade.html-Cj3lyBcS.js b/assets/facade.html-BODpRH45.js
similarity index 99%
rename from assets/facade.html-Cj3lyBcS.js
rename to assets/facade.html-BODpRH45.js
index b422d55..4f0cb57 100644
--- a/assets/facade.html-Cj3lyBcS.js
+++ b/assets/facade.html-BODpRH45.js
@@ -1,4 +1,4 @@
-import{_ as s,o as a,c as t,a as p,e,b as n,f as o}from"./app-B69Gl_S-.js";const c={},i=n("p",null,'当某个程序员得意地说出"啊，在调用那个类之前需要先调用这个类。在调用那个方法之前需要先在这个类中注册一下"的时候，就意味着我们需要引人Facade了。',-1),l=n("p",null,"对于那些能够明确地用语言描述出来的知识，我们不应该将它们隐藏在自己脑袋中，而是应该用代码将它们表现出来。",-1),r=n("p",{style:{"text-align":"right"}},"—————《图解设计模式》",-1),u=o(`<ol><li><strong>简化接口</strong>：外观模式为复杂的子系统提供了一个简单的接口，使得客户端代码不需要了解子系统的内部细节。</li><li><strong>松散耦合</strong>：通过引入外观类，客户端代码与子系统之间的耦合度降低，增强了代码的可维护性和可扩展性。</li><li><strong>更好的分层</strong>：外观模式有助于分层设计，使得每一层只关注自己的职责，层与层之间通过外观类进行交互。</li></ol><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><p>在这个示例中，我们使用了外观模式（Facade Pattern）来简化与复杂子系统的交互。外观模式通过提供一个统一的接口来隐藏子系统的复杂性，使得客户端代码可以更容易地使用子系统的功能。</p><img src="https://www.plantuml.com/plantuml/svg/VLBBJiCm4BpdAtnq1Vc175117BXGUki1SLZiRMh5ZsYz0K7LVyUEQf9MWOjVE-EPMNiT6OW7Pojb8KRn20mF454SAo5kKf6D4WwCpOL67CLhXr-DY4p6jszb8Ku9NQlWqtPG74YkPlGMUKkXHsA3KUfqqNjIs833mb_zT_EfEdjxOcTtP1XfT5T_Zkk2p89p1vVLqGyRjYZ7SQRy4OpErHu8MeB-81t62EqInXhVoGFXljHkXOAUJV0BuDms3Z9Fe3LDb24Y-SluXQDiY2Xd1wbvENS-EkVyxSSsUNo6hhJZh_Qx1DcXLS5XPen-xfEV57Aoj3Vs-aL61qbiagdhk-c3DEA5Ml3c6t9yeOB6A-ZilPR0Q_GwVRmV" alt=""><h2 id="代码实现" tabindex="-1"><a class="header-anchor" href="#代码实现"><span>代码实现</span></a></h2><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// dataBase.ts</span>
+import{_ as s,o as a,c as t,a as p,e,b as n,f as o}from"./app-B4LGNJZ0.js";const c={},i=n("p",null,'当某个程序员得意地说出"啊，在调用那个类之前需要先调用这个类。在调用那个方法之前需要先在这个类中注册一下"的时候，就意味着我们需要引人Facade了。',-1),l=n("p",null,"对于那些能够明确地用语言描述出来的知识，我们不应该将它们隐藏在自己脑袋中，而是应该用代码将它们表现出来。",-1),r=n("p",{style:{"text-align":"right"}},"—————《图解设计模式》",-1),u=o(`<ol><li><strong>简化接口</strong>：外观模式为复杂的子系统提供了一个简单的接口，使得客户端代码不需要了解子系统的内部细节。</li><li><strong>松散耦合</strong>：通过引入外观类，客户端代码与子系统之间的耦合度降低，增强了代码的可维护性和可扩展性。</li><li><strong>更好的分层</strong>：外观模式有助于分层设计，使得每一层只关注自己的职责，层与层之间通过外观类进行交互。</li></ol><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><p>在这个示例中，我们使用了外观模式（Facade Pattern）来简化与复杂子系统的交互。外观模式通过提供一个统一的接口来隐藏子系统的复杂性，使得客户端代码可以更容易地使用子系统的功能。</p><img src="https://www.plantuml.com/plantuml/svg/VLBBJiCm4BpdAtnq1Vc175117BXGUki1SLZiRMh5ZsYz0K7LVyUEQf9MWOjVE-EPMNiT6OW7Pojb8KRn20mF454SAo5kKf6D4WwCpOL67CLhXr-DY4p6jszb8Ku9NQlWqtPG74YkPlGMUKkXHsA3KUfqqNjIs833mb_zT_EfEdjxOcTtP1XfT5T_Zkk2p89p1vVLqGyRjYZ7SQRy4OpErHu8MeB-81t62EqInXhVoGFXljHkXOAUJV0BuDms3Z9Fe3LDb24Y-SluXQDiY2Xd1wbvENS-EkVyxSSsUNo6hhJZh_Qx1DcXLS5XPen-xfEV57Aoj3Vs-aL61qbiagdhk-c3DEA5Ml3c6t9yeOB6A-ZilPR0Q_GwVRmV" alt=""><h2 id="代码实现" tabindex="-1"><a class="header-anchor" href="#代码实现"><span>代码实现</span></a></h2><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// dataBase.ts</span>
 <span class="token keyword">export</span> <span class="token keyword">class</span> <span class="token class-name">DataBase</span> <span class="token punctuation">{</span>
   <span class="token keyword">static</span> mailData<span class="token operator">:</span> <span class="token punctuation">{</span> <span class="token punctuation">[</span>key<span class="token operator">:</span> <span class="token builtin">string</span><span class="token punctuation">]</span><span class="token operator">:</span> <span class="token builtin">string</span> <span class="token punctuation">}</span> <span class="token operator">=</span> <span class="token punctuation">{</span>
     <span class="token string-property property">&#39;hyuki@hyuki.com&#39;</span><span class="token operator">:</span> <span class="token string">&#39;Hiroshi Yuki&#39;</span><span class="token punctuation">,</span>
diff --git a/assets/factory_method.html-B20phxz9.js b/assets/factory_method.html-NuMbQ7is.js
similarity index 99%
rename from assets/factory_method.html-B20phxz9.js
rename to assets/factory_method.html-NuMbQ7is.js
index c33b447..85ba25e 100644
--- a/assets/factory_method.html-B20phxz9.js
+++ b/assets/factory_method.html-NuMbQ7is.js
@@ -1,4 +1,4 @@
-import{_ as n,o as s,c as a,a as t,b as p,f as e}from"./app-B69Gl_S-.js";const o={},c=p("p",null,"在 Factory Method 模式中，我们定义一个用于创建对象的接口，但由子类决定要实例化的类是哪一个。Factory Method 使一个类的实例化延迟到其子类。",-1),i=e(`<h2 id="为什么要使用-factory-method" tabindex="-1"><a class="header-anchor" href="#为什么要使用-factory-method"><span>为什么要使用 Factory Method</span></a></h2><p>使用 Factory Method 模式有以下几个好处：</p><ol><li><strong>解耦创建和使用</strong>：客户端代码不需要知道具体的产品类，只需要依赖抽象产品接口，降低了耦合性。</li><li><strong>扩展性强</strong>：增加新的产品类时，只需添加新的子类工厂，不需要修改现有代码，符合开闭原则。</li><li><strong>灵活性高</strong>：可以通过子类来定制产品的创建过程，满足不同的需求。</li></ol><p>通过使用 Factory Method 模式，我们可以更灵活地管理对象的创建过程，提高代码的可维护性和可扩展性。</p><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/XP9DJiGm38NtFOMN0wXpWAugWP1OmHwn2AcdYcYJoauP4EBkE6dw4-Y8JMkzFjlFdrgpL-J7lYlgfRAgHnwKHZYHb6T7R_1L01ZhaKv1VoBNZDf75U06HiR3LGNlpZIYV1VoKA_iIOb7TuePxgLqzBbqQ4BbyU3E5ga2iHhRoeGqE9hAP4hQFrx2rh3aczt3z5vistWISBrHEojxFCPeKzY7krj53PX-wB17wta5SSnFBo5BjOiZA2twns0CycADdBORPqZuuT4sswqvlhILvrdFBndLIy2c9SbwaTVase_FQ_wuCwBycx8ihtU8LIaU5pFoOtvsQFlrQTDK2nBvEty0" alt=""><p>@enduml</p><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// product.ts</span>
+import{_ as n,o as s,c as a,a as t,b as p,f as e}from"./app-B4LGNJZ0.js";const o={},c=p("p",null,"在 Factory Method 模式中，我们定义一个用于创建对象的接口，但由子类决定要实例化的类是哪一个。Factory Method 使一个类的实例化延迟到其子类。",-1),i=e(`<h2 id="为什么要使用-factory-method" tabindex="-1"><a class="header-anchor" href="#为什么要使用-factory-method"><span>为什么要使用 Factory Method</span></a></h2><p>使用 Factory Method 模式有以下几个好处：</p><ol><li><strong>解耦创建和使用</strong>：客户端代码不需要知道具体的产品类，只需要依赖抽象产品接口，降低了耦合性。</li><li><strong>扩展性强</strong>：增加新的产品类时，只需添加新的子类工厂，不需要修改现有代码，符合开闭原则。</li><li><strong>灵活性高</strong>：可以通过子类来定制产品的创建过程，满足不同的需求。</li></ol><p>通过使用 Factory Method 模式，我们可以更灵活地管理对象的创建过程，提高代码的可维护性和可扩展性。</p><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/XP9DJiGm38NtFOMN0wXpWAugWP1OmHwn2AcdYcYJoauP4EBkE6dw4-Y8JMkzFjlFdrgpL-J7lYlgfRAgHnwKHZYHb6T7R_1L01ZhaKv1VoBNZDf75U06HiR3LGNlpZIYV1VoKA_iIOb7TuePxgLqzBbqQ4BbyU3E5ga2iHhRoeGqE9hAP4hQFrx2rh3aczt3z5vistWISBrHEojxFCPeKzY7krj53PX-wB17wta5SSnFBo5BjOiZA2twns0CycADdBORPqZuuT4sswqvlhILvrdFBndLIy2c9SbwaTVase_FQ_wuCwBycx8ihtU8LIaU5pFoOtvsQFlrQTDK2nBvEty0" alt=""><p>@enduml</p><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// product.ts</span>
 <span class="token keyword">export</span> <span class="token keyword">interface</span> <span class="token class-name">Product</span> <span class="token punctuation">{</span>
   <span class="token function">use</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">:</span> <span class="token keyword">void</span><span class="token punctuation">;</span>
 <span class="token punctuation">}</span>
diff --git a/assets/figure_bed.html-BME-hebA.js b/assets/figure_bed.html-vyc89ngd.js
similarity index 96%
rename from assets/figure_bed.html-BME-hebA.js
rename to assets/figure_bed.html-vyc89ngd.js
index e263f65..4670b40 100644
--- a/assets/figure_bed.html-BME-hebA.js
+++ b/assets/figure_bed.html-vyc89ngd.js
@@ -1 +1 @@
-import{_ as e,o,c as n,b as t}from"./app-B69Gl_S-.js";const i={},a=t("p",null,"参考",-1),r=t("ul",null,[t("li",null,"https://zhuanlan.zhihu.com/p/347342082")],-1),c=[a,r];function l(h,p){return o(),n("div",null,c)}const u=e(i,[["render",l],["__file","figure_bed.html.vue"]]),m=JSON.parse('{"path":"/tech/figure_bed.html","title":"github 图床","lang":"zh-CN","frontmatter":{"title":"github 图床","date":"2024-11-01T00:00:00.000Z","description":"参考 https://zhuanlan.zhihu.com/p/347342082","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/figure_bed.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"github 图床"}],["meta",{"property":"og:description","content":"参考 https://zhuanlan.zhihu.com/p/347342082"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:published_time","content":"2024-11-01T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"github 图床\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-11-01T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.04,"words":12},"filePathRelative":"tech/figure_bed.md","localizedDate":"2024年11月1日","excerpt":"<p>参考</p>\\n<ul>\\n<li>https://zhuanlan.zhihu.com/p/347342082</li>\\n</ul>\\n","autoDesc":true}');export{u as comp,m as data};
+import{_ as e,o,c as n,b as t}from"./app-B4LGNJZ0.js";const i={},a=t("p",null,"参考",-1),r=t("ul",null,[t("li",null,"https://zhuanlan.zhihu.com/p/347342082")],-1),c=[a,r];function l(h,p){return o(),n("div",null,c)}const u=e(i,[["render",l],["__file","figure_bed.html.vue"]]),m=JSON.parse('{"path":"/tech/figure_bed.html","title":"github 图床","lang":"zh-CN","frontmatter":{"title":"github 图床","date":"2024-11-01T00:00:00.000Z","description":"参考 https://zhuanlan.zhihu.com/p/347342082","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/figure_bed.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"github 图床"}],["meta",{"property":"og:description","content":"参考 https://zhuanlan.zhihu.com/p/347342082"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:published_time","content":"2024-11-01T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"github 图床\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-11-01T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.04,"words":12},"filePathRelative":"tech/figure_bed.md","localizedDate":"2024年11月1日","excerpt":"<p>参考</p>\\n<ul>\\n<li>https://zhuanlan.zhihu.com/p/347342082</li>\\n</ul>\\n","autoDesc":true}');export{u as comp,m as data};
diff --git a/assets/flowDb-0da60e67-C3mEtQas.js b/assets/flowDb-0da60e67-XaXEQp9e.js
similarity index 99%
rename from assets/flowDb-0da60e67-C3mEtQas.js
rename to assets/flowDb-0da60e67-XaXEQp9e.js
index 0ee1cb7..1f53f5f 100644
--- a/assets/flowDb-0da60e67-C3mEtQas.js
+++ b/assets/flowDb-0da60e67-XaXEQp9e.js
@@ -1,4 +1,4 @@
-import{c as et,v as me,s as ye,g as ve,a as Ve,b as Le,x as Ie,y as Re,l as J1,z as dt,A as Ne,j as we,h as w1}from"./mermaid.core-ChLYKTZm.js";var pt=function(){var e=function(f1,a,o,f){for(o=o||{},f=f1.length;f--;o[f1[f]]=a);return o},u=[1,4],i=[1,3],n=[1,5],c=[1,8,9,10,11,27,34,36,38,42,58,81,82,83,84,85,86,99,102,103,106,108,111,112,113,118,119,120,121],l=[2,2],h=[1,13],U=[1,14],F=[1,15],w=[1,16],X=[1,23],o1=[1,25],p1=[1,26],A1=[1,27],C=[1,49],k=[1,48],l1=[1,29],U1=[1,30],G1=[1,31],M1=[1,32],K1=[1,33],x=[1,44],B=[1,46],m=[1,42],y=[1,47],v=[1,43],V=[1,50],L=[1,45],I=[1,51],R=[1,52],Y1=[1,34],j1=[1,35],z1=[1,36],X1=[1,37],I1=[1,57],b=[1,8,9,10,11,27,32,34,36,38,42,58,81,82,83,84,85,86,99,102,103,106,108,111,112,113,118,119,120,121],q=[1,61],Q=[1,60],Z=[1,62],H1=[8,9,11,73,75],k1=[1,88],b1=[1,93],g1=[1,92],D1=[1,89],F1=[1,85],T1=[1,91],S1=[1,87],C1=[1,94],_1=[1,90],x1=[1,95],B1=[1,86],W1=[8,9,10,11,73,75],N=[8,9,10,11,44,73,75],M=[8,9,10,11,29,42,44,46,48,50,52,54,56,58,61,63,65,66,68,73,75,86,99,102,103,106,108,111,112,113],Et=[8,9,11,42,58,73,75,86,99,102,103,106,108,111,112,113],R1=[42,58,86,99,102,103,106,108,111,112,113],kt=[1,121],bt=[1,120],gt=[1,128],Dt=[1,142],Ft=[1,143],Tt=[1,144],St=[1,145],Ct=[1,130],_t=[1,132],xt=[1,136],Bt=[1,137],mt=[1,138],yt=[1,139],vt=[1,140],Vt=[1,141],Lt=[1,146],It=[1,147],Rt=[1,126],Nt=[1,127],wt=[1,134],Ot=[1,129],Pt=[1,133],Ut=[1,131],nt=[8,9,10,11,27,32,34,36,38,42,58,81,82,83,84,85,86,99,102,103,106,108,111,112,113,118,119,120,121],Gt=[1,149],T=[8,9,11],K=[8,9,10,11,14,42,58,86,102,103,106,108,111,112,113],p=[1,169],O=[1,165],P=[1,166],A=[1,170],d=[1,167],E=[1,168],m1=[75,113,116],g=[8,9,10,11,12,14,27,29,32,42,58,73,81,82,83,84,85,86,87,102,106,108,111,112,113],Mt=[10,103],h1=[31,47,49,51,53,55,60,62,64,65,67,69,113,114,115],J=[1,235],$=[1,233],t1=[1,237],e1=[1,231],s1=[1,232],u1=[1,234],i1=[1,236],r1=[1,238],y1=[1,255],Kt=[8,9,11,103],W=[8,9,10,11,58,81,102,103,106,107,108,109],at={trace:function(){},yy:{},symbols_:{error:2,start:3,graphConfig:4,document:5,line:6,statement:7,SEMI:8,NEWLINE:9,SPACE:10,EOF:11,GRAPH:12,NODIR:13,DIR:14,FirstStmtSeparator:15,ending:16,endToken:17,spaceList:18,spaceListNewline:19,vertexStatement:20,separator:21,styleStatement:22,linkStyleStatement:23,classDefStatement:24,classStatement:25,clickStatement:26,subgraph:27,textNoTags:28,SQS:29,text:30,SQE:31,end:32,direction:33,acc_title:34,acc_title_value:35,acc_descr:36,acc_descr_value:37,acc_descr_multiline_value:38,link:39,node:40,styledVertex:41,AMP:42,vertex:43,STYLE_SEPARATOR:44,idString:45,DOUBLECIRCLESTART:46,DOUBLECIRCLEEND:47,PS:48,PE:49,"(-":50,"-)":51,STADIUMSTART:52,STADIUMEND:53,SUBROUTINESTART:54,SUBROUTINEEND:55,VERTEX_WITH_PROPS_START:56,"NODE_STRING[field]":57,COLON:58,"NODE_STRING[value]":59,PIPE:60,CYLINDERSTART:61,CYLINDEREND:62,DIAMOND_START:63,DIAMOND_STOP:64,TAGEND:65,TRAPSTART:66,TRAPEND:67,INVTRAPSTART:68,INVTRAPEND:69,linkStatement:70,arrowText:71,TESTSTR:72,START_LINK:73,edgeText:74,LINK:75,edgeTextToken:76,STR:77,MD_STR:78,textToken:79,keywords:80,STYLE:81,LINKSTYLE:82,CLASSDEF:83,CLASS:84,CLICK:85,DOWN:86,UP:87,textNoTagsToken:88,stylesOpt:89,"idString[vertex]":90,"idString[class]":91,CALLBACKNAME:92,CALLBACKARGS:93,HREF:94,LINK_TARGET:95,"STR[link]":96,"STR[tooltip]":97,alphaNum:98,DEFAULT:99,numList:100,INTERPOLATE:101,NUM:102,COMMA:103,style:104,styleComponent:105,NODE_STRING:106,UNIT:107,BRKT:108,PCT:109,idStringToken:110,MINUS:111,MULT:112,UNICODE_TEXT:113,TEXT:114,TAGSTART:115,EDGE_TEXT:116,alphaNumToken:117,direction_tb:118,direction_bt:119,direction_rl:120,direction_lr:121,$accept:0,$end:1},terminals_:{2:"error",8:"SEMI",9:"NEWLINE",10:"SPACE",11:"EOF",12:"GRAPH",13:"NODIR",14:"DIR",27:"subgraph",29:"SQS",31:"SQE",32:"end",34:"acc_title",35:"acc_title_value",36:"acc_descr",37:"acc_descr_value",38:"acc_descr_multiline_value",42:"AMP",44:"STYLE_SEPARATOR",46:"DOUBLECIRCLESTART",47:"DOUBLECIRCLEEND",48:"PS",49:"PE",50:"(-",51:"-)",52:"STADIUMSTART",53:"STADIUMEND",54:"SUBROUTINESTART",55:"SUBROUTINEEND",56:"VERTEX_WITH_PROPS_START",57:"NODE_STRING[field]",58:"COLON",59:"NODE_STRING[value]",60:"PIPE",61:"CYLINDERSTART",62:"CYLINDEREND",63:"DIAMOND_START",64:"DIAMOND_STOP",65:"TAGEND",66:"TRAPSTART",67:"TRAPEND",68:"INVTRAPSTART",69:"INVTRAPEND",72:"TESTSTR",73:"START_LINK",75:"LINK",77:"STR",78:"MD_STR",81:"STYLE",82:"LINKSTYLE",83:"CLASSDEF",84:"CLASS",85:"CLICK",86:"DOWN",87:"UP",90:"idString[vertex]",91:"idString[class]",92:"CALLBACKNAME",93:"CALLBACKARGS",94:"HREF",95:"LINK_TARGET",96:"STR[link]",97:"STR[tooltip]",99:"DEFAULT",101:"INTERPOLATE",102:"NUM",103:"COMMA",106:"NODE_STRING",107:"UNIT",108:"BRKT",109:"PCT",111:"MINUS",112:"MULT",113:"UNICODE_TEXT",114:"TEXT",115:"TAGSTART",116:"EDGE_TEXT",118:"direction_tb",119:"direction_bt",120:"direction_rl",121:"direction_lr"},productions_:[0,[3,2],[5,0],[5,2],[6,1],[6,1],[6,1],[6,1],[6,1],[4,2],[4,2],[4,2],[4,3],[16,2],[16,1],[17,1],[17,1],[17,1],[15,1],[15,1],[15,2],[19,2],[19,2],[19,1],[19,1],[18,2],[18,1],[7,2],[7,2],[7,2],[7,2],[7,2],[7,2],[7,9],[7,6],[7,4],[7,1],[7,2],[7,2],[7,1],[21,1],[21,1],[21,1],[20,3],[20,4],[20,2],[20,1],[40,1],[40,5],[41,1],[41,3],[43,4],[43,4],[43,6],[43,4],[43,4],[43,4],[43,8],[43,4],[43,4],[43,4],[43,6],[43,4],[43,4],[43,4],[43,4],[43,4],[43,1],[39,2],[39,3],[39,3],[39,1],[39,3],[74,1],[74,2],[74,1],[74,1],[70,1],[71,3],[30,1],[30,2],[30,1],[30,1],[80,1],[80,1],[80,1],[80,1],[80,1],[80,1],[80,1],[80,1],[80,1],[80,1],[80,1],[28,1],[28,2],[28,1],[28,1],[24,5],[25,5],[26,2],[26,4],[26,3],[26,5],[26,3],[26,5],[26,5],[26,7],[26,2],[26,4],[26,2],[26,4],[26,4],[26,6],[22,5],[23,5],[23,5],[23,9],[23,9],[23,7],[23,7],[100,1],[100,3],[89,1],[89,3],[104,1],[104,2],[105,1],[105,1],[105,1],[105,1],[105,1],[105,1],[105,1],[105,1],[110,1],[110,1],[110,1],[110,1],[110,1],[110,1],[110,1],[110,1],[110,1],[110,1],[110,1],[79,1],[79,1],[79,1],[79,1],[88,1],[88,1],[88,1],[88,1],[88,1],[88,1],[88,1],[88,1],[88,1],[88,1],[88,1],[76,1],[76,1],[117,1],[117,1],[117,1],[117,1],[117,1],[117,1],[117,1],[117,1],[117,1],[117,1],[117,1],[45,1],[45,2],[98,1],[98,2],[33,1],[33,1],[33,1],[33,1]],performAction:function(a,o,f,r,S,t,N1){var s=t.length-1;switch(S){case 2:this.$=[];break;case 3:(!Array.isArray(t[s])||t[s].length>0)&&t[s-1].push(t[s]),this.$=t[s-1];break;case 4:case 176:this.$=t[s];break;case 11:r.setDirection("TB"),this.$="TB";break;case 12:r.setDirection(t[s-1]),this.$=t[s-1];break;case 27:this.$=t[s-1].nodes;break;case 28:case 29:case 30:case 31:case 32:this.$=[];break;case 33:this.$=r.addSubGraph(t[s-6],t[s-1],t[s-4]);break;case 34:this.$=r.addSubGraph(t[s-3],t[s-1],t[s-3]);break;case 35:this.$=r.addSubGraph(void 0,t[s-1],void 0);break;case 37:this.$=t[s].trim(),r.setAccTitle(this.$);break;case 38:case 39:this.$=t[s].trim(),r.setAccDescription(this.$);break;case 43:r.addLink(t[s-2].stmt,t[s],t[s-1]),this.$={stmt:t[s],nodes:t[s].concat(t[s-2].nodes)};break;case 44:r.addLink(t[s-3].stmt,t[s-1],t[s-2]),this.$={stmt:t[s-1],nodes:t[s-1].concat(t[s-3].nodes)};break;case 45:this.$={stmt:t[s-1],nodes:t[s-1]};break;case 46:this.$={stmt:t[s],nodes:t[s]};break;case 47:this.$=[t[s]];break;case 48:this.$=t[s-4].concat(t[s]);break;case 49:this.$=t[s];break;case 50:this.$=t[s-2],r.setClass(t[s-2],t[s]);break;case 51:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"square");break;case 52:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"doublecircle");break;case 53:this.$=t[s-5],r.addVertex(t[s-5],t[s-2],"circle");break;case 54:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"ellipse");break;case 55:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"stadium");break;case 56:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"subroutine");break;case 57:this.$=t[s-7],r.addVertex(t[s-7],t[s-1],"rect",void 0,void 0,void 0,Object.fromEntries([[t[s-5],t[s-3]]]));break;case 58:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"cylinder");break;case 59:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"round");break;case 60:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"diamond");break;case 61:this.$=t[s-5],r.addVertex(t[s-5],t[s-2],"hexagon");break;case 62:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"odd");break;case 63:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"trapezoid");break;case 64:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"inv_trapezoid");break;case 65:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"lean_right");break;case 66:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"lean_left");break;case 67:this.$=t[s],r.addVertex(t[s]);break;case 68:t[s-1].text=t[s],this.$=t[s-1];break;case 69:case 70:t[s-2].text=t[s-1],this.$=t[s-2];break;case 71:this.$=t[s];break;case 72:var Y=r.destructLink(t[s],t[s-2]);this.$={type:Y.type,stroke:Y.stroke,length:Y.length,text:t[s-1]};break;case 73:this.$={text:t[s],type:"text"};break;case 74:this.$={text:t[s-1].text+""+t[s],type:t[s-1].type};break;case 75:this.$={text:t[s],type:"string"};break;case 76:this.$={text:t[s],type:"markdown"};break;case 77:var Y=r.destructLink(t[s]);this.$={type:Y.type,stroke:Y.stroke,length:Y.length};break;case 78:this.$=t[s-1];break;case 79:this.$={text:t[s],type:"text"};break;case 80:this.$={text:t[s-1].text+""+t[s],type:t[s-1].type};break;case 81:this.$={text:t[s],type:"string"};break;case 82:case 97:this.$={text:t[s],type:"markdown"};break;case 94:this.$={text:t[s],type:"text"};break;case 95:this.$={text:t[s-1].text+""+t[s],type:t[s-1].type};break;case 96:this.$={text:t[s],type:"text"};break;case 98:this.$=t[s-4],r.addClass(t[s-2],t[s]);break;case 99:this.$=t[s-4],r.setClass(t[s-2],t[s]);break;case 100:case 108:this.$=t[s-1],r.setClickEvent(t[s-1],t[s]);break;case 101:case 109:this.$=t[s-3],r.setClickEvent(t[s-3],t[s-2]),r.setTooltip(t[s-3],t[s]);break;case 102:this.$=t[s-2],r.setClickEvent(t[s-2],t[s-1],t[s]);break;case 103:this.$=t[s-4],r.setClickEvent(t[s-4],t[s-3],t[s-2]),r.setTooltip(t[s-4],t[s]);break;case 104:this.$=t[s-2],r.setLink(t[s-2],t[s]);break;case 105:this.$=t[s-4],r.setLink(t[s-4],t[s-2]),r.setTooltip(t[s-4],t[s]);break;case 106:this.$=t[s-4],r.setLink(t[s-4],t[s-2],t[s]);break;case 107:this.$=t[s-6],r.setLink(t[s-6],t[s-4],t[s]),r.setTooltip(t[s-6],t[s-2]);break;case 110:this.$=t[s-1],r.setLink(t[s-1],t[s]);break;case 111:this.$=t[s-3],r.setLink(t[s-3],t[s-2]),r.setTooltip(t[s-3],t[s]);break;case 112:this.$=t[s-3],r.setLink(t[s-3],t[s-2],t[s]);break;case 113:this.$=t[s-5],r.setLink(t[s-5],t[s-4],t[s]),r.setTooltip(t[s-5],t[s-2]);break;case 114:this.$=t[s-4],r.addVertex(t[s-2],void 0,void 0,t[s]);break;case 115:this.$=t[s-4],r.updateLink([t[s-2]],t[s]);break;case 116:this.$=t[s-4],r.updateLink(t[s-2],t[s]);break;case 117:this.$=t[s-8],r.updateLinkInterpolate([t[s-6]],t[s-2]),r.updateLink([t[s-6]],t[s]);break;case 118:this.$=t[s-8],r.updateLinkInterpolate(t[s-6],t[s-2]),r.updateLink(t[s-6],t[s]);break;case 119:this.$=t[s-6],r.updateLinkInterpolate([t[s-4]],t[s]);break;case 120:this.$=t[s-6],r.updateLinkInterpolate(t[s-4],t[s]);break;case 121:case 123:this.$=[t[s]];break;case 122:case 124:t[s-2].push(t[s]),this.$=t[s-2];break;case 126:this.$=t[s-1]+t[s];break;case 174:this.$=t[s];break;case 175:this.$=t[s-1]+""+t[s];break;case 177:this.$=t[s-1]+""+t[s];break;case 178:this.$={stmt:"dir",value:"TB"};break;case 179:this.$={stmt:"dir",value:"BT"};break;case 180:this.$={stmt:"dir",value:"RL"};break;case 181:this.$={stmt:"dir",value:"LR"};break}},table:[{3:1,4:2,9:u,10:i,12:n},{1:[3]},e(c,l,{5:6}),{4:7,9:u,10:i,12:n},{4:8,9:u,10:i,12:n},{13:[1,9],14:[1,10]},{1:[2,1],6:11,7:12,8:h,9:U,10:F,11:w,20:17,22:18,23:19,24:20,25:21,26:22,27:X,33:24,34:o1,36:p1,38:A1,40:28,41:38,42:C,43:39,45:40,58:k,81:l1,82:U1,83:G1,84:M1,85:K1,86:x,99:B,102:m,103:y,106:v,108:V,110:41,111:L,112:I,113:R,118:Y1,119:j1,120:z1,121:X1},e(c,[2,9]),e(c,[2,10]),e(c,[2,11]),{8:[1,54],9:[1,55],10:I1,15:53,18:56},e(b,[2,3]),e(b,[2,4]),e(b,[2,5]),e(b,[2,6]),e(b,[2,7]),e(b,[2,8]),{8:q,9:Q,11:Z,21:58,39:59,70:63,73:[1,64],75:[1,65]},{8:q,9:Q,11:Z,21:66},{8:q,9:Q,11:Z,21:67},{8:q,9:Q,11:Z,21:68},{8:q,9:Q,11:Z,21:69},{8:q,9:Q,11:Z,21:70},{8:q,9:Q,10:[1,71],11:Z,21:72},e(b,[2,36]),{35:[1,73]},{37:[1,74]},e(b,[2,39]),e(H1,[2,46],{18:75,10:I1}),{10:[1,76]},{10:[1,77]},{10:[1,78]},{10:[1,79]},{14:k1,42:b1,58:g1,77:[1,83],86:D1,92:[1,80],94:[1,81],98:82,102:F1,103:T1,106:S1,108:C1,111:_1,112:x1,113:B1,117:84},e(b,[2,178]),e(b,[2,179]),e(b,[2,180]),e(b,[2,181]),e(W1,[2,47]),e(W1,[2,49],{44:[1,96]}),e(N,[2,67],{110:109,29:[1,97],42:C,46:[1,98],48:[1,99],50:[1,100],52:[1,101],54:[1,102],56:[1,103],58:k,61:[1,104],63:[1,105],65:[1,106],66:[1,107],68:[1,108],86:x,99:B,102:m,103:y,106:v,108:V,111:L,112:I,113:R}),e(M,[2,174]),e(M,[2,135]),e(M,[2,136]),e(M,[2,137]),e(M,[2,138]),e(M,[2,139]),e(M,[2,140]),e(M,[2,141]),e(M,[2,142]),e(M,[2,143]),e(M,[2,144]),e(M,[2,145]),e(c,[2,12]),e(c,[2,18]),e(c,[2,19]),{9:[1,110]},e(Et,[2,26],{18:111,10:I1}),e(b,[2,27]),{40:112,41:38,42:C,43:39,45:40,58:k,86:x,99:B,102:m,103:y,106:v,108:V,110:41,111:L,112:I,113:R},e(b,[2,40]),e(b,[2,41]),e(b,[2,42]),e(R1,[2,71],{71:113,60:[1,115],72:[1,114]}),{74:116,76:117,77:[1,118],78:[1,119],113:kt,116:bt},e([42,58,60,72,86,99,102,103,106,108,111,112,113],[2,77]),e(b,[2,28]),e(b,[2,29]),e(b,[2,30]),e(b,[2,31]),e(b,[2,32]),{10:gt,12:Dt,14:Ft,27:Tt,28:122,32:St,42:Ct,58:_t,73:xt,77:[1,124],78:[1,125],80:135,81:Bt,82:mt,83:yt,84:vt,85:Vt,86:Lt,87:It,88:123,102:Rt,106:Nt,108:wt,111:Ot,112:Pt,113:Ut},e(nt,l,{5:148}),e(b,[2,37]),e(b,[2,38]),e(H1,[2,45],{42:Gt}),{42:C,45:150,58:k,86:x,99:B,102:m,103:y,106:v,108:V,110:41,111:L,112:I,113:R},{99:[1,151],100:152,102:[1,153]},{42:C,45:154,58:k,86:x,99:B,102:m,103:y,106:v,108:V,110:41,111:L,112:I,113:R},{42:C,45:155,58:k,86:x,99:B,102:m,103:y,106:v,108:V,110:41,111:L,112:I,113:R},e(T,[2,100],{10:[1,156],93:[1,157]}),{77:[1,158]},e(T,[2,108],{117:160,10:[1,159],14:k1,42:b1,58:g1,86:D1,102:F1,103:T1,106:S1,108:C1,111:_1,112:x1,113:B1}),e(T,[2,110],{10:[1,161]}),e(K,[2,176]),e(K,[2,163]),e(K,[2,164]),e(K,[2,165]),e(K,[2,166]),e(K,[2,167]),e(K,[2,168]),e(K,[2,169]),e(K,[2,170]),e(K,[2,171]),e(K,[2,172]),e(K,[2,173]),{42:C,45:162,58:k,86:x,99:B,102:m,103:y,106:v,108:V,110:41,111:L,112:I,113:R},{30:163,65:p,77:O,78:P,79:164,113:A,114:d,115:E},{30:171,65:p,77:O,78:P,79:164,113:A,114:d,115:E},{30:173,48:[1,172],65:p,77:O,78:P,79:164,113:A,114:d,115:E},{30:174,65:p,77:O,78:P,79:164,113:A,114:d,115:E},{30:175,65:p,77:O,78:P,79:164,113:A,114:d,115:E},{30:176,65:p,77:O,78:P,79:164,113:A,114:d,115:E},{106:[1,177]},{30:178,65:p,77:O,78:P,79:164,113:A,114:d,115:E},{30:179,63:[1,180],65:p,77:O,78:P,79:164,113:A,114:d,115:E},{30:181,65:p,77:O,78:P,79:164,113:A,114:d,115:E},{30:182,65:p,77:O,78:P,79:164,113:A,114:d,115:E},{30:183,65:p,77:O,78:P,79:164,113:A,114:d,115:E},e(M,[2,175]),e(c,[2,20]),e(Et,[2,25]),e(H1,[2,43],{18:184,10:I1}),e(R1,[2,68],{10:[1,185]}),{10:[1,186]},{30:187,65:p,77:O,78:P,79:164,113:A,114:d,115:E},{75:[1,188],76:189,113:kt,116:bt},e(m1,[2,73]),e(m1,[2,75]),e(m1,[2,76]),e(m1,[2,161]),e(m1,[2,162]),{8:q,9:Q,10:gt,11:Z,12:Dt,14:Ft,21:191,27:Tt,29:[1,190],32:St,42:Ct,58:_t,73:xt,80:135,81:Bt,82:mt,83:yt,84:vt,85:Vt,86:Lt,87:It,88:192,102:Rt,106:Nt,108:wt,111:Ot,112:Pt,113:Ut},e(g,[2,94]),e(g,[2,96]),e(g,[2,97]),e(g,[2,150]),e(g,[2,151]),e(g,[2,152]),e(g,[2,153]),e(g,[2,154]),e(g,[2,155]),e(g,[2,156]),e(g,[2,157]),e(g,[2,158]),e(g,[2,159]),e(g,[2,160]),e(g,[2,83]),e(g,[2,84]),e(g,[2,85]),e(g,[2,86]),e(g,[2,87]),e(g,[2,88]),e(g,[2,89]),e(g,[2,90]),e(g,[2,91]),e(g,[2,92]),e(g,[2,93]),{6:11,7:12,8:h,9:U,10:F,11:w,20:17,22:18,23:19,24:20,25:21,26:22,27:X,32:[1,193],33:24,34:o1,36:p1,38:A1,40:28,41:38,42:C,43:39,45:40,58:k,81:l1,82:U1,83:G1,84:M1,85:K1,86:x,99:B,102:m,103:y,106:v,108:V,110:41,111:L,112:I,113:R,118:Y1,119:j1,120:z1,121:X1},{10:I1,18:194},{10:[1,195],42:C,58:k,86:x,99:B,102:m,103:y,106:v,108:V,110:109,111:L,112:I,113:R},{10:[1,196]},{10:[1,197],103:[1,198]},e(Mt,[2,121]),{10:[1,199],42:C,58:k,86:x,99:B,102:m,103:y,106:v,108:V,110:109,111:L,112:I,113:R},{10:[1,200],42:C,58:k,86:x,99:B,102:m,103:y,106:v,108:V,110:109,111:L,112:I,113:R},{77:[1,201]},e(T,[2,102],{10:[1,202]}),e(T,[2,104],{10:[1,203]}),{77:[1,204]},e(K,[2,177]),{77:[1,205],95:[1,206]},e(W1,[2,50],{110:109,42:C,58:k,86:x,99:B,102:m,103:y,106:v,108:V,111:L,112:I,113:R}),{31:[1,207],65:p,79:208,113:A,114:d,115:E},e(h1,[2,79]),e(h1,[2,81]),e(h1,[2,82]),e(h1,[2,146]),e(h1,[2,147]),e(h1,[2,148]),e(h1,[2,149]),{47:[1,209],65:p,79:208,113:A,114:d,115:E},{30:210,65:p,77:O,78:P,79:164,113:A,114:d,115:E},{49:[1,211],65:p,79:208,113:A,114:d,115:E},{51:[1,212],65:p,79:208,113:A,114:d,115:E},{53:[1,213],65:p,79:208,113:A,114:d,115:E},{55:[1,214],65:p,79:208,113:A,114:d,115:E},{58:[1,215]},{62:[1,216],65:p,79:208,113:A,114:d,115:E},{64:[1,217],65:p,79:208,113:A,114:d,115:E},{30:218,65:p,77:O,78:P,79:164,113:A,114:d,115:E},{31:[1,219],65:p,79:208,113:A,114:d,115:E},{65:p,67:[1,220],69:[1,221],79:208,113:A,114:d,115:E},{65:p,67:[1,223],69:[1,222],79:208,113:A,114:d,115:E},e(H1,[2,44],{42:Gt}),e(R1,[2,70]),e(R1,[2,69]),{60:[1,224],65:p,79:208,113:A,114:d,115:E},e(R1,[2,72]),e(m1,[2,74]),{30:225,65:p,77:O,78:P,79:164,113:A,114:d,115:E},e(nt,l,{5:226}),e(g,[2,95]),e(b,[2,35]),{41:227,42:C,43:39,45:40,58:k,86:x,99:B,102:m,103:y,106:v,108:V,110:41,111:L,112:I,113:R},{10:J,58:$,81:t1,89:228,102:e1,104:229,105:230,106:s1,107:u1,108:i1,109:r1},{10:J,58:$,81:t1,89:239,101:[1,240],102:e1,104:229,105:230,106:s1,107:u1,108:i1,109:r1},{10:J,58:$,81:t1,89:241,101:[1,242],102:e1,104:229,105:230,106:s1,107:u1,108:i1,109:r1},{102:[1,243]},{10:J,58:$,81:t1,89:244,102:e1,104:229,105:230,106:s1,107:u1,108:i1,109:r1},{42:C,45:245,58:k,86:x,99:B,102:m,103:y,106:v,108:V,110:41,111:L,112:I,113:R},e(T,[2,101]),{77:[1,246]},{77:[1,247],95:[1,248]},e(T,[2,109]),e(T,[2,111],{10:[1,249]}),e(T,[2,112]),e(N,[2,51]),e(h1,[2,80]),e(N,[2,52]),{49:[1,250],65:p,79:208,113:A,114:d,115:E},e(N,[2,59]),e(N,[2,54]),e(N,[2,55]),e(N,[2,56]),{106:[1,251]},e(N,[2,58]),e(N,[2,60]),{64:[1,252],65:p,79:208,113:A,114:d,115:E},e(N,[2,62]),e(N,[2,63]),e(N,[2,65]),e(N,[2,64]),e(N,[2,66]),e([10,42,58,86,99,102,103,106,108,111,112,113],[2,78]),{31:[1,253],65:p,79:208,113:A,114:d,115:E},{6:11,7:12,8:h,9:U,10:F,11:w,20:17,22:18,23:19,24:20,25:21,26:22,27:X,32:[1,254],33:24,34:o1,36:p1,38:A1,40:28,41:38,42:C,43:39,45:40,58:k,81:l1,82:U1,83:G1,84:M1,85:K1,86:x,99:B,102:m,103:y,106:v,108:V,110:41,111:L,112:I,113:R,118:Y1,119:j1,120:z1,121:X1},e(W1,[2,48]),e(T,[2,114],{103:y1}),e(Kt,[2,123],{105:256,10:J,58:$,81:t1,102:e1,106:s1,107:u1,108:i1,109:r1}),e(W,[2,125]),e(W,[2,127]),e(W,[2,128]),e(W,[2,129]),e(W,[2,130]),e(W,[2,131]),e(W,[2,132]),e(W,[2,133]),e(W,[2,134]),e(T,[2,115],{103:y1}),{10:[1,257]},e(T,[2,116],{103:y1}),{10:[1,258]},e(Mt,[2,122]),e(T,[2,98],{103:y1}),e(T,[2,99],{110:109,42:C,58:k,86:x,99:B,102:m,103:y,106:v,108:V,111:L,112:I,113:R}),e(T,[2,103]),e(T,[2,105],{10:[1,259]}),e(T,[2,106]),{95:[1,260]},{49:[1,261]},{60:[1,262]},{64:[1,263]},{8:q,9:Q,11:Z,21:264},e(b,[2,34]),{10:J,58:$,81:t1,102:e1,104:265,105:230,106:s1,107:u1,108:i1,109:r1},e(W,[2,126]),{14:k1,42:b1,58:g1,86:D1,98:266,102:F1,103:T1,106:S1,108:C1,111:_1,112:x1,113:B1,117:84},{14:k1,42:b1,58:g1,86:D1,98:267,102:F1,103:T1,106:S1,108:C1,111:_1,112:x1,113:B1,117:84},{95:[1,268]},e(T,[2,113]),e(N,[2,53]),{30:269,65:p,77:O,78:P,79:164,113:A,114:d,115:E},e(N,[2,61]),e(nt,l,{5:270}),e(Kt,[2,124],{105:256,10:J,58:$,81:t1,102:e1,106:s1,107:u1,108:i1,109:r1}),e(T,[2,119],{117:160,10:[1,271],14:k1,42:b1,58:g1,86:D1,102:F1,103:T1,106:S1,108:C1,111:_1,112:x1,113:B1}),e(T,[2,120],{117:160,10:[1,272],14:k1,42:b1,58:g1,86:D1,102:F1,103:T1,106:S1,108:C1,111:_1,112:x1,113:B1}),e(T,[2,107]),{31:[1,273],65:p,79:208,113:A,114:d,115:E},{6:11,7:12,8:h,9:U,10:F,11:w,20:17,22:18,23:19,24:20,25:21,26:22,27:X,32:[1,274],33:24,34:o1,36:p1,38:A1,40:28,41:38,42:C,43:39,45:40,58:k,81:l1,82:U1,83:G1,84:M1,85:K1,86:x,99:B,102:m,103:y,106:v,108:V,110:41,111:L,112:I,113:R,118:Y1,119:j1,120:z1,121:X1},{10:J,58:$,81:t1,89:275,102:e1,104:229,105:230,106:s1,107:u1,108:i1,109:r1},{10:J,58:$,81:t1,89:276,102:e1,104:229,105:230,106:s1,107:u1,108:i1,109:r1},e(N,[2,57]),e(b,[2,33]),e(T,[2,117],{103:y1}),e(T,[2,118],{103:y1})],defaultActions:{},parseError:function(a,o){if(o.recoverable)this.trace(a);else{var f=new Error(a);throw f.hash=o,f}},parse:function(a){var o=this,f=[0],r=[],S=[null],t=[],N1=this.table,s="",Y=0,Yt=0,Ce=2,jt=1,_e=t.slice.call(arguments,1),_=Object.create(this.lexer),d1={yy:{}};for(var ot in this.yy)Object.prototype.hasOwnProperty.call(this.yy,ot)&&(d1.yy[ot]=this.yy[ot]);_.setInput(a,d1.yy),d1.yy.lexer=_,d1.yy.parser=this,typeof _.yylloc>"u"&&(_.yylloc={});var lt=_.yylloc;t.push(lt);var xe=_.options&&_.options.ranges;typeof d1.yy.parseError=="function"?this.parseError=d1.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function Be(){var a1;return a1=r.pop()||_.lex()||jt,typeof a1!="number"&&(a1 instanceof Array&&(r=a1,a1=r.pop()),a1=o.symbols_[a1]||a1),a1}for(var G,E1,j,ht,v1={},q1,n1,zt,Q1;;){if(E1=f[f.length-1],this.defaultActions[E1]?j=this.defaultActions[E1]:((G===null||typeof G>"u")&&(G=Be()),j=N1[E1]&&N1[E1][G]),typeof j>"u"||!j.length||!j[0]){var ft="";Q1=[];for(q1 in N1[E1])this.terminals_[q1]&&q1>Ce&&Q1.push("'"+this.terminals_[q1]+"'");_.showPosition?ft="Parse error on line "+(Y+1)+`:
+import{c as et,v as me,s as ye,g as ve,a as Ve,b as Le,x as Ie,y as Re,l as J1,z as dt,A as Ne,j as we,h as w1}from"./mermaid.core-DNo_7Q2B.js";var pt=function(){var e=function(f1,a,o,f){for(o=o||{},f=f1.length;f--;o[f1[f]]=a);return o},u=[1,4],i=[1,3],n=[1,5],c=[1,8,9,10,11,27,34,36,38,42,58,81,82,83,84,85,86,99,102,103,106,108,111,112,113,118,119,120,121],l=[2,2],h=[1,13],U=[1,14],F=[1,15],w=[1,16],X=[1,23],o1=[1,25],p1=[1,26],A1=[1,27],C=[1,49],k=[1,48],l1=[1,29],U1=[1,30],G1=[1,31],M1=[1,32],K1=[1,33],x=[1,44],B=[1,46],m=[1,42],y=[1,47],v=[1,43],V=[1,50],L=[1,45],I=[1,51],R=[1,52],Y1=[1,34],j1=[1,35],z1=[1,36],X1=[1,37],I1=[1,57],b=[1,8,9,10,11,27,32,34,36,38,42,58,81,82,83,84,85,86,99,102,103,106,108,111,112,113,118,119,120,121],q=[1,61],Q=[1,60],Z=[1,62],H1=[8,9,11,73,75],k1=[1,88],b1=[1,93],g1=[1,92],D1=[1,89],F1=[1,85],T1=[1,91],S1=[1,87],C1=[1,94],_1=[1,90],x1=[1,95],B1=[1,86],W1=[8,9,10,11,73,75],N=[8,9,10,11,44,73,75],M=[8,9,10,11,29,42,44,46,48,50,52,54,56,58,61,63,65,66,68,73,75,86,99,102,103,106,108,111,112,113],Et=[8,9,11,42,58,73,75,86,99,102,103,106,108,111,112,113],R1=[42,58,86,99,102,103,106,108,111,112,113],kt=[1,121],bt=[1,120],gt=[1,128],Dt=[1,142],Ft=[1,143],Tt=[1,144],St=[1,145],Ct=[1,130],_t=[1,132],xt=[1,136],Bt=[1,137],mt=[1,138],yt=[1,139],vt=[1,140],Vt=[1,141],Lt=[1,146],It=[1,147],Rt=[1,126],Nt=[1,127],wt=[1,134],Ot=[1,129],Pt=[1,133],Ut=[1,131],nt=[8,9,10,11,27,32,34,36,38,42,58,81,82,83,84,85,86,99,102,103,106,108,111,112,113,118,119,120,121],Gt=[1,149],T=[8,9,11],K=[8,9,10,11,14,42,58,86,102,103,106,108,111,112,113],p=[1,169],O=[1,165],P=[1,166],A=[1,170],d=[1,167],E=[1,168],m1=[75,113,116],g=[8,9,10,11,12,14,27,29,32,42,58,73,81,82,83,84,85,86,87,102,106,108,111,112,113],Mt=[10,103],h1=[31,47,49,51,53,55,60,62,64,65,67,69,113,114,115],J=[1,235],$=[1,233],t1=[1,237],e1=[1,231],s1=[1,232],u1=[1,234],i1=[1,236],r1=[1,238],y1=[1,255],Kt=[8,9,11,103],W=[8,9,10,11,58,81,102,103,106,107,108,109],at={trace:function(){},yy:{},symbols_:{error:2,start:3,graphConfig:4,document:5,line:6,statement:7,SEMI:8,NEWLINE:9,SPACE:10,EOF:11,GRAPH:12,NODIR:13,DIR:14,FirstStmtSeparator:15,ending:16,endToken:17,spaceList:18,spaceListNewline:19,vertexStatement:20,separator:21,styleStatement:22,linkStyleStatement:23,classDefStatement:24,classStatement:25,clickStatement:26,subgraph:27,textNoTags:28,SQS:29,text:30,SQE:31,end:32,direction:33,acc_title:34,acc_title_value:35,acc_descr:36,acc_descr_value:37,acc_descr_multiline_value:38,link:39,node:40,styledVertex:41,AMP:42,vertex:43,STYLE_SEPARATOR:44,idString:45,DOUBLECIRCLESTART:46,DOUBLECIRCLEEND:47,PS:48,PE:49,"(-":50,"-)":51,STADIUMSTART:52,STADIUMEND:53,SUBROUTINESTART:54,SUBROUTINEEND:55,VERTEX_WITH_PROPS_START:56,"NODE_STRING[field]":57,COLON:58,"NODE_STRING[value]":59,PIPE:60,CYLINDERSTART:61,CYLINDEREND:62,DIAMOND_START:63,DIAMOND_STOP:64,TAGEND:65,TRAPSTART:66,TRAPEND:67,INVTRAPSTART:68,INVTRAPEND:69,linkStatement:70,arrowText:71,TESTSTR:72,START_LINK:73,edgeText:74,LINK:75,edgeTextToken:76,STR:77,MD_STR:78,textToken:79,keywords:80,STYLE:81,LINKSTYLE:82,CLASSDEF:83,CLASS:84,CLICK:85,DOWN:86,UP:87,textNoTagsToken:88,stylesOpt:89,"idString[vertex]":90,"idString[class]":91,CALLBACKNAME:92,CALLBACKARGS:93,HREF:94,LINK_TARGET:95,"STR[link]":96,"STR[tooltip]":97,alphaNum:98,DEFAULT:99,numList:100,INTERPOLATE:101,NUM:102,COMMA:103,style:104,styleComponent:105,NODE_STRING:106,UNIT:107,BRKT:108,PCT:109,idStringToken:110,MINUS:111,MULT:112,UNICODE_TEXT:113,TEXT:114,TAGSTART:115,EDGE_TEXT:116,alphaNumToken:117,direction_tb:118,direction_bt:119,direction_rl:120,direction_lr:121,$accept:0,$end:1},terminals_:{2:"error",8:"SEMI",9:"NEWLINE",10:"SPACE",11:"EOF",12:"GRAPH",13:"NODIR",14:"DIR",27:"subgraph",29:"SQS",31:"SQE",32:"end",34:"acc_title",35:"acc_title_value",36:"acc_descr",37:"acc_descr_value",38:"acc_descr_multiline_value",42:"AMP",44:"STYLE_SEPARATOR",46:"DOUBLECIRCLESTART",47:"DOUBLECIRCLEEND",48:"PS",49:"PE",50:"(-",51:"-)",52:"STADIUMSTART",53:"STADIUMEND",54:"SUBROUTINESTART",55:"SUBROUTINEEND",56:"VERTEX_WITH_PROPS_START",57:"NODE_STRING[field]",58:"COLON",59:"NODE_STRING[value]",60:"PIPE",61:"CYLINDERSTART",62:"CYLINDEREND",63:"DIAMOND_START",64:"DIAMOND_STOP",65:"TAGEND",66:"TRAPSTART",67:"TRAPEND",68:"INVTRAPSTART",69:"INVTRAPEND",72:"TESTSTR",73:"START_LINK",75:"LINK",77:"STR",78:"MD_STR",81:"STYLE",82:"LINKSTYLE",83:"CLASSDEF",84:"CLASS",85:"CLICK",86:"DOWN",87:"UP",90:"idString[vertex]",91:"idString[class]",92:"CALLBACKNAME",93:"CALLBACKARGS",94:"HREF",95:"LINK_TARGET",96:"STR[link]",97:"STR[tooltip]",99:"DEFAULT",101:"INTERPOLATE",102:"NUM",103:"COMMA",106:"NODE_STRING",107:"UNIT",108:"BRKT",109:"PCT",111:"MINUS",112:"MULT",113:"UNICODE_TEXT",114:"TEXT",115:"TAGSTART",116:"EDGE_TEXT",118:"direction_tb",119:"direction_bt",120:"direction_rl",121:"direction_lr"},productions_:[0,[3,2],[5,0],[5,2],[6,1],[6,1],[6,1],[6,1],[6,1],[4,2],[4,2],[4,2],[4,3],[16,2],[16,1],[17,1],[17,1],[17,1],[15,1],[15,1],[15,2],[19,2],[19,2],[19,1],[19,1],[18,2],[18,1],[7,2],[7,2],[7,2],[7,2],[7,2],[7,2],[7,9],[7,6],[7,4],[7,1],[7,2],[7,2],[7,1],[21,1],[21,1],[21,1],[20,3],[20,4],[20,2],[20,1],[40,1],[40,5],[41,1],[41,3],[43,4],[43,4],[43,6],[43,4],[43,4],[43,4],[43,8],[43,4],[43,4],[43,4],[43,6],[43,4],[43,4],[43,4],[43,4],[43,4],[43,1],[39,2],[39,3],[39,3],[39,1],[39,3],[74,1],[74,2],[74,1],[74,1],[70,1],[71,3],[30,1],[30,2],[30,1],[30,1],[80,1],[80,1],[80,1],[80,1],[80,1],[80,1],[80,1],[80,1],[80,1],[80,1],[80,1],[28,1],[28,2],[28,1],[28,1],[24,5],[25,5],[26,2],[26,4],[26,3],[26,5],[26,3],[26,5],[26,5],[26,7],[26,2],[26,4],[26,2],[26,4],[26,4],[26,6],[22,5],[23,5],[23,5],[23,9],[23,9],[23,7],[23,7],[100,1],[100,3],[89,1],[89,3],[104,1],[104,2],[105,1],[105,1],[105,1],[105,1],[105,1],[105,1],[105,1],[105,1],[110,1],[110,1],[110,1],[110,1],[110,1],[110,1],[110,1],[110,1],[110,1],[110,1],[110,1],[79,1],[79,1],[79,1],[79,1],[88,1],[88,1],[88,1],[88,1],[88,1],[88,1],[88,1],[88,1],[88,1],[88,1],[88,1],[76,1],[76,1],[117,1],[117,1],[117,1],[117,1],[117,1],[117,1],[117,1],[117,1],[117,1],[117,1],[117,1],[45,1],[45,2],[98,1],[98,2],[33,1],[33,1],[33,1],[33,1]],performAction:function(a,o,f,r,S,t,N1){var s=t.length-1;switch(S){case 2:this.$=[];break;case 3:(!Array.isArray(t[s])||t[s].length>0)&&t[s-1].push(t[s]),this.$=t[s-1];break;case 4:case 176:this.$=t[s];break;case 11:r.setDirection("TB"),this.$="TB";break;case 12:r.setDirection(t[s-1]),this.$=t[s-1];break;case 27:this.$=t[s-1].nodes;break;case 28:case 29:case 30:case 31:case 32:this.$=[];break;case 33:this.$=r.addSubGraph(t[s-6],t[s-1],t[s-4]);break;case 34:this.$=r.addSubGraph(t[s-3],t[s-1],t[s-3]);break;case 35:this.$=r.addSubGraph(void 0,t[s-1],void 0);break;case 37:this.$=t[s].trim(),r.setAccTitle(this.$);break;case 38:case 39:this.$=t[s].trim(),r.setAccDescription(this.$);break;case 43:r.addLink(t[s-2].stmt,t[s],t[s-1]),this.$={stmt:t[s],nodes:t[s].concat(t[s-2].nodes)};break;case 44:r.addLink(t[s-3].stmt,t[s-1],t[s-2]),this.$={stmt:t[s-1],nodes:t[s-1].concat(t[s-3].nodes)};break;case 45:this.$={stmt:t[s-1],nodes:t[s-1]};break;case 46:this.$={stmt:t[s],nodes:t[s]};break;case 47:this.$=[t[s]];break;case 48:this.$=t[s-4].concat(t[s]);break;case 49:this.$=t[s];break;case 50:this.$=t[s-2],r.setClass(t[s-2],t[s]);break;case 51:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"square");break;case 52:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"doublecircle");break;case 53:this.$=t[s-5],r.addVertex(t[s-5],t[s-2],"circle");break;case 54:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"ellipse");break;case 55:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"stadium");break;case 56:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"subroutine");break;case 57:this.$=t[s-7],r.addVertex(t[s-7],t[s-1],"rect",void 0,void 0,void 0,Object.fromEntries([[t[s-5],t[s-3]]]));break;case 58:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"cylinder");break;case 59:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"round");break;case 60:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"diamond");break;case 61:this.$=t[s-5],r.addVertex(t[s-5],t[s-2],"hexagon");break;case 62:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"odd");break;case 63:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"trapezoid");break;case 64:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"inv_trapezoid");break;case 65:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"lean_right");break;case 66:this.$=t[s-3],r.addVertex(t[s-3],t[s-1],"lean_left");break;case 67:this.$=t[s],r.addVertex(t[s]);break;case 68:t[s-1].text=t[s],this.$=t[s-1];break;case 69:case 70:t[s-2].text=t[s-1],this.$=t[s-2];break;case 71:this.$=t[s];break;case 72:var Y=r.destructLink(t[s],t[s-2]);this.$={type:Y.type,stroke:Y.stroke,length:Y.length,text:t[s-1]};break;case 73:this.$={text:t[s],type:"text"};break;case 74:this.$={text:t[s-1].text+""+t[s],type:t[s-1].type};break;case 75:this.$={text:t[s],type:"string"};break;case 76:this.$={text:t[s],type:"markdown"};break;case 77:var Y=r.destructLink(t[s]);this.$={type:Y.type,stroke:Y.stroke,length:Y.length};break;case 78:this.$=t[s-1];break;case 79:this.$={text:t[s],type:"text"};break;case 80:this.$={text:t[s-1].text+""+t[s],type:t[s-1].type};break;case 81:this.$={text:t[s],type:"string"};break;case 82:case 97:this.$={text:t[s],type:"markdown"};break;case 94:this.$={text:t[s],type:"text"};break;case 95:this.$={text:t[s-1].text+""+t[s],type:t[s-1].type};break;case 96:this.$={text:t[s],type:"text"};break;case 98:this.$=t[s-4],r.addClass(t[s-2],t[s]);break;case 99:this.$=t[s-4],r.setClass(t[s-2],t[s]);break;case 100:case 108:this.$=t[s-1],r.setClickEvent(t[s-1],t[s]);break;case 101:case 109:this.$=t[s-3],r.setClickEvent(t[s-3],t[s-2]),r.setTooltip(t[s-3],t[s]);break;case 102:this.$=t[s-2],r.setClickEvent(t[s-2],t[s-1],t[s]);break;case 103:this.$=t[s-4],r.setClickEvent(t[s-4],t[s-3],t[s-2]),r.setTooltip(t[s-4],t[s]);break;case 104:this.$=t[s-2],r.setLink(t[s-2],t[s]);break;case 105:this.$=t[s-4],r.setLink(t[s-4],t[s-2]),r.setTooltip(t[s-4],t[s]);break;case 106:this.$=t[s-4],r.setLink(t[s-4],t[s-2],t[s]);break;case 107:this.$=t[s-6],r.setLink(t[s-6],t[s-4],t[s]),r.setTooltip(t[s-6],t[s-2]);break;case 110:this.$=t[s-1],r.setLink(t[s-1],t[s]);break;case 111:this.$=t[s-3],r.setLink(t[s-3],t[s-2]),r.setTooltip(t[s-3],t[s]);break;case 112:this.$=t[s-3],r.setLink(t[s-3],t[s-2],t[s]);break;case 113:this.$=t[s-5],r.setLink(t[s-5],t[s-4],t[s]),r.setTooltip(t[s-5],t[s-2]);break;case 114:this.$=t[s-4],r.addVertex(t[s-2],void 0,void 0,t[s]);break;case 115:this.$=t[s-4],r.updateLink([t[s-2]],t[s]);break;case 116:this.$=t[s-4],r.updateLink(t[s-2],t[s]);break;case 117:this.$=t[s-8],r.updateLinkInterpolate([t[s-6]],t[s-2]),r.updateLink([t[s-6]],t[s]);break;case 118:this.$=t[s-8],r.updateLinkInterpolate(t[s-6],t[s-2]),r.updateLink(t[s-6],t[s]);break;case 119:this.$=t[s-6],r.updateLinkInterpolate([t[s-4]],t[s]);break;case 120:this.$=t[s-6],r.updateLinkInterpolate(t[s-4],t[s]);break;case 121:case 123:this.$=[t[s]];break;case 122:case 124:t[s-2].push(t[s]),this.$=t[s-2];break;case 126:this.$=t[s-1]+t[s];break;case 174:this.$=t[s];break;case 175:this.$=t[s-1]+""+t[s];break;case 177:this.$=t[s-1]+""+t[s];break;case 178:this.$={stmt:"dir",value:"TB"};break;case 179:this.$={stmt:"dir",value:"BT"};break;case 180:this.$={stmt:"dir",value:"RL"};break;case 181:this.$={stmt:"dir",value:"LR"};break}},table:[{3:1,4:2,9:u,10:i,12:n},{1:[3]},e(c,l,{5:6}),{4:7,9:u,10:i,12:n},{4:8,9:u,10:i,12:n},{13:[1,9],14:[1,10]},{1:[2,1],6:11,7:12,8:h,9:U,10:F,11:w,20:17,22:18,23:19,24:20,25:21,26:22,27:X,33:24,34:o1,36:p1,38:A1,40:28,41:38,42:C,43:39,45:40,58:k,81:l1,82:U1,83:G1,84:M1,85:K1,86:x,99:B,102:m,103:y,106:v,108:V,110:41,111:L,112:I,113:R,118:Y1,119:j1,120:z1,121:X1},e(c,[2,9]),e(c,[2,10]),e(c,[2,11]),{8:[1,54],9:[1,55],10:I1,15:53,18:56},e(b,[2,3]),e(b,[2,4]),e(b,[2,5]),e(b,[2,6]),e(b,[2,7]),e(b,[2,8]),{8:q,9:Q,11:Z,21:58,39:59,70:63,73:[1,64],75:[1,65]},{8:q,9:Q,11:Z,21:66},{8:q,9:Q,11:Z,21:67},{8:q,9:Q,11:Z,21:68},{8:q,9:Q,11:Z,21:69},{8:q,9:Q,11:Z,21:70},{8:q,9:Q,10:[1,71],11:Z,21:72},e(b,[2,36]),{35:[1,73]},{37:[1,74]},e(b,[2,39]),e(H1,[2,46],{18:75,10:I1}),{10:[1,76]},{10:[1,77]},{10:[1,78]},{10:[1,79]},{14:k1,42:b1,58:g1,77:[1,83],86:D1,92:[1,80],94:[1,81],98:82,102:F1,103:T1,106:S1,108:C1,111:_1,112:x1,113:B1,117:84},e(b,[2,178]),e(b,[2,179]),e(b,[2,180]),e(b,[2,181]),e(W1,[2,47]),e(W1,[2,49],{44:[1,96]}),e(N,[2,67],{110:109,29:[1,97],42:C,46:[1,98],48:[1,99],50:[1,100],52:[1,101],54:[1,102],56:[1,103],58:k,61:[1,104],63:[1,105],65:[1,106],66:[1,107],68:[1,108],86:x,99:B,102:m,103:y,106:v,108:V,111:L,112:I,113:R}),e(M,[2,174]),e(M,[2,135]),e(M,[2,136]),e(M,[2,137]),e(M,[2,138]),e(M,[2,139]),e(M,[2,140]),e(M,[2,141]),e(M,[2,142]),e(M,[2,143]),e(M,[2,144]),e(M,[2,145]),e(c,[2,12]),e(c,[2,18]),e(c,[2,19]),{9:[1,110]},e(Et,[2,26],{18:111,10:I1}),e(b,[2,27]),{40:112,41:38,42:C,43:39,45:40,58:k,86:x,99:B,102:m,103:y,106:v,108:V,110:41,111:L,112:I,113:R},e(b,[2,40]),e(b,[2,41]),e(b,[2,42]),e(R1,[2,71],{71:113,60:[1,115],72:[1,114]}),{74:116,76:117,77:[1,118],78:[1,119],113:kt,116:bt},e([42,58,60,72,86,99,102,103,106,108,111,112,113],[2,77]),e(b,[2,28]),e(b,[2,29]),e(b,[2,30]),e(b,[2,31]),e(b,[2,32]),{10:gt,12:Dt,14:Ft,27:Tt,28:122,32:St,42:Ct,58:_t,73:xt,77:[1,124],78:[1,125],80:135,81:Bt,82:mt,83:yt,84:vt,85:Vt,86:Lt,87:It,88:123,102:Rt,106:Nt,108:wt,111:Ot,112:Pt,113:Ut},e(nt,l,{5:148}),e(b,[2,37]),e(b,[2,38]),e(H1,[2,45],{42:Gt}),{42:C,45:150,58:k,86:x,99:B,102:m,103:y,106:v,108:V,110:41,111:L,112:I,113:R},{99:[1,151],100:152,102:[1,153]},{42:C,45:154,58:k,86:x,99:B,102:m,103:y,106:v,108:V,110:41,111:L,112:I,113:R},{42:C,45:155,58:k,86:x,99:B,102:m,103:y,106:v,108:V,110:41,111:L,112:I,113:R},e(T,[2,100],{10:[1,156],93:[1,157]}),{77:[1,158]},e(T,[2,108],{117:160,10:[1,159],14:k1,42:b1,58:g1,86:D1,102:F1,103:T1,106:S1,108:C1,111:_1,112:x1,113:B1}),e(T,[2,110],{10:[1,161]}),e(K,[2,176]),e(K,[2,163]),e(K,[2,164]),e(K,[2,165]),e(K,[2,166]),e(K,[2,167]),e(K,[2,168]),e(K,[2,169]),e(K,[2,170]),e(K,[2,171]),e(K,[2,172]),e(K,[2,173]),{42:C,45:162,58:k,86:x,99:B,102:m,103:y,106:v,108:V,110:41,111:L,112:I,113:R},{30:163,65:p,77:O,78:P,79:164,113:A,114:d,115:E},{30:171,65:p,77:O,78:P,79:164,113:A,114:d,115:E},{30:173,48:[1,172],65:p,77:O,78:P,79:164,113:A,114:d,115:E},{30:174,65:p,77:O,78:P,79:164,113:A,114:d,115:E},{30:175,65:p,77:O,78:P,79:164,113:A,114:d,115:E},{30:176,65:p,77:O,78:P,79:164,113:A,114:d,115:E},{106:[1,177]},{30:178,65:p,77:O,78:P,79:164,113:A,114:d,115:E},{30:179,63:[1,180],65:p,77:O,78:P,79:164,113:A,114:d,115:E},{30:181,65:p,77:O,78:P,79:164,113:A,114:d,115:E},{30:182,65:p,77:O,78:P,79:164,113:A,114:d,115:E},{30:183,65:p,77:O,78:P,79:164,113:A,114:d,115:E},e(M,[2,175]),e(c,[2,20]),e(Et,[2,25]),e(H1,[2,43],{18:184,10:I1}),e(R1,[2,68],{10:[1,185]}),{10:[1,186]},{30:187,65:p,77:O,78:P,79:164,113:A,114:d,115:E},{75:[1,188],76:189,113:kt,116:bt},e(m1,[2,73]),e(m1,[2,75]),e(m1,[2,76]),e(m1,[2,161]),e(m1,[2,162]),{8:q,9:Q,10:gt,11:Z,12:Dt,14:Ft,21:191,27:Tt,29:[1,190],32:St,42:Ct,58:_t,73:xt,80:135,81:Bt,82:mt,83:yt,84:vt,85:Vt,86:Lt,87:It,88:192,102:Rt,106:Nt,108:wt,111:Ot,112:Pt,113:Ut},e(g,[2,94]),e(g,[2,96]),e(g,[2,97]),e(g,[2,150]),e(g,[2,151]),e(g,[2,152]),e(g,[2,153]),e(g,[2,154]),e(g,[2,155]),e(g,[2,156]),e(g,[2,157]),e(g,[2,158]),e(g,[2,159]),e(g,[2,160]),e(g,[2,83]),e(g,[2,84]),e(g,[2,85]),e(g,[2,86]),e(g,[2,87]),e(g,[2,88]),e(g,[2,89]),e(g,[2,90]),e(g,[2,91]),e(g,[2,92]),e(g,[2,93]),{6:11,7:12,8:h,9:U,10:F,11:w,20:17,22:18,23:19,24:20,25:21,26:22,27:X,32:[1,193],33:24,34:o1,36:p1,38:A1,40:28,41:38,42:C,43:39,45:40,58:k,81:l1,82:U1,83:G1,84:M1,85:K1,86:x,99:B,102:m,103:y,106:v,108:V,110:41,111:L,112:I,113:R,118:Y1,119:j1,120:z1,121:X1},{10:I1,18:194},{10:[1,195],42:C,58:k,86:x,99:B,102:m,103:y,106:v,108:V,110:109,111:L,112:I,113:R},{10:[1,196]},{10:[1,197],103:[1,198]},e(Mt,[2,121]),{10:[1,199],42:C,58:k,86:x,99:B,102:m,103:y,106:v,108:V,110:109,111:L,112:I,113:R},{10:[1,200],42:C,58:k,86:x,99:B,102:m,103:y,106:v,108:V,110:109,111:L,112:I,113:R},{77:[1,201]},e(T,[2,102],{10:[1,202]}),e(T,[2,104],{10:[1,203]}),{77:[1,204]},e(K,[2,177]),{77:[1,205],95:[1,206]},e(W1,[2,50],{110:109,42:C,58:k,86:x,99:B,102:m,103:y,106:v,108:V,111:L,112:I,113:R}),{31:[1,207],65:p,79:208,113:A,114:d,115:E},e(h1,[2,79]),e(h1,[2,81]),e(h1,[2,82]),e(h1,[2,146]),e(h1,[2,147]),e(h1,[2,148]),e(h1,[2,149]),{47:[1,209],65:p,79:208,113:A,114:d,115:E},{30:210,65:p,77:O,78:P,79:164,113:A,114:d,115:E},{49:[1,211],65:p,79:208,113:A,114:d,115:E},{51:[1,212],65:p,79:208,113:A,114:d,115:E},{53:[1,213],65:p,79:208,113:A,114:d,115:E},{55:[1,214],65:p,79:208,113:A,114:d,115:E},{58:[1,215]},{62:[1,216],65:p,79:208,113:A,114:d,115:E},{64:[1,217],65:p,79:208,113:A,114:d,115:E},{30:218,65:p,77:O,78:P,79:164,113:A,114:d,115:E},{31:[1,219],65:p,79:208,113:A,114:d,115:E},{65:p,67:[1,220],69:[1,221],79:208,113:A,114:d,115:E},{65:p,67:[1,223],69:[1,222],79:208,113:A,114:d,115:E},e(H1,[2,44],{42:Gt}),e(R1,[2,70]),e(R1,[2,69]),{60:[1,224],65:p,79:208,113:A,114:d,115:E},e(R1,[2,72]),e(m1,[2,74]),{30:225,65:p,77:O,78:P,79:164,113:A,114:d,115:E},e(nt,l,{5:226}),e(g,[2,95]),e(b,[2,35]),{41:227,42:C,43:39,45:40,58:k,86:x,99:B,102:m,103:y,106:v,108:V,110:41,111:L,112:I,113:R},{10:J,58:$,81:t1,89:228,102:e1,104:229,105:230,106:s1,107:u1,108:i1,109:r1},{10:J,58:$,81:t1,89:239,101:[1,240],102:e1,104:229,105:230,106:s1,107:u1,108:i1,109:r1},{10:J,58:$,81:t1,89:241,101:[1,242],102:e1,104:229,105:230,106:s1,107:u1,108:i1,109:r1},{102:[1,243]},{10:J,58:$,81:t1,89:244,102:e1,104:229,105:230,106:s1,107:u1,108:i1,109:r1},{42:C,45:245,58:k,86:x,99:B,102:m,103:y,106:v,108:V,110:41,111:L,112:I,113:R},e(T,[2,101]),{77:[1,246]},{77:[1,247],95:[1,248]},e(T,[2,109]),e(T,[2,111],{10:[1,249]}),e(T,[2,112]),e(N,[2,51]),e(h1,[2,80]),e(N,[2,52]),{49:[1,250],65:p,79:208,113:A,114:d,115:E},e(N,[2,59]),e(N,[2,54]),e(N,[2,55]),e(N,[2,56]),{106:[1,251]},e(N,[2,58]),e(N,[2,60]),{64:[1,252],65:p,79:208,113:A,114:d,115:E},e(N,[2,62]),e(N,[2,63]),e(N,[2,65]),e(N,[2,64]),e(N,[2,66]),e([10,42,58,86,99,102,103,106,108,111,112,113],[2,78]),{31:[1,253],65:p,79:208,113:A,114:d,115:E},{6:11,7:12,8:h,9:U,10:F,11:w,20:17,22:18,23:19,24:20,25:21,26:22,27:X,32:[1,254],33:24,34:o1,36:p1,38:A1,40:28,41:38,42:C,43:39,45:40,58:k,81:l1,82:U1,83:G1,84:M1,85:K1,86:x,99:B,102:m,103:y,106:v,108:V,110:41,111:L,112:I,113:R,118:Y1,119:j1,120:z1,121:X1},e(W1,[2,48]),e(T,[2,114],{103:y1}),e(Kt,[2,123],{105:256,10:J,58:$,81:t1,102:e1,106:s1,107:u1,108:i1,109:r1}),e(W,[2,125]),e(W,[2,127]),e(W,[2,128]),e(W,[2,129]),e(W,[2,130]),e(W,[2,131]),e(W,[2,132]),e(W,[2,133]),e(W,[2,134]),e(T,[2,115],{103:y1}),{10:[1,257]},e(T,[2,116],{103:y1}),{10:[1,258]},e(Mt,[2,122]),e(T,[2,98],{103:y1}),e(T,[2,99],{110:109,42:C,58:k,86:x,99:B,102:m,103:y,106:v,108:V,111:L,112:I,113:R}),e(T,[2,103]),e(T,[2,105],{10:[1,259]}),e(T,[2,106]),{95:[1,260]},{49:[1,261]},{60:[1,262]},{64:[1,263]},{8:q,9:Q,11:Z,21:264},e(b,[2,34]),{10:J,58:$,81:t1,102:e1,104:265,105:230,106:s1,107:u1,108:i1,109:r1},e(W,[2,126]),{14:k1,42:b1,58:g1,86:D1,98:266,102:F1,103:T1,106:S1,108:C1,111:_1,112:x1,113:B1,117:84},{14:k1,42:b1,58:g1,86:D1,98:267,102:F1,103:T1,106:S1,108:C1,111:_1,112:x1,113:B1,117:84},{95:[1,268]},e(T,[2,113]),e(N,[2,53]),{30:269,65:p,77:O,78:P,79:164,113:A,114:d,115:E},e(N,[2,61]),e(nt,l,{5:270}),e(Kt,[2,124],{105:256,10:J,58:$,81:t1,102:e1,106:s1,107:u1,108:i1,109:r1}),e(T,[2,119],{117:160,10:[1,271],14:k1,42:b1,58:g1,86:D1,102:F1,103:T1,106:S1,108:C1,111:_1,112:x1,113:B1}),e(T,[2,120],{117:160,10:[1,272],14:k1,42:b1,58:g1,86:D1,102:F1,103:T1,106:S1,108:C1,111:_1,112:x1,113:B1}),e(T,[2,107]),{31:[1,273],65:p,79:208,113:A,114:d,115:E},{6:11,7:12,8:h,9:U,10:F,11:w,20:17,22:18,23:19,24:20,25:21,26:22,27:X,32:[1,274],33:24,34:o1,36:p1,38:A1,40:28,41:38,42:C,43:39,45:40,58:k,81:l1,82:U1,83:G1,84:M1,85:K1,86:x,99:B,102:m,103:y,106:v,108:V,110:41,111:L,112:I,113:R,118:Y1,119:j1,120:z1,121:X1},{10:J,58:$,81:t1,89:275,102:e1,104:229,105:230,106:s1,107:u1,108:i1,109:r1},{10:J,58:$,81:t1,89:276,102:e1,104:229,105:230,106:s1,107:u1,108:i1,109:r1},e(N,[2,57]),e(b,[2,33]),e(T,[2,117],{103:y1}),e(T,[2,118],{103:y1})],defaultActions:{},parseError:function(a,o){if(o.recoverable)this.trace(a);else{var f=new Error(a);throw f.hash=o,f}},parse:function(a){var o=this,f=[0],r=[],S=[null],t=[],N1=this.table,s="",Y=0,Yt=0,Ce=2,jt=1,_e=t.slice.call(arguments,1),_=Object.create(this.lexer),d1={yy:{}};for(var ot in this.yy)Object.prototype.hasOwnProperty.call(this.yy,ot)&&(d1.yy[ot]=this.yy[ot]);_.setInput(a,d1.yy),d1.yy.lexer=_,d1.yy.parser=this,typeof _.yylloc>"u"&&(_.yylloc={});var lt=_.yylloc;t.push(lt);var xe=_.options&&_.options.ranges;typeof d1.yy.parseError=="function"?this.parseError=d1.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function Be(){var a1;return a1=r.pop()||_.lex()||jt,typeof a1!="number"&&(a1 instanceof Array&&(r=a1,a1=r.pop()),a1=o.symbols_[a1]||a1),a1}for(var G,E1,j,ht,v1={},q1,n1,zt,Q1;;){if(E1=f[f.length-1],this.defaultActions[E1]?j=this.defaultActions[E1]:((G===null||typeof G>"u")&&(G=Be()),j=N1[E1]&&N1[E1][G]),typeof j>"u"||!j.length||!j[0]){var ft="";Q1=[];for(q1 in N1[E1])this.terminals_[q1]&&q1>Ce&&Q1.push("'"+this.terminals_[q1]+"'");_.showPosition?ft="Parse error on line "+(Y+1)+`:
 `+_.showPosition()+`
 Expecting `+Q1.join(", ")+", got '"+(this.terminals_[G]||G)+"'":ft="Parse error on line "+(Y+1)+": Unexpected "+(G==jt?"end of input":"'"+(this.terminals_[G]||G)+"'"),this.parseError(ft,{text:_.match,token:this.terminals_[G]||G,line:_.yylineno,loc:lt,expected:Q1})}if(j[0]instanceof Array&&j.length>1)throw new Error("Parse Error: multiple actions possible at state: "+E1+", token: "+G);switch(j[0]){case 1:f.push(G),S.push(_.yytext),t.push(_.yylloc),f.push(j[1]),G=null,Yt=_.yyleng,s=_.yytext,Y=_.yylineno,lt=_.yylloc;break;case 2:if(n1=this.productions_[j[1]][1],v1.$=S[S.length-n1],v1._$={first_line:t[t.length-(n1||1)].first_line,last_line:t[t.length-1].last_line,first_column:t[t.length-(n1||1)].first_column,last_column:t[t.length-1].last_column},xe&&(v1._$.range=[t[t.length-(n1||1)].range[0],t[t.length-1].range[1]]),ht=this.performAction.apply(v1,[s,Yt,Y,d1.yy,j[1],S,t].concat(_e)),typeof ht<"u")return ht;n1&&(f=f.slice(0,-1*n1*2),S=S.slice(0,-1*n1),t=t.slice(0,-1*n1)),f.push(this.productions_[j[1]][0]),S.push(v1.$),t.push(v1._$),zt=N1[f[f.length-2]][f[f.length-1]],f.push(zt);break;case 3:return!0}}return!0}},Se=function(){var f1={EOF:1,parseError:function(o,f){if(this.yy.parser)this.yy.parser.parseError(o,f);else throw new Error(o)},setInput:function(a,o){return this.yy=o||this.yy||{},this._input=a,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var a=this._input[0];this.yytext+=a,this.yyleng++,this.offset++,this.match+=a,this.matched+=a;var o=a.match(/(?:\r\n?|\n).*/g);return o?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),a},unput:function(a){var o=a.length,f=a.split(/(?:\r\n?|\n)/g);this._input=a+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-o),this.offset-=o;var r=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),f.length-1&&(this.yylineno-=f.length-1);var S=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:f?(f.length===r.length?this.yylloc.first_column:0)+r[r.length-f.length].length-f[0].length:this.yylloc.first_column-o},this.options.ranges&&(this.yylloc.range=[S[0],S[0]+this.yyleng-o]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){if(this.options.backtrack_lexer)this._backtrack=!0;else return this.parseError("Lexical error on line "+(this.yylineno+1)+`. You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).
 `+this.showPosition(),{text:"",token:null,line:this.yylineno});return this},less:function(a){this.unput(this.match.slice(a))},pastInput:function(){var a=this.matched.substr(0,this.matched.length-this.match.length);return(a.length>20?"...":"")+a.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var a=this.match;return a.length<20&&(a+=this._input.substr(0,20-a.length)),(a.substr(0,20)+(a.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var a=this.pastInput(),o=new Array(a.length+1).join("-");return a+this.upcomingInput()+`
diff --git a/assets/flowDiagram-622f9fc1-C8iBq7aS.js b/assets/flowDiagram-622f9fc1-BpT3eoaF.js
similarity index 97%
rename from assets/flowDiagram-622f9fc1-C8iBq7aS.js
rename to assets/flowDiagram-622f9fc1-BpT3eoaF.js
index bb37059..76b1d4d 100644
--- a/assets/flowDiagram-622f9fc1-C8iBq7aS.js
+++ b/assets/flowDiagram-622f9fc1-BpT3eoaF.js
@@ -1,4 +1,4 @@
-import{p as Lt,f as V}from"./flowDb-0da60e67-C3mEtQas.js";import{h as S,f as tt,G as _t}from"./graph-T5JS4vfK.js";import{h as x,o as U,p as Y,q as et,c as G,r as rt,j as at,l as R,t as z,u as Et}from"./mermaid.core-ChLYKTZm.js";import{u as Tt,r as Nt,p as At,l as Ct,d as M}from"./layout-DUYLy6Ue.js";import{a as N,b as nt,i as st,c as E,e as it,d as ot,f as It,g as Bt,s as Mt}from"./styles-422bd1c9-CXxGUMW8.js";import{l as Dt}from"./line-D0jG_HZ-.js";import"./app-B69Gl_S-.js";import"./index-9620d214-B8uh0R2i.js";import"./clone-CI3kFeqi.js";import"./edges-5962ec63-B19hLEst.js";import"./createText-4a4f35c9-BuT3nXUz.js";import"./channel-DJsAcM5I.js";import"./array-BKyUJesY.js";import"./path-CbwjOpE9.js";function Rt(r){if(!r.ok)throw new Error(r.status+" "+r.statusText);return r.text()}function Gt(r,e){return fetch(r,e).then(Rt)}function Pt(r){return(e,t)=>Gt(e,t).then(n=>new DOMParser().parseFromString(n,r))}var Ut=Pt("image/svg+xml"),H={normal:Wt,vee:Vt,undirected:zt};function $t(r){H=r}function Wt(r,e,t,n){var a=r.append("marker").attr("id",e).attr("viewBox","0 0 10 10").attr("refX",9).attr("refY",5).attr("markerUnits","strokeWidth").attr("markerWidth",8).attr("markerHeight",6).attr("orient","auto"),s=a.append("path").attr("d","M 0 0 L 10 5 L 0 10 z").style("stroke-width",1).style("stroke-dasharray","1,0");N(s,t[n+"Style"]),t[n+"Class"]&&s.attr("class",t[n+"Class"])}function Vt(r,e,t,n){var a=r.append("marker").attr("id",e).attr("viewBox","0 0 10 10").attr("refX",9).attr("refY",5).attr("markerUnits","strokeWidth").attr("markerWidth",8).attr("markerHeight",6).attr("orient","auto"),s=a.append("path").attr("d","M 0 0 L 10 5 L 0 10 L 4 5 z").style("stroke-width",1).style("stroke-dasharray","1,0");N(s,t[n+"Style"]),t[n+"Class"]&&s.attr("class",t[n+"Class"])}function zt(r,e,t,n){var a=r.append("marker").attr("id",e).attr("viewBox","0 0 10 10").attr("refX",9).attr("refY",5).attr("markerUnits","strokeWidth").attr("markerWidth",8).attr("markerHeight",6).attr("orient","auto"),s=a.append("path").attr("d","M 0 5 L 10 5").style("stroke-width",1).style("stroke-dasharray","1,0");N(s,t[n+"Style"]),t[n+"Class"]&&s.attr("class",t[n+"Class"])}function Yt(r,e){var t=r;return t.node().appendChild(e.label),N(t,e.labelStyle),t}function Ht(r,e){for(var t=r.append("text"),n=Xt(e.label).split(`
+import{p as Lt,f as V}from"./flowDb-0da60e67-XaXEQp9e.js";import{h as S,f as tt,G as _t}from"./graph-B1296pfd.js";import{h as x,o as U,p as Y,q as et,c as G,r as rt,j as at,l as R,t as z,u as Et}from"./mermaid.core-DNo_7Q2B.js";import{u as Tt,r as Nt,p as At,l as Ct,d as M}from"./layout-qMafh1ee.js";import{a as N,b as nt,i as st,c as E,e as it,d as ot,f as It,g as Bt,s as Mt}from"./styles-422bd1c9-CFsDtXUv.js";import{l as Dt}from"./line-BqHmcuby.js";import"./app-B4LGNJZ0.js";import"./index-9620d214-BlfbO5wW.js";import"./clone-C3EvpqoY.js";import"./edges-5962ec63-ApWhby2b.js";import"./createText-4a4f35c9-CISzj231.js";import"./channel-yU22lAlC.js";import"./array-BKyUJesY.js";import"./path-CbwjOpE9.js";function Rt(r){if(!r.ok)throw new Error(r.status+" "+r.statusText);return r.text()}function Gt(r,e){return fetch(r,e).then(Rt)}function Pt(r){return(e,t)=>Gt(e,t).then(n=>new DOMParser().parseFromString(n,r))}var Ut=Pt("image/svg+xml"),H={normal:Wt,vee:Vt,undirected:zt};function $t(r){H=r}function Wt(r,e,t,n){var a=r.append("marker").attr("id",e).attr("viewBox","0 0 10 10").attr("refX",9).attr("refY",5).attr("markerUnits","strokeWidth").attr("markerWidth",8).attr("markerHeight",6).attr("orient","auto"),s=a.append("path").attr("d","M 0 0 L 10 5 L 0 10 z").style("stroke-width",1).style("stroke-dasharray","1,0");N(s,t[n+"Style"]),t[n+"Class"]&&s.attr("class",t[n+"Class"])}function Vt(r,e,t,n){var a=r.append("marker").attr("id",e).attr("viewBox","0 0 10 10").attr("refX",9).attr("refY",5).attr("markerUnits","strokeWidth").attr("markerWidth",8).attr("markerHeight",6).attr("orient","auto"),s=a.append("path").attr("d","M 0 0 L 10 5 L 0 10 L 4 5 z").style("stroke-width",1).style("stroke-dasharray","1,0");N(s,t[n+"Style"]),t[n+"Class"]&&s.attr("class",t[n+"Class"])}function zt(r,e,t,n){var a=r.append("marker").attr("id",e).attr("viewBox","0 0 10 10").attr("refX",9).attr("refY",5).attr("markerUnits","strokeWidth").attr("markerWidth",8).attr("markerHeight",6).attr("orient","auto"),s=a.append("path").attr("d","M 0 5 L 10 5").style("stroke-width",1).style("stroke-dasharray","1,0");N(s,t[n+"Style"]),t[n+"Class"]&&s.attr("class",t[n+"Class"])}function Yt(r,e){var t=r;return t.node().appendChild(e.label),N(t,e.labelStyle),t}function Ht(r,e){for(var t=r.append("text"),n=Xt(e.label).split(`
 `),a=0;a<n.length;a++)t.append("tspan").attr("xml:space","preserve").attr("dy","1em").attr("x","1").text(n[a]);return N(t,e.labelStyle),t}function Xt(r){for(var e="",t=!1,n,a=0;a<r.length;++a)if(n=r[a],t){switch(n){case"n":e+=`
 `;break;default:e+=n}t=!1}else n==="\\"?t=!0:e+=n;return e}function J(r,e,t){var n=e.label,a=r.append("g");e.labelType==="svg"?Yt(a,e):typeof n!="string"||e.labelType==="html"?nt(a,e):Ht(a,e);var s=a.node().getBBox(),i;switch(t){case"top":i=-e.height/2;break;case"bottom":i=e.height/2-s.height;break;default:i=-s.height/2}return a.attr("transform","translate("+-s.width/2+","+i+")"),a}var X=function(r,e){var t=e.nodes().filter(function(s){return st(e,s)}),n=r.selectAll("g.cluster").data(t,function(s){return s});E(n.exit(),e).style("opacity",0).remove();var a=n.enter().append("g").attr("class","cluster").attr("id",function(s){var i=e.node(s);return i.id}).style("opacity",0).each(function(s){var i=e.node(s),o=x(this);x(this).append("rect");var c=o.append("g").attr("class","label");J(c,i,i.clusterLabelPos)});return n=n.merge(a),n=E(n,e).style("opacity",1),n.selectAll("rect").each(function(s){var i=e.node(s),o=x(this);N(o,i.style)}),n};function Ft(r){X=r}let F=function(r,e){var t=r.selectAll("g.edgeLabel").data(e.edges(),function(a){return it(a)}).classed("update",!0);t.exit().remove(),t.enter().append("g").classed("edgeLabel",!0).style("opacity",0),t=r.selectAll("g.edgeLabel"),t.each(function(a){var s=x(this);s.select(".label").remove();var i=e.edge(a),o=J(s,e.edge(a),0).classed("label",!0),c=o.node().getBBox();i.labelId&&o.attr("id",i.labelId),S(i,"width")||(i.width=c.width),S(i,"height")||(i.height=c.height)});var n;return t.exit?n=t.exit():n=t.selectAll(null),E(n,e).style("opacity",0).remove(),t};function qt(r){F=r}function O(r,e){return r.intersect(e)}var q=function(r,e,t){var n=r.selectAll("g.edgePath").data(e.edges(),function(i){return it(i)}).classed("update",!0),a=Ot(n,e);jt(n,e);var s=n.merge!==void 0?n.merge(a):n;return E(s,e).style("opacity",1),s.each(function(i){var o=x(this),c=e.edge(i);c.elem=this,c.id&&o.attr("id",c.id),ot(o,c.class,(o.classed("update")?"update ":"")+"edgePath")}),s.selectAll("path.path").each(function(i){var o=e.edge(i);o.arrowheadId=Tt("arrowhead");var c=x(this).attr("marker-end",function(){return"url("+Kt(location.href,o.arrowheadId)+")"}).style("fill","none");E(c,e).attr("d",function(d){return Jt(e,d)}),N(c,o.style)}),s.selectAll("defs *").remove(),s.selectAll("defs").each(function(i){var o=e.edge(i),c=t[o.arrowhead];c(x(this),o.arrowheadId,o,"arrowhead")}),s};function Qt(r){q=r}function Kt(r,e){var t=r.split("#")[0];return t+"#"+e}function Jt(r,e){var t=r.edge(e),n=r.node(e.v),a=r.node(e.w),s=t.points.slice(1,t.points.length-1);return s.unshift(O(n,s[0])),s.push(O(a,s[s.length-1])),lt(t,s)}function lt(r,e){var t=(Dt||Ut.line)().x(function(n){return n.x}).y(function(n){return n.y});return(t.curve||t.interpolate)(r.curve),t(e)}function Zt(r){var e=r.getBBox(),t=r.ownerSVGElement.getScreenCTM().inverse().multiply(r.getScreenCTM()).translate(e.width/2,e.height/2);return{x:t.e,y:t.f}}function Ot(r,e){var t=r.enter().append("g").attr("class","edgePath").style("opacity",0);return t.append("path").attr("class","path").attr("d",function(n){var a=e.edge(n),s=e.node(n.v).elem,i=Nt(a.points.length).map(function(){return Zt(s)});return lt(a,i)}),t.append("defs"),t}function jt(r,e){var t=r.exit();E(t,e).style("opacity",0).remove()}var Q=function(r,e,t){var n=e.nodes().filter(function(i){return!st(e,i)}),a=r.selectAll("g.node").data(n,function(i){return i}).classed("update",!0);a.exit().remove(),a.enter().append("g").attr("class","node").style("opacity",0),a=r.selectAll("g.node"),a.each(function(i){var o=e.node(i),c=x(this);ot(c,o.class,(c.classed("update")?"update ":"")+"node"),c.select("g.label").remove();var d=c.append("g").attr("class","label"),l=J(d,o),v=t[o.shape],h=At(l.node().getBBox(),"width","height");o.elem=this,o.id&&c.attr("id",o.id),o.labelId&&d.attr("id",o.labelId),S(o,"width")&&(h.width=o.width),S(o,"height")&&(h.height=o.height),h.width+=o.paddingLeft+o.paddingRight,h.height+=o.paddingTop+o.paddingBottom,d.attr("transform","translate("+(o.paddingLeft-o.paddingRight)/2+","+(o.paddingTop-o.paddingBottom)/2+")");var u=x(this);u.select(".label-container").remove();var p=v(u,h,o).classed("label-container",!0);N(p,o.style);var y=p.node().getBBox();o.width=y.width,o.height=y.height});var s;return a.exit?s=a.exit():s=a.selectAll(null),E(s,e).style("opacity",0).remove(),a};function te(r){Q=r}function ee(r,e){var t=r.filter(function(){return!x(this).classed("update")});function n(a){var s=e.node(a);return"translate("+s.x+","+s.y+")"}t.attr("transform",n),E(r,e).style("opacity",1).attr("transform",n),E(t.selectAll("rect"),e).attr("width",function(a){return e.node(a).width}).attr("height",function(a){return e.node(a).height}).attr("x",function(a){var s=e.node(a);return-s.width/2}).attr("y",function(a){var s=e.node(a);return-s.height/2})}function re(r,e){var t=r.filter(function(){return!x(this).classed("update")});function n(a){var s=e.edge(a);return S(s,"x")?"translate("+s.x+","+s.y+")":""}t.attr("transform",n),E(r,e).style("opacity",1).attr("transform",n)}function ae(r,e){var t=r.filter(function(){return!x(this).classed("update")});function n(a){var s=e.node(a);return"translate("+s.x+","+s.y+")"}t.attr("transform",n),E(r,e).style("opacity",1).attr("transform",n)}function ct(r,e,t,n){var a=r.x,s=r.y,i=a-n.x,o=s-n.y,c=Math.sqrt(e*e*o*o+t*t*i*i),d=Math.abs(e*t*i/c);n.x<a&&(d=-d);var l=Math.abs(e*t*o/c);return n.y<s&&(l=-l),{x:a+d,y:s+l}}function ne(r,e,t){return ct(r,e,e,t)}function se(r,e,t,n){var a,s,i,o,c,d,l,v,h,u,p,y,f,g,k;if(a=e.y-r.y,i=r.x-e.x,c=e.x*r.y-r.x*e.y,h=a*t.x+i*t.y+c,u=a*n.x+i*n.y+c,!(h!==0&&u!==0&&j(h,u))&&(s=n.y-t.y,o=t.x-n.x,d=n.x*t.y-t.x*n.y,l=s*r.x+o*r.y+d,v=s*e.x+o*e.y+d,!(l!==0&&v!==0&&j(l,v))&&(p=a*o-s*i,p!==0)))return y=Math.abs(p/2),f=i*d-o*c,g=f<0?(f-y)/p:(f+y)/p,f=s*c-a*d,k=f<0?(f-y)/p:(f+y)/p,{x:g,y:k}}function j(r,e){return r*e>0}function T(r,e,t){var n=r.x,a=r.y,s=[],i=Number.POSITIVE_INFINITY,o=Number.POSITIVE_INFINITY;e.forEach(function(p){i=Math.min(i,p.x),o=Math.min(o,p.y)});for(var c=n-r.width/2-i,d=a-r.height/2-o,l=0;l<e.length;l++){var v=e[l],h=e[l<e.length-1?l+1:0],u=se(r,t,{x:c+v.x,y:d+v.y},{x:c+h.x,y:d+h.y});u&&s.push(u)}return s.length?(s.length>1&&s.sort(function(p,y){var f=p.x-t.x,g=p.y-t.y,k=Math.sqrt(f*f+g*g),I=y.x-t.x,_=y.y-t.y,$=Math.sqrt(I*I+_*_);return k<$?-1:k===$?0:1}),s[0]):(console.log("NO INTERSECTION FOUND, RETURN NODE CENTER",r),r)}function Z(r,e){var t=r.x,n=r.y,a=e.x-t,s=e.y-n,i=r.width/2,o=r.height/2,c,d;return Math.abs(s)*i>Math.abs(a)*o?(s<0&&(o=-o),c=s===0?0:o*a/s,d=o):(a<0&&(i=-i),c=i,d=a===0?0:i*s/a),{x:t+c,y:n+d}}var K={rect:oe,ellipse:le,circle:ce,diamond:de};function ie(r){K=r}function oe(r,e,t){var n=r.insert("rect",":first-child").attr("rx",t.rx).attr("ry",t.ry).attr("x",-e.width/2).attr("y",-e.height/2).attr("width",e.width).attr("height",e.height);return t.intersect=function(a){return Z(t,a)},n}function le(r,e,t){var n=e.width/2,a=e.height/2,s=r.insert("ellipse",":first-child").attr("x",-e.width/2).attr("y",-e.height/2).attr("rx",n).attr("ry",a);return t.intersect=function(i){return ct(t,n,a,i)},s}function ce(r,e,t){var n=Math.max(e.width,e.height)/2,a=r.insert("circle",":first-child").attr("x",-e.width/2).attr("y",-e.height/2).attr("r",n);return t.intersect=function(s){return ne(t,n,s)},a}function de(r,e,t){var n=e.width*Math.SQRT2/2,a=e.height*Math.SQRT2/2,s=[{x:0,y:-a},{x:-n,y:0},{x:0,y:a},{x:n,y:0}],i=r.insert("polygon",":first-child").attr("points",s.map(function(o){return o.x+","+o.y}).join(" "));return t.intersect=function(o){return T(t,s,o)},i}function he(){var r=function(e,t){pe(t);var n=D(e,"output"),a=D(n,"clusters"),s=D(n,"edgePaths"),i=F(D(n,"edgeLabels"),t),o=Q(D(n,"nodes"),t,K);Ct(t),ae(o,t),re(i,t),q(s,t,H);var c=X(a,t);ee(c,t),ve(t)};return r.createNodes=function(e){return arguments.length?(te(e),r):Q},r.createClusters=function(e){return arguments.length?(Ft(e),r):X},r.createEdgeLabels=function(e){return arguments.length?(qt(e),r):F},r.createEdgePaths=function(e){return arguments.length?(Qt(e),r):q},r.shapes=function(e){return arguments.length?(ie(e),r):K},r.arrows=function(e){return arguments.length?($t(e),r):H},r}var ue={paddingLeft:10,paddingRight:10,paddingTop:10,paddingBottom:10,rx:0,ry:0,shape:"rect"},fe={arrowhead:"normal",curve:U};function pe(r){r.nodes().forEach(function(e){var t=r.node(e);!S(t,"label")&&!r.children(e).length&&(t.label=e),S(t,"paddingX")&&M(t,{paddingLeft:t.paddingX,paddingRight:t.paddingX}),S(t,"paddingY")&&M(t,{paddingTop:t.paddingY,paddingBottom:t.paddingY}),S(t,"padding")&&M(t,{paddingLeft:t.padding,paddingRight:t.padding,paddingTop:t.padding,paddingBottom:t.padding}),M(t,ue),tt(["paddingLeft","paddingRight","paddingTop","paddingBottom"],function(n){t[n]=Number(t[n])}),S(t,"width")&&(t._prevWidth=t.width),S(t,"height")&&(t._prevHeight=t.height)}),r.edges().forEach(function(e){var t=r.edge(e);S(t,"label")||(t.label=""),M(t,fe)})}function ve(r){tt(r.nodes(),function(e){var t=r.node(e);S(t,"_prevWidth")?t.width=t._prevWidth:delete t.width,S(t,"_prevHeight")?t.height=t._prevHeight:delete t.height,delete t._prevWidth,delete t._prevHeight})}function D(r,e){var t=r.select("g."+e);return t.empty()&&(t=r.append("g").attr("class",e)),t}function dt(r,e,t){const n=e.width,a=e.height,s=(n+a)*.9,i=[{x:s/2,y:0},{x:s,y:-s/2},{x:s/2,y:-s},{x:0,y:-s/2}],o=A(r,s,s,i);return t.intersect=function(c){return T(t,i,c)},o}function ht(r,e,t){const a=e.height,s=a/4,i=e.width+2*s,o=[{x:s,y:0},{x:i-s,y:0},{x:i,y:-a/2},{x:i-s,y:-a},{x:s,y:-a},{x:0,y:-a/2}],c=A(r,i,a,o);return t.intersect=function(d){return T(t,o,d)},c}function ut(r,e,t){const n=e.width,a=e.height,s=[{x:-a/2,y:0},{x:n,y:0},{x:n,y:-a},{x:-a/2,y:-a},{x:0,y:-a/2}],i=A(r,n,a,s);return t.intersect=function(o){return T(t,s,o)},i}function ft(r,e,t){const n=e.width,a=e.height,s=[{x:-2*a/6,y:0},{x:n-a/6,y:0},{x:n+2*a/6,y:-a},{x:a/6,y:-a}],i=A(r,n,a,s);return t.intersect=function(o){return T(t,s,o)},i}function pt(r,e,t){const n=e.width,a=e.height,s=[{x:2*a/6,y:0},{x:n+a/6,y:0},{x:n-2*a/6,y:-a},{x:-a/6,y:-a}],i=A(r,n,a,s);return t.intersect=function(o){return T(t,s,o)},i}function vt(r,e,t){const n=e.width,a=e.height,s=[{x:-2*a/6,y:0},{x:n+2*a/6,y:0},{x:n-a/6,y:-a},{x:a/6,y:-a}],i=A(r,n,a,s);return t.intersect=function(o){return T(t,s,o)},i}function gt(r,e,t){const n=e.width,a=e.height,s=[{x:a/6,y:0},{x:n-a/6,y:0},{x:n+2*a/6,y:-a},{x:-2*a/6,y:-a}],i=A(r,n,a,s);return t.intersect=function(o){return T(t,s,o)},i}function yt(r,e,t){const n=e.width,a=e.height,s=[{x:0,y:0},{x:n+a/2,y:0},{x:n,y:-a/2},{x:n+a/2,y:-a},{x:0,y:-a}],i=A(r,n,a,s);return t.intersect=function(o){return T(t,s,o)},i}function wt(r,e,t){const n=e.height,a=e.width+n/4,s=r.insert("rect",":first-child").attr("rx",n/2).attr("ry",n/2).attr("x",-a/2).attr("y",-n/2).attr("width",a).attr("height",n);return t.intersect=function(i){return Z(t,i)},s}function mt(r,e,t){const n=e.width,a=e.height,s=[{x:0,y:0},{x:n,y:0},{x:n,y:-a},{x:0,y:-a},{x:0,y:0},{x:-8,y:0},{x:n+8,y:0},{x:n+8,y:-a},{x:-8,y:-a},{x:-8,y:0}],i=A(r,n,a,s);return t.intersect=function(o){return T(t,s,o)},i}function xt(r,e,t){const n=e.width,a=n/2,s=a/(2.5+n/50),i=e.height+s,o="M 0,"+s+" a "+a+","+s+" 0,0,0 "+n+" 0 a "+a+","+s+" 0,0,0 "+-n+" 0 l 0,"+i+" a "+a+","+s+" 0,0,0 "+n+" 0 l 0,"+-i,c=r.attr("label-offset-y",s).insert("path",":first-child").attr("d",o).attr("transform","translate("+-n/2+","+-(i/2+s)+")");return t.intersect=function(d){const l=Z(t,d),v=l.x-t.x;if(a!=0&&(Math.abs(v)<t.width/2||Math.abs(v)==t.width/2&&Math.abs(l.y-t.y)>t.height/2-s)){let h=s*s*(1-v*v/(a*a));h!=0&&(h=Math.sqrt(h)),h=s-h,d.y-t.y>0&&(h=-h),l.y+=h}return l},c}function ge(r){r.shapes().question=dt,r.shapes().hexagon=ht,r.shapes().stadium=wt,r.shapes().subroutine=mt,r.shapes().cylinder=xt,r.shapes().rect_left_inv_arrow=ut,r.shapes().lean_right=ft,r.shapes().lean_left=pt,r.shapes().trapezoid=vt,r.shapes().inv_trapezoid=gt,r.shapes().rect_right_inv_arrow=yt}function ye(r){r({question:dt}),r({hexagon:ht}),r({stadium:wt}),r({subroutine:mt}),r({cylinder:xt}),r({rect_left_inv_arrow:ut}),r({lean_right:ft}),r({lean_left:pt}),r({trapezoid:vt}),r({inv_trapezoid:gt}),r({rect_right_inv_arrow:yt})}function A(r,e,t,n){return r.insert("polygon",":first-child").attr("points",n.map(function(a){return a.x+","+a.y}).join(" ")).attr("transform","translate("+-e/2+","+t/2+")")}const we={addToRender:ge,addToRenderV2:ye},bt={},me=function(r){const e=Object.keys(r);for(const t of e)bt[t]=r[t]},kt=async function(r,e,t,n,a,s){const i=n?n.select(`[id="${t}"]`):x(`[id="${t}"]`),o=a||document,c=Object.keys(r);for(const d of c){const l=r[d];let v="default";l.classes.length>0&&(v=l.classes.join(" "));const h=Y(l.styles);let u=l.text!==void 0?l.text:l.id,p;if(et(G().flowchart.htmlLabels)){const g={label:await rt(u.replace(/fa[blrs]?:fa-[\w-]+/g,k=>`<i class='${k.replace(":"," ")}'></i>`),G())};p=nt(i,g).node(),p.parentNode.removeChild(p)}else{const g=o.createElementNS("http://www.w3.org/2000/svg","text");g.setAttribute("style",h.labelStyle.replace("color:","fill:"));const k=u.split(at.lineBreakRegex);for(const I of k){const _=o.createElementNS("http://www.w3.org/2000/svg","tspan");_.setAttributeNS("http://www.w3.org/XML/1998/namespace","xml:space","preserve"),_.setAttribute("dy","1em"),_.setAttribute("x","1"),_.textContent=I,g.appendChild(_)}p=g}let y=0,f="";switch(l.type){case"round":y=5,f="rect";break;case"square":f="rect";break;case"diamond":f="question";break;case"hexagon":f="hexagon";break;case"odd":f="rect_left_inv_arrow";break;case"lean_right":f="lean_right";break;case"lean_left":f="lean_left";break;case"trapezoid":f="trapezoid";break;case"inv_trapezoid":f="inv_trapezoid";break;case"odd_right":f="rect_left_inv_arrow";break;case"circle":f="circle";break;case"ellipse":f="ellipse";break;case"stadium":f="stadium";break;case"subroutine":f="subroutine";break;case"cylinder":f="cylinder";break;case"group":f="rect";break;default:f="rect"}R.warn("Adding node",l.id,l.domId),e.setNode(s.db.lookUpDomId(l.id),{labelType:"svg",labelStyle:h.labelStyle,shape:f,label:p,rx:y,ry:y,class:v,style:h.style,id:s.db.lookUpDomId(l.id)})}},St=async function(r,e,t){let n=0,a,s;if(r.defaultStyle!==void 0){const i=Y(r.defaultStyle);a=i.style,s=i.labelStyle}for(const i of r){n++;const o="L-"+i.start+"-"+i.end,c="LS-"+i.start,d="LE-"+i.end,l={};i.type==="arrow_open"?l.arrowhead="none":l.arrowhead="normal";let v="",h="";if(i.style!==void 0){const u=Y(i.style);v=u.style,h=u.labelStyle}else switch(i.stroke){case"normal":v="fill:none",a!==void 0&&(v=a),s!==void 0&&(h=s);break;case"dotted":v="fill:none;stroke-width:2px;stroke-dasharray:3;";break;case"thick":v=" stroke-width: 3.5px;fill:none";break}l.style=v,l.labelStyle=h,i.interpolate!==void 0?l.curve=z(i.interpolate,U):r.defaultInterpolate!==void 0?l.curve=z(r.defaultInterpolate,U):l.curve=z(bt.curve,U),i.text===void 0?i.style!==void 0&&(l.arrowheadStyle="fill: #333"):(l.arrowheadStyle="fill: #333",l.labelpos="c",et(G().flowchart.htmlLabels)?(l.labelType="html",l.label=`<span id="L-${o}" class="edgeLabel L-${c}' L-${d}" style="${l.labelStyle}">${await rt(i.text.replace(/fa[blrs]?:fa-[\w-]+/g,u=>`<i class='${u.replace(":"," ")}'></i>`),G())}</span>`):(l.labelType="text",l.label=i.text.replace(at.lineBreakRegex,`
 `),i.style===void 0&&(l.style=l.style||"stroke: #333; stroke-width: 1.5px;fill:none"),l.labelStyle=l.labelStyle.replace("color:","fill:"))),l.id=o,l.class=c+" "+d,l.minlen=i.length||1,e.setEdge(t.db.lookUpDomId(i.start),t.db.lookUpDomId(i.end),l,n)}},xe=function(r,e){return R.info("Extracting classes"),e.db.getClasses()},be=async function(r,e,t,n){R.info("Drawing flowchart");const{securityLevel:a,flowchart:s}=G();let i;a==="sandbox"&&(i=x("#i"+e));const o=a==="sandbox"?x(i.nodes()[0].contentDocument.body):x("body"),c=a==="sandbox"?i.nodes()[0].contentDocument:document;let d=n.db.getDirection();d===void 0&&(d="TD");const l=s.nodeSpacing||50,v=s.rankSpacing||50,h=new _t({multigraph:!0,compound:!0}).setGraph({rankdir:d,nodesep:l,ranksep:v,marginx:8,marginy:8}).setDefaultEdgeLabel(function(){return{}});let u;const p=n.db.getSubGraphs();for(let w=p.length-1;w>=0;w--)u=p[w],n.db.addVertex(u.id,u.title,"group",void 0,u.classes);const y=n.db.getVertices();R.warn("Get vertices",y);const f=n.db.getEdges();let g=0;for(g=p.length-1;g>=0;g--){u=p[g],Mt("cluster").append("text");for(let w=0;w<u.nodes.length;w++)R.warn("Setting subgraph",u.nodes[w],n.db.lookUpDomId(u.nodes[w]),n.db.lookUpDomId(u.id)),h.setParent(n.db.lookUpDomId(u.nodes[w]),n.db.lookUpDomId(u.id))}await kt(y,h,e,o,c,n),await St(f,h,n);const k=new he;we.addToRender(k),k.arrows().none=function(b,L,m,B){const C=b.append("marker").attr("id",L).attr("viewBox","0 0 10 10").attr("refX",9).attr("refY",5).attr("markerUnits","strokeWidth").attr("markerWidth",8).attr("markerHeight",6).attr("orient","auto").append("path").attr("d","M 0 0 L 0 0 L 0 0 z");N(C,m[B+"Style"])},k.arrows().normal=function(b,L){b.append("marker").attr("id",L).attr("viewBox","0 0 10 10").attr("refX",9).attr("refY",5).attr("markerUnits","strokeWidth").attr("markerWidth",8).attr("markerHeight",6).attr("orient","auto").append("path").attr("d","M 0 0 L 10 5 L 0 10 z").attr("class","arrowheadPath").style("stroke-width",1).style("stroke-dasharray","1,0")};const I=o.select(`[id="${e}"]`),_=o.select("#"+e+" g");for(k(_,h),_.selectAll("g.node").attr("title",function(){return n.db.getTooltip(this.id)}),n.db.indexNodes("subGraph"+g),g=0;g<p.length;g++)if(u=p[g],u.title!=="undefined"){const w=c.querySelectorAll("#"+e+' [id="'+n.db.lookUpDomId(u.id)+'"] rect'),b=c.querySelectorAll("#"+e+' [id="'+n.db.lookUpDomId(u.id)+'"]'),L=w[0].x.baseVal.value,m=w[0].y.baseVal.value,B=w[0].width.baseVal.value,C=x(b[0]).select(".label");C.attr("transform",`translate(${L+B/2}, ${m+14})`),C.attr("id",e+"Text");for(let W=0;W<u.classes.length;W++)b[0].classList.add(u.classes[W])}if(!s.htmlLabels){const w=c.querySelectorAll('[id="'+e+'"] .edgeLabel .label');for(const b of w){const L=b.getBBox(),m=c.createElementNS("http://www.w3.org/2000/svg","rect");m.setAttribute("rx",0),m.setAttribute("ry",0),m.setAttribute("width",L.width),m.setAttribute("height",L.height),b.insertBefore(m,b.firstChild)}}Et(h,I,s.diagramPadding,s.useMaxWidth),Object.keys(y).forEach(function(w){const b=y[w];if(b.link){const L=o.select("#"+e+' [id="'+n.db.lookUpDomId(w)+'"]');if(L){const m=c.createElementNS("http://www.w3.org/2000/svg","a");m.setAttributeNS("http://www.w3.org/2000/svg","class",b.classes.join(" ")),m.setAttributeNS("http://www.w3.org/2000/svg","href",b.link),m.setAttributeNS("http://www.w3.org/2000/svg","rel","noopener"),a==="sandbox"?m.setAttributeNS("http://www.w3.org/2000/svg","target","_top"):b.linkTarget&&m.setAttributeNS("http://www.w3.org/2000/svg","target",b.linkTarget);const B=L.insert(function(){return m},":first-child"),P=L.select(".label-container");P&&B.append(function(){return P.node()});const C=L.select(".label");C&&B.append(function(){return C.node()})}}})},ke={setConf:me,addVertices:kt,addEdges:St,getClasses:xe,draw:be},Pe={parser:Lt,db:V,renderer:It,styles:Bt,init:r=>{r.flowchart||(r.flowchart={}),r.flowchart.arrowMarkerAbsolute=r.arrowMarkerAbsolute,ke.setConf(r.flowchart),V.clear(),V.setGen("gen-1")}};export{Pe as diagram};
diff --git a/assets/flowDiagram-v2-a33b4996-BQrZXIe9.js b/assets/flowDiagram-v2-a33b4996-BQrZXIe9.js
new file mode 100644
index 0000000..a7fe857
--- /dev/null
+++ b/assets/flowDiagram-v2-a33b4996-BQrZXIe9.js
@@ -0,0 +1 @@
+import{p as e,f as o}from"./flowDb-0da60e67-XaXEQp9e.js";import{f as t,g as a}from"./styles-422bd1c9-CFsDtXUv.js";import{aq as i}from"./mermaid.core-DNo_7Q2B.js";import"./graph-B1296pfd.js";import"./layout-qMafh1ee.js";import"./index-9620d214-BlfbO5wW.js";import"./clone-C3EvpqoY.js";import"./edges-5962ec63-ApWhby2b.js";import"./createText-4a4f35c9-CISzj231.js";import"./line-BqHmcuby.js";import"./array-BKyUJesY.js";import"./path-CbwjOpE9.js";import"./channel-yU22lAlC.js";import"./app-B4LGNJZ0.js";const n={parser:e,db:o,renderer:t,styles:a,init:r=>{r.flowchart||(r.flowchart={}),r.flowchart.arrowMarkerAbsolute=r.arrowMarkerAbsolute,i({flowchart:{arrowMarkerAbsolute:r.arrowMarkerAbsolute}}),t.setConf(r.flowchart),o.clear(),o.setGen("gen-2")}};export{n as diagram};
diff --git a/assets/flowDiagram-v2-a33b4996-BVubizbB.js b/assets/flowDiagram-v2-a33b4996-BVubizbB.js
deleted file mode 100644
index d91b42f..0000000
--- a/assets/flowDiagram-v2-a33b4996-BVubizbB.js
+++ /dev/null
@@ -1 +0,0 @@
-import{p as e,f as o}from"./flowDb-0da60e67-C3mEtQas.js";import{f as t,g as a}from"./styles-422bd1c9-CXxGUMW8.js";import{aq as i}from"./mermaid.core-ChLYKTZm.js";import"./graph-T5JS4vfK.js";import"./layout-DUYLy6Ue.js";import"./index-9620d214-B8uh0R2i.js";import"./clone-CI3kFeqi.js";import"./edges-5962ec63-B19hLEst.js";import"./createText-4a4f35c9-BuT3nXUz.js";import"./line-D0jG_HZ-.js";import"./array-BKyUJesY.js";import"./path-CbwjOpE9.js";import"./channel-DJsAcM5I.js";import"./app-B69Gl_S-.js";const n={parser:e,db:o,renderer:t,styles:a,init:r=>{r.flowchart||(r.flowchart={}),r.flowchart.arrowMarkerAbsolute=r.arrowMarkerAbsolute,i({flowchart:{arrowMarkerAbsolute:r.arrowMarkerAbsolute}}),t.setConf(r.flowchart),o.clear(),o.setGen("gen-2")}};export{n as diagram};
diff --git a/assets/flowchart-elk-definition-930acc39-Q-ihdrlR.js b/assets/flowchart-elk-definition-930acc39-D2d6YT5I.js
similarity index 99%
rename from assets/flowchart-elk-definition-930acc39-Q-ihdrlR.js
rename to assets/flowchart-elk-definition-930acc39-D2d6YT5I.js
index 67d932f..8cbf595 100644
--- a/assets/flowchart-elk-definition-930acc39-Q-ihdrlR.js
+++ b/assets/flowchart-elk-definition-930acc39-D2d6YT5I.js
@@ -1,4 +1,4 @@
-import{d as xNe,p as FNe}from"./flowDb-0da60e67-C3mEtQas.js";import{aB as Nse,aC as BNe,l as Ba,h as IO,a$ as xU,u as RNe,p as E0n,t as j0n,o as $U,j as KNe}from"./mermaid.core-ChLYKTZm.js";import{i as _Ne,a as HNe,l as qNe,b as UNe,k as GNe,m as zNe}from"./edges-5962ec63-B19hLEst.js";import{l as XNe}from"./line-D0jG_HZ-.js";import"./app-B69Gl_S-.js";import"./createText-4a4f35c9-BuT3nXUz.js";import"./array-BKyUJesY.js";import"./path-CbwjOpE9.js";function NU(ct){throw new Error('Could not dynamically require "'+ct+'". Please configure the dynamicRequireTargets or/and ignoreDynamicRequires option of @rollup/plugin-commonjs appropriately for this require call to work.')}var Bse={exports:{}};(function(ct,_t){(function(Xt){ct.exports=Xt()})(function(){return function(){function Xt(gt,Sr,Di){function y(Ht,Jt){if(!Sr[Ht]){if(!gt[Ht]){var ze=typeof NU=="function"&&NU;if(!Jt&&ze)return ze(Ht,!0);if(Wt)return Wt(Ht,!0);var Yi=new Error("Cannot find module '"+Ht+"'");throw Yi.code="MODULE_NOT_FOUND",Yi}var Ri=Sr[Ht]={exports:{}};gt[Ht][0].call(Ri.exports,function(En){var hu=gt[Ht][1][En];return y(hu||En)},Ri,Ri.exports,Xt,gt,Sr,Di)}return Sr[Ht].exports}for(var Wt=typeof NU=="function"&&NU,Bu=0;Bu<Di.length;Bu++)y(Di[Bu]);return y}return Xt}()({1:[function(Xt,gt,Sr){Object.defineProperty(Sr,"__esModule",{value:!0});var Di=function(){function Ht(Jt,ze){for(var Yi=0;Yi<ze.length;Yi++){var Ri=ze[Yi];Ri.enumerable=Ri.enumerable||!1,Ri.configurable=!0,"value"in Ri&&(Ri.writable=!0),Object.defineProperty(Jt,Ri.key,Ri)}}return function(Jt,ze,Yi){return ze&&Ht(Jt.prototype,ze),Yi&&Ht(Jt,Yi),Jt}}();function y(Ht,Jt){if(!(Ht instanceof Jt))throw new TypeError("Cannot call a class as a function")}var Wt=function(){function Ht(){var Jt=this,ze=arguments.length>0&&arguments[0]!==void 0?arguments[0]:{},Yi=ze.defaultLayoutOptions,Ri=Yi===void 0?{}:Yi,En=ze.algorithms,hu=En===void 0?["layered","stress","mrtree","radial","force","disco","sporeOverlap","sporeCompaction","rectpacking"]:En,Qc=ze.workerFactory,Ru=ze.workerUrl;if(y(this,Ht),this.defaultLayoutOptions=Ri,this.initialized=!1,typeof Ru>"u"&&typeof Qc>"u")throw new Error("Cannot construct an ELK without both 'workerUrl' and 'workerFactory'.");var Pr=Qc;typeof Ru<"u"&&typeof Qc>"u"&&(Pr=function(N1){return new Worker(N1)});var Cf=Pr(Ru);if(typeof Cf.postMessage!="function")throw new TypeError("Created worker does not provide the required 'postMessage' function.");this.worker=new Bu(Cf),this.worker.postMessage({cmd:"register",algorithms:hu}).then(function(L1){return Jt.initialized=!0}).catch(console.err)}return Di(Ht,[{key:"layout",value:function(ze){var Yi=arguments.length>1&&arguments[1]!==void 0?arguments[1]:{},Ri=Yi.layoutOptions,En=Ri===void 0?this.defaultLayoutOptions:Ri,hu=Yi.logging,Qc=hu===void 0?!1:hu,Ru=Yi.measureExecutionTime,Pr=Ru===void 0?!1:Ru;return ze?this.worker.postMessage({cmd:"layout",graph:ze,layoutOptions:En,options:{logging:Qc,measureExecutionTime:Pr}}):Promise.reject(new Error("Missing mandatory parameter 'graph'."))}},{key:"knownLayoutAlgorithms",value:function(){return this.worker.postMessage({cmd:"algorithms"})}},{key:"knownLayoutOptions",value:function(){return this.worker.postMessage({cmd:"options"})}},{key:"knownLayoutCategories",value:function(){return this.worker.postMessage({cmd:"categories"})}},{key:"terminateWorker",value:function(){this.worker&&this.worker.terminate()}}]),Ht}();Sr.default=Wt;var Bu=function(){function Ht(Jt){var ze=this;if(y(this,Ht),Jt===void 0)throw new Error("Missing mandatory parameter 'worker'.");this.resolvers={},this.worker=Jt,this.worker.onmessage=function(Yi){setTimeout(function(){ze.receive(ze,Yi)},0)}}return Di(Ht,[{key:"postMessage",value:function(ze){var Yi=this.id||0;this.id=Yi+1,ze.id=Yi;var Ri=this;return new Promise(function(En,hu){Ri.resolvers[Yi]=function(Qc,Ru){Qc?(Ri.convertGwtStyleError(Qc),hu(Qc)):En(Ru)},Ri.worker.postMessage(ze)})}},{key:"receive",value:function(ze,Yi){var Ri=Yi.data,En=ze.resolvers[Ri.id];En&&(delete ze.resolvers[Ri.id],Ri.error?En(Ri.error):En(null,Ri.data))}},{key:"terminate",value:function(){this.worker&&this.worker.terminate()}},{key:"convertGwtStyleError",value:function(ze){if(ze){var Yi=ze.__java$exception;Yi&&(Yi.cause&&Yi.cause.backingJsObject&&(ze.cause=Yi.cause.backingJsObject,this.convertGwtStyleError(ze.cause)),delete ze.__java$exception)}}}]),Ht}()},{}],2:[function(Xt,gt,Sr){(function(Di){(function(){var y;typeof window<"u"?y=window:typeof Di<"u"?y=Di:typeof self<"u"&&(y=self);var Wt;function Bu(){}function Ht(){}function Jt(){}function ze(){}function Yi(){}function Ri(){}function En(){}function hu(){}function Qc(){}function Ru(){}function Pr(){}function Cf(){}function L1(){}function N1(){}function og(){}function V3(){}function $1(){}function ul(){}function C0n(){}function M0n(){}function J2(){}function F(){}function T0n(){}function mE(){}function A0n(){}function S0n(){}function P0n(){}function I0n(){}function O0n(){}function FU(){}function D0n(){}function L0n(){}function N0n(){}function OO(){}function $0n(){}function x0n(){}function F0n(){}function DO(){}function B0n(){}function R0n(){}function BU(){}function K0n(){}function _0n(){}function yu(){}function ju(){}function Q2(){}function Y2(){}function H0n(){}function q0n(){}function U0n(){}function G0n(){}function RU(){}function Eu(){}function Z2(){}function np(){}function z0n(){}function X0n(){}function LO(){}function V0n(){}function W0n(){}function J0n(){}function Q0n(){}function Y0n(){}function Z0n(){}function nbn(){}function ebn(){}function tbn(){}function ibn(){}function rbn(){}function cbn(){}function ubn(){}function obn(){}function sbn(){}function fbn(){}function hbn(){}function lbn(){}function abn(){}function dbn(){}function bbn(){}function wbn(){}function gbn(){}function pbn(){}function mbn(){}function vbn(){}function kbn(){}function ybn(){}function jbn(){}function Ebn(){}function Cbn(){}function Mbn(){}function Tbn(){}function KU(){}function Abn(){}function Sbn(){}function Pbn(){}function Ibn(){}function NO(){}function $O(){}function vE(){}function Obn(){}function Dbn(){}function xO(){}function Lbn(){}function Nbn(){}function $bn(){}function kE(){}function xbn(){}function Fbn(){}function Bbn(){}function Rbn(){}function Kbn(){}function _bn(){}function Hbn(){}function qbn(){}function Ubn(){}function _U(){}function Gbn(){}function zbn(){}function HU(){}function Xbn(){}function Vbn(){}function Wbn(){}function Jbn(){}function Qbn(){}function Ybn(){}function Zbn(){}function nwn(){}function ewn(){}function twn(){}function iwn(){}function rwn(){}function cwn(){}function FO(){}function uwn(){}function own(){}function swn(){}function fwn(){}function hwn(){}function lwn(){}function awn(){}function dwn(){}function bwn(){}function qU(){}function UU(){}function wwn(){}function gwn(){}function pwn(){}function mwn(){}function vwn(){}function kwn(){}function ywn(){}function jwn(){}function Ewn(){}function Cwn(){}function Mwn(){}function Twn(){}function Awn(){}function Swn(){}function Pwn(){}function Iwn(){}function Own(){}function Dwn(){}function Lwn(){}function Nwn(){}function $wn(){}function xwn(){}function Fwn(){}function Bwn(){}function Rwn(){}function Kwn(){}function _wn(){}function Hwn(){}function qwn(){}function Uwn(){}function Gwn(){}function zwn(){}function Xwn(){}function Vwn(){}function Wwn(){}function Jwn(){}function Qwn(){}function Ywn(){}function Zwn(){}function ngn(){}function egn(){}function tgn(){}function ign(){}function rgn(){}function cgn(){}function ugn(){}function ogn(){}function sgn(){}function fgn(){}function hgn(){}function lgn(){}function agn(){}function dgn(){}function bgn(){}function wgn(){}function ggn(){}function pgn(){}function mgn(){}function vgn(){}function kgn(){}function ygn(){}function jgn(){}function Egn(){}function Cgn(){}function Mgn(){}function Tgn(){}function Agn(){}function Sgn(){}function Pgn(){}function Ign(){}function Ogn(){}function Dgn(){}function Lgn(){}function Ngn(){}function $gn(){}function xgn(){}function Fgn(){}function Bgn(){}function Rgn(){}function Kgn(){}function _gn(){}function Hgn(){}function qgn(){}function Ugn(){}function Ggn(){}function zgn(){}function Xgn(){}function Vgn(){}function Wgn(){}function Jgn(){}function Qgn(){}function Ygn(){}function Zgn(){}function n2n(){}function e2n(){}function t2n(){}function i2n(){}function r2n(){}function c2n(){}function u2n(){}function GU(){}function o2n(){}function s2n(){}function f2n(){}function h2n(){}function l2n(){}function a2n(){}function d2n(){}function b2n(){}function w2n(){}function g2n(){}function p2n(){}function m2n(){}function v2n(){}function k2n(){}function y2n(){}function j2n(){}function E2n(){}function C2n(){}function M2n(){}function T2n(){}function A2n(){}function S2n(){}function P2n(){}function I2n(){}function O2n(){}function D2n(){}function L2n(){}function N2n(){}function $2n(){}function x2n(){}function F2n(){}function B2n(){}function R2n(){}function K2n(){}function _2n(){}function H2n(){}function q2n(){}function U2n(){}function G2n(){}function z2n(){}function X2n(){}function V2n(){}function W2n(){}function J2n(){}function Q2n(){}function Y2n(){}function Z2n(){}function npn(){}function epn(){}function tpn(){}function ipn(){}function rpn(){}function cpn(){}function upn(){}function opn(){}function spn(){}function fpn(){}function hpn(){}function lpn(){}function apn(){}function dpn(){}function bpn(){}function wpn(){}function gpn(){}function ppn(){}function mpn(){}function vpn(){}function kpn(){}function ypn(){}function jpn(){}function Epn(){}function Cpn(){}function Mpn(){}function zU(){}function Tpn(){}function Apn(){}function Spn(){}function Ppn(){}function Ipn(){}function Opn(){}function Dpn(){}function Lpn(){}function Npn(){}function $pn(){}function XU(){}function xpn(){}function Fpn(){}function Bpn(){}function Rpn(){}function Kpn(){}function _pn(){}function VU(){}function WU(){}function Hpn(){}function JU(){}function QU(){}function qpn(){}function Upn(){}function Gpn(){}function zpn(){}function Xpn(){}function Vpn(){}function Wpn(){}function Jpn(){}function Qpn(){}function Ypn(){}function Zpn(){}function YU(){}function n3n(){}function e3n(){}function t3n(){}function i3n(){}function r3n(){}function c3n(){}function u3n(){}function o3n(){}function s3n(){}function f3n(){}function h3n(){}function l3n(){}function a3n(){}function d3n(){}function b3n(){}function w3n(){}function g3n(){}function p3n(){}function m3n(){}function v3n(){}function k3n(){}function y3n(){}function j3n(){}function E3n(){}function C3n(){}function M3n(){}function T3n(){}function A3n(){}function S3n(){}function P3n(){}function I3n(){}function O3n(){}function D3n(){}function L3n(){}function N3n(){}function $3n(){}function x3n(){}function F3n(){}function B3n(){}function R3n(){}function K3n(){}function _3n(){}function H3n(){}function q3n(){}function U3n(){}function G3n(){}function z3n(){}function X3n(){}function V3n(){}function W3n(){}function J3n(){}function Q3n(){}function Y3n(){}function Z3n(){}function n4n(){}function e4n(){}function t4n(){}function i4n(){}function r4n(){}function c4n(){}function u4n(){}function o4n(){}function s4n(){}function f4n(){}function h4n(){}function l4n(){}function a4n(){}function d4n(){}function b4n(){}function w4n(){}function g4n(){}function p4n(){}function m4n(){}function v4n(){}function k4n(){}function y4n(){}function j4n(){}function E4n(){}function C4n(){}function M4n(){}function T4n(){}function A4n(){}function S4n(){}function P4n(){}function I4n(){}function O4n(){}function _se(){}function D4n(){}function L4n(){}function N4n(){}function $4n(){}function x4n(){}function F4n(){}function B4n(){}function R4n(){}function K4n(){}function _4n(){}function H4n(){}function q4n(){}function U4n(){}function G4n(){}function z4n(){}function X4n(){}function V4n(){}function W4n(){}function J4n(){}function Q4n(){}function Y4n(){}function Z4n(){}function nmn(){}function emn(){}function tmn(){}function imn(){}function rmn(){}function BO(){}function RO(){}function cmn(){}function KO(){}function umn(){}function omn(){}function smn(){}function fmn(){}function hmn(){}function lmn(){}function amn(){}function dmn(){}function bmn(){}function wmn(){}function ZU(){}function gmn(){}function pmn(){}function mmn(){}function Hse(){}function vmn(){}function kmn(){}function ymn(){}function jmn(){}function Emn(){}function Cmn(){}function Mmn(){}function Ra(){}function Tmn(){}function ep(){}function nG(){}function Amn(){}function Smn(){}function Pmn(){}function Imn(){}function Omn(){}function Dmn(){}function Lmn(){}function Nmn(){}function $mn(){}function xmn(){}function Fmn(){}function Bmn(){}function Rmn(){}function Kmn(){}function _mn(){}function Hmn(){}function qmn(){}function Umn(){}function Gmn(){}function hn(){}function zmn(){}function Xmn(){}function Vmn(){}function Wmn(){}function Jmn(){}function Qmn(){}function Ymn(){}function Zmn(){}function nvn(){}function evn(){}function tvn(){}function ivn(){}function rvn(){}function _O(){}function cvn(){}function uvn(){}function ovn(){}function yE(){}function svn(){}function HO(){}function jE(){}function fvn(){}function eG(){}function hvn(){}function lvn(){}function avn(){}function dvn(){}function bvn(){}function wvn(){}function EE(){}function gvn(){}function pvn(){}function CE(){}function mvn(){}function ME(){}function vvn(){}function tG(){}function kvn(){}function qO(){}function iG(){}function yvn(){}function jvn(){}function Evn(){}function Cvn(){}function qse(){}function Mvn(){}function Tvn(){}function Avn(){}function Svn(){}function Pvn(){}function Ivn(){}function Ovn(){}function Dvn(){}function Lvn(){}function Nvn(){}function W3(){}function UO(){}function $vn(){}function xvn(){}function Fvn(){}function Bvn(){}function Rvn(){}function Kvn(){}function _vn(){}function Hvn(){}function qvn(){}function Uvn(){}function Gvn(){}function zvn(){}function Xvn(){}function Vvn(){}function Wvn(){}function Jvn(){}function Qvn(){}function Yvn(){}function Zvn(){}function n6n(){}function e6n(){}function t6n(){}function i6n(){}function r6n(){}function c6n(){}function u6n(){}function o6n(){}function s6n(){}function f6n(){}function h6n(){}function l6n(){}function a6n(){}function d6n(){}function b6n(){}function w6n(){}function g6n(){}function p6n(){}function m6n(){}function v6n(){}function k6n(){}function y6n(){}function j6n(){}function E6n(){}function C6n(){}function M6n(){}function T6n(){}function A6n(){}function S6n(){}function P6n(){}function I6n(){}function O6n(){}function D6n(){}function L6n(){}function N6n(){}function $6n(){}function x6n(){}function F6n(){}function B6n(){}function R6n(){}function K6n(){}function _6n(){}function H6n(){}function q6n(){}function U6n(){}function G6n(){}function z6n(){}function X6n(){}function V6n(){}function W6n(){}function J6n(){}function Q6n(){}function Y6n(){}function Z6n(){}function n5n(){}function e5n(){}function t5n(){}function i5n(){}function r5n(){}function c5n(){}function u5n(){}function o5n(){}function s5n(){}function f5n(){}function h5n(){}function l5n(){}function a5n(){}function d5n(){}function b5n(){}function w5n(){}function g5n(){}function p5n(){}function m5n(){}function v5n(){}function k5n(){}function y5n(){}function j5n(){}function E5n(){}function C5n(){}function M5n(){}function T5n(){}function A5n(){}function rG(){}function S5n(){}function P5n(){}function GO(){n6()}function I5n(){u7()}function O5n(){aA()}function D5n(){Q$()}function L5n(){M5()}function N5n(){ann()}function $5n(){qs()}function x5n(){jZ()}function F5n(){zk()}function B5n(){o7()}function R5n(){$7()}function K5n(){aCn()}function _5n(){Hp()}function H5n(){KLn()}function q5n(){yQ()}function U5n(){SOn()}function G5n(){jQ()}function z5n(){pNn()}function X5n(){AOn()}function V5n(){cm()}function W5n(){nxn()}function J5n(){Z$n()}function Q5n(){EDn()}function Y5n(){exn()}function Z5n(){ca()}function n8n(){ZE()}function e8n(){ltn()}function t8n(){cn()}function i8n(){txn()}function r8n(){Pxn()}function c8n(){POn()}function u8n(){nKn()}function o8n(){IOn()}function s8n(){bUn()}function f8n(){qnn()}function h8n(){kl()}function l8n(){wBn()}function a8n(){lc()}function d8n(){ROn()}function b8n(){_p()}function w8n(){Men()}function g8n(){ua()}function p8n(){Ten()}function m8n(){Bf()}function v8n(){Qk()}function k8n(){EF()}function y8n(){Dx()}function cf(){wSn()}function j8n(){YM()}function E8n(){mA()}function cG(){qe()}function C8n(){NT()}function M8n(){YY()}function uG(){D$()}function oG(){KA()}function T8n(){Fen()}function sG(n){Jn(n)}function A8n(n){this.a=n}function TE(n){this.a=n}function S8n(n){this.a=n}function P8n(n){this.a=n}function I8n(n){this.a=n}function O8n(n){this.a=n}function D8n(n){this.a=n}function L8n(n){this.a=n}function fG(n){this.a=n}function hG(n){this.a=n}function N8n(n){this.a=n}function $8n(n){this.a=n}function zO(n){this.a=n}function x8n(n){this.a=n}function F8n(n){this.a=n}function XO(n){this.a=n}function VO(n){this.a=n}function B8n(n){this.a=n}function WO(n){this.a=n}function R8n(n){this.a=n}function K8n(n){this.a=n}function _8n(n){this.a=n}function lG(n){this.b=n}function H8n(n){this.c=n}function q8n(n){this.a=n}function U8n(n){this.a=n}function G8n(n){this.a=n}function z8n(n){this.a=n}function X8n(n){this.a=n}function V8n(n){this.a=n}function W8n(n){this.a=n}function J8n(n){this.a=n}function Q8n(n){this.a=n}function Y8n(n){this.a=n}function Z8n(n){this.a=n}function n9n(n){this.a=n}function e9n(n){this.a=n}function aG(n){this.a=n}function dG(n){this.a=n}function AE(n){this.a=n}function z9(n){this.a=n}function Ka(){this.a=[]}function t9n(n,e){n.a=e}function Use(n,e){n.a=e}function Gse(n,e){n.b=e}function zse(n,e){n.b=e}function Xse(n,e){n.b=e}function bG(n,e){n.j=e}function Vse(n,e){n.g=e}function Wse(n,e){n.i=e}function Jse(n,e){n.c=e}function Qse(n,e){n.c=e}function Yse(n,e){n.d=e}function Zse(n,e){n.d=e}function _a(n,e){n.k=e}function nfe(n,e){n.c=e}function wG(n,e){n.c=e}function gG(n,e){n.a=e}function efe(n,e){n.a=e}function tfe(n,e){n.f=e}function ife(n,e){n.a=e}function rfe(n,e){n.b=e}function JO(n,e){n.d=e}function SE(n,e){n.i=e}function pG(n,e){n.o=e}function cfe(n,e){n.r=e}function ufe(n,e){n.a=e}function ofe(n,e){n.b=e}function i9n(n,e){n.e=e}function sfe(n,e){n.f=e}function mG(n,e){n.g=e}function ffe(n,e){n.e=e}function hfe(n,e){n.f=e}function lfe(n,e){n.f=e}function QO(n,e){n.a=e}function YO(n,e){n.b=e}function afe(n,e){n.n=e}function dfe(n,e){n.a=e}function bfe(n,e){n.c=e}function wfe(n,e){n.c=e}function gfe(n,e){n.c=e}function pfe(n,e){n.a=e}function mfe(n,e){n.a=e}function vfe(n,e){n.d=e}function kfe(n,e){n.d=e}function yfe(n,e){n.e=e}function jfe(n,e){n.e=e}function Efe(n,e){n.g=e}function Cfe(n,e){n.f=e}function Mfe(n,e){n.j=e}function Tfe(n,e){n.a=e}function Afe(n,e){n.a=e}function Sfe(n,e){n.b=e}function r9n(n){n.b=n.a}function c9n(n){n.c=n.d.d}function vG(n){this.a=n}function kG(n){this.a=n}function yG(n){this.a=n}function Ha(n){this.a=n}function qa(n){this.a=n}function X9(n){this.a=n}function u9n(n){this.a=n}function jG(n){this.a=n}function V9(n){this.a=n}function PE(n){this.a=n}function ol(n){this.a=n}function Sb(n){this.a=n}function o9n(n){this.a=n}function s9n(n){this.a=n}function ZO(n){this.b=n}function J3(n){this.b=n}function Q3(n){this.b=n}function nD(n){this.a=n}function f9n(n){this.a=n}function eD(n){this.c=n}function C(n){this.c=n}function h9n(n){this.c=n}function Xv(n){this.d=n}function EG(n){this.a=n}function Te(n){this.a=n}function l9n(n){this.a=n}function CG(n){this.a=n}function MG(n){this.a=n}function TG(n){this.a=n}function AG(n){this.a=n}function SG(n){this.a=n}function PG(n){this.a=n}function Y3(n){this.a=n}function a9n(n){this.a=n}function d9n(n){this.a=n}function Z3(n){this.a=n}function b9n(n){this.a=n}function w9n(n){this.a=n}function g9n(n){this.a=n}function p9n(n){this.a=n}function m9n(n){this.a=n}function v9n(n){this.a=n}function k9n(n){this.a=n}function y9n(n){this.a=n}function j9n(n){this.a=n}function E9n(n){this.a=n}function C9n(n){this.a=n}function M9n(n){this.a=n}function T9n(n){this.a=n}function A9n(n){this.a=n}function S9n(n){this.a=n}function Vv(n){this.a=n}function P9n(n){this.a=n}function I9n(n){this.a=n}function O9n(n){this.a=n}function D9n(n){this.a=n}function IE(n){this.a=n}function L9n(n){this.a=n}function N9n(n){this.a=n}function n4(n){this.a=n}function IG(n){this.a=n}function $9n(n){this.a=n}function x9n(n){this.a=n}function F9n(n){this.a=n}function B9n(n){this.a=n}function R9n(n){this.a=n}function K9n(n){this.a=n}function OG(n){this.a=n}function DG(n){this.a=n}function LG(n){this.a=n}function Wv(n){this.a=n}function OE(n){this.e=n}function e4(n){this.a=n}function _9n(n){this.a=n}function tp(n){this.a=n}function NG(n){this.a=n}function H9n(n){this.a=n}function q9n(n){this.a=n}function U9n(n){this.a=n}function G9n(n){this.a=n}function z9n(n){this.a=n}function X9n(n){this.a=n}function V9n(n){this.a=n}function W9n(n){this.a=n}function J9n(n){this.a=n}function Q9n(n){this.a=n}function Y9n(n){this.a=n}function $G(n){this.a=n}function Z9n(n){this.a=n}function n7n(n){this.a=n}function e7n(n){this.a=n}function t7n(n){this.a=n}function i7n(n){this.a=n}function r7n(n){this.a=n}function c7n(n){this.a=n}function u7n(n){this.a=n}function o7n(n){this.a=n}function s7n(n){this.a=n}function f7n(n){this.a=n}function h7n(n){this.a=n}function l7n(n){this.a=n}function a7n(n){this.a=n}function d7n(n){this.a=n}function b7n(n){this.a=n}function w7n(n){this.a=n}function g7n(n){this.a=n}function p7n(n){this.a=n}function m7n(n){this.a=n}function v7n(n){this.a=n}function k7n(n){this.a=n}function y7n(n){this.a=n}function j7n(n){this.a=n}function E7n(n){this.a=n}function C7n(n){this.a=n}function M7n(n){this.a=n}function T7n(n){this.a=n}function A7n(n){this.a=n}function S7n(n){this.a=n}function P7n(n){this.a=n}function I7n(n){this.a=n}function O7n(n){this.a=n}function D7n(n){this.a=n}function L7n(n){this.a=n}function N7n(n){this.a=n}function $7n(n){this.a=n}function x7n(n){this.a=n}function F7n(n){this.c=n}function B7n(n){this.b=n}function R7n(n){this.a=n}function K7n(n){this.a=n}function _7n(n){this.a=n}function H7n(n){this.a=n}function q7n(n){this.a=n}function U7n(n){this.a=n}function G7n(n){this.a=n}function z7n(n){this.a=n}function X7n(n){this.a=n}function V7n(n){this.a=n}function W7n(n){this.a=n}function J7n(n){this.a=n}function Q7n(n){this.a=n}function Y7n(n){this.a=n}function Z7n(n){this.a=n}function nkn(n){this.a=n}function ekn(n){this.a=n}function tkn(n){this.a=n}function ikn(n){this.a=n}function rkn(n){this.a=n}function ckn(n){this.a=n}function ukn(n){this.a=n}function okn(n){this.a=n}function skn(n){this.a=n}function fkn(n){this.a=n}function hkn(n){this.a=n}function lkn(n){this.a=n}function sl(n){this.a=n}function sg(n){this.a=n}function akn(n){this.a=n}function dkn(n){this.a=n}function bkn(n){this.a=n}function wkn(n){this.a=n}function gkn(n){this.a=n}function pkn(n){this.a=n}function mkn(n){this.a=n}function vkn(n){this.a=n}function kkn(n){this.a=n}function ykn(n){this.a=n}function jkn(n){this.a=n}function Ekn(n){this.a=n}function Ckn(n){this.a=n}function Mkn(n){this.a=n}function Tkn(n){this.a=n}function Akn(n){this.a=n}function Skn(n){this.a=n}function Pkn(n){this.a=n}function Ikn(n){this.a=n}function Okn(n){this.a=n}function Dkn(n){this.a=n}function Lkn(n){this.a=n}function Nkn(n){this.a=n}function $kn(n){this.a=n}function xkn(n){this.a=n}function Fkn(n){this.a=n}function DE(n){this.a=n}function Bkn(n){this.f=n}function Rkn(n){this.a=n}function Kkn(n){this.a=n}function _kn(n){this.a=n}function Hkn(n){this.a=n}function qkn(n){this.a=n}function Ukn(n){this.a=n}function Gkn(n){this.a=n}function zkn(n){this.a=n}function Xkn(n){this.a=n}function Vkn(n){this.a=n}function Wkn(n){this.a=n}function Jkn(n){this.a=n}function Qkn(n){this.a=n}function Ykn(n){this.a=n}function Zkn(n){this.a=n}function nyn(n){this.a=n}function eyn(n){this.a=n}function tyn(n){this.a=n}function iyn(n){this.a=n}function ryn(n){this.a=n}function cyn(n){this.a=n}function uyn(n){this.a=n}function oyn(n){this.a=n}function syn(n){this.a=n}function fyn(n){this.a=n}function hyn(n){this.a=n}function lyn(n){this.a=n}function ayn(n){this.a=n}function tD(n){this.a=n}function xG(n){this.a=n}function lt(n){this.b=n}function dyn(n){this.a=n}function byn(n){this.a=n}function wyn(n){this.a=n}function gyn(n){this.a=n}function pyn(n){this.a=n}function myn(n){this.a=n}function vyn(n){this.a=n}function kyn(n){this.b=n}function yyn(n){this.a=n}function W9(n){this.a=n}function jyn(n){this.a=n}function Eyn(n){this.a=n}function FG(n){this.c=n}function LE(n){this.e=n}function NE(n){this.a=n}function $E(n){this.a=n}function iD(n){this.a=n}function Cyn(n){this.d=n}function Myn(n){this.a=n}function BG(n){this.a=n}function RG(n){this.a=n}function Wd(n){this.e=n}function Pfe(){this.a=0}function de(){Hu(this)}function Z(){pL(this)}function rD(){sIn(this)}function Tyn(){}function Jd(){this.c=Gdn}function Ayn(n,e){n.b+=e}function Ife(n,e){e.Wb(n)}function Ofe(n){return n.a}function Dfe(n){return n.a}function Lfe(n){return n.a}function Nfe(n){return n.a}function $fe(n){return n.a}function M(n){return n.e}function xfe(){return null}function Ffe(){return null}function Bfe(){Cz(),pLe()}function Rfe(n){n.b.Of(n.e)}function Syn(n){n.b=new CD}function Jv(n,e){n.b=e-n.b}function Qv(n,e){n.a=e-n.a}function Bn(n,e){n.push(e)}function Pyn(n,e){n.sort(e)}function Iyn(n,e){e.jd(n.a)}function Kfe(n,e){gi(e,n)}function _fe(n,e,t){n.Yd(t,e)}function J9(n,e){n.e=e,e.b=n}function KG(n){uh(),this.a=n}function Oyn(n){uh(),this.a=n}function Dyn(n){uh(),this.a=n}function cD(n){m0(),this.a=n}function Lyn(n){O4(),VK.le(n)}function _G(){_G=F,new de}function Ua(){YTn.call(this)}function HG(){YTn.call(this)}function qG(){Ua.call(this)}function uD(){Ua.call(this)}function Nyn(){Ua.call(this)}function Q9(){Ua.call(this)}function Cu(){Ua.call(this)}function ip(){Ua.call(this)}function Pe(){Ua.call(this)}function Bo(){Ua.call(this)}function $yn(){Ua.call(this)}function nc(){Ua.call(this)}function xyn(){Ua.call(this)}function Fyn(){this.a=this}function xE(){this.Bb|=256}function Byn(){this.b=new GMn}function Pb(n,e){n.length=e}function FE(n,e){nn(n.a,e)}function Hfe(n,e){bnn(n.c,e)}function qfe(n,e){fi(n.b,e)}function Ufe(n,e){uA(n.a,e)}function Gfe(n,e){cx(n.a,e)}function t4(n,e){it(n.e,e)}function rp(n){jA(n.c,n.b)}function zfe(n,e){n.kc().Nb(e)}function UG(n){this.a=B5e(n)}function ni(){this.a=new de}function Ryn(){this.a=new de}function GG(){this.a=new rCn}function BE(){this.a=new Z}function oD(){this.a=new Z}function zG(){this.a=new Z}function hs(){this.a=new cbn}function Ga(){this.a=new NLn}function XG(){this.a=new _U}function VG(){this.a=new TOn}function WG(){this.a=new BAn}function Kyn(){this.a=new Z}function _yn(){this.a=new Z}function Hyn(){this.a=new Z}function JG(){this.a=new Z}function qyn(){this.d=new Z}function Uyn(){this.a=new zOn}function Gyn(){this.a=new ni}function zyn(){this.a=new de}function Xyn(){this.b=new de}function Vyn(){this.b=new Z}function QG(){this.e=new Z}function Wyn(){this.a=new Z5n}function Jyn(){this.d=new Z}function Qyn(){QIn.call(this)}function Yyn(){QIn.call(this)}function Zyn(){Z.call(this)}function YG(){qG.call(this)}function ZG(){BE.call(this)}function njn(){qC.call(this)}function ejn(){JG.call(this)}function Yv(){Tyn.call(this)}function sD(){Yv.call(this)}function cp(){Tyn.call(this)}function nz(){cp.call(this)}function tjn(){rz.call(this)}function ijn(){rz.call(this)}function rjn(){rz.call(this)}function cjn(){cz.call(this)}function Zv(){svn.call(this)}function ez(){svn.call(this)}function Mu(){Ct.call(this)}function ujn(){yjn.call(this)}function ojn(){yjn.call(this)}function sjn(){de.call(this)}function fjn(){de.call(this)}function hjn(){de.call(this)}function fD(){cxn.call(this)}function ljn(){ni.call(this)}function ajn(){xE.call(this)}function hD(){BX.call(this)}function tz(){de.call(this)}function lD(){BX.call(this)}function aD(){de.call(this)}function djn(){de.call(this)}function iz(){ME.call(this)}function bjn(){iz.call(this)}function wjn(){ME.call(this)}function gjn(){rG.call(this)}function rz(){this.a=new ni}function pjn(){this.a=new de}function mjn(){this.a=new Z}function cz(){this.a=new de}function up(){this.a=new Ct}function vjn(){this.j=new Z}function kjn(){this.a=new mEn}function yjn(){this.a=new mvn}function uz(){this.a=new Z4n}function n6(){n6=F,KK=new Ht}function dD(){dD=F,_K=new Ejn}function bD(){bD=F,HK=new jjn}function jjn(){XO.call(this,"")}function Ejn(){XO.call(this,"")}function Cjn(n){S$n.call(this,n)}function Mjn(n){S$n.call(this,n)}function oz(n){fG.call(this,n)}function sz(n){XEn.call(this,n)}function Xfe(n){XEn.call(this,n)}function Vfe(n){sz.call(this,n)}function Wfe(n){sz.call(this,n)}function Jfe(n){sz.call(this,n)}function Tjn(n){zN.call(this,n)}function Ajn(n){zN.call(this,n)}function Sjn(n){uSn.call(this,n)}function Pjn(n){Oz.call(this,n)}function e6(n){WE.call(this,n)}function fz(n){WE.call(this,n)}function Ijn(n){WE.call(this,n)}function hz(n){mje.call(this,n)}function lz(n){hz.call(this,n)}function ec(n){APn.call(this,n)}function Ojn(n){ec.call(this,n)}function op(){z9.call(this,{})}function Djn(){Djn=F,dQn=new M0n}function RE(){RE=F,GK=new STn}function Ljn(){Ljn=F,oun=new Bu}function az(){az=F,sun=new N1}function KE(){KE=F,P8=new $1}function wD(n){b4(),this.a=n}function gD(n){RQ(),this.a=n}function Qd(n){nN(),this.f=n}function pD(n){nN(),this.f=n}function Njn(n){bSn(),this.a=n}function $jn(n){n.b=null,n.c=0}function Qfe(n,e){n.e=e,bqn(n,e)}function Yfe(n,e){n.a=e,cEe(n)}function mD(n,e,t){n.a[e.g]=t}function Zfe(n,e,t){kke(t,n,e)}function nhe(n,e){Wae(e.i,n.n)}function xjn(n,e){v6e(n).Cd(e)}function ehe(n,e){n.a.ec().Mc(e)}function Fjn(n,e){return n.g-e.g}function the(n,e){return n*n/e}function on(n){return Jn(n),n}function $(n){return Jn(n),n}function Y9(n){return Jn(n),n}function ihe(n){return new AE(n)}function rhe(n){return new qb(n)}function dz(n){return Jn(n),n}function che(n){return Jn(n),n}function _E(n){ec.call(this,n)}function Ir(n){ec.call(this,n)}function Bjn(n){ec.call(this,n)}function vD(n){APn.call(this,n)}function i4(n){ec.call(this,n)}function Gn(n){ec.call(this,n)}function Or(n){ec.call(this,n)}function Rjn(n){ec.call(this,n)}function sp(n){ec.call(this,n)}function Kl(n){ec.call(this,n)}function _l(n){ec.call(this,n)}function fp(n){ec.call(this,n)}function nh(n){ec.call(this,n)}function kD(n){ec.call(this,n)}function Le(n){ec.call(this,n)}function Ku(n){Jn(n),this.a=n}function bz(n){return ld(n),n}function t6(n){TW(n,n.length)}function i6(n){return n.b==n.c}function Ib(n){return!!n&&n.b}function uhe(n){return!!n&&n.k}function ohe(n){return!!n&&n.j}function she(n,e,t){n.c.Ef(e,t)}function Kjn(n,e){n.be(e),e.ae(n)}function hp(n){uh(),this.a=Se(n)}function yD(){this.a=Oe(Se(ur))}function _jn(){throw M(new Pe)}function fhe(){throw M(new Pe)}function wz(){throw M(new Pe)}function Hjn(){throw M(new Pe)}function hhe(){throw M(new Pe)}function lhe(){throw M(new Pe)}function HE(){HE=F,O4()}function Hl(){X9.call(this,"")}function r6(){X9.call(this,"")}function x1(){X9.call(this,"")}function lp(){X9.call(this,"")}function gz(n){Ir.call(this,n)}function pz(n){Ir.call(this,n)}function eh(n){Gn.call(this,n)}function r4(n){Q3.call(this,n)}function qjn(n){r4.call(this,n)}function jD(n){BC.call(this,n)}function ED(n){JX.call(this,n,0)}function CD(){sJ.call(this,12,3)}function T(n,e){return kOn(n,e)}function qE(n,e){return o$(n,e)}function ahe(n,e){return n.a-e.a}function dhe(n,e){return n.a-e.a}function bhe(n,e){return n.a-e.a}function whe(n,e){return e in n.a}function Ujn(n){return n.a?n.b:0}function ghe(n){return n.a?n.b:0}function phe(n,e,t){e.Cd(n.a[t])}function mhe(n,e,t){e.Pe(n.a[t])}function vhe(n,e){n.b=new rr(e)}function khe(n,e){return n.b=e,n}function Gjn(n,e){return n.c=e,n}function zjn(n,e){return n.f=e,n}function yhe(n,e){return n.g=e,n}function mz(n,e){return n.a=e,n}function vz(n,e){return n.f=e,n}function jhe(n,e){return n.k=e,n}function kz(n,e){return n.a=e,n}function Ehe(n,e){return n.e=e,n}function yz(n,e){return n.e=e,n}function Che(n,e){return n.f=e,n}function Mhe(n,e){n.b=!0,n.d=e}function The(n,e){return n.b-e.b}function Ahe(n,e){return n.g-e.g}function She(n,e){return n?0:e-1}function Xjn(n,e){return n?0:e-1}function Phe(n,e){return n?e-1:0}function Ihe(n,e){return n.s-e.s}function Ohe(n,e){return e.rg(n)}function Yd(n,e){return n.b=e,n}function UE(n,e){return n.a=e,n}function Zd(n,e){return n.c=e,n}function n0(n,e){return n.d=e,n}function e0(n,e){return n.e=e,n}function jz(n,e){return n.f=e,n}function c6(n,e){return n.a=e,n}function c4(n,e){return n.b=e,n}function u4(n,e){return n.c=e,n}function an(n,e){return n.c=e,n}function Sn(n,e){return n.b=e,n}function dn(n,e){return n.d=e,n}function bn(n,e){return n.e=e,n}function Dhe(n,e){return n.f=e,n}function wn(n,e){return n.g=e,n}function gn(n,e){return n.a=e,n}function pn(n,e){return n.i=e,n}function mn(n,e){return n.j=e,n}function Lhe(n,e){ca(),ic(e,n)}function Nhe(n,e,t){Jbe(n.a,e,t)}function GE(n){$L.call(this,n)}function Vjn(n){Z5e.call(this,n)}function Wjn(n){SIn.call(this,n)}function Ez(n){SIn.call(this,n)}function F1(n){S0.call(this,n)}function Jjn(n){CN.call(this,n)}function Qjn(n){CN.call(this,n)}function Yjn(){DX.call(this,"")}function Li(){this.a=0,this.b=0}function Zjn(){this.b=0,this.a=0}function nEn(n,e){n.b=0,Zb(n,e)}function eEn(n,e){return n.k=e,n}function $he(n,e){return n.j=e,n}function xhe(n,e){n.c=e,n.b=!0}function tEn(){tEn=F,TQn=Xke()}function B1(){B1=F,voe=rke()}function iEn(){iEn=F,Ti=gye()}function Cz(){Cz=F,Oa=z4()}function o4(){o4=F,Udn=cke()}function rEn(){rEn=F,ise=uke()}function Mz(){Mz=F,yc=tEe()}function uf(n){return n.e&&n.e()}function cEn(n){return n.l|n.m<<22}function uEn(n,e){return n.c._b(e)}function oEn(n,e){return rBn(n.b,e)}function MD(n){return n?n.d:null}function Fhe(n){return n?n.g:null}function Bhe(n){return n?n.i:null}function za(n){return ll(n),n.o}function fg(n,e){return n.a+=e,n}function TD(n,e){return n.a+=e,n}function ql(n,e){return n.a+=e,n}function t0(n,e){return n.a+=e,n}function Tz(n,e){for(;n.Bd(e););}function zE(n){this.a=new ap(n)}function sEn(){throw M(new Pe)}function fEn(){throw M(new Pe)}function hEn(){throw M(new Pe)}function lEn(){throw M(new Pe)}function aEn(){throw M(new Pe)}function dEn(){throw M(new Pe)}function Ul(n){this.a=new iN(n)}function bEn(){this.a=new K5(Rln)}function wEn(){this.b=new K5(rln)}function gEn(){this.a=new K5(f1n)}function pEn(){this.b=new K5(Fq)}function mEn(){this.b=new K5(Fq)}function XE(n){this.a=0,this.b=n}function Az(n){zGn(),ILe(this,n)}function s4(n){return z1(n),n.a}function Z9(n){return n.b!=n.d.c}function Sz(n,e){return n.d[e.p]}function vEn(n,e){return XTe(n,e)}function Pz(n,e,t){n.splice(e,t)}function hg(n,e){for(;n.Re(e););}function kEn(n){n.c?Dqn(n):Lqn(n)}function yEn(){throw M(new Pe)}function jEn(){throw M(new Pe)}function EEn(){throw M(new Pe)}function CEn(){throw M(new Pe)}function MEn(){throw M(new Pe)}function TEn(){throw M(new Pe)}function AEn(){throw M(new Pe)}function SEn(){throw M(new Pe)}function PEn(){throw M(new Pe)}function IEn(){throw M(new Pe)}function Rhe(){throw M(new nc)}function Khe(){throw M(new nc)}function n7(n){this.a=new OEn(n)}function OEn(n){Ume(this,n,jje())}function e7(n){return!n||oIn(n)}function t7(n){return Zf[n]!=-1}function _he(){cP!=0&&(cP=0),uP=-1}function DEn(){RK==null&&(RK=[])}function i7(n,e){Cg.call(this,n,e)}function f4(n,e){i7.call(this,n,e)}function LEn(n,e){this.a=n,this.b=e}function NEn(n,e){this.a=n,this.b=e}function $En(n,e){this.a=n,this.b=e}function xEn(n,e){this.a=n,this.b=e}function FEn(n,e){this.a=n,this.b=e}function BEn(n,e){this.a=n,this.b=e}function REn(n,e){this.a=n,this.b=e}function h4(n,e){this.e=n,this.d=e}function Iz(n,e){this.b=n,this.c=e}function KEn(n,e){this.b=n,this.a=e}function _En(n,e){this.b=n,this.a=e}function HEn(n,e){this.b=n,this.a=e}function qEn(n,e){this.b=n,this.a=e}function UEn(n,e){this.a=n,this.b=e}function AD(n,e){this.a=n,this.b=e}function GEn(n,e){this.a=n,this.f=e}function i0(n,e){this.g=n,this.i=e}function je(n,e){this.f=n,this.g=e}function zEn(n,e){this.b=n,this.c=e}function XEn(n){KX(n.dc()),this.c=n}function Hhe(n,e){this.a=n,this.b=e}function VEn(n,e){this.a=n,this.b=e}function WEn(n){this.a=u(Se(n),15)}function Oz(n){this.a=u(Se(n),15)}function JEn(n){this.a=u(Se(n),85)}function VE(n){this.b=u(Se(n),85)}function WE(n){this.b=u(Se(n),51)}function JE(){this.q=new y.Date}function SD(n,e){this.a=n,this.b=e}function QEn(n,e){return Zc(n.b,e)}function r7(n,e){return n.b.Hc(e)}function YEn(n,e){return n.b.Ic(e)}function ZEn(n,e){return n.b.Qc(e)}function nCn(n,e){return n.b.Hc(e)}function eCn(n,e){return n.c.uc(e)}function tCn(n,e){return rt(n.c,e)}function of(n,e){return n.a._b(e)}function iCn(n,e){return n>e&&e<Y5}function u6(n){return n.f.c+n.i.c}function qhe(n){return zPn(),n?aQn:lQn}function ap(n){wFn.call(this,n,0)}function rCn(){iN.call(this,null)}function dp(n){this.c=n,i$n(this)}function Ct(){jTn(this),vo(this)}function fl(){fl=F,pQn=new T0n}function l4(){l4=F,fv=new S0n}function Ob(){Ob=F,n_=new qMn}function QE(){QE=F,SQn=new UMn}function a4(){a4=F,$un=new R0n}function Dz(){i$.call(this,null)}function Xa(){Xa=F,v3=new V0n}function qt(n,e){z1(n),n.a.Nb(e)}function Uhe(n,e){return n.a.Xc(e)}function Ghe(n,e){return n.a.Yc(e)}function PD(n,e){return n.a.$c(e)}function ID(n,e){return n.a._c(e)}function zhe(n,e){return n.Gc(e),n}function Xhe(n,e){return Bi(n,e),n}function Vhe(n,e){aF(_(n.a),e)}function Whe(n,e){aF(_(n.a),e)}function cCn(n,e){return n.Gc(e),n}function Jhe(n,e){return n.a.f=e,n}function uCn(n,e){return n.a.d=e,n}function oCn(n,e){return n.a.g=e,n}function sCn(n,e){return n.a.j=e,n}function Is(n,e){return n.a.a=e,n}function Os(n,e){return n.a.d=e,n}function Ds(n,e){return n.a.e=e,n}function Ls(n,e){return n.a.g=e,n}function c7(n,e){return n.a.f=e,n}function Qhe(n){return n.b=!1,n}function fCn(){fCn=F,BQn=new Z0n}function YE(){YE=F,b_=new bAn}function Lz(){Lz=F,jZn=new zbn}function hCn(){hCn=F,EZn=new Zbn}function Nz(){Nz=F,CZn=new wPn}function $z(){$z=F,Oon=new iwn}function lCn(){lCn=F,LZn=new dwn}function o6(){o6=F,$Zn=new bwn}function u7(){u7=F,RZn=new _wn}function o7(){o7=F,BZn=new Li}function aCn(){aCn=F,qZn=new Mgn}function s6(){s6=F,QZn=new upn}function ZE(){ZE=F,b2=new Ipn}function nC(){nC=F,Jte=new Zmn}function eC(){eC=F,Bq=new bCn}function tC(){tC=F,Rq=new dAn}function f6(){f6=F,Hj=new bIn}function dCn(){Y$n(),this.c=new CD}function bCn(){je.call(this,VXn,0)}function Yhe(n,e,t){Dr(n.d,e.f,t)}function Zhe(n,e,t,i){P9e(n,i,e,t)}function nle(n,e,t,i){nTe(i,n,e,t)}function ele(n,e,t,i){IDe(i,n,e,t)}function h6(n,e){s1(n.c.c,e.b,e)}function r0(n,e){s1(n.c.b,e.c,e)}function tle(n){return n.e.b+n.f.b}function ile(n){return n.e.a+n.f.a}function rle(n){return n.b?n.b:n.a}function cle(n){return(n.c+n.a)/2}function wCn(n,e){return R7e(n.a,e)}function l6(n,e){return n.a=e.g,n}function xz(){xz=F,qdn=new djn}function gCn(){gCn=F,Roe=new hjn}function c0(){c0=F,poe=new nvn}function pCn(){pCn=F,Moe=new lvn}function mCn(){mCn=F,Boe=new fjn}function R1(){R1=F,Ss=new tz}function iC(){iC=F,yO=new de}function a6(){a6=F,MU=new TTn}function Gl(){Gl=F,dE=new ATn}function OD(){OD=F,Zoe=new T6n}function dr(){dr=F,ese=new A6n}function K1(){K1=F,$a=new P5n}function Fz(){Fz=F,n0n=new Z}function rC(n){return u(n,44).ld()}function DD(n){return n.b<n.d.gc()}function ule(n,e){return e.split(n)}function LD(n,e){return Ec(n,e)>0}function ND(n,e){return Ec(n,e)<0}function vCn(n,e){return JL(n.a,e)}function ole(n,e){yOn.call(this,n,e)}function Bz(n){wN(),uSn.call(this,n)}function Rz(n,e){bPn(n,n.length,e)}function s7(n,e){HPn(n,n.length,e)}function d6(n,e){return n.a.get(e)}function kCn(n,e){return Zc(n.e,e)}function Kz(n){return Jn(n),!1}function _z(n){this.a=u(Se(n),229)}function cC(n){In.call(this,n,21)}function uC(n,e){je.call(this,n,e)}function $D(n,e){je.call(this,n,e)}function yCn(n,e){this.b=n,this.a=e}function oC(n,e){this.d=n,this.e=e}function jCn(n,e){this.a=n,this.b=e}function ECn(n,e){this.a=n,this.b=e}function CCn(n,e){this.a=n,this.b=e}function MCn(n,e){this.a=n,this.b=e}function bp(n,e){this.a=n,this.b=e}function TCn(n,e){this.b=n,this.a=e}function Hz(n,e){this.b=n,this.a=e}function qz(n,e){je.call(this,n,e)}function Uz(n,e){je.call(this,n,e)}function lg(n,e){je.call(this,n,e)}function xD(n,e){je.call(this,n,e)}function FD(n,e){je.call(this,n,e)}function BD(n,e){je.call(this,n,e)}function sC(n,e){je.call(this,n,e)}function Gz(n,e){this.b=n,this.a=e}function fC(n,e){je.call(this,n,e)}function zz(n,e){this.b=n,this.a=e}function hC(n,e){je.call(this,n,e)}function ACn(n,e){this.b=n,this.a=e}function Xz(n,e){je.call(this,n,e)}function RD(n,e){je.call(this,n,e)}function f7(n,e){je.call(this,n,e)}function b6(n,e,t){n.splice(e,0,t)}function sle(n,e,t){n.Mb(t)&&e.Cd(t)}function fle(n,e,t){e.Pe(n.a.Ye(t))}function hle(n,e,t){e.Dd(n.a.Ze(t))}function lle(n,e,t){e.Cd(n.a.Kb(t))}function ale(n,e){return Au(n.c,e)}function dle(n,e){return Au(n.e,e)}function lC(n,e){je.call(this,n,e)}function aC(n,e){je.call(this,n,e)}function w6(n,e){je.call(this,n,e)}function Vz(n,e){je.call(this,n,e)}function ei(n,e){je.call(this,n,e)}function dC(n,e){je.call(this,n,e)}function SCn(n,e){this.a=n,this.b=e}function PCn(n,e){this.a=n,this.b=e}function ICn(n,e){this.a=n,this.b=e}function OCn(n,e){this.a=n,this.b=e}function DCn(n,e){this.a=n,this.b=e}function LCn(n,e){this.a=n,this.b=e}function NCn(n,e){this.b=n,this.a=e}function $Cn(n,e){this.b=n,this.a=e}function Wz(n,e){this.b=n,this.a=e}function d4(n,e){this.c=n,this.d=e}function xCn(n,e){this.e=n,this.d=e}function FCn(n,e){this.a=n,this.b=e}function BCn(n,e){this.a=n,this.b=e}function RCn(n,e){this.a=n,this.b=e}function KCn(n,e){this.b=n,this.a=e}function _Cn(n,e){this.b=e,this.c=n}function bC(n,e){je.call(this,n,e)}function h7(n,e){je.call(this,n,e)}function KD(n,e){je.call(this,n,e)}function Jz(n,e){je.call(this,n,e)}function g6(n,e){je.call(this,n,e)}function _D(n,e){je.call(this,n,e)}function HD(n,e){je.call(this,n,e)}function l7(n,e){je.call(this,n,e)}function Qz(n,e){je.call(this,n,e)}function qD(n,e){je.call(this,n,e)}function p6(n,e){je.call(this,n,e)}function Yz(n,e){je.call(this,n,e)}function m6(n,e){je.call(this,n,e)}function v6(n,e){je.call(this,n,e)}function Db(n,e){je.call(this,n,e)}function UD(n,e){je.call(this,n,e)}function GD(n,e){je.call(this,n,e)}function Zz(n,e){je.call(this,n,e)}function a7(n,e){je.call(this,n,e)}function ag(n,e){je.call(this,n,e)}function zD(n,e){je.call(this,n,e)}function wC(n,e){je.call(this,n,e)}function d7(n,e){je.call(this,n,e)}function Lb(n,e){je.call(this,n,e)}function gC(n,e){je.call(this,n,e)}function nX(n,e){je.call(this,n,e)}function XD(n,e){je.call(this,n,e)}function VD(n,e){je.call(this,n,e)}function WD(n,e){je.call(this,n,e)}function JD(n,e){je.call(this,n,e)}function QD(n,e){je.call(this,n,e)}function YD(n,e){je.call(this,n,e)}function ZD(n,e){je.call(this,n,e)}function HCn(n,e){this.b=n,this.a=e}function eX(n,e){je.call(this,n,e)}function qCn(n,e){this.a=n,this.b=e}function UCn(n,e){this.a=n,this.b=e}function GCn(n,e){this.a=n,this.b=e}function tX(n,e){je.call(this,n,e)}function iX(n,e){je.call(this,n,e)}function zCn(n,e){this.a=n,this.b=e}function ble(n,e){return k4(),e!=n}function b7(n){return oe(n.a),n.b}function nL(n){return yCe(n,n.c),n}function XCn(){return tEn(),new TQn}function VCn(){VC(),this.a=new kV}function WCn(){OA(),this.a=new ni}function JCn(){NN(),this.b=new ni}function QCn(n,e){this.b=n,this.d=e}function YCn(n,e){this.a=n,this.b=e}function ZCn(n,e){this.a=n,this.b=e}function nMn(n,e){this.a=n,this.b=e}function eMn(n,e){this.b=n,this.a=e}function rX(n,e){je.call(this,n,e)}function cX(n,e){je.call(this,n,e)}function pC(n,e){je.call(this,n,e)}function u0(n,e){je.call(this,n,e)}function eL(n,e){je.call(this,n,e)}function mC(n,e){je.call(this,n,e)}function uX(n,e){je.call(this,n,e)}function oX(n,e){je.call(this,n,e)}function w7(n,e){je.call(this,n,e)}function sX(n,e){je.call(this,n,e)}function tL(n,e){je.call(this,n,e)}function vC(n,e){je.call(this,n,e)}function iL(n,e){je.call(this,n,e)}function rL(n,e){je.call(this,n,e)}function cL(n,e){je.call(this,n,e)}function uL(n,e){je.call(this,n,e)}function fX(n,e){je.call(this,n,e)}function oL(n,e){je.call(this,n,e)}function hX(n,e){je.call(this,n,e)}function g7(n,e){je.call(this,n,e)}function sL(n,e){je.call(this,n,e)}function lX(n,e){je.call(this,n,e)}function p7(n,e){je.call(this,n,e)}function aX(n,e){je.call(this,n,e)}function tMn(n,e){this.b=n,this.a=e}function iMn(n,e){this.b=n,this.a=e}function rMn(n,e){this.b=n,this.a=e}function cMn(n,e){this.b=n,this.a=e}function dX(n,e){this.a=n,this.b=e}function uMn(n,e){this.a=n,this.b=e}function oMn(n,e){this.a=n,this.b=e}function V(n,e){this.a=n,this.b=e}function k6(n,e){je.call(this,n,e)}function m7(n,e){je.call(this,n,e)}function wp(n,e){je.call(this,n,e)}function y6(n,e){je.call(this,n,e)}function v7(n,e){je.call(this,n,e)}function fL(n,e){je.call(this,n,e)}function kC(n,e){je.call(this,n,e)}function j6(n,e){je.call(this,n,e)}function hL(n,e){je.call(this,n,e)}function yC(n,e){je.call(this,n,e)}function dg(n,e){je.call(this,n,e)}function k7(n,e){je.call(this,n,e)}function E6(n,e){je.call(this,n,e)}function C6(n,e){je.call(this,n,e)}function y7(n,e){je.call(this,n,e)}function jC(n,e){je.call(this,n,e)}function bg(n,e){je.call(this,n,e)}function lL(n,e){je.call(this,n,e)}function sMn(n,e){je.call(this,n,e)}function EC(n,e){je.call(this,n,e)}function fMn(n,e){this.a=n,this.b=e}function hMn(n,e){this.a=n,this.b=e}function lMn(n,e){this.a=n,this.b=e}function aMn(n,e){this.a=n,this.b=e}function dMn(n,e){this.a=n,this.b=e}function bMn(n,e){this.a=n,this.b=e}function bi(n,e){this.a=n,this.b=e}function wMn(n,e){this.a=n,this.b=e}function gMn(n,e){this.a=n,this.b=e}function pMn(n,e){this.a=n,this.b=e}function mMn(n,e){this.a=n,this.b=e}function vMn(n,e){this.a=n,this.b=e}function kMn(n,e){this.a=n,this.b=e}function yMn(n,e){this.b=n,this.a=e}function jMn(n,e){this.b=n,this.a=e}function EMn(n,e){this.b=n,this.a=e}function CMn(n,e){this.b=n,this.a=e}function MMn(n,e){this.a=n,this.b=e}function TMn(n,e){this.a=n,this.b=e}function CC(n,e){je.call(this,n,e)}function AMn(n,e){this.a=n,this.b=e}function SMn(n,e){this.a=n,this.b=e}function gp(n,e){je.call(this,n,e)}function PMn(n,e){this.f=n,this.c=e}function bX(n,e){return Au(n.g,e)}function wle(n,e){return Au(e.b,n)}function IMn(n,e){return wx(n.a,e)}function gle(n,e){return-n.b.af(e)}function ple(n,e){n&&Xe(hE,n,e)}function wX(n,e){n.i=null,kT(n,e)}function mle(n,e,t){yKn(e,oF(n,t))}function vle(n,e,t){yKn(e,oF(n,t))}function kle(n,e){VMe(n.a,u(e,58))}function OMn(n,e){U4e(n.a,u(e,12))}function MC(n,e){this.a=n,this.b=e}function DMn(n,e){this.a=n,this.b=e}function LMn(n,e){this.a=n,this.b=e}function NMn(n,e){this.a=n,this.b=e}function $Mn(n,e){this.a=n,this.b=e}function xMn(n,e){this.d=n,this.b=e}function FMn(n,e){this.e=n,this.a=e}function j7(n,e){this.b=n,this.c=e}function gX(n,e){this.i=n,this.g=e}function pX(n,e){this.d=n,this.e=e}function yle(n,e){cme(new ne(n),e)}function TC(n){return Rk(n.c,n.b)}function Kr(n){return n?n.md():null}function x(n){return n??null}function Ai(n){return typeof n===nB}function Nb(n){return typeof n===i3}function $b(n){return typeof n===dtn}function o0(n,e){return Ec(n,e)==0}function AC(n,e){return Ec(n,e)>=0}function M6(n,e){return Ec(n,e)!=0}function SC(n,e){return jve(n.Kc(),e)}function _1(n,e){return n.Rd().Xb(e)}function BMn(n){return eo(n),n.d.gc()}function PC(n){return F6(n==null),n}function T6(n,e){return n.a+=""+e,n}function Er(n,e){return n.a+=""+e,n}function A6(n,e){return n.a+=""+e,n}function Dc(n,e){return n.a+=""+e,n}function Be(n,e){return n.a+=""+e,n}function mX(n,e){return n.a+=""+e,n}function jle(n){return""+(Jn(n),n)}function RMn(n){Hu(this),f5(this,n)}function KMn(){oJ(),dW.call(this)}function _Mn(n,e){mW.call(this,n,e)}function HMn(n,e){mW.call(this,n,e)}function IC(n,e){mW.call(this,n,e)}function ir(n,e){xt(n,e,n.c.b,n.c)}function wg(n,e){xt(n,e,n.a,n.a.a)}function vX(n){return Ln(n,0),null}function qMn(){this.b=0,this.a=!1}function UMn(){this.b=0,this.a=!1}function GMn(){this.b=new ap(Qb(12))}function zMn(){zMn=F,kYn=Ce(jx())}function XMn(){XMn=F,HZn=Ce(iqn())}function VMn(){VMn=F,lre=Ce(xxn())}function kX(){kX=F,_G(),fun=new de}function sf(n){return n.a=0,n.b=0,n}function WMn(n,e){return n.a=e.g+1,n}function aL(n,e){Kb.call(this,n,e)}function Mn(n,e){Dt.call(this,n,e)}function gg(n,e){gX.call(this,n,e)}function JMn(n,e){T7.call(this,n,e)}function dL(n,e){Y4.call(this,n,e)}function Ue(n,e){iC(),Xe(yO,n,e)}function QMn(n,e){n.q.setTime(id(e))}function Ele(n){y.clearTimeout(n)}function Cle(n){return Se(n),new S6(n)}function YMn(n,e){return x(n)===x(e)}function ZMn(n,e){return n.a.a.a.cc(e)}function bL(n,e){return qo(n.a,0,e)}function yX(n){return Awe(u(n,74))}function pp(n){return wi((Jn(n),n))}function Mle(n){return wi((Jn(n),n))}function nTn(n){return Yc(n.l,n.m,n.h)}function jX(n,e){return jc(n.a,e.a)}function Tle(n,e){return KPn(n.a,e.a)}function Ale(n,e){return bt(n.a,e.a)}function th(n,e){return n.indexOf(e)}function Sle(n,e){return n.j[e.p]==2}function s0(n,e){return n==e?0:n?1:-1}function OC(n){return n<10?"0"+n:""+n}function Vr(n){return typeof n===dtn}function Ple(n){return n==rb||n==Iw}function Ile(n){return n==rb||n==Pw}function eTn(n,e){return jc(n.g,e.g)}function EX(n){return qr(n.b.b,n,0)}function tTn(){rM.call(this,0,0,0,0)}function ih(){CG.call(this,new Ql)}function CX(n,e){F4(n,0,n.length,e)}function Ole(n,e){return nn(n.a,e),e}function Dle(n,e){return xs(),e.a+=n}function Lle(n,e){return xs(),e.a+=n}function Nle(n,e){return xs(),e.c+=n}function $le(n,e){return nn(n.c,e),n}function MX(n,e){return Mo(n.a,e),n}function iTn(n){this.a=XCn(),this.b=n}function rTn(n){this.a=XCn(),this.b=n}function rr(n){this.a=n.a,this.b=n.b}function S6(n){this.a=n,GO.call(this)}function cTn(n){this.a=n,GO.call(this)}function mp(){Ho.call(this,0,0,0,0)}function DC(n){return Mo(new ii,n)}function uTn(n){return jM(u(n,123))}function fo(n){return n.vh()&&n.wh()}function pg(n){return n!=Jf&&n!=Sa}function hl(n){return n==Br||n==Xr}function mg(n){return n==us||n==Vf}function oTn(n){return n==S2||n==A2}function xle(n,e){return jc(n.g,e.g)}function sTn(n,e){return new Y4(e,n)}function Fle(n,e){return new Y4(e,n)}function TX(n){return rbe(n.b.Kc(),n.a)}function wL(n,e){um(n,e),G4(n,n.D)}function gL(n,e,t){aT(n,e),lT(n,t)}function vg(n,e,t){I0(n,e),P0(n,t)}function Ro(n,e,t){eu(n,e),tu(n,t)}function E7(n,e,t){_4(n,e),q4(n,t)}function C7(n,e,t){H4(n,e),U4(n,t)}function fTn(n,e,t){sV.call(this,n,e,t)}function AX(n){PMn.call(this,n,!0)}function hTn(){uC.call(this,"Tail",3)}function lTn(){uC.call(this,"Head",1)}function H1(n){dh(),mve.call(this,n)}function f0(n){rM.call(this,n,n,n,n)}function pL(n){n.c=K(ki,Fn,1,0,5,1)}function SX(n){return n.b&&xF(n),n.a}function PX(n){return n.b&&xF(n),n.c}function Ble(n,e){qf||(n.b=e)}function Rle(n,e){return n[n.length]=e}function Kle(n,e){return n[n.length]=e}function _le(n,e){return Yb(e,Af(n))}function Hle(n,e){return Yb(e,Af(n))}function qle(n,e){return pT(dN(n.d),e)}function Ule(n,e){return pT(dN(n.g),e)}function Gle(n,e){return pT(dN(n.j),e)}function Ni(n,e){Dt.call(this,n.b,e)}function zle(n,e){ve(Sc(n.a),DOn(e))}function Xle(n,e){ve(no(n.a),LOn(e))}function Vle(n,e,t){Ro(t,t.i+n,t.j+e)}function aTn(n,e,t){$t(n.c[e.g],e.g,t)}function Wle(n,e,t){u(n.c,71).Gi(e,t)}function mL(n,e,t){return $t(n,e,t),t}function dTn(n){nu(n.Sf(),new D9n(n))}function kg(n){return n!=null?mt(n):0}function Jle(n){return n==null?0:mt(n)}function P6(n){nt(),Wd.call(this,n)}function bTn(n){this.a=n,qV.call(this,n)}function Mf(){Mf=F,y.Math.log(2)}function Ko(){Ko=F,rl=(pCn(),Moe)}function wTn(){wTn=F,YH=new j5(aU)}function Ie(){Ie=F,new gTn,new Z}function gTn(){new de,new de,new de}function Qle(){throw M(new Kl(QJn))}function Yle(){throw M(new Kl(QJn))}function Zle(){throw M(new Kl(YJn))}function n1e(){throw M(new Kl(YJn))}function vL(n){this.a=n,VE.call(this,n)}function kL(n){this.a=n,VE.call(this,n)}function pTn(n,e){m0(),this.a=n,this.b=e}function e1e(n,e){Se(e),Tg(n).Jc(new Ru)}function Yt(n,e){QL(n.c,n.c.length,e)}function tc(n){return n.a<n.c.c.length}function IX(n){return n.a<n.c.a.length}function mTn(n,e){return n.a?n.b:e.We()}function jc(n,e){return n<e?-1:n>e?1:0}function OX(n,e){return Ec(n,e)>0?n:e}function Yc(n,e,t){return{l:n,m:e,h:t}}function t1e(n,e){n.a!=null&&OMn(e,n.a)}function i1e(n){Zi(n,null),Ii(n,null)}function r1e(n,e,t){return Xe(n.g,t,e)}function yg(n,e,t){return nZ(e,t,n.c)}function c1e(n,e,t){return Xe(n.k,t,e)}function u1e(n,e,t){return GOe(n,e,t),t}function o1e(n,e){return ko(),e.n.b+=n}function vTn(n){nJ.call(this),this.b=n}function DX(n){vV.call(this),this.a=n}function kTn(){uC.call(this,"Range",2)}function LC(n){this.b=n,this.a=new Z}function yTn(n){this.b=new $bn,this.a=n}function jTn(n){n.a=new OO,n.c=new OO}function ETn(n){n.a=new de,n.d=new de}function CTn(n){$N(n,null),xN(n,null)}function MTn(n,e){return XOe(n.a,e,null)}function s1e(n,e){return Xe(n.a,e.a,e)}function Ki(n){return new V(n.a,n.b)}function LX(n){return new V(n.c,n.d)}function f1e(n){return new V(n.c,n.d)}function I6(n,e){return cOe(n.c,n.b,e)}function O(n,e){return n!=null&&Tx(n,e)}function yL(n,e){return Yve(n.Kc(),e)!=-1}function NC(n){return n.Ob()?n.Pb():null}function h1e(n){this.b=(Dn(),new eD(n))}function NX(n){this.a=n,de.call(this)}function TTn(){T7.call(this,null,null)}function ATn(){_C.call(this,null,null)}function STn(){je.call(this,"INSTANCE",0)}function PTn(){LZ(),this.a=new K5(Ion)}function ITn(n){return hh(n,0,n.length)}function l1e(n,e){return new VTn(n.Kc(),e)}function $X(n,e){return n.a.Bc(e)!=null}function OTn(n,e){me(n),n.Gc(u(e,15))}function a1e(n,e,t){n.c.bd(e,u(t,136))}function d1e(n,e,t){n.c.Ui(e,u(t,136))}function DTn(n,e){n.c&&(tW(e),rOn(e))}function b1e(n,e){n.q.setHours(e),G5(n,e)}function w1e(n,e){a0(e,n.a.a.a,n.a.a.b)}function g1e(n,e,t,i){$t(n.a[e.g],t.g,i)}function jL(n,e,t){return n.a[e.g][t.g]}function p1e(n,e){return n.e[e.c.p][e.p]}function m1e(n,e){return n.c[e.c.p][e.p]}function Tf(n,e){return n.a[e.c.p][e.p]}function v1e(n,e){return n.j[e.p]=IMe(e)}function EL(n,e){return n.a.Bc(e)!=null}function k1e(n,e){return $(R(e.a))<=n}function y1e(n,e){return $(R(e.a))>=n}function j1e(n,e){return RJ(n.f,e.Pg())}function vp(n,e){return n.a*e.a+n.b*e.b}function E1e(n,e){return n.a<IV(e)?-1:1}function C1e(n,e){return RJ(n.b,e.Pg())}function M1e(n,e,t){return t?e!=0:e!=n-1}function LTn(n,e,t){n.a=e^1502,n.b=t^LB}function T1e(n,e,t){return n.a=e,n.b=t,n}function rh(n,e){return n.a*=e,n.b*=e,n}function nn(n,e){return Bn(n.c,e),!0}function O6(n,e,t){return $t(n.g,e,t),t}function ti(n,e,t){R7.call(this,n,e,t)}function $C(n,e,t){ti.call(this,n,e,t)}function xX(n,e,t){QC.call(this,n,e,t)}function NTn(n,e,t){QC.call(this,n,e,t)}function $Tn(n,e,t){xX.call(this,n,e,t)}function Tu(n,e,t){ti.call(this,n,e,t)}function xTn(n,e,t){$C.call(this,n,e,t)}function FX(n,e,t){R7.call(this,n,e,t)}function jg(n,e,t){R7.call(this,n,e,t)}function FTn(n,e,t){FX.call(this,n,e,t)}function xC(n){n.j=K(jun,J,319,0,0,1)}function Eg(){this.a=K(ki,Fn,1,8,5,1)}function BX(){this.Bb|=256,this.Bb|=512}function ne(n){this.i=n,this.f=this.i.j}function q1(n){this.c=n,this.a=this.c.a}function Cg(n,e){this.a=n,VE.call(this,e)}function RX(n,e){return H5e(n,new x1,e).a}function KX(n){if(!n)throw M(new Q9)}function _X(n){if(!n)throw M(new Cu)}function HX(){HX=F,HX(),PQn=new F0n}function BTn(){BTn=F,OD(),nse=new T8n}function b4(){b4=F,Dun=new wD(null)}function A1e(n){X7(n,MWn),AA(n,GDe(n))}function RTn(n){n.a=u(Un(n.b.a,4),129)}function KTn(n){n.a=u(Un(n.b.a,4),129)}function _Tn(n){n.b.Qb(),--n.d.f.d,fM(n.d)}function qX(n){this.a=n,H8n.call(this,n.d)}function HTn(n,e){this.a=n,ED.call(this,e)}function qTn(n,e){this.a=n,ED.call(this,e)}function UTn(n,e){this.a=n,ED.call(this,e)}function UX(n,e){this.a=e,ED.call(this,n)}function GTn(n,e){this.a=e,zN.call(this,n)}function zTn(n,e){this.a=n,zN.call(this,e)}function XTn(n,e){this.a=e,WE.call(this,n)}function VTn(n,e){this.a=e,WE.call(this,n)}function re(n,e){return Se(e),new XTn(n,e)}function WTn(n,e){return new k_n(n.a,n.b,e)}function GX(n,e,t){return n.indexOf(e,t)}function FC(n,e){return n.lastIndexOf(e)}function D6(n){return n==null?gu:Jr(n)}function S1e(n){return n==null?null:n.name}function P1e(n){return n.l+n.m*o3+n.h*vd}function I1e(n){return Z9(n.a)?NOn(n):null}function ls(n){X9.call(this,(Jn(n),n))}function mo(n){X9.call(this,(Jn(n),n))}function JTn(n){XO.call(this,u(Se(n),34))}function QTn(n){XO.call(this,u(Se(n),34))}function CL(n){CG.call(this,new VJ(n))}function BC(n){Q3.call(this,n),this.a=n}function zX(n){J3.call(this,n),this.a=n}function XX(n){r4.call(this,n),this.a=n}function YTn(){xC(this),MM(this),this.je()}function ZTn(n){this.a=n,ZO.call(this,n)}function ho(n){return oe(n.a!=null),n.a}function nAn(n,e){return nn(e.a,n.a),n.a}function eAn(n,e){return nn(e.b,n.a),n.a}function h0(n,e){return nn(e.a,n.a),n.a}function M7(n,e,t){return L$(n,e,e,t),n}function RC(n,e){return++n.b,nn(n.a,e)}function VX(n,e){return++n.b,du(n.a,e)}function O1e(n,e){return bt(n.c.d,e.c.d)}function D1e(n,e){return bt(n.c.c,e.c.c)}function L1e(n,e){return bt(n.n.a,e.n.a)}function lu(n,e){return u(ot(n.b,e),15)}function N1e(n,e){return n.n.b=(Jn(e),e)}function $1e(n,e){return n.n.b=(Jn(e),e)}function Au(n,e){return!!e&&n.b[e.g]==e}function L6(n){return tc(n.a)||tc(n.b)}function l0(n){return n.$H||(n.$H=++bNe)}function x1e(n){return n.a!=null?n.a:null}function F1e(n,e){return bt(n.e.b,e.e.b)}function B1e(n,e){return bt(n.e.a,e.e.a)}function R1e(n,e,t){return FDn(n,e,t,n.b)}function WX(n,e,t){return FDn(n,e,t,n.c)}function K1e(n){return xs(),!!n&&!n.dc()}function tAn(){s6(),this.b=new w7n(this)}function KC(){KC=F,bP=new Dt(gXn,0)}function _n(){_n=F,wa=!1,ov=!0}function zl(n){var e;e=n.a,n.a=n.b,n.b=e}function T7(n,e){a6(),this.a=n,this.b=e}function _C(n,e){Gl(),this.b=n,this.c=e}function ML(n,e){nN(),this.f=e,this.d=n}function JX(n,e){BJ(e,n),this.d=n,this.c=e}function QX(n,e){oZ.call(this,n,e,null)}function iAn(n,e,t,i){vW.call(this,n,e,t,i)}function kp(n){this.d=n,ne.call(this,n)}function yp(n){this.c=n,ne.call(this,n)}function A7(n){this.c=n,kp.call(this,n)}function _1e(n){return new Xb(3,n)}function Dh(n){return Co(n,mw),new Gc(n)}function rAn(n){return O4(),parseInt(n)||-1}function H1e(n){return RE(),Ee((lOn(),oQn),n)}function w4(n,e,t){return GX(n,wu(e),t)}function TL(n,e){return new iSn(n,n.gc(),e)}function q1e(n,e){return eN(n.c).Md().Xb(e)}function g4(n,e,t){var i;i=n.fd(e),i.Rb(t)}function YX(n,e,t){u(dk(n,e),21).Fc(t)}function U1e(n,e,t){cx(n.a,t),uA(n.a,e)}function S7(n){O(n,158)&&u(n,158).pi()}function cAn(n){UV.call(this,n,null,null)}function AL(n){Ob(),this.b=n,this.a=!0}function uAn(n){QE(),this.b=n,this.a=!0}function p4(n){return oe(n.b!=0),n.a.a.c}function Ns(n){return oe(n.b!=0),n.c.b.c}function G1e(n,e){return L$(n,e,e+1,""),n}function kt(n,e){return!!n.q&&Zc(n.q,e)}function oAn(n){return n.b=u(VW(n.a),44)}function z1e(n){return n.f!=null?n.f:""+n.g}function SL(n){return n.f!=null?n.f:""+n.g}function X1e(n,e){return n>0?e/(n*n):e*100}function V1e(n,e){return n>0?e*e/n:e*e*100}function xb(n,e){return u(Lf(n.a,e),34)}function W1e(n,e){return ca(),Pn(n,e.e,e)}function J1e(n,e,t){return nC(),t.Mg(n,e)}function Q1e(n){return kl(),n.e.a+n.f.a/2}function Y1e(n,e,t){return kl(),t.e.a-n*e}function Z1e(n){return kl(),n.e.b+n.f.b/2}function nae(n,e,t){return kl(),t.e.b-n*e}function sAn(n){n.d=new cAn(n),n.e=new de}function fAn(){this.a=new C0,this.b=new C0}function hAn(n){this.c=n,this.a=1,this.b=1}function lAn(n){YF(),Syn(this),this.Ff(n)}function eae(n,e,t){YM(),n.pf(e)&&t.Cd(n)}function tae(n,e,t){return nn(e,jBn(n,t))}function a0(n,e,t){return n.a+=e,n.b+=t,n}function iae(n,e,t){return n.a*=e,n.b*=t,n}function ZX(n,e){return n.a=e.a,n.b=e.b,n}function HC(n){return n.a=-n.a,n.b=-n.b,n}function N6(n,e,t){return n.a-=e,n.b-=t,n}function aAn(n){Ct.call(this),c5(this,n)}function dAn(){je.call(this,"GROW_TREE",0)}function bAn(){je.call(this,"POLYOMINO",0)}function lo(n,e,t){Iu.call(this,n,e,t,2)}function rae(n,e,t){k5(Sc(n.a),e,DOn(t))}function wAn(n,e){a6(),T7.call(this,n,e)}function nV(n,e){Gl(),_C.call(this,n,e)}function gAn(n,e){Gl(),nV.call(this,n,e)}function pAn(n,e){Gl(),_C.call(this,n,e)}function cae(n,e){return n.c.Fc(u(e,136))}function uae(n,e,t){k5(no(n.a),e,LOn(t))}function mAn(n){this.c=n,eu(n,0),tu(n,0)}function PL(n,e){Ko(),oM.call(this,n,e)}function vAn(n,e){Ko(),PL.call(this,n,e)}function eV(n,e){Ko(),PL.call(this,n,e)}function tV(n,e){Ko(),oM.call(this,n,e)}function kAn(n,e){Ko(),eV.call(this,n,e)}function yAn(n,e){Ko(),tV.call(this,n,e)}function jAn(n,e){Ko(),oM.call(this,n,e)}function oae(n,e,t){return e.zl(n.e,n.c,t)}function sae(n,e,t){return e.Al(n.e,n.c,t)}function iV(n,e,t){return qA(ak(n,e),t)}function IL(n,e){return na(n.e,u(e,54))}function fae(n){return n==null?null:NDe(n)}function hae(n){return n==null?null:Aje(n)}function lae(n){return n==null?null:Jr(n)}function aae(n){return n==null?null:Jr(n)}function un(n){return F6(n==null||Nb(n)),n}function R(n){return F6(n==null||$b(n)),n}function Oe(n){return F6(n==null||Ai(n)),n}function ll(n){n.o==null&&cMe(n)}function rV(n){if(!n)throw M(new Q9)}function dae(n){if(!n)throw M(new uD)}function oe(n){if(!n)throw M(new nc)}function Fb(n){if(!n)throw M(new Cu)}function EAn(n){if(!n)throw M(new Bo)}function m4(){m4=F,aE=new ujn,new ojn}function Mg(){Mg=F,O2=new lt("root")}function cV(){cxn.call(this),this.Bb|=hr}function bae(n,e){this.d=n,c9n(this),this.b=e}function uV(n,e){i$.call(this,n),this.a=e}function oV(n,e){i$.call(this,n),this.a=e}function sV(n,e,t){VM.call(this,n,e,t,null)}function CAn(n,e,t){VM.call(this,n,e,t,null)}function P7(n,e){this.c=n,h4.call(this,n,e)}function $6(n,e){this.a=n,P7.call(this,n,e)}function fV(n){this.q=new y.Date(id(n))}function MAn(n){return n>8?0:n+1}function TAn(n,e){qf||nn(n.a,e)}function wae(n,e){return o7(),Q4(e.d.i,n)}function gae(n,e){return Hp(),new tUn(e,n)}function pae(n,e,t){return n.Ne(e,t)<=0?t:e}function mae(n,e,t){return n.Ne(e,t)<=0?e:t}function vae(n,e){return u(Lf(n.b,e),143)}function kae(n,e){return u(Lf(n.c,e),233)}function OL(n){return u(sn(n.a,n.b),294)}function AAn(n){return new V(n.c,n.d+n.a)}function SAn(n){return Jn(n),n?1231:1237}function PAn(n){return ko(),oTn(u(n,203))}function Bb(){Bb=F,ron=yn((go(),Gd))}function yae(n,e){e.a?MCe(n,e):EL(n.a,e.b)}function I7(n,e,t){++n.j,n.tj(),t$(n,e,t)}function IAn(n,e,t){++n.j,n.qj(e,n.Zi(e,t))}function OAn(n,e,t){var i;i=n.fd(e),i.Rb(t)}function hV(n,e,t){return t=So(n,e,6,t),t}function lV(n,e,t){return t=So(n,e,3,t),t}function aV(n,e,t){return t=So(n,e,9,t),t}function ch(n,e){return X7(e,xtn),n.f=e,n}function dV(n,e){return(e&et)%n.d.length}function DAn(n,e,t){return zen(n.c,n.b,e,t)}function LAn(n,e){this.c=n,S0.call(this,e)}function NAn(n,e){this.a=n,kyn.call(this,e)}function O7(n,e){this.a=n,kyn.call(this,e)}function Dt(n,e){lt.call(this,n),this.a=e}function bV(n,e){FG.call(this,n),this.a=e}function DL(n,e){FG.call(this,n),this.a=e}function jae(n){VY.call(this,0,0),this.f=n}function $An(n,e,t){return n.a+=hh(e,0,t),n}function D7(n){return!n.a&&(n.a=new C0n),n.a}function wV(n,e){var t;return t=n.e,n.e=e,t}function gV(n,e){var t;return t=e,!!n.Fe(t)}function Eae(n,e){return _n(),n==e?0:n?1:-1}function Rb(n,e){n.a.bd(n.b,e),++n.b,n.c=-1}function L7(n){n.b?L7(n.b):n.f.c.zc(n.e,n.d)}function xAn(n){Hu(n.e),n.d.b=n.d,n.d.a=n.d}function Cae(n,e,t){Xa(),t9n(n,e.Ve(n.a,t))}function pV(n,e,t){return Pp(n,u(e,22),t)}function $s(n,e){return qE(new Array(e),n)}function Mae(n){return Ae(U1(n,32))^Ae(n)}function LL(n){return String.fromCharCode(n)}function Tae(n){return n==null?null:n.message}function Aae(n,e,t){return n.apply(e,t)}function Sae(n,e){var t;t=n[DB],t.call(n,e)}function Pae(n,e){var t;t=n[DB],t.call(n,e)}function Iae(n,e){return o7(),!Q4(e.d.i,n)}function mV(n,e,t,i){rM.call(this,n,e,t,i)}function FAn(){qC.call(this),this.a=new Li}function vV(){this.n=new Li,this.o=new Li}function BAn(){this.b=new Li,this.c=new Z}function RAn(){this.a=new Z,this.b=new Z}function KAn(){this.a=new _U,this.b=new Byn}function kV(){this.b=new Ql,this.a=new Ql}function _An(){this.b=new ni,this.a=new ni}function HAn(){this.b=new de,this.a=new de}function qAn(){this.b=new wEn,this.a=new H3n}function UAn(){this.a=new n8n,this.b=new Lpn}function GAn(){this.a=new Z,this.d=new Z}function qC(){this.n=new cp,this.i=new mp}function zAn(n){this.a=(Co(n,mw),new Gc(n))}function XAn(n){this.a=(Co(n,mw),new Gc(n))}function Oae(n){return n<100?null:new F1(n)}function Dae(n,e){return n.n.a=(Jn(e),e+10)}function Lae(n,e){return n.n.a=(Jn(e),e+10)}function Nae(n,e){return e==n||km(TA(e),n)}function VAn(n,e){return Xe(n.a,e,"")==null}function $ae(n,e){var t;return t=e.qi(n.a),t}function tt(n,e){return n.a+=e.a,n.b+=e.b,n}function mi(n,e){return n.a-=e.a,n.b-=e.b,n}function xae(n){return Pb(n.j.c,0),n.a=-1,n}function yV(n,e,t){return t=So(n,e,11,t),t}function Fae(n,e,t){t!=null&&mT(e,Fx(n,t))}function Bae(n,e,t){t!=null&&vT(e,Fx(n,t))}function jp(n,e,t,i){q.call(this,n,e,t,i)}function jV(n,e,t,i){q.call(this,n,e,t,i)}function WAn(n,e,t,i){jV.call(this,n,e,t,i)}function JAn(n,e,t,i){bM.call(this,n,e,t,i)}function NL(n,e,t,i){bM.call(this,n,e,t,i)}function EV(n,e,t,i){bM.call(this,n,e,t,i)}function QAn(n,e,t,i){NL.call(this,n,e,t,i)}function CV(n,e,t,i){NL.call(this,n,e,t,i)}function Nn(n,e,t,i){EV.call(this,n,e,t,i)}function YAn(n,e,t,i){CV.call(this,n,e,t,i)}function ZAn(n,e,t,i){jW.call(this,n,e,t,i)}function Kb(n,e){Ir.call(this,k8+n+Td+e)}function MV(n,e){return n.jk().wi().ri(n,e)}function TV(n,e){return n.jk().wi().ti(n,e)}function nSn(n,e){return Jn(n),x(n)===x(e)}function An(n,e){return Jn(n),x(n)===x(e)}function Rae(n,e){return n.b.Bd(new ECn(n,e))}function Kae(n,e){return n.b.Bd(new CCn(n,e))}function eSn(n,e){return n.b.Bd(new MCn(n,e))}function _ae(n,e){return n.e=u(n.d.Kb(e),159)}function AV(n,e,t){return n.lastIndexOf(e,t)}function Hae(n,e,t){return bt(n[e.a],n[t.a])}function qae(n,e){return U(e,(cn(),Cj),n)}function Uae(n,e){return jc(e.a.d.p,n.a.d.p)}function Gae(n,e){return jc(n.a.d.p,e.a.d.p)}function zae(n,e){return bt(n.c-n.s,e.c-e.s)}function Xae(n,e){return bt(n.b.e.a,e.b.e.a)}function Vae(n,e){return bt(n.c.e.a,e.c.e.a)}function tSn(n){return n.c?qr(n.c.a,n,0):-1}function Ep(n){return n==Ud||n==tl||n==qc}function SV(n,e){this.c=n,oN.call(this,n,e)}function iSn(n,e,t){this.a=n,JX.call(this,e,t)}function rSn(n){this.c=n,IC.call(this,Ey,0)}function cSn(n,e,t){this.c=e,this.b=t,this.a=n}function N7(n){k4(),this.d=n,this.a=new Eg}function uSn(n){uh(),this.a=(Dn(),new r4(n))}function Wae(n,e){hl(n.f)?QCe(n,e):Sye(n,e)}function oSn(n,e){sbe.call(this,n,n.length,e)}function Jae(n,e){qf||e&&(n.d=e)}function sSn(n,e){return O(e,15)&&xqn(n.c,e)}function Qae(n,e,t){return u(n.c,71).Wk(e,t)}function UC(n,e,t){return u(n.c,71).Xk(e,t)}function Yae(n,e,t){return oae(n,u(e,343),t)}function PV(n,e,t){return sae(n,u(e,343),t)}function Zae(n,e,t){return PKn(n,u(e,343),t)}function fSn(n,e,t){return _ye(n,u(e,343),t)}function x6(n,e){return e==null?null:tw(n.b,e)}function IV(n){return $b(n)?(Jn(n),n):n.ue()}function GC(n){return!isNaN(n)&&!isFinite(n)}function $L(n){jTn(this),vo(this),Bi(this,n)}function _u(n){pL(this),zV(this.c,0,n.Pc())}function _o(n,e,t){this.a=n,this.b=e,this.c=t}function hSn(n,e,t){this.a=n,this.b=e,this.c=t}function lSn(n,e,t){this.d=n,this.b=t,this.a=e}function aSn(n){this.a=n,fl(),vc(Date.now())}function dSn(n){bo(n.a),GJ(n.c,n.b),n.b=null}function xL(){xL=F,Oun=new $0n,AQn=new x0n}function bSn(){bSn=F,Ioe=K(ki,Fn,1,0,5,1)}function wSn(){wSn=F,Voe=K(ki,Fn,1,0,5,1)}function OV(){OV=F,Woe=K(ki,Fn,1,0,5,1)}function uh(){uh=F,new KG((Dn(),Dn(),sr))}function nde(n){return B4(),Ee((yNn(),IQn),n)}function ede(n){return Gu(),Ee((lNn(),xQn),n)}function tde(n){return YT(),Ee((JDn(),HQn),n)}function ide(n){return cT(),Ee((QDn(),qQn),n)}function rde(n){return NA(),Ee((Jxn(),UQn),n)}function cde(n){return bf(),Ee((fNn(),XQn),n)}function ude(n){return Uu(),Ee((sNn(),WQn),n)}function ode(n){return bu(),Ee((hNn(),QQn),n)}function sde(n){return VA(),Ee((zMn(),kYn),n)}function fde(n){return N0(),Ee((ENn(),jYn),n)}function hde(n){return Vp(),Ee((MNn(),CYn),n)}function lde(n){return A5(),Ee((CNn(),AYn),n)}function ade(n){return YE(),Ee((jDn(),SYn),n)}function dde(n){return uT(),Ee((YDn(),GYn),n)}function bde(n){return i5(),Ee((aNn(),pZn),n)}function wde(n){return Vi(),Ee((u$n(),yZn),n)}function gde(n){return nm(),Ee((ANn(),TZn),n)}function pde(n){return dd(),Ee((TNn(),DZn),n)}function DV(n,e){if(!n)throw M(new Gn(e))}function v4(n){if(!n)throw M(new Or(btn))}function FL(n,e){if(n!=e)throw M(new Bo)}function gSn(n,e,t){this.a=n,this.b=e,this.c=t}function LV(n,e,t){this.a=n,this.b=e,this.c=t}function pSn(n,e,t){this.a=n,this.b=e,this.c=t}function zC(n,e,t){this.b=n,this.a=e,this.c=t}function NV(n,e,t){this.b=n,this.c=e,this.a=t}function $V(n,e,t){this.a=n,this.b=e,this.c=t}function XC(n,e,t){this.e=e,this.b=n,this.d=t}function mSn(n,e,t){this.b=n,this.a=e,this.c=t}function mde(n,e,t){return Xa(),n.a.Yd(e,t),e}function BL(n){var e;return e=new ubn,e.e=n,e}function xV(n){var e;return e=new qyn,e.b=n,e}function $7(){$7=F,CP=new sgn,MP=new fgn}function VC(){VC=F,XZn=new xgn,zZn=new Fgn}function xs(){xs=F,YZn=new G2n,ZZn=new z2n}function vde(n){return D0(),Ee((qLn(),fne),n)}function kde(n){return tr(),Ee((XMn(),HZn),n)}function yde(n){return OT(),Ee((PNn(),GZn),n)}function jde(n){return $f(),Ee((SNn(),tne),n)}function Ede(n){return ow(),Ee((o$n(),rne),n)}function Cde(n){return DA(),Ee(($xn(),hne),n)}function Mde(n){return Yp(),Ee((D$n(),lne),n)}function Tde(n){return QM(),Ee((cLn(),ane),n)}function Ade(n){return u5(),Ee((_Ln(),dne),n)}function Sde(n){return bT(),Ee((HLn(),bne),n)}function Pde(n){return o1(),Ee((s$n(),wne),n)}function Ide(n){return pk(),Ee((eLn(),gne),n)}function Ode(n){return jm(),Ee(($$n(),jne),n)}function Dde(n){return pr(),Ee((aFn(),Ene),n)}function Lde(n){return Z4(),Ee((GLn(),Cne),n)}function Nde(n){return vl(),Ee((zLn(),Tne),n)}function $de(n){return KM(),Ee((nLn(),Ane),n)}function xde(n){return Jk(),Ee((N$n(),yne),n)}function Fde(n){return hd(),Ee((ULn(),mne),n)}function Bde(n){return vA(),Ee((L$n(),vne),n)}function Rde(n){return hk(),Ee((tLn(),kne),n)}function Kde(n){return Yo(),Ee((h$n(),Sne),n)}function _de(n){return a1(),Ee((Xxn(),Yte),n)}function Hde(n){return g5(),Ee((XLn(),Zte),n)}function qde(n){return cw(),Ee((INn(),nie),n)}function Ude(n){return T5(),Ee((f$n(),eie),n)}function Gde(n){return gs(),Ee((dFn(),tie),n)}function zde(n){return lh(),Ee((ONn(),iie),n)}function Xde(n){return wk(),Ee((iLn(),rie),n)}function Vde(n){return gr(),Ee((JLn(),uie),n)}function Wde(n){return ST(),Ee((VLn(),oie),n)}function Jde(n){return d5(),Ee((WLn(),sie),n)}function Qde(n){return om(),Ee((QLn(),fie),n)}function Yde(n){return dT(),Ee((YLn(),hie),n)}function Zde(n){return DT(),Ee((ZLn(),lie),n)}function n0e(n){return O0(),Ee((oNn(),Aie),n)}function e0e(n){return n5(),Ee((rLn(),Die),n)}function t0e(n){return sh(),Ee((sLn(),Rie),n)}function i0e(n){return Sf(),Ee((fLn(),_ie),n)}function r0e(n){return lf(),Ee((hLn(),tre),n)}function c0e(n){return M0(),Ee((lLn(),fre),n)}function u0e(n){return Qp(),Ee((BNn(),hre),n)}function o0e(n){return q5(),Ee((VMn(),lre),n)}function s0e(n){return b5(),Ee((nNn(),are),n)}function f0e(n){return w5(),Ee((FNn(),$re),n)}function h0e(n){return FM(),Ee((uLn(),xre),n)}function l0e(n){return yT(),Ee((oLn(),_re),n)}function a0e(n){return wA(),Ee((l$n(),qre),n)}function d0e(n){return Ok(),Ee((eNn(),Gre),n)}function b0e(n){return ZM(),Ee((aLn(),Ure),n)}function w0e(n){return sA(),Ee((xNn(),lce),n)}function g0e(n){return AT(),Ee((tNn(),ace),n)}function p0e(n){return XT(),Ee((iNn(),dce),n)}function m0e(n){return rA(),Ee((rNn(),wce),n)}function v0e(n){return _T(),Ee((cNn(),mce),n)}function k0e(n){return GM(),Ee((dLn(),Rce),n)}function y0e(n){return V4(),Ee((ZDn(),_Zn),n)}function j0e(n){return Vn(),Ee((x$n(),xZn),n)}function E0e(n){return nT(),Ee((uNn(),Kce),n)}function C0e(n){return N$(),Ee((bLn(),_ce),n)}function M0e(n){return R5(),Ee((a$n(),qce),n)}function T0e(n){return eC(),Ee((IDn(),Gce),n)}function A0e(n){return Fk(),Ee((bNn(),Uce),n)}function S0e(n){return tC(),Ee((ODn(),Xce),n)}function P0e(n){return ck(),Ee((wLn(),Vce),n)}function I0e(n){return Yk(),Ee((d$n(),Wce),n)}function O0e(n){return f6(),Ee((DDn(),lue),n)}function D0e(n){return Ak(),Ee((gLn(),aue),n)}function L0e(n){return gf(),Ee((w$n(),mue),n)}function N0e(n){return l1(),Ee((Lxn(),kue),n)}function $0e(n){return Rh(),Ee((F$n(),yue),n)}function x0e(n){return wd(),Ee((B$n(),Aue),n)}function F0e(n){return ci(),Ee((b$n(),zue),n)}function B0e(n){return Nf(),Ee((wNn(),Xue),n)}function R0e(n){return El(),Ee((RNn(),Vue),n)}function K0e(n){return pA(),Ee((R$n(),Wue),n)}function _0e(n){return jl(),Ee((dNn(),Que),n)}function H0e(n){return To(),Ee((KNn(),Zue),n)}function q0e(n){return lw(),Ee((Wxn(),noe),n)}function U0e(n){return Fg(),Ee((g$n(),eoe),n)}function G0e(n){return Oi(),Ee((K$n(),toe),n)}function z0e(n){return zu(),Ee((_$n(),ioe),n)}function X0e(n){return tn(),Ee((p$n(),roe),n)}function V0e(n){return go(),Ee((_Nn(),foe),n)}function W0e(n){return io(),Ee((Vxn(),hoe),n)}function J0e(n){return Gp(),Ee((gNn(),loe),n)}function Q0e(n,e){return Jn(n),n+(Jn(e),e)}function Y0e(n){return RL(),Ee((pLn(),aoe),n)}function Z0e(n){return qT(),Ee((HNn(),doe),n)}function nbe(n){return LT(),Ee((qNn(),goe),n)}function k4(){k4=F,tln=(tn(),Wn),II=Zn}function RL(){RL=F,vdn=new VSn,kdn=new LPn}function ebe(n){return!n.e&&(n.e=new Z),n.e}function KL(n,e){this.c=n,this.a=e,this.b=e-n}function vSn(n,e,t){this.a=n,this.b=e,this.c=t}function _L(n,e,t){this.a=n,this.b=e,this.c=t}function FV(n,e,t){this.a=n,this.b=e,this.c=t}function BV(n,e,t){this.a=n,this.b=e,this.c=t}function kSn(n,e,t){this.a=n,this.b=e,this.c=t}function ySn(n,e,t){this.a=n,this.b=e,this.c=t}function Xl(n,e,t){this.e=n,this.a=e,this.c=t}function jSn(n,e,t){Ko(),tJ.call(this,n,e,t)}function HL(n,e,t){Ko(),RW.call(this,n,e,t)}function RV(n,e,t){Ko(),RW.call(this,n,e,t)}function KV(n,e,t){Ko(),RW.call(this,n,e,t)}function ESn(n,e,t){Ko(),HL.call(this,n,e,t)}function _V(n,e,t){Ko(),HL.call(this,n,e,t)}function CSn(n,e,t){Ko(),_V.call(this,n,e,t)}function MSn(n,e,t){Ko(),RV.call(this,n,e,t)}function TSn(n,e,t){Ko(),KV.call(this,n,e,t)}function qL(n){rM.call(this,n.d,n.c,n.a,n.b)}function HV(n){rM.call(this,n.d,n.c,n.a,n.b)}function qV(n){this.d=n,c9n(this),this.b=nwe(n.d)}function tbe(n){return Cm(),Ee((Nxn(),Poe),n)}function x7(n,e){return Se(n),Se(e),new NEn(n,e)}function Cp(n,e){return Se(n),Se(e),new RSn(n,e)}function ibe(n,e){return Se(n),Se(e),new KSn(n,e)}function rbe(n,e){return Se(n),Se(e),new qEn(n,e)}function UL(n){return oe(n.b!=0),Xo(n,n.a.a)}function cbe(n){return oe(n.b!=0),Xo(n,n.c.b)}function ube(n){return!n.c&&(n.c=new W3),n.c}function y4(n){var e;return e=new Z,b$(e,n),e}function obe(n){var e;return e=new ni,b$(e,n),e}function ASn(n){var e;return e=new GG,A$(e,n),e}function F7(n){var e;return e=new Ct,A$(e,n),e}function u(n,e){return F6(n==null||Tx(n,e)),n}function sbe(n,e,t){TPn.call(this,e,t),this.a=n}function SSn(n,e){this.c=n,this.b=e,this.a=!1}function PSn(){this.a=";,;",this.b="",this.c=""}function ISn(n,e,t){this.b=n,_Mn.call(this,e,t)}function UV(n,e,t){this.c=n,oC.call(this,e,t)}function GV(n,e,t){d4.call(this,n,e),this.b=t}function zV(n,e,t){Bnn(t,0,n,e,t.length,!1)}function Lh(n,e,t,i,r){n.b=e,n.c=t,n.d=i,n.a=r}function XV(n,e,t,i,r){n.d=e,n.c=t,n.a=i,n.b=r}function fbe(n,e){e&&(n.b=e,n.a=(z1(e),e.a))}function B7(n,e){if(!n)throw M(new Gn(e))}function Mp(n,e){if(!n)throw M(new Or(e))}function VV(n,e){if(!n)throw M(new Bjn(e))}function hbe(n,e){return ZE(),jc(n.d.p,e.d.p)}function lbe(n,e){return kl(),bt(n.e.b,e.e.b)}function abe(n,e){return kl(),bt(n.e.a,e.e.a)}function dbe(n,e){return jc(GSn(n.d),GSn(e.d))}function WC(n,e){return e&&vM(n,e.d)?e:null}function bbe(n,e){return e==(tn(),Wn)?n.c:n.d}function WV(n){return Q1(dwe(Vr(n)?ds(n):n))}function wbe(n){return new V(n.c+n.b,n.d+n.a)}function OSn(n){return n!=null&&!lx(n,N9,$9)}function gbe(n,e){return(fBn(n)<<4|fBn(e))&ui}function DSn(n,e,t,i,r){n.c=e,n.d=t,n.b=i,n.a=r}function JV(n){var e,t;e=n.b,t=n.c,n.b=t,n.c=e}function QV(n){var e,t;t=n.d,e=n.a,n.d=e,n.a=t}function pbe(n,e){var t;return t=n.c,PQ(n,e),t}function YV(n,e){return e<0?n.g=-1:n.g=e,n}function JC(n,e){return Mme(n),n.a*=e,n.b*=e,n}function LSn(n,e,t){A$n.call(this,e,t),this.d=n}function R7(n,e,t){pX.call(this,n,e),this.c=t}function QC(n,e,t){pX.call(this,n,e),this.c=t}function ZV(n){OV(),ME.call(this),this.ci(n)}function NSn(){$4(),Bwe.call(this,(R1(),Ss))}function $Sn(n){return nt(),new Nh(0,n)}function xSn(){xSn=F,AU=(Dn(),new nD(IK))}function YC(){YC=F,new hZ((bD(),HK),(dD(),_K))}function FSn(){FSn=F,pun=K(Gi,J,17,256,0,1)}function BSn(){this.b=$(R(rn((qs(),y_))))}function GL(n){this.b=n,this.a=Wa(this.b.a).Od()}function RSn(n,e){this.b=n,this.a=e,GO.call(this)}function KSn(n,e){this.a=n,this.b=e,GO.call(this)}function _Sn(n,e,t){this.a=n,gg.call(this,e,t)}function HSn(n,e,t){this.a=n,gg.call(this,e,t)}function j4(n,e,t){var i;i=new qb(t),df(n,e,i)}function nW(n,e,t){var i;return i=n[e],n[e]=t,i}function ZC(n){var e;return e=n.slice(),o$(e,n)}function nM(n){var e;return e=n.n,n.a.b+e.d+e.a}function qSn(n){var e;return e=n.n,n.e.b+e.d+e.a}function eW(n){var e;return e=n.n,n.e.a+e.b+e.c}function tW(n){n.a.b=n.b,n.b.a=n.a,n.a=n.b=null}function xe(n,e){return xt(n,e,n.c.b,n.c),!0}function mbe(n){return n.a?n.a:vN(n)}function vbe(n){return Lp(),Kh(n)==At(ia(n))}function kbe(n){return Lp(),ia(n)==At(Kh(n))}function d0(n,e){return O5(n,new d4(e.a,e.b))}function ybe(n,e){return yM(),Nx(n,e),new lIn(n,e)}function jbe(n,e){return n.c<e.c?-1:n.c==e.c?0:1}function USn(n){return n.b.c.length-n.e.c.length}function GSn(n){return n.e.c.length-n.g.c.length}function zL(n){return n.e.c.length+n.g.c.length}function K7(n){return n==0||isNaN(n)?n:n<0?-1:1}function Ebe(n){return!fr(n)&&n.c.i.c==n.d.i.c}function Cbe(n){return ko(),(tn(),su).Hc(n.j)}function Mbe(n,e,t){return kl(),t.e.a+t.f.a+n*e}function Tbe(n,e,t){return kl(),t.e.b+t.f.b+n*e}function Abe(n,e,t){return Xe(n.b,u(t.b,18),e)}function Sbe(n,e,t){return Xe(n.b,u(t.b,18),e)}function Pbe(n,e,t){wDe(n.a,n.b,n.c,u(e,166),t)}function iW(n,e,t,i){iZ.call(this,n,e,t,i,0,0)}function zSn(n){OV(),ZV.call(this,n),this.a=-1}function XSn(n,e){TPn.call(this,e,1040),this.a=n}function VSn(){sMn.call(this,"COUNT_CHILDREN",0)}function eM(n,e){j7.call(this,n,e),this.a=this}function Nt(n,e){var t;return t=bN(n,e),t.i=2,t}function tM(n,e){var t;return++n.j,t=n.Cj(e),t}function Re(n,e,t){return n.a=-1,YX(n,e.g,t),n}function Ibe(n,e){return nn(n,new V(e.a,e.b))}function WSn(n){return _p(),K(NI,OS,40,n,0,1)}function JSn(n){return n.e.Rd().gc()*n.c.Rd().gc()}function XL(n,e,t){return new cSn(Kwe(n)._e(),t,e)}function Obe(n,e){IQ(n,e==null?null:(Jn(e),e))}function Dbe(n,e){SQ(n,e==null?null:(Jn(e),e))}function Lbe(n,e){SQ(n,e==null?null:(Jn(e),e))}function F6(n){if(!n)throw M(new i4(null))}function rW(n){if(n.c.e!=n.a)throw M(new Bo)}function cW(n){if(n.e.c!=n.b)throw M(new Bo)}function iM(n){for(Se(n);n.Ob();)n.Pb(),n.Qb()}function VL(n){m0(),this.a=(Dn(),new nD(Se(n)))}function uW(n){this.c=n,this.b=this.c.d.vc().Kc()}function Nbe(n){n.a.ld(),u(n.a.md(),16).gc(),wz()}function QSn(n,e){return n.a+=hh(e,0,e.length),n}function sn(n,e){return Ln(e,n.c.length),n.c[e]}function YSn(n,e){return Ln(e,n.a.length),n.a[e]}function $be(n,e){return Jn(e),kk(e,(Jn(n),n))}function xbe(n,e){return Jn(n),kk(n,(Jn(e),e))}function Va(n,e,t,i,r,c){return jKn(n,e,t,i,r,0,c)}function Fbe(n,e){return $t(e,0,oW(e[0],Ml(1)))}function Bbe(n,e){return Ml(nr(Ml(n.a).a,e.a))}function oW(n,e){return Bbe(u(n,168),u(e,168))}function ZSn(){ZSn=F,mun=K(tb,J,168,256,0,1)}function nPn(){nPn=F,yun=K(ib,J,191,256,0,1)}function ePn(){ePn=F,bun=K(p3,J,222,256,0,1)}function tPn(){tPn=F,gun=K(I8,J,180,128,0,1)}function sW(){Lh(this,!1,!1,!1,!1)}function fW(n){CG.call(this,new Ql),Bi(this,n)}function B6(n){this.a=new ap(n.gc()),Bi(this,n)}function iPn(n){this.c=n,this.a=new dp(this.c.a)}function rPn(n){this.a=n,this.c=new de,o6e(this)}function cPn(){this.d=new V(0,0),this.e=new ni}function Tn(n,e){Xa(),i$.call(this,n),this.a=e}function rM(n,e,t,i){XV(this,n,e,t,i)}function Rbe(n,e,t){return jc(e.d[n.g],t.d[n.g])}function Kbe(n,e,t){return jc(n.d[e.p],n.d[t.p])}function _be(n,e,t){return jc(n.d[e.p],n.d[t.p])}function Hbe(n,e,t){return jc(n.d[e.p],n.d[t.p])}function qbe(n,e,t){return jc(n.d[e.p],n.d[t.p])}function cM(n,e,t){return y.Math.min(t/n,1/e)}function uPn(n,e){return n?0:y.Math.max(0,e-1)}function WL(n,e){return n==null?e==null:An(n,e)}function Ube(n,e){return n==null?e==null:JT(n,e)}function oPn(n){return n.q?n.q:(Dn(),Dn(),Wh)}function sPn(n){return n.c-u(sn(n.a,n.b),294).b}function ao(n){return n.c?n.c.f:n.e.b}function Su(n){return n.c?n.c.g:n.e.a}function Gbe(n,e){return n.a==null&&qqn(n),n.a[e]}function fPn(n){var e;return e=CKn(n),e?fPn(e):n}function uM(n,e){return nt(),new SW(n,e)}function Nh(n,e){nt(),Wd.call(this,n),this.a=e}function oM(n,e){Ko(),LE.call(this,e),this.a=n}function R6(n,e,t){this.a=n,ti.call(this,e,t,2)}function hPn(n){this.b=new Ct,this.a=n,this.c=-1}function lPn(n){JX.call(this,0,0),this.a=n,this.b=0}function sM(n){S0.call(this,n.gc()),Bt(this,n)}function fM(n){n.b?fM(n.b):n.d.dc()&&n.f.c.Bc(n.e)}function hW(n){return Array.isArray(n)&&n.Tm===J2}function JL(n,e){return O(e,22)&&Au(n,u(e,22))}function aPn(n,e){return O(e,22)&&kme(n,u(e,22))}function wr(n,e){return BFn(n,e,J3e(n,n.b.Ce(e)))}function zbe(n,e){return n.a.get(e)!==void 0}function lW(n){return to(n,26)*Z5+to(n,27)*n8}function dPn(n,e){return Rme(new U0n,new b9n(n),e)}function QL(n,e,t){xFn(0,e,n.length),F4(n,0,e,t)}function b0(n,e,t){zb(e,n.c.length),b6(n.c,e,t)}function hM(n,e,t){var i;n&&(i=n.i,i.c=e,i.b=t)}function lM(n,e,t){var i;n&&(i=n.i,i.d=e,i.a=t)}function bPn(n,e,t){var i;for(i=0;i<e;++i)n[i]=t}function Xbe(n,e){var t;for(t=0;t<e;++t)n[t]=-1}function yt(n,e){var t;return t=yn(n),eY(t,e),t}function Vbe(n,e){return!n&&(n=[]),n[n.length]=e,n}function YL(n,e){tt(n.c,e),n.b.c+=e.a,n.b.d+=e.b}function Wbe(n,e){YL(n,mi(new V(e.a,e.b),n.c))}function ZL(n,e){this.b=new Ct,this.a=n,this.c=e}function wPn(){this.b=new twn,this.c=new WIn(this)}function aW(){this.d=new ibn,this.e=new VIn(this)}function dW(){oJ(),this.f=new Ct,this.e=new Ct}function gPn(){ko(),this.k=new de,this.d=new ni}function nN(){nN=F,moe=new Ni((qe(),oo),0)}function pPn(){pPn=F,cQn=new lPn(K(ki,Fn,1,0,5,1))}function Jbe(n,e,t){return fi(n,new bp(e.a,t.a))}function Qbe(n,e,t){return-jc(n.f[e.p],n.f[t.p])}function Ybe(n,e,t){DHn(t,n,1),nn(e,new DCn(t,n))}function Zbe(n,e,t){I5(t,n,1),nn(e,new $Cn(t,n))}function mPn(n,e,t){this.a=n,$C.call(this,e,t,22)}function vPn(n,e,t){this.a=n,$C.call(this,e,t,14)}function kPn(n,e,t,i){Ko(),rDn.call(this,n,e,t,i)}function yPn(n,e,t,i){Ko(),rDn.call(this,n,e,t,i)}function Pu(n,e,t){return n.a=-1,YX(n,e.g+1,t),n}function bW(n,e,t){return t=So(n,u(e,54),7,t),t}function wW(n,e,t){return t=So(n,u(e,54),3,t),t}function Ae(n){return Vr(n)?n|0:cEn(n)}function jPn(n){return nt(),new IN(10,n,0)}function EPn(n){var e;return e=n.f,e||(n.f=n.Dc())}function Tp(n){var e;return e=n.i,e||(n.i=n.bc())}function aM(n){if(n.e.j!=n.d)throw M(new Bo)}function Wa(n){return n.c?n.c:n.c=n.Sd()}function eN(n){return n.d?n.d:n.d=n.Td()}function K6(n,e){return q8e(ak(n,e))?e.zi():null}function nwe(n){return O(n,15)?u(n,15).ed():n.Kc()}function gW(n){return n.Qc(K(ki,Fn,1,n.gc(),5,1))}function CPn(n){return n!=null&&uN(n)&&n.Tm!==J2}function pW(n){return!Array.isArray(n)&&n.Tm===J2}function MPn(n,e){return Se(e),n.a.Jd(e)&&!n.b.Jd(e)}function ewe(n,e){return Yc(n.l&e.l,n.m&e.m,n.h&e.h)}function twe(n,e){return Yc(n.l|e.l,n.m|e.m,n.h|e.h)}function iwe(n,e){return Yc(n.l^e.l,n.m^e.m,n.h^e.h)}function Fs(n,e){return Q1(t_n(Vr(n)?ds(n):n,e))}function w0(n,e){return Q1(Xnn(Vr(n)?ds(n):n,e))}function U1(n,e){return Q1(Bje(Vr(n)?ds(n):n,e))}function rwe(n,e){return Eae((Jn(n),n),(Jn(e),e))}function tN(n,e){return bt((Jn(n),n),(Jn(e),e))}function dM(n){this.b=new Gc(11),this.a=(j0(),n)}function te(n){this.a=(pPn(),cQn),this.d=u(Se(n),51)}function TPn(n,e){this.c=0,this.d=n,this.b=e|64|wh}function mW(n,e){this.e=n,this.d=e&64?e|wh:e}function iN(n){this.b=null,this.a=(j0(),n||Pun)}function APn(n){xC(this),this.g=n,MM(this),this.je()}function Ja(n){K1(),this.a=0,this.b=n-1,this.c=1}function vW(n,e,t,i){this.a=n,VM.call(this,n,e,t,i)}function cwe(n,e,t){n.a.Mb(t)&&(n.b=!0,e.Cd(t))}function kW(n){n.d||(n.d=n.b.Kc(),n.c=n.b.gc())}function E4(n,e){if(n<0||n>=e)throw M(new YG)}function _b(n,e){return $k(n,(Jn(e),new a9n(e)))}function Ap(n,e){return $k(n,(Jn(e),new d9n(e)))}function SPn(n,e,t){return VLe(n,u(e,12),u(t,12))}function PPn(n){return Ou(),u(n,12).g.c.length!=0}function IPn(n){return Ou(),u(n,12).e.c.length!=0}function uwe(n,e){return Hp(),bt(e.a.o.a,n.a.o.a)}function owe(n,e){e.Bb&kc&&!n.a.o&&(n.a.o=e)}function swe(n,e){e.Ug("General 'Rotator",1),jDe(n)}function fwe(n,e,t){e.qf(t,$(R(ee(n.b,t)))*n.a)}function OPn(n,e,t){return Xg(),W4(n,e)&&W4(n,t)}function _6(n){return zu(),!n.Hc(Fl)&&!n.Hc(Pa)}function hwe(n){return n.e?qJ(n.e):null}function H6(n){return Vr(n)?""+n:$qn(n)}function yW(n){var e;for(e=n;e.f;)e=e.f;return e}function lwe(n,e,t){return $t(e,0,oW(e[0],t[0])),e}function Vl(n,e,t,i){var r;r=n.i,r.i=e,r.a=t,r.b=i}function q(n,e,t,i){ti.call(this,n,e,t),this.b=i}function Ci(n,e,t,i,r){c$.call(this,n,e,t,i,r,-1)}function q6(n,e,t,i,r){ok.call(this,n,e,t,i,r,-1)}function bM(n,e,t,i){R7.call(this,n,e,t),this.b=i}function DPn(n){PMn.call(this,n,!1),this.a=!1}function LPn(){sMn.call(this,"LOOKAHEAD_LAYOUT",1)}function NPn(n){this.b=n,kp.call(this,n),RTn(this)}function $Pn(n){this.b=n,A7.call(this,n),KTn(this)}function Hb(n,e,t){this.a=n,jp.call(this,e,t,5,6)}function jW(n,e,t,i){this.b=n,ti.call(this,e,t,i)}function xPn(n,e){this.b=n,H8n.call(this,n.b),this.a=e}function FPn(n){this.a=kRn(n.a),this.b=new _u(n.b)}function EW(n,e){m0(),Hhe.call(this,n,FT(new Ku(e)))}function wM(n,e){return nt(),new BW(n,e,0)}function rN(n,e){return nt(),new BW(6,n,e)}function _i(n,e){for(Jn(e);n.Ob();)e.Cd(n.Pb())}function Zc(n,e){return Ai(e)?AN(n,e):!!wr(n.f,e)}function cN(n,e){return e.Vh()?na(n.b,u(e,54)):e}function awe(n,e){return An(n.substr(0,e.length),e)}function $h(n){return new te(new UX(n.a.length,n.a))}function gM(n){return new V(n.c+n.b/2,n.d+n.a/2)}function dwe(n){return Yc(~n.l&ro,~n.m&ro,~n.h&Il)}function uN(n){return typeof n===vy||typeof n===eB}function Hu(n){n.f=new iTn(n),n.i=new rTn(n),++n.g}function BPn(n){if(!n)throw M(new nc);return n.d}function Sp(n){var e;return e=a5(n),oe(e!=null),e}function bwe(n){var e;return e=I5e(n),oe(e!=null),e}function C4(n,e){var t;return t=n.a.gc(),BJ(e,t),t-e}function fi(n,e){var t;return t=n.a.zc(e,n),t==null}function _7(n,e){return n.a.zc(e,(_n(),wa))==null}function CW(n){return new Tn(null,vwe(n,n.length))}function MW(n,e,t){return cGn(n,u(e,42),u(t,176))}function Pp(n,e,t){return Ks(n.a,e),nW(n.b,e.g,t)}function wwe(n,e,t){E4(t,n.a.c.length),Go(n.a,t,e)}function B(n,e,t,i){xFn(e,t,n.length),gwe(n,e,t,i)}function gwe(n,e,t,i){var r;for(r=e;r<t;++r)n[r]=i}function TW(n,e){var t;for(t=0;t<e;++t)n[t]=!1}function Qa(n,e,t){dh(),this.e=n,this.d=e,this.a=t}function AW(n,e,t){this.c=n,this.a=e,Dn(),this.b=t}function oN(n,e){this.d=n,ne.call(this,n),this.e=e}function ff(n,e,t){return $6e(n,e.g,t),Ks(n.c,e),n}function pwe(n){return Qg(n,(ci(),Br)),n.d=!0,n}function sN(n){return!n.j&&Mfe(n,kSe(n.g,n.b)),n.j}function RPn(n){n.a=null,n.e=null,Hu(n.b),n.d=0,++n.c}function U6(n){Fb(n.b!=-1),Yl(n.c,n.a=n.b),n.b=-1}function SW(n,e){Wd.call(this,1),this.a=n,this.b=e}function mwe(n,e){return n>0?y.Math.log(n/e):-100}function KPn(n,e){return Ec(n,e)<0?-1:Ec(n,e)>0?1:0}function H7(n,e){OTn(n,O(e,160)?e:u(e,2036).Rl())}function PW(n,e){if(n==null)throw M(new sp(e))}function vwe(n,e){return yme(e,n.length),new XSn(n,e)}function IW(n,e){return e?Bi(n,e):!1}function kwe(){return RE(),S(T(uQn,1),G,549,0,[GK])}function G6(n){return n.e==0?n:new Qa(-n.e,n.d,n.a)}function ywe(n,e){return bt(n.c.c+n.c.b,e.c.c+e.c.b)}function q7(n,e){xt(n.d,e,n.b.b,n.b),++n.a,n.c=null}function _Pn(n,e){return n.c?_Pn(n.c,e):nn(n.b,e),n}function jwe(n,e,t){var i;return i=Jb(n,e),qN(n,e,t),i}function HPn(n,e,t){var i;for(i=0;i<e;++i)$t(n,i,t)}function qPn(n,e,t,i,r){for(;e<t;)i[r++]=Xi(n,e++)}function M4(n,e,t,i,r){Qx(n,u(ot(e.k,t),15),t,i,r)}function g0(n,e){qt(_r(n.Oc(),new lpn),new C7n(e))}function Ewe(n,e){return bt(n.e.a+n.f.a,e.e.a+e.f.a)}function Cwe(n,e){return bt(n.e.b+n.f.b,e.e.b+e.f.b)}function fN(n){return y.Math.abs(n.d.e-n.e.e)-n.a}function Mwe(n){return n==St?nj:n==li?"-INF":""+n}function Twe(n){return n==St?nj:n==li?"-INF":""+n}function Awe(n){return Lp(),At(Kh(n))==At(ia(n))}function Swe(n,e,t){return u(n.c.hd(e,u(t,136)),44)}function Pwe(n,e){Ip(n,new qb(e.f!=null?e.f:""+e.g))}function Iwe(n,e){Ip(n,new qb(e.f!=null?e.f:""+e.g))}function Bt(n,e){return n.Si()&&(e=gOn(n,e)),n.Fi(e)}function hN(n,e){return e=n.Yk(null,e),BKn(n,null,e)}function Owe(n,e){++n.j,Jx(n,n.i,e),nCe(n,u(e,343))}function OW(n){n?ZZ(n,(fl(),pQn)):$ge((fl(),n))}function p0(n){this.d=(Jn(n),n),this.a=0,this.c=Ey}function lN(n,e){this.d=j5e(n),this.c=e,this.a=.5*e}function UPn(n){nJ.call(this),this.a=n,nn(n.a,this)}function GPn(){Ql.call(this),this.a=!0,this.b=!0}function zPn(){zPn=F,lQn=new dG(!1),aQn=new dG(!0)}function z6(n){var e;return e=n.g,e||(n.g=new fG(n))}function pM(n){var e;return e=n.k,e||(n.k=new hG(n))}function DW(n){var e;return e=n.k,e||(n.k=new hG(n))}function Dwe(n){var e;return e=n.i,e||(n.i=new x8n(n))}function XPn(n){var e;return e=n.f,e||(n.f=new qX(n))}function aN(n){var e;return e=n.j,e||(n.j=new W8n(n))}function dN(n){var e;return e=n.d,e||(n.d=new VO(n))}function VPn(n,e,t){return nt(),new qOn(n,e,t)}function WPn(n,e){return ek(e,n.c.b.c.gc()),new LEn(n,e)}function LW(n,e){var t;return t=n.a.gc(),ek(e,t),t-1-e}function w(n,e,t){var i;return i=bN(n,e),G$n(t,i),i}function bN(n,e){var t;return t=new YQ,t.j=n,t.d=e,t}function Se(n){if(n==null)throw M(new ip);return n}function qb(n){if(n==null)throw M(new ip);this.a=n}function JPn(n){_G(),this.b=new Z,this.a=n,COe(this,n)}function NW(n){this.b=n,this.a=u(as(this.b.a.e),227)}function m0(){m0=F,uh(),qK=new PN((Dn(),Dn(),sr))}function wN(){wN=F,uh(),uun=new Bz((Dn(),Dn(),hP))}function G1(){G1=F,Hn=ZEe(),On(),tg&&nke()}function mM(n){n.s=NaN,n.c=NaN,kHn(n,n.e),kHn(n,n.j)}function se(n){return(n.i==null&&bh(n),n.i).length}function QPn(n,e){return u(Wa(n.a).Md().Xb(e),44).ld()}function ee(n,e){return Ai(e)?Nc(n,e):Kr(wr(n.f,e))}function Lwe(n,e){return Lp(),n==Kh(e)?ia(e):Kh(e)}function Nwe(n,e,t,i){return t==0||(t-i)/t<n.e||e>=n.g}function $t(n,e,t){return dae(t==null||oPe(n,t)),n[e]=t}function $W(n,e){return zn(e,n.length+1),n.substr(e)}function gN(n,e){for(Jn(e);n.c<n.d;)n.Se(e,n.c++)}function xW(n){this.d=n,this.c=n.a.d.a,this.b=n.a.e.g}function YPn(n){this.c=n,this.a=new Ct,this.b=new Ct}function Lc(n){this.c=new Li,this.a=new Z,this.b=n}function ZPn(n){this.b=new Z,this.a=new Z,this.c=n}function $we(n,e,t){u(e.b,68),nu(e.a,new FV(n,t,e))}function xwe(n,e){return Hp(),u(Cr(n,e.d),15).Fc(e)}function Ip(n,e){var t;t=n.a.length,Jb(n,t),qN(n,t,e)}function nIn(n,e){var t;t=console[n],t.call(console,e)}function eIn(n,e){var t;++n.j,t=n.Ej(),n.rj(n.Zi(t,e))}function pN(n,e,t){var i;return i=T$(n,e,t),yen(n,i)}function v0(n){return!n.d&&(n.d=new ti(jr,n,1)),n.d}function Fwe(n){return!n.a&&(n.a=new ti(Ia,n,4)),n.a}function T4(n,e){return n.a+=String.fromCharCode(e),n}function Ya(n,e){return n.a+=String.fromCharCode(e),n}function FW(n,e,t){this.a=n,FG.call(this,e),this.b=t}function tIn(n,e,t){this.a=n,vJ.call(this,8,e,null,t)}function BW(n,e,t){Wd.call(this,n),this.a=e,this.b=t}function RW(n,e,t){LE.call(this,e),this.a=n,this.b=t}function iIn(n){this.c=n,this.b=this.c.a,this.a=this.c.e}function Bwe(n){this.a=(Jn(Fe),Fe),this.b=n,new tz}function rIn(n){zW(n.a),n.b=K(ki,Fn,1,n.b.length,5,1)}function bo(n){Fb(n.c!=-1),n.d.gd(n.c),n.b=n.c,n.c=-1}function X6(n){return y.Math.sqrt(n.a*n.a+n.b*n.b)}function vM(n,e){return qx(n.c,n.f,e,n.b,n.a,n.e,n.d)}function k0(n,e){return E4(e,n.a.c.length),sn(n.a,e)}function oh(n,e){return x(n)===x(e)||n!=null&&rt(n,e)}function cIn(n){return O(n,102)&&(u(n,19).Bb&kc)!=0}function uIn(n){return as(n),O(n,484)?u(n,484):Jr(n)}function oIn(n){return n?n.dc():!n.Kc().Ob()}function Rwe(n){return rg?AN(rg,n):!1}function Kwe(n){return 0>=n?new Dz:Gme(n-1)}function Hi(n){return!n.a&&n.c?n.c.b:n.a}function KW(n){return O(n,616)?n:new oOn(n)}function z1(n){n.c?z1(n.c):(ea(n),n.d=!0)}function V6(n){n.c?n.c.$e():(n.d=!0,fTe(n))}function sIn(n){n.b=!1,n.c=!1,n.d=!1,n.a=!1}function fIn(n){var e,t;return e=n.c.i.c,t=n.d.i.c,e==t}function _we(n,e){var t;t=n.Ih(e),t>=0?n.ki(t):Pnn(n,e)}function hIn(n,e){n.c<0||n.b.b<n.c?ir(n.b,e):n.a.tf(e)}function Hwe(n,e){ve((!n.a&&(n.a=new O7(n,n)),n.a),e)}function qwe(n,e){YL(u(e.b,68),n),nu(e.a,new IG(n))}function Uwe(n,e){return jc(e.j.c.length,n.j.c.length)}function Gwe(n,e,t){return qp(),t.Lg(n,u(e.ld(),149))}function as(n){if(n==null)throw M(new ip);return n}function Jn(n){if(n==null)throw M(new ip);return n}function zwe(n){if(n.p!=4)throw M(new Cu);return n.e}function Xwe(n){if(n.p!=3)throw M(new Cu);return n.e}function Vwe(n){if(n.p!=3)throw M(new Cu);return n.j}function Wwe(n){if(n.p!=4)throw M(new Cu);return n.j}function Jwe(n){if(n.p!=6)throw M(new Cu);return n.f}function Qwe(n){if(n.p!=6)throw M(new Cu);return n.k}function _W(n){return!n.b&&(n.b=new NE(new aD)),n.b}function y0(n){return n.c==-2&&gfe(n,Uye(n.g,n.b)),n.c}function A4(n,e){var t;return t=bN("",n),t.n=e,t.i=1,t}function kM(n,e,t,i){i0.call(this,n,t),this.a=e,this.f=i}function HW(n,e,t,i){i0.call(this,n,e),this.d=t,this.a=i}function lIn(n,e){h1e.call(this,zme(Se(n),Se(e))),this.a=e}function ii(){vjn.call(this),Pb(this.j.c,0),this.a=-1}function aIn(){unn.call(this,vs,(o4(),Udn)),mIe(this)}function dIn(){unn.call(this,Sd,(rEn(),ise)),hOe(this)}function bIn(){je.call(this,"DELAUNAY_TRIANGULATION",0)}function Ywe(n){return String.fromCharCode.apply(null,n)}function Xe(n,e,t){return Ai(e)?Dr(n,e,t):Vc(n.f,e,t)}function qW(n){return Dn(),n?n.Oe():(j0(),j0(),Iun)}function Zwe(n){return Co(n,cB),oT(nr(nr(5,n),n/10|0))}function wIn(n,e){return YC(),new hZ(new QTn(n),new JTn(e))}function yM(){yM=F,rQn=new lz(S(T(Pd,1),WA,44,0,[]))}function gIn(n){return!n.d&&(n.d=new Q3(n.c.Cc())),n.d}function S4(n){return!n.a&&(n.a=new qjn(n.c.vc())),n.a}function pIn(n){return!n.b&&(n.b=new r4(n.c.ec())),n.b}function xh(n,e){for(;e-- >0;)n=n<<1|(n<0?1:0);return n}function mIn(n,e){var t;return t=new Lc(n),Bn(e.c,t),t}function vIn(n,e){n.u.Hc((zu(),Fl))&&zEe(n,e),h4e(n,e)}function mc(n,e){return x(n)===x(e)||n!=null&&rt(n,e)}function Cr(n,e){return JL(n.a,e)?n.b[u(e,22).g]:null}function nge(){return YE(),S(T(oon,1),G,489,0,[b_])}function ege(){return eC(),S(T($1n,1),G,490,0,[Bq])}function tge(){return tC(),S(T(zce,1),G,558,0,[Rq])}function ige(){return f6(),S(T(tan,1),G,539,0,[Hj])}function jM(n){return!n.n&&(n.n=new q(Ar,n,1,7)),n.n}function mN(n){return!n.c&&(n.c=new q(Qu,n,9,9)),n.c}function UW(n){return!n.c&&(n.c=new Nn(he,n,5,8)),n.c}function rge(n){return!n.b&&(n.b=new Nn(he,n,4,7)),n.b}function U7(n){return n.j.c.length=0,zW(n.c),xae(n.a),n}function P4(n){return n.e==rv&&jfe(n,Y8e(n.g,n.b)),n.e}function G7(n){return n.f==rv&&Cfe(n,q7e(n.g,n.b)),n.f}function Ve(n,e,t,i){return Hxn(n,e,t,!1),BT(n,i),n}function kIn(n,e){this.b=n,oN.call(this,n,e),RTn(this)}function yIn(n,e){this.b=n,SV.call(this,n,e),KTn(this)}function W6(n){this.d=n,this.a=this.d.b,this.b=this.d.c}function GW(n,e){this.b=n,this.c=e,this.a=new dp(this.b)}function Xi(n,e){return zn(e,n.length),n.charCodeAt(e)}function cge(n,e){DY(n,$(yl(e,"x")),$(yl(e,"y")))}function uge(n,e){DY(n,$(yl(e,"x")),$(yl(e,"y")))}function ut(n,e){return ea(n),new Tn(n,new tQ(e,n.a))}function _r(n,e){return ea(n),new Tn(n,new _J(e,n.a))}function Ub(n,e){return ea(n),new uV(n,new ILn(e,n.a))}function EM(n,e){return ea(n),new oV(n,new OLn(e,n.a))}function oge(n,e){return new GIn(u(Se(n),50),u(Se(e),50))}function sge(n,e){return bt(n.d.c+n.d.b/2,e.d.c+e.d.b/2)}function jIn(n,e,t){t.a?tu(n,e.b-n.f/2):eu(n,e.a-n.g/2)}function fge(n,e){return bt(n.g.c+n.g.b/2,e.g.c+e.g.b/2)}function hge(n,e){return $z(),bt((Jn(n),n),(Jn(e),e))}function lge(n){return n!=null&&r7(jO,n.toLowerCase())}function zW(n){var e;for(e=n.Kc();e.Ob();)e.Pb(),e.Qb()}function Tg(n){var e;return e=n.b,!e&&(n.b=e=new N8n(n)),e}function vN(n){var e;return e=Wme(n),e||null}function EIn(n,e){var t,i;return t=n/e,i=wi(t),t>i&&++i,i}function age(n,e,t){var i;i=u(n.d.Kb(t),159),i&&i.Nb(e)}function dge(n,e,t){wIe(n.a,t),zve(t),xCe(n.b,t),$Ie(e,t)}function CM(n,e,t,i){this.a=n,this.c=e,this.b=t,this.d=i}function XW(n,e,t,i){this.c=n,this.b=e,this.a=t,this.d=i}function CIn(n,e,t,i){this.c=n,this.b=e,this.d=t,this.a=i}function Ho(n,e,t,i){this.c=n,this.d=e,this.b=t,this.a=i}function MIn(n,e,t,i){this.a=n,this.d=e,this.c=t,this.b=i}function kN(n,e,t,i){this.a=n,this.e=e,this.d=t,this.c=i}function TIn(n,e,t,i){this.a=n,this.c=e,this.d=t,this.b=i}function yN(n,e,t){this.a=ktn,this.d=n,this.b=e,this.c=t}function Op(n,e,t,i){je.call(this,n,e),this.a=t,this.b=i}function AIn(n,e){this.d=(Jn(n),n),this.a=16449,this.c=e}function SIn(n){this.a=new Z,this.e=K(ye,J,53,n,0,2)}function bge(n){n.Ug("No crossing minimization",1),n.Vg()}function PIn(){ec.call(this,"There is no more element.")}function IIn(n,e,t,i){this.a=n,this.b=e,this.c=t,this.d=i}function OIn(n,e,t,i){this.a=n,this.b=e,this.c=t,this.d=i}function Za(n,e,t,i){this.e=n,this.a=e,this.c=t,this.d=i}function DIn(n,e,t,i){this.a=n,this.c=e,this.d=t,this.b=i}function LIn(n,e,t,i){Ko(),DLn.call(this,e,t,i),this.a=n}function NIn(n,e,t,i){Ko(),DLn.call(this,e,t,i),this.a=n}function jN(n,e,t){var i,r;return i=utn(n),r=e.ti(t,i),r}function al(n){var e,t;return t=(e=new Jd,e),K4(t,n),t}function EN(n){var e,t;return t=(e=new Jd,e),fnn(t,n),t}function wge(n,e){var t;return t=ee(n.f,e),HQ(e,t),null}function $In(n){return!n.b&&(n.b=new q(Vt,n,12,3)),n.b}function xIn(n){return F6(n==null||uN(n)&&n.Tm!==J2),n}function MM(n){return n.n&&(n.e!==Fzn&&n.je(),n.j=null),n}function I4(n){if(eo(n.d),n.d.d!=n.c)throw M(new Bo)}function VW(n){return oe(n.b<n.d.gc()),n.d.Xb(n.c=n.b++)}function vo(n){n.a.a=n.c,n.c.b=n.a,n.a.b=n.c.a=null,n.b=0}function CN(n){this.f=n,this.c=this.f.e,n.f>0&&bKn(this)}function FIn(n,e){this.a=n,bae.call(this,n,u(n.d,15).fd(e))}function gge(n,e){return bt(Su(n)*ao(n),Su(e)*ao(e))}function pge(n,e){return bt(Su(n)*ao(n),Su(e)*ao(e))}function mge(n){return _0(n)&&on(un(z(n,(cn(),Nd))))}function vge(n,e){return Pn(n,u(v(e,(cn(),Cv)),17),e)}function kge(n,e){return u(v(n,(W(),T3)),15).Fc(e),e}function WW(n,e){return n.b=e.b,n.c=e.c,n.d=e.d,n.a=e.a,n}function BIn(n,e,t,i){this.b=n,this.c=i,IC.call(this,e,t)}function yge(n,e,t){n.i=0,n.e=0,e!=t&&yFn(n,e,t)}function jge(n,e,t){n.i=0,n.e=0,e!=t&&jFn(n,e,t)}function Ege(n,e,t){return s6(),J5e(u(ee(n.e,e),529),t)}function Dp(n){var e;return e=n.f,e||(n.f=new h4(n,n.c))}function RIn(n,e){return xg(n.j,e.s,e.c)+xg(e.e,n.s,n.c)}function KIn(n,e){n.e&&!n.e.a&&(Ayn(n.e,e),KIn(n.e,e))}function _In(n,e){n.d&&!n.d.a&&(Ayn(n.d,e),_In(n.d,e))}function Cge(n,e){return-bt(Su(n)*ao(n),Su(e)*ao(e))}function Mge(n){return u(n.ld(),149).Pg()+":"+Jr(n.md())}function HIn(){tF(this,new oG),this.wb=(G1(),Hn),o4()}function qIn(n){this.b=new Z,hi(this.b,this.b),this.a=n}function JW(n,e){new Ct,this.a=new Mu,this.b=n,this.c=e}function j0(){j0=F,Pun=new FU,ZK=new FU,Iun=new D0n}function Dn(){Dn=F,sr=new A0n,Wh=new P0n,hP=new I0n}function QW(){QW=F,RQn=new nbn,_Qn=new aW,KQn=new ebn}function Lp(){Lp=F,mP=new Z,m_=new de,p_=new Z}function TM(n,e){if(n==null)throw M(new sp(e));return n}function AM(n){return!n.a&&(n.a=new q(Qe,n,10,11)),n.a}function ft(n){return!n.q&&(n.q=new q(As,n,11,10)),n.q}function _(n){return!n.s&&(n.s=new q(ku,n,21,17)),n.s}function Tge(n){return Se(n),IRn(new te(re(n.a.Kc(),new En)))}function Age(n,e){return wo(n),wo(e),Fjn(u(n,22),u(e,22))}function nd(n,e,t){var i,r;i=IV(t),r=new AE(i),df(n,e,r)}function MN(n,e,t,i,r,c){ok.call(this,n,e,t,i,r,c?-2:-1)}function UIn(n,e,t,i){pX.call(this,e,t),this.b=n,this.a=i}function GIn(n,e){Vfe.call(this,new iN(n)),this.a=n,this.b=e}function YW(n){this.b=n,this.c=n,n.e=null,n.c=null,this.a=1}function Sge(n){xs();var e;e=u(n.g,10),e.n.a=n.d.c+e.d.b}function O4(){O4=F;var n,e;e=!$8e(),n=new V3,VK=e?new og:n}function TN(n){return Dn(),O(n,59)?new jD(n):new BC(n)}function SM(n){return O(n,16)?new B6(u(n,16)):obe(n.Kc())}function Pge(n){return new HTn(n,n.e.Rd().gc()*n.c.Rd().gc())}function Ige(n){return new qTn(n,n.e.Rd().gc()*n.c.Rd().gc())}function ZW(n){return n&&n.hashCode?n.hashCode():l0(n)}function AN(n,e){return e==null?!!wr(n.f,null):zbe(n.i,e)}function Oge(n,e){var t;return t=$X(n.a,e),t&&(e.d=null),t}function zIn(n,e,t){return n.f?n.f.ef(e,t):!1}function z7(n,e,t,i){$t(n.c[e.g],t.g,i),$t(n.c[t.g],e.g,i)}function SN(n,e,t,i){$t(n.c[e.g],e.g,t),$t(n.b[e.g],e.g,i)}function Dge(n,e,t){return $(R(t.a))<=n&&$(R(t.b))>=e}function XIn(n,e){this.g=n,this.d=S(T(Qh,1),b1,10,0,[e])}function VIn(n){this.c=n,this.b=new Ul(u(Se(new tbn),50))}function WIn(n){this.c=n,this.b=new Ul(u(Se(new ewn),50))}function JIn(n){this.b=n,this.a=new Ul(u(Se(new Nbn),50))}function QIn(){this.b=new ni,this.d=new Ct,this.e=new ZG}function nJ(){this.c=new Li,this.d=new Li,this.e=new Li}function E0(){this.a=new Mu,this.b=(Co(3,mw),new Gc(3))}function Wl(n,e){this.e=n,this.a=ki,this.b=Qqn(e),this.c=e}function PM(n){this.c=n.c,this.d=n.d,this.b=n.b,this.a=n.a}function YIn(n,e,t,i,r,c){this.a=n,k$.call(this,e,t,i,r,c)}function ZIn(n,e,t,i,r,c){this.a=n,k$.call(this,e,t,i,r,c)}function X1(n,e,t,i,r,c,s){return new GN(n.e,e,t,i,r,c,s)}function Lge(n,e,t){return t>=0&&An(n.substr(t,e.length),e)}function nOn(n,e){return O(e,149)&&An(n.b,u(e,149).Pg())}function Nge(n,e){return n.a?e.Gh().Kc():u(e.Gh(),71).Ii()}function eOn(n,e){var t;return t=n.b.Qc(e),WDn(t,n.b.gc()),t}function X7(n,e){if(n==null)throw M(new sp(e));return n}function Hr(n){return n.u||(Zu(n),n.u=new NAn(n,n)),n.u}function PN(n){this.a=(Dn(),O(n,59)?new jD(n):new BC(n))}function au(n){var e;return e=u(Un(n,16),29),e||n.ii()}function IM(n,e){var t;return t=za(n.Rm),e==null?t:t+": "+e}function qo(n,e,t){return Fi(e,t,n.length),n.substr(e,t-e)}function tOn(n,e){qC.call(this),lQ(this),this.a=n,this.c=e}function $ge(n){n&&IM(n,n.ie())}function xge(n){HE(),y.setTimeout(function(){throw n},0)}function Fge(){return YT(),S(T(Bun,1),G,436,0,[o_,Fun])}function Bge(){return cT(),S(T(Kun,1),G,435,0,[Run,s_])}function Rge(){return uT(),S(T(bon,1),G,432,0,[v_,vP])}function Kge(){return V4(),S(T(KZn,1),G,517,0,[dj,L_])}function _ge(){return KM(),S(T(Qsn,1),G,429,0,[fH,Jsn])}function Hge(){return pk(),S(T($sn,1),G,428,0,[WP,Nsn])}function qge(){return QM(),S(T(Asn,1),G,431,0,[Tsn,V_])}function Uge(){return wk(),S(T(qhn,1),G,430,0,[UH,GH])}function Gge(){return n5(),S(T(Oie,1),G,531,0,[r9,i9])}function zge(){return yT(),S(T(Rln,1),G,501,0,[RI,D2])}function Xge(){return sh(),S(T(Bie,1),G,523,0,[mb,y1])}function Vge(){return Sf(),S(T(Kie,1),G,522,0,[Rd,zf])}function Wge(){return lf(),S(T(ere,1),G,528,0,[zw,ja])}function Jge(){return hk(),S(T(Bsn,1),G,488,0,[Fsn,QP])}function Qge(){return GM(),S(T(S1n,1),G,491,0,[$q,A1n])}function Yge(){return N$(),S(T(N1n,1),G,492,0,[D1n,L1n])}function Zge(){return FM(),S(T(Bln,1),G,433,0,[dq,Fln])}function n2e(){return ZM(),S(T(_ln,1),G,434,0,[Kln,vq])}function e2e(){return M0(),S(T(sre,1),G,465,0,[Ea,P2])}function t2e(){return ck(),S(T(x1n,1),G,438,0,[Kq,JI])}function i2e(){return Ak(),S(T(ran,1),G,437,0,[YI,ian])}function r2e(){return RL(),S(T(dO,1),G,347,0,[vdn,kdn])}function OM(n,e,t,i){return t>=0?n.Uh(e,t,i):n.Ch(null,t,i)}function V7(n){return n.b.b==0?n.a.sf():UL(n.b)}function c2e(n){if(n.p!=5)throw M(new Cu);return Ae(n.f)}function u2e(n){if(n.p!=5)throw M(new Cu);return Ae(n.k)}function eJ(n){return x(n.a)===x((D$(),CU))&&rOe(n),n.a}function o2e(n,e){n.b=e,n.c>0&&n.b>0&&(n.g=cM(n.c,n.b,n.a))}function s2e(n,e){n.c=e,n.c>0&&n.b>0&&(n.g=cM(n.c,n.b,n.a))}function iOn(n,e){ufe(this,new V(n.a,n.b)),ofe(this,F7(e))}function C0(){Wfe.call(this,new ap(Qb(12))),KX(!0),this.a=2}function IN(n,e,t){nt(),Wd.call(this,n),this.b=e,this.a=t}function tJ(n,e,t){Ko(),LE.call(this,e),this.a=n,this.b=t}function rOn(n){var e;e=n.c.d.b,n.b=e,n.a=n.c.d,e.a=n.c.d.b=n}function f2e(n){return n.b==0?null:(oe(n.b!=0),Xo(n,n.a.a))}function Nc(n,e){return e==null?Kr(wr(n.f,null)):d6(n.i,e)}function cOn(n,e,t,i,r){return new rF(n,(B4(),i_),e,t,i,r)}function DM(n,e){return zDn(e),Lme(n,K(ye,Ke,28,e,15,1),e)}function LM(n,e){return TM(n,"set1"),TM(e,"set2"),new VEn(n,e)}function h2e(n,e){var t=XK[n.charCodeAt(0)];return t??n}function uOn(n,e){var t,i;return t=e,i=new DO,LGn(n,t,i),i.d}function ON(n,e,t,i){var r;r=new FAn,e.a[t.g]=r,Pp(n.b,i,r)}function l2e(n,e){var t;return t=Ime(n.f,e),tt(HC(t),n.f.d)}function W7(n){var e;_me(n.a),dTn(n.a),e=new IE(n.a),HY(e)}function a2e(n,e){_qn(n,!0),nu(n.e.Rf(),new NV(n,!0,e))}function d2e(n,e){return Lp(),n==At(Kh(e))||n==At(ia(e))}function b2e(n,e){return kl(),u(v(e,(lc(),Sh)),17).a==n}function wi(n){return Math.max(Math.min(n,et),-2147483648)|0}function oOn(n){this.a=u(Se(n),277),this.b=(Dn(),new XX(n))}function sOn(n,e,t){this.i=new Z,this.b=n,this.g=e,this.a=t}function iJ(n,e,t){this.a=new Z,this.e=n,this.f=e,this.c=t}function NM(n,e,t){this.c=new Z,this.e=n,this.f=e,this.b=t}function fOn(n){qC.call(this),lQ(this),this.a=n,this.c=!0}function w2e(n){function e(){}return e.prototype=n||{},new e}function g2e(n){if(n.Ae())return null;var e=n.n;return rP[e]}function J7(n){return n.Db>>16!=3?null:u(n.Cb,27)}function Af(n){return n.Db>>16!=9?null:u(n.Cb,27)}function hOn(n){return n.Db>>16!=6?null:u(n.Cb,74)}function M0(){M0=F,Ea=new cX(s3,0),P2=new cX(f3,1)}function sh(){sh=F,mb=new tX(f3,0),y1=new tX(s3,1)}function Sf(){Sf=F,Rd=new iX(_B,0),zf=new iX("UP",1)}function lOn(){lOn=F,oQn=Ce((RE(),S(T(uQn,1),G,549,0,[GK])))}function aOn(n){var e;return e=new zE(Qb(n.length)),eY(e,n),e}function dOn(n,e){return n.b+=e.b,n.c+=e.c,n.d+=e.d,n.a+=e.a,n}function p2e(n,e){return Zxn(n,e)?(W$n(n),!0):!1}function dl(n,e){if(e==null)throw M(new ip);return F8e(n,e)}function Q7(n,e){var t;t=n.q.getHours(),n.q.setDate(e),G5(n,t)}function rJ(n,e,t){var i;i=n.Ih(e),i>=0?n.bi(i,t):ten(n,e,t)}function bOn(n,e){var t;return t=n.Ih(e),t>=0?n.Wh(t):hF(n,e)}function wOn(n,e){var t;for(Se(e),t=n.a;t;t=t.c)e.Yd(t.g,t.i)}function DN(n,e,t){var i;i=vFn(n,e,t),n.b=new ET(i.c.length)}function Ag(n,e,t){$M(),n&&Xe(yU,n,e),n&&Xe(hE,n,t)}function m2e(n,e){return VC(),_n(),u(e.a,17).a<n}function v2e(n,e){return VC(),_n(),u(e.b,17).a<n}function LN(n,e){return y.Math.abs(n)<y.Math.abs(e)?n:e}function k2e(n){return!n.a&&(n.a=new q(Qe,n,10,11)),n.a.i>0}function cJ(n){var e;return e=n.d,e=n.bj(n.f),ve(n,e),e.Ob()}function gOn(n,e){var t;return t=new fW(e),_Kn(t,n),new _u(t)}function y2e(n){if(n.p!=0)throw M(new Cu);return M6(n.f,0)}function j2e(n){if(n.p!=0)throw M(new Cu);return M6(n.k,0)}function pOn(n){return n.Db>>16!=7?null:u(n.Cb,241)}function D4(n){return n.Db>>16!=6?null:u(n.Cb,241)}function mOn(n){return n.Db>>16!=7?null:u(n.Cb,167)}function At(n){return n.Db>>16!=11?null:u(n.Cb,27)}function Gb(n){return n.Db>>16!=17?null:u(n.Cb,29)}function vOn(n){return n.Db>>16!=3?null:u(n.Cb,155)}function uJ(n){var e;return ea(n),e=new ni,ut(n,new M9n(e))}function kOn(n,e){var t=n.a=n.a||[];return t[e]||(t[e]=n.ve(e))}function E2e(n,e){var t;t=n.q.getHours(),n.q.setMonth(e),G5(n,t)}function yOn(n,e){xC(this),this.f=e,this.g=n,MM(this),this.je()}function jOn(n,e){this.a=n,this.c=Ki(this.a),this.b=new PM(e)}function EOn(n,e,t){this.a=e,this.c=n,this.b=(Se(t),new _u(t))}function COn(n,e,t){this.a=e,this.c=n,this.b=(Se(t),new _u(t))}function MOn(n){this.a=n,this.b=K(Sie,J,2043,n.e.length,0,2)}function TOn(){this.a=new ih,this.e=new ni,this.g=0,this.i=0}function $M(){$M=F,yU=new de,hE=new de,ple(MQn,new wvn)}function AOn(){AOn=F,aie=Pu(new ii,(Vi(),zr),(tr(),bj))}function oJ(){oJ=F,die=Pu(new ii,(Vi(),zr),(tr(),bj))}function SOn(){SOn=F,wie=Pu(new ii,(Vi(),zr),(tr(),bj))}function POn(){POn=F,Lie=Re(new ii,(Vi(),zr),(tr(),x8))}function ko(){ko=F,xie=Re(new ii,(Vi(),zr),(tr(),x8))}function IOn(){IOn=F,Fie=Re(new ii,(Vi(),zr),(tr(),x8))}function NN(){NN=F,Hie=Re(new ii,(Vi(),zr),(tr(),x8))}function J6(n,e,t,i,r,c){return new ml(n.e,e,n.Lj(),t,i,r,c)}function Dr(n,e,t){return e==null?Vc(n.f,null,t):$0(n.i,e,t)}function Zi(n,e){n.c&&du(n.c.g,n),n.c=e,n.c&&nn(n.c.g,n)}function $i(n,e){n.c&&du(n.c.a,n),n.c=e,n.c&&nn(n.c.a,n)}function ic(n,e){n.i&&du(n.i.j,n),n.i=e,n.i&&nn(n.i.j,n)}function Ii(n,e){n.d&&du(n.d.e,n),n.d=e,n.d&&nn(n.d.e,n)}function $N(n,e){n.a&&du(n.a.k,n),n.a=e,n.a&&nn(n.a.k,n)}function xN(n,e){n.b&&du(n.b.f,n),n.b=e,n.b&&nn(n.b.f,n)}function OOn(n,e){$we(n,n.b,n.c),u(n.b.b,68),e&&u(e.b,68).b}function C2e(n,e){return bt(u(n.c,65).c.e.b,u(e.c,65).c.e.b)}function M2e(n,e){return bt(u(n.c,65).c.e.a,u(e.c,65).c.e.a)}function T2e(n){return Y$(),_n(),u(n.a,86).d.e!=0}function xM(n,e){O(n.Cb,184)&&(u(n.Cb,184).tb=null),zc(n,e)}function FN(n,e){O(n.Cb,90)&&hw(Zu(u(n.Cb,90)),4),zc(n,e)}function A2e(n,e){LY(n,e),O(n.Cb,90)&&hw(Zu(u(n.Cb,90)),2)}function S2e(n,e){var t,i;t=e.c,i=t!=null,i&&Ip(n,new qb(e.c))}function DOn(n){var e,t;return t=(o4(),e=new Jd,e),K4(t,n),t}function LOn(n){var e,t;return t=(o4(),e=new Jd,e),K4(t,n),t}function NOn(n){for(var e;;)if(e=n.Pb(),!n.Ob())return e}function P2e(n,e,t){return nn(n.a,(yM(),Nx(e,t),new i0(e,t))),n}function $c(n,e){return dr(),a$(e)?new eM(e,n):new j7(e,n)}function Y7(n){return dh(),Ec(n,0)>=0?ta(n):G6(ta(n1(n)))}function I2e(n){var e;return e=u(ZC(n.b),9),new _o(n.a,e,n.c)}function $On(n,e){var t;return t=u(tw(Dp(n.a),e),16),t?t.gc():0}function xOn(n,e,t){var i;oBn(e,t,n.c.length),i=t-e,Pz(n.c,e,i)}function Jl(n,e,t){oBn(e,t,n.gc()),this.c=n,this.a=e,this.b=t-e}function Np(n){this.c=new Ct,this.b=n.b,this.d=n.c,this.a=n.a}function BN(n){this.a=y.Math.cos(n),this.b=y.Math.sin(n)}function ed(n,e,t,i){this.c=n,this.d=i,$N(this,e),xN(this,t)}function sJ(n,e){Xfe.call(this,new ap(Qb(n))),Co(e,Ozn),this.a=e}function FOn(n,e,t){return new rF(n,(B4(),t_),null,!1,e,t)}function BOn(n,e,t){return new rF(n,(B4(),r_),e,t,null,!1)}function O2e(){return Gu(),S(T(xr,1),G,108,0,[xun,Yr,Aw])}function D2e(){return bu(),S(T(JQn,1),G,472,0,[vf,pa,zs])}function L2e(){return Uu(),S(T(VQn,1),G,471,0,[Mh,ga,Gs])}function N2e(){return bf(),S(T(Sw,1),G,237,0,[bc,Wc,wc])}function $2e(){return i5(),S(T(Pon,1),G,391,0,[E_,j_,C_])}function x2e(){return D0(),S(T(R_,1),G,372,0,[ub,ma,cb])}function F2e(){return u5(),S(T(Psn,1),G,322,0,[B8,pj,Ssn])}function B2e(){return bT(),S(T(Osn,1),G,351,0,[Isn,VP,W_])}function R2e(){return hd(),S(T(pne,1),G,460,0,[Y_,mv,p2])}function K2e(){return Z4(),S(T(sH,1),G,299,0,[uH,oH,mj])}function _2e(){return vl(),S(T(Mne,1),G,311,0,[vj,v2,E3])}function H2e(){return g5(),S(T(Lhn,1),G,390,0,[FH,Dhn,MI])}function q2e(){return gr(),S(T(cie,1),G,463,0,[n9,Vu,Jc])}function U2e(){return ST(),S(T(zhn,1),G,387,0,[Uhn,zH,Ghn])}function G2e(){return d5(),S(T(Xhn,1),G,349,0,[VH,XH,Ij])}function z2e(){return om(),S(T(Whn,1),G,350,0,[WH,Vhn,e9])}function X2e(){return dT(),S(T(Yhn,1),G,352,0,[Qhn,JH,Jhn])}function V2e(){return DT(),S(T(Zhn,1),G,388,0,[QH,Ov,Gw])}function W2e(){return O0(),S(T(Tie,1),G,464,0,[Oj,t9,PI])}function Pf(n){return cc(S(T(Ei,1),J,8,0,[n.i.n,n.n,n.a]))}function J2e(){return b5(),S(T(gln,1),G,392,0,[wln,nq,Lj])}function ROn(){ROn=F,Fre=Pu(new ii,(Qp(),u9),(q5(),uln))}function FM(){FM=F,dq=new uX("DFS",0),Fln=new uX("BFS",1)}function KOn(n,e,t){var i;i=new E3n,i.b=e,i.a=t,++e.b,nn(n.d,i)}function Q2e(n,e,t){var i;i=new rr(t.d),tt(i,n),DY(e,i.a,i.b)}function Y2e(n,e){LTn(n,Ae(vi(w0(e,24),YA)),Ae(vi(e,YA)))}function zb(n,e){if(n<0||n>e)throw M(new Ir(Ptn+n+Itn+e))}function Ln(n,e){if(n<0||n>=e)throw M(new Ir(Ptn+n+Itn+e))}function zn(n,e){if(n<0||n>=e)throw M(new gz(Ptn+n+Itn+e))}function In(n,e){this.b=(Jn(n),n),this.a=e&vw?e:e|64|wh}function fJ(n){var e;return ea(n),e=(j0(),j0(),ZK),fT(n,e)}function Z2e(n,e,t){var i;return i=V5(n,e,!1),i.b<=e&&i.a<=t}function npe(){return nT(),S(T(O1n,1),G,439,0,[xq,I1n,P1n])}function epe(){return _T(),S(T(a1n,1),G,394,0,[l1n,Oq,h1n])}function tpe(){return XT(),S(T(f1n,1),G,445,0,[Bj,qI,Mq])}function ipe(){return rA(),S(T(bce,1),G,456,0,[Tq,Sq,Aq])}function rpe(){return Ok(),S(T(Uln,1),G,393,0,[KI,Hln,qln])}function cpe(){return AT(),S(T(s1n,1),G,300,0,[Cq,o1n,u1n])}function upe(){return jl(),S(T(ldn,1),G,346,0,[uO,M1,M9])}function ope(){return Fk(),S(T(Fq,1),G,444,0,[XI,VI,WI])}function spe(){return Nf(),S(T(Zan,1),G,278,0,[Bv,Jw,Rv])}function fpe(){return Gp(),S(T(mdn,1),G,280,0,[pdn,Yw,aO])}function T0(n){return Se(n),O(n,16)?new _u(u(n,16)):y4(n.Kc())}function hJ(n,e){return n&&n.equals?n.equals(e):x(n)===x(e)}function vi(n,e){return Q1(ewe(Vr(n)?ds(n):n,Vr(e)?ds(e):e))}function hf(n,e){return Q1(twe(Vr(n)?ds(n):n,Vr(e)?ds(e):e))}function RN(n,e){return Q1(iwe(Vr(n)?ds(n):n,Vr(e)?ds(e):e))}function hpe(n,e){var t;return t=(Jn(n),n).g,rV(!!t),Jn(e),t(e)}function _On(n,e){var t,i;return i=C4(n,e),t=n.a.fd(i),new zEn(n,t)}function lpe(n){return n.Db>>16!=6?null:u(dF(n),241)}function ape(n){if(n.p!=2)throw M(new Cu);return Ae(n.f)&ui}function dpe(n){if(n.p!=2)throw M(new Cu);return Ae(n.k)&ui}function E(n){return oe(n.a<n.c.c.length),n.b=n.a++,n.c.c[n.b]}function bpe(n,e){n.b=n.b|e.b,n.c=n.c|e.c,n.d=n.d|e.d,n.a=n.a|e.a}function wpe(n,e){var t;t=$(R(n.a.of((qe(),iO)))),tzn(n,e,t)}function HOn(n,e){Qa.call(this,1,2,S(T(ye,1),Ke,28,15,[n,e]))}function qOn(n,e,t){Wd.call(this,25),this.b=n,this.a=e,this.c=t}function yo(n){nt(),Wd.call(this,n),this.c=!1,this.a=!1}function gpe(n){return n.a==($4(),TO)&&mfe(n,IAe(n.g,n.b)),n.a}function $p(n){return n.d==($4(),TO)&&kfe(n,PPe(n.g,n.b)),n.d}function ppe(n,e){return r5(),n.c==e.c?bt(e.d,n.d):bt(e.c,n.c)}function mpe(n,e){return r5(),n.c==e.c?bt(e.d,n.d):bt(n.c,e.c)}function vpe(n,e){return r5(),n.c==e.c?bt(n.d,e.d):bt(n.c,e.c)}function kpe(n,e){return r5(),n.c==e.c?bt(n.d,e.d):bt(e.c,n.c)}function lJ(n,e){return aPn(n.a,e)?nW(n.b,u(e,22).g,null):null}function ype(n){return nr(Fs(vc(to(n,32)),32),vc(to(n,32)))}function aJ(n){return n.b==null||n.b.length==0?"n_"+n.a:"n_"+n.b}function td(n){return n.c==null||n.c.length==0?"n_"+n.g:"n_"+n.c}function UOn(n,e){var t;for(t=n+"";t.length<e;)t="0"+t;return t}function jpe(n,e){var t;t=u(ee(n.g,e),60),nu(e.d,new BCn(n,t))}function Epe(n,e){var t,i;return t=XRn(n),i=XRn(e),t<i?-1:t>i?1:0}function GOn(n,e){var t,i;return t=s$(e),i=t,u(ee(n.c,i),17).a}function KN(n,e,t){var i;i=n.d[e.p],n.d[e.p]=n.d[t.p],n.d[t.p]=i}function Cpe(n,e,t){var i;n.n&&e&&t&&(i=new uvn,nn(n.e,i))}function _N(n,e){if(fi(n.a,e),e.d)throw M(new ec(nXn));e.d=n}function dJ(n,e){this.a=new Z,this.d=new Z,this.f=n,this.c=e}function zOn(){this.c=new PTn,this.a=new $Ln,this.b=new Xyn,lCn()}function XOn(){qp(),this.b=new de,this.a=new de,this.c=new Z}function VOn(n,e,t){this.d=n,this.j=e,this.e=t,this.o=-1,this.p=3}function WOn(n,e,t){this.d=n,this.k=e,this.f=t,this.o=-1,this.p=5}function JOn(n,e,t,i,r,c){dQ.call(this,n,e,t,i,r),c&&(this.o=-2)}function QOn(n,e,t,i,r,c){bQ.call(this,n,e,t,i,r),c&&(this.o=-2)}function YOn(n,e,t,i,r,c){OJ.call(this,n,e,t,i,r),c&&(this.o=-2)}function ZOn(n,e,t,i,r,c){pQ.call(this,n,e,t,i,r),c&&(this.o=-2)}function nDn(n,e,t,i,r,c){DJ.call(this,n,e,t,i,r),c&&(this.o=-2)}function eDn(n,e,t,i,r,c){wQ.call(this,n,e,t,i,r),c&&(this.o=-2)}function tDn(n,e,t,i,r,c){gQ.call(this,n,e,t,i,r),c&&(this.o=-2)}function iDn(n,e,t,i,r,c){LJ.call(this,n,e,t,i,r),c&&(this.o=-2)}function rDn(n,e,t,i){LE.call(this,t),this.b=n,this.c=e,this.d=i}function cDn(n,e){this.f=n,this.a=($4(),MO),this.c=MO,this.b=e}function uDn(n,e){this.g=n,this.d=($4(),TO),this.a=TO,this.b=e}function bJ(n,e){!n.c&&(n.c=new Rt(n,0)),HA(n.c,(at(),F9),e)}function Mpe(n,e){return oMe(n,e,O(e,102)&&(u(e,19).Bb&hr)!=0)}function Tpe(n,e){return KPn(vc(n.q.getTime()),vc(e.q.getTime()))}function oDn(n){return XL(n.e.Rd().gc()*n.c.Rd().gc(),16,new O8n(n))}function Ape(n){return!!n.u&&Sc(n.u.a).i!=0&&!(n.n&&Ix(n.n))}function Spe(n){return!!n.a&&no(n.a.a).i!=0&&!(n.b&&Ox(n.b))}function wJ(n,e){return e==0?!!n.o&&n.o.f!=0:Cx(n,e)}function Ppe(n,e,t){var i;return i=u(n.Zb().xc(e),16),!!i&&i.Hc(t)}function sDn(n,e,t){var i;return i=u(n.Zb().xc(e),16),!!i&&i.Mc(t)}function fDn(n,e){var t;return t=1-e,n.a[t]=jT(n.a[t],t),jT(n,e)}function hDn(n,e){var t,i;return i=vi(n,mr),t=Fs(e,32),hf(t,i)}function lDn(n,e,t){var i;i=(Se(n),new _u(n)),O7e(new EOn(i,e,t))}function Z7(n,e,t){var i;i=(Se(n),new _u(n)),D7e(new COn(i,e,t))}function fc(n,e,t,i,r,c){return Hxn(n,e,t,c),CY(n,i),MY(n,r),n}function aDn(n,e,t,i){return n.a+=""+qo(e==null?gu:Jr(e),t,i),n}function xi(n,e){this.a=n,Xv.call(this,n),zb(e,n.gc()),this.b=e}function dDn(n){this.a=K(ki,Fn,1,QQ(y.Math.max(8,n))<<1,5,1)}function nk(n){return u(xf(n,K(Qh,b1,10,n.c.length,0,1)),199)}function fh(n){return u(xf(n,K(O_,rR,18,n.c.length,0,1)),483)}function bDn(n){return n.a?n.e.length==0?n.a.a:n.a.a+(""+n.e):n.c}function Q6(n){for(;n.d>0&&n.a[--n.d]==0;);n.a[n.d++]==0&&(n.e=0)}function wDn(n){return oe(n.b.b!=n.d.a),n.c=n.b=n.b.b,--n.a,n.c.c}function Ipe(n,e,t){n.a=e,n.c=t,n.b.a.$b(),vo(n.d),Pb(n.e.a.c,0)}function gDn(n,e){var t;n.e=new uz,t=aw(e),Yt(t,n.c),Iqn(n,t,0)}function ri(n,e,t,i){var r;r=new nG,r.a=e,r.b=t,r.c=i,xe(n.a,r)}function Q(n,e,t,i){var r;r=new nG,r.a=e,r.b=t,r.c=i,xe(n.b,r)}function pDn(n,e,t){if(n<0||e<n||e>t)throw M(new Ir(qje(n,e,t)))}function ek(n,e){if(n<0||n>=e)throw M(new Ir(kEe(n,e)));return n}function Ope(n){if(!("stack"in n))try{throw n}catch{}return n}function Sg(n){return s6(),O(n.g,10)?u(n.g,10):null}function Dpe(n){return Tg(n).dc()?!1:(e1e(n,new Pr),!0)}function id(n){var e;return Vr(n)?(e=n,e==-0?0:e):X4e(n)}function mDn(n,e){return O(e,44)?xx(n.a,u(e,44)):!1}function vDn(n,e){return O(e,44)?xx(n.a,u(e,44)):!1}function kDn(n,e){return O(e,44)?xx(n.a,u(e,44)):!1}function gJ(n){var e;return z1(n),e=new L0n,hg(n.a,new j9n(e)),e}function pJ(){var n,e,t;return e=(t=(n=new Jd,n),t),nn(n0n,e),e}function BM(n){var e;return z1(n),e=new N0n,hg(n.a,new E9n(e)),e}function Lpe(n,e){return n.a<=n.b?(e.Dd(n.a++),!0):!1}function yDn(n){P$.call(this,n,(B4(),e_),null,!1,null,!1)}function jDn(){jDn=F,SYn=Ce((YE(),S(T(oon,1),G,489,0,[b_])))}function EDn(){EDn=F,eln=wIn(Y(1),Y(4)),nln=wIn(Y(1),Y(2))}function Npe(n,e){return new _L(e,N6(Ki(e.e),n,n),(_n(),!0))}function RM(n){return new Gc((Co(n,cB),oT(nr(nr(5,n),n/10|0))))}function $pe(n){return XL(n.e.Rd().gc()*n.c.Rd().gc(),273,new I8n(n))}function CDn(n){return u(xf(n,K(FZn,DXn,12,n.c.length,0,1)),2042)}function xpe(n){return ko(),!fr(n)&&!(!fr(n)&&n.c.i.c==n.d.i.c)}function Fpe(n,e){return _p(),u(v(e,(lc(),I2)),17).a>=n.gc()}function Y6(n,e){vLe(e,n),JV(n.d),JV(u(v(n,(cn(),mI)),214))}function HN(n,e){kLe(e,n),QV(n.d),QV(u(v(n,(cn(),mI)),214))}function Bpe(n,e,t){n.d&&du(n.d.e,n),n.d=e,n.d&&b0(n.d.e,t,n)}function Rpe(n,e,t){return t.f.c.length>0?MW(n.a,e,t):MW(n.b,e,t)}function Kpe(n,e,t){var i;i=i9e();try{return Aae(n,e,t)}finally{D3e(i)}}function A0(n,e){var t,i;return t=dl(n,e),i=null,t&&(i=t.pe()),i}function Z6(n,e){var t,i;return t=dl(n,e),i=null,t&&(i=t.se()),i}function L4(n,e){var t,i;return t=Jb(n,e),i=null,t&&(i=t.se()),i}function bl(n,e){var t,i;return t=dl(n,e),i=null,t&&(i=gnn(t)),i}function _pe(n,e,t){var i;return i=wm(t),FA(n.g,i,e),FA(n.i,e,t),e}function mJ(n,e,t){this.d=new $7n(this),this.e=n,this.i=e,this.f=t}function MDn(n,e,t,i){this.e=null,this.c=n,this.d=e,this.a=t,this.b=i}function TDn(n,e,t,i){ETn(this),this.c=n,this.e=e,this.f=t,this.b=i}function vJ(n,e,t,i){this.d=n,this.n=e,this.g=t,this.o=i,this.p=-1}function ADn(n,e,t,i){return O(t,59)?new iAn(n,e,t,i):new vW(n,e,t,i)}function N4(n){return O(n,16)?u(n,16).dc():!n.Kc().Ob()}function SDn(n){if(n.e.g!=n.b)throw M(new Bo);return!!n.c&&n.d>0}function be(n){return oe(n.b!=n.d.c),n.c=n.b,n.b=n.b.a,++n.a,n.c.c}function kJ(n,e){Jn(e),$t(n.a,n.c,e),n.c=n.c+1&n.a.length-1,JRn(n)}function V1(n,e){Jn(e),n.b=n.b-1&n.a.length-1,$t(n.a,n.b,e),JRn(n)}function PDn(n){var e;e=n.Gh(),this.a=O(e,71)?u(e,71).Ii():e.Kc()}function Hpe(n){return new In(Ame(u(n.a.md(),16).gc(),n.a.ld()),16)}function IDn(){IDn=F,Gce=Ce((eC(),S(T($1n,1),G,490,0,[Bq])))}function ODn(){ODn=F,Xce=Ce((tC(),S(T(zce,1),G,558,0,[Rq])))}function DDn(){DDn=F,lue=Ce((f6(),S(T(tan,1),G,539,0,[Hj])))}function qpe(){return dd(),S(T(Lon,1),G,389,0,[Ow,Don,P_,I_])}function Upe(){return B4(),S(T(lP,1),G,304,0,[e_,t_,i_,r_])}function Gpe(){return Vp(),S(T(EYn,1),G,332,0,[uj,cj,oj,sj])}function zpe(){return A5(),S(T(TYn,1),G,406,0,[fj,wP,gP,hj])}function Xpe(){return N0(),S(T(yYn,1),G,417,0,[rj,ij,a_,d_])}function Vpe(){return nm(),S(T(MZn,1),G,416,0,[rb,Iw,Pw,a2])}function Wpe(){return $f(),S(T(ene,1),G,421,0,[j3,lv,av,B_])}function Jpe(){return OT(),S(T(UZn,1),G,371,0,[F_,HP,qP,wj])}function Qpe(){return cw(),S(T(RH,1),G,203,0,[TI,BH,S2,A2])}function Ype(){return lh(),S(T(Hhn,1),G,284,0,[k1,_hn,HH,qH])}function Zpe(n){var e;return n.j==(tn(),ae)&&(e=mHn(n),Au(e,Zn))}function n3e(n,e){var t;t=e.a,Zi(t,e.c.d),Ii(t,e.d.d),nw(t.a,n.n)}function yJ(n,e){var t;return t=u(Lf(n.b,e),67),!t&&(t=new Ct),t}function xp(n){return s6(),O(n.g,154)?u(n.g,154):null}function e3e(n){n.a=null,n.e=null,Pb(n.b.c,0),Pb(n.f.c,0),n.c=null}function KM(){KM=F,fH=new Zz(qm,0),Jsn=new Zz("TOP_LEFT",1)}function n5(){n5=F,r9=new eX("UPPER",0),i9=new eX("LOWER",1)}function t3e(n,e){return vp(new V(e.e.a+e.f.a/2,e.e.b+e.f.b/2),n)}function LDn(n,e){return u(ho(_b(u(ot(n.k,e),15).Oc(),b2)),113)}function NDn(n,e){return u(ho(Ap(u(ot(n.k,e),15).Oc(),b2)),113)}function i3e(){return Qp(),S(T(rln,1),G,405,0,[LI,c9,u9,o9])}function r3e(){return w5(),S(T(xln,1),G,353,0,[aq,BI,lq,hq])}function c3e(){return sA(),S(T(c1n,1),G,354,0,[Eq,i1n,r1n,t1n])}function u3e(){return go(),S(T(I9,1),G,386,0,[rE,Gd,iE,Qw])}function o3e(){return To(),S(T(Yue,1),G,291,0,[nE,nl,Ta,Zj])}function s3e(){return El(),S(T(aU,1),G,223,0,[lU,Yj,Kv,F3])}function f3e(){return qT(),S(T(Cdn,1),G,320,0,[wU,ydn,Edn,jdn])}function h3e(){return LT(),S(T(woe,1),G,415,0,[gU,Tdn,Mdn,Adn])}function l3e(n){return $M(),Zc(yU,n)?u(ee(yU,n),341).Qg():null}function Uo(n,e,t){return e<0?hF(n,t):u(t,69).wk().Bk(n,n.hi(),e)}function a3e(n,e,t){var i;return i=wm(t),FA(n.j,i,e),Xe(n.k,e,t),e}function d3e(n,e,t){var i;return i=wm(t),FA(n.d,i,e),Xe(n.e,e,t),e}function $Dn(n){var e,t;return e=(B1(),t=new HO,t),n&&AA(e,n),e}function jJ(n){var e;return e=n.aj(n.i),n.i>0&&Ic(n.g,0,e,0,n.i),e}function xDn(n,e){var t;for(t=n.j.c.length;t<e;t++)nn(n.j,n.Ng())}function FDn(n,e,t,i){var r;return r=i[e.g][t.g],$(R(v(n.a,r)))}function BDn(n,e){iC();var t;return t=u(ee(yO,n),57),!t||t.fk(e)}function b3e(n){if(n.p!=1)throw M(new Cu);return Ae(n.f)<<24>>24}function w3e(n){if(n.p!=1)throw M(new Cu);return Ae(n.k)<<24>>24}function g3e(n){if(n.p!=7)throw M(new Cu);return Ae(n.k)<<16>>16}function p3e(n){if(n.p!=7)throw M(new Cu);return Ae(n.f)<<16>>16}function Pg(n,e){return e.e==0||n.e==0?O8:(Am(),vF(n,e))}function RDn(n,e){return x(e)===x(n)?"(this Map)":e==null?gu:Jr(e)}function m3e(n,e,t){return tN(R(Kr(wr(n.f,e))),R(Kr(wr(n.f,t))))}function v3e(n,e,t){var i;i=u(ee(n.g,t),60),nn(n.a.c,new bi(e,i))}function KDn(n,e,t){n.i=0,n.e=0,e!=t&&(jFn(n,e,t),yFn(n,e,t))}function k3e(n,e,t,i,r){var c;c=yMe(r,t,i),nn(e,dEe(r,c)),rje(n,r,e)}function EJ(n,e,t,i,r){this.i=n,this.a=e,this.e=t,this.j=i,this.f=r}function _Dn(n,e){nJ.call(this),this.a=n,this.b=e,nn(this.a.b,this)}function HDn(n){this.b=new de,this.c=new de,this.d=new de,this.a=n}function qDn(n,e){var t;return t=new lp,n.Gd(t),t.a+="..",e.Hd(t),t.a}function UDn(n,e){var t;for(t=e;t;)a0(n,t.i,t.j),t=At(t);return n}function GDn(n,e,t){var i;return i=wm(t),Xe(n.b,i,e),Xe(n.c,e,t),e}function wl(n){var e;for(e=0;n.Ob();)n.Pb(),e=nr(e,1);return oT(e)}function Fh(n,e){dr();var t;return t=u(n,69).vk(),kje(t,e),t.xl(e)}function y3e(n,e,t){if(t){var i=t.oe();n.a[e]=i(t)}else delete n.a[e]}function CJ(n,e){var t;t=n.q.getHours(),n.q.setFullYear(e+fa),G5(n,t)}function j3e(n,e){return u(e==null?Kr(wr(n.f,null)):d6(n.i,e),288)}function MJ(n,e){return n==(Vn(),zt)&&e==zt?4:n==zt||e==zt?8:32}function _M(n,e,t){return RA(n,e,t,O(e,102)&&(u(e,19).Bb&hr)!=0)}function E3e(n,e,t){return Om(n,e,t,O(e,102)&&(u(e,19).Bb&hr)!=0)}function C3e(n,e,t){return bMe(n,e,t,O(e,102)&&(u(e,19).Bb&hr)!=0)}function TJ(n){n.b!=n.c&&(n.a=K(ki,Fn,1,8,5,1),n.b=0,n.c=0)}function e5(n){return oe(n.a<n.c.a.length),n.b=n.a,i$n(n),n.c.b[n.b]}function Sc(n){return n.n||(Zu(n),n.n=new mPn(n,jr,n),Hr(n)),n.n}function zDn(n){if(n<0)throw M(new Rjn("Negative array size: "+n))}function qN(n,e,t){if(t){var i=t.oe();t=i(t)}else t=void 0;n.a[e]=t}function XDn(n,e){cm();var t;return t=n.j.g-e.j.g,t!=0?t:0}function M3e(n,e){return fl(),ve(_(n.a),e)}function T3e(n,e){return fl(),ve(_(n.a),e)}function gl(n,e){dh(),Qa.call(this,n,1,S(T(ye,1),Ke,28,15,[e]))}function Xb(n,e){nt(),Wd.call(this,n),this.a=e,this.c=-1,this.b=-1}function Vb(n,e,t,i){VOn.call(this,1,t,i),this.c=n,this.b=e}function UN(n,e,t,i){WOn.call(this,1,t,i),this.c=n,this.b=e}function GN(n,e,t,i,r,c,s){k$.call(this,e,i,r,c,s),this.c=n,this.a=t}function rd(n,e,t){this.e=n,this.a=ki,this.b=Qqn(e),this.c=e,this.d=t}function zN(n){this.e=n,this.c=this.e.a,this.b=this.e.g,this.d=this.e.i}function AJ(n){this.d=n,this.b=this.d.a.entries(),this.a=this.b.next()}function VDn(n){this.c=n,this.a=u(ws(n),156),this.b=this.a.jk().wi()}function Ql(){de.call(this),sAn(this),this.d.b=this.d,this.d.a=this.d}function xt(n,e,t,i){var r;r=new OO,r.c=e,r.b=t,r.a=i,i.b=t.a=r,++n.b}function A3e(n,e){var t;return t=e!=null?Nc(n,e):Kr(wr(n.f,e)),PC(t)}function S3e(n,e){var t;return t=e!=null?Nc(n,e):Kr(wr(n.f,e)),PC(t)}function Wr(n,e){var t;return e.b.Kb(GNn(n,e.c.Xe(),(t=new A9n(e),t)))}function P3e(n,e){var t;return zDn(e),t=n.slice(0,e),t.length=e,o$(t,n)}function WDn(n,e){var t;for(t=0;t<e;++t)$t(n,t,new EG(u(n[t],44)))}function I3e(n,e){var t;for(t=n.d-1;t>=0&&n.a[t]===e[t];t--);return t<0}function HM(n){var e;return n?new fW(n):(e=new ih,A$(e,n),e)}function O3e(n,e){var t,i;i=!1;do t=lFn(n,e),i=i|t;while(t);return i}function D3e(n){n&&rme((az(),sun)),--cP,n&&uP!=-1&&(Ele(uP),uP=-1)}function qM(n){nnn(),LTn(this,Ae(vi(w0(n,24),YA)),Ae(vi(n,YA)))}function JDn(){JDn=F,HQn=Ce((YT(),S(T(Bun,1),G,436,0,[o_,Fun])))}function QDn(){QDn=F,qQn=Ce((cT(),S(T(Kun,1),G,435,0,[Run,s_])))}function YDn(){YDn=F,GYn=Ce((uT(),S(T(bon,1),G,432,0,[v_,vP])))}function ZDn(){ZDn=F,_Zn=Ce((V4(),S(T(KZn,1),G,517,0,[dj,L_])))}function nLn(){nLn=F,Ane=Ce((KM(),S(T(Qsn,1),G,429,0,[fH,Jsn])))}function eLn(){eLn=F,gne=Ce((pk(),S(T($sn,1),G,428,0,[WP,Nsn])))}function tLn(){tLn=F,kne=Ce((hk(),S(T(Bsn,1),G,488,0,[Fsn,QP])))}function iLn(){iLn=F,rie=Ce((wk(),S(T(qhn,1),G,430,0,[UH,GH])))}function rLn(){rLn=F,Die=Ce((n5(),S(T(Oie,1),G,531,0,[r9,i9])))}function cLn(){cLn=F,ane=Ce((QM(),S(T(Asn,1),G,431,0,[Tsn,V_])))}function uLn(){uLn=F,xre=Ce((FM(),S(T(Bln,1),G,433,0,[dq,Fln])))}function oLn(){oLn=F,_re=Ce((yT(),S(T(Rln,1),G,501,0,[RI,D2])))}function sLn(){sLn=F,Rie=Ce((sh(),S(T(Bie,1),G,523,0,[mb,y1])))}function fLn(){fLn=F,_ie=Ce((Sf(),S(T(Kie,1),G,522,0,[Rd,zf])))}function hLn(){hLn=F,tre=Ce((lf(),S(T(ere,1),G,528,0,[zw,ja])))}function lLn(){lLn=F,fre=Ce((M0(),S(T(sre,1),G,465,0,[Ea,P2])))}function aLn(){aLn=F,Ure=Ce((ZM(),S(T(_ln,1),G,434,0,[Kln,vq])))}function dLn(){dLn=F,Rce=Ce((GM(),S(T(S1n,1),G,491,0,[$q,A1n])))}function bLn(){bLn=F,_ce=Ce((N$(),S(T(N1n,1),G,492,0,[D1n,L1n])))}function wLn(){wLn=F,Vce=Ce((ck(),S(T(x1n,1),G,438,0,[Kq,JI])))}function gLn(){gLn=F,aue=Ce((Ak(),S(T(ran,1),G,437,0,[YI,ian])))}function pLn(){pLn=F,aoe=Ce((RL(),S(T(dO,1),G,347,0,[vdn,kdn])))}function L3e(){return ci(),S(T(E9,1),G,88,0,[Wf,Xr,Br,Vf,us])}function N3e(){return tn(),S(T(lr,1),Mc,64,0,[sc,Xn,Zn,ae,Wn])}function $3e(n,e,t){return u(e==null?Vc(n.f,null,t):$0(n.i,e,t),288)}function x3e(n){return(n.k==(Vn(),zt)||n.k==Zt)&&kt(n,(W(),H8))}function XN(n){return n.c&&n.d?aJ(n.c)+"->"+aJ(n.d):"e_"+l0(n)}function qi(n,e){var t,i;for(Jn(e),i=n.Kc();i.Ob();)t=i.Pb(),e.Cd(t)}function F3e(n,e){var t;t=new op,nd(t,"x",e.a),nd(t,"y",e.b),Ip(n,t)}function B3e(n,e){var t;t=new op,nd(t,"x",e.a),nd(t,"y",e.b),Ip(n,t)}function mLn(n,e){var t;for(t=e;t;)a0(n,-t.i,-t.j),t=At(t);return n}function SJ(n,e){var t,i;for(t=e,i=0;t>0;)i+=n.a[t],t-=t&-t;return i}function Go(n,e,t){var i;return i=(Ln(e,n.c.length),n.c[e]),n.c[e]=t,i}function PJ(n,e,t){n.a.c.length=0,fOe(n,e,t),n.a.c.length==0||xSe(n,e)}function tk(n){n.i=0,s7(n.b,null),s7(n.c,null),n.a=null,n.e=null,++n.g}function UM(){UM=F,qf=!0,DQn=!1,LQn=!1,$Qn=!1,NQn=!1}function VN(n){UM(),!qf&&(this.c=n,this.e=!0,this.a=new Z)}function vLn(n,e){this.c=0,this.b=e,HMn.call(this,n,17493),this.a=this.c}function kLn(n){jzn(),Syn(this),this.a=new Ct,sY(this,n),xe(this.a,n)}function yLn(){pL(this),this.b=new V(St,St),this.a=new V(li,li)}function GM(){GM=F,$q=new fX(cin,0),A1n=new fX("TARGET_WIDTH",1)}function Ig(n,e){return(ea(n),s4(new Tn(n,new tQ(e,n.a)))).Bd(v3)}function R3e(){return Vi(),S(T(Ion,1),G,367,0,[Xs,Jh,Oc,Kc,zr])}function K3e(){return ow(),S(T(ine,1),G,375,0,[gj,zP,XP,GP,UP])}function _3e(){return o1(),S(T(Lsn,1),G,348,0,[J_,Dsn,Q_,pv,gv])}function H3e(){return T5(),S(T($hn,1),G,323,0,[Nhn,KH,_H,Y8,Z8])}function q3e(){return Yo(),S(T(hfn,1),G,171,0,[Ej,U8,ka,G8,xw])}function U3e(){return wA(),S(T(Hre,1),G,368,0,[pq,bq,mq,wq,gq])}function G3e(){return R5(),S(T(Hce,1),G,373,0,[L2,D3,g9,w9,_j])}function z3e(){return Yk(),S(T(K1n,1),G,324,0,[F1n,_q,R1n,Hq,B1n])}function X3e(){return gf(),S(T(Zh,1),G,170,0,[xn,pi,Ph,Kd,E1])}function V3e(){return Fg(),S(T(A9,1),G,256,0,[Aa,eE,adn,T9,ddn])}function W3e(n){return HE(),function(){return Kpe(n,this,arguments)}}function fr(n){return!n.c||!n.d?!1:!!n.c.i&&n.c.i==n.d.i}function IJ(n,e){return O(e,143)?An(n.c,u(e,143).c):!1}function Zu(n){return n.t||(n.t=new myn(n),k5(new Njn(n),0,n.t)),n.t}function jLn(n){this.b=n,ne.call(this,n),this.a=u(Un(this.b.a,4),129)}function ELn(n){this.b=n,yp.call(this,n),this.a=u(Un(this.b.a,4),129)}function Bs(n,e,t,i,r){LLn.call(this,e,i,r),this.c=n,this.b=t}function OJ(n,e,t,i,r){VOn.call(this,e,i,r),this.c=n,this.a=t}function DJ(n,e,t,i,r){WOn.call(this,e,i,r),this.c=n,this.a=t}function LJ(n,e,t,i,r){LLn.call(this,e,i,r),this.c=n,this.a=t}function WN(n,e){var t;return t=u(Lf(n.d,e),23),t||u(Lf(n.e,e),23)}function CLn(n,e){var t,i;return t=e.ld(),i=n.Fe(t),!!i&&mc(i.e,e.md())}function MLn(n,e){var t;return t=e.ld(),new i0(t,n.e.pc(t,u(e.md(),16)))}function J3e(n,e){var t;return t=n.a.get(e),t??K(ki,Fn,1,0,5,1)}function TLn(n){var e;return e=n.length,An(Yn.substr(Yn.length-e,e),n)}function fe(n){if(pe(n))return n.c=n.a,n.a.Pb();throw M(new nc)}function NJ(n,e){return e==0||n.e==0?n:e>0?wqn(n,e):RBn(n,-e)}function Fp(n,e){return e==0||n.e==0?n:e>0?RBn(n,e):wqn(n,-e)}function $J(n){ole.call(this,n==null?gu:Jr(n),O(n,82)?u(n,82):null)}function ALn(n){var e;return n.c||(e=n.r,O(e,90)&&(n.c=u(e,29))),n.c}function JN(n){var e;return e=new E0,Ur(e,n),U(e,(cn(),Fr),null),e}function SLn(n){var e,t;return e=n.c.i,t=n.d.i,e.k==(Vn(),Zt)&&t.k==Zt}function QN(n){var e,t,i;return e=n&ro,t=n>>22&ro,i=n<0?Il:0,Yc(e,t,i)}function Q3e(n){var e,t,i,r;for(t=n,i=0,r=t.length;i<r;++i)e=t[i],V6(e)}function Y3e(n,e){var t,i;t=u(o5e(n.c,e),16),t&&(i=t.gc(),t.$b(),n.d-=i)}function YN(n,e,t){var i;return i=n.Ih(e),i>=0?n.Lh(i,t,!0):H0(n,e,t)}function Z3e(n,e,t){return bt(vp(pm(n),Ki(e.b)),vp(pm(n),Ki(t.b)))}function n4e(n,e,t){return bt(vp(pm(n),Ki(e.e)),vp(pm(n),Ki(t.e)))}function e4e(n,e){return y.Math.min(W1(e.a,n.d.d.c),W1(e.b,n.d.d.c))}function ik(n,e){n._i(n.i+1),O6(n,n.i,n.Zi(n.i,e)),n.Mi(n.i++,e),n.Ni()}function t5(n){var e,t;++n.j,e=n.g,t=n.i,n.g=null,n.i=0,n.Oi(t,e),n.Ni()}function PLn(n,e,t){var i;i=new NX(n.a),f5(i,n.a.a),Vc(i.f,e,t),n.a.a=i}function xJ(n,e,t,i){var r;for(r=0;r<dP;r++)hM(n.a[r][e.g],t,i[e.g])}function FJ(n,e,t,i){var r;for(r=0;r<h_;r++)lM(n.a[e.g][r],t,i[e.g])}function ot(n,e){var t;return t=u(n.c.xc(e),16),!t&&(t=n.ic(e)),n.pc(e,t)}function t4e(n){var e;return e=(Se(n),n?new _u(n):y4(n.Kc())),ny(e),FT(e)}function If(n){var e,t;return Se(n),e=Zwe(n.length),t=new Gc(e),eY(t,n),t}function ZN(n,e,t,i){var r;return r=K(ye,Ke,28,e,15,1),Eye(r,n,e,t,i),r}function BJ(n,e){if(n<0||n>e)throw M(new Ir(Mnn(n,e,"index")));return n}function Yl(n,e){var t;return t=(Ln(e,n.c.length),n.c[e]),Pz(n.c,e,1),t}function RJ(n,e){var t,i;return t=(Jn(n),n),i=(Jn(e),e),t==i?0:t<i?-1:1}function KJ(n){var e;return e=n.e+n.f,isNaN(e)&&GC(n.d)?n.d:e}function i4e(n){return n.e=3,n.d=n.Yb(),n.e!=2?(n.e=0,!0):!1}function pl(n,e){return n.a?Be(n.a,n.b):n.a=new mo(n.d),A6(n.a,e),n}function Bp(n,e){return Ai(e)?e==null?Hnn(n.f,null):Gxn(n.i,e):Hnn(n.f,e)}function ILn(n,e){_Mn.call(this,e.zd(),e.yd()&-6),Jn(n),this.a=n,this.b=e}function OLn(n,e){HMn.call(this,e.zd(),e.yd()&-6),Jn(n),this.a=n,this.b=e}function _J(n,e){IC.call(this,e.zd(),e.yd()&-6),Jn(n),this.a=n,this.b=e}function DLn(n,e,t){LE.call(this,t),this.b=n,this.c=e,this.d=(gx(),TU)}function LLn(n,e,t){this.d=n,this.k=e?1:0,this.f=t?1:0,this.o=-1,this.p=0}function Of(n){this.c=n,this.a=new C(this.c.a),this.b=new C(this.c.b)}function zM(){this.e=new Z,this.c=new Z,this.d=new Z,this.b=new Z}function NLn(){this.g=new zG,this.b=new zG,this.a=new Z,this.k=new Z}function $Ln(){this.a=new JG,this.b=new ejn,this.d=new cwn,this.e=new lwn}function xLn(n,e,t){this.a=n,this.c=e,this.d=t,nn(e.e,this),nn(t.b,this)}function HJ(n,e,t){var i,r;for(i=0,r=0;r<e.length;r++)i+=n.tg(e[r],i,t)}function r4e(n,e){var t;return t=EOe(n,e),n.b=new ET(t.c.length),HIe(n,t)}function c4e(n,e){var t;t=n.q.getHours()+(e/60|0),n.q.setMinutes(e),G5(n,t)}function n$(n){var e;return e=n.b,e.b==0?null:u(Zo(e,0),65).b}function qJ(n){if(n.a){if(n.e)return qJ(n.e)}else return n;return null}function u4e(n,e){return n.p<e.p?1:n.p>e.p?-1:0}function FLn(n){var e;return n.a||(e=n.r,O(e,156)&&(n.a=u(e,156))),n.a}function o4e(n,e,t){var i;return++n.e,--n.f,i=u(n.d[e].gd(t),136),i.md()}function s4e(n){var e,t;return e=n.ld(),t=u(n.md(),16),x7(t.Nc(),new L8n(e))}function BLn(n,e){return Zc(n.a,e)?(Bp(n.a,e),!0):!1}function Rp(n,e,t){return ek(e,n.e.Rd().gc()),ek(t,n.c.Rd().gc()),n.a[e][t]}function XM(n,e,t){this.a=n,this.b=e,this.c=t,nn(n.t,this),nn(e.i,this)}function VM(n,e,t,i){this.f=n,this.e=e,this.d=t,this.b=i,this.c=i?i.d:null}function rk(){this.b=new Ct,this.a=new Ct,this.b=new Ct,this.a=new Ct}function $4(){$4=F;var n,e;MO=(o4(),e=new xE,e),TO=(n=new fD,n)}function f4e(n){var e;return ea(n),e=new ISn(n,n.a.e,n.a.d|4),new uV(n,e)}function RLn(n){var e;for(z1(n),e=0;n.a.Bd(new W0n);)e=nr(e,1);return e}function WM(n,e){return Jn(e),n.c<n.d?(n.Se(e,n.c++),!0):!1}function Gc(n){pL(this),B7(n>=0,"Initial capacity must not be negative")}function JM(){JM=F,p9=new lt("org.eclipse.elk.labels.labelManager")}function KLn(){KLn=F,ysn=new Dt("separateLayerConnections",(OT(),F_))}function lf(){lf=F,zw=new rX("REGULAR",0),ja=new rX("CRITICAL",1)}function ck(){ck=F,Kq=new lX("FIXED",0),JI=new lX("CENTER_NODE",1)}function QM(){QM=F,Tsn=new Jz("QUADRATIC",0),V_=new Jz("SCANLINE",1)}function _Ln(){_Ln=F,dne=Ce((u5(),S(T(Psn,1),G,322,0,[B8,pj,Ssn])))}function HLn(){HLn=F,bne=Ce((bT(),S(T(Osn,1),G,351,0,[Isn,VP,W_])))}function qLn(){qLn=F,fne=Ce((D0(),S(T(R_,1),G,372,0,[ub,ma,cb])))}function ULn(){ULn=F,mne=Ce((hd(),S(T(pne,1),G,460,0,[Y_,mv,p2])))}function GLn(){GLn=F,Cne=Ce((Z4(),S(T(sH,1),G,299,0,[uH,oH,mj])))}function zLn(){zLn=F,Tne=Ce((vl(),S(T(Mne,1),G,311,0,[vj,v2,E3])))}function XLn(){XLn=F,Zte=Ce((g5(),S(T(Lhn,1),G,390,0,[FH,Dhn,MI])))}function VLn(){VLn=F,oie=Ce((ST(),S(T(zhn,1),G,387,0,[Uhn,zH,Ghn])))}function WLn(){WLn=F,sie=Ce((d5(),S(T(Xhn,1),G,349,0,[VH,XH,Ij])))}function JLn(){JLn=F,uie=Ce((gr(),S(T(cie,1),G,463,0,[n9,Vu,Jc])))}function QLn(){QLn=F,fie=Ce((om(),S(T(Whn,1),G,350,0,[WH,Vhn,e9])))}function YLn(){YLn=F,hie=Ce((dT(),S(T(Yhn,1),G,352,0,[Qhn,JH,Jhn])))}function ZLn(){ZLn=F,lie=Ce((DT(),S(T(Zhn,1),G,388,0,[QH,Ov,Gw])))}function nNn(){nNn=F,are=Ce((b5(),S(T(gln,1),G,392,0,[wln,nq,Lj])))}function eNn(){eNn=F,Gre=Ce((Ok(),S(T(Uln,1),G,393,0,[KI,Hln,qln])))}function tNn(){tNn=F,ace=Ce((AT(),S(T(s1n,1),G,300,0,[Cq,o1n,u1n])))}function iNn(){iNn=F,dce=Ce((XT(),S(T(f1n,1),G,445,0,[Bj,qI,Mq])))}function rNn(){rNn=F,wce=Ce((rA(),S(T(bce,1),G,456,0,[Tq,Sq,Aq])))}function cNn(){cNn=F,mce=Ce((_T(),S(T(a1n,1),G,394,0,[l1n,Oq,h1n])))}function uNn(){uNn=F,Kce=Ce((nT(),S(T(O1n,1),G,439,0,[xq,I1n,P1n])))}function oNn(){oNn=F,Aie=Ce((O0(),S(T(Tie,1),G,464,0,[Oj,t9,PI])))}function sNn(){sNn=F,WQn=Ce((Uu(),S(T(VQn,1),G,471,0,[Mh,ga,Gs])))}function fNn(){fNn=F,XQn=Ce((bf(),S(T(Sw,1),G,237,0,[bc,Wc,wc])))}function hNn(){hNn=F,QQn=Ce((bu(),S(T(JQn,1),G,472,0,[vf,pa,zs])))}function lNn(){lNn=F,xQn=Ce((Gu(),S(T(xr,1),G,108,0,[xun,Yr,Aw])))}function aNn(){aNn=F,pZn=Ce((i5(),S(T(Pon,1),G,391,0,[E_,j_,C_])))}function dNn(){dNn=F,Que=Ce((jl(),S(T(ldn,1),G,346,0,[uO,M1,M9])))}function bNn(){bNn=F,Uce=Ce((Fk(),S(T(Fq,1),G,444,0,[XI,VI,WI])))}function wNn(){wNn=F,Xue=Ce((Nf(),S(T(Zan,1),G,278,0,[Bv,Jw,Rv])))}function gNn(){gNn=F,loe=Ce((Gp(),S(T(mdn,1),G,280,0,[pdn,Yw,aO])))}function Df(n,e){return!n.o&&(n.o=new Iu((Cc(),il),T1,n,0)),wx(n.o,e)}function h4e(n,e){var t;n.C&&(t=u(Cr(n.b,e),127).n,t.d=n.C.d,t.a=n.C.a)}function UJ(n){var e,t,i,r;r=n.d,e=n.a,t=n.b,i=n.c,n.d=t,n.a=i,n.b=r,n.c=e}function l4e(n){return!n.g&&(n.g=new CE),!n.g.b&&(n.g.b=new byn(n)),n.g.b}function uk(n){return!n.g&&(n.g=new CE),!n.g.c&&(n.g.c=new pyn(n)),n.g.c}function a4e(n){return!n.g&&(n.g=new CE),!n.g.d&&(n.g.d=new wyn(n)),n.g.d}function d4e(n){return!n.g&&(n.g=new CE),!n.g.a&&(n.g.a=new gyn(n)),n.g.a}function b4e(n,e,t,i){return t&&(i=t.Rh(e,Ot(t.Dh(),n.c.uk()),null,i)),i}function w4e(n,e,t,i){return t&&(i=t.Th(e,Ot(t.Dh(),n.c.uk()),null,i)),i}function e$(n,e,t,i){var r;return r=K(ye,Ke,28,e+1,15,1),vPe(r,n,e,t,i),r}function K(n,e,t,i,r,c){var s;return s=_Rn(r,i),r!=10&&S(T(n,c),e,t,r,s),s}function g4e(n,e,t){var i,r;for(r=new Y4(e,n),i=0;i<t;++i)iA(r);return r}function t$(n,e,t){var i,r;if(t!=null)for(i=0;i<e;++i)r=t[i],n.Qi(i,r)}function GJ(n,e){var t;return t=new DO,t.c=!0,t.d=e.md(),LGn(n,e.ld(),t)}function p4e(n,e){var t;t=n.q.getHours()+(e/3600|0),n.q.setSeconds(e),G5(n,t)}function zJ(n,e){var t,i;return t=e,i=TN(y4(new f$(n,t))),iM(new f$(n,t)),i}function m4e(n,e){e.Ug("Label management",1),PC(v(n,(JM(),p9))),e.Vg()}function v4e(n,e,t,i){LUn(n,e,t,Om(n,e,i,O(e,102)&&(u(e,19).Bb&hr)!=0))}function XJ(n,e,t){u(n.b,68),u(n.b,68),u(n.b,68),nu(n.a,new gSn(t,e,n))}function Fi(n,e,t){if(n<0||e>t||e<n)throw M(new gz(ZA+n+Stn+e+Mtn+t))}function i$(n){n?(this.c=n,this.b=null):(this.c=null,this.b=new Z)}function r$(n,e){oC.call(this,n,e),this.a=K(lNe,WA,447,2,0,1),this.b=!0}function VJ(n){wFn.call(this,n,0),sAn(this),this.d.b=this.d,this.d.a=this.d}function WJ(n){this.e=n,this.b=this.e.a.entries(),this.a=K(ki,Fn,1,0,5,1)}function pNn(){pNn=F,bie=Pu(Re(new ii,(Vi(),Xs),(tr(),N_)),zr,bj)}function k4e(){return vA(),S(T(xsn,1),G,283,0,[nH,Z_,tH,eH,iH,JP])}function y4e(){return Jk(),S(T(qsn,1),G,281,0,[YP,Ksn,Hsn,Rsn,_sn,rH])}function j4e(){return jm(),S(T(Wsn,1),G,282,0,[R8,Gsn,Vsn,Xsn,zsn,Usn])}function E4e(){return Yp(),S(T(wv,1),G,232,0,[bv,F8,dv,Nw,g2,w2])}function C4e(){return Vn(),S(T(D_,1),G,273,0,[zt,Mi,Zt,_c,Ac,Uf])}function M4e(){return zu(),S(T(oO,1),G,279,0,[Pa,Fl,tE,P9,S9,B3])}function T4e(){return Oi(),S(T(bdn,1),G,101,0,[Sa,Jf,_v,Ud,tl,qc])}function A4e(){return pA(),S(T(cdn,1),G,321,0,[dU,tdn,rdn,ndn,idn,edn])}function S4e(){return Rh(),S(T(fan,1),G,255,0,[Vq,qj,Uj,eO,ZI,nO])}function P4e(){return wd(),S(T(Yq,1),G,298,0,[Qq,y9,k9,Jq,m9,v9])}function JJ(n){var e;return!n.a&&n.b!=-1&&(e=n.c.Dh(),n.a=$n(e,n.b)),n.a}function ve(n,e){return n.Si()&&n.Hc(e)?!1:(n.Hi(e),!0)}function af(n,e){return X7(e,"Horizontal alignment cannot be null"),n.b=e,n}function mNn(n,e,t){nt();var i;return i=oa(n,e),t&&i&&Rwe(n)&&(i=null),i}function QJ(n,e,t){var i;i=n.b[t.c.p][t.p],i.b+=e.b,i.c+=e.c,i.a+=e.a,++i.a}function YJ(n,e,t){var i;n.d[e.g]=t,i=n.g.c,i[e.g]=y.Math.max(i[e.g],t+1)}function W1(n,e){var t,i;return t=n.a-e.a,i=n.b-e.b,y.Math.sqrt(t*t+i*i)}function ZJ(n,e){var t,i;for(i=e.Kc();i.Ob();)t=u(i.Pb(),36),sUn(n,t,0,0)}function Zl(n,e,t){var i,r;for(r=n.Kc();r.Ob();)i=u(r.Pb(),36),Sm(i,e,t)}function I4e(n){var e,t;for(t=ge(n.a,0);t.b!=t.d.c;)e=u(be(t),65),Dnn(e)}function vNn(n,e){return kCn(n.e,e)||s1(n.e,e,new fRn(e)),u(Lf(n.e,e),113)}function qu(n,e,t,i){return Jn(n),Jn(e),Jn(t),Jn(i),new AW(n,e,new B0n)}function Iu(n,e,t,i){this.ak(),this.a=e,this.b=n,this.c=new jW(this,e,t,i)}function c$(n,e,t,i,r,c){vJ.call(this,e,i,r,c),this.c=n,this.b=t}function ok(n,e,t,i,r,c){vJ.call(this,e,i,r,c),this.c=n,this.a=t}function sk(n,e){var t,i,r;return r=n.r,i=n.d,t=V5(n,e,!0),t.b!=r||t.a!=i}function fk(n,e,t){var i,r;return r=(i=Mm(n.b,e),i),r?qA(ak(n,r),t):null}function O4e(n,e,t){var i,r,c;i=dl(n,t),r=null,i&&(r=gnn(i)),c=r,uRn(e,t,c)}function D4e(n,e,t){var i,r,c;i=dl(n,t),r=null,i&&(r=gnn(i)),c=r,uRn(e,t,c)}function x4(n,e){var t;return t=n.Ih(e),t>=0?n.Lh(t,!0,!0):H0(n,e,!0)}function L4e(n,e,t){var i;return i=vFn(n,e,t),n.b=new ET(i.c.length),den(n,i)}function N4e(n){if(n.b<=0)throw M(new nc);return--n.b,n.a-=n.c.c,Y(n.a)}function $4e(n){var e;if(!n.a)throw M(new PIn);return e=n.a,n.a=At(n.a),e}function x4e(n){for(;!n.a;)if(!eSn(n.c,new C9n(n)))return!1;return!0}function Kp(n){var e;return Se(n),O(n,204)?(e=u(n,204),e):new _8n(n)}function F4e(n){YM(),u(n.of((qe(),Ww)),181).Fc((zu(),tE)),n.qf(sU,null)}function YM(){YM=F,wue=new Emn,pue=new Cmn,gue=M6e((qe(),sU),wue,Ma,pue)}function ZM(){ZM=F,Kln=new sX("LEAF_NUMBER",0),vq=new sX("NODE_SIZE",1)}function u$(n){n.a=K(ye,Ke,28,n.b+1,15,1),n.c=K(ye,Ke,28,n.b,15,1),n.d=0}function B4e(n,e){n.a.Ne(e.d,n.b)>0&&(nn(n.c,new GV(e.c,e.d,n.d)),n.b=e.d)}function nQ(n,e){if(n.g==null||e>=n.i)throw M(new aL(e,n.i));return n.g[e]}function kNn(n,e,t){if(rm(n,t),t!=null&&!n.fk(t))throw M(new uD);return t}function o$(n,e){return gk(e)!=10&&S(wo(e),e.Sm,e.__elementTypeId$,gk(e),n),n}function F4(n,e,t,i){var r;i=(j0(),i||Pun),r=n.slice(e,t),Tnn(r,n,e,t,-e,i)}function zo(n,e,t,i,r){return e<0?H0(n,t,i):u(t,69).wk().yk(n,n.hi(),e,i,r)}function R4e(n,e){return bt($(R(v(n,(W(),fb)))),$(R(v(e,fb))))}function yNn(){yNn=F,IQn=Ce((B4(),S(T(lP,1),G,304,0,[e_,t_,i_,r_])))}function B4(){B4=F,e_=new uC("All",0),t_=new lTn,i_=new kTn,r_=new hTn}function Uu(){Uu=F,Mh=new FD(s3,0),ga=new FD(qm,1),Gs=new FD(f3,2)}function jNn(){jNn=F,KA(),s0n=St,mse=li,f0n=new V9(St),vse=new V9(li)}function ENn(){ENn=F,jYn=Ce((N0(),S(T(yYn,1),G,417,0,[rj,ij,a_,d_])))}function CNn(){CNn=F,AYn=Ce((A5(),S(T(TYn,1),G,406,0,[fj,wP,gP,hj])))}function MNn(){MNn=F,CYn=Ce((Vp(),S(T(EYn,1),G,332,0,[uj,cj,oj,sj])))}function TNn(){TNn=F,DZn=Ce((dd(),S(T(Lon,1),G,389,0,[Ow,Don,P_,I_])))}function ANn(){ANn=F,TZn=Ce((nm(),S(T(MZn,1),G,416,0,[rb,Iw,Pw,a2])))}function SNn(){SNn=F,tne=Ce(($f(),S(T(ene,1),G,421,0,[j3,lv,av,B_])))}function PNn(){PNn=F,GZn=Ce((OT(),S(T(UZn,1),G,371,0,[F_,HP,qP,wj])))}function INn(){INn=F,nie=Ce((cw(),S(T(RH,1),G,203,0,[TI,BH,S2,A2])))}function ONn(){ONn=F,iie=Ce((lh(),S(T(Hhn,1),G,284,0,[k1,_hn,HH,qH])))}function hk(){hk=F,Fsn=new Yz(kh,0),QP=new Yz("IMPROVE_STRAIGHTNESS",1)}function DNn(n,e){var t,i;return i=e/n.c.Rd().gc()|0,t=e%n.c.Rd().gc(),Rp(n,i,t)}function LNn(n){var e;if(n.nl())for(e=n.i-1;e>=0;--e)L(n,e);return jJ(n)}function eQ(n){var e,t;if(!n.b)return null;for(t=n.b;e=t.a[0];)t=e;return t}function NNn(n){var e,t;if(!n.b)return null;for(t=n.b;e=t.a[1];)t=e;return t}function K4e(n){return O(n,180)?""+u(n,180).a:n==null?null:Jr(n)}function _4e(n){return O(n,180)?""+u(n,180).a:n==null?null:Jr(n)}function $Nn(n,e){if(e.a)throw M(new ec(nXn));fi(n.a,e),e.a=n,!n.j&&(n.j=e)}function tQ(n,e){IC.call(this,e.zd(),e.yd()&-16449),Jn(n),this.a=n,this.c=e}function H4e(n,e){return new _L(e,a0(Ki(e.e),e.f.a+n,e.f.b+n),(_n(),!1))}function q4e(n,e){return k4(),nn(n,new bi(e,Y(e.e.c.length+e.g.c.length)))}function U4e(n,e){return k4(),nn(n,new bi(e,Y(e.e.c.length+e.g.c.length)))}function xNn(){xNn=F,lce=Ce((sA(),S(T(c1n,1),G,354,0,[Eq,i1n,r1n,t1n])))}function FNn(){FNn=F,$re=Ce((w5(),S(T(xln,1),G,353,0,[aq,BI,lq,hq])))}function BNn(){BNn=F,hre=Ce((Qp(),S(T(rln,1),G,405,0,[LI,c9,u9,o9])))}function RNn(){RNn=F,Vue=Ce((El(),S(T(aU,1),G,223,0,[lU,Yj,Kv,F3])))}function KNn(){KNn=F,Zue=Ce((To(),S(T(Yue,1),G,291,0,[nE,nl,Ta,Zj])))}function _Nn(){_Nn=F,foe=Ce((go(),S(T(I9,1),G,386,0,[rE,Gd,iE,Qw])))}function HNn(){HNn=F,doe=Ce((qT(),S(T(Cdn,1),G,320,0,[wU,ydn,Edn,jdn])))}function qNn(){qNn=F,goe=Ce((LT(),S(T(woe,1),G,415,0,[gU,Tdn,Mdn,Adn])))}function nT(){nT=F,xq=new oL(mVn,0),I1n=new oL(Crn,1),P1n=new oL(kh,2)}function Wb(n,e,t,i,r){return Jn(n),Jn(e),Jn(t),Jn(i),Jn(r),new AW(n,e,i)}function UNn(n,e){var t;return t=u(Bp(n.e,e),400),t?(tW(t),t.e):null}function du(n,e){var t;return t=qr(n,e,0),t==-1?!1:(Yl(n,t),!0)}function GNn(n,e,t){var i;return z1(n),i=new LO,i.a=e,n.a.Nb(new TCn(i,t)),i.a}function G4e(n){var e;return z1(n),e=K(Pi,Tr,28,0,15,1),hg(n.a,new y9n(e)),e}function iQ(n){var e;if(!E$(n))throw M(new nc);return n.e=1,e=n.d,n.d=null,e}function n1(n){var e;return Vr(n)&&(e=0-n,!isNaN(e))?e:Q1(tm(n))}function qr(n,e,t){for(;t<n.c.length;++t)if(mc(e,n.c[t]))return t;return-1}function s$(n){var e,t;return t=u(sn(n.j,0),12),e=u(v(t,(W(),st)),12),e}function f$(n,e){var t;this.f=n,this.b=e,t=u(ee(n.b,e),260),this.c=t?t.b:null}function zNn(){xs(),this.b=new de,this.f=new de,this.g=new de,this.e=new de}function eT(n){xC(this),this.g=n?IM(n,n.ie()):null,this.f=n,MM(this),this.je()}function h$(n){var e;e=n.jj(),e!=null&&n.d!=-1&&u(e,94).xh(n),n.i&&n.i.oj()}function lk(n){var e;for(e=n.p+1;e<n.c.a.c.length;++e)--u(sn(n.c.a,e),10).p}function XNn(n){Fb(!!n.c),FL(n.f.g,n.d),n.c.Qb(),n.c=null,n.b=GQ(n),n.d=n.f.g}function no(n){return n.b||(n.b=new vPn(n,jr,n),!n.a&&(n.a=new O7(n,n))),n.b}function ak(n,e){var t,i;return t=u(e,690),i=t.xi(),!i&&t.Ai(i=new FMn(n,e)),i}function Lr(n,e){var t,i;return t=u(e,692),i=t.$k(),!i&&t.cl(i=new uDn(n,e)),i}function rQ(n,e){s6();var t,i;return t=xp(n),i=xp(e),!!t&&!!i&&!pRn(t.k,i.k)}function tT(n,e){return mc(e,sn(n.f,0))||mc(e,sn(n.f,1))||mc(e,sn(n.f,2))}function dk(n,e){if(e<0)throw M(new Ir(DVn+e));return xDn(n,e+1),sn(n.j,e)}function VNn(n,e,t,i){if(!n)throw M(new Gn(H5(e,S(T(ki,1),Fn,1,5,[t,i]))))}function ml(n,e,t,i,r,c,s){k$.call(this,e,i,r,c,s),this.c=n,this.b=t}function Bh(n,e,t){var i,r;for(i=10,r=0;r<t-1;r++)e<i&&(n.a+="0"),i*=10;n.a+=e}function iT(n){var e,t;return t=n.length,e=K(fs,gh,28,t,15,1),qPn(n,0,t,e,0),e}function bk(n){ePn();var e,t;return e=n+128,t=bun[e],!t&&(t=bun[e]=new u9n(n)),t}function WNn(n){return FL(n.d.a.e.g,n.b),oe(n.c!=n.d.a.d),n.a=n.c,n.c=n.c.a,n.a}function z4e(n){switch(n.g){case 0:return et;case 1:return-1;default:return 0}}function X4e(n){return DZ(n,(R4(),aun))<0?-P1e(tm(n)):n.l+n.m*o3+n.h*vd}function JNn(n){(this.q?this.q:(Dn(),Dn(),Wh)).Ac(n.q?n.q:(Dn(),Dn(),Wh))}function V4e(n,e){Ep(u(u(n.f,27).of((qe(),j9)),101))&&e8e(mN(u(n.f,27)),e)}function l$(n,e){var t;return t=Ot(n.d,e),t>=0?tA(n,t,!0,!0):H0(n,e,!0)}function cQ(n){var e;return e=cd(Un(n,32)),e==null&&(iu(n),e=cd(Un(n,32))),e}function uQ(n){var e;return n.Oh()||(e=se(n.Dh())-n.ji(),n.$h().Mk(e)),n.zh()}function QNn(n,e){con=new kE,MYn=e,L8=n,u(L8.b,68),XJ(L8,con,null),aGn(L8)}function i5(){i5=F,E_=new RD("XY",0),j_=new RD("X",1),C_=new RD("Y",2)}function bu(){bu=F,vf=new BD("TOP",0),pa=new BD(qm,1),zs=new BD(Ftn,2)}function vl(){vl=F,vj=new GD(kh,0),v2=new GD("TOP",1),E3=new GD(Ftn,2)}function wk(){wk=F,UH=new nX("INPUT_ORDER",0),GH=new nX("PORT_DEGREE",1)}function R4(){R4=F,hun=Yc(ro,ro,524287),bQn=Yc(0,0,Ty),lun=QN(1),QN(2),aun=QN(0)}function a$(n){var e;return n.d!=n.r&&(e=ws(n),n.e=!!e&&e.lk()==bJn,n.d=e),n.e}function d$(n,e,t){var i;return i=n.g[e],O6(n,e,n.Zi(e,t)),n.Ri(e,t,i),n.Ni(),i}function rT(n,e){var t;return t=n.dd(e),t>=0?(n.gd(t),!0):!1}function b$(n,e){var t;for(Se(n),Se(e),t=!1;e.Ob();)t=t|n.Fc(e.Pb());return t}function Lf(n,e){var t;return t=u(ee(n.e,e),400),t?(DTn(n,t),t.e):null}function YNn(n){var e,t;return e=n/60|0,t=n%60,t==0?""+e:""+e+":"+(""+t)}function Jb(n,e){var t=n.a[e],i=(K$(),WK)[typeof t];return i?i(t):wY(typeof t)}function rc(n,e){var t,i;return ea(n),i=new _J(e,n.a),t=new rSn(i),new Tn(n,t)}function w$(n){var e;return e=n.b.c.length==0?null:sn(n.b,0),e!=null&&M$(n,0),e}function W4e(n,e){var t,i,r;r=e.c.i,t=u(ee(n.f,r),60),i=t.d.c-t.e.c,BQ(e.a,i,0)}function oQ(n,e){var t;for(++n.d,++n.c[e],t=e+1;t<n.a.length;)++n.a[t],t+=t&-t}function ZNn(n,e,t,i){nt(),Wd.call(this,26),this.c=n,this.a=e,this.d=t,this.b=i}function n$n(n,e){for(;e[0]<n.length&&th(` 	\r
+import{d as xNe,p as FNe}from"./flowDb-0da60e67-XaXEQp9e.js";import{aB as Nse,aC as BNe,l as Ba,h as IO,a$ as xU,u as RNe,p as E0n,t as j0n,o as $U,j as KNe}from"./mermaid.core-DNo_7Q2B.js";import{i as _Ne,a as HNe,l as qNe,b as UNe,k as GNe,m as zNe}from"./edges-5962ec63-ApWhby2b.js";import{l as XNe}from"./line-BqHmcuby.js";import"./app-B4LGNJZ0.js";import"./createText-4a4f35c9-CISzj231.js";import"./array-BKyUJesY.js";import"./path-CbwjOpE9.js";function NU(ct){throw new Error('Could not dynamically require "'+ct+'". Please configure the dynamicRequireTargets or/and ignoreDynamicRequires option of @rollup/plugin-commonjs appropriately for this require call to work.')}var Bse={exports:{}};(function(ct,_t){(function(Xt){ct.exports=Xt()})(function(){return function(){function Xt(gt,Sr,Di){function y(Ht,Jt){if(!Sr[Ht]){if(!gt[Ht]){var ze=typeof NU=="function"&&NU;if(!Jt&&ze)return ze(Ht,!0);if(Wt)return Wt(Ht,!0);var Yi=new Error("Cannot find module '"+Ht+"'");throw Yi.code="MODULE_NOT_FOUND",Yi}var Ri=Sr[Ht]={exports:{}};gt[Ht][0].call(Ri.exports,function(En){var hu=gt[Ht][1][En];return y(hu||En)},Ri,Ri.exports,Xt,gt,Sr,Di)}return Sr[Ht].exports}for(var Wt=typeof NU=="function"&&NU,Bu=0;Bu<Di.length;Bu++)y(Di[Bu]);return y}return Xt}()({1:[function(Xt,gt,Sr){Object.defineProperty(Sr,"__esModule",{value:!0});var Di=function(){function Ht(Jt,ze){for(var Yi=0;Yi<ze.length;Yi++){var Ri=ze[Yi];Ri.enumerable=Ri.enumerable||!1,Ri.configurable=!0,"value"in Ri&&(Ri.writable=!0),Object.defineProperty(Jt,Ri.key,Ri)}}return function(Jt,ze,Yi){return ze&&Ht(Jt.prototype,ze),Yi&&Ht(Jt,Yi),Jt}}();function y(Ht,Jt){if(!(Ht instanceof Jt))throw new TypeError("Cannot call a class as a function")}var Wt=function(){function Ht(){var Jt=this,ze=arguments.length>0&&arguments[0]!==void 0?arguments[0]:{},Yi=ze.defaultLayoutOptions,Ri=Yi===void 0?{}:Yi,En=ze.algorithms,hu=En===void 0?["layered","stress","mrtree","radial","force","disco","sporeOverlap","sporeCompaction","rectpacking"]:En,Qc=ze.workerFactory,Ru=ze.workerUrl;if(y(this,Ht),this.defaultLayoutOptions=Ri,this.initialized=!1,typeof Ru>"u"&&typeof Qc>"u")throw new Error("Cannot construct an ELK without both 'workerUrl' and 'workerFactory'.");var Pr=Qc;typeof Ru<"u"&&typeof Qc>"u"&&(Pr=function(N1){return new Worker(N1)});var Cf=Pr(Ru);if(typeof Cf.postMessage!="function")throw new TypeError("Created worker does not provide the required 'postMessage' function.");this.worker=new Bu(Cf),this.worker.postMessage({cmd:"register",algorithms:hu}).then(function(L1){return Jt.initialized=!0}).catch(console.err)}return Di(Ht,[{key:"layout",value:function(ze){var Yi=arguments.length>1&&arguments[1]!==void 0?arguments[1]:{},Ri=Yi.layoutOptions,En=Ri===void 0?this.defaultLayoutOptions:Ri,hu=Yi.logging,Qc=hu===void 0?!1:hu,Ru=Yi.measureExecutionTime,Pr=Ru===void 0?!1:Ru;return ze?this.worker.postMessage({cmd:"layout",graph:ze,layoutOptions:En,options:{logging:Qc,measureExecutionTime:Pr}}):Promise.reject(new Error("Missing mandatory parameter 'graph'."))}},{key:"knownLayoutAlgorithms",value:function(){return this.worker.postMessage({cmd:"algorithms"})}},{key:"knownLayoutOptions",value:function(){return this.worker.postMessage({cmd:"options"})}},{key:"knownLayoutCategories",value:function(){return this.worker.postMessage({cmd:"categories"})}},{key:"terminateWorker",value:function(){this.worker&&this.worker.terminate()}}]),Ht}();Sr.default=Wt;var Bu=function(){function Ht(Jt){var ze=this;if(y(this,Ht),Jt===void 0)throw new Error("Missing mandatory parameter 'worker'.");this.resolvers={},this.worker=Jt,this.worker.onmessage=function(Yi){setTimeout(function(){ze.receive(ze,Yi)},0)}}return Di(Ht,[{key:"postMessage",value:function(ze){var Yi=this.id||0;this.id=Yi+1,ze.id=Yi;var Ri=this;return new Promise(function(En,hu){Ri.resolvers[Yi]=function(Qc,Ru){Qc?(Ri.convertGwtStyleError(Qc),hu(Qc)):En(Ru)},Ri.worker.postMessage(ze)})}},{key:"receive",value:function(ze,Yi){var Ri=Yi.data,En=ze.resolvers[Ri.id];En&&(delete ze.resolvers[Ri.id],Ri.error?En(Ri.error):En(null,Ri.data))}},{key:"terminate",value:function(){this.worker&&this.worker.terminate()}},{key:"convertGwtStyleError",value:function(ze){if(ze){var Yi=ze.__java$exception;Yi&&(Yi.cause&&Yi.cause.backingJsObject&&(ze.cause=Yi.cause.backingJsObject,this.convertGwtStyleError(ze.cause)),delete ze.__java$exception)}}}]),Ht}()},{}],2:[function(Xt,gt,Sr){(function(Di){(function(){var y;typeof window<"u"?y=window:typeof Di<"u"?y=Di:typeof self<"u"&&(y=self);var Wt;function Bu(){}function Ht(){}function Jt(){}function ze(){}function Yi(){}function Ri(){}function En(){}function hu(){}function Qc(){}function Ru(){}function Pr(){}function Cf(){}function L1(){}function N1(){}function og(){}function V3(){}function $1(){}function ul(){}function C0n(){}function M0n(){}function J2(){}function F(){}function T0n(){}function mE(){}function A0n(){}function S0n(){}function P0n(){}function I0n(){}function O0n(){}function FU(){}function D0n(){}function L0n(){}function N0n(){}function OO(){}function $0n(){}function x0n(){}function F0n(){}function DO(){}function B0n(){}function R0n(){}function BU(){}function K0n(){}function _0n(){}function yu(){}function ju(){}function Q2(){}function Y2(){}function H0n(){}function q0n(){}function U0n(){}function G0n(){}function RU(){}function Eu(){}function Z2(){}function np(){}function z0n(){}function X0n(){}function LO(){}function V0n(){}function W0n(){}function J0n(){}function Q0n(){}function Y0n(){}function Z0n(){}function nbn(){}function ebn(){}function tbn(){}function ibn(){}function rbn(){}function cbn(){}function ubn(){}function obn(){}function sbn(){}function fbn(){}function hbn(){}function lbn(){}function abn(){}function dbn(){}function bbn(){}function wbn(){}function gbn(){}function pbn(){}function mbn(){}function vbn(){}function kbn(){}function ybn(){}function jbn(){}function Ebn(){}function Cbn(){}function Mbn(){}function Tbn(){}function KU(){}function Abn(){}function Sbn(){}function Pbn(){}function Ibn(){}function NO(){}function $O(){}function vE(){}function Obn(){}function Dbn(){}function xO(){}function Lbn(){}function Nbn(){}function $bn(){}function kE(){}function xbn(){}function Fbn(){}function Bbn(){}function Rbn(){}function Kbn(){}function _bn(){}function Hbn(){}function qbn(){}function Ubn(){}function _U(){}function Gbn(){}function zbn(){}function HU(){}function Xbn(){}function Vbn(){}function Wbn(){}function Jbn(){}function Qbn(){}function Ybn(){}function Zbn(){}function nwn(){}function ewn(){}function twn(){}function iwn(){}function rwn(){}function cwn(){}function FO(){}function uwn(){}function own(){}function swn(){}function fwn(){}function hwn(){}function lwn(){}function awn(){}function dwn(){}function bwn(){}function qU(){}function UU(){}function wwn(){}function gwn(){}function pwn(){}function mwn(){}function vwn(){}function kwn(){}function ywn(){}function jwn(){}function Ewn(){}function Cwn(){}function Mwn(){}function Twn(){}function Awn(){}function Swn(){}function Pwn(){}function Iwn(){}function Own(){}function Dwn(){}function Lwn(){}function Nwn(){}function $wn(){}function xwn(){}function Fwn(){}function Bwn(){}function Rwn(){}function Kwn(){}function _wn(){}function Hwn(){}function qwn(){}function Uwn(){}function Gwn(){}function zwn(){}function Xwn(){}function Vwn(){}function Wwn(){}function Jwn(){}function Qwn(){}function Ywn(){}function Zwn(){}function ngn(){}function egn(){}function tgn(){}function ign(){}function rgn(){}function cgn(){}function ugn(){}function ogn(){}function sgn(){}function fgn(){}function hgn(){}function lgn(){}function agn(){}function dgn(){}function bgn(){}function wgn(){}function ggn(){}function pgn(){}function mgn(){}function vgn(){}function kgn(){}function ygn(){}function jgn(){}function Egn(){}function Cgn(){}function Mgn(){}function Tgn(){}function Agn(){}function Sgn(){}function Pgn(){}function Ign(){}function Ogn(){}function Dgn(){}function Lgn(){}function Ngn(){}function $gn(){}function xgn(){}function Fgn(){}function Bgn(){}function Rgn(){}function Kgn(){}function _gn(){}function Hgn(){}function qgn(){}function Ugn(){}function Ggn(){}function zgn(){}function Xgn(){}function Vgn(){}function Wgn(){}function Jgn(){}function Qgn(){}function Ygn(){}function Zgn(){}function n2n(){}function e2n(){}function t2n(){}function i2n(){}function r2n(){}function c2n(){}function u2n(){}function GU(){}function o2n(){}function s2n(){}function f2n(){}function h2n(){}function l2n(){}function a2n(){}function d2n(){}function b2n(){}function w2n(){}function g2n(){}function p2n(){}function m2n(){}function v2n(){}function k2n(){}function y2n(){}function j2n(){}function E2n(){}function C2n(){}function M2n(){}function T2n(){}function A2n(){}function S2n(){}function P2n(){}function I2n(){}function O2n(){}function D2n(){}function L2n(){}function N2n(){}function $2n(){}function x2n(){}function F2n(){}function B2n(){}function R2n(){}function K2n(){}function _2n(){}function H2n(){}function q2n(){}function U2n(){}function G2n(){}function z2n(){}function X2n(){}function V2n(){}function W2n(){}function J2n(){}function Q2n(){}function Y2n(){}function Z2n(){}function npn(){}function epn(){}function tpn(){}function ipn(){}function rpn(){}function cpn(){}function upn(){}function opn(){}function spn(){}function fpn(){}function hpn(){}function lpn(){}function apn(){}function dpn(){}function bpn(){}function wpn(){}function gpn(){}function ppn(){}function mpn(){}function vpn(){}function kpn(){}function ypn(){}function jpn(){}function Epn(){}function Cpn(){}function Mpn(){}function zU(){}function Tpn(){}function Apn(){}function Spn(){}function Ppn(){}function Ipn(){}function Opn(){}function Dpn(){}function Lpn(){}function Npn(){}function $pn(){}function XU(){}function xpn(){}function Fpn(){}function Bpn(){}function Rpn(){}function Kpn(){}function _pn(){}function VU(){}function WU(){}function Hpn(){}function JU(){}function QU(){}function qpn(){}function Upn(){}function Gpn(){}function zpn(){}function Xpn(){}function Vpn(){}function Wpn(){}function Jpn(){}function Qpn(){}function Ypn(){}function Zpn(){}function YU(){}function n3n(){}function e3n(){}function t3n(){}function i3n(){}function r3n(){}function c3n(){}function u3n(){}function o3n(){}function s3n(){}function f3n(){}function h3n(){}function l3n(){}function a3n(){}function d3n(){}function b3n(){}function w3n(){}function g3n(){}function p3n(){}function m3n(){}function v3n(){}function k3n(){}function y3n(){}function j3n(){}function E3n(){}function C3n(){}function M3n(){}function T3n(){}function A3n(){}function S3n(){}function P3n(){}function I3n(){}function O3n(){}function D3n(){}function L3n(){}function N3n(){}function $3n(){}function x3n(){}function F3n(){}function B3n(){}function R3n(){}function K3n(){}function _3n(){}function H3n(){}function q3n(){}function U3n(){}function G3n(){}function z3n(){}function X3n(){}function V3n(){}function W3n(){}function J3n(){}function Q3n(){}function Y3n(){}function Z3n(){}function n4n(){}function e4n(){}function t4n(){}function i4n(){}function r4n(){}function c4n(){}function u4n(){}function o4n(){}function s4n(){}function f4n(){}function h4n(){}function l4n(){}function a4n(){}function d4n(){}function b4n(){}function w4n(){}function g4n(){}function p4n(){}function m4n(){}function v4n(){}function k4n(){}function y4n(){}function j4n(){}function E4n(){}function C4n(){}function M4n(){}function T4n(){}function A4n(){}function S4n(){}function P4n(){}function I4n(){}function O4n(){}function _se(){}function D4n(){}function L4n(){}function N4n(){}function $4n(){}function x4n(){}function F4n(){}function B4n(){}function R4n(){}function K4n(){}function _4n(){}function H4n(){}function q4n(){}function U4n(){}function G4n(){}function z4n(){}function X4n(){}function V4n(){}function W4n(){}function J4n(){}function Q4n(){}function Y4n(){}function Z4n(){}function nmn(){}function emn(){}function tmn(){}function imn(){}function rmn(){}function BO(){}function RO(){}function cmn(){}function KO(){}function umn(){}function omn(){}function smn(){}function fmn(){}function hmn(){}function lmn(){}function amn(){}function dmn(){}function bmn(){}function wmn(){}function ZU(){}function gmn(){}function pmn(){}function mmn(){}function Hse(){}function vmn(){}function kmn(){}function ymn(){}function jmn(){}function Emn(){}function Cmn(){}function Mmn(){}function Ra(){}function Tmn(){}function ep(){}function nG(){}function Amn(){}function Smn(){}function Pmn(){}function Imn(){}function Omn(){}function Dmn(){}function Lmn(){}function Nmn(){}function $mn(){}function xmn(){}function Fmn(){}function Bmn(){}function Rmn(){}function Kmn(){}function _mn(){}function Hmn(){}function qmn(){}function Umn(){}function Gmn(){}function hn(){}function zmn(){}function Xmn(){}function Vmn(){}function Wmn(){}function Jmn(){}function Qmn(){}function Ymn(){}function Zmn(){}function nvn(){}function evn(){}function tvn(){}function ivn(){}function rvn(){}function _O(){}function cvn(){}function uvn(){}function ovn(){}function yE(){}function svn(){}function HO(){}function jE(){}function fvn(){}function eG(){}function hvn(){}function lvn(){}function avn(){}function dvn(){}function bvn(){}function wvn(){}function EE(){}function gvn(){}function pvn(){}function CE(){}function mvn(){}function ME(){}function vvn(){}function tG(){}function kvn(){}function qO(){}function iG(){}function yvn(){}function jvn(){}function Evn(){}function Cvn(){}function qse(){}function Mvn(){}function Tvn(){}function Avn(){}function Svn(){}function Pvn(){}function Ivn(){}function Ovn(){}function Dvn(){}function Lvn(){}function Nvn(){}function W3(){}function UO(){}function $vn(){}function xvn(){}function Fvn(){}function Bvn(){}function Rvn(){}function Kvn(){}function _vn(){}function Hvn(){}function qvn(){}function Uvn(){}function Gvn(){}function zvn(){}function Xvn(){}function Vvn(){}function Wvn(){}function Jvn(){}function Qvn(){}function Yvn(){}function Zvn(){}function n6n(){}function e6n(){}function t6n(){}function i6n(){}function r6n(){}function c6n(){}function u6n(){}function o6n(){}function s6n(){}function f6n(){}function h6n(){}function l6n(){}function a6n(){}function d6n(){}function b6n(){}function w6n(){}function g6n(){}function p6n(){}function m6n(){}function v6n(){}function k6n(){}function y6n(){}function j6n(){}function E6n(){}function C6n(){}function M6n(){}function T6n(){}function A6n(){}function S6n(){}function P6n(){}function I6n(){}function O6n(){}function D6n(){}function L6n(){}function N6n(){}function $6n(){}function x6n(){}function F6n(){}function B6n(){}function R6n(){}function K6n(){}function _6n(){}function H6n(){}function q6n(){}function U6n(){}function G6n(){}function z6n(){}function X6n(){}function V6n(){}function W6n(){}function J6n(){}function Q6n(){}function Y6n(){}function Z6n(){}function n5n(){}function e5n(){}function t5n(){}function i5n(){}function r5n(){}function c5n(){}function u5n(){}function o5n(){}function s5n(){}function f5n(){}function h5n(){}function l5n(){}function a5n(){}function d5n(){}function b5n(){}function w5n(){}function g5n(){}function p5n(){}function m5n(){}function v5n(){}function k5n(){}function y5n(){}function j5n(){}function E5n(){}function C5n(){}function M5n(){}function T5n(){}function A5n(){}function rG(){}function S5n(){}function P5n(){}function GO(){n6()}function I5n(){u7()}function O5n(){aA()}function D5n(){Q$()}function L5n(){M5()}function N5n(){ann()}function $5n(){qs()}function x5n(){jZ()}function F5n(){zk()}function B5n(){o7()}function R5n(){$7()}function K5n(){aCn()}function _5n(){Hp()}function H5n(){KLn()}function q5n(){yQ()}function U5n(){SOn()}function G5n(){jQ()}function z5n(){pNn()}function X5n(){AOn()}function V5n(){cm()}function W5n(){nxn()}function J5n(){Z$n()}function Q5n(){EDn()}function Y5n(){exn()}function Z5n(){ca()}function n8n(){ZE()}function e8n(){ltn()}function t8n(){cn()}function i8n(){txn()}function r8n(){Pxn()}function c8n(){POn()}function u8n(){nKn()}function o8n(){IOn()}function s8n(){bUn()}function f8n(){qnn()}function h8n(){kl()}function l8n(){wBn()}function a8n(){lc()}function d8n(){ROn()}function b8n(){_p()}function w8n(){Men()}function g8n(){ua()}function p8n(){Ten()}function m8n(){Bf()}function v8n(){Qk()}function k8n(){EF()}function y8n(){Dx()}function cf(){wSn()}function j8n(){YM()}function E8n(){mA()}function cG(){qe()}function C8n(){NT()}function M8n(){YY()}function uG(){D$()}function oG(){KA()}function T8n(){Fen()}function sG(n){Jn(n)}function A8n(n){this.a=n}function TE(n){this.a=n}function S8n(n){this.a=n}function P8n(n){this.a=n}function I8n(n){this.a=n}function O8n(n){this.a=n}function D8n(n){this.a=n}function L8n(n){this.a=n}function fG(n){this.a=n}function hG(n){this.a=n}function N8n(n){this.a=n}function $8n(n){this.a=n}function zO(n){this.a=n}function x8n(n){this.a=n}function F8n(n){this.a=n}function XO(n){this.a=n}function VO(n){this.a=n}function B8n(n){this.a=n}function WO(n){this.a=n}function R8n(n){this.a=n}function K8n(n){this.a=n}function _8n(n){this.a=n}function lG(n){this.b=n}function H8n(n){this.c=n}function q8n(n){this.a=n}function U8n(n){this.a=n}function G8n(n){this.a=n}function z8n(n){this.a=n}function X8n(n){this.a=n}function V8n(n){this.a=n}function W8n(n){this.a=n}function J8n(n){this.a=n}function Q8n(n){this.a=n}function Y8n(n){this.a=n}function Z8n(n){this.a=n}function n9n(n){this.a=n}function e9n(n){this.a=n}function aG(n){this.a=n}function dG(n){this.a=n}function AE(n){this.a=n}function z9(n){this.a=n}function Ka(){this.a=[]}function t9n(n,e){n.a=e}function Use(n,e){n.a=e}function Gse(n,e){n.b=e}function zse(n,e){n.b=e}function Xse(n,e){n.b=e}function bG(n,e){n.j=e}function Vse(n,e){n.g=e}function Wse(n,e){n.i=e}function Jse(n,e){n.c=e}function Qse(n,e){n.c=e}function Yse(n,e){n.d=e}function Zse(n,e){n.d=e}function _a(n,e){n.k=e}function nfe(n,e){n.c=e}function wG(n,e){n.c=e}function gG(n,e){n.a=e}function efe(n,e){n.a=e}function tfe(n,e){n.f=e}function ife(n,e){n.a=e}function rfe(n,e){n.b=e}function JO(n,e){n.d=e}function SE(n,e){n.i=e}function pG(n,e){n.o=e}function cfe(n,e){n.r=e}function ufe(n,e){n.a=e}function ofe(n,e){n.b=e}function i9n(n,e){n.e=e}function sfe(n,e){n.f=e}function mG(n,e){n.g=e}function ffe(n,e){n.e=e}function hfe(n,e){n.f=e}function lfe(n,e){n.f=e}function QO(n,e){n.a=e}function YO(n,e){n.b=e}function afe(n,e){n.n=e}function dfe(n,e){n.a=e}function bfe(n,e){n.c=e}function wfe(n,e){n.c=e}function gfe(n,e){n.c=e}function pfe(n,e){n.a=e}function mfe(n,e){n.a=e}function vfe(n,e){n.d=e}function kfe(n,e){n.d=e}function yfe(n,e){n.e=e}function jfe(n,e){n.e=e}function Efe(n,e){n.g=e}function Cfe(n,e){n.f=e}function Mfe(n,e){n.j=e}function Tfe(n,e){n.a=e}function Afe(n,e){n.a=e}function Sfe(n,e){n.b=e}function r9n(n){n.b=n.a}function c9n(n){n.c=n.d.d}function vG(n){this.a=n}function kG(n){this.a=n}function yG(n){this.a=n}function Ha(n){this.a=n}function qa(n){this.a=n}function X9(n){this.a=n}function u9n(n){this.a=n}function jG(n){this.a=n}function V9(n){this.a=n}function PE(n){this.a=n}function ol(n){this.a=n}function Sb(n){this.a=n}function o9n(n){this.a=n}function s9n(n){this.a=n}function ZO(n){this.b=n}function J3(n){this.b=n}function Q3(n){this.b=n}function nD(n){this.a=n}function f9n(n){this.a=n}function eD(n){this.c=n}function C(n){this.c=n}function h9n(n){this.c=n}function Xv(n){this.d=n}function EG(n){this.a=n}function Te(n){this.a=n}function l9n(n){this.a=n}function CG(n){this.a=n}function MG(n){this.a=n}function TG(n){this.a=n}function AG(n){this.a=n}function SG(n){this.a=n}function PG(n){this.a=n}function Y3(n){this.a=n}function a9n(n){this.a=n}function d9n(n){this.a=n}function Z3(n){this.a=n}function b9n(n){this.a=n}function w9n(n){this.a=n}function g9n(n){this.a=n}function p9n(n){this.a=n}function m9n(n){this.a=n}function v9n(n){this.a=n}function k9n(n){this.a=n}function y9n(n){this.a=n}function j9n(n){this.a=n}function E9n(n){this.a=n}function C9n(n){this.a=n}function M9n(n){this.a=n}function T9n(n){this.a=n}function A9n(n){this.a=n}function S9n(n){this.a=n}function Vv(n){this.a=n}function P9n(n){this.a=n}function I9n(n){this.a=n}function O9n(n){this.a=n}function D9n(n){this.a=n}function IE(n){this.a=n}function L9n(n){this.a=n}function N9n(n){this.a=n}function n4(n){this.a=n}function IG(n){this.a=n}function $9n(n){this.a=n}function x9n(n){this.a=n}function F9n(n){this.a=n}function B9n(n){this.a=n}function R9n(n){this.a=n}function K9n(n){this.a=n}function OG(n){this.a=n}function DG(n){this.a=n}function LG(n){this.a=n}function Wv(n){this.a=n}function OE(n){this.e=n}function e4(n){this.a=n}function _9n(n){this.a=n}function tp(n){this.a=n}function NG(n){this.a=n}function H9n(n){this.a=n}function q9n(n){this.a=n}function U9n(n){this.a=n}function G9n(n){this.a=n}function z9n(n){this.a=n}function X9n(n){this.a=n}function V9n(n){this.a=n}function W9n(n){this.a=n}function J9n(n){this.a=n}function Q9n(n){this.a=n}function Y9n(n){this.a=n}function $G(n){this.a=n}function Z9n(n){this.a=n}function n7n(n){this.a=n}function e7n(n){this.a=n}function t7n(n){this.a=n}function i7n(n){this.a=n}function r7n(n){this.a=n}function c7n(n){this.a=n}function u7n(n){this.a=n}function o7n(n){this.a=n}function s7n(n){this.a=n}function f7n(n){this.a=n}function h7n(n){this.a=n}function l7n(n){this.a=n}function a7n(n){this.a=n}function d7n(n){this.a=n}function b7n(n){this.a=n}function w7n(n){this.a=n}function g7n(n){this.a=n}function p7n(n){this.a=n}function m7n(n){this.a=n}function v7n(n){this.a=n}function k7n(n){this.a=n}function y7n(n){this.a=n}function j7n(n){this.a=n}function E7n(n){this.a=n}function C7n(n){this.a=n}function M7n(n){this.a=n}function T7n(n){this.a=n}function A7n(n){this.a=n}function S7n(n){this.a=n}function P7n(n){this.a=n}function I7n(n){this.a=n}function O7n(n){this.a=n}function D7n(n){this.a=n}function L7n(n){this.a=n}function N7n(n){this.a=n}function $7n(n){this.a=n}function x7n(n){this.a=n}function F7n(n){this.c=n}function B7n(n){this.b=n}function R7n(n){this.a=n}function K7n(n){this.a=n}function _7n(n){this.a=n}function H7n(n){this.a=n}function q7n(n){this.a=n}function U7n(n){this.a=n}function G7n(n){this.a=n}function z7n(n){this.a=n}function X7n(n){this.a=n}function V7n(n){this.a=n}function W7n(n){this.a=n}function J7n(n){this.a=n}function Q7n(n){this.a=n}function Y7n(n){this.a=n}function Z7n(n){this.a=n}function nkn(n){this.a=n}function ekn(n){this.a=n}function tkn(n){this.a=n}function ikn(n){this.a=n}function rkn(n){this.a=n}function ckn(n){this.a=n}function ukn(n){this.a=n}function okn(n){this.a=n}function skn(n){this.a=n}function fkn(n){this.a=n}function hkn(n){this.a=n}function lkn(n){this.a=n}function sl(n){this.a=n}function sg(n){this.a=n}function akn(n){this.a=n}function dkn(n){this.a=n}function bkn(n){this.a=n}function wkn(n){this.a=n}function gkn(n){this.a=n}function pkn(n){this.a=n}function mkn(n){this.a=n}function vkn(n){this.a=n}function kkn(n){this.a=n}function ykn(n){this.a=n}function jkn(n){this.a=n}function Ekn(n){this.a=n}function Ckn(n){this.a=n}function Mkn(n){this.a=n}function Tkn(n){this.a=n}function Akn(n){this.a=n}function Skn(n){this.a=n}function Pkn(n){this.a=n}function Ikn(n){this.a=n}function Okn(n){this.a=n}function Dkn(n){this.a=n}function Lkn(n){this.a=n}function Nkn(n){this.a=n}function $kn(n){this.a=n}function xkn(n){this.a=n}function Fkn(n){this.a=n}function DE(n){this.a=n}function Bkn(n){this.f=n}function Rkn(n){this.a=n}function Kkn(n){this.a=n}function _kn(n){this.a=n}function Hkn(n){this.a=n}function qkn(n){this.a=n}function Ukn(n){this.a=n}function Gkn(n){this.a=n}function zkn(n){this.a=n}function Xkn(n){this.a=n}function Vkn(n){this.a=n}function Wkn(n){this.a=n}function Jkn(n){this.a=n}function Qkn(n){this.a=n}function Ykn(n){this.a=n}function Zkn(n){this.a=n}function nyn(n){this.a=n}function eyn(n){this.a=n}function tyn(n){this.a=n}function iyn(n){this.a=n}function ryn(n){this.a=n}function cyn(n){this.a=n}function uyn(n){this.a=n}function oyn(n){this.a=n}function syn(n){this.a=n}function fyn(n){this.a=n}function hyn(n){this.a=n}function lyn(n){this.a=n}function ayn(n){this.a=n}function tD(n){this.a=n}function xG(n){this.a=n}function lt(n){this.b=n}function dyn(n){this.a=n}function byn(n){this.a=n}function wyn(n){this.a=n}function gyn(n){this.a=n}function pyn(n){this.a=n}function myn(n){this.a=n}function vyn(n){this.a=n}function kyn(n){this.b=n}function yyn(n){this.a=n}function W9(n){this.a=n}function jyn(n){this.a=n}function Eyn(n){this.a=n}function FG(n){this.c=n}function LE(n){this.e=n}function NE(n){this.a=n}function $E(n){this.a=n}function iD(n){this.a=n}function Cyn(n){this.d=n}function Myn(n){this.a=n}function BG(n){this.a=n}function RG(n){this.a=n}function Wd(n){this.e=n}function Pfe(){this.a=0}function de(){Hu(this)}function Z(){pL(this)}function rD(){sIn(this)}function Tyn(){}function Jd(){this.c=Gdn}function Ayn(n,e){n.b+=e}function Ife(n,e){e.Wb(n)}function Ofe(n){return n.a}function Dfe(n){return n.a}function Lfe(n){return n.a}function Nfe(n){return n.a}function $fe(n){return n.a}function M(n){return n.e}function xfe(){return null}function Ffe(){return null}function Bfe(){Cz(),pLe()}function Rfe(n){n.b.Of(n.e)}function Syn(n){n.b=new CD}function Jv(n,e){n.b=e-n.b}function Qv(n,e){n.a=e-n.a}function Bn(n,e){n.push(e)}function Pyn(n,e){n.sort(e)}function Iyn(n,e){e.jd(n.a)}function Kfe(n,e){gi(e,n)}function _fe(n,e,t){n.Yd(t,e)}function J9(n,e){n.e=e,e.b=n}function KG(n){uh(),this.a=n}function Oyn(n){uh(),this.a=n}function Dyn(n){uh(),this.a=n}function cD(n){m0(),this.a=n}function Lyn(n){O4(),VK.le(n)}function _G(){_G=F,new de}function Ua(){YTn.call(this)}function HG(){YTn.call(this)}function qG(){Ua.call(this)}function uD(){Ua.call(this)}function Nyn(){Ua.call(this)}function Q9(){Ua.call(this)}function Cu(){Ua.call(this)}function ip(){Ua.call(this)}function Pe(){Ua.call(this)}function Bo(){Ua.call(this)}function $yn(){Ua.call(this)}function nc(){Ua.call(this)}function xyn(){Ua.call(this)}function Fyn(){this.a=this}function xE(){this.Bb|=256}function Byn(){this.b=new GMn}function Pb(n,e){n.length=e}function FE(n,e){nn(n.a,e)}function Hfe(n,e){bnn(n.c,e)}function qfe(n,e){fi(n.b,e)}function Ufe(n,e){uA(n.a,e)}function Gfe(n,e){cx(n.a,e)}function t4(n,e){it(n.e,e)}function rp(n){jA(n.c,n.b)}function zfe(n,e){n.kc().Nb(e)}function UG(n){this.a=B5e(n)}function ni(){this.a=new de}function Ryn(){this.a=new de}function GG(){this.a=new rCn}function BE(){this.a=new Z}function oD(){this.a=new Z}function zG(){this.a=new Z}function hs(){this.a=new cbn}function Ga(){this.a=new NLn}function XG(){this.a=new _U}function VG(){this.a=new TOn}function WG(){this.a=new BAn}function Kyn(){this.a=new Z}function _yn(){this.a=new Z}function Hyn(){this.a=new Z}function JG(){this.a=new Z}function qyn(){this.d=new Z}function Uyn(){this.a=new zOn}function Gyn(){this.a=new ni}function zyn(){this.a=new de}function Xyn(){this.b=new de}function Vyn(){this.b=new Z}function QG(){this.e=new Z}function Wyn(){this.a=new Z5n}function Jyn(){this.d=new Z}function Qyn(){QIn.call(this)}function Yyn(){QIn.call(this)}function Zyn(){Z.call(this)}function YG(){qG.call(this)}function ZG(){BE.call(this)}function njn(){qC.call(this)}function ejn(){JG.call(this)}function Yv(){Tyn.call(this)}function sD(){Yv.call(this)}function cp(){Tyn.call(this)}function nz(){cp.call(this)}function tjn(){rz.call(this)}function ijn(){rz.call(this)}function rjn(){rz.call(this)}function cjn(){cz.call(this)}function Zv(){svn.call(this)}function ez(){svn.call(this)}function Mu(){Ct.call(this)}function ujn(){yjn.call(this)}function ojn(){yjn.call(this)}function sjn(){de.call(this)}function fjn(){de.call(this)}function hjn(){de.call(this)}function fD(){cxn.call(this)}function ljn(){ni.call(this)}function ajn(){xE.call(this)}function hD(){BX.call(this)}function tz(){de.call(this)}function lD(){BX.call(this)}function aD(){de.call(this)}function djn(){de.call(this)}function iz(){ME.call(this)}function bjn(){iz.call(this)}function wjn(){ME.call(this)}function gjn(){rG.call(this)}function rz(){this.a=new ni}function pjn(){this.a=new de}function mjn(){this.a=new Z}function cz(){this.a=new de}function up(){this.a=new Ct}function vjn(){this.j=new Z}function kjn(){this.a=new mEn}function yjn(){this.a=new mvn}function uz(){this.a=new Z4n}function n6(){n6=F,KK=new Ht}function dD(){dD=F,_K=new Ejn}function bD(){bD=F,HK=new jjn}function jjn(){XO.call(this,"")}function Ejn(){XO.call(this,"")}function Cjn(n){S$n.call(this,n)}function Mjn(n){S$n.call(this,n)}function oz(n){fG.call(this,n)}function sz(n){XEn.call(this,n)}function Xfe(n){XEn.call(this,n)}function Vfe(n){sz.call(this,n)}function Wfe(n){sz.call(this,n)}function Jfe(n){sz.call(this,n)}function Tjn(n){zN.call(this,n)}function Ajn(n){zN.call(this,n)}function Sjn(n){uSn.call(this,n)}function Pjn(n){Oz.call(this,n)}function e6(n){WE.call(this,n)}function fz(n){WE.call(this,n)}function Ijn(n){WE.call(this,n)}function hz(n){mje.call(this,n)}function lz(n){hz.call(this,n)}function ec(n){APn.call(this,n)}function Ojn(n){ec.call(this,n)}function op(){z9.call(this,{})}function Djn(){Djn=F,dQn=new M0n}function RE(){RE=F,GK=new STn}function Ljn(){Ljn=F,oun=new Bu}function az(){az=F,sun=new N1}function KE(){KE=F,P8=new $1}function wD(n){b4(),this.a=n}function gD(n){RQ(),this.a=n}function Qd(n){nN(),this.f=n}function pD(n){nN(),this.f=n}function Njn(n){bSn(),this.a=n}function $jn(n){n.b=null,n.c=0}function Qfe(n,e){n.e=e,bqn(n,e)}function Yfe(n,e){n.a=e,cEe(n)}function mD(n,e,t){n.a[e.g]=t}function Zfe(n,e,t){kke(t,n,e)}function nhe(n,e){Wae(e.i,n.n)}function xjn(n,e){v6e(n).Cd(e)}function ehe(n,e){n.a.ec().Mc(e)}function Fjn(n,e){return n.g-e.g}function the(n,e){return n*n/e}function on(n){return Jn(n),n}function $(n){return Jn(n),n}function Y9(n){return Jn(n),n}function ihe(n){return new AE(n)}function rhe(n){return new qb(n)}function dz(n){return Jn(n),n}function che(n){return Jn(n),n}function _E(n){ec.call(this,n)}function Ir(n){ec.call(this,n)}function Bjn(n){ec.call(this,n)}function vD(n){APn.call(this,n)}function i4(n){ec.call(this,n)}function Gn(n){ec.call(this,n)}function Or(n){ec.call(this,n)}function Rjn(n){ec.call(this,n)}function sp(n){ec.call(this,n)}function Kl(n){ec.call(this,n)}function _l(n){ec.call(this,n)}function fp(n){ec.call(this,n)}function nh(n){ec.call(this,n)}function kD(n){ec.call(this,n)}function Le(n){ec.call(this,n)}function Ku(n){Jn(n),this.a=n}function bz(n){return ld(n),n}function t6(n){TW(n,n.length)}function i6(n){return n.b==n.c}function Ib(n){return!!n&&n.b}function uhe(n){return!!n&&n.k}function ohe(n){return!!n&&n.j}function she(n,e,t){n.c.Ef(e,t)}function Kjn(n,e){n.be(e),e.ae(n)}function hp(n){uh(),this.a=Se(n)}function yD(){this.a=Oe(Se(ur))}function _jn(){throw M(new Pe)}function fhe(){throw M(new Pe)}function wz(){throw M(new Pe)}function Hjn(){throw M(new Pe)}function hhe(){throw M(new Pe)}function lhe(){throw M(new Pe)}function HE(){HE=F,O4()}function Hl(){X9.call(this,"")}function r6(){X9.call(this,"")}function x1(){X9.call(this,"")}function lp(){X9.call(this,"")}function gz(n){Ir.call(this,n)}function pz(n){Ir.call(this,n)}function eh(n){Gn.call(this,n)}function r4(n){Q3.call(this,n)}function qjn(n){r4.call(this,n)}function jD(n){BC.call(this,n)}function ED(n){JX.call(this,n,0)}function CD(){sJ.call(this,12,3)}function T(n,e){return kOn(n,e)}function qE(n,e){return o$(n,e)}function ahe(n,e){return n.a-e.a}function dhe(n,e){return n.a-e.a}function bhe(n,e){return n.a-e.a}function whe(n,e){return e in n.a}function Ujn(n){return n.a?n.b:0}function ghe(n){return n.a?n.b:0}function phe(n,e,t){e.Cd(n.a[t])}function mhe(n,e,t){e.Pe(n.a[t])}function vhe(n,e){n.b=new rr(e)}function khe(n,e){return n.b=e,n}function Gjn(n,e){return n.c=e,n}function zjn(n,e){return n.f=e,n}function yhe(n,e){return n.g=e,n}function mz(n,e){return n.a=e,n}function vz(n,e){return n.f=e,n}function jhe(n,e){return n.k=e,n}function kz(n,e){return n.a=e,n}function Ehe(n,e){return n.e=e,n}function yz(n,e){return n.e=e,n}function Che(n,e){return n.f=e,n}function Mhe(n,e){n.b=!0,n.d=e}function The(n,e){return n.b-e.b}function Ahe(n,e){return n.g-e.g}function She(n,e){return n?0:e-1}function Xjn(n,e){return n?0:e-1}function Phe(n,e){return n?e-1:0}function Ihe(n,e){return n.s-e.s}function Ohe(n,e){return e.rg(n)}function Yd(n,e){return n.b=e,n}function UE(n,e){return n.a=e,n}function Zd(n,e){return n.c=e,n}function n0(n,e){return n.d=e,n}function e0(n,e){return n.e=e,n}function jz(n,e){return n.f=e,n}function c6(n,e){return n.a=e,n}function c4(n,e){return n.b=e,n}function u4(n,e){return n.c=e,n}function an(n,e){return n.c=e,n}function Sn(n,e){return n.b=e,n}function dn(n,e){return n.d=e,n}function bn(n,e){return n.e=e,n}function Dhe(n,e){return n.f=e,n}function wn(n,e){return n.g=e,n}function gn(n,e){return n.a=e,n}function pn(n,e){return n.i=e,n}function mn(n,e){return n.j=e,n}function Lhe(n,e){ca(),ic(e,n)}function Nhe(n,e,t){Jbe(n.a,e,t)}function GE(n){$L.call(this,n)}function Vjn(n){Z5e.call(this,n)}function Wjn(n){SIn.call(this,n)}function Ez(n){SIn.call(this,n)}function F1(n){S0.call(this,n)}function Jjn(n){CN.call(this,n)}function Qjn(n){CN.call(this,n)}function Yjn(){DX.call(this,"")}function Li(){this.a=0,this.b=0}function Zjn(){this.b=0,this.a=0}function nEn(n,e){n.b=0,Zb(n,e)}function eEn(n,e){return n.k=e,n}function $he(n,e){return n.j=e,n}function xhe(n,e){n.c=e,n.b=!0}function tEn(){tEn=F,TQn=Xke()}function B1(){B1=F,voe=rke()}function iEn(){iEn=F,Ti=gye()}function Cz(){Cz=F,Oa=z4()}function o4(){o4=F,Udn=cke()}function rEn(){rEn=F,ise=uke()}function Mz(){Mz=F,yc=tEe()}function uf(n){return n.e&&n.e()}function cEn(n){return n.l|n.m<<22}function uEn(n,e){return n.c._b(e)}function oEn(n,e){return rBn(n.b,e)}function MD(n){return n?n.d:null}function Fhe(n){return n?n.g:null}function Bhe(n){return n?n.i:null}function za(n){return ll(n),n.o}function fg(n,e){return n.a+=e,n}function TD(n,e){return n.a+=e,n}function ql(n,e){return n.a+=e,n}function t0(n,e){return n.a+=e,n}function Tz(n,e){for(;n.Bd(e););}function zE(n){this.a=new ap(n)}function sEn(){throw M(new Pe)}function fEn(){throw M(new Pe)}function hEn(){throw M(new Pe)}function lEn(){throw M(new Pe)}function aEn(){throw M(new Pe)}function dEn(){throw M(new Pe)}function Ul(n){this.a=new iN(n)}function bEn(){this.a=new K5(Rln)}function wEn(){this.b=new K5(rln)}function gEn(){this.a=new K5(f1n)}function pEn(){this.b=new K5(Fq)}function mEn(){this.b=new K5(Fq)}function XE(n){this.a=0,this.b=n}function Az(n){zGn(),ILe(this,n)}function s4(n){return z1(n),n.a}function Z9(n){return n.b!=n.d.c}function Sz(n,e){return n.d[e.p]}function vEn(n,e){return XTe(n,e)}function Pz(n,e,t){n.splice(e,t)}function hg(n,e){for(;n.Re(e););}function kEn(n){n.c?Dqn(n):Lqn(n)}function yEn(){throw M(new Pe)}function jEn(){throw M(new Pe)}function EEn(){throw M(new Pe)}function CEn(){throw M(new Pe)}function MEn(){throw M(new Pe)}function TEn(){throw M(new Pe)}function AEn(){throw M(new Pe)}function SEn(){throw M(new Pe)}function PEn(){throw M(new Pe)}function IEn(){throw M(new Pe)}function Rhe(){throw M(new nc)}function Khe(){throw M(new nc)}function n7(n){this.a=new OEn(n)}function OEn(n){Ume(this,n,jje())}function e7(n){return!n||oIn(n)}function t7(n){return Zf[n]!=-1}function _he(){cP!=0&&(cP=0),uP=-1}function DEn(){RK==null&&(RK=[])}function i7(n,e){Cg.call(this,n,e)}function f4(n,e){i7.call(this,n,e)}function LEn(n,e){this.a=n,this.b=e}function NEn(n,e){this.a=n,this.b=e}function $En(n,e){this.a=n,this.b=e}function xEn(n,e){this.a=n,this.b=e}function FEn(n,e){this.a=n,this.b=e}function BEn(n,e){this.a=n,this.b=e}function REn(n,e){this.a=n,this.b=e}function h4(n,e){this.e=n,this.d=e}function Iz(n,e){this.b=n,this.c=e}function KEn(n,e){this.b=n,this.a=e}function _En(n,e){this.b=n,this.a=e}function HEn(n,e){this.b=n,this.a=e}function qEn(n,e){this.b=n,this.a=e}function UEn(n,e){this.a=n,this.b=e}function AD(n,e){this.a=n,this.b=e}function GEn(n,e){this.a=n,this.f=e}function i0(n,e){this.g=n,this.i=e}function je(n,e){this.f=n,this.g=e}function zEn(n,e){this.b=n,this.c=e}function XEn(n){KX(n.dc()),this.c=n}function Hhe(n,e){this.a=n,this.b=e}function VEn(n,e){this.a=n,this.b=e}function WEn(n){this.a=u(Se(n),15)}function Oz(n){this.a=u(Se(n),15)}function JEn(n){this.a=u(Se(n),85)}function VE(n){this.b=u(Se(n),85)}function WE(n){this.b=u(Se(n),51)}function JE(){this.q=new y.Date}function SD(n,e){this.a=n,this.b=e}function QEn(n,e){return Zc(n.b,e)}function r7(n,e){return n.b.Hc(e)}function YEn(n,e){return n.b.Ic(e)}function ZEn(n,e){return n.b.Qc(e)}function nCn(n,e){return n.b.Hc(e)}function eCn(n,e){return n.c.uc(e)}function tCn(n,e){return rt(n.c,e)}function of(n,e){return n.a._b(e)}function iCn(n,e){return n>e&&e<Y5}function u6(n){return n.f.c+n.i.c}function qhe(n){return zPn(),n?aQn:lQn}function ap(n){wFn.call(this,n,0)}function rCn(){iN.call(this,null)}function dp(n){this.c=n,i$n(this)}function Ct(){jTn(this),vo(this)}function fl(){fl=F,pQn=new T0n}function l4(){l4=F,fv=new S0n}function Ob(){Ob=F,n_=new qMn}function QE(){QE=F,SQn=new UMn}function a4(){a4=F,$un=new R0n}function Dz(){i$.call(this,null)}function Xa(){Xa=F,v3=new V0n}function qt(n,e){z1(n),n.a.Nb(e)}function Uhe(n,e){return n.a.Xc(e)}function Ghe(n,e){return n.a.Yc(e)}function PD(n,e){return n.a.$c(e)}function ID(n,e){return n.a._c(e)}function zhe(n,e){return n.Gc(e),n}function Xhe(n,e){return Bi(n,e),n}function Vhe(n,e){aF(_(n.a),e)}function Whe(n,e){aF(_(n.a),e)}function cCn(n,e){return n.Gc(e),n}function Jhe(n,e){return n.a.f=e,n}function uCn(n,e){return n.a.d=e,n}function oCn(n,e){return n.a.g=e,n}function sCn(n,e){return n.a.j=e,n}function Is(n,e){return n.a.a=e,n}function Os(n,e){return n.a.d=e,n}function Ds(n,e){return n.a.e=e,n}function Ls(n,e){return n.a.g=e,n}function c7(n,e){return n.a.f=e,n}function Qhe(n){return n.b=!1,n}function fCn(){fCn=F,BQn=new Z0n}function YE(){YE=F,b_=new bAn}function Lz(){Lz=F,jZn=new zbn}function hCn(){hCn=F,EZn=new Zbn}function Nz(){Nz=F,CZn=new wPn}function $z(){$z=F,Oon=new iwn}function lCn(){lCn=F,LZn=new dwn}function o6(){o6=F,$Zn=new bwn}function u7(){u7=F,RZn=new _wn}function o7(){o7=F,BZn=new Li}function aCn(){aCn=F,qZn=new Mgn}function s6(){s6=F,QZn=new upn}function ZE(){ZE=F,b2=new Ipn}function nC(){nC=F,Jte=new Zmn}function eC(){eC=F,Bq=new bCn}function tC(){tC=F,Rq=new dAn}function f6(){f6=F,Hj=new bIn}function dCn(){Y$n(),this.c=new CD}function bCn(){je.call(this,VXn,0)}function Yhe(n,e,t){Dr(n.d,e.f,t)}function Zhe(n,e,t,i){P9e(n,i,e,t)}function nle(n,e,t,i){nTe(i,n,e,t)}function ele(n,e,t,i){IDe(i,n,e,t)}function h6(n,e){s1(n.c.c,e.b,e)}function r0(n,e){s1(n.c.b,e.c,e)}function tle(n){return n.e.b+n.f.b}function ile(n){return n.e.a+n.f.a}function rle(n){return n.b?n.b:n.a}function cle(n){return(n.c+n.a)/2}function wCn(n,e){return R7e(n.a,e)}function l6(n,e){return n.a=e.g,n}function xz(){xz=F,qdn=new djn}function gCn(){gCn=F,Roe=new hjn}function c0(){c0=F,poe=new nvn}function pCn(){pCn=F,Moe=new lvn}function mCn(){mCn=F,Boe=new fjn}function R1(){R1=F,Ss=new tz}function iC(){iC=F,yO=new de}function a6(){a6=F,MU=new TTn}function Gl(){Gl=F,dE=new ATn}function OD(){OD=F,Zoe=new T6n}function dr(){dr=F,ese=new A6n}function K1(){K1=F,$a=new P5n}function Fz(){Fz=F,n0n=new Z}function rC(n){return u(n,44).ld()}function DD(n){return n.b<n.d.gc()}function ule(n,e){return e.split(n)}function LD(n,e){return Ec(n,e)>0}function ND(n,e){return Ec(n,e)<0}function vCn(n,e){return JL(n.a,e)}function ole(n,e){yOn.call(this,n,e)}function Bz(n){wN(),uSn.call(this,n)}function Rz(n,e){bPn(n,n.length,e)}function s7(n,e){HPn(n,n.length,e)}function d6(n,e){return n.a.get(e)}function kCn(n,e){return Zc(n.e,e)}function Kz(n){return Jn(n),!1}function _z(n){this.a=u(Se(n),229)}function cC(n){In.call(this,n,21)}function uC(n,e){je.call(this,n,e)}function $D(n,e){je.call(this,n,e)}function yCn(n,e){this.b=n,this.a=e}function oC(n,e){this.d=n,this.e=e}function jCn(n,e){this.a=n,this.b=e}function ECn(n,e){this.a=n,this.b=e}function CCn(n,e){this.a=n,this.b=e}function MCn(n,e){this.a=n,this.b=e}function bp(n,e){this.a=n,this.b=e}function TCn(n,e){this.b=n,this.a=e}function Hz(n,e){this.b=n,this.a=e}function qz(n,e){je.call(this,n,e)}function Uz(n,e){je.call(this,n,e)}function lg(n,e){je.call(this,n,e)}function xD(n,e){je.call(this,n,e)}function FD(n,e){je.call(this,n,e)}function BD(n,e){je.call(this,n,e)}function sC(n,e){je.call(this,n,e)}function Gz(n,e){this.b=n,this.a=e}function fC(n,e){je.call(this,n,e)}function zz(n,e){this.b=n,this.a=e}function hC(n,e){je.call(this,n,e)}function ACn(n,e){this.b=n,this.a=e}function Xz(n,e){je.call(this,n,e)}function RD(n,e){je.call(this,n,e)}function f7(n,e){je.call(this,n,e)}function b6(n,e,t){n.splice(e,0,t)}function sle(n,e,t){n.Mb(t)&&e.Cd(t)}function fle(n,e,t){e.Pe(n.a.Ye(t))}function hle(n,e,t){e.Dd(n.a.Ze(t))}function lle(n,e,t){e.Cd(n.a.Kb(t))}function ale(n,e){return Au(n.c,e)}function dle(n,e){return Au(n.e,e)}function lC(n,e){je.call(this,n,e)}function aC(n,e){je.call(this,n,e)}function w6(n,e){je.call(this,n,e)}function Vz(n,e){je.call(this,n,e)}function ei(n,e){je.call(this,n,e)}function dC(n,e){je.call(this,n,e)}function SCn(n,e){this.a=n,this.b=e}function PCn(n,e){this.a=n,this.b=e}function ICn(n,e){this.a=n,this.b=e}function OCn(n,e){this.a=n,this.b=e}function DCn(n,e){this.a=n,this.b=e}function LCn(n,e){this.a=n,this.b=e}function NCn(n,e){this.b=n,this.a=e}function $Cn(n,e){this.b=n,this.a=e}function Wz(n,e){this.b=n,this.a=e}function d4(n,e){this.c=n,this.d=e}function xCn(n,e){this.e=n,this.d=e}function FCn(n,e){this.a=n,this.b=e}function BCn(n,e){this.a=n,this.b=e}function RCn(n,e){this.a=n,this.b=e}function KCn(n,e){this.b=n,this.a=e}function _Cn(n,e){this.b=e,this.c=n}function bC(n,e){je.call(this,n,e)}function h7(n,e){je.call(this,n,e)}function KD(n,e){je.call(this,n,e)}function Jz(n,e){je.call(this,n,e)}function g6(n,e){je.call(this,n,e)}function _D(n,e){je.call(this,n,e)}function HD(n,e){je.call(this,n,e)}function l7(n,e){je.call(this,n,e)}function Qz(n,e){je.call(this,n,e)}function qD(n,e){je.call(this,n,e)}function p6(n,e){je.call(this,n,e)}function Yz(n,e){je.call(this,n,e)}function m6(n,e){je.call(this,n,e)}function v6(n,e){je.call(this,n,e)}function Db(n,e){je.call(this,n,e)}function UD(n,e){je.call(this,n,e)}function GD(n,e){je.call(this,n,e)}function Zz(n,e){je.call(this,n,e)}function a7(n,e){je.call(this,n,e)}function ag(n,e){je.call(this,n,e)}function zD(n,e){je.call(this,n,e)}function wC(n,e){je.call(this,n,e)}function d7(n,e){je.call(this,n,e)}function Lb(n,e){je.call(this,n,e)}function gC(n,e){je.call(this,n,e)}function nX(n,e){je.call(this,n,e)}function XD(n,e){je.call(this,n,e)}function VD(n,e){je.call(this,n,e)}function WD(n,e){je.call(this,n,e)}function JD(n,e){je.call(this,n,e)}function QD(n,e){je.call(this,n,e)}function YD(n,e){je.call(this,n,e)}function ZD(n,e){je.call(this,n,e)}function HCn(n,e){this.b=n,this.a=e}function eX(n,e){je.call(this,n,e)}function qCn(n,e){this.a=n,this.b=e}function UCn(n,e){this.a=n,this.b=e}function GCn(n,e){this.a=n,this.b=e}function tX(n,e){je.call(this,n,e)}function iX(n,e){je.call(this,n,e)}function zCn(n,e){this.a=n,this.b=e}function ble(n,e){return k4(),e!=n}function b7(n){return oe(n.a),n.b}function nL(n){return yCe(n,n.c),n}function XCn(){return tEn(),new TQn}function VCn(){VC(),this.a=new kV}function WCn(){OA(),this.a=new ni}function JCn(){NN(),this.b=new ni}function QCn(n,e){this.b=n,this.d=e}function YCn(n,e){this.a=n,this.b=e}function ZCn(n,e){this.a=n,this.b=e}function nMn(n,e){this.a=n,this.b=e}function eMn(n,e){this.b=n,this.a=e}function rX(n,e){je.call(this,n,e)}function cX(n,e){je.call(this,n,e)}function pC(n,e){je.call(this,n,e)}function u0(n,e){je.call(this,n,e)}function eL(n,e){je.call(this,n,e)}function mC(n,e){je.call(this,n,e)}function uX(n,e){je.call(this,n,e)}function oX(n,e){je.call(this,n,e)}function w7(n,e){je.call(this,n,e)}function sX(n,e){je.call(this,n,e)}function tL(n,e){je.call(this,n,e)}function vC(n,e){je.call(this,n,e)}function iL(n,e){je.call(this,n,e)}function rL(n,e){je.call(this,n,e)}function cL(n,e){je.call(this,n,e)}function uL(n,e){je.call(this,n,e)}function fX(n,e){je.call(this,n,e)}function oL(n,e){je.call(this,n,e)}function hX(n,e){je.call(this,n,e)}function g7(n,e){je.call(this,n,e)}function sL(n,e){je.call(this,n,e)}function lX(n,e){je.call(this,n,e)}function p7(n,e){je.call(this,n,e)}function aX(n,e){je.call(this,n,e)}function tMn(n,e){this.b=n,this.a=e}function iMn(n,e){this.b=n,this.a=e}function rMn(n,e){this.b=n,this.a=e}function cMn(n,e){this.b=n,this.a=e}function dX(n,e){this.a=n,this.b=e}function uMn(n,e){this.a=n,this.b=e}function oMn(n,e){this.a=n,this.b=e}function V(n,e){this.a=n,this.b=e}function k6(n,e){je.call(this,n,e)}function m7(n,e){je.call(this,n,e)}function wp(n,e){je.call(this,n,e)}function y6(n,e){je.call(this,n,e)}function v7(n,e){je.call(this,n,e)}function fL(n,e){je.call(this,n,e)}function kC(n,e){je.call(this,n,e)}function j6(n,e){je.call(this,n,e)}function hL(n,e){je.call(this,n,e)}function yC(n,e){je.call(this,n,e)}function dg(n,e){je.call(this,n,e)}function k7(n,e){je.call(this,n,e)}function E6(n,e){je.call(this,n,e)}function C6(n,e){je.call(this,n,e)}function y7(n,e){je.call(this,n,e)}function jC(n,e){je.call(this,n,e)}function bg(n,e){je.call(this,n,e)}function lL(n,e){je.call(this,n,e)}function sMn(n,e){je.call(this,n,e)}function EC(n,e){je.call(this,n,e)}function fMn(n,e){this.a=n,this.b=e}function hMn(n,e){this.a=n,this.b=e}function lMn(n,e){this.a=n,this.b=e}function aMn(n,e){this.a=n,this.b=e}function dMn(n,e){this.a=n,this.b=e}function bMn(n,e){this.a=n,this.b=e}function bi(n,e){this.a=n,this.b=e}function wMn(n,e){this.a=n,this.b=e}function gMn(n,e){this.a=n,this.b=e}function pMn(n,e){this.a=n,this.b=e}function mMn(n,e){this.a=n,this.b=e}function vMn(n,e){this.a=n,this.b=e}function kMn(n,e){this.a=n,this.b=e}function yMn(n,e){this.b=n,this.a=e}function jMn(n,e){this.b=n,this.a=e}function EMn(n,e){this.b=n,this.a=e}function CMn(n,e){this.b=n,this.a=e}function MMn(n,e){this.a=n,this.b=e}function TMn(n,e){this.a=n,this.b=e}function CC(n,e){je.call(this,n,e)}function AMn(n,e){this.a=n,this.b=e}function SMn(n,e){this.a=n,this.b=e}function gp(n,e){je.call(this,n,e)}function PMn(n,e){this.f=n,this.c=e}function bX(n,e){return Au(n.g,e)}function wle(n,e){return Au(e.b,n)}function IMn(n,e){return wx(n.a,e)}function gle(n,e){return-n.b.af(e)}function ple(n,e){n&&Xe(hE,n,e)}function wX(n,e){n.i=null,kT(n,e)}function mle(n,e,t){yKn(e,oF(n,t))}function vle(n,e,t){yKn(e,oF(n,t))}function kle(n,e){VMe(n.a,u(e,58))}function OMn(n,e){U4e(n.a,u(e,12))}function MC(n,e){this.a=n,this.b=e}function DMn(n,e){this.a=n,this.b=e}function LMn(n,e){this.a=n,this.b=e}function NMn(n,e){this.a=n,this.b=e}function $Mn(n,e){this.a=n,this.b=e}function xMn(n,e){this.d=n,this.b=e}function FMn(n,e){this.e=n,this.a=e}function j7(n,e){this.b=n,this.c=e}function gX(n,e){this.i=n,this.g=e}function pX(n,e){this.d=n,this.e=e}function yle(n,e){cme(new ne(n),e)}function TC(n){return Rk(n.c,n.b)}function Kr(n){return n?n.md():null}function x(n){return n??null}function Ai(n){return typeof n===nB}function Nb(n){return typeof n===i3}function $b(n){return typeof n===dtn}function o0(n,e){return Ec(n,e)==0}function AC(n,e){return Ec(n,e)>=0}function M6(n,e){return Ec(n,e)!=0}function SC(n,e){return jve(n.Kc(),e)}function _1(n,e){return n.Rd().Xb(e)}function BMn(n){return eo(n),n.d.gc()}function PC(n){return F6(n==null),n}function T6(n,e){return n.a+=""+e,n}function Er(n,e){return n.a+=""+e,n}function A6(n,e){return n.a+=""+e,n}function Dc(n,e){return n.a+=""+e,n}function Be(n,e){return n.a+=""+e,n}function mX(n,e){return n.a+=""+e,n}function jle(n){return""+(Jn(n),n)}function RMn(n){Hu(this),f5(this,n)}function KMn(){oJ(),dW.call(this)}function _Mn(n,e){mW.call(this,n,e)}function HMn(n,e){mW.call(this,n,e)}function IC(n,e){mW.call(this,n,e)}function ir(n,e){xt(n,e,n.c.b,n.c)}function wg(n,e){xt(n,e,n.a,n.a.a)}function vX(n){return Ln(n,0),null}function qMn(){this.b=0,this.a=!1}function UMn(){this.b=0,this.a=!1}function GMn(){this.b=new ap(Qb(12))}function zMn(){zMn=F,kYn=Ce(jx())}function XMn(){XMn=F,HZn=Ce(iqn())}function VMn(){VMn=F,lre=Ce(xxn())}function kX(){kX=F,_G(),fun=new de}function sf(n){return n.a=0,n.b=0,n}function WMn(n,e){return n.a=e.g+1,n}function aL(n,e){Kb.call(this,n,e)}function Mn(n,e){Dt.call(this,n,e)}function gg(n,e){gX.call(this,n,e)}function JMn(n,e){T7.call(this,n,e)}function dL(n,e){Y4.call(this,n,e)}function Ue(n,e){iC(),Xe(yO,n,e)}function QMn(n,e){n.q.setTime(id(e))}function Ele(n){y.clearTimeout(n)}function Cle(n){return Se(n),new S6(n)}function YMn(n,e){return x(n)===x(e)}function ZMn(n,e){return n.a.a.a.cc(e)}function bL(n,e){return qo(n.a,0,e)}function yX(n){return Awe(u(n,74))}function pp(n){return wi((Jn(n),n))}function Mle(n){return wi((Jn(n),n))}function nTn(n){return Yc(n.l,n.m,n.h)}function jX(n,e){return jc(n.a,e.a)}function Tle(n,e){return KPn(n.a,e.a)}function Ale(n,e){return bt(n.a,e.a)}function th(n,e){return n.indexOf(e)}function Sle(n,e){return n.j[e.p]==2}function s0(n,e){return n==e?0:n?1:-1}function OC(n){return n<10?"0"+n:""+n}function Vr(n){return typeof n===dtn}function Ple(n){return n==rb||n==Iw}function Ile(n){return n==rb||n==Pw}function eTn(n,e){return jc(n.g,e.g)}function EX(n){return qr(n.b.b,n,0)}function tTn(){rM.call(this,0,0,0,0)}function ih(){CG.call(this,new Ql)}function CX(n,e){F4(n,0,n.length,e)}function Ole(n,e){return nn(n.a,e),e}function Dle(n,e){return xs(),e.a+=n}function Lle(n,e){return xs(),e.a+=n}function Nle(n,e){return xs(),e.c+=n}function $le(n,e){return nn(n.c,e),n}function MX(n,e){return Mo(n.a,e),n}function iTn(n){this.a=XCn(),this.b=n}function rTn(n){this.a=XCn(),this.b=n}function rr(n){this.a=n.a,this.b=n.b}function S6(n){this.a=n,GO.call(this)}function cTn(n){this.a=n,GO.call(this)}function mp(){Ho.call(this,0,0,0,0)}function DC(n){return Mo(new ii,n)}function uTn(n){return jM(u(n,123))}function fo(n){return n.vh()&&n.wh()}function pg(n){return n!=Jf&&n!=Sa}function hl(n){return n==Br||n==Xr}function mg(n){return n==us||n==Vf}function oTn(n){return n==S2||n==A2}function xle(n,e){return jc(n.g,e.g)}function sTn(n,e){return new Y4(e,n)}function Fle(n,e){return new Y4(e,n)}function TX(n){return rbe(n.b.Kc(),n.a)}function wL(n,e){um(n,e),G4(n,n.D)}function gL(n,e,t){aT(n,e),lT(n,t)}function vg(n,e,t){I0(n,e),P0(n,t)}function Ro(n,e,t){eu(n,e),tu(n,t)}function E7(n,e,t){_4(n,e),q4(n,t)}function C7(n,e,t){H4(n,e),U4(n,t)}function fTn(n,e,t){sV.call(this,n,e,t)}function AX(n){PMn.call(this,n,!0)}function hTn(){uC.call(this,"Tail",3)}function lTn(){uC.call(this,"Head",1)}function H1(n){dh(),mve.call(this,n)}function f0(n){rM.call(this,n,n,n,n)}function pL(n){n.c=K(ki,Fn,1,0,5,1)}function SX(n){return n.b&&xF(n),n.a}function PX(n){return n.b&&xF(n),n.c}function Ble(n,e){qf||(n.b=e)}function Rle(n,e){return n[n.length]=e}function Kle(n,e){return n[n.length]=e}function _le(n,e){return Yb(e,Af(n))}function Hle(n,e){return Yb(e,Af(n))}function qle(n,e){return pT(dN(n.d),e)}function Ule(n,e){return pT(dN(n.g),e)}function Gle(n,e){return pT(dN(n.j),e)}function Ni(n,e){Dt.call(this,n.b,e)}function zle(n,e){ve(Sc(n.a),DOn(e))}function Xle(n,e){ve(no(n.a),LOn(e))}function Vle(n,e,t){Ro(t,t.i+n,t.j+e)}function aTn(n,e,t){$t(n.c[e.g],e.g,t)}function Wle(n,e,t){u(n.c,71).Gi(e,t)}function mL(n,e,t){return $t(n,e,t),t}function dTn(n){nu(n.Sf(),new D9n(n))}function kg(n){return n!=null?mt(n):0}function Jle(n){return n==null?0:mt(n)}function P6(n){nt(),Wd.call(this,n)}function bTn(n){this.a=n,qV.call(this,n)}function Mf(){Mf=F,y.Math.log(2)}function Ko(){Ko=F,rl=(pCn(),Moe)}function wTn(){wTn=F,YH=new j5(aU)}function Ie(){Ie=F,new gTn,new Z}function gTn(){new de,new de,new de}function Qle(){throw M(new Kl(QJn))}function Yle(){throw M(new Kl(QJn))}function Zle(){throw M(new Kl(YJn))}function n1e(){throw M(new Kl(YJn))}function vL(n){this.a=n,VE.call(this,n)}function kL(n){this.a=n,VE.call(this,n)}function pTn(n,e){m0(),this.a=n,this.b=e}function e1e(n,e){Se(e),Tg(n).Jc(new Ru)}function Yt(n,e){QL(n.c,n.c.length,e)}function tc(n){return n.a<n.c.c.length}function IX(n){return n.a<n.c.a.length}function mTn(n,e){return n.a?n.b:e.We()}function jc(n,e){return n<e?-1:n>e?1:0}function OX(n,e){return Ec(n,e)>0?n:e}function Yc(n,e,t){return{l:n,m:e,h:t}}function t1e(n,e){n.a!=null&&OMn(e,n.a)}function i1e(n){Zi(n,null),Ii(n,null)}function r1e(n,e,t){return Xe(n.g,t,e)}function yg(n,e,t){return nZ(e,t,n.c)}function c1e(n,e,t){return Xe(n.k,t,e)}function u1e(n,e,t){return GOe(n,e,t),t}function o1e(n,e){return ko(),e.n.b+=n}function vTn(n){nJ.call(this),this.b=n}function DX(n){vV.call(this),this.a=n}function kTn(){uC.call(this,"Range",2)}function LC(n){this.b=n,this.a=new Z}function yTn(n){this.b=new $bn,this.a=n}function jTn(n){n.a=new OO,n.c=new OO}function ETn(n){n.a=new de,n.d=new de}function CTn(n){$N(n,null),xN(n,null)}function MTn(n,e){return XOe(n.a,e,null)}function s1e(n,e){return Xe(n.a,e.a,e)}function Ki(n){return new V(n.a,n.b)}function LX(n){return new V(n.c,n.d)}function f1e(n){return new V(n.c,n.d)}function I6(n,e){return cOe(n.c,n.b,e)}function O(n,e){return n!=null&&Tx(n,e)}function yL(n,e){return Yve(n.Kc(),e)!=-1}function NC(n){return n.Ob()?n.Pb():null}function h1e(n){this.b=(Dn(),new eD(n))}function NX(n){this.a=n,de.call(this)}function TTn(){T7.call(this,null,null)}function ATn(){_C.call(this,null,null)}function STn(){je.call(this,"INSTANCE",0)}function PTn(){LZ(),this.a=new K5(Ion)}function ITn(n){return hh(n,0,n.length)}function l1e(n,e){return new VTn(n.Kc(),e)}function $X(n,e){return n.a.Bc(e)!=null}function OTn(n,e){me(n),n.Gc(u(e,15))}function a1e(n,e,t){n.c.bd(e,u(t,136))}function d1e(n,e,t){n.c.Ui(e,u(t,136))}function DTn(n,e){n.c&&(tW(e),rOn(e))}function b1e(n,e){n.q.setHours(e),G5(n,e)}function w1e(n,e){a0(e,n.a.a.a,n.a.a.b)}function g1e(n,e,t,i){$t(n.a[e.g],t.g,i)}function jL(n,e,t){return n.a[e.g][t.g]}function p1e(n,e){return n.e[e.c.p][e.p]}function m1e(n,e){return n.c[e.c.p][e.p]}function Tf(n,e){return n.a[e.c.p][e.p]}function v1e(n,e){return n.j[e.p]=IMe(e)}function EL(n,e){return n.a.Bc(e)!=null}function k1e(n,e){return $(R(e.a))<=n}function y1e(n,e){return $(R(e.a))>=n}function j1e(n,e){return RJ(n.f,e.Pg())}function vp(n,e){return n.a*e.a+n.b*e.b}function E1e(n,e){return n.a<IV(e)?-1:1}function C1e(n,e){return RJ(n.b,e.Pg())}function M1e(n,e,t){return t?e!=0:e!=n-1}function LTn(n,e,t){n.a=e^1502,n.b=t^LB}function T1e(n,e,t){return n.a=e,n.b=t,n}function rh(n,e){return n.a*=e,n.b*=e,n}function nn(n,e){return Bn(n.c,e),!0}function O6(n,e,t){return $t(n.g,e,t),t}function ti(n,e,t){R7.call(this,n,e,t)}function $C(n,e,t){ti.call(this,n,e,t)}function xX(n,e,t){QC.call(this,n,e,t)}function NTn(n,e,t){QC.call(this,n,e,t)}function $Tn(n,e,t){xX.call(this,n,e,t)}function Tu(n,e,t){ti.call(this,n,e,t)}function xTn(n,e,t){$C.call(this,n,e,t)}function FX(n,e,t){R7.call(this,n,e,t)}function jg(n,e,t){R7.call(this,n,e,t)}function FTn(n,e,t){FX.call(this,n,e,t)}function xC(n){n.j=K(jun,J,319,0,0,1)}function Eg(){this.a=K(ki,Fn,1,8,5,1)}function BX(){this.Bb|=256,this.Bb|=512}function ne(n){this.i=n,this.f=this.i.j}function q1(n){this.c=n,this.a=this.c.a}function Cg(n,e){this.a=n,VE.call(this,e)}function RX(n,e){return H5e(n,new x1,e).a}function KX(n){if(!n)throw M(new Q9)}function _X(n){if(!n)throw M(new Cu)}function HX(){HX=F,HX(),PQn=new F0n}function BTn(){BTn=F,OD(),nse=new T8n}function b4(){b4=F,Dun=new wD(null)}function A1e(n){X7(n,MWn),AA(n,GDe(n))}function RTn(n){n.a=u(Un(n.b.a,4),129)}function KTn(n){n.a=u(Un(n.b.a,4),129)}function _Tn(n){n.b.Qb(),--n.d.f.d,fM(n.d)}function qX(n){this.a=n,H8n.call(this,n.d)}function HTn(n,e){this.a=n,ED.call(this,e)}function qTn(n,e){this.a=n,ED.call(this,e)}function UTn(n,e){this.a=n,ED.call(this,e)}function UX(n,e){this.a=e,ED.call(this,n)}function GTn(n,e){this.a=e,zN.call(this,n)}function zTn(n,e){this.a=n,zN.call(this,e)}function XTn(n,e){this.a=e,WE.call(this,n)}function VTn(n,e){this.a=e,WE.call(this,n)}function re(n,e){return Se(e),new XTn(n,e)}function WTn(n,e){return new k_n(n.a,n.b,e)}function GX(n,e,t){return n.indexOf(e,t)}function FC(n,e){return n.lastIndexOf(e)}function D6(n){return n==null?gu:Jr(n)}function S1e(n){return n==null?null:n.name}function P1e(n){return n.l+n.m*o3+n.h*vd}function I1e(n){return Z9(n.a)?NOn(n):null}function ls(n){X9.call(this,(Jn(n),n))}function mo(n){X9.call(this,(Jn(n),n))}function JTn(n){XO.call(this,u(Se(n),34))}function QTn(n){XO.call(this,u(Se(n),34))}function CL(n){CG.call(this,new VJ(n))}function BC(n){Q3.call(this,n),this.a=n}function zX(n){J3.call(this,n),this.a=n}function XX(n){r4.call(this,n),this.a=n}function YTn(){xC(this),MM(this),this.je()}function ZTn(n){this.a=n,ZO.call(this,n)}function ho(n){return oe(n.a!=null),n.a}function nAn(n,e){return nn(e.a,n.a),n.a}function eAn(n,e){return nn(e.b,n.a),n.a}function h0(n,e){return nn(e.a,n.a),n.a}function M7(n,e,t){return L$(n,e,e,t),n}function RC(n,e){return++n.b,nn(n.a,e)}function VX(n,e){return++n.b,du(n.a,e)}function O1e(n,e){return bt(n.c.d,e.c.d)}function D1e(n,e){return bt(n.c.c,e.c.c)}function L1e(n,e){return bt(n.n.a,e.n.a)}function lu(n,e){return u(ot(n.b,e),15)}function N1e(n,e){return n.n.b=(Jn(e),e)}function $1e(n,e){return n.n.b=(Jn(e),e)}function Au(n,e){return!!e&&n.b[e.g]==e}function L6(n){return tc(n.a)||tc(n.b)}function l0(n){return n.$H||(n.$H=++bNe)}function x1e(n){return n.a!=null?n.a:null}function F1e(n,e){return bt(n.e.b,e.e.b)}function B1e(n,e){return bt(n.e.a,e.e.a)}function R1e(n,e,t){return FDn(n,e,t,n.b)}function WX(n,e,t){return FDn(n,e,t,n.c)}function K1e(n){return xs(),!!n&&!n.dc()}function tAn(){s6(),this.b=new w7n(this)}function KC(){KC=F,bP=new Dt(gXn,0)}function _n(){_n=F,wa=!1,ov=!0}function zl(n){var e;e=n.a,n.a=n.b,n.b=e}function T7(n,e){a6(),this.a=n,this.b=e}function _C(n,e){Gl(),this.b=n,this.c=e}function ML(n,e){nN(),this.f=e,this.d=n}function JX(n,e){BJ(e,n),this.d=n,this.c=e}function QX(n,e){oZ.call(this,n,e,null)}function iAn(n,e,t,i){vW.call(this,n,e,t,i)}function kp(n){this.d=n,ne.call(this,n)}function yp(n){this.c=n,ne.call(this,n)}function A7(n){this.c=n,kp.call(this,n)}function _1e(n){return new Xb(3,n)}function Dh(n){return Co(n,mw),new Gc(n)}function rAn(n){return O4(),parseInt(n)||-1}function H1e(n){return RE(),Ee((lOn(),oQn),n)}function w4(n,e,t){return GX(n,wu(e),t)}function TL(n,e){return new iSn(n,n.gc(),e)}function q1e(n,e){return eN(n.c).Md().Xb(e)}function g4(n,e,t){var i;i=n.fd(e),i.Rb(t)}function YX(n,e,t){u(dk(n,e),21).Fc(t)}function U1e(n,e,t){cx(n.a,t),uA(n.a,e)}function S7(n){O(n,158)&&u(n,158).pi()}function cAn(n){UV.call(this,n,null,null)}function AL(n){Ob(),this.b=n,this.a=!0}function uAn(n){QE(),this.b=n,this.a=!0}function p4(n){return oe(n.b!=0),n.a.a.c}function Ns(n){return oe(n.b!=0),n.c.b.c}function G1e(n,e){return L$(n,e,e+1,""),n}function kt(n,e){return!!n.q&&Zc(n.q,e)}function oAn(n){return n.b=u(VW(n.a),44)}function z1e(n){return n.f!=null?n.f:""+n.g}function SL(n){return n.f!=null?n.f:""+n.g}function X1e(n,e){return n>0?e/(n*n):e*100}function V1e(n,e){return n>0?e*e/n:e*e*100}function xb(n,e){return u(Lf(n.a,e),34)}function W1e(n,e){return ca(),Pn(n,e.e,e)}function J1e(n,e,t){return nC(),t.Mg(n,e)}function Q1e(n){return kl(),n.e.a+n.f.a/2}function Y1e(n,e,t){return kl(),t.e.a-n*e}function Z1e(n){return kl(),n.e.b+n.f.b/2}function nae(n,e,t){return kl(),t.e.b-n*e}function sAn(n){n.d=new cAn(n),n.e=new de}function fAn(){this.a=new C0,this.b=new C0}function hAn(n){this.c=n,this.a=1,this.b=1}function lAn(n){YF(),Syn(this),this.Ff(n)}function eae(n,e,t){YM(),n.pf(e)&&t.Cd(n)}function tae(n,e,t){return nn(e,jBn(n,t))}function a0(n,e,t){return n.a+=e,n.b+=t,n}function iae(n,e,t){return n.a*=e,n.b*=t,n}function ZX(n,e){return n.a=e.a,n.b=e.b,n}function HC(n){return n.a=-n.a,n.b=-n.b,n}function N6(n,e,t){return n.a-=e,n.b-=t,n}function aAn(n){Ct.call(this),c5(this,n)}function dAn(){je.call(this,"GROW_TREE",0)}function bAn(){je.call(this,"POLYOMINO",0)}function lo(n,e,t){Iu.call(this,n,e,t,2)}function rae(n,e,t){k5(Sc(n.a),e,DOn(t))}function wAn(n,e){a6(),T7.call(this,n,e)}function nV(n,e){Gl(),_C.call(this,n,e)}function gAn(n,e){Gl(),nV.call(this,n,e)}function pAn(n,e){Gl(),_C.call(this,n,e)}function cae(n,e){return n.c.Fc(u(e,136))}function uae(n,e,t){k5(no(n.a),e,LOn(t))}function mAn(n){this.c=n,eu(n,0),tu(n,0)}function PL(n,e){Ko(),oM.call(this,n,e)}function vAn(n,e){Ko(),PL.call(this,n,e)}function eV(n,e){Ko(),PL.call(this,n,e)}function tV(n,e){Ko(),oM.call(this,n,e)}function kAn(n,e){Ko(),eV.call(this,n,e)}function yAn(n,e){Ko(),tV.call(this,n,e)}function jAn(n,e){Ko(),oM.call(this,n,e)}function oae(n,e,t){return e.zl(n.e,n.c,t)}function sae(n,e,t){return e.Al(n.e,n.c,t)}function iV(n,e,t){return qA(ak(n,e),t)}function IL(n,e){return na(n.e,u(e,54))}function fae(n){return n==null?null:NDe(n)}function hae(n){return n==null?null:Aje(n)}function lae(n){return n==null?null:Jr(n)}function aae(n){return n==null?null:Jr(n)}function un(n){return F6(n==null||Nb(n)),n}function R(n){return F6(n==null||$b(n)),n}function Oe(n){return F6(n==null||Ai(n)),n}function ll(n){n.o==null&&cMe(n)}function rV(n){if(!n)throw M(new Q9)}function dae(n){if(!n)throw M(new uD)}function oe(n){if(!n)throw M(new nc)}function Fb(n){if(!n)throw M(new Cu)}function EAn(n){if(!n)throw M(new Bo)}function m4(){m4=F,aE=new ujn,new ojn}function Mg(){Mg=F,O2=new lt("root")}function cV(){cxn.call(this),this.Bb|=hr}function bae(n,e){this.d=n,c9n(this),this.b=e}function uV(n,e){i$.call(this,n),this.a=e}function oV(n,e){i$.call(this,n),this.a=e}function sV(n,e,t){VM.call(this,n,e,t,null)}function CAn(n,e,t){VM.call(this,n,e,t,null)}function P7(n,e){this.c=n,h4.call(this,n,e)}function $6(n,e){this.a=n,P7.call(this,n,e)}function fV(n){this.q=new y.Date(id(n))}function MAn(n){return n>8?0:n+1}function TAn(n,e){qf||nn(n.a,e)}function wae(n,e){return o7(),Q4(e.d.i,n)}function gae(n,e){return Hp(),new tUn(e,n)}function pae(n,e,t){return n.Ne(e,t)<=0?t:e}function mae(n,e,t){return n.Ne(e,t)<=0?e:t}function vae(n,e){return u(Lf(n.b,e),143)}function kae(n,e){return u(Lf(n.c,e),233)}function OL(n){return u(sn(n.a,n.b),294)}function AAn(n){return new V(n.c,n.d+n.a)}function SAn(n){return Jn(n),n?1231:1237}function PAn(n){return ko(),oTn(u(n,203))}function Bb(){Bb=F,ron=yn((go(),Gd))}function yae(n,e){e.a?MCe(n,e):EL(n.a,e.b)}function I7(n,e,t){++n.j,n.tj(),t$(n,e,t)}function IAn(n,e,t){++n.j,n.qj(e,n.Zi(e,t))}function OAn(n,e,t){var i;i=n.fd(e),i.Rb(t)}function hV(n,e,t){return t=So(n,e,6,t),t}function lV(n,e,t){return t=So(n,e,3,t),t}function aV(n,e,t){return t=So(n,e,9,t),t}function ch(n,e){return X7(e,xtn),n.f=e,n}function dV(n,e){return(e&et)%n.d.length}function DAn(n,e,t){return zen(n.c,n.b,e,t)}function LAn(n,e){this.c=n,S0.call(this,e)}function NAn(n,e){this.a=n,kyn.call(this,e)}function O7(n,e){this.a=n,kyn.call(this,e)}function Dt(n,e){lt.call(this,n),this.a=e}function bV(n,e){FG.call(this,n),this.a=e}function DL(n,e){FG.call(this,n),this.a=e}function jae(n){VY.call(this,0,0),this.f=n}function $An(n,e,t){return n.a+=hh(e,0,t),n}function D7(n){return!n.a&&(n.a=new C0n),n.a}function wV(n,e){var t;return t=n.e,n.e=e,t}function gV(n,e){var t;return t=e,!!n.Fe(t)}function Eae(n,e){return _n(),n==e?0:n?1:-1}function Rb(n,e){n.a.bd(n.b,e),++n.b,n.c=-1}function L7(n){n.b?L7(n.b):n.f.c.zc(n.e,n.d)}function xAn(n){Hu(n.e),n.d.b=n.d,n.d.a=n.d}function Cae(n,e,t){Xa(),t9n(n,e.Ve(n.a,t))}function pV(n,e,t){return Pp(n,u(e,22),t)}function $s(n,e){return qE(new Array(e),n)}function Mae(n){return Ae(U1(n,32))^Ae(n)}function LL(n){return String.fromCharCode(n)}function Tae(n){return n==null?null:n.message}function Aae(n,e,t){return n.apply(e,t)}function Sae(n,e){var t;t=n[DB],t.call(n,e)}function Pae(n,e){var t;t=n[DB],t.call(n,e)}function Iae(n,e){return o7(),!Q4(e.d.i,n)}function mV(n,e,t,i){rM.call(this,n,e,t,i)}function FAn(){qC.call(this),this.a=new Li}function vV(){this.n=new Li,this.o=new Li}function BAn(){this.b=new Li,this.c=new Z}function RAn(){this.a=new Z,this.b=new Z}function KAn(){this.a=new _U,this.b=new Byn}function kV(){this.b=new Ql,this.a=new Ql}function _An(){this.b=new ni,this.a=new ni}function HAn(){this.b=new de,this.a=new de}function qAn(){this.b=new wEn,this.a=new H3n}function UAn(){this.a=new n8n,this.b=new Lpn}function GAn(){this.a=new Z,this.d=new Z}function qC(){this.n=new cp,this.i=new mp}function zAn(n){this.a=(Co(n,mw),new Gc(n))}function XAn(n){this.a=(Co(n,mw),new Gc(n))}function Oae(n){return n<100?null:new F1(n)}function Dae(n,e){return n.n.a=(Jn(e),e+10)}function Lae(n,e){return n.n.a=(Jn(e),e+10)}function Nae(n,e){return e==n||km(TA(e),n)}function VAn(n,e){return Xe(n.a,e,"")==null}function $ae(n,e){var t;return t=e.qi(n.a),t}function tt(n,e){return n.a+=e.a,n.b+=e.b,n}function mi(n,e){return n.a-=e.a,n.b-=e.b,n}function xae(n){return Pb(n.j.c,0),n.a=-1,n}function yV(n,e,t){return t=So(n,e,11,t),t}function Fae(n,e,t){t!=null&&mT(e,Fx(n,t))}function Bae(n,e,t){t!=null&&vT(e,Fx(n,t))}function jp(n,e,t,i){q.call(this,n,e,t,i)}function jV(n,e,t,i){q.call(this,n,e,t,i)}function WAn(n,e,t,i){jV.call(this,n,e,t,i)}function JAn(n,e,t,i){bM.call(this,n,e,t,i)}function NL(n,e,t,i){bM.call(this,n,e,t,i)}function EV(n,e,t,i){bM.call(this,n,e,t,i)}function QAn(n,e,t,i){NL.call(this,n,e,t,i)}function CV(n,e,t,i){NL.call(this,n,e,t,i)}function Nn(n,e,t,i){EV.call(this,n,e,t,i)}function YAn(n,e,t,i){CV.call(this,n,e,t,i)}function ZAn(n,e,t,i){jW.call(this,n,e,t,i)}function Kb(n,e){Ir.call(this,k8+n+Td+e)}function MV(n,e){return n.jk().wi().ri(n,e)}function TV(n,e){return n.jk().wi().ti(n,e)}function nSn(n,e){return Jn(n),x(n)===x(e)}function An(n,e){return Jn(n),x(n)===x(e)}function Rae(n,e){return n.b.Bd(new ECn(n,e))}function Kae(n,e){return n.b.Bd(new CCn(n,e))}function eSn(n,e){return n.b.Bd(new MCn(n,e))}function _ae(n,e){return n.e=u(n.d.Kb(e),159)}function AV(n,e,t){return n.lastIndexOf(e,t)}function Hae(n,e,t){return bt(n[e.a],n[t.a])}function qae(n,e){return U(e,(cn(),Cj),n)}function Uae(n,e){return jc(e.a.d.p,n.a.d.p)}function Gae(n,e){return jc(n.a.d.p,e.a.d.p)}function zae(n,e){return bt(n.c-n.s,e.c-e.s)}function Xae(n,e){return bt(n.b.e.a,e.b.e.a)}function Vae(n,e){return bt(n.c.e.a,e.c.e.a)}function tSn(n){return n.c?qr(n.c.a,n,0):-1}function Ep(n){return n==Ud||n==tl||n==qc}function SV(n,e){this.c=n,oN.call(this,n,e)}function iSn(n,e,t){this.a=n,JX.call(this,e,t)}function rSn(n){this.c=n,IC.call(this,Ey,0)}function cSn(n,e,t){this.c=e,this.b=t,this.a=n}function N7(n){k4(),this.d=n,this.a=new Eg}function uSn(n){uh(),this.a=(Dn(),new r4(n))}function Wae(n,e){hl(n.f)?QCe(n,e):Sye(n,e)}function oSn(n,e){sbe.call(this,n,n.length,e)}function Jae(n,e){qf||e&&(n.d=e)}function sSn(n,e){return O(e,15)&&xqn(n.c,e)}function Qae(n,e,t){return u(n.c,71).Wk(e,t)}function UC(n,e,t){return u(n.c,71).Xk(e,t)}function Yae(n,e,t){return oae(n,u(e,343),t)}function PV(n,e,t){return sae(n,u(e,343),t)}function Zae(n,e,t){return PKn(n,u(e,343),t)}function fSn(n,e,t){return _ye(n,u(e,343),t)}function x6(n,e){return e==null?null:tw(n.b,e)}function IV(n){return $b(n)?(Jn(n),n):n.ue()}function GC(n){return!isNaN(n)&&!isFinite(n)}function $L(n){jTn(this),vo(this),Bi(this,n)}function _u(n){pL(this),zV(this.c,0,n.Pc())}function _o(n,e,t){this.a=n,this.b=e,this.c=t}function hSn(n,e,t){this.a=n,this.b=e,this.c=t}function lSn(n,e,t){this.d=n,this.b=t,this.a=e}function aSn(n){this.a=n,fl(),vc(Date.now())}function dSn(n){bo(n.a),GJ(n.c,n.b),n.b=null}function xL(){xL=F,Oun=new $0n,AQn=new x0n}function bSn(){bSn=F,Ioe=K(ki,Fn,1,0,5,1)}function wSn(){wSn=F,Voe=K(ki,Fn,1,0,5,1)}function OV(){OV=F,Woe=K(ki,Fn,1,0,5,1)}function uh(){uh=F,new KG((Dn(),Dn(),sr))}function nde(n){return B4(),Ee((yNn(),IQn),n)}function ede(n){return Gu(),Ee((lNn(),xQn),n)}function tde(n){return YT(),Ee((JDn(),HQn),n)}function ide(n){return cT(),Ee((QDn(),qQn),n)}function rde(n){return NA(),Ee((Jxn(),UQn),n)}function cde(n){return bf(),Ee((fNn(),XQn),n)}function ude(n){return Uu(),Ee((sNn(),WQn),n)}function ode(n){return bu(),Ee((hNn(),QQn),n)}function sde(n){return VA(),Ee((zMn(),kYn),n)}function fde(n){return N0(),Ee((ENn(),jYn),n)}function hde(n){return Vp(),Ee((MNn(),CYn),n)}function lde(n){return A5(),Ee((CNn(),AYn),n)}function ade(n){return YE(),Ee((jDn(),SYn),n)}function dde(n){return uT(),Ee((YDn(),GYn),n)}function bde(n){return i5(),Ee((aNn(),pZn),n)}function wde(n){return Vi(),Ee((u$n(),yZn),n)}function gde(n){return nm(),Ee((ANn(),TZn),n)}function pde(n){return dd(),Ee((TNn(),DZn),n)}function DV(n,e){if(!n)throw M(new Gn(e))}function v4(n){if(!n)throw M(new Or(btn))}function FL(n,e){if(n!=e)throw M(new Bo)}function gSn(n,e,t){this.a=n,this.b=e,this.c=t}function LV(n,e,t){this.a=n,this.b=e,this.c=t}function pSn(n,e,t){this.a=n,this.b=e,this.c=t}function zC(n,e,t){this.b=n,this.a=e,this.c=t}function NV(n,e,t){this.b=n,this.c=e,this.a=t}function $V(n,e,t){this.a=n,this.b=e,this.c=t}function XC(n,e,t){this.e=e,this.b=n,this.d=t}function mSn(n,e,t){this.b=n,this.a=e,this.c=t}function mde(n,e,t){return Xa(),n.a.Yd(e,t),e}function BL(n){var e;return e=new ubn,e.e=n,e}function xV(n){var e;return e=new qyn,e.b=n,e}function $7(){$7=F,CP=new sgn,MP=new fgn}function VC(){VC=F,XZn=new xgn,zZn=new Fgn}function xs(){xs=F,YZn=new G2n,ZZn=new z2n}function vde(n){return D0(),Ee((qLn(),fne),n)}function kde(n){return tr(),Ee((XMn(),HZn),n)}function yde(n){return OT(),Ee((PNn(),GZn),n)}function jde(n){return $f(),Ee((SNn(),tne),n)}function Ede(n){return ow(),Ee((o$n(),rne),n)}function Cde(n){return DA(),Ee(($xn(),hne),n)}function Mde(n){return Yp(),Ee((D$n(),lne),n)}function Tde(n){return QM(),Ee((cLn(),ane),n)}function Ade(n){return u5(),Ee((_Ln(),dne),n)}function Sde(n){return bT(),Ee((HLn(),bne),n)}function Pde(n){return o1(),Ee((s$n(),wne),n)}function Ide(n){return pk(),Ee((eLn(),gne),n)}function Ode(n){return jm(),Ee(($$n(),jne),n)}function Dde(n){return pr(),Ee((aFn(),Ene),n)}function Lde(n){return Z4(),Ee((GLn(),Cne),n)}function Nde(n){return vl(),Ee((zLn(),Tne),n)}function $de(n){return KM(),Ee((nLn(),Ane),n)}function xde(n){return Jk(),Ee((N$n(),yne),n)}function Fde(n){return hd(),Ee((ULn(),mne),n)}function Bde(n){return vA(),Ee((L$n(),vne),n)}function Rde(n){return hk(),Ee((tLn(),kne),n)}function Kde(n){return Yo(),Ee((h$n(),Sne),n)}function _de(n){return a1(),Ee((Xxn(),Yte),n)}function Hde(n){return g5(),Ee((XLn(),Zte),n)}function qde(n){return cw(),Ee((INn(),nie),n)}function Ude(n){return T5(),Ee((f$n(),eie),n)}function Gde(n){return gs(),Ee((dFn(),tie),n)}function zde(n){return lh(),Ee((ONn(),iie),n)}function Xde(n){return wk(),Ee((iLn(),rie),n)}function Vde(n){return gr(),Ee((JLn(),uie),n)}function Wde(n){return ST(),Ee((VLn(),oie),n)}function Jde(n){return d5(),Ee((WLn(),sie),n)}function Qde(n){return om(),Ee((QLn(),fie),n)}function Yde(n){return dT(),Ee((YLn(),hie),n)}function Zde(n){return DT(),Ee((ZLn(),lie),n)}function n0e(n){return O0(),Ee((oNn(),Aie),n)}function e0e(n){return n5(),Ee((rLn(),Die),n)}function t0e(n){return sh(),Ee((sLn(),Rie),n)}function i0e(n){return Sf(),Ee((fLn(),_ie),n)}function r0e(n){return lf(),Ee((hLn(),tre),n)}function c0e(n){return M0(),Ee((lLn(),fre),n)}function u0e(n){return Qp(),Ee((BNn(),hre),n)}function o0e(n){return q5(),Ee((VMn(),lre),n)}function s0e(n){return b5(),Ee((nNn(),are),n)}function f0e(n){return w5(),Ee((FNn(),$re),n)}function h0e(n){return FM(),Ee((uLn(),xre),n)}function l0e(n){return yT(),Ee((oLn(),_re),n)}function a0e(n){return wA(),Ee((l$n(),qre),n)}function d0e(n){return Ok(),Ee((eNn(),Gre),n)}function b0e(n){return ZM(),Ee((aLn(),Ure),n)}function w0e(n){return sA(),Ee((xNn(),lce),n)}function g0e(n){return AT(),Ee((tNn(),ace),n)}function p0e(n){return XT(),Ee((iNn(),dce),n)}function m0e(n){return rA(),Ee((rNn(),wce),n)}function v0e(n){return _T(),Ee((cNn(),mce),n)}function k0e(n){return GM(),Ee((dLn(),Rce),n)}function y0e(n){return V4(),Ee((ZDn(),_Zn),n)}function j0e(n){return Vn(),Ee((x$n(),xZn),n)}function E0e(n){return nT(),Ee((uNn(),Kce),n)}function C0e(n){return N$(),Ee((bLn(),_ce),n)}function M0e(n){return R5(),Ee((a$n(),qce),n)}function T0e(n){return eC(),Ee((IDn(),Gce),n)}function A0e(n){return Fk(),Ee((bNn(),Uce),n)}function S0e(n){return tC(),Ee((ODn(),Xce),n)}function P0e(n){return ck(),Ee((wLn(),Vce),n)}function I0e(n){return Yk(),Ee((d$n(),Wce),n)}function O0e(n){return f6(),Ee((DDn(),lue),n)}function D0e(n){return Ak(),Ee((gLn(),aue),n)}function L0e(n){return gf(),Ee((w$n(),mue),n)}function N0e(n){return l1(),Ee((Lxn(),kue),n)}function $0e(n){return Rh(),Ee((F$n(),yue),n)}function x0e(n){return wd(),Ee((B$n(),Aue),n)}function F0e(n){return ci(),Ee((b$n(),zue),n)}function B0e(n){return Nf(),Ee((wNn(),Xue),n)}function R0e(n){return El(),Ee((RNn(),Vue),n)}function K0e(n){return pA(),Ee((R$n(),Wue),n)}function _0e(n){return jl(),Ee((dNn(),Que),n)}function H0e(n){return To(),Ee((KNn(),Zue),n)}function q0e(n){return lw(),Ee((Wxn(),noe),n)}function U0e(n){return Fg(),Ee((g$n(),eoe),n)}function G0e(n){return Oi(),Ee((K$n(),toe),n)}function z0e(n){return zu(),Ee((_$n(),ioe),n)}function X0e(n){return tn(),Ee((p$n(),roe),n)}function V0e(n){return go(),Ee((_Nn(),foe),n)}function W0e(n){return io(),Ee((Vxn(),hoe),n)}function J0e(n){return Gp(),Ee((gNn(),loe),n)}function Q0e(n,e){return Jn(n),n+(Jn(e),e)}function Y0e(n){return RL(),Ee((pLn(),aoe),n)}function Z0e(n){return qT(),Ee((HNn(),doe),n)}function nbe(n){return LT(),Ee((qNn(),goe),n)}function k4(){k4=F,tln=(tn(),Wn),II=Zn}function RL(){RL=F,vdn=new VSn,kdn=new LPn}function ebe(n){return!n.e&&(n.e=new Z),n.e}function KL(n,e){this.c=n,this.a=e,this.b=e-n}function vSn(n,e,t){this.a=n,this.b=e,this.c=t}function _L(n,e,t){this.a=n,this.b=e,this.c=t}function FV(n,e,t){this.a=n,this.b=e,this.c=t}function BV(n,e,t){this.a=n,this.b=e,this.c=t}function kSn(n,e,t){this.a=n,this.b=e,this.c=t}function ySn(n,e,t){this.a=n,this.b=e,this.c=t}function Xl(n,e,t){this.e=n,this.a=e,this.c=t}function jSn(n,e,t){Ko(),tJ.call(this,n,e,t)}function HL(n,e,t){Ko(),RW.call(this,n,e,t)}function RV(n,e,t){Ko(),RW.call(this,n,e,t)}function KV(n,e,t){Ko(),RW.call(this,n,e,t)}function ESn(n,e,t){Ko(),HL.call(this,n,e,t)}function _V(n,e,t){Ko(),HL.call(this,n,e,t)}function CSn(n,e,t){Ko(),_V.call(this,n,e,t)}function MSn(n,e,t){Ko(),RV.call(this,n,e,t)}function TSn(n,e,t){Ko(),KV.call(this,n,e,t)}function qL(n){rM.call(this,n.d,n.c,n.a,n.b)}function HV(n){rM.call(this,n.d,n.c,n.a,n.b)}function qV(n){this.d=n,c9n(this),this.b=nwe(n.d)}function tbe(n){return Cm(),Ee((Nxn(),Poe),n)}function x7(n,e){return Se(n),Se(e),new NEn(n,e)}function Cp(n,e){return Se(n),Se(e),new RSn(n,e)}function ibe(n,e){return Se(n),Se(e),new KSn(n,e)}function rbe(n,e){return Se(n),Se(e),new qEn(n,e)}function UL(n){return oe(n.b!=0),Xo(n,n.a.a)}function cbe(n){return oe(n.b!=0),Xo(n,n.c.b)}function ube(n){return!n.c&&(n.c=new W3),n.c}function y4(n){var e;return e=new Z,b$(e,n),e}function obe(n){var e;return e=new ni,b$(e,n),e}function ASn(n){var e;return e=new GG,A$(e,n),e}function F7(n){var e;return e=new Ct,A$(e,n),e}function u(n,e){return F6(n==null||Tx(n,e)),n}function sbe(n,e,t){TPn.call(this,e,t),this.a=n}function SSn(n,e){this.c=n,this.b=e,this.a=!1}function PSn(){this.a=";,;",this.b="",this.c=""}function ISn(n,e,t){this.b=n,_Mn.call(this,e,t)}function UV(n,e,t){this.c=n,oC.call(this,e,t)}function GV(n,e,t){d4.call(this,n,e),this.b=t}function zV(n,e,t){Bnn(t,0,n,e,t.length,!1)}function Lh(n,e,t,i,r){n.b=e,n.c=t,n.d=i,n.a=r}function XV(n,e,t,i,r){n.d=e,n.c=t,n.a=i,n.b=r}function fbe(n,e){e&&(n.b=e,n.a=(z1(e),e.a))}function B7(n,e){if(!n)throw M(new Gn(e))}function Mp(n,e){if(!n)throw M(new Or(e))}function VV(n,e){if(!n)throw M(new Bjn(e))}function hbe(n,e){return ZE(),jc(n.d.p,e.d.p)}function lbe(n,e){return kl(),bt(n.e.b,e.e.b)}function abe(n,e){return kl(),bt(n.e.a,e.e.a)}function dbe(n,e){return jc(GSn(n.d),GSn(e.d))}function WC(n,e){return e&&vM(n,e.d)?e:null}function bbe(n,e){return e==(tn(),Wn)?n.c:n.d}function WV(n){return Q1(dwe(Vr(n)?ds(n):n))}function wbe(n){return new V(n.c+n.b,n.d+n.a)}function OSn(n){return n!=null&&!lx(n,N9,$9)}function gbe(n,e){return(fBn(n)<<4|fBn(e))&ui}function DSn(n,e,t,i,r){n.c=e,n.d=t,n.b=i,n.a=r}function JV(n){var e,t;e=n.b,t=n.c,n.b=t,n.c=e}function QV(n){var e,t;t=n.d,e=n.a,n.d=e,n.a=t}function pbe(n,e){var t;return t=n.c,PQ(n,e),t}function YV(n,e){return e<0?n.g=-1:n.g=e,n}function JC(n,e){return Mme(n),n.a*=e,n.b*=e,n}function LSn(n,e,t){A$n.call(this,e,t),this.d=n}function R7(n,e,t){pX.call(this,n,e),this.c=t}function QC(n,e,t){pX.call(this,n,e),this.c=t}function ZV(n){OV(),ME.call(this),this.ci(n)}function NSn(){$4(),Bwe.call(this,(R1(),Ss))}function $Sn(n){return nt(),new Nh(0,n)}function xSn(){xSn=F,AU=(Dn(),new nD(IK))}function YC(){YC=F,new hZ((bD(),HK),(dD(),_K))}function FSn(){FSn=F,pun=K(Gi,J,17,256,0,1)}function BSn(){this.b=$(R(rn((qs(),y_))))}function GL(n){this.b=n,this.a=Wa(this.b.a).Od()}function RSn(n,e){this.b=n,this.a=e,GO.call(this)}function KSn(n,e){this.a=n,this.b=e,GO.call(this)}function _Sn(n,e,t){this.a=n,gg.call(this,e,t)}function HSn(n,e,t){this.a=n,gg.call(this,e,t)}function j4(n,e,t){var i;i=new qb(t),df(n,e,i)}function nW(n,e,t){var i;return i=n[e],n[e]=t,i}function ZC(n){var e;return e=n.slice(),o$(e,n)}function nM(n){var e;return e=n.n,n.a.b+e.d+e.a}function qSn(n){var e;return e=n.n,n.e.b+e.d+e.a}function eW(n){var e;return e=n.n,n.e.a+e.b+e.c}function tW(n){n.a.b=n.b,n.b.a=n.a,n.a=n.b=null}function xe(n,e){return xt(n,e,n.c.b,n.c),!0}function mbe(n){return n.a?n.a:vN(n)}function vbe(n){return Lp(),Kh(n)==At(ia(n))}function kbe(n){return Lp(),ia(n)==At(Kh(n))}function d0(n,e){return O5(n,new d4(e.a,e.b))}function ybe(n,e){return yM(),Nx(n,e),new lIn(n,e)}function jbe(n,e){return n.c<e.c?-1:n.c==e.c?0:1}function USn(n){return n.b.c.length-n.e.c.length}function GSn(n){return n.e.c.length-n.g.c.length}function zL(n){return n.e.c.length+n.g.c.length}function K7(n){return n==0||isNaN(n)?n:n<0?-1:1}function Ebe(n){return!fr(n)&&n.c.i.c==n.d.i.c}function Cbe(n){return ko(),(tn(),su).Hc(n.j)}function Mbe(n,e,t){return kl(),t.e.a+t.f.a+n*e}function Tbe(n,e,t){return kl(),t.e.b+t.f.b+n*e}function Abe(n,e,t){return Xe(n.b,u(t.b,18),e)}function Sbe(n,e,t){return Xe(n.b,u(t.b,18),e)}function Pbe(n,e,t){wDe(n.a,n.b,n.c,u(e,166),t)}function iW(n,e,t,i){iZ.call(this,n,e,t,i,0,0)}function zSn(n){OV(),ZV.call(this,n),this.a=-1}function XSn(n,e){TPn.call(this,e,1040),this.a=n}function VSn(){sMn.call(this,"COUNT_CHILDREN",0)}function eM(n,e){j7.call(this,n,e),this.a=this}function Nt(n,e){var t;return t=bN(n,e),t.i=2,t}function tM(n,e){var t;return++n.j,t=n.Cj(e),t}function Re(n,e,t){return n.a=-1,YX(n,e.g,t),n}function Ibe(n,e){return nn(n,new V(e.a,e.b))}function WSn(n){return _p(),K(NI,OS,40,n,0,1)}function JSn(n){return n.e.Rd().gc()*n.c.Rd().gc()}function XL(n,e,t){return new cSn(Kwe(n)._e(),t,e)}function Obe(n,e){IQ(n,e==null?null:(Jn(e),e))}function Dbe(n,e){SQ(n,e==null?null:(Jn(e),e))}function Lbe(n,e){SQ(n,e==null?null:(Jn(e),e))}function F6(n){if(!n)throw M(new i4(null))}function rW(n){if(n.c.e!=n.a)throw M(new Bo)}function cW(n){if(n.e.c!=n.b)throw M(new Bo)}function iM(n){for(Se(n);n.Ob();)n.Pb(),n.Qb()}function VL(n){m0(),this.a=(Dn(),new nD(Se(n)))}function uW(n){this.c=n,this.b=this.c.d.vc().Kc()}function Nbe(n){n.a.ld(),u(n.a.md(),16).gc(),wz()}function QSn(n,e){return n.a+=hh(e,0,e.length),n}function sn(n,e){return Ln(e,n.c.length),n.c[e]}function YSn(n,e){return Ln(e,n.a.length),n.a[e]}function $be(n,e){return Jn(e),kk(e,(Jn(n),n))}function xbe(n,e){return Jn(n),kk(n,(Jn(e),e))}function Va(n,e,t,i,r,c){return jKn(n,e,t,i,r,0,c)}function Fbe(n,e){return $t(e,0,oW(e[0],Ml(1)))}function Bbe(n,e){return Ml(nr(Ml(n.a).a,e.a))}function oW(n,e){return Bbe(u(n,168),u(e,168))}function ZSn(){ZSn=F,mun=K(tb,J,168,256,0,1)}function nPn(){nPn=F,yun=K(ib,J,191,256,0,1)}function ePn(){ePn=F,bun=K(p3,J,222,256,0,1)}function tPn(){tPn=F,gun=K(I8,J,180,128,0,1)}function sW(){Lh(this,!1,!1,!1,!1)}function fW(n){CG.call(this,new Ql),Bi(this,n)}function B6(n){this.a=new ap(n.gc()),Bi(this,n)}function iPn(n){this.c=n,this.a=new dp(this.c.a)}function rPn(n){this.a=n,this.c=new de,o6e(this)}function cPn(){this.d=new V(0,0),this.e=new ni}function Tn(n,e){Xa(),i$.call(this,n),this.a=e}function rM(n,e,t,i){XV(this,n,e,t,i)}function Rbe(n,e,t){return jc(e.d[n.g],t.d[n.g])}function Kbe(n,e,t){return jc(n.d[e.p],n.d[t.p])}function _be(n,e,t){return jc(n.d[e.p],n.d[t.p])}function Hbe(n,e,t){return jc(n.d[e.p],n.d[t.p])}function qbe(n,e,t){return jc(n.d[e.p],n.d[t.p])}function cM(n,e,t){return y.Math.min(t/n,1/e)}function uPn(n,e){return n?0:y.Math.max(0,e-1)}function WL(n,e){return n==null?e==null:An(n,e)}function Ube(n,e){return n==null?e==null:JT(n,e)}function oPn(n){return n.q?n.q:(Dn(),Dn(),Wh)}function sPn(n){return n.c-u(sn(n.a,n.b),294).b}function ao(n){return n.c?n.c.f:n.e.b}function Su(n){return n.c?n.c.g:n.e.a}function Gbe(n,e){return n.a==null&&qqn(n),n.a[e]}function fPn(n){var e;return e=CKn(n),e?fPn(e):n}function uM(n,e){return nt(),new SW(n,e)}function Nh(n,e){nt(),Wd.call(this,n),this.a=e}function oM(n,e){Ko(),LE.call(this,e),this.a=n}function R6(n,e,t){this.a=n,ti.call(this,e,t,2)}function hPn(n){this.b=new Ct,this.a=n,this.c=-1}function lPn(n){JX.call(this,0,0),this.a=n,this.b=0}function sM(n){S0.call(this,n.gc()),Bt(this,n)}function fM(n){n.b?fM(n.b):n.d.dc()&&n.f.c.Bc(n.e)}function hW(n){return Array.isArray(n)&&n.Tm===J2}function JL(n,e){return O(e,22)&&Au(n,u(e,22))}function aPn(n,e){return O(e,22)&&kme(n,u(e,22))}function wr(n,e){return BFn(n,e,J3e(n,n.b.Ce(e)))}function zbe(n,e){return n.a.get(e)!==void 0}function lW(n){return to(n,26)*Z5+to(n,27)*n8}function dPn(n,e){return Rme(new U0n,new b9n(n),e)}function QL(n,e,t){xFn(0,e,n.length),F4(n,0,e,t)}function b0(n,e,t){zb(e,n.c.length),b6(n.c,e,t)}function hM(n,e,t){var i;n&&(i=n.i,i.c=e,i.b=t)}function lM(n,e,t){var i;n&&(i=n.i,i.d=e,i.a=t)}function bPn(n,e,t){var i;for(i=0;i<e;++i)n[i]=t}function Xbe(n,e){var t;for(t=0;t<e;++t)n[t]=-1}function yt(n,e){var t;return t=yn(n),eY(t,e),t}function Vbe(n,e){return!n&&(n=[]),n[n.length]=e,n}function YL(n,e){tt(n.c,e),n.b.c+=e.a,n.b.d+=e.b}function Wbe(n,e){YL(n,mi(new V(e.a,e.b),n.c))}function ZL(n,e){this.b=new Ct,this.a=n,this.c=e}function wPn(){this.b=new twn,this.c=new WIn(this)}function aW(){this.d=new ibn,this.e=new VIn(this)}function dW(){oJ(),this.f=new Ct,this.e=new Ct}function gPn(){ko(),this.k=new de,this.d=new ni}function nN(){nN=F,moe=new Ni((qe(),oo),0)}function pPn(){pPn=F,cQn=new lPn(K(ki,Fn,1,0,5,1))}function Jbe(n,e,t){return fi(n,new bp(e.a,t.a))}function Qbe(n,e,t){return-jc(n.f[e.p],n.f[t.p])}function Ybe(n,e,t){DHn(t,n,1),nn(e,new DCn(t,n))}function Zbe(n,e,t){I5(t,n,1),nn(e,new $Cn(t,n))}function mPn(n,e,t){this.a=n,$C.call(this,e,t,22)}function vPn(n,e,t){this.a=n,$C.call(this,e,t,14)}function kPn(n,e,t,i){Ko(),rDn.call(this,n,e,t,i)}function yPn(n,e,t,i){Ko(),rDn.call(this,n,e,t,i)}function Pu(n,e,t){return n.a=-1,YX(n,e.g+1,t),n}function bW(n,e,t){return t=So(n,u(e,54),7,t),t}function wW(n,e,t){return t=So(n,u(e,54),3,t),t}function Ae(n){return Vr(n)?n|0:cEn(n)}function jPn(n){return nt(),new IN(10,n,0)}function EPn(n){var e;return e=n.f,e||(n.f=n.Dc())}function Tp(n){var e;return e=n.i,e||(n.i=n.bc())}function aM(n){if(n.e.j!=n.d)throw M(new Bo)}function Wa(n){return n.c?n.c:n.c=n.Sd()}function eN(n){return n.d?n.d:n.d=n.Td()}function K6(n,e){return q8e(ak(n,e))?e.zi():null}function nwe(n){return O(n,15)?u(n,15).ed():n.Kc()}function gW(n){return n.Qc(K(ki,Fn,1,n.gc(),5,1))}function CPn(n){return n!=null&&uN(n)&&n.Tm!==J2}function pW(n){return!Array.isArray(n)&&n.Tm===J2}function MPn(n,e){return Se(e),n.a.Jd(e)&&!n.b.Jd(e)}function ewe(n,e){return Yc(n.l&e.l,n.m&e.m,n.h&e.h)}function twe(n,e){return Yc(n.l|e.l,n.m|e.m,n.h|e.h)}function iwe(n,e){return Yc(n.l^e.l,n.m^e.m,n.h^e.h)}function Fs(n,e){return Q1(t_n(Vr(n)?ds(n):n,e))}function w0(n,e){return Q1(Xnn(Vr(n)?ds(n):n,e))}function U1(n,e){return Q1(Bje(Vr(n)?ds(n):n,e))}function rwe(n,e){return Eae((Jn(n),n),(Jn(e),e))}function tN(n,e){return bt((Jn(n),n),(Jn(e),e))}function dM(n){this.b=new Gc(11),this.a=(j0(),n)}function te(n){this.a=(pPn(),cQn),this.d=u(Se(n),51)}function TPn(n,e){this.c=0,this.d=n,this.b=e|64|wh}function mW(n,e){this.e=n,this.d=e&64?e|wh:e}function iN(n){this.b=null,this.a=(j0(),n||Pun)}function APn(n){xC(this),this.g=n,MM(this),this.je()}function Ja(n){K1(),this.a=0,this.b=n-1,this.c=1}function vW(n,e,t,i){this.a=n,VM.call(this,n,e,t,i)}function cwe(n,e,t){n.a.Mb(t)&&(n.b=!0,e.Cd(t))}function kW(n){n.d||(n.d=n.b.Kc(),n.c=n.b.gc())}function E4(n,e){if(n<0||n>=e)throw M(new YG)}function _b(n,e){return $k(n,(Jn(e),new a9n(e)))}function Ap(n,e){return $k(n,(Jn(e),new d9n(e)))}function SPn(n,e,t){return VLe(n,u(e,12),u(t,12))}function PPn(n){return Ou(),u(n,12).g.c.length!=0}function IPn(n){return Ou(),u(n,12).e.c.length!=0}function uwe(n,e){return Hp(),bt(e.a.o.a,n.a.o.a)}function owe(n,e){e.Bb&kc&&!n.a.o&&(n.a.o=e)}function swe(n,e){e.Ug("General 'Rotator",1),jDe(n)}function fwe(n,e,t){e.qf(t,$(R(ee(n.b,t)))*n.a)}function OPn(n,e,t){return Xg(),W4(n,e)&&W4(n,t)}function _6(n){return zu(),!n.Hc(Fl)&&!n.Hc(Pa)}function hwe(n){return n.e?qJ(n.e):null}function H6(n){return Vr(n)?""+n:$qn(n)}function yW(n){var e;for(e=n;e.f;)e=e.f;return e}function lwe(n,e,t){return $t(e,0,oW(e[0],t[0])),e}function Vl(n,e,t,i){var r;r=n.i,r.i=e,r.a=t,r.b=i}function q(n,e,t,i){ti.call(this,n,e,t),this.b=i}function Ci(n,e,t,i,r){c$.call(this,n,e,t,i,r,-1)}function q6(n,e,t,i,r){ok.call(this,n,e,t,i,r,-1)}function bM(n,e,t,i){R7.call(this,n,e,t),this.b=i}function DPn(n){PMn.call(this,n,!1),this.a=!1}function LPn(){sMn.call(this,"LOOKAHEAD_LAYOUT",1)}function NPn(n){this.b=n,kp.call(this,n),RTn(this)}function $Pn(n){this.b=n,A7.call(this,n),KTn(this)}function Hb(n,e,t){this.a=n,jp.call(this,e,t,5,6)}function jW(n,e,t,i){this.b=n,ti.call(this,e,t,i)}function xPn(n,e){this.b=n,H8n.call(this,n.b),this.a=e}function FPn(n){this.a=kRn(n.a),this.b=new _u(n.b)}function EW(n,e){m0(),Hhe.call(this,n,FT(new Ku(e)))}function wM(n,e){return nt(),new BW(n,e,0)}function rN(n,e){return nt(),new BW(6,n,e)}function _i(n,e){for(Jn(e);n.Ob();)e.Cd(n.Pb())}function Zc(n,e){return Ai(e)?AN(n,e):!!wr(n.f,e)}function cN(n,e){return e.Vh()?na(n.b,u(e,54)):e}function awe(n,e){return An(n.substr(0,e.length),e)}function $h(n){return new te(new UX(n.a.length,n.a))}function gM(n){return new V(n.c+n.b/2,n.d+n.a/2)}function dwe(n){return Yc(~n.l&ro,~n.m&ro,~n.h&Il)}function uN(n){return typeof n===vy||typeof n===eB}function Hu(n){n.f=new iTn(n),n.i=new rTn(n),++n.g}function BPn(n){if(!n)throw M(new nc);return n.d}function Sp(n){var e;return e=a5(n),oe(e!=null),e}function bwe(n){var e;return e=I5e(n),oe(e!=null),e}function C4(n,e){var t;return t=n.a.gc(),BJ(e,t),t-e}function fi(n,e){var t;return t=n.a.zc(e,n),t==null}function _7(n,e){return n.a.zc(e,(_n(),wa))==null}function CW(n){return new Tn(null,vwe(n,n.length))}function MW(n,e,t){return cGn(n,u(e,42),u(t,176))}function Pp(n,e,t){return Ks(n.a,e),nW(n.b,e.g,t)}function wwe(n,e,t){E4(t,n.a.c.length),Go(n.a,t,e)}function B(n,e,t,i){xFn(e,t,n.length),gwe(n,e,t,i)}function gwe(n,e,t,i){var r;for(r=e;r<t;++r)n[r]=i}function TW(n,e){var t;for(t=0;t<e;++t)n[t]=!1}function Qa(n,e,t){dh(),this.e=n,this.d=e,this.a=t}function AW(n,e,t){this.c=n,this.a=e,Dn(),this.b=t}function oN(n,e){this.d=n,ne.call(this,n),this.e=e}function ff(n,e,t){return $6e(n,e.g,t),Ks(n.c,e),n}function pwe(n){return Qg(n,(ci(),Br)),n.d=!0,n}function sN(n){return!n.j&&Mfe(n,kSe(n.g,n.b)),n.j}function RPn(n){n.a=null,n.e=null,Hu(n.b),n.d=0,++n.c}function U6(n){Fb(n.b!=-1),Yl(n.c,n.a=n.b),n.b=-1}function SW(n,e){Wd.call(this,1),this.a=n,this.b=e}function mwe(n,e){return n>0?y.Math.log(n/e):-100}function KPn(n,e){return Ec(n,e)<0?-1:Ec(n,e)>0?1:0}function H7(n,e){OTn(n,O(e,160)?e:u(e,2036).Rl())}function PW(n,e){if(n==null)throw M(new sp(e))}function vwe(n,e){return yme(e,n.length),new XSn(n,e)}function IW(n,e){return e?Bi(n,e):!1}function kwe(){return RE(),S(T(uQn,1),G,549,0,[GK])}function G6(n){return n.e==0?n:new Qa(-n.e,n.d,n.a)}function ywe(n,e){return bt(n.c.c+n.c.b,e.c.c+e.c.b)}function q7(n,e){xt(n.d,e,n.b.b,n.b),++n.a,n.c=null}function _Pn(n,e){return n.c?_Pn(n.c,e):nn(n.b,e),n}function jwe(n,e,t){var i;return i=Jb(n,e),qN(n,e,t),i}function HPn(n,e,t){var i;for(i=0;i<e;++i)$t(n,i,t)}function qPn(n,e,t,i,r){for(;e<t;)i[r++]=Xi(n,e++)}function M4(n,e,t,i,r){Qx(n,u(ot(e.k,t),15),t,i,r)}function g0(n,e){qt(_r(n.Oc(),new lpn),new C7n(e))}function Ewe(n,e){return bt(n.e.a+n.f.a,e.e.a+e.f.a)}function Cwe(n,e){return bt(n.e.b+n.f.b,e.e.b+e.f.b)}function fN(n){return y.Math.abs(n.d.e-n.e.e)-n.a}function Mwe(n){return n==St?nj:n==li?"-INF":""+n}function Twe(n){return n==St?nj:n==li?"-INF":""+n}function Awe(n){return Lp(),At(Kh(n))==At(ia(n))}function Swe(n,e,t){return u(n.c.hd(e,u(t,136)),44)}function Pwe(n,e){Ip(n,new qb(e.f!=null?e.f:""+e.g))}function Iwe(n,e){Ip(n,new qb(e.f!=null?e.f:""+e.g))}function Bt(n,e){return n.Si()&&(e=gOn(n,e)),n.Fi(e)}function hN(n,e){return e=n.Yk(null,e),BKn(n,null,e)}function Owe(n,e){++n.j,Jx(n,n.i,e),nCe(n,u(e,343))}function OW(n){n?ZZ(n,(fl(),pQn)):$ge((fl(),n))}function p0(n){this.d=(Jn(n),n),this.a=0,this.c=Ey}function lN(n,e){this.d=j5e(n),this.c=e,this.a=.5*e}function UPn(n){nJ.call(this),this.a=n,nn(n.a,this)}function GPn(){Ql.call(this),this.a=!0,this.b=!0}function zPn(){zPn=F,lQn=new dG(!1),aQn=new dG(!0)}function z6(n){var e;return e=n.g,e||(n.g=new fG(n))}function pM(n){var e;return e=n.k,e||(n.k=new hG(n))}function DW(n){var e;return e=n.k,e||(n.k=new hG(n))}function Dwe(n){var e;return e=n.i,e||(n.i=new x8n(n))}function XPn(n){var e;return e=n.f,e||(n.f=new qX(n))}function aN(n){var e;return e=n.j,e||(n.j=new W8n(n))}function dN(n){var e;return e=n.d,e||(n.d=new VO(n))}function VPn(n,e,t){return nt(),new qOn(n,e,t)}function WPn(n,e){return ek(e,n.c.b.c.gc()),new LEn(n,e)}function LW(n,e){var t;return t=n.a.gc(),ek(e,t),t-1-e}function w(n,e,t){var i;return i=bN(n,e),G$n(t,i),i}function bN(n,e){var t;return t=new YQ,t.j=n,t.d=e,t}function Se(n){if(n==null)throw M(new ip);return n}function qb(n){if(n==null)throw M(new ip);this.a=n}function JPn(n){_G(),this.b=new Z,this.a=n,COe(this,n)}function NW(n){this.b=n,this.a=u(as(this.b.a.e),227)}function m0(){m0=F,uh(),qK=new PN((Dn(),Dn(),sr))}function wN(){wN=F,uh(),uun=new Bz((Dn(),Dn(),hP))}function G1(){G1=F,Hn=ZEe(),On(),tg&&nke()}function mM(n){n.s=NaN,n.c=NaN,kHn(n,n.e),kHn(n,n.j)}function se(n){return(n.i==null&&bh(n),n.i).length}function QPn(n,e){return u(Wa(n.a).Md().Xb(e),44).ld()}function ee(n,e){return Ai(e)?Nc(n,e):Kr(wr(n.f,e))}function Lwe(n,e){return Lp(),n==Kh(e)?ia(e):Kh(e)}function Nwe(n,e,t,i){return t==0||(t-i)/t<n.e||e>=n.g}function $t(n,e,t){return dae(t==null||oPe(n,t)),n[e]=t}function $W(n,e){return zn(e,n.length+1),n.substr(e)}function gN(n,e){for(Jn(e);n.c<n.d;)n.Se(e,n.c++)}function xW(n){this.d=n,this.c=n.a.d.a,this.b=n.a.e.g}function YPn(n){this.c=n,this.a=new Ct,this.b=new Ct}function Lc(n){this.c=new Li,this.a=new Z,this.b=n}function ZPn(n){this.b=new Z,this.a=new Z,this.c=n}function $we(n,e,t){u(e.b,68),nu(e.a,new FV(n,t,e))}function xwe(n,e){return Hp(),u(Cr(n,e.d),15).Fc(e)}function Ip(n,e){var t;t=n.a.length,Jb(n,t),qN(n,t,e)}function nIn(n,e){var t;t=console[n],t.call(console,e)}function eIn(n,e){var t;++n.j,t=n.Ej(),n.rj(n.Zi(t,e))}function pN(n,e,t){var i;return i=T$(n,e,t),yen(n,i)}function v0(n){return!n.d&&(n.d=new ti(jr,n,1)),n.d}function Fwe(n){return!n.a&&(n.a=new ti(Ia,n,4)),n.a}function T4(n,e){return n.a+=String.fromCharCode(e),n}function Ya(n,e){return n.a+=String.fromCharCode(e),n}function FW(n,e,t){this.a=n,FG.call(this,e),this.b=t}function tIn(n,e,t){this.a=n,vJ.call(this,8,e,null,t)}function BW(n,e,t){Wd.call(this,n),this.a=e,this.b=t}function RW(n,e,t){LE.call(this,e),this.a=n,this.b=t}function iIn(n){this.c=n,this.b=this.c.a,this.a=this.c.e}function Bwe(n){this.a=(Jn(Fe),Fe),this.b=n,new tz}function rIn(n){zW(n.a),n.b=K(ki,Fn,1,n.b.length,5,1)}function bo(n){Fb(n.c!=-1),n.d.gd(n.c),n.b=n.c,n.c=-1}function X6(n){return y.Math.sqrt(n.a*n.a+n.b*n.b)}function vM(n,e){return qx(n.c,n.f,e,n.b,n.a,n.e,n.d)}function k0(n,e){return E4(e,n.a.c.length),sn(n.a,e)}function oh(n,e){return x(n)===x(e)||n!=null&&rt(n,e)}function cIn(n){return O(n,102)&&(u(n,19).Bb&kc)!=0}function uIn(n){return as(n),O(n,484)?u(n,484):Jr(n)}function oIn(n){return n?n.dc():!n.Kc().Ob()}function Rwe(n){return rg?AN(rg,n):!1}function Kwe(n){return 0>=n?new Dz:Gme(n-1)}function Hi(n){return!n.a&&n.c?n.c.b:n.a}function KW(n){return O(n,616)?n:new oOn(n)}function z1(n){n.c?z1(n.c):(ea(n),n.d=!0)}function V6(n){n.c?n.c.$e():(n.d=!0,fTe(n))}function sIn(n){n.b=!1,n.c=!1,n.d=!1,n.a=!1}function fIn(n){var e,t;return e=n.c.i.c,t=n.d.i.c,e==t}function _we(n,e){var t;t=n.Ih(e),t>=0?n.ki(t):Pnn(n,e)}function hIn(n,e){n.c<0||n.b.b<n.c?ir(n.b,e):n.a.tf(e)}function Hwe(n,e){ve((!n.a&&(n.a=new O7(n,n)),n.a),e)}function qwe(n,e){YL(u(e.b,68),n),nu(e.a,new IG(n))}function Uwe(n,e){return jc(e.j.c.length,n.j.c.length)}function Gwe(n,e,t){return qp(),t.Lg(n,u(e.ld(),149))}function as(n){if(n==null)throw M(new ip);return n}function Jn(n){if(n==null)throw M(new ip);return n}function zwe(n){if(n.p!=4)throw M(new Cu);return n.e}function Xwe(n){if(n.p!=3)throw M(new Cu);return n.e}function Vwe(n){if(n.p!=3)throw M(new Cu);return n.j}function Wwe(n){if(n.p!=4)throw M(new Cu);return n.j}function Jwe(n){if(n.p!=6)throw M(new Cu);return n.f}function Qwe(n){if(n.p!=6)throw M(new Cu);return n.k}function _W(n){return!n.b&&(n.b=new NE(new aD)),n.b}function y0(n){return n.c==-2&&gfe(n,Uye(n.g,n.b)),n.c}function A4(n,e){var t;return t=bN("",n),t.n=e,t.i=1,t}function kM(n,e,t,i){i0.call(this,n,t),this.a=e,this.f=i}function HW(n,e,t,i){i0.call(this,n,e),this.d=t,this.a=i}function lIn(n,e){h1e.call(this,zme(Se(n),Se(e))),this.a=e}function ii(){vjn.call(this),Pb(this.j.c,0),this.a=-1}function aIn(){unn.call(this,vs,(o4(),Udn)),mIe(this)}function dIn(){unn.call(this,Sd,(rEn(),ise)),hOe(this)}function bIn(){je.call(this,"DELAUNAY_TRIANGULATION",0)}function Ywe(n){return String.fromCharCode.apply(null,n)}function Xe(n,e,t){return Ai(e)?Dr(n,e,t):Vc(n.f,e,t)}function qW(n){return Dn(),n?n.Oe():(j0(),j0(),Iun)}function Zwe(n){return Co(n,cB),oT(nr(nr(5,n),n/10|0))}function wIn(n,e){return YC(),new hZ(new QTn(n),new JTn(e))}function yM(){yM=F,rQn=new lz(S(T(Pd,1),WA,44,0,[]))}function gIn(n){return!n.d&&(n.d=new Q3(n.c.Cc())),n.d}function S4(n){return!n.a&&(n.a=new qjn(n.c.vc())),n.a}function pIn(n){return!n.b&&(n.b=new r4(n.c.ec())),n.b}function xh(n,e){for(;e-- >0;)n=n<<1|(n<0?1:0);return n}function mIn(n,e){var t;return t=new Lc(n),Bn(e.c,t),t}function vIn(n,e){n.u.Hc((zu(),Fl))&&zEe(n,e),h4e(n,e)}function mc(n,e){return x(n)===x(e)||n!=null&&rt(n,e)}function Cr(n,e){return JL(n.a,e)?n.b[u(e,22).g]:null}function nge(){return YE(),S(T(oon,1),G,489,0,[b_])}function ege(){return eC(),S(T($1n,1),G,490,0,[Bq])}function tge(){return tC(),S(T(zce,1),G,558,0,[Rq])}function ige(){return f6(),S(T(tan,1),G,539,0,[Hj])}function jM(n){return!n.n&&(n.n=new q(Ar,n,1,7)),n.n}function mN(n){return!n.c&&(n.c=new q(Qu,n,9,9)),n.c}function UW(n){return!n.c&&(n.c=new Nn(he,n,5,8)),n.c}function rge(n){return!n.b&&(n.b=new Nn(he,n,4,7)),n.b}function U7(n){return n.j.c.length=0,zW(n.c),xae(n.a),n}function P4(n){return n.e==rv&&jfe(n,Y8e(n.g,n.b)),n.e}function G7(n){return n.f==rv&&Cfe(n,q7e(n.g,n.b)),n.f}function Ve(n,e,t,i){return Hxn(n,e,t,!1),BT(n,i),n}function kIn(n,e){this.b=n,oN.call(this,n,e),RTn(this)}function yIn(n,e){this.b=n,SV.call(this,n,e),KTn(this)}function W6(n){this.d=n,this.a=this.d.b,this.b=this.d.c}function GW(n,e){this.b=n,this.c=e,this.a=new dp(this.b)}function Xi(n,e){return zn(e,n.length),n.charCodeAt(e)}function cge(n,e){DY(n,$(yl(e,"x")),$(yl(e,"y")))}function uge(n,e){DY(n,$(yl(e,"x")),$(yl(e,"y")))}function ut(n,e){return ea(n),new Tn(n,new tQ(e,n.a))}function _r(n,e){return ea(n),new Tn(n,new _J(e,n.a))}function Ub(n,e){return ea(n),new uV(n,new ILn(e,n.a))}function EM(n,e){return ea(n),new oV(n,new OLn(e,n.a))}function oge(n,e){return new GIn(u(Se(n),50),u(Se(e),50))}function sge(n,e){return bt(n.d.c+n.d.b/2,e.d.c+e.d.b/2)}function jIn(n,e,t){t.a?tu(n,e.b-n.f/2):eu(n,e.a-n.g/2)}function fge(n,e){return bt(n.g.c+n.g.b/2,e.g.c+e.g.b/2)}function hge(n,e){return $z(),bt((Jn(n),n),(Jn(e),e))}function lge(n){return n!=null&&r7(jO,n.toLowerCase())}function zW(n){var e;for(e=n.Kc();e.Ob();)e.Pb(),e.Qb()}function Tg(n){var e;return e=n.b,!e&&(n.b=e=new N8n(n)),e}function vN(n){var e;return e=Wme(n),e||null}function EIn(n,e){var t,i;return t=n/e,i=wi(t),t>i&&++i,i}function age(n,e,t){var i;i=u(n.d.Kb(t),159),i&&i.Nb(e)}function dge(n,e,t){wIe(n.a,t),zve(t),xCe(n.b,t),$Ie(e,t)}function CM(n,e,t,i){this.a=n,this.c=e,this.b=t,this.d=i}function XW(n,e,t,i){this.c=n,this.b=e,this.a=t,this.d=i}function CIn(n,e,t,i){this.c=n,this.b=e,this.d=t,this.a=i}function Ho(n,e,t,i){this.c=n,this.d=e,this.b=t,this.a=i}function MIn(n,e,t,i){this.a=n,this.d=e,this.c=t,this.b=i}function kN(n,e,t,i){this.a=n,this.e=e,this.d=t,this.c=i}function TIn(n,e,t,i){this.a=n,this.c=e,this.d=t,this.b=i}function yN(n,e,t){this.a=ktn,this.d=n,this.b=e,this.c=t}function Op(n,e,t,i){je.call(this,n,e),this.a=t,this.b=i}function AIn(n,e){this.d=(Jn(n),n),this.a=16449,this.c=e}function SIn(n){this.a=new Z,this.e=K(ye,J,53,n,0,2)}function bge(n){n.Ug("No crossing minimization",1),n.Vg()}function PIn(){ec.call(this,"There is no more element.")}function IIn(n,e,t,i){this.a=n,this.b=e,this.c=t,this.d=i}function OIn(n,e,t,i){this.a=n,this.b=e,this.c=t,this.d=i}function Za(n,e,t,i){this.e=n,this.a=e,this.c=t,this.d=i}function DIn(n,e,t,i){this.a=n,this.c=e,this.d=t,this.b=i}function LIn(n,e,t,i){Ko(),DLn.call(this,e,t,i),this.a=n}function NIn(n,e,t,i){Ko(),DLn.call(this,e,t,i),this.a=n}function jN(n,e,t){var i,r;return i=utn(n),r=e.ti(t,i),r}function al(n){var e,t;return t=(e=new Jd,e),K4(t,n),t}function EN(n){var e,t;return t=(e=new Jd,e),fnn(t,n),t}function wge(n,e){var t;return t=ee(n.f,e),HQ(e,t),null}function $In(n){return!n.b&&(n.b=new q(Vt,n,12,3)),n.b}function xIn(n){return F6(n==null||uN(n)&&n.Tm!==J2),n}function MM(n){return n.n&&(n.e!==Fzn&&n.je(),n.j=null),n}function I4(n){if(eo(n.d),n.d.d!=n.c)throw M(new Bo)}function VW(n){return oe(n.b<n.d.gc()),n.d.Xb(n.c=n.b++)}function vo(n){n.a.a=n.c,n.c.b=n.a,n.a.b=n.c.a=null,n.b=0}function CN(n){this.f=n,this.c=this.f.e,n.f>0&&bKn(this)}function FIn(n,e){this.a=n,bae.call(this,n,u(n.d,15).fd(e))}function gge(n,e){return bt(Su(n)*ao(n),Su(e)*ao(e))}function pge(n,e){return bt(Su(n)*ao(n),Su(e)*ao(e))}function mge(n){return _0(n)&&on(un(z(n,(cn(),Nd))))}function vge(n,e){return Pn(n,u(v(e,(cn(),Cv)),17),e)}function kge(n,e){return u(v(n,(W(),T3)),15).Fc(e),e}function WW(n,e){return n.b=e.b,n.c=e.c,n.d=e.d,n.a=e.a,n}function BIn(n,e,t,i){this.b=n,this.c=i,IC.call(this,e,t)}function yge(n,e,t){n.i=0,n.e=0,e!=t&&yFn(n,e,t)}function jge(n,e,t){n.i=0,n.e=0,e!=t&&jFn(n,e,t)}function Ege(n,e,t){return s6(),J5e(u(ee(n.e,e),529),t)}function Dp(n){var e;return e=n.f,e||(n.f=new h4(n,n.c))}function RIn(n,e){return xg(n.j,e.s,e.c)+xg(e.e,n.s,n.c)}function KIn(n,e){n.e&&!n.e.a&&(Ayn(n.e,e),KIn(n.e,e))}function _In(n,e){n.d&&!n.d.a&&(Ayn(n.d,e),_In(n.d,e))}function Cge(n,e){return-bt(Su(n)*ao(n),Su(e)*ao(e))}function Mge(n){return u(n.ld(),149).Pg()+":"+Jr(n.md())}function HIn(){tF(this,new oG),this.wb=(G1(),Hn),o4()}function qIn(n){this.b=new Z,hi(this.b,this.b),this.a=n}function JW(n,e){new Ct,this.a=new Mu,this.b=n,this.c=e}function j0(){j0=F,Pun=new FU,ZK=new FU,Iun=new D0n}function Dn(){Dn=F,sr=new A0n,Wh=new P0n,hP=new I0n}function QW(){QW=F,RQn=new nbn,_Qn=new aW,KQn=new ebn}function Lp(){Lp=F,mP=new Z,m_=new de,p_=new Z}function TM(n,e){if(n==null)throw M(new sp(e));return n}function AM(n){return!n.a&&(n.a=new q(Qe,n,10,11)),n.a}function ft(n){return!n.q&&(n.q=new q(As,n,11,10)),n.q}function _(n){return!n.s&&(n.s=new q(ku,n,21,17)),n.s}function Tge(n){return Se(n),IRn(new te(re(n.a.Kc(),new En)))}function Age(n,e){return wo(n),wo(e),Fjn(u(n,22),u(e,22))}function nd(n,e,t){var i,r;i=IV(t),r=new AE(i),df(n,e,r)}function MN(n,e,t,i,r,c){ok.call(this,n,e,t,i,r,c?-2:-1)}function UIn(n,e,t,i){pX.call(this,e,t),this.b=n,this.a=i}function GIn(n,e){Vfe.call(this,new iN(n)),this.a=n,this.b=e}function YW(n){this.b=n,this.c=n,n.e=null,n.c=null,this.a=1}function Sge(n){xs();var e;e=u(n.g,10),e.n.a=n.d.c+e.d.b}function O4(){O4=F;var n,e;e=!$8e(),n=new V3,VK=e?new og:n}function TN(n){return Dn(),O(n,59)?new jD(n):new BC(n)}function SM(n){return O(n,16)?new B6(u(n,16)):obe(n.Kc())}function Pge(n){return new HTn(n,n.e.Rd().gc()*n.c.Rd().gc())}function Ige(n){return new qTn(n,n.e.Rd().gc()*n.c.Rd().gc())}function ZW(n){return n&&n.hashCode?n.hashCode():l0(n)}function AN(n,e){return e==null?!!wr(n.f,null):zbe(n.i,e)}function Oge(n,e){var t;return t=$X(n.a,e),t&&(e.d=null),t}function zIn(n,e,t){return n.f?n.f.ef(e,t):!1}function z7(n,e,t,i){$t(n.c[e.g],t.g,i),$t(n.c[t.g],e.g,i)}function SN(n,e,t,i){$t(n.c[e.g],e.g,t),$t(n.b[e.g],e.g,i)}function Dge(n,e,t){return $(R(t.a))<=n&&$(R(t.b))>=e}function XIn(n,e){this.g=n,this.d=S(T(Qh,1),b1,10,0,[e])}function VIn(n){this.c=n,this.b=new Ul(u(Se(new tbn),50))}function WIn(n){this.c=n,this.b=new Ul(u(Se(new ewn),50))}function JIn(n){this.b=n,this.a=new Ul(u(Se(new Nbn),50))}function QIn(){this.b=new ni,this.d=new Ct,this.e=new ZG}function nJ(){this.c=new Li,this.d=new Li,this.e=new Li}function E0(){this.a=new Mu,this.b=(Co(3,mw),new Gc(3))}function Wl(n,e){this.e=n,this.a=ki,this.b=Qqn(e),this.c=e}function PM(n){this.c=n.c,this.d=n.d,this.b=n.b,this.a=n.a}function YIn(n,e,t,i,r,c){this.a=n,k$.call(this,e,t,i,r,c)}function ZIn(n,e,t,i,r,c){this.a=n,k$.call(this,e,t,i,r,c)}function X1(n,e,t,i,r,c,s){return new GN(n.e,e,t,i,r,c,s)}function Lge(n,e,t){return t>=0&&An(n.substr(t,e.length),e)}function nOn(n,e){return O(e,149)&&An(n.b,u(e,149).Pg())}function Nge(n,e){return n.a?e.Gh().Kc():u(e.Gh(),71).Ii()}function eOn(n,e){var t;return t=n.b.Qc(e),WDn(t,n.b.gc()),t}function X7(n,e){if(n==null)throw M(new sp(e));return n}function Hr(n){return n.u||(Zu(n),n.u=new NAn(n,n)),n.u}function PN(n){this.a=(Dn(),O(n,59)?new jD(n):new BC(n))}function au(n){var e;return e=u(Un(n,16),29),e||n.ii()}function IM(n,e){var t;return t=za(n.Rm),e==null?t:t+": "+e}function qo(n,e,t){return Fi(e,t,n.length),n.substr(e,t-e)}function tOn(n,e){qC.call(this),lQ(this),this.a=n,this.c=e}function $ge(n){n&&IM(n,n.ie())}function xge(n){HE(),y.setTimeout(function(){throw n},0)}function Fge(){return YT(),S(T(Bun,1),G,436,0,[o_,Fun])}function Bge(){return cT(),S(T(Kun,1),G,435,0,[Run,s_])}function Rge(){return uT(),S(T(bon,1),G,432,0,[v_,vP])}function Kge(){return V4(),S(T(KZn,1),G,517,0,[dj,L_])}function _ge(){return KM(),S(T(Qsn,1),G,429,0,[fH,Jsn])}function Hge(){return pk(),S(T($sn,1),G,428,0,[WP,Nsn])}function qge(){return QM(),S(T(Asn,1),G,431,0,[Tsn,V_])}function Uge(){return wk(),S(T(qhn,1),G,430,0,[UH,GH])}function Gge(){return n5(),S(T(Oie,1),G,531,0,[r9,i9])}function zge(){return yT(),S(T(Rln,1),G,501,0,[RI,D2])}function Xge(){return sh(),S(T(Bie,1),G,523,0,[mb,y1])}function Vge(){return Sf(),S(T(Kie,1),G,522,0,[Rd,zf])}function Wge(){return lf(),S(T(ere,1),G,528,0,[zw,ja])}function Jge(){return hk(),S(T(Bsn,1),G,488,0,[Fsn,QP])}function Qge(){return GM(),S(T(S1n,1),G,491,0,[$q,A1n])}function Yge(){return N$(),S(T(N1n,1),G,492,0,[D1n,L1n])}function Zge(){return FM(),S(T(Bln,1),G,433,0,[dq,Fln])}function n2e(){return ZM(),S(T(_ln,1),G,434,0,[Kln,vq])}function e2e(){return M0(),S(T(sre,1),G,465,0,[Ea,P2])}function t2e(){return ck(),S(T(x1n,1),G,438,0,[Kq,JI])}function i2e(){return Ak(),S(T(ran,1),G,437,0,[YI,ian])}function r2e(){return RL(),S(T(dO,1),G,347,0,[vdn,kdn])}function OM(n,e,t,i){return t>=0?n.Uh(e,t,i):n.Ch(null,t,i)}function V7(n){return n.b.b==0?n.a.sf():UL(n.b)}function c2e(n){if(n.p!=5)throw M(new Cu);return Ae(n.f)}function u2e(n){if(n.p!=5)throw M(new Cu);return Ae(n.k)}function eJ(n){return x(n.a)===x((D$(),CU))&&rOe(n),n.a}function o2e(n,e){n.b=e,n.c>0&&n.b>0&&(n.g=cM(n.c,n.b,n.a))}function s2e(n,e){n.c=e,n.c>0&&n.b>0&&(n.g=cM(n.c,n.b,n.a))}function iOn(n,e){ufe(this,new V(n.a,n.b)),ofe(this,F7(e))}function C0(){Wfe.call(this,new ap(Qb(12))),KX(!0),this.a=2}function IN(n,e,t){nt(),Wd.call(this,n),this.b=e,this.a=t}function tJ(n,e,t){Ko(),LE.call(this,e),this.a=n,this.b=t}function rOn(n){var e;e=n.c.d.b,n.b=e,n.a=n.c.d,e.a=n.c.d.b=n}function f2e(n){return n.b==0?null:(oe(n.b!=0),Xo(n,n.a.a))}function Nc(n,e){return e==null?Kr(wr(n.f,null)):d6(n.i,e)}function cOn(n,e,t,i,r){return new rF(n,(B4(),i_),e,t,i,r)}function DM(n,e){return zDn(e),Lme(n,K(ye,Ke,28,e,15,1),e)}function LM(n,e){return TM(n,"set1"),TM(e,"set2"),new VEn(n,e)}function h2e(n,e){var t=XK[n.charCodeAt(0)];return t??n}function uOn(n,e){var t,i;return t=e,i=new DO,LGn(n,t,i),i.d}function ON(n,e,t,i){var r;r=new FAn,e.a[t.g]=r,Pp(n.b,i,r)}function l2e(n,e){var t;return t=Ime(n.f,e),tt(HC(t),n.f.d)}function W7(n){var e;_me(n.a),dTn(n.a),e=new IE(n.a),HY(e)}function a2e(n,e){_qn(n,!0),nu(n.e.Rf(),new NV(n,!0,e))}function d2e(n,e){return Lp(),n==At(Kh(e))||n==At(ia(e))}function b2e(n,e){return kl(),u(v(e,(lc(),Sh)),17).a==n}function wi(n){return Math.max(Math.min(n,et),-2147483648)|0}function oOn(n){this.a=u(Se(n),277),this.b=(Dn(),new XX(n))}function sOn(n,e,t){this.i=new Z,this.b=n,this.g=e,this.a=t}function iJ(n,e,t){this.a=new Z,this.e=n,this.f=e,this.c=t}function NM(n,e,t){this.c=new Z,this.e=n,this.f=e,this.b=t}function fOn(n){qC.call(this),lQ(this),this.a=n,this.c=!0}function w2e(n){function e(){}return e.prototype=n||{},new e}function g2e(n){if(n.Ae())return null;var e=n.n;return rP[e]}function J7(n){return n.Db>>16!=3?null:u(n.Cb,27)}function Af(n){return n.Db>>16!=9?null:u(n.Cb,27)}function hOn(n){return n.Db>>16!=6?null:u(n.Cb,74)}function M0(){M0=F,Ea=new cX(s3,0),P2=new cX(f3,1)}function sh(){sh=F,mb=new tX(f3,0),y1=new tX(s3,1)}function Sf(){Sf=F,Rd=new iX(_B,0),zf=new iX("UP",1)}function lOn(){lOn=F,oQn=Ce((RE(),S(T(uQn,1),G,549,0,[GK])))}function aOn(n){var e;return e=new zE(Qb(n.length)),eY(e,n),e}function dOn(n,e){return n.b+=e.b,n.c+=e.c,n.d+=e.d,n.a+=e.a,n}function p2e(n,e){return Zxn(n,e)?(W$n(n),!0):!1}function dl(n,e){if(e==null)throw M(new ip);return F8e(n,e)}function Q7(n,e){var t;t=n.q.getHours(),n.q.setDate(e),G5(n,t)}function rJ(n,e,t){var i;i=n.Ih(e),i>=0?n.bi(i,t):ten(n,e,t)}function bOn(n,e){var t;return t=n.Ih(e),t>=0?n.Wh(t):hF(n,e)}function wOn(n,e){var t;for(Se(e),t=n.a;t;t=t.c)e.Yd(t.g,t.i)}function DN(n,e,t){var i;i=vFn(n,e,t),n.b=new ET(i.c.length)}function Ag(n,e,t){$M(),n&&Xe(yU,n,e),n&&Xe(hE,n,t)}function m2e(n,e){return VC(),_n(),u(e.a,17).a<n}function v2e(n,e){return VC(),_n(),u(e.b,17).a<n}function LN(n,e){return y.Math.abs(n)<y.Math.abs(e)?n:e}function k2e(n){return!n.a&&(n.a=new q(Qe,n,10,11)),n.a.i>0}function cJ(n){var e;return e=n.d,e=n.bj(n.f),ve(n,e),e.Ob()}function gOn(n,e){var t;return t=new fW(e),_Kn(t,n),new _u(t)}function y2e(n){if(n.p!=0)throw M(new Cu);return M6(n.f,0)}function j2e(n){if(n.p!=0)throw M(new Cu);return M6(n.k,0)}function pOn(n){return n.Db>>16!=7?null:u(n.Cb,241)}function D4(n){return n.Db>>16!=6?null:u(n.Cb,241)}function mOn(n){return n.Db>>16!=7?null:u(n.Cb,167)}function At(n){return n.Db>>16!=11?null:u(n.Cb,27)}function Gb(n){return n.Db>>16!=17?null:u(n.Cb,29)}function vOn(n){return n.Db>>16!=3?null:u(n.Cb,155)}function uJ(n){var e;return ea(n),e=new ni,ut(n,new M9n(e))}function kOn(n,e){var t=n.a=n.a||[];return t[e]||(t[e]=n.ve(e))}function E2e(n,e){var t;t=n.q.getHours(),n.q.setMonth(e),G5(n,t)}function yOn(n,e){xC(this),this.f=e,this.g=n,MM(this),this.je()}function jOn(n,e){this.a=n,this.c=Ki(this.a),this.b=new PM(e)}function EOn(n,e,t){this.a=e,this.c=n,this.b=(Se(t),new _u(t))}function COn(n,e,t){this.a=e,this.c=n,this.b=(Se(t),new _u(t))}function MOn(n){this.a=n,this.b=K(Sie,J,2043,n.e.length,0,2)}function TOn(){this.a=new ih,this.e=new ni,this.g=0,this.i=0}function $M(){$M=F,yU=new de,hE=new de,ple(MQn,new wvn)}function AOn(){AOn=F,aie=Pu(new ii,(Vi(),zr),(tr(),bj))}function oJ(){oJ=F,die=Pu(new ii,(Vi(),zr),(tr(),bj))}function SOn(){SOn=F,wie=Pu(new ii,(Vi(),zr),(tr(),bj))}function POn(){POn=F,Lie=Re(new ii,(Vi(),zr),(tr(),x8))}function ko(){ko=F,xie=Re(new ii,(Vi(),zr),(tr(),x8))}function IOn(){IOn=F,Fie=Re(new ii,(Vi(),zr),(tr(),x8))}function NN(){NN=F,Hie=Re(new ii,(Vi(),zr),(tr(),x8))}function J6(n,e,t,i,r,c){return new ml(n.e,e,n.Lj(),t,i,r,c)}function Dr(n,e,t){return e==null?Vc(n.f,null,t):$0(n.i,e,t)}function Zi(n,e){n.c&&du(n.c.g,n),n.c=e,n.c&&nn(n.c.g,n)}function $i(n,e){n.c&&du(n.c.a,n),n.c=e,n.c&&nn(n.c.a,n)}function ic(n,e){n.i&&du(n.i.j,n),n.i=e,n.i&&nn(n.i.j,n)}function Ii(n,e){n.d&&du(n.d.e,n),n.d=e,n.d&&nn(n.d.e,n)}function $N(n,e){n.a&&du(n.a.k,n),n.a=e,n.a&&nn(n.a.k,n)}function xN(n,e){n.b&&du(n.b.f,n),n.b=e,n.b&&nn(n.b.f,n)}function OOn(n,e){$we(n,n.b,n.c),u(n.b.b,68),e&&u(e.b,68).b}function C2e(n,e){return bt(u(n.c,65).c.e.b,u(e.c,65).c.e.b)}function M2e(n,e){return bt(u(n.c,65).c.e.a,u(e.c,65).c.e.a)}function T2e(n){return Y$(),_n(),u(n.a,86).d.e!=0}function xM(n,e){O(n.Cb,184)&&(u(n.Cb,184).tb=null),zc(n,e)}function FN(n,e){O(n.Cb,90)&&hw(Zu(u(n.Cb,90)),4),zc(n,e)}function A2e(n,e){LY(n,e),O(n.Cb,90)&&hw(Zu(u(n.Cb,90)),2)}function S2e(n,e){var t,i;t=e.c,i=t!=null,i&&Ip(n,new qb(e.c))}function DOn(n){var e,t;return t=(o4(),e=new Jd,e),K4(t,n),t}function LOn(n){var e,t;return t=(o4(),e=new Jd,e),K4(t,n),t}function NOn(n){for(var e;;)if(e=n.Pb(),!n.Ob())return e}function P2e(n,e,t){return nn(n.a,(yM(),Nx(e,t),new i0(e,t))),n}function $c(n,e){return dr(),a$(e)?new eM(e,n):new j7(e,n)}function Y7(n){return dh(),Ec(n,0)>=0?ta(n):G6(ta(n1(n)))}function I2e(n){var e;return e=u(ZC(n.b),9),new _o(n.a,e,n.c)}function $On(n,e){var t;return t=u(tw(Dp(n.a),e),16),t?t.gc():0}function xOn(n,e,t){var i;oBn(e,t,n.c.length),i=t-e,Pz(n.c,e,i)}function Jl(n,e,t){oBn(e,t,n.gc()),this.c=n,this.a=e,this.b=t-e}function Np(n){this.c=new Ct,this.b=n.b,this.d=n.c,this.a=n.a}function BN(n){this.a=y.Math.cos(n),this.b=y.Math.sin(n)}function ed(n,e,t,i){this.c=n,this.d=i,$N(this,e),xN(this,t)}function sJ(n,e){Xfe.call(this,new ap(Qb(n))),Co(e,Ozn),this.a=e}function FOn(n,e,t){return new rF(n,(B4(),t_),null,!1,e,t)}function BOn(n,e,t){return new rF(n,(B4(),r_),e,t,null,!1)}function O2e(){return Gu(),S(T(xr,1),G,108,0,[xun,Yr,Aw])}function D2e(){return bu(),S(T(JQn,1),G,472,0,[vf,pa,zs])}function L2e(){return Uu(),S(T(VQn,1),G,471,0,[Mh,ga,Gs])}function N2e(){return bf(),S(T(Sw,1),G,237,0,[bc,Wc,wc])}function $2e(){return i5(),S(T(Pon,1),G,391,0,[E_,j_,C_])}function x2e(){return D0(),S(T(R_,1),G,372,0,[ub,ma,cb])}function F2e(){return u5(),S(T(Psn,1),G,322,0,[B8,pj,Ssn])}function B2e(){return bT(),S(T(Osn,1),G,351,0,[Isn,VP,W_])}function R2e(){return hd(),S(T(pne,1),G,460,0,[Y_,mv,p2])}function K2e(){return Z4(),S(T(sH,1),G,299,0,[uH,oH,mj])}function _2e(){return vl(),S(T(Mne,1),G,311,0,[vj,v2,E3])}function H2e(){return g5(),S(T(Lhn,1),G,390,0,[FH,Dhn,MI])}function q2e(){return gr(),S(T(cie,1),G,463,0,[n9,Vu,Jc])}function U2e(){return ST(),S(T(zhn,1),G,387,0,[Uhn,zH,Ghn])}function G2e(){return d5(),S(T(Xhn,1),G,349,0,[VH,XH,Ij])}function z2e(){return om(),S(T(Whn,1),G,350,0,[WH,Vhn,e9])}function X2e(){return dT(),S(T(Yhn,1),G,352,0,[Qhn,JH,Jhn])}function V2e(){return DT(),S(T(Zhn,1),G,388,0,[QH,Ov,Gw])}function W2e(){return O0(),S(T(Tie,1),G,464,0,[Oj,t9,PI])}function Pf(n){return cc(S(T(Ei,1),J,8,0,[n.i.n,n.n,n.a]))}function J2e(){return b5(),S(T(gln,1),G,392,0,[wln,nq,Lj])}function ROn(){ROn=F,Fre=Pu(new ii,(Qp(),u9),(q5(),uln))}function FM(){FM=F,dq=new uX("DFS",0),Fln=new uX("BFS",1)}function KOn(n,e,t){var i;i=new E3n,i.b=e,i.a=t,++e.b,nn(n.d,i)}function Q2e(n,e,t){var i;i=new rr(t.d),tt(i,n),DY(e,i.a,i.b)}function Y2e(n,e){LTn(n,Ae(vi(w0(e,24),YA)),Ae(vi(e,YA)))}function zb(n,e){if(n<0||n>e)throw M(new Ir(Ptn+n+Itn+e))}function Ln(n,e){if(n<0||n>=e)throw M(new Ir(Ptn+n+Itn+e))}function zn(n,e){if(n<0||n>=e)throw M(new gz(Ptn+n+Itn+e))}function In(n,e){this.b=(Jn(n),n),this.a=e&vw?e:e|64|wh}function fJ(n){var e;return ea(n),e=(j0(),j0(),ZK),fT(n,e)}function Z2e(n,e,t){var i;return i=V5(n,e,!1),i.b<=e&&i.a<=t}function npe(){return nT(),S(T(O1n,1),G,439,0,[xq,I1n,P1n])}function epe(){return _T(),S(T(a1n,1),G,394,0,[l1n,Oq,h1n])}function tpe(){return XT(),S(T(f1n,1),G,445,0,[Bj,qI,Mq])}function ipe(){return rA(),S(T(bce,1),G,456,0,[Tq,Sq,Aq])}function rpe(){return Ok(),S(T(Uln,1),G,393,0,[KI,Hln,qln])}function cpe(){return AT(),S(T(s1n,1),G,300,0,[Cq,o1n,u1n])}function upe(){return jl(),S(T(ldn,1),G,346,0,[uO,M1,M9])}function ope(){return Fk(),S(T(Fq,1),G,444,0,[XI,VI,WI])}function spe(){return Nf(),S(T(Zan,1),G,278,0,[Bv,Jw,Rv])}function fpe(){return Gp(),S(T(mdn,1),G,280,0,[pdn,Yw,aO])}function T0(n){return Se(n),O(n,16)?new _u(u(n,16)):y4(n.Kc())}function hJ(n,e){return n&&n.equals?n.equals(e):x(n)===x(e)}function vi(n,e){return Q1(ewe(Vr(n)?ds(n):n,Vr(e)?ds(e):e))}function hf(n,e){return Q1(twe(Vr(n)?ds(n):n,Vr(e)?ds(e):e))}function RN(n,e){return Q1(iwe(Vr(n)?ds(n):n,Vr(e)?ds(e):e))}function hpe(n,e){var t;return t=(Jn(n),n).g,rV(!!t),Jn(e),t(e)}function _On(n,e){var t,i;return i=C4(n,e),t=n.a.fd(i),new zEn(n,t)}function lpe(n){return n.Db>>16!=6?null:u(dF(n),241)}function ape(n){if(n.p!=2)throw M(new Cu);return Ae(n.f)&ui}function dpe(n){if(n.p!=2)throw M(new Cu);return Ae(n.k)&ui}function E(n){return oe(n.a<n.c.c.length),n.b=n.a++,n.c.c[n.b]}function bpe(n,e){n.b=n.b|e.b,n.c=n.c|e.c,n.d=n.d|e.d,n.a=n.a|e.a}function wpe(n,e){var t;t=$(R(n.a.of((qe(),iO)))),tzn(n,e,t)}function HOn(n,e){Qa.call(this,1,2,S(T(ye,1),Ke,28,15,[n,e]))}function qOn(n,e,t){Wd.call(this,25),this.b=n,this.a=e,this.c=t}function yo(n){nt(),Wd.call(this,n),this.c=!1,this.a=!1}function gpe(n){return n.a==($4(),TO)&&mfe(n,IAe(n.g,n.b)),n.a}function $p(n){return n.d==($4(),TO)&&kfe(n,PPe(n.g,n.b)),n.d}function ppe(n,e){return r5(),n.c==e.c?bt(e.d,n.d):bt(e.c,n.c)}function mpe(n,e){return r5(),n.c==e.c?bt(e.d,n.d):bt(n.c,e.c)}function vpe(n,e){return r5(),n.c==e.c?bt(n.d,e.d):bt(n.c,e.c)}function kpe(n,e){return r5(),n.c==e.c?bt(n.d,e.d):bt(e.c,n.c)}function lJ(n,e){return aPn(n.a,e)?nW(n.b,u(e,22).g,null):null}function ype(n){return nr(Fs(vc(to(n,32)),32),vc(to(n,32)))}function aJ(n){return n.b==null||n.b.length==0?"n_"+n.a:"n_"+n.b}function td(n){return n.c==null||n.c.length==0?"n_"+n.g:"n_"+n.c}function UOn(n,e){var t;for(t=n+"";t.length<e;)t="0"+t;return t}function jpe(n,e){var t;t=u(ee(n.g,e),60),nu(e.d,new BCn(n,t))}function Epe(n,e){var t,i;return t=XRn(n),i=XRn(e),t<i?-1:t>i?1:0}function GOn(n,e){var t,i;return t=s$(e),i=t,u(ee(n.c,i),17).a}function KN(n,e,t){var i;i=n.d[e.p],n.d[e.p]=n.d[t.p],n.d[t.p]=i}function Cpe(n,e,t){var i;n.n&&e&&t&&(i=new uvn,nn(n.e,i))}function _N(n,e){if(fi(n.a,e),e.d)throw M(new ec(nXn));e.d=n}function dJ(n,e){this.a=new Z,this.d=new Z,this.f=n,this.c=e}function zOn(){this.c=new PTn,this.a=new $Ln,this.b=new Xyn,lCn()}function XOn(){qp(),this.b=new de,this.a=new de,this.c=new Z}function VOn(n,e,t){this.d=n,this.j=e,this.e=t,this.o=-1,this.p=3}function WOn(n,e,t){this.d=n,this.k=e,this.f=t,this.o=-1,this.p=5}function JOn(n,e,t,i,r,c){dQ.call(this,n,e,t,i,r),c&&(this.o=-2)}function QOn(n,e,t,i,r,c){bQ.call(this,n,e,t,i,r),c&&(this.o=-2)}function YOn(n,e,t,i,r,c){OJ.call(this,n,e,t,i,r),c&&(this.o=-2)}function ZOn(n,e,t,i,r,c){pQ.call(this,n,e,t,i,r),c&&(this.o=-2)}function nDn(n,e,t,i,r,c){DJ.call(this,n,e,t,i,r),c&&(this.o=-2)}function eDn(n,e,t,i,r,c){wQ.call(this,n,e,t,i,r),c&&(this.o=-2)}function tDn(n,e,t,i,r,c){gQ.call(this,n,e,t,i,r),c&&(this.o=-2)}function iDn(n,e,t,i,r,c){LJ.call(this,n,e,t,i,r),c&&(this.o=-2)}function rDn(n,e,t,i){LE.call(this,t),this.b=n,this.c=e,this.d=i}function cDn(n,e){this.f=n,this.a=($4(),MO),this.c=MO,this.b=e}function uDn(n,e){this.g=n,this.d=($4(),TO),this.a=TO,this.b=e}function bJ(n,e){!n.c&&(n.c=new Rt(n,0)),HA(n.c,(at(),F9),e)}function Mpe(n,e){return oMe(n,e,O(e,102)&&(u(e,19).Bb&hr)!=0)}function Tpe(n,e){return KPn(vc(n.q.getTime()),vc(e.q.getTime()))}function oDn(n){return XL(n.e.Rd().gc()*n.c.Rd().gc(),16,new O8n(n))}function Ape(n){return!!n.u&&Sc(n.u.a).i!=0&&!(n.n&&Ix(n.n))}function Spe(n){return!!n.a&&no(n.a.a).i!=0&&!(n.b&&Ox(n.b))}function wJ(n,e){return e==0?!!n.o&&n.o.f!=0:Cx(n,e)}function Ppe(n,e,t){var i;return i=u(n.Zb().xc(e),16),!!i&&i.Hc(t)}function sDn(n,e,t){var i;return i=u(n.Zb().xc(e),16),!!i&&i.Mc(t)}function fDn(n,e){var t;return t=1-e,n.a[t]=jT(n.a[t],t),jT(n,e)}function hDn(n,e){var t,i;return i=vi(n,mr),t=Fs(e,32),hf(t,i)}function lDn(n,e,t){var i;i=(Se(n),new _u(n)),O7e(new EOn(i,e,t))}function Z7(n,e,t){var i;i=(Se(n),new _u(n)),D7e(new COn(i,e,t))}function fc(n,e,t,i,r,c){return Hxn(n,e,t,c),CY(n,i),MY(n,r),n}function aDn(n,e,t,i){return n.a+=""+qo(e==null?gu:Jr(e),t,i),n}function xi(n,e){this.a=n,Xv.call(this,n),zb(e,n.gc()),this.b=e}function dDn(n){this.a=K(ki,Fn,1,QQ(y.Math.max(8,n))<<1,5,1)}function nk(n){return u(xf(n,K(Qh,b1,10,n.c.length,0,1)),199)}function fh(n){return u(xf(n,K(O_,rR,18,n.c.length,0,1)),483)}function bDn(n){return n.a?n.e.length==0?n.a.a:n.a.a+(""+n.e):n.c}function Q6(n){for(;n.d>0&&n.a[--n.d]==0;);n.a[n.d++]==0&&(n.e=0)}function wDn(n){return oe(n.b.b!=n.d.a),n.c=n.b=n.b.b,--n.a,n.c.c}function Ipe(n,e,t){n.a=e,n.c=t,n.b.a.$b(),vo(n.d),Pb(n.e.a.c,0)}function gDn(n,e){var t;n.e=new uz,t=aw(e),Yt(t,n.c),Iqn(n,t,0)}function ri(n,e,t,i){var r;r=new nG,r.a=e,r.b=t,r.c=i,xe(n.a,r)}function Q(n,e,t,i){var r;r=new nG,r.a=e,r.b=t,r.c=i,xe(n.b,r)}function pDn(n,e,t){if(n<0||e<n||e>t)throw M(new Ir(qje(n,e,t)))}function ek(n,e){if(n<0||n>=e)throw M(new Ir(kEe(n,e)));return n}function Ope(n){if(!("stack"in n))try{throw n}catch{}return n}function Sg(n){return s6(),O(n.g,10)?u(n.g,10):null}function Dpe(n){return Tg(n).dc()?!1:(e1e(n,new Pr),!0)}function id(n){var e;return Vr(n)?(e=n,e==-0?0:e):X4e(n)}function mDn(n,e){return O(e,44)?xx(n.a,u(e,44)):!1}function vDn(n,e){return O(e,44)?xx(n.a,u(e,44)):!1}function kDn(n,e){return O(e,44)?xx(n.a,u(e,44)):!1}function gJ(n){var e;return z1(n),e=new L0n,hg(n.a,new j9n(e)),e}function pJ(){var n,e,t;return e=(t=(n=new Jd,n),t),nn(n0n,e),e}function BM(n){var e;return z1(n),e=new N0n,hg(n.a,new E9n(e)),e}function Lpe(n,e){return n.a<=n.b?(e.Dd(n.a++),!0):!1}function yDn(n){P$.call(this,n,(B4(),e_),null,!1,null,!1)}function jDn(){jDn=F,SYn=Ce((YE(),S(T(oon,1),G,489,0,[b_])))}function EDn(){EDn=F,eln=wIn(Y(1),Y(4)),nln=wIn(Y(1),Y(2))}function Npe(n,e){return new _L(e,N6(Ki(e.e),n,n),(_n(),!0))}function RM(n){return new Gc((Co(n,cB),oT(nr(nr(5,n),n/10|0))))}function $pe(n){return XL(n.e.Rd().gc()*n.c.Rd().gc(),273,new I8n(n))}function CDn(n){return u(xf(n,K(FZn,DXn,12,n.c.length,0,1)),2042)}function xpe(n){return ko(),!fr(n)&&!(!fr(n)&&n.c.i.c==n.d.i.c)}function Fpe(n,e){return _p(),u(v(e,(lc(),I2)),17).a>=n.gc()}function Y6(n,e){vLe(e,n),JV(n.d),JV(u(v(n,(cn(),mI)),214))}function HN(n,e){kLe(e,n),QV(n.d),QV(u(v(n,(cn(),mI)),214))}function Bpe(n,e,t){n.d&&du(n.d.e,n),n.d=e,n.d&&b0(n.d.e,t,n)}function Rpe(n,e,t){return t.f.c.length>0?MW(n.a,e,t):MW(n.b,e,t)}function Kpe(n,e,t){var i;i=i9e();try{return Aae(n,e,t)}finally{D3e(i)}}function A0(n,e){var t,i;return t=dl(n,e),i=null,t&&(i=t.pe()),i}function Z6(n,e){var t,i;return t=dl(n,e),i=null,t&&(i=t.se()),i}function L4(n,e){var t,i;return t=Jb(n,e),i=null,t&&(i=t.se()),i}function bl(n,e){var t,i;return t=dl(n,e),i=null,t&&(i=gnn(t)),i}function _pe(n,e,t){var i;return i=wm(t),FA(n.g,i,e),FA(n.i,e,t),e}function mJ(n,e,t){this.d=new $7n(this),this.e=n,this.i=e,this.f=t}function MDn(n,e,t,i){this.e=null,this.c=n,this.d=e,this.a=t,this.b=i}function TDn(n,e,t,i){ETn(this),this.c=n,this.e=e,this.f=t,this.b=i}function vJ(n,e,t,i){this.d=n,this.n=e,this.g=t,this.o=i,this.p=-1}function ADn(n,e,t,i){return O(t,59)?new iAn(n,e,t,i):new vW(n,e,t,i)}function N4(n){return O(n,16)?u(n,16).dc():!n.Kc().Ob()}function SDn(n){if(n.e.g!=n.b)throw M(new Bo);return!!n.c&&n.d>0}function be(n){return oe(n.b!=n.d.c),n.c=n.b,n.b=n.b.a,++n.a,n.c.c}function kJ(n,e){Jn(e),$t(n.a,n.c,e),n.c=n.c+1&n.a.length-1,JRn(n)}function V1(n,e){Jn(e),n.b=n.b-1&n.a.length-1,$t(n.a,n.b,e),JRn(n)}function PDn(n){var e;e=n.Gh(),this.a=O(e,71)?u(e,71).Ii():e.Kc()}function Hpe(n){return new In(Ame(u(n.a.md(),16).gc(),n.a.ld()),16)}function IDn(){IDn=F,Gce=Ce((eC(),S(T($1n,1),G,490,0,[Bq])))}function ODn(){ODn=F,Xce=Ce((tC(),S(T(zce,1),G,558,0,[Rq])))}function DDn(){DDn=F,lue=Ce((f6(),S(T(tan,1),G,539,0,[Hj])))}function qpe(){return dd(),S(T(Lon,1),G,389,0,[Ow,Don,P_,I_])}function Upe(){return B4(),S(T(lP,1),G,304,0,[e_,t_,i_,r_])}function Gpe(){return Vp(),S(T(EYn,1),G,332,0,[uj,cj,oj,sj])}function zpe(){return A5(),S(T(TYn,1),G,406,0,[fj,wP,gP,hj])}function Xpe(){return N0(),S(T(yYn,1),G,417,0,[rj,ij,a_,d_])}function Vpe(){return nm(),S(T(MZn,1),G,416,0,[rb,Iw,Pw,a2])}function Wpe(){return $f(),S(T(ene,1),G,421,0,[j3,lv,av,B_])}function Jpe(){return OT(),S(T(UZn,1),G,371,0,[F_,HP,qP,wj])}function Qpe(){return cw(),S(T(RH,1),G,203,0,[TI,BH,S2,A2])}function Ype(){return lh(),S(T(Hhn,1),G,284,0,[k1,_hn,HH,qH])}function Zpe(n){var e;return n.j==(tn(),ae)&&(e=mHn(n),Au(e,Zn))}function n3e(n,e){var t;t=e.a,Zi(t,e.c.d),Ii(t,e.d.d),nw(t.a,n.n)}function yJ(n,e){var t;return t=u(Lf(n.b,e),67),!t&&(t=new Ct),t}function xp(n){return s6(),O(n.g,154)?u(n.g,154):null}function e3e(n){n.a=null,n.e=null,Pb(n.b.c,0),Pb(n.f.c,0),n.c=null}function KM(){KM=F,fH=new Zz(qm,0),Jsn=new Zz("TOP_LEFT",1)}function n5(){n5=F,r9=new eX("UPPER",0),i9=new eX("LOWER",1)}function t3e(n,e){return vp(new V(e.e.a+e.f.a/2,e.e.b+e.f.b/2),n)}function LDn(n,e){return u(ho(_b(u(ot(n.k,e),15).Oc(),b2)),113)}function NDn(n,e){return u(ho(Ap(u(ot(n.k,e),15).Oc(),b2)),113)}function i3e(){return Qp(),S(T(rln,1),G,405,0,[LI,c9,u9,o9])}function r3e(){return w5(),S(T(xln,1),G,353,0,[aq,BI,lq,hq])}function c3e(){return sA(),S(T(c1n,1),G,354,0,[Eq,i1n,r1n,t1n])}function u3e(){return go(),S(T(I9,1),G,386,0,[rE,Gd,iE,Qw])}function o3e(){return To(),S(T(Yue,1),G,291,0,[nE,nl,Ta,Zj])}function s3e(){return El(),S(T(aU,1),G,223,0,[lU,Yj,Kv,F3])}function f3e(){return qT(),S(T(Cdn,1),G,320,0,[wU,ydn,Edn,jdn])}function h3e(){return LT(),S(T(woe,1),G,415,0,[gU,Tdn,Mdn,Adn])}function l3e(n){return $M(),Zc(yU,n)?u(ee(yU,n),341).Qg():null}function Uo(n,e,t){return e<0?hF(n,t):u(t,69).wk().Bk(n,n.hi(),e)}function a3e(n,e,t){var i;return i=wm(t),FA(n.j,i,e),Xe(n.k,e,t),e}function d3e(n,e,t){var i;return i=wm(t),FA(n.d,i,e),Xe(n.e,e,t),e}function $Dn(n){var e,t;return e=(B1(),t=new HO,t),n&&AA(e,n),e}function jJ(n){var e;return e=n.aj(n.i),n.i>0&&Ic(n.g,0,e,0,n.i),e}function xDn(n,e){var t;for(t=n.j.c.length;t<e;t++)nn(n.j,n.Ng())}function FDn(n,e,t,i){var r;return r=i[e.g][t.g],$(R(v(n.a,r)))}function BDn(n,e){iC();var t;return t=u(ee(yO,n),57),!t||t.fk(e)}function b3e(n){if(n.p!=1)throw M(new Cu);return Ae(n.f)<<24>>24}function w3e(n){if(n.p!=1)throw M(new Cu);return Ae(n.k)<<24>>24}function g3e(n){if(n.p!=7)throw M(new Cu);return Ae(n.k)<<16>>16}function p3e(n){if(n.p!=7)throw M(new Cu);return Ae(n.f)<<16>>16}function Pg(n,e){return e.e==0||n.e==0?O8:(Am(),vF(n,e))}function RDn(n,e){return x(e)===x(n)?"(this Map)":e==null?gu:Jr(e)}function m3e(n,e,t){return tN(R(Kr(wr(n.f,e))),R(Kr(wr(n.f,t))))}function v3e(n,e,t){var i;i=u(ee(n.g,t),60),nn(n.a.c,new bi(e,i))}function KDn(n,e,t){n.i=0,n.e=0,e!=t&&(jFn(n,e,t),yFn(n,e,t))}function k3e(n,e,t,i,r){var c;c=yMe(r,t,i),nn(e,dEe(r,c)),rje(n,r,e)}function EJ(n,e,t,i,r){this.i=n,this.a=e,this.e=t,this.j=i,this.f=r}function _Dn(n,e){nJ.call(this),this.a=n,this.b=e,nn(this.a.b,this)}function HDn(n){this.b=new de,this.c=new de,this.d=new de,this.a=n}function qDn(n,e){var t;return t=new lp,n.Gd(t),t.a+="..",e.Hd(t),t.a}function UDn(n,e){var t;for(t=e;t;)a0(n,t.i,t.j),t=At(t);return n}function GDn(n,e,t){var i;return i=wm(t),Xe(n.b,i,e),Xe(n.c,e,t),e}function wl(n){var e;for(e=0;n.Ob();)n.Pb(),e=nr(e,1);return oT(e)}function Fh(n,e){dr();var t;return t=u(n,69).vk(),kje(t,e),t.xl(e)}function y3e(n,e,t){if(t){var i=t.oe();n.a[e]=i(t)}else delete n.a[e]}function CJ(n,e){var t;t=n.q.getHours(),n.q.setFullYear(e+fa),G5(n,t)}function j3e(n,e){return u(e==null?Kr(wr(n.f,null)):d6(n.i,e),288)}function MJ(n,e){return n==(Vn(),zt)&&e==zt?4:n==zt||e==zt?8:32}function _M(n,e,t){return RA(n,e,t,O(e,102)&&(u(e,19).Bb&hr)!=0)}function E3e(n,e,t){return Om(n,e,t,O(e,102)&&(u(e,19).Bb&hr)!=0)}function C3e(n,e,t){return bMe(n,e,t,O(e,102)&&(u(e,19).Bb&hr)!=0)}function TJ(n){n.b!=n.c&&(n.a=K(ki,Fn,1,8,5,1),n.b=0,n.c=0)}function e5(n){return oe(n.a<n.c.a.length),n.b=n.a,i$n(n),n.c.b[n.b]}function Sc(n){return n.n||(Zu(n),n.n=new mPn(n,jr,n),Hr(n)),n.n}function zDn(n){if(n<0)throw M(new Rjn("Negative array size: "+n))}function qN(n,e,t){if(t){var i=t.oe();t=i(t)}else t=void 0;n.a[e]=t}function XDn(n,e){cm();var t;return t=n.j.g-e.j.g,t!=0?t:0}function M3e(n,e){return fl(),ve(_(n.a),e)}function T3e(n,e){return fl(),ve(_(n.a),e)}function gl(n,e){dh(),Qa.call(this,n,1,S(T(ye,1),Ke,28,15,[e]))}function Xb(n,e){nt(),Wd.call(this,n),this.a=e,this.c=-1,this.b=-1}function Vb(n,e,t,i){VOn.call(this,1,t,i),this.c=n,this.b=e}function UN(n,e,t,i){WOn.call(this,1,t,i),this.c=n,this.b=e}function GN(n,e,t,i,r,c,s){k$.call(this,e,i,r,c,s),this.c=n,this.a=t}function rd(n,e,t){this.e=n,this.a=ki,this.b=Qqn(e),this.c=e,this.d=t}function zN(n){this.e=n,this.c=this.e.a,this.b=this.e.g,this.d=this.e.i}function AJ(n){this.d=n,this.b=this.d.a.entries(),this.a=this.b.next()}function VDn(n){this.c=n,this.a=u(ws(n),156),this.b=this.a.jk().wi()}function Ql(){de.call(this),sAn(this),this.d.b=this.d,this.d.a=this.d}function xt(n,e,t,i){var r;r=new OO,r.c=e,r.b=t,r.a=i,i.b=t.a=r,++n.b}function A3e(n,e){var t;return t=e!=null?Nc(n,e):Kr(wr(n.f,e)),PC(t)}function S3e(n,e){var t;return t=e!=null?Nc(n,e):Kr(wr(n.f,e)),PC(t)}function Wr(n,e){var t;return e.b.Kb(GNn(n,e.c.Xe(),(t=new A9n(e),t)))}function P3e(n,e){var t;return zDn(e),t=n.slice(0,e),t.length=e,o$(t,n)}function WDn(n,e){var t;for(t=0;t<e;++t)$t(n,t,new EG(u(n[t],44)))}function I3e(n,e){var t;for(t=n.d-1;t>=0&&n.a[t]===e[t];t--);return t<0}function HM(n){var e;return n?new fW(n):(e=new ih,A$(e,n),e)}function O3e(n,e){var t,i;i=!1;do t=lFn(n,e),i=i|t;while(t);return i}function D3e(n){n&&rme((az(),sun)),--cP,n&&uP!=-1&&(Ele(uP),uP=-1)}function qM(n){nnn(),LTn(this,Ae(vi(w0(n,24),YA)),Ae(vi(n,YA)))}function JDn(){JDn=F,HQn=Ce((YT(),S(T(Bun,1),G,436,0,[o_,Fun])))}function QDn(){QDn=F,qQn=Ce((cT(),S(T(Kun,1),G,435,0,[Run,s_])))}function YDn(){YDn=F,GYn=Ce((uT(),S(T(bon,1),G,432,0,[v_,vP])))}function ZDn(){ZDn=F,_Zn=Ce((V4(),S(T(KZn,1),G,517,0,[dj,L_])))}function nLn(){nLn=F,Ane=Ce((KM(),S(T(Qsn,1),G,429,0,[fH,Jsn])))}function eLn(){eLn=F,gne=Ce((pk(),S(T($sn,1),G,428,0,[WP,Nsn])))}function tLn(){tLn=F,kne=Ce((hk(),S(T(Bsn,1),G,488,0,[Fsn,QP])))}function iLn(){iLn=F,rie=Ce((wk(),S(T(qhn,1),G,430,0,[UH,GH])))}function rLn(){rLn=F,Die=Ce((n5(),S(T(Oie,1),G,531,0,[r9,i9])))}function cLn(){cLn=F,ane=Ce((QM(),S(T(Asn,1),G,431,0,[Tsn,V_])))}function uLn(){uLn=F,xre=Ce((FM(),S(T(Bln,1),G,433,0,[dq,Fln])))}function oLn(){oLn=F,_re=Ce((yT(),S(T(Rln,1),G,501,0,[RI,D2])))}function sLn(){sLn=F,Rie=Ce((sh(),S(T(Bie,1),G,523,0,[mb,y1])))}function fLn(){fLn=F,_ie=Ce((Sf(),S(T(Kie,1),G,522,0,[Rd,zf])))}function hLn(){hLn=F,tre=Ce((lf(),S(T(ere,1),G,528,0,[zw,ja])))}function lLn(){lLn=F,fre=Ce((M0(),S(T(sre,1),G,465,0,[Ea,P2])))}function aLn(){aLn=F,Ure=Ce((ZM(),S(T(_ln,1),G,434,0,[Kln,vq])))}function dLn(){dLn=F,Rce=Ce((GM(),S(T(S1n,1),G,491,0,[$q,A1n])))}function bLn(){bLn=F,_ce=Ce((N$(),S(T(N1n,1),G,492,0,[D1n,L1n])))}function wLn(){wLn=F,Vce=Ce((ck(),S(T(x1n,1),G,438,0,[Kq,JI])))}function gLn(){gLn=F,aue=Ce((Ak(),S(T(ran,1),G,437,0,[YI,ian])))}function pLn(){pLn=F,aoe=Ce((RL(),S(T(dO,1),G,347,0,[vdn,kdn])))}function L3e(){return ci(),S(T(E9,1),G,88,0,[Wf,Xr,Br,Vf,us])}function N3e(){return tn(),S(T(lr,1),Mc,64,0,[sc,Xn,Zn,ae,Wn])}function $3e(n,e,t){return u(e==null?Vc(n.f,null,t):$0(n.i,e,t),288)}function x3e(n){return(n.k==(Vn(),zt)||n.k==Zt)&&kt(n,(W(),H8))}function XN(n){return n.c&&n.d?aJ(n.c)+"->"+aJ(n.d):"e_"+l0(n)}function qi(n,e){var t,i;for(Jn(e),i=n.Kc();i.Ob();)t=i.Pb(),e.Cd(t)}function F3e(n,e){var t;t=new op,nd(t,"x",e.a),nd(t,"y",e.b),Ip(n,t)}function B3e(n,e){var t;t=new op,nd(t,"x",e.a),nd(t,"y",e.b),Ip(n,t)}function mLn(n,e){var t;for(t=e;t;)a0(n,-t.i,-t.j),t=At(t);return n}function SJ(n,e){var t,i;for(t=e,i=0;t>0;)i+=n.a[t],t-=t&-t;return i}function Go(n,e,t){var i;return i=(Ln(e,n.c.length),n.c[e]),n.c[e]=t,i}function PJ(n,e,t){n.a.c.length=0,fOe(n,e,t),n.a.c.length==0||xSe(n,e)}function tk(n){n.i=0,s7(n.b,null),s7(n.c,null),n.a=null,n.e=null,++n.g}function UM(){UM=F,qf=!0,DQn=!1,LQn=!1,$Qn=!1,NQn=!1}function VN(n){UM(),!qf&&(this.c=n,this.e=!0,this.a=new Z)}function vLn(n,e){this.c=0,this.b=e,HMn.call(this,n,17493),this.a=this.c}function kLn(n){jzn(),Syn(this),this.a=new Ct,sY(this,n),xe(this.a,n)}function yLn(){pL(this),this.b=new V(St,St),this.a=new V(li,li)}function GM(){GM=F,$q=new fX(cin,0),A1n=new fX("TARGET_WIDTH",1)}function Ig(n,e){return(ea(n),s4(new Tn(n,new tQ(e,n.a)))).Bd(v3)}function R3e(){return Vi(),S(T(Ion,1),G,367,0,[Xs,Jh,Oc,Kc,zr])}function K3e(){return ow(),S(T(ine,1),G,375,0,[gj,zP,XP,GP,UP])}function _3e(){return o1(),S(T(Lsn,1),G,348,0,[J_,Dsn,Q_,pv,gv])}function H3e(){return T5(),S(T($hn,1),G,323,0,[Nhn,KH,_H,Y8,Z8])}function q3e(){return Yo(),S(T(hfn,1),G,171,0,[Ej,U8,ka,G8,xw])}function U3e(){return wA(),S(T(Hre,1),G,368,0,[pq,bq,mq,wq,gq])}function G3e(){return R5(),S(T(Hce,1),G,373,0,[L2,D3,g9,w9,_j])}function z3e(){return Yk(),S(T(K1n,1),G,324,0,[F1n,_q,R1n,Hq,B1n])}function X3e(){return gf(),S(T(Zh,1),G,170,0,[xn,pi,Ph,Kd,E1])}function V3e(){return Fg(),S(T(A9,1),G,256,0,[Aa,eE,adn,T9,ddn])}function W3e(n){return HE(),function(){return Kpe(n,this,arguments)}}function fr(n){return!n.c||!n.d?!1:!!n.c.i&&n.c.i==n.d.i}function IJ(n,e){return O(e,143)?An(n.c,u(e,143).c):!1}function Zu(n){return n.t||(n.t=new myn(n),k5(new Njn(n),0,n.t)),n.t}function jLn(n){this.b=n,ne.call(this,n),this.a=u(Un(this.b.a,4),129)}function ELn(n){this.b=n,yp.call(this,n),this.a=u(Un(this.b.a,4),129)}function Bs(n,e,t,i,r){LLn.call(this,e,i,r),this.c=n,this.b=t}function OJ(n,e,t,i,r){VOn.call(this,e,i,r),this.c=n,this.a=t}function DJ(n,e,t,i,r){WOn.call(this,e,i,r),this.c=n,this.a=t}function LJ(n,e,t,i,r){LLn.call(this,e,i,r),this.c=n,this.a=t}function WN(n,e){var t;return t=u(Lf(n.d,e),23),t||u(Lf(n.e,e),23)}function CLn(n,e){var t,i;return t=e.ld(),i=n.Fe(t),!!i&&mc(i.e,e.md())}function MLn(n,e){var t;return t=e.ld(),new i0(t,n.e.pc(t,u(e.md(),16)))}function J3e(n,e){var t;return t=n.a.get(e),t??K(ki,Fn,1,0,5,1)}function TLn(n){var e;return e=n.length,An(Yn.substr(Yn.length-e,e),n)}function fe(n){if(pe(n))return n.c=n.a,n.a.Pb();throw M(new nc)}function NJ(n,e){return e==0||n.e==0?n:e>0?wqn(n,e):RBn(n,-e)}function Fp(n,e){return e==0||n.e==0?n:e>0?RBn(n,e):wqn(n,-e)}function $J(n){ole.call(this,n==null?gu:Jr(n),O(n,82)?u(n,82):null)}function ALn(n){var e;return n.c||(e=n.r,O(e,90)&&(n.c=u(e,29))),n.c}function JN(n){var e;return e=new E0,Ur(e,n),U(e,(cn(),Fr),null),e}function SLn(n){var e,t;return e=n.c.i,t=n.d.i,e.k==(Vn(),Zt)&&t.k==Zt}function QN(n){var e,t,i;return e=n&ro,t=n>>22&ro,i=n<0?Il:0,Yc(e,t,i)}function Q3e(n){var e,t,i,r;for(t=n,i=0,r=t.length;i<r;++i)e=t[i],V6(e)}function Y3e(n,e){var t,i;t=u(o5e(n.c,e),16),t&&(i=t.gc(),t.$b(),n.d-=i)}function YN(n,e,t){var i;return i=n.Ih(e),i>=0?n.Lh(i,t,!0):H0(n,e,t)}function Z3e(n,e,t){return bt(vp(pm(n),Ki(e.b)),vp(pm(n),Ki(t.b)))}function n4e(n,e,t){return bt(vp(pm(n),Ki(e.e)),vp(pm(n),Ki(t.e)))}function e4e(n,e){return y.Math.min(W1(e.a,n.d.d.c),W1(e.b,n.d.d.c))}function ik(n,e){n._i(n.i+1),O6(n,n.i,n.Zi(n.i,e)),n.Mi(n.i++,e),n.Ni()}function t5(n){var e,t;++n.j,e=n.g,t=n.i,n.g=null,n.i=0,n.Oi(t,e),n.Ni()}function PLn(n,e,t){var i;i=new NX(n.a),f5(i,n.a.a),Vc(i.f,e,t),n.a.a=i}function xJ(n,e,t,i){var r;for(r=0;r<dP;r++)hM(n.a[r][e.g],t,i[e.g])}function FJ(n,e,t,i){var r;for(r=0;r<h_;r++)lM(n.a[e.g][r],t,i[e.g])}function ot(n,e){var t;return t=u(n.c.xc(e),16),!t&&(t=n.ic(e)),n.pc(e,t)}function t4e(n){var e;return e=(Se(n),n?new _u(n):y4(n.Kc())),ny(e),FT(e)}function If(n){var e,t;return Se(n),e=Zwe(n.length),t=new Gc(e),eY(t,n),t}function ZN(n,e,t,i){var r;return r=K(ye,Ke,28,e,15,1),Eye(r,n,e,t,i),r}function BJ(n,e){if(n<0||n>e)throw M(new Ir(Mnn(n,e,"index")));return n}function Yl(n,e){var t;return t=(Ln(e,n.c.length),n.c[e]),Pz(n.c,e,1),t}function RJ(n,e){var t,i;return t=(Jn(n),n),i=(Jn(e),e),t==i?0:t<i?-1:1}function KJ(n){var e;return e=n.e+n.f,isNaN(e)&&GC(n.d)?n.d:e}function i4e(n){return n.e=3,n.d=n.Yb(),n.e!=2?(n.e=0,!0):!1}function pl(n,e){return n.a?Be(n.a,n.b):n.a=new mo(n.d),A6(n.a,e),n}function Bp(n,e){return Ai(e)?e==null?Hnn(n.f,null):Gxn(n.i,e):Hnn(n.f,e)}function ILn(n,e){_Mn.call(this,e.zd(),e.yd()&-6),Jn(n),this.a=n,this.b=e}function OLn(n,e){HMn.call(this,e.zd(),e.yd()&-6),Jn(n),this.a=n,this.b=e}function _J(n,e){IC.call(this,e.zd(),e.yd()&-6),Jn(n),this.a=n,this.b=e}function DLn(n,e,t){LE.call(this,t),this.b=n,this.c=e,this.d=(gx(),TU)}function LLn(n,e,t){this.d=n,this.k=e?1:0,this.f=t?1:0,this.o=-1,this.p=0}function Of(n){this.c=n,this.a=new C(this.c.a),this.b=new C(this.c.b)}function zM(){this.e=new Z,this.c=new Z,this.d=new Z,this.b=new Z}function NLn(){this.g=new zG,this.b=new zG,this.a=new Z,this.k=new Z}function $Ln(){this.a=new JG,this.b=new ejn,this.d=new cwn,this.e=new lwn}function xLn(n,e,t){this.a=n,this.c=e,this.d=t,nn(e.e,this),nn(t.b,this)}function HJ(n,e,t){var i,r;for(i=0,r=0;r<e.length;r++)i+=n.tg(e[r],i,t)}function r4e(n,e){var t;return t=EOe(n,e),n.b=new ET(t.c.length),HIe(n,t)}function c4e(n,e){var t;t=n.q.getHours()+(e/60|0),n.q.setMinutes(e),G5(n,t)}function n$(n){var e;return e=n.b,e.b==0?null:u(Zo(e,0),65).b}function qJ(n){if(n.a){if(n.e)return qJ(n.e)}else return n;return null}function u4e(n,e){return n.p<e.p?1:n.p>e.p?-1:0}function FLn(n){var e;return n.a||(e=n.r,O(e,156)&&(n.a=u(e,156))),n.a}function o4e(n,e,t){var i;return++n.e,--n.f,i=u(n.d[e].gd(t),136),i.md()}function s4e(n){var e,t;return e=n.ld(),t=u(n.md(),16),x7(t.Nc(),new L8n(e))}function BLn(n,e){return Zc(n.a,e)?(Bp(n.a,e),!0):!1}function Rp(n,e,t){return ek(e,n.e.Rd().gc()),ek(t,n.c.Rd().gc()),n.a[e][t]}function XM(n,e,t){this.a=n,this.b=e,this.c=t,nn(n.t,this),nn(e.i,this)}function VM(n,e,t,i){this.f=n,this.e=e,this.d=t,this.b=i,this.c=i?i.d:null}function rk(){this.b=new Ct,this.a=new Ct,this.b=new Ct,this.a=new Ct}function $4(){$4=F;var n,e;MO=(o4(),e=new xE,e),TO=(n=new fD,n)}function f4e(n){var e;return ea(n),e=new ISn(n,n.a.e,n.a.d|4),new uV(n,e)}function RLn(n){var e;for(z1(n),e=0;n.a.Bd(new W0n);)e=nr(e,1);return e}function WM(n,e){return Jn(e),n.c<n.d?(n.Se(e,n.c++),!0):!1}function Gc(n){pL(this),B7(n>=0,"Initial capacity must not be negative")}function JM(){JM=F,p9=new lt("org.eclipse.elk.labels.labelManager")}function KLn(){KLn=F,ysn=new Dt("separateLayerConnections",(OT(),F_))}function lf(){lf=F,zw=new rX("REGULAR",0),ja=new rX("CRITICAL",1)}function ck(){ck=F,Kq=new lX("FIXED",0),JI=new lX("CENTER_NODE",1)}function QM(){QM=F,Tsn=new Jz("QUADRATIC",0),V_=new Jz("SCANLINE",1)}function _Ln(){_Ln=F,dne=Ce((u5(),S(T(Psn,1),G,322,0,[B8,pj,Ssn])))}function HLn(){HLn=F,bne=Ce((bT(),S(T(Osn,1),G,351,0,[Isn,VP,W_])))}function qLn(){qLn=F,fne=Ce((D0(),S(T(R_,1),G,372,0,[ub,ma,cb])))}function ULn(){ULn=F,mne=Ce((hd(),S(T(pne,1),G,460,0,[Y_,mv,p2])))}function GLn(){GLn=F,Cne=Ce((Z4(),S(T(sH,1),G,299,0,[uH,oH,mj])))}function zLn(){zLn=F,Tne=Ce((vl(),S(T(Mne,1),G,311,0,[vj,v2,E3])))}function XLn(){XLn=F,Zte=Ce((g5(),S(T(Lhn,1),G,390,0,[FH,Dhn,MI])))}function VLn(){VLn=F,oie=Ce((ST(),S(T(zhn,1),G,387,0,[Uhn,zH,Ghn])))}function WLn(){WLn=F,sie=Ce((d5(),S(T(Xhn,1),G,349,0,[VH,XH,Ij])))}function JLn(){JLn=F,uie=Ce((gr(),S(T(cie,1),G,463,0,[n9,Vu,Jc])))}function QLn(){QLn=F,fie=Ce((om(),S(T(Whn,1),G,350,0,[WH,Vhn,e9])))}function YLn(){YLn=F,hie=Ce((dT(),S(T(Yhn,1),G,352,0,[Qhn,JH,Jhn])))}function ZLn(){ZLn=F,lie=Ce((DT(),S(T(Zhn,1),G,388,0,[QH,Ov,Gw])))}function nNn(){nNn=F,are=Ce((b5(),S(T(gln,1),G,392,0,[wln,nq,Lj])))}function eNn(){eNn=F,Gre=Ce((Ok(),S(T(Uln,1),G,393,0,[KI,Hln,qln])))}function tNn(){tNn=F,ace=Ce((AT(),S(T(s1n,1),G,300,0,[Cq,o1n,u1n])))}function iNn(){iNn=F,dce=Ce((XT(),S(T(f1n,1),G,445,0,[Bj,qI,Mq])))}function rNn(){rNn=F,wce=Ce((rA(),S(T(bce,1),G,456,0,[Tq,Sq,Aq])))}function cNn(){cNn=F,mce=Ce((_T(),S(T(a1n,1),G,394,0,[l1n,Oq,h1n])))}function uNn(){uNn=F,Kce=Ce((nT(),S(T(O1n,1),G,439,0,[xq,I1n,P1n])))}function oNn(){oNn=F,Aie=Ce((O0(),S(T(Tie,1),G,464,0,[Oj,t9,PI])))}function sNn(){sNn=F,WQn=Ce((Uu(),S(T(VQn,1),G,471,0,[Mh,ga,Gs])))}function fNn(){fNn=F,XQn=Ce((bf(),S(T(Sw,1),G,237,0,[bc,Wc,wc])))}function hNn(){hNn=F,QQn=Ce((bu(),S(T(JQn,1),G,472,0,[vf,pa,zs])))}function lNn(){lNn=F,xQn=Ce((Gu(),S(T(xr,1),G,108,0,[xun,Yr,Aw])))}function aNn(){aNn=F,pZn=Ce((i5(),S(T(Pon,1),G,391,0,[E_,j_,C_])))}function dNn(){dNn=F,Que=Ce((jl(),S(T(ldn,1),G,346,0,[uO,M1,M9])))}function bNn(){bNn=F,Uce=Ce((Fk(),S(T(Fq,1),G,444,0,[XI,VI,WI])))}function wNn(){wNn=F,Xue=Ce((Nf(),S(T(Zan,1),G,278,0,[Bv,Jw,Rv])))}function gNn(){gNn=F,loe=Ce((Gp(),S(T(mdn,1),G,280,0,[pdn,Yw,aO])))}function Df(n,e){return!n.o&&(n.o=new Iu((Cc(),il),T1,n,0)),wx(n.o,e)}function h4e(n,e){var t;n.C&&(t=u(Cr(n.b,e),127).n,t.d=n.C.d,t.a=n.C.a)}function UJ(n){var e,t,i,r;r=n.d,e=n.a,t=n.b,i=n.c,n.d=t,n.a=i,n.b=r,n.c=e}function l4e(n){return!n.g&&(n.g=new CE),!n.g.b&&(n.g.b=new byn(n)),n.g.b}function uk(n){return!n.g&&(n.g=new CE),!n.g.c&&(n.g.c=new pyn(n)),n.g.c}function a4e(n){return!n.g&&(n.g=new CE),!n.g.d&&(n.g.d=new wyn(n)),n.g.d}function d4e(n){return!n.g&&(n.g=new CE),!n.g.a&&(n.g.a=new gyn(n)),n.g.a}function b4e(n,e,t,i){return t&&(i=t.Rh(e,Ot(t.Dh(),n.c.uk()),null,i)),i}function w4e(n,e,t,i){return t&&(i=t.Th(e,Ot(t.Dh(),n.c.uk()),null,i)),i}function e$(n,e,t,i){var r;return r=K(ye,Ke,28,e+1,15,1),vPe(r,n,e,t,i),r}function K(n,e,t,i,r,c){var s;return s=_Rn(r,i),r!=10&&S(T(n,c),e,t,r,s),s}function g4e(n,e,t){var i,r;for(r=new Y4(e,n),i=0;i<t;++i)iA(r);return r}function t$(n,e,t){var i,r;if(t!=null)for(i=0;i<e;++i)r=t[i],n.Qi(i,r)}function GJ(n,e){var t;return t=new DO,t.c=!0,t.d=e.md(),LGn(n,e.ld(),t)}function p4e(n,e){var t;t=n.q.getHours()+(e/3600|0),n.q.setSeconds(e),G5(n,t)}function zJ(n,e){var t,i;return t=e,i=TN(y4(new f$(n,t))),iM(new f$(n,t)),i}function m4e(n,e){e.Ug("Label management",1),PC(v(n,(JM(),p9))),e.Vg()}function v4e(n,e,t,i){LUn(n,e,t,Om(n,e,i,O(e,102)&&(u(e,19).Bb&hr)!=0))}function XJ(n,e,t){u(n.b,68),u(n.b,68),u(n.b,68),nu(n.a,new gSn(t,e,n))}function Fi(n,e,t){if(n<0||e>t||e<n)throw M(new gz(ZA+n+Stn+e+Mtn+t))}function i$(n){n?(this.c=n,this.b=null):(this.c=null,this.b=new Z)}function r$(n,e){oC.call(this,n,e),this.a=K(lNe,WA,447,2,0,1),this.b=!0}function VJ(n){wFn.call(this,n,0),sAn(this),this.d.b=this.d,this.d.a=this.d}function WJ(n){this.e=n,this.b=this.e.a.entries(),this.a=K(ki,Fn,1,0,5,1)}function pNn(){pNn=F,bie=Pu(Re(new ii,(Vi(),Xs),(tr(),N_)),zr,bj)}function k4e(){return vA(),S(T(xsn,1),G,283,0,[nH,Z_,tH,eH,iH,JP])}function y4e(){return Jk(),S(T(qsn,1),G,281,0,[YP,Ksn,Hsn,Rsn,_sn,rH])}function j4e(){return jm(),S(T(Wsn,1),G,282,0,[R8,Gsn,Vsn,Xsn,zsn,Usn])}function E4e(){return Yp(),S(T(wv,1),G,232,0,[bv,F8,dv,Nw,g2,w2])}function C4e(){return Vn(),S(T(D_,1),G,273,0,[zt,Mi,Zt,_c,Ac,Uf])}function M4e(){return zu(),S(T(oO,1),G,279,0,[Pa,Fl,tE,P9,S9,B3])}function T4e(){return Oi(),S(T(bdn,1),G,101,0,[Sa,Jf,_v,Ud,tl,qc])}function A4e(){return pA(),S(T(cdn,1),G,321,0,[dU,tdn,rdn,ndn,idn,edn])}function S4e(){return Rh(),S(T(fan,1),G,255,0,[Vq,qj,Uj,eO,ZI,nO])}function P4e(){return wd(),S(T(Yq,1),G,298,0,[Qq,y9,k9,Jq,m9,v9])}function JJ(n){var e;return!n.a&&n.b!=-1&&(e=n.c.Dh(),n.a=$n(e,n.b)),n.a}function ve(n,e){return n.Si()&&n.Hc(e)?!1:(n.Hi(e),!0)}function af(n,e){return X7(e,"Horizontal alignment cannot be null"),n.b=e,n}function mNn(n,e,t){nt();var i;return i=oa(n,e),t&&i&&Rwe(n)&&(i=null),i}function QJ(n,e,t){var i;i=n.b[t.c.p][t.p],i.b+=e.b,i.c+=e.c,i.a+=e.a,++i.a}function YJ(n,e,t){var i;n.d[e.g]=t,i=n.g.c,i[e.g]=y.Math.max(i[e.g],t+1)}function W1(n,e){var t,i;return t=n.a-e.a,i=n.b-e.b,y.Math.sqrt(t*t+i*i)}function ZJ(n,e){var t,i;for(i=e.Kc();i.Ob();)t=u(i.Pb(),36),sUn(n,t,0,0)}function Zl(n,e,t){var i,r;for(r=n.Kc();r.Ob();)i=u(r.Pb(),36),Sm(i,e,t)}function I4e(n){var e,t;for(t=ge(n.a,0);t.b!=t.d.c;)e=u(be(t),65),Dnn(e)}function vNn(n,e){return kCn(n.e,e)||s1(n.e,e,new fRn(e)),u(Lf(n.e,e),113)}function qu(n,e,t,i){return Jn(n),Jn(e),Jn(t),Jn(i),new AW(n,e,new B0n)}function Iu(n,e,t,i){this.ak(),this.a=e,this.b=n,this.c=new jW(this,e,t,i)}function c$(n,e,t,i,r,c){vJ.call(this,e,i,r,c),this.c=n,this.b=t}function ok(n,e,t,i,r,c){vJ.call(this,e,i,r,c),this.c=n,this.a=t}function sk(n,e){var t,i,r;return r=n.r,i=n.d,t=V5(n,e,!0),t.b!=r||t.a!=i}function fk(n,e,t){var i,r;return r=(i=Mm(n.b,e),i),r?qA(ak(n,r),t):null}function O4e(n,e,t){var i,r,c;i=dl(n,t),r=null,i&&(r=gnn(i)),c=r,uRn(e,t,c)}function D4e(n,e,t){var i,r,c;i=dl(n,t),r=null,i&&(r=gnn(i)),c=r,uRn(e,t,c)}function x4(n,e){var t;return t=n.Ih(e),t>=0?n.Lh(t,!0,!0):H0(n,e,!0)}function L4e(n,e,t){var i;return i=vFn(n,e,t),n.b=new ET(i.c.length),den(n,i)}function N4e(n){if(n.b<=0)throw M(new nc);return--n.b,n.a-=n.c.c,Y(n.a)}function $4e(n){var e;if(!n.a)throw M(new PIn);return e=n.a,n.a=At(n.a),e}function x4e(n){for(;!n.a;)if(!eSn(n.c,new C9n(n)))return!1;return!0}function Kp(n){var e;return Se(n),O(n,204)?(e=u(n,204),e):new _8n(n)}function F4e(n){YM(),u(n.of((qe(),Ww)),181).Fc((zu(),tE)),n.qf(sU,null)}function YM(){YM=F,wue=new Emn,pue=new Cmn,gue=M6e((qe(),sU),wue,Ma,pue)}function ZM(){ZM=F,Kln=new sX("LEAF_NUMBER",0),vq=new sX("NODE_SIZE",1)}function u$(n){n.a=K(ye,Ke,28,n.b+1,15,1),n.c=K(ye,Ke,28,n.b,15,1),n.d=0}function B4e(n,e){n.a.Ne(e.d,n.b)>0&&(nn(n.c,new GV(e.c,e.d,n.d)),n.b=e.d)}function nQ(n,e){if(n.g==null||e>=n.i)throw M(new aL(e,n.i));return n.g[e]}function kNn(n,e,t){if(rm(n,t),t!=null&&!n.fk(t))throw M(new uD);return t}function o$(n,e){return gk(e)!=10&&S(wo(e),e.Sm,e.__elementTypeId$,gk(e),n),n}function F4(n,e,t,i){var r;i=(j0(),i||Pun),r=n.slice(e,t),Tnn(r,n,e,t,-e,i)}function zo(n,e,t,i,r){return e<0?H0(n,t,i):u(t,69).wk().yk(n,n.hi(),e,i,r)}function R4e(n,e){return bt($(R(v(n,(W(),fb)))),$(R(v(e,fb))))}function yNn(){yNn=F,IQn=Ce((B4(),S(T(lP,1),G,304,0,[e_,t_,i_,r_])))}function B4(){B4=F,e_=new uC("All",0),t_=new lTn,i_=new kTn,r_=new hTn}function Uu(){Uu=F,Mh=new FD(s3,0),ga=new FD(qm,1),Gs=new FD(f3,2)}function jNn(){jNn=F,KA(),s0n=St,mse=li,f0n=new V9(St),vse=new V9(li)}function ENn(){ENn=F,jYn=Ce((N0(),S(T(yYn,1),G,417,0,[rj,ij,a_,d_])))}function CNn(){CNn=F,AYn=Ce((A5(),S(T(TYn,1),G,406,0,[fj,wP,gP,hj])))}function MNn(){MNn=F,CYn=Ce((Vp(),S(T(EYn,1),G,332,0,[uj,cj,oj,sj])))}function TNn(){TNn=F,DZn=Ce((dd(),S(T(Lon,1),G,389,0,[Ow,Don,P_,I_])))}function ANn(){ANn=F,TZn=Ce((nm(),S(T(MZn,1),G,416,0,[rb,Iw,Pw,a2])))}function SNn(){SNn=F,tne=Ce(($f(),S(T(ene,1),G,421,0,[j3,lv,av,B_])))}function PNn(){PNn=F,GZn=Ce((OT(),S(T(UZn,1),G,371,0,[F_,HP,qP,wj])))}function INn(){INn=F,nie=Ce((cw(),S(T(RH,1),G,203,0,[TI,BH,S2,A2])))}function ONn(){ONn=F,iie=Ce((lh(),S(T(Hhn,1),G,284,0,[k1,_hn,HH,qH])))}function hk(){hk=F,Fsn=new Yz(kh,0),QP=new Yz("IMPROVE_STRAIGHTNESS",1)}function DNn(n,e){var t,i;return i=e/n.c.Rd().gc()|0,t=e%n.c.Rd().gc(),Rp(n,i,t)}function LNn(n){var e;if(n.nl())for(e=n.i-1;e>=0;--e)L(n,e);return jJ(n)}function eQ(n){var e,t;if(!n.b)return null;for(t=n.b;e=t.a[0];)t=e;return t}function NNn(n){var e,t;if(!n.b)return null;for(t=n.b;e=t.a[1];)t=e;return t}function K4e(n){return O(n,180)?""+u(n,180).a:n==null?null:Jr(n)}function _4e(n){return O(n,180)?""+u(n,180).a:n==null?null:Jr(n)}function $Nn(n,e){if(e.a)throw M(new ec(nXn));fi(n.a,e),e.a=n,!n.j&&(n.j=e)}function tQ(n,e){IC.call(this,e.zd(),e.yd()&-16449),Jn(n),this.a=n,this.c=e}function H4e(n,e){return new _L(e,a0(Ki(e.e),e.f.a+n,e.f.b+n),(_n(),!1))}function q4e(n,e){return k4(),nn(n,new bi(e,Y(e.e.c.length+e.g.c.length)))}function U4e(n,e){return k4(),nn(n,new bi(e,Y(e.e.c.length+e.g.c.length)))}function xNn(){xNn=F,lce=Ce((sA(),S(T(c1n,1),G,354,0,[Eq,i1n,r1n,t1n])))}function FNn(){FNn=F,$re=Ce((w5(),S(T(xln,1),G,353,0,[aq,BI,lq,hq])))}function BNn(){BNn=F,hre=Ce((Qp(),S(T(rln,1),G,405,0,[LI,c9,u9,o9])))}function RNn(){RNn=F,Vue=Ce((El(),S(T(aU,1),G,223,0,[lU,Yj,Kv,F3])))}function KNn(){KNn=F,Zue=Ce((To(),S(T(Yue,1),G,291,0,[nE,nl,Ta,Zj])))}function _Nn(){_Nn=F,foe=Ce((go(),S(T(I9,1),G,386,0,[rE,Gd,iE,Qw])))}function HNn(){HNn=F,doe=Ce((qT(),S(T(Cdn,1),G,320,0,[wU,ydn,Edn,jdn])))}function qNn(){qNn=F,goe=Ce((LT(),S(T(woe,1),G,415,0,[gU,Tdn,Mdn,Adn])))}function nT(){nT=F,xq=new oL(mVn,0),I1n=new oL(Crn,1),P1n=new oL(kh,2)}function Wb(n,e,t,i,r){return Jn(n),Jn(e),Jn(t),Jn(i),Jn(r),new AW(n,e,i)}function UNn(n,e){var t;return t=u(Bp(n.e,e),400),t?(tW(t),t.e):null}function du(n,e){var t;return t=qr(n,e,0),t==-1?!1:(Yl(n,t),!0)}function GNn(n,e,t){var i;return z1(n),i=new LO,i.a=e,n.a.Nb(new TCn(i,t)),i.a}function G4e(n){var e;return z1(n),e=K(Pi,Tr,28,0,15,1),hg(n.a,new y9n(e)),e}function iQ(n){var e;if(!E$(n))throw M(new nc);return n.e=1,e=n.d,n.d=null,e}function n1(n){var e;return Vr(n)&&(e=0-n,!isNaN(e))?e:Q1(tm(n))}function qr(n,e,t){for(;t<n.c.length;++t)if(mc(e,n.c[t]))return t;return-1}function s$(n){var e,t;return t=u(sn(n.j,0),12),e=u(v(t,(W(),st)),12),e}function f$(n,e){var t;this.f=n,this.b=e,t=u(ee(n.b,e),260),this.c=t?t.b:null}function zNn(){xs(),this.b=new de,this.f=new de,this.g=new de,this.e=new de}function eT(n){xC(this),this.g=n?IM(n,n.ie()):null,this.f=n,MM(this),this.je()}function h$(n){var e;e=n.jj(),e!=null&&n.d!=-1&&u(e,94).xh(n),n.i&&n.i.oj()}function lk(n){var e;for(e=n.p+1;e<n.c.a.c.length;++e)--u(sn(n.c.a,e),10).p}function XNn(n){Fb(!!n.c),FL(n.f.g,n.d),n.c.Qb(),n.c=null,n.b=GQ(n),n.d=n.f.g}function no(n){return n.b||(n.b=new vPn(n,jr,n),!n.a&&(n.a=new O7(n,n))),n.b}function ak(n,e){var t,i;return t=u(e,690),i=t.xi(),!i&&t.Ai(i=new FMn(n,e)),i}function Lr(n,e){var t,i;return t=u(e,692),i=t.$k(),!i&&t.cl(i=new uDn(n,e)),i}function rQ(n,e){s6();var t,i;return t=xp(n),i=xp(e),!!t&&!!i&&!pRn(t.k,i.k)}function tT(n,e){return mc(e,sn(n.f,0))||mc(e,sn(n.f,1))||mc(e,sn(n.f,2))}function dk(n,e){if(e<0)throw M(new Ir(DVn+e));return xDn(n,e+1),sn(n.j,e)}function VNn(n,e,t,i){if(!n)throw M(new Gn(H5(e,S(T(ki,1),Fn,1,5,[t,i]))))}function ml(n,e,t,i,r,c,s){k$.call(this,e,i,r,c,s),this.c=n,this.b=t}function Bh(n,e,t){var i,r;for(i=10,r=0;r<t-1;r++)e<i&&(n.a+="0"),i*=10;n.a+=e}function iT(n){var e,t;return t=n.length,e=K(fs,gh,28,t,15,1),qPn(n,0,t,e,0),e}function bk(n){ePn();var e,t;return e=n+128,t=bun[e],!t&&(t=bun[e]=new u9n(n)),t}function WNn(n){return FL(n.d.a.e.g,n.b),oe(n.c!=n.d.a.d),n.a=n.c,n.c=n.c.a,n.a}function z4e(n){switch(n.g){case 0:return et;case 1:return-1;default:return 0}}function X4e(n){return DZ(n,(R4(),aun))<0?-P1e(tm(n)):n.l+n.m*o3+n.h*vd}function JNn(n){(this.q?this.q:(Dn(),Dn(),Wh)).Ac(n.q?n.q:(Dn(),Dn(),Wh))}function V4e(n,e){Ep(u(u(n.f,27).of((qe(),j9)),101))&&e8e(mN(u(n.f,27)),e)}function l$(n,e){var t;return t=Ot(n.d,e),t>=0?tA(n,t,!0,!0):H0(n,e,!0)}function cQ(n){var e;return e=cd(Un(n,32)),e==null&&(iu(n),e=cd(Un(n,32))),e}function uQ(n){var e;return n.Oh()||(e=se(n.Dh())-n.ji(),n.$h().Mk(e)),n.zh()}function QNn(n,e){con=new kE,MYn=e,L8=n,u(L8.b,68),XJ(L8,con,null),aGn(L8)}function i5(){i5=F,E_=new RD("XY",0),j_=new RD("X",1),C_=new RD("Y",2)}function bu(){bu=F,vf=new BD("TOP",0),pa=new BD(qm,1),zs=new BD(Ftn,2)}function vl(){vl=F,vj=new GD(kh,0),v2=new GD("TOP",1),E3=new GD(Ftn,2)}function wk(){wk=F,UH=new nX("INPUT_ORDER",0),GH=new nX("PORT_DEGREE",1)}function R4(){R4=F,hun=Yc(ro,ro,524287),bQn=Yc(0,0,Ty),lun=QN(1),QN(2),aun=QN(0)}function a$(n){var e;return n.d!=n.r&&(e=ws(n),n.e=!!e&&e.lk()==bJn,n.d=e),n.e}function d$(n,e,t){var i;return i=n.g[e],O6(n,e,n.Zi(e,t)),n.Ri(e,t,i),n.Ni(),i}function rT(n,e){var t;return t=n.dd(e),t>=0?(n.gd(t),!0):!1}function b$(n,e){var t;for(Se(n),Se(e),t=!1;e.Ob();)t=t|n.Fc(e.Pb());return t}function Lf(n,e){var t;return t=u(ee(n.e,e),400),t?(DTn(n,t),t.e):null}function YNn(n){var e,t;return e=n/60|0,t=n%60,t==0?""+e:""+e+":"+(""+t)}function Jb(n,e){var t=n.a[e],i=(K$(),WK)[typeof t];return i?i(t):wY(typeof t)}function rc(n,e){var t,i;return ea(n),i=new _J(e,n.a),t=new rSn(i),new Tn(n,t)}function w$(n){var e;return e=n.b.c.length==0?null:sn(n.b,0),e!=null&&M$(n,0),e}function W4e(n,e){var t,i,r;r=e.c.i,t=u(ee(n.f,r),60),i=t.d.c-t.e.c,BQ(e.a,i,0)}function oQ(n,e){var t;for(++n.d,++n.c[e],t=e+1;t<n.a.length;)++n.a[t],t+=t&-t}function ZNn(n,e,t,i){nt(),Wd.call(this,26),this.c=n,this.a=e,this.d=t,this.b=i}function n$n(n,e){for(;e[0]<n.length&&th(` 	\r
 `,wu(Xi(n,e[0])))>=0;)++e[0]}function J4e(n,e){eu(n,e==null||GC((Jn(e),e))||isNaN((Jn(e),e))?0:(Jn(e),e))}function Q4e(n,e){tu(n,e==null||GC((Jn(e),e))||isNaN((Jn(e),e))?0:(Jn(e),e))}function Y4e(n,e){I0(n,e==null||GC((Jn(e),e))||isNaN((Jn(e),e))?0:(Jn(e),e))}function Z4e(n,e){P0(n,e==null||GC((Jn(e),e))||isNaN((Jn(e),e))?0:(Jn(e),e))}function nme(n,e,t){return vp(new V(t.e.a+t.f.a/2,t.e.b+t.f.b/2),n)==(Jn(e),e)}function eme(n,e){return O(e,102)&&u(e,19).Bb&hr?new dL(e,n):new Y4(e,n)}function tme(n,e){return O(e,102)&&u(e,19).Bb&hr?new dL(e,n):new Y4(e,n)}function gk(n){return n.__elementTypeCategory$==null?10:n.__elementTypeCategory$}function e$n(n,e){return e==(xL(),xL(),AQn)?n.toLocaleLowerCase():n.toLowerCase()}function t$n(n){if(!n.e)throw M(new nc);return n.c=n.a=n.e,n.e=n.e.e,--n.d,n.a.f}function sQ(n){if(!n.c)throw M(new nc);return n.e=n.a=n.c,n.c=n.c.c,++n.d,n.a.f}function i$n(n){var e;for(++n.a,e=n.c.a.length;n.a<e;++n.a)if(n.c.b[n.a])return}function ime(n){var e,t;if(n.a){t=null;do e=n.a,n.a=null,t=d_n(e,t);while(n.a);n.a=t}}function rme(n){var e,t;if(n.b){t=null;do e=n.b,n.b=null,t=d_n(e,t);while(n.b);n.b=t}}function cme(n,e){var t;for(t=0;n.e!=n.i.gc();)Pbe(e,ce(n),Y(t)),t!=et&&++t}function ume(n,e){var t;return t=x0(n.e.c,e.e.c),t==0?bt(n.e.d,e.e.d):t}function ome(n,e){var t,i;for(i=e.c,t=i+1;t<=e.f;t++)n.a[t]>n.a[i]&&(i=t);return i}function r$n(n){var e;return e=u(v(n,(W(),ob)),313),e?e.a==n:!1}function c$n(n){var e;return e=u(v(n,(W(),ob)),313),e?e.i==n:!1}function u$n(){u$n=F,yZn=Ce((Vi(),S(T(Ion,1),G,367,0,[Xs,Jh,Oc,Kc,zr])))}function o$n(){o$n=F,rne=Ce((ow(),S(T(ine,1),G,375,0,[gj,zP,XP,GP,UP])))}function s$n(){s$n=F,wne=Ce((o1(),S(T(Lsn,1),G,348,0,[J_,Dsn,Q_,pv,gv])))}function f$n(){f$n=F,eie=Ce((T5(),S(T($hn,1),G,323,0,[Nhn,KH,_H,Y8,Z8])))}function h$n(){h$n=F,Sne=Ce((Yo(),S(T(hfn,1),G,171,0,[Ej,U8,ka,G8,xw])))}function l$n(){l$n=F,qre=Ce((wA(),S(T(Hre,1),G,368,0,[pq,bq,mq,wq,gq])))}function a$n(){a$n=F,qce=Ce((R5(),S(T(Hce,1),G,373,0,[L2,D3,g9,w9,_j])))}function d$n(){d$n=F,Wce=Ce((Yk(),S(T(K1n,1),G,324,0,[F1n,_q,R1n,Hq,B1n])))}function b$n(){b$n=F,zue=Ce((ci(),S(T(E9,1),G,88,0,[Wf,Xr,Br,Vf,us])))}function w$n(){w$n=F,mue=Ce((gf(),S(T(Zh,1),G,170,0,[xn,pi,Ph,Kd,E1])))}function g$n(){g$n=F,eoe=Ce((Fg(),S(T(A9,1),G,256,0,[Aa,eE,adn,T9,ddn])))}function p$n(){p$n=F,roe=Ce((tn(),S(T(lr,1),Mc,64,0,[sc,Xn,Zn,ae,Wn])))}function cT(){cT=F,Run=new Uz("BY_SIZE",0),s_=new Uz("BY_SIZE_AND_SHAPE",1)}function uT(){uT=F,v_=new Xz("EADES",0),vP=new Xz("FRUCHTERMAN_REINGOLD",1)}function pk(){pk=F,WP=new Qz("READING_DIRECTION",0),Nsn=new Qz("ROTATION",1)}function r5(){r5=F,PZn=new rwn,IZn=new own,AZn=new swn,SZn=new uwn,OZn=new fwn}function m$n(n){this.b=new Z,this.a=new Z,this.c=new Z,this.d=new Z,this.e=n}function v$n(n){this.g=n,this.f=new Z,this.a=y.Math.min(this.g.c.c,this.g.d.c)}function k$n(n,e,t){qC.call(this),lQ(this),this.a=n,this.c=t,this.b=e.d,this.f=e.e}function sme(n,e,t){var i,r;for(r=new C(t);r.a<r.c.c.length;)i=E(r),WZ(n,e,i)}function df(n,e,t){var i;if(e==null)throw M(new ip);return i=dl(n,e),y3e(n,e,t),i}function g$(n,e){var t;return t=u(ee(n.a,e),137),t||(t=new xO,Xe(n.a,e,t)),t}function $n(n,e){var t;return t=(n.i==null&&bh(n),n.i),e>=0&&e<t.length?t[e]:null}function fme(n,e){var t;return t=e>0?e-1:e,eEn($he(U$n(YV(new up,t),n.n),n.j),n.k)}function Nr(n){var e,t;t=(e=new hD,e),ve((!n.q&&(n.q=new q(As,n,11,10)),n.q),t)}function fQ(n){return(n.i&2?"interface ":n.i&1?"":"class ")+(ll(n),n.o)}function oT(n){return Ec(n,et)>0?et:Ec(n,Wi)<0?Wi:Ae(n)}function Qb(n){return n<3?(Co(n,$zn),n+1):n<Y5?wi(n/.75+1):et}function y$n(n,e){return Jn(e),kW(n),n.d.Ob()?(e.Cd(n.d.Pb()),!0):!1}function hme(n,e){var t,i;return t=u(tw(n.d,e),16),t?(i=e,n.e.pc(i,t)):null}function lme(n,e,t,i){var r;n.j=-1,Rnn(n,pnn(n,e,t),(dr(),r=u(e,69).vk(),r.xl(i)))}function ame(n,e){return _p(),-jc(u(v(n,(lc(),I2)),17).a,u(v(e,I2),17).a)}function j$n(n,e){return!!s5(n,e,Ae(er(Uh,xh(Ae(er(e==null?0:mt(e),Gh)),15))))}function dme(){return Cm(),S(T(kO,1),G,245,0,[kU,mO,vO,pO,vU,gO,wO,mU])}function bme(){return l1(),S(T(vue,1),G,285,0,[uan,yi,Zr,N2,Qi,Pt,L3,Xf])}function wme(){return DA(),S(T(Msn,1),G,276,0,[__,U_,K_,X_,q_,H_,z_,G_])}function gme(n){var e;return e=$(R(v(n,(cn(),m1)))),e<0&&(e=0,U(n,m1,e)),e}function sT(n,e){var t,i;for(i=n.Kc();i.Ob();)t=u(i.Pb(),72),U(t,(W(),A3),e)}function pme(n,e,t){var i;i=y.Math.max(0,n.b/2-.5),I5(t,i,1),nn(e,new PCn(t,i))}function mme(n,e,t){var i;return i=n.a.e[u(e.a,10).p]-n.a.e[u(t.a,10).p],wi(K7(i))}function fT(n,e){var t;return ea(n),t=new BIn(n,n.a.zd(),n.a.yd()|4,e),new Tn(n,t)}function p$(n){var e;Fb(!!n.c),e=n.c.a,Xo(n.d,n.c),n.b==n.c?n.b=e:--n.a,n.c=null}function E$n(n){return n.a>=-.01&&n.a<=Kf&&(n.a=0),n.b>=-.01&&n.b<=Kf&&(n.b=0),n}function Og(n){Xg();var e,t;for(t=Arn,e=0;e<n.length;e++)n[e]>t&&(t=n[e]);return t}function C$n(n,e){var t;if(t=oy(n.Dh(),e),!t)throw M(new Gn(da+e+sK));return t}function Yb(n,e){var t;for(t=n;At(t);)if(t=At(t),t==e)return!0;return!1}function vme(n,e){var t,i,r;for(i=e.a.ld(),t=u(e.a.md(),16).gc(),r=0;r<t;r++)n.Cd(i)}function nu(n,e){var t,i,r,c;for(Jn(e),i=n.c,r=0,c=i.length;r<c;++r)t=i[r],e.Cd(t)}function M$n(n,e,t,i,r,c){var s;s=JN(i),Zi(s,r),Ii(s,c),Pn(n.a,i,new zC(s,e,t.f))}function T$n(n,e){ht(n,(_h(),Iq),e.f),ht(n,pce,e.e),ht(n,Pq,e.d),ht(n,gce,e.c)}function A$n(n,e){this.a=new de,this.e=new de,this.b=(g5(),MI),this.c=n,this.b=e}function S$n(n){this.d=n,this.c=n.c.vc().Kc(),this.b=null,this.a=null,this.e=(RE(),GK)}function Xo(n,e){var t;return t=e.c,e.a.b=e.b,e.b.a=e.a,e.a=e.b=null,e.c=null,--n.b,t}function kme(n,e){return e&&n.b[e.g]==e?($t(n.b,e.g,null),--n.c,!0):!1}function yme(n,e){if(0>n||n>e)throw M(new pz("fromIndex: 0, toIndex: "+n+Mtn+e))}function S0(n){if(n<0)throw M(new Gn("Illegal Capacity: "+n));this.g=this.aj(n)}function hQ(n,e){return Mf(),Rs(sa),y.Math.abs(n-e)<=sa||n==e||isNaN(n)&&isNaN(e)}function m$(n,e){var t,i,r,c;for(i=n.d,r=0,c=i.length;r<c;++r)t=i[r],Tf(n.g,t).a=e}function jme(n,e,t){var i,r,c;for(r=e[t],i=0;i<r.length;i++)c=r[i],n.e[c.c.p][c.p]=i}function Eme(n){var e;for(e=0;e<n.c.length;e++)(Ln(e,n.c.length),u(n.c[e],12)).p=e}function Cme(n){var e,t;for(e=n.a.d.j,t=n.c.d.j;e!=t;)Ks(n.b,e),e=RT(e);Ks(n.b,e)}function Mme(n){var e;return e=y.Math.sqrt(n.a*n.a+n.b*n.b),e>0&&(n.a/=e,n.b/=e),n}function jo(n){var e;return n.w?n.w:(e=lpe(n),e&&!e.Vh()&&(n.w=e),e)}function K4(n,e){var t,i;i=n.a,t=w5e(n,e,null),i!=e&&!n.e&&(t=Nm(n,e,t)),t&&t.oj()}function P$n(n,e,t){var i,r;i=e;do r=$(n.p[i.p])+t,n.p[i.p]=r,i=n.a[i.p];while(i!=e)}function I$n(n,e,t){var i=function(){return n.apply(i,arguments)};return e.apply(i,t),i}function Tme(n){var e;return n==null?null:(e=u(n,195),Bye(e,e.length))}function L(n,e){if(n.g==null||e>=n.i)throw M(new aL(e,n.i));return n.Wi(e,n.g[e])}function Ame(n,e){Dn();var t,i;for(i=new Z,t=0;t<n;++t)Bn(i.c,e);return new jD(i)}function O$n(n){return ea(n),Mp(!0,"n may not be negative"),new Tn(n,new uxn(n.a))}function lQ(n){n.b=(Uu(),ga),n.f=(bu(),pa),n.d=(Co(2,mw),new Gc(2)),n.e=new Li}function hT(n){this.b=(Se(n),new _u(n)),this.a=new Z,this.d=new Z,this.e=new Li}function bf(){bf=F,bc=new xD("BEGIN",0),Wc=new xD(qm,1),wc=new xD("END",2)}function Nf(){Nf=F,Bv=new fL(qm,0),Jw=new fL("HEAD",1),Rv=new fL("TAIL",2)}function _p(){_p=F,Bre=ah(ah(ah(l6(new ii,(Qp(),c9)),(q5(),ZH)),sln),aln)}function kl(){kl=F,Kre=ah(ah(ah(l6(new ii,(Qp(),o9)),(q5(),hln)),cln),fln)}function D$n(){D$n=F,lne=Ce((Yp(),S(T(wv,1),G,232,0,[bv,F8,dv,Nw,g2,w2])))}function L$n(){L$n=F,vne=Ce((vA(),S(T(xsn,1),G,283,0,[nH,Z_,tH,eH,iH,JP])))}function N$n(){N$n=F,yne=Ce((Jk(),S(T(qsn,1),G,281,0,[YP,Ksn,Hsn,Rsn,_sn,rH])))}function $$n(){$$n=F,jne=Ce((jm(),S(T(Wsn,1),G,282,0,[R8,Gsn,Vsn,Xsn,zsn,Usn])))}function x$n(){x$n=F,xZn=Ce((Vn(),S(T(D_,1),G,273,0,[zt,Mi,Zt,_c,Ac,Uf])))}function F$n(){F$n=F,yue=Ce((Rh(),S(T(fan,1),G,255,0,[Vq,qj,Uj,eO,ZI,nO])))}function B$n(){B$n=F,Aue=Ce((wd(),S(T(Yq,1),G,298,0,[Qq,y9,k9,Jq,m9,v9])))}function R$n(){R$n=F,Wue=Ce((pA(),S(T(cdn,1),G,321,0,[dU,tdn,rdn,ndn,idn,edn])))}function K$n(){K$n=F,toe=Ce((Oi(),S(T(bdn,1),G,101,0,[Sa,Jf,_v,Ud,tl,qc])))}function _$n(){_$n=F,ioe=Ce((zu(),S(T(oO,1),G,279,0,[Pa,Fl,tE,P9,S9,B3])))}function H$n(){H$n=F,dP=(bf(),S(T(Sw,1),G,237,0,[bc,Wc,wc])).length,h_=dP}function Sme(){return lw(),S(T(yr,1),G,95,0,[Js,xl,Qs,Zs,el,Cs,Lo,Ys,Es])}function Pme(n,e){return ca(),jc(n.b.c.length-n.e.c.length,e.b.c.length-e.e.c.length)}function Dg(n,e){return Bhe(o5(n,e,Ae(er(Uh,xh(Ae(er(e==null?0:mt(e),Gh)),15)))))}function aQ(n,e){return Mf(),Rs(sa),y.Math.abs(n-e)<=sa||n==e||isNaN(n)&&isNaN(e)}function lT(n,e){var t;t=n.b,n.b=e,n.Db&4&&!(n.Db&1)&&it(n,new Vb(n,1,t,n.b))}function _4(n,e){var t;t=n.b,n.b=e,n.Db&4&&!(n.Db&1)&&it(n,new Vb(n,3,t,n.b))}function P0(n,e){var t;t=n.f,n.f=e,n.Db&4&&!(n.Db&1)&&it(n,new Vb(n,3,t,n.f))}function I0(n,e){var t;t=n.g,n.g=e,n.Db&4&&!(n.Db&1)&&it(n,new Vb(n,4,t,n.g))}function eu(n,e){var t;t=n.i,n.i=e,n.Db&4&&!(n.Db&1)&&it(n,new Vb(n,5,t,n.i))}function tu(n,e){var t;t=n.j,n.j=e,n.Db&4&&!(n.Db&1)&&it(n,new Vb(n,6,t,n.j))}function H4(n,e){var t;t=n.j,n.j=e,n.Db&4&&!(n.Db&1)&&it(n,new Vb(n,1,t,n.j))}function q4(n,e){var t;t=n.c,n.c=e,n.Db&4&&!(n.Db&1)&&it(n,new Vb(n,4,t,n.c))}function U4(n,e){var t;t=n.k,n.k=e,n.Db&4&&!(n.Db&1)&&it(n,new Vb(n,2,t,n.k))}function aT(n,e){var t;t=n.a,n.a=e,n.Db&4&&!(n.Db&1)&&it(n,new Vb(n,0,t,n.a))}function e1(n,e){var t;t=n.s,n.s=e,n.Db&4&&!(n.Db&1)&&it(n,new UN(n,4,t,n.s))}function Zb(n,e){var t;t=n.t,n.t=e,n.Db&4&&!(n.Db&1)&&it(n,new UN(n,5,t,n.t))}function v$(n,e){var t;t=n.d,n.d=e,n.Db&4&&!(n.Db&1)&&it(n,new UN(n,2,t,n.d))}function G4(n,e){var t;t=n.F,n.F=e,n.Db&4&&!(n.Db&1)&&it(n,new Ci(n,1,5,t,e))}function mk(n,e){var t;return t=u(ee((iC(),yO),n),57),t?t.gk(e):K(ki,Fn,1,e,5,1)}function Ime(n,e){var t;return t=mi(Ki(u(ee(n.g,e),8)),LX(u(ee(n.f,e),470).b)),t}function Ome(n,e){var t,i,r;return t=(i=(B1(),r=new eG,r),e&&oen(i,e),i),TQ(t,n),t}function yl(n,e){var t,i;return t=e in n.a,t&&(i=dl(n,e).re(),i)?i.a:null}function q$n(n,e,t){if(rm(n,t),!n.kl()&&t!=null&&!n.fk(t))throw M(new uD);return t}function U$n(n,e){return n.n=e,n.n?(n.f=new Z,n.e=new Z):(n.f=null,n.e=null),n}function G$n(n,e){if(n){e.n=n;var t=g2e(e);if(!t){rP[n]=[e];return}t.Rm=e}}function cd(n){var e;return F6(n==null||Array.isArray(n)&&(e=gk(n),!(e>=14&&e<=16))),n}function Ee(n,e){var t;return Jn(e),t=n[":"+e],B7(!!t,"Enum constant undefined: "+e),t}function we(n,e,t,i,r,c){var s;return s=bN(n,e),G$n(t,s),s.i=r?8:0,s.f=i,s.e=r,s.g=c,s}function dQ(n,e,t,i,r){this.d=e,this.k=i,this.f=r,this.o=-1,this.p=1,this.c=n,this.a=t}function bQ(n,e,t,i,r){this.d=e,this.k=i,this.f=r,this.o=-1,this.p=2,this.c=n,this.a=t}function wQ(n,e,t,i,r){this.d=e,this.k=i,this.f=r,this.o=-1,this.p=6,this.c=n,this.a=t}function gQ(n,e,t,i,r){this.d=e,this.k=i,this.f=r,this.o=-1,this.p=7,this.c=n,this.a=t}function pQ(n,e,t,i,r){this.d=e,this.j=i,this.e=r,this.o=-1,this.p=4,this.c=n,this.a=t}function z$n(n,e){var t,i,r,c;for(i=e,r=0,c=i.length;r<c;++r)t=i[r],$Nn(n.a,t);return n}function Eo(n){var e,t,i,r;for(t=n,i=0,r=t.length;i<r;++i)e=t[i],Se(e);return new cTn(n)}function mQ(n){var e;return e=mi(Ki(n.d.d),n.c.d),vm(e,n.c.e.a,n.c.e.b),tt(e,n.c.d)}function vQ(n){var e;return e=mi(Ki(n.c.d),n.d.d),vm(e,n.d.e.a,n.d.e.b),tt(e,n.d.d)}function Dme(n){var e=/function(?:\s+([\w$]+))?\s*\(/,t=e.exec(n);return t&&t[1]||uB}function Lme(n,e,t){var i,r;return r=n.length,i=y.Math.min(t,r),Bnn(n,0,e,0,i,!0),e}function X$n(n,e,t){var i,r;for(r=e.Kc();r.Ob();)i=u(r.Pb(),74),fi(n,u(t.Kb(i),27))}function Nme(n,e){Ep(u(v(u(n.e,10),(cn(),Kt)),101))&&(Dn(),Yt(u(n.e,10).j,e))}function $me(){return NA(),S(T(ton,1),G,257,0,[eon,Qun,Yun,Jun,f_,non,Zun,Wun,Vun])}function xme(){return a1(),S(T(Ohn,1),G,265,0,[xH,Shn,Phn,$H,Ahn,Ihn,CI,Pv,Iv])}function O0(){O0=F,Oj=new ZD("BARYCENTER",0),t9=new ZD(qXn,1),PI=new ZD(UXn,2)}function dT(){dT=F,Qhn=new QD("NO",0),JH=new QD(cin,1),Jhn=new QD("LOOK_BACK",2)}function bT(){bT=F,Isn=new HD("ARD",0),VP=new HD("MSD",1),W_=new HD("MANUAL",2)}function gr(){gr=F,n9=new XD(i8,0),Vu=new XD("INPUT",1),Jc=new XD("OUTPUT",2)}function z4(){return zq||(zq=new Jqn,Lg(zq,S(T(l2,1),Fn,134,0,[new cG]))),zq}function Rs(n){if(!(n>=0))throw M(new Gn("tolerance ("+n+") must be >= 0"));return n}function V$n(n,e){var t;return O(e,44)?n.c.Mc(e):(t=wx(n,e),VT(n,e),t)}function Mr(n,e,t){return ad(n,e),zc(n,t),e1(n,0),Zb(n,1),u1(n,!0),c1(n,!0),n}function vk(n,e){var t;if(t=n.gc(),e<0||e>t)throw M(new Kb(e,t));return new SV(n,e)}function wT(n,e){n.b=y.Math.max(n.b,e.d),n.e+=e.r+(n.a.c.length==0?0:n.c),nn(n.a,e)}function W$n(n){Fb(n.c>=0),_8e(n.d,n.c)<0&&(n.a=n.a-1&n.d.a.length-1,n.b=n.d.c),n.c=-1}function gT(n){var e,t;for(t=n.c.Cc().Kc();t.Ob();)e=u(t.Pb(),16),e.$b();n.c.$b(),n.d=0}function Fme(n){var e,t,i,r;for(t=n.a,i=0,r=t.length;i<r;++i)e=t[i],HPn(e,e.length,null)}function c5(n,e){var t,i,r,c;for(i=e,r=0,c=i.length;r<c;++r)t=i[r],xt(n,t,n.c.b,n.c)}function J$n(n,e){var t,i;for(t=0,i=n.gc();t<i;++t)if(mc(e,n.Xb(t)))return t;return-1}function kQ(n){var e,t;if(n==0)return 32;for(t=0,e=1;!(e&n);e<<=1)++t;return t}function Co(n,e){if(n<0)throw M(new Gn(e+" cannot be negative but was: "+n));return n}function Bme(n,e){typeof window===vy&&typeof window.$gwt===vy&&(window.$gwt[n]=e)}function pT(n,e){return Fhe(s5(n.a,e,Ae(er(Uh,xh(Ae(er(e==null?0:mt(e),Gh)),15)))))}function Rme(n,e,t){return Wb(n,new m9n(e),new z0n,new v9n(t),S(T(xr,1),G,108,0,[]))}function Kme(){return io(),S(T(gdn,1),G,264,0,[Hv,uE,sO,O9,fO,lO,hO,bU,cE])}function Q$n(){Q$n=F,wQn=S(T(ye,1),Ke,28,15,[0,8,4,12,2,10,6,14,1,9,5,13,3,11,7,15])}function u5(){u5=F,B8=new _D("LAYER_SWEEP",0),pj=new _D(sR,1),Ssn=new _D(kh,2)}function yQ(){yQ=F,gie=Re(Re(Re(new ii,(Vi(),Xs),(tr(),d2)),Jh,Lw),Oc,Dw)}function Y$n(){Y$n=F,pie=Re(Re(Re(new ii,(Vi(),Xs),(tr(),d2)),Jh,Lw),Oc,Dw)}function jQ(){jQ=F,mie=Re(Re(Re(new ii,(Vi(),Xs),(tr(),d2)),Jh,Lw),Oc,Dw)}function Z$n(){Z$n=F,vie=Re(Re(Re(new ii,(Vi(),Xs),(tr(),d2)),Jh,Lw),Oc,Dw)}function nxn(){nxn=F,kie=Re(Re(Re(new ii,(Vi(),Xs),(tr(),d2)),Jh,Lw),Oc,Dw)}function exn(){exn=F,yie=Re(Re(Re(new ii,(Vi(),Xs),(tr(),d2)),Jh,Lw),Oc,Dw)}function txn(){txn=F,Cie=Pu(Re(Re(new ii,(Vi(),Oc),(tr(),NP)),Kc,PP),zr,LP)}function _me(n){var e,t;for(t=new C(zRn(n));t.a<t.c.c.length;)e=u(E(t),695),e._f()}function Hme(){DEn();for(var n=RK,e=0;e<arguments.length;e++)n.push(arguments[e])}function ixn(n){Lz(),this.g=new de,this.f=new de,this.b=new de,this.c=new C0,this.i=n}function EQ(){this.f=new Li,this.d=new nz,this.c=new Li,this.a=new Z,this.b=new Z}function rxn(n,e,t,i){this.ak(),this.a=e,this.b=n,this.c=null,this.c=new ZAn(this,e,t,i)}function k$(n,e,t,i,r){this.d=n,this.n=e,this.g=t,this.o=i,this.p=-1,r||(this.o=-2-i-1)}function cxn(){BX.call(this),this.n=-1,this.g=null,this.i=null,this.j=null,this.Bb|=Us}function uxn(n){IC.call(this,n.Ad(64)?OX(0,bs(n.zd(),1)):Ey,n.yd()),this.b=1,this.a=n}function qme(n,e){return _p(),u(v(e,(lc(),I2)),17).a<n.gc()&&u(v(e,I2),17).a>=0}function CQ(n,e){n.r>0&&n.c<n.r&&(n.c+=e,n.i&&n.i.d>0&&n.g!=0&&CQ(n.i,e/n.r*n.i.d))}function MQ(n,e){var t;t=n.c,n.c=e,n.Db&4&&!(n.Db&1)&&it(n,new Ci(n,1,1,t,n.c))}function y$(n,e){var t;t=n.c,n.c=e,n.Db&4&&!(n.Db&1)&&it(n,new Ci(n,1,4,t,n.c))}function X4(n,e){var t;t=n.k,n.k=e,n.Db&4&&!(n.Db&1)&&it(n,new Ci(n,1,2,t,n.k))}function j$(n,e){var t;t=n.D,n.D=e,n.Db&4&&!(n.Db&1)&&it(n,new Ci(n,1,2,t,n.D))}function mT(n,e){var t;t=n.f,n.f=e,n.Db&4&&!(n.Db&1)&&it(n,new Ci(n,1,8,t,n.f))}function vT(n,e){var t;t=n.i,n.i=e,n.Db&4&&!(n.Db&1)&&it(n,new Ci(n,1,7,t,n.i))}function TQ(n,e){var t;t=n.a,n.a=e,n.Db&4&&!(n.Db&1)&&it(n,new Ci(n,1,8,t,n.a))}function AQ(n,e){var t;t=n.b,n.b=e,n.Db&4&&!(n.Db&1)&&it(n,new Ci(n,1,0,t,n.b))}function SQ(n,e){var t;t=n.b,n.b=e,n.Db&4&&!(n.Db&1)&&it(n,new Ci(n,1,0,t,n.b))}function PQ(n,e){var t;t=n.c,n.c=e,n.Db&4&&!(n.Db&1)&&it(n,new Ci(n,1,1,t,n.c))}function IQ(n,e){var t;t=n.d,n.d=e,n.Db&4&&!(n.Db&1)&&it(n,new Ci(n,1,1,t,n.d))}function Ume(n,e,t){var i;n.b=e,n.a=t,i=(n.a&512)==512?new gjn:new rG,n.c=rAe(i,n.b,n.a)}function oxn(n,e){return Sl(n.e,e)?(dr(),a$(e)?new eM(e,n):new j7(e,n)):new $Mn(e,n)}function Gme(n){var e,t;return 0>n?new Dz:(e=n+1,t=new vLn(e,n),new oV(null,t))}function zme(n,e){Dn();var t;return t=new ap(1),Ai(n)?Dr(t,n,e):Vc(t.f,n,e),new eD(t)}function Xme(n,e){var t,i;return t=n.c,i=e.e[n.p],i>0?u(sn(t.a,i-1),10):null}function Vme(n,e){var t,i;return t=n.o+n.p,i=e.o+e.p,t<i?-1:t==i?0:1}function Wme(n){var e;return e=v(n,(W(),st)),O(e,167)?MBn(u(e,167)):null}function sxn(n){var e;return n=y.Math.max(n,2),e=QQ(n),n>e?(e<<=1,e>0?e:Y5):e}function E$(n){switch(_X(n.e!=3),n.e){case 2:return!1;case 0:return!0}return i4e(n)}function fxn(n,e){var t;return O(e,8)?(t=u(e,8),n.a==t.a&&n.b==t.b):!1}function Jme(n,e){var t;t=new kE,u(e.b,68),u(e.b,68),u(e.b,68),nu(e.a,new BV(n,t,e))}function hxn(n,e){var t,i;for(i=e.vc().Kc();i.Ob();)t=u(i.Pb(),44),Vk(n,t.ld(),t.md())}function OQ(n,e){var t;t=n.d,n.d=e,n.Db&4&&!(n.Db&1)&&it(n,new Ci(n,1,11,t,n.d))}function kT(n,e){var t;t=n.j,n.j=e,n.Db&4&&!(n.Db&1)&&it(n,new Ci(n,1,13,t,n.j))}function DQ(n,e){var t;t=n.b,n.b=e,n.Db&4&&!(n.Db&1)&&it(n,new Ci(n,1,21,t,n.b))}function Qme(n,e){(UM(),qf?null:e.c).length==0&&TAn(e,new BU),Dr(n.a,qf?null:e.c,e)}function Yme(n,e){e.Ug("Hierarchical port constraint processing",1),g9e(n),xLe(n),e.Vg()}function D0(){D0=F,ub=new KD("START",0),ma=new KD("MIDDLE",1),cb=new KD("END",2)}function yT(){yT=F,RI=new oX("P1_NODE_PLACEMENT",0),D2=new oX("P2_EDGE_ROUTING",1)}function J1(){J1=F,y3=new lt(Jtn),jP=new lt(MXn),$8=new lt(TXn),lj=new lt(AXn)}function L0(n){var e;return FL(n.f.g,n.d),oe(n.b),n.c=n.a,e=u(n.a.Pb(),44),n.b=GQ(n),e}function LQ(n){var e;return n.b==null?(Gl(),Gl(),dE):(e=n.ul()?n.tl():n.sl(),e)}function lxn(n,e){var t;return t=e==null?-1:qr(n.b,e,0),t<0?!1:(M$(n,t),!0)}function Ks(n,e){var t;return Jn(e),t=e.g,n.b[t]?!1:($t(n.b,t,e),++n.c,!0)}function jT(n,e){var t,i;return t=1-e,i=n.a[t],n.a[t]=i.a[e],i.a[e]=n,n.b=!0,i.b=!1,i}function Zme(n,e){var t,i;for(i=e.Kc();i.Ob();)t=u(i.Pb(),272),n.b=!0,fi(n.e,t),t.b=n}function nve(n,e){var t,i;return t=u(v(n,(cn(),Hw)),8),i=u(v(e,Hw),8),bt(t.b,i.b)}function C$(n,e,t){var i,r,c;return c=e>>5,r=e&31,i=vi(U1(n.n[t][c],Ae(Fs(r,1))),3),i}function axn(n,e,t){var i,r,c;for(c=n.a.length-1,r=n.b,i=0;i<t;r=r+1&c,++i)$t(e,i,n.a[r])}function M$(n,e){var t;t=Yl(n.b,n.b.c.length-1),e<n.b.c.length&&(Go(n.b,e,t),$_n(n,e))}function dxn(n,e){var t;return t=u(ee(n.c,e),467),t||(t=new Jyn,t.c=e,Xe(n.c,t.c,t)),t}function eve(n,e){var t,i;i=new Z,t=e;do Bn(i.c,t),t=u(ee(n.k,t),18);while(t);return i}function T$(n,e,t){var i;return i=new Z,hen(n,e,i,t,!0,!0),n.b=new ET(i.c.length),i}function ud(n,e){var t,i;for(t=n.Pc(),F4(t,0,t.length,e),i=0;i<t.length;i++)n.hd(i,t[i])}function NQ(n){var e,t;for(t=new ne(n);t.e!=t.i.gc();)e=u(ce(t),27),eu(e,0),tu(e,0)}function bxn(n){this.e=n,this.d=new zE(Qb(Tp(this.e).gc())),this.c=this.e.a,this.b=this.e.c}function ET(n){this.b=n,this.a=K(ye,Ke,28,n+1,15,1),this.c=K(ye,Ke,28,n,15,1),this.d=0}function wxn(n,e,t){A$n.call(this,e,t),this.d=K(Qh,b1,10,n.a.c.length,0,1),xf(n.a,this.d)}function gxn(n,e,t){mJ.call(this,n,e,t),this.a=new de,this.b=new de,this.d=new q7n(this)}function pxn(n){aW.call(this),this.b=$(R(v(n,(cn(),Vs)))),this.a=u(v(n,$l),223)}function A$(n,e){var t;return O(e,16)?(t=u(e,16),n.Gc(t)):b$(n,u(Se(e),20).Kc())}function tve(n,e){qt(ut(new Tn(null,new In(new Ha(n.b),1)),new fMn(n,e)),new lMn(n,e))}function ive(n,e){e.Ug(HXn,1),qt(rc(new Tn(null,new In(n.b,16)),new Awn),new Swn),e.Vg()}function mt(n){return Ai(n)?t1(n):$b(n)?pp(n):Nb(n)?SAn(n):pW(n)?n.Hb():hW(n)?l0(n):ZW(n)}function mxn(n){var e,t;for(t=n.c.a.ec().Kc();t.Ob();)e=u(t.Pb(),219),efe(e,new FPn(e.f))}function $Q(n){var e,t;for(t=n.c.a.ec().Kc();t.Ob();)e=u(t.Pb(),219),tfe(e,new QKn(e.e))}function zc(n,e){var t;t=n.zb,n.zb=e,n.Db&4&&!(n.Db&1)&&it(n,new Ci(n,1,1,t,n.zb))}function CT(n,e){var t;t=n.xb,n.xb=e,n.Db&4&&!(n.Db&1)&&it(n,new Ci(n,1,3,t,n.xb))}function MT(n,e){var t;t=n.yb,n.yb=e,n.Db&4&&!(n.Db&1)&&it(n,new Ci(n,1,2,t,n.yb))}function Ft(n,e){var t,i;t=(i=new fD,i),t.n=e,ve((!n.s&&(n.s=new q(ku,n,21,17)),n.s),t)}function jt(n,e){var t,i;i=(t=new cV,t),i.n=e,ve((!n.s&&(n.s=new q(ku,n,21,17)),n.s),i)}function Bi(n,e){var t,i,r;for(Jn(e),t=!1,r=e.Kc();r.Ob();)i=r.Pb(),t=t|n.Fc(i);return t}function vxn(n){var e,t,i;for(e=0,i=n.Kc();i.Ob();)t=i.Pb(),e+=t!=null?mt(t):0,e=~~e;return e}function S$(n,e){var t=n.a,i=0;for(var r in t)t.hasOwnProperty(r)&&(e[i++]=r);return e}function kxn(n){var e;return n==0?"UTC":(n<0?(n=-n,e="UTC+"):e="UTC-",e+YNn(n))}function xQ(n){return n.a<54?n.f<0?-1:n.f>0?1:0:(!n.c&&(n.c=Y7(vc(n.f))),n.c).e}function yxn(n,e){e?n.B==null&&(n.B=n.D,n.D=null):n.B!=null&&(n.D=n.B,n.B=null)}function rve(n,e){return nm(),n==rb&&e==Iw||n==Iw&&e==rb||n==a2&&e==Pw||n==Pw&&e==a2}function cve(n,e){return nm(),n==rb&&e==Pw||n==rb&&e==a2||n==Iw&&e==a2||n==Iw&&e==Pw}function jxn(n,e){return Mf(),Rs(Kf),y.Math.abs(0-e)<=Kf||e==0||isNaN(0)&&isNaN(e)?0:n/e}function Exn(n,e){return $(R(ho($k(_r(new Tn(null,new In(n.c.b,16)),new I7n(n)),e))))}function FQ(n,e){return $(R(ho($k(_r(new Tn(null,new In(n.c.b,16)),new P7n(n)),e))))}function uve(){return pr(),S(T(cH,1),G,259,0,[ZP,cs,K8,nI,yv,m2,_8,vv,kv,eI])}function ove(){return gs(),S(T(Khn,1),G,243,0,[AI,Sj,Pj,Fhn,Bhn,xhn,Rhn,SI,pb,Uw])}function sve(n,e){var t;e.Ug("General Compactor",1),t=d8e(u(z(n,(ua(),yq)),393)),t.Cg(n)}function fve(n,e){var t,i;return t=u(z(n,(ua(),_I)),17),i=u(z(e,_I),17),jc(t.a,i.a)}function BQ(n,e,t){var i,r;for(r=ge(n,0);r.b!=r.d.c;)i=u(be(r),8),i.a+=e,i.b+=t;return n}function o5(n,e,t){var i;for(i=n.b[t&n.f];i;i=i.b)if(t==i.a&&oh(e,i.g))return i;return null}function s5(n,e,t){var i;for(i=n.c[t&n.f];i;i=i.d)if(t==i.f&&oh(e,i.i))return i;return null}function hve(n,e,t){var i,r,c;for(i=0,r=0;r<t;r++)c=e[r],n[r]=c<<1|i,i=c>>>31;i!=0&&(n[t]=i)}function P$(n,e,t,i,r,c){var s;this.c=n,s=new Z,pZ(n,s,e,n.b,t,i,r,c),this.a=new xi(s,0)}function Cxn(){this.c=new XE(0),this.b=new XE(Trn),this.d=new XE(lVn),this.a=new XE(QB)}function Vo(n,e,t,i,r,c,s){je.call(this,n,e),this.d=t,this.e=i,this.c=r,this.b=c,this.a=If(s)}function Ut(n,e,t,i,r,c,s,f,h,l,a,d,g){return P_n(n,e,t,i,r,c,s,f,h,l,a,d,g),sx(n,!1),n}function lve(n){return n.b.c.i.k==(Vn(),Zt)?u(v(n.b.c.i,(W(),st)),12):n.b.c}function Mxn(n){return n.b.d.i.k==(Vn(),Zt)?u(v(n.b.d.i,(W(),st)),12):n.b.d}function ave(n){var e;return e=BM(n),o0(e.a,0)?(QE(),QE(),SQn):(QE(),new uAn(e.b))}function I$(n){var e;return e=gJ(n),o0(e.a,0)?(Ob(),Ob(),n_):(Ob(),new AL(e.b))}function O$(n){var e;return e=gJ(n),o0(e.a,0)?(Ob(),Ob(),n_):(Ob(),new AL(e.c))}function Txn(n){switch(n.g){case 2:return tn(),Wn;case 4:return tn(),Zn;default:return n}}function Axn(n){switch(n.g){case 1:return tn(),ae;case 3:return tn(),Xn;default:return n}}function Sxn(n){switch(n.g){case 0:return new hmn;case 1:return new lmn;default:return null}}function Hp(){Hp=F,x_=new Dt("edgelabelcenterednessanalysis.includelabel",(_n(),wa))}function RQ(){RQ=F,Mie=ah(WMn(Re(Re(new ii,(Vi(),Oc),(tr(),NP)),Kc,PP),zr),LP)}function Pxn(){Pxn=F,Pie=ah(WMn(Re(Re(new ii,(Vi(),Oc),(tr(),NP)),Kc,PP),zr),LP)}function D$(){D$=F,x9=new ljn,CU=S(T(ku,1),s2,179,0,[]),Joe=S(T(As,1),Gcn,62,0,[])}function V4(){V4=F,dj=new Vz("TO_INTERNAL_LTR",0),L_=new Vz("TO_INPUT_DIRECTION",1)}function Ou(){Ou=F,Ron=new wwn,Fon=new gwn,Bon=new pwn,xon=new mwn,Kon=new vwn,_on=new kwn}function dve(n,e){e.Ug(HXn,1),HY(Qhe(new IE((o6(),new kN(n,!1,!1,new qU))))),e.Vg()}function bve(n,e,t){t.Ug("DFS Treeifying phase",1),O8e(n,e),PTe(n,e),n.a=null,n.b=null,t.Vg()}function kk(n,e){return _n(),Ai(n)?RJ(n,Oe(e)):$b(n)?tN(n,R(e)):Nb(n)?rwe(n,un(e)):n.Fd(e)}function f5(n,e){var t,i;for(Jn(e),i=e.vc().Kc();i.Ob();)t=u(i.Pb(),44),n.zc(t.ld(),t.md())}function wve(n,e,t){var i;for(i=t.Kc();i.Ob();)if(!_M(n,e,i.Pb()))return!1;return!0}function gve(n,e,t,i,r){var c;return t&&(c=Ot(e.Dh(),n.c),r=t.Rh(e,-1-(c==-1?i:c),null,r)),r}function pve(n,e,t,i,r){var c;return t&&(c=Ot(e.Dh(),n.c),r=t.Th(e,-1-(c==-1?i:c),null,r)),r}function Ixn(n){var e;if(n.b==-2){if(n.e==0)e=-1;else for(e=0;n.a[e]==0;e++);n.b=e}return n.b}function mve(n){if(Jn(n),n.length==0)throw M(new eh("Zero length BigInteger"));ESe(this,n)}function KQ(n){this.i=n.gc(),this.i>0&&(this.g=this.aj(this.i+(this.i/8|0)+1),n.Qc(this.g))}function Oxn(n,e,t){this.g=n,this.d=e,this.e=t,this.a=new Z,IEe(this),Dn(),Yt(this.a,null)}function _Q(n,e){e.q=n,n.d=y.Math.max(n.d,e.r),n.b+=e.d+(n.a.c.length==0?0:n.c),nn(n.a,e)}function W4(n,e){var t,i,r,c;return r=n.c,t=n.c+n.b,c=n.d,i=n.d+n.a,e.a>r&&e.a<t&&e.b>c&&e.b<i}function nw(n,e){var t,i;for(i=ge(n,0);i.b!=i.d.c;)t=u(be(i),8),t.a+=e.a,t.b+=e.b;return n}function vve(n){var e,t,i;for(i=0,t=new C(n.b);t.a<t.c.c.length;)e=u(E(t),30),e.p=i,++i}function kve(n){var e,t,i;return n.j==(tn(),Xn)&&(e=mHn(n),t=Au(e,Zn),i=Au(e,Wn),i||i&&t)}function yve(n,e){var t;return t=tnn(n),Lnn(new V(t.c,t.d),new V(t.b,t.a),n.Mf(),e,n.ag())}function HQ(n,e){var t;t=u(e,190),nd(t,"x",n.i),nd(t,"y",n.j),nd(t,dK,n.g),nd(t,aK,n.f)}function TT(n,e){var t;O(e,85)?(u(n.c,79).Gk(),t=u(e,85),hxn(n,t)):u(n.c,79).Wb(e)}function h5(n,e){var t,i;for(Jn(e),i=n.vc().Kc();i.Ob();)t=u(i.Pb(),44),e.Yd(t.ld(),t.md())}function jve(n,e){var t;for(Se(e);n.Ob();)if(t=n.Pb(),!UQ(u(t,10)))return!1;return!0}function Eve(){var n;return c_||(c_=new Ryn,n=new VN(""),Ble(n,(a4(),$un)),Qme(c_,n)),c_}function Dxn(n,e){return Wb(new w9n(n),new g9n(e),new p9n(e),new G0n,S(T(xr,1),G,108,0,[]))}function AT(){AT=F,Cq=new iL(kh,0),o1n=new iL("POLAR_COORDINATE",1),u1n=new iL("ID",2)}function ST(){ST=F,Uhn=new VD("EQUALLY",0),zH=new VD(eS,1),Ghn=new VD("NORTH_SOUTH",2)}function J4(){J4=F,N8=new Dt("debugSVG",(_n(),!1)),uon=new Dt("overlapsExisted",!0)}function Lxn(){Lxn=F,kue=Ce((l1(),S(T(vue,1),G,285,0,[uan,yi,Zr,N2,Qi,Pt,L3,Xf])))}function Nxn(){Nxn=F,Poe=Ce((Cm(),S(T(kO,1),G,245,0,[kU,mO,vO,pO,vU,gO,wO,mU])))}function $xn(){$xn=F,hne=Ce((DA(),S(T(Msn,1),G,276,0,[__,U_,K_,X_,q_,H_,z_,G_])))}function xxn(){return q5(),S(T(TNe,1),G,262,0,[ZH,sln,aln,dln,lln,oln,bln,cln,hln,fln,uln])}function od(n,e,t){var i,r;return r=u(x6(n.d,e),17),i=u(x6(n.b,t),17),!r||!i?null:Rp(n,r.a,i.a)}function Fxn(n,e){var t;return t=TF(z4(),n),t?(ht(e,(qe(),H2),t),!0):!1}function Bxn(n){return Bb(),n.A.Hc((go(),Qw))&&!n.B.Hc((io(),uE))?NBn(n):null}function Rxn(){this.a=u(rn((qs(),kP)),17).a,this.c=$(R(rn(yP))),this.b=$(R(rn(k_)))}function sd(n){this.f=n,this.e=new AJ(this.f.i),this.a=this.e,this.b=GQ(this),this.d=this.f.g}function Rt(n,e){QC.call(this,Qoe,n,e),this.b=this,this.a=ru(n.Dh(),$n(this.e.Dh(),this.c))}function Cve(n,e){var t,i;for(i=new C(e.b);i.a<i.c.c.length;)t=u(E(i),30),n.a[t.p]=ije(t)}function Mo(n,e){var t;for(t=0;t<e.j.c.length;t++)u(dk(n,t),21).Gc(u(dk(e,t),16));return n}function L$(n,e,t,i){var r;r=n.a.length,t>r?t=r:zn(e,t+1),n.a=qo(n.a,0,e)+(""+i)+$W(n.a,t)}function Kxn(n,e){n.a=nr(n.a,1),n.c=y.Math.min(n.c,e),n.b=y.Math.max(n.b,e),n.d=nr(n.d,e)}function Mve(n,e){return e<n.b.gc()?u(n.b.Xb(e),10):e==n.b.gc()?n.a:u(sn(n.e,e-n.b.gc()-1),10)}function Tve(n,e,t){return bt(vp(pm(n),new V(e.e.a,e.e.b)),vp(pm(n),new V(t.e.a,t.e.b)))}function Ave(n,e,t){return n==(O0(),PI)?new Wpn:to(e,1)!=0?new Ez(t.length):new Wjn(t.length)}function it(n,e){var t,i,r;if(t=n.th(),t!=null&&n.wh())for(i=0,r=t.length;i<r;++i)t[i].dj(e)}function Sve(n,e){var t,i,r;for(t=n.c.Xe(),r=e.Kc();r.Ob();)i=r.Pb(),n.a.Yd(t,i);return n.b.Kb(t)}function Q4(n,e){var t,i;for(t=n,i=Hi(t).e;i;){if(t=i,t==e)return!0;i=Hi(t).e}return!1}function Q1(n){var e;return e=n.h,e==0?n.l+n.m*o3:e==Il?n.l+n.m*o3-vd:n}function Pve(n,e,t){var i,r;return i=n.a.f[e.p],r=n.a.f[t.p],i<r?-1:i==r?0:1}function Ive(n,e){var t,i;for(i=new C(e);i.a<i.c.c.length;)t=u(E(i),72),nn(n.d,t),Yye(n,t)}function Ove(n,e){var t;e.Ug("Edge and layer constraint edge reversal",1),t=KAe(n),pDe(t),e.Vg()}function Dve(n,e){var t,i;for(i=new ne(n);i.e!=i.i.gc();)t=u(ce(i),27),Ro(t,t.i+e.b,t.j+e.d)}function _xn(n){var e;n.d==null?(++n.e,n.f=0,ZFn(null)):(++n.e,e=n.d,n.d=null,n.f=0,ZFn(e))}function Lve(n){var e;if(n.a==n.b.a)throw M(new nc);return e=n.a,n.c=e,n.a=u(as(n.a.e),227),e}function Un(n,e){var t;return n.Db&e?(t=Rx(n,e),t==-1?n.Eb:cd(n.Eb)[t]):null}function hc(n,e){var t,i;return t=(i=new uG,i),t.G=e,!n.rb&&(n.rb=new Hb(n,Ef,n)),ve(n.rb,t),t}function We(n,e){var t,i;return t=(i=new xE,i),t.G=e,!n.rb&&(n.rb=new Hb(n,Ef,n)),ve(n.rb,t),t}function Hxn(n,e,t,i){O(n.Cb,184)&&(u(n.Cb,184).tb=null),zc(n,t),e&&JEe(n,e),i&&n.gl(!0)}function qxn(n,e){n.c&&(cUn(n,e,!0),qt(new Tn(null,new In(e,16)),new x7n(n))),cUn(n,e,!1)}function Nve(n){wTn();var e;return vCn(YH,n)||(e=new M3n,e.a=n,pV(YH,n,e)),u(Cr(YH,n),645)}function PT(n){var e;if(n.g>1||n.Ob())return++n.a,n.g=0,e=n.i,n.Ob(),e;throw M(new nc)}function Uxn(n){switch(n.a.g){case 1:return new WCn;case 3:return new WRn;default:return new s8n}}function qQ(n,e){switch(e){case 1:return!!n.n&&n.n.i!=0;case 2:return n.k!=null}return wJ(n,e)}function vc(n){return Ay<n&&n<vd?n<0?y.Math.ceil(n):y.Math.floor(n):Q1(sTe(n))}function yk(n){var e;return n<128?(tPn(),e=gun[n],!e&&(e=gun[n]=new jG(n)),e):new jG(n)}function $ve(n,e){var t;try{e.de()}catch(i){if(i=It(i),O(i,82))t=i,Bn(n.c,t);else throw M(i)}}function ds(n){var e,t,i,r;return r=n,i=0,r<0&&(r+=vd,i=Il),t=wi(r/o3),e=wi(r-t*o3),Yc(e,t,i)}function jk(n){var e,t,i;for(i=0,t=new dp(n.a);t.a<t.c.a.length;)e=e5(t),n.b.Hc(e)&&++i;return i}function xve(n){var e,t,i;for(e=1,i=n.Kc();i.Ob();)t=i.Pb(),e=31*e+(t==null?0:mt(t)),e=~~e;return e}function Ur(n,e){var t;return e&&(t=e.nf(),t.dc()||(n.q?f5(n.q,t):n.q=new RMn(t))),n}function Gxn(n,e){var t;return t=n.a.get(e),t===void 0?++n.d:(Pae(n.a,e),--n.c,++n.b.g),t}function Fve(n,e){var t,i,r;return t=e.p-n.p,t==0?(i=n.f.a*n.f.b,r=e.f.a*e.f.b,bt(i,r)):t}function Bve(n,e){var t,i;return t=n.j,i=e.j,t!=i?t.g-i.g:n.p==e.p?0:t==(tn(),Xn)?n.p-e.p:e.p-n.p}function l5(n,e,t,i,r){$t(n.c[e.g],t.g,i),$t(n.c[t.g],e.g,i),$t(n.b[e.g],t.g,r),$t(n.b[t.g],e.g,r)}function fd(n,e,t){this.b=(Jn(n),n),this.d=(Jn(e),e),this.e=(Jn(t),t),this.c=this.d+(""+this.e)}function Y4(n,e){this.b=n,this.e=e,this.d=e.j,this.f=(dr(),u(n,69).xk()),this.k=ru(e.e.Dh(),n)}function Ek(n){this.n=new Z,this.e=new Ct,this.j=new Ct,this.k=new Z,this.f=new Z,this.p=n}function zxn(n){n.r=new ni,n.w=new ni,n.t=new Z,n.i=new Z,n.d=new ni,n.a=new mp,n.c=new de}function N0(){N0=F,rj=new sC("UP",0),ij=new sC(_B,1),a_=new sC(s3,2),d_=new sC(f3,3)}function Z4(){Z4=F,uH=new UD("ONE_SIDED",0),oH=new UD("TWO_SIDED",1),mj=new UD("OFF",2)}function N$(){N$=F,D1n=new hX("EQUAL_BETWEEN_STRUCTURES",0),L1n=new hX("TO_ASPECT_RATIO",1)}function Xxn(){Xxn=F,Yte=Ce((a1(),S(T(Ohn,1),G,265,0,[xH,Shn,Phn,$H,Ahn,Ihn,CI,Pv,Iv])))}function Vxn(){Vxn=F,hoe=Ce((io(),S(T(gdn,1),G,264,0,[Hv,uE,sO,O9,fO,lO,hO,bU,cE])))}function Wxn(){Wxn=F,noe=Ce((lw(),S(T(yr,1),G,95,0,[Js,xl,Qs,Zs,el,Cs,Lo,Ys,Es])))}function Jxn(){Jxn=F,UQn=Ce((NA(),S(T(ton,1),G,257,0,[eon,Qun,Yun,Jun,f_,non,Zun,Wun,Vun])))}function UQ(n){var e;return e=u(v(n,(W(),gc)),64),n.k==(Vn(),Zt)&&(e==(tn(),Wn)||e==Zn)}function Rve(n,e,t){var i,r;r=u(v(n,(cn(),Fr)),75),r&&(i=new Mu,J$(i,0,r),nw(i,t),Bi(e,i))}function IT(n,e,t){var i,r,c,s;s=Hi(n),i=s.d,r=s.c,c=n.n,e&&(c.a=c.a-i.b-r.a),t&&(c.b=c.b-i.d-r.b)}function Kve(n,e){var t,i;return t=n.f.c.length,i=e.f.c.length,t<i?-1:t==i?0:1}function _ve(n){return n.b.c.length!=0&&u(sn(n.b,0),72).a?u(sn(n.b,0),72).a:vN(n)}function Hve(n){var e;if(n){if(e=n,e.dc())throw M(new nc);return e.Xb(e.gc()-1)}return NOn(n.Kc())}function Qxn(n){var e;return Ec(n,0)<0&&(n=WV(n)),e=Ae(U1(n,32)),64-(e!=0?iy(e):iy(Ae(n))+32)}function qve(){return UM(),qf?new VN(null):wHn(Eve(),"com.google.common.base.Strings")}function $$(n,e,t,i){return t==1?(!n.n&&(n.n=new q(Ar,n,1,7)),cr(n.n,e,i)):hnn(n,e,t,i)}function Ck(n,e){var t,i;return i=(t=new UO,t),zc(i,e),ve((!n.A&&(n.A=new Tu(fu,n,7)),n.A),i),i}function Uve(n,e,t){var i,r,c,s;return c=null,s=e,r=A0(s,gK),i=new wMn(n,t),c=(yke(i.a,i.b,r),r),c}function x$(n){var e;return(!n.a||!(n.Bb&1)&&n.a.Vh())&&(e=ws(n),O(e,156)&&(n.a=u(e,156))),n.a}function Mk(n,e){var t,i;for(Jn(e),i=e.Kc();i.Ob();)if(t=i.Pb(),!n.Hc(t))return!1;return!0}function Gve(n,e){var t,i,r;return t=n.l+e.l,i=n.m+e.m+(t>>22),r=n.h+e.h+(i>>22),Yc(t&ro,i&ro,r&Il)}function Yxn(n,e){var t,i,r;return t=n.l-e.l,i=n.m-e.m+(t>>22),r=n.h-e.h+(i>>22),Yc(t&ro,i&ro,r&Il)}function zve(n){var e,t;for(RDe(n),t=new C(n.d);t.a<t.c.c.length;)e=u(E(t),105),e.i&&Nje(e)}function It(n){var e;return O(n,82)?n:(e=n&&n.__java$exception,e||(e=new GFn(n),Lyn(e)),e)}function Tk(n){if(O(n,193))return u(n,123);if(n)return null;throw M(new sp(CWn))}function GQ(n){return n.a.Ob()?!0:n.a!=n.e?!1:(n.a=new WJ(n.f.f),n.a.Ob())}function Zxn(n,e){if(e==null)return!1;for(;n.a!=n.b;)if(rt(e,xT(n)))return!0;return!1}function nFn(n,e){return!n||!e||n==e?!1:KBn(n.d.c,e.d.c+e.d.b)&&KBn(e.d.c,n.d.c+n.d.b)}function hi(n,e){var t,i;return t=e.Pc(),i=t.length,i==0?!1:(zV(n.c,n.c.length,t),!0)}function Xve(n,e,t){var i,r;for(r=e.vc().Kc();r.Ob();)i=u(r.Pb(),44),n.yc(i.ld(),i.md(),t);return n}function F$(n){var e,t,i;for(e=new Ct,i=ge(n.d,0);i.b!=i.d.c;)t=u(be(i),65),xe(e,t.c);return e}function eFn(n,e){var t,i;for(i=new C(n.b);i.a<i.c.c.length;)t=u(E(i),72),U(t,(W(),A3),e)}function Vve(n,e,t){var i,r;for(r=new C(n.b);r.a<r.c.c.length;)i=u(E(r),27),Ro(i,i.i+e,i.j+t)}function tFn(n,e){if(!n)throw M(new Gn(H5("value already present: %s",S(T(ki,1),Fn,1,5,[e]))))}function Wve(n,e,t,i,r){return Xg(),y.Math.min(IGn(n,e,t,i,r),IGn(t,i,n,e,HC(new V(r.a,r.b))))}function Jve(n,e,t,i){u(t.b,68),u(t.b,68),u(i.b,68),u(i.b,68),u(i.b,68),nu(i.a,new FV(n,e,i))}function Qve(n,e){n.d==(ci(),Br)||n.d==us?u(e.a,60).c.Fc(u(e.b,60)):u(e.b,60).c.Fc(u(e.a,60))}function iFn(n,e){var t;return t=Dh(e.a.gc()),qt(fT(new Tn(null,new In(e,1)),n.i),new oMn(n,t)),t}function rFn(n){var e,t;return t=(e=new UO,e),zc(t,"T"),ve((!n.d&&(n.d=new Tu(fu,n,11)),n.d),t),t}function zQ(n){var e,t,i,r;for(e=1,t=0,r=n.gc();t<r;++t)i=n.Vi(t),e=31*e+(i==null?0:mt(i));return e}function cFn(n,e,t,i){var r;return ek(e,n.e.Rd().gc()),ek(t,n.c.Rd().gc()),r=n.a[e][t],$t(n.a[e],t,i),r}function S(n,e,t,i,r){return r.Rm=n,r.Sm=e,r.Tm=J2,r.__elementTypeId$=t,r.__elementTypeCategory$=i,r}function OT(){OT=F,F_=new dC(kh,0),HP=new dC(GXn,1),qP=new dC(zXn,2),wj=new dC("BOTH",3)}function $f(){$f=F,j3=new bC(qm,0),lv=new bC(s3,1),av=new bC(f3,2),B_=new bC("TOP",3)}function nm(){nm=F,rb=new lC("Q1",0),Iw=new lC("Q4",1),Pw=new lC("Q2",2),a2=new lC("Q3",3)}function DT(){DT=F,QH=new YD("OFF",0),Ov=new YD("SINGLE_EDGE",1),Gw=new YD("MULTI_EDGE",2)}function Ak(){Ak=F,YI=new aX("MINIMUM_SPANNING_TREE",0),ian=new aX("MAXIMUM_SPANNING_TREE",1)}function qp(){qp=F,bue=new mmn,due=new pmn}function XQ(n){var e,t;return t=(B1(),e=new jE,e),n&&ve((!n.a&&(n.a=new q(Mt,n,6,6)),n.a),t),t}function B$(n){var e,t,i,r;for(r=new Z,i=n.Kc();i.Ob();)t=u(i.Pb(),27),e=aw(t),hi(r,e);return r}function Yve(n,e){var t,i;for(TM(e,"predicate"),i=0;n.Ob();i++)if(t=n.Pb(),e.Lb(t))return i;return-1}function Up(n,e){var t,i;if(i=0,n<64&&n<=e)for(e=e<64?e:63,t=n;t<=e;t++)i=hf(i,Fs(1,t));return i}function Zve(n,e){var t,i;return t=n.c,i=e.e[n.p],i<t.a.c.length-1?u(sn(t.a,i+1),10):null}function VQ(n){Dn();var e,t,i;for(i=0,t=n.Kc();t.Ob();)e=t.Pb(),i=i+(e!=null?mt(e):0),i=i|0;return i}function n6e(n){var e,t,i;return e=u(n.e&&n.e(),9),i=(t=e.slice(),u(o$(t,e),9)),new _o(e,i,e.length)}function uFn(n,e,t){var i;Hu(n.a),nu(t.i,new Pkn(n)),i=new LC(u(ee(n.a,e.b),68)),JBn(n,i,e),t.f=i}function e6e(n){var e;U0(n,!0),e=d1,kt(n,(cn(),Tv))&&(e+=u(v(n,Tv),17).a),U(n,Tv,Y(e))}function t6e(n){var e;return e=new ul,e.a=n,e.b=a6e(n),e.c=K(fn,J,2,2,6,1),e.c[0]=kxn(n),e.c[1]=kxn(n),e}function oFn(n){var e,t,i;return t=n.n,i=n.o,e=n.d,new Ho(t.a-e.b,t.b-e.d,i.a+(e.b+e.c),i.b+(e.d+e.a))}function i6e(n,e){return!n||!e||n==e?!1:x0(n.b.c,e.b.c+e.b.b)<0&&x0(e.b.c,n.b.c+n.b.b)<0}function sFn(n){switch(n.g){case 1:return Ta;case 2:return nl;case 3:return Zj;default:return nE}}function r6e(n){switch(u(v(n,(cn(),ou)),171).g){case 2:case 4:return!0;default:return!1}}function Sk(n,e,t){switch(t.g){case 2:n.b=e;break;case 1:n.c=e;break;case 4:n.d=e;break;case 3:n.a=e}}function WQ(n,e){switch(e){case 0:!n.o&&(n.o=new Iu((Cc(),il),T1,n,0)),n.o.c.$b();return}cF(n,e)}function c6e(n,e){var t,i;return t=u(u(ee(n.g,e.a),42).a,68),i=u(u(ee(n.g,e.b),42).a,68),xUn(t,i)}function JQ(n,e,t){var i;if(i=n.gc(),e>i)throw M(new Kb(e,i));return n.Si()&&(t=gOn(n,t)),n.Ei(e,t)}function em(n,e,t,i,r){var c,s;for(s=t;s<=r;s++)for(c=e;c<=i;c++)Rg(n,c,s)||xA(n,c,s,!0,!1)}function u6e(n){Xg();var e,t,i;for(t=K(Ei,J,8,2,0,1),i=0,e=0;e<2;e++)i+=.5,t[e]=Z9e(i,n);return t}function tm(n){var e,t,i;return e=~n.l+1&ro,t=~n.m+(e==0?1:0)&ro,i=~n.h+(e==0&&t==0?1:0)&Il,Yc(e,t,i)}function QQ(n){var e;if(n<0)return Wi;if(n==0)return 0;for(e=Y5;!(e&n);e>>=1);return e}function R$(n,e,t){return n>=128?!1:n<64?M6(vi(Fs(1,n),t),0):M6(vi(Fs(1,n-64),e),0)}function Pk(n,e,t){return t==null?(!n.q&&(n.q=new de),Bp(n.q,e)):(!n.q&&(n.q=new de),Xe(n.q,e,t)),n}function U(n,e,t){return t==null?(!n.q&&(n.q=new de),Bp(n.q,e)):(!n.q&&(n.q=new de),Xe(n.q,e,t)),n}function fFn(n){var e,t;return t=new zM,Ur(t,n),U(t,(J1(),y3),n),e=new de,$Pe(n,t,e),fDe(n,t,e),t}function hFn(n){var e,t;return e=n.t-n.k[n.o.p]*n.d+n.j[n.o.p]>n.f,t=n.u+n.e[n.o.p]*n.d>n.f*n.s*n.d,e||t}function lFn(n,e){var t,i,r,c;for(t=!1,i=n.a[e].length,c=0;c<i-1;c++)r=c+1,t=t|L8e(n,e,c,r);return t}function o6e(n){var e,t,i,r;for(t=n.a,i=0,r=t.length;i<r;++i)e=t[i],mFn(n,e,(tn(),ae)),mFn(n,e,Xn)}function aFn(){aFn=F,Ene=Ce((pr(),S(T(cH,1),G,259,0,[ZP,cs,K8,nI,yv,m2,_8,vv,kv,eI])))}function dFn(){dFn=F,tie=Ce((gs(),S(T(Khn,1),G,243,0,[AI,Sj,Pj,Fhn,Bhn,xhn,Rhn,SI,pb,Uw])))}function hd(){hd=F,Y_=new qD(kh,0),mv=new qD("INCOMING_ONLY",1),p2=new qD("OUTGOING_ONLY",2)}function K$(){K$=F,WK={boolean:qhe,number:ihe,string:rhe,object:D_n,function:D_n,undefined:Ffe}}function YQ(){this.o=null,this.k=null,this.j=null,this.d=null,this.b=null,this.n=null,this.a=null}function ZQ(n,e){this.c=n,this.d=e,this.b=this.d/this.c.c.Rd().gc()|0,this.a=this.d%this.c.c.Rd().gc()}function bFn(n,e){this.b=n,gg.call(this,(u(L(_((G1(),Hn).o),10),19),e.i),e.g),this.a=(D$(),CU)}function nY(n,e,t){this.q=new y.Date,this.q.setFullYear(n+fa,e,t),this.q.setHours(0,0,0,0),G5(this,0)}function wFn(n,e){B7(n>=0,"Negative initial capacity"),B7(e>=0,"Non-positive load factor"),Hu(this)}function s6e(n,e,t,i,r){var c,s;if(s=n.length,c=t.length,e<0||i<0||r<0||e+r>s||i+r>c)throw M(new qG)}function eY(n,e){Dn();var t,i,r,c,s;for(s=!1,i=e,r=0,c=i.length;r<c;++r)t=i[r],s=s|n.Fc(t);return s}function gFn(n,e,t){var i,r;return i=new r$(e,t),r=new DO,n.b=yqn(n,n.b,i,r),r.b||++n.c,n.b.b=!1,r.d}function a5(n){var e;return e=n.a[n.b],e==null?null:($t(n.a,n.b,null),n.b=n.b+1&n.a.length-1,e)}function pFn(n){var e,t;return t=iy(n.h),t==32?(e=iy(n.m),e==32?iy(n.l)+32:e+20-10):t-12}function tY(n){var e;return(!n.c||!(n.Bb&1)&&n.c.Db&64)&&(e=ws(n),O(e,90)&&(n.c=u(e,29))),n.c}function Y1(n){var e,t;for(t=new C(n.a.b);t.a<t.c.c.length;)e=u(E(t),60),e.d.c=-e.d.c-e.d.b;uen(n)}function Z1(n){var e,t;for(t=new C(n.a.b);t.a<t.c.c.length;)e=u(E(t),86),e.g.c=-e.g.c-e.g.b;PA(n)}function mFn(n,e,t){var i,r,c,s;for(s=p5(e,t),c=0,r=s.Kc();r.Ob();)i=u(r.Pb(),12),Xe(n.c,i,Y(c++))}function vFn(n,e,t){var i;return i=new Z,hen(n,e,i,(tn(),Zn),!0,!1),hen(n,t,i,Wn,!1,!1),i}function cc(n){var e,t,i,r,c;for(e=new Li,i=n,r=0,c=i.length;r<c;++r)t=i[r],e.a+=t.a,e.b+=t.b;return e}function _$(n,e,t){var i,r,c,s;return c=null,s=e,r=A0(s,"labels"),i=new MMn(n,t),c=(GCe(i.a,i.b,r),r),c}function f6e(n,e,t,i){var r;return r=Qnn(n,e,t,i),!r&&(r=p5e(n,t,i),r&&!Jg(n,e,r))?null:r}function h6e(n,e,t,i){var r;return r=Ynn(n,e,t,i),!r&&(r=rx(n,t,i),r&&!Jg(n,e,r))?null:r}function l6e(n,e,t){if(Se(e),t.Ob())for(mX(e,uIn(t.Pb()));t.Ob();)mX(e,n.a),mX(e,uIn(t.Pb()));return e}function kFn(n,e){var t;for(t=0;t<n.a.a.length;t++)if(!u(YSn(n.a,t),178).Lb(e))return!1;return!0}function a6e(n){var e;return n==0?"Etc/GMT":(n<0?(n=-n,e="Etc/GMT-"):e="Etc/GMT+",e+YNn(n))}function iY(n){var e;return n.b<=0?!1:(e=th("MLydhHmsSDkK",wu(Xi(n.c,0))),e>1||e>=0&&n.b<3)}function H$(n){var e,t,i;e=~n.l+1&ro,t=~n.m+(e==0?1:0)&ro,i=~n.h+(e==0&&t==0?1:0)&Il,n.l=e,n.m=t,n.h=i}function rY(n){Dn();var e,t,i;for(i=1,t=n.Kc();t.Ob();)e=t.Pb(),i=31*i+(e!=null?mt(e):0),i=i|0;return i}function d6e(n,e,t,i,r){var c;return c=Xnn(n,e),t&&H$(c),r&&(n=u7e(n,e),i?ba=tm(n):ba=Yc(n.l,n.m,n.h)),c}function yFn(n,e,t){n.g=uF(n,e,(tn(),Zn),n.b),n.d=uF(n,t,Zn,n.b),!(n.g.c==0||n.d.c==0)&&YKn(n)}function jFn(n,e,t){n.g=uF(n,e,(tn(),Wn),n.j),n.d=uF(n,t,Wn,n.j),!(n.g.c==0||n.d.c==0)&&YKn(n)}function cY(n,e){switch(e){case 7:return!!n.e&&n.e.i!=0;case 8:return!!n.d&&n.d.i!=0}return qY(n,e)}function b6e(n,e){switch(e.g){case 0:O(n.b,641)||(n.b=new Rxn);break;case 1:O(n.b,642)||(n.b=new BSn)}}function EFn(n){switch(n.g){case 0:return new gmn;default:throw M(new Gn(xS+(n.f!=null?n.f:""+n.g)))}}function CFn(n){switch(n.g){case 0:return new wmn;default:throw M(new Gn(xS+(n.f!=null?n.f:""+n.g)))}}function w6e(n,e,t){return!s4(ut(new Tn(null,new In(n.c,16)),new Z3(new hMn(e,t)))).Bd((Xa(),v3))}function MFn(n,e){return vp(pm(u(v(e,(lc(),vb)),88)),new V(n.c.e.a-n.b.e.a,n.c.e.b-n.b.e.b))<=0}function g6e(n,e){for(;n.g==null&&!n.c?cJ(n):n.g==null||n.i!=0&&u(n.g[n.i-1],51).Ob();)kle(e,CA(n))}function ld(n){var e,t;for(t=new C(n.a.b);t.a<t.c.c.length;)e=u(E(t),86),e.f.$b();Yfe(n.b,n),uqn(n)}function Ik(n){var e,t,i;for(e=new Mu,i=ge(n,0);i.b!=i.d.c;)t=u(be(i),8),g4(e,0,new rr(t));return e}function im(n){var e;return z1(n),e=new LO,n.a.Bd(e)?(b4(),new wD(Jn(e.a))):(b4(),b4(),Dun)}function uY(n,e,t){switch(e){case 0:!n.o&&(n.o=new Iu((Cc(),il),T1,n,0)),TT(n.o,t);return}sF(n,e,t)}function q$(n,e,t){this.g=n,this.e=new Li,this.f=new Li,this.d=new Ct,this.b=new Ct,this.a=e,this.c=t}function U$(n,e,t,i){this.b=new Z,this.n=new Z,this.i=i,this.j=t,this.s=n,this.t=e,this.r=0,this.d=0}function rm(n,e){if(!n.Li()&&e==null)throw M(new Gn("The 'no null' constraint is violated"));return e}function t1(n){var e,t;for(e=0,t=0;t<n.length;t++)e=(e<<5)-e+(zn(t,n.length),n.charCodeAt(t))|0;return e}function TFn(n,e){var t,i,r;for(r=n.b;r;){if(t=n.a.Ne(e,r.d),t==0)return r;i=t<0?0:1,r=r.a[i]}return null}function p6e(n,e,t){var i,r;i=(_n(),!!yX(t)),r=u(e.xc(i),15),r||(r=new Z,e.zc(i,r)),r.Fc(t)}function m6e(n,e){var t,i;return t=u(z(n,(Bf(),Rj)),17).a,i=u(z(e,Rj),17).a,t==i||t<i?-1:t>i?1:0}function v6e(n){return nn(n.c,(qp(),bue)),hQ(n.a,$(R(rn((bx(),EI)))))?new tvn:new $kn(n)}function k6e(n){for(;!n.d||!n.d.Ob();)if(n.b&&!i6(n.b))n.d=u(Sp(n.b),51);else return null;return n.d}function oY(n){switch(n.g){case 1:return lVn;default:case 2:return 0;case 3:return QB;case 4:return Trn}}function y6e(){nt();var n;return IU||(n=_1e(oa("M",!0)),n=uM(oa("M",!1),n),IU=n,IU)}function LT(){LT=F,gU=new CC("ELK",0),Tdn=new CC("JSON",1),Mdn=new CC("DOT",2),Adn=new CC("SVG",3)}function d5(){d5=F,VH=new WD("STACKED",0),XH=new WD("REVERSE_STACKED",1),Ij=new WD("SEQUENCED",2)}function b5(){b5=F,wln=new eL(kh,0),nq=new eL("MIDDLE_TO_MIDDLE",1),Lj=new eL("AVOID_OVERLAP",2)}function cm(){cm=F,Esn=new Ygn,Csn=new Zgn,JZn=new Jgn,WZn=new n2n,VZn=new Qgn,jsn=(Jn(VZn),new O0n)}function NT(){NT=F,hdn=new f0(15),Jue=new Ni((qe(),C1),hdn),C9=N3,udn=Pue,odn=Hd,fdn=K2,sdn=Vw}function Lg(n,e){var t,i,r,c,s;for(i=e,r=0,c=i.length;r<c;++r)t=i[r],s=new YPn(n),t.hf(s),VPe(s);Hu(n.f)}function G$(n,e){var t;return e===n?!0:O(e,229)?(t=u(e,229),rt(n.Zb(),t.Zb())):!1}function sY(n,e){return tqn(n,e)?(Pn(n.b,u(v(e,(W(),Nl)),21),e),xe(n.a,e),!0):!1}function j6e(n){var e,t;e=u(v(n,(W(),Xu)),10),e&&(t=e.c,du(t.a,e),t.a.c.length==0&&du(Hi(e).b,t))}function E6e(n,e){return kt(n,(W(),dt))&&kt(e,dt)?u(v(e,dt),17).a-u(v(n,dt),17).a:0}function C6e(n,e){return kt(n,(W(),dt))&&kt(e,dt)?u(v(n,dt),17).a-u(v(e,dt),17).a:0}function AFn(n){return qf?K(OQn,Jzn,581,0,0,1):u(xf(n.a,K(OQn,Jzn,581,n.a.c.length,0,1)),856)}function M6e(n,e,t,i){return yM(),new lz(S(T(Pd,1),WA,44,0,[(Nx(n,e),new i0(n,e)),(Nx(t,i),new i0(t,i))]))}function Ng(n,e,t){var i,r;return r=(i=new hD,i),Mr(r,e,t),ve((!n.q&&(n.q=new q(As,n,11,10)),n.q),r),r}function z$(n){var e,t,i,r;for(r=ule(Toe,n),t=r.length,i=K(fn,J,2,t,6,1),e=0;e<t;++e)i[e]=r[e];return i}function fY(n,e){var t;e*2+1>=n.b.c.length||(fY(n,2*e+1),t=2*e+2,t<n.b.c.length&&fY(n,t),$_n(n,e))}function T6e(n,e){var t,i;for(i=ge(n,0);i.b!=i.d.c;)t=u(be(i),219),t.e.length>0&&(e.Cd(t),t.i&&E5e(t))}function hY(n,e,t){var i;for(i=t-1;i>=0&&n[i]===e[i];i--);return i<0?0:ND(vi(n[i],mr),vi(e[i],mr))?-1:1}function SFn(n,e,t){var i,r;this.g=n,this.c=e,this.a=this,this.d=this,r=sxn(t),i=K(sQn,Cy,227,r,0,1),this.b=i}function X$(n,e,t,i,r){var c,s;for(s=t;s<=r;s++)for(c=e;c<=i;c++)if(Rg(n,c,s))return!0;return!1}function A6e(n,e){var t,i;for(i=n.Zb().Cc().Kc();i.Ob();)if(t=u(i.Pb(),16),t.Hc(e))return!0;return!1}function PFn(n,e,t){var i,r,c,s;for(Jn(t),s=!1,c=n.fd(e),r=t.Kc();r.Ob();)i=r.Pb(),c.Rb(i),s=!0;return s}function V$(n,e){var t,i;return i=u(Un(n.a,4),129),t=K(jU,MK,424,e,0,1),i!=null&&Ic(i,0,t,0,i.length),t}function IFn(n,e){var t;return t=new jF((n.f&256)!=0,n.i,n.a,n.d,(n.f&16)!=0,n.j,n.g,e),n.e!=null||(t.c=n),t}function S6e(n,e){var t;return n===e?!0:O(e,85)?(t=u(e,85),dnn(Wa(n),t.vc())):!1}function OFn(n,e,t){var i,r;for(r=t.Kc();r.Ob();)if(i=u(r.Pb(),44),n.Be(e,i.md()))return!0;return!1}function DFn(n,e,t){return n.d[e.p][t.p]||(O9e(n,e,t),n.d[e.p][t.p]=!0,n.d[t.p][e.p]=!0),n.a[e.p][t.p]}function P6e(n,e){var t;return!n||n==e||!kt(e,(W(),sb))?!1:(t=u(v(e,(W(),sb)),10),t!=n)}function W$(n){switch(n.i){case 2:return!0;case 1:return!1;case-1:++n.c;default:return n.$l()}}function LFn(n){switch(n.i){case-2:return!0;case-1:return!1;case 1:--n.c;default:return n._l()}}function NFn(n){yOn.call(this,"The given string does not match the expected format for individual spacings.",n)}function I6e(n,e){var t;e.Ug("Min Size Preprocessing",1),t=jnn(n),ht(n,(_h(),a9),t.a),ht(n,UI,t.b),e.Vg()}function O6e(n){var e,t,i;for(e=0,i=K(Ei,J,8,n.b,0,1),t=ge(n,0);t.b!=t.d.c;)i[e++]=u(be(t),8);return i}function J$(n,e,t){var i,r,c;for(i=new Ct,c=ge(t,0);c.b!=c.d.c;)r=u(be(c),8),xe(i,new rr(r));PFn(n,e,i)}function D6e(n,e){var t;return t=nr(n,e),ND(RN(n,e),0)|AC(RN(n,t),0)?t:nr(Ey,RN(U1(t,63),1))}function L6e(n,e){var t,i;return t=u(n.d.Bc(e),16),t?(i=n.e.hc(),i.Gc(t),n.e.d-=t.gc(),t.$b(),i):null}function $Fn(n){var e;if(e=n.a.c.length,e>0)return E4(e-1,n.a.c.length),Yl(n.a,e-1);throw M(new $yn)}function xFn(n,e,t){if(n>e)throw M(new Gn(ZA+n+Qzn+e));if(n<0||e>t)throw M(new pz(ZA+n+Stn+e+Mtn+t))}function um(n,e){n.D==null&&n.B!=null&&(n.D=n.B,n.B=null),j$(n,e==null?null:(Jn(e),e)),n.C&&n.hl(null)}function N6e(n,e){var t;t=rn((bx(),EI))!=null&&e.Sg()!=null?$(R(e.Sg()))/$(R(rn(EI))):1,Xe(n.b,e,t)}function lY(n,e){var t,i;if(i=n.c[e],i!=0)for(n.c[e]=0,n.d-=i,t=e+1;t<n.a.length;)n.a[t]-=i,t+=t&-t}function ew(n){var e;++n.j,n.i==0?n.g=null:n.i<n.g.length&&(e=n.g,n.g=n.aj(n.i),Ic(e,0,n.g,0,n.i))}function $6e(n,e,t){if(e<0)throw M(new Ir(DVn+e));e<n.j.c.length?Go(n.j,e,t):(xDn(n,e),nn(n.j,t))}function FFn(n){if(!n.a||!(n.a.i&8))throw M(new Or("Enumeration class expected for layout option "+n.f))}function aY(n){var e;return e=(!n.a&&(n.a=new q(Bl,n,9,5)),n.a),e.i!=0?rle(u(L(e,0),694)):null}function x6e(n){var e;for(Se(n),DV(!0,"numberToAdvance must be nonnegative"),e=0;e<0&&pe(n);e++)fe(n);return e}function Q$(){Q$=F,fon=(YE(),b_),son=new Mn(_tn,fon),PYn=new lt(Htn),IYn=new lt(qtn),OYn=new lt(Utn)}function w5(){w5=F,aq=new mC(tin,0),BI=new mC(bVn,1),lq=new mC("FAN",2),hq=new mC("CONSTRAINT",3)}function Ok(){Ok=F,KI=new tL(kh,0),Hln=new tL("RADIAL_COMPACTION",1),qln=new tL("WEDGE_COMPACTION",2)}function om(){om=F,WH=new JD("CONSERVATIVE",0),Vhn=new JD("CONSERVATIVE_SOFT",1),e9=new JD("SLOPPY",2)}function Gu(){Gu=F,xun=new $D("CONCURRENT",0),Yr=new $D("IDENTITY_FINISH",1),Aw=new $D("UNORDERED",2)}function Y$(){Y$=F,T_=aOn(S(T(E9,1),G,88,0,[(ci(),Br),Xr])),A_=aOn(S(T(E9,1),G,88,0,[us,Vf]))}function wo(n){return Ai(n)?fn:$b(n)?si:Nb(n)?Gt:pW(n)||hW(n)?n.Rm:n.Rm||Array.isArray(n)&&T(fQn,1)||fQn}function F6e(n){return n?n.i&1?n==so?Gt:n==ye?Gi:n==cg?sv:n==Pi?si:n==xa?tb:n==X2?ib:n==Fu?p3:I8:n:null}function $g(n){return(n.c!=n.b.b||n.i!=n.g.b)&&(Pb(n.a.c,0),hi(n.a,n.b),hi(n.a,n.g),n.c=n.b.b,n.i=n.g.b),n.a}function B6e(n,e){var t,i;for(t=n.a.length-1;e!=n.b;)i=e-1&t,$t(n.a,e,n.a[i]),e=i;$t(n.a,n.b,null),n.b=n.b+1&t}function R6e(n,e){var t,i;for(t=n.a.length-1,n.c=n.c-1&t;e!=n.c;)i=e+1&t,$t(n.a,e,n.a[i]),e=i;$t(n.a,n.c,null)}function dY(n,e,t){var i,r;return zb(e,n.c.length),i=t.Pc(),r=i.length,r==0?!1:(zV(n.c,e,i),!0)}function BFn(n,e,t){var i,r,c,s;for(r=t,c=0,s=r.length;c<s;++c)if(i=r[c],n.b.Be(e,i.ld()))return i;return null}function Dk(n){var e,t,i,r,c;for(c=1,t=n,i=0,r=t.length;i<r;++i)e=t[i],c=31*c+(e!=null?mt(e):0),c=c|0;return c}function Ce(n){var e,t,i,r,c;for(e={},i=n,r=0,c=i.length;r<c;++r)t=i[r],e[":"+(t.f!=null?t.f:""+t.g)]=t;return e}function K6e(n){var e,t;if(n==null)return null;for(e=0,t=n.length;e<t;e++)if(!OSn(n[e]))return n[e];return null}function Z$(n,e){return!n||e&&!n.j||O(n,127)&&u(n,127).a.b==0?0:n.jf()}function $T(n,e){return!n||e&&!n.k||O(n,127)&&u(n,127).a.a==0?0:n.kf()}function RFn(n,e){return kt(n,(W(),dt))&&kt(e,dt)?jc(u(v(n,dt),17).a,u(v(e,dt),17).a):0}function KFn(n){var e,t,i;for(i=0,t=new te(re(n.a.Kc(),new En));pe(t);)e=u(fe(t),18),e.c.i==e.d.i||++i;return i}function _Fn(n,e){var t,i,r;for(r=e-n.f,i=new C(n.d);i.a<i.c.c.length;)t=u(E(i),315),xBn(t,t.e,t.f+r);n.f=e}function ad(n,e){var t,i,r;i=n.Yk(e,null),r=null,e&&(r=(o4(),t=new Jd,t),K4(r,n.r)),i=Ff(n,r,i),i&&i.oj()}function HFn(n,e){var t,i,r;t=n,r=0;do{if(t==e)return r;if(i=t.e,!i)throw M(new Q9);t=Hi(i),++r}while(!0)}function _6e(n){var e,t,i,r;for(i=n.b.a,t=i.a.ec().Kc();t.Ob();)e=u(t.Pb(),567),r=new zHn(e,n.e,n.f),nn(n.g,r)}function H6e(n){var e;return e=new v$n(n),Z7(n.a,OZn,new Ku(S(T(aj,1),Fn,382,0,[e]))),e.d&&nn(e.f,e.d),e.f}function qFn(n,e){var t;for(t=0;t<e.length;t++)if(n==(zn(t,e.length),e.charCodeAt(t)))return!0;return!1}function q6e(n,e){return e<n.length&&(zn(e,n.length),n.charCodeAt(e)!=63)&&(zn(e,n.length),n.charCodeAt(e)!=35)}function UFn(n,e,t,i){ETn(this),this.c=K(Qh,b1,10,n.a.c.length,0,1),this.e=e,xf(n.a,this.c),this.f=t,this.b=i}function GFn(n){Ljn(),xC(this),MM(this),this.e=n,bqn(this,n),this.g=n==null?gu:Jr(n),this.a="",this.b=n,this.a=""}function bY(){this.a=new amn,this.f=new jkn(this),this.b=new Ekn(this),this.i=new Ckn(this),this.e=new Mkn(this)}function zFn(){Jfe.call(this,new VJ(Qb(16))),Co(2,Ozn),this.b=2,this.a=new HW(null,null,0,null),J9(this.a,this.a)}function wY(n){throw K$(),M(new Ojn("Unexpected typeof result '"+n+"'; please report this bug to the GWT team"))}function nx(n,e,t){return y.Math.abs(e-n)<PS||y.Math.abs(t-n)<PS?!0:e-n>PS?n-t>PS:t-n>PS}function XFn(n,e){var t;for(t=0;t<e.length;t++)if(n==(zn(t,e.length),e.charCodeAt(t)))return!0;return!1}function U6e(n){var e,t;if(n==null)return!1;for(e=0,t=n.length;e<t;e++)if(!OSn(n[e]))return!1;return!0}function gY(n,e){var t,i,r;return i=!1,t=e.q.d,e.d<n.b&&(r=cen(e.q,n.b),e.q.d>r&&(EKn(e.q,r),i=t!=e.q.d)),i}function VFn(n,e){var t,i,r,c,s,f,h,l;return h=e.i,l=e.j,i=n.f,r=i.i,c=i.j,s=h-r,f=l-c,t=y.Math.sqrt(s*s+f*f),t}function pY(n,e){var t,i;return i=WT(n),i||(t=(UF(),$Hn(e)),i=new Cyn(t),ve(i.El(),n)),i}function Lk(n,e){var t,i;return t=u(n.c.Bc(e),16),t?(i=n.hc(),i.Gc(t),n.d-=t.gc(),t.$b(),n.mc(i)):n.jc()}function G6e(n,e){var t,i;for(i=to(n.d,1)!=0,t=!0;t;)t=!1,t=e.c.mg(e.e,i),t=t|sy(n,e,i,!1),i=!i;$Q(n)}function WFn(n,e,t,i){var r,c;n.a=e,c=i?0:1,n.f=(r=new s_n(n.c,n.a,t,c),new Kqn(t,n.a,r,n.e,n.b,n.c==(O0(),t9)))}function xT(n){var e;return oe(n.a!=n.b),e=n.d.a[n.a],EAn(n.b==n.d.c&&e!=null),n.c=n.a,n.a=n.a+1&n.d.a.length-1,e}function JFn(n){var e;if(n.c!=0)return n.c;for(e=0;e<n.a.length;e++)n.c=n.c*33+(n.a[e]&-1);return n.c=n.c*n.e,n.c}function z6e(n){var e;if(!(n.c.c<0?n.a>=n.c.b:n.a<=n.c.b))throw M(new nc);return e=n.a,n.a+=n.c.c,++n.b,Y(e)}function ex(n){var e;return e=new DX(n.a),Ur(e,n),U(e,(W(),st),n),e.o.a=n.g,e.o.b=n.f,e.n.a=n.i,e.n.b=n.j,e}function tx(n){return(tn(),mu).Hc(n.j)?$(R(v(n,(W(),jv)))):cc(S(T(Ei,1),J,8,0,[n.i.n,n.n,n.a])).b}function X6e(n){var e;return e=DC(Cie),u(v(n,(W(),Hc)),21).Hc((pr(),yv))&&Re(e,(Vi(),Oc),(tr(),FP)),e}function V6e(n){var e,t,i,r;for(r=new ni,i=new C(n);i.a<i.c.c.length;)t=u(E(i),27),e=wAe(t),Bi(r,e);return r}function W6e(n){var e,t;for(t=new C(n.r);t.a<t.c.c.length;)if(e=u(E(t),10),n.n[e.p]<=0)return e;return null}function J6e(n,e,t){var i,r;for(r=e.a.a.ec().Kc();r.Ob();)if(i=u(r.Pb(),60),zIn(n,i,t))return!0;return!1}function Q6e(n,e,t,i){var r,c;for(c=n.Kc();c.Ob();)r=u(c.Pb(),72),r.n.a=e.a+(i.a-r.o.a)/2,r.n.b=e.b,e.b+=r.o.b+t}function Y6e(n,e,t){var i;i=new sHn(n,e),Pn(n.r,e.ag(),i),t&&!_6(n.u)&&(i.c=new fOn(n.d),nu(e.Rf(),new L9n(i)))}function Ec(n,e){var t;return Vr(n)&&Vr(e)&&(t=n-e,!isNaN(t))?t:DZ(Vr(n)?ds(n):n,Vr(e)?ds(e):e)}function mY(n,e){var t,i,r;for(r=1,t=n,i=e>=0?e:-e;i>0;)i%2==0?(t*=t,i=i/2|0):(r*=t,i-=1);return e<0?1/r:r}function Z6e(n,e){var t,i,r;for(r=1,t=n,i=e>=0?e:-e;i>0;)i%2==0?(t*=t,i=i/2|0):(r*=t,i-=1);return e<0?1/r:r}function na(n,e){var t,i,r,c;return c=(r=n?WT(n):null,O_n((i=e,r&&r.Gl(),i))),c==e&&(t=WT(n),t&&t.Gl()),c}function QFn(n,e,t){var i,r;return r=n.f,n.f=e,n.Db&4&&!(n.Db&1)&&(i=new Ci(n,1,0,r,e),t?t.nj(i):t=i),t}function YFn(n,e,t){var i,r;return r=n.b,n.b=e,n.Db&4&&!(n.Db&1)&&(i=new Ci(n,1,3,r,e),t?t.nj(i):t=i),t}function vY(n,e,t){var i,r;return r=n.a,n.a=e,n.Db&4&&!(n.Db&1)&&(i=new Ci(n,1,1,r,e),t?t.nj(i):t=i),t}function ZFn(n){var e,t;if(n!=null)for(t=0;t<n.length;++t)e=n[t],e&&(u(e.g,379),e.i)}function n5e(n,e,t,i,r,c,s,f){var h;for(h=t;c<s;)h>=i||e<t&&f.Ne(n[e],n[h])<=0?$t(r,c++,n[e++]):$t(r,c++,n[h++])}function e5e(n,e,t,i,r){e==0||i==0||(e==1?r[i]=lZ(r,t,i,n[0]):i==1?r[e]=lZ(r,n,e,t[0]):ECe(n,t,r,e,i))}function t5e(n,e,t){var i,r,c,s;for(i=t/n.gc(),r=0,s=n.Kc();s.Ob();)c=u(s.Pb(),186),_Fn(c,c.f+i*r),gke(c,e,i),++r}function i5e(n){var e,t,i;for(i=0,t=new C(n.a);t.a<t.c.c.length;)e=u(E(t),172),i=y.Math.max(i,e.g);return i}function r5e(n){var e,t,i;for(i=new C(n.b);i.a<i.c.c.length;)t=u(E(i),219),e=t.c.kg()?t.f:t.a,e&&PIe(e,t.j)}function g5(){g5=F,FH=new zD("DUMMY_NODE_OVER",0),Dhn=new zD("DUMMY_NODE_UNDER",1),MI=new zD("EQUAL",2)}function Gp(){Gp=F,pdn=new lL("PARALLEL_NODE",0),Yw=new lL("HIERARCHICAL_NODE",1),aO=new lL("ROOT_NODE",2)}function jl(){jl=F,uO=new hL("INHERIT",0),M1=new hL("INCLUDE_CHILDREN",1),M9=new hL("SEPARATE_CHILDREN",2)}function kY(n,e){switch(e){case 1:!n.n&&(n.n=new q(Ar,n,1,7)),me(n.n);return;case 2:X4(n,null);return}WQ(n,e)}function nBn(n){switch(n.g){case 0:return new omn;case 1:return new fmn;case 2:return new smn;default:return null}}function i1(n){switch(uh(),n.c){case 0:return wN(),uun;case 1:return new hp(B_n(new dp(n)));default:return new Sjn(n)}}function eBn(n){switch(uh(),n.gc()){case 0:return wN(),uun;case 1:return new hp(n.Kc().Pb());default:return new Bz(n)}}function FT(n){var e;switch(n.gc()){case 0:return qK;case 1:return new VL(Se(n.Xb(0)));default:return e=n,new PN(e)}}function Y(n){var e,t;return n>-129&&n<128?(FSn(),e=n+128,t=pun[e],!t&&(t=pun[e]=new vG(n)),t):new vG(n)}function sm(n){var e,t;return n>-129&&n<128?(nPn(),e=n+128,t=yun[e],!t&&(t=yun[e]=new yG(n)),t):new yG(n)}function tBn(n,e){var t;n.a.c.length>0&&(t=u(sn(n.a,n.a.c.length-1),579),sY(t,e))||nn(n.a,new kLn(e))}function c5e(n){xs();var e,t;e=n.d.c-n.e.c,t=u(n.g,154),nu(t.b,new p7n(e)),nu(t.c,new m7n(e)),qi(t.i,new v7n(e))}function iBn(n){var e;return e=new x1,e.a+="VerticalSegment ",Dc(e,n.e),e.a+=" ",Be(e,RX(new yD,new C(n.k))),e.a}function ix(n,e){var t,i,r;for(t=0,r=uc(n,e).Kc();r.Ob();)i=u(r.Pb(),12),t+=v(i,(W(),Xu))!=null?1:0;return t}function xg(n,e,t){var i,r,c;for(i=0,c=ge(n,0);c.b!=c.d.c&&(r=$(R(be(c))),!(r>t));)r>=e&&++i;return i}function rBn(n,e){Se(n);try{return n._b(e)}catch(t){if(t=It(t),O(t,212)||O(t,169))return!1;throw M(t)}}function yY(n,e){Se(n);try{return n.Hc(e)}catch(t){if(t=It(t),O(t,212)||O(t,169))return!1;throw M(t)}}function u5e(n,e){Se(n);try{return n.Mc(e)}catch(t){if(t=It(t),O(t,212)||O(t,169))return!1;throw M(t)}}function tw(n,e){Se(n);try{return n.xc(e)}catch(t){if(t=It(t),O(t,212)||O(t,169))return null;throw M(t)}}function o5e(n,e){Se(n);try{return n.Bc(e)}catch(t){if(t=It(t),O(t,212)||O(t,169))return null;throw M(t)}}function p5(n,e){switch(e.g){case 2:case 1:return uc(n,e);case 3:case 4:return Qo(uc(n,e))}return Dn(),Dn(),sr}function m5(n){var e;return n.Db&64?_s(n):(e=new ls(_s(n)),e.a+=" (name: ",Er(e,n.zb),e.a+=")",e.a)}function s5e(n){var e;return e=u(Lf(n.c.c,""),233),e||(e=new Np(u4(c4(new ep,""),"Other")),s1(n.c.c,"",e)),e}function jY(n,e,t){var i,r;return r=n.sb,n.sb=e,n.Db&4&&!(n.Db&1)&&(i=new Ci(n,1,4,r,e),t?t.nj(i):t=i),t}function EY(n,e,t){var i,r;return r=n.r,n.r=e,n.Db&4&&!(n.Db&1)&&(i=new Ci(n,1,8,r,n.r),t?t.nj(i):t=i),t}function f5e(n,e,t){var i,r;return i=new ml(n.e,4,13,(r=e.c,r||(On(),Yf)),null,f1(n,e),!1),t?t.nj(i):t=i,t}function h5e(n,e,t){var i,r;return i=new ml(n.e,3,13,null,(r=e.c,r||(On(),Yf)),f1(n,e),!1),t?t.nj(i):t=i,t}function r1(n,e){var t,i;return t=u(e,691),i=t.el(),!i&&t.fl(i=O(e,90)?new xMn(n,u(e,29)):new cDn(n,u(e,156))),i}function Nk(n,e,t){var i;n._i(n.i+1),i=n.Zi(e,t),e!=n.i&&Ic(n.g,e,n.g,e+1,n.i-e),$t(n.g,e,i),++n.i,n.Mi(e,t),n.Ni()}function l5e(n,e){var t;return e.a&&(t=e.a.a.length,n.a?Be(n.a,n.b):n.a=new mo(n.d),aDn(n.a,e.a,e.d.length,t)),n}function a5e(n,e){var t;n.c=e,n.a=p8e(e),n.a<54&&(n.f=(t=e.d>1?hDn(e.a[0],e.a[1]):hDn(e.a[0],0),id(e.e>0?t:n1(t))))}function $k(n,e){var t;return t=new LO,n.a.Bd(t)?(b4(),new wD(Jn(GNn(n,t.a,e)))):(z1(n),b4(),b4(),Dun)}function cBn(n,e){var t;n.c.length!=0&&(t=u(xf(n,K(Qh,b1,10,n.c.length,0,1)),199),CX(t,new rgn),Y_n(t,e))}function uBn(n,e){var t;n.c.length!=0&&(t=u(xf(n,K(Qh,b1,10,n.c.length,0,1)),199),CX(t,new cgn),Y_n(t,e))}function rt(n,e){return Ai(n)?An(n,e):$b(n)?nSn(n,e):Nb(n)?(Jn(n),x(n)===x(e)):pW(n)?n.Fb(e):hW(n)?YMn(n,e):hJ(n,e)}function Wo(n,e,t){if(e<0)Pnn(n,t);else{if(!t.rk())throw M(new Gn(da+t.xe()+p8));u(t,69).wk().Ek(n,n.hi(),e)}}function oBn(n,e,t){if(n<0||e>t)throw M(new Ir(ZA+n+Stn+e+", size: "+t));if(n>e)throw M(new Gn(ZA+n+Qzn+e))}function sBn(n){var e;return n.Db&64?_s(n):(e=new ls(_s(n)),e.a+=" (source: ",Er(e,n.d),e.a+=")",e.a)}function fBn(n){return n>=65&&n<=70?n-65+10:n>=97&&n<=102?n-97+10:n>=48&&n<=57?n-48:0}function d5e(n){VA();var e,t,i,r;for(t=jx(),i=0,r=t.length;i<r;++i)if(e=t[i],qr(e.a,n,0)!=-1)return e;return l_}function b5e(n,e){var t,i,r,c;if(e.ej(n.a),c=u(Un(n.a,8),2035),c!=null)for(t=c,i=0,r=t.length;i<r;++i)null.Um()}function c1(n,e){var t;t=(n.Bb&256)!=0,e?n.Bb|=256:n.Bb&=-257,n.Db&4&&!(n.Db&1)&&it(n,new Bs(n,1,2,t,e))}function CY(n,e){var t;t=(n.Bb&256)!=0,e?n.Bb|=256:n.Bb&=-257,n.Db&4&&!(n.Db&1)&&it(n,new Bs(n,1,8,t,e))}function BT(n,e){var t;t=(n.Bb&256)!=0,e?n.Bb|=256:n.Bb&=-257,n.Db&4&&!(n.Db&1)&&it(n,new Bs(n,1,8,t,e))}function u1(n,e){var t;t=(n.Bb&512)!=0,e?n.Bb|=512:n.Bb&=-513,n.Db&4&&!(n.Db&1)&&it(n,new Bs(n,1,3,t,e))}function MY(n,e){var t;t=(n.Bb&512)!=0,e?n.Bb|=512:n.Bb&=-513,n.Db&4&&!(n.Db&1)&&it(n,new Bs(n,1,9,t,e))}function w5e(n,e,t){var i,r;return r=n.a,n.a=e,n.Db&4&&!(n.Db&1)&&(i=new Ci(n,1,5,r,n.a),t?zZ(t,i):t=i),t}function v5(n,e){var t;return n.b==-1&&n.a&&(t=n.a.pk(),n.b=t?n.c.Hh(n.a.Lj(),t):Ot(n.c.Dh(),n.a)),n.c.yh(n.b,e)}function hBn(n,e){var t,i;for(i=new ne(n);i.e!=i.i.gc();)if(t=u(ce(i),29),x(e)===x(t))return!0;return!1}function TY(n){var e,t;return e=n.k,e==(Vn(),Zt)?(t=u(v(n,(W(),gc)),64),t==(tn(),Xn)||t==ae):!1}function lBn(n){var e;return e=gJ(n),o0(e.a,0)?(Ob(),Ob(),n_):(Ob(),new AL(LD(e.a,0)?KJ(e)/id(e.a):0))}function xk(n,e){this.e=e,this.a=Qxn(n),this.a<54?this.f=id(n):this.c=(dh(),Ec(n,0)>=0?ta(n):G6(ta(n1(n))))}function aBn(n,e,t,i,r,c){this.e=new Z,this.f=(gr(),n9),nn(this.e,n),this.d=e,this.a=t,this.b=i,this.f=r,this.c=c}function g5e(n,e,t){n.n=Va(xa,[J,SB],[376,28],14,[t,wi(y.Math.ceil(e/32))],2),n.o=e,n.p=t,n.j=e-1>>1,n.k=t-1>>1}function dBn(n){return n-=n>>1&1431655765,n=(n>>2&858993459)+(n&858993459),n=(n>>4)+n&252645135,n+=n>>8,n+=n>>16,n&63}function bBn(n,e){var t,i;for(i=new ne(n);i.e!=i.i.gc();)if(t=u(ce(i),142),x(e)===x(t))return!0;return!1}function p5e(n,e,t){var i,r,c;return c=(r=Mm(n.b,e),r),c&&(i=u(qA(ak(n,c),""),29),i)?Qnn(n,i,e,t):null}function rx(n,e,t){var i,r,c;return c=(r=Mm(n.b,e),r),c&&(i=u(qA(ak(n,c),""),29),i)?Ynn(n,i,e,t):null}function m5e(n,e){var t;if(t=Dg(n.i,e),t==null)throw M(new nh("Node did not exist in input."));return HQ(e,t),null}function v5e(n,e){var t;if(t=oy(n,e),O(t,331))return u(t,35);throw M(new Gn(da+e+"' is not a valid attribute"))}function k5(n,e,t){var i;if(i=n.gc(),e>i)throw M(new Kb(e,i));if(n.Si()&&n.Hc(t))throw M(new Gn(Vy));n.Gi(e,t)}function k5e(n,e){e.Ug("Sort end labels",1),qt(ut(rc(new Tn(null,new In(n.b,16)),new Hwn),new qwn),new Uwn),e.Vg()}function ci(){ci=F,Wf=new v7(i8,0),Xr=new v7(f3,1),Br=new v7(s3,2),Vf=new v7(_B,3),us=new v7("UP",4)}function Fk(){Fk=F,XI=new sL("P1_STRUCTURE",0),VI=new sL("P2_PROCESSING_ORDER",1),WI=new sL("P3_EXECUTION",2)}function wBn(){wBn=F,Rre=ah(ah(l6(ah(ah(l6(Re(new ii,(Qp(),c9),(q5(),ZH)),u9),lln),dln),o9),oln),bln)}function y5e(n){switch(u(v(n,(W(),Od)),311).g){case 1:U(n,Od,(vl(),E3));break;case 2:U(n,Od,(vl(),v2))}}function j5e(n){switch(n){case 0:return new rjn;case 1:return new tjn;case 2:return new ijn;default:throw M(new Q9)}}function gBn(n){switch(n.g){case 2:return Xr;case 1:return Br;case 4:return Vf;case 3:return us;default:return Wf}}function AY(n,e){switch(n.b.g){case 0:case 1:return e;case 2:case 3:return new Ho(e.d,0,e.a,e.b);default:return null}}function SY(n){switch(n.g){case 1:return Wn;case 2:return Xn;case 3:return Zn;case 4:return ae;default:return sc}}function Bk(n){switch(n.g){case 1:return ae;case 2:return Wn;case 3:return Xn;case 4:return Zn;default:return sc}}function RT(n){switch(n.g){case 1:return Zn;case 2:return ae;case 3:return Wn;case 4:return Xn;default:return sc}}function PY(n,e,t,i){switch(e){case 1:return!n.n&&(n.n=new q(Ar,n,1,7)),n.n;case 2:return n.k}return yZ(n,e,t,i)}function y5(n,e,t){var i,r;return n.Pj()?(r=n.Qj(),i=lF(n,e,t),n.Jj(n.Ij(7,Y(t),i,e,r)),i):lF(n,e,t)}function cx(n,e){var t,i,r;n.d==null?(++n.e,--n.f):(r=e.ld(),t=e.Bi(),i=(t&et)%n.d.length,o4e(n,i,RHn(n,i,t,r)))}function fm(n,e){var t;t=(n.Bb&Us)!=0,e?n.Bb|=Us:n.Bb&=-1025,n.Db&4&&!(n.Db&1)&&it(n,new Bs(n,1,10,t,e))}function hm(n,e){var t;t=(n.Bb&vw)!=0,e?n.Bb|=vw:n.Bb&=-4097,n.Db&4&&!(n.Db&1)&&it(n,new Bs(n,1,12,t,e))}function lm(n,e){var t;t=(n.Bb&$u)!=0,e?n.Bb|=$u:n.Bb&=-8193,n.Db&4&&!(n.Db&1)&&it(n,new Bs(n,1,15,t,e))}function am(n,e){var t;t=(n.Bb&Tw)!=0,e?n.Bb|=Tw:n.Bb&=-2049,n.Db&4&&!(n.Db&1)&&it(n,new Bs(n,1,11,t,e))}function E5e(n){var e;n.g&&(e=n.c.kg()?n.f:n.a,len(e.a,n.o,!0),len(e.a,n.o,!1),U(n.o,(cn(),Kt),(Oi(),Ud)))}function C5e(n){var e;if(!n.a)throw M(new Or("Cannot offset an unassigned cut."));e=n.c-n.b,n.b+=e,_In(n,e),KIn(n,e)}function M5e(n,e){var t;if(t=ee(n.k,e),t==null)throw M(new nh("Port did not exist in input."));return HQ(e,t),null}function T5e(n){var e,t;for(t=xHn(jo(n)).Kc();t.Ob();)if(e=Oe(t.Pb()),U5(n,e))return A3e((mCn(),Boe),e);return null}function pBn(n){var e,t;for(t=n.p.a.ec().Kc();t.Ob();)if(e=u(t.Pb(),218),e.f&&n.b[e.c]<-1e-10)return e;return null}function A5e(n){var e,t;for(t=Ya(new x1,91),e=!0;n.Ob();)e||(t.a+=ur),e=!1,Dc(t,n.Pb());return(t.a+="]",t).a}function S5e(n){var e,t,i;for(e=new Z,i=new C(n.b);i.a<i.c.c.length;)t=u(E(i),602),hi(e,u(t.Cf(),16));return e}function ux(n,e){var t,i;for(i=new C(e);i.a<i.c.c.length;)t=u(E(i),42),du(n.b.b,t.b),Oge(u(t.a,194),u(t.b,86))}function P5e(n,e){var t;return t=bt(n.b.c,e.b.c),t!=0||(t=bt(n.a.a,e.a.a),t!=0)?t:bt(n.a.b,e.a.b)}function bt(n,e){return n<e?-1:n>e?1:n==e?n==0?bt(1/n,1/e):0:isNaN(n)?isNaN(e)?0:1:-1}function I5e(n){var e;return e=n.a[n.c-1&n.a.length-1],e==null?null:(n.c=n.c-1&n.a.length-1,$t(n.a,n.c,null),e)}function O5e(n){var e,t,i;for(i=0,t=n.length,e=0;e<t;e++)n[e]==32||n[e]==13||n[e]==10||n[e]==9||(n[i++]=n[e]);return i}function D5e(n,e){var t,i,r,c,s;for(s=ru(n.e.Dh(),e),c=0,t=u(n.g,124),r=0;r<n.i;++r)i=t[r],s.am(i.Lk())&&++c;return c}function L5e(n,e,t){var i,r;for(r=O(e,102)&&u(e,19).Bb&hr?new dL(e,n):new Y4(e,n),i=0;i<t;++i)iA(r);return r}function mBn(n,e,t){var i,r;if(n.c)cnn(n.c,e,t);else for(r=new C(n.b);r.a<r.c.c.length;)i=u(E(r),163),mBn(i,e,t)}function N5e(n,e,t){var i,r;return i=u(e.of(n.a),34),r=u(t.of(n.a),34),i!=null&&r!=null?kk(i,r):i!=null?-1:r!=null?1:0}function IY(n,e){var t,i,r;for(Jn(e),t=!1,i=new C(n);i.a<i.c.c.length;)r=E(i),e.Hc(r)&&(U6(i),t=!0);return t}function yn(n){var e,t,i,r;return t=(e=u(uf((i=n.Rm,r=i.f,r==ke?i:r)),9),new _o(e,u($s(e,e.length),9),0)),Ks(t,n),t}function KT(n){var e,t;return t=u(v(n,(cn(),Do)),88),t==(ci(),Wf)?(e=$(R(v(n,oI))),e>=1?Xr:Vf):t}function $5e(n){switch(u(v(n,(cn(),$l)),223).g){case 1:return new Ppn;case 3:return new Npn;default:return new Spn}}function ea(n){if(n.c)ea(n.c);else if(n.d)throw M(new Or("Stream already terminated, can't be modified or used"))}function $0(n,e,t){var i;return i=n.a.get(e),n.a.set(e,t===void 0?null:t),i===void 0?(++n.c,++n.b.g):++n.d,i}function x5e(n,e,t){var i,r;for(r=n.a.ec().Kc();r.Ob();)if(i=u(r.Pb(),10),Mk(t,u(sn(e,i.p),16)))return i;return null}function OY(n,e,t){var i;return i=0,e&&(mg(n.a)?i+=e.f.a/2:i+=e.f.b/2),t&&(mg(n.a)?i+=t.f.a/2:i+=t.f.b/2),i}function F5e(n,e,t){var i;i=t,!i&&(i=YV(new up,0)),i.Ug(PXn,2),jRn(n.b,e,i.eh(1)),YIe(n,e,i.eh(1)),eLe(e,i.eh(1)),i.Vg()}function DY(n,e,t){var i,r;return i=(B1(),r=new yE,r),aT(i,e),lT(i,t),n&&ve((!n.a&&(n.a=new ti(xo,n,5)),n.a),i),i}function ox(n){var e;return n.Db&64?_s(n):(e=new ls(_s(n)),e.a+=" (identifier: ",Er(e,n.k),e.a+=")",e.a)}function sx(n,e){var t;t=(n.Bb&kc)!=0,e?n.Bb|=kc:n.Bb&=-32769,n.Db&4&&!(n.Db&1)&&it(n,new Bs(n,1,18,t,e))}function LY(n,e){var t;t=(n.Bb&kc)!=0,e?n.Bb|=kc:n.Bb&=-32769,n.Db&4&&!(n.Db&1)&&it(n,new Bs(n,1,18,t,e))}function dm(n,e){var t;t=(n.Bb&wh)!=0,e?n.Bb|=wh:n.Bb&=-16385,n.Db&4&&!(n.Db&1)&&it(n,new Bs(n,1,16,t,e))}function NY(n,e){var t;t=(n.Bb&hr)!=0,e?n.Bb|=hr:n.Bb&=-65537,n.Db&4&&!(n.Db&1)&&it(n,new Bs(n,1,20,t,e))}function $Y(n){var e;return e=K(fs,gh,28,2,15,1),n-=hr,e[0]=(n>>10)+Sy&ui,e[1]=(n&1023)+56320&ui,hh(e,0,e.length)}function B5e(n){var e;return e=sw(n),e>34028234663852886e22?St:e<-34028234663852886e22?li:e}function nr(n,e){var t;return Vr(n)&&Vr(e)&&(t=n+e,Ay<t&&t<vd)?t:Q1(Gve(Vr(n)?ds(n):n,Vr(e)?ds(e):e))}function er(n,e){var t;return Vr(n)&&Vr(e)&&(t=n*e,Ay<t&&t<vd)?t:Q1(KIe(Vr(n)?ds(n):n,Vr(e)?ds(e):e))}function bs(n,e){var t;return Vr(n)&&Vr(e)&&(t=n-e,Ay<t&&t<vd)?t:Q1(Yxn(Vr(n)?ds(n):n,Vr(e)?ds(e):e))}function uc(n,e){var t;return n.i||Snn(n),t=u(Cr(n.g,e),42),t?new Jl(n.j,u(t.a,17).a,u(t.b,17).a):(Dn(),Dn(),sr)}function R5e(n){return Y$(),_n(),!!(yBn(u(n.a,86).j,u(n.b,88))||u(n.a,86).d.e!=0&&yBn(u(n.a,86).j,u(n.b,88)))}function K5e(n,e){return An(e.b&&e.c?td(e.b)+"->"+td(e.c):"e_"+mt(e),n.b&&n.c?td(n.b)+"->"+td(n.c):"e_"+mt(n))}function _5e(n,e){return An(e.b&&e.c?td(e.b)+"->"+td(e.c):"e_"+mt(e),n.b&&n.c?td(n.b)+"->"+td(n.c):"e_"+mt(n))}function x0(n,e){return Mf(),Rs(sa),y.Math.abs(n-e)<=sa||n==e||isNaN(n)&&isNaN(e)?0:n<e?-1:n>e?1:s0(isNaN(n),isNaN(e))}function El(){El=F,lU=new kC(i8,0),Yj=new kC("POLYLINE",1),Kv=new kC("ORTHOGONAL",2),F3=new kC("SPLINES",3)}function _T(){_T=F,l1n=new uL("ASPECT_RATIO_DRIVEN",0),Oq=new uL("MAX_SCALE_DRIVEN",1),h1n=new uL("AREA_DRIVEN",2)}function H5e(n,e,t){var i;try{l6e(n,e,t)}catch(r){throw r=It(r),O(r,606)?(i=r,M(new $J(i))):M(r)}return e}function q5e(n){var e,t,i;for(t=0,i=n.length;t<i;t++)if(n[t]==null)throw M(new sp("at index "+t));return e=n,new Ku(e)}function Cl(n){var e,t,i;for(e=new Z,i=new C(n.j);i.a<i.c.c.length;)t=u(E(i),12),nn(e,t.b);return Se(e),new S6(e)}function ji(n){var e,t,i;for(e=new Z,i=new C(n.j);i.a<i.c.c.length;)t=u(E(i),12),nn(e,t.e);return Se(e),new S6(e)}function Qt(n){var e,t,i;for(e=new Z,i=new C(n.j);i.a<i.c.c.length;)t=u(E(i),12),nn(e,t.g);return Se(e),new S6(e)}function U5e(n,e){var t,i,r;for(r=new de,i=e.vc().Kc();i.Ob();)t=u(i.Pb(),44),Xe(r,t.ld(),Sve(n,u(t.md(),15)));return r}function G5e(n){var e,t;for(t=NCe(jo(Gb(n))).Kc();t.Ob();)if(e=Oe(t.Pb()),U5(n,e))return S3e((gCn(),Roe),e);return null}function fx(n,e){var t,i,r;for(r=0,i=u(e.Kb(n),20).Kc();i.Ob();)t=u(i.Pb(),18),on(un(v(t,(W(),Gf))))||++r;return r}function vBn(n){var e,t,i,r;for(e=new XAn(n.Rd().gc()),r=0,i=Kp(n.Rd().Kc());i.Ob();)t=i.Pb(),P2e(e,t,Y(r++));return Sje(e.a)}function hx(n,e,t,i){var r,c;return Jn(i),Jn(t),r=n.xc(e),c=r==null?t:cCn(u(r,15),u(t,16)),c==null?n.Bc(e):n.zc(e,c),c}function z5e(n,e,t,i){var r,c,s;for(r=e+1;r<t;++r)for(c=r;c>e&&i.Ne(n[c-1],n[c])>0;--c)s=n[c],$t(n,c,n[c-1]),$t(n,c-1,s)}function vn(n,e){var t,i,r,c,s;if(t=e.f,s1(n.c.d,t,e),e.g!=null)for(r=e.g,c=0,s=r.length;c<s;++c)i=r[c],s1(n.c.e,i,e)}function kBn(n,e){var t,i;for(t=ge(n,0);t.b!=t.d.c;){if(i=Y9(R(be(t))),i==e)return;if(i>e){wDn(t);break}}q7(t,e)}function X5e(n,e){var t,i,r;i=Sg(e),r=$(R(rw(i,(cn(),Vs)))),t=y.Math.max(0,r/2-.5),I5(e,t,1),nn(n,new NCn(e,t))}function V5e(n,e,t){var i;t.Ug("Straight Line Edge Routing",1),t.dh(e,xrn),i=u(z(e,(Mg(),O2)),27),iGn(n,i),t.dh(e,DS)}function xY(n,e){n.n.c.length==0&&nn(n.n,new NM(n.s,n.t,n.i)),nn(n.b,e),gZ(u(sn(n.n,n.n.c.length-1),209),e),RUn(n,e)}function j5(n){var e;this.a=(e=u(n.e&&n.e(),9),new _o(e,u($s(e,e.length),9),0)),this.b=K(ki,Fn,1,this.a.a.length,5,1)}function Jr(n){var e;return Array.isArray(n)&&n.Tm===J2?za(wo(n))+"@"+(e=mt(n)>>>0,e.toString(16)):n.toString()}function W5e(n,e){return n.h==Ty&&n.m==0&&n.l==0?(e&&(ba=Yc(0,0,0)),nTn((R4(),lun))):(e&&(ba=Yc(n.l,n.m,n.h)),Yc(0,0,0))}function J5e(n,e){switch(e.g){case 2:return n.b;case 1:return n.c;case 4:return n.d;case 3:return n.a;default:return!1}}function yBn(n,e){switch(e.g){case 2:return n.b;case 1:return n.c;case 4:return n.d;case 3:return n.a;default:return!1}}function FY(n,e,t,i){switch(e){case 3:return n.f;case 4:return n.g;case 5:return n.i;case 6:return n.j}return PY(n,e,t,i)}function HT(n,e){if(e==n.d)return n.e;if(e==n.e)return n.d;throw M(new Gn("Node "+e+" not part of edge "+n))}function Q5e(n,e){var t;if(t=oy(n.Dh(),e),O(t,102))return u(t,19);throw M(new Gn(da+e+"' is not a valid reference"))}function Jo(n,e,t,i){if(e<0)ten(n,t,i);else{if(!t.rk())throw M(new Gn(da+t.xe()+p8));u(t,69).wk().Ck(n,n.hi(),e,i)}}function eo(n){var e;if(n.b){if(eo(n.b),n.b.d!=n.c)throw M(new Bo)}else n.d.dc()&&(e=u(n.f.c.xc(n.e),16),e&&(n.d=e))}function Y5e(n){Bb();var e,t,i,r;for(e=n.o.b,i=u(u(ot(n.r,(tn(),ae)),21),87).Kc();i.Ob();)t=u(i.Pb(),117),r=t.e,r.b+=e}function Z5e(n){var e,t,i;for(this.a=new ih,i=new C(n);i.a<i.c.c.length;)t=u(E(i),16),e=new cPn,Zme(e,t),fi(this.a,e)}function n8e(n,e){var t,i,r;for(i=eSe(n,e),r=i[i.length-1]/2,t=0;t<i.length;t++)if(i[t]>=r)return e.c+t;return e.c+e.b.gc()}function e8e(n,e){m4();var t,i,r,c;for(i=LNn(n),r=e,F4(i,0,i.length,r),t=0;t<i.length;t++)c=H7e(n,i[t],t),t!=c&&y5(n,t,c)}function lx(n,e,t){var i,r;for(i=0,r=n.length;i<r;i++)if(R$((zn(i,n.length),n.charCodeAt(i)),e,t))return!0;return!1}function t8e(n,e){var t,i;for(i=n.e.a.ec().Kc();i.Ob();)if(t=u(i.Pb(),272),fje(e,t.d)||mEe(e,t.d))return!0;return!1}function BY(n,e,t,i,r){var c,s,f;for(s=r;e.b!=e.c;)c=u(Sp(e),10),f=u(uc(c,i).Xb(0),12),n.d[f.p]=s++,Bn(t.c,f);return s}function RY(n,e){var t,i,r,c,s,f;for(i=0,t=0,c=e,s=0,f=c.length;s<f;++s)r=c[s],r>0&&(i+=r,++t);return t>1&&(i+=n.d*(t-1)),i}function i8e(n){var e,t,i,r,c;return c=enn(n),t=e7(n.c),i=!t,i&&(r=new Ka,df(c,"knownLayouters",r),e=new lyn(r),qi(n.c,e)),c}function KY(n){var e,t,i;for(i=new Hl,i.a+="[",e=0,t=n.gc();e<t;)Er(i,D6(n.Vi(e))),++e<t&&(i.a+=ur);return i.a+="]",i.a}function r8e(n){return n.e==null?n:(!n.c&&(n.c=new jF((n.f&256)!=0,n.i,n.a,n.d,(n.f&16)!=0,n.j,n.g,null)),n.c)}function c8e(n){return n.k!=(Vn(),zt)?!1:Ig(new Tn(null,new p0(new te(re(Qt(n).a.Kc(),new En)))),new mpn)}function Qo(n){var e,t;return O(n,307)?(t=t4e(u(n,307)),e=t,e):O(n,441)?u(n,441).a:O(n,59)?new Pjn(n):new Oz(n)}function u8e(n){var e;return n==null?!0:(e=n.length,e>0&&(zn(e-1,n.length),n.charCodeAt(e-1)==58)&&!lx(n,N9,$9))}function _Y(n,e){var t;return x(n)===x(e)?!0:O(e,92)?(t=u(e,92),n.e==t.e&&n.d==t.d&&I3e(n,t.a)):!1}function zp(n){switch(tn(),n.g){case 4:return Xn;case 1:return Zn;case 3:return ae;case 2:return Wn;default:return sc}}function o8e(n){var e,t;if(n.b)return n.b;for(t=qf?null:n.d;t;){if(e=qf?null:t.b,e)return e;t=qf?null:t.d}return a4(),$un}function HY(n){var e,t,i;for(i=$(R(n.a.of((qe(),iO)))),t=new C(n.a.Sf());t.a<t.c.c.length;)e=u(E(t),695),tzn(n,e,i)}function s8e(n){var e,t,i,r;for(e=(n.j==null&&(n.j=(O4(),r=VK.me(n),Tke(r))),n.j),t=0,i=e.length;t<i;++t);}function ax(n,e){var t,i;for(i=new C(e);i.a<i.c.c.length;)t=u(E(i),42),nn(n.b.b,u(t.b,86)),_N(u(t.a,194),u(t.b,86))}function f8e(n,e,t){var i,r;for(r=n.a.b,i=r.c.length;i<t;i++)b0(r,0,new Lc(n.a));$i(e,u(sn(r,r.c.length-t),30)),n.b[e.p]=t}function h8e(n,e,t,i,r){ko(),Hs(Ds(Os(Is(Ls(new hs,0),r.d.e-n),e),r.d)),Hs(Ds(Os(Is(Ls(new hs,0),t-r.a.e),r.a),i))}function jBn(n,e){var t;return n.d?Zc(n.b,e)?u(ee(n.b,e),47):(t=e.dg(),Xe(n.b,e,t),t):e.dg()}function l8e(n){var e=n.e;function t(i){return!i||i.length==0?"":"	"+i.join(`
 	`)}return e&&(e.stack||t(n[oB]))}function qY(n,e){switch(e){case 3:return n.f!=0;case 4:return n.g!=0;case 5:return n.i!=0;case 6:return n.j!=0}return qQ(n,e)}function EBn(n){switch(n.g){case 0:return new W4n;case 1:return new Y4n;default:throw M(new Gn(cR+(n.f!=null?n.f:""+n.g)))}}function a8e(n){switch(n.g){case 0:return new J4n;case 1:return new Q4n;default:throw M(new Gn(GR+(n.f!=null?n.f:""+n.g)))}}function d8e(n){switch(n.g){case 1:return new H4n;case 2:return new fAn;default:throw M(new Gn(GR+(n.f!=null?n.f:""+n.g)))}}function CBn(n){switch(n.g){case 0:return new cz;case 1:return new cjn;default:throw M(new Gn(xS+(n.f!=null?n.f:""+n.g)))}}function dx(){nnn();var n,e,t;t=hNe+++Date.now(),n=wi(y.Math.floor(t*Iy))&YA,e=wi(t-n*Ctn),this.a=n^1502,this.b=e^LB}function Yo(){Yo=F,Ej=new a7(kh,0),U8=new a7("FIRST",1),ka=new a7(GXn,2),G8=new a7("LAST",3),xw=new a7(zXn,4)}function qT(){qT=F,wU=new EC(Crn,0),ydn=new EC("GROUP_DEC",1),Edn=new EC("GROUP_MIXED",2),jdn=new EC("GROUP_INC",3)}function b8e(n,e){var t,i,r,c;e&&(r=yl(e,"x"),t=new tyn(n),H4(t.a,(Jn(r),r)),c=yl(e,"y"),i=new ryn(n),U4(i.a,(Jn(c),c)))}function w8e(n,e){var t,i,r,c;e&&(r=yl(e,"x"),t=new uyn(n),_4(t.a,(Jn(r),r)),c=yl(e,"y"),i=new oyn(n),q4(i.a,(Jn(c),c)))}function g8e(n,e){var t,i,r,c;for(r=new Gc(e.gc()),i=e.Kc();i.Ob();)t=i.Pb(),c=IF(n,u(t,58)),c&&Bn(r.c,c);return r}function iw(n,e,t){var i,r;for(r=n.Kc();r.Ob();)if(i=r.Pb(),x(e)===x(i)||e!=null&&rt(e,i))return t&&r.Qb(),!0;return!1}function MBn(n){var e,t,i;return t=n.jh(),t?(e=n.Eh(),O(e,167)&&(i=MBn(u(e,167)),i!=null)?i+"."+t:t):null}function p8e(n){var e,t,i;return n.e==0?0:(e=n.d<<5,t=n.a[n.d-1],n.e<0&&(i=Ixn(n),i==n.d-1&&(--t,t=t|0)),e-=iy(t),e)}function m8e(n){var e,t,i;return n<fP.length?fP[n]:(t=n>>5,e=n&31,i=K(ye,Ke,28,t+1,15,1),i[t]=1<<e,new Qa(1,t+1,i))}function TBn(n,e){var t,i;if(e){for(t=0;t<n.i;++t)if(i=u(n.g[t],378),i.mj(e))return!1;return ve(n,e)}else return!1}function UY(n,e,t){var i,r;if(++n.j,t.dc())return!1;for(r=t.Kc();r.Ob();)i=r.Pb(),n.qj(e,n.Zi(e,i)),++e;return!0}function v8e(n,e,t,i){var r,c;if(c=t-e,c<3)for(;c<3;)n*=10,++c;else{for(r=1;c>3;)r*=10,--c;n=(n+(r>>1))/r|0}return i.i=n,!0}function Ot(n,e){var t,i,r;if(t=(n.i==null&&bh(n),n.i),i=e.Lj(),i!=-1){for(r=t.length;i<r;++i)if(t[i]==e)return i}return-1}function k8e(n){var e,t,i,r,c;for(t=u(n.g,689),i=n.i-1;i>=0;--i)for(e=t[i],r=0;r<i;++r)if(c=t[r],DUn(n,e,c)){Jp(n,i);break}}function GY(n){var e,t,i,r;for(e=new Ka,r=new J3(n.b.Kc());r.b.Ob();)i=u(r.b.Pb(),701),t=xje(i),jwe(e,e.a.length,t);return e.a}function zY(n){var e;return!n.c&&(n.c=new pbn),Yt(n.d,new vbn),vAe(n),e=hAe(n),qt(new Tn(null,new In(n.d,16)),new N9n(n)),e}function y8e(n,e){e.Ug("End label post-processing",1),qt(ut(rc(new Tn(null,new In(n.b,16)),new Nwn),new $wn),new xwn),e.Vg()}function XY(n){bx(),this.c=If(S(T(PNe,1),Fn,845,0,[Jte])),this.b=new de,this.a=n,Xe(this.b,EI,1),nu(Qte,new Nkn(this))}function ABn(n,e,t){H$n(),njn.call(this),this.a=Va(zQn,[J,$tn],[603,217],0,[dP,h_],2),this.c=new mp,this.g=n,this.f=e,this.d=t}function VY(n,e){this.n=Va(xa,[J,SB],[376,28],14,[e,wi(y.Math.ceil(n/32))],2),this.o=n,this.p=e,this.j=n-1>>1,this.k=e-1>>1}function j8e(n){YM(),u(n.of((qe(),Ma)),181).Hc((io(),hO))&&(u(n.of(Ww),181).Fc((zu(),B3)),u(n.of(Ma),181).Mc(hO))}function SBn(n){var e,t;e=n.d==(Yp(),dv),t=GZ(n),e&&!t||!e&&t?U(n.a,(cn(),Th),(Rh(),Uj)):U(n.a,(cn(),Th),(Rh(),qj))}function bx(){bx=F,nC(),EI=(cn(),gb),Qte=If(S(T(Xq,1),Ern,149,0,[Tj,Vs,M2,wb,qw,IH,Av,Sv,OH,J8,C2,Bd,T2]))}function E8e(n,e){var t;return t=u(Wr(n,qu(new ju,new yu,new Eu,S(T(xr,1),G,108,0,[(Gu(),Yr)]))),15),t.Qc(WSn(t.gc()))}function PBn(n,e){var t,i;if(i=new Y3(n.a.ad(e,!0)),i.a.gc()<=1)throw M(new ip);return t=i.a.ec().Kc(),t.Pb(),u(t.Pb(),40)}function C8e(n,e,t){var i,r;return i=$(n.p[e.i.p])+$(n.d[e.i.p])+e.n.b+e.a.b,r=$(n.p[t.i.p])+$(n.d[t.i.p])+t.n.b+t.a.b,r-i}function WY(n,e){var t;return n.i>0&&(e.length<n.i&&(t=mk(wo(e).c,n.i),e=t),Ic(n.g,0,e,0,n.i)),e.length>n.i&&$t(e,n.i,null),e}function UT(n){var e;return n.Db&64?m5(n):(e=new ls(m5(n)),e.a+=" (instanceClassName: ",Er(e,n.D),e.a+=")",e.a)}function GT(n){var e,t,i,r;for(r=0,t=0,i=n.length;t<i;t++)e=(zn(t,n.length),n.charCodeAt(t)),e<64&&(r=hf(r,Fs(1,e)));return r}function M8e(n,e,t){var i,r;for(i=vi(t,mr),r=0;Ec(i,0)!=0&&r<e;r++)i=nr(i,vi(n[r],mr)),n[r]=Ae(i),i=w0(i,32);return Ae(i)}function Rk(n,e){var t,i,r,c;for(c=ru(n.e.Dh(),e),t=u(n.g,124),r=0;r<n.i;++r)if(i=t[r],c.am(i.Lk()))return!1;return!0}function wx(n,e){var t,i,r;return n.f>0?(n._j(),i=e==null?0:mt(e),r=(i&et)%n.d.length,t=RHn(n,r,i,e),t!=-1):!1}function IBn(n,e){var t,i;n.a=nr(n.a,1),n.c=y.Math.min(n.c,e),n.b=y.Math.max(n.b,e),n.d+=e,t=e-n.f,i=n.e+t,n.f=i-n.e-t,n.e=i}function JY(n,e){switch(e){case 3:P0(n,0);return;case 4:I0(n,0);return;case 5:eu(n,0);return;case 6:tu(n,0);return}kY(n,e)}function F0(n,e){switch(e.g){case 1:return Cp(n.j,(Ou(),Fon));case 2:return Cp(n.j,(Ou(),Ron));default:return Dn(),Dn(),sr}}function QY(n){m0();var e;switch(e=n.Pc(),e.length){case 0:return qK;case 1:return new VL(Se(e[0]));default:return new PN(q5e(e))}}function OBn(n,e){n.Xj();try{n.d.bd(n.e++,e),n.f=n.d.j,n.g=-1}catch(t){throw t=It(t),O(t,77)?M(new Bo):M(t)}}function gx(){gx=F,TU=new Tvn,zdn=new Avn,Xdn=new Svn,Vdn=new Pvn,Wdn=new Ivn,Jdn=new Ovn,Qdn=new Dvn,Ydn=new Lvn,Zdn=new Nvn}function zT(n,e){kX();var t,i;return t=D7((KE(),KE(),P8)),i=null,e==t&&(i=u(Nc(fun,n),624)),i||(i=new JPn(n),e==t&&Dr(fun,n,i)),i}function DBn(n){cw();var e;return(n.q?n.q:(Dn(),Dn(),Wh))._b((cn(),db))?e=u(v(n,db),203):e=u(v(Hi(n),W8),203),e}function rw(n,e){var t,i;return i=null,kt(n,(cn(),yI))&&(t=u(v(n,yI),96),t.pf(e)&&(i=t.of(e))),i==null&&(i=v(Hi(n),e)),i}function LBn(n,e){var t,i,r;return O(e,44)?(t=u(e,44),i=t.ld(),r=tw(n.Rc(),i),oh(r,t.md())&&(r!=null||n.Rc()._b(i))):!1}function wf(n,e){var t,i,r;return n.f>0&&(n._j(),i=e==null?0:mt(e),r=(i&et)%n.d.length,t=xnn(n,r,i,e),t)?t.md():null}function Xc(n,e,t){var i,r,c;return n.Pj()?(i=n.i,c=n.Qj(),Nk(n,i,e),r=n.Ij(3,null,e,i,c),t?t.nj(r):t=r):Nk(n,n.i,e),t}function T8e(n,e,t){var i,r;return i=new ml(n.e,4,10,(r=e.c,O(r,90)?u(r,29):(On(),Ps)),null,f1(n,e),!1),t?t.nj(i):t=i,t}function A8e(n,e,t){var i,r;return i=new ml(n.e,3,10,null,(r=e.c,O(r,90)?u(r,29):(On(),Ps)),f1(n,e),!1),t?t.nj(i):t=i,t}function NBn(n){Bb();var e;return e=new rr(u(n.e.of((qe(),K2)),8)),n.B.Hc((io(),Hv))&&(e.a<=0&&(e.a=20),e.b<=0&&(e.b=20)),e}function ta(n){dh();var e,t;return t=Ae(n),e=Ae(U1(n,32)),e!=0?new HOn(t,e):t>10||t<0?new gl(1,t):kQn[t]}function Kk(n,e){var t;return Vr(n)&&Vr(e)&&(t=n%e,Ay<t&&t<vd)?t:Q1((Jen(Vr(n)?ds(n):n,Vr(e)?ds(e):e,!0),ba))}function E5(n,e){var t;bDe(e),t=u(v(n,(cn(),bI)),283),t&&U(n,bI,I7e(t)),zl(n.c),zl(n.f),UJ(n.d),UJ(u(v(n,mI),214))}function S8e(n){var e,t,i,r;for(i=uEe(n),Yt(i,RZn),r=n.d,r.c.length=0,t=new C(i);t.a<t.c.c.length;)e=u(E(t),466),hi(r,e.b)}function px(n){var e;n.c!=0&&(e=u(sn(n.a,n.b),294),e.b==1?(++n.b,n.b<n.a.c.length&&r9n(u(sn(n.a,n.b),294))):--e.b,--n.c)}function P8e(n){var e;e=n.a;do e=u(fe(new te(re(Qt(e).a.Kc(),new En))),18).d.i,e.k==(Vn(),Mi)&&nn(n.e,e);while(e.k==(Vn(),Mi))}function $Bn(n){this.e=K(ye,Ke,28,n.length,15,1),this.c=K(so,Xh,28,n.length,16,1),this.b=K(so,Xh,28,n.length,16,1),this.f=0}function I8e(n){var e,t;for(n.j=K(Pi,Tr,28,n.p.c.length,15,1),t=new C(n.p);t.a<t.c.c.length;)e=u(E(t),10),n.j[e.p]=e.o.b/n.i}function O8e(n,e){var t,i,r,c;for(c=e.b.b,n.a=new Ct,n.b=K(ye,Ke,28,c,15,1),t=0,r=ge(e.b,0);r.b!=r.d.c;)i=u(be(r),40),i.g=t++}function xBn(n,e,t){var i,r,c,s;for(c=e-n.e,s=t-n.f,r=new C(n.a);r.a<r.c.c.length;)i=u(E(r),172),Uk(i,i.s+c,i.t+s);n.e=e,n.f=t}function _k(n,e){var t,i;for(i=e.length,t=0;t<i;t+=2)xc(n,(zn(t,e.length),e.charCodeAt(t)),(zn(t+1,e.length),e.charCodeAt(t+1)))}function D8e(n,e){e.Ug("Min Size Postprocessing",1),ht(n,(_h(),Xw),y.Math.max($(R(z(n,Xw))),$(R(z(n,a9))))),e.Vg()}function YY(){YY=F,wdn=new f0(15),uoe=new Ni((qe(),C1),wdn),soe=new Ni(qd,15),ooe=new Ni(fU,Y(0)),coe=new Ni($2,Gm)}function go(){go=F,rE=new jC("PORTS",0),Gd=new jC("PORT_LABELS",1),iE=new jC("NODE_LABELS",2),Qw=new jC("MINIMUM_SIZE",3)}function XT(){XT=F,Bj=new rL("P1_WIDTH_APPROXIMATION",0),qI=new rL("P2_PACKING",1),Mq=new rL("P3_WHITESPACE_ELIMINATION",2)}function FBn(n){if(n.b==null){for(;n.a.Ob();)if(n.b=n.a.Pb(),!u(n.b,54).Jh())return!0;return n.b=null,!1}else return!0}function bm(n,e,t){var i,r,c;for(r=null,c=n.b;c;){if(i=n.a.Ne(e,c.d),t&&i==0)return c;i>=0?c=c.a[1]:(r=c,c=c.a[0])}return r}function Hk(n,e,t){var i,r,c;for(r=null,c=n.b;c;){if(i=n.a.Ne(e,c.d),t&&i==0)return c;i<=0?c=c.a[0]:(r=c,c=c.a[1])}return r}function L8e(n,e,t,i){var r,c,s;return r=!1,xOe(n.f,t,i)&&(e9e(n.f,n.a[e][t],n.a[e][i]),c=n.a[e],s=c[i],c[i]=c[t],c[t]=s,r=!0),r}function BBn(n,e,t){var i,r,c,s;for(r=u(ee(n.b,t),183),i=0,s=new C(e.j);s.a<s.c.c.length;)c=u(E(s),113),r[c.d.p]&&++i;return i}function ZY(n,e,t){var i,r;i=u(Nc(Gv,e),122),r=u(Nc(_9,e),122),t?(Dr(Gv,n,i),Dr(_9,n,r)):(Dr(_9,n,i),Dr(Gv,n,r))}function RBn(n,e){var t,i,r,c;return t=e>>5,e&=31,r=n.d+t+(e==0?0:1),i=K(ye,Ke,28,r,15,1),Oye(i,n.a,t,e),c=new Qa(n.e,r,i),Q6(c),c}function N8e(n,e){var t,i,r;for(i=new te(re(Qt(n).a.Kc(),new En));pe(i);)if(t=u(fe(i),18),r=t.d.i,r.c==e)return!1;return!0}function nZ(n,e,t){var i,r,c,s,f;return s=n.k,f=e.k,i=t[s.g][f.g],r=R(rw(n,i)),c=R(rw(e,i)),y.Math.max((Jn(r),r),(Jn(c),c))}function $8e(){return Error.stackTraceLimit>0?(y.Error.stackTraceLimit=Error.stackTraceLimit=64,!0):"stack"in new Error}function x8e(n,e){return Mf(),Mf(),Rs(sa),(y.Math.abs(n-e)<=sa||n==e||isNaN(n)&&isNaN(e)?0:n<e?-1:n>e?1:s0(isNaN(n),isNaN(e)))>0}function eZ(n,e){return Mf(),Mf(),Rs(sa),(y.Math.abs(n-e)<=sa||n==e||isNaN(n)&&isNaN(e)?0:n<e?-1:n>e?1:s0(isNaN(n),isNaN(e)))<0}function KBn(n,e){return Mf(),Mf(),Rs(sa),(y.Math.abs(n-e)<=sa||n==e||isNaN(n)&&isNaN(e)?0:n<e?-1:n>e?1:s0(isNaN(n),isNaN(e)))<=0}function mx(n,e){for(var t=0;!e[t]||e[t]=="";)t++;for(var i=e[t++];t<e.length;t++)!e[t]||e[t]==""||(i+=n+e[t]);return i}function _Bn(n){var e,t;return e=u(Un(n.a,4),129),e!=null?(t=K(jU,MK,424,e.length,0,1),Ic(e,0,t,0,e.length),t):Ioe}function HBn(n){var e,t,i,r,c;if(n==null)return null;for(c=new Z,t=z$(n),i=0,r=t.length;i<r;++i)e=t[i],nn(c,Fc(e,!0));return c}function qBn(n){var e,t,i,r,c;if(n==null)return null;for(c=new Z,t=z$(n),i=0,r=t.length;i<r;++i)e=t[i],nn(c,Fc(e,!0));return c}function UBn(n){var e,t,i,r,c;if(n==null)return null;for(c=new Z,t=z$(n),i=0,r=t.length;i<r;++i)e=t[i],nn(c,Fc(e,!0));return c}function GBn(n,e){var t,i,r;if(n.c)P0(n.c,e);else for(t=e-ao(n),r=new C(n.a);r.a<r.c.c.length;)i=u(E(r),163),GBn(i,ao(i)+t)}function zBn(n,e){var t,i,r;if(n.c)I0(n.c,e);else for(t=e-Su(n),r=new C(n.d);r.a<r.c.c.length;)i=u(E(r),163),zBn(i,Su(i)+t)}function hh(n,e,t){var i,r,c,s;for(c=e+t,Fi(e,c,n.length),s="",r=e;r<c;)i=y.Math.min(r+1e4,c),s+=Ywe(n.slice(r,i)),r=i;return s}function tZ(n){switch(n.g){case 12:case 13:case 14:case 15:case 16:case 17:case 18:case 19:case 20:return!0;default:return!1}}function o1(){o1=F,J_=new l7(cin,0),Dsn=new l7(VXn,1),Q_=new l7(sR,2),pv=new l7(tin,3),gv=new l7("GREEDY_MODEL_ORDER",4)}function lh(){lh=F,k1=new gC(kh,0),_hn=new gC("NODES_AND_EDGES",1),HH=new gC("PREFER_EDGES",2),qH=new gC("PREFER_NODES",3)}function iZ(n,e,t,i,r,c){this.a=n,this.c=e,this.b=t,this.f=i,this.d=r,this.e=c,this.c>0&&this.b>0&&(this.g=cM(this.c,this.b,this.a))}function F8e(n,e){var t=n.a,i;e=String(e),t.hasOwnProperty(e)&&(i=t[e]);var r=(K$(),WK)[typeof i],c=r?r(i):wY(typeof i);return c}function wm(n){var e,t,i;if(i=null,e=Eh in n.a,t=!e,t)throw M(new nh("Every element must have an id."));return i=Zp(dl(n,Eh)),i}function B0(n){var e,t;for(t=a_n(n),e=null;n.c==2;)Ye(n),e||(e=(nt(),nt(),new P6(2)),pd(e,t),t=e),t.Jm(a_n(n));return t}function VT(n,e){var t,i,r;return n._j(),i=e==null?0:mt(e),r=(i&et)%n.d.length,t=xnn(n,r,i,e),t?(V$n(n,t),t.md()):null}function XBn(n,e){return n.e>e.e?1:n.e<e.e?-1:n.d>e.d?n.e:n.d<e.d?-e.e:n.e*hY(n.a,e.a,n.d)}function VBn(n){return n>=48&&n<48+y.Math.min(10,10)?n-48:n>=97&&n<97?n-97+10:n>=65&&n<65?n-65+10:-1}function B8e(n,e){if(e.c==n)return e.d;if(e.d==n)return e.c;throw M(new Gn("Input edge is not connected to the input port."))}function R8e(n){if(JT(nv,n))return _n(),ov;if(JT(cK,n))return _n(),wa;throw M(new Gn("Expecting true or false"))}function rZ(n){switch(typeof n){case nB:return t1(n);case dtn:return pp(n);case i3:return SAn(n);default:return n==null?0:l0(n)}}function ah(n,e){if(n.a<0)throw M(new Or("Did not call before(...) or after(...) before calling add(...)."));return YX(n,n.a,e),n}function cZ(n){return $M(),O(n,162)?u(ee(hE,MQn),295).Rg(n):Zc(hE,wo(n))?u(ee(hE,wo(n)),295).Rg(n):null}function iu(n){var e,t;return n.Db&32||(t=(e=u(Un(n,16),29),se(e||n.ii())-se(n.ii())),t!=0&&Xp(n,32,K(ki,Fn,1,t,5,1))),n}function Xp(n,e,t){var i;n.Db&e?t==null?jCe(n,e):(i=Rx(n,e),i==-1?n.Eb=t:$t(cd(n.Eb),i,t)):t!=null&&GTe(n,e,t)}function K8e(n,e,t,i){var r,c;e.c.length!=0&&(r=$Me(t,i),c=xEe(e),qt(fT(new Tn(null,new In(c,1)),new L3n),new MIn(n,t,r,i)))}function _8e(n,e){var t,i,r,c;return i=n.a.length-1,t=e-n.b&i,c=n.c-e&i,r=n.c-n.b&i,EAn(t<r),t>=c?(R6e(n,e),-1):(B6e(n,e),1)}function WT(n){var e,t,i;if(i=n.Jh(),!i)for(e=0,t=n.Ph();t;t=t.Ph()){if(++e>PB)return t.Qh();if(i=t.Jh(),i||t==n)break}return i}function WBn(n,e){var t;return x(e)===x(n)?!0:!O(e,21)||(t=u(e,21),t.gc()!=n.gc())?!1:n.Ic(t)}function H8e(n,e){return n.e<e.e?-1:n.e>e.e?1:n.f<e.f?-1:n.f>e.f?1:mt(n)-mt(e)}function JT(n,e){return Jn(n),e==null?!1:An(n,e)?!0:n.length==e.length&&An(n.toLowerCase(),e.toLowerCase())}function Ml(n){var e,t;return Ec(n,-129)>0&&Ec(n,128)<0?(ZSn(),e=Ae(n)+128,t=mun[e],!t&&(t=mun[e]=new kG(n)),t):new kG(n)}function dd(){dd=F,Ow=new aC(kh,0),Don=new aC("INSIDE_PORT_SIDE_GROUPS",1),P_=new aC("GROUP_MODEL_ORDER",2),I_=new aC(tin,3)}function q8e(n){var e;return n.b||xhe(n,(e=$ae(n.e,n.a),!e||!An(cK,wf((!e.b&&(e.b=new lo((On(),ar),pc,e)),e.b),"qualified")))),n.c}function U8e(n,e){var t,i;for(t=(zn(e,n.length),n.charCodeAt(e)),i=e+1;i<n.length&&(zn(i,n.length),n.charCodeAt(i)==t);)++i;return i-e}function G8e(n,e){(!e&&console.groupCollapsed!=null?console.groupCollapsed:console.group??console.log).call(console,n)}function z8e(n,e,t,i){i==n,u(t.b,68),u(t.b,68),u(i.b,68),u(i.b,68).c.b,XJ(i,e,n)}function X8e(n){var e,t;for(e=new C(n.g);e.a<e.c.c.length;)u(E(e),568);t=new hqn(n.g,$(n.a),n.c),yDe(t),n.g=t.b,n.d=t.a}function JBn(n,e,t){var i,r,c;for(c=new C(t.a);c.a<c.c.c.length;)r=u(E(c),225),i=new LC(u(ee(n.a,r.b),68)),nn(e.a,i),JBn(n,i,r)}function V8e(n,e,t){var i,r,c;return i=u(L(no(n.a),e),89),c=(r=i.c,r||(On(),Yf)),(c.Vh()?na(n.b,u(c,54)):c)==t?BA(i):K4(i,t),c}function uZ(n,e,t){e.b=y.Math.max(e.b,-t.a),e.c=y.Math.max(e.c,t.a-n.a),e.d=y.Math.max(e.d,-t.b),e.a=y.Math.max(e.a,t.b-n.b)}function oZ(n,e,t){this.c=n,this.f=new Z,this.e=new Li,this.j=new sW,this.n=new sW,this.b=e,this.g=new Ho(e.c,e.d,e.b,e.a),this.a=t}function vx(n){var e,t,i,r;for(this.a=new ih,this.d=new ni,this.e=0,t=n,i=0,r=t.length;i<r;++i)e=t[i],!this.f&&(this.f=e),_N(this,e)}function QBn(n){dh(),n.length==0?(this.e=0,this.d=1,this.a=S(T(ye,1),Ke,28,15,[0])):(this.e=1,this.d=n.length,this.a=n,Q6(this))}function C5(n,e,t){njn.call(this),this.a=K(zQn,$tn,217,(bf(),S(T(Sw,1),G,237,0,[bc,Wc,wc])).length,0,1),this.b=n,this.d=e,this.c=t}function W8e(n){var e,t,i,r,c,s;for(s=u(v(n,(W(),st)),12),U(s,jv,n.i.n.b),e=fh(n.e),i=e,r=0,c=i.length;r<c;++r)t=i[r],Ii(t,s)}function J8e(n){var e,t,i,r,c,s;for(t=u(v(n,(W(),st)),12),U(t,jv,n.i.n.b),e=fh(n.g),r=e,c=0,s=r.length;c<s;++c)i=r[c],Zi(i,t)}function Q8e(n,e){NN();var t,i;for(i=new te(re(Cl(n).a.Kc(),new En));pe(i);)if(t=u(fe(i),18),t.d.i==e||t.c.i==e)return t;return null}function YBn(n,e){var t,i;return t=e.qi(n.a),t&&(i=Oe(wf((!t.b&&(t.b=new lo((On(),ar),pc,t)),t.b),Je)),i!=null)?i:e.xe()}function Y8e(n,e){var t,i;return t=e.qi(n.a),t&&(i=Oe(wf((!t.b&&(t.b=new lo((On(),ar),pc,t)),t.b),Je)),i!=null)?i:e.xe()}function Z8e(n,e){var t,i;return t=jc(n.a.c.p,e.a.c.p),t!=0?t:(i=jc(n.a.d.i.p,e.a.d.i.p),i!=0?i:jc(e.a.d.p,n.a.d.p))}function n9e(n,e){var t,i,r,c;for(i=0,r=e.gc();i<r;++i)t=e.Tl(i),O(t,102)&&u(t,19).Bb&kc&&(c=e.Ul(i),c!=null&&IF(n,u(c,58)))}function ZBn(n,e){var t,i,r;if(nn(mP,n),e.Fc(n),t=u(ee(m_,n),21),t)for(r=t.Kc();r.Ob();)i=u(r.Pb(),27),qr(mP,i,0)!=-1||ZBn(i,e)}function e9e(n,e,t){var i,r;eF(n.e,e,t,(tn(),Wn)),eF(n.i,e,t,Zn),n.a&&(r=u(v(e,(W(),st)),12),i=u(v(t,st),12),KN(n.g,r,i))}function nRn(n,e,t){var i,r,c;i=e.c.p,c=e.p,n.b[i][c]=new XIn(n,e),t&&(n.a[i][c]=new F7n(e),r=u(v(e,(W(),sb)),10),r&&Pn(n.d,r,e))}function t9e(n,e,t){var i,r,c,s;return c=e.j,s=t.j,c!=s?c.g-s.g:(i=n.f[e.p],r=n.f[t.p],i==0&&r==0?0:i==0?-1:r==0?1:bt(i,r))}function i9e(){var n;return cP!=0&&(n=Date.now(),n-hQn>2e3&&(hQn=n,uP=y.setTimeout(_he,10))),cP++==0?(ime((az(),sun)),!0):!1}function r9e(n,e,t){var i;(DQn?(o8e(n),!0):LQn||$Qn?(a4(),!0):NQn&&(a4(),!1))&&(i=new aSn(e),i.b=t,aje(n,i))}function kx(n,e){var t;t=!n.A.Hc((go(),Gd))||n.q==(Oi(),qc),n.u.Hc((zu(),Fl))?t?XDe(n,e):UGn(n,e):n.u.Hc(Pa)&&(t?dDe(n,e):czn(n,e))}function eRn(n){var e;x(z(n,(qe(),B2)))===x((jl(),uO))&&(At(n)?(e=u(z(At(n),B2),346),ht(n,B2,e)):ht(n,B2,M9))}function c9e(n){var e,t;return kt(n.d.i,(cn(),Cv))?(e=u(v(n.c.i,Cv),17),t=u(v(n.d.i,Cv),17),jc(e.a,t.a)>0):!1}function tRn(n,e,t){return new Ho(y.Math.min(n.a,e.a)-t/2,y.Math.min(n.b,e.b)-t/2,y.Math.abs(n.a-e.a)+t,y.Math.abs(n.b-e.b)+t)}function iRn(n){var e;this.d=new Z,this.j=new Li,this.g=new Li,e=n.g.b,this.f=u(v(Hi(e),(cn(),Do)),88),this.e=$(R(nA(e,qw)))}function rRn(n){this.d=new Z,this.e=new Ql,this.c=K(ye,Ke,28,(tn(),S(T(lr,1),Mc,64,0,[sc,Xn,Zn,ae,Wn])).length,15,1),this.b=n}function sZ(n,e,t){var i;switch(i=t[n.g][e],n.g){case 1:case 3:return new V(0,i);case 2:case 4:return new V(i,0);default:return null}}function cRn(n,e,t){var i,r;r=u(V7(e.f),205);try{r.rf(n,t),hIn(e.f,r)}catch(c){throw c=It(c),O(c,103)?(i=c,M(i)):M(c)}}function uRn(n,e,t){var i,r,c,s,f,h;return i=null,f=Zen(z4(),e),c=null,f&&(r=null,h=Qen(f,t),s=null,h!=null&&(s=n.qf(f,h)),r=s,c=r),i=c,i}function yx(n,e,t,i){var r;if(r=n.length,e>=r)return r;for(e=e>0?e:0;e<r&&!R$((zn(e,n.length),n.charCodeAt(e)),t,i);e++);return e}function xf(n,e){var t,i;for(i=n.c.length,e.length<i&&(e=qE(new Array(i),e)),t=0;t<i;++t)$t(e,t,n.c[t]);return e.length>i&&$t(e,i,null),e}function oRn(n,e){var t,i;for(i=n.a.length,e.length<i&&(e=qE(new Array(i),e)),t=0;t<i;++t)$t(e,t,n.a[t]);return e.length>i&&$t(e,i,null),e}function gm(n,e){var t,i;if(++n.j,e!=null&&(t=(i=n.a.Cb,O(i,99)?u(i,99).th():null),hCe(e,t))){Xp(n.a,4,t);return}Xp(n.a,4,u(e,129))}function u9e(n){var e;if(n==null)return null;if(e=lMe(Fc(n,!0)),e==null)throw M(new kD("Invalid hexBinary value: '"+n+"'"));return e}function QT(n,e,t){var i;e.a.length>0&&(nn(n.b,new SSn(e.a,t)),i=e.a.length,0<i?e.a=qo(e.a,0,0):0>i&&(e.a+=ITn(K(fs,gh,28,-i,15,1))))}function sRn(n,e,t){var i,r,c;if(!t[e.d])for(t[e.d]=!0,r=new C($g(e));r.a<r.c.c.length;)i=u(E(r),218),c=HT(i,e),sRn(n,c,t)}function s1(n,e,t){var i,r,c;return r=u(ee(n.e,e),400),r?(c=wV(r,t),DTn(n,r),c):(i=new UV(n,e,t),Xe(n.e,e,i),rOn(i),null)}function o9e(n,e,t,i){var r,c,s;return r=new ml(n.e,1,13,(s=e.c,s||(On(),Yf)),(c=t.c,c||(On(),Yf)),f1(n,e),!1),i?i.nj(r):i=r,i}function jx(){return VA(),S(T(vYn,1),G,164,0,[pYn,gYn,mYn,sYn,oYn,fYn,aYn,lYn,hYn,wYn,bYn,dYn,cYn,rYn,uYn,tYn,eYn,iYn,ZQn,YQn,nYn,l_])}function pm(n){switch(n.g){case 4:return new V(0,-1);case 1:return new V(1,0);case 2:return new V(-1,0);default:return new V(0,1)}}function Ex(n){switch(n.g){case 1:return ci(),us;case 4:return ci(),Br;case 2:return ci(),Xr;case 3:return ci(),Vf}return ci(),Wf}function s9e(n){var e;switch(e=n.hj(null),e){case 10:return 0;case 15:return 1;case 14:return 2;case 11:return 3;case 21:return 4}return-1}function gf(){gf=F,xn=new m7("PARENTS",0),pi=new m7("NODES",1),Ph=new m7("EDGES",2),Kd=new m7("PORTS",3),E1=new m7("LABELS",4)}function f9e(n,e,t){var i;switch(i=t.q.getFullYear()-fa+fa,i<0&&(i=-i),e){case 1:n.a+=i;break;case 2:Bh(n,i%100,2);break;default:Bh(n,i,e)}}function ge(n,e){var t,i;if(zb(e,n.b),e>=n.b>>1)for(i=n.c,t=n.b;t>e;--t)i=i.b;else for(i=n.a.a,t=0;t<e;++t)i=i.a;return new lSn(n,e,i)}function YT(){YT=F,o_=new qz("NUM_OF_EXTERNAL_SIDES_THAN_NUM_OF_EXTENSIONS_LAST",0),Fun=new qz("CORNER_CASES_THAN_SINGLE_SIDE_LAST",1)}function fRn(n){this.b=new Z,this.e=new Z,this.d=n,this.a=!s4(ut(new Tn(null,new p0(new Of(n.b))),new Z3(new vpn))).Bd((Xa(),v3))}function hRn(n,e){var t,i,r,c;for(t=0,r=new C(e.a);r.a<r.c.c.length;)i=u(E(r),10),c=i.o.a+i.d.c+i.d.b+n.j,t=y.Math.max(t,c);return t}function lRn(n,e){var t,i,r;r=e.d.i,i=r.k,!(i==(Vn(),zt)||i==Uf)&&(t=new te(re(Qt(r).a.Kc(),new En)),pe(t)&&Xe(n.k,e,u(fe(t),18)))}function h9e(n,e){return kl(),bt((n.a.b==0?new V(n.c.e.a,n.c.e.b):u(p4(n.a),8)).b,(e.a.b==0?new V(e.c.e.a,e.c.e.b):u(p4(e.a),8)).b)}function l9e(n,e){return kl(),bt((n.a.b==0?new V(n.c.e.a,n.c.e.b):u(p4(n.a),8)).a,(e.a.b==0?new V(e.c.e.a,e.c.e.b):u(p4(e.a),8)).a)}function a9e(n,e){return kl(),bt((n.a.b==0?new V(n.b.e.a,n.b.e.b):u(Ns(n.a),8)).a,(e.a.b==0?new V(e.b.e.a,e.b.e.b):u(Ns(e.a),8)).a)}function d9e(n,e){return kl(),bt((n.a.b==0?new V(n.b.e.a,n.b.e.b):u(Ns(n.a),8)).b,(e.a.b==0?new V(e.b.e.a,e.b.e.b):u(Ns(e.a),8)).b)}function Fg(){Fg=F,Aa=new k7("DISTRIBUTED",0),eE=new k7("JUSTIFIED",1),adn=new k7("BEGIN",2),T9=new k7(qm,3),ddn=new k7("END",4)}function Cx(n,e){var t,i,r;return i=$n(n.Dh(),e),t=e-n.ji(),t<0?(r=n.Ih(i),r>=0?n.Wh(r):hF(n,i)):t<0?hF(n,i):u(i,69).wk().Bk(n,n.hi(),t)}function aRn(n){var e,t,i;for(i=(!n.o&&(n.o=new Iu((Cc(),il),T1,n,0)),n.o),t=i.c.Kc();t.e!=t.i.gc();)e=u(t.Yj(),44),e.md();return uk(i)}function rn(n){var e;if(O(n.a,4)){if(e=cZ(n.a),e==null)throw M(new Or(NVn+n.b+"'. "+LVn+(ll(lE),lE.k)+bcn));return e}else return n.a}function b9e(n,e){var t,i;if(n.j.length!=e.j.length)return!1;for(t=0,i=n.j.length;t<i;t++)if(!An(n.j[t],e.j[t]))return!1;return!0}function ce(n){var e;try{return e=n.i.Xb(n.e),n.Xj(),n.g=n.e++,e}catch(t){throw t=It(t),O(t,77)?(n.Xj(),M(new nc)):M(t)}}function Mx(n){var e;try{return e=n.c.Vi(n.e),n.Xj(),n.g=n.e++,e}catch(t){throw t=It(t),O(t,77)?(n.Xj(),M(new nc)):M(t)}}function ZT(n){var e,t,i,r;for(r=0,t=0,i=n.length;t<i;t++)e=(zn(t,n.length),n.charCodeAt(t)),e>=64&&e<128&&(r=hf(r,Fs(1,e-64)));return r}function nA(n,e){var t,i;return i=null,kt(n,(qe(),$3))&&(t=u(v(n,$3),96),t.pf(e)&&(i=t.of(e))),i==null&&Hi(n)&&(i=v(Hi(n),e)),i}function w9e(n,e){var t;return t=u(v(n,(cn(),Fr)),75),yL(e,LZn)?t?vo(t):(t=new Mu,U(n,Fr,t)):t&&U(n,Fr,null),t}function M5(){M5=F,aon=(qe(),qan),g_=Ean,DYn=$2,lon=C1,xYn=(aA(),Uun),$Yn=Hun,FYn=zun,NYn=_un,LYn=(Q$(),son),w_=PYn,hon=IYn,pP=OYn}function eA(n){switch($z(),this.c=new Z,this.d=n,n.g){case 0:case 2:this.a=qW(Oon),this.b=St;break;case 3:case 1:this.a=Oon,this.b=li}}function g9e(n){var e;Ep(u(v(n,(cn(),Kt)),101))&&(e=n.b,nHn((Ln(0,e.c.length),u(e.c[0],30))),nHn(u(sn(e,e.c.length-1),30)))}function p9e(n,e){e.Ug("Self-Loop post-processing",1),qt(ut(ut(rc(new Tn(null,new In(n.b,16)),new s2n),new f2n),new h2n),new l2n),e.Vg()}function dRn(n,e,t){var i,r;if(n.c)eu(n.c,n.c.i+e),tu(n.c,n.c.j+t);else for(r=new C(n.b);r.a<r.c.c.length;)i=u(E(r),163),dRn(i,e,t)}function m9e(n){var e;if(n==null)return null;if(e=iLe(Fc(n,!0)),e==null)throw M(new kD("Invalid base64Binary value: '"+n+"'"));return e}function Zo(n,e){var t;t=n.fd(e);try{return t.Pb()}catch(i){throw i=It(i),O(i,112)?M(new Ir("Can't get element "+e)):M(i)}}function bRn(n,e){var t,i,r;for(t=n.o,r=u(u(ot(n.r,e),21),87).Kc();r.Ob();)i=u(r.Pb(),117),i.e.a=y7e(i,t.a),i.e.b=t.b*$(R(i.b.of(bP)))}function v9e(n,e){var t,i,r;for(r=new Gc(e.gc()),i=e.Kc();i.Ob();)t=u(i.Pb(),293),t.c==t.f?Em(n,t,t.c):Hje(n,t)||Bn(r.c,t);return r}function wRn(n){var e;return e=new x1,e.a+="n",n.k!=(Vn(),zt)&&Be(Be((e.a+="(",e),SL(n.k).toLowerCase()),")"),Be((e.a+="_",e),Gk(n)),e.a}function k9e(n,e){var t,i,r,c;return r=n.k,t=$(R(v(n,(W(),fb)))),c=e.k,i=$(R(v(e,fb))),c!=(Vn(),Zt)?-1:r!=Zt?1:t==i?0:t<i?-1:1}function y9e(n,e){var t,i;return t=u(u(ee(n.g,e.a),42).a,68),i=u(u(ee(n.g,e.b),42).a,68),W1(e.a,e.b)-W1(e.a,LX(t.b))-W1(e.b,LX(i.b))}function gRn(n,e){var t;switch(t=u(Cr(n.b,e),127).n,e.g){case 1:n.t>=0&&(t.d=n.t);break;case 3:n.t>=0&&(t.a=n.t)}n.C&&(t.b=n.C.b,t.c=n.C.c)}function T5(){T5=F,Nhn=new d7(Crn,0),KH=new d7(sR,1),_H=new d7("LINEAR_SEGMENTS",2),Y8=new d7("BRANDES_KOEPF",3),Z8=new d7(sVn,4)}function A5(){A5=F,fj=new hC(eS,0),wP=new hC(HB,1),gP=new hC(qB,2),hj=new hC(UB,3),fj.a=!1,wP.a=!0,gP.a=!1,hj.a=!0}function Vp(){Vp=F,uj=new fC(eS,0),cj=new fC(HB,1),oj=new fC(qB,2),sj=new fC(UB,3),uj.a=!1,cj.a=!0,oj.a=!1,sj.a=!0}function Wp(n,e,t,i){var r;return t>=0?n.Sh(e,t,i):(n.Ph()&&(i=(r=n.Fh(),r>=0?n.Ah(i):n.Ph().Th(n,-1-r,null,i))),n.Ch(e,t,i))}function fZ(n,e){switch(e){case 7:!n.e&&(n.e=new Nn(Vt,n,7,4)),me(n.e);return;case 8:!n.d&&(n.d=new Nn(Vt,n,8,5)),me(n.d);return}JY(n,e)}function ht(n,e,t){return t==null?(!n.o&&(n.o=new Iu((Cc(),il),T1,n,0)),VT(n.o,e)):(!n.o&&(n.o=new Iu((Cc(),il),T1,n,0)),Vk(n.o,e,t)),n}function pRn(n,e){Dn();var t,i,r,c;for(t=n,c=e,O(n,21)&&!O(e,21)&&(t=e,c=n),r=t.Kc();r.Ob();)if(i=r.Pb(),c.Hc(i))return!1;return!0}function j9e(n,e,t,i){if(e.a<i.a)return!0;if(e.a==i.a){if(e.b<i.b)return!0;if(e.b==i.b&&n.b>t.b)return!0}return!1}function Tx(n,e){return Ai(n)?!!iQn[e]:n.Sm?!!n.Sm[e]:$b(n)?!!tQn[e]:Nb(n)?!!eQn[e]:!1}function E9e(n){var e;e=n.a;do e=u(fe(new te(re(ji(e).a.Kc(),new En))),18).c.i,e.k==(Vn(),Mi)&&n.b.Fc(e);while(e.k==(Vn(),Mi));n.b=Qo(n.b)}function mRn(n,e){var t,i,r;for(r=n,i=new te(re(ji(e).a.Kc(),new En));pe(i);)t=u(fe(i),18),t.c.i.c&&(r=y.Math.max(r,t.c.i.c.p));return r}function C9e(n,e){var t,i,r;for(r=0,i=u(u(ot(n.r,e),21),87).Kc();i.Ob();)t=u(i.Pb(),117),r+=t.d.d+t.b.Mf().b+t.d.a,i.Ob()&&(r+=n.w);return r}function M9e(n,e){var t,i,r;for(r=0,i=u(u(ot(n.r,e),21),87).Kc();i.Ob();)t=u(i.Pb(),117),r+=t.d.b+t.b.Mf().a+t.d.c,i.Ob()&&(r+=n.w);return r}function vRn(n){var e,t,i,r;if(i=0,r=aw(n),r.c.length==0)return 1;for(t=new C(r);t.a<t.c.c.length;)e=u(E(t),27),i+=vRn(e);return i}function T9e(n){var e,t,i;for(i=n.c.a,n.p=(Se(i),new _u(i)),t=new C(i);t.a<t.c.c.length;)e=u(E(t),10),e.p=fEe(e).a;Dn(),Yt(n.p,new Vpn)}function A9e(n,e,t){var i,r,c,s;return i=n.dd(e),i!=-1&&(n.Pj()?(c=n.Qj(),s=tM(n,i),r=n.Ij(4,s,null,i,c),t?t.nj(r):t=r):tM(n,i)),t}function cr(n,e,t){var i,r,c,s;return i=n.dd(e),i!=-1&&(n.Pj()?(c=n.Qj(),s=Jp(n,i),r=n.Ij(4,s,null,i,c),t?t.nj(r):t=r):Jp(n,i)),t}function S9e(n,e,t,i){var r,c,s;t.Xh(e)&&(dr(),a$(e)?(r=u(t.Mh(e),160),n9e(n,r)):(c=(s=e,s?u(i,54).gi(s):null),c&&Ife(t.Mh(e),c)))}function tA(n,e,t,i){var r,c,s;return c=$n(n.Dh(),e),r=e-n.ji(),r<0?(s=n.Ih(c),s>=0?n.Lh(s,t,!0):H0(n,c,t)):u(c,69).wk().yk(n,n.hi(),r,t,i)}function P9e(n,e,t,i){var r,c;c=e.pf((qe(),R2))?u(e.of(R2),21):n.j,r=d5e(c),r!=(VA(),l_)&&(t&&!tZ(r)||bnn(aMe(n,r,i),e))}function I9e(n){switch(n.g){case 1:return N0(),rj;case 3:return N0(),ij;case 2:return N0(),d_;case 4:return N0(),a_;default:return null}}function O9e(n,e,t){if(n.e)switch(n.b){case 1:yge(n.c,e,t);break;case 0:jge(n.c,e,t)}else KDn(n.c,e,t);n.a[e.p][t.p]=n.c.i,n.a[t.p][e.p]=n.c.e}function kRn(n){var e,t;if(n==null)return null;for(t=K(Qh,J,199,n.length,0,2),e=0;e<t.length;e++)t[e]=u(P3e(n[e],n[e].length),199);return t}function iA(n){var e;if(W$(n))return aM(n),n.ul()&&(e=x5(n.e,n.b,n.c,n.a,n.j),n.j=e),n.g=n.a,++n.a,++n.c,n.i=0,n.j;throw M(new nc)}function D9e(n,e){var t,i,r,c;return c=n.o,t=n.p,c<t?c*=c:t*=t,i=c+t,c=e.o,t=e.p,c<t?c*=c:t*=t,r=c+t,i<r?-1:i==r?0:1}function f1(n,e){var t,i,r;if(r=eKn(n,e),r>=0)return r;if(n.ol()){for(i=0;i<n.i;++i)if(t=n.pl(u(n.g[i],58)),x(t)===x(e))return i}return-1}function Bg(n,e,t){var i,r;if(r=n.gc(),e>=r)throw M(new Kb(e,r));if(n.Si()&&(i=n.dd(t),i>=0&&i!=e))throw M(new Gn(Vy));return n.Xi(e,t)}function hZ(n,e){if(this.a=u(Se(n),253),this.b=u(Se(e),253),n.Ed(e)>0||n==(dD(),_K)||e==(bD(),HK))throw M(new Gn("Invalid range: "+qDn(n,e)))}function yRn(n){var e,t;for(this.b=new Z,this.c=n,this.a=!1,t=new C(n.a);t.a<t.c.c.length;)e=u(E(t),10),this.a=this.a|e.k==(Vn(),zt)}function L9e(n,e){var t,i,r;for(t=h0(new Ga,n),r=new C(e);r.a<r.c.c.length;)i=u(E(r),125),Hs(Ds(Os(Ls(Is(new hs,0),0),t),i));return t}function jRn(n,e,t){t.Ug("Compound graph preprocessor",1),n.a=new C0,KGn(n,e,null),TIe(n,e),QMe(n),U(e,(W(),efn),n.a),n.a=null,Hu(n.b),t.Vg()}function ERn(n,e,t){var i,r,c;for(r=new te(re((e?ji(n):Qt(n)).a.Kc(),new En));pe(r);)i=u(fe(r),18),c=e?i.c.i:i.d.i,c.k==(Vn(),Ac)&&$i(c,t)}function N9e(n,e){var t,i,r;for(e.Ug("Untreeify",1),t=u(v(n,(pt(),yln)),15),r=t.Kc();r.Ob();)i=u(r.Pb(),65),xe(i.b.d,i),xe(i.c.b,i);e.Vg()}function $9e(n){var e,t,i;for(i=u(ot(n.a,(ow(),zP)),15).Kc();i.Ob();)t=u(i.Pb(),105),e=EZ(t),M4(n,t,e[0],(D0(),cb),0),M4(n,t,e[1],ub,1)}function x9e(n){var e,t,i;for(i=u(ot(n.a,(ow(),XP)),15).Kc();i.Ob();)t=u(i.Pb(),105),e=EZ(t),M4(n,t,e[0],(D0(),cb),0),M4(n,t,e[1],ub,1)}function cw(){cw=F,TI=new wC(kh,0),BH=new wC("PORT_POSITION",1),S2=new wC("NODE_SIZE_WHERE_SPACE_PERMITS",2),A2=new wC("NODE_SIZE",3)}function rA(){rA=F,Tq=new cL("INTERACTIVE_NODE_REORDERER",0),Sq=new cL("MIN_SIZE_PRE_PROCESSOR",1),Aq=new cL("MIN_SIZE_POST_PROCESSOR",2)}function Rh(){Rh=F,Vq=new k6("AUTOMATIC",0),qj=new k6(s3,1),Uj=new k6(f3,2),eO=new k6("TOP",3),ZI=new k6(Ftn,4),nO=new k6(qm,5)}function lZ(n,e,t,i){Am();var r,c;for(r=0,c=0;c<t;c++)r=nr(er(vi(e[c],mr),vi(i,mr)),vi(Ae(r),mr)),n[c]=Ae(r),r=U1(r,32);return Ae(r)}function aZ(n,e,t){var i,r;for(r=0,i=0;i<h_;i++)r=y.Math.max(r,Z$(n.a[e.g][i],t));return e==(bf(),Wc)&&n.b&&(r=y.Math.max(r,n.b.b)),r}function cA(n,e){var t,i;if(rV(e>0),(e&-e)==e)return wi(e*to(n,31)*4656612873077393e-25);do t=to(n,31),i=t%e;while(t-i+(e-1)<0);return wi(i)}function F9e(n,e,t){switch(t.g){case 1:n.a=e.a/2,n.b=0;break;case 2:n.a=e.a,n.b=e.b/2;break;case 3:n.a=e.a/2,n.b=e.b;break;case 4:n.a=0,n.b=e.b/2}}function qk(n,e,t,i){var r,c;for(r=e;r<n.c.length;r++)if(c=(Ln(r,n.c.length),u(n.c[r],12)),t.Mb(c))Bn(i.c,c);else return r;return n.c.length}function Ax(n){switch(n.g){case 0:return null;case 1:return new Cxn;case 2:return new uz;default:throw M(new Gn(GR+(n.f!=null?n.f:""+n.g)))}}function Uk(n,e,t){var i,r;for(Vve(n,e-n.s,t-n.t),r=new C(n.n);r.a<r.c.c.length;)i=u(E(r),209),ffe(i,i.e+e-n.s),hfe(i,i.f+t-n.t);n.s=e,n.t=t}function B9e(n){var e,t,i,r,c;for(t=0,r=new C(n.a);r.a<r.c.c.length;)i=u(E(r),125),i.d=t++;return e=Xye(n),c=null,e.c.length>1&&(c=L9e(n,e)),c}function CRn(n){var e;return e=$(R(z(n,(qe(),Qj))))*y.Math.sqrt((!n.a&&(n.a=new q(Qe,n,10,11)),n.a).i),new V(e,e/$(R(z(n,rO))))}function Sx(n){var e;return n.f&&n.f.Vh()&&(e=u(n.f,54),n.f=u(na(n,e),84),n.f!=e&&n.Db&4&&!(n.Db&1)&&it(n,new Ci(n,9,8,e,n.f))),n.f}function Px(n){var e;return n.i&&n.i.Vh()&&(e=u(n.i,54),n.i=u(na(n,e),84),n.i!=e&&n.Db&4&&!(n.Db&1)&&it(n,new Ci(n,9,7,e,n.i))),n.i}function br(n){var e;return n.b&&n.b.Db&64&&(e=n.b,n.b=u(na(n,e),19),n.b!=e&&n.Db&4&&!(n.Db&1)&&it(n,new Ci(n,9,21,e,n.b))),n.b}function uA(n,e){var t,i,r;n.d==null?(++n.e,++n.f):(i=e.Bi(),uTe(n,n.f+1),r=(i&et)%n.d.length,t=n.d[r],!t&&(t=n.d[r]=n.dk()),t.Fc(e),++n.f)}function dZ(n,e,t){var i;return e.tk()?!1:e.Ik()!=-2?(i=e.ik(),i==null?t==null:rt(i,t)):e.qk()==n.e.Dh()&&t==null}function oA(){var n;Co(16,$zn),n=sxn(16),this.b=K(UK,Cy,303,n,0,1),this.c=K(UK,Cy,303,n,0,1),this.a=null,this.e=null,this.i=0,this.f=n-1,this.g=0}function Tl(n){vV.call(this),this.k=(Vn(),zt),this.j=(Co(6,mw),new Gc(6)),this.b=(Co(2,mw),new Gc(2)),this.d=new sD,this.f=new nz,this.a=n}function R9e(n){var e,t;n.c.length<=1||(e=Sqn(n,(tn(),ae)),w_n(n,u(e.a,17).a,u(e.b,17).a),t=Sqn(n,Wn),w_n(n,u(t.a,17).a,u(t.b,17).a))}function K9e(n,e,t){var i,r;for(r=n.a.b,i=r.c.length;i<t;i++)b0(r,r.c.length,new Lc(n.a));$i(e,(Ln(t-1,r.c.length),u(r.c[t-1],30))),n.b[e.p]=t}function MRn(n,e){var t,i,r;for(n.b[e.g]=1,i=ge(e.d,0);i.b!=i.d.c;)t=u(be(i),65),r=t.c,n.b[r.g]==1?xe(n.a,t):n.b[r.g]==2?n.b[r.g]=1:MRn(n,r)}function TRn(n,e,t,i){var r,c,s;for(r=u(ot(i?n.a:n.b,e),21),s=r.Kc();s.Ob();)if(c=u(s.Pb(),27),LA(n,t,c))return!0;return!1}function Ix(n){var e,t;for(t=new ne(n);t.e!=t.i.gc();)if(e=u(ce(t),89),e.e||(!e.d&&(e.d=new ti(jr,e,1)),e.d).i!=0)return!0;return!1}function Ox(n){var e,t;for(t=new ne(n);t.e!=t.i.gc();)if(e=u(ce(t),89),e.e||(!e.d&&(e.d=new ti(jr,e,1)),e.d).i!=0)return!0;return!1}function _9e(n){var e,t,i;for(e=0,i=new C(n.c.a);i.a<i.c.c.length;)t=u(E(i),10),e+=wl(new te(re(Qt(t).a.Kc(),new En)));return e/n.c.a.c.length}function Dx(){Dx=F,ean=(EF(),Q1n),nan=new f0(8),new Ni((qe(),C1),nan),new Ni(qd,8),hue=W1n,Y1n=tue,Z1n=iue,fue=new Ni(zj,(_n(),!1))}function H9e(n,e,t){var i;t.Ug("Shrinking tree compaction",1),on(un(v(e,(J4(),N8))))?(Jme(n,e.f),QNn(e.f,(i=e.c,i))):QNn(e.f,e.c),t.Vg()}function bZ(n,e,t,i){switch(e){case 7:return!n.e&&(n.e=new Nn(Vt,n,7,4)),n.e;case 8:return!n.d&&(n.d=new Nn(Vt,n,8,5)),n.d}return FY(n,e,t,i)}function Lx(n){var e;return n.a&&n.a.Vh()&&(e=u(n.a,54),n.a=u(na(n,e),142),n.a!=e&&n.Db&4&&!(n.Db&1)&&it(n,new Ci(n,9,5,e,n.a))),n.a}function bd(n){return n<48||n>102?-1:n<=57?n-48:n<65?-1:n<=70?n-65+10:n<97?-1:n-97+10}function Nx(n,e){if(n==null)throw M(new sp("null key in entry: null="+e));if(e==null)throw M(new sp("null value in entry: "+n+"=null"))}function q9e(n,e){for(var t,i;n.Ob();)if(!e.Ob()||(t=n.Pb(),i=e.Pb(),!(x(t)===x(i)||t!=null&&rt(t,i))))return!1;return!e.Ob()}function ARn(n,e){var t;return t=S(T(Pi,1),Tr,28,15,[Z$(n.a[0],e),Z$(n.a[1],e),Z$(n.a[2],e)]),n.d&&(t[0]=y.Math.max(t[0],t[2]),t[2]=t[0]),t}function SRn(n,e){var t;return t=S(T(Pi,1),Tr,28,15,[$T(n.a[0],e),$T(n.a[1],e),$T(n.a[2],e)]),n.d&&(t[0]=y.Math.max(t[0],t[2]),t[2]=t[0]),t}function wZ(n,e,t){Ep(u(v(e,(cn(),Kt)),101))||(PJ(n,e,h1(e,t)),PJ(n,e,h1(e,(tn(),ae))),PJ(n,e,h1(e,Xn)),Dn(),Yt(e.j,new N7n(n)))}function PRn(n){var e,t;for(n.c||sOe(n),t=new Mu,e=new C(n.a),E(e);e.a<e.c.c.length;)xe(t,u(E(e),418).a);return oe(t.b!=0),Xo(t,t.c.b),t}function U9e(n,e,t){var i,r,c,s,f;for(f=n.r+e,n.r+=e,n.d+=t,i=t/n.n.c.length,r=0,s=new C(n.n);s.a<s.c.c.length;)c=u(E(s),209),iMe(c,f,i,r),++r}function G9e(n){var e,t,i;for(n.b.a.$b(),n.a=K(aP,Fn,60,n.c.c.a.b.c.length,0,1),e=0,i=new C(n.c.c.a.b);i.a<i.c.c.length;)t=u(E(i),60),t.f=e++}function z9e(n){var e,t,i;for(n.b.a.$b(),n.a=K(M_,Fn,86,n.c.a.a.b.c.length,0,1),e=0,i=new C(n.c.a.a.b);i.a<i.c.c.length;)t=u(E(i),86),t.i=e++}function IRn(n){var e;if(e=x6e(n),!pe(n))throw M(new Ir("position (0) must be less than the number of elements that remained ("+e+")"));return fe(n)}function X9e(n,e){var t;return n.a||(t=K(Pi,Tr,28,0,15,1),hg(n.b.a,new k9n(t)),Pyn(t,I$n(mE.prototype.Me,mE,[])),n.a=new oSn(t,n.d)),WM(n.a,e)}function ORn(n,e,t){var i;try{return Rg(n,e+n.j,t+n.k)}catch(r){throw r=It(r),O(r,77)?(i=r,M(new Ir(i.g+iS+e+ur+t+")."))):M(r)}}function V9e(n,e,t){var i;try{return NRn(n,e+n.j,t+n.k)}catch(r){throw r=It(r),O(r,77)?(i=r,M(new Ir(i.g+iS+e+ur+t+")."))):M(r)}}function W9e(n,e,t){var i;try{return $Rn(n,e+n.j,t+n.k)}catch(r){throw r=It(r),O(r,77)?(i=r,M(new Ir(i.g+iS+e+ur+t+")."))):M(r)}}function DRn(n){switch(n.g){case 1:return tn(),Wn;case 4:return tn(),Xn;case 3:return tn(),Zn;case 2:return tn(),ae;default:return tn(),sc}}function J9e(n,e,t){e.k==(Vn(),zt)&&t.k==Mi&&(n.d=ix(e,(tn(),ae)),n.b=ix(e,Xn)),t.k==zt&&e.k==Mi&&(n.d=ix(t,(tn(),Xn)),n.b=ix(t,ae))}function $x(n,e){var t,i,r;for(r=uc(n,e),i=r.Kc();i.Ob();)if(t=u(i.Pb(),12),v(t,(W(),Xu))!=null||L6(new Of(t.b)))return!0;return!1}function Q9e(n,e,t){t.Ug("Linear segments node placement",1),n.b=u(v(e,(W(),j2)),312),FLe(n,e),dIe(n,e),IIe(n,e),bLe(n),n.a=null,n.b=null,t.Vg()}function gZ(n,e){return eu(e,n.e+n.d+(n.c.c.length==0?0:n.b)),tu(e,n.f),n.a=y.Math.max(n.a,e.f),n.d+=e.g+(n.c.c.length==0?0:n.b),nn(n.c,e),!0}function Y9e(n,e,t){var i,r,c,s;for(s=0,i=t/n.a.c.length,c=new C(n.a);c.a<c.c.c.length;)r=u(E(c),172),Uk(r,r.s,r.t+s*i),U9e(r,n.d-r.r+e,i),++s}function Z9e(n,e){var t,i,r,c,s,f;for(r=e.length-1,s=0,f=0,i=0;i<=r;i++)c=e[i],t=pje(r,i)*mY(1-n,r-i)*mY(n,i),s+=c.a*t,f+=c.b*t;return new V(s,f)}function LRn(n,e){var t,i,r,c,s;for(t=e.gc(),n._i(n.i+t),c=e.Kc(),s=n.i,n.i+=t,i=s;i<n.i;++i)r=c.Pb(),O6(n,i,n.Zi(i,r)),n.Mi(i,r),n.Ni();return t!=0}function n7e(n,e,t){var i,r,c;return n.Pj()?(i=n.Ej(),c=n.Qj(),++n.j,n.qj(i,n.Zi(i,e)),r=n.Ij(3,null,e,i,c),t?t.nj(r):t=r):IAn(n,n.Ej(),e),t}function e7e(n,e,t){var i,r,c;return i=u(L(Sc(n.a),e),89),c=(r=i.c,O(r,90)?u(r,29):(On(),Ps)),(c.Db&64?na(n.b,c):c)==t?BA(i):K4(i,t),c}function t7e(n){var e;return n==null?null:new H1((e=Fc(n,!0),e.length>0&&(zn(0,e.length),e.charCodeAt(0)==43)?(zn(1,e.length+1),e.substr(1)):e))}function i7e(n){var e;return n==null?null:new H1((e=Fc(n,!0),e.length>0&&(zn(0,e.length),e.charCodeAt(0)==43)?(zn(1,e.length+1),e.substr(1)):e))}function pZ(n,e,t,i,r,c,s,f){var h,l;i&&(h=i.a[0],h&&pZ(n,e,t,h,r,c,s,f),qx(n,t,i.d,r,c,s,f)&&e.Fc(i),l=i.a[1],l&&pZ(n,e,t,l,r,c,s,f))}function Rg(n,e,t){try{return o0(C$(n,e,t),1)}catch(i){throw i=It(i),O(i,333)?M(new Ir(GB+n.o+"*"+n.p+zB+e+ur+t+XB)):M(i)}}function NRn(n,e,t){try{return o0(C$(n,e,t),0)}catch(i){throw i=It(i),O(i,333)?M(new Ir(GB+n.o+"*"+n.p+zB+e+ur+t+XB)):M(i)}}function $Rn(n,e,t){try{return o0(C$(n,e,t),2)}catch(i){throw i=It(i),O(i,333)?M(new Ir(GB+n.o+"*"+n.p+zB+e+ur+t+XB)):M(i)}}function xRn(n,e){if(n.g==-1)throw M(new Cu);n.Xj();try{n.d.hd(n.g,e),n.f=n.d.j}catch(t){throw t=It(t),O(t,77)?M(new Bo):M(t)}}function r7e(n){var e,t,i,r,c;for(i=new C(n.b);i.a<i.c.c.length;)for(t=u(E(i),30),e=0,c=new C(t.a);c.a<c.c.c.length;)r=u(E(c),10),r.p=e++}function S5(n,e){var t,i,r,c;for(c=n.gc(),e.length<c&&(e=qE(new Array(c),e)),r=e,i=n.Kc(),t=0;t<c;++t)$t(r,t,i.Pb());return e.length>c&&$t(e,c,null),e}function c7e(n,e){var t,i;if(i=n.gc(),e==null){for(t=0;t<i;t++)if(n.Xb(t)==null)return t}else for(t=0;t<i;t++)if(rt(e,n.Xb(t)))return t;return-1}function xx(n,e){var t,i,r;return t=e.ld(),r=e.md(),i=n.xc(t),!(!(x(r)===x(i)||r!=null&&rt(r,i))||i==null&&!n._b(t))}function u7e(n,e){var t,i,r;return e<=22?(t=n.l&(1<<e)-1,i=r=0):e<=44?(t=n.l,i=n.m&(1<<e-22)-1,r=0):(t=n.l,i=n.m,r=n.h&(1<<e-44)-1),Yc(t,i,r)}function o7e(n,e){switch(e.g){case 1:return n.f.n.d+n.t;case 3:return n.f.n.a+n.t;case 2:return n.f.n.c+n.s;case 4:return n.f.n.b+n.s;default:return 0}}function s7e(n,e){var t,i;switch(i=e.c,t=e.a,n.b.g){case 0:t.d=n.e-i.a-i.d;break;case 1:t.d+=n.e;break;case 2:t.c=n.e-i.a-i.d;break;case 3:t.c=n.e+i.d}}function mZ(n,e,t,i){var r,c;this.a=e,this.c=i,r=n.a,zse(this,new V(-r.c,-r.d)),tt(this.b,t),c=i/2,e.a?N6(this.b,0,c):N6(this.b,c,0),nn(n.c,this)}function FRn(n,e,t,i){var r;this.c=n,this.d=e,r=new Ct,xt(r,t,r.c.b,r.c),this.a=r,this.b=u(v(i,(lc(),vb)),88),this.e=$(R(v(i,Lln))),Ezn(this)}function sA(){sA=F,Eq=new vC(kh,0),i1n=new vC(WXn,1),r1n=new vC("EDGE_LENGTH_BY_POSITION",2),t1n=new vC("CROSSING_MINIMIZATION_BY_POSITION",3)}function Fx(n,e){var t,i;if(t=u(Dg(n.g,e),27),t)return t;if(i=u(Dg(n.j,e),123),i)return i;throw M(new nh("Referenced shape does not exist: "+e))}function vZ(n,e){var t,i;if(O(e,253)){i=u(e,253);try{return t=n.Ed(i),t==0}catch(r){if(r=It(r),O(r,212))return!1;throw M(r)}}return!1}function f7e(n,e){if(n.c==e)return n.d;if(n.d==e)return n.c;throw M(new Gn("Node 'one' must be either source or target of edge 'edge'."))}function h7e(n,e){if(n.c.i==e)return n.d.i;if(n.d.i==e)return n.c.i;throw M(new Gn("Node "+e+" is neither source nor target of edge "+n))}function l7e(n,e,t){t.Ug("Self-Loop ordering",1),qt(_r(ut(ut(rc(new Tn(null,new In(e.b,16)),new i2n),new r2n),new c2n),new u2n),new u7n(n)),t.Vg()}function a7e(n,e){var t;switch(e.g){case 2:case 4:t=n.a,n.c.d.n.b<t.d.n.b&&(t=n.c),Vl(n,e,($f(),B_),t);break;case 1:case 3:Vl(n,e,($f(),j3),null)}}function Bx(n,e,t,i,r,c){var s,f,h,l,a;for(s=ake(e,t,c),f=t==(tn(),Xn)||t==Wn?-1:1,l=n[t.g],a=0;a<l.length;a++)h=l[a],h>0&&(h+=r),l[a]=s,s+=f*(h+i)}function BRn(n){var e,t,i;for(i=n.f,n.n=K(Pi,Tr,28,i,15,1),n.d=K(Pi,Tr,28,i,15,1),e=0;e<i;e++)t=u(sn(n.c.b,e),30),n.n[e]=hRn(n,t),n.d[e]=eqn(n,t)}function Rx(n,e){var t,i,r;for(r=0,i=2;i<e;i<<=1)n.Db&i&&++r;if(r==0){for(t=e<<=1;t<=128;t<<=1)if(n.Db&t)return 0;return-1}else return r}function RRn(n,e){var t,i,r,c,s;for(s=ru(n.e.Dh(),e),c=null,t=u(n.g,124),r=0;r<n.i;++r)i=t[r],s.am(i.Lk())&&(!c&&(c=new EE),ve(c,i));c&&uzn(n,c)}function KRn(n){var e,t,i;if(!n)return null;if(n.dc())return"";for(i=new Hl,t=n.Kc();t.Ob();)e=t.Pb(),Er(i,Oe(e)),i.a+=" ";return bL(i,i.a.length-1)}function _Rn(n,e){var t=new Array(e),i;switch(n){case 14:case 15:i=0;break;case 16:i=!1;break;default:return t}for(var r=0;r<e;++r)t[r]=i;return t}function R0(n){var e,t,i;for(t=new C(n.a.b);t.a<t.c.c.length;)e=u(E(t),60),e.c.$b();hl(n.d)?i=n.a.c:i=n.a.d,nu(i,new O9n(n)),n.c.df(n),vqn(n)}function HRn(n){var e,t,i,r;for(t=new C(n.e.c);t.a<t.c.c.length;){for(e=u(E(t),290),r=new C(e.b);r.a<r.c.c.length;)i=u(E(r),454),Uen(i);W_n(e)}}function fA(n){var e,t,i,r,c;for(i=0,c=0,r=0,t=new C(n.a);t.a<t.c.c.length;)e=u(E(t),172),c=y.Math.max(c,e.r),i+=e.d+(r>0?n.c:0),++r;n.b=i,n.d=c}function qRn(n,e){var t;return t=S(T(Pi,1),Tr,28,15,[aZ(n,(bf(),bc),e),aZ(n,Wc,e),aZ(n,wc,e)]),n.f&&(t[0]=y.Math.max(t[0],t[2]),t[2]=t[0]),t}function d7e(n,e,t){var i;try{xA(n,e+n.j,t+n.k,!1,!0)}catch(r){throw r=It(r),O(r,77)?(i=r,M(new Ir(i.g+iS+e+ur+t+")."))):M(r)}}function b7e(n,e,t){var i;try{xA(n,e+n.j,t+n.k,!0,!1)}catch(r){throw r=It(r),O(r,77)?(i=r,M(new Ir(i.g+iS+e+ur+t+")."))):M(r)}}function URn(n){var e;kt(n,(cn(),ab))&&(e=u(v(n,ab),21),e.Hc((lw(),Js))?(e.Mc(Js),e.Fc(Qs)):e.Hc(Qs)&&(e.Mc(Qs),e.Fc(Js)))}function GRn(n){var e;kt(n,(cn(),ab))&&(e=u(v(n,ab),21),e.Hc((lw(),Zs))?(e.Mc(Zs),e.Fc(Cs)):e.Hc(Cs)&&(e.Mc(Cs),e.Fc(Zs)))}function Kx(n,e,t,i){var r,c,s,f;return n.a==null&&gje(n,e),s=e.b.j.c.length,c=t.d.p,f=i.d.p,r=f-1,r<0&&(r=s-1),c<=r?n.a[r]-n.a[c]:n.a[s-1]-n.a[c]+n.a[r]}function w7e(n){var e,t;if(!n.b)for(n.b=RM(u(n.f,27).kh().i),t=new ne(u(n.f,27).kh());t.e!=t.i.gc();)e=u(ce(t),135),nn(n.b,new pD(e));return n.b}function g7e(n){var e,t;if(!n.e)for(n.e=RM(mN(u(n.f,27)).i),t=new ne(mN(u(n.f,27)));t.e!=t.i.gc();)e=u(ce(t),123),nn(n.e,new Bkn(e));return n.e}function zRn(n){var e,t;if(!n.a)for(n.a=RM(AM(u(n.f,27)).i),t=new ne(AM(u(n.f,27)));t.e!=t.i.gc();)e=u(ce(t),27),nn(n.a,new ML(n,e));return n.a}function K0(n){var e;if(!n.C&&(n.D!=null||n.B!=null))if(e=iDe(n),e)n.hl(e);else try{n.hl(null)}catch(t){if(t=It(t),!O(t,63))throw M(t)}return n.C}function p7e(n){switch(n.q.g){case 5:gKn(n,(tn(),Xn)),gKn(n,ae);break;case 4:mGn(n,(tn(),Xn)),mGn(n,ae);break;default:y_n(n,(tn(),Xn)),y_n(n,ae)}}function m7e(n){switch(n.q.g){case 5:pKn(n,(tn(),Zn)),pKn(n,Wn);break;case 4:vGn(n,(tn(),Zn)),vGn(n,Wn);break;default:j_n(n,(tn(),Zn)),j_n(n,Wn)}}function Kg(n,e){var t,i,r;for(r=new Li,i=n.Kc();i.Ob();)t=u(i.Pb(),36),Sm(t,r.a,0),r.a+=t.f.a+e,r.b=y.Math.max(r.b,t.f.b);return r.b>0&&(r.b+=e),r}function hA(n,e){var t,i,r;for(r=new Li,i=n.Kc();i.Ob();)t=u(i.Pb(),36),Sm(t,0,r.b),r.b+=t.f.b+e,r.a=y.Math.max(r.a,t.f.a);return r.a>0&&(r.a+=e),r}function XRn(n){var e,t,i;for(i=et,t=new C(n.a);t.a<t.c.c.length;)e=u(E(t),10),kt(e,(W(),dt))&&(i=y.Math.min(i,u(v(e,dt),17).a));return i}function VRn(n,e){var t,i;if(e.length==0)return 0;for(t=pN(n.a,e[0],(tn(),Wn)),t+=pN(n.a,e[e.length-1],Zn),i=0;i<e.length;i++)t+=eje(n,i,e);return t}function WRn(){_5(),this.c=new Z,this.i=new Z,this.e=new ih,this.f=new ih,this.g=new ih,this.j=new Z,this.a=new Z,this.b=new de,this.k=new de}function _x(n,e){var t,i;return n.Db>>16==6?n.Cb.Th(n,5,jf,e):(i=br(u($n((t=u(Un(n,16),29),t||n.ii()),n.Db>>16),19)),n.Cb.Th(n,i.n,i.f,e))}function v7e(n){O4();var e=n.e;if(e&&e.stack){var t=e.stack,i=e+`
 `;return t.substring(0,i.length)==i&&(t=t.substring(i.length)),t.split(`
diff --git a/assets/flyweight.html-CWx8TgTS.js b/assets/flyweight.html-DUTi0_Qx.js
similarity index 99%
rename from assets/flyweight.html-CWx8TgTS.js
rename to assets/flyweight.html-DUTi0_Qx.js
index b7da2f0..61e74f0 100644
--- a/assets/flyweight.html-CWx8TgTS.js
+++ b/assets/flyweight.html-DUTi0_Qx.js
@@ -1,4 +1,4 @@
-import{_ as n,o as s,c as a,f as t}from"./app-B69Gl_S-.js";const p={},o=t(`<h2 id="为什么使用-flyweight-模式" tabindex="-1"><a class="header-anchor" href="#为什么使用-flyweight-模式"><span>为什么使用 Flyweight 模式</span></a></h2><p>Flyweight 模式是一种结构型设计模式，它通过共享尽可能多的相同对象来减少内存使用，从而提高性能。在需要生成大量细粒度对象的场景中，Flyweight 模式非常有用。通过共享对象，Flyweight 模式可以显著减少内存消耗，并提高应用程序的效率。</p><h2 id="实例代码" tabindex="-1"><a class="header-anchor" href="#实例代码"><span>实例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/RL7B2i8m4BpdA_ROKli3GKfH43nuyYWUrZJMG4rAinL4_7VJz5rxMsPsPcTtKqjOKVqic2ZGMjYfVF_02ZuC80RXIerFoS5IfNJkmRlHb27X18oWT1K58OUNKHdxihdT0GMPwjsvbiOK74vORbk3JT-MUDeb8YN0EgQGP3HVkBJ9Z7RYkW62q2VePBcaewDG2zd4-PD6JKU71ilzHi5iXRCdk_GtbJSoExHUhjvsciWLW-NwUHQ7YUDac3mEdA3z0giaIwNEt0z_" alt=""><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuKfCBialKd3EoKpDA-62K0gwTWfEcUd19KMPUUbM2dcfvGYkXfAXaR6I9aXRPbbYIIf2XWlEWkftpaWiSWCRNscba9vQufa7j3GlELK3LJUICYvKBWvpe48QweRgc2QX6s6ZgmkJib8eIYqfBSfJG34W9PMG4GHSOKIfAuoeuGfZIbrXZDqLc498SGMBRg3R82a7sLXega0r02g8FQ4L0AaI3QBJ5am3E1hnAZ0Yf03Jyr1x7LBpKe2v1000" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// bigChar.ts</span>
+import{_ as n,o as s,c as a,f as t}from"./app-B4LGNJZ0.js";const p={},o=t(`<h2 id="为什么使用-flyweight-模式" tabindex="-1"><a class="header-anchor" href="#为什么使用-flyweight-模式"><span>为什么使用 Flyweight 模式</span></a></h2><p>Flyweight 模式是一种结构型设计模式，它通过共享尽可能多的相同对象来减少内存使用，从而提高性能。在需要生成大量细粒度对象的场景中，Flyweight 模式非常有用。通过共享对象，Flyweight 模式可以显著减少内存消耗，并提高应用程序的效率。</p><h2 id="实例代码" tabindex="-1"><a class="header-anchor" href="#实例代码"><span>实例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/RL7B2i8m4BpdA_ROKli3GKfH43nuyYWUrZJMG4rAinL4_7VJz5rxMsPsPcTtKqjOKVqic2ZGMjYfVF_02ZuC80RXIerFoS5IfNJkmRlHb27X18oWT1K58OUNKHdxihdT0GMPwjsvbiOK74vORbk3JT-MUDeb8YN0EgQGP3HVkBJ9Z7RYkW62q2VePBcaewDG2zd4-PD6JKU71ilzHi5iXRCdk_GtbJSoExHUhjvsciWLW-NwUHQ7YUDac3mEdA3z0giaIwNEt0z_" alt=""><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuKfCBialKd3EoKpDA-62K0gwTWfEcUd19KMPUUbM2dcfvGYkXfAXaR6I9aXRPbbYIIf2XWlEWkftpaWiSWCRNscba9vQufa7j3GlELK3LJUICYvKBWvpe48QweRgc2QX6s6ZgmkJib8eIYqfBSfJG34W9PMG4GHSOKIfAuoeuGfZIbrXZDqLc498SGMBRg3R82a7sLXega0r02g8FQ4L0AaI3QBJ5am3E1hnAZ0Yf03Jyr1x7LBpKe2v1000" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// bigChar.ts</span>
 <span class="token keyword">export</span> <span class="token keyword">class</span> <span class="token class-name">BigChar</span> <span class="token punctuation">{</span>
   charname<span class="token operator">:</span> <span class="token builtin">string</span><span class="token punctuation">;</span>
   fontdata<span class="token operator">:</span> <span class="token builtin">string</span><span class="token punctuation">;</span>
diff --git a/assets/ganttDiagram-a649f789-B8bnTgqC.js b/assets/ganttDiagram-a649f789-B7dFucT2.js
similarity index 99%
rename from assets/ganttDiagram-a649f789-B8bnTgqC.js
rename to assets/ganttDiagram-a649f789-B7dFucT2.js
index 6362164..4d6f4be 100644
--- a/assets/ganttDiagram-a649f789-B8bnTgqC.js
+++ b/assets/ganttDiagram-a649f789-B7dFucT2.js
@@ -1,4 +1,4 @@
-import{au as Be,av as Ze,aw as Xe,ax as qe,ay as Dn,az as Kt,aA as Mn,aB as ye,aC as ke,aD as nt,c as wt,s as Sn,g as _n,x as Un,y as Yn,b as Fn,a as Ln,A as An,m as En,l as qt,h as Pt,i as In,j as Wn,z as On}from"./mermaid.core-ChLYKTZm.js";import{b as Hn,t as Ue,c as Nn,a as Vn,l as zn}from"./linear-CRQH6hcv.js";import{i as Pn}from"./init-Gi6I4Gst.js";import"./app-B69Gl_S-.js";function Rn(t,e){let n;if(e===void 0)for(const r of t)r!=null&&(n<r||n===void 0&&r>=r)&&(n=r);else{let r=-1;for(let i of t)(i=e(i,++r,t))!=null&&(n<i||n===void 0&&i>=i)&&(n=i)}return n}function Bn(t,e){let n;if(e===void 0)for(const r of t)r!=null&&(n>r||n===void 0&&r>=r)&&(n=r);else{let r=-1;for(let i of t)(i=e(i,++r,t))!=null&&(n>i||n===void 0&&i>=i)&&(n=i)}return n}function Zn(t){return t}var Bt=1,te=2,ue=3,Rt=4,Ye=1e-6;function Xn(t){return"translate("+t+",0)"}function qn(t){return"translate(0,"+t+")"}function Gn(t){return e=>+t(e)}function jn(t,e){return e=Math.max(0,t.bandwidth()-e*2)/2,t.round()&&(e=Math.round(e)),n=>+t(n)+e}function Qn(){return!this.__axis}function Ge(t,e){var n=[],r=null,i=null,s=6,a=6,k=3,Y=typeof window<"u"&&window.devicePixelRatio>1?0:.5,g=t===Bt||t===Rt?-1:1,b=t===Rt||t===te?"x":"y",U=t===Bt||t===ue?Xn:qn;function C(v){var q=r??(e.ticks?e.ticks.apply(e,n):e.domain()),y=i??(e.tickFormat?e.tickFormat.apply(e,n):Zn),L=Math.max(s,0)+k,O=e.range(),W=+O[0]+Y,B=+O[O.length-1]+Y,Z=(e.bandwidth?jn:Gn)(e.copy(),Y),Q=v.selection?v.selection():v,x=Q.selectAll(".domain").data([null]),E=Q.selectAll(".tick").data(q,e).order(),T=E.exit(),F=E.enter().append("g").attr("class","tick"),D=E.select("line"),w=E.select("text");x=x.merge(x.enter().insert("path",".tick").attr("class","domain").attr("stroke","currentColor")),E=E.merge(F),D=D.merge(F.append("line").attr("stroke","currentColor").attr(b+"2",g*s)),w=w.merge(F.append("text").attr("fill","currentColor").attr(b,g*L).attr("dy",t===Bt?"0em":t===ue?"0.71em":"0.32em")),v!==Q&&(x=x.transition(v),E=E.transition(v),D=D.transition(v),w=w.transition(v),T=T.transition(v).attr("opacity",Ye).attr("transform",function(o){return isFinite(o=Z(o))?U(o+Y):this.getAttribute("transform")}),F.attr("opacity",Ye).attr("transform",function(o){var d=this.parentNode.__axis;return U((d&&isFinite(d=d(o))?d:Z(o))+Y)})),T.remove(),x.attr("d",t===Rt||t===te?a?"M"+g*a+","+W+"H"+Y+"V"+B+"H"+g*a:"M"+Y+","+W+"V"+B:a?"M"+W+","+g*a+"V"+Y+"H"+B+"V"+g*a:"M"+W+","+Y+"H"+B),E.attr("opacity",1).attr("transform",function(o){return U(Z(o)+Y)}),D.attr(b+"2",g*s),w.attr(b,g*L).text(y),Q.filter(Qn).attr("fill","none").attr("font-size",10).attr("font-family","sans-serif").attr("text-anchor",t===te?"start":t===Rt?"end":"middle"),Q.each(function(){this.__axis=Z})}return C.scale=function(v){return arguments.length?(e=v,C):e},C.ticks=function(){return n=Array.from(arguments),C},C.tickArguments=function(v){return arguments.length?(n=v==null?[]:Array.from(v),C):n.slice()},C.tickValues=function(v){return arguments.length?(r=v==null?null:Array.from(v),C):r&&r.slice()},C.tickFormat=function(v){return arguments.length?(i=v,C):i},C.tickSize=function(v){return arguments.length?(s=a=+v,C):s},C.tickSizeInner=function(v){return arguments.length?(s=+v,C):s},C.tickSizeOuter=function(v){return arguments.length?(a=+v,C):a},C.tickPadding=function(v){return arguments.length?(k=+v,C):k},C.offset=function(v){return arguments.length?(Y=+v,C):Y},C}function Jn(t){return Ge(Bt,t)}function $n(t){return Ge(ue,t)}const Kn=Math.PI/180,tr=180/Math.PI,Gt=18,je=.96422,Qe=1,Je=.82521,$e=4/29,Ct=6/29,Ke=3*Ct*Ct,er=Ct*Ct*Ct;function tn(t){if(t instanceof ot)return new ot(t.l,t.a,t.b,t.opacity);if(t instanceof ut)return en(t);t instanceof Xe||(t=Dn(t));var e=ie(t.r),n=ie(t.g),r=ie(t.b),i=ee((.2225045*e+.7168786*n+.0606169*r)/Qe),s,a;return e===n&&n===r?s=a=i:(s=ee((.4360747*e+.3850649*n+.1430804*r)/je),a=ee((.0139322*e+.0971045*n+.7141733*r)/Je)),new ot(116*i-16,500*(s-i),200*(i-a),t.opacity)}function nr(t,e,n,r){return arguments.length===1?tn(t):new ot(t,e,n,r??1)}function ot(t,e,n,r){this.l=+t,this.a=+e,this.b=+n,this.opacity=+r}Be(ot,nr,Ze(qe,{brighter(t){return new ot(this.l+Gt*(t??1),this.a,this.b,this.opacity)},darker(t){return new ot(this.l-Gt*(t??1),this.a,this.b,this.opacity)},rgb(){var t=(this.l+16)/116,e=isNaN(this.a)?t:t+this.a/500,n=isNaN(this.b)?t:t-this.b/200;return e=je*ne(e),t=Qe*ne(t),n=Je*ne(n),new Xe(re(3.1338561*e-1.6168667*t-.4906146*n),re(-.9787684*e+1.9161415*t+.033454*n),re(.0719453*e-.2289914*t+1.4052427*n),this.opacity)}}));function ee(t){return t>er?Math.pow(t,1/3):t/Ke+$e}function ne(t){return t>Ct?t*t*t:Ke*(t-$e)}function re(t){return 255*(t<=.0031308?12.92*t:1.055*Math.pow(t,1/2.4)-.055)}function ie(t){return(t/=255)<=.04045?t/12.92:Math.pow((t+.055)/1.055,2.4)}function rr(t){if(t instanceof ut)return new ut(t.h,t.c,t.l,t.opacity);if(t instanceof ot||(t=tn(t)),t.a===0&&t.b===0)return new ut(NaN,0<t.l&&t.l<100?0:NaN,t.l,t.opacity);var e=Math.atan2(t.b,t.a)*tr;return new ut(e<0?e+360:e,Math.sqrt(t.a*t.a+t.b*t.b),t.l,t.opacity)}function fe(t,e,n,r){return arguments.length===1?rr(t):new ut(t,e,n,r??1)}function ut(t,e,n,r){this.h=+t,this.c=+e,this.l=+n,this.opacity=+r}function en(t){if(isNaN(t.h))return new ot(t.l,0,0,t.opacity);var e=t.h*Kn;return new ot(t.l,Math.cos(e)*t.c,Math.sin(e)*t.c,t.opacity)}Be(ut,fe,Ze(qe,{brighter(t){return new ut(this.h,this.c,this.l+Gt*(t??1),this.opacity)},darker(t){return new ut(this.h,this.c,this.l-Gt*(t??1),this.opacity)},rgb(){return en(this).rgb()}}));function ir(t){return function(e,n){var r=t((e=fe(e)).h,(n=fe(n)).h),i=Kt(e.c,n.c),s=Kt(e.l,n.l),a=Kt(e.opacity,n.opacity);return function(k){return e.h=r(k),e.c=i(k),e.l=s(k),e.opacity=a(k),e+""}}}const sr=ir(Mn);function ar(t,e){t=t.slice();var n=0,r=t.length-1,i=t[n],s=t[r],a;return s<i&&(a=n,n=r,r=a,a=i,i=s,s=a),t[n]=e.floor(i),t[r]=e.ceil(s),t}const se=new Date,ae=new Date;function K(t,e,n,r){function i(s){return t(s=arguments.length===0?new Date:new Date(+s)),s}return i.floor=s=>(t(s=new Date(+s)),s),i.ceil=s=>(t(s=new Date(s-1)),e(s,1),t(s),s),i.round=s=>{const a=i(s),k=i.ceil(s);return s-a<k-s?a:k},i.offset=(s,a)=>(e(s=new Date(+s),a==null?1:Math.floor(a)),s),i.range=(s,a,k)=>{const Y=[];if(s=i.ceil(s),k=k==null?1:Math.floor(k),!(s<a)||!(k>0))return Y;let g;do Y.push(g=new Date(+s)),e(s,k),t(s);while(g<s&&s<a);return Y},i.filter=s=>K(a=>{if(a>=a)for(;t(a),!s(a);)a.setTime(a-1)},(a,k)=>{if(a>=a)if(k<0)for(;++k<=0;)for(;e(a,-1),!s(a););else for(;--k>=0;)for(;e(a,1),!s(a););}),n&&(i.count=(s,a)=>(se.setTime(+s),ae.setTime(+a),t(se),t(ae),Math.floor(n(se,ae))),i.every=s=>(s=Math.floor(s),!isFinite(s)||!(s>0)?null:s>1?i.filter(r?a=>r(a)%s===0:a=>i.count(0,a)%s===0):i)),i}const Mt=K(()=>{},(t,e)=>{t.setTime(+t+e)},(t,e)=>e-t);Mt.every=t=>(t=Math.floor(t),!isFinite(t)||!(t>0)?null:t>1?K(e=>{e.setTime(Math.floor(e/t)*t)},(e,n)=>{e.setTime(+e+n*t)},(e,n)=>(n-e)/t):Mt);Mt.range;const ft=1e3,rt=ft*60,ht=rt*60,dt=ht*24,pe=dt*7,Fe=dt*30,oe=dt*365,gt=K(t=>{t.setTime(t-t.getMilliseconds())},(t,e)=>{t.setTime(+t+e*ft)},(t,e)=>(e-t)/ft,t=>t.getUTCSeconds());gt.range;const At=K(t=>{t.setTime(t-t.getMilliseconds()-t.getSeconds()*ft)},(t,e)=>{t.setTime(+t+e*rt)},(t,e)=>(e-t)/rt,t=>t.getMinutes());At.range;const or=K(t=>{t.setUTCSeconds(0,0)},(t,e)=>{t.setTime(+t+e*rt)},(t,e)=>(e-t)/rt,t=>t.getUTCMinutes());or.range;const Et=K(t=>{t.setTime(t-t.getMilliseconds()-t.getSeconds()*ft-t.getMinutes()*rt)},(t,e)=>{t.setTime(+t+e*ht)},(t,e)=>(e-t)/ht,t=>t.getHours());Et.range;const cr=K(t=>{t.setUTCMinutes(0,0,0)},(t,e)=>{t.setTime(+t+e*ht)},(t,e)=>(e-t)/ht,t=>t.getUTCHours());cr.range;const yt=K(t=>t.setHours(0,0,0,0),(t,e)=>t.setDate(t.getDate()+e),(t,e)=>(e-t-(e.getTimezoneOffset()-t.getTimezoneOffset())*rt)/dt,t=>t.getDate()-1);yt.range;const Te=K(t=>{t.setUTCHours(0,0,0,0)},(t,e)=>{t.setUTCDate(t.getUTCDate()+e)},(t,e)=>(e-t)/dt,t=>t.getUTCDate()-1);Te.range;const lr=K(t=>{t.setUTCHours(0,0,0,0)},(t,e)=>{t.setUTCDate(t.getUTCDate()+e)},(t,e)=>(e-t)/dt,t=>Math.floor(t/dt));lr.range;function Tt(t){return K(e=>{e.setDate(e.getDate()-(e.getDay()+7-t)%7),e.setHours(0,0,0,0)},(e,n)=>{e.setDate(e.getDate()+n*7)},(e,n)=>(n-e-(n.getTimezoneOffset()-e.getTimezoneOffset())*rt)/pe)}const Ot=Tt(0),It=Tt(1),nn=Tt(2),rn=Tt(3),kt=Tt(4),sn=Tt(5),an=Tt(6);Ot.range;It.range;nn.range;rn.range;kt.range;sn.range;an.range;function vt(t){return K(e=>{e.setUTCDate(e.getUTCDate()-(e.getUTCDay()+7-t)%7),e.setUTCHours(0,0,0,0)},(e,n)=>{e.setUTCDate(e.getUTCDate()+n*7)},(e,n)=>(n-e)/pe)}const on=vt(0),jt=vt(1),ur=vt(2),fr=vt(3),St=vt(4),hr=vt(5),dr=vt(6);on.range;jt.range;ur.range;fr.range;St.range;hr.range;dr.range;const Wt=K(t=>{t.setDate(1),t.setHours(0,0,0,0)},(t,e)=>{t.setMonth(t.getMonth()+e)},(t,e)=>e.getMonth()-t.getMonth()+(e.getFullYear()-t.getFullYear())*12,t=>t.getMonth());Wt.range;const mr=K(t=>{t.setUTCDate(1),t.setUTCHours(0,0,0,0)},(t,e)=>{t.setUTCMonth(t.getUTCMonth()+e)},(t,e)=>e.getUTCMonth()-t.getUTCMonth()+(e.getUTCFullYear()-t.getUTCFullYear())*12,t=>t.getUTCMonth());mr.range;const mt=K(t=>{t.setMonth(0,1),t.setHours(0,0,0,0)},(t,e)=>{t.setFullYear(t.getFullYear()+e)},(t,e)=>e.getFullYear()-t.getFullYear(),t=>t.getFullYear());mt.every=t=>!isFinite(t=Math.floor(t))||!(t>0)?null:K(e=>{e.setFullYear(Math.floor(e.getFullYear()/t)*t),e.setMonth(0,1),e.setHours(0,0,0,0)},(e,n)=>{e.setFullYear(e.getFullYear()+n*t)});mt.range;const pt=K(t=>{t.setUTCMonth(0,1),t.setUTCHours(0,0,0,0)},(t,e)=>{t.setUTCFullYear(t.getUTCFullYear()+e)},(t,e)=>e.getUTCFullYear()-t.getUTCFullYear(),t=>t.getUTCFullYear());pt.every=t=>!isFinite(t=Math.floor(t))||!(t>0)?null:K(e=>{e.setUTCFullYear(Math.floor(e.getUTCFullYear()/t)*t),e.setUTCMonth(0,1),e.setUTCHours(0,0,0,0)},(e,n)=>{e.setUTCFullYear(e.getUTCFullYear()+n*t)});pt.range;function gr(t,e,n,r,i,s){const a=[[gt,1,ft],[gt,5,5*ft],[gt,15,15*ft],[gt,30,30*ft],[s,1,rt],[s,5,5*rt],[s,15,15*rt],[s,30,30*rt],[i,1,ht],[i,3,3*ht],[i,6,6*ht],[i,12,12*ht],[r,1,dt],[r,2,2*dt],[n,1,pe],[e,1,Fe],[e,3,3*Fe],[t,1,oe]];function k(g,b,U){const C=b<g;C&&([g,b]=[b,g]);const v=U&&typeof U.range=="function"?U:Y(g,b,U),q=v?v.range(g,+b+1):[];return C?q.reverse():q}function Y(g,b,U){const C=Math.abs(b-g)/U,v=Hn(([,,L])=>L).right(a,C);if(v===a.length)return t.every(Ue(g/oe,b/oe,U));if(v===0)return Mt.every(Math.max(Ue(g,b,U),1));const[q,y]=a[C/a[v-1][2]<a[v][2]/C?v-1:v];return q.every(y)}return[k,Y]}const[yr,kr]=gr(mt,Wt,Ot,yt,Et,At);function ce(t){if(0<=t.y&&t.y<100){var e=new Date(-1,t.m,t.d,t.H,t.M,t.S,t.L);return e.setFullYear(t.y),e}return new Date(t.y,t.m,t.d,t.H,t.M,t.S,t.L)}function le(t){if(0<=t.y&&t.y<100){var e=new Date(Date.UTC(-1,t.m,t.d,t.H,t.M,t.S,t.L));return e.setUTCFullYear(t.y),e}return new Date(Date.UTC(t.y,t.m,t.d,t.H,t.M,t.S,t.L))}function Yt(t,e,n){return{y:t,m:e,d:n,H:0,M:0,S:0,L:0}}function pr(t){var e=t.dateTime,n=t.date,r=t.time,i=t.periods,s=t.days,a=t.shortDays,k=t.months,Y=t.shortMonths,g=Ft(i),b=Lt(i),U=Ft(s),C=Lt(s),v=Ft(a),q=Lt(a),y=Ft(k),L=Lt(k),O=Ft(Y),W=Lt(Y),B={a:c,A:X,b:f,B:h,c:null,d:Oe,e:Oe,f:zr,g:Jr,G:Kr,H:Hr,I:Nr,j:Vr,L:cn,m:Pr,M:Rr,p:_,q:G,Q:Ve,s:ze,S:Br,u:Zr,U:Xr,V:qr,w:Gr,W:jr,x:null,X:null,y:Qr,Y:$r,Z:ti,"%":Ne},Z={a:H,A:V,b:I,B:z,c:null,d:He,e:He,f:ii,g:mi,G:yi,H:ei,I:ni,j:ri,L:un,m:si,M:ai,p:st,q:it,Q:Ve,s:ze,S:oi,u:ci,U:li,V:ui,w:fi,W:hi,x:null,X:null,y:di,Y:gi,Z:ki,"%":Ne},Q={a:D,A:w,b:o,B:d,c:m,d:Ie,e:Ie,f:Er,g:Ee,G:Ae,H:We,I:We,j:Yr,L:Ar,m:Ur,M:Fr,p:F,q:_r,Q:Wr,s:Or,S:Lr,u:wr,U:Cr,V:Dr,w:xr,W:Mr,x:u,X:S,y:Ee,Y:Ae,Z:Sr,"%":Ir};B.x=x(n,B),B.X=x(r,B),B.c=x(e,B),Z.x=x(n,Z),Z.X=x(r,Z),Z.c=x(e,Z);function x(p,A){return function(M){var l=[],R=-1,N=0,j=p.length,J,et,Ut;for(M instanceof Date||(M=new Date(+M));++R<j;)p.charCodeAt(R)===37&&(l.push(p.slice(N,R)),(et=Le[J=p.charAt(++R)])!=null?J=p.charAt(++R):et=J==="e"?" ":"0",(Ut=A[J])&&(J=Ut(M,et)),l.push(J),N=R+1);return l.push(p.slice(N,R)),l.join("")}}function E(p,A){return function(M){var l=Yt(1900,void 0,1),R=T(l,p,M+="",0),N,j;if(R!=M.length)return null;if("Q"in l)return new Date(l.Q);if("s"in l)return new Date(l.s*1e3+("L"in l?l.L:0));if(A&&!("Z"in l)&&(l.Z=0),"p"in l&&(l.H=l.H%12+l.p*12),l.m===void 0&&(l.m="q"in l?l.q:0),"V"in l){if(l.V<1||l.V>53)return null;"w"in l||(l.w=1),"Z"in l?(N=le(Yt(l.y,0,1)),j=N.getUTCDay(),N=j>4||j===0?jt.ceil(N):jt(N),N=Te.offset(N,(l.V-1)*7),l.y=N.getUTCFullYear(),l.m=N.getUTCMonth(),l.d=N.getUTCDate()+(l.w+6)%7):(N=ce(Yt(l.y,0,1)),j=N.getDay(),N=j>4||j===0?It.ceil(N):It(N),N=yt.offset(N,(l.V-1)*7),l.y=N.getFullYear(),l.m=N.getMonth(),l.d=N.getDate()+(l.w+6)%7)}else("W"in l||"U"in l)&&("w"in l||(l.w="u"in l?l.u%7:"W"in l?1:0),j="Z"in l?le(Yt(l.y,0,1)).getUTCDay():ce(Yt(l.y,0,1)).getDay(),l.m=0,l.d="W"in l?(l.w+6)%7+l.W*7-(j+5)%7:l.w+l.U*7-(j+6)%7);return"Z"in l?(l.H+=l.Z/100|0,l.M+=l.Z%100,le(l)):ce(l)}}function T(p,A,M,l){for(var R=0,N=A.length,j=M.length,J,et;R<N;){if(l>=j)return-1;if(J=A.charCodeAt(R++),J===37){if(J=A.charAt(R++),et=Q[J in Le?A.charAt(R++):J],!et||(l=et(p,M,l))<0)return-1}else if(J!=M.charCodeAt(l++))return-1}return l}function F(p,A,M){var l=g.exec(A.slice(M));return l?(p.p=b.get(l[0].toLowerCase()),M+l[0].length):-1}function D(p,A,M){var l=v.exec(A.slice(M));return l?(p.w=q.get(l[0].toLowerCase()),M+l[0].length):-1}function w(p,A,M){var l=U.exec(A.slice(M));return l?(p.w=C.get(l[0].toLowerCase()),M+l[0].length):-1}function o(p,A,M){var l=O.exec(A.slice(M));return l?(p.m=W.get(l[0].toLowerCase()),M+l[0].length):-1}function d(p,A,M){var l=y.exec(A.slice(M));return l?(p.m=L.get(l[0].toLowerCase()),M+l[0].length):-1}function m(p,A,M){return T(p,e,A,M)}function u(p,A,M){return T(p,n,A,M)}function S(p,A,M){return T(p,r,A,M)}function c(p){return a[p.getDay()]}function X(p){return s[p.getDay()]}function f(p){return Y[p.getMonth()]}function h(p){return k[p.getMonth()]}function _(p){return i[+(p.getHours()>=12)]}function G(p){return 1+~~(p.getMonth()/3)}function H(p){return a[p.getUTCDay()]}function V(p){return s[p.getUTCDay()]}function I(p){return Y[p.getUTCMonth()]}function z(p){return k[p.getUTCMonth()]}function st(p){return i[+(p.getUTCHours()>=12)]}function it(p){return 1+~~(p.getUTCMonth()/3)}return{format:function(p){var A=x(p+="",B);return A.toString=function(){return p},A},parse:function(p){var A=E(p+="",!1);return A.toString=function(){return p},A},utcFormat:function(p){var A=x(p+="",Z);return A.toString=function(){return p},A},utcParse:function(p){var A=E(p+="",!0);return A.toString=function(){return p},A}}}var Le={"-":"",_:" ",0:"0"},tt=/^\s*\d+/,Tr=/^%/,vr=/[\\^$*+?|[\]().{}]/g;function P(t,e,n){var r=t<0?"-":"",i=(r?-t:t)+"",s=i.length;return r+(s<n?new Array(n-s+1).join(e)+i:i)}function br(t){return t.replace(vr,"\\$&")}function Ft(t){return new RegExp("^(?:"+t.map(br).join("|")+")","i")}function Lt(t){return new Map(t.map((e,n)=>[e.toLowerCase(),n]))}function xr(t,e,n){var r=tt.exec(e.slice(n,n+1));return r?(t.w=+r[0],n+r[0].length):-1}function wr(t,e,n){var r=tt.exec(e.slice(n,n+1));return r?(t.u=+r[0],n+r[0].length):-1}function Cr(t,e,n){var r=tt.exec(e.slice(n,n+2));return r?(t.U=+r[0],n+r[0].length):-1}function Dr(t,e,n){var r=tt.exec(e.slice(n,n+2));return r?(t.V=+r[0],n+r[0].length):-1}function Mr(t,e,n){var r=tt.exec(e.slice(n,n+2));return r?(t.W=+r[0],n+r[0].length):-1}function Ae(t,e,n){var r=tt.exec(e.slice(n,n+4));return r?(t.y=+r[0],n+r[0].length):-1}function Ee(t,e,n){var r=tt.exec(e.slice(n,n+2));return r?(t.y=+r[0]+(+r[0]>68?1900:2e3),n+r[0].length):-1}function Sr(t,e,n){var r=/^(Z)|([+-]\d\d)(?::?(\d\d))?/.exec(e.slice(n,n+6));return r?(t.Z=r[1]?0:-(r[2]+(r[3]||"00")),n+r[0].length):-1}function _r(t,e,n){var r=tt.exec(e.slice(n,n+1));return r?(t.q=r[0]*3-3,n+r[0].length):-1}function Ur(t,e,n){var r=tt.exec(e.slice(n,n+2));return r?(t.m=r[0]-1,n+r[0].length):-1}function Ie(t,e,n){var r=tt.exec(e.slice(n,n+2));return r?(t.d=+r[0],n+r[0].length):-1}function Yr(t,e,n){var r=tt.exec(e.slice(n,n+3));return r?(t.m=0,t.d=+r[0],n+r[0].length):-1}function We(t,e,n){var r=tt.exec(e.slice(n,n+2));return r?(t.H=+r[0],n+r[0].length):-1}function Fr(t,e,n){var r=tt.exec(e.slice(n,n+2));return r?(t.M=+r[0],n+r[0].length):-1}function Lr(t,e,n){var r=tt.exec(e.slice(n,n+2));return r?(t.S=+r[0],n+r[0].length):-1}function Ar(t,e,n){var r=tt.exec(e.slice(n,n+3));return r?(t.L=+r[0],n+r[0].length):-1}function Er(t,e,n){var r=tt.exec(e.slice(n,n+6));return r?(t.L=Math.floor(r[0]/1e3),n+r[0].length):-1}function Ir(t,e,n){var r=Tr.exec(e.slice(n,n+1));return r?n+r[0].length:-1}function Wr(t,e,n){var r=tt.exec(e.slice(n));return r?(t.Q=+r[0],n+r[0].length):-1}function Or(t,e,n){var r=tt.exec(e.slice(n));return r?(t.s=+r[0],n+r[0].length):-1}function Oe(t,e){return P(t.getDate(),e,2)}function Hr(t,e){return P(t.getHours(),e,2)}function Nr(t,e){return P(t.getHours()%12||12,e,2)}function Vr(t,e){return P(1+yt.count(mt(t),t),e,3)}function cn(t,e){return P(t.getMilliseconds(),e,3)}function zr(t,e){return cn(t,e)+"000"}function Pr(t,e){return P(t.getMonth()+1,e,2)}function Rr(t,e){return P(t.getMinutes(),e,2)}function Br(t,e){return P(t.getSeconds(),e,2)}function Zr(t){var e=t.getDay();return e===0?7:e}function Xr(t,e){return P(Ot.count(mt(t)-1,t),e,2)}function ln(t){var e=t.getDay();return e>=4||e===0?kt(t):kt.ceil(t)}function qr(t,e){return t=ln(t),P(kt.count(mt(t),t)+(mt(t).getDay()===4),e,2)}function Gr(t){return t.getDay()}function jr(t,e){return P(It.count(mt(t)-1,t),e,2)}function Qr(t,e){return P(t.getFullYear()%100,e,2)}function Jr(t,e){return t=ln(t),P(t.getFullYear()%100,e,2)}function $r(t,e){return P(t.getFullYear()%1e4,e,4)}function Kr(t,e){var n=t.getDay();return t=n>=4||n===0?kt(t):kt.ceil(t),P(t.getFullYear()%1e4,e,4)}function ti(t){var e=t.getTimezoneOffset();return(e>0?"-":(e*=-1,"+"))+P(e/60|0,"0",2)+P(e%60,"0",2)}function He(t,e){return P(t.getUTCDate(),e,2)}function ei(t,e){return P(t.getUTCHours(),e,2)}function ni(t,e){return P(t.getUTCHours()%12||12,e,2)}function ri(t,e){return P(1+Te.count(pt(t),t),e,3)}function un(t,e){return P(t.getUTCMilliseconds(),e,3)}function ii(t,e){return un(t,e)+"000"}function si(t,e){return P(t.getUTCMonth()+1,e,2)}function ai(t,e){return P(t.getUTCMinutes(),e,2)}function oi(t,e){return P(t.getUTCSeconds(),e,2)}function ci(t){var e=t.getUTCDay();return e===0?7:e}function li(t,e){return P(on.count(pt(t)-1,t),e,2)}function fn(t){var e=t.getUTCDay();return e>=4||e===0?St(t):St.ceil(t)}function ui(t,e){return t=fn(t),P(St.count(pt(t),t)+(pt(t).getUTCDay()===4),e,2)}function fi(t){return t.getUTCDay()}function hi(t,e){return P(jt.count(pt(t)-1,t),e,2)}function di(t,e){return P(t.getUTCFullYear()%100,e,2)}function mi(t,e){return t=fn(t),P(t.getUTCFullYear()%100,e,2)}function gi(t,e){return P(t.getUTCFullYear()%1e4,e,4)}function yi(t,e){var n=t.getUTCDay();return t=n>=4||n===0?St(t):St.ceil(t),P(t.getUTCFullYear()%1e4,e,4)}function ki(){return"+0000"}function Ne(){return"%"}function Ve(t){return+t}function ze(t){return Math.floor(+t/1e3)}var xt,Qt;pi({dateTime:"%x, %X",date:"%-m/%-d/%Y",time:"%-I:%M:%S %p",periods:["AM","PM"],days:["Sunday","Monday","Tuesday","Wednesday","Thursday","Friday","Saturday"],shortDays:["Sun","Mon","Tue","Wed","Thu","Fri","Sat"],months:["January","February","March","April","May","June","July","August","September","October","November","December"],shortMonths:["Jan","Feb","Mar","Apr","May","Jun","Jul","Aug","Sep","Oct","Nov","Dec"]});function pi(t){return xt=pr(t),Qt=xt.format,xt.parse,xt.utcFormat,xt.utcParse,xt}function Ti(t){return new Date(t)}function vi(t){return t instanceof Date?+t:+new Date(+t)}function hn(t,e,n,r,i,s,a,k,Y,g){var b=Nn(),U=b.invert,C=b.domain,v=g(".%L"),q=g(":%S"),y=g("%I:%M"),L=g("%I %p"),O=g("%a %d"),W=g("%b %d"),B=g("%B"),Z=g("%Y");function Q(x){return(Y(x)<x?v:k(x)<x?q:a(x)<x?y:s(x)<x?L:r(x)<x?i(x)<x?O:W:n(x)<x?B:Z)(x)}return b.invert=function(x){return new Date(U(x))},b.domain=function(x){return arguments.length?C(Array.from(x,vi)):C().map(Ti)},b.ticks=function(x){var E=C();return t(E[0],E[E.length-1],x??10)},b.tickFormat=function(x,E){return E==null?Q:g(E)},b.nice=function(x){var E=C();return(!x||typeof x.range!="function")&&(x=e(E[0],E[E.length-1],x??10)),x?C(ar(E,x)):b},b.copy=function(){return Vn(b,hn(t,e,n,r,i,s,a,k,Y,g))},b}function bi(){return Pn.apply(hn(yr,kr,mt,Wt,Ot,yt,Et,At,gt,Qt).domain([new Date(2e3,0,1),new Date(2e3,0,2)]),arguments)}var dn={exports:{}};(function(t,e){(function(n,r){t.exports=r()})(ye,function(){var n="day";return function(r,i,s){var a=function(g){return g.add(4-g.isoWeekday(),n)},k=i.prototype;k.isoWeekYear=function(){return a(this).year()},k.isoWeek=function(g){if(!this.$utils().u(g))return this.add(7*(g-this.isoWeek()),n);var b,U,C,v,q=a(this),y=(b=this.isoWeekYear(),U=this.$u,C=(U?s.utc:s)().year(b).startOf("year"),v=4-C.isoWeekday(),C.isoWeekday()>4&&(v+=7),C.add(v,n));return q.diff(y,"week")+1},k.isoWeekday=function(g){return this.$utils().u(g)?this.day()||7:this.day(this.day()%7?g:g-7)};var Y=k.startOf;k.startOf=function(g,b){var U=this.$utils(),C=!!U.u(b)||b;return U.p(g)==="isoweek"?C?this.date(this.date()-(this.isoWeekday()-1)).startOf("day"):this.date(this.date()-1-(this.isoWeekday()-1)+7).endOf("day"):Y.bind(this)(g,b)}}})})(dn);var xi=dn.exports;const wi=ke(xi);var mn={exports:{}};(function(t,e){(function(n,r){t.exports=r()})(ye,function(){var n={LTS:"h:mm:ss A",LT:"h:mm A",L:"MM/DD/YYYY",LL:"MMMM D, YYYY",LLL:"MMMM D, YYYY h:mm A",LLLL:"dddd, MMMM D, YYYY h:mm A"},r=/(\[[^[]*\])|([-_:/.,()\s]+)|(A|a|YYYY|YY?|MM?M?M?|Do|DD?|hh?|HH?|mm?|ss?|S{1,3}|z|ZZ?)/g,i=/\d\d/,s=/\d\d?/,a=/\d*[^-_:/,()\s\d]+/,k={},Y=function(y){return(y=+y)+(y>68?1900:2e3)},g=function(y){return function(L){this[y]=+L}},b=[/[+-]\d\d:?(\d\d)?|Z/,function(y){(this.zone||(this.zone={})).offset=function(L){if(!L||L==="Z")return 0;var O=L.match(/([+-]|\d\d)/g),W=60*O[1]+(+O[2]||0);return W===0?0:O[0]==="+"?-W:W}(y)}],U=function(y){var L=k[y];return L&&(L.indexOf?L:L.s.concat(L.f))},C=function(y,L){var O,W=k.meridiem;if(W){for(var B=1;B<=24;B+=1)if(y.indexOf(W(B,0,L))>-1){O=B>12;break}}else O=y===(L?"pm":"PM");return O},v={A:[a,function(y){this.afternoon=C(y,!1)}],a:[a,function(y){this.afternoon=C(y,!0)}],S:[/\d/,function(y){this.milliseconds=100*+y}],SS:[i,function(y){this.milliseconds=10*+y}],SSS:[/\d{3}/,function(y){this.milliseconds=+y}],s:[s,g("seconds")],ss:[s,g("seconds")],m:[s,g("minutes")],mm:[s,g("minutes")],H:[s,g("hours")],h:[s,g("hours")],HH:[s,g("hours")],hh:[s,g("hours")],D:[s,g("day")],DD:[i,g("day")],Do:[a,function(y){var L=k.ordinal,O=y.match(/\d+/);if(this.day=O[0],L)for(var W=1;W<=31;W+=1)L(W).replace(/\[|\]/g,"")===y&&(this.day=W)}],M:[s,g("month")],MM:[i,g("month")],MMM:[a,function(y){var L=U("months"),O=(U("monthsShort")||L.map(function(W){return W.slice(0,3)})).indexOf(y)+1;if(O<1)throw new Error;this.month=O%12||O}],MMMM:[a,function(y){var L=U("months").indexOf(y)+1;if(L<1)throw new Error;this.month=L%12||L}],Y:[/[+-]?\d+/,g("year")],YY:[i,function(y){this.year=Y(y)}],YYYY:[/\d{4}/,g("year")],Z:b,ZZ:b};function q(y){var L,O;L=y,O=k&&k.formats;for(var W=(y=L.replace(/(\[[^\]]+])|(LTS?|l{1,4}|L{1,4})/g,function(F,D,w){var o=w&&w.toUpperCase();return D||O[w]||n[w]||O[o].replace(/(\[[^\]]+])|(MMMM|MM|DD|dddd)/g,function(d,m,u){return m||u.slice(1)})})).match(r),B=W.length,Z=0;Z<B;Z+=1){var Q=W[Z],x=v[Q],E=x&&x[0],T=x&&x[1];W[Z]=T?{regex:E,parser:T}:Q.replace(/^\[|\]$/g,"")}return function(F){for(var D={},w=0,o=0;w<B;w+=1){var d=W[w];if(typeof d=="string")o+=d.length;else{var m=d.regex,u=d.parser,S=F.slice(o),c=m.exec(S)[0];u.call(D,c),F=F.replace(c,"")}}return function(X){var f=X.afternoon;if(f!==void 0){var h=X.hours;f?h<12&&(X.hours+=12):h===12&&(X.hours=0),delete X.afternoon}}(D),D}}return function(y,L,O){O.p.customParseFormat=!0,y&&y.parseTwoDigitYear&&(Y=y.parseTwoDigitYear);var W=L.prototype,B=W.parse;W.parse=function(Z){var Q=Z.date,x=Z.utc,E=Z.args;this.$u=x;var T=E[1];if(typeof T=="string"){var F=E[2]===!0,D=E[3]===!0,w=F||D,o=E[2];D&&(o=E[2]),k=this.$locale(),!F&&o&&(k=O.Ls[o]),this.$d=function(S,c,X){try{if(["x","X"].indexOf(c)>-1)return new Date((c==="X"?1e3:1)*S);var f=q(c)(S),h=f.year,_=f.month,G=f.day,H=f.hours,V=f.minutes,I=f.seconds,z=f.milliseconds,st=f.zone,it=new Date,p=G||(h||_?1:it.getDate()),A=h||it.getFullYear(),M=0;h&&!_||(M=_>0?_-1:it.getMonth());var l=H||0,R=V||0,N=I||0,j=z||0;return st?new Date(Date.UTC(A,M,p,l,R,N,j+60*st.offset*1e3)):X?new Date(Date.UTC(A,M,p,l,R,N,j)):new Date(A,M,p,l,R,N,j)}catch{return new Date("")}}(Q,T,x),this.init(),o&&o!==!0&&(this.$L=this.locale(o).$L),w&&Q!=this.format(T)&&(this.$d=new Date("")),k={}}else if(T instanceof Array)for(var d=T.length,m=1;m<=d;m+=1){E[1]=T[m-1];var u=O.apply(this,E);if(u.isValid()){this.$d=u.$d,this.$L=u.$L,this.init();break}m===d&&(this.$d=new Date(""))}else B.call(this,Z)}}})})(mn);var Ci=mn.exports;const Di=ke(Ci);var gn={exports:{}};(function(t,e){(function(n,r){t.exports=r()})(ye,function(){return function(n,r){var i=r.prototype,s=i.format;i.format=function(a){var k=this,Y=this.$locale();if(!this.isValid())return s.bind(this)(a);var g=this.$utils(),b=(a||"YYYY-MM-DDTHH:mm:ssZ").replace(/\[([^\]]+)]|Q|wo|ww|w|WW|W|zzz|z|gggg|GGGG|Do|X|x|k{1,2}|S/g,function(U){switch(U){case"Q":return Math.ceil((k.$M+1)/3);case"Do":return Y.ordinal(k.$D);case"gggg":return k.weekYear();case"GGGG":return k.isoWeekYear();case"wo":return Y.ordinal(k.week(),"W");case"w":case"ww":return g.s(k.week(),U==="w"?1:2,"0");case"W":case"WW":return g.s(k.isoWeek(),U==="W"?1:2,"0");case"k":case"kk":return g.s(String(k.$H===0?24:k.$H),U==="k"?1:2,"0");case"X":return Math.floor(k.$d.getTime()/1e3);case"x":return k.$d.getTime();case"z":return"["+k.offsetName()+"]";case"zzz":return"["+k.offsetName("long")+"]";default:return U}});return s.bind(this)(b)}}})})(gn);var Mi=gn.exports;const Si=ke(Mi);var he=function(){var t=function(w,o,d,m){for(d=d||{},m=w.length;m--;d[w[m]]=o);return d},e=[6,8,10,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,30,32,33,35,37],n=[1,25],r=[1,26],i=[1,27],s=[1,28],a=[1,29],k=[1,30],Y=[1,31],g=[1,9],b=[1,10],U=[1,11],C=[1,12],v=[1,13],q=[1,14],y=[1,15],L=[1,16],O=[1,18],W=[1,19],B=[1,20],Z=[1,21],Q=[1,22],x=[1,24],E=[1,32],T={trace:function(){},yy:{},symbols_:{error:2,start:3,gantt:4,document:5,EOF:6,line:7,SPACE:8,statement:9,NL:10,weekday:11,weekday_monday:12,weekday_tuesday:13,weekday_wednesday:14,weekday_thursday:15,weekday_friday:16,weekday_saturday:17,weekday_sunday:18,dateFormat:19,inclusiveEndDates:20,topAxis:21,axisFormat:22,tickInterval:23,excludes:24,includes:25,todayMarker:26,title:27,acc_title:28,acc_title_value:29,acc_descr:30,acc_descr_value:31,acc_descr_multiline_value:32,section:33,clickStatement:34,taskTxt:35,taskData:36,click:37,callbackname:38,callbackargs:39,href:40,clickStatementDebug:41,$accept:0,$end:1},terminals_:{2:"error",4:"gantt",6:"EOF",8:"SPACE",10:"NL",12:"weekday_monday",13:"weekday_tuesday",14:"weekday_wednesday",15:"weekday_thursday",16:"weekday_friday",17:"weekday_saturday",18:"weekday_sunday",19:"dateFormat",20:"inclusiveEndDates",21:"topAxis",22:"axisFormat",23:"tickInterval",24:"excludes",25:"includes",26:"todayMarker",27:"title",28:"acc_title",29:"acc_title_value",30:"acc_descr",31:"acc_descr_value",32:"acc_descr_multiline_value",33:"section",35:"taskTxt",36:"taskData",37:"click",38:"callbackname",39:"callbackargs",40:"href"},productions_:[0,[3,3],[5,0],[5,2],[7,2],[7,1],[7,1],[7,1],[11,1],[11,1],[11,1],[11,1],[11,1],[11,1],[11,1],[9,1],[9,1],[9,1],[9,1],[9,1],[9,1],[9,1],[9,1],[9,1],[9,1],[9,2],[9,2],[9,1],[9,1],[9,1],[9,2],[34,2],[34,3],[34,3],[34,4],[34,3],[34,4],[34,2],[41,2],[41,3],[41,3],[41,4],[41,3],[41,4],[41,2]],performAction:function(o,d,m,u,S,c,X){var f=c.length-1;switch(S){case 1:return c[f-1];case 2:this.$=[];break;case 3:c[f-1].push(c[f]),this.$=c[f-1];break;case 4:case 5:this.$=c[f];break;case 6:case 7:this.$=[];break;case 8:u.setWeekday("monday");break;case 9:u.setWeekday("tuesday");break;case 10:u.setWeekday("wednesday");break;case 11:u.setWeekday("thursday");break;case 12:u.setWeekday("friday");break;case 13:u.setWeekday("saturday");break;case 14:u.setWeekday("sunday");break;case 15:u.setDateFormat(c[f].substr(11)),this.$=c[f].substr(11);break;case 16:u.enableInclusiveEndDates(),this.$=c[f].substr(18);break;case 17:u.TopAxis(),this.$=c[f].substr(8);break;case 18:u.setAxisFormat(c[f].substr(11)),this.$=c[f].substr(11);break;case 19:u.setTickInterval(c[f].substr(13)),this.$=c[f].substr(13);break;case 20:u.setExcludes(c[f].substr(9)),this.$=c[f].substr(9);break;case 21:u.setIncludes(c[f].substr(9)),this.$=c[f].substr(9);break;case 22:u.setTodayMarker(c[f].substr(12)),this.$=c[f].substr(12);break;case 24:u.setDiagramTitle(c[f].substr(6)),this.$=c[f].substr(6);break;case 25:this.$=c[f].trim(),u.setAccTitle(this.$);break;case 26:case 27:this.$=c[f].trim(),u.setAccDescription(this.$);break;case 28:u.addSection(c[f].substr(8)),this.$=c[f].substr(8);break;case 30:u.addTask(c[f-1],c[f]),this.$="task";break;case 31:this.$=c[f-1],u.setClickEvent(c[f-1],c[f],null);break;case 32:this.$=c[f-2],u.setClickEvent(c[f-2],c[f-1],c[f]);break;case 33:this.$=c[f-2],u.setClickEvent(c[f-2],c[f-1],null),u.setLink(c[f-2],c[f]);break;case 34:this.$=c[f-3],u.setClickEvent(c[f-3],c[f-2],c[f-1]),u.setLink(c[f-3],c[f]);break;case 35:this.$=c[f-2],u.setClickEvent(c[f-2],c[f],null),u.setLink(c[f-2],c[f-1]);break;case 36:this.$=c[f-3],u.setClickEvent(c[f-3],c[f-1],c[f]),u.setLink(c[f-3],c[f-2]);break;case 37:this.$=c[f-1],u.setLink(c[f-1],c[f]);break;case 38:case 44:this.$=c[f-1]+" "+c[f];break;case 39:case 40:case 42:this.$=c[f-2]+" "+c[f-1]+" "+c[f];break;case 41:case 43:this.$=c[f-3]+" "+c[f-2]+" "+c[f-1]+" "+c[f];break}},table:[{3:1,4:[1,2]},{1:[3]},t(e,[2,2],{5:3}),{6:[1,4],7:5,8:[1,6],9:7,10:[1,8],11:17,12:n,13:r,14:i,15:s,16:a,17:k,18:Y,19:g,20:b,21:U,22:C,23:v,24:q,25:y,26:L,27:O,28:W,30:B,32:Z,33:Q,34:23,35:x,37:E},t(e,[2,7],{1:[2,1]}),t(e,[2,3]),{9:33,11:17,12:n,13:r,14:i,15:s,16:a,17:k,18:Y,19:g,20:b,21:U,22:C,23:v,24:q,25:y,26:L,27:O,28:W,30:B,32:Z,33:Q,34:23,35:x,37:E},t(e,[2,5]),t(e,[2,6]),t(e,[2,15]),t(e,[2,16]),t(e,[2,17]),t(e,[2,18]),t(e,[2,19]),t(e,[2,20]),t(e,[2,21]),t(e,[2,22]),t(e,[2,23]),t(e,[2,24]),{29:[1,34]},{31:[1,35]},t(e,[2,27]),t(e,[2,28]),t(e,[2,29]),{36:[1,36]},t(e,[2,8]),t(e,[2,9]),t(e,[2,10]),t(e,[2,11]),t(e,[2,12]),t(e,[2,13]),t(e,[2,14]),{38:[1,37],40:[1,38]},t(e,[2,4]),t(e,[2,25]),t(e,[2,26]),t(e,[2,30]),t(e,[2,31],{39:[1,39],40:[1,40]}),t(e,[2,37],{38:[1,41]}),t(e,[2,32],{40:[1,42]}),t(e,[2,33]),t(e,[2,35],{39:[1,43]}),t(e,[2,34]),t(e,[2,36])],defaultActions:{},parseError:function(o,d){if(d.recoverable)this.trace(o);else{var m=new Error(o);throw m.hash=d,m}},parse:function(o){var d=this,m=[0],u=[],S=[null],c=[],X=this.table,f="",h=0,_=0,G=2,H=1,V=c.slice.call(arguments,1),I=Object.create(this.lexer),z={yy:{}};for(var st in this.yy)Object.prototype.hasOwnProperty.call(this.yy,st)&&(z.yy[st]=this.yy[st]);I.setInput(o,z.yy),z.yy.lexer=I,z.yy.parser=this,typeof I.yylloc>"u"&&(I.yylloc={});var it=I.yylloc;c.push(it);var p=I.options&&I.options.ranges;typeof z.yy.parseError=="function"?this.parseError=z.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function A(){var ct;return ct=u.pop()||I.lex()||H,typeof ct!="number"&&(ct instanceof Array&&(u=ct,ct=u.pop()),ct=d.symbols_[ct]||ct),ct}for(var M,l,R,N,j={},J,et,Ut,zt;;){if(l=m[m.length-1],this.defaultActions[l]?R=this.defaultActions[l]:((M===null||typeof M>"u")&&(M=A()),R=X[l]&&X[l][M]),typeof R>"u"||!R.length||!R[0]){var $t="";zt=[];for(J in X[l])this.terminals_[J]&&J>G&&zt.push("'"+this.terminals_[J]+"'");I.showPosition?$t="Parse error on line "+(h+1)+`:
+import{au as Be,av as Ze,aw as Xe,ax as qe,ay as Dn,az as Kt,aA as Mn,aB as ye,aC as ke,aD as nt,c as wt,s as Sn,g as _n,x as Un,y as Yn,b as Fn,a as Ln,A as An,m as En,l as qt,h as Pt,i as In,j as Wn,z as On}from"./mermaid.core-DNo_7Q2B.js";import{b as Hn,t as Ue,c as Nn,a as Vn,l as zn}from"./linear-Cb1OAgs3.js";import{i as Pn}from"./init-Gi6I4Gst.js";import"./app-B4LGNJZ0.js";function Rn(t,e){let n;if(e===void 0)for(const r of t)r!=null&&(n<r||n===void 0&&r>=r)&&(n=r);else{let r=-1;for(let i of t)(i=e(i,++r,t))!=null&&(n<i||n===void 0&&i>=i)&&(n=i)}return n}function Bn(t,e){let n;if(e===void 0)for(const r of t)r!=null&&(n>r||n===void 0&&r>=r)&&(n=r);else{let r=-1;for(let i of t)(i=e(i,++r,t))!=null&&(n>i||n===void 0&&i>=i)&&(n=i)}return n}function Zn(t){return t}var Bt=1,te=2,ue=3,Rt=4,Ye=1e-6;function Xn(t){return"translate("+t+",0)"}function qn(t){return"translate(0,"+t+")"}function Gn(t){return e=>+t(e)}function jn(t,e){return e=Math.max(0,t.bandwidth()-e*2)/2,t.round()&&(e=Math.round(e)),n=>+t(n)+e}function Qn(){return!this.__axis}function Ge(t,e){var n=[],r=null,i=null,s=6,a=6,k=3,Y=typeof window<"u"&&window.devicePixelRatio>1?0:.5,g=t===Bt||t===Rt?-1:1,b=t===Rt||t===te?"x":"y",U=t===Bt||t===ue?Xn:qn;function C(v){var q=r??(e.ticks?e.ticks.apply(e,n):e.domain()),y=i??(e.tickFormat?e.tickFormat.apply(e,n):Zn),L=Math.max(s,0)+k,O=e.range(),W=+O[0]+Y,B=+O[O.length-1]+Y,Z=(e.bandwidth?jn:Gn)(e.copy(),Y),Q=v.selection?v.selection():v,x=Q.selectAll(".domain").data([null]),E=Q.selectAll(".tick").data(q,e).order(),T=E.exit(),F=E.enter().append("g").attr("class","tick"),D=E.select("line"),w=E.select("text");x=x.merge(x.enter().insert("path",".tick").attr("class","domain").attr("stroke","currentColor")),E=E.merge(F),D=D.merge(F.append("line").attr("stroke","currentColor").attr(b+"2",g*s)),w=w.merge(F.append("text").attr("fill","currentColor").attr(b,g*L).attr("dy",t===Bt?"0em":t===ue?"0.71em":"0.32em")),v!==Q&&(x=x.transition(v),E=E.transition(v),D=D.transition(v),w=w.transition(v),T=T.transition(v).attr("opacity",Ye).attr("transform",function(o){return isFinite(o=Z(o))?U(o+Y):this.getAttribute("transform")}),F.attr("opacity",Ye).attr("transform",function(o){var d=this.parentNode.__axis;return U((d&&isFinite(d=d(o))?d:Z(o))+Y)})),T.remove(),x.attr("d",t===Rt||t===te?a?"M"+g*a+","+W+"H"+Y+"V"+B+"H"+g*a:"M"+Y+","+W+"V"+B:a?"M"+W+","+g*a+"V"+Y+"H"+B+"V"+g*a:"M"+W+","+Y+"H"+B),E.attr("opacity",1).attr("transform",function(o){return U(Z(o)+Y)}),D.attr(b+"2",g*s),w.attr(b,g*L).text(y),Q.filter(Qn).attr("fill","none").attr("font-size",10).attr("font-family","sans-serif").attr("text-anchor",t===te?"start":t===Rt?"end":"middle"),Q.each(function(){this.__axis=Z})}return C.scale=function(v){return arguments.length?(e=v,C):e},C.ticks=function(){return n=Array.from(arguments),C},C.tickArguments=function(v){return arguments.length?(n=v==null?[]:Array.from(v),C):n.slice()},C.tickValues=function(v){return arguments.length?(r=v==null?null:Array.from(v),C):r&&r.slice()},C.tickFormat=function(v){return arguments.length?(i=v,C):i},C.tickSize=function(v){return arguments.length?(s=a=+v,C):s},C.tickSizeInner=function(v){return arguments.length?(s=+v,C):s},C.tickSizeOuter=function(v){return arguments.length?(a=+v,C):a},C.tickPadding=function(v){return arguments.length?(k=+v,C):k},C.offset=function(v){return arguments.length?(Y=+v,C):Y},C}function Jn(t){return Ge(Bt,t)}function $n(t){return Ge(ue,t)}const Kn=Math.PI/180,tr=180/Math.PI,Gt=18,je=.96422,Qe=1,Je=.82521,$e=4/29,Ct=6/29,Ke=3*Ct*Ct,er=Ct*Ct*Ct;function tn(t){if(t instanceof ot)return new ot(t.l,t.a,t.b,t.opacity);if(t instanceof ut)return en(t);t instanceof Xe||(t=Dn(t));var e=ie(t.r),n=ie(t.g),r=ie(t.b),i=ee((.2225045*e+.7168786*n+.0606169*r)/Qe),s,a;return e===n&&n===r?s=a=i:(s=ee((.4360747*e+.3850649*n+.1430804*r)/je),a=ee((.0139322*e+.0971045*n+.7141733*r)/Je)),new ot(116*i-16,500*(s-i),200*(i-a),t.opacity)}function nr(t,e,n,r){return arguments.length===1?tn(t):new ot(t,e,n,r??1)}function ot(t,e,n,r){this.l=+t,this.a=+e,this.b=+n,this.opacity=+r}Be(ot,nr,Ze(qe,{brighter(t){return new ot(this.l+Gt*(t??1),this.a,this.b,this.opacity)},darker(t){return new ot(this.l-Gt*(t??1),this.a,this.b,this.opacity)},rgb(){var t=(this.l+16)/116,e=isNaN(this.a)?t:t+this.a/500,n=isNaN(this.b)?t:t-this.b/200;return e=je*ne(e),t=Qe*ne(t),n=Je*ne(n),new Xe(re(3.1338561*e-1.6168667*t-.4906146*n),re(-.9787684*e+1.9161415*t+.033454*n),re(.0719453*e-.2289914*t+1.4052427*n),this.opacity)}}));function ee(t){return t>er?Math.pow(t,1/3):t/Ke+$e}function ne(t){return t>Ct?t*t*t:Ke*(t-$e)}function re(t){return 255*(t<=.0031308?12.92*t:1.055*Math.pow(t,1/2.4)-.055)}function ie(t){return(t/=255)<=.04045?t/12.92:Math.pow((t+.055)/1.055,2.4)}function rr(t){if(t instanceof ut)return new ut(t.h,t.c,t.l,t.opacity);if(t instanceof ot||(t=tn(t)),t.a===0&&t.b===0)return new ut(NaN,0<t.l&&t.l<100?0:NaN,t.l,t.opacity);var e=Math.atan2(t.b,t.a)*tr;return new ut(e<0?e+360:e,Math.sqrt(t.a*t.a+t.b*t.b),t.l,t.opacity)}function fe(t,e,n,r){return arguments.length===1?rr(t):new ut(t,e,n,r??1)}function ut(t,e,n,r){this.h=+t,this.c=+e,this.l=+n,this.opacity=+r}function en(t){if(isNaN(t.h))return new ot(t.l,0,0,t.opacity);var e=t.h*Kn;return new ot(t.l,Math.cos(e)*t.c,Math.sin(e)*t.c,t.opacity)}Be(ut,fe,Ze(qe,{brighter(t){return new ut(this.h,this.c,this.l+Gt*(t??1),this.opacity)},darker(t){return new ut(this.h,this.c,this.l-Gt*(t??1),this.opacity)},rgb(){return en(this).rgb()}}));function ir(t){return function(e,n){var r=t((e=fe(e)).h,(n=fe(n)).h),i=Kt(e.c,n.c),s=Kt(e.l,n.l),a=Kt(e.opacity,n.opacity);return function(k){return e.h=r(k),e.c=i(k),e.l=s(k),e.opacity=a(k),e+""}}}const sr=ir(Mn);function ar(t,e){t=t.slice();var n=0,r=t.length-1,i=t[n],s=t[r],a;return s<i&&(a=n,n=r,r=a,a=i,i=s,s=a),t[n]=e.floor(i),t[r]=e.ceil(s),t}const se=new Date,ae=new Date;function K(t,e,n,r){function i(s){return t(s=arguments.length===0?new Date:new Date(+s)),s}return i.floor=s=>(t(s=new Date(+s)),s),i.ceil=s=>(t(s=new Date(s-1)),e(s,1),t(s),s),i.round=s=>{const a=i(s),k=i.ceil(s);return s-a<k-s?a:k},i.offset=(s,a)=>(e(s=new Date(+s),a==null?1:Math.floor(a)),s),i.range=(s,a,k)=>{const Y=[];if(s=i.ceil(s),k=k==null?1:Math.floor(k),!(s<a)||!(k>0))return Y;let g;do Y.push(g=new Date(+s)),e(s,k),t(s);while(g<s&&s<a);return Y},i.filter=s=>K(a=>{if(a>=a)for(;t(a),!s(a);)a.setTime(a-1)},(a,k)=>{if(a>=a)if(k<0)for(;++k<=0;)for(;e(a,-1),!s(a););else for(;--k>=0;)for(;e(a,1),!s(a););}),n&&(i.count=(s,a)=>(se.setTime(+s),ae.setTime(+a),t(se),t(ae),Math.floor(n(se,ae))),i.every=s=>(s=Math.floor(s),!isFinite(s)||!(s>0)?null:s>1?i.filter(r?a=>r(a)%s===0:a=>i.count(0,a)%s===0):i)),i}const Mt=K(()=>{},(t,e)=>{t.setTime(+t+e)},(t,e)=>e-t);Mt.every=t=>(t=Math.floor(t),!isFinite(t)||!(t>0)?null:t>1?K(e=>{e.setTime(Math.floor(e/t)*t)},(e,n)=>{e.setTime(+e+n*t)},(e,n)=>(n-e)/t):Mt);Mt.range;const ft=1e3,rt=ft*60,ht=rt*60,dt=ht*24,pe=dt*7,Fe=dt*30,oe=dt*365,gt=K(t=>{t.setTime(t-t.getMilliseconds())},(t,e)=>{t.setTime(+t+e*ft)},(t,e)=>(e-t)/ft,t=>t.getUTCSeconds());gt.range;const At=K(t=>{t.setTime(t-t.getMilliseconds()-t.getSeconds()*ft)},(t,e)=>{t.setTime(+t+e*rt)},(t,e)=>(e-t)/rt,t=>t.getMinutes());At.range;const or=K(t=>{t.setUTCSeconds(0,0)},(t,e)=>{t.setTime(+t+e*rt)},(t,e)=>(e-t)/rt,t=>t.getUTCMinutes());or.range;const Et=K(t=>{t.setTime(t-t.getMilliseconds()-t.getSeconds()*ft-t.getMinutes()*rt)},(t,e)=>{t.setTime(+t+e*ht)},(t,e)=>(e-t)/ht,t=>t.getHours());Et.range;const cr=K(t=>{t.setUTCMinutes(0,0,0)},(t,e)=>{t.setTime(+t+e*ht)},(t,e)=>(e-t)/ht,t=>t.getUTCHours());cr.range;const yt=K(t=>t.setHours(0,0,0,0),(t,e)=>t.setDate(t.getDate()+e),(t,e)=>(e-t-(e.getTimezoneOffset()-t.getTimezoneOffset())*rt)/dt,t=>t.getDate()-1);yt.range;const Te=K(t=>{t.setUTCHours(0,0,0,0)},(t,e)=>{t.setUTCDate(t.getUTCDate()+e)},(t,e)=>(e-t)/dt,t=>t.getUTCDate()-1);Te.range;const lr=K(t=>{t.setUTCHours(0,0,0,0)},(t,e)=>{t.setUTCDate(t.getUTCDate()+e)},(t,e)=>(e-t)/dt,t=>Math.floor(t/dt));lr.range;function Tt(t){return K(e=>{e.setDate(e.getDate()-(e.getDay()+7-t)%7),e.setHours(0,0,0,0)},(e,n)=>{e.setDate(e.getDate()+n*7)},(e,n)=>(n-e-(n.getTimezoneOffset()-e.getTimezoneOffset())*rt)/pe)}const Ot=Tt(0),It=Tt(1),nn=Tt(2),rn=Tt(3),kt=Tt(4),sn=Tt(5),an=Tt(6);Ot.range;It.range;nn.range;rn.range;kt.range;sn.range;an.range;function vt(t){return K(e=>{e.setUTCDate(e.getUTCDate()-(e.getUTCDay()+7-t)%7),e.setUTCHours(0,0,0,0)},(e,n)=>{e.setUTCDate(e.getUTCDate()+n*7)},(e,n)=>(n-e)/pe)}const on=vt(0),jt=vt(1),ur=vt(2),fr=vt(3),St=vt(4),hr=vt(5),dr=vt(6);on.range;jt.range;ur.range;fr.range;St.range;hr.range;dr.range;const Wt=K(t=>{t.setDate(1),t.setHours(0,0,0,0)},(t,e)=>{t.setMonth(t.getMonth()+e)},(t,e)=>e.getMonth()-t.getMonth()+(e.getFullYear()-t.getFullYear())*12,t=>t.getMonth());Wt.range;const mr=K(t=>{t.setUTCDate(1),t.setUTCHours(0,0,0,0)},(t,e)=>{t.setUTCMonth(t.getUTCMonth()+e)},(t,e)=>e.getUTCMonth()-t.getUTCMonth()+(e.getUTCFullYear()-t.getUTCFullYear())*12,t=>t.getUTCMonth());mr.range;const mt=K(t=>{t.setMonth(0,1),t.setHours(0,0,0,0)},(t,e)=>{t.setFullYear(t.getFullYear()+e)},(t,e)=>e.getFullYear()-t.getFullYear(),t=>t.getFullYear());mt.every=t=>!isFinite(t=Math.floor(t))||!(t>0)?null:K(e=>{e.setFullYear(Math.floor(e.getFullYear()/t)*t),e.setMonth(0,1),e.setHours(0,0,0,0)},(e,n)=>{e.setFullYear(e.getFullYear()+n*t)});mt.range;const pt=K(t=>{t.setUTCMonth(0,1),t.setUTCHours(0,0,0,0)},(t,e)=>{t.setUTCFullYear(t.getUTCFullYear()+e)},(t,e)=>e.getUTCFullYear()-t.getUTCFullYear(),t=>t.getUTCFullYear());pt.every=t=>!isFinite(t=Math.floor(t))||!(t>0)?null:K(e=>{e.setUTCFullYear(Math.floor(e.getUTCFullYear()/t)*t),e.setUTCMonth(0,1),e.setUTCHours(0,0,0,0)},(e,n)=>{e.setUTCFullYear(e.getUTCFullYear()+n*t)});pt.range;function gr(t,e,n,r,i,s){const a=[[gt,1,ft],[gt,5,5*ft],[gt,15,15*ft],[gt,30,30*ft],[s,1,rt],[s,5,5*rt],[s,15,15*rt],[s,30,30*rt],[i,1,ht],[i,3,3*ht],[i,6,6*ht],[i,12,12*ht],[r,1,dt],[r,2,2*dt],[n,1,pe],[e,1,Fe],[e,3,3*Fe],[t,1,oe]];function k(g,b,U){const C=b<g;C&&([g,b]=[b,g]);const v=U&&typeof U.range=="function"?U:Y(g,b,U),q=v?v.range(g,+b+1):[];return C?q.reverse():q}function Y(g,b,U){const C=Math.abs(b-g)/U,v=Hn(([,,L])=>L).right(a,C);if(v===a.length)return t.every(Ue(g/oe,b/oe,U));if(v===0)return Mt.every(Math.max(Ue(g,b,U),1));const[q,y]=a[C/a[v-1][2]<a[v][2]/C?v-1:v];return q.every(y)}return[k,Y]}const[yr,kr]=gr(mt,Wt,Ot,yt,Et,At);function ce(t){if(0<=t.y&&t.y<100){var e=new Date(-1,t.m,t.d,t.H,t.M,t.S,t.L);return e.setFullYear(t.y),e}return new Date(t.y,t.m,t.d,t.H,t.M,t.S,t.L)}function le(t){if(0<=t.y&&t.y<100){var e=new Date(Date.UTC(-1,t.m,t.d,t.H,t.M,t.S,t.L));return e.setUTCFullYear(t.y),e}return new Date(Date.UTC(t.y,t.m,t.d,t.H,t.M,t.S,t.L))}function Yt(t,e,n){return{y:t,m:e,d:n,H:0,M:0,S:0,L:0}}function pr(t){var e=t.dateTime,n=t.date,r=t.time,i=t.periods,s=t.days,a=t.shortDays,k=t.months,Y=t.shortMonths,g=Ft(i),b=Lt(i),U=Ft(s),C=Lt(s),v=Ft(a),q=Lt(a),y=Ft(k),L=Lt(k),O=Ft(Y),W=Lt(Y),B={a:c,A:X,b:f,B:h,c:null,d:Oe,e:Oe,f:zr,g:Jr,G:Kr,H:Hr,I:Nr,j:Vr,L:cn,m:Pr,M:Rr,p:_,q:G,Q:Ve,s:ze,S:Br,u:Zr,U:Xr,V:qr,w:Gr,W:jr,x:null,X:null,y:Qr,Y:$r,Z:ti,"%":Ne},Z={a:H,A:V,b:I,B:z,c:null,d:He,e:He,f:ii,g:mi,G:yi,H:ei,I:ni,j:ri,L:un,m:si,M:ai,p:st,q:it,Q:Ve,s:ze,S:oi,u:ci,U:li,V:ui,w:fi,W:hi,x:null,X:null,y:di,Y:gi,Z:ki,"%":Ne},Q={a:D,A:w,b:o,B:d,c:m,d:Ie,e:Ie,f:Er,g:Ee,G:Ae,H:We,I:We,j:Yr,L:Ar,m:Ur,M:Fr,p:F,q:_r,Q:Wr,s:Or,S:Lr,u:wr,U:Cr,V:Dr,w:xr,W:Mr,x:u,X:S,y:Ee,Y:Ae,Z:Sr,"%":Ir};B.x=x(n,B),B.X=x(r,B),B.c=x(e,B),Z.x=x(n,Z),Z.X=x(r,Z),Z.c=x(e,Z);function x(p,A){return function(M){var l=[],R=-1,N=0,j=p.length,J,et,Ut;for(M instanceof Date||(M=new Date(+M));++R<j;)p.charCodeAt(R)===37&&(l.push(p.slice(N,R)),(et=Le[J=p.charAt(++R)])!=null?J=p.charAt(++R):et=J==="e"?" ":"0",(Ut=A[J])&&(J=Ut(M,et)),l.push(J),N=R+1);return l.push(p.slice(N,R)),l.join("")}}function E(p,A){return function(M){var l=Yt(1900,void 0,1),R=T(l,p,M+="",0),N,j;if(R!=M.length)return null;if("Q"in l)return new Date(l.Q);if("s"in l)return new Date(l.s*1e3+("L"in l?l.L:0));if(A&&!("Z"in l)&&(l.Z=0),"p"in l&&(l.H=l.H%12+l.p*12),l.m===void 0&&(l.m="q"in l?l.q:0),"V"in l){if(l.V<1||l.V>53)return null;"w"in l||(l.w=1),"Z"in l?(N=le(Yt(l.y,0,1)),j=N.getUTCDay(),N=j>4||j===0?jt.ceil(N):jt(N),N=Te.offset(N,(l.V-1)*7),l.y=N.getUTCFullYear(),l.m=N.getUTCMonth(),l.d=N.getUTCDate()+(l.w+6)%7):(N=ce(Yt(l.y,0,1)),j=N.getDay(),N=j>4||j===0?It.ceil(N):It(N),N=yt.offset(N,(l.V-1)*7),l.y=N.getFullYear(),l.m=N.getMonth(),l.d=N.getDate()+(l.w+6)%7)}else("W"in l||"U"in l)&&("w"in l||(l.w="u"in l?l.u%7:"W"in l?1:0),j="Z"in l?le(Yt(l.y,0,1)).getUTCDay():ce(Yt(l.y,0,1)).getDay(),l.m=0,l.d="W"in l?(l.w+6)%7+l.W*7-(j+5)%7:l.w+l.U*7-(j+6)%7);return"Z"in l?(l.H+=l.Z/100|0,l.M+=l.Z%100,le(l)):ce(l)}}function T(p,A,M,l){for(var R=0,N=A.length,j=M.length,J,et;R<N;){if(l>=j)return-1;if(J=A.charCodeAt(R++),J===37){if(J=A.charAt(R++),et=Q[J in Le?A.charAt(R++):J],!et||(l=et(p,M,l))<0)return-1}else if(J!=M.charCodeAt(l++))return-1}return l}function F(p,A,M){var l=g.exec(A.slice(M));return l?(p.p=b.get(l[0].toLowerCase()),M+l[0].length):-1}function D(p,A,M){var l=v.exec(A.slice(M));return l?(p.w=q.get(l[0].toLowerCase()),M+l[0].length):-1}function w(p,A,M){var l=U.exec(A.slice(M));return l?(p.w=C.get(l[0].toLowerCase()),M+l[0].length):-1}function o(p,A,M){var l=O.exec(A.slice(M));return l?(p.m=W.get(l[0].toLowerCase()),M+l[0].length):-1}function d(p,A,M){var l=y.exec(A.slice(M));return l?(p.m=L.get(l[0].toLowerCase()),M+l[0].length):-1}function m(p,A,M){return T(p,e,A,M)}function u(p,A,M){return T(p,n,A,M)}function S(p,A,M){return T(p,r,A,M)}function c(p){return a[p.getDay()]}function X(p){return s[p.getDay()]}function f(p){return Y[p.getMonth()]}function h(p){return k[p.getMonth()]}function _(p){return i[+(p.getHours()>=12)]}function G(p){return 1+~~(p.getMonth()/3)}function H(p){return a[p.getUTCDay()]}function V(p){return s[p.getUTCDay()]}function I(p){return Y[p.getUTCMonth()]}function z(p){return k[p.getUTCMonth()]}function st(p){return i[+(p.getUTCHours()>=12)]}function it(p){return 1+~~(p.getUTCMonth()/3)}return{format:function(p){var A=x(p+="",B);return A.toString=function(){return p},A},parse:function(p){var A=E(p+="",!1);return A.toString=function(){return p},A},utcFormat:function(p){var A=x(p+="",Z);return A.toString=function(){return p},A},utcParse:function(p){var A=E(p+="",!0);return A.toString=function(){return p},A}}}var Le={"-":"",_:" ",0:"0"},tt=/^\s*\d+/,Tr=/^%/,vr=/[\\^$*+?|[\]().{}]/g;function P(t,e,n){var r=t<0?"-":"",i=(r?-t:t)+"",s=i.length;return r+(s<n?new Array(n-s+1).join(e)+i:i)}function br(t){return t.replace(vr,"\\$&")}function Ft(t){return new RegExp("^(?:"+t.map(br).join("|")+")","i")}function Lt(t){return new Map(t.map((e,n)=>[e.toLowerCase(),n]))}function xr(t,e,n){var r=tt.exec(e.slice(n,n+1));return r?(t.w=+r[0],n+r[0].length):-1}function wr(t,e,n){var r=tt.exec(e.slice(n,n+1));return r?(t.u=+r[0],n+r[0].length):-1}function Cr(t,e,n){var r=tt.exec(e.slice(n,n+2));return r?(t.U=+r[0],n+r[0].length):-1}function Dr(t,e,n){var r=tt.exec(e.slice(n,n+2));return r?(t.V=+r[0],n+r[0].length):-1}function Mr(t,e,n){var r=tt.exec(e.slice(n,n+2));return r?(t.W=+r[0],n+r[0].length):-1}function Ae(t,e,n){var r=tt.exec(e.slice(n,n+4));return r?(t.y=+r[0],n+r[0].length):-1}function Ee(t,e,n){var r=tt.exec(e.slice(n,n+2));return r?(t.y=+r[0]+(+r[0]>68?1900:2e3),n+r[0].length):-1}function Sr(t,e,n){var r=/^(Z)|([+-]\d\d)(?::?(\d\d))?/.exec(e.slice(n,n+6));return r?(t.Z=r[1]?0:-(r[2]+(r[3]||"00")),n+r[0].length):-1}function _r(t,e,n){var r=tt.exec(e.slice(n,n+1));return r?(t.q=r[0]*3-3,n+r[0].length):-1}function Ur(t,e,n){var r=tt.exec(e.slice(n,n+2));return r?(t.m=r[0]-1,n+r[0].length):-1}function Ie(t,e,n){var r=tt.exec(e.slice(n,n+2));return r?(t.d=+r[0],n+r[0].length):-1}function Yr(t,e,n){var r=tt.exec(e.slice(n,n+3));return r?(t.m=0,t.d=+r[0],n+r[0].length):-1}function We(t,e,n){var r=tt.exec(e.slice(n,n+2));return r?(t.H=+r[0],n+r[0].length):-1}function Fr(t,e,n){var r=tt.exec(e.slice(n,n+2));return r?(t.M=+r[0],n+r[0].length):-1}function Lr(t,e,n){var r=tt.exec(e.slice(n,n+2));return r?(t.S=+r[0],n+r[0].length):-1}function Ar(t,e,n){var r=tt.exec(e.slice(n,n+3));return r?(t.L=+r[0],n+r[0].length):-1}function Er(t,e,n){var r=tt.exec(e.slice(n,n+6));return r?(t.L=Math.floor(r[0]/1e3),n+r[0].length):-1}function Ir(t,e,n){var r=Tr.exec(e.slice(n,n+1));return r?n+r[0].length:-1}function Wr(t,e,n){var r=tt.exec(e.slice(n));return r?(t.Q=+r[0],n+r[0].length):-1}function Or(t,e,n){var r=tt.exec(e.slice(n));return r?(t.s=+r[0],n+r[0].length):-1}function Oe(t,e){return P(t.getDate(),e,2)}function Hr(t,e){return P(t.getHours(),e,2)}function Nr(t,e){return P(t.getHours()%12||12,e,2)}function Vr(t,e){return P(1+yt.count(mt(t),t),e,3)}function cn(t,e){return P(t.getMilliseconds(),e,3)}function zr(t,e){return cn(t,e)+"000"}function Pr(t,e){return P(t.getMonth()+1,e,2)}function Rr(t,e){return P(t.getMinutes(),e,2)}function Br(t,e){return P(t.getSeconds(),e,2)}function Zr(t){var e=t.getDay();return e===0?7:e}function Xr(t,e){return P(Ot.count(mt(t)-1,t),e,2)}function ln(t){var e=t.getDay();return e>=4||e===0?kt(t):kt.ceil(t)}function qr(t,e){return t=ln(t),P(kt.count(mt(t),t)+(mt(t).getDay()===4),e,2)}function Gr(t){return t.getDay()}function jr(t,e){return P(It.count(mt(t)-1,t),e,2)}function Qr(t,e){return P(t.getFullYear()%100,e,2)}function Jr(t,e){return t=ln(t),P(t.getFullYear()%100,e,2)}function $r(t,e){return P(t.getFullYear()%1e4,e,4)}function Kr(t,e){var n=t.getDay();return t=n>=4||n===0?kt(t):kt.ceil(t),P(t.getFullYear()%1e4,e,4)}function ti(t){var e=t.getTimezoneOffset();return(e>0?"-":(e*=-1,"+"))+P(e/60|0,"0",2)+P(e%60,"0",2)}function He(t,e){return P(t.getUTCDate(),e,2)}function ei(t,e){return P(t.getUTCHours(),e,2)}function ni(t,e){return P(t.getUTCHours()%12||12,e,2)}function ri(t,e){return P(1+Te.count(pt(t),t),e,3)}function un(t,e){return P(t.getUTCMilliseconds(),e,3)}function ii(t,e){return un(t,e)+"000"}function si(t,e){return P(t.getUTCMonth()+1,e,2)}function ai(t,e){return P(t.getUTCMinutes(),e,2)}function oi(t,e){return P(t.getUTCSeconds(),e,2)}function ci(t){var e=t.getUTCDay();return e===0?7:e}function li(t,e){return P(on.count(pt(t)-1,t),e,2)}function fn(t){var e=t.getUTCDay();return e>=4||e===0?St(t):St.ceil(t)}function ui(t,e){return t=fn(t),P(St.count(pt(t),t)+(pt(t).getUTCDay()===4),e,2)}function fi(t){return t.getUTCDay()}function hi(t,e){return P(jt.count(pt(t)-1,t),e,2)}function di(t,e){return P(t.getUTCFullYear()%100,e,2)}function mi(t,e){return t=fn(t),P(t.getUTCFullYear()%100,e,2)}function gi(t,e){return P(t.getUTCFullYear()%1e4,e,4)}function yi(t,e){var n=t.getUTCDay();return t=n>=4||n===0?St(t):St.ceil(t),P(t.getUTCFullYear()%1e4,e,4)}function ki(){return"+0000"}function Ne(){return"%"}function Ve(t){return+t}function ze(t){return Math.floor(+t/1e3)}var xt,Qt;pi({dateTime:"%x, %X",date:"%-m/%-d/%Y",time:"%-I:%M:%S %p",periods:["AM","PM"],days:["Sunday","Monday","Tuesday","Wednesday","Thursday","Friday","Saturday"],shortDays:["Sun","Mon","Tue","Wed","Thu","Fri","Sat"],months:["January","February","March","April","May","June","July","August","September","October","November","December"],shortMonths:["Jan","Feb","Mar","Apr","May","Jun","Jul","Aug","Sep","Oct","Nov","Dec"]});function pi(t){return xt=pr(t),Qt=xt.format,xt.parse,xt.utcFormat,xt.utcParse,xt}function Ti(t){return new Date(t)}function vi(t){return t instanceof Date?+t:+new Date(+t)}function hn(t,e,n,r,i,s,a,k,Y,g){var b=Nn(),U=b.invert,C=b.domain,v=g(".%L"),q=g(":%S"),y=g("%I:%M"),L=g("%I %p"),O=g("%a %d"),W=g("%b %d"),B=g("%B"),Z=g("%Y");function Q(x){return(Y(x)<x?v:k(x)<x?q:a(x)<x?y:s(x)<x?L:r(x)<x?i(x)<x?O:W:n(x)<x?B:Z)(x)}return b.invert=function(x){return new Date(U(x))},b.domain=function(x){return arguments.length?C(Array.from(x,vi)):C().map(Ti)},b.ticks=function(x){var E=C();return t(E[0],E[E.length-1],x??10)},b.tickFormat=function(x,E){return E==null?Q:g(E)},b.nice=function(x){var E=C();return(!x||typeof x.range!="function")&&(x=e(E[0],E[E.length-1],x??10)),x?C(ar(E,x)):b},b.copy=function(){return Vn(b,hn(t,e,n,r,i,s,a,k,Y,g))},b}function bi(){return Pn.apply(hn(yr,kr,mt,Wt,Ot,yt,Et,At,gt,Qt).domain([new Date(2e3,0,1),new Date(2e3,0,2)]),arguments)}var dn={exports:{}};(function(t,e){(function(n,r){t.exports=r()})(ye,function(){var n="day";return function(r,i,s){var a=function(g){return g.add(4-g.isoWeekday(),n)},k=i.prototype;k.isoWeekYear=function(){return a(this).year()},k.isoWeek=function(g){if(!this.$utils().u(g))return this.add(7*(g-this.isoWeek()),n);var b,U,C,v,q=a(this),y=(b=this.isoWeekYear(),U=this.$u,C=(U?s.utc:s)().year(b).startOf("year"),v=4-C.isoWeekday(),C.isoWeekday()>4&&(v+=7),C.add(v,n));return q.diff(y,"week")+1},k.isoWeekday=function(g){return this.$utils().u(g)?this.day()||7:this.day(this.day()%7?g:g-7)};var Y=k.startOf;k.startOf=function(g,b){var U=this.$utils(),C=!!U.u(b)||b;return U.p(g)==="isoweek"?C?this.date(this.date()-(this.isoWeekday()-1)).startOf("day"):this.date(this.date()-1-(this.isoWeekday()-1)+7).endOf("day"):Y.bind(this)(g,b)}}})})(dn);var xi=dn.exports;const wi=ke(xi);var mn={exports:{}};(function(t,e){(function(n,r){t.exports=r()})(ye,function(){var n={LTS:"h:mm:ss A",LT:"h:mm A",L:"MM/DD/YYYY",LL:"MMMM D, YYYY",LLL:"MMMM D, YYYY h:mm A",LLLL:"dddd, MMMM D, YYYY h:mm A"},r=/(\[[^[]*\])|([-_:/.,()\s]+)|(A|a|YYYY|YY?|MM?M?M?|Do|DD?|hh?|HH?|mm?|ss?|S{1,3}|z|ZZ?)/g,i=/\d\d/,s=/\d\d?/,a=/\d*[^-_:/,()\s\d]+/,k={},Y=function(y){return(y=+y)+(y>68?1900:2e3)},g=function(y){return function(L){this[y]=+L}},b=[/[+-]\d\d:?(\d\d)?|Z/,function(y){(this.zone||(this.zone={})).offset=function(L){if(!L||L==="Z")return 0;var O=L.match(/([+-]|\d\d)/g),W=60*O[1]+(+O[2]||0);return W===0?0:O[0]==="+"?-W:W}(y)}],U=function(y){var L=k[y];return L&&(L.indexOf?L:L.s.concat(L.f))},C=function(y,L){var O,W=k.meridiem;if(W){for(var B=1;B<=24;B+=1)if(y.indexOf(W(B,0,L))>-1){O=B>12;break}}else O=y===(L?"pm":"PM");return O},v={A:[a,function(y){this.afternoon=C(y,!1)}],a:[a,function(y){this.afternoon=C(y,!0)}],S:[/\d/,function(y){this.milliseconds=100*+y}],SS:[i,function(y){this.milliseconds=10*+y}],SSS:[/\d{3}/,function(y){this.milliseconds=+y}],s:[s,g("seconds")],ss:[s,g("seconds")],m:[s,g("minutes")],mm:[s,g("minutes")],H:[s,g("hours")],h:[s,g("hours")],HH:[s,g("hours")],hh:[s,g("hours")],D:[s,g("day")],DD:[i,g("day")],Do:[a,function(y){var L=k.ordinal,O=y.match(/\d+/);if(this.day=O[0],L)for(var W=1;W<=31;W+=1)L(W).replace(/\[|\]/g,"")===y&&(this.day=W)}],M:[s,g("month")],MM:[i,g("month")],MMM:[a,function(y){var L=U("months"),O=(U("monthsShort")||L.map(function(W){return W.slice(0,3)})).indexOf(y)+1;if(O<1)throw new Error;this.month=O%12||O}],MMMM:[a,function(y){var L=U("months").indexOf(y)+1;if(L<1)throw new Error;this.month=L%12||L}],Y:[/[+-]?\d+/,g("year")],YY:[i,function(y){this.year=Y(y)}],YYYY:[/\d{4}/,g("year")],Z:b,ZZ:b};function q(y){var L,O;L=y,O=k&&k.formats;for(var W=(y=L.replace(/(\[[^\]]+])|(LTS?|l{1,4}|L{1,4})/g,function(F,D,w){var o=w&&w.toUpperCase();return D||O[w]||n[w]||O[o].replace(/(\[[^\]]+])|(MMMM|MM|DD|dddd)/g,function(d,m,u){return m||u.slice(1)})})).match(r),B=W.length,Z=0;Z<B;Z+=1){var Q=W[Z],x=v[Q],E=x&&x[0],T=x&&x[1];W[Z]=T?{regex:E,parser:T}:Q.replace(/^\[|\]$/g,"")}return function(F){for(var D={},w=0,o=0;w<B;w+=1){var d=W[w];if(typeof d=="string")o+=d.length;else{var m=d.regex,u=d.parser,S=F.slice(o),c=m.exec(S)[0];u.call(D,c),F=F.replace(c,"")}}return function(X){var f=X.afternoon;if(f!==void 0){var h=X.hours;f?h<12&&(X.hours+=12):h===12&&(X.hours=0),delete X.afternoon}}(D),D}}return function(y,L,O){O.p.customParseFormat=!0,y&&y.parseTwoDigitYear&&(Y=y.parseTwoDigitYear);var W=L.prototype,B=W.parse;W.parse=function(Z){var Q=Z.date,x=Z.utc,E=Z.args;this.$u=x;var T=E[1];if(typeof T=="string"){var F=E[2]===!0,D=E[3]===!0,w=F||D,o=E[2];D&&(o=E[2]),k=this.$locale(),!F&&o&&(k=O.Ls[o]),this.$d=function(S,c,X){try{if(["x","X"].indexOf(c)>-1)return new Date((c==="X"?1e3:1)*S);var f=q(c)(S),h=f.year,_=f.month,G=f.day,H=f.hours,V=f.minutes,I=f.seconds,z=f.milliseconds,st=f.zone,it=new Date,p=G||(h||_?1:it.getDate()),A=h||it.getFullYear(),M=0;h&&!_||(M=_>0?_-1:it.getMonth());var l=H||0,R=V||0,N=I||0,j=z||0;return st?new Date(Date.UTC(A,M,p,l,R,N,j+60*st.offset*1e3)):X?new Date(Date.UTC(A,M,p,l,R,N,j)):new Date(A,M,p,l,R,N,j)}catch{return new Date("")}}(Q,T,x),this.init(),o&&o!==!0&&(this.$L=this.locale(o).$L),w&&Q!=this.format(T)&&(this.$d=new Date("")),k={}}else if(T instanceof Array)for(var d=T.length,m=1;m<=d;m+=1){E[1]=T[m-1];var u=O.apply(this,E);if(u.isValid()){this.$d=u.$d,this.$L=u.$L,this.init();break}m===d&&(this.$d=new Date(""))}else B.call(this,Z)}}})})(mn);var Ci=mn.exports;const Di=ke(Ci);var gn={exports:{}};(function(t,e){(function(n,r){t.exports=r()})(ye,function(){return function(n,r){var i=r.prototype,s=i.format;i.format=function(a){var k=this,Y=this.$locale();if(!this.isValid())return s.bind(this)(a);var g=this.$utils(),b=(a||"YYYY-MM-DDTHH:mm:ssZ").replace(/\[([^\]]+)]|Q|wo|ww|w|WW|W|zzz|z|gggg|GGGG|Do|X|x|k{1,2}|S/g,function(U){switch(U){case"Q":return Math.ceil((k.$M+1)/3);case"Do":return Y.ordinal(k.$D);case"gggg":return k.weekYear();case"GGGG":return k.isoWeekYear();case"wo":return Y.ordinal(k.week(),"W");case"w":case"ww":return g.s(k.week(),U==="w"?1:2,"0");case"W":case"WW":return g.s(k.isoWeek(),U==="W"?1:2,"0");case"k":case"kk":return g.s(String(k.$H===0?24:k.$H),U==="k"?1:2,"0");case"X":return Math.floor(k.$d.getTime()/1e3);case"x":return k.$d.getTime();case"z":return"["+k.offsetName()+"]";case"zzz":return"["+k.offsetName("long")+"]";default:return U}});return s.bind(this)(b)}}})})(gn);var Mi=gn.exports;const Si=ke(Mi);var he=function(){var t=function(w,o,d,m){for(d=d||{},m=w.length;m--;d[w[m]]=o);return d},e=[6,8,10,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,30,32,33,35,37],n=[1,25],r=[1,26],i=[1,27],s=[1,28],a=[1,29],k=[1,30],Y=[1,31],g=[1,9],b=[1,10],U=[1,11],C=[1,12],v=[1,13],q=[1,14],y=[1,15],L=[1,16],O=[1,18],W=[1,19],B=[1,20],Z=[1,21],Q=[1,22],x=[1,24],E=[1,32],T={trace:function(){},yy:{},symbols_:{error:2,start:3,gantt:4,document:5,EOF:6,line:7,SPACE:8,statement:9,NL:10,weekday:11,weekday_monday:12,weekday_tuesday:13,weekday_wednesday:14,weekday_thursday:15,weekday_friday:16,weekday_saturday:17,weekday_sunday:18,dateFormat:19,inclusiveEndDates:20,topAxis:21,axisFormat:22,tickInterval:23,excludes:24,includes:25,todayMarker:26,title:27,acc_title:28,acc_title_value:29,acc_descr:30,acc_descr_value:31,acc_descr_multiline_value:32,section:33,clickStatement:34,taskTxt:35,taskData:36,click:37,callbackname:38,callbackargs:39,href:40,clickStatementDebug:41,$accept:0,$end:1},terminals_:{2:"error",4:"gantt",6:"EOF",8:"SPACE",10:"NL",12:"weekday_monday",13:"weekday_tuesday",14:"weekday_wednesday",15:"weekday_thursday",16:"weekday_friday",17:"weekday_saturday",18:"weekday_sunday",19:"dateFormat",20:"inclusiveEndDates",21:"topAxis",22:"axisFormat",23:"tickInterval",24:"excludes",25:"includes",26:"todayMarker",27:"title",28:"acc_title",29:"acc_title_value",30:"acc_descr",31:"acc_descr_value",32:"acc_descr_multiline_value",33:"section",35:"taskTxt",36:"taskData",37:"click",38:"callbackname",39:"callbackargs",40:"href"},productions_:[0,[3,3],[5,0],[5,2],[7,2],[7,1],[7,1],[7,1],[11,1],[11,1],[11,1],[11,1],[11,1],[11,1],[11,1],[9,1],[9,1],[9,1],[9,1],[9,1],[9,1],[9,1],[9,1],[9,1],[9,1],[9,2],[9,2],[9,1],[9,1],[9,1],[9,2],[34,2],[34,3],[34,3],[34,4],[34,3],[34,4],[34,2],[41,2],[41,3],[41,3],[41,4],[41,3],[41,4],[41,2]],performAction:function(o,d,m,u,S,c,X){var f=c.length-1;switch(S){case 1:return c[f-1];case 2:this.$=[];break;case 3:c[f-1].push(c[f]),this.$=c[f-1];break;case 4:case 5:this.$=c[f];break;case 6:case 7:this.$=[];break;case 8:u.setWeekday("monday");break;case 9:u.setWeekday("tuesday");break;case 10:u.setWeekday("wednesday");break;case 11:u.setWeekday("thursday");break;case 12:u.setWeekday("friday");break;case 13:u.setWeekday("saturday");break;case 14:u.setWeekday("sunday");break;case 15:u.setDateFormat(c[f].substr(11)),this.$=c[f].substr(11);break;case 16:u.enableInclusiveEndDates(),this.$=c[f].substr(18);break;case 17:u.TopAxis(),this.$=c[f].substr(8);break;case 18:u.setAxisFormat(c[f].substr(11)),this.$=c[f].substr(11);break;case 19:u.setTickInterval(c[f].substr(13)),this.$=c[f].substr(13);break;case 20:u.setExcludes(c[f].substr(9)),this.$=c[f].substr(9);break;case 21:u.setIncludes(c[f].substr(9)),this.$=c[f].substr(9);break;case 22:u.setTodayMarker(c[f].substr(12)),this.$=c[f].substr(12);break;case 24:u.setDiagramTitle(c[f].substr(6)),this.$=c[f].substr(6);break;case 25:this.$=c[f].trim(),u.setAccTitle(this.$);break;case 26:case 27:this.$=c[f].trim(),u.setAccDescription(this.$);break;case 28:u.addSection(c[f].substr(8)),this.$=c[f].substr(8);break;case 30:u.addTask(c[f-1],c[f]),this.$="task";break;case 31:this.$=c[f-1],u.setClickEvent(c[f-1],c[f],null);break;case 32:this.$=c[f-2],u.setClickEvent(c[f-2],c[f-1],c[f]);break;case 33:this.$=c[f-2],u.setClickEvent(c[f-2],c[f-1],null),u.setLink(c[f-2],c[f]);break;case 34:this.$=c[f-3],u.setClickEvent(c[f-3],c[f-2],c[f-1]),u.setLink(c[f-3],c[f]);break;case 35:this.$=c[f-2],u.setClickEvent(c[f-2],c[f],null),u.setLink(c[f-2],c[f-1]);break;case 36:this.$=c[f-3],u.setClickEvent(c[f-3],c[f-1],c[f]),u.setLink(c[f-3],c[f-2]);break;case 37:this.$=c[f-1],u.setLink(c[f-1],c[f]);break;case 38:case 44:this.$=c[f-1]+" "+c[f];break;case 39:case 40:case 42:this.$=c[f-2]+" "+c[f-1]+" "+c[f];break;case 41:case 43:this.$=c[f-3]+" "+c[f-2]+" "+c[f-1]+" "+c[f];break}},table:[{3:1,4:[1,2]},{1:[3]},t(e,[2,2],{5:3}),{6:[1,4],7:5,8:[1,6],9:7,10:[1,8],11:17,12:n,13:r,14:i,15:s,16:a,17:k,18:Y,19:g,20:b,21:U,22:C,23:v,24:q,25:y,26:L,27:O,28:W,30:B,32:Z,33:Q,34:23,35:x,37:E},t(e,[2,7],{1:[2,1]}),t(e,[2,3]),{9:33,11:17,12:n,13:r,14:i,15:s,16:a,17:k,18:Y,19:g,20:b,21:U,22:C,23:v,24:q,25:y,26:L,27:O,28:W,30:B,32:Z,33:Q,34:23,35:x,37:E},t(e,[2,5]),t(e,[2,6]),t(e,[2,15]),t(e,[2,16]),t(e,[2,17]),t(e,[2,18]),t(e,[2,19]),t(e,[2,20]),t(e,[2,21]),t(e,[2,22]),t(e,[2,23]),t(e,[2,24]),{29:[1,34]},{31:[1,35]},t(e,[2,27]),t(e,[2,28]),t(e,[2,29]),{36:[1,36]},t(e,[2,8]),t(e,[2,9]),t(e,[2,10]),t(e,[2,11]),t(e,[2,12]),t(e,[2,13]),t(e,[2,14]),{38:[1,37],40:[1,38]},t(e,[2,4]),t(e,[2,25]),t(e,[2,26]),t(e,[2,30]),t(e,[2,31],{39:[1,39],40:[1,40]}),t(e,[2,37],{38:[1,41]}),t(e,[2,32],{40:[1,42]}),t(e,[2,33]),t(e,[2,35],{39:[1,43]}),t(e,[2,34]),t(e,[2,36])],defaultActions:{},parseError:function(o,d){if(d.recoverable)this.trace(o);else{var m=new Error(o);throw m.hash=d,m}},parse:function(o){var d=this,m=[0],u=[],S=[null],c=[],X=this.table,f="",h=0,_=0,G=2,H=1,V=c.slice.call(arguments,1),I=Object.create(this.lexer),z={yy:{}};for(var st in this.yy)Object.prototype.hasOwnProperty.call(this.yy,st)&&(z.yy[st]=this.yy[st]);I.setInput(o,z.yy),z.yy.lexer=I,z.yy.parser=this,typeof I.yylloc>"u"&&(I.yylloc={});var it=I.yylloc;c.push(it);var p=I.options&&I.options.ranges;typeof z.yy.parseError=="function"?this.parseError=z.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function A(){var ct;return ct=u.pop()||I.lex()||H,typeof ct!="number"&&(ct instanceof Array&&(u=ct,ct=u.pop()),ct=d.symbols_[ct]||ct),ct}for(var M,l,R,N,j={},J,et,Ut,zt;;){if(l=m[m.length-1],this.defaultActions[l]?R=this.defaultActions[l]:((M===null||typeof M>"u")&&(M=A()),R=X[l]&&X[l][M]),typeof R>"u"||!R.length||!R[0]){var $t="";zt=[];for(J in X[l])this.terminals_[J]&&J>G&&zt.push("'"+this.terminals_[J]+"'");I.showPosition?$t="Parse error on line "+(h+1)+`:
 `+I.showPosition()+`
 Expecting `+zt.join(", ")+", got '"+(this.terminals_[M]||M)+"'":$t="Parse error on line "+(h+1)+": Unexpected "+(M==H?"end of input":"'"+(this.terminals_[M]||M)+"'"),this.parseError($t,{text:I.match,token:this.terminals_[M]||M,line:I.yylineno,loc:it,expected:zt})}if(R[0]instanceof Array&&R.length>1)throw new Error("Parse Error: multiple actions possible at state: "+l+", token: "+M);switch(R[0]){case 1:m.push(M),S.push(I.yytext),c.push(I.yylloc),m.push(R[1]),M=null,_=I.yyleng,f=I.yytext,h=I.yylineno,it=I.yylloc;break;case 2:if(et=this.productions_[R[1]][1],j.$=S[S.length-et],j._$={first_line:c[c.length-(et||1)].first_line,last_line:c[c.length-1].last_line,first_column:c[c.length-(et||1)].first_column,last_column:c[c.length-1].last_column},p&&(j._$.range=[c[c.length-(et||1)].range[0],c[c.length-1].range[1]]),N=this.performAction.apply(j,[f,_,h,z.yy,R[1],S,c].concat(V)),typeof N<"u")return N;et&&(m=m.slice(0,-1*et*2),S=S.slice(0,-1*et),c=c.slice(0,-1*et)),m.push(this.productions_[R[1]][0]),S.push(j.$),c.push(j._$),Ut=X[m[m.length-2]][m[m.length-1]],m.push(Ut);break;case 3:return!0}}return!0}},F=function(){var w={EOF:1,parseError:function(d,m){if(this.yy.parser)this.yy.parser.parseError(d,m);else throw new Error(d)},setInput:function(o,d){return this.yy=d||this.yy||{},this._input=o,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var o=this._input[0];this.yytext+=o,this.yyleng++,this.offset++,this.match+=o,this.matched+=o;var d=o.match(/(?:\r\n?|\n).*/g);return d?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),o},unput:function(o){var d=o.length,m=o.split(/(?:\r\n?|\n)/g);this._input=o+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-d),this.offset-=d;var u=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),m.length-1&&(this.yylineno-=m.length-1);var S=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:m?(m.length===u.length?this.yylloc.first_column:0)+u[u.length-m.length].length-m[0].length:this.yylloc.first_column-d},this.options.ranges&&(this.yylloc.range=[S[0],S[0]+this.yyleng-d]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){if(this.options.backtrack_lexer)this._backtrack=!0;else return this.parseError("Lexical error on line "+(this.yylineno+1)+`. You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).
 `+this.showPosition(),{text:"",token:null,line:this.yylineno});return this},less:function(o){this.unput(this.match.slice(o))},pastInput:function(){var o=this.matched.substr(0,this.matched.length-this.match.length);return(o.length>20?"...":"")+o.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var o=this.match;return o.length<20&&(o+=this._input.substr(0,20-o.length)),(o.substr(0,20)+(o.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var o=this.pastInput(),d=new Array(o.length+1).join("-");return o+this.upcomingInput()+`
diff --git a/assets/gitGraphDiagram-23af1bdb-BuC3CTB9.js b/assets/gitGraphDiagram-23af1bdb-Dd7cNN9F.js
similarity index 99%
rename from assets/gitGraphDiagram-23af1bdb-BuC3CTB9.js
rename to assets/gitGraphDiagram-23af1bdb-Dd7cNN9F.js
index 074d938..3159266 100644
--- a/assets/gitGraphDiagram-23af1bdb-BuC3CTB9.js
+++ b/assets/gitGraphDiagram-23af1bdb-Dd7cNN9F.js
@@ -1,4 +1,4 @@
-import{c as C,s as vt,g as Ct,a as Ot,b as Pt,x as At,y as Gt,l as B,j as D,A as St,h as It,z as Nt,as as Ht,at as Bt}from"./mermaid.core-ChLYKTZm.js";import"./app-B69Gl_S-.js";var mt=function(){var r=function(G,o,u,d){for(u=u||{},d=G.length;d--;u[G[d]]=o);return u},n=[1,3],l=[1,6],h=[1,4],i=[1,5],c=[2,5],p=[1,12],m=[5,7,13,19,21,23,24,26,28,31,37,40,47],x=[7,13,19,21,23,24,26,28,31,37,40],y=[7,12,13,19,21,23,24,26,28,31,37,40],a=[7,13,47],R=[1,42],_=[1,41],b=[7,13,29,32,35,38,47],f=[1,55],k=[1,56],g=[1,57],E=[7,13,32,35,42,47],z={trace:function(){},yy:{},symbols_:{error:2,start:3,eol:4,GG:5,document:6,EOF:7,":":8,DIR:9,options:10,body:11,OPT:12,NL:13,line:14,statement:15,commitStatement:16,mergeStatement:17,cherryPickStatement:18,acc_title:19,acc_title_value:20,acc_descr:21,acc_descr_value:22,acc_descr_multiline_value:23,section:24,branchStatement:25,CHECKOUT:26,ref:27,BRANCH:28,ORDER:29,NUM:30,CHERRY_PICK:31,COMMIT_ID:32,STR:33,PARENT_COMMIT:34,COMMIT_TAG:35,EMPTYSTR:36,MERGE:37,COMMIT_TYPE:38,commitType:39,COMMIT:40,commit_arg:41,COMMIT_MSG:42,NORMAL:43,REVERSE:44,HIGHLIGHT:45,ID:46,";":47,$accept:0,$end:1},terminals_:{2:"error",5:"GG",7:"EOF",8:":",9:"DIR",12:"OPT",13:"NL",19:"acc_title",20:"acc_title_value",21:"acc_descr",22:"acc_descr_value",23:"acc_descr_multiline_value",24:"section",26:"CHECKOUT",28:"BRANCH",29:"ORDER",30:"NUM",31:"CHERRY_PICK",32:"COMMIT_ID",33:"STR",34:"PARENT_COMMIT",35:"COMMIT_TAG",36:"EMPTYSTR",37:"MERGE",38:"COMMIT_TYPE",40:"COMMIT",42:"COMMIT_MSG",43:"NORMAL",44:"REVERSE",45:"HIGHLIGHT",46:"ID",47:";"},productions_:[0,[3,2],[3,3],[3,4],[3,5],[6,0],[6,2],[10,2],[10,1],[11,0],[11,2],[14,2],[14,1],[15,1],[15,1],[15,1],[15,2],[15,2],[15,1],[15,1],[15,1],[15,2],[25,2],[25,4],[18,3],[18,5],[18,5],[18,7],[18,7],[18,5],[18,5],[18,5],[18,7],[18,7],[18,7],[18,7],[17,2],[17,4],[17,4],[17,4],[17,6],[17,6],[17,6],[17,6],[17,6],[17,6],[17,8],[17,8],[17,8],[17,8],[17,8],[17,8],[16,2],[16,3],[16,3],[16,5],[16,5],[16,3],[16,5],[16,5],[16,5],[16,5],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,3],[16,5],[16,5],[16,5],[16,5],[16,5],[16,5],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[41,0],[41,1],[39,1],[39,1],[39,1],[27,1],[27,1],[4,1],[4,1],[4,1]],performAction:function(o,u,d,s,T,t,X){var e=t.length-1;switch(T){case 2:return t[e];case 3:return t[e-1];case 4:return s.setDirection(t[e-3]),t[e-1];case 6:s.setOptions(t[e-1]),this.$=t[e];break;case 7:t[e-1]+=t[e],this.$=t[e-1];break;case 9:this.$=[];break;case 10:t[e-1].push(t[e]),this.$=t[e-1];break;case 11:this.$=t[e-1];break;case 16:this.$=t[e].trim(),s.setAccTitle(this.$);break;case 17:case 18:this.$=t[e].trim(),s.setAccDescription(this.$);break;case 19:s.addSection(t[e].substr(8)),this.$=t[e].substr(8);break;case 21:s.checkout(t[e]);break;case 22:s.branch(t[e]);break;case 23:s.branch(t[e-2],t[e]);break;case 24:s.cherryPick(t[e],"",void 0);break;case 25:s.cherryPick(t[e-2],"",void 0,t[e]);break;case 26:s.cherryPick(t[e-2],"",t[e]);break;case 27:s.cherryPick(t[e-4],"",t[e],t[e-2]);break;case 28:s.cherryPick(t[e-4],"",t[e-2],t[e]);break;case 29:s.cherryPick(t[e],"",t[e-2]);break;case 30:s.cherryPick(t[e],"","");break;case 31:s.cherryPick(t[e-2],"","");break;case 32:s.cherryPick(t[e-4],"","",t[e-2]);break;case 33:s.cherryPick(t[e-4],"","",t[e]);break;case 34:s.cherryPick(t[e-2],"",t[e-4],t[e]);break;case 35:s.cherryPick(t[e-2],"","",t[e]);break;case 36:s.merge(t[e],"","","");break;case 37:s.merge(t[e-2],t[e],"","");break;case 38:s.merge(t[e-2],"",t[e],"");break;case 39:s.merge(t[e-2],"","",t[e]);break;case 40:s.merge(t[e-4],t[e],"",t[e-2]);break;case 41:s.merge(t[e-4],"",t[e],t[e-2]);break;case 42:s.merge(t[e-4],"",t[e-2],t[e]);break;case 43:s.merge(t[e-4],t[e-2],t[e],"");break;case 44:s.merge(t[e-4],t[e-2],"",t[e]);break;case 45:s.merge(t[e-4],t[e],t[e-2],"");break;case 46:s.merge(t[e-6],t[e-4],t[e-2],t[e]);break;case 47:s.merge(t[e-6],t[e],t[e-4],t[e-2]);break;case 48:s.merge(t[e-6],t[e-4],t[e],t[e-2]);break;case 49:s.merge(t[e-6],t[e-2],t[e-4],t[e]);break;case 50:s.merge(t[e-6],t[e],t[e-2],t[e-4]);break;case 51:s.merge(t[e-6],t[e-2],t[e],t[e-4]);break;case 52:s.commit(t[e]);break;case 53:s.commit("","",s.commitType.NORMAL,t[e]);break;case 54:s.commit("","",t[e],"");break;case 55:s.commit("","",t[e],t[e-2]);break;case 56:s.commit("","",t[e-2],t[e]);break;case 57:s.commit("",t[e],s.commitType.NORMAL,"");break;case 58:s.commit("",t[e-2],s.commitType.NORMAL,t[e]);break;case 59:s.commit("",t[e],s.commitType.NORMAL,t[e-2]);break;case 60:s.commit("",t[e-2],t[e],"");break;case 61:s.commit("",t[e],t[e-2],"");break;case 62:s.commit("",t[e-4],t[e-2],t[e]);break;case 63:s.commit("",t[e-4],t[e],t[e-2]);break;case 64:s.commit("",t[e-2],t[e-4],t[e]);break;case 65:s.commit("",t[e],t[e-4],t[e-2]);break;case 66:s.commit("",t[e],t[e-2],t[e-4]);break;case 67:s.commit("",t[e-2],t[e],t[e-4]);break;case 68:s.commit(t[e],"",s.commitType.NORMAL,"");break;case 69:s.commit(t[e],"",s.commitType.NORMAL,t[e-2]);break;case 70:s.commit(t[e-2],"",s.commitType.NORMAL,t[e]);break;case 71:s.commit(t[e-2],"",t[e],"");break;case 72:s.commit(t[e],"",t[e-2],"");break;case 73:s.commit(t[e],t[e-2],s.commitType.NORMAL,"");break;case 74:s.commit(t[e-2],t[e],s.commitType.NORMAL,"");break;case 75:s.commit(t[e-4],"",t[e-2],t[e]);break;case 76:s.commit(t[e-4],"",t[e],t[e-2]);break;case 77:s.commit(t[e-2],"",t[e-4],t[e]);break;case 78:s.commit(t[e],"",t[e-4],t[e-2]);break;case 79:s.commit(t[e],"",t[e-2],t[e-4]);break;case 80:s.commit(t[e-2],"",t[e],t[e-4]);break;case 81:s.commit(t[e-4],t[e],t[e-2],"");break;case 82:s.commit(t[e-4],t[e-2],t[e],"");break;case 83:s.commit(t[e-2],t[e],t[e-4],"");break;case 84:s.commit(t[e],t[e-2],t[e-4],"");break;case 85:s.commit(t[e],t[e-4],t[e-2],"");break;case 86:s.commit(t[e-2],t[e-4],t[e],"");break;case 87:s.commit(t[e-4],t[e],s.commitType.NORMAL,t[e-2]);break;case 88:s.commit(t[e-4],t[e-2],s.commitType.NORMAL,t[e]);break;case 89:s.commit(t[e-2],t[e],s.commitType.NORMAL,t[e-4]);break;case 90:s.commit(t[e],t[e-2],s.commitType.NORMAL,t[e-4]);break;case 91:s.commit(t[e],t[e-4],s.commitType.NORMAL,t[e-2]);break;case 92:s.commit(t[e-2],t[e-4],s.commitType.NORMAL,t[e]);break;case 93:s.commit(t[e-6],t[e-4],t[e-2],t[e]);break;case 94:s.commit(t[e-6],t[e-4],t[e],t[e-2]);break;case 95:s.commit(t[e-6],t[e-2],t[e-4],t[e]);break;case 96:s.commit(t[e-6],t[e],t[e-4],t[e-2]);break;case 97:s.commit(t[e-6],t[e-2],t[e],t[e-4]);break;case 98:s.commit(t[e-6],t[e],t[e-2],t[e-4]);break;case 99:s.commit(t[e-4],t[e-6],t[e-2],t[e]);break;case 100:s.commit(t[e-4],t[e-6],t[e],t[e-2]);break;case 101:s.commit(t[e-2],t[e-6],t[e-4],t[e]);break;case 102:s.commit(t[e],t[e-6],t[e-4],t[e-2]);break;case 103:s.commit(t[e-2],t[e-6],t[e],t[e-4]);break;case 104:s.commit(t[e],t[e-6],t[e-2],t[e-4]);break;case 105:s.commit(t[e],t[e-4],t[e-2],t[e-6]);break;case 106:s.commit(t[e-2],t[e-4],t[e],t[e-6]);break;case 107:s.commit(t[e],t[e-2],t[e-4],t[e-6]);break;case 108:s.commit(t[e-2],t[e],t[e-4],t[e-6]);break;case 109:s.commit(t[e-4],t[e-2],t[e],t[e-6]);break;case 110:s.commit(t[e-4],t[e],t[e-2],t[e-6]);break;case 111:s.commit(t[e-2],t[e-4],t[e-6],t[e]);break;case 112:s.commit(t[e],t[e-4],t[e-6],t[e-2]);break;case 113:s.commit(t[e-2],t[e],t[e-6],t[e-4]);break;case 114:s.commit(t[e],t[e-2],t[e-6],t[e-4]);break;case 115:s.commit(t[e-4],t[e-2],t[e-6],t[e]);break;case 116:s.commit(t[e-4],t[e],t[e-6],t[e-2]);break;case 117:this.$="";break;case 118:this.$=t[e];break;case 119:this.$=s.commitType.NORMAL;break;case 120:this.$=s.commitType.REVERSE;break;case 121:this.$=s.commitType.HIGHLIGHT;break}},table:[{3:1,4:2,5:n,7:l,13:h,47:i},{1:[3]},{3:7,4:2,5:n,7:l,13:h,47:i},{6:8,7:c,8:[1,9],9:[1,10],10:11,13:p},r(m,[2,124]),r(m,[2,125]),r(m,[2,126]),{1:[2,1]},{7:[1,13]},{6:14,7:c,10:11,13:p},{8:[1,15]},r(x,[2,9],{11:16,12:[1,17]}),r(y,[2,8]),{1:[2,2]},{7:[1,18]},{6:19,7:c,10:11,13:p},{7:[2,6],13:[1,22],14:20,15:21,16:23,17:24,18:25,19:[1,26],21:[1,27],23:[1,28],24:[1,29],25:30,26:[1,31],28:[1,35],31:[1,34],37:[1,33],40:[1,32]},r(y,[2,7]),{1:[2,3]},{7:[1,36]},r(x,[2,10]),{4:37,7:l,13:h,47:i},r(x,[2,12]),r(a,[2,13]),r(a,[2,14]),r(a,[2,15]),{20:[1,38]},{22:[1,39]},r(a,[2,18]),r(a,[2,19]),r(a,[2,20]),{27:40,33:R,46:_},r(a,[2,117],{41:43,32:[1,46],33:[1,48],35:[1,44],38:[1,45],42:[1,47]}),{27:49,33:R,46:_},{32:[1,50],35:[1,51]},{27:52,33:R,46:_},{1:[2,4]},r(x,[2,11]),r(a,[2,16]),r(a,[2,17]),r(a,[2,21]),r(b,[2,122]),r(b,[2,123]),r(a,[2,52]),{33:[1,53]},{39:54,43:f,44:k,45:g},{33:[1,58]},{33:[1,59]},r(a,[2,118]),r(a,[2,36],{32:[1,60],35:[1,62],38:[1,61]}),{33:[1,63]},{33:[1,64],36:[1,65]},r(a,[2,22],{29:[1,66]}),r(a,[2,53],{32:[1,68],38:[1,67],42:[1,69]}),r(a,[2,54],{32:[1,71],35:[1,70],42:[1,72]}),r(E,[2,119]),r(E,[2,120]),r(E,[2,121]),r(a,[2,57],{35:[1,73],38:[1,74],42:[1,75]}),r(a,[2,68],{32:[1,78],35:[1,76],38:[1,77]}),{33:[1,79]},{39:80,43:f,44:k,45:g},{33:[1,81]},r(a,[2,24],{34:[1,82],35:[1,83]}),{32:[1,84]},{32:[1,85]},{30:[1,86]},{39:87,43:f,44:k,45:g},{33:[1,88]},{33:[1,89]},{33:[1,90]},{33:[1,91]},{33:[1,92]},{33:[1,93]},{39:94,43:f,44:k,45:g},{33:[1,95]},{33:[1,96]},{39:97,43:f,44:k,45:g},{33:[1,98]},r(a,[2,37],{35:[1,100],38:[1,99]}),r(a,[2,38],{32:[1,102],35:[1,101]}),r(a,[2,39],{32:[1,103],38:[1,104]}),{33:[1,105]},{33:[1,106],36:[1,107]},{33:[1,108]},{33:[1,109]},r(a,[2,23]),r(a,[2,55],{32:[1,110],42:[1,111]}),r(a,[2,59],{38:[1,112],42:[1,113]}),r(a,[2,69],{32:[1,115],38:[1,114]}),r(a,[2,56],{32:[1,116],42:[1,117]}),r(a,[2,61],{35:[1,118],42:[1,119]}),r(a,[2,72],{32:[1,121],35:[1,120]}),r(a,[2,58],{38:[1,122],42:[1,123]}),r(a,[2,60],{35:[1,124],42:[1,125]}),r(a,[2,73],{35:[1,127],38:[1,126]}),r(a,[2,70],{32:[1,129],38:[1,128]}),r(a,[2,71],{32:[1,131],35:[1,130]}),r(a,[2,74],{35:[1,133],38:[1,132]}),{39:134,43:f,44:k,45:g},{33:[1,135]},{33:[1,136]},{33:[1,137]},{33:[1,138]},{39:139,43:f,44:k,45:g},r(a,[2,25],{35:[1,140]}),r(a,[2,26],{34:[1,141]}),r(a,[2,31],{34:[1,142]}),r(a,[2,29],{34:[1,143]}),r(a,[2,30],{34:[1,144]}),{33:[1,145]},{33:[1,146]},{39:147,43:f,44:k,45:g},{33:[1,148]},{39:149,43:f,44:k,45:g},{33:[1,150]},{33:[1,151]},{33:[1,152]},{33:[1,153]},{33:[1,154]},{33:[1,155]},{33:[1,156]},{39:157,43:f,44:k,45:g},{33:[1,158]},{33:[1,159]},{33:[1,160]},{39:161,43:f,44:k,45:g},{33:[1,162]},{39:163,43:f,44:k,45:g},{33:[1,164]},{33:[1,165]},{33:[1,166]},{39:167,43:f,44:k,45:g},{33:[1,168]},r(a,[2,43],{35:[1,169]}),r(a,[2,44],{38:[1,170]}),r(a,[2,42],{32:[1,171]}),r(a,[2,45],{35:[1,172]}),r(a,[2,40],{38:[1,173]}),r(a,[2,41],{32:[1,174]}),{33:[1,175],36:[1,176]},{33:[1,177]},{33:[1,178]},{33:[1,179]},{33:[1,180]},r(a,[2,66],{42:[1,181]}),r(a,[2,79],{32:[1,182]}),r(a,[2,67],{42:[1,183]}),r(a,[2,90],{38:[1,184]}),r(a,[2,80],{32:[1,185]}),r(a,[2,89],{38:[1,186]}),r(a,[2,65],{42:[1,187]}),r(a,[2,78],{32:[1,188]}),r(a,[2,64],{42:[1,189]}),r(a,[2,84],{35:[1,190]}),r(a,[2,77],{32:[1,191]}),r(a,[2,83],{35:[1,192]}),r(a,[2,63],{42:[1,193]}),r(a,[2,91],{38:[1,194]}),r(a,[2,62],{42:[1,195]}),r(a,[2,85],{35:[1,196]}),r(a,[2,86],{35:[1,197]}),r(a,[2,92],{38:[1,198]}),r(a,[2,76],{32:[1,199]}),r(a,[2,87],{38:[1,200]}),r(a,[2,75],{32:[1,201]}),r(a,[2,81],{35:[1,202]}),r(a,[2,82],{35:[1,203]}),r(a,[2,88],{38:[1,204]}),{33:[1,205]},{39:206,43:f,44:k,45:g},{33:[1,207]},{33:[1,208]},{39:209,43:f,44:k,45:g},{33:[1,210]},r(a,[2,27]),r(a,[2,32]),r(a,[2,28]),r(a,[2,33]),r(a,[2,34]),r(a,[2,35]),{33:[1,211]},{33:[1,212]},{33:[1,213]},{39:214,43:f,44:k,45:g},{33:[1,215]},{39:216,43:f,44:k,45:g},{33:[1,217]},{33:[1,218]},{33:[1,219]},{33:[1,220]},{33:[1,221]},{33:[1,222]},{33:[1,223]},{39:224,43:f,44:k,45:g},{33:[1,225]},{33:[1,226]},{33:[1,227]},{39:228,43:f,44:k,45:g},{33:[1,229]},{39:230,43:f,44:k,45:g},{33:[1,231]},{33:[1,232]},{33:[1,233]},{39:234,43:f,44:k,45:g},r(a,[2,46]),r(a,[2,48]),r(a,[2,47]),r(a,[2,49]),r(a,[2,51]),r(a,[2,50]),r(a,[2,107]),r(a,[2,108]),r(a,[2,105]),r(a,[2,106]),r(a,[2,110]),r(a,[2,109]),r(a,[2,114]),r(a,[2,113]),r(a,[2,112]),r(a,[2,111]),r(a,[2,116]),r(a,[2,115]),r(a,[2,104]),r(a,[2,103]),r(a,[2,102]),r(a,[2,101]),r(a,[2,99]),r(a,[2,100]),r(a,[2,98]),r(a,[2,97]),r(a,[2,96]),r(a,[2,95]),r(a,[2,93]),r(a,[2,94])],defaultActions:{7:[2,1],13:[2,2],18:[2,3],36:[2,4]},parseError:function(o,u){if(u.recoverable)this.trace(o);else{var d=new Error(o);throw d.hash=u,d}},parse:function(o){var u=this,d=[0],s=[],T=[null],t=[],X=this.table,e="",rt=0,ft=0,wt=2,pt=1,Lt=t.slice.call(arguments,1),O=Object.create(this.lexer),F={yy:{}};for(var ct in this.yy)Object.prototype.hasOwnProperty.call(this.yy,ct)&&(F.yy[ct]=this.yy[ct]);O.setInput(o,F.yy),F.yy.lexer=O,F.yy.parser=this,typeof O.yylloc>"u"&&(O.yylloc={});var ot=O.yylloc;t.push(ot);var Rt=O.options&&O.options.ranges;typeof F.yy.parseError=="function"?this.parseError=F.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function Mt(){var q;return q=s.pop()||O.lex()||pt,typeof q!="number"&&(q instanceof Array&&(s=q,q=s.pop()),q=u.symbols_[q]||q),q}for(var N,K,V,lt,J={},it,j,bt,st;;){if(K=d[d.length-1],this.defaultActions[K]?V=this.defaultActions[K]:((N===null||typeof N>"u")&&(N=Mt()),V=X[K]&&X[K][N]),typeof V>"u"||!V.length||!V[0]){var ht="";st=[];for(it in X[K])this.terminals_[it]&&it>wt&&st.push("'"+this.terminals_[it]+"'");O.showPosition?ht="Parse error on line "+(rt+1)+`:
+import{c as C,s as vt,g as Ct,a as Ot,b as Pt,x as At,y as Gt,l as B,j as D,A as St,h as It,z as Nt,as as Ht,at as Bt}from"./mermaid.core-DNo_7Q2B.js";import"./app-B4LGNJZ0.js";var mt=function(){var r=function(G,o,u,d){for(u=u||{},d=G.length;d--;u[G[d]]=o);return u},n=[1,3],l=[1,6],h=[1,4],i=[1,5],c=[2,5],p=[1,12],m=[5,7,13,19,21,23,24,26,28,31,37,40,47],x=[7,13,19,21,23,24,26,28,31,37,40],y=[7,12,13,19,21,23,24,26,28,31,37,40],a=[7,13,47],R=[1,42],_=[1,41],b=[7,13,29,32,35,38,47],f=[1,55],k=[1,56],g=[1,57],E=[7,13,32,35,42,47],z={trace:function(){},yy:{},symbols_:{error:2,start:3,eol:4,GG:5,document:6,EOF:7,":":8,DIR:9,options:10,body:11,OPT:12,NL:13,line:14,statement:15,commitStatement:16,mergeStatement:17,cherryPickStatement:18,acc_title:19,acc_title_value:20,acc_descr:21,acc_descr_value:22,acc_descr_multiline_value:23,section:24,branchStatement:25,CHECKOUT:26,ref:27,BRANCH:28,ORDER:29,NUM:30,CHERRY_PICK:31,COMMIT_ID:32,STR:33,PARENT_COMMIT:34,COMMIT_TAG:35,EMPTYSTR:36,MERGE:37,COMMIT_TYPE:38,commitType:39,COMMIT:40,commit_arg:41,COMMIT_MSG:42,NORMAL:43,REVERSE:44,HIGHLIGHT:45,ID:46,";":47,$accept:0,$end:1},terminals_:{2:"error",5:"GG",7:"EOF",8:":",9:"DIR",12:"OPT",13:"NL",19:"acc_title",20:"acc_title_value",21:"acc_descr",22:"acc_descr_value",23:"acc_descr_multiline_value",24:"section",26:"CHECKOUT",28:"BRANCH",29:"ORDER",30:"NUM",31:"CHERRY_PICK",32:"COMMIT_ID",33:"STR",34:"PARENT_COMMIT",35:"COMMIT_TAG",36:"EMPTYSTR",37:"MERGE",38:"COMMIT_TYPE",40:"COMMIT",42:"COMMIT_MSG",43:"NORMAL",44:"REVERSE",45:"HIGHLIGHT",46:"ID",47:";"},productions_:[0,[3,2],[3,3],[3,4],[3,5],[6,0],[6,2],[10,2],[10,1],[11,0],[11,2],[14,2],[14,1],[15,1],[15,1],[15,1],[15,2],[15,2],[15,1],[15,1],[15,1],[15,2],[25,2],[25,4],[18,3],[18,5],[18,5],[18,7],[18,7],[18,5],[18,5],[18,5],[18,7],[18,7],[18,7],[18,7],[17,2],[17,4],[17,4],[17,4],[17,6],[17,6],[17,6],[17,6],[17,6],[17,6],[17,8],[17,8],[17,8],[17,8],[17,8],[17,8],[16,2],[16,3],[16,3],[16,5],[16,5],[16,3],[16,5],[16,5],[16,5],[16,5],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,3],[16,5],[16,5],[16,5],[16,5],[16,5],[16,5],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,7],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[16,9],[41,0],[41,1],[39,1],[39,1],[39,1],[27,1],[27,1],[4,1],[4,1],[4,1]],performAction:function(o,u,d,s,T,t,X){var e=t.length-1;switch(T){case 2:return t[e];case 3:return t[e-1];case 4:return s.setDirection(t[e-3]),t[e-1];case 6:s.setOptions(t[e-1]),this.$=t[e];break;case 7:t[e-1]+=t[e],this.$=t[e-1];break;case 9:this.$=[];break;case 10:t[e-1].push(t[e]),this.$=t[e-1];break;case 11:this.$=t[e-1];break;case 16:this.$=t[e].trim(),s.setAccTitle(this.$);break;case 17:case 18:this.$=t[e].trim(),s.setAccDescription(this.$);break;case 19:s.addSection(t[e].substr(8)),this.$=t[e].substr(8);break;case 21:s.checkout(t[e]);break;case 22:s.branch(t[e]);break;case 23:s.branch(t[e-2],t[e]);break;case 24:s.cherryPick(t[e],"",void 0);break;case 25:s.cherryPick(t[e-2],"",void 0,t[e]);break;case 26:s.cherryPick(t[e-2],"",t[e]);break;case 27:s.cherryPick(t[e-4],"",t[e],t[e-2]);break;case 28:s.cherryPick(t[e-4],"",t[e-2],t[e]);break;case 29:s.cherryPick(t[e],"",t[e-2]);break;case 30:s.cherryPick(t[e],"","");break;case 31:s.cherryPick(t[e-2],"","");break;case 32:s.cherryPick(t[e-4],"","",t[e-2]);break;case 33:s.cherryPick(t[e-4],"","",t[e]);break;case 34:s.cherryPick(t[e-2],"",t[e-4],t[e]);break;case 35:s.cherryPick(t[e-2],"","",t[e]);break;case 36:s.merge(t[e],"","","");break;case 37:s.merge(t[e-2],t[e],"","");break;case 38:s.merge(t[e-2],"",t[e],"");break;case 39:s.merge(t[e-2],"","",t[e]);break;case 40:s.merge(t[e-4],t[e],"",t[e-2]);break;case 41:s.merge(t[e-4],"",t[e],t[e-2]);break;case 42:s.merge(t[e-4],"",t[e-2],t[e]);break;case 43:s.merge(t[e-4],t[e-2],t[e],"");break;case 44:s.merge(t[e-4],t[e-2],"",t[e]);break;case 45:s.merge(t[e-4],t[e],t[e-2],"");break;case 46:s.merge(t[e-6],t[e-4],t[e-2],t[e]);break;case 47:s.merge(t[e-6],t[e],t[e-4],t[e-2]);break;case 48:s.merge(t[e-6],t[e-4],t[e],t[e-2]);break;case 49:s.merge(t[e-6],t[e-2],t[e-4],t[e]);break;case 50:s.merge(t[e-6],t[e],t[e-2],t[e-4]);break;case 51:s.merge(t[e-6],t[e-2],t[e],t[e-4]);break;case 52:s.commit(t[e]);break;case 53:s.commit("","",s.commitType.NORMAL,t[e]);break;case 54:s.commit("","",t[e],"");break;case 55:s.commit("","",t[e],t[e-2]);break;case 56:s.commit("","",t[e-2],t[e]);break;case 57:s.commit("",t[e],s.commitType.NORMAL,"");break;case 58:s.commit("",t[e-2],s.commitType.NORMAL,t[e]);break;case 59:s.commit("",t[e],s.commitType.NORMAL,t[e-2]);break;case 60:s.commit("",t[e-2],t[e],"");break;case 61:s.commit("",t[e],t[e-2],"");break;case 62:s.commit("",t[e-4],t[e-2],t[e]);break;case 63:s.commit("",t[e-4],t[e],t[e-2]);break;case 64:s.commit("",t[e-2],t[e-4],t[e]);break;case 65:s.commit("",t[e],t[e-4],t[e-2]);break;case 66:s.commit("",t[e],t[e-2],t[e-4]);break;case 67:s.commit("",t[e-2],t[e],t[e-4]);break;case 68:s.commit(t[e],"",s.commitType.NORMAL,"");break;case 69:s.commit(t[e],"",s.commitType.NORMAL,t[e-2]);break;case 70:s.commit(t[e-2],"",s.commitType.NORMAL,t[e]);break;case 71:s.commit(t[e-2],"",t[e],"");break;case 72:s.commit(t[e],"",t[e-2],"");break;case 73:s.commit(t[e],t[e-2],s.commitType.NORMAL,"");break;case 74:s.commit(t[e-2],t[e],s.commitType.NORMAL,"");break;case 75:s.commit(t[e-4],"",t[e-2],t[e]);break;case 76:s.commit(t[e-4],"",t[e],t[e-2]);break;case 77:s.commit(t[e-2],"",t[e-4],t[e]);break;case 78:s.commit(t[e],"",t[e-4],t[e-2]);break;case 79:s.commit(t[e],"",t[e-2],t[e-4]);break;case 80:s.commit(t[e-2],"",t[e],t[e-4]);break;case 81:s.commit(t[e-4],t[e],t[e-2],"");break;case 82:s.commit(t[e-4],t[e-2],t[e],"");break;case 83:s.commit(t[e-2],t[e],t[e-4],"");break;case 84:s.commit(t[e],t[e-2],t[e-4],"");break;case 85:s.commit(t[e],t[e-4],t[e-2],"");break;case 86:s.commit(t[e-2],t[e-4],t[e],"");break;case 87:s.commit(t[e-4],t[e],s.commitType.NORMAL,t[e-2]);break;case 88:s.commit(t[e-4],t[e-2],s.commitType.NORMAL,t[e]);break;case 89:s.commit(t[e-2],t[e],s.commitType.NORMAL,t[e-4]);break;case 90:s.commit(t[e],t[e-2],s.commitType.NORMAL,t[e-4]);break;case 91:s.commit(t[e],t[e-4],s.commitType.NORMAL,t[e-2]);break;case 92:s.commit(t[e-2],t[e-4],s.commitType.NORMAL,t[e]);break;case 93:s.commit(t[e-6],t[e-4],t[e-2],t[e]);break;case 94:s.commit(t[e-6],t[e-4],t[e],t[e-2]);break;case 95:s.commit(t[e-6],t[e-2],t[e-4],t[e]);break;case 96:s.commit(t[e-6],t[e],t[e-4],t[e-2]);break;case 97:s.commit(t[e-6],t[e-2],t[e],t[e-4]);break;case 98:s.commit(t[e-6],t[e],t[e-2],t[e-4]);break;case 99:s.commit(t[e-4],t[e-6],t[e-2],t[e]);break;case 100:s.commit(t[e-4],t[e-6],t[e],t[e-2]);break;case 101:s.commit(t[e-2],t[e-6],t[e-4],t[e]);break;case 102:s.commit(t[e],t[e-6],t[e-4],t[e-2]);break;case 103:s.commit(t[e-2],t[e-6],t[e],t[e-4]);break;case 104:s.commit(t[e],t[e-6],t[e-2],t[e-4]);break;case 105:s.commit(t[e],t[e-4],t[e-2],t[e-6]);break;case 106:s.commit(t[e-2],t[e-4],t[e],t[e-6]);break;case 107:s.commit(t[e],t[e-2],t[e-4],t[e-6]);break;case 108:s.commit(t[e-2],t[e],t[e-4],t[e-6]);break;case 109:s.commit(t[e-4],t[e-2],t[e],t[e-6]);break;case 110:s.commit(t[e-4],t[e],t[e-2],t[e-6]);break;case 111:s.commit(t[e-2],t[e-4],t[e-6],t[e]);break;case 112:s.commit(t[e],t[e-4],t[e-6],t[e-2]);break;case 113:s.commit(t[e-2],t[e],t[e-6],t[e-4]);break;case 114:s.commit(t[e],t[e-2],t[e-6],t[e-4]);break;case 115:s.commit(t[e-4],t[e-2],t[e-6],t[e]);break;case 116:s.commit(t[e-4],t[e],t[e-6],t[e-2]);break;case 117:this.$="";break;case 118:this.$=t[e];break;case 119:this.$=s.commitType.NORMAL;break;case 120:this.$=s.commitType.REVERSE;break;case 121:this.$=s.commitType.HIGHLIGHT;break}},table:[{3:1,4:2,5:n,7:l,13:h,47:i},{1:[3]},{3:7,4:2,5:n,7:l,13:h,47:i},{6:8,7:c,8:[1,9],9:[1,10],10:11,13:p},r(m,[2,124]),r(m,[2,125]),r(m,[2,126]),{1:[2,1]},{7:[1,13]},{6:14,7:c,10:11,13:p},{8:[1,15]},r(x,[2,9],{11:16,12:[1,17]}),r(y,[2,8]),{1:[2,2]},{7:[1,18]},{6:19,7:c,10:11,13:p},{7:[2,6],13:[1,22],14:20,15:21,16:23,17:24,18:25,19:[1,26],21:[1,27],23:[1,28],24:[1,29],25:30,26:[1,31],28:[1,35],31:[1,34],37:[1,33],40:[1,32]},r(y,[2,7]),{1:[2,3]},{7:[1,36]},r(x,[2,10]),{4:37,7:l,13:h,47:i},r(x,[2,12]),r(a,[2,13]),r(a,[2,14]),r(a,[2,15]),{20:[1,38]},{22:[1,39]},r(a,[2,18]),r(a,[2,19]),r(a,[2,20]),{27:40,33:R,46:_},r(a,[2,117],{41:43,32:[1,46],33:[1,48],35:[1,44],38:[1,45],42:[1,47]}),{27:49,33:R,46:_},{32:[1,50],35:[1,51]},{27:52,33:R,46:_},{1:[2,4]},r(x,[2,11]),r(a,[2,16]),r(a,[2,17]),r(a,[2,21]),r(b,[2,122]),r(b,[2,123]),r(a,[2,52]),{33:[1,53]},{39:54,43:f,44:k,45:g},{33:[1,58]},{33:[1,59]},r(a,[2,118]),r(a,[2,36],{32:[1,60],35:[1,62],38:[1,61]}),{33:[1,63]},{33:[1,64],36:[1,65]},r(a,[2,22],{29:[1,66]}),r(a,[2,53],{32:[1,68],38:[1,67],42:[1,69]}),r(a,[2,54],{32:[1,71],35:[1,70],42:[1,72]}),r(E,[2,119]),r(E,[2,120]),r(E,[2,121]),r(a,[2,57],{35:[1,73],38:[1,74],42:[1,75]}),r(a,[2,68],{32:[1,78],35:[1,76],38:[1,77]}),{33:[1,79]},{39:80,43:f,44:k,45:g},{33:[1,81]},r(a,[2,24],{34:[1,82],35:[1,83]}),{32:[1,84]},{32:[1,85]},{30:[1,86]},{39:87,43:f,44:k,45:g},{33:[1,88]},{33:[1,89]},{33:[1,90]},{33:[1,91]},{33:[1,92]},{33:[1,93]},{39:94,43:f,44:k,45:g},{33:[1,95]},{33:[1,96]},{39:97,43:f,44:k,45:g},{33:[1,98]},r(a,[2,37],{35:[1,100],38:[1,99]}),r(a,[2,38],{32:[1,102],35:[1,101]}),r(a,[2,39],{32:[1,103],38:[1,104]}),{33:[1,105]},{33:[1,106],36:[1,107]},{33:[1,108]},{33:[1,109]},r(a,[2,23]),r(a,[2,55],{32:[1,110],42:[1,111]}),r(a,[2,59],{38:[1,112],42:[1,113]}),r(a,[2,69],{32:[1,115],38:[1,114]}),r(a,[2,56],{32:[1,116],42:[1,117]}),r(a,[2,61],{35:[1,118],42:[1,119]}),r(a,[2,72],{32:[1,121],35:[1,120]}),r(a,[2,58],{38:[1,122],42:[1,123]}),r(a,[2,60],{35:[1,124],42:[1,125]}),r(a,[2,73],{35:[1,127],38:[1,126]}),r(a,[2,70],{32:[1,129],38:[1,128]}),r(a,[2,71],{32:[1,131],35:[1,130]}),r(a,[2,74],{35:[1,133],38:[1,132]}),{39:134,43:f,44:k,45:g},{33:[1,135]},{33:[1,136]},{33:[1,137]},{33:[1,138]},{39:139,43:f,44:k,45:g},r(a,[2,25],{35:[1,140]}),r(a,[2,26],{34:[1,141]}),r(a,[2,31],{34:[1,142]}),r(a,[2,29],{34:[1,143]}),r(a,[2,30],{34:[1,144]}),{33:[1,145]},{33:[1,146]},{39:147,43:f,44:k,45:g},{33:[1,148]},{39:149,43:f,44:k,45:g},{33:[1,150]},{33:[1,151]},{33:[1,152]},{33:[1,153]},{33:[1,154]},{33:[1,155]},{33:[1,156]},{39:157,43:f,44:k,45:g},{33:[1,158]},{33:[1,159]},{33:[1,160]},{39:161,43:f,44:k,45:g},{33:[1,162]},{39:163,43:f,44:k,45:g},{33:[1,164]},{33:[1,165]},{33:[1,166]},{39:167,43:f,44:k,45:g},{33:[1,168]},r(a,[2,43],{35:[1,169]}),r(a,[2,44],{38:[1,170]}),r(a,[2,42],{32:[1,171]}),r(a,[2,45],{35:[1,172]}),r(a,[2,40],{38:[1,173]}),r(a,[2,41],{32:[1,174]}),{33:[1,175],36:[1,176]},{33:[1,177]},{33:[1,178]},{33:[1,179]},{33:[1,180]},r(a,[2,66],{42:[1,181]}),r(a,[2,79],{32:[1,182]}),r(a,[2,67],{42:[1,183]}),r(a,[2,90],{38:[1,184]}),r(a,[2,80],{32:[1,185]}),r(a,[2,89],{38:[1,186]}),r(a,[2,65],{42:[1,187]}),r(a,[2,78],{32:[1,188]}),r(a,[2,64],{42:[1,189]}),r(a,[2,84],{35:[1,190]}),r(a,[2,77],{32:[1,191]}),r(a,[2,83],{35:[1,192]}),r(a,[2,63],{42:[1,193]}),r(a,[2,91],{38:[1,194]}),r(a,[2,62],{42:[1,195]}),r(a,[2,85],{35:[1,196]}),r(a,[2,86],{35:[1,197]}),r(a,[2,92],{38:[1,198]}),r(a,[2,76],{32:[1,199]}),r(a,[2,87],{38:[1,200]}),r(a,[2,75],{32:[1,201]}),r(a,[2,81],{35:[1,202]}),r(a,[2,82],{35:[1,203]}),r(a,[2,88],{38:[1,204]}),{33:[1,205]},{39:206,43:f,44:k,45:g},{33:[1,207]},{33:[1,208]},{39:209,43:f,44:k,45:g},{33:[1,210]},r(a,[2,27]),r(a,[2,32]),r(a,[2,28]),r(a,[2,33]),r(a,[2,34]),r(a,[2,35]),{33:[1,211]},{33:[1,212]},{33:[1,213]},{39:214,43:f,44:k,45:g},{33:[1,215]},{39:216,43:f,44:k,45:g},{33:[1,217]},{33:[1,218]},{33:[1,219]},{33:[1,220]},{33:[1,221]},{33:[1,222]},{33:[1,223]},{39:224,43:f,44:k,45:g},{33:[1,225]},{33:[1,226]},{33:[1,227]},{39:228,43:f,44:k,45:g},{33:[1,229]},{39:230,43:f,44:k,45:g},{33:[1,231]},{33:[1,232]},{33:[1,233]},{39:234,43:f,44:k,45:g},r(a,[2,46]),r(a,[2,48]),r(a,[2,47]),r(a,[2,49]),r(a,[2,51]),r(a,[2,50]),r(a,[2,107]),r(a,[2,108]),r(a,[2,105]),r(a,[2,106]),r(a,[2,110]),r(a,[2,109]),r(a,[2,114]),r(a,[2,113]),r(a,[2,112]),r(a,[2,111]),r(a,[2,116]),r(a,[2,115]),r(a,[2,104]),r(a,[2,103]),r(a,[2,102]),r(a,[2,101]),r(a,[2,99]),r(a,[2,100]),r(a,[2,98]),r(a,[2,97]),r(a,[2,96]),r(a,[2,95]),r(a,[2,93]),r(a,[2,94])],defaultActions:{7:[2,1],13:[2,2],18:[2,3],36:[2,4]},parseError:function(o,u){if(u.recoverable)this.trace(o);else{var d=new Error(o);throw d.hash=u,d}},parse:function(o){var u=this,d=[0],s=[],T=[null],t=[],X=this.table,e="",rt=0,ft=0,wt=2,pt=1,Lt=t.slice.call(arguments,1),O=Object.create(this.lexer),F={yy:{}};for(var ct in this.yy)Object.prototype.hasOwnProperty.call(this.yy,ct)&&(F.yy[ct]=this.yy[ct]);O.setInput(o,F.yy),F.yy.lexer=O,F.yy.parser=this,typeof O.yylloc>"u"&&(O.yylloc={});var ot=O.yylloc;t.push(ot);var Rt=O.options&&O.options.ranges;typeof F.yy.parseError=="function"?this.parseError=F.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function Mt(){var q;return q=s.pop()||O.lex()||pt,typeof q!="number"&&(q instanceof Array&&(s=q,q=s.pop()),q=u.symbols_[q]||q),q}for(var N,K,V,lt,J={},it,j,bt,st;;){if(K=d[d.length-1],this.defaultActions[K]?V=this.defaultActions[K]:((N===null||typeof N>"u")&&(N=Mt()),V=X[K]&&X[K][N]),typeof V>"u"||!V.length||!V[0]){var ht="";st=[];for(it in X[K])this.terminals_[it]&&it>wt&&st.push("'"+this.terminals_[it]+"'");O.showPosition?ht="Parse error on line "+(rt+1)+`:
 `+O.showPosition()+`
 Expecting `+st.join(", ")+", got '"+(this.terminals_[N]||N)+"'":ht="Parse error on line "+(rt+1)+": Unexpected "+(N==pt?"end of input":"'"+(this.terminals_[N]||N)+"'"),this.parseError(ht,{text:O.match,token:this.terminals_[N]||N,line:O.yylineno,loc:ot,expected:st})}if(V[0]instanceof Array&&V.length>1)throw new Error("Parse Error: multiple actions possible at state: "+K+", token: "+N);switch(V[0]){case 1:d.push(N),T.push(O.yytext),t.push(O.yylloc),d.push(V[1]),N=null,ft=O.yyleng,e=O.yytext,rt=O.yylineno,ot=O.yylloc;break;case 2:if(j=this.productions_[V[1]][1],J.$=T[T.length-j],J._$={first_line:t[t.length-(j||1)].first_line,last_line:t[t.length-1].last_line,first_column:t[t.length-(j||1)].first_column,last_column:t[t.length-1].last_column},Rt&&(J._$.range=[t[t.length-(j||1)].range[0],t[t.length-1].range[1]]),lt=this.performAction.apply(J,[e,ft,rt,F.yy,V[1],T,t].concat(Lt)),typeof lt<"u")return lt;j&&(d=d.slice(0,-1*j*2),T=T.slice(0,-1*j),t=t.slice(0,-1*j)),d.push(this.productions_[V[1]][0]),T.push(J.$),t.push(J._$),bt=X[d[d.length-2]][d[d.length-1]],d.push(bt);break;case 3:return!0}}return!0}},M=function(){var G={EOF:1,parseError:function(u,d){if(this.yy.parser)this.yy.parser.parseError(u,d);else throw new Error(u)},setInput:function(o,u){return this.yy=u||this.yy||{},this._input=o,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var o=this._input[0];this.yytext+=o,this.yyleng++,this.offset++,this.match+=o,this.matched+=o;var u=o.match(/(?:\r\n?|\n).*/g);return u?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),o},unput:function(o){var u=o.length,d=o.split(/(?:\r\n?|\n)/g);this._input=o+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-u),this.offset-=u;var s=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),d.length-1&&(this.yylineno-=d.length-1);var T=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:d?(d.length===s.length?this.yylloc.first_column:0)+s[s.length-d.length].length-d[0].length:this.yylloc.first_column-u},this.options.ranges&&(this.yylloc.range=[T[0],T[0]+this.yyleng-u]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){if(this.options.backtrack_lexer)this._backtrack=!0;else return this.parseError("Lexical error on line "+(this.yylineno+1)+`. You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).
 `+this.showPosition(),{text:"",token:null,line:this.yylineno});return this},less:function(o){this.unput(this.match.slice(o))},pastInput:function(){var o=this.matched.substr(0,this.matched.length-this.match.length);return(o.length>20?"...":"")+o.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var o=this.match;return o.length<20&&(o+=this._input.substr(0,20-o.length)),(o.substr(0,20)+(o.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var o=this.pastInput(),u=new Array(o.length+1).join("-");return o+this.upcomingInput()+`
diff --git "a/assets/github \345\267\245\344\275\234\346\265\201.html-CFTCrRk5.js" "b/assets/github \345\267\245\344\275\234\346\265\201.html-DJORqAx-.js"
similarity index 97%
rename from "assets/github \345\267\245\344\275\234\346\265\201.html-CFTCrRk5.js"
rename to "assets/github \345\267\245\344\275\234\346\265\201.html-DJORqAx-.js"
index 815eb6f..3f53f6d 100644
--- "a/assets/github \345\267\245\344\275\234\346\265\201.html-CFTCrRk5.js"	
+++ "b/assets/github \345\267\245\344\275\234\346\265\201.html-DJORqAx-.js"	
@@ -1 +1 @@
-import{_ as n,r as o,o as i,c as r,b as t,e as a,d as c}from"./app-B69Gl_S-.js";const h={},l=t("h1",{id:"github-工作流程",tabindex:"-1"},[t("a",{class:"header-anchor",href:"#github-工作流程"},[t("span",null,"github 工作流程")])],-1),s={href:"https://www.bilibili.com/video/BV19e4y1q7JJ",target:"_blank",rel:"noopener noreferrer"},p=t("div",{class:"hint-container info"},[t("p",{class:"hint-container-title"},"相关信息"),t("p",null,"TODO")],-1);function g(u,d){const e=o("ExternalLinkIcon");return i(),r("div",null,[l,t("p",null,[t("a",s,[a("十分钟学会正确的github工作流，和开源作者们使用同一套流程"),c(e)])]),p])}const b=n(h,[["render",g],["__file","github 工作流.html.vue"]]),_=JSON.parse('{"path":"/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html","title":"github 工作流程","lang":"zh-CN","frontmatter":{"description":"github 工作流程 十分钟学会正确的github工作流，和开源作者们使用同一套流程 相关信息 TODO","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"github 工作流程"}],["meta",{"property":"og:description","content":"github 工作流程 十分钟学会正确的github工作流，和开源作者们使用同一套流程 相关信息 TODO"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"github 工作流程\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.11,"words":34},"filePathRelative":"tech/github 工作流.md","excerpt":"\\n<p><a href=\\"https://www.bilibili.com/video/BV19e4y1q7JJ\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">十分钟学会正确的github工作流，和开源作者们使用同一套流程</a></p>\\n<div class=\\"hint-container info\\">\\n<p class=\\"hint-container-title\\">相关信息</p>\\n<p>TODO</p>\\n</div>\\n","autoDesc":true}');export{b as comp,_ as data};
+import{_ as n,r as o,o as i,c as r,b as t,e as a,d as c}from"./app-B4LGNJZ0.js";const h={},l=t("h1",{id:"github-工作流程",tabindex:"-1"},[t("a",{class:"header-anchor",href:"#github-工作流程"},[t("span",null,"github 工作流程")])],-1),s={href:"https://www.bilibili.com/video/BV19e4y1q7JJ",target:"_blank",rel:"noopener noreferrer"},p=t("div",{class:"hint-container info"},[t("p",{class:"hint-container-title"},"相关信息"),t("p",null,"TODO")],-1);function g(u,d){const e=o("ExternalLinkIcon");return i(),r("div",null,[l,t("p",null,[t("a",s,[a("十分钟学会正确的github工作流，和开源作者们使用同一套流程"),c(e)])]),p])}const b=n(h,[["render",g],["__file","github 工作流.html.vue"]]),_=JSON.parse('{"path":"/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html","title":"github 工作流程","lang":"zh-CN","frontmatter":{"description":"github 工作流程 十分钟学会正确的github工作流，和开源作者们使用同一套流程 相关信息 TODO","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"github 工作流程"}],["meta",{"property":"og:description","content":"github 工作流程 十分钟学会正确的github工作流，和开源作者们使用同一套流程 相关信息 TODO"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"github 工作流程\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.11,"words":34},"filePathRelative":"tech/github 工作流.md","excerpt":"\\n<p><a href=\\"https://www.bilibili.com/video/BV19e4y1q7JJ\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">十分钟学会正确的github工作流，和开源作者们使用同一套流程</a></p>\\n<div class=\\"hint-container info\\">\\n<p class=\\"hint-container-title\\">相关信息</p>\\n<p>TODO</p>\\n</div>\\n","autoDesc":true}');export{b as comp,_ as data};
diff --git a/assets/graph-T5JS4vfK.js b/assets/graph-B1296pfd.js
similarity index 99%
rename from assets/graph-T5JS4vfK.js
rename to assets/graph-B1296pfd.js
index 1a0bc1f..6eea7a4 100644
--- a/assets/graph-T5JS4vfK.js
+++ b/assets/graph-B1296pfd.js
@@ -1 +1 @@
-import{B as I,C as Ze,S as m,D as y,E as Te,F as qe,G as Xe,H as Je,I as Ee,J as G,K as X,L as Qe,M as me,N as We,O as C,P as x,Q as Oe,R as ve,T as ze,U as Z,V as Ve,W as ke,X as P,Y as en,Z as nn,_ as rn,$ as re,a0 as tn,a1 as sn,a2 as an,a3 as we,a4 as un,a5 as j,a6 as fn,a7 as on,a8 as M,a9 as te,aa as ie}from"./mermaid.core-ChLYKTZm.js";var dn="[object Symbol]";function J(e){return typeof e=="symbol"||I(e)&&Ze(e)==dn}function $e(e,n){for(var r=-1,t=e==null?0:e.length,i=Array(t);++r<t;)i[r]=n(e[r],r,e);return i}var hn=1/0,se=m?m.prototype:void 0,ae=se?se.toString:void 0;function Le(e){if(typeof e=="string")return e;if(y(e))return $e(e,Le)+"";if(J(e))return ae?ae.call(e):"";var n=e+"";return n=="0"&&1/e==-hn?"-0":n}function gn(){}function Pe(e,n){for(var r=-1,t=e==null?0:e.length;++r<t&&n(e[r],r,e)!==!1;);return e}function ln(e,n,r,t){for(var i=e.length,s=r+-1;++s<i;)if(n(e[s],s,e))return s;return-1}function cn(e){return e!==e}function _n(e,n,r){for(var t=r-1,i=e.length;++t<i;)if(e[t]===n)return t;return-1}function pn(e,n,r){return n===n?_n(e,n,r):ln(e,cn,r)}function bn(e,n){var r=e==null?0:e.length;return!!r&&pn(e,n,0)>-1}function T(e){return Te(e)?qe(e):Xe(e)}var yn=/\.|\[(?:[^[\]]*|(["'])(?:(?!\1)[^\\]|\\.)*?\1)\]/,An=/^\w*$/;function Q(e,n){if(y(e))return!1;var r=typeof e;return r=="number"||r=="symbol"||r=="boolean"||e==null||J(e)?!0:An.test(e)||!yn.test(e)||n!=null&&e in Object(n)}var Tn=500;function En(e){var n=Je(e,function(t){return r.size===Tn&&r.clear(),t}),r=n.cache;return n}var mn=/[^.[\]]+|\[(?:(-?\d+(?:\.\d+)?)|(["'])((?:(?!\2)[^\\]|\\.)*?)\2)\]|(?=(?:\.|\[\])(?:\.|\[\]|$))/g,On=/\\(\\)?/g,vn=En(function(e){var n=[];return e.charCodeAt(0)===46&&n.push(""),e.replace(mn,function(r,t,i,s){n.push(i?s.replace(On,"$1"):t||r)}),n});function wn(e){return e==null?"":Le(e)}function Ie(e,n){return y(e)?e:Q(e,n)?[e]:vn(wn(e))}var $n=1/0;function U(e){if(typeof e=="string"||J(e))return e;var n=e+"";return n=="0"&&1/e==-$n?"-0":n}function Ce(e,n){n=Ie(n,e);for(var r=0,t=n.length;e!=null&&r<t;)e=e[U(n[r++])];return r&&r==t?e:void 0}function Ln(e,n,r){var t=e==null?void 0:Ce(e,n);return t===void 0?r:t}function W(e,n){for(var r=-1,t=n.length,i=e.length;++r<t;)e[i+r]=n[r];return e}var ue=m?m.isConcatSpreadable:void 0;function Pn(e){return y(e)||Ee(e)||!!(ue&&e&&e[ue])}function In(e,n,r,t,i){var s=-1,a=e.length;for(r||(r=Pn),i||(i=[]);++s<a;){var u=e[s];r(u)?W(i,u):t||(i[i.length]=u)}return i}function Cn(e,n,r,t){var i=-1,s=e==null?0:e.length;for(t&&s&&(r=e[++i]);++i<s;)r=n(r,e[i],i,e);return r}function Sn(e,n){return e&&G(n,T(n),e)}function Nn(e,n){return e&&G(n,X(n),e)}function Se(e,n){for(var r=-1,t=e==null?0:e.length,i=0,s=[];++r<t;){var a=e[r];n(a,r,e)&&(s[i++]=a)}return s}function Ne(){return[]}var Fn=Object.prototype,Mn=Fn.propertyIsEnumerable,fe=Object.getOwnPropertySymbols,z=fe?function(e){return e==null?[]:(e=Object(e),Se(fe(e),function(n){return Mn.call(e,n)}))}:Ne;function Rn(e,n){return G(e,z(e),n)}var Dn=Object.getOwnPropertySymbols,Fe=Dn?function(e){for(var n=[];e;)W(n,z(e)),e=Qe(e);return n}:Ne;function xn(e,n){return G(e,Fe(e),n)}function Me(e,n,r){var t=n(e);return y(e)?t:W(t,r(e))}function q(e){return Me(e,T,z)}function Gn(e){return Me(e,X,Fe)}var Un=Object.prototype,jn=Un.hasOwnProperty;function Bn(e){var n=e.length,r=new e.constructor(n);return n&&typeof e[0]=="string"&&jn.call(e,"index")&&(r.index=e.index,r.input=e.input),r}function Kn(e,n){var r=n?me(e.buffer):e.buffer;return new e.constructor(r,e.byteOffset,e.byteLength)}var Hn=/\w*$/;function Yn(e){var n=new e.constructor(e.source,Hn.exec(e));return n.lastIndex=e.lastIndex,n}var oe=m?m.prototype:void 0,de=oe?oe.valueOf:void 0;function Zn(e){return de?Object(de.call(e)):{}}var qn="[object Boolean]",Xn="[object Date]",Jn="[object Map]",Qn="[object Number]",Wn="[object RegExp]",zn="[object Set]",Vn="[object String]",kn="[object Symbol]",er="[object ArrayBuffer]",nr="[object DataView]",rr="[object Float32Array]",tr="[object Float64Array]",ir="[object Int8Array]",sr="[object Int16Array]",ar="[object Int32Array]",ur="[object Uint8Array]",fr="[object Uint8ClampedArray]",or="[object Uint16Array]",dr="[object Uint32Array]";function hr(e,n,r){var t=e.constructor;switch(n){case er:return me(e);case qn:case Xn:return new t(+e);case nr:return Kn(e,r);case rr:case tr:case ir:case sr:case ar:case ur:case fr:case or:case dr:return We(e,r);case Jn:return new t;case Qn:case Vn:return new t(e);case Wn:return Yn(e);case zn:return new t;case kn:return Zn(e)}}var gr="[object Map]";function lr(e){return I(e)&&C(e)==gr}var he=x&&x.isMap,cr=he?Oe(he):lr,_r="[object Set]";function pr(e){return I(e)&&C(e)==_r}var ge=x&&x.isSet,br=ge?Oe(ge):pr,yr=1,Ar=2,Tr=4,Re="[object Arguments]",Er="[object Array]",mr="[object Boolean]",Or="[object Date]",vr="[object Error]",De="[object Function]",wr="[object GeneratorFunction]",$r="[object Map]",Lr="[object Number]",xe="[object Object]",Pr="[object RegExp]",Ir="[object Set]",Cr="[object String]",Sr="[object Symbol]",Nr="[object WeakMap]",Fr="[object ArrayBuffer]",Mr="[object DataView]",Rr="[object Float32Array]",Dr="[object Float64Array]",xr="[object Int8Array]",Gr="[object Int16Array]",Ur="[object Int32Array]",jr="[object Uint8Array]",Br="[object Uint8ClampedArray]",Kr="[object Uint16Array]",Hr="[object Uint32Array]",d={};d[Re]=d[Er]=d[Fr]=d[Mr]=d[mr]=d[Or]=d[Rr]=d[Dr]=d[xr]=d[Gr]=d[Ur]=d[$r]=d[Lr]=d[xe]=d[Pr]=d[Ir]=d[Cr]=d[Sr]=d[jr]=d[Br]=d[Kr]=d[Hr]=!0;d[vr]=d[De]=d[Nr]=!1;function B(e,n,r,t,i,s){var a,u=n&yr,f=n&Ar,l=n&Tr;if(a!==void 0)return a;if(!ve(e))return e;var g=y(e);if(g){if(a=Bn(e),!u)return ze(e,a)}else{var o=C(e),h=o==De||o==wr;if(Z(e))return Ve(e,u);if(o==xe||o==Re||h&&!i){if(a=f||h?{}:ke(e),!u)return f?xn(e,Nn(a,e)):Rn(e,Sn(a,e))}else{if(!d[o])return i?e:{};a=hr(e,o,u)}}s||(s=new P);var A=s.get(e);if(A)return A;s.set(e,a),br(e)?e.forEach(function(c){a.add(B(c,n,r,c,e,s))}):cr(e)&&e.forEach(function(c,_){a.set(_,B(c,n,r,_,e,s))});var p=l?f?Gn:q:f?X:T,b=g?void 0:p(e);return Pe(b||e,function(c,_){b&&(_=c,c=e[_]),en(a,_,B(c,n,r,_,e,s))}),a}var Yr="__lodash_hash_undefined__";function Zr(e){return this.__data__.set(e,Yr),this}function qr(e){return this.__data__.has(e)}function S(e){var n=-1,r=e==null?0:e.length;for(this.__data__=new nn;++n<r;)this.add(e[n])}S.prototype.add=S.prototype.push=Zr;S.prototype.has=qr;function Xr(e,n){for(var r=-1,t=e==null?0:e.length;++r<t;)if(n(e[r],r,e))return!0;return!1}function Ge(e,n){return e.has(n)}var Jr=1,Qr=2;function Ue(e,n,r,t,i,s){var a=r&Jr,u=e.length,f=n.length;if(u!=f&&!(a&&f>u))return!1;var l=s.get(e),g=s.get(n);if(l&&g)return l==n&&g==e;var o=-1,h=!0,A=r&Qr?new S:void 0;for(s.set(e,n),s.set(n,e);++o<u;){var p=e[o],b=n[o];if(t)var c=a?t(b,p,o,n,e,s):t(p,b,o,e,n,s);if(c!==void 0){if(c)continue;h=!1;break}if(A){if(!Xr(n,function(_,O){if(!Ge(A,O)&&(p===_||i(p,_,r,t,s)))return A.push(O)})){h=!1;break}}else if(!(p===b||i(p,b,r,t,s))){h=!1;break}}return s.delete(e),s.delete(n),h}function Wr(e){var n=-1,r=Array(e.size);return e.forEach(function(t,i){r[++n]=[i,t]}),r}function V(e){var n=-1,r=Array(e.size);return e.forEach(function(t){r[++n]=t}),r}var zr=1,Vr=2,kr="[object Boolean]",et="[object Date]",nt="[object Error]",rt="[object Map]",tt="[object Number]",it="[object RegExp]",st="[object Set]",at="[object String]",ut="[object Symbol]",ft="[object ArrayBuffer]",ot="[object DataView]",le=m?m.prototype:void 0,K=le?le.valueOf:void 0;function dt(e,n,r,t,i,s,a){switch(r){case ot:if(e.byteLength!=n.byteLength||e.byteOffset!=n.byteOffset)return!1;e=e.buffer,n=n.buffer;case ft:return!(e.byteLength!=n.byteLength||!s(new re(e),new re(n)));case kr:case et:case tt:return rn(+e,+n);case nt:return e.name==n.name&&e.message==n.message;case it:case at:return e==n+"";case rt:var u=Wr;case st:var f=t&zr;if(u||(u=V),e.size!=n.size&&!f)return!1;var l=a.get(e);if(l)return l==n;t|=Vr,a.set(e,n);var g=Ue(u(e),u(n),t,i,s,a);return a.delete(e),g;case ut:if(K)return K.call(e)==K.call(n)}return!1}var ht=1,gt=Object.prototype,lt=gt.hasOwnProperty;function ct(e,n,r,t,i,s){var a=r&ht,u=q(e),f=u.length,l=q(n),g=l.length;if(f!=g&&!a)return!1;for(var o=f;o--;){var h=u[o];if(!(a?h in n:lt.call(n,h)))return!1}var A=s.get(e),p=s.get(n);if(A&&p)return A==n&&p==e;var b=!0;s.set(e,n),s.set(n,e);for(var c=a;++o<f;){h=u[o];var _=e[h],O=n[h];if(t)var ne=a?t(O,_,h,n,e,s):t(_,O,h,e,n,s);if(!(ne===void 0?_===O||i(_,O,r,t,s):ne)){b=!1;break}c||(c=h=="constructor")}if(b&&!c){var N=e.constructor,F=n.constructor;N!=F&&"constructor"in e&&"constructor"in n&&!(typeof N=="function"&&N instanceof N&&typeof F=="function"&&F instanceof F)&&(b=!1)}return s.delete(e),s.delete(n),b}var _t=1,ce="[object Arguments]",_e="[object Array]",R="[object Object]",pt=Object.prototype,pe=pt.hasOwnProperty;function bt(e,n,r,t,i,s){var a=y(e),u=y(n),f=a?_e:C(e),l=u?_e:C(n);f=f==ce?R:f,l=l==ce?R:l;var g=f==R,o=l==R,h=f==l;if(h&&Z(e)){if(!Z(n))return!1;a=!0,g=!1}if(h&&!g)return s||(s=new P),a||tn(e)?Ue(e,n,r,t,i,s):dt(e,n,f,r,t,i,s);if(!(r&_t)){var A=g&&pe.call(e,"__wrapped__"),p=o&&pe.call(n,"__wrapped__");if(A||p){var b=A?e.value():e,c=p?n.value():n;return s||(s=new P),i(b,c,r,t,s)}}return h?(s||(s=new P),ct(e,n,r,t,i,s)):!1}function k(e,n,r,t,i){return e===n?!0:e==null||n==null||!I(e)&&!I(n)?e!==e&&n!==n:bt(e,n,r,t,k,i)}var yt=1,At=2;function Tt(e,n,r,t){var i=r.length,s=i;if(e==null)return!s;for(e=Object(e);i--;){var a=r[i];if(a[2]?a[1]!==e[a[0]]:!(a[0]in e))return!1}for(;++i<s;){a=r[i];var u=a[0],f=e[u],l=a[1];if(a[2]){if(f===void 0&&!(u in e))return!1}else{var g=new P,o;if(!(o===void 0?k(l,f,yt|At,t,g):o))return!1}}return!0}function je(e){return e===e&&!ve(e)}function Et(e){for(var n=T(e),r=n.length;r--;){var t=n[r],i=e[t];n[r]=[t,i,je(i)]}return n}function Be(e,n){return function(r){return r==null?!1:r[e]===n&&(n!==void 0||e in Object(r))}}function mt(e){var n=Et(e);return n.length==1&&n[0][2]?Be(n[0][0],n[0][1]):function(r){return r===e||Tt(r,e,n)}}function Ot(e,n){return e!=null&&n in Object(e)}function Ke(e,n,r){n=Ie(n,e);for(var t=-1,i=n.length,s=!1;++t<i;){var a=U(n[t]);if(!(s=e!=null&&r(e,a)))break;e=e[a]}return s||++t!=i?s:(i=e==null?0:e.length,!!i&&sn(i)&&an(a,i)&&(y(e)||Ee(e)))}function vt(e,n){return e!=null&&Ke(e,n,Ot)}var wt=1,$t=2;function Lt(e,n){return Q(e)&&je(n)?Be(U(e),n):function(r){var t=Ln(r,e);return t===void 0&&t===n?vt(r,e):k(n,t,wt|$t)}}function Pt(e){return function(n){return n==null?void 0:n[e]}}function It(e){return function(n){return Ce(n,e)}}function Ct(e){return Q(e)?Pt(U(e)):It(e)}function He(e){return typeof e=="function"?e:e==null?we:typeof e=="object"?y(e)?Lt(e[0],e[1]):mt(e):Ct(e)}function St(e,n){return e&&un(e,n,T)}function Nt(e,n){return function(r,t){if(r==null)return r;if(!Te(r))return e(r,t);for(var i=r.length,s=-1,a=Object(r);++s<i&&t(a[s],s,a)!==!1;);return r}}var ee=Nt(St);function Ft(e){return typeof e=="function"?e:we}function v(e,n){var r=y(e)?Pe:ee;return r(e,Ft(n))}function Mt(e,n){var r=[];return ee(e,function(t,i,s){n(t,i,s)&&r.push(t)}),r}function D(e,n){var r=y(e)?Se:Mt;return r(e,He(n))}var Rt=Object.prototype,Dt=Rt.hasOwnProperty;function xt(e,n){return e!=null&&Dt.call(e,n)}function E(e,n){return e!=null&&Ke(e,n,xt)}function Gt(e,n){return $e(n,function(r){return e[r]})}function H(e){return e==null?[]:Gt(e,T(e))}function $(e){return e===void 0}function Ut(e,n,r,t,i){return i(e,function(s,a,u){r=t?(t=!1,s):n(r,s,a,u)}),r}function jt(e,n,r){var t=y(e)?Cn:Ut,i=arguments.length<3;return t(e,He(n),r,i,ee)}var Bt=1/0,Kt=j&&1/V(new j([,-0]))[1]==Bt?function(e){return new j(e)}:gn,Ht=200;function Yt(e,n,r){var t=-1,i=bn,s=e.length,a=!0,u=[],f=u;if(s>=Ht){var l=Kt(e);if(l)return V(l);a=!1,i=Ge,f=new S}else f=u;e:for(;++t<s;){var g=e[t],o=g;if(g=g!==0?g:0,a&&o===o){for(var h=f.length;h--;)if(f[h]===o)continue e;u.push(g)}else i(f,o,r)||(f!==u&&f.push(o),u.push(g))}return u}var Zt=fn(function(e){return Yt(In(e,1,on,!0))}),qt="\0",w="\0",be="
";class Ye{constructor(n={}){this._isDirected=E(n,"directed")?n.directed:!0,this._isMultigraph=E(n,"multigraph")?n.multigraph:!1,this._isCompound=E(n,"compound")?n.compound:!1,this._label=void 0,this._defaultNodeLabelFn=M(void 0),this._defaultEdgeLabelFn=M(void 0),this._nodes={},this._isCompound&&(this._parent={},this._children={},this._children[w]={}),this._in={},this._preds={},this._out={},this._sucs={},this._edgeObjs={},this._edgeLabels={}}isDirected(){return this._isDirected}isMultigraph(){return this._isMultigraph}isCompound(){return this._isCompound}setGraph(n){return this._label=n,this}graph(){return this._label}setDefaultNodeLabel(n){return te(n)||(n=M(n)),this._defaultNodeLabelFn=n,this}nodeCount(){return this._nodeCount}nodes(){return T(this._nodes)}sources(){var n=this;return D(this.nodes(),function(r){return ie(n._in[r])})}sinks(){var n=this;return D(this.nodes(),function(r){return ie(n._out[r])})}setNodes(n,r){var t=arguments,i=this;return v(n,function(s){t.length>1?i.setNode(s,r):i.setNode(s)}),this}setNode(n,r){return E(this._nodes,n)?(arguments.length>1&&(this._nodes[n]=r),this):(this._nodes[n]=arguments.length>1?r:this._defaultNodeLabelFn(n),this._isCompound&&(this._parent[n]=w,this._children[n]={},this._children[w][n]=!0),this._in[n]={},this._preds[n]={},this._out[n]={},this._sucs[n]={},++this._nodeCount,this)}node(n){return this._nodes[n]}hasNode(n){return E(this._nodes,n)}removeNode(n){var r=this;if(E(this._nodes,n)){var t=function(i){r.removeEdge(r._edgeObjs[i])};delete this._nodes[n],this._isCompound&&(this._removeFromParentsChildList(n),delete this._parent[n],v(this.children(n),function(i){r.setParent(i)}),delete this._children[n]),v(T(this._in[n]),t),delete this._in[n],delete this._preds[n],v(T(this._out[n]),t),delete this._out[n],delete this._sucs[n],--this._nodeCount}return this}setParent(n,r){if(!this._isCompound)throw new Error("Cannot set parent in a non-compound graph");if($(r))r=w;else{r+="";for(var t=r;!$(t);t=this.parent(t))if(t===n)throw new Error("Setting "+r+" as parent of "+n+" would create a cycle");this.setNode(r)}return this.setNode(n),this._removeFromParentsChildList(n),this._parent[n]=r,this._children[r][n]=!0,this}_removeFromParentsChildList(n){delete this._children[this._parent[n]][n]}parent(n){if(this._isCompound){var r=this._parent[n];if(r!==w)return r}}children(n){if($(n)&&(n=w),this._isCompound){var r=this._children[n];if(r)return T(r)}else{if(n===w)return this.nodes();if(this.hasNode(n))return[]}}predecessors(n){var r=this._preds[n];if(r)return T(r)}successors(n){var r=this._sucs[n];if(r)return T(r)}neighbors(n){var r=this.predecessors(n);if(r)return Zt(r,this.successors(n))}isLeaf(n){var r;return this.isDirected()?r=this.successors(n):r=this.neighbors(n),r.length===0}filterNodes(n){var r=new this.constructor({directed:this._isDirected,multigraph:this._isMultigraph,compound:this._isCompound});r.setGraph(this.graph());var t=this;v(this._nodes,function(a,u){n(u)&&r.setNode(u,a)}),v(this._edgeObjs,function(a){r.hasNode(a.v)&&r.hasNode(a.w)&&r.setEdge(a,t.edge(a))});var i={};function s(a){var u=t.parent(a);return u===void 0||r.hasNode(u)?(i[a]=u,u):u in i?i[u]:s(u)}return this._isCompound&&v(r.nodes(),function(a){r.setParent(a,s(a))}),r}setDefaultEdgeLabel(n){return te(n)||(n=M(n)),this._defaultEdgeLabelFn=n,this}edgeCount(){return this._edgeCount}edges(){return H(this._edgeObjs)}setPath(n,r){var t=this,i=arguments;return jt(n,function(s,a){return i.length>1?t.setEdge(s,a,r):t.setEdge(s,a),a}),this}setEdge(){var n,r,t,i,s=!1,a=arguments[0];typeof a=="object"&&a!==null&&"v"in a?(n=a.v,r=a.w,t=a.name,arguments.length===2&&(i=arguments[1],s=!0)):(n=a,r=arguments[1],t=arguments[3],arguments.length>2&&(i=arguments[2],s=!0)),n=""+n,r=""+r,$(t)||(t=""+t);var u=L(this._isDirected,n,r,t);if(E(this._edgeLabels,u))return s&&(this._edgeLabels[u]=i),this;if(!$(t)&&!this._isMultigraph)throw new Error("Cannot set a named edge when isMultigraph = false");this.setNode(n),this.setNode(r),this._edgeLabels[u]=s?i:this._defaultEdgeLabelFn(n,r,t);var f=Xt(this._isDirected,n,r,t);return n=f.v,r=f.w,Object.freeze(f),this._edgeObjs[u]=f,ye(this._preds[r],n),ye(this._sucs[n],r),this._in[r][u]=f,this._out[n][u]=f,this._edgeCount++,this}edge(n,r,t){var i=arguments.length===1?Y(this._isDirected,arguments[0]):L(this._isDirected,n,r,t);return this._edgeLabels[i]}hasEdge(n,r,t){var i=arguments.length===1?Y(this._isDirected,arguments[0]):L(this._isDirected,n,r,t);return E(this._edgeLabels,i)}removeEdge(n,r,t){var i=arguments.length===1?Y(this._isDirected,arguments[0]):L(this._isDirected,n,r,t),s=this._edgeObjs[i];return s&&(n=s.v,r=s.w,delete this._edgeLabels[i],delete this._edgeObjs[i],Ae(this._preds[r],n),Ae(this._sucs[n],r),delete this._in[r][i],delete this._out[n][i],this._edgeCount--),this}inEdges(n,r){var t=this._in[n];if(t){var i=H(t);return r?D(i,function(s){return s.v===r}):i}}outEdges(n,r){var t=this._out[n];if(t){var i=H(t);return r?D(i,function(s){return s.w===r}):i}}nodeEdges(n,r){var t=this.inEdges(n,r);if(t)return t.concat(this.outEdges(n,r))}}Ye.prototype._nodeCount=0;Ye.prototype._edgeCount=0;function ye(e,n){e[n]?e[n]++:e[n]=1}function Ae(e,n){--e[n]||delete e[n]}function L(e,n,r,t){var i=""+n,s=""+r;if(!e&&i>s){var a=i;i=s,s=a}return i+be+s+be+($(t)?qt:t)}function Xt(e,n,r,t){var i=""+n,s=""+r;if(!e&&i>s){var a=i;i=s,s=a}var u={v:i,w:s};return t&&(u.name=t),u}function Y(e,n){return L(e,n.v,n.w,n.name)}export{Ye as G,B as a,In as b,He as c,ln as d,ee as e,v as f,$e as g,E as h,J as i,Ft as j,T as k,St as l,Ie as m,Ce as n,vt as o,wn as p,$ as q,D as r,jt as s,U as t,H as v};
+import{B as I,C as Ze,S as m,D as y,E as Te,F as qe,G as Xe,H as Je,I as Ee,J as G,K as X,L as Qe,M as me,N as We,O as C,P as x,Q as Oe,R as ve,T as ze,U as Z,V as Ve,W as ke,X as P,Y as en,Z as nn,_ as rn,$ as re,a0 as tn,a1 as sn,a2 as an,a3 as we,a4 as un,a5 as j,a6 as fn,a7 as on,a8 as M,a9 as te,aa as ie}from"./mermaid.core-DNo_7Q2B.js";var dn="[object Symbol]";function J(e){return typeof e=="symbol"||I(e)&&Ze(e)==dn}function $e(e,n){for(var r=-1,t=e==null?0:e.length,i=Array(t);++r<t;)i[r]=n(e[r],r,e);return i}var hn=1/0,se=m?m.prototype:void 0,ae=se?se.toString:void 0;function Le(e){if(typeof e=="string")return e;if(y(e))return $e(e,Le)+"";if(J(e))return ae?ae.call(e):"";var n=e+"";return n=="0"&&1/e==-hn?"-0":n}function gn(){}function Pe(e,n){for(var r=-1,t=e==null?0:e.length;++r<t&&n(e[r],r,e)!==!1;);return e}function ln(e,n,r,t){for(var i=e.length,s=r+-1;++s<i;)if(n(e[s],s,e))return s;return-1}function cn(e){return e!==e}function _n(e,n,r){for(var t=r-1,i=e.length;++t<i;)if(e[t]===n)return t;return-1}function pn(e,n,r){return n===n?_n(e,n,r):ln(e,cn,r)}function bn(e,n){var r=e==null?0:e.length;return!!r&&pn(e,n,0)>-1}function T(e){return Te(e)?qe(e):Xe(e)}var yn=/\.|\[(?:[^[\]]*|(["'])(?:(?!\1)[^\\]|\\.)*?\1)\]/,An=/^\w*$/;function Q(e,n){if(y(e))return!1;var r=typeof e;return r=="number"||r=="symbol"||r=="boolean"||e==null||J(e)?!0:An.test(e)||!yn.test(e)||n!=null&&e in Object(n)}var Tn=500;function En(e){var n=Je(e,function(t){return r.size===Tn&&r.clear(),t}),r=n.cache;return n}var mn=/[^.[\]]+|\[(?:(-?\d+(?:\.\d+)?)|(["'])((?:(?!\2)[^\\]|\\.)*?)\2)\]|(?=(?:\.|\[\])(?:\.|\[\]|$))/g,On=/\\(\\)?/g,vn=En(function(e){var n=[];return e.charCodeAt(0)===46&&n.push(""),e.replace(mn,function(r,t,i,s){n.push(i?s.replace(On,"$1"):t||r)}),n});function wn(e){return e==null?"":Le(e)}function Ie(e,n){return y(e)?e:Q(e,n)?[e]:vn(wn(e))}var $n=1/0;function U(e){if(typeof e=="string"||J(e))return e;var n=e+"";return n=="0"&&1/e==-$n?"-0":n}function Ce(e,n){n=Ie(n,e);for(var r=0,t=n.length;e!=null&&r<t;)e=e[U(n[r++])];return r&&r==t?e:void 0}function Ln(e,n,r){var t=e==null?void 0:Ce(e,n);return t===void 0?r:t}function W(e,n){for(var r=-1,t=n.length,i=e.length;++r<t;)e[i+r]=n[r];return e}var ue=m?m.isConcatSpreadable:void 0;function Pn(e){return y(e)||Ee(e)||!!(ue&&e&&e[ue])}function In(e,n,r,t,i){var s=-1,a=e.length;for(r||(r=Pn),i||(i=[]);++s<a;){var u=e[s];r(u)?W(i,u):t||(i[i.length]=u)}return i}function Cn(e,n,r,t){var i=-1,s=e==null?0:e.length;for(t&&s&&(r=e[++i]);++i<s;)r=n(r,e[i],i,e);return r}function Sn(e,n){return e&&G(n,T(n),e)}function Nn(e,n){return e&&G(n,X(n),e)}function Se(e,n){for(var r=-1,t=e==null?0:e.length,i=0,s=[];++r<t;){var a=e[r];n(a,r,e)&&(s[i++]=a)}return s}function Ne(){return[]}var Fn=Object.prototype,Mn=Fn.propertyIsEnumerable,fe=Object.getOwnPropertySymbols,z=fe?function(e){return e==null?[]:(e=Object(e),Se(fe(e),function(n){return Mn.call(e,n)}))}:Ne;function Rn(e,n){return G(e,z(e),n)}var Dn=Object.getOwnPropertySymbols,Fe=Dn?function(e){for(var n=[];e;)W(n,z(e)),e=Qe(e);return n}:Ne;function xn(e,n){return G(e,Fe(e),n)}function Me(e,n,r){var t=n(e);return y(e)?t:W(t,r(e))}function q(e){return Me(e,T,z)}function Gn(e){return Me(e,X,Fe)}var Un=Object.prototype,jn=Un.hasOwnProperty;function Bn(e){var n=e.length,r=new e.constructor(n);return n&&typeof e[0]=="string"&&jn.call(e,"index")&&(r.index=e.index,r.input=e.input),r}function Kn(e,n){var r=n?me(e.buffer):e.buffer;return new e.constructor(r,e.byteOffset,e.byteLength)}var Hn=/\w*$/;function Yn(e){var n=new e.constructor(e.source,Hn.exec(e));return n.lastIndex=e.lastIndex,n}var oe=m?m.prototype:void 0,de=oe?oe.valueOf:void 0;function Zn(e){return de?Object(de.call(e)):{}}var qn="[object Boolean]",Xn="[object Date]",Jn="[object Map]",Qn="[object Number]",Wn="[object RegExp]",zn="[object Set]",Vn="[object String]",kn="[object Symbol]",er="[object ArrayBuffer]",nr="[object DataView]",rr="[object Float32Array]",tr="[object Float64Array]",ir="[object Int8Array]",sr="[object Int16Array]",ar="[object Int32Array]",ur="[object Uint8Array]",fr="[object Uint8ClampedArray]",or="[object Uint16Array]",dr="[object Uint32Array]";function hr(e,n,r){var t=e.constructor;switch(n){case er:return me(e);case qn:case Xn:return new t(+e);case nr:return Kn(e,r);case rr:case tr:case ir:case sr:case ar:case ur:case fr:case or:case dr:return We(e,r);case Jn:return new t;case Qn:case Vn:return new t(e);case Wn:return Yn(e);case zn:return new t;case kn:return Zn(e)}}var gr="[object Map]";function lr(e){return I(e)&&C(e)==gr}var he=x&&x.isMap,cr=he?Oe(he):lr,_r="[object Set]";function pr(e){return I(e)&&C(e)==_r}var ge=x&&x.isSet,br=ge?Oe(ge):pr,yr=1,Ar=2,Tr=4,Re="[object Arguments]",Er="[object Array]",mr="[object Boolean]",Or="[object Date]",vr="[object Error]",De="[object Function]",wr="[object GeneratorFunction]",$r="[object Map]",Lr="[object Number]",xe="[object Object]",Pr="[object RegExp]",Ir="[object Set]",Cr="[object String]",Sr="[object Symbol]",Nr="[object WeakMap]",Fr="[object ArrayBuffer]",Mr="[object DataView]",Rr="[object Float32Array]",Dr="[object Float64Array]",xr="[object Int8Array]",Gr="[object Int16Array]",Ur="[object Int32Array]",jr="[object Uint8Array]",Br="[object Uint8ClampedArray]",Kr="[object Uint16Array]",Hr="[object Uint32Array]",d={};d[Re]=d[Er]=d[Fr]=d[Mr]=d[mr]=d[Or]=d[Rr]=d[Dr]=d[xr]=d[Gr]=d[Ur]=d[$r]=d[Lr]=d[xe]=d[Pr]=d[Ir]=d[Cr]=d[Sr]=d[jr]=d[Br]=d[Kr]=d[Hr]=!0;d[vr]=d[De]=d[Nr]=!1;function B(e,n,r,t,i,s){var a,u=n&yr,f=n&Ar,l=n&Tr;if(a!==void 0)return a;if(!ve(e))return e;var g=y(e);if(g){if(a=Bn(e),!u)return ze(e,a)}else{var o=C(e),h=o==De||o==wr;if(Z(e))return Ve(e,u);if(o==xe||o==Re||h&&!i){if(a=f||h?{}:ke(e),!u)return f?xn(e,Nn(a,e)):Rn(e,Sn(a,e))}else{if(!d[o])return i?e:{};a=hr(e,o,u)}}s||(s=new P);var A=s.get(e);if(A)return A;s.set(e,a),br(e)?e.forEach(function(c){a.add(B(c,n,r,c,e,s))}):cr(e)&&e.forEach(function(c,_){a.set(_,B(c,n,r,_,e,s))});var p=l?f?Gn:q:f?X:T,b=g?void 0:p(e);return Pe(b||e,function(c,_){b&&(_=c,c=e[_]),en(a,_,B(c,n,r,_,e,s))}),a}var Yr="__lodash_hash_undefined__";function Zr(e){return this.__data__.set(e,Yr),this}function qr(e){return this.__data__.has(e)}function S(e){var n=-1,r=e==null?0:e.length;for(this.__data__=new nn;++n<r;)this.add(e[n])}S.prototype.add=S.prototype.push=Zr;S.prototype.has=qr;function Xr(e,n){for(var r=-1,t=e==null?0:e.length;++r<t;)if(n(e[r],r,e))return!0;return!1}function Ge(e,n){return e.has(n)}var Jr=1,Qr=2;function Ue(e,n,r,t,i,s){var a=r&Jr,u=e.length,f=n.length;if(u!=f&&!(a&&f>u))return!1;var l=s.get(e),g=s.get(n);if(l&&g)return l==n&&g==e;var o=-1,h=!0,A=r&Qr?new S:void 0;for(s.set(e,n),s.set(n,e);++o<u;){var p=e[o],b=n[o];if(t)var c=a?t(b,p,o,n,e,s):t(p,b,o,e,n,s);if(c!==void 0){if(c)continue;h=!1;break}if(A){if(!Xr(n,function(_,O){if(!Ge(A,O)&&(p===_||i(p,_,r,t,s)))return A.push(O)})){h=!1;break}}else if(!(p===b||i(p,b,r,t,s))){h=!1;break}}return s.delete(e),s.delete(n),h}function Wr(e){var n=-1,r=Array(e.size);return e.forEach(function(t,i){r[++n]=[i,t]}),r}function V(e){var n=-1,r=Array(e.size);return e.forEach(function(t){r[++n]=t}),r}var zr=1,Vr=2,kr="[object Boolean]",et="[object Date]",nt="[object Error]",rt="[object Map]",tt="[object Number]",it="[object RegExp]",st="[object Set]",at="[object String]",ut="[object Symbol]",ft="[object ArrayBuffer]",ot="[object DataView]",le=m?m.prototype:void 0,K=le?le.valueOf:void 0;function dt(e,n,r,t,i,s,a){switch(r){case ot:if(e.byteLength!=n.byteLength||e.byteOffset!=n.byteOffset)return!1;e=e.buffer,n=n.buffer;case ft:return!(e.byteLength!=n.byteLength||!s(new re(e),new re(n)));case kr:case et:case tt:return rn(+e,+n);case nt:return e.name==n.name&&e.message==n.message;case it:case at:return e==n+"";case rt:var u=Wr;case st:var f=t&zr;if(u||(u=V),e.size!=n.size&&!f)return!1;var l=a.get(e);if(l)return l==n;t|=Vr,a.set(e,n);var g=Ue(u(e),u(n),t,i,s,a);return a.delete(e),g;case ut:if(K)return K.call(e)==K.call(n)}return!1}var ht=1,gt=Object.prototype,lt=gt.hasOwnProperty;function ct(e,n,r,t,i,s){var a=r&ht,u=q(e),f=u.length,l=q(n),g=l.length;if(f!=g&&!a)return!1;for(var o=f;o--;){var h=u[o];if(!(a?h in n:lt.call(n,h)))return!1}var A=s.get(e),p=s.get(n);if(A&&p)return A==n&&p==e;var b=!0;s.set(e,n),s.set(n,e);for(var c=a;++o<f;){h=u[o];var _=e[h],O=n[h];if(t)var ne=a?t(O,_,h,n,e,s):t(_,O,h,e,n,s);if(!(ne===void 0?_===O||i(_,O,r,t,s):ne)){b=!1;break}c||(c=h=="constructor")}if(b&&!c){var N=e.constructor,F=n.constructor;N!=F&&"constructor"in e&&"constructor"in n&&!(typeof N=="function"&&N instanceof N&&typeof F=="function"&&F instanceof F)&&(b=!1)}return s.delete(e),s.delete(n),b}var _t=1,ce="[object Arguments]",_e="[object Array]",R="[object Object]",pt=Object.prototype,pe=pt.hasOwnProperty;function bt(e,n,r,t,i,s){var a=y(e),u=y(n),f=a?_e:C(e),l=u?_e:C(n);f=f==ce?R:f,l=l==ce?R:l;var g=f==R,o=l==R,h=f==l;if(h&&Z(e)){if(!Z(n))return!1;a=!0,g=!1}if(h&&!g)return s||(s=new P),a||tn(e)?Ue(e,n,r,t,i,s):dt(e,n,f,r,t,i,s);if(!(r&_t)){var A=g&&pe.call(e,"__wrapped__"),p=o&&pe.call(n,"__wrapped__");if(A||p){var b=A?e.value():e,c=p?n.value():n;return s||(s=new P),i(b,c,r,t,s)}}return h?(s||(s=new P),ct(e,n,r,t,i,s)):!1}function k(e,n,r,t,i){return e===n?!0:e==null||n==null||!I(e)&&!I(n)?e!==e&&n!==n:bt(e,n,r,t,k,i)}var yt=1,At=2;function Tt(e,n,r,t){var i=r.length,s=i;if(e==null)return!s;for(e=Object(e);i--;){var a=r[i];if(a[2]?a[1]!==e[a[0]]:!(a[0]in e))return!1}for(;++i<s;){a=r[i];var u=a[0],f=e[u],l=a[1];if(a[2]){if(f===void 0&&!(u in e))return!1}else{var g=new P,o;if(!(o===void 0?k(l,f,yt|At,t,g):o))return!1}}return!0}function je(e){return e===e&&!ve(e)}function Et(e){for(var n=T(e),r=n.length;r--;){var t=n[r],i=e[t];n[r]=[t,i,je(i)]}return n}function Be(e,n){return function(r){return r==null?!1:r[e]===n&&(n!==void 0||e in Object(r))}}function mt(e){var n=Et(e);return n.length==1&&n[0][2]?Be(n[0][0],n[0][1]):function(r){return r===e||Tt(r,e,n)}}function Ot(e,n){return e!=null&&n in Object(e)}function Ke(e,n,r){n=Ie(n,e);for(var t=-1,i=n.length,s=!1;++t<i;){var a=U(n[t]);if(!(s=e!=null&&r(e,a)))break;e=e[a]}return s||++t!=i?s:(i=e==null?0:e.length,!!i&&sn(i)&&an(a,i)&&(y(e)||Ee(e)))}function vt(e,n){return e!=null&&Ke(e,n,Ot)}var wt=1,$t=2;function Lt(e,n){return Q(e)&&je(n)?Be(U(e),n):function(r){var t=Ln(r,e);return t===void 0&&t===n?vt(r,e):k(n,t,wt|$t)}}function Pt(e){return function(n){return n==null?void 0:n[e]}}function It(e){return function(n){return Ce(n,e)}}function Ct(e){return Q(e)?Pt(U(e)):It(e)}function He(e){return typeof e=="function"?e:e==null?we:typeof e=="object"?y(e)?Lt(e[0],e[1]):mt(e):Ct(e)}function St(e,n){return e&&un(e,n,T)}function Nt(e,n){return function(r,t){if(r==null)return r;if(!Te(r))return e(r,t);for(var i=r.length,s=-1,a=Object(r);++s<i&&t(a[s],s,a)!==!1;);return r}}var ee=Nt(St);function Ft(e){return typeof e=="function"?e:we}function v(e,n){var r=y(e)?Pe:ee;return r(e,Ft(n))}function Mt(e,n){var r=[];return ee(e,function(t,i,s){n(t,i,s)&&r.push(t)}),r}function D(e,n){var r=y(e)?Se:Mt;return r(e,He(n))}var Rt=Object.prototype,Dt=Rt.hasOwnProperty;function xt(e,n){return e!=null&&Dt.call(e,n)}function E(e,n){return e!=null&&Ke(e,n,xt)}function Gt(e,n){return $e(n,function(r){return e[r]})}function H(e){return e==null?[]:Gt(e,T(e))}function $(e){return e===void 0}function Ut(e,n,r,t,i){return i(e,function(s,a,u){r=t?(t=!1,s):n(r,s,a,u)}),r}function jt(e,n,r){var t=y(e)?Cn:Ut,i=arguments.length<3;return t(e,He(n),r,i,ee)}var Bt=1/0,Kt=j&&1/V(new j([,-0]))[1]==Bt?function(e){return new j(e)}:gn,Ht=200;function Yt(e,n,r){var t=-1,i=bn,s=e.length,a=!0,u=[],f=u;if(s>=Ht){var l=Kt(e);if(l)return V(l);a=!1,i=Ge,f=new S}else f=u;e:for(;++t<s;){var g=e[t],o=g;if(g=g!==0?g:0,a&&o===o){for(var h=f.length;h--;)if(f[h]===o)continue e;u.push(g)}else i(f,o,r)||(f!==u&&f.push(o),u.push(g))}return u}var Zt=fn(function(e){return Yt(In(e,1,on,!0))}),qt="\0",w="\0",be="
";class Ye{constructor(n={}){this._isDirected=E(n,"directed")?n.directed:!0,this._isMultigraph=E(n,"multigraph")?n.multigraph:!1,this._isCompound=E(n,"compound")?n.compound:!1,this._label=void 0,this._defaultNodeLabelFn=M(void 0),this._defaultEdgeLabelFn=M(void 0),this._nodes={},this._isCompound&&(this._parent={},this._children={},this._children[w]={}),this._in={},this._preds={},this._out={},this._sucs={},this._edgeObjs={},this._edgeLabels={}}isDirected(){return this._isDirected}isMultigraph(){return this._isMultigraph}isCompound(){return this._isCompound}setGraph(n){return this._label=n,this}graph(){return this._label}setDefaultNodeLabel(n){return te(n)||(n=M(n)),this._defaultNodeLabelFn=n,this}nodeCount(){return this._nodeCount}nodes(){return T(this._nodes)}sources(){var n=this;return D(this.nodes(),function(r){return ie(n._in[r])})}sinks(){var n=this;return D(this.nodes(),function(r){return ie(n._out[r])})}setNodes(n,r){var t=arguments,i=this;return v(n,function(s){t.length>1?i.setNode(s,r):i.setNode(s)}),this}setNode(n,r){return E(this._nodes,n)?(arguments.length>1&&(this._nodes[n]=r),this):(this._nodes[n]=arguments.length>1?r:this._defaultNodeLabelFn(n),this._isCompound&&(this._parent[n]=w,this._children[n]={},this._children[w][n]=!0),this._in[n]={},this._preds[n]={},this._out[n]={},this._sucs[n]={},++this._nodeCount,this)}node(n){return this._nodes[n]}hasNode(n){return E(this._nodes,n)}removeNode(n){var r=this;if(E(this._nodes,n)){var t=function(i){r.removeEdge(r._edgeObjs[i])};delete this._nodes[n],this._isCompound&&(this._removeFromParentsChildList(n),delete this._parent[n],v(this.children(n),function(i){r.setParent(i)}),delete this._children[n]),v(T(this._in[n]),t),delete this._in[n],delete this._preds[n],v(T(this._out[n]),t),delete this._out[n],delete this._sucs[n],--this._nodeCount}return this}setParent(n,r){if(!this._isCompound)throw new Error("Cannot set parent in a non-compound graph");if($(r))r=w;else{r+="";for(var t=r;!$(t);t=this.parent(t))if(t===n)throw new Error("Setting "+r+" as parent of "+n+" would create a cycle");this.setNode(r)}return this.setNode(n),this._removeFromParentsChildList(n),this._parent[n]=r,this._children[r][n]=!0,this}_removeFromParentsChildList(n){delete this._children[this._parent[n]][n]}parent(n){if(this._isCompound){var r=this._parent[n];if(r!==w)return r}}children(n){if($(n)&&(n=w),this._isCompound){var r=this._children[n];if(r)return T(r)}else{if(n===w)return this.nodes();if(this.hasNode(n))return[]}}predecessors(n){var r=this._preds[n];if(r)return T(r)}successors(n){var r=this._sucs[n];if(r)return T(r)}neighbors(n){var r=this.predecessors(n);if(r)return Zt(r,this.successors(n))}isLeaf(n){var r;return this.isDirected()?r=this.successors(n):r=this.neighbors(n),r.length===0}filterNodes(n){var r=new this.constructor({directed:this._isDirected,multigraph:this._isMultigraph,compound:this._isCompound});r.setGraph(this.graph());var t=this;v(this._nodes,function(a,u){n(u)&&r.setNode(u,a)}),v(this._edgeObjs,function(a){r.hasNode(a.v)&&r.hasNode(a.w)&&r.setEdge(a,t.edge(a))});var i={};function s(a){var u=t.parent(a);return u===void 0||r.hasNode(u)?(i[a]=u,u):u in i?i[u]:s(u)}return this._isCompound&&v(r.nodes(),function(a){r.setParent(a,s(a))}),r}setDefaultEdgeLabel(n){return te(n)||(n=M(n)),this._defaultEdgeLabelFn=n,this}edgeCount(){return this._edgeCount}edges(){return H(this._edgeObjs)}setPath(n,r){var t=this,i=arguments;return jt(n,function(s,a){return i.length>1?t.setEdge(s,a,r):t.setEdge(s,a),a}),this}setEdge(){var n,r,t,i,s=!1,a=arguments[0];typeof a=="object"&&a!==null&&"v"in a?(n=a.v,r=a.w,t=a.name,arguments.length===2&&(i=arguments[1],s=!0)):(n=a,r=arguments[1],t=arguments[3],arguments.length>2&&(i=arguments[2],s=!0)),n=""+n,r=""+r,$(t)||(t=""+t);var u=L(this._isDirected,n,r,t);if(E(this._edgeLabels,u))return s&&(this._edgeLabels[u]=i),this;if(!$(t)&&!this._isMultigraph)throw new Error("Cannot set a named edge when isMultigraph = false");this.setNode(n),this.setNode(r),this._edgeLabels[u]=s?i:this._defaultEdgeLabelFn(n,r,t);var f=Xt(this._isDirected,n,r,t);return n=f.v,r=f.w,Object.freeze(f),this._edgeObjs[u]=f,ye(this._preds[r],n),ye(this._sucs[n],r),this._in[r][u]=f,this._out[n][u]=f,this._edgeCount++,this}edge(n,r,t){var i=arguments.length===1?Y(this._isDirected,arguments[0]):L(this._isDirected,n,r,t);return this._edgeLabels[i]}hasEdge(n,r,t){var i=arguments.length===1?Y(this._isDirected,arguments[0]):L(this._isDirected,n,r,t);return E(this._edgeLabels,i)}removeEdge(n,r,t){var i=arguments.length===1?Y(this._isDirected,arguments[0]):L(this._isDirected,n,r,t),s=this._edgeObjs[i];return s&&(n=s.v,r=s.w,delete this._edgeLabels[i],delete this._edgeObjs[i],Ae(this._preds[r],n),Ae(this._sucs[n],r),delete this._in[r][i],delete this._out[n][i],this._edgeCount--),this}inEdges(n,r){var t=this._in[n];if(t){var i=H(t);return r?D(i,function(s){return s.v===r}):i}}outEdges(n,r){var t=this._out[n];if(t){var i=H(t);return r?D(i,function(s){return s.w===r}):i}}nodeEdges(n,r){var t=this.inEdges(n,r);if(t)return t.concat(this.outEdges(n,r))}}Ye.prototype._nodeCount=0;Ye.prototype._edgeCount=0;function ye(e,n){e[n]?e[n]++:e[n]=1}function Ae(e,n){--e[n]||delete e[n]}function L(e,n,r,t){var i=""+n,s=""+r;if(!e&&i>s){var a=i;i=s,s=a}return i+be+s+be+($(t)?qt:t)}function Xt(e,n,r,t){var i=""+n,s=""+r;if(!e&&i>s){var a=i;i=s,s=a}var u={v:i,w:s};return t&&(u.name=t),u}function Y(e,n){return L(e,n.v,n.w,n.name)}export{Ye as G,B as a,In as b,He as c,ln as d,ee as e,v as f,$e as g,E as h,J as i,Ft as j,T as k,St as l,Ie as m,Ce as n,vt as o,wn as p,$ as q,D as r,jt as s,U as t,H as v};
diff --git a/assets/image-Dc9IOqtq.png b/assets/image-Dc9IOqtq.png
new file mode 100644
index 0000000000000000000000000000000000000000..e328a9e1bd2a5b8301d0547b1e566ad88683a0f7
GIT binary patch
literal 196365
zcmeFZc{rDC`#ma2LM6#OlqoU`Nv329p(HYsq=;n5EXquhIUyvP3?WlUrplZ$MaIly
z6f*7g>AUxF{GR9e9>@N7|FL^IdV9nDx$o;buk&2zTI;-nwKY|ClQWVN5fSY^t*UsA
zh-e2X5fSkbGGhG8DjCsn{LePWb1Di%+0D!oL_`OPPAi@~@49We&rSOL%$D3d!_lzv
z=vH=xv>%$2c88wv3s^@zh~_Nd*>^oiEkl*!z_~ZHYM~cO4DFPd)Lut(tx3JfYm~j>
z&1xJm=hkTdLFL=VMEi!UkL#o3&5s<D#+<E2-!?lZIg)wO%M+3O`}cq;ul$Ohow%(S
z*=?eK|DHcYU9Cw(eDGht=Y<a3R$Ui*<=SOSMYQc-zk_OW_x|@v>*_lWQg5mAu}U!g
z=N5?AMW(m^`!k4$x6W+~s@eJ+64*rg@6VuGnN-!tI5%bfpHHVE@-@|X{Os9;&8ba2
zm7%ITJNKLY@82Y^qB6!7QbSHot|t87`@Q{6=-@#iA+3W{n<c77dV0%+gG{44|8pNi
zzA1<1XZubB)yQq9jotO%m3l!T&$;>4hV0YM|9&ls1WUrHuh0MQWxxF{N02CTMK9+N
z58HpgrbUg#k1{jQ`|pxfmJ%rrnU)7U_WbYH<W3W@FKGGs*ZTcuo7X3ase*leG5Y=V
z{qNT}u?up$XlW__`vCv%57#wkz#m|4BpBCZ<yg`?XV6+y!5~BwQNPx4dHuuk;Ez>%
z-}MjSzL)>?x$C01p~}1?!jzYU>3{wD_4Vsl-K{NcV`F0-9UVPAm5g)WdU_<8HQ73=
ze%!n&W}vJ4wLXH)wA}sIcw2gBjwu}-U1vv!i<6TXJ$C^!ZKzVlIh$+O-1$#AJ3C*$
ze*M&`?cvIo^7Q-q1q;MvQ(6XZ7#J8F;p3wqCr_61*&O*8_44J*2M-?n`Qt8?^xbP0
zeSouzOUKu*8(T!><<FlzyL$cl%%#^#2XR|u_~yeorj>$6j^GOu<Kt8zQ}}i#r^k%@
zNS<Y9XTNx{|6xkQk2i1LbaZqKIi_{@eEW8sS<}YG=FFKh_K6EyTRBgkJ}oaVFDxv~
z&fa5s@L|TEMQuaFZ(dj43BRl_`hs7bok!^@Pu|!Q*xuE}qu-hJ&Pl5L)vK8oYKF$f
zeH|U##q+Zs#2VZF&*=2^2}UT`zqFP}OiD^Bx9JqbCA;&lXeCOV(bBU2voujxSGPFU
zVp@D-@N<Sb3o|qE_U-MTKQl5iy6^R+4=5}ux^m^pP7)G&28OHF)>(LH{Q3O(^A|4+
z_4OYecN}fc)Y9PIFC-Y(u(7gmNnZYTdHDwZeQ9aw>6t_;Gc&Vm*RGkH=iL~5UmHp%
zWcbE*rl)Xic}`1HQ&31KvwdRao4>NFw28X9y1RR6QBjevuWxB->BEN)@n=X#NNjA!
z&mRrLLqkW79MR{G9bjUhtZPa<MkiqKBqzt-+S=OI*4Dzp0)OJZmfhk-E|JPQj5a3x
z`Sa)Km1fF4d$MzK=!`U%9Y}uup80nBHqrk5`?2D0rSXKLqoad^gZ}>hl%(5zgrYub
zoIc%M?om`&`0M4x{HI>5R?Uw}JXddOX|<?CuwpL<jvf;iudS;qEiUFaDsCNE%(eVT
zt*6&HGBSeuy;OfM;o-x{si~HS;uJ!azP{UfvJ#G78QOoPF+Mdj^NOu4GaDNl6Vue-
zV4l;&xl^Z36}S|v64t)Jx~-?srmb09PcN|fLF>d)L!3}qNr}M4*ER3n5tU#5J>C7{
z!mFP@f4VQvvLrUuQ5YE-GBGnxkBo@jnl<wB+F&?p#cx{Sx%PV|$D}+YEKE#9q^-TZ
zn!?J$!jD|ydXHF@d%|%??jCgxc6O3wE>8hr;(wgtEeRa%e%)c_J!5@kw;V?s4^anm
zQeRz}AG~+(UPVPk*{!)Z1qIBqp2hL;`dgbDo!Q2TQBjK-=No_A#DRKWU0ol}bj)*Q
z-g&A+#(gQPq$J^^CGCL&N{Wi~OiX+{JcypYat}S>&V^M^)`;bWVU@#&4~vM1ut#R4
zr40=YQPa}W?%(f-aJ>HQO;fzcDH9VD1B0H{R^da3QZq6#JQfcIR`c@m9(SD|$ZDy6
zbNw3*sAhVb)QJ=Ql|DX8<7Z`LWVpDv`1oFY`EtI>sPFrC@1dGt^Xh<SSy_$P1q2<F
zgzb$RH{wMvhs4Lz2P-ljv+I2*ZX;paH84JIZD*JL>{)k?sho;R{pZi0O?vlzm}t*L
zn$SIe{?VgH=gysDWJ2gEJ2))h^dNwC?q(Fb()`G<$ga&=tV&?$hUD^WUweByN2IDE
zyThkw-Xgm`YK>;Usf;#jgfyZT0XNo?Vt@VmkHuA7V9%aCs5wYDI2FiHy}9OhaQXuR
zNP`vGqdw+aH5uRv0lS$xvW;ylEuXx6$<N2<vA(h}I%*}6$il{!laayo)2;RESK~65
z86367#zv%wn%Y_{*UZe!(W6Hf6hB$y;cT4O)eTMwbXy#~eC3MIvnwZcblPJD3@t4!
zH&=!ukT3J~`S%3oJB~GPZmhj{{#?+gm@39)<Ik^4bzz4hRY`~kTjaJB_n$qGm6a6~
z5>i@Hf-FdW?w#a6O49lX6m}o`a-1HP6D}I(&!0bc?q+Ss0i;>$U=8lYoXX9ISo)x#
zpu2Z#{B}@~Q&5!Ugw+qn#KgF{x$UMGme<iaDlKiqQ@P;!7C9GZe0i$VzA+wAB7*1f
zYd9Gmj(lJ#>el?|_>LVrR(wP#ZLF;&ohQF!olRHe{QM!3Ln}pAfadve=4K=qq&xg6
zcllHF3%wk2@g0k<Z?T3<OiULqUfjO@&XXsc(r4PN3kC+vupTQbu5Y`<7-!}OtGDmm
z6Mg@F*Xzsb#>Om1_Qo}wQCBxCb$S*Rr4vD8Ex{V0XJAl@#X58<!20S{|G>cXCn5GU
zDJ?=rj`S2e48QZ;jwNMdVd?Ab<&O_}c7F2Duc?eDPqcr($jYMf%xPW0?NILCjUyCF
z_pGAgJ0f-U=MN#%ikkGRr%qLWis3^XU$(StPC5~&w=J=$!u{7|G_MZQGVXoV)BDVs
zaDV?D{tA(?v9dm!(hsBRhchxWTM~|{C@A>JA8brIag2jwyFE$v^XCs`Jl<qw@%St3
z+O@0d)}hq2w78ESKUN3s?a#lmH(Ysman)ABW2)m7DJkjIt5;Wu%cS0wm6oPCudc08
zB-g5HX{AUy4Aq4*`Mca<?cA~d<o}5p2a4zbKgxA`+u9svdynH2QdJwr7AKtkAQMDK
zN0X8Gy?wimi1Po;9bk^4wz;_}Dk`d`rslCcTigEBEDuTF#3UK}pOrO^g}Zx>4;ffZ
zjZwrxaalEt7N?M!nmX<AV|n(-r&=k=4<Cl?RK@C_KVNXUftHu|StN%_@^ME}tv7x<
z25y!-d-e>KEG;d~ILW^3&*Ai?ulRWe1_oy4-p`-?TDCF>cXyHh0v4&V(#P9dR<?40
zj2LG*0>PG+W+5+6^eMq_@$tf=N6dVDd=3r{EG$WP?~+vA?)+LYGcm!7gmvi9;MCMN
zkHa&)y}d}>_TS#Tdi$1HpybUP7i?#deLt<n1JjTiPuY|zvz4{AK!1O6F|qm8b==qi
zz6+{qYUIim1tVA-hvB;5prHGzoG2|lJqBXsd3g?PX-ZkUj|&QB*Lx8)eH>d%k@LyU
z$Z#I2*+ui_B7X-`o}g(3zkZJiyGTTRXh_ISXXjcSnF>q#f7Sa`)cd(tOU=#A<KyG3
z93lbcN=izLqfH!CWJt8gvpnL1FQ%ub-@5;L{`&Rn`1tt9$hN?}Z1X<5!kwI)j4C|c
zKHNV<Lw*^@Z0>t`^(BF*k8ho)VoOW^#IfUQ067xk;#^c@rvmrvCL?<n<>u(P2=EgV
z9nHzbrT5C<tGdr<Y;5e~$B$3mAw8|8*3;d6fR;9`>=a7N9Dul=*L#oP8v1~8ueINZ
zb~ZV0njZP32UTV@H8o)jN0k*7Evx)?;A85J=~#QyhC2VAzKDED9b5nmp_gMac-h*<
z=39y5*zIlGIXO9h&-U?I3Kl$i`&Qb~(NRlF>#YbjL_$hR3b1|tw{f|m1!Xm>wCjzH
zKhDwL6CXYVRCw~_NvX;ZGO3}VA*u?oudw<1yN!(+=SQDD<pvT#G+(_sp&lpri!~T%
zGUL@N7HVq0X5w7^m&5fDbTl*ri4k^DzcVga$fn?z&&Y>;RZ(OL-1F4`XlgcP2=KKi
z+asbzS6BD<@82ZE+X{0oT(~eab;{Qbr#@?UcS8e3Wd%*jPPQsx{=<js8ymyq5AyKx
z&h%HZ*&kSsh>UL;^I4g%>gb4-KS)V0{I0rsyK~cz1y>=HxAJE%>gxUi@N_+2*BKfy
z@A?+osF@<0B!4iB`8ai7N-*$dVc{<S7l@gZmMfwO$Z+b04^vX?FI~DL`0hI@r;g5k
zliRZ#-QC@Y4CK~<cPLiAO-)VK$#Y>fwi0C-8A?HEafHKjLQ2Y7jB)aEpE~F04N2rJ
zWJ*pdvg&}{Yg0Lutp*i`sV~uYbae&YN>C;)FQ87Z=-9n`x2aTTYaheYe{@#w?D^5w
zc<>c1s~RDh+IEY6QG0u1P@#%eojb~HtT_pFdmkBzv-2;T&g@?%G+$EVG`K^9gPW30
z(AisWU{UIaFI!oqNxnkrn3@V5a>72kx)%HS5l5;{mm2;`SBY>JdWSq*Hfwr@JrYsE
z%*;HWT&FNMDML-s#J}>OdeErU>FRV>9trVDb@eGgOoh{0H>|!Wb)&^lRt`|*L}jk<
zTBB{6Pm0vH78t)g7pXrlP_AMjCntx3MeO_d<;!)Hi@AszzZZ4&*y0u2f1#>_goj-A
z#o~w7y05R~#m3S`s-D-@?kciRF{=Y^A}1r0zh#vycJ-XHvhti#YMZsWxjE0adkjap
zd3kp=ZLx7U;K7`n3V^p!IPcxlw6I{Gq&B*6VRUj5h(e7!ijH6Zeq3Cq$2Q<jFHcXL
zz+lB803P&59*?#XIUH<krjlhmNGa*%4^pA*q)5Ac_E6`(QzZ$s)|z^17s>msyi4}q
z-v;+w_32ja?dTYto(9qgwIfN2iTSm`lIii1IH*SE^*hCX^!MXvOpD7tcAl9K!LBQ3
zw)a<f+1T4_u}411$Uyk`&+_VCyf`s3qIi(%gXK@$kw?irx&uL)nK)0nXV2~{6iJqJ
zAl`ALN>$q9_jFiTSaY)`nyj|AHYCK07u|;I!jYV#K8~Qyy1Kik8OmRxk4;Lte)a0<
zgH${;A+KIt2RfTG{NB+)%gh|cK843X5#@I+6xjT3f3N1pj~~FUH01vB2Z7av(bSn*
zMQ|7i9upP4Ir1Sg>!_Q)KK<nT4I5<(!MHW-Kd;Wy`yVaI{fA~}O>}hbyqWTl(p=`*
z9$BnH8&CERwA=@zbL-e@DX%LhEghX{uGvXDJG;}TKLT##7?oI9S#|tsWW9X(vbs8O
zyeat`Hw*d;Mn-SZD-iqMmQvWNSNvotYTsY+DlJXnAXTYfUP=nvHOD%RJnS)gz@nmC
zNKu}io*EjBsBsrw>WkQR35zDYOiO$1wdV4+=xBgBPQS3IC_5DyiWds_{^>7$94FDJ
z>Fak5RNdJ{;`i{Ofvc<JW*B?bYUOe2v9U1(Qq)Jwef#zyAeQI)DFolFNk-I{d9I31
zS_|;;G11W6O;%qDRkT25MUIP$iz_N9(0=yinEm&cMkRy*H8SdLZJkHmbB#l{(8ovj
zuR|@zL5TOH1yv39NI*`#m->iiUw2;h)29;>6HVW`?yFqfUm;3a4d^Gp&#%q#Dj|X4
zyH!vNhuC|IyxIQBoYd5l2dPMRGmgy6gl8+(a)?B#Mx!`&bZjoR$Q{;7mNtJ+f|eWE
z;WXCv<Hw7JhCu(7PoI+h(5I{hU_gN5*->DlqV~tA9WY35RhLR)Wng&r@}<T>DqvF0
zB&lDQI2N!|ae~Hb?2(F!idgH-ODcA(5pnVHS?TGg4pJe4w-Xb$=0En1R1GUlXOniF
zUz%w5_Vz|k2?YA-(<cgAe$_K)4!o_RSF}i#*=_O<D&?IVH(?>3EvWKyb4z&rSwe|L
zZ<t!&vWG!*<jXUil~<`dI`5k6BV^EWpXJL#Q?08TGeFr_k3wJWu?!qPpQuSuNSz)i
zJlL0CVq|ybOw+Ha&Y9_H?NfPve(!<F9B<w%HWIwXB_ScfO+^Nzgj6}Rv0CmaTbZAK
zl%1W}xa>u0ssma_Hl|<@8VIA4+)+pluP-;;ym_;fgG_U9!BsEYXmvP3j*LVBUEQ5K
zcYK~*upsw;?J{FvZ$G!2NdjAcv+1EYI*d~1sSA#d`DQ-bWK*_uBUgSj#QE(trzWYY
zPaPK1+{W<_qN%kEAmqE(=AsW4ftR<$qBaD?2MXYa52`>Tq6yf^yGYLzvPWr6EiPaF
z0gQ~cCqY9(SeS>Ozh>*}Fd0yX+ah=Aslw;aC(*#QX1sOfTZl_m@BQ+{X|$0+TwI(z
zl829PYJ6P(>{;LBNz2QZl{l$uYieG;dbJ??RVF*BWejve;N81CJUmonBvs#>kW!mi
zGWm`id6bk?TU(1zNl56P>df(v<zITx@B=XInvG5Rm_W*jTYD;_erFq(k?vvU0qPqY
z>-6~2($pk=^ys$=ud;!~yt@}_#uj}(uw<4A(Vn?#XJ=CC#Op4&0E)xIM{ofxT|r@?
zR+1Fg(llR{|0zz|FSi~3nLm|?*d2r<z5eI{>zeBW)F&n;){L1i4AlbuE9}05eJm+i
zMNdORzN3#!N=Bx9`4=dNn!37AA3yF3Rs=eYj;0aY@(BaptOS7l_U8I{vu;mM51o+7
z$jy=i2M)~6&W^`+0{S&HH_w(6AuI3P%ZdYqBp@O#?zQ^!a>SyKBd6W<>%SHkPesgp
zZEyFOA2=CNH1}TblT|*>Td-g@=&tfxbF5OoTHD$NXJ!P1goFeIXJ=-N4GlvpGuBjH
zTz+GpT;{&_dGKv$h1a}#^$J-pZe3bYMP>PcGa8m_*Ph45UT}4F75d1)?ywvZ!28cw
zNk^=(UaYXNSSFwh1iPl@y=TvO6Es+b&2A$Z+St5kRcLbzZp$b^9n8zi>${XcV3>7&
z5?GR#CZxD{WvDi^;nSy9pEc@W^dJ5dblNFboNNS1@AxLGhuN9SI1JUCxHY?EavOLT
zeI<|t@`rs-!Gt=U92S7qQ!uZz)cySV=z$$Yel*r^3k#jm%oE^Eq$=XJq@*Nk-ASsi
zzu)xq>C@-We`#t$>P}npSm13*kvk?K@q2lBu3Tg_Q+Ws>E^gDIs;-XD@V|Ta@oc~A
zE`R0O-jeiZ&)g<HXRw|aNl!RLO_5rq{*Q22d4NR_`ncrm{ul9q=8HB#Zu;`|D{5NU
zY=FNIU7tCgQ4Rm7soDJXYhigg%T`V+S%5j4tY>as9ta!sb$j>hsf+6XTC>Qr>n-+8
z)_d~!@xbtKdw2K8;f2rb?PoMJaDjk5Ebim2sV0o9ZH;JT5A55=aKgpb$cWjy+A=lG
z+mUm0aTO2;nT3X2$-uxJy-oSCdEi3>?0Il-s?D1P&X0pPw5O1t3-a^V<_GU+?^=kX
z59q7#@~8`A$ka@F-+ymQ@5V@`vITAEkI~T%5G#l}HntSt>ndG}dza{G85oXV`;vti
z_S{MJXj}Lx&RIKRoqwnjk5y1-WL|sL)(9zCd=Z!8;jw;qdm9LiqgIU{K762>+(l?U
z5ytp+_Uu{kVBkQ63fn(VEF~VZzsGzWtPP67IpNV?T-50eiRe(!m4ac}Tz`VIj?N#s
zh}_@e>eYmll&uV69NDDfj>;D=miTOKG99z4`Ic3t4vOIRZFCx>L7}1c-LH4Zke003
z%4nJk(?>=|0wZ!#f2^tD6c;b7Z^&Kslnt#7iHO)jN(Dp-4?pALB4KiqvO3$eQWmv~
zJ<{6JGCDSvyXIcb!zwcpQqty!;#0_d<wdH;#KgL~y3ixK$mmY>mN=F_dTV{{+UvZ$
zNR;@$t-hy_<52Cuf-9C+p)emQ_2<u<o`&;ot*Te9WQK-@R#eEAsyuA<S%_oabEP3x
zz&P&QEty|E{r#13zb)7QL-}bEC_lqF78Vu&?o)BQ5okuad68gbVq?Kg>+sMpFeH3^
zp%)h$Oa7FFvKox<t?8~d^bBrptDtz6RyaBL1V$w$0`>_3G-PJpn(7d!3JbI=6St@d
z66!Mvtsb<za^+ihcO(H<S(uwI{GKr^=%x<<HajjQ_36V05Xq!FcBGEc?@C2$b)_X)
zKtESrS-I~0dv<Yg-CQDtqwUrO=rh4u1c!!}6&HIx^C@gCn~y_w`&MMHr>#vddE;?h
zoZjWj8IS27hBy3hk=b(l`dk+k4#gU$Rl)Z+&IKrUR7i9x6ciLw-)&GC^1BI`Qz?|T
zyQgP#WW>po!h};c#njZa(xR5!Y3EBoF*K1?Tjck2o}C9tk4vE=MAVs#(s=4wS&f2{
z0j@=U);V|XuEfr!j~02XGVWs7We~!w%lkcjnfKJ!*6!%bvPBnNF19&r@4N4xXZ{vB
zG@<YAU<74ujs*QBY7&mwCu^IUN+fO!)lz`c+_x_hp=S%C;mH%l+y-?1s9rZ+Tv)}d
z?;~Y_{su|)T`a_$K1tJOc{V99FwoD>FFE;phI-sx_r|nucBxE8Esu^Lm61tOPH&rV
zBE8f0{kw^w;oADDBW@J@j1Euq=_qd0O)^2>>OrsqpL%-San7Q+&xC}Ark{J}I#etC
zvb-F3;{_-H00hdq^446k*=pJ1*=OhN?d_c|<Lh2nqGdPt1iy2C08g+%;Cv$3<V-GJ
z<XtH^ES0p0&k`^MAC;w%C?Oy#Tj4QnnWqn)1w22_G!7&#5FQ@BqR?e45u-+6-Js(D
zE(w8Z_u8evg|5Uf*KC`=!h~Aw$&)9`m##xVICkt<rYEa=iq4G#l%yO751N6qMsDW2
z@X~elCs(*~wT*AB#n+CGr%#@MiJqF6kn#Baa{0*k^fZtSS83wI7cXogu8@#)?iv0^
zRhrKsNSooh5w9%()1nS*@$>T|c?1Q0z?Sc)rpD4RF*43ys7I55YQKj~_L2O-B@mXs
zCco}wm0np{;P{^0IJ^L`_!gQ@L4k5OV<AvrrdG=6j~@qUXx@6QNgO(44iW(RNGPp9
zsn3>d@{};;6xuH#A)nvV3HkZ?Aga+ZUbx_L^CtQ3-Qf`tS{fSD*D{=L-9jJt8oV?L
z8q_9Kywd(w`aViq6noIjSW&QTs7);`EkZmzh+4^8vyT!I5}rOC1?7!Guuv>W5@=2z
zuFNMOQ0_Q(4~(Mw+uVwZO~efz4OnF1_Ti<vSs@WhK0(3X3k#?a)6iC2rn?rP@{l}8
zN&*FKfBCXFayUQ_$T6R1dN&BDJnAs|GH}oUE9)B@s7~?tVC2e2kEW-lPJpcq-hVh*
z)~hs*R*y9T3LY}oB@2tz{HG8L0NvPR+|PsgZ)@}I6pg5#D*axJgTc*hwKU$w&d#pL
z-uC(P&%x?IfFwUhmwpqmjMP+f=pJ}#uv;h$fK*HQS6Z+zU>oiFN(&)Lw56*+?-JnU
z4X!ftyn0ALKmb3EU80xsmImykB6D|lN2o%(OKY=sy;`~C62Ipk9pC@xBl^QxM;8&r
zptLhL`yWHnF*gSx2tL!e%H?f9Kman;M!%6xcvzUUj0_0)9i4q`ZOGri(>=i{JCS^_
zK-sj-yY_Q8CLWsua|7kjZxM<p?tTAZO-V^f`b&kDcmE$R06qNx1s!8sXXi2C&SHm4
zKq%Tp*Q+uXR@c!df=BM@>KdP%)Jzb)Jow&UJ(eFL&uC5Xemo$S6iagVJNwFmCaWu#
zFSE#ccGcBcL14+E$I}w1t;I$4GiPSFKI{_Q$u>7WuBxdC8Djl^IxSl(E32zlkE1ik
zZZ)UK$#HT%iL<e5Qy6#plXT*i?e*)2HR2y<XUkgDkf9?xo30#=atrMQNE5KE+;pnJ
zQZy<mYI(Xl->ixlxuf7L60(bn3n(f<9-enC+K<-)*H%{I6BCCWCnqLAK(R>PASmrO
zeBKqEwSIzxBPG?-+w0j|?7*QMrmdsHbkr&g0gUr^So6{N(9qA(rbLt2JLdWb7wigP
zZ&;l9<d<hi_UP3>X{>&ppiH%R_b;TiOopsmIQg)85d9$M;lnB_Dxg|7aWUM3={2$q
z1|=|MXb*19_68%{K>%|c(?r6Fh<mdcR(Q*lJFWpJSnKrZVElp};xMeNckJiv?!LbM
zAT9GeeSnHvbKhlrHa$C8-h;)zh5Gv70d>{);g!b9_hfgfK79OG;=S>Qpu(oevK%-N
z^Wecb9i8pIzxA?Mc((r^s>(ZiLMM6bg?1P7KPm^o$lzOn>M{F*rtyC<6eRA#BQ_nO
zk=XeUI+6gc9_N6PTsyL3@n1?i__=i}g8H9N?%(teM)|LrJpKasv_h@wfAJGkCg4l`
zFBQxk{{i0qY6X9efF;T~C;Y#-7ykc8`?s0q|8u+6FUK#R-Ug9U)^nw`qvQA9oIi5e
zd#ZE6n;(fmgSa)^SUF8eA0RFvVRhw--h~Sm^uHrwz%qFw&4BEOs&2{~*8r0C!>3Ph
zMXVmCxI;&zyvavwBv_Q4J-e~C3{QuV;PSUm?}isZV1m;q6?&4Idg#Q7HP{OHX{Wx?
zHver2L7yXcAbZZ`Ilk6^iR_Nzhi1#(%J-Nb(VZ$DK|y2{RP}XVMs%RKETrt6g8ONA
z5b}6A%r~=rJ2%(*_nC<%K&LUuv+xIj2tg+5<N925dS;<$LgV`SI-g$llc!HN{T#|O
z*(tOx<#(sZdbtBpq@D_drC|TQeG7Y;J<aGlK7W1?6XU!vq;%!V7%FCLOibznbNUN9
zI{7H^7xS%HKpFX**VSh*Sw144*$%a4wy&%R_?AmO7Wr(L>E81;g$GelUS3{wf<~_3
zI`7@v<5>vF68In)y(;uvEc*QJ$g=cw4z%37ydSHpFKw=`wj|4}naWXg^z=OZTY~3?
zhQOc1BqoMBR(;q@H*iA|f*J}gioe!W^*nkDI1}u<&ic51^e{armGm$s<^XWez`y_y
zkiPzh;RSaez5XqDIq2!=mO*nNd-e}=p6@SW870|9wPH_5CH5by-97e0BmZ9Fc%`!C
z4g@qvE%uIEceX&kxPsb7n+|Oq<xuWEr%zoSMDx1=0jNv<itHfrO-=iK2A*t>`sj%&
zjz@!E;(wZ3InR~bZ|*hxsPNtZ=bNC&J~25N8y&qK_A21=rW7$cg|RUJ0;l(PcL5@z
zmjk0{>T!gmIu|Gx{TrGWsKWqgxw*oO;Q{tm;K|TCffWErHuJ4$hX>cd;*#k5;RQqt
z_E$NK{v>-Om?E&R8#1q&%3n^UtkQv<|FiTAnCGv4a30J#K%89uq|cZE${oOj-<>=7
zBy7!QJ)4h4yl@pdHQbDvS#CkWBh(InR45(5sRvyR#yXt<;XLODe50b;p@0P`4xv@}
z4k=+fhXZO2NL_3Sw#U@icw>9qx{bTSGbB#$9cafY6$I8tFIxjqU%k5ed`UI49oH1L
z|1N#>XnswNA}}-`J+yajE-rK}ta9FOK~4x=$$^as!m%8cWaXzZP`4;PeYxh_{S{X0
z*+tM6tgkpYIbq?`{Rzq;0G~0;1-NC{3xFS1bQ7z`7DXu2+b8f0H|CcLowj0D|FSTe
z=guL_V_v?TE>g09YXe0V3Z9_h8;uJW-gt1@L4_;3mE-GM1xoQdNFZI)laM~qLwK$d
zYBLrNo{qKWs*P6p=%6ZH!sW^Y<26R{?|?hpXC9J7(s$1O^<Hec#ngfV{$6flW+u-`
zjeZ_FB3cON(`G^8;c%3U<0Hhx#X-xW<(_}N@sLA|Q9xY$7jy+^J=~G1a?;f4TK(Wi
z#~KqHL2f*Meq_aBOMIDx=K$HdCZVup_N*T$+EJ+9i)XO$8U6O{TR*5)Jd^22^zp<d
zO|aB*J{5t1DriGYe+om;7ZQpH4(1gS+S=jMHrH1MjJq76WKnPn^5-l4JOv)=MS__{
z4;mcK4KTNTS44t_71~$e@y$%8g$ncPt<3)SKW>6adzO~=^Lixx^%D{G6uWn`NI6;m
zWxF6p!pLHB?%dBNmgEwnY!H@VVU2o9L+D|U0VyOdZb^xM?d^qLOBqT3l`OHz8?gxv
z3qR;>!g7F)4(&BS$PpeMX2io<1Y>|Xs2fd9O_h7hspp=_<#5W~_=t1}#+r(bZi|7S
zC+6$Fgf(h?p`H!4rt8<PO%B`7?(LP=ry;xju2K!|z{=;PTNF%&CMMwdW~QdruAd#N
z)E-K{5PVM$hB%PyK=obqy|sfka4Iik8zm$qZBQr=!Fls#W+r7qG93OS!=y)#ps^-@
zS(Dmbotxe4EGsJuR%WxOInT>@XXEmI5?AT(fIvXNl}D+;xY{Al$|w)b35mxwKvy1z
zeXpNGB(X^rJ;wtsb)Z@As^OK6jtgk{f@-Y$vw%Kt4BQ3^hfcUWCtzxzprqsv;(xNb
z{}O@1q9h$&hg#8`v}U^c%J$kdg9^`*Cr?JS{tEPJ8DL89F^W&Zcs1X*nNd#h^bQ~p
z6;7et-F>v5^I;3EM`QDAY3Yq!-=E5#NBf6k3*Nk${Z^!<q*UA9o{x-D?{=5_r|Vm|
z0kGq^!3ub6=)!8?r5Jzk-ba)g<OMkN^)6NLRFQwxh2fDAlE5<xYlAuK59)`Lu=S@-
z4WHm}0J4X$fLoJh6%rQCo%_EPPR(TLZm=Zi%R0kqSXo)Ag2AVv<{-{tD$7HAlfoDb
zw*m?W1V~8gXd*c{(qUlJ+w2;;Yy(~zl`cB^OG_xe+E?mq)0JzE)&cgJ%7GT1?7y`A
z))e7*$nQp7EiILDvZtr4hIkGeB)mWsPCNJ`>cQ~jz&it_Tu2D1X<{KXxq1-C5#9fi
zDQ&1OXp;*Up#1W<s;CLZeFNnNX9s+S4dO3sB@)##fCr$!yeuiXcw<-4?fPNo!hx?~
z@#orqadF`LA^2^&!AoPF-_4S;(}||5yF1~*1A>kQ+E7nVFBJ?qT2)XH1VkYouDt(=
znJ_)F6&f*xz!*F{{*DCQHI|CnKXp4DX)#W+X7C0qTLjKjT^-Ju%I9=k0p>ni8%4><
z$sr+X3JUMzp6hA{*AL?mm6eq>G&JCtuBu1U&j=tU(ZFW?x%=k)jReyZ_sr>^CjqL%
z%;8jdF583CN|+vb5#J&=-^Tyf6q;6Ejt_;41EpL>8OgE}i=d}>xOneC=PqOjG^OzR
zB-dJqBxtNVNIFSvpoit==0=Z-Z>Ow|*RVnxmDvJQ;Hikhmf;0!F#|9=ehMcv5Y(;p
zXR>JLwM-FMLVJHG#7SXM;-aG=vZWg9S)VmsdtI+(3iWT<IH-ECpr8PaO>|rwyo%2K
z`zu_&T6;?*_O-UQ_Vk2IhH7SZ;+*R0!q|CBXnO_ulFV-y-O%UY{y_$N`EY{KnB}5I
zCi0mm+vi1uD9|p4Cvlc*Y{3-?<3Jcf3EWN$Xg6KmU0y$M0`N=s#f7sx(GY4jvs4=g
zZ%j^3w$3Rn&z<UxZ5c~9;1Ljbm7Tr$dD$FnK91~MB)zU3j9AF@LN+x%PlPFlZ%Cd$
zQW*D(JT`w#GQgaYG`*t2WIV3m_3LxvQ)C+hX-OBy%M@<p!IA(803Z1JHFdxGjw_Gb
zCkUI0%|L|Rxl;{~N@#7`xo6hL5gn!m9BJ|?LQ6KtN1<E#>-DOQmZHe~Wj^Am_AqiP
ze-YocWiq*O2R=sBf5gDn@EpsZg;#&wc2hr?C`-)g1NIoV>N$9Mm4}Bn;p(!Er%&(d
z;VbniZZ(&`eqA83NjZX3{;Pl_T!G=Ksi`QJ3&ZvPze%ck?*7$$R{k=rdjPc_CMF&g
z6-Dub6BV>7RC8pJQoE!{C^Zuk40LpQCMJR_KbnUZ5V`QhcmhX*Q&|1;XSOSk1NauL
z^-9(L5GtHs=(3cQlwqNvD6Iq%=jIO(&k>=a4fvj|%{BX_Z$_r3TM&aeRPNb!zpia)
z;1dzad;VPQMmUNzF#7rm!C5CP+zMa`wwPcY(bS}Udy=NK@~o@t3K~~9W!G*7jsX$E
z%nL%aIwcTM1ndJr6T<e*5~CwA?lV2&z=EimxH_^e2*|_W3NkXjc6Op8kahbx0-6IZ
zTT~_V*M|-r0&g1;7RE0ipj7z>Ko$3ZkFI0$M4g<Pnu3ef4RQ(0L*Vk^BEsi@SSc+l
z1Btpe`SnHLTy@pp4Oy>0PLREUB$B0^j|f9F<l(`EK)J}tRpMu1R8&simAY$|76lBs
z2t5ouZq`#ITi?7M)mp$ig478YLZm7uXl=Ng;d)vHWPzwS9z<T9i;si`3*HQi=j!1B
zo<dPc37))xVB#5q&r4HPH7FuN<ph1{oT|6?=AE5;vyDoq+1NnA8cVaKy?=bK1{%8@
z$S&Z%-oCz#_4RC%a)S#OxLu_W(+8h8aRO@w3^+GB`UWWjs|xywyt&uw=$dH8U#eAx
zpMM%wLU?aMFTwX{@WwVlo73tqF#&Cg0(-w}*FI1By`i<AT3Ucpc2QDFJB@1tg#+xN
z98vGz-)-vx8;FI)5U`ml=Y!(n;>gIeQ1N5<^pd6B{Prm0KKkFf-Enz>PHe8Xq`jqO
z4u&lFp;s;*S_<ocjt)}l?%lgzyjX$Frsn46CMVtJ2dW^&J5@4>CN_b9t@K#7gY!Bi
zr5{0!hxS1RMDFwa$kS5v<_&;7YKc2G4@TKv^YdhT_o^J|qpM~eLoRcJu?r@JKTAnc
z&g5QyOe(zv^lkWQUqI2rwIFl+TwVr7yCpCG4h0WQly+>jaF|*KxT&<hY1}Ey&I(NG
zneC9b(M;k0F|x63jkj?uvH0J!AozlRP3rpiY@ywN(;FQFLKk$5-M2Ra($dn1l(pI&
z=rN%W!0!cu2Q=b0a5DP(@rdHruYcZpL%mEN3@8kMflzCWn?Vaea(Ttm8|efj8r*X5
zTY&J~*x2A;X9tIaU2Qvt;R5l%>U|+Kpy9B`a!?-;T77+eFl_|+WF=@2Ec2Z&FLLnm
z!pfo?!OHSi8uLLw+k3}Sq8q^mqpO7Dv-~XqT-;-mgZuGF^lt4(P!>=4Y_7u=0)Gft
zMR?=7VJg1W?+i=bcyAL9*YNOg1gp&C*jN!90oXrj&lT<YWrcZ_Nib(fouJt9^&X&L
z9Py|J5AKF^4$FpVK{Ccy2=?)N_hfI5r~+quczD38245A*V`3uHp9FN5*q+?ndDvy(
z{~8aRM(OA~mJ7oHz_N%4sNrEO;^NPrQh@9TDu@-WSN2!u0&?Ka3=Is_z?y}GG$+fP
z0H2OzATEBOGK;>ig&iV03_OVSU-)6<CR3jcU1MW`6$UVq0EVZa<e_4=bxs5BgI31E
z*!5S0$98yd)(KCe>A~7U40(4Eg%ptmm#Mb4Hp(ElIBXs^9Y2G9hah|6V9(OMaFir)
z=U4<JkZTA}fUBK*n9-UmySbILmIw>R0sbb#3rb7tf{2I58m8F#`g%BNmR&_rZMd+z
z($dT<rOco$xw-4mpD8G$dGI;F4T)d@SB-uX*82ju90`KSepgzVz-qYBU4M>zM1jB_
z80hFMf)^loLniCwbdZ*ttROKe;aT6kLk?3N*9mj1A|nujo|z!o>`6v$NP?IIq(!ES
zii~6svu;KB+531$XJd&$GA3wTICl<vE97m+OIZy{1s()(q#+ClO!t)?gFe#z`Z9_=
zR#Db@l18lr$jP`H^4e(>W9STMF0g!n>L6=T!m&g!f<n^8+8q%Tltn0GGD7(tGoFJ7
zerIQ06K(DLW{+V^@kAuTqZ%t{Jc(untc0cI-40h6Bc=0>(ucucjZdNuwzRcfCj^f%
z6h<(#B{zS3f?iJI#oF=mVtPh~xK(33EFzdyNlYxe(!vT!7xEW;vPjHuY44z*o&H{a
zLRR*BON%}1{XErR888BX0RtF3Adq0;E1=zibjE>)1_<>9XN!{bPOSwrM+ow$T;QUh
zxIlsU^WL8VJUD#958~nuM}5TeBC*j(KS!A3-W(vZKrBK|z==Agpa8j0OiWBeLjxkk
zbz57^4cy0}{L;fwyb6PW@pAbSZ5}XE*q`#dSC+EzSCmW~<2_6gVT$a(kQuR#xGmr;
z*pkPcT(Qt*W{>f+gcBLjg42lJHT}sGOH3$DeCBfEiv-7jCxY$wt!bq<rV3yV8TZ_o
zq*;lY(ecVKa1YB7cJ{Q?RD!O$P8D8147vn|wgr6_u)eXL15C6gy1LG-k53}~9`JPM
zWDUlQ0kor`fdOInCF><lP6+4dbTHv`GBAfx<@y(72zb4q#-a3}Fq>eDKplY4nO6<_
zsjH?I0-W^lA)}Os-`qQJY&hg_8p9ia(?hm<cOOCk^&UQxx8~KPQb{I8M$;1$c+P_Y
z0%y3RaGBATluGM1b|Il0d<K3L$r&mvJmWAm5T>?3<RSH-VB;Z_msNpo2r7kCl9<c1
zK15_|>v)7YJ-s!SE-mdd8iXYWb>J51$CjcA*tLb<zu)BM>KEB10l;Ds2{{kkA%tt+
zTl1&bR<Yl&F6P%k;RNJCeoPWJC)m`%8DXiuZ&+6deE@8P;UOREP*k)R_d!Vsj{_5Q
zF65{5w6yt~X)P641MFLV{vxcEXi{=syf}fBiN*{CB8~e8iaEaE^6>%J|9D7jI$o|q
z5G)nZ1)~C450o5)M34q$ta5cfZlZxh-i7t(gzLN+q5?JvJiJ{`!By~HrvfPV(b3Iy
z=A;1IVM9pvnw&Lqx_J{iUI(T_h>3~cz(0%r0yP2Ibz`1j{=m6~A}M|O6Ak87png@l
zE)d5JF0LYHS&vQsd4wG{DR*~<T8QGe1<411*H(7#_)}TG$Q7JVnBxoztTAEG0R{_H
z9Xxq7Fj+o0jqSjMS3*KJut~6D8elkl_wXs<ZszTKD!vHG?oHBEspLhRBjJPIEzHfm
zA07Qj(g71%{NAHv)w$@qfp^d;Uo<fI<H?FT0GzS(>sL$CiNj75%dmPZC6v3&JVc9u
z3nQM8N5L`RbDq6=g$CDqX{H_knUN8`2xb<Rz}-yTfWNRqKo3J<NmOJ<g@FrN=J4U2
z{UP5~^!YpBG$Ux>SDKk|@?h0KRm6_hLkI^Uhs39$VGF?<@D~UbHi+I*=NF)-gZ6QN
zsXL6chy4RUqUf-NcM`P(M-R$h9v*=pCWG#UjTlb_lN@0_>kp|QKmXG5a*D{M0IUx-
z8ZKcNZ)o}T2d1V#v<Cg&La{h;q6{bvF!XDE{goe|Vi5Ew3jIa)rkG6#tgaG%iCaMO
z!4ZM$3C{|6K(Ti(n!1?#_o?>nO8}5DFaX^HOEPUJ;oqpK&lwqo6~m+h*1E?zz#X>*
zeg?AOX$=iZGBRN?F=i2qyU1hE;PdhpP-3}O8o;}u2?dlW#HmCNi4irxLYx__Q(xIF
zu!sA$63p_uu}t8l#f}{V(L4X^S04zuf~)NTd)X?G!{OpdjbcQGht7-Xu{=P8g$2T_
z7QV~L*%?gUN6Xh{oXQ@T0GL7!@IgNW9s<XQLi!bF7{osIs9kO^%J}@^A`_@AIJ=QZ
z$`r}~hyP?m#l=;^4On4J9{_lYWD3H8Fg(!LQuwRlPL&T~H05ywLE0kYl4f#$=nqdc
zD9&I-i%Rbe)RuhcZD7ri`EH`vgR6tp9iv6)_)i`RsWQWkW7@}9N$CfyWN%xxm-YfX
zoY&IYE5rQ+)G{P=Kw1R_1ytq_AI1^;Su;OSWRS{HWRRtCkWM&_w}MLoqYsLH3I<kh
zV+1wucN-&2oj?Gnk*FNlnopb3mR42>7&TQ@%u}++c{8&_qef!<0eKw*69)SFOPjfB
zl+|F3Z7yB91b#m$DcoHM?e<JxnI76YeD=7LH!5PGP3Ke1B$Vb^(D~Zh@)_saj(a1h
z|GFbrz*cwl^Z<YhUVLo{23Y5*MsQfzTU1D-r>7bT?A+V|Dnsb^k*}wFOLSCJ0yVhz
zGD$RIW)|~bz(i15=a-h4Pq@59%)p8Z<hsDNiD(3`Mad%drMfyD6ENa=-=R)_esY?V
z`t;eeZGhQTRf9-7GRbr*uRIqP7Vxl$M8FD#zDoaFp)EOQ8~J#7FQTWx*+-ls^3nUD
zu4q>lqZFYy?Bh@d>_n6N(^Z<X`lh2JN-ieWKyILYo^Rg*fe#N7Y&suM#gRZ4<iGdy
zl)_?7?w|JbX~%(<R_;rGUDvR(LKFa~aMG_f69$^bgj^YG$;jAP;H|KFj=Y$duSla3
z_TPJ*M;tI-2SgjC$_bJSzEFy%4_S}>R^Q)tsQ^wq$oj~ut(u=(TXQef??KBeO^u;4
zBy;2wa8~$-T}p(Z5=;o-BS%Io3kJt~Dj}c)qF~1EOZibQE+s?+^y=njjAw<YWqh_4
zgNG_E4*7)OtirsqVq0tLz}y_cQI&S(DWk^!;{{0bbNPa01n%0ob0=Ueb+DLKBR$4l
z(4K<FhMC?1XV^GF1t<>1f8`l1E}WD!Gd?bf5jenzG%amVNtv04{S_D>Pkk@<Xj6<X
zLzj&t1u%41s<*DbUhAP)utI7hTxposd%yfu=rsA6dSN(kY+zIY5pewYak4iy^<B6g
z$``tuh@owP)u*+zieA6|gF1pXs5Q6**au1)CNsdkA+HT>2nkcd1%C1uX4$T-yS2fv
z`s7IsMp_h7$KlBFT)7XYn58Aj&YesQ46tUx5+a0%MF;{7pfNKR(1T=ws5^J|EHwA3
zWieRxaZ<t0PEAe*U<B`Ootdzp$y@lh@3_3NcNG+Q0CRJnVKBHJn03&BBcYw<e1HRM
z#%Yz`jeZYniB1*RLMcV<NX+EG01%1*JG-dEkRq}XI{LJ!3)=Npv8i-)aj3PfZf-EB
z;NYp~=tL>9hqIjcjr3?FNcYPDW_FBbAC6ST>44n^eaQHN!hzIlGn*JQ>4hf}k{`0-
z$zAA#vaMVIFfjHC)CLRIk|1L^Ee(wrQY8qqRQu!56Ckd5Z@6Rs;d4)t^<vDSfa5wt
zRU@+<7=>UX#PnkJV(z#{uv!M(a|AH~)e967o{@P^Ci0cA@C|rPsZ(|WKc7jII4&s(
z+>2BL8$L4pt^PFDO!Thn8_WF!SC6!tXrwB$w5zaG{m9f56UK0X+P81tj+2Z#xDLh`
z{V0+|RaF%RUV(}*f)@?>)5!_>Oo?I+qhxRpA@gJ6ne_z<GX}@fU%i4y0$+L*7l&%C
z&kyhTBGwBf0^%G1w4I&c=2u@?UeGdF8n^j@ZK1XAg<rxRDlDuG5)_(VUmuH1oGjRW
z(5@JcL#9OzK@m5q^ezYI3p@atCMHG~W8-F=tdchd&`V(oWo=<A0LL7O1<4Uz`cPzX
zS{l2cpdD<1Ak#3o*8cPi;IMJ0*Za2R2Vjg5SeQu#($Ef1Py7wD4AeD7dV1vJ#}p3`
zV33+28KQxJLB368??&%SfG1Rs`g<&=j`^O7IFC^bTtmT}Y3>)s@BxM;a5ND`7*<Pd
zQ3uD_+13mTDg0w*oKM@V@pFkHm+JB^)uZKTE!>3`1%I&=?e6WBK72S6`ZxN?+S<$L
zJJCks0AW-Z!^`@wEra2I0Y+XZJ@xhBg9oCPAE?+Pi!V3CZpBc%^633$&JG19hcH`J
zb}bVx2EeyMM}qSaj0spP<xGjIVm;4vGBG8D@nsr%`k;I6NV@2akx+0~YfBS41w+8)
zfUQBn!LaoFgq6>lJ+xL$Q<GK1g2Z1TLCSd&O-<`Qfw%@_RbfmYPzPgKogE#k^QmIg
zpxoSt+gn!`JFR2`N_Oez&xaD%4HOiJy+^_s?}GOSl{VIt7#9=c?`H~B0V)m17MRmx
z>njuhtl8JLwu>b<Vd>p>1fwp-#)4({PNt`)x1Br=0)OLICo&HgC+FR4uI7dY)L^K8
z==U*#v%0#9wT_e9n|0h@IUWCRH?t&FM2%!zS(!)YWhJyKU>8?`c-vA<5RUg)PPDFL
z-e|n&QInO5k`j<NFCSlhUEPq}JizC87g+XV$B#2?yi5OaYYToRuy`~F4q%oSNMK%K
zYu1tcuk*j~T1-K~Qi{(eud9GaU^R@Ycr^u(#!mp!`QN+$4yHiuROF7zJd+r}<_2T|
z2V}SgH-(Y~i1}YNgi=za+6(aM+z3Nb5l$VbX=yn$ea0XmR5>5U#}C}9s^wUKw+nAV
zm{-muuxWGsDe?zls~@P{-&6YC6f``b9js;GLUBY`gh;Pdb+olrafle~iEEgdWPt;N
zmp)j861&_EL<Ic?%MmPeS1kjxH~n9~9;hsyh2Iy6QK6GMeQz7MV*t0Z(x>Sg;EM^v
zf=C71Nh#;&=jBr_Ko7?IPJm9n=wn>RSX=wHIekPuVJN5g#-YE19P%kNaMbGP43CXv
zVuoXA$WKl%19k=p2?C=6UIA1@R_G|85nkqC`PYOU5vr@FH`i0B4l{bp$*diFQ)bjT
zY$XWeSw8Cvfp9!{6NQ_1!ElKa4j`Z%gN_nQ04U;wQ;pqU`3(GvbBce*nFXekLuuQL
ziHsD1A4@cWpC<U(`RAxF82=8b8K>EW{R#>~KO!%RNXR<1t+cijzF&WZ?m`>AGiP=i
zxZ>dB3<Od#_@yK$wBxiG85#Xqp4+N63~u|0>28!ELNKyB=;|JDcMS^<-|hWyS9LC~
zkHtfC4Pxx=GXHlq4b18Z7%Yu^++Xm`DJhcho(ZHV=#g0Rg*v_?F;b4B8lnm7NuAVm
z2M$b3P3>itoChbc(%j$OU2^T~5lp)X3VLJm1urW3aTBhHCx6^9qOHPokNBLoH@bD%
z5N0SL$13h)=og2xq2Z{wxROlrd_M)u+s~h)PsND3l;wx}t*zPx8CX?NM;Ics6vY@7
zAtq4&P~PFNfbp%W(stqJlB{2|F6u4lp;sp57(rq25<pj7UsFTLAgTx^L{G2ih5A0V
zN{E&xPI#c*g&DrJl`5%PspXjojs@USPL7cGg~*mMR5eh@h5#p^;LuE|Y-qRYWuwUk
zD?LyM*>esQFItteIyxuZmw3LLgb?PVPIq>*0g3?(LfvNG&_;}-Ge)w+dj!HzfpOPB
zx@h|WYc(`Al@|wI)gaxWE+m3_`{Q=Q+1VMde2{W}jvS8A+YDAVLJ@_4uhbtq?y>7@
z1G?0v#zr`~@yZfpb^mK`va_43t54xgG7SxozQ_e&iUtJ^r#e1UQc4Q;l*f+j##cUr
zeJQ>9Lv6`8&<cnGBrJ3_qzB`2ck#&?h#ByOb898P%*Y@NM(gJTD`A>GZNL#HknkD@
z9OYxzd(LBYY3?Qnpm7ql&XfBlsRAohfitx;K;RT2cf-bjU)<cJTagMoz>fBT&j1Vo
zO?IeQf5~*^@5^}P6rtJQ5`lXYW)u?z1q%%EBAZw5<v{NXrjK+lYcHM}Z`MdPy~P;r
zf^mHomL!x7*pMF|z?dJ}bEGr{7#R@F<A?874@yH|LHn3BNHM4KX>1WZE?5Qy_Q<*j
zHXnE!-!8#y4fitk5@ez=-R(TWD<l?|`+XpjdV%1C7;|;&7_NeVk3vQnzgC2)pkay$
z!dw>)3642I-_qCDhk_=hZD(tX$^Z9E74E?`u;!xPq12-(sKf#<YpZ3p-|_Pcpk!dD
z2`*#o_w@2YEe6;jurVoD*6BeCY@$(-zwRW)*wo(c2s8vgYAK|L3R==TdG`IXxaRTW
zCBP1k6DkX45a@t2=z0Mu5P^Q-0;cX14>vPZjUbDng+ScF>#_cBM|nnmz9af>#4+v%
zO_Jg-*x51Z(0Pdyb~M_M8n8gP&AI-{ErjpFB_|-YiT1;2!1nKt0)`y=7OG-_G9tZq
zadjOn<d=X-yiexsvcVh^-%>wdGCWF{s5z4&Yn-+03}A^!(B>Rna7B{~|2=gW;b5R(
z;qMSQzU5s~K~ZG2LEdIyWxaPKx_WSlKDgWVHxeQt^X%RY$*xTh);uik%fIh4sm$i<
zZQZ;hID%JL@LucQZ#(cjI~#rFi3AN4hgHCQZJ|4$#DNOnhCm~^M}U?q3gRNpC3Xjp
z9E?LDUT|PM^y2ALh}5vM{`5(y6#JrXq^wN(^(qR~eUmvM7+-)2F?Fh^@*^mSY`q=M
zZhMR%{gD9Ej&XbBn!RA8#KdT};vYwug6|SNb_|di%_-QnQ(;g7!5NKf>*vPAt7X`I
ze|r%%U6{~ct*oq|Ek;#E<IWUO;VCO8BLg-2z6LjViu7UoJ%M+ufK9-@`<dMeWBX+^
zH2bRNL++FyCAJ8?xk99*j0~pL4Dnt8^yz*ZvZdK%;Qfe$6-7lvc%eh~*ST`WK6p@i
zW6;lR6%)LoHwNTI6POtpL$tOI5u6xF(r)L#5rL5NJA9_tXcoW{icS$;M^K4Dq1r@P
z%rWAEwNKseGH!_ae%{E)6WztimACb(y?DU~vbH5$dA!B@;WLEjkY;oZ^tj#>&P3Zp
z1YTtTrIWnkhfO^s5*$RV7Zm#H_wVOT&!N*n(}Cqf(K5Vvao6{m$|=%Vq%Bm5Bs6{S
zFs8J?F%}UL!U)SC6qp??HK|i)v09-&4LdWK;aQJkcbM9`G*_CQR{ZC;U^!j*Zoc23
zfI``c>-<8}4(clMrjd~a(ZsNm1(}^B+5P!E&G~3<ReQBLmWgsfFY|AW-fQkH$G}8W
zQF2osUEFykKB>fU&at6)OmA%s<FN<X*<ZsWT_d}rAV`%HJ;^J>qCFo}(6##}D1-MC
z-VHSdutYxVpx<_dU^iD+1pX~(4K}8G(Ys^ecI@y60>pTRi1rYi`~Ne2cJX32-pOED
zI59ih(cZrOX9rY-$1Tu0yMgjS{(zLf@5~f1I6Z9(+J&llyLJ;nQ$?APmnSMFJs3k0
zDtDh9^&N(^n~<?GGgZ(ptE!G8+L1n%&cM7V=`v04Wn%I0%o6G_gcTbrE9J^@uEU47
zC-PE~p32YM9<?X1+P5C=@<;LUs#{fQIn*&~*R8DySO^xGtSrpz9}<<Ow>!0^v`-%Y
z#gh~Ba3zzwZ>bN?Pj??>Wle_5Y3<J+_REnUM<Ar*IVoUonwq*($m;hPJvID#8Bd>5
z2P;w$k06Vnfr5a76Yc$bnqg%WrV9KJ_;KRUGwxS!d3fNB3|#QX!bXWocmEhQ*<I9g
z^lIQCp;BE(W9RBh|Dh9;y+~A7)NWxwfbjMUoHCHvLDv|0C$+SAXw;w*V-vc&y3poe
z1RCiD$LVBz)9kF>{MSdfsoROuCdbDiCr{%|6w{jYCIlT9L&DHtgtdp@b3h>`(5+S`
zN-Y_O$Uu`DmAMFjx_<G3kE(Gy3yqxI7T7<Cy5ZB*sINfZz&|w&4O63|%0doiS)}(Z
zQC2=XiK748MNXb}g|6{fyD38yb+s__{{4%{Oc;IxCT_EL*~c*huGAt=AML`xw3HjD
zvE0haExarQr0RY6HgfI3Bfw&$_@?&!kprnUl&9kX13Mv+)LL9+4U4iD`s_ka$i2kV
zT>uOW5>l7A&HWB$A+MoOE=AMpGr>WZo104%T8}?5B8U-XF|jXQU1Z!1uF>>0T56zB
z_wL=vJ%tR7nt^vm#h<v9jp<6<7!l*+_fVR!il`||WuLRN1);+1*>ewhVcV`R@Y;eH
z@LBy4hhqWn=Al=lFX>5~cPa$pbI@m>JXwX#7#1at#TNK6foTdzI*}wK#Kho|$PgOQ
zYT>0(v$PyRhYFhMm~EGtjZNZ%2gL8K+r>)Xi9IeV>inBy5+G>oCMUO`-vu)i^g#Jf
z!vh0Ebz4Q}hLF&0yK;R4;pTW{7^D!RmI2lQJ^%gi@EN3+Ag!m^(fjvX0XTtM?q8Q_
zwe*hT)EGW%VKDE5dWnGwQZ;5KCcH1;CM4h&FVtJcB1_(Y2IG9otPq^ANR0*xujh#K
z_y2)we9%}Gj0P^(*VNn-S_|+g+IW!MpO|_l5j&=t-ryq0&7&pCsoG$k2=6e1eGEj!
zA=+(?(ezn<z$M@i;rnYtw<x#g5E+31kBzOf$OA&$wR^X}dAvd@Mhow7>47ZrHc$0&
zc`$~Rgzkdjs*K~b==~1eA>pw_uU1@Af?i<!2c1~D5!4F|&*CgW{~(sSVr~7QstO`B
zbdI|DNxWVS+qB)h7X{r{MdXZj?MtrgmoM>l3jUot>)`+gS{QHGW=DZ<glGXx0G109
z)>?2$7?T+s8p7tMv7P;pPsRmyRl?C^2=DtqhQOw@3CY6S1V;hD5Y9Hv;X7AWny&tS
zd%Vwsld}K~A8!2|4-K*Jz|hcZ49tvPBxOzpC3^C)$9=IxZvM3&ai-(pcjP}7kWdj~
z4<Eq91P#g!kL2$D2b&6#2hlRIka_MIBtFW0nW%VsS)^)OT0r41pwMuHCWA7;+tvuu
z6r2M;J{=gi`x(5IkkDRwanU}insF^4wcF3W;9Oa!vTZ(`q4x3}KORCv`0pr^npNEh
zQ})2Z3b1a(>0mgSAj^Ej^#|YY_#?CXhFDW`^Y6ckPwSU2Bx*4qb%yZl;VQvUlca1q
zKq9_qYdg!lXXodu5UPN1G9sKue*6&e9N}(vr4P887Ye{YXw&#<8-Tzav)<(AL)v?K
ztRv|*HAo=Bq?3FwURVNPMe8ji?<%03w~I%F>igotLP>Ek(e;n>^TN4q$>KJ#U^&xR
zxFS{2$z04es{*zMXgqvj9V5-3ElzApuflmaSo&CQ$2AQ#%9E|Qp!|}!!QDev63J0f
z`Jjx!;Q+##9f+`PPuQKwP*6idPIyNFs8WFPcO?!(YWGwK<RT8^?OF@8YPW5d4hx2C
z>XG}ycvB6dKvk9bwQHZ=)q~)Qj}qR-bd^*MZz?@$V)M9l`^g^IcN9*Y+ILCs@f#K$
z^|151f{VQuN6%o&A9%evUgVB1-Yckw>LRRz_mS8EP$F;vJN&NS!muy;;A6*@an2@Y
z&PR40It+LV7!G(Vjnz|A`=q}pR1TjmL+pn;`%{QO!o0lS4IPW{2~@mvs_D1S66L;^
z7aLK<JGfYjlM&c>eZj8z6#I;tgZspea$yjTn6wLI-!}77v>%wHeqUGjh9Im@+qw(1
zFMm>(X633ICeZqg(UNj<Y&?``y(hMh!t}NMbU%o#`?vM?YY%mG=|7y3YzjjbXBfQO
z?@urlZqJLxn;=L?ZY!ihSiBwo5fmNeE#lMd_LUm}$kv1D_Xj^|1S8`?x`d#DpGAKi
z-@XrqMbv9E;dm6fzDgf9zk>s{+cgrNY6gQ42i@{sBiNk2xv2@`%dAn<FqIOkG4I>A
z?ZYH|BNz4cfvMs-6!AKwHuh{s2M0{DHh|@uKV^ktas#q<L4g<rMd+hPMkh~h6LolZ
z`qCvB5M@EfLB)spCFm?(4<dPh5G@d45lsxyGr$ly%8k*kW@fi(6;A;!YiRIGNijb0
z!`VP_eh?k4p{13Xa+&fMtW%wxop^E7BZz3=h3GFJ;sIK~yNS?;!H$aef4~C(pR?rg
z;~+N~EQ=eXi{S-;Obv+_A|RUZOM>pIlI~P{E{R4L=jZRYjape<B}`Dzdy0td-k?(=
z!hdE*$R0<#9vR=zQeQt49k0la*F3=cr@k?@05%YQmV+!?v(d%r>D8d$;o!V*fi|x_
z`JBxJE2;7;BxSsx6K}hy|ErXMV1Wd5(1fPd?cSLBdK~Wps2^7Y3oO}5ZM>4OxLESo
zF%0quS}ft!5tpp3$<j8TW@a9}AyIl^bFLsYbsK#&nr4k8>h|;G06GT?gz{tQ6_56m
zIs^4hJ=cBlIzRuT<<Ajb5do2>V2=^hgm->K@lV>P)qoG}?2JoF@|ujMe-gW}xCp}w
zYN)9&JtclRXfiCm<;-I)(o_dn#4>Yoa)89HUq9o>1!G?3ju`W&H7FWUsWtD6&{SOq
z@P8Nm(EQzPpQ;NckPhQay&+P@>rabX?b>g2_aNRvNqqPE*zoZ7e0v}zScDI@T)2Am
z8N3D*6b%T&s|+^u%96o~KY#xwZ6krE>HBlukk>&~^#j<U!>5Ar=0}7nLg49MF1Y5)
z(MtdvU_aS8ID8*b6rY5P!xJ+^py`9IH<Lt5qSI2`aKM;)MRYNI!yr#UlB2s5u{UR>
z#<RoJhx^tL5DD6#C@2FD3?k++i4}oILUaN55T)%rY8`xX<uX=-N*QASZj9$F$o$ap
z;AI@)wHEbXsG+|jF+z&P8#U2Q5OaRN^t6VG1VMMb`!y1<|3!7=q^nnFAphTH1_8-1
z(wNB3MS5iR{d)z{LlYysFu@Qun2oI;-~${tmH3Ipcns;l+dMWn$e=^`d0hFn=~u{H
zFk0jNv3SVpswxo%H4GeM%+VdH9|W<QorxuTK1fQ#L1f7zB4C~h$ryl>jm=b1kwh)H
z{tiv~J@(t|!UssS)uazBRfJPVsXl>==ssy3yim{>6(4WltqSsC9j6&Jwa%&IW}&~I
zv9p^6s1lV_^p&U<#w&ifbADSYKL_a~D*E&PV(-2Ga_;*-{&pcc6seG-Av0Pi(vFZy
zoMfk>5Xx#uTf?f%5{e>DD|<H-6&cBCYse_8BBM0E_c!0qPv7fL_+IDd_PJfxc{=Mj
z-tX7zIUdi)<MD+2FP=6+E~<Oao><L|^y}9)=3HT=U3~tJn|JRn6Ugw7k0U=HG;}D#
zO$7x7hFS?w52?J>uGJ^MU~(G#_00t0t{~KW<+sOCkB1!LFavbSA${7L>kbAd7%4Nd
zi`qMCdsF|zGkbszehnFmTBvTBO5#^){_t6zQU!H`mc&QQANBMwbfR4gY&#~;@^D#3
zx!>hhC=)wMKj@1d25MEFN}CmnGI&2kI)S{%nFV8#THtBj=iN~kkMyM;-rgLd%X~ZO
z7c%e4nUVl>QtF5oZiTpSTqM!*nJG-}wd;(ZyDBL?!5Z}9^1cqyS8<y~>rW7&wE~r_
z3jWDt*kCnM`o^C>=b!eFWyE#*w4qC<_VqhVVU2SGu-bi=`EC4SVk)Y$vv6dn3TSL!
z*VJHK#=T|ygQd^`Y=AM#O5E7bCLU4@o=*|^?gAm@u$B@+{SP0smE)O*3w7w}kdz4y
z0RcbZC!coXi4T0OWv<ts4<+}kjQVAUt83(OwJJ<~@87#e(ReS#xaiKErNOSRfs{T!
zJ1ZZRPXiurp{MR66&F2JEVeR!=<nwzai=PI$1h4Y>~EOwQi(x!@Op6Rq1!P45zZ~+
zVW<Wq&<KNtgJ*dJpIe}&*|)Fkof|}*Zn0PWs--xcXNxQb_VIeEp{~wHma1-R{`Cun
zXtM3%apT8Jcafd-;Sw@}zsAWhww-SIG0|N|gP(VMkJd(+BXW#XH8iBQe;n=;4>cQz
zzWwW-2?@r*!jTTw&I^~A7_TnTd?9SWss3_<`cOSaZ`knj^9y;$&JkB@IFi3<qb)+{
zkOyjOujE+U)kU21gEWN#slv8X^WxVk3XxZ?UZtdq==~2gBWBYO`($5!@M*W<2#afr
z6aG_<njWrpfWg3_phKv!%JH$Q|JYqaqa`au?Z|kaXY=_|0GSMX2AulRyW9`z2;G{{
zR~aM&F&U3>!6pGd%1&%c$brerar}jChi&v+40$Tt$t8wrPPU>qSkH;Yc{gsXME{uh
zGC5}mEDHw*2jmJ*lUmo$f?DRz*jA*dS~6E=iILE(H86gM6kGL!DGvCck%584ymZ6{
zh-;$7KIRj7)_r>P&>cMZ3Y|e=U?34cwxG;a5+W&HVZGJV4BV7mk3Pah8|lKH{TJ{}
z<Lonn1e+81edA8#O$DA_?|9#~WuB+0{Ml0{PIOIK&*Yf0i1rdp``Oii6(B2~o;umR
z(hoVDK7W3p%UG>h9wMcF#}$Da90K)&GqyF}SUP#$BxaTauu%O}q5f%TXpjDK+crTd
zhi$;q5GD~A2f!1J0Tj&0@C3fRo>>#?;?buY71q{#cc5A8NfV3mZo8{3$KkJYXT*p6
z=f;g2ymqE|R@XM<CrdhI5~pbxNwE$FmL$~Up%+$EZoTP&pPxuo^;W~UJ)?4vYLa}Q
z%Y^$En#?#G$_9bII|5Ah@_?sLn^s6egpj|f$xG}Mw<{1p1=|M(E2Ryy3>3W=Euty)
zIQ^92HBHRs1@ENv4VlT3ub7f{xt(%lms-j@hS5N8>1Xwv;~_ntntOF5l{%OOC(JlC
zr^fFRlVkKbqBY9V8?LT=+j)JVk&AqK|94eY+2_wMTe_4!RntM{(7}VQbLURBG!PXC
z2F~<v;RECOM~gf?1x7Vpp!Djz4}%R2yB9C#Hwou>d;zJRI8v82AhLIG<e!UTU@t`f
z{t^S6<MZWSU#tvebcBEVxZ|JX<mJ0h>?0CMT)JIYeO~Wqe>~4XU4_^M7Q*1S`){iU
zXnQgCf@h=Xu_jcdv$*XRu{=@HL>#}B!GCyo9(V+19M%on0Fr3iM609cJ!!nJ<}~$a
z$J83!TA8}63k<}#3R1hEPUgv&_UTq8HTmTaT(i86Re$+np|0Asv)#Z(43y~u6Q5A`
zN<IX~n0V)0X?nhNP9ZG<fR60f-#>n=bvI_xWnGw?H1W{Z&6~0FiFAAGV4$D4Kp|6K
zHh4<r8h5lXS@OznLg(unwpnztE0o-Sl2os#+BsY~YS|EF-yp~N<aBf+sOb{>*cd1V
z1O(s=PW8G8GZ1Iz1S_$4M>79){CN4(!4yCg9#RG}_AA9&JKSLE?Ruo4VCt^M&Doz>
z-Bes$3~Hk~e4gT^<z8O8ZTHsk|1B)q3BS|?d8@z&##6#fn$*S1*8YkoL@)4ZBDA83
z+~oz=RFvZ}Muz)6spZ)WH@85>2xuQLwxtY3VR-rKRn)49gbRCn`tInQC=5wcQ(usV
zFD`o#<M*A;i8vkgyG|!msO9VGA_64|UhZnPB9owr*t*Fmj^HM$kNnuQ<7s*M_L;s#
zic;%s^G-c*3yRNou4x7tLemn4;skV^??Pox9~XlB_`-!<Iir%kTF>)%*Dy<^x6>qS
zl-8~_nvr~YO5WY*_R;Znc%Bq^oaPF`{cYMbK;c9yIsvkRa{QwQ4<wF!LP%O!*56!u
zA%16&wz&+9xnyQ8NgiY<dOPQmUj#%0bO?9~r;JaZF21f$XMjjZJY{NTp<=e<tKFd1
z4>vClZ&xkc?)|{^!o`b#wcL9KlM27i>Fh|x48x++RJsZht&-AxvMFtuTH!pLZQ)wO
z=11>9uO)S3e(=On$MM#xM;MGsFV*1-IXpoyBO@#O>hdanr(%4xrTTna`bfoRnU4%r
z#i50iHn}p&PP>sv&I^N9C!YG80z2DnXv4yE?_>kT@`qx0k#J;8b#-MDiiFEP^Q@eL
z!oiG;q$zg&=5?81^7O?Ec#lq-X4BLo^Xt@Vn)nzR4Iaf@hlucy?OBC@XT)4j;_11?
zQwix`4eck6b9Rvt{yMysG?x{vrJ10lpdhi_p2Dx#Tl3N)w6c--YjF-_q$2FJ!8)mh
z_ok-Ko;OeP**|E7Z$5g2VdJXm8yn!`sl)AEyjV-5fGI}>7%MUjaFpwdReqg>Iot8$
z#R{IP!)NQlI%o*(U+)YDI@i(BF;GMh7oKj-^<z#W*#6^-^GC2kRVt{gg1--rdoNjF
z&@C2BA@ui;W#qUvZ>1pFl{UJ{OxjPJI+cdSbjV%@T~`;E2hg8{=^nK~`VA%#0;Qfe
zjsq)7YqA-(xp)1##GC5t=pdnptctnj0iX(}s!NWhKq|BeM<q+^%0*oYxfAM4aeL3m
zbjS^qt6O*P{t5OPekpQV3B5OoggG&zY7<H5KLeEGOIO&<yXz-4@+B@tfQQ)^E-ZSQ
zYV^{vV+CRsicv~FDzx9t-@L1OzN80#^=g@ihmq$kzI8XzLzSb7GS-rkk|=&*EX(`p
z%Dw28c+`VxB~JP?9~}xZ!)c->6j<wKaH;d>|Cv60S5%aAVN85NLOsB=_(*Q9rM~`W
zE(O;pZp}h8!Y~G~=sJIX#QFrCm~!SGzYAyiR~<*GGn-dLHUD5Ths-yC`jT!NoRaR?
zy4E*)JencF-J~&;U@z$*u6|D^fzeGjO>>2jjv^TdAt(uQASjoOl&~-45z5NQ{PFRW
z+F(<1_pa>W-!yW7doof7n9PqF)$3RJ$=Mf&X=zDDzej=0DdU?;7=uY3gI7e%0_)<9
zkz7f!4*xF8Q=zE2iRH?oyL%cM{6xB!v$I{8TA|?NRD#ISSkZ}l84<v+IBp@sGaW?I
zL$M;H7)oflD15mDOD$mt_x!n!v~Y<{O$FaUI>orvn?oDIR~e<S9%j6XudJNhA}_CS
zt2x|8W(wdxlspI1)?=%DELW2O1#h^nu8tRvCowGuC3sdCp3|E^V2NlX8s&RgSFRxc
z+!qz)NvbZsrU_GL<Hi>FTKSQfP)M%5FOt#fo<*}&Yi0}d4>$>43g@}&HZ!KjFR!ob
z6?ltpJ%X#Q&XsGV<|Y*~U|WkdQ^K6Po5wLR3JGZyXn`3SeCxyu((|rE0H)uEun;_N
zthu?Ou55053+Uo#qm4vz;ujQ9+_E^R_&GqCsI471c9hj%3F|~gQ&dRd;a0dvT(^``
zp4Ua~b>w(IQ@C%x`C#+|4~gy`a|ru7<$VUJ@7=t0tDc@7aSwId){5=g)PKM3cj?rL
zrc9WL*=Z-)955L<Qcgyu5AjpRyq~(d|Jt>O&DIbCc$#~l>3bO!%U*&`n0UI=wbQw|
zl?>nG4ka2)labQmr)4e_tSXqyxGqqLqzr=b1ZvrVkSP1Z!|{6`gDbb}IIu>sLpff+
z3HbC}O{U6Pckbooh40?oi$V!+RveWR?`>FMI$(hJwT4-shtLS9;S{=bL5wV(*+XQC
zS(ZSNuJc!mL7)aLPVn=ff`21TE9Ou3=T5>UfFugPgcm^b$S;F%8vbZHkWO))MC45%
zzhQH)2+_kmJKsQ2+bJq=O=<9q!8@^MfYDe`QewtAAqH>h)GOW&P3U%F9)~r#3ztp&
zx=9!gZrms`NNSiRR<<}YkF1Os03eC!G}ntf!8juSN)HtkBsOpB>N@$Z<vUwV)ODA0
zUSV%!ZtjcK6D|`5VIb|tj!Dmyh6h4bdHc?t?$ek^qCW#y)7R76m69?+Z#x9Oix+=#
z_G#nb-vXzDeA5ug%gMpan0GCZ9zUL8uf&zDc6;eWRs{u_J*;yuPGXzR(Clz{h+2d6
z6X%zy^pNDQi26t&ZOG6fR)ND38Ir##575(N3q>O32ow3-+%%g5JyccUkEDWGT=;wm
zD_Z99L>c;TRGAzxs&2vR7Ck5n83Y&1TenV<b^y5GyjC>zD4BGP`@r@0dLos1N1z-j
zD+_JN&|m@v6FGhywE-6rY>v73WjYJcR)EiyRe6%SLk3|493P*Akb#W~L?MqSWA#SU
z4;dJUyrx?1{h}aqgJX+hL0IhrE!~fvG)zEky?ejFLY9m)584@H9g6*p8#|LiM~=L}
zv;*3LW^<wTDK@#ByLd6nej~uVz$r~Sa?P~QJtm(H4n8P;DCy(GdmZ(p)y>#u#DGxJ
z|B%Z-<^_irpWsX*%xBcxmE=Ud9n8!HKJf3~xnUhS=g#feuP^SIZb=m7$3oG$N+vBX
znb7eu@I5J$2@zchs4@B$tjSibSu+`ypQh%$+qXxD{4$_OVa5t(@%Y7yF4MXa&bddd
zp*a}Pc<}8<BV%KgU%?FIZWa|~Wo9y@$6gQoJ_+!WDHG#yN<03$mr*l85H_$EP1wSP
zufSLsPjG(7gQ$cl6h-TepbaW1@kVaA8=&_c7u`+#pvwa-_$Sg+?6*F1RE~ecp*6n?
zb2}p6yjV)3d-v1iW<|LI>Xbi%AexW4Zf**$t61j5@8O#YD!(twJ8!@O^vt5W8eClp
zes>dvr>CHL9yoQ>B~Kh7K633E{_}elbr;+gYd=nzH!la#nJA_WAu|MXUQj4pZRE0?
zFj{9Ab5Kq^JUs>S6`azcLrY6a2BBR1{J9M-@1CoHuvUr1Je7dY&+XH8Cs(XeE3q->
zl+d||xrc&Z3VMdS`P(jZjPa|=<K`wc5=&A2aK(p)7jOh%WcTUYclg{Zx`PHGg*KCG
z)0Zyh`%%MV6UYzQzH=v=mUJ3Fb{C1VS?C0nkq#|8LFVWUTpT&GQm^ku4y~nwd;j(=
z-nVv81d@jq6cjM(5-3DKOAIr$r{TH=28wKC4;D6jNxm4h3=I+z7{!<ra?znf3s<f*
z(pTz}<bal8?)fEHCG2MWeEo9(+>f}&@R<A)(|g7+{PN&fQ*_`440n`v^EmtwKqJc0
z^f5d=sBYn<-40A>@(Fhd0s=?%HRpQpdFC`X+6MNx4S}6ufR)Rf;CbxO$-pqGpx|s^
z<7@h~=)2$$6#IUwR@FZ{OHp1}QBiU8<_6Wy?Wicp{^V5%J3JtX+2{)wF1(59VL^ck
zDf775w87sw`Bq1~*n@O@3Xgyz%m5BZps}e5_kQp*>FfIx)?c-HJ~;gyMz~~|anUYf
zozc*aK@L?_E%++*0yHjN6&2}|=&I!^6bk&%`m=C?!5~!>!v`tVFoj4&`@A;0E)uw5
zjnBPJ1O@Hy_SAt79o`}_VHe?;;c{YPBL2gy9&_7`4u#RYc<|t02qJ}E)bHGfp|dZb
z>i>vnDDIz;wjXOdWRLD=vPa|tT7pZKsPJa&*s;)g-@Sf4i>+M*&BWnS#gncvj77qP
zIV<GR%sj3-B2nH4*Dvaj#GBHq2vHB(Zz58%PzfQLRP<TXK3{l-w1mif<w~L>qPPAq
zlsc1*ODEb3rYfY3_XwwVbfzbTfKQnJ_xN!cxrf|qPGfG{k5s6>{{Du)+9NMjhHo_P
zy)e8pW%%CFYXt9Gs_2(5uMuSuz6jI#W5-BRRDvY0Ze6-as~A(t9iIfkdAqdK&f+H^
z9rb`Xw~CLGw<Eu%5!pWV2jKRQ;?NK>YW6Te{9<n}n>{_-f)B?9-G}=D1rnLn{ZaS$
zLdsgmf(W$G2t^p$>MCOwWHtC5^P-gGWL-TySjmDwGAQW8{M`M3>m&>w7>CES&(>X9
zjwmx+Ttu60e*N|hPRj$13bI&sq)|CjtS|&m*J7@Y&XG(df(Kkun{-~G&f^W+C8B?H
z1}A1P^f1Beja-w=-%-p5MlrvJdpI0$fx``AMSWqdt<4J}cu$`(BY*`iH*dlhWby;n
z{~5dkSwF}q22cU3SIZ0wBRq3g%vq=f<$$B=(D$-?ek9q8l7sPN899PaoH&jGoEzAu
z8yM<qW)H*!MLFVnAA|y2JgN>{b42ep;^|MD1sn@7#&xCQy?*@_?hi0$A+;uVSaN5n
z)xOdh+nKYPiR#D7raRB)UFOy%1IdZkmi+fGtU)w%8)9M(A3DUXbs9h3n>WCfj9cT6
zI*#;|U*wBc1f!7kR6hu&xPTBHqi=dJPdu8Dp~7aQhYzJjrdxIW3W1nP<K(F#*k?SS
z-WnQ|A5i^5JK6%Mo6_HI+Ps-Mp3QDh#LFK&+RJh`21j@{k(PLZ6duZ|s_e>`Q2C>y
zNTT50y&SfPV5nGITWh%Rhr{;8vwM-~$OxQ^moMkIIKO$)=p<I?+^yTVwTkHV$YRpU
zGH|_m_Jr~?VCc|mpjU9Kz<-9Bnm(lz+_mIJe*S^;=X(ZqiF3Wc`UTO7RY=?!g<!B0
z)c9J~BO#a)fw+h$w(|xfQ`1@`zGz=*oH9?tQf3YaBS|_ni%tRApL=m^zB`Ew-vvPj
z#Dr`A{!kc|d`8|G^J>fXU!IX6PBb47fvWTY2`H+HV?rS-Fcf!m+)UrXDk@$WYfEU*
zXmyy`NnSl9#NEJ#bmo}w<2bqS>Njjyh;V{mOz>ch7bOZHrl1paalsvTp>Qf~m{t@J
z*Py*c8k}Ya2bDnHrCr14qrq=P4qfGUiQr3(cP2ZV5Dbm99r+voCIM(yVq%^L>j)x+
zm)+8|7$O2Mn`wXNhbKpyni7lu_Ljs@NAks{n^N%zh&vl>0CYqz0PV}xN={aD^y-21
zDGMg&9mvbelaLuEWhLn^WJb8<1D?u)`+oSagnxq+{@39bp-^otoeS)P%izVHo;5^O
zgkeY^aha(M>v+Ya)o}1)Zc#u$rGWVbeRJAtN|x@cp+VAvClo@33QQfmVQ{=1#=58{
zg*&aPD!7<YhA)<s!d*=<vQeQ^r;^*ZD=3~Au>+Jrl__5R?dMO5E+mY1OG?0z=U(tt
zmy4PS?N`AEmIA#Ci4+7hPlu|9i3yd+H0*kkk|b4C=p773i~#bnj}f(%vgQpOm)I&%
zz*Ul}b|T)=l=0Pp>a*QGF}N0%r7&M9s==CuXh!xUnNn=wCb9=xrzcP3OY6bjBvb9*
zDLfp5QkF5uDmtZ<5ZK7kv9a`(tNi@3&zxaXmL6L1qk>vDMX#^Kz1Ctysr(;W3ZR%$
zNk=Fo`HHeHFL$@FtsFLZXA5n;sBhP({Gs!%C0m^P2U7&j_k*4~{}G<|V^(<Gw_BuO
z(L!SE0EFSIqDkgal4MSB+K416De5<7lz6eG>N~xskNSy-<ae}G?$e|@KF|&UT!Tm5
zOC5C|MI~W_Ry&t}nY)e6l0?)7@sW!cM-3Zx@8!!rcEcoEe$YGE4a<8lu3@-h0d=D=
z8C#Y@HI69{Z<5%}*QDlVh7Zt7JmDoE-SP2{Sv=B?*)va>t3*vC><T3Q!LFb)V3a1x
zY31{Cpv7ZG8R&x~LR|lkp%HTApFmbPny?a$P6&7bX^8f=?zClWLSXeG9g|flGV4#(
z)smT70Kuqi7}u*XZX^o1yH`<=Q^_qh?91UK@kOj+zvGORD+PUZepRNSE0sFms$m&K
z6)p<(GBHC)d8(WEVS>PxKlr(BD^B#}PX?9%kXCc&!t5X*(u)^kevhU}O>q%x_6V1t
z)wtb|WQg$6HdgN1nvB0*z3OW1g69(LJ7&_vIHPRJ2*LXprJdzj&<P4YCfBUG48muF
zn@nsc5hE4>x-4c2ZGCPvyhu7$KR$Xx1Ct(r>?M4HW5;0e?um-BCDQyb6E;UMU1{(#
zgVFW$gZRH>vsH&7Hqe8oID*!L?2^$5LFlXALY6Wy@yc$uiV?|JgSK#RX}sV#SeyJP
z?poXF59cT^z*^!^VOaNZ%JGoK-hKHJ3eo7qsaV|5C@ZO1ahYS%3HBv*5;U1iLJS8f
zef0P-?h+_bFch}JUJXSj;e-B#QUtaistBQ4|7+9X<3BvHh^I!lU0f2#nc=@P+01jM
zfkaYqE?JvbK~F^6Ue$u!aPFKrR6%($y<-b-lVA^7{fmnUs!fEo4-|qXFDA9D&`fc3
za&~5H(GFgNG-1N<&E9fxj(S;#5AR7yp*nGb#fahpGb2JJ&w=8mtL<r?5B;Mheo1&}
z!7l;A1~3=4IGnpd1jcX<=+{RMbdo1}cV#J|(j<150k)tzfRs8qH4H)cc{Y16z{#L+
zXl)Gv;~|D-HdCwda7cta28sb-v7#Ko?Ie*b#->B)$FysVZY66~6}sMd>FOsNnGU`~
z&<ChBA3D_6QU7uBeV`+VyXYWbN-`S<g3#^}2Mur0BCI=sG8h%$i7XW2Y)Pi*Y`VP9
z`ZT{3Nw*80B(&2+R*q)xzJ13U7*yf8&rQUvj(V816K${5wJUz_A4q9JlLB(Y{|O*K
za&p`!SxN&U^6^urlteg`qI7`n&h#mxF2D5d-TXBaXA~dIlrx_z-qqb+LeI<(LG|;D
zNgYsYUE5DoqKktq(Sy*V39~#TPsPP3YVJWKfYwTdXELfDb_Q>qc=F~DbXUR#AWoq9
zepNfcCXg7JWxp1I3UxJy2;Yz^48N|g(T=wRxCbrXNW&w%Jjx~?!#>>zAFKNJKg1k~
z2H{~vMGh3CW5+&Hai1$BeeLhstsA1XcDfKI)jnsq1{*fqBtlW~!okGeW_^2WP{Ve}
zA<&r>45SPE2p`y9#Khd<Nm44XtWA<h2xV_fwe<lPZl$n9DLq|6u7WO<6w!hfA#;qH
zi+%g&x;mUOERdP<uhJz#FK1{~>;(#GRPd=Bhj9}V45bdFtrx!z=03AQ0L%~&=Qv2w
zfdh2z_Nlq0w^jL8w94EGx@l^vF1>~c<Cn{qpWVGXdEUH=M~|BLx=1RyZM=ixmbF}2
zpb4r_P;N>F;%wy6$&);xEwUm&_R(cs<v}_+tZs6p1)-*)UB?!c_S?M|r1=y~0T7#R
zj_o8;Jc@N0OItt)smBfHw>2QnA#^1jN_h7JyP0ixQcz4KCkL{GBJ;Q7<jJH<fzG(l
z`Y$lgcfnVGI1iUI$x0%qiGRfxuvP<5tio{R5OY-=wBUN9kq-rwr?+WaM?Aohj71k+
zR7npbpSzC<`kG1AgX_`yY37-$lIWVZu^|9C|0nK%n;R-2jb_BTpp4+)eetg)fCB!Q
z^y{4WUtPWAk5&>GEKa!R$s}=-6~BKKW>|PH*zI#V<jO#u6?BAbex2HXkX4~T$mYMW
zHe-bk--FGn+me#Z;K!z%iruuS%eKO9rp?k_q`V%}Q-3FyHpxv^93j)e5Q>!<4ihFo
zpYZ0Xk#z}gO!~NAR|6Zh2j1nDmzNs@m%#B6izQ~NWA!c=c)|0cH|4xSCx8+0@cv{`
zf62&ndP<;QSh9lP1tk)dDL+&227=q)bU)o9&*CNq@L=lrpin^iGbRzuvl304KffMc
z?%~652tx@)+`?H$>^aR<NnM&s`CptB_qoKShmRlQ-Xh?qnA*klWdq&Y>gtG>5`)bv
z=EIF7RM743->=zlKxP?X9(S=8E(|9D(j^m8(IwtHDouQkBxlg)V|pR6$<l2%f0vck
z$?t#jy=c;yE-0-Z%M}0|<sT6vQ|x=Y!?YG0B{<l`NU9>TIk%ryyQ;TLfgkR~fCXG|
z9vxQ?q3EO+assO14C~Yn#W(RSahXKiPX;-6O9R0|Sv3YW7C@c-E;-4wn{ku&->f#@
zO2}%G=LU_nnR*<jN%)G|!wjuzG0eQv+IP>x)LKos=DFX#eM7j;rMacp!hi}YFd3_;
zb>~Tg!HNY#SGErSKP~_a&cI3##nARvmWK}GU4qd&PFAQINmtvvbo~5J0m8(A{}AGs
zKERX%Gh@SK$-R4r-+pkQqhPrBqETp@V`8>m>?MC5-alR;nQuR@_VY{kULQ8gyYq&J
z?cdeThLDM;PPM(`s)ALai;DqZtzNkMG5lPFRI+oYtjXNGXjqHU5m8$I+^F`WBB82b
zTm|w{vvc#yjwenWX1)}oAXInYf8DQ2yJ#pD0147n@@F}m=iC<3neu07I2^6iK3Ls3
zx4ED?e9Rnrb$US>2-{-SH}-i-i3{$_DE0?{k7$wl<k1*N(rioHx+><jK}VObngBI?
zVfOPm8-z{Jb!Dcl7Ra?zncZJJT&kA(ys)SU&OJ4v)G1%D9~7OqEp{rk@EU8aDL+8m
z4E@v}cDBL%tWn#%FHyq4-^>C&fA>yGH{zQ&IK=gh@zqC5IyM#6ES`6i%*QtXAK<f7
z%z>-bUeX&T@1TXJIl%QgYAXyO<bsVGYnpPom~h|VO97Tp8&cg!#n1jTv-(7NP0h%7
zZygH$_`dSBcf3sH>&nSS?W@bAr|f_)-vjs)m0EDtd>6e3A$&<eQ!ukqeV%+fz%U{(
zihS?_?pfUVd&#4m{kkjq8Z4t;QhcMJ^3t+7O{_o{#OvR>aU)}KBEf5!vx~moG^*@0
zZwFLYJoLyLUM<FzoosqSm|YVPV4N_JBY-U{%;SFjoVRNr8Z@XhUX)_lpdDw@?eQUa
zl8I(P*ILj>AnY!?5!D~KW%_jOK`qJk@`t~tyH)wo82L0#B%O$^s<mXHK%r9LWeyCw
zR^Ovd$8$f<YS2%nL!s5zU)B<3xk%-~rh!rer8+u83TZu6t9Nc&<z@*PYsyzTV*x9Y
zHCff&Kym!IasM7U0(|IL`oLWcIEPznhJ^HW(#<(lVLv8%dk<)Mtm&NAnr6S~L)TdG
zz~RGbIf{W0D;@=X=-<(MQhNLroD3M8i4MKJctI+m$P#NTDn$lzH525m=76xS3hw#w
zVoq)97kt7f2SEUAH}B1@YYcmGSKNwa{JVZ(tr6SyVx`_zaK68CJZBZDf`BH@v1zX!
zoqoy|Wzeq#ak%U24u|m_@Ap90CsUme94u;UH(y+LtJ;sKOkqJ<wmH7F$acx<)jL#Y
zpn|(yR@PnZ=9Yl>VV{HX;e|rY5MjOJqYe#)u&L`JlKy3sfBCZ6`jCCOb!*D6J;iGi
z0Uptk*2USi{N78!rHR|kh-rt`@V+YtBwDjJ4*<<LHC6lK`XVH0t-NnWNx(>!{|yc+
z`q`d%kkSAT6aF=t>_|1=j>J9b!}q;Y2oJ0wMUz)mUW|AA7L)$ppYJt8_+DZ5qYmtB
zT_i)|plp*^DHfR9oC1KZfB+>$MG#~_Cz>RPY{IRpJW+B@kgmLXHFxIBW*&s1+?DM?
zt?#eON2XK1hKEZ4Md&X6eE&&lzyA*Mt#D_jqMhZC4HTd28}uvVLr34rE)Q1&(^rsn
zC^>6p#yh{;0+Y^-o*ZiOzyB^lz(gLW+z1P^)b|`2_k!EwkGmRuA|<}%&K;BAZBeN#
zuc**eRRy;F3GA9y(b=7V4$MZw!i(g4bVyuNiArc6y{x-L$p^fg5I)`cBxAAc*p}&v
zV0~4Uo0wsBTwfpiI7C|p&LA|+LH+xKL=Q*Z0USqtO5s6!PsCxAO_ZYvq6A#O{i+z<
z?2jMJwc&eqU2k_R{@<_P+7ZUU8^+`i7v>JV`ES#DU9()F-i?JRjWsmWw4-6cZ>tOa
z!u!-vuQE-Z+O!11Ls@xws%4l3vwcWoct<ZLUSjycQ(Lfr!>q*^bIFp8GOekXJf?P>
zCz*jT5av2$lg9Io;4;&m@d?X%dVYv{@2wx<s7HWen*4+&{B42d(%~7OZMr8f7Z~PO
zzAMa1tB=W}R;Iq9QDqJ%_$+}>(oYO?%XX(yqsK5XHl~wl>GE!Opt*&f-aA}@$O<*h
z+MyRmI{uC%9XvSkx$@B@7PUI)9^7LhF+9nkb=XQt(Y@Oc7^%SMsOf{wt<HfCi-xrh
z*9I~-6}3&8?B^99=484_MKn}4W^EA1S&7q!$UXdBTav86K+O^^Xo6)sZY;lsoeeF$
znBHs3ADT*ScdJ2$V>N1<o#U*+!orAB)YMn6k~WXw6M;~X@#%bVfx>75MTP*tDCs-Y
z@@2+acmLH(%Ze&{=~7H?XhuF!{ZJ`@DygW@lf*2~@33!+oBln^F8$A3%d6DtvE{;b
zW#bMgq$@be3(U5@!ICGW|LSS}KmR{ZNvI1fB~~}>6r$e$`m0=0a)+{W>^!TF0;}|Y
z{na2XvKrK=B+++$|NqY~_#@-ln73N^HRT6-Js6$N=lWlNwMqy9SK4a){P_R*OJHgD
z6@Ja?TG?~m{@3Re{+^`-pS45cLD`Ih|MQpp|BvK<JeI$w<iC08E(5^`iCbJ18L0(E
zH(3uN&^?Qa5Mxh%*KSzP>=HWzW&nt@Dd<Yqwa@K^WCmg-T_9^XNN~BwzWOX1V1>>G
z?<)K8<8cq0?AN=cT*+D@rkaAA`WRs;9dAF^*!u6T+DUHA5_<OhXZGw#+DWyWHY`A6
zV$5%_v`kwN1ikq-T{_#x>g!_{B)1QGC-7acyy)4JK3K|H^sQ^hk0Ey2r|H3=-V;Z{
zHr}dy;-(OZya!NUeRP*=a5_Zsh5g*F=bozeDUpy=i=hHyPZfg}^r5SxHt<Oyd)nJm
zmWM2T<*tUa46>`){p{-dDe<QXpAfl#?EOvq#M|*bxr(VVI^Ngx(w}5W3!+=s;duts
zijY9*Nhk`EF+sQX7s*unT>?2}ltSXel8Rq3*{`F}65y0AP4t{hJTi!n9UtEIOeiAc
z$;im4X=t>!|E{Mgr)5$Z)sfc9m=gdA_!a&}-h@8<dHP(-w`-ecFX*SK3FPy$p#kCB
z%kxWj!=AdbscpJqN6v2mQ2GnR$9VD+Z7IOhQd57Q`jSq83j-Qd?>o9O`nq&|o*pAb
z47r~^4Fo3v?`F=1oK@(%c0t^Ne~ukB9C7MJCxd0k3jh__OOZwM1_KZ@U01myr=nS_
zzpY4!$n<Hr$=)n2Rg5iYOI$*k&(sy{7=Ejgl9J9EaT28LHDGuvflg7v1_U_cl&_&-
zv)sx#R7yx=G$F8Uf+6OCm@tM?NGNhnTN{z^9Q=)3&h(05jo$oG=_Ocy3gaHI-Z#9i
zK1z~w3i#B~EYW8Jp<|~+vm{c8ZfaW1W?|k&nyshFyl-V6D|-n+t&_937|Z%1kJAFA
zKqVw2ocTpKxFBi%3vxn*fJR3F+vp6AMcC#5gX)r?J1Xv~D;DrJ>EU^-fQis_Xl8h-
z|M%wjUlc{~J=tl=s9V@!0@^TPLS1P`KYCTc*cO-w&GevQ!}ddRt^b@<zd>Kd8l;0~
zi<t=21X$`Yd-sK}3_11l;9E!K2&P_aFTqL!O*FbR&}#yJ+p$5IY21Lw1d~?ynV6Z%
zaW7v`PrUu}{0-DLpFGL(lp#AO_ElF01P24$J7TG->ZZB5q3fY@1)i~2h~$g#EvBEC
zb(8yX=Z@e_Jz<aR<TGOq7cBEKGK1~TXovg`u0YA(5ptsC_ivC5Dh<3J<}fo*ET$0V
zykV)v3!tZi$xYigXy8DBugm!R+jqOlU!$~KKvCbm?XRW9(?z_&Tq7&tk#uA_-8hr5
z6;HDzLmutNBTT)ISb;f=0PwT&1s3^k{n@lvqf+F{*6EESgN`vbpJQw5309(}C~Rq?
z0de>K^8P(F$A|j*O12LS)lu0U)85i=JSk{uUkNH9;t&*lS{RiV8=zvrJb0k^ko*pX
z@UTNX0%>wTuDgPhqO0rS8z$jzy#Q{No>k`?2s<^lZ}+6U$JM6mAVW3na5dJ5I1$BI
zv3C15ltS(Hjs!03UksoAYS^rEjGDZV$p7p4arXWJA_e+y%S`#AV|p^yoFASJ1qpM4
zf&Dd=j`Ulzo{Mq(cqw~-v9Eei95$x^avvYA3bDAUp#eRr)QfZiD3e8s&A$ruXyt^h
zTTzb!H-i19FxGV*<WI53A!8PV7&&aZpq~3{-Pof?4|>Bfw9z~BSwz9zyLB!^^VCzG
z3VcH<7izDI$BuQmyv0s?p|>|U$Hw@0Hm6c8a)S|>G8F<5Lv<O@lC76{uXF&KATGyL
zyPcPxrhNi0o5ZG4kcqskwO6LRrZOi2P(RXIgM>K7C`&)l0z9S>gBmha^(q9w9m-+5
z{a@hSKW9!WI1UgQlp3peYuwmgL2R9Zfloldils|`4?AVsrTH?oRO7VYy<(~fhs5SW
zrxmZ2iPOO3AYWMym@N&~OgMG)=z<@6QZGrB=JJjiQ1Uxl^cB7>3;WnpEe1*r(g%xW
zgA8|0?EilgF*U_;vu9srV}_)PR0I=C?f(70a|6PjKK_5*;rTe_lQr1j&ioRMo6E#f
zgIR}5a(SOTX$tv{PUi{@6ls=dM|rb`4xOM50<hn|aU;^jBRq^Cgkp^`mEPgPsznNs
zbLP&4cN)se`BXx04x=&4$In4;JC6`DfW+#r+tojFy`UO^Nj`z2GQ&mMKNEvmCWb;}
ztG^2}#jmEzVtwUkL&Ky4MFYOw3j3<*?jurDGd*3~ns)r*>d+ahSDzyisczageTSNO
zoOTlHf0%oi1x<w7-VgkMdA5#Dl<Vtyiv}(}KN>bso$zdyEnX~a4P-#ZTt0Z+y4>IE
z%A~@Kgj&rxz$Yv$mm4@>!23so8h`#949x=nH<~KwdpR>wDra?5ETGb7BDMeC4#e|J
ziroq8==&LGy?F5#j<v6s`gy`9<YSwR6tSS1USs=?J0VM(r(RBT)T7Hpj&l%gsX_bt
z`*;(;ZP~hg`?mq<g(~TGQx#aJ9nWYwLYY>N;nd&rRbU{{>@he<OICIcuO8JVSPPk(
zLns988k55MZb9YCfCgw-lY!KVd<(Es7MLPX=RRGzd|At4kVxiGRu*%X6#&9SigI()
zIrPDpFZ1;VY&A1dKi=NuCj?J@EQ^C(J!oecULp*f;Odc?OH?EcOqsY@;_G!Mzz1p}
z`Z@K1hHlz)638?1(~MdQeoBe-<^MFX!Ma%Y(*Hv^Sh~mMHO~QJD5L=DvCl=W0wJkW
zr})KA@idv2e98`@KbNtlo#TipO0MY0@uzcR;vf3^^C%1)sTb-F_t)EA!k=ahx9y<D
z%29HMU8x8%cI|rX>>N*Pg!5>rqab0X>d~9Ph55ipmDv*QLSrJc60E^1A<bbFru#>Y
zNt?ps#fk^T$NFZz8$AfAj3FU>Ch0ci8M9}vLzu-pkPph}xh1W3(y!|GkQEWBFs8zH
z3LcW>HH-3GDdHW`VE=_3zd-HH=O>h?IqCSoo@97W(<Aw2-99GQOMQF{rV7UdyMh%f
z1pgx9cFR+l%8&o~m|3b&ceQuB-pQJ+#q&W_lQ&wc#el_8S<pT6WFR)f@}iTH?jIw}
zbT6W`^^f>nzDF|kGghxLRoZ!@F6HECy5(Sx0{l+iW6~_Qw1S926$`5Y{c79#9cnQ^
z0M&#r(mUY0@UJd$IXX=(2ADKQht)oTf2rTh(MZ|=ilvLzP*KqypFFwsvV~`)^8pvV
z^g_yMcX#(|=^Z^fvuNWw=o>Kr9|iLp$iQiW0X^U~H=G#;&!nzy!AbKYS{rO&0a@Y`
z!yp6lAa)=z)o?0+i1{3Rp!zQ>Uy>r=(4%Si=bxJrdd9-Xp{wMlgQ4f<hB+Q7y6PYn
z<yldb*4Ed9#}cLE9xDWOE<Mcb!{v}+n_?#!n{Q8~BgF<25Lj~cZy8(g=g8-b)2S;6
zcnm2``z&|7XyvjJxN-5~#Td5-+JaZn6)>c*5}A;JDK#j(CU4#Cu&&5l@+0X$KUuKd
zRGcfle~GUz6?Xf)9crt;6n<M?`aJa1CXvhtUe1UShMPAw4s2u~Flx$ccpnd@dWc5g
zC7R8a>DLXCf#x}ccOC%W=hUhC)Z*R>(`L_^vlk}HtXUfis&9q#iA;wXD-aRqgu5N*
z#q$k4D=anNiTlkHL~{SCrs!0ylFkWcKuw%b{I<zT9D=lz@dx-6y?TnGa8sB+;IK9a
ztIOC}`L-Pq;(=qv%w`yZ{AS|B!So_I$Q@o$^btm?@*5xj(=uMq6dx&mTXBoIk&!FM
z5HpdoGHWGS+fKU5oo2q^iKxqIl3YXzAfwy?1oh0lwr3)>T@yCeL09?LVRZ13vP(*D
zQ=w8S(&-qbK!C~*zG3h-DT2b3S;eS#OQfwu*?Te3Te4yWuZFbANT8`woVk}G3{C`E
zqG!*{pn!xaS>d9~wlE5Tckkbi8adJ^Dk>c6Gy-81foK}R8yN5G9y;^uWZ^h*?m<uu
z?f{LYe3b5!4qrGjZZ0(h3BIGr(@s~J2u=6}>|Pff3{|Q_s=ua&2H%3M>djwru%|c#
zun&l7b0GY#GZz3a;$JypvCaS)sRM66N?ME5-k1Ki&0fP2uM)@%Cr&I>o0LA#E8`yk
z4?;0d6T6#NuO?fn<d0{0UT0rRemhZ#Uss!DHn6KB62F67J)Tad>C+N3QH&p_5#o~K
zeaXz$Q_!9R+p#PSySg6?w>#ao%d>WFKP#X`6X!Z>C-J4e!WxGvLUU#GOCjQBq^ey$
zC>$kPY3V2a5%Cge5f(O%Jdx?p7y+;NF7PDyQ}M@S&twVS)$~jJPl3)`Bt88zIUP@R
zc1#06QP^DzZF^3yMDNVxpAn{&lic1fd~WQ8x#mpX8GZ`0WA;$AwG}xgzl1B)yZ1Wu
zK&hu<Y3QJwqj-3#L@)y1$;)F6-1t3?Ur04XGy_Ex^>jV2NcxP51gld1!yFhwI{#MN
z&*T(kmH0wV1G8ePh!;<vB7qpg?sY41p217RW8J$~V-U^D^!DyWU0(GAV=EPP^~HQq
z;syEX&-#ZJ`X<hx*HQ<_L>?Ygzrx&HQ`184;)2=@@q_#ca@cA`1x8Lhw9O%tQ9tD%
zezQDUv{MZ1VB>pxc|Fjv(oQ0haNZf@`?3rU9#UeWyNAa?NQR3S&m>q~>xw>=N>xD2
z`5_RQ&iRzlJn|?w-$|lP28uvnbd7W~>}n<^?lW6;3sdotBUO{CFoS{1XhCP#^obM_
z@dUS1u0BB*DhmxP4tF2~P08U?niz(I=fcyW#sRcoY=>=$*6e<Ag8H|$v1UBjH!fhz
zQK1tMBeeF}%r`ACOL1(6FT>BqWEqg2W9Osl!w)CFiL<(0>h~#+H97n<pbTmyN^Dvp
z60pSca1?q2Dle}ZPc#GuB<kM3eftdN#r$X5G}hcNVY=fQRyFt8qepM*>(RRfG5Dlg
zrS-r*wT)_%Nkh|jPNO3vsx@mEt^Uhcg&@b*!&!^j@ELoFt0lBmOi2Mq(5Qm3z>%PE
zhk(c#iCG|Q1YtFdLFv`an-#q(BKj+oUWMgG_A;o4ZKD2eA23eAHDR^gj$|t_{*h((
zg+H1oeF040-25fBtfg0(`SKI!G^iXI@Ijr@`X=a8RpOeh@`4bBF*S;;hN}C6$vIb&
zltLJ!4)<gKcq4C<>IHz+PMZdlHoh2zU`2(6k<l4a6SF{49k48!jNj0d!I^6ByMvTm
z!L}P1P{Is;>eRCrFW$d%$Ft%+tc7uQc5bt0Bg>``*^AFDFG#RsS5r&xXI`@p+X0>d
z^dj~<U|b7fgytVa<$<>YM~xfE`~*;l7f4dUjtCnYDn7C)V|OOAZROX+iE|@YqEr+{
z`Pp{iW<7yd?#y39y~;VH%;s^-VJ!)n1Kx!&eb(2PJ$nhzMOXI?MJwq<ypb)!2e9gb
zx-B!)8zmA1J2dwfeV<{<Vy7e<VFhBr(R^D~B{;y@%Ea>LNqZ=JkRi>@3As$21=WS4
z`RdJ98c0Te^vu+T%oVZOquNOu8BMSvmcM%WlKDNPbvTu8i9PSy@ev@%N-w?2)D^QE
zUJ7@K^WDAu0a^+PXyw?IBc*s)R>p~H{Q4DIb)Qvr1vQOa9w_a^K^k|)v=|$+UR;ox
z6MeDYrwC43p<We1@S|czs=A(qV~nO@_P%?f!}j>i7zGeT*lx3A`SOz#416lM<s@#n
zaV_^n-C_xKC*aI|KUKuQ1g&)5JgM%PKbo2Zed#6tsP_E?5!Pir9G;q|T*26uILFt-
zUegpNJOvIW$!F9ew;pyG$n}7~LPbsmDo`d`!#-UPFyGnHVHx@(`(p9!;*BPm5!1H)
zqw!;2C;PQtb}S!@cUfdJ=;*ZJ2c~8AopLUqq~hc8%Aj1$-1}?BT+9gm*cN;}x4!;o
zTU|@R=g~!LPJRp;`?JmPOMqoAGxqM?lTvJ7^D2myC|qLU!^_D%fA(w{Jn*A$qNnx9
z9D#uW9`?pT&zaARp(bL$#=l5lL?<NA_rn7qcoP$U#^prVUb_~tXdpa1ysD}y<-M{_
z8^_iZS>dLePO*jIy&1WCKVH>=ukSzqKrRC5p^yM!a&S;6T}MIn0NU*{<QPH$^q?@j
zhd^S)2#VDJTdCj$E+c30!ED&%`3{p0xL}0W_2)}Ai%`o!xuuO`(lRqEi331a#t1k6
zwi@LEmqT4W2<n8_Vzs_~uR}Oye;Xf`-g80S=D0Zb<!ju!zNU7d;NdQ1j}Lghe9r%I
z0nVH|x7y!-!sN;8n`*l+&9d25LsjwAg#kQ-(ofhbv(X~9;Iyoh?Oljwf*U3TWulp{
zio!#aT<6dy5>ffTy2f{WUoMgQJ3U=Y?v;v2hc3%0d$U&DcYj)1E;1^#OMT5&X41%8
zSj;2PKqB7a9}LO^Ns97{)s-yLcprQd;1j9@0M{(MM^hZJ8^Rqwz03zT0PqHPeJ)nf
z@pgOoA3&pgCk*>8y5|dR368=#I%i>v_!%*lA7p7+iJum?438XKA>q6k7$jcabH+7Q
zyy6kH_uRRk-@W4`#$YOCZ;#ykmRvlkMmUvTCEGwv!&70icwx7~tz%CjG$7<R;h?*5
zad9-tz#QF^f6jG4O}i&8Z3Xo=!XCDM%rOFjl29hB3-n7=GYLgRRW^~x-R{)E-U2qC
ztpaZ{UY2_KLn=hIxVWJ#Y#uwduYWQQUj#jDW!z6c<;UOmI@sDtms`WT!2a0#*cD;}
zSSL(6I8mHhyrJMjr0m%PjR+}~&I^yHChQ$7-8ZIJY=QnfY)~6(06p`ZN{Wi$`QNzW
zAF&(w&<x~~2ukq-tVnkPl^f|QsJcaHtHQneVBVBH>b-lToe?$zfPdq`=H?a%Wt8DU
z)d>v_8MzP|n9ElzSL9Ep63}&r4;KstHrN;rigR0dizV2!iR4*E<RGq`Xkr=v9n_vW
zk4UAoWs{Z1;kOH+tP#K<&Im@%e8y@&I#ZHO$BuA$-*NQP{3BQrl>fvIS|}h!a+&>y
zy#Nwn?dGFLKY#pqB%FS$9I9#VW=>8hZyQ%P2}OP*tX*OwOnb<40%q~Yu6<QokZ;8`
zb;%E`RAuTwflnv=68W28+Ve+Ej<wSnC=T%IrRxHT!?aTbEb=mcmX`rf5c4X$rSM{c
z^omj>dGB68(6O8kEUBQ-GS!q=SDHGCRg2pkbU|`CR(WHqS3reg>R<ig!^X{H_^`xg
z={b^9r!lcdW<%>|WMl;K<4I*@7&bz1Q;4?(m+1ICE?nZE;FAD5%IHf@7r_pL+McQu
z#FWmTr;_L&Ko5^u4%(IK#$Nyx;tV;v;obU<e)H)Q6^UZaJ-pR;jbOm&5Sl58o386c
z$6iCXprhl--<6S)OekW$LN=E47Iv|~4V|c~jARo&A>asE9c*rc4VxG8DRrod-TOp*
z&E_t^apzC5M|u1DJ>TQQ#^^HI0MnV~;!^eY?M-)sfj#I#mJ&ONfyc+R1A;>o<P1~(
zP;=5BQj6n;%Y5L7+v5xSL)-cB04S{WpqJRSbEjdzMgAQE4=JC+;QnvzmoNA3-@kbF
zY$_mlw^-wmBTpVXwkjZCKGR<6527;p8#Xjt*!)>qzW1dn#Vh+E^<qD8Wu>K=Su-<x
z0hLDY>8N*q&xj##^#=?<bmhf!;FkoN&ttS*S=sO9a&+EcbQKqtrP9qhPNd#Jv&KcF
zCiPX?kiZ$@*bs&7w95($qwgN0DZ-iH|F!d5vEu%sI<Dpz|JUr1Q`@|cQjo7fd38VS
z8RY}+Ads+{vCbm01GX8ZFnk9`WdYh{kDHyTHpm`EDS{9cvh$heV|Ze)0#I?&OOZ&J
zw!kFh7*M6btS8z@k7@q{G^~WU$iI&KfeAjH18Tym#1r=64xfN%31aBks;jCRnwrd4
zzKJ8D5V}=2*&lETG>0<1fi%Izq{I|@WLa*cpacBzi9Iu7<#;v4TNs0V@+VMZXNj-b
zD+&wL!+7N&T!2*rKD9Zy3tbRLl!T|OsfmBubd-{meElcwVoe0sS+W@D68pyrTp>_A
z0O--U5`<LsXQ8{gwPbCC{uZ20n6J~$(9Nf%rSY99AIXG*e$CM4kSk3Q)jb>nmEOJa
ziQlzvABZP=22EFWKTO5P&;owu<tta1MVtYYhnb$1HXo=J*}}wjnnz|*l%(Nmz!EQ^
zRED1x#*-cI5!U4ENpQ1fPMNZR%G}*u*iV7}fB$}5#}$`;IrUDtLq?fZ-L!MhUc9(}
z{C#`PV3sj+N6~oFE%5xPbBvA8e*L<VqynsEu9;wSKtV>zaRd-jwp$;IkU)0TfCkZN
z@j5V|kh#5HDk7UVjq*zEE1!YC%`6qB1_uSsB#)Ok1-VwLrkLjp&xWd%d5?gMvX(X_
z1$2irSoiw1)LBWjzO+aH)Vu)-UId<Jg1#-H1O$%r8j5zT@{)f6$Gf#Z+{Q)E*F)w;
zKaE2VMQTF2hsKu2uv>ceT!<o}u8tKjw99lur_gbV#d)_(x0H^AuJVjNl`4@jAX^VU
zevO^;?f092uB|bJVMmov>r=gq<w5T-cqSH10C~R2BkSpaA3u3g;MzI<Dx=JW<^4%-
z)MpUo-Xl$9zZ}vW=ZQia_^Z(~`K6(nqEtL=EkVb<Z5zG=QR6a*J9KpzIWyLU`NTkz
zIJL2;hFaTd$p)JPLXp4(ki;z`l~4a1IfWk(YO>Jf=p()?`gry}BB-Od^;#hP@f9T)
zB`uAW09&jU)JT%+C~Wh4m{Bk6-79PyMa7QIhuzD`v4t+uY<A>j?Vw5$i5#4q#`W=8
zJ(}%c!EB~rJN=zIT_OqrJF_iWE|bUa^D%kO0EKx9$=yNsA;F1bz953Fa%N-;v>fF<
zAcGjIYz>|6AS|5cqIA5U@~7eSq9?4Wi3*oFl1TGMHULpzwyMz?Sd#XK;VgQ6CTeTx
zA-KVRPYH}c5+!!1GKa`l{B2SoNe<T|d%RaXGRL>bDVyaYZ#LHyaM`No2%I8Sfmsf*
z)rvTtGG-eotR=08^vzJ5g?(s8a9#0eBIqzylkvREk4w6)vCj!xY^#hitRe)7Q#n5k
zA)$W%{%aWOHl(=>WIKIlF2PXMrS9$$R=pw$c{~hpD=V>7C?FpW9X4#Fp<%v<uyBq@
zRa}$!`|N%~nPFo%is_IL^VMdEiogKKX*dQ+=pHVwbF2)+GJgO5d34e}7NhaIyaHQp
z$aB<a=t}}AI{p1mgF+dEqDUReRwGUlO&<UZH3e~uIsisObmz3adojCbWz1WwMG_Os
zID?!LIF4G0^x}fsxA4$7Mp%^f5Qg2?Fa-blmP;kEi^>ZdS3)n?g22fO3gYN-lR2J1
zuOu<t4G$OjaNam5biFDHoTm*G_-D5Wqir??!MX2ui(FpL8ZrKvU`p-}hrndr4_{^*
zL^o|osd6ntlR{<(OO^oeWI}B_rpBH`wi|4OQmvWbJwo^U&z}WOhGu5!w_c$VoICdw
zwX~LO6K^A~a`X9x)ggX<28M<dRg@s`7pzmPN2?WXZwL&*KJn{V#giN$e7?XxxU8Xk
zIRYY6L`1tb8D$;I9RM>)*Th%)$mDNsU`-@I)lK-Pz%3w>Z-_(8Rzgf>>T;M*cyZ&n
z420tIY4hctb5z4jo*Ahr4&F)Vx{YVDzJ42vOtQrSjDm9|5+rU6Y=uM>H1xDE-E4uB
zg7^T8py_uw5wz_*Z%P;1jq<xo9A-c8IS1-VdggxP=yTczyX0M5A({rZI3WK<X-aR#
z^JCh|0y<w}fN3AJGkm!_t4H_Ue3th^ss<6KmgT=!6?os=Uc5?c>pO~4+7NfK=l4+7
z>JjKsNZ`AF_wMKF>ii#-{I;oCP7(P51u<QjpYU9$0M>c04NnsGEt1Uykt8O*)qZ?i
zDo*0I#7V+4{xL+%Z1!D8=P$*!=gJj`&o0!-zRMKlJVQc|I^V*{C^ps`!U8rRYW@0Q
z#!L^+s^2pgF5s8TaG61o<-elQ``T#$VFZ8!+b%%JNVpd~CqOCCE(74L^!Hz2kW7BX
zdP*`f6th2iG5CZ^bxQ6%S;sK%lHUSO#G5D#9~cnQqUP`EvOI`Xg;@e-i`o?wzlJ6z
z=gyzEH@Qv|1JM_2Ilm8&2C3!prMY4&SFa91zgpT85SvmMIt`#@?0?ZtS&Y9FHb()h
zL=I1Bvt(=p^yjEo|MYYXl#*;s&IN8OY%ak~PDyo;#+Dz%0E*lDA|Z=nW&*-Z1Ag`B
z(M~ZHL``55dJ|MD^gVT}Teyo9!Bp7!XR@&e#e<MQ0to=YG5{mf=3&E53hRRn54s+O
z2Muwbt#6lC*D04?A^U>D@=0?uCn@%AACRbatqmyD_~Ye{OM}Ulcx*TpT*=L41-v-k
zZdSH?1asW&+sjcB-6$wn(86)g{-)lqpJ1)Y^p~}8jE>#qU$ZMapnjgbd@Ls&dH8jr
z1DFk^At)tM&pznC)b(KeQ#J6@5VfPBbjk|*{X?I%Vw^`JlEFE0?#cPNIg88nn5QHk
zOVNyj3&lm|tZ6+#n6ZZAMvoxxfMu#6b_6q~mjGMAOUUguo{@|&`7$)GKZuh)Jr+&n
zo}-%Qb_!Lg`%j?n^?!ta0}oCr9etf=N|vAy)zUh^Kkqj-c*mM%&#Pa57InNG(eMJl
z-q8|)iIB<3yF-M|lh+O)0(BpnkFDdJ>?*_Eqec!l^pgNgW1ID7M33329YG}kfn?Bl
zJ8h}>>K3>$v?Odq22rQs0lZF*2VJJNgS7yEfeY;3PwvQnxUo6t-ZR+EdHjX#6cs7%
z6rgFITU3Y#Ot^89WkQiv=7T2#Q4MgNX#pof-pV1P44SL393VfxyRvfRCxcKK=AcW^
z6QQYlCN_-9zeIh{t)8i6NYq^OaTi}aBcleaIB~<4l$svu>VvekZNwtcBUZ)WX2gdA
zGRre+`PMnM@8E5d7<ybLQk7dKaL15tu;7uTJY871#jTr8R)vx9R5DKoRyrw%D5ROd
z^7>G&$MM&MHO39F*VEE0p|){p(S$g@0dqiS9DA+XY%_`t+V0q*nrAEHA!QK3fLr)G
zMSDCIw{)}E%YNhY=gx^=1lSp-_EaV$K^P&acNR>pu||Y;4L8^0<A!CiAdVVa=#kd5
z`ayTO<aO0I%`dM7sf<(w903zg_eNa$UBz8O5<>3+icPu<1r7F6965RN!kIHt4(1jX
zeCV6-k$eGU)val0D2suo?K8@F+(a^!FinC52)VBEVvNZUCP{}0JD9n@`7=J%)+(gd
z)2HL}-H@kqeV@$%5UZv9A;ugJ3^kc~FTA75V4K%*`s5{=X&Ao9rd5@dJ1Z#sYWY5-
zIIAy<n&!+VHJ&(mQnODV?)e5Q(>Jm+duvG9fl`nmfq#;=ae5i&l5l{0NEIr#=He1`
zDI6Wo0(mY7wV>*-ImIO<>QHGmU+rhj06G{{jB;qCL#ev~RvT=Oz1caQfC9J&aP<Do
z8}?&vT>Xe23+VT*0d^1Qhuz-h<Mp!dc@RKMxF~5U$CGC`)%ME;)*nk3yDP{*28WET
zRmpS*G;!>}feOkdRThBeIE&@E8wmNcfGs1RSWDAMd=}9#_z3oKQTZt1d#S2Mj(tnV
zL$ctUIA}{Z?ZOyaDk6Mb25n_`<I1KbfC@;k$;2F<*!|M`ipV-!#!Yf?5XUQ;Xnf{h
z=D21nYc2TCMB_w8hV(Tn^d7}7``U;8lH0tWT&AEKgKVs-F_0RJFhv-#9Zsz`8t584
zBreVYe$tuaOdM{pelWJ+uI_FMpMj%B?Zz3>%1TV}+x21qVg&XQDadfI1VF*Icju8D
z7j*mlr%yL}cV@#sGG_d4{>i7nfDFmZrkhI^FE)&F$$Lq0h^i|8ozKFBva2+r^1-_M
z8-KQ81f0?@f8r!FmMQUiK!3pXX;F3e_emO^I$;?1_0+%r;{IiqQAU|d(*m86FwPmE
zY819+D#x=ljKsF9x7RsbkkKsw3E{P3P@v5S0C-IBNZ7N7<vcey%4a`3V5!t2#IFfO
zJU>Q06h4?TO=liXP^XB?9>~!GQM`2JijX8xQ8;D60iwDwRB;vUfXA12y&3ysi5Aea
zPD)BMrcAL8x#QAIi^=vZi>D!I6Z8fQ0On(9cz#h4@pz<eco#!C>mxy{SDSc@?pUtl
zG<mYM(H<(O8)<j~y``@Ivm;D%Y;bgGZ|-TL_qpY-M#sI3Scim^V05s|2Wj6^qx>(+
zp|iu@)7FmsPj@T>816~RM`fLx?VWVTooxP31(nUCN9ajn3aXg}krV*BpoBn#;DQ3V
zNqm4U7XB&>n*h2Gq!?H#synQNb4N%df6u=bn4}(D{_54f-Mh2U`eSF5`Mhp*FbZ(+
za*ZwfjlH`WPjyGhP0FCBpr7QOxp-!~GH5kCyGueDWslpeSx|O)Xj)Im-I+MLpEYnF
z{o%_Os_i*o0KfyHvxANg;=>bHh~$)byi+P2ur>ZC2?Qpk^>P9`xf)C%>`nju$;sjS
zddtg?=Uf`?ZeQ|GM^1Zgj$Eki>)hvsO!TR<d=ueJR6RIgORdF40mHNSXpGJW(>(&~
z%;Cw^L1ZA5t#nGXq2LrW8*z3Ac@M_b@-v@ux>F9E0H93wjBsp$s@c|GSeh#2T9UF<
zMBZk-EBJt)dCHiWFr?+AnYiF3P!OtHvVHzAmM3H1a}Kj?x3cb)pPa@1C;<}0hM%U1
zhBpGYQSu!>{t4nE_1vr<mh#5=5C7O~DB%9Arj~uaSaHbSuFCuflfi>ORHcmv2*m!2
zHY?fMjtjhO3(+0FbL87+uH@A)L}C!jN;Lp$!co^D){K;x`N<T}&evRh;1j$!OeUUW
zhFvSshp**ktzlZpvk^}tpLOz&<!CtnB%LTOnmC}h?ibjI>+I;X9u`UL2SM`1{*PgX
zd+*o%WAYYzse}LUxtV?;kH#e8ck>;i_~WDyU<_kj<z0RaDxvMI_!EhyKc?c4m6ykr
zoJ3D2)9PHan}FfV(e*Jw?~hvd46e1Mt<-tc^rZJ<z1}OcsMRLvDkJO5yVJEtBcGFZ
zPd(}&(ZGma*sA{UA(s!#E1~ZgJ!-tehlNFSUUpV#M^Bvsrj)%nkEV8?6E|h}uwlEB
zlB(ao|H-^f_DK1QUO5NK>;CGabVLe-Sz>eXR2~4`ImhmRCY?DL3ZDk?7@&XL=Bqqx
zngZqcXz{8`-+tGZEuC`o5on#d&1?E-nlQ6f@9-0+80c~|D6WG_#_oU%<<alUKT6TG
z&?F)@g^vAtIYG(sf*J7u(h2Ng8ey5?II#+X+EVe_$4UROcY1Z*!w%_)a?H-4S4l{u
zYtVm^Z#k%}ZvskH&|z%IIxK)e@`d()sGWt~ISNamy6)5L5#A)(dBaMU>Cy90ZHZ5r
zjU0KaX#rt_s!Mn0KBp{34&&%vV+(|nrk#camO&+kF?djTt+mn2Un}(>7_`$jQElh}
z7CPG5>0)55{#9gaNE^yArXW_k>5|L<ji!t2P11vCO!0W(Xca{+Z5n}u1r)^EyO9Qr
zb*4{eBqiIuro%`#M&DFzKAl@)wvJp>Sw+Pcs)V1h=cP-7i0FXT%n^>ilCY`Ivpt!a
zS@>pV__Oc3{}gR&Kkq@nth(tuz{T-h^hoS5;(AjXqE=_jC^JND%eW!>`V=H^bLbF#
z=jdWEa{-U6q$E~C4IVaZT+0H81TtF<RaEHBuuNyqw9z8b#^`AFPnOb3EI3JIF=ch;
zs#V6KAYqXq@M5PUKk6$x-renO5XqKGOc}K%+<-w*URH)Y9}(%$z~|Km_}FwEiCWwC
z?Hg-iGHveMvFstj`MNH}nrf$XTdA(#>HF@@8+g7g>=SwuM~uTWh#@wIo9Htx_!B`H
zc-mzkeRq#DYHac#>Oi*U#UUB=x;J#lkeat|d#bADu+`!tK2QT0G3zEdgn3q(d~6G=
z+dD2}Y-npB9W;P5In8i;{>nMirU}r2qTE^7xPhC<TTCu&t*vQg7~Ld|Xp%eL8{As-
z6z95)O}hxt)U*f6e1IisrD(Z993ic8D<MkrY6~>wu36KKhR^ZPoB5pRMQut^)?HdV
z^ZJ~e5cNnYp{xT?1lGVo=kWkGDZA6nyWiQmX%mcOxK30KtX2Bn(BPhWJJ~#poMw5u
z|6$jo6k`v50$PUd$ZwqVU;FRZ9k(@v@!^uQaD?S$WU_5MXmne?FO}Fr<+WghR>7C%
ztDDPnXLXAc?e7+kuL?{V2i<M({kDr_FMkFg0rBN-Ub+-06f^<N|2QZn`BF3hmzIug
zBlNouj^5E53<>B*dkFi79T@I{@=<{U<V0B9zIoFgh{R62nSE;$GQ+y)GJQyee`smh
z0ZE4|d2r@d0tJy{_RN`viwCs7?UXda4@%j-HLg^vjuR$;1z68nfHx7w^88v5lq(R)
zk8M#mb->h*7Chmm2LdpO9@Ho#%55cHPzD()Xdg3u7*{#Ad6)ogF@XR>GVL?W*m(Qr
zI*L!iLbkCRAgXUVv=ncJ`23+nbQ`_x$Wfk79D%h^b%DH$w{~Lk<mmWu8Fct?{%KRd
z-F3G`eqP?-k5l)60jT{qIp_|Xc}5p6A4CLxexhV2t&Feqtt4Z#@)-KLFK+fpA3;Hh
z$QqMyJdp7<z7pDY1vK0DOj2L{HzxRy;Ok7E;xJfx@-(pVsxE>H2w5<~3%kvJ;kT(U
zIpJH2YJenfT?mStd<$qT+_gVLb%Au|agb>$1Bz0wU(~vp5|!%%-rNCbfs;~jX$<C(
zMql`+HDA5}X6KLm!u%S_G=m+E&UDacl=)lz(cTsI_^vYC|I21Af0h~n^hGPSdc8b-
zT1mTJc7Tb-mJ+oL?5Op&!w?tQT5KPQMfeU!Jr#v$&S|m}ekueXjvwc@SYv)(=B3#=
zA!cYK1J=do4!N-!N|%c(=1k9kAUGVfagBkk90G)uGk<%5fFaWc?7?N|>tWxXQvKlk
z;JMp1=Tt?-Jokl24F_3yL|;{NyG;gX00p|2z9O$Ld}7)jL$y*`Q_PvZzseHNkDM_R
zzI9h+yk`tnEliQHa&&|nCviEHkvL#H4=j61%#_w+iNC;4xS^2S=gcuDhu7U|=pj+6
zs~iu1V}yiE`xsUuvm=bstfn!LiRa<rAL$J^Toz_$Gq@KgPj>TrM8lLP`H`8~l_h-S
z=LH4Q2}KM(C`9vT%v!Jee_Vjh&<F0`zfbkeZ0`1R>FQh>BLWvWviM~?pM{wr#Wf=$
z+PmYT-A-A5$x{7Ty@B-+ls<Y+niJ4d3Txb1;i7nK(&txRp@D)lOFY7@GBH#Q7EN{a
z0)|VTo~!uu0DSOQ0C@oo=q%u<a`0SKn1We9%_N}kLH$i%Vt4_9i$=A%y=@&;@2gjo
z!%}OnFcLR7yOQsUyG4ZgF!~@Pqle%td{kN+m#H`mGi!~GmYFSQ0WQD}m{RpD$QEEJ
zU37O)4ge5Aj^*D|Q;fl9n>M`IBe<<aU?VRoUFGVk?C}qyawZ;FI%{fd5e6GWcf+nA
zyF*-H_Oj+g?1QYZ6#te1O|$rU<bpr=(!a=Mv2MXH8yX>`X6hiw0_VS5D?eoAF;>;L
zZ>z%Is%rvEW4uRU?WA;DqGu%!0`F!5&e;od?d+l<Ky&B-FBr+n%gbA9um}8GV<Vdf
zj8*CobB$_wFBx>l-KXK(H=XSz)MpSb83YN2O>~p&C;9j>gM1@wlXJDT_2ib(5*~Mk
z-!#hZH<ZKOxGQ$+wtq~(awdN`(J<&+aK6R*(X9lvto&foI`1ZCTn01pU#n_{*8FVD
zz4W&T{{=?9!R9go0V*5}NDez@Uk;~Q>lo&+Hz}!cu7g0mthe#VKFq?}&-j0wvZ5!S
z^{4EYcGPv>*~(%7U*F^GWn4WAnM4_b^}gnTp!Rr4Ji;Ev$>~d_WIT69cF`SxT|P%v
z<(P_6x0Q>7@BiwgyU0L|<hfAqsJ43ss_<L4@IRS~2nDpa+<Gx<sziDOD#@0X-dczu
zw#3E3+R3YF<nQ@9dmE@x5GJk>+!5g;KCEk+A6Y0s8@<hzu5E16@a(#md;`|@?%uvG
z*1s)d3z5}@jNkxL&@vE1qE2y1nJRDI>DdK37*KNZK;_crEXszcS1*7&8QBDA`9noz
z@uv8#(#rq>)S%ftH8eVJL6>$KEdY6ij#F}EzeH1S{6_QL*^gtmPeI~G6BU_@i?D$c
zc@CL{b}9D{__JmWfqrC)<62>l%{|&TJ_T3VwC`t$%T}{yX}q}f`-PUUyASA&I)juF
zYVu{#!QtO2Z749<Fv%>6#q4Pl4{>~rny=9JGE<zWx1D*1;Bnu1!&jJ<e`wpfBYTbK
z(}#(a!`fSkS1Nz@G9r>Xc=2MdufC8*U<>5F7(fTv_-((E=f7vqZdZ@efNL<}hR7L<
z_S>D~E5WDdIv`P$I69i*zkGoA1;Z}a3SoPsbc?57IBe_TK2BomX}X2hrHO*5fSdrP
zW@Dp0V#Lm_3x53kX&j^t<|^Kuyle<;?QLvY89H?HgQcKGAsAkKTeKEiF#!~JUxq`f
zU0k-cu(~oZIQVtrFX6l9tWV8%7dXDJUiD2VI(GEvKD<Ux<dMpV^7s*oMGB5FVOCSa
zdI<-L0UN;=n?3L@+T6r-L7*LwPwNs%A8Di4OvJ@w+ZwdwM%VjcQmA<DHGXI$mGEDp
z*aB`Hhl|k#HcaY4MZ|5!2mrLjdw~oj#|=4b+|PZ$KBw42lksFbb4Gb{4__s4yP0g|
zU};uLih8`A;Ir6JC7C+t4F&OP(%~2C7A`bNgmsy)ay(Bzr6Hl_rQgmd^Wki`4a2D8
z8YCza4Z%fj<kg-VY?@za8EzT3j<MdpeXmM`zgV7}#RQP{65Njd6wVghAcA&8?H7=E
zt0(iPPW{GfB3HBHk?&1q2c`7F^r!^Dmj^;J1mj>hSK?*#XFJxy{b1MhqoR~@{uxe?
zQjWvOQEWVBs!ajP>GQiwaTXey1KNW01c7nF{$CX1fDX2?-Pp}+EWeJ5ZT30AK_IM~
zu=45HfddhL=C?CF{~xyA1Fq-3Z~rGrCA26cl?DneP1-1uIE}IzvP;9BEmB4rNJJWT
zCsOt(Dh<iV$|{vnStY47{?8BBec!*w|Guxs{kR_Y<vi8*`}w@zuW`JN<9MaL(9A9$
z+!^;g+t<ErmU;Fnd#SlQDg7vV$><|C*JX7PP*D&V+HxRGBIw~U>t$CdV1Pgo6J0P~
zw*)3!6L=kvg<}Zy!)GWw3^lo`9p)-}{~&!U-W3~bU}z{`Z`t`&Y*9=5166-t-%)2S
zlyj~5zbWdnfD^8#Orn1uw%9xy<B@GP2!X86ek&J`pp?K$%0XSW-_EhCK0RDzSq=Wc
zEq$~kliKwBo;F!^RG<uSFqhZT>ajlM+mW{1Nv~lWdKDj(P#5cc1Uikdp1P@>fU<Mv
zBsj-_;AD@eDaV)ssHw5NG^|;4%k)&H{>9R=-A)IBEk_-*RUUwaFk9lV&p9w=j=O6Q
zr|S%T&N~!Xxfk$g;clTy<K7E_c(lEg@*8G{d=&e0Fl&Jc$Z*fuws?Hcb*x|&*K%HY
zR}}jXA3ai~%`jI-W;%xqN6lG!cF%#Wx90q?><rknNy#Mp@6ZL3KM@%}K77uDflW!B
zbc?W0$l`R+v=DS3q4%HtNZghS*MY=_Q3>?`hY>*{`!IU<+sR04;p$f%H)LOQOiFSF
zCFHg76NsUl>iD9|K-Hx;a|O$&Km|b@nBshr3Wtw0<WtYno}>&MaBv}Fz1qu{7y4TZ
z2muQxK?nig;1vka0SgUM`^7Bwqb^8bXdbS-sCNXHd)a~op|{;t3=j6Y7u?##&mS#h
zU-8V&@%FI#`KyANIU*>k{zO}75Hp>fQ7ouvYg771xc9xZB1{0$Rsx4o+XZDQqz>gl
zM;%>~UCna@V^9h2VkG$B@g+GdDUU$g;KR^OetUg2XQpXEXa!<5GuTD*=XXH#@}AWp
zt4>!0>lobG(7@moCT%F92*pib-}DSFHK>=(u=afTPml(gJJiR#{##Hkbc5^Hf5YN2
z_;jhWQv-g8)tgp1dnqy30>#b~QHnBS@FYg^?fx@4!$>K>f<~3id#rcMJlbU!_y#VO
z+pCws$;M{I7nK_0gdZQ_IIwt$S^8)wXl7;y_w5@^89<NVhF!GQ6eUH)7dV=NvuGRl
znidl%86lwUIxgP_$_^Rb^t<}{X#T&z%d@w<yH^vn4%CaXvoRPLugqozx2>MNICjfm
zfi$<aVq^rc0h^oeuMq#_Q{eE*ue{saA>GCM_7b%xlr)g@<6kxk7PVnV7<Q+s+pnB<
zYI+y-0^_Vz4J+-7*RXPCr2B`8%1SyO+i6{+?@>Cr=W(dI4{79X#;>Y$e1}KPE}JBD
zFVR0G)(e(js;ei?nx$~XFHk}@(R5{)otlR(<JQ69CRSgiZd@VF21Ry^w3q6)AGm|n
zZTzF7Js9W$NpY=VeUNB*KHX<MZhR@`%p9kOtVNb+#Jk-@W_U;xBL5yc)?Gx4>_Pk^
zH}daek~bmA*|D@84B>^@TSmWl+Oj4BdLZwY(!FVvt!FdZnc)<uP?Jcu0HsviF7FM4
zt91a#c`Vds!d!LoN(e?-60+Dl3rp?n)zLhpKYpn?FNBaOC3XJxtm>=+iHB7q+-|Xt
zrnR}5K|4z-vSIVn!E?emc%mX`XFf31fIi&x<A<$@Z?t*aVpV_GdP^1%7)6ZV{#gL@
zng4b<6&m&Uj^=@05-OeB>>3Hu=Vo7=$R13hl=MDbHbqdab!ys!DSzaONQvdh|AOVW
z;Ec4cByOJ~3&$Qx87Ogv!hg}i3ts=;jZY}8X#`B-Y7~q_uf>|v#Reu=^>XQHBx4Gz
ziBku}xQS8?!Bn9X3(_W&Pm}@#AAhu@*n2(=GS|k=@5sM4z_w^hWhRNL8J%JIUrr9R
zAc7vfx66$CTtnt6q;Ek8fB(K9Z))n(ww-&D{b=6o*{$;yJp7)RPwr>X9W2=hX~Mg%
zpjb$kNSrwSV8@W2C#-wKM6**;eG4XO$rB4Scm3k-dGFT$v4;*vD~iqVS{4>ZtW?g6
zIdv9H8UtBu#*AY;2sJhMZXItf;fXa^QPFBw34Roeo5-o~xuieQo5CL8z(gy<6k+|E
zw)DEtC$iLK5Rv##w?T)QP#}<6>+@@s*=BHO=C?GQ5S8ipsJC{j251JCGBF_EaJZny
zW_3HU`0e$M%kx?W%62~Om)JYvw#R6Isq<>U!l6I=r$w#XpsZQ9&(gBTv&2sO3PY8x
zjIIb+G7)yizb;2|fu>{bT&3m8J*AzshYl@Hw9LxPl#gJLeCD@?eX-YZI3%#0U^I1!
zNs`=EYIW{C%N6!FL*r$!n7^MNrQQ(}e^0aCoA4Zf+!(#8Jn{MW#!jLe{<d8DhWdI8
zH6RlkeH075jio@>fK${L>&|7#$Z{;mMCx-C*GQ!K!d@|O`9|7EN@k*hKi?Lcb9vKE
zw(2f5JN%Z_>MOP~sC4X8cKF~yGz*Y#TTT!q8)exSXMxR`<4;D#JQy%DhM)#551`^C
z^EGbX9MmO(Dg?LLfg^D|1MlrJOb74nmG-<jp`ScDi`30ffe{mYcz~Q>mm-{PG5b(D
z?L?iDq;0!wBkL6@N=epGN`PnhU2b8-<90f3ZmFFbye;DqBWR&VaWq!H=0yj)Q@h=T
z`xfQ@>r9le_c)}^W!wRm{wHL{eixqKl`Gj-Fo&#OoBxJoK`#HGzVa}y`T7;Y=|F-4
zpBY(R!E|PBr?Rr($;A;SoSa4u8@3cMS*7ew(~nLabur5k<kW@+z*VN48R_YG;giBB
zM7_<o0KmR_b?ETn`!CmcpZkGr7d3{ISk;FQVJ_=CeycEKU&{zU^a<9_8SC|L=jMEt
zh&mI9j^^3y4fsp_Q#P;zgO__owXWydT3SX~3$-T+7n3^1R9~UTpE<Mh=LdjJG{PWA
zX*QvOL)5?iF%M<kz~iS+Z~9k>eR|j?E*m;q)j5(QY+E~Q`BJ9!^hY2Q{4BVpzrp;%
zjr%Jr-(tEBl+NjB-hrx>Q{dLQK4?9X;*%^_W``$dG4wVPAz=i3B|oT}lA`g80ox`X
z6E>z$(URl!_4K+neMVG~et)3B_FOh~p}sQ+wt{+36&sRIjg}=IVF}xP;-uo5PdH4c
z?Yk=(fm4i2=g%KM0((>$YO6CG_dGO(4<`0`6$k@9vOP+_Q#$XPcoSq+cQriZbp6#i
z8_A#W=9~E;AOeJaTJ9)CVcdk(a&<v8ghyF%QR<oFPXhpu=;ayK?l9ET6IgRFl`y2~
z7WbB1$bTLrm>PV0V7Lwh@AwDZIlff;!q-MTTT_EVW8v)k-`9<aG2Z&bs8R#!9F4bf
z!`K9PW^iA4*E;=BoHUQhC_MkB2}Z}QzrgAtlqpeio|t&qB;kU_0)w0ZrQuedjN~Ch
zbllt1d0nNRCe5ljpY_g@Q#(E`>{cE})f5%=kSY@pAAf?aFS@H12qyMW0AMPSX?07}
zH$>nnAl*-{c|PHolmmXMku>cTaaurs-n}c!3bcHvD55FgKSX^@%f5f_GTjKWzJfvz
z)jA><KPN5n6q5v|ED#rsEOQ>X#s19VUeT0L-@+T;J%8s<eG@n!1kj3zc^Qi)gW4~D
z4;2h838Rh|<FnVafGZ$6`S;)Z!!NDE7@vPN=n5GxZAy>v|G?j*T!SeTG-nYa4YZS6
zLtLM(fa*!H%wlNeJ(jC$<!`(JG84vTHc7lYQun=OPNW?WDzK8M8NV;Di@=|g-0m{y
zJS~^icE-1S0-&IF;x^4|m&6^{ubVH|CYo_S*ye@v61E;hKt#8~um|u)#tpNdClCPv
z79~VO2n@tZaA-0P2s^(QiscKFt^CXZ@L%%s*r6u5Bhnx^*W0{XYH0AZp}WjK>|~e=
z`DWWiVTU!#TE?kG&pbDOGwXc3UaLmE0BauI`}>4lrH-xr{3d9rtDlbqGdHWKuy({a
zc?fTiPd`L90(+Wk9OGA4%o!%2<aqIKltRl_iG35%MdH%H_U1&iW8i((W!uK5?2C&F
zeG<=%mIZlh7wC6pL^YE(X-xac%d@!UGmEs~COA1U`Cw>owQA3mnc35)Lu3E)W%rXW
zjgnW_d>H@%LM)U;yLMY(vB)%Riu(0CYq;ORVa|Qj97`uJ^7b`@u<YVO;aY%*P~g1=
zR$qWu!qK2Sgfu%CmPpN)>>scWa_`+kRoXHuq={mVJs9sle6X?j7dv0z1J?<4VEmMz
zs4}1?GauaB#A7D;s@QGM9MBL_Iz@WJzr3;Y-4AwMC<YgT?7C~%%u#}M=fI(u-n?Li
zV6;86^fwuc`&4gGnX-wV7Cf2`m4`1V_8{YU)gLRZ;Uh^&O3I?xe*eCE(s9BBGB~xX
z7a!I$r-Y&K0No9oHw%lmj~^!=JGL$79g9CuWNbZem17Hs6ucaLtuf$8av5FVjQaye
z+N$_N&zw^^blN%-2(AalZZsOOd(oTa={BAf@56Qm+MUbmXVS~_5)|p7@{)V<hlDM-
zA|VpNN^~m67ezl}_s|7FSG2k)u342hcT7&8Y7|U7qHad?^BbFgBLHL<L}^ix<U7qa
z8FjIR6Wz;j5+da4p6LwgSp0ghTpS)s+@6~#V5s#9p7q{q2Q%<0&;mrk>T1C!iu!>k
zn8v#H{wl;graD5>jV%PbA==(t`7!d;sbONF(fjt{MX`8Lo>d=gd^>=$!MlS_C|tPC
z`*ihLEUr#8xVG|R?>SEa;{?}Zz)83cY)APiLvz&8oOR<b)Yui7d+<#wa^a_;{iVj^
z%-Fo``?@w%GcZ2FuZVLttrkuN`=jA62*cluhHE8LTRv!ei%1s@vBxsNT@<aL*<Lw~
z;1GZVdKz9hXh0;3ju-bxIKoq4&R1!^q4~S2^JfMg?4IKa;~cJ1xyAC-Ap0c3_U(6m
zNW-BXq-ALNMKLkQ{tMM-NWbnXv4k+d9-PoPn~gR9XwDg>6Hk!`4sECAk2$FL$)lw;
z^mbv+Gjg@NE9nyW=(dnku)VrkZK>gaD@TK;FCecIz^Dzd7GHsY1PL<Etp1gv;SWJ6
z5s)yyBXO|e=)BW8%MHsVw-G7zng2a>Z8<S#taBDV>GHC&W~j64-d?6?07wM_*IcsX
zILvNl!20pLxJQp4hkS0^GF>@U>j2fVxF|kc1Zg}w9zPZ&S{)r*Ah_|&#wZVF%hqXc
z$3HG5F!<=xgXZ+S6T=Wa-9-oc7^?S*njmFk?-v-y9av&&Zaz>MH=A_$kq>8rT#sG%
zT}3>AO_PjrcuyPFt?MGw8{C++vvl<EJBUAzr*<{%c5^?wB1KHHeqV4LdxFJg@Nq7j
z{e=JrXxM#a3y2kpN;qGi)*!TC-B9S_3z(zR&N%u^(bhf#?9gqfF@~_mnWW6|%k><0
zqLfPpZY{2J`@9@t<AVG5K~Gos_>3zu8Z(A{qT1@}DClOmx%Ihmo&3e-UPHy`dZ!bm
z+!tUG$Y(rT_a#Gil`?wcQ>2M)1HYoZK&%ZKLaR~pls2EDiwom#l0XYHP<4d#+|WtA
z3V-wnzK<0Ngf!}GbQg=l^SSWW8g(2#@EC^Yy=+hk248pQXdHFuwknsZ6C{!IaQk-G
zlRvHc$u=zFJh2I9Rb{S(;#wj8@KT*$UI<&KGTOAgnzEBmkgY3KbVk>Vawx;UYP^2D
zqq;2gT$$wq>IQN0SUMb*=Lv{MjkU9Qixhh)CkrSc#X@auQR}PQx2<VL^yA0CzOJz_
ze0C^jJ=1e~7eFR{epyr?PV#;F?17P>X48Q)4+mOGtlNe8G{yM90o@3=4#HuIvoon5
z8y6#l#`e0~?(xJ*t1n%5CvfOq%;Bd4olz5Y-Bqe`CleCy%<ZqTvxD#sCQQV|b)NVt
z^G9_8y6mYIeT8i}qH}}CM*mf3K^i{w0*DV*V&T1elo4?5t+#b?gz}7jfY)Jl`3Lpm
z%=^op#dUA$#XN^{9EqIK32n#8<ZyyN?+*!Cfx51l8N)3a<MV_!prZ6~b2BU|6OV+7
zmvZWnJMf7_dRiY?3*m)97t2_w;@zVt11@D`42iafiD1gGa(TJfp}jB)pe8*o?Glfq
z1Qr@6h}Ivx5m}I`T=zK=U1f7>n}`I}S%w38iLu&3(tY~L!37I|m%%LU+q2I>??%SO
zG7a<+2?=xYnSmopDFTg#xfkFPvo~c%BBMvMa21a#ta^5)h0$_A*2kvduXKW&$heD)
z5PoCKle=8U>i6$u)CxJNoJZ%rGp9}^gH8ePW(_>JCO6~*-7w>Mo|&J5?U+G+R*g+f
zHqVnw`NQ}8%q4~!IFo6Uw5IhfaF{pmFdhN}cEho-N<Pk0g|A~3^NXiN8RPyD{@k{T
zQ%u*q^q{>E{kxC%1Wa*}v05sTyMt2#b300)Gn#OAn=ix1$lowHb$a<&><?J^g*uQc
z7T8vwzxG_q(@`?^jw;g6&d$5H%qn=>Qdkb|lR`?wc9puX!O>!2h83EJ!LXL&tGeB7
zWOzbEq4rM4rwc|jQ$I+O0U3NmjQrt#^cXmN=o)HMOeu@S7{M~<c?%1N2BNOZ(&fuD
zE?$I(_v057^O~B^pV`(ZBQL+zeJkXEa(Iy-9yrS^s-4)3biAbn)`eo@JGjwcz9&<L
z1awnbE^x$j`mv9DEyF^ukdSHk4}ylXvrND2Dv{lNgXr<ED2Xu=0c&XAS5`Ia(C1%2
zJD)!jQ0=&bVGzPw8w>B=727@jUO@rGp4(s8Y)4s+@Bqikct@;0?iCl4wwr(uXtChP
zMcj60lKPCjkpzY81>{YD9f~AyR<YUl664Y`GUSe4<Y*FAA-??d#k7RsDd~`Di?mDk
zJ27;I3<)W%#A^XJa4pd8y&cF<ymxOWSRf7#@yfbC-rNDa6PBm3KgPiUF?HhVQ1Ost
zYCR}cNVSArEHQq{mRp#}5VK@G)A#GRR>B)#KQ71?%v*-6-vg}Lq#AN*#;siTUbql|
zl#b~xRy%Oq7^G2Q1*;5)(a3o5l*}8N)Pn~B!uE_$;ToPkT}$ZVdm$ziW*hb!!@5iL
z)8g+#LZV$M$@MF643b1KeRu{t%Ybt_HjPMi9ttrC(is<(MaU=9(zd=|3|gF;iacgB
zWO`7#aWB8}W}$6S1yjKuaT>IBy7;TY=4KL#`4UypKax}$r7^s3c@d18#YIDQ?Q%r_
zT2Y|_t?JPd0s<kV;+@w#32KMi+81#i<AcHsA|(*qUzL>sEy_z$zRz}c?o#&;N08$w
z7Ha(m5a!G>7@|^w&NTPhs-<wWbSCj`3H9UzJGCzi1=cIkW^ViiIZC}^O3-5Ob77kp
zhD-GB9kyzS)l2vJWvumv!i#Pa=c(P}f3u_(Y{J`<9s+})JE<cv9~sTIw<k}~_Joy(
zoQ;9EMX5^^zvD3}<q@<~(UwHggG#FzOyBtUVWUQ6Egv%0Z}xw20iKT(U1)8LxHMqx
z+U;*vlD|+g093M16gbi2p7=J1FX%y`GjBv~|3p}6z~(@ZO$HFIH|G$dZin_j%|-)B
z!9-9@bGT#g6Xd!Z0K?Vw>d~X_tykF9w$-0{e(NrC>Jr{9w+ZQwv@{MwU80K#ExP|K
zUABxRe5wZH;TA{vB7ViiAwANZl2dUl{U3}BP@4)ZzFMe1bH6bHi|REZZQQNeHl0`T
z6&AkzA^WR=;?JKS`JyMHe>mgF2x)SuH$xTmqXvig-2=#kjTId|b>l|!Iyr)*Sj$Ix
z)HF@Y<A?6BuE1VhSPQ<Q(bf0fhTa{H;;i`kru;buAQF)!XPNqk_HOGcu&#P0T(?V<
zUBaOjg5Bb-n*<HCvJ#2N;!AG^)@AVI2@1q~XiE$T;5;Jp0viC=mfS{mU<yICQ6Y+8
zJ-7)v!8m7)!%m%qG$zTkz5<uwiC$esg;KRFG(-wvEH`AlOn8-1Q9=1t5CVHEnFOth
zVIs{b)6I*eZo}m!DhanKfgYdp4rS8&FJBI`IvOh@`t@(ObPhWO5)Rlk8f`!K`kE1E
z&JUk<hfl#v$FGzT6O1+8dG9%?Ox;%b`LUq~-vRfW;DSDj*NJ@hMnr(Zuc&Cp(>348
zc|>7F6K><fQ=qlX98R#6n4vfO0Li+yUt925v4%i4gHR8;jLO&~0ug`6Y#lZ3y?c=S
zM!<0r$QacRW;zAsG8D#8PhdsO4?VPkP8O0oxJtn)SeT6b$Xpa)tYKdMORS(3sTqKZ
z^k5zj_I<0dbYHV(KEy0w8r~L(+Um6nYuWSi-qV*m>k_Y6??&bn<TxmGY?1_8Ad{G!
zoD>%My^Vy`_x^pbP74u3CF(cL;N8Fg8CVsRY}BW)*QsQAN<erV`8!v>GH$^v28L+L
zBR(eQl$r#MAuLr2cwjM`Bxi&IP|<92yT2H|<F-3y21-&>z`~FEY-AxY{Wsb?_jH#r
z%HJw0Il!!c>KXskDjkVT_Usn$%b@8lJRwC3cLySMUR6DuUg#T4ps7R&bKTeIRlKIz
zql%>+>s{w<a5L)rWcb2(-bi=dyMO<dwI*$!E?c%L2j{vsF-Hl#8a+ORm@`sc-ERE&
zyLem`&O!Hd?&L|%RF`x5m0N;-|8r{kqR7X*66@E&iHU)T=pN2t_CRv$GssMI!yPUx
z7acM_pKM!)M9-5zf;)B;!GYmF<ZUmwdjI~rnbe@D0*cOK<bpAGpx*(Oh+4YD!=vj5
zOI%yfSeSOKr;qyAHAC!Vzy4BpDY!vVNirdMp4OU}-+Tt^<9LzA&JP4J$24o>!i5^1
zbr3s9^+Z@gGC6>K-@_f<2oVTbn8p>iT|_Hsr2KmD)246VI<GIUFjnt){t5*21||p8
z$Ur=xPKOS?Vo(A?C;iV~!xF?Zx0xm6yyMzZiE!5|=tY(;bx@He-a*p<V8u9zU&6Ad
zZUZNBbogG0^2_19(bQ;YECe=yUIanK%`FQrRW|ks<p_**G*s480dRIx!_jAVb=ytv
z9Br>IEzX0S%reoXOJRZ1WrNtCKgfus+Xw44MwY|GayzKCU1!b0YF|*7eW~Q{eP~z&
zLtHbKB4uSh0;XDqktk+Z#Rj#?!r~TX1U-kKRwLZuiB<3zW3}1zKbPL|BoX4-D2Mau
zD1YcO5wsFb5x26-og$4X0YYyR8-S;^jDDH>pbUA^sYE@2xK?1dez(O_bkCkX)m*UF
z3s<kWmUs6uB4mT7G28EY`S9rFg5e<z#;4Ee^B-)$PbvU<1;7+~D#lxUSUOwejQ#uf
z=iAbpXO{@O0;n|!w)<mZV1whvNVwvk0<(=bnvr&S;n?j5rU5$Y^ka5$CE$G#nh)C<
zR!0u7B8zK8caWGUNB|h;@Y>K1wo(?&^p#y=U~^<R%|~qP98`Z15rw=G2z2zc!B#E^
zgTYg>U$a?>4b|yLm{``@dFn%8?g5HLnp$v;&`ndBoi4eHTML6y(imq@5NJ~K62Fg@
zXN%sY%I7*-ZYU$&GaI5SSyIOx2MEDyLU(N^Es6LOsuqFGFD1pT9KS<!>M|I^8_>$^
zo7mp)zNd*9Zi5tPSh3sNU*Xfk8yGeBO2xNtmaKm^9DttiD@_=aB!LUHXc4NaAU{tU
zcj^gvtpYLPupn|zDn1`b$1wYncRYrYkQ#Zr#Bxj=$gs5^KSF1k$3TRc6eoj$jNewz
zbQkub(rWWEX%od)K4fLV9ST(?%nPoiC_0Xy@?^fpWluZYby{AKcUa>`RXlh&cDO)t
z?D(~|j``Gac*!B0D^!x9Cn5YJ0by3hXC!Egcdmzi%`54*lV!><?1T{{JqXlyVy4Gy
z=6Z;X)T)G$N9&c9{{DPio4bSNEIkpJT3SO1MUmq*@jytY+}U8MCfM-U6<oe}G2O=s
zWR(#SicQj?RSBda?2MMH1Tm+Bydbhd8w4C*0<I}9hbaxQFQoJk9KF1}V^^*yM#sj_
zH~K?fSC*Bf938Hr;_l@o58FE?hC<gD-O2m+PhY$UzY<gNk-$NlGmY_ZifpD1g%;18
z%k<)H$d`!XcY>q_#7JIJSbY9xGumnvm2=V&W+Plq9Sv<-Fkr>=nG_Gj2GI@CAF3pu
zAK;5I2!}VgOi+@Rm9<dHmyg4E<R;?C<m5Xz(Xh~KdI$_-VSgLM09uYNC(I)35b)l+
ze;<?e+uR;p$8Nh~yGf-&RmZJ>O($e#);k?PE*ATkJBDsn`e;ehLFrlhs0e{ZxU)%0
zrRQqU^$#1y-T+Ln_^5&n5(q<Zur-~ONbeJ!wTWA75mB0(3!qhP?QnH<QL{|mH17{4
z#tp#V(%v}Gia%s=UJH#YP2#p%v(>eG(J<!PqcmnQFz<-Vc^i&a{HvrcR`wF=9vl%g
z#}k<ozqy#PPp)28=uKEyi8u%B-_kOW79Ab|w?)KG^4V6bG-z>;UY$05I&0~Ir$)S9
zNl}%QMBMJBY5ZwxRQpDv7C~1elFcgrOr1*Z)-yJ?T=mHrI|#}E`dTCJ7k+<)QK|!W
zi;25ZUl$b(A3L@kYAe5)Cq}-?R+Z|*U{V;b<A-s6+K?#-u04nZXN;SP1B6j#&v2pG
zdI^yg85S5#X(<hsw75K-I!c-QMi-(kqw7G87BmaC|BP9)*f~21!eZ2bWapvSG5)dZ
zJ<eFi`JOHOm|BbpYA7g3V{AnBFf*{8Y{k#h*&G`vX@PVYi2u$UY*omXI0p*b&Uuby
zlL<td<4WX)sUCKs#ihhw9M;taI~hl#(W7x*x#eGVchB3NEiDhGNZS`nRf+6N!B&$I
z9#0aBE(Tf1OyOS)*ggK(G$H7t)*~Odtp8XXFQ=r0yU6|8?TL_zAOb-3W<zn(JLjSD
z;Q=JFV2kdDoqT<K&~dzb|9&2A4vCXBib$y0xfP#WM*Y@J{}K~ct}A3#oOnFJw+Q3Z
z0>EUQoiEJ4ogW%=*4Mz+Nknq_>lu1yJ+seyW^YaFI&PedUH7Rn4xS?8tfc$OckgyI
zq-)f;7|C$SaJ%k>4p!<PrEHJ97(4jf&#{~Dj~1`{T6FeZ<KUO2t7aX(c4ouzEi+Cy
zq2Uo^Z!RD4ar(i@$55cKpg`J`;E8L~12FQH*OJrI>zT`ug!{_M+L#|nn|Hn6<c&JB
zGsU|<6W06IZkHR<8;a6%xV#DqT4RnxxdnmfGIk(=TCJE68oNDfOQ5KgY-hU}vt`gP
z>SjBGGvrEGeH7NYn-u8#i;5^Yn3A&lW_jYhd`=LD1ONqJI6u_3R2g?3p!LM}&z}bb
zdaQZlUyG%4-MlJD$>ajT$pzGjn+0#2x{z7?a2*}0vd^#TyU&B>yas(W1t>iR#unuN
z!xqXgT&OgL4IfU3R}2GLYU=eIR%FrLyPDkHyulq_&)P@Pb)i}Mh!JMRs$HrpZ1q|}
z(wNu@Wy|wGgf`%)oJp*Jzr_NK>v3Ml1Sl`aL#rt*0s^q)K8Tuh!v-@w!};uJthgO&
zF`@33)kLB#F&BFR`ZPGV2FAw7Xc?PpEsAwkU}%+#fFCFVY-7rlZ?v0~kqPYqjfdFV
zDoCDyqelKxO%`9W_vZ2Ann(m*y&9N4P7x~CPof{)W=Hb2ANAY<N<HdwwAXxc)`kMC
z2yD<&<-f~{nMgg^j~D<bqV*;7)n0n4Iq{m$*Uy=Ah>C$~Q%6S!p}>oW53N>Rbk&&&
z$O$Y=T-(3@8TADAhQZ^n|30+)#wK12^-U7$3J;HZIL*WN?bvdb!32($5wmslgYrE2
zuHfQ8uIPcGg4a=6=E|<9wv|y*+BIPK=`vVmd=df-vnxDR?F0y(<5E3)#eLViJS&L4
z==$Iazhl60f<1vNKkTBe957XFOUpyuUbUwNn+AAsrwEB?Ch%soJG@AKur}Zfkzk=P
z9^@`l((&YJ9_i+jWeA<rE0-AQfmwi%!hC>%#=AhqZUM~6E>{wW=^XjUD(ZSpHt&?*
zfFg>QjTCMdh2Dne;y-ZH$IddUD@Cxd(3c;(cCB%P$!dT9M@Tnj&2mFe0sl#Sdv7Nd
z3MWb<h=Pf2+5v8t)6*Y4e{P94*5%7<p%DT^vqzMdjnNsCm>r$y;Hv8CCT&^(n=h_;
znvJ#u%n**CY58?XQn#*@LFp8p(uQx~(732LC0b0ru@-P0Vr5louIrBA5*|4Z7HZ(t
zw?z=AK|pVHXfN*3TZ0aa>8)UfS^4Tke!doaz-hp_d!30K5?G1!l(cr>0AaOvkQ$(#
zp~zmhxphu>)jHg%2dKQdzV;mD4^IY~Xk6SZ;<nacyPcjK8yZ>xw<6X9%h5S*E;%!A
z#*A$tJARE2<{oIE0eD7?8bzT3Oan3QB(LG?SCZ>>I<R`9^*9D@X+LO_gn);oEy<d@
zw<J*$wU*kJ2XN0AY}uKeTqwN0lPAO1?F5LW=OJhS@sTXBLAAay5u~?|xHuz^h5GSB
z53DKQV2Ng(%9EehTdmXC`wO$^^1#maIJYe<o%@h*t12yo?v3~bOBRYd9Oni~4O;Ak
za{C11zz?P|+T3ozDd#9{^4F>=>Ih063|?9hM<4B1`T6rE9z5sE(=iFJePRvaiUqPq
zIbBSX87GV#GsYzAm4pF2l~xgBmn~xiA<o6)aaVdBR&gkXyh;5=eOQKc7W@FWI#*XF
z<M1bChWNv9;GPZH@>&=>0A0`x{M=dWrB6RkjYlLxc8x+(aMHxMQ>L5MlE9y25-i~g
zX$6^D0lF~T0s+{pml<AO$!)*`cRv64bCvb$SQgWd&famnp0?ubi4&J$q4est8zT<h
zZIX;(@(q(nJb;-yK+1qa{sm_fVhwfs<cSmYb#>YB0T5lE*t-{7oGIDJ?!SC)`>-93
zi_HC{-eNk86C8x88OZev4dKk+A<wLv49L$>do)voQr!AEuaYy4j%Ml*yEB>OSlTZx
z5Q~4D1`a$#T>z;Xpn*0cYh8Va%TR0i9d)Al{(F&a^{LmtcI67V<&{xeI;{RZtQ{R}
zAsgeu@@*P*P6Ikfo1dPX(wZ9AY12Y(#XSu7V=%aQ`Bh9aDdnDj6PJt=bUEJMAkIwA
zfATb2e*a#%AKRUgEEytaJ$rV^x2PS{6i`gSQ`j;?GFMEVygMr^i>rf4EWQ4tu|$g8
zlErpOC#Nq14spx=4jv{fM1W+DHi$^sem&*WgeIygfK(x5@i_3vL7@&|AG5Lmk^)<Q
zs-?Hf=IiQ=8H4Fe-jbD)cW#DHJl2%gRj*^6UoUr=nYRn~jPIge|L~bfWEBsM;(;W`
z-UO>TgA9$06%-WYd^Il+d~wof9CxH*$2h&rruI>*VUlqa-oEWHy_wlLwlT2NAikK$
zYwf)#-GxN4`Q91kc@gKfFbjS00tKc;S!lImqRE6o0vCZs;7Jbod*rB5z8He1-d7Cc
z#{<H7EnW;kPc9_hKI;A=Ol_#6Fn>FHt>VVVNr!(mHDS>~5`Y1XH@5W9Thm)l-YDq&
zH}IgNW(Gf#;u*I%thT;;)Nlz&p>P^xwIyT<J7fne{EH$nQGgVAWsB?YISs$gx+^}z
zdp+e5&zO>l$4qHT9c$IyLqC4AhdqTFQxUjXof1Au`AZFF!}0vXa0C#d&_xdZuC`O=
z{T=@s{A&pE=+gN{N1Gg8KUf`7izZN)tvB3e8mtzts?V?1!u>c!nZD8_$Y5CIO<EGQ
z9i7H+uajk=fpvTn+^jy{Ses~gq_kwpk(9Fo5ALhH(KY8hUZp5X3e!x#wJDUK(m;(!
zk`YuPCob*^o78ILS5i;_A+TlA0#RBT*46x&B=z$=sUYHDyF$@#;|o^1&$9??W$l@Z
z7ePW-KTdU^oB5ESP+6pqbDqe;_<=%sq<`M(k6BGJ?Xo;#!PffAfUytbWLvL#v+~<{
zXt%35(ndoZumHrVwUv=Ev$(xmAfQ>ETJ>Z<_it*-d;QSXdUst#8g|MO5D03!kFWi=
z-(Mv6i~D-CsSW?7j&sAON(<?|nQzVE6>H5~obJNsD$repCTJE){f0*x(*{;=z3onX
zWeq?|`nXk#!6K1-s*KjR4@n4QOvXW=pWxRNq~3Bl0G8dYUDD6O{K?0y>iuM7=xEb;
zb2t_j71{h7eP%~zj2`|P)H+l%<Y%^1Xb;njEh{bk+jdP=Fh=KDXT%@9dNt{foz26`
z%w$)%-EcUYDt?B|FTCF0$-c}5do{|1_Ip5zhq?oqgPGIRQ_~^3&zSME@EV2ySUe?I
zY&LuOV$Tl+xt~R?ukUrf{U+~Wl(5N|QZ~?dhD7(SB32dVs%(M&0ZWT6mKkR6ClPH<
zJ0$bEhzyoE?~+E27|gnu%jH`(5)?n4{PgXB(g}6VnZaA~-)~E9_Ys*Jb3n16<CVmg
zDSgz+dk|<r3Ir@Tu}|ctDSk(F+9iV2zdjH>+oh`t8b<?>>B9xRD*+dHK*_7+ec+<O
zUQ(j?>`G=QaV~+D`&TSm67c)<KiwVLX3To<+)F9UgJ7_;-w2zGT$Kn@?Gv0KKyn&t
zK3r#Yh)l_$cS_<x>S0D*M1#6WHxCy-`u;lhO&lo7lc6?+vpo7Mb`|aDD?(;P28rzu
z$@=|{ZNJY|cV7JCVhbdW<nC8_T=Q~0na|B;;_iwR1L+9LrhJ{$w)#bLxyvKG*zr6+
zcMjtxA9>ktS?S#Z+Sl-FJJ!@n>U8HpUe^pV@?k}j0~;@kPkt*O-Dl|QJ@!Yz!v9EL
zo1kD3(JJQt{uNsB>B|@H%~zstq1Oc#mBPU6^L2bj=#$^&+L|x>c;DG7LGjD@3yh|@
zt6Tq(tCsw@N{dD7K^PBJ{!rO%a1XUEG3!+H{RWBiY`^=;0Wo*mrrdIQa&TKvcAy;&
zG@#a^VqzFcZSEzrt7EhjxEkwk>0pt(K{6;kK6y^MCs{EMEZn{PN#MWzZtdH3z!9Em
zArn~|k42>E&8>|*o&>YifC1G#-26GH{D-kDlb73Wt#g(>a0@-G5|I@)yURcxe-{zf
z)prT*oYEz~9u|scVDR9rJ;OXm`P7;MIM%XmYgib1E1l7!`)+8mv>({q=6S&-jW|w9
zgjZkktbyW}$oXK($KTgu3%!88+0UHa-0*AGRomHWQMtA|6l8n+`88cRQ~&cj&&74I
zuRM2oMYjI``^W$JcNC|Is6=d+AEn;=fBwdQ{!teZw^3cAa@~C21T7Rk{D1%P-~XYT
z%5~{8Y`(qH|N2K=L~qUK$7a2~*7e?he~$n8>+bd(e&uO5qD=ntSpMf9brIimQ@DjU
zS9jar_5c0jE`R<<c9d)vhcT(^RQ>;tuhP7MAKS5^PE4np$p8Ah!KxY@3;TMT%K!C`
zI3+*%v28z}^>Pst{okM0b|NV_s&ZRy@PEC=KcD5#|EQ?r$2QmfJMg^J|M3*U_VVOa
z^Lj>f`=7t@Uk@_-`6Pbq^Et-u{r``rAT^99|M!KK8+9GNZvg&mv?kz`zSq^=+nr_c
zUtsJa7)-I?XlLGlqO>q0(jc5=_!I!2K!YX*IsP;eZS=R{yLTU(b}AtdE-nM^cm|X>
z^hH)B1l9&Z1)>%McR}yc(fFZbPvF>Df6lrC_#d@>$Ki?jy3naq`MH0%MDJHRGoa%d
z($O)!6$`C5-IG1`?^FHWO?Z&qW}3;j^psw*Vg+z8l@dzM^PL$vv{k02@n;6Mci*L0
zq>kzYc^PDh6Trq=T5;%c_FlDqS+3qyDu;i@{2rTAg!Y%1r;)4iOqks7L&_s^JD!sX
z`U`hZnxi%0B4m_N8qtfG^3`ai;g+meuz=;oC5tljq_lN(fclZRnuElGjyod&3NP|m
zvgG@(U(ea-Hhp@6-h%Pa!^1qvm9&-e1^<PrDtO8n9ywt!@u|@HwyGn<_e~TAO%Qz{
zwKCB7^||Z^N!B_b*Z&5A7seotU!c#(K0($cpDX68?8!;|dzdOF4B?PWIO9L`Tb$~{
zKQ=@PN=i3af$Zv9HZ^5D*6}{DQFyuAEtL6h?mRP1CFt9z*{~?3QOI(9Ynvz;TS%R_
z4LfRDWTdZn<FNoR%wkT#yMaT362zH*lJE+=aOCl}vdVTolcKtig_GxaODZb5I7QRA
z7@l)sTOHLW&99_{1dSQwxM@S>jSju}6Uo;#fA^pVl8rFriBjPOtLue%(2uYrgjb{y
zZBLU%KUkiuPAv)iM%7)Oxl|6x&v}m=LSxvf8-4QYTU$2-26n<#1>+E~uX)#vsJ){0
z;~R!iI@ltP#wgjeu;upg;p~kq81h}~@0D(j7H)C$^1($NQzYnMUSD79OGN}NyS1?f
zjG3Hg+G$STjsXHK&)vvD%NH&LrEZ?`V_?xoh>EZjoVP3IoTq%@^z${rpt(yD9Rr;X
z{fU~#jvwb9?A*3?>cs!z0z^b??h$j~kMT$|OB(5~>9#(tUV>P1<jAJ)-xW;*)bajP
z$GL0Nh!Kn_4qzF@cdm$0%&#Zof+tc}!@~BRCA&ZoYvChoh57mw`RMmRYuSvl&ooF>
zaqvU{ueL<0-_=c{FJ>h*lL-EtQ2EZczwY0RbxxWqbk04@@s^tigLb}#m;QPnTi}Da
z%WM6VMrmu)mt$SO82;3)*-}X5>A-k02~8O;X<+gp>K)6Lf6>;X!ny~{gdoT~D%XB9
zAQ<oY?6B7y2gBQw>^*a{I7z?C1EISNo-3PjNKfiIghfn2E^9|jwFcj%TiGfh*D=VU
zcu|JG5@cV1z-A?fUAs~rEy1;0PRmKuVOLOg)_?MWG$E^7ba0(jMTR&A*TTAMTHZw&
zt~$@?SZR!JEpmYW48mi>IC-Q4I}Daa<t9Guy`|z1m<s+Yfvq(szS+w5nI21V`p<Dk
z)!4$hF;{Nh6lRBs!y^2Z)&>N$_Ey)6EyTfw)LWaS8Byll1T_ZI|Bsd!1k5zXljHTf
ztJhooJK*ep!Y&1Y;%pJ=<_V$ziehoO-bU9sxzKg&<6gDL>a!LbUe1p2aDjFH5ASag
zuwP7b;`w%&BhU(=X@2HRWcfNIur<-affbwSOG}SG*vrrP&Ag?2ySmfFi3g2*US<u8
zfEmTCxHCq5OXH_Ubb{8ho#JkG&f|r%oo%T~7)X2=x;VJYMrns)&vd#le9W|leASIF
z<~;*!Z{4~T4RCOX>^qbB*k>?gdG%_ihs(Hec{KVUJti0HRGxB+7?R4#$^!4qgKX4!
z3f#xs{5qi|+CCNT&&sz!9xp(oOf>W&t3agw%7;U@`Yud&`2?VH62NFmWOpcW0^x4f
ztduU7{>~!<2c#*Eka2W!iey>{1)Vk!`pu|O9~=A^W|UE(b9P|iVWiF7Zm+L2aY}M#
zjP>aA*w{k!BSH<hXp!a)t>STg^XsWqn2-UuV;zZ^MOhhhsi&3;t2fPIQz%d_<P`2|
z@R~qutf+%%Mow%QLsG-_8gL<^?;F5YI(a@kgFY}JFgoTfffFO{H3T-K<D8C&m}Ad~
z4&;*;YFRsKWCVGSCrJWC&nRTH`weO{`CIfNgqZ~2uPQMvGy=YpJdqO-zxi~+v$&*@
z+zR^woEi|{)3b8%3TwMD_uO@14e*$mXCh#TSok=%SK>;W6Qy)`%whNiL^r1TBpiz<
z^}9l!`2%Jhcb0-33@<^~QtNuhFFyy*%6*(yol&DEyt{3h2nP{>S=mkq6t7<=fGu%-
zQCfiX1+Gv((bexil~}nX_o;m1<lw_@!-B2V{r~I?6c#L<C?Vy+KEh{-()SGoGcXy)
zFO{c#;)H^-@>}RMdt=9^02fdg`@Ft_YU}cqE6sdg@E{bw4<A2fmq$%`cl9IV4(jUY
z6lZ6<18&j*l%MwqCF(Q6BPAw1q#Gv$6Jyza4aiR2dlQrcG}YYH^ij>Kkq)m}%iPh%
za>4g_BxAvoo1INju+?Bf<_Kg%kqG`LE{5aCnZ(R&_l_Ml&pZ`pvY6!k`(vOfX=$uy
zM8Ial(}Y-pTP@INuVhI$)JHJ1hh7cw4TuJsp1@Y+P1CHaPRw1D!L>o~iX{31pGPpl
zcD-OndH&=HIK9jaQ51MOI<Q8bQaI0=wI@8B28BU^ktajCCEnf%`}f~1GeyA_v3ob@
zBtGTY2*x249c6BC?AXHP%Q3gel}I8+o0z;PC|JV7;g=&*pL==5VN@9WZi%H6K1(kE
zF~`c=$A>>$595v|k3$Eso)&|!!r%`a5abqS2omL4wzdn%ywJ6mEMHz#TtDT3p47dP
z5{iC->Tx-6450(3JUc`1cWfJ?h~-#*!x3RZ%mLv|z@!3k|ML3k4=lqFRI~IN{P|a7
zW3}w`xiN}g;;L$EPjfT)8c9j-YHG@W1s7!y-JnPUBU8qu!?Xl{+_!&!K)_clhkExm
z($z%-kxv^YY~K6*EsF(hpgmHLUvdk<3U7g1O}{3P)vsS?X&>8-fpS1EQtGgTW(tl4
zj!nvRQ8{iI*1ez(7-B=Jdv~Wh<P|VypbMvVOZk{)SPPtSO3L}L5t5TDIkj|KIq}0z
zzs5lqmIs0hj4qg3vt@?;CBnETQR(`-Wqlkq4Y1<ns6dZKzxonR2_tlld^K{gmPw{~
z)NpAz-T<U)7@u%lC<I9IxawWX60+^BTODw5I9D4jlre?klU>ZnK%!xL44Dm@9W*{V
zrw74s=D<kh{8^|IkCzVwKUg0;fv;Q~3fW{E|B02<SWMM<j+{Gh{N)B3d6U!bkcCVR
zm8!%j=3r~8&)4CR0eUmBT!e`S=Rj!7H|fkh`EJPHf`8L>q0_m(y2t*&zM^8$xk3rc
z23jmm7W=YGEk7q`0h|ZSWZ9P!zGn|a+EZuGem$VK;KPGNloOFnYnS@?2uc(xQvMX=
z7L$Wd)z#Q+UZZ%0U_<DH9|C|CEX`$rQNn}e{A>#gYwDhdKK?E5JzQo8Z<}&HssX?F
zdbYo>`Fw!+Q=dK$=r{RH!nr2W;)^~kBHG#Y;<BeuD`4r}W#Q1sk>t6lC09K)V+GWh
zXYTI)o#GT!oWUaNTJjiiQxYTplz@B(tp)UyD*%sWD0+NAB5!X%crW};F%gF|pL)18
zZs){faO7>MjTucNZiBD^uugCqJbIZhP){=AMMBI?!z>Z-g`x_ixf19@IM-28FRu76
zfXGLQktoI{hR&bQ-MBxRP6?l|FkHCsVr3O}6<QR;p1I<L7rZRIQ0&?}I<lnxIa4pJ
zuwaeAHK4lWZwW5TKzyqP9(;f>efqR%W}BM*;Q2zj-LvNbQ{lV2`e*ROA)*^Tb(=eP
z)6d!&WHYFqs;Wt_l3tXRv8c!ePgpxOQYy0vWW3YC5`id*DH<ArO)f1B<^GL`2#GlH
zZx43VNk$6J^yHN{SaI_3;~nSYl?`_udGBK_+8qEj&`{`pW&zdq{C~6v&dyPkH{2`1
z5(ed{jEp~Q0H*#A;te3DZFe5F<kkF<`85pd!R^5PDUBof3QwMZ<jPJyLKz5p36C+(
z5nFF<qKMpp<4^;A#%!eegt)|nZqDr4$%9G=Q$VVw<wHvJ)iz&*`a#10YXm|E@o5!4
zFBdOrXli1ahmsZc=wgmPxDyZ}K4p6KKYkqIm2-ay@eEg11Hm$!7CuZ|+*<kqVH6tb
z>NZ!FK>~?%_khvM=yARD<Jm&#;<64GK2Um5Iio`WvI_w6ap^<7!HHw;_xaUjb~e~k
z6Jf{6E)BWv&rNsc!K&mpd`WePh1||ahYE{UiSk3!@qiy^)O!5U@Khi~G7*Cq`j)jU
z!loF57{oxe>83dY4Dh@>L4qnsxEMCTafJ8*q5dkzgQG_x{ughTH48A<;fpe*et|ZW
zTAGU~s7q_NG3nCKNb1LfIezBMB*zH37{TI@2?N8Dy^vH9Ek@hZu#oNuaTFdyKJ`+M
zaMkHI;Hqs5t4MM0m_@xYe*7X19Ft7SEv+4WwEoj~6H*-7hCI>V>n|=L9kULcj95V2
z5GR96N!`F59J)EKQ38!;)q6dujd+sLd+>!w!_gD;cIFj5ctD0ykdyn(g#pH*BIl8S
zC(wx#@rW+@^wz>G^~>fTA11?_qHVpo`S<>n%l2k$RSZJ|<<1YKexueJy0+g=>duR7
z;lMeCR%OVed!FgSBhJY=mYPZ_fpC&ELbVokM_oM~>#KtYg_R1?5B%^-NA$)f5x`JZ
zP)ud^5lB-Cdw_7OnrVlcn+oRS)Rg9y7IMiv?m7f>IXR3pQB7*As8E1-EnN7M^(u05
zv5eb*j02~AtTI7}c$qm65;>f!p1fbEs|c%r=54EBPRJ1^&O!VUR+_lz^oy)wHcuZ&
zcgAty^iZ6@FX<y8QI@`-2YcHHG}KCTPz<Vw7mOz1K^Nuc8<Wk!EB3;YjJ<iYo#PoE
z{+b?*oJ4ESlx(ZuKZC;O0QUu=se!(}bQA3%RXNoI{R6)UVPZ(3*QJXW+41dmHDF=w
zlT(}wt}MmMRY>ztxNv7dW+|_vwCS$|8%m+-(;Z%dKAftkVU~v8X%%22<Q~s%`j%bL
zz;iL<K3)shIU{EN$gi@0`Wf{D)POm2%u(&<`%@9){6b`bsz^mm607t->*|?$!B2?_
zioOlbZaGPo3Mc$G|3wsGnHx9Ow)k#o%__9~RHVq!7!sviV}htRdh{SYPdb{dyLV#;
zH7HvAxkQ);lU;bhEdG8)oMxDC+FUA!aAgqKu?hAj0aN<bt|Y-Oo)T)z*s*W|u(74z
zh0rfpfKu?2$CCS}9Lh>l|4>!MnTY2{Vz9<cm+2KH>h4rwPYB7#`8dP~s`LG^v7C2_
zmopisppK+02HwC*58%nBYk;0dMj10nmN{bDegyx!hMH_$VR0+GnD-w)vR5WAahWAN
zIjvNxPtyf=cd-DsaRb;ag)7kc+07A;#O^RHjMbcM2GxoMOC9wf2aKk9#eyjyiog{s
zM(X1uK*cd>+Oz<ALy)oDU+O#aY@*v3ZV7U1jR*(z$26LcGJg<tSS*J(L+g(RmP1tN
zxN>`cPu!bp68USrD>0ab*+_O$;@1q=-H)`3l_2SiRL#+qP4R9&b*HZi{U(@yhXBNP
z)XGn6JSVH7o*o`vfP7*9rZHsv<4%W%tEuV3wxXv?KEpyMLfIOefe@1WNe+aoh?V-n
zB6(g4hlNFaDyqD2LD$CdfLKTsh0;){iG224?PnIS|0;VHq4UrzQ7u;`<k4$Va>Dq8
z9q?skkos#k_9KM#8C;T+WAJdcCqD(#c9h#TJK0xBv4WnGXqc3?RIpPH#ZwEWyT0<5
zL(`}#joor{a!QT$!0@)U-G#IOnU3p^!#!>h58QQ8sept58(NfQO=w@o8K!!mh^bV@
zLYR7k2l}{X)ssOmF>-hHH-OL~F_0o}_UxBHc|7*arKJ=q&e;Zxu}D=k!;J9mpcJ^-
z&J`6d8(LtbB?r|RD>CxHnXQed5)p}Z<QHYSz?4zflgwtKHO9YEpyZUiFU1yx3YPN{
z9TjDQLiFIManpRL=zy|-D{y+Drv+2wI5TVD?UkW#q#0$*t@j--U`GC^<xS@FUVO8&
zX8pKvf-VzYE4&))Eh6@od9Q)6OT9u)d!(}&hAU+mR$&bHIAv3dNUN{7R@8r#huoj=
z&lbY~OV*SZ%}~F2Mcp550I`DSXrfWix#8U+T4G(J{f$v3kvIXsG&yXi27`*tH-1j9
zWW|o+!|sU&M^#mia*m=T`8f3pLCDbig)XRENgWP3uxPPyTKC2|N4N*_@=DA8Oe8%#
zP%iJ1d<DeVub&a8%5WBHpNIkQcON5qWxi|@H~nEvBe4`fmm^2MRy|cbuG?nsrAw`6
zTw+t4r&}Xk5zQ_>I&OjO7oniV_DSAp5(yoFUAnsz^*lQ}+7pz2bLZj4&;2d?&#5Pr
zEK>kiK@O><G~WJWm`cfs7SV9olc97sUV`ce&kC$K;)E{2_h}>KP0L||*qn<(#{l9L
z<e?Z_h|C2Y4hufn0{Lx6Uu`hrsn58POX_OKFq{|v-WM88C&TF=f&<Pl(K_&BN~lVR
z<=-hr_AhJD{$Eq~IPd7()kQUek3q~qeFs@c*wY4<&R07-`{IrR8h3StAugCFZ2sI$
zJw4Vk#N{CIs<=Hcp?9Wwb0s*J{K=w{gu?ehlgAXS4)J)waBBRfF{CT;)xj$Wz^)g(
zB#6q~OMG%=6$6JyZ0|L&-{8ShytY;~v!(GiHZDVlHdoy4roOqZu8tCFBx~GZpv702
zto_PSRHCrLB!e#Dg|`vw4H~K=KIP{;d$vDnq+M(K6kP#bpPRWPnnDQ?1fAW(e;D?2
zG>{(utcMsXfPGXzk;-F>Jnk%H{tpA4)VGTa#h3OrI%JcC5C=SU2^9-{ie35P@hN<*
zU4zV<P9$!D112TA8)%2dO=u+IMs7yA9xx+MH;p(xe7NL&eclQidTkk0V>m{kVHdJw
z^J-4jx2#SlwP-pewB3)5+as&iQJIvB*i(+c+F3c=(dZC8`&DS~sO`AQXs%REb3M}m
zk6On(Fnu~TaAxRS9HjYBSskr)fZHe*BU*gS4x@b8OkquQdE!oM|7iGY^2nVD!d^9!
z(K`~`wbjdEx=y_ttX>aLAeaR|cu?*pi`2<~qNh?mLWjl02UG#XSF9*;6{-Rv$cK0D
zU<xMU?P3<5GAhi2C`8a=rhuE6)^SOp4opKC15rR@%n!H;+}E>nuiiP;$Q@*MzjfQT
z?XzWfhKEa!>~gZ`<n+^r4-Z1(OcMvk`sDQCJM+xwa0v!vbuBqqyY$-Vy)u6doVus|
z%q_e{OG{TWS7oHW<bYUyJ&igUFt)H7lAx^IrS`;eDfm20mD6+t3Qt8xs8_u8Z6&GQ
zAy(7h%n5LZkO;WzGIeS?ge`-~WF}U#)7tUC(YhpUBC>{J*%u=iW45HKlN1E26ND1c
z78IYw#YhXx;~l@g+V%oA^UbT=t<Ax=5U&|5dvcPF2CrB-ci7j0A{D~clRG`MY`uE@
zSNXeHD1SFU8M3$1a)_0EC8SP_+GR4R<Fx;-!ra=&hnk*dh~%HYt3S=rZH?~zrNTH{
zd-ux6J6hn7($LqNf9Hn_i(6X1TrP)BZhAenTVG(0jXXtqfULF#fx_(3=USrE2`ot|
zucHdRJT=}WPV@wP;s>csP|C+LLkEH<79a241*=0m6D%5uIRw-%#r};xpD9jP{~;Rx
z;NU!o?~RNK6j4E8t-pT@OJDa9u)`?#&~pQ+jiFBA5MiAF#re~xY=7+0Nf+&nrBiqr
zkg_x#{eUf3tzrX6Bh59FE8)v6%AgRNH+L@Qf>6VWi%7<Wm$tz%!DOnC_U?$RPNS0G
z45^JA8F^O|a0!(QPZ{qC+5k1`!c7&~T?xgvOgun=G-d6y$i6g>IG53*++_EZ<TtYW
zB_#PAR<K&9EYHkMnN#``02%kw>w-H$)&_aNjtHlRvu5v$mVe(ve+L-C<0M`HGh2U$
z2tpd<2S^x@lc}gUXmjQaJnY28VJ#RQds4ohD)`pgb0W^^k#~-a0%k;nchZ~|pAv$y
zn6vj9W-nF?PYbLTVlY1kiw^v-8!W7jaaSG_u~_jCZ4V6jps>(-zOa~-Y9Ac8YLgsb
z0^nLlcLyC!&3^1Cf7(nrk1qmE3U)axKgL$|CZ|p|B9j8iNfS{AX~nXm{tA!aMCwPi
zP?4)V8MFgzh=rR7P$8gWZ&InSiiYW2Ju>cG1d>B~L6m*;Kc>F!`tb~N5@b#Q{}mQa
z#U@`~{xy~?&vmrJJjmOiT!YvE&3uEv;HT8NF{U~8kgkv<&CJLxa3AnkPxeTeGO?1!
zNZg^$y5akzhW<{}h1!ErfZX6c<b1HfmHQP+{?4r{erqy*_<h!G=$j}xMSEc?MbXNq
zRp{GSwHFJ#z*97JbjB<yJ^)3xB+_J>z+^>fQT^^69k=zMA^?5R)^-ht*AE|__b$`t
zaJX%0(J(hZG|A$f$rgN7L2LLs6z_%#?Z)c<a9wGI$e19;kL;Gv=z>B|v22$gG-#ed
zcCgxZ<fvK0BOYy?0Z;&P2w$1bDkf$&Ipx%;rOdY<_XW16J0hup?rg@UMr$${q3y~W
zOlCki2@_CPK&<K0APw7y>?-skc7Z)~*_MS1Qz9T-aJL??V;?=9sFV*wgW_}&R=^|X
z>_2dz;OS=)$H=)?RQTS&IyifllsGjOSj8yjslo=C@aQ}!0WOg4%a$FCiqb7G95(BC
zVjGZ7O?9;)163w2DAcGE2j!dx6T}PyE4YBxjYB?wTu`=icnIMnR;;^B>7Eqga!LD8
z@ks5of}DbGPv<dYOv<rzHNypG@#5`^1`$AZeeKh;CxR$ky)yRheFE~idDA9Hm-Ne#
zgUlCsdQNk7EsS48@fkQYg40G7Ur1TaLIJV~-@kmz?|(-PxIuTS6;GxhLHOOQYA=Mi
z#Dk<!!h;k@8Utz{uECQ1>--$%BH9DV!6t+1%*j%Qd9a({KZ~kbe&wWb<BoL>f6u+<
z8y=PD1Pt|5Z0fFond~_bB;aGhD(%XSO~$R0$Z%XBM(w&3S(ujaa;Ai^wYLAJ@5d~?
zu80VYNf(iFLt(nH>Su6$=UAp2jPw{+g2h^I{z^}fsmlpB)6q%Gy2JurCF2!JF}Vf(
z8+`36xnPX*nTkT9Y=~VximB0_%1ME)4s9rM(Yw%@@VI-=*AAQ_oAPE~>y3N@%cGb{
znH~)XM=z(VV($<1IS%AFJ3FeUGPk_}@r`lndM_Uh=ZXU544p48*-8iQnW-Tg=7GML
zudOay1J!G1WaNjUvy7Ht8PF5h#wbo+4oucZJz}cg2Wm(_IC;0-c51v<zybh~pzmHE
zir%lZ@KgjYU}d}x-~`k*BNrGECIELxYEGE&z0rIT^KcV`WZFqF-uldxum!nelfQ$b
zPB*A)1jzS>RVyXOy$-Efhk6*NczSQz4n{lA-@aWz(FRCB6-nx2!p@|SzeH5>d2#-o
zpl@if>GaiLgmjO72j&1YIm%yZK7=l|YSGkZttYO<1!b>>Oy3UGIgJp+$-rQ};NCqd
zNz;Jp0+L*&L<_AD&<s!-fMi~LK%fK5guqJ2?@>nG0Mo$EPJGA_n-w%UH6IfLJ1T{#
zI_=nGKIz1Xwbc4cs_SB7O!V~pF&-H*ewPVp%X0m`@POMA|3Srj2&j0Eed6PqM@dMj
zMO-abTNFWyj17GLQ-#GDWt_7C9Eb=zePd%Sr4yY^I_U=vybx&L4_1RxMTCbp`fTv>
z_1)vuqL82g3GfEsyw>$^xSRVlw_MiHJ9HoF0`oaei?Ak~s%!oBw%J?%iwm%B9bMF{
zG#7L(FW$UiQl&9`xEVo_N8*1qHTl$MQd#ES#&Z)r8`lBI+1P||&FIQdwQ+y|)u#Hr
zB%we&KMeK>SSNHN$!9Y%O5t{b8PO2d{1C-@E%bqG%KlKvfqna~#^|EDW;o)`Wlx98
zUpjbZ_2!QJyLZQ98NhiS_Rn#=zR~oPHlaWJtq2gj**n@=nDEl_l9H3%?YV%q>caMr
zhdT9ixD*eq#<Md;)<i`G*wrKIfNwiu`0#5uvh&%f&>6+v8X=@BKz^-}BP|vd?L~;g
zVd7@|TAR|$X<4u!g({m85;SG%oN-BScqrC7yEP~7n7^IC)^R1AaI}FomFNTI|IV$j
zt+nZN%s(^)KUPi|-#zE*E%)!Po|#MM3WbxH8IGH53Ku22>Ep}gUJ<uC0e4`Y5DbCA
z28*QX?>CVdvAzV;;BgT186S-t^5`LVYhXZ^n$B7O9Y8dM0J89+O;X2Lk;G9E5f^j+
zZW^*595A32Ar8eJru>YKWez_l$?#dhtvQPP3F^}9{{92r!$2nEv8J~JQ_j?RomZLS
zjxjc7$5}d@3xSe-U7;j7X~a%|fX=4bmE=po_(q2&hdLU$Bxe{K``NRv`O3HxjESt{
zBb9~`w=nz=F<<%eA!Y<9WYnBGNt#q4&<vjS1399?1M5)z^^!Ra`vA`4tNX8pW^5t(
z-XgGLOk59r+@n~8OZ1iex$DmIUiy;=&=}TP?^0oq$QqfWTiTf12<8rRADT}3)$)-U
znTg3d+;l19Nb15$AYI+?ojZq!$w23V4g?aprR9Abv0K()Y2XZ5?9CCaCLjcYcHnZ1
zIU#%!=XLBi*2t8QlkA`nP$Vi5Gdk*%dEcz`O=K%jc$=-Li_ZS-+w&h-c7lemmvz~n
zp*bn-j+cICbJZTo(4G<!$lk!<j#viX3jF-Fb0*1Hp|j!MC>Gmc&DPQvW9Hr551@T}
z+kj{KkyXIvfMSW$@7e28*nwft&5#9TeJ-^BQ0LN~J$J4gOr4gLoV;&e-;cBVl(<&H
zyNBNEIYKYOE@t1pUgF{v0~Al6J!_<|Z&UXr+MUBiyr|vzX7q-}CA1)F{Zw|C?7p+S
z=F=x>nMdK9BPa(B#l_`2bTf?*AOz4%(K8(}2ktLY=+_UYyzdPSOv;5&p5eTtS{qbo
z=+JQS%#!$?34h5Y*}nvK;IG*k&SwK7tT5PnS+`I7#>~#o{z`o$B@g1F&(2lEfzTp8
zdJhlt;42dK1Ta-5y3W_cX@Me6MW&3RSjzQU!PNZt=7BO?*Pi0yI&&_um{_EJ82e9h
z!(}#K&%#S3;$ABFoJyzH+3&OGE*J0|Y8HSWid6;{==M#!TS}G)TPd;z&F?8pA}>JG
zk&ce{S7KyHtAPmaG?3)2TU)@<K_wgJ1FU8u^GrWH?D0FQ7Sd1Tu3dKip%#H7AYNQW
zdHeCWKJ;WwO|h$kQJ`IfVr7$rCx8QfB|Uqx0XHQxb8kjh>I_!ZQd2W99ptmopg>1&
zfSaGcKQnfX+OyZM|K?aQjo^54`bFnwe$!q&KXIk7d;_ClkVw=eWOjB(2b_M08iOJ>
zaZBq`MhXc7GZA^f+Z#Lf@Ohu3;ib&h=p6umDd(z`G=SyHudO~46qHT&el*QbDW5KS
z$A`DngSG57?ytWCNNGc3L2<FvxVx>TBD9`ZNY8b47U<i8GCnbJa6<tM{l6x_ip=K$
ze}o7+YQ7K$?d`<_Rti(@hT^iacvj0Z9~(OK=uW$OVhZ#;hRj9}H)(>8G=7qie7puJ
znrA^udtl7EqP@fBzWPTlA|)0{B<ulU8Y3>A=8~R#^k~qP;HX@xF+yko4@3+(1K2jD
z1I3fm1VtsmWQj-0(1;C(4-fQa*8zN~#KEH%2dy>iK4{>;ow;oQR1wiT;fAm?gQ*Mm
zf)ZZu*KbHlj~{zdS5l7?jFOY#B-`5iGcubqXCo`4>4W4p&XgG!CifqlI8xx;MQSVT
zX!4aNX2i0ABDRpWlBr0-%`+Wk^!M0F5l+G9Kl79mO3fLMF#rElI-TA0YG?l$DxWD)
zD(JRvZk(`c+3yp@>yNQ>1Jn|(>9lDL2n%vQOCM}<y}1GBCX9G{__vd3hL-r0pPnRN
z+Dx#9K&R91-km!k6j1i|=yUcLh~(EZv*k;`tmE+=6%a;f+Vl~2YP|+q%(b;0Vq$WI
zGmgId{wZNyM8r&%H=sD&Pz%jH@t>hmIdJffCMVn26^`#(h`kMb#Zh=w`1ss+*QNHy
zyT|$UIb^~~;+(J<zyWaM$+Iy2?H#8L-OD+HB}v5M$3!`=wacxM88ZGre7tHOETSq2
z*HF0R=B?z(y1F9UXIzcR%PUwHp6O5&|1%Ntd6@}ULpq>mj&AiC)77<4;Bv{yTy;J$
z7#1D0iDbDwMf;8%A;1N)D#K~v0c>M{*ZEBVDkQCUCLQ=UGcKdYL?ZRTSGizxBkvxD
z9MWT~ONlg<3EFj^KSN_k13Bj)U=5*0y83{QM@wshW~>nBpp+ouWBHVq{_nPUkOFKe
z41lYdQzp;rtDwM~sJqWKhV%msU(#SKrG~md{N936@fzyZoA7a96!0#XSficOXI~+}
z91iUC5sc@!Hx<=WGVgY1(X)}x<6>fL?j4En+5TG!^D^rcODH^$J8H_C@P2!w=|~`}
z4mg7&7xQ32vTbNsou(kUEySqwAdgF{wEDt#Di4?mj1(BCRv2QwNM^SE!(WnJZ+pJ%
zb6eY{%<b_^59xz3t)4%BKD{S)-~0AG1z$A1T=Stw+`*GV&)WJnee#e)@P;7ugQiYU
zi)OfgAS%jv{(KAPs1cg6@dpo@F@$QI25cc~ox!jYy(J|K)ot>rQx5j8N&WZZ4Yu#u
z<4cyMBTn#T2|J#4_;CLScYZ|z9yt<lz-jvQRXpvX{y1;M$Fs%}#^?xY8K6c_SAEq8
z=Ax#?4zR$W(NZw5mFO%1sJ<3_CObPDJdL<2=W!B87_KROYM7cx+Wea@^YSzh#$3Aw
zPv<!Uf4WCNjKJDG+2aOUh;$Y1aklYfQjzhz&F*c1jzM{z>o;tGklX;=syx<=&Lb;D
z|3n0c7!EFk88BDA93f|@lp|#yKNTVcy~uBln&;_DP&pXp@bCcuHenF|=xLQ>MkmAc
z9g&g3kPIl1;!vjO4DArto`1{G$mr~uGeb7uZ*>d_1=DN*DicmSGYY1?a0__&ppoph
z0~Ba59={&U0Ky<2fg?qhQd#b=bneU<16|#Uj~~As@}qM;VzHSGZIu8UEbnBrH@SH!
z!ZRvyi9e%l7(OeVG=7fic`c+#15K#lI2|!^6!cJh6ev7y+}MN;HL~jO_?7DpcE$9C
zBAnPpTL++g*mULbm>5~rY%V>b<Gg$KUMVCuaqe=h#!s2@0L~In5W;`1X><dX;#>GY
z45lNdN=fCwe57azZ2vh6;38Fv;#**?v7wMCfGf7z=b_{Ahuy~s!4x38`7Vx>Oh|d>
znm|$eM-Wa`Pj{QFLVtCi<ziguB@v@|z<c&|w*M+;cmm`N3zxc*NC}FEPLwulGa0et
zR%N&PT>mj_UndOP*$FZ>8ey$~2?n)1PJ>0oR!L!WID#n^N>55n+QOzUH%8OO+`1pk
z9{NL=iFvr7pu++HY?}hkWYE9E<cs*A3>ikMszPzq1YBbvgXJ~>PvEfNlX<@ev_0j@
z6}q}{6DA1z5}=(xY$+%xX8M2w5E+g+C|dr)k`m3+OOFO5)h#Jm|1xta+!Vs0+B5r<
ziaFeTc{w>Up6xm1S<`^<3A6pAr4`wy%KJJo66lqIn@)t?%L@y8eyjrs`T5E>i>AMW
z0uo9nbN+q$_4UFNdxDHd1J2)@^5>7KhJTb!u^eQ!D%`K!$~x=jjT_D?8}#Gbn4*%g
z)8O}VbC+bKPuVZ>e%qS5aVv&dwl~H`MwUR|C(8o0ro&hO!D1!=y8%nb#=O2-#Z_Z&
z`=eE8r&UTBzZ>&1{`=+4jh88%xuO6%ykyMQXg;+dlze`nhZ3EHPx$4ew)5KywA99q
z9h9R>kco>E2xSCNH#jfn`}e8?%}O!$=LHg8*k8tzLov?!4$XK+I8HaX<mb-$mM@yk
z0odMqkc~0LA%NXG6LcGpIfUMvphazc=ib5li-1e7UcU|jU>X<!=A#FivGqjfdf0HO
ztmOFb_eN#m?y!W{)G&AtuU2ktz~i8m|Nk1mXsak$t-Y;{iHCxYOHh-c&F%fY2V1n!
zR8gon?Y_OV$L{gSai2eaJV4Jgm*FW-&STlKYj9zhh8-rHo0|`;!3RRvTWhFouNK|h
z+>Eo8=kn!;uun9-6EyJ{8Ft0XOsIF>ABy9_Dyh&u;iCiOik=aJv|`h-PhY)SzId^K
zBt5BngU*>@vz=Wo41@{02jsC5W2Sf_M&7uCXlUe>l&pZIl)7g-B-o1=S3{y}`0=^a
zh#HVBLmyhoZ{NFTj&~lZE;DHbc08!N2o}f+X0ONIlJT~k<A{I@Y9-O?@M9HmNuh~m
zUuq!Ll7N?;K8^Ft%kuKX12b4j#SvsD77b6Q!Mo1J7JwzH+6|V<gjMohqLI&lzk{=o
z?mYn)@y@_42c<NG<pMBmNGjUe8#!xGJ_xWpG(aXw40?IA+5(D8q(T6~MlZ7yeGInQ
z;EE{Nu+#7Hs4}2q!p?wu2)Kp=t-OLl${>H}82B!nN>0}2X=OUE<YR-5p4>Ub-qYW|
zo_VQ2vx2^me)%%Bave#8%Mm4KP2?veMZ2g)+w&W%pF9=47VN}GiMpuYh}n33KMS0m
zeB%b<a&LGh^t!|(25m6gNvc2+#76~b>Hm+gHxJ9PZQH(^G>|4!lbn&rSPGS>6hbO8
zWNeUxP$UV>MaEJnV}%l-Tp?q#%2>w8&`1bnNJxFZ!}Z<o^DN(cFU$A*@h<Oup|kTi
z_I(@Hb=}s@>8jsKWLLBzbeEi()M*EwT=F}Nfg18iB&s|w7Q+>}F+LLjaF*X^w;)S9
zJm%^1=cc;4?C@QPunPtdV3gzEy>qAHW-woHyj6@;1F)PNgE#<6n7srZO+E8x-68wI
z;z3IsS+U~NjajeJ=Lk&}fbr9fk18vL-9dseaY@OyPDi^bDK(s)#5({QrH$oEo>_EV
z{rWqGjj6qX9>CTF#}5ooo_}*<B^~e{cd@?voduDZ&l+iOSrtcT0uG2O3)k(3XrB2N
z<PU00Ft!EGy)iz*p(Enuc&D=HkiC1UBzru)yWklPjrdiP&skc^H-JmiGWBKg6=U(U
ztgXYTBnVlBxtdS^Y3LW}O2Fow5xhk)Hk3S6cR~(B7e%xP`dQzrE)l^l{W^LFeR<X<
z2<XV_oIkp#rrk^T@O@R))z9+v_}v(^*M8M2E|5kVkcDoBp&+1l;5QyBGqCE6AAxY9
z!2k_mClAmhv*7rX#>XRUG+XxIINo4qajf}VYz4LN=x9j&kd`JV?waWYwGH#}fXxYI
z9|Y|t+HIh3Kr!aFR;(bn3FgaGV%B?Yb?pxrkq6GwAAbGN9P3oo_y5KCmI@f((jJ|Q
ze(sn3b~h1XpI3haBfFZQN$9!A&YW6{)4!vAn3x8wLWRwbS-r6bH-{t3#o@IiAH4T>
z5CXHM-heE7g1*1+@qENv!>cP8RDfDzp8xstUnpt_#H1dqcp3Yunj$`}iGGU<H5O9?
zwkrP}W5$JIZM`rw&qOoWLXRF1=>fPtGhk+5NTTF~y1O3_3$r>J^p5z08wi&_x`Ekp
zI%nEae@tT8$&pFH(R6vFX0cxPDNarm1P;;$L<L7((82=Cq@FmT+<a7Nk#yMfMT@l5
z)dSe}jS_?EhdHO=M9pbc4DkT{<wtUQajIx+Y~<YX4fy}y86n|MY@ky@0Kipa_Y+|n
z0SF(k6z=lVC+f1-bRTJxy*2Tvx^?&N$F(;Fs}m@E=4*%n!WI&{M!t^#obTQ}No@jF
zh($$I8%qByMLV)t;U_5v;8%FZR1E|I((I3xkMoUuc7_h%?|qx*198YkE4K9s+SLUk
z$CTU-c6IXbctbQ0yeG|z+(&@lz+<q!us>)!d>Mmwtnnb+@etUlIsg?OYeG6{KxT<v
zh4Mu)WUHIJ>*5~Vu!wcSEIz6+f(m!(@8rW<NMLRS6|M1ljeqwnb9V<e>?e}*xgZf8
zd$cBYdx<+0?A(Bqt;(IV<o==iT(M&C(xRmAr+KNwXH=Wk-$MtTzzHQa^(`DX;<3UH
zO{8`JGgfylTEyyXn+3a}*>2y~cri<=xS5BK8<(^5YcOUm2qPmDys7q$K4$~preEdC
zLi|#sQ35x7_<%KT#Fi~g7Ow3P@>SUv-2wN5mIDzem~;n$2|&~I@S^$iKh)Q+gU`a5
zV3_rvZh3zv!WaQ(7=*YAFnt+=4m1l)7$EoK0Ksq>Uz&tU1u_xUFmHu|9WRVlCNHRK
zX*YjwiD2RrG@6huP?VcmGmafYBI^aDfGGwNTXICgp+k4nW*xLkoilqj>?}AA$U$%P
zOxT97ZJZ-gtNG0GYo+l2*>o6H)z;5WGrREQxI(5#!zmciY0^2uG5pF=_>++PAF<gz
zL2Pz!Q1@+L?<%ndfXbA*XrS@Kssl}{_ivkcjA>==Ht;1nYWWA1i}h8x8i!U)>F`VW
z>x#=nmdcV}sl9*PFO@CO@BSF&!=)QHjtnffh=PcM)#BZALwVpKtA5`}XM=QXDU)c{
zdy_6aIl4)+*e9#D`@AV*ja%$f$}VlwsIPzm$Gy&mpR;yWpV(3^077<bQlFHUZxEP7
zM~#NQd#8MCXizQGU|T4fUIygygAn>s?I+1~gzTxmvddL9Vm!M0RbF1!8<O6j%i1a~
zIy*@=fM|UvG~vU=Jaa(<_tWBRCA}~qbW6j!T7l+<Zn#iKo-$vV?3s09b<sLF3{>CF
z=a1&OWbsj1SxT!%Z?pTc-#EjG@hFtgv-sm@&!TFLf32$So_wetl?zQ1e>FKdbnQmJ
zdmFc|{dN&b7i)uLmZ>u^<dGFN+DF4D-z}4l8pa429JEfy`>k>@3X!e@dmGKL%350^
zZH%9RFnr!8oN?qn$CH!d`JbDPN=5&3<;<C(%D)<Z4;c{G`G3tXTUpUamU&0a{L36$
z*)p?E1w@gKX%76dqR~6k!r2yI{?#7Sd7?DDC?H4|KPaX%fnHUtV{xn;e1w>VzsvNd
zq&~5daq9o;13IGlO@d^VwEoVkx5-EWQS;1EpP&=Hqu3$SLu~H9P3>Q<u!{ioPn|a2
zMEImUS(iS$`=pmSEcmx@6%)SPCRbtJT;IV);eUO~e}2CkJ%m5pdq85$f1BX$(hcoM
zM9BCx|M}~G`N@C(N7ETWSaRl3_X;`TTmJnhG4cO=u5&!!Vz_+wJ^yXqe02nWxcWp&
zuHAqB`v3a*t@%O%bWM!b{Qv$;{?eww!XFME*~#yJ9>M?lx4FFp7Qc&RMBV@W`&d-X
z7bXnnr|D&M`)`jypU3E|I#5SO>i_<?|1)j&e?IDezHd{6@OJYpv`zlocbP5R``ODo
zH%dwTU;j2_xGhJimvraS|2EBkX*_>;X@;ZAfdBRw{(oQTmg6bjnyC&00aB<p0LKn(
zs4~9imdQ4lw-ZJk+*xZJ>AIj-b#2Gu&v$Fne%<Ks8TK?fVTAi^oBrh%Hen8>aXJ%{
z#y@CU9+zx#y|3PcZj&Wr=8jl0Y(h%hhJ72fK5e>p`StH*=C9ta*LoU#E%L|jKO1xI
znXiAnw#6*{`jHjqE{tjjAqPRN!I>b>NW5+>QessWKIB-?PGEK2i#f>a3537|vpNC*
zC_#*G?pD6Im0ua0j`D+4FB_V1)YC{^%2GDe#W}QjNkG)jrq`+z2itx(Gf|!ReL##2
zMHmG)m1@K7QVHw6xH|qI$dj)<HA!02rz>k|ErNe}bjkBjN3NKZC4XWcXa;TN_$YeH
zi6>06-Mk4E$`%KuZjsf*6l_Ll`fU#%vP)I$+7+EMBO+w2V+*bO#*lT~7B43ML21qt
z$J_?=mfS%<awR9H&t~(vVwTZ_<9|m&j@6w8;_BD0mV%tZq++BnW(dP@;DGv|y{2;`
zW3K}xTlZBy)8Sqo_-?Fx!OTJH+Qw_-=mhCiE}IDFMRR~IsjcOs#`CEUZGWE@{C*IP
z(OJV!muKnAlc<D^%uMb{_wHg@MqT7Cr!BjD)hc232wuf>b$N1!3oRvyn$@k$`Sl#L
zk?f%An9?rQeeb*aKIsKHV@(olp-k6$c{Kt7m)ix4PNFlwSr+1vWac<WC9;~D(qeu_
z43cxe3bB=HIi~Snq!QrSd3f+P$<Ay5x3#?kSU{Dt)w=Jm_8@JscqmyaYyXsSv~b&Y
z>^O8UaP+!KmP$rPwn^+#o@S#POKC#Yp@|%B)TqcCM~8@6IzXyXOyD3Rw$(gT*e@io
zgi%ogH>5s%2ZAZ^7g14Zr%wHPyd**-8!=v6NjB$z_xa^vKZ0j@95@@KF?ghz8IP<I
z=##o2?Q&k)e1pU1{%+!h*GtLFR35sWtyXby!b`h$joG7V1Nx*G^KyYH*NGf8EnLv}
z^0Ydtnk<zbJ$*VF|Ma=z^yQ(QSy#7sz^m3@=yB=B$hbk7bsazEJ35BdZ%2zyWq|;h
z(=lN1s{BK#fj<>>j$8@y__Ei!FXp_kgdMQIKobSY7pTQ}TL2Bb!sNM<GlgLrgl6VG
zp5<*Fm69MQLS@K$c}7JpUc7hzKD!5WRP^96S;5BlLeCN<Jkb{Y8-takCfnIDDDcmS
zH*-;yf>)~5@7k?cGKswfAdD2+P)~AF5>tG(TGybMqyBN8Jv;KjNYzLRA)IVM*xOUT
z#&mnq^m&5`SaV&S4!|sCzAGz7<tpJ+5Bf@*H@U!Aqu+nD0Fx)vE1C`%uyorkCE0Ms
z0Ppfs=gkYCy{2lC4W*=IN{j=6aVylexqp+`)zFlZkFQ&o0h+Tpi0%W9o#p^UyRh%3
zlx-o>U@OQ55WUg2U~sEw8BJY-$q+mvsu94elaR-H+P^Nb;t7#2iI;y)dqii2hX))t
zUmbRU3C=~#;&FWO=eOL$&k%rwZQJ-bHgp^_>~>eFt5Q@U)%H=0-W?s+0*?T*oINS5
zXhM08Dqi5e(*N3w<Eoddj#)txpTnRj2mv+^DJIuhVMzT+Eez+wbm)1W4@D=hF!6Ex
zT(QV%CLjPw*$OpeBv#><kpkjFPo;ck%@Mm(L>Zo#8cT_odYC*J+XcJw`wvUK-y6dw
z@{YNVbW!v(E}w%%4b<=;5cr%UD4q^oZS+(@$`WW0G>$6j-|~YF@xA}qPL@g%Ar7GI
z%$3pgZfa{)?!Vdbso(o^vY|}4a9_ERu%QSKlYWb^1WQkc7-igXqPW&pp#m3BIUmgt
z>t43sJIC`xHB4zk4=U7!{8A+)vY{gSV*U$H9)qPTz!o&g?ia=@>5LwY8TkUhE1Dn9
zIS<kze;smQyu!H>K)}Eq$z$)t;Yi^$Wy&_JRru{`8UR)^9*WQwAQ_+?VAV{kM))|}
zb-#bKfBgLU^`+HE(PbdH2D^e*J#0tJM^y=$>e2;=<HK|NvoewS2~1dS1pe9f#v;i<
zb?P0EBoh<09lb(D#CuLycV*?dj0;f+s&Cj7Y@-thyH3v!)*KrXL(Y&{2a)ufegVND
z5+DZZAsLmV*h#5?+>C)Gp25?nyFvJMfA&=ov=dA~5s2qFI#y!e3lZA$%8qjtzOT3~
zSYFU^@-2PmTPhvLfIuXwLfuVg`LJ}Uw2zDGDi8|ZKa-+-6tzDy`Kgm_mO5zi<y4}e
z**K|*U!iaT;X*}3KNl-L2jKu~a}ETy^MioIE3=k4vMtVUwEL~38#i8YkQh>9Xplg{
zI}=tZQ8c@M3(+%a?NZ=PDB$~%iCG?#6YzaGKZD~5Cz{e#!ZI2&18^OKH{Rgbrsr*+
zjaQ0eUJ^FD`j&v$;DR1<(^|=$g-2vFBzJ<5%!(CO=6_;x&7)g)e|sghj0AwTocB)K
z4N8_VA_ts`7|h`fYHw59o3V?1KgGrL*5+W+8y}6beA03H9JC{bbo7nTd1#9S;0rGt
zeSHBch5>}<P*6bD=ZBZt{lqOwQX3c&L8k?zEC@6RG)z>1HKXIxRt|S<CDD?7!TG6}
z!O9kXC1X&A0Cf^V)Oz>s^jTXL62aWN%7W{_0~oG+K+WjwXWIuA6~<to`}!y{6~LH@
zl%@Q$R}6vVvDok)9K*3(uT3vG>6{D8I>weUsboG}MK+wcu?7zx{_mfEXfpyqMm9a~
zI5b*c{!&&J7*HW&9~_R|#Rn4-TopgXpEAXvm5nXPNBDB+AaTB@;J`=+&qIPP|B-9b
zsZ#_*=&_lhdRxf6h%;!U_!GVu5D(uFVJC4;u1lAHGBT=~g+3acYj8NP3b@a0=~8?z
zmywR$mj(k8UAVB<$1MkJ6v~<(LV~5Ar_Wxnfc|&K**vfq!S9jfO0WZb_jF4j6hf-O
ztaWY95^Q;|E<mOZjY(pKSNQ<K$-ze>(I+Qtm;JbB8mf`xG{IjRaqN&3;t}l6RXi(c
zSoW#g@4J8JRe?Uf0;m$OHP}&54I7Xbe{aa8cgG3%EMfw`?{pZ&KWjm_yg>W%PZS_?
z;n`@-?bqVq_w3m-G<WmS{RntQ=gtgX0*HGoTV@hyk>}&UGo<9>G0GP@nGbc_CMz3C
z$lznB4N1HTii*d&@5S7#XHPA-6R@o_XS&{*FJ%d_#Wo^D4-sRh98TWavCp3LO%(60
zq$D=gpHE~81vMJEnz|1)l(FV20xK>S-9An8HSHam$haG_DT|5whAljB=nz}-5Ez1N
zdK+tEw@OvUOi;_AZk6T~xd0MEn0YLWJMDW)d_qK9T<uNq*mg9uP&O1nL-4L8uC7cn
zU@R9V^7QsrdYKOf0bm)`c~!=B({=vrX&gAP1dIBN45dzTlmnpqd3oA656t=~9$oR^
z0Xm;qm;k}zpFb2*G0@29QE91M;}j72;9NW?2_K<qeFqH+VCsi58__bQR&BF?&z}1@
z(>yGG&uRNieg%4a3p*;PZ=h2tt^qvOu3yi%Wj+5@ylvv*_8Gypx;dmgbldRH4WB+q
zFX$$Zd43VO^D5{Jb2-kF?nGJFa6iEL6H`*q;<1`fiQUSlyxL}1rKrKiY{a*V!NlNr
z2>j6_M@~<BM4rRSJR}0LbIi1&qx^>413Z@IF(kf!{|_eTWAB!7)>TzinXCyu+*@A<
zet|c|YkQbxzITdXcu#;>>E%U{gpEQAB>^O#plShKxmMA=#2E+`EfYIxL+t#$=32y5
z19cJ45#IxNVW3T_VdBwc+eDEPr31U#uOjLvQZ_zKi0B9@H2iQW%F$A3=AuP}aZh*m
zN6bO(wAN9<4TVuC)Nf@)@|F&hCr1G=@f^bqB@Y&Kc(F44EtLX45Xh11n|a~Fne=qF
zKk#^Y&bY<{RPpUM5!vOh$VL>BU-=^`3GrXeiC$`sN4R3xGmkbfV7p|u**mt0Z15oB
z^r{}$92|?93>!<yH4jU_xDTqyssBuENv|P%aXr1L;@b5epVM=locW%D6Ih;+3qis^
zblxLahPm6R3aOQ#k*N$?VWWmE#4DH0hNM^ug$aRX)chQJPlfKCPy8wlyYbUrmMlk_
zg0BPD?&z)p^GxbzR0GF8SJ!F|Mki_M2cB8rv;1U$%;3mAV*|R^hsQr>Pmwp@5ul98
zk%Qp;q+sEi%}8V97{3T8A!rju<gi4MkYfN5+KBU~!S1Qb$}vS|JThh=(K+$6S=ks-
zh@yglZWa<rtSHONqfCqBXkwD^uK<<7c?xF7!JW$9`Ks@1fkA?XLzoAUNJ0WC0`Nxu
zaR1=w&%leZX&(CDb6ayr9~|5ps5%(<c%DnG&qdkj@6S4+Y1*=?M=RxD$tx-flp-t8
zeSH3OjTRiTHnw07q|h{$U}2F(EsWiWpx$CM7oASzgIkYQhKN{8W@~S6kMk6oFFIg-
zc>?M0)>ckEImJa$t~{Mag8a&2-<24O%c#W=en5s{HJAt6xvZOe9ioE`-VRZ_-VuJt
zJuHTJop^Wa#UG#Lf~QTR7~-z*TyX>7i7H8L=5J%6#&tjmLhTBY$>(;PEoT``p#swk
zfC<|HuUl1B#SMVD;hjMW<Iua5i^B6SmRRUDTStW@<mODlL0rKk+D7~P`Wor!l`<*E
zhPY)J840$^tMFIl5#PzONG)ku-D-qh;msTAmN6tzo(}r~V4M-7bK5fH5l5L81&(&@
zU+TUFT?#Ikc*XBC<VRx<qbM(5c)nZJf-8S{!QmKUboMc10o#l;CR_<r0E+%*S{A^?
zubw^Iz<32it=N*IBBN*~S@LcLMvZ4cMM-y0bZyf!7@#Ce-lez-j_(#_&2b>JQzi?p
z|F>_i@K{<T8%mX}ImQn+YSaNT3tK5-5v(wmhh53fsZl2K1$4ytPk^+NgMuV=q_0Sm
zKT)bcw*EjHfu+BT>OEGi(7`Z0j248EdkQ1_m<_~4J`ZxS=dcAOkl>}I8@LE^+Gx+W
zgXuH1NkK@>!DSr@nM3(QB|!N@1haPx8i%<WzdRV{wQHI^9#hqJl93@5s;j9@%T8q+
zjfp4@5j*QQ<%jik87^k@7A|6Tx|4yHN?4}}y0Nu2HB_6>dE*R|!xzSPSh#tuZYzhM
zYT_edPgxLIoVAR#w*onV9*KM9X~0m9KmekHpdBsW-yszrAXYKp(UT`A6S3$v9y5j+
z)4s9<D=Mf~Hk@&LsYV(by;8y-{@fl>NSbk6{g{1EJZscw1a#ZJyNQ2@Q!yV9nqO<p
z$Z9+yP=e{<+x+rlisR{yZN?TdDd*4cah)b?&nAkOdm8Bv1I9u?L+`{JbUgi&*T4W&
z_nti|Hz9}vJKB3&Dyc;As%LV&aO;8jO+N1}`YGs!JGZp2HSKH}%{71@ZtJchIUx;D
z1oVMnX%^9c;yUJT6HsMzL<A?=7z%+yjXE-s)!Z1)8{dgSY{iNXI6F&OlFmSU+4~~c
zkIT!0=$5s!sfp78pmX?8Luzvfg*N6Vdl@&3C{&XA-qOP7(L~bnXqx#)CwX@&yzbKV
zQ{|=mg@tvbpxU(sH;^A}r>I4ZmYTX0AIerK%Q9*$d@wjOU}vMhs~5hBjC55+uKM`t
zQ+rm3tzY7uEgbdqdqWS@os-Sg-$VyaHWy-&T`DV=c^*{HWLT1f#3H8X#2)#)z1JJ{
zJX$!tc_b2=6_N!S8f=5Yd&lsadJLY;S^Crd`*ZEGUdCq_Cy=oS7=OfL+nRDlTOq7q
zrBH>kN=jvn37s(am;F;psv$bEp_~5vdR$agPjls1E1tErBU$W98XdWo$(lln?4d)u
zMq*Ok#uuhggs9_P3IakoUDry)5cB5G=hx)1;eqv)NFjRrk=mlY3)OmXN{>-J9JARS
zi2BM{bC;Zoqz%Hj@L9Xvri>|aR^RDI89-MxZQ`>Oo8PNDqzb%gh^Q@T(|LV}b^UTM
z6*ROG-C$<gS9#h$`G9~#T96aNo+f}8U~PDZ2BIb1G!7_^6gi@IU$0G4mi(q*85z;4
z`ZKAJfFdYL*k2%Cvews^T{qecHwb#!ORE-IT8fVvoT6|151ke|9%P`ZgRWx@$%)6>
z;a|h8TrCa#di`h4Dp71|KF`<~(*@ms^_AW8R|)Z!-A+YyM~B>3yVgfT12pXblAzaO
zQ6UKd^lUyp6b|1hg*n?wQrap}|58aL`h^$0*dsW|Z~eiH>Fy&auCC&_262U0H`dZk
zHIfNa^pe15&jBZ2zcx2EZsi>?2}mj>&d|*gtB(4OjIj~uR`g9IuZK5ZmX+ZdQfT}h
z>1%<CpTkNiOMW0A0uH3*rG~ECm84u-of0HetdzKPri|)i49b?FY4N4soZBU%QeV$8
z-_7RV>Z&TSM|K(3ec~<f!AI(N*w{zVu7M8AhUyzFV=^7{6Dlv_U#~uWIvlmj?hkJ6
zcrBP^gD=wfICcF>m-;%;4B*4i^Ve|88Xi0(K4FqONte`U`nj<Y>vy3CX0r6l7dD~j
z#Fow+#2!D|Epm7>XOe84<KA^d*qgRLlY_O6aoL$A&gebD*x2)L+-iHM*R^LpbtWrV
zf?vKNn*u>XXiZ;hIU?aueEi9zB;}qxTYg;feXpV{g}(YyMn=4Xj`Umt^4P$(3T7>_
zLb<CMnn-c<>G=hgOuL(Pw>%bNL5syLLs}ZvBa3Fs`NpOV)N~ea6ZA@b+Zjn(i8j1T
zRQXJbXljp^A3us8jP^DaRuk$yDgv`ju)VS2YYOQRabaxhJ8(S8da7q!u;TOOHO@#o
z2In0N*suX3D}DDEvi5FLM3<p|C5@$b?g&PW!0~@T0e0kRI7W4Ak8ox6#oN_kg^3Cj
z1eD_cT)I?zw)cnxO&r>=mQ5QIJLLp(cce7h8h&53dS_)RYNs`ScMh_iiF@I;e0Zpc
za*5vs1{;>j_KuQconAWvVd5~a7h8IS%8d;GZU`(WubB-L#EA4m_~k^n8nep@g)C4I
zUHTO&N1j`T`_gUa+qVmA(HJpCRiXM}ZTR0|DKzjN?(T^WuIDFODoOQyTUY1OZz+<`
zgalzMZMnxKnl9=+8rxd!X7~PfZ#OSlazYTy?0@>mw#oPWuk}ShGPsTqX_=L7D3na@
zFMW|J_s_e)EoV$zet<>*f2vMNBHs-kGDJ%39c3X^6BXExrlzgCcD0}ID(@S7;|KOu
z1cXf!l%(`$f}Iq3AdwIx3k;B_W&Xh{4f6z|B+3{nkTR1<kqwJLaj{}(h|?AH{m!BG
zg0;slUHX9%ioOBl1A`%UAxK#|pr;^D;8I7o1rXjeDc!5AJ)y6KNQt#Fn1i*9ws6Z*
zCqI)4DSdPO#udyz4iJJRCIEhBca>=)U8{iZXewfbYm!8bgM+pLgvmqIt#heBf(_y>
zUp8rp3(TK^&?k68B$wT<Co)^63rMS@MqNZC;-xI=BV~!IiJ?x~x-qZJWadBd75Q+N
zVEM5kK++jHZA@5`d9=Uu;ZZ&+QkH~o@$U%PN8T!yT>XG6K};;FZKhNrL6Z9kxYTcm
zt*Uv*wY9WN^DydqwC8eEm-g5GV`vSC;Yh~=0WMGEbnnc3*{x^KOlWX#E8FEv4U|*)
z@%=ks0N%V}R~3eAknqUlXS)pi*w~2Qz%rxf;LRaD*~A{qE2ikQ_qq3NaK}-l*rcvL
zl))JGcfOpLP4g%iteTB<KQ$`GW(OOaM~xabaG*s$Nkh7Z+q}EnG%KZV-#_3=Xoc-d
zhpkOp{q0`-(X#PwvZ0ui`PP*vqnDfMAffOY`GPM4hG}{7hwb_R7s|;obHHku-km+5
zYXCYK-lTg-eG`x{QT+G*>dh~oKUd#fd@QxFYQ^7;iT6>UWK5i9QTY&<o9Vyho{uUj
zvN!+sBPRFmeHbBkN_}lZgD`HGl7h*6^XU~*p@|I9^=??rFbqv-aD*TeVr2m38s+$~
zVOnTW_G=Bz*WZL>J*S)C_kqDN1t>qv_ajT=?P|GITkYf<Ta&Aaqlk1Vnh_R}ioT8Y
zZr$+t)mY@($abjAk`ls<T{dv^;<-im_fGEL`QZIWB=JMh(IRfRuC5>Z>l(9TZH{yN
zXuIes1dJw0!=Yjk^V(>{cp+ft9Oq1x2Wi`XpKI-WlV!9fBSxq^mXw+@5RW&88b-}-
zAL+VX?70uiqgaIVWW~ZcbM`YF!$}S~@Hl)~-fi?DKt1NYR3wWQ)3Tr}=~!fQCu1FT
z(uY@3wz`w7t-W4kD`%fNki0lyocQ%rkV9}e9ug)ToK4&yY1`QE-K}1pVlvYWAz4am
z7lp+aSHB*orNSSR`|gt{sJR;6>nh2TEjYE{W&`(+92Zn2|KQ%eU98*T_ex{&$utIn
z-c(hw_?NzKqG6w-_rq7SRgZ^^Dw-ib08N^QE^Q<DpUXTwnW5%488~RruiwAzPb!+Z
z9x?O>;1&Pca>>#SD)H~y+TU1<d^1w@e~SE=SkZB!1vs7k0Cv(*lyGXtUO#`n?PY}J
zaIh?fBH8On=1jaWdctSwOG>HpnVHZsXcxMUc|ugivIESH2Cw3WXterHMjmKQZk4?_
z;?P54=(p79`0+{f{7iDOx0o#fyN7qVyWBJ+NYv~buxy@>*gEQ)!fJ1VwynDx;P1eJ
zvf1f$bg!`SV1y>Y)^74-X7r_`zk#HkoTMqz+tks%8ADgj4ljp`#Ov~}k}2@UOy;lr
ze<meL%YnXGuP9N7aqI>3$|U)a^8g$Xo(#UyQdZ(?dU$*i#2b1F7`wnfzk2vPd#+sB
z+q{x(m=3A7Q>L&f{OFF+5<eay@npTqjI^1FUs;B_WsMiZwG?N9YP7VJ2f)vU8O|M|
zRI-H0MsGY3$)0f^@i)E9AQ(zM;u54@`IS6<`7bP6O$bd7YiU=}fm)GHEd&6eqRI2?
z&4f`?RS2)f+aF(3g<Ub2{Dqv{frA93h||<BAtB<C2XC~r_&JmklffP-7r{rGeLMSK
zp(n;=4-GZHx10agqBYSCO(0zewrC{EE<sFUF}C1N*iOZQCUPJ4IsEVe8Y4{)E38_9
z*Cf`EU1zV6lNw7ELPX%M6dpJX_>4^N<*QfY1`qC1NfM$H;tKVwf1o7w?!$+xP@9}n
z8fx_f3lS@Q(WJdakS11Op)_;uTsg75*d@6~tA-|m$CE#ixn1XZ+^^rOE&IN)k>4Kw
zKIDlvpQneuLQ<GJ-Ys#?0!BLG;_y|Cyf;61G`}Y%8Zc+r$t$D`bNPXd&}Pt4-eb~K
z$=-8~f<-paCd|M?LC$b=oPJ{idP}$<q}pWP{!MN>b%8^0%@fqtUmngJbb&xbI3fAa
zm}F=B16nxQ$oq?c=@9`kxTm#pD%-`Zx_+UQ;SI}gidYy%HAp_F&^SnAN3)xE>lO^%
z>>+)mvkb7+4qjOaeHhpyyRYmQ8a!ZZ@%@WA?QqIqSpanOxg;PrFsqsx=FeImA1YVC
z4TGu^zzf_F_mx9svtAulh(fnW!GK5$T-|^5L>fI_FdbdR{O#By!<~c00bTFdHZQjg
z11Hy$Q<7grhByy)F{1t4q<cfk)1AQ#u9`3`y6m-fj16IhTAHefC*o$>$70OKRPn^#
z=&(vC%NiQCF3hk<ea=9ram1d#b4;P4lh?1mEGUr7P6i}4_H9sda1t8>2(FhnA-6A7
ztl$|x{+^=KMaebFJ$iKVGfnXb{Z*ikPscni>G41wF=nq|5CAAneZ_V?!NL%lF~z&X
zN~CmyUXJEnLt{STH=RrGKYzwrFp0?_j4OkJ%$*!^E6b=~0mw6d<4adNM=fGJlQL+=
zZm?onUCmPIX1y#e^EKahGbT*v<kwGZB~YD9$Ik8BVHt@Ff7}I-%s^@wJ^a9DmXi=U
z_9J-d>PA*~UrEWsRlR&!&EY$I4HXmH#jCutOGQ3GK|v^3c<!`-c;Z>D?Qvp&r*dK`
z`*VV&xJSJA@bGZ{-{zh90{6f_^e2!|zNN;Wbxb!F8_qFBqL13DYl~-<Oi5+sM({)q
zO+(Mfo_`+Z!aaF<o}}JEi~ubS27{XfJuT$}rJ2~$l0tisOx`pIXJde6m*g49FLx3b
zID+Db#JcH7f2yaX5<bGgA-IJB^rxITJ`NY`%!ewC3OsE=oidvyI0cJ?V!=KUj=TJU
z`2DJnAMfH7J9H?%k$3e1G!Ay|YNZsHkZ_rXK6eVVIh%rm=jSmagcaIcCnth6<+DMj
z*P(Alxr${CgfJpFBN%09byNQiUmM$F<*L6r5%2*Y+5w86>=qe2k{ZbEEIFJ|IiYV1
zV{4!4>TvVwqB}r@ECrDXC0|36!38Rwr<@1cMfIJd5Ityb<mg<XS%#*fIime)UZFH!
zDPsJyORM{=iLx*Mj}|~{HzR)%fzNa2s77)?E@x*mB@jGzh~-0YINWbxsgSF>taB}s
z^{gW6Scv>LZmjh-W*CSZVN`ubqQjyl;d^Ca8f^si6rvJLii)zm<TT_|lci*23>Q?R
z=Xdw;2;DehOJpR4Efqe54A{R||GrAHybS{ekSU&ge4a7zN?Qlm4!X8IqQAa8u(|W~
z02ZyzVN$-;8*(fSo2CrkPQT26r|8iIFD|$O@+Ux+>Xy|o1VG;4dh9pI4R|gVkil^p
zjTtnPEeyK=^TGJLxx0rSc^cx^RZ-FKlN4e9$-{?>jkmBUjg$!TDJv(Jx5$qlxaY_b
zh4h!{XU?D)1%k~j8Vcsj;UNMszy)xC-QzJZZMa3|ZD`r2+1m2)7Q+#KV9rA}anYN@
zPF7G;7_}C49q%sK97XKdafgr-9BS$(iqFrHB0zO6JE7dY`=*vgHNQ%f47>><mi(NZ
zaDrr@PR=2(OMtq=Zp#6ki)3+1%tku|uMJ;<^(*z!xdoS#=>Wdhf*(yo;C=A~^dTb-
zf352l(;@PcP-7m3X@iu_xHOgwOVjJmSO7tlHj8gT+@v*SAqIZK(Xp{(uzg&*bbzrH
zeoPF<y`ppA{!=G*yn8r6SMy%eH%z=Qv*Qj8^C@Nt$?by&16~{(XPEm^i?56l#_72!
zu4()CZy8~gSfDLS-2;RX&9<eB7o`)#hOs~69IBqmMJiE(h?YIfEz%UHhYn%dESJ&M
z;Uci<T&ybbJyS^R7cpLM&>%GQ?Aa0)ml_#i`#DZBc;PjFW!u$>M|#uy0?B{?QZJOz
zHiLyzk64J<QFkvd&lN<O8wdG{IfvfG(ZNrn!4H^*r|$HjjU|^Yee@O<d|<w{l2n%{
z_FC~O-Kct)NP)>iV8Gy>`s2RHBbKx-1LoDxZ0lInbZkZ%QGqguuFkQ_Rctk?RW;K)
z1R5vZK*AH#?%y=7#D;XqQhQp7+Jq&kBfuH{Sa(z>BbX>FDw+Uk+g2<&aT9Y~T#g1k
z1JxCg!*kif*=R!mfc*n7G(3|BjES5<O)Y_=AUS4fRhK#Fy7%r~M}Vdl1}!NrmT6rE
z;+;FgB&E}sXU;rIHgWRLmM;&Wx=U>CWYmRmz$KoZ{$ziS5@-5fKku|Qf51i_JVR>Y
z!_kWUf;tu)=oye>`yZpFxjWZl=~Un_mtkw@A4nJ;m@~JJ=bcay*BtHd;*yKjj+q)*
z1|Bpw#p1PMWHl85pTQTmo-knvRR*9{g%5ZuKLnYCu#m94JchM54h|I;S86;7`vw(F
z!D(eBIVeeN+&TtQcmbJ{IztR!y2PMLw-*&swl_jv>k?OqZX-utXzsV?;6Yx|0^lZk
zRNaf<40V{C<Mu_VMy{`@H-9EJtyL?s8UqfXIFNb1o6GvXiOV`DYd8jA7>lm@b#2Xv
z5S=`G_7jstpv1`4^@a^Y%txidPvLH`6IEC<#QOq(%j>b3kc*lNGQZ$#caf6R{+%nI
zoi9TCNGCOYx(^i!<iNoFa>M3~L53uRhiTLJ%1i<T&@xQe-jh3ni~@~@!KhLDtos6f
zQJ?dVr-I5>D?2P)__DZoOWMQS31j$K!lU9HapqMYBF@iR1-vEp_}KcM!GWzzGO$e}
zH&^WWW7$v|^!S7XrWfh{xy&Iyt#o5^+WhHVGGl<-Xd?hs%btWN;{-@KMbV9NgBvO6
z(0C98R_Kq|p*{pIfB$S|L9+Yrsve+uI1@=mmGpTy2aY&SakQ_(d4BqIJ%9-d1E~67
zNW~v?h5e)&?9rnKg^ft5k)jrf6OiHPmCqR$fFM4Nrw>FH11T*iNSyw<&79%3UB0{l
z*bcOXKoc68PsD-R1Sq??wkfwq8@d6p&4M*9v!|4bRHm8TwKOGzH8Qe-%xdRoDp|jI
z`xa);b&MY!521yn2h#qkN?&<-4ChiL@ZuPH$o;xw*Di@J>KG}5Z)Nll7$-smY!oM#
zV{3cKOH5qc%5^CbLq4+>$QGdw2rQW+bZq}f(Me$sNAYeFu;*cADWqTnhYgc1)LeKb
zS52q(h#7p=!mEBEW0Ga1@;O>`kYrV4`Uxf9;dc3?;A;Y+*R96Ss6$TDWfBSw!p{fc
zM1`1nzJ$6{b$Cx;2Vz8g#a5i*Q|@3=;{!d8?k!A>MHoFaHND*2Q2D@9u7?rGJ<0hJ
zOxB>#z-^egoI%Q*J)5~+XDTnh%HE1mj96lTZ98q6WfXux@O5fsC_{Q=I%b(Rt2Jvz
z`0Z!#01hMgpH7?Dw#0gYKrA)~C4=J+15e`{&PHmfeFO$gOHD1$?kN$3k`%W$Rw3;x
zy+8Q*QJ`8!3pb<Ztrja*oMx<&Wk7r%2k&v?)cwOmHY|4kyR(w_Uqx>b9H$THJ9n<|
z+@WI|-10owsEwrV=B-<7fDaily+YQrH8mRb1fDYqoMp@R0!trm*riP}YUz{J-BJ;B
z0nlSCNMS)lS-efEK)>k^7DqdWsaDxChRP_nWbi<d=mqoa%;)hRh;DFBXaksB^h8E8
zqHA#FS~idv8e)aTus0Al)2G+azk+p!Os(K4Gm~}(7gK;brdD`~#l@4HodxVu%$R40
ze6j<MY@p*~mVKilqTm8nqy)h0nsx+IXDZ4Lkw~n+8dWo>_u$#-Scv>YOSE>a;o_+P
z-n0q(V`IO5`z94Qg%?F91~K#t_=Hl6fJI?Sl4Y5X*z}_aC_!T}3Ik9P98?jhMecZy
ze9C2UAhTjlb_^xDI)u#VT$Y*JPkG;r;A6-f97KyqlRh}P%v+jLEfy3cr&6Hb*7ox&
z;g3~Tf;nj_?B8NiHXm0t&%{B>+dsGI+$dAi&RMpcbmqm0CRFZ%tXD%j`=$$6E&W%1
zZ8J>J*|apvgR`ekcjexpK7RX_a;*|)AePL#<Vnzx<K~tqOqbQXc|)ati)@*nzlN>T
zk<Mj;`3A5mFE2O;pV6-^Etn@PexZ5|DoLn$j){3MRor)!y=!F43Y2reo-7Qok{7si
zx@vLp5UyL&^3}|yymT!8)T!MiUV8iZBupZKqiVdf`HIJ$^y@ZpqEfi6?y<Wv^YNXc
zPZ$GHf(<OklTYX2OCB;~&k&LCuYMNy7e-OupzokyA@$#5-2mX9suc|d?x`F&G6+UA
zU~9(x`bpkN;N-(df_c-KjnFhBmUcT)3k*77KrxvW`V8q@>#!@7ZKz);0Qp>t)h^o2
zSdX!ld6m061IH=+%#za5YVT~obU>Z32<Za-y;GJPK$IK2VOL9C_mEOulrj@mFehD!
zdC{xu$kY{Er;i<rjm4`ZE30GWv{S6GmOm~=XF$5)cUtg|M^~kr$D&m=)20P=1u~JW
z-_MdqzH0E)9U)sL!?-jntPXKd8#ov5^!;*2rj;vJ*i+)dqvHX1+rmPrFx%l9FuIr>
zR2y4wiP0{@PMkaEOxJW|Ql368{z4QY@NpJ6_A}BRp{j#U0wcK2vTO1uU;+7$dPDx)
zJ$}`qTSYgm0AzU&=G--G7c~_IfQQ6Q3VyW_@gpTYN-QMG)EuV6tot?-4+W!KwDBB9
zuw4dC!E{iTU|Z~<*!SVwF^NIJgGQ<fo){1)lJcyLz-tS#9&5XTI%&m|6A_BQt4v$C
z@NnrNRpUKm$(argxu)U83dO$psJNa!6~rpLi#62LcCKGE?Zk}Vzkf4qm6_j9Hk7Qu
z6ci*fvSiF)Ag@x<!xh&~|2marFih3ciph2EjGoY|B14<(_)XvG6mkq;C}3D->@~u=
z*xK0WqtHe`l#wCUg2m3^9fQ-Dmmop-7;6^1?4G^z8C~M5S6JEeF<VgCR%<i@i*tYA
z$vKVGB-|lNMC7{&!St?VLJW{3i&0@#R$k?e(gLt{8Kq_Jtc_?qwwhF5k-l_c@zars
z^ANIBtx4g<GZiWsAhD{{ZJWG%|J>f){T84uA_>5I28&(!tEEE5DL7rfC=PqB!ul&3
z-Nmpj9D1?>$%EQ9(Og@$vx0)hf?sPWKdC49vII)xR#?>?8oQD4wDkyFNW1(fCetZX
zAtLDUc*g7{WqJa@n*s|Laom50VpfJj2TCq>D`jU?kqe1pK4%Va1dkkH{Ik#C!Kdl4
z;1|fl)M1K+uTc<rrFd=$(`7lDATh`AiE59+fpJxag&FabPk2LZlj`I{hJYETjv(+_
zTt8|TlvCjM#lE2G%4e3AMtY3dX9(L!+zVbSc5et3B;-}@0h-Q9gQfSa1x%nE<l*3U
zDHpjX$waWTqtYCrBfY1rS>b_;YKp_ahKpTJb+!FP)dOUpCSwSMY4PjxhYww5&H}^8
zm?W|&)KpQCke>_P;b7Th|65!m#8wyl)6dt}CCX$<SGs4!L)1c(C(Aj!D5&-ZVg=|J
zXu$9QjRjws{nOXh)K6jXGh%${-MfI`?7l-b9l$N8Vq`Lx3X1^E=Q-5KFK`*5XXiLD
zj#x$bA$b5V!~b!J^39LHD*-Y9EDE+SbOJn|lLNPmPcj4Uq9NqGA&n${P`x6i0Oq0y
zhx8M_Vx}au^Yf;ReF+o8?NXO6Su%89mh6@S4!&E_#0rH&208#2v0U=_cs$P3V_W49
znyZ7w!vVXP*VooAR=o)X!1gC$4-yqr?N6)dCgKX+0tbs?zGCEdkL}WdoujyV?4p!x
zNoyV>d*Hs2Bp|~wzeicgphk?;^17*Z6JE+$r#@u%2-qQu>Fh_612Sf`eEXJ_kzt|j
zGk^X;+}vOQr}sIdB*n|Tnw^c_mhJ=11iCEFD}k8n01yx8LNXBabF|b?o(TNm-1FfK
z2rxFHIxJsbe&%eykIy6S4W*%qi*sk!_>WHuGv290Sx5J5ogqEkRh2<XJdNWiYw4kw
z9BP`1MCRbWeIC>o1=ZYe-1n4WgyQ1rfUSXP%M{4wY%DVkY%?CTLPsSE43@HuQ5(&i
z3mv{X6zSMcXp>Cq>cYQwn7QUVhZg#pjx{uN<e*NRs5@+!!prNrcQ)kjuUe3mndw8d
z$cyqfTQqg5V1$5FkU3Ov=iKBOh<!{=)g5NZh6={W{NI29GOdz{8}L9eUh!lIk3^))
zZ@}N@xd7mKxVp||ke<BBxq`Z&r-$wf?k9}Zdq=py5g~m0*J+<4%25ef?`V4Xo>&XY
zC|;!i?<I%ydqOWxqysjU#=n2S!)_OQZI*i^dYV4BAENp<Zz5;Cv#zyO#)v-t9;#zB
z`{Oozk+PVg8p+mk#1dc<^b{1J^8^(SF`d7GYn6$qX>y7)!4tqz%4~3OVd8?SI!6Zw
zr7lq+hE~-0koBlRf|bSJ4x-Epo^EGvUp&Z;vJsPE_Dc@X)05lk50a)}-GdX?aQ;AY
zW>C!lZ^cPK?oPo@HakQ%e`k00Zre5mP5tr!{ShN-K7WR1+kJh1>zvapOG5cEicm&X
z#ynV}RUnFYqAOh`b)rG<#5{e-ipAa^F{h~vy5bddVO&M4zI+hw*yKQ>HwBE-;h@}!
zN5^j5SG~1I$#JqEtx;iV>9QqDB2HyfxD!gbun4z%47O2MjIz9p!Qk`f2dK`#c5bhO
z?&aDb|0OulF6Sl|=xg@usjIE+!@-={fc%wPE$K9$x!FcJ{fo<DBc|Vf0NpC6ZF_Bo
z?c?YJ6#002L#QUckr#E74dwCRiz3z-3<QvwAo)9pE{-5G#Cg|F!@J(hyHl|sxFY>d
z?;5u(WkS6mIff4g(5|YfnRnj3l)-uk)<^89jkf{#b(v1S4EsJ+q{L<l;xgs?QL_ya
zE$4_yq#Fpe#NoVZP+}?&IC+v75P@(}dh~!3dGzunq3jw$PNWGuUic^w2c9CVlcc5t
zJMUoS;MkQ8c@gK(!cj<4*(J|=0UQm*NX#M!2(Q@S^S8=H^X4sQNdl|A@c&NPF!Hdi
zk`x^>+t4MS?md=&m?MVecF1O_h(gqo@V?|-?x1b7YWBWI_(U(17yG<I{=iyB{}U%$
z9xDel%k{;}y1Q|@^udiD9)jHx)d=lSUbu`x9S*c?jS$3I5+Py^2F3yT)!u?(K~~ld
zLM{^>jg82K4+BRiY!Spq2*$4LVwQw<f#d@vmmAq>_CW5Q!WK@h#5C!_f)Pwb4_4Lr
z;V!kS&;2{AG>+U;YMY^{z7zCP(tEhVmI8s|h716+668DxszUri!d^pl3f@R^D)u=G
zEM#(xD)F0i>8>^)gm(l)Lb#?xS@QfYV<1jW@$|>~*9rUyfj&9vtXrfTd;jiTwYM=6
z;h76$zo=od;awg2&p$%T<f4s2Tz~03&1uu_LV$(7`|;=ZdYXRrW?>aY3QLxM+v?~R
zy%cE$4HvZq5_>Tn>Cc!lA^S(n%nsw<U+Sk?Ea!FHxkC*mbM}i^8t@QcB-fW&Yi<jK
zx7g>@*Yv6_2nz2W8OtKWEVPto3`cEA5EN20C2T_jYtNjoG3srz5HL{Zi~Zw}Xe!k`
zFU7N$)g_6F#zSM)ugd>*>;w`*!*CJbKDWU|dXSu_rKm|!$K!pp`M3QnY1{b2jv7)h
zu2~YSw+;I{Z0OO0UBwrD&^UItf|#H&7ZV6rXuH|WpaE77Jf~=<1wF*(2@3dSuCC=}
zWn!9Qyhw@m;f99Y>g0Ava&rimA+Lrg8Ie^1wN_(e%uvKh`3omb(5pyf%T&#M3VLK~
zD?hfc<X!PPIj2hU^f=+)(}iSk70k5md#`-|_AP^rvev<LlfbrMlQFTel`L?2axH`A
z3azz)fzSKLBV0!#<sl}sx7a1t&{gwW{kicq6yF?gfwJB0ZyF&II2G(#I0v+>D_5+L
zylbsgN8f3&Sy*Ojkrp{VNt4+U9QNkUP4JmDcB`Ca8CQcC&jZi+p@u-W<kl^!t4}y)
zCMAh~ybj__BT1Er*aYQ5+~bK#Izxu+prF;x$PVflxAiC+mvwdDK$BhQX{Dqi5(QIF
zQXgWkb~0b_d8~O?1`z2Ym}IRoX-REPfF%e=>?dKf<3fLrI-ErjE;GU4(Kxx6zTRuT
zH(0FI25lpw?%oq}?{aB=vuZ0NI^ITy=S-S)(FV#o%6N=YePXYy&<p<vTQL<bfn0Og
zhv;~)SG&A?GHGI%5&xKoK?#^L_F&r1pmJwXDEhbD@ikCe;L0#mUX>TSu5b<(l@Nfr
zsu@32I+hm&_g>AvvA0)@Hd0hj&>|=W_q@4GquU0lr+dY1ybyz<NQrB0TVDP!%A70Q
zP^Qf=FppWXXpYe=@B(0G=v+mY0olqiXo2$b#5?Uoaf7Hnx3-y?u$uu+@$xE$!zMl_
zKZi#f8yUrgg-Lc1{C`oKpTSFE?-8-ZGLedd618qR$c`Uuc2~^X1j%u6^odYq#D)Y=
zDiZ=Ci(}l}bTguzs8iRi5#J`ct(dE_fTb$k<{k0aT;_>x8oG#3+mU9dZ&cbU7X4rf
zMQP{GrY0sMM~#wLwPVT&&|fkX$^&k+c*L&iYFDB-F&F=3j*<9z^iEpiHpxCp;$oH;
z?Br!qxkJqe-7>G~@lw3vgf&W_)78~vQsRwxe~HrzDJ?_>;)`B0Bh974!fMOoc@n$U
z2H&lN&lBwK#}|+G&L3Sn=UI5U?#5@2A74QI0aF4^l-{vO$`VIVa=%&oq8h?6eLU~7
zQO}^j#+pKgnn_z*yxz&v=s-?R5Scw79A6}G%Mq{k3H8x}Vs#aj&`($!nOI!DdHZ&k
z9%2S%!ejxLmc$r+`0!5k6+3qBq`<Fk_UCUsnt9{u)%oB+DD6>N-_-KMc^RC5r7K0a
zvRV|E&R)PQ2}VCOFKB4wXTNZN*)H>%MS>>A#`>0SReNY-3mMEj?Ivldq;DH<pd;<&
zN^ePj%UO!A6P$rJ|1#3rjcqT*k&dZF;<73m*1}K-;MTKg`P6dr3XQ4*^^ojL9&ru$
z>)kgxz+z=_!)bmb%U(Tw`r}`lxwCWsVFh9rFM}P9o)Gh#zTr+8RS<^_GZW+m1r6Q5
zu&U5jAbW-NGc#tWbcv#1hcF_Pv-xD#JvPO>dhr76F(1JbTXtXxoa<9WvZM%PG7XsO
z?eM%KuY$)3!OfCs(mB2J=#?11lkBAk>nA@y5-=*uuz2@~>`qi1AHYEd9yA@NUX`A5
zBRp#2G4NhN)6YYh<#I^>^t)?qGAj0|`%^ShF_DKD1mNTa<OJ-9+*khOi66<FcTC%b
zq$}f?*o6e<A}lt8O9poQS<k_siMg4eVdWsBh0P>ZF|bFZG7514N!@rKx(>3G-zzv;
zG4An$2VZznyj&u+ciQm1Q;18mrcbYa`<8(~>p7jGtnpx$ZeNI1JhzZ7Jk*4J7z8$Y
zH-FwdRz^|4=~05=l$%knuek)&S8SIV;83L@OS2GfasgmHNz1gm(nk9&M2Ndd=x+Uv
zE&Mh>8iiap*>FG(5)6saMefD9Co)@W{vGV0XwR4n26yMEd7mu>0^_BhhF-h1Dev*)
zk^1^d>$39`!{}Syb~L;6-W>A#nYZx^0M?B2^E*eJ59$b{Hl;cXonKXMnwpYA8J&6l
z{IAwlke#x3-<z6Tm^)<b8c|LA$bZ^DuO}1_G1t0zVTR$u$njkcTe^(5k+<^+sd)&i
zGCfkh&YU@Y7Azg<vm1$ggMH*)y{7YHv{dj;a@95n6(Kl<pQDT$yZ)1=-?<YG11S~x
zFZ2%<H-cv!8f9RRx9ui4C!T(x#kJG~JQ|O(7W4SyXU^Px{CF>l?+6C#>fXKujG+=R
zcv(%Wmzo{E?B>Y4@ikPB$C^~!Web|1>vPMqAjq5prpWt2Zoj4hp>pocs*JJc$vj3z
zzOYvukYJ^l(mFKLNZRNieI+21$gNrn9KtW0JS3q4&|@zfg%0M{&st0SDE1dJaZPao
zU$SlCW{V)Hlglt22)HR3qAL|0&rp6?*kXS0-@5|QK}Q<m=%)L2zQx!P$Rb=n2&W)r
zq1e!xRB?t?nrkOvBgZeBJa4@Dw2|W^5^S-fcF(RNU<vE#r^qmQa{KmtkUB!ysX-Ed
zr_caDXe9#-q>TUB+t%!|Spt6Oi0Qg*2M=Of@D;?jArQ$aI(E7c%o(?Ak=fVd^qDiA
zPE`TJNe}x0fCOv-&IN&;x%kS8r^EE$vL6CmwMc5{&Cy@&H-(ADEHPgFA1#0lJPiB~
z*u4K1KWOT1i}JsHtQ<|hNj4v%1IP==iTrZ`j4WhW`D}(s_5q34GLkw@O=s2W)dUf<
zb?=4EmA5pPy1R=#`-F0-d?#By6}KjX++-#XRNpCG*ppJ&b;l6ZW1y{EQnZT51JgIL
zWP%8a=H}YPi#-ePl$79@x}Sb~o(~}e@F}Qf+i%Cnb0}$GKxp^AO@ZXFv1uR(d2W#$
zKL?q}CsUxS+$qo6ZI;~N*uQ_IcT;U#aN)`D-gW5ph^ry)ubH(h{rRMi-unD3BXvX=
z%jwEMvgtu31JrUQIymFx_DPq0TpkJwMWKkk=`4fXM2n7~X8QDID%XK}za2#e4v!H2
zvKZ?FWnB3MH0<(zeay5zzk3%o+aq84USqwy$Uw?csLx_z@OHJB)9gD%rsr>tFBsxz
zr4xiAlthHCxbC~}%e*i?k(L&vQr+y6A{muev=G*c!63o(RX_G!jt~cP&ZTUVEAR%|
zICt(`Y^)<AYq!j%?e*BR8ch?uJAz-@OCIjroWRXYoEke>?d-}M4enF~cSd>I(cmnY
zzalSK{l}kt8nTz>U$0=S9PkG`pWl}xU$CSuCpUy0)B=&ABV&pczYR(nawQYK4udCE
zt&5@>#GjOCzC_t#1vM51Trl&3FWdX~o$qB44bjk$A%P#r=$XHnFXewx%&_UVmK9mo
z{4<##-LS!=cH-;ioBLvYEBXYC-E8xM)AjlD=QnRymV@{rbY;=GC)hE-?CN`kQE?{N
zS~|ScX9O>9G9iV6i$*VZawVk&X_?N6DLfif^bih{UBQPSe87+;?<OCT(wD;QUZfxQ
z=SzJTzeghs4LRLvpN3Ikv4SeZq5?x!g)NmBxYbtFIU9cH2xR1<EzpcdnltEW+v8#C
zeS*f@*y^ZYZZY&*tqF8?uz}~i&JlZJVi4deruPrY4)_%vKjj3oRWznHlPB}*CN-*;
z^a&Mte>ZAnnu>AU3XK3jd)AwX$JH(MvJV-xTsi~<kQ+Zl2MiHQe>cx(m@#8nvwvB~
z>9c1&z8H@U8=tTTkeEfv3+T=m7-WS&lw7a~O3PyQ?0x7Msg%sG>qP2(RcrhB?j3<$
zV&*V(iQePs4XC{6bDX-q%FHzI9wR1SAV2g1AO*JPwBOJdjA<t=atcxT9KK(F`oOq%
zRy90r5HSilWL1st(N5+uVg<4UdeGi|SS$mY0pGU~YO)h@N2xjNAm0+z9TLE1QtT%F
z^%)p8jGp5Y*oW;1g_M$R?d&C`gaYerZfTjgxu3o2*VN&e(XG${4ei@SHZ)ssAe3DI
zeqp!9fkiXS*wmz7R<gOdCIae!kKlL$ZW9a-NES42fx97_@7p&Ure%tWtLiRHTg%D_
z7UsN|DW}<m!?s4sW3An<vwiwyq)66ip?2ZiG{(PT$vS#?I5=8FW>+Vcw%S+zF7BtV
zj&a9^n_cJ24?jp+@TgfZ;A(i<l`HCp9=d6>^H0`6EU&g1=njOC)*3&8C11owsOdzy
z!c8hUZP{aU9KR5{TmVJPLcqNbjoTc+A7x>9avxrPcQKhHdA5A+h$nxxXvm^k#L7kT
z>pfxtgwZ{0Khc*h`-fRthR}N7qI9G0A2#=V-MK|RL7N^m_y#}<96YGeQzfj6x>&o+
zLF0L4-S_J!`FJQX_;iIFV)b+(v5>7rws#Q5Rd6eS9YZGM9*rnSJ-L*S>^*Vk!sCF&
zIe%I-9`?>*7l@0C3%zY<BB(HLn+BgWW~S9K$D)R(%{QTyJq)5lKx}x9q)^+bl{Sdi
zUDe>ZP5NHdLwQj%xE$m-Y-H%d1?EH5Bdhsnh#$7YN|<L0y@uv{jv4ra#>h*WM-`jq
ztp8Fs8FCQh!*}e6qPDaequ{#$+`JA(nWzzLAMMa9Nb3*=kUkw<wwaXxk~cb^TX<D^
zM{DX{uRS(Zw`6#ev@`f2m}w1X`wP%4G{ZNuQ}_(ux`jn$E34_a+Wl&eAm{>rS<nj!
z4ZQX=SpjA3dUm&!$-2HV@z`YWZf@R;{A+7K5~rj_jgc33=G?jUY>2)!mA}0tUk(zF
zDgr{!-z*SOcvZSrXB+t;b8t{sy*HHzlj|>RwBzVK$$6x+@cV#kM-+6h9)QrSWIQdq
zx6B9A6&@plU5!N|>Zl#+3#gF>f``>}1K=0QZSpJcGiDIxSYxgb6>`Zi<KPHQn{@c*
zy?ej&cOXh?J)U%2XZq^kj=;O=Rw=Q|smFXp&HiRhmm{|MTSi)JQZUmPy6{T(fkAeC
zRPbd@d?b_Yo|1NN=370H!Jv%~u*y2M+_1js=^vB;wBjLK^cfl8lo_rp4eBIBpWOL!
zG|rg0It=wKTh2%xN=!;d_)|_&dskCgeR&xf8D?Dso|-~D_#=As2Tz|CzmkzYB~#!{
zKYL{CM#gafB_2L_z}nR=?wUcvbUaGtGG~bZlFou%K_jc*OS;tVzTea3O+Ou-@Zwra
zp9-^({gY?{DKez*THarj;q!Mqjv|s-5$Gc(caG@J6+3i=f|1rrsBNUBQxcTsn~t*8
zjXjo}oU7ODZ{tOVmWmSZ_4xU71h6@n_VBpSu`!rWINrIXkbOQsXW29YJB+V^w5RE1
zFit~V-DAm;X`@nVU-ov@XieS1Ci~!5$i-jy=cuC03(;oLM^|IV`kETxJqE@s&SY8C
z4+tx)0z7Y^Nk$xg(d(Its%k4J*0(s-h(eMpqdQFgvB3~1Rr1vV?RR2!vl!q_-FNQK
z;lZEm)e8SrOQG$-e0BWz8WbiKC%*OiI~PYI4PC<1q*`>VxAZmLjF<`RjNHyV0Fl*D
zY2Tmala!+h86oE`5=j6iLN|^jIAM6O{c(i!v*i5&tFVKIn1k6tqI>`W7CLBGRR$z+
zQ?3CXL2LsPTzu{iS7b!O9i8((AHT6z?U<w8OlNcn=$^SmDu=YWy;ExV7If9Z+7^8Y
zDNBJ<NJl?EVbLNj&s+K@B!WWBZx<F?^WJG)8}$^_gG{4U%f9l_wD^byFdW~pzdBjX
zu6HXn%uDl!zd9Fq2L*L7Dn~B#p+;+*+?e%X_jW1UPC%fvY$3IiTn4NqP`G?)2RNaI
zAc=AM(r-P<KGcvayYg4G>I-EI;(VCeN_^NUIP*q3c6iq%lWm@Of1WIFGAME2);&9}
zUg-<^BQ6=b?O9l7>6r`GE?6t&D;L?LY{CxNlUJqI=BJAWg(enuDmAe?^6to(r@!o8
zw|lq*TmBgG_S&B<Ek?5zKF)c6>TGKM?_KzU_mY(&hQN*C!%JX*L!0q+P2ZRX5CZ7R
zIe0!{@nmPWi#0;Sqhc->p_s&?IE8kvMENMZ64u-32M4VSdM49YwfCZpn|rqp^x&Ys
zFEbZIJ_N|DeY|M$5G7eyOx)_n;c9Q*-YU4#-}PWM631;*>|D3=I(S_n$RttlOoHB~
zPdHs)k*>p*jUQjXTJ_UIjuvxEe^)I{WJ$}-Xl<*qlw!ZhHK-nO5Ft{oLkjw3i`JO^
zLOK8J#^$RjDQ{knn!3Zag3Hb@8`}(E)Jw(~mjp)PNdtaUe`(p78-rHLM;|=+0VvFU
z1QaIKS@wcY!*kkd>gy*giq-46z5m%qAos4=Wo`QTh3xVETrp-d3AS%WAMM{W%9`7T
zq@3sUxnz9JMI{T}4RBPGQXeuBF=STXl2gePDyL4pM{slSW4h?AJ5S|L{eI`I)5flx
ztiICW4qhmzw{S5zF?D~*>9LjmGHdj;cCRN!U7YHsuw^ZnI1B~)9y&O7cO+iC*n+sF
zWOUM_AwDwweVAsTVrJB1#CxmRL+U2A9>g`^HiR@2%g>wVx*6He2kZd;Y5ODUb(M5T
zS5nxyyUCtbs%3fub$ypyemK(|Fe((7Wzv1W4DqS#pJ^d-y6B}AmIsdz`+d00#Gxut
zI%}hX?05D{J>7IUU1y@Rk?CQ~M)1&``o!?{WR<m-Ul5U)E<Aba)UbJ3Tb(wAXq`gv
zbpO6RYQNlE7x?iRwP!k;XCK;HGV?f%a9Cdah$Xk^w~#JzH-*TS)@dZr1oMNcV*|eN
znE!QISpXD`qy}Q{vvw5OX9XpvmzQmP-2SiKU$@wQ+*3#~#reR0I}jM<s_7-KQI#y7
zLAC)`>14j!)rqk4?cKv=&bw(Yr{0~VWPhu+8O#n5Pbh^74*er5M_rt*a?D^s)bJ=K
z!>D1p-QKh{>$$(gp6s28^W-AaPcV}r1Rp@<x+Sq^3cafDmzX$G<e?Ld$s2ThJW$!a
z+GY^r=p+~FI*+dAqGEH;&8x3^L{0az?mL~wz?Y3#FV#7Mn}A@b1?YqVl&<U8<qwz-
zOun$bZ_Geb(<@ZtPz3ztNfUkRrn<!?I}A)ed)Cgz1~SOv;xJ*Z=GwKAjU(n;JWjg3
zGNy2#c!))?pEG740QVOccHJ_wXJ!AW34N6xs7Ol73)u7*11z7Jb@>r3JS!64#P*s4
zALACQ(&i56KkkH9)5bQh*(!iG(m~&4cbk4H+$3>JY)>J?1WHbJ;8`AS=Rk5YY5&pc
zQbt3wO`hhJ9C4o8L=#jpM)}!rgUg*-W$vl4f9T_j%Z@C8qdGI0qTTD+kNEyQw-=$=
z0iA&Ohxl@zAK*E>jC@Nc&vaJ%#aEI??_+`$3_Z%#<<e5pvH;#%FQ}GZnaN&q@}w1u
z94KPWb=d7uEy#c}nLe;Pg`fMyoePF}4&kA+9h6tAGG<HFsI_lw>v~OFeo23OQD;TP
zNfVc_mSaHW3oHlgRE4R0>Xh^1$JY$|-R(>~^B@Ne7Eh#VoHWzts*b__+nmDQSOBm>
zf%CTg#vYnqLAYq8vex(z6=l}cpJ?R!&EI8V8$H(hyoT%C*{|DJpHu{z3&E#T=@|q}
zH$FQ#{Q1bKwq~7JnOs`>^ZQe0hAzqn{euFI^DVo1$h<v;P(a?kzVJil(CqH>d%o`p
z1CY{hkCTo{()B?qISZ%=-S^r=$7R2bZuQ%va|yD919alV_v<S(V|*vsx%c<sZG=e5
zL|1NI_u)y*mQ^{iY)2>JENv)Yd|*(0(zFroIqb91jg4w~GO|lfKdA#dg`I@lDSAyh
zR|rDw&v#)Wbk{q~9Wt9+9V{*hq)z6I-Y{y^!Oab2NnAZ2O{^OlD=(cRpaBdVJUn!N
zd_}bU<%`Ev4{m-iYLVAfoqa=oRU!l>KkR|IsXTZ4-aSUo;!4Ezu8#MNE$7Fw?3(WO
zk*UNtSvVi`RY0xSHHmENOUEsouVXNxhJd%8#Y*R|j(c|XLO>@SpVM2PD+k}MXCRE-
zeaxD~sE$}RsqLI4+Pgku1LDB1O)WGP-lDspgn9xD%Q%4HQagBn<-QHRS7Kty`E5^_
zb}Ol#hWQbNedWlhJ0||YQ)I`u%97n55Ro`cdV+f0%<LLp4GAl<AK*41%f0hzw!ZMk
zRfF(|F{8v1+g&;n|C|Eed9<sGR4A97j)*n_vmw@>>0t<dbyV8Q{e?CXsHK@+04z>=
zwl{p`kPqZ4&ZoiRoB9d1Odi%r_pYxSGubV~B7-4u^_{wNJ0?~n>YC4?>;ZQ<K14cJ
za#QM8kNyTn?@u~X^Un7dekYiQm!@%NQSW1pot8#QTJz|m5b7}`gcwkF6XkacTtZjf
z_UF$8=iN{iKnIXc;*!#B&Bc9YbUB1K5+oK6yyBgX0SXscSyTXQHv;mDt(j=!M*oQf
zTVlG5y^dWNa!it`3Cb@XTI`4K{O=U|qh~RpY;3e`EN^gGvoh*PTwM4IJ!}$J(5`c@
z$<K8=&@JAjastewh_H5c6rX&JUlp*jTenz3YwYX3?u({A*o<0v;!}b``tjr8J8n*u
z>rprKYgv+2iMrc-Er&qWp4(YRqzC@NkTAI=T5_ssPim`)%T2VkL)r#>a}|7j=p%yK
znkSu4U6JN;roGTdQ|;(K7cbuMsg+K!J?&E}{=9z_4JZCl=xz-lbiW<$vAyWEy~=iL
zL9a*z#;hEdo)Xjf`27M|=93{#+^DUSX?ydQC_sII_%-R_yYqqha+7zo$f%@^zPexV
zkOc=Qd8V>Un4F?<X1*FjaHeTYH?``&R~kJy>hc0XZBOXhBCp0$lZi90D@<|AbP}e#
z-8-I?mQJ3%Q{<TIS@nf)ATKR>*=Fw<AFolr!TesIx~Z(wV_eMMLP|!e`{|C3Rv!mk
zp4xI)$KZSd@=?>Q852)!My}iXG^f4DMIXssOwqcCJ{LbK8_4s7UY(qNEZ+7FI1$c@
zpFe)2npm+Wb`Khz#>VudBw<;QTkzHEdz@;9KEtEY%4#v&LMZ+E>y9eznJO2w6HS!m
zd<k?jAPK`puG;EX_lM*2+I_3zwpkkeIX5OC^dwa0YyL^Oci!`n(Y-IwG)x`KREjX|
zuydjYdne+OI)CdV7~@k4x}Qm&GS=p_5Vvs^jEbq^Dk#}4Ke6gT%TZBO<-Jqiqa{KF
zOUgZWP3REzsr#-T`z6N;D;?zhv`h&ny*wi-(FB&a9A{#jvr(PjiSPwN>sgk_RgIan
zo`oOwhm12BQ!fp7x~fAFBP`wEdX|SS{Z<2?(vEu!j1O`{I6WRVOfZT%23@Gq+=G6U
zIIlwRkI6x}TsQVpg*@+PvM0W{mSOsL*mM-0-f`%iw&H4#64W6-wX8flBL4*S+J|VA
z@<mw7`Qk%=37f-aNJa2nz<ZGYJiu^&XWfpaS9O|E%(H8SGL&gP*)2T_hh(Otcx>8a
z7SpZh&We~`cH4{GjK)|eIWSQ`7$5p&QpD|g%sN)^@~pRgIr>ebeeYcl9{6-5300?^
z-F%nUEnCKrKYCV5ajJIfGnV5#2#Ak(9e^81PLgEcA6W)08(WHYY%7}`*MMTE_UxHL
ziF|$IdH~u-H#$g5)Ielqk_GgS?)y&jeq#5NK~XJeah!L59zAu(Cwun`*9V;67!~7_
z=voj--o;IjhpQZ5Kcr{3J^rkWqQG0Rdd<*?UQyOOpLefwaza8Z{r!zMlr;gCQ*UC+
zgsd~}eV=IOoPD3to4z9nc$9;%cf`n%-<zAYcQ55qQc6!<6LE2X(pc&7DoAId&(vIU
z_fel)$kK5tfB{_s<qL>zYVwhL_B?>FFOQ`f#J>n5F9cHj>)0jifo8cK#pRSqH)~7M
z%l0oJfAQtG%l!w9+*QkIvOML%Op?3qK-1mDS2zAR%bEmoeZAs=ta+REB$(DoEkSB}
zci4U1|A)OZ59c!f+rCVzR8mP&gea*fL<tF@g%%~WFqA@zHkD|xeJj~2ijuUb(SkN*
zsSuL(WfYYtDlN96EYIs|e#_L{|3A<19QS?9G52p0zSnhquJ>}j&+~jQzI3#X!smK}
zU_k^vms}_c%K;gNSu*%6rbDY&l%2EF@I?>pB?-m;ic@ySTDdjxHiG_)NMf|1K3K|s
z`1m(t(nm;(C>^(z9PBpGKrr2|_@psNgpw_Pq(f>%BQFm{iE_G`;xiATb0e=CF&}U{
zOo>@uH4ddA=9s#6tr>)J)zmi&Gr|1F6FXb-jxTclVEs%uKd(4%Y`m~JF$?VwRm!VU
z^TKr2T|z7nwg1czjd=F@p&rfbDE|vl;!VFl{9;!-@urotVO(5T*g_|#2~dOU-%ixs
zU}fQ4;U3xC5)o(hhu>?jG=cRG6s4mxo?-2vAWg}Q^;O}gPI(gY@uV?cRxz%zkGsxf
z0z4P-07}P$2dP+%A_tyJbN+=D)sg`1wzg|f(&R)N4iZrZ73{iepQ48X;392^c5oeI
zx5KwniiKG%5*(J}@CNoQQfJX2{AO#4Oym@0*8?KDiA=qd?U?zKQfdKuB8@Un87}Jo
zn<MUK^!9L@zyV{bjeA_~5|mxj(7<fTx3)s$F;K<O5hPam#b+m9U&E6RC&ko_Tfru0
z0tmI@Vg13Q?kq~BbDDhoflw-D?LVh3(wD!D5eEC%iLiZIw@UT<&2q}2#*S)kd+jDo
zI?fqj{;|C@`Ou+-yrsMigKs2<eL9cBgPXfMTD`O2tl4MbVt|CJ@42~96OT)w_~T=?
z@YaEg+cTUbw6rzXS-Z@C&!vNdq)dwrZWvBnns}kGgZQ;LzgGCIaxyaJJ|<yX1izjh
zvYIa`oLK^uGG!T`n4Sk3HJzx+Clv(p^HW?bX`JXRf-gp{xGwB5;of?w;kk$$g1HAy
zwNh~|57!LTT)3I_Bh+gZb7be{gSntV>Zh~xA>-2gT}xdjDiysLVYxGQ7VCF0D%g^)
zdb~L1;_9Aj4!{p_IiNY7K!=ICc><_Pw}$?R|3e((2{1=|*A(t@`mgwD|9*SS>sdHM
z2=q31PEZj}+0hw;TU9!@TF9TaKQE!5hZ=OS@+Pp@6g_1BzO$;3QsiHk2{C74`4n#l
z_~Dk81-vGL%+=Mkfz-cu;HjhU6C;@oEP=VoqkQ#Y>Cp7*H6x<fnyN$Yq~pS7rgQtP
zOs7fql(TRO$r+RsaJg!?ySl79Lgs)KlB0GOB0nX*TmKKBeRrdTEWkbHW-r#1B>|w|
z9d>!w&h>{+?;%$(s5CJV-;paQC=p$fF2XjAt5=F2AVIf;bR(xa(oREFV;UXM#V3|x
z^b?_>l#j32?H-(Io#JAj0e3an>c#Eb-Mes@8Gu~E{}?R4<F+jxR`C+S<&E5{8@mQf
zPPoUuAbNkR(`Qc|3lL|;m(YVgOq`D0bj6o=Iv)16;{wf;yHD-@U8+?+n>O)sVvhd}
z-udANVSDz#n0*BFPe-M6<*VnEj1SkshRId5dxVgb9>H{&|K;0^4LCvCa-N(zw}EI>
zg?xt!h|IXHV>eFi0}=!C%boJk%zsEKf($%2H+(q@hWri0g8cmtMaA8z1b=P&oZaK$
znNCi9gYwEfpQrD$I(j%a7NCKeb~e}p0u|afdM|7nn{Iph;7w%?Vm4@EV3K26MEW4{
zeL<94pqPW^+Z)DV|3G{4J1i5Zem674+_J?}o|Go#>dEH~7Pcb^UajvdDtap@Sg+oH
zbQFd-QP?SH?VA!1(CO)pfv_$Am@{&y+LZilus+Je#73yAo9HGUh>fKQ2?;5JHo;6H
z?v5Y!)PPvgQ;y~I`9MVo*F@lm5lPUTpj^RhLJ}<xR3_8Hq0%Cpmpb+kZc-X_tJ=hN
zDSkT)t{q-k1{)18br8*&CuYIv1aXE~KljxDHTXJ;iWqhZ5`j~`Cy!hb<-UTm&#&Jl
zr(^Z%-B!nADT87%Fv<;xO;8^?H2$sotcEb}DuVtVs{=ajv)P(ZBYx!gakdr39~~?R
z$}S&~*g0U_<2!dkr7k-sUpjK6eUrCx`gOrUJV?R!&^<R^6g+p#zntSPjd8u%n<LNL
z!0~^$2IKw(DJ~*dXaOdI|2T9ul#f)u&}`sHg=dVJwYw_KROue*ZFtlZVt@RoS6*q5
zwH9g0Qf-h%nWf#jbB9FF{EMFJBOpJOjKt96H*oBOA>Xlm`*VNXh|ky!f~z}v^!E#0
zJ*ED{zz<7l1;6H=MOWz2Ir9X5=+yvkA3k)+8fX&#ndik`rXvsDvUD4*?6NOY!&dba
z2^z3aIi2l}IaS*-sg01BZ}9e(I`D`#4M>bT4h3H7<Hzv$ZcyNfufw7LK=L+K9;x>B
zORMFO%!MAG{>=sGJ)cW{ImhoQM?G@ss=GrpQzC((de<LZk>=>~tjq8+EN-luHqenz
z-ms3!3Kj~9FC;ivvA1$mVQH3M7PS@%LL9VHE|9+Z%F8#i#&RgzJul1P7iRK=pv{X#
ziW}N{JNw`m+AyCdj8Q=_q8kJLspI}Q-`;e2!!>4S-R1Q(opXX2Mn+_aMJQvf6W{a<
zxrxp&_Jx0;cqLwD5n(xn#MVn^CNT;BO9mX&t^Wl;v%{_!quN1JrbC<-XE@cuQPklR
zJ*{w(&dZuk-103paT}cH3EDBH-EoKP*iFtf;ojbn3!dLU-mb$kTWRVtlm@+<y4fD;
zr;_47%~*PJySI1mAPoYEC#SQ&FgUn#?nhf2o0qR&yDnU4oH+HI)CTs^lJy|3o1E%0
zN{Ws&q<Z?G-#e1TP)m;)JzAjS$~p8AnUd#H0Cpd|MVe5ds|8hScsP=PvFkp@VxH5v
zJsJ=NQV|?*3>4m7hMOG_7zi7Rjkrn~TWVp_#pAoZbSZXPI|8@hGDwUQZVGZ0ukqGX
zr}B!(9GLd$!SOrPnW7sV8Un4+g8$$m3w-tZGNKh9CW{v*$@S^%@WTf#y6xGIXCcSl
z{?u~Xb(47P2eZiM5&B1Yb0Q}hI~2+4i`fr9hQ`We6hrg;r#kBDCrRABC0v=9<=?Vq
z$}cwwbX;!i>Z&_NZPjnEzqsztgP;5+{O<neSi8W5h`LkBiVoPa*a6{W;v(vH^cfS~
zckh4@j)38yl&tOamgUEZb;;lW+UG=0f0A?PDX~u2WA*6nU6fVYpweu|d-SNAgoM(u
z!u%eC+vN8tA)9g0lqEbXjeSx3dw83AZwa~sCue69v?E_&2X-iX^JeXvTm7~e+i)+D
z(UM;vfH7p$uFGDO%6bCd#<EWJPkV)oy4>SkEGs8BQJ?})vt;)TA)jGMU~F8&$I^{R
zqy&Go6?z12to=}TU^wC?8ait7vr`UZxUP!2-wKX{A2Id2@1_m-N%OB%M{oel)0Qi`
zdGj5hwdu5AF|TP5qVU9t$E-Kup30jk3|Q}1S5Cb>Ajf$nPZ-u5Q*P!vBG<n8*IJHP
zM#@Tdj4WstqFU4IC|X|b4nS)rK`60mfV@2HwB6z16I!1ZSWi=thW*g+;aSwRg}f<Y
zFUCk_gCTx`g5&Di2a;d<%bdJCfsOz4DQff`jgKV)u2UwvtdV)U4^qg5$_c*R3;cwo
zV>I*lGY}+`>bjh}$*vksAHjye^BC$xX{i8+k?F}0%=RcBD4k>jnOe@WlfGgYv1V+=
z(psiwa97m#oJ7`&n*`SL5VSZQpGvRv)sNwzhPn*!nlfdlg^J(_>9cuqU=vOjOY!dJ
zmcru`4pP$@C8NocD*=UdbozvxXVAgMQBh}6IclG`WK{an6mY$YgB4(3fOsGHCc;u$
znyNFi>*g=dmb(QHXN}thN6IeBybWJJhAa(%K+yDHVo9gG8r%?F%)FoiZ7<4=&!|Fp
zf+7I+VQW)moG73p0hts)GtR3^Ibz=HsoM$Ny7yXaDu8B5fCVPt8Ta!XOn~HYF^m&@
z94PcS(6~dMOwW13AoKvDIlu(~H9%aY+4}KKmM->-xPy#F-4>1|95hWeJ$AglzFy@I
zd#>s+qYzG@%HYA_&s?^K#`X%gSPdRHs}MHDS}Fpi<zCL=Z7NcoRa#zBIAEg9h?`0a
zrWmuN1-?zLpc#z#W~tl4Tfou{i!j>|0)}#d)`ogF=L}(01hVywh>GRptZr4oKy{&8
z7nTKAFWbF$?=A(Sg9R=yNT$XamLi^~%b^(M2jC_UKjQ?KS^xR79gZy&&&-tWCPtDG
zSo0_6bm!JBdCi4lA?CQtu)b6IUKkAxHwxwTiNr(}8V9_@e+1*a;O1+X49H@65gony
z({p4Jiz(zQ?p%zO8w29=<+0v~sQ&cn@$vLza10mUiXL>uE5=dE(<o0^B<;>a!x!V$
zEe%!Gj=6n0x5vAMj&tJjCs()p1^`4J{{Weu%cb0PIk>RC>K+p*kEl&D%#^UErmE_=
zjb*^W{Hau0ABlkc{l*BbAeZPb2t~<WFeQ-oj_uA`pF?7O69x_H)-43Fu$8Bg>c`@1
zkq`}0O7UliAtIhQA9@Bo2%x-wh8l?*VbuQC23fe**lDv78&`-$w`12cI2aM-FnxM5
zVOzU$isbu4<K6QI>3>raOwjo3?4d?`Vt;mFyA4Y^Ny@&2Kg}({<6iVz7U~mvLdCCI
zRH=fc!1D|iIesLu7JU5pthHL;nzc46Z@X5-dBthmqZi{UK!SUd1k>n>Vz1p+43A*@
z;t&gPaN)w*sJ6B()$SY@0T!(q7U=XRZ)8J#eb{jG>&GwJY0!qPU9kdh+!v{fdrUum
z_blcS_lWXS&ULBiq%m~pgl)?hjTCiM6u)RD-Al$Vyo;^UX>m10QJ>9^op+<qp^|yv
zragKzrZqa}WFzZ4X&;AUi)8nA#O*A&UJhWwPGPDYl^EX%f&0O2v>_O}?2+pd4R|B3
z@6~?a2}bWbU<U(8@7c2_Ja0WDeu`xZvVfo<>wTj-G_7|YwT}*`gzB75SddikZjwA;
zyx>aLwj5Vtx9!reXASA?3kwKWd&Ul!0fk4`9T?@h9XJ4Z68V7KE;GY=wv!T1wRLpJ
zJO`#taxMppOH4CO&577z$B*Pv&~8(Qc*1vJSS3s`^ZSIFT09>b=p<xt18+?)m)h#$
z(XX<LJ<hEi9*fBwPMY29I~<DsI$AOt@xWQ+&;=<<^(Rnh9>+zIQUT$V5W*-uXYtDJ
zho4J9LCo}npT&@u=zm}u^~u_G>+qZ_0^SMl>I{fXl0JUq2sbc+S(%%o<J761Kw(s0
z>cfY(e7N|6WxQKgLv%L#c#MbyikZo&<Iu~61kUeKKVC{Az{jwSXbDHf?ZWojhN`FM
z-*df3W2JN_+kQE0tO$hyvWH3bBZ(;@MP+RgDw+e<eIXFYxj95KJ8aHaruUR8z+gjX
z9)o8O9=wkGonqdbxdboLy(gF>6f^il-vs8Jg~Sz-4V2(TMf>|GDB!iSL)dsnWTBPI
z7aM01pOBF1cJDACPS*ev?fI-r6Xq5P+cD@Gp^wMt9=FENpV6x=_A;Be$|favf5z6N
z;z5scTt+c4wK&*uxvoT$Gov8pk?45v^4Mlr5OFdYAwk9AeR<`A87=vpS|ne~n@^Ir
zvtKHWwzkA*x4Vk?EbrVYnQ~eAMON`D$!ypPov0GyZG;x|*0V!bP2x2%zk2YXSCIm0
z35e>H<kq#Vk)9q4Wn~yI8}vb{M&%6~@zA_gIz?}$emQKRf{ywE^2A-cRNL$K+?ne<
zK;O$0!HU&Uh#B)UHZ*<v)(Q+lV4Z}?cb8sphSwWBXE@1Lag7@BttY1td2!4WEbPWs
zIga?s3-7kj4E^>a=K{I6+zh%Jpf1iOzgH||-9lNmfp1p*a__r&ybS<2CoA7DE_lj?
z4O^Y;(BfGewU{2A0kdV<i_EFJwmL<--1a1Fkr^+frpD;6I+mjzftMD_0nv!=`UX$$
zBRIF^?30ccb=xk{ek-ycEWLL7aRTAN<m={gUoZ@#Po+TMOwKXZ2W@~b$Arfv1lGS$
zRDG!~ruvqinGG&GP}f8Dq#<Pz0S`&%Fl2jQs`sU)j$S&Q=tEP8^T9^K9xQ7V!9s`I
z)Fik%jUBsz^X=9%1kjTR4+Vpr1rM0YphR?-J2!rOBGLdV03PxyA^|A4km~A}F>ETx
z31=le{0*BS;LoLSLFH;p?bsU8)^Nse=ml}{?6b6Xt@Q1z#l~lpCOXCYsMXXjYI1h0
zew~H+g{CYJ6EmGPD_82X_nr5Wt;>{>P<-$KfM1NgXkhmNCsFI%@+8b+)CN!P8(m>l
zIG1%JRDtp1UYeff#_~|$5ehifce`zdfZ(N|i(k4F0uVK>zX`}3=9P7TeJ5t2!#PQU
zrC&ri1n%gf8VSWGg*(HyLzLPzaJ<~nT@}UrKJo^fUyAdPr84&Vg1-j!hLfzSv<OBl
zFGuix*BtrcKPP#PYuCQ$z11T<&Q0!8`Ov%_!NJDk_J!L%B!Kl=GSp`VW^63}W9rPC
z{ZP^3>7UG)<6qx}kB9P%2RTKxS5I9{&9EtNiFa7H^eevoxu%9yf=lNNgHpgA#^D+o
zRja>6YyE!Y%Wt(!&5+c&bY2)?o$vi4mPD|)G0O+0mE<~W#T2o}>;1iiPU_->4Cn3h
zo#cwlT~dpAdl?Bsyh}>5si^Vxqa0(IeAVi)+pf`z!pkTIuZN`<DA~^>-i9JR2wniq
zC0#i-9m?IT6Yf#zeJCrNkTgP=-;on&!NLmqFh`>a2Qq%cl#Nti{KtKo=b&nXGQIgM
zrNsEi$!W`2`$V;B%=o|z=l;I2$S~?*F6x8Bb5C;`d%byY6U|9OmP4i9sX>ztmqfgK
z=uGNx^ut^CcMi9}M0wjcqeRpFEolB!$Bc<`v&9Hx*V;c}V?-Vpb;$k#c8uB^2Cr1Q
zL~LT<$UFhf-JzqlGnyuCi-v4~N|HERdqw+{m9xwac)imk0+^CTp*Si&_jC;-;VUZ&
zy6&`E#uLfEZ+#{3RsPr4EA*&EiS+DTXyFV)@PV*KlY>vV>oEP4New_+paqn(^DnI!
zG=BVmeuK>&HV_V(8tup&NE`+z12i-kcm{k6hQ_5!vMrXQrc(q2RnJOTGl0O122O}r
z+1IZFcFtogCz*M;#45cnJsREIyiA{BT3?Lp`ShsEA-yM>NyjM(u>0%RrX~@dA(V3d
z?h79F$MnCBDinVCdMddEek~3B0q_v6C(A!w)xT-SRGy;(Zh%YRqoq3@jIe}xp5b;+
zi6IC27gnj6Bv-FYD`Bj`;MX*hcJk!O?bs`%;g86woEfWG#Gc5C=JjH4>Y9+U=SMJ{
z#3--Nj8k|xfUrd*chQX*F4dWzkbjS+TCRWp={@nPle##ZYW2j4vbrX2#pTQUhsf<#
zO6xQe?RZ$&3X&4xQrIoR1==307&G@>`iT<^zFCy@nci%Be6}Y3N`|bw2I~;WTC+5)
zI)q3GcsIY478{z~4`1}9?0Y-lVXwCf(h068G8xN>_6#>FR_O6<V1?3t3#ApzT$XQ<
z4diWPWeja-A*8>tD_`XhYYTKthV*9H0->m97=G}e0}dzMJU{L39B`f2pAw1M!mA)+
zFeFyfrL(ttPBt36cg|c5nY3d#0rDVv_A_2po!AZ)PTJZJ_BgZQ$p;g~(XoW*5pb-V
z!)3q8Pni4jSYT7`-@V&3eY)wwcpH4<BBP_d5m)djAdL%QFJHQ65)qGa9Z&T+`^K?T
z0?`Rx(n;yo7=1JZm(kcjNVvD6=S8zOTX_=fit_<Jq3;9&by08PMdbQv6ej3LX*^6i
zc~WWVOd2E}SX%C)WIMswvt7H06EUQqb8Ub!uUT^igTd4`B6b-yKKTc31JE_$5Q9el
zZ+529YY%*GYUbS~Sn`o3T`<*@WMhwowRPzB?PC#B@F3}6D|T)pXE7aug{nMhbIQ$r
zc{M;kGzKi4VKEtN?~-$FuJF1LK7Ab()H#O<y1!RkEjp;Ypa+koLZ;98Sk4I~@5DV-
zbwSS;8^$fLv-9R!K->w*d!nN1ntVn?#T-273tWp^FW1WpZo3XjGGQ-mK`1Jp!^ud;
zAOJ38KyIk8>C=&??dso}hEamS((<NP1Q5g3@lx@atYWo28T9Z&v_>!^V(^!^qVQH_
z9Xd#+@azBbKtE^2WV4MXG~%8^#pfQ`ngza%ptItO2y(SCAx^^EMeeMtt>uRcVV#=e
zAn?3E6FGWx#vZu_Px5d~Y^<ZLZGiovikN!P9P-E|xHq_th2~{zO6t7fkx)J-ZW+8`
z6wAUB2lSE%pjMz#H_e#1V2si{$!y3LRN|mV@K?zzSQ<X6-lZm=SD^EeU?lNG&!xv;
zIvPbqMOxH-rF(~GewjZZZcy!U`8CgickP4qm6+%aTa^8pd^Bb{-<~Y+quGU9Lixl*
z&SuLE`Sphci!=+1eE4Fn&)U2A>tF<-^9EYQZk_m@<=$WuoN5jStj19gDypj7if>%V
zFm}l<*E<O18Nvbc^x~t#+=9$_2@p(!E&}QT2zL-~w<FhT+BCsU_nnoK?2WP&B<1|6
z5@}Di%Uy&z3(FNRqADt9F59gR4OR}--1Oh4xrpVhblEvxUHu(Do|m4ZwhZfw>v5xD
zs?D&ruu%NE^{&cV?5@(xS<S&R8H+W?5yy(uCu+~0p~f{<WcJ#TON#>L6>;EqV}%?H
zpt(XuAsBBq!&!`IarT!EA3oGFFZ<cE{%`G?W?ms(xO6n(VPF-)>oLIRjInf~%-*eY
zYzl;W6`Mx7t`zq^PrVmtYX#iUOLH9Y{{4iHhbEVH%EP%ae^DyoA*%4h%dT5Cjb9-T
zG1fy@h~n90Ql6)0-B0Xjb>WrNzFCTEb}I!s`54Aoggf?e?d91Z5qBpl&hu4wn25X*
zFlosuqZi$B!?{*TKfv1Nj<s{?_9-1dY@NAz{j=09--L6LGsOH^`OQF6vnjsqi#1Qp
zpD?UBX46trQLb~m<e2_}m$F<s$pvLkNa#`p`;VA7+?8`YOQG1~Laf|`k~W6}Y&7Pr
z+Oy|8lNIODxfd_%U+!_TT0^Gm8uNQ{3k~C}eIE9)IQ?ksklqqp=gH$ms{ZAAOC7Mu
z)ZtA*eYtnL`IhSNghQ2k>Mk5oGF}lJy!FhaRDHGU7Q)YdXw&OckENF#tmM|*rZM}|
zV{KmCfTJUhD+KBx4KSH*@j9*%u#&hTbdB2D!iKh_ffE&ap38T=xqB!@i(1bEdJ~?9
zZrn5;n~ZU-J97>=jGs`9w}<K6LmzrT_PDZW;>mtXo_tsSZgcAKsNx|hbAlK3I<ev5
zZ)IL-`C*wJ-Y16X?MlckOKidC6Y9+H++5A1xz`hQ6!T2xZCyS?rmARp;iNK$M|uy}
zK6?CE0QPf&d(L>i@~D_^c3j1C#dq3=t%e`}t$69X#AEqyZQ}cGcDogmF-RPP#X5E|
zVgJIY=Unl^0a?Lg&AjIKub&Tw=Os&YlIm=~G$^L1&(h1&7mGb|7KON;7$~Q&q~7_V
zt!h?fg{G&`q!a6!4Lz-U?(4m$Zm>y@{MHTU_G`)KfjpZXe}JdL{gYd6P()DMFd5*6
z&(+O#8y1W74S5eb8jsCu=e4se8R2-U{oZQR7gyG?(e^PBD`tSmW3XX!({i=DBP=zV
zPBWs*qlYAorHr#}{gOU$Yum8){w8H0B5((kl$8s{H?{>-jvP94E(RIG;C9jF*1iLq
z<C=Hs?W(M-yc4Z8alrxsLa4ZXbk+s>YziaZ+>+|~UBWGh#@b#L7WA-0g%g)P_v*ZQ
zzIgtpuOwQ~U)6DGPuIu&p{#%B_U-4SXi`+4gIez_-bsCpn<$o70|v{r^<c8!8kO+~
z^WmY{B_-*+?G+gxw~yDbaL&D?qkv0_0d~AsH@Bl5P;*$|VW{oc(n-oKO6A5%`Sm;Y
z(G`#~$Ld{e>*2j2-$YGubH@pEr~TO$k@ff_LgG)t2D81x@gehCJx6UwZrf>%!*gGC
z>7_~%z<@pTXwV;c>O!Kvv?4zCz-j3P?`hWYBa!UVWyuqbsgp(5*C>8gP}^L7DW}7+
zoJpGzpI$dFZ!Nd3={9<^K^S}P;J1~L5ALq}7U(gq{L~70R;*(|1^@GG^Yqr)gOhEB
zKs7i@`2r8n$!@xnDmah%6Q3L)VQ|sz{YF*5^s@O7v$)>+@>3?})i-0uuDOX;jG{GV
zTve;3b;tEh%M~}Lk3WS4HgiP4(zbC^B?6rwM%iCk>j@U<>zmnp=8fM(%XKFgyWw+!
zxRO4L8tO^4l}Egdz!;$~WgY4eoRV%^dGPQeB3^y`Xb4=$sDD~OyHQ=+?;oTn)p_9f
z4S2C3KRB^ycyH}qm091UqYC##$Jk@Xf`p58P?F19=R~cI83>cl<5sj5pi88Y+0GJ&
zn+x>jIXJK@^RYl?M7>%*KqV~4Q$6cKr|T=zsc$%qv~MnP?LD)8^KTy4MJj@QUI<3W
z#Bge-I?D-eO+}~c3EdRE#D+K?FS*k-<3jU+eL?41-*-{$<wn*VP*VJ?-vnM-mJB5q
zdqf*FSN2v2bRzqrml8mrojX0&_SJfqcec2il>{m0bN3!JQIrxg9dkRT3UFjLmxb;%
zzSb~pf>?3=$)qHen7f~P>$gqYXBzlgO3Lk4R<DZNUJjDk3}J`XOnLL+!_*6oQ*UQk
zs9auI9+-2+;o_Mf>Qt}wL(WIZ_Pato-$F|Rn$$AYP+n0~(4ofjc6iM*vd#;?w$c|b
z6!sSR^iO*6VMIjDNq};!m6cmx<Wb`>7N2rKX4oFRC^kPA;k@0Wb7!1GwobPmYWTUX
zzjRgO)ygsal=Z`!-`A`=)_F;RnxeFbF$l{wZ^s$M#l?;E3v#)#-C9MOz88UfBYd|j
zYo|_oHq0pK^Bl#`){38vp1ECYpEd8)gvn#JygzV&UC}`Q_Zd~w9Sn9I7Srsew<~Jz
z-sgO%z|{;nB1=6FHQeVt5QT=GNlI!~-C(C7vrR>{Z_Y)7Nyoa9<*JS@7d4D4>AF7J
z_{;Ai@XM+CCwc}>%(AuJ9Vye?rL$N&;TLZ%*|4eC_qrLO+a#ZXWPe(@>cqL1YEok2
z#$uhDTiUbnEGKfsAEk?2_8+VYOXxLJYp_&j0mds$OZdEMi^^=-0jBMRzspY(Yrk3S
zuWuCFa(k+n%F4<SM)~9a^(TM-@{lQFD#_QY6qWvmudQAtt|%I}u4%%@E&u*u|NT~D
zC%)Lnyi?Er;cJIh^%AozNh|E()#JaP<3Haj!55P>#|C%)AHH@VM$F>X?Rmao8~=U@
z|N2&&XfX@tfO`{6|A((tm9#gOUiYzfTgh+#`9=S^6`QZ~#bG<UD~bQ}YsQtTViA{C
zMJZGa{N=_8f44VZv~yZ5)$@P&+SoDe!g3B=X;%FDpI`Lf+jK~iFG?hA3;rLzb~mld
zW|fa6uREo6694Cy1Nh?qH;?jQsPw^qa{>PMvHpMaSpWA?{_mswzYuKOa%!_zI;uz`
zD+;%$S13>jZzq}Es@!k0=|7W@-)}+yHo37fw(vEwD-1w-7s`X=07jGesh3RR&xR}s
zHa!gbLgzr`L6ZjYjkP0~2QimsB|w?pw9Fp6%6$y8XvB*pSvAFv;Y&!&AprukoT#dB
z=vm26V%UgBB{erd00zC@2nkVVKw60@+MDs)u5t|-u(l~3jd%2g$N+X0v*#P%MSpVc
z+$?o3j6<8AY->IOOh%uZuiwNnadtIKeodhTyq9_GnE991U?{nB*R0Xmk*icWbx3av
zMsJ!Uv=1+W@W>)@mBlHbl5EUvYhc6l?hPZFjA%c=6q?dr%KwtRwk)4U*57IYb&4y-
zAT${z2GrZ9zT?e9<a8j`Fl3v8?4IExj7<Se1nQkXcdn(3eTwBPJ-lFra`^rGamz~d
z7_2a*p{W6}2GoKa#=4fu*RNNmIVzpD5FALsgs~(S(2JX!5!B-+gC{CJ)eK<RI-KfK
z5Ft!eA#DJ(d+5dlk66P13H}`a$tGl1raRnAc<20k=~BcuFZioaGuW4GV-?_)Rzhnc
zFg)P4u$}`BQZLmhvPQn?g2#HeGJ_L(q^XYbqZjSO?ut<X78I}}j*L>2*#QuXCDQCu
z_6W0``91FL<Gd>JMZMI}(K5B#L?;BN?x6OP`)E9n;qW(Ms{gUbjJYx!iz@y?AaShu
z^ztSCg|Rp|&tvzYo}M><jWdzcLc0!m8bUL!0JBd!_LG*brLhzCG0ms^=38*Hz>Mb|
zKi_7r>eT(`s5DVTvZJh4V*{%L*`7t83Vde72V)w8RW7#i@M+;WdeWytqex+4GYowH
zGkLf+psIyz!M|Nb!ZMrnt~Dj+rNpnb-2fFzo{3@sCQgumVErV{Qisv?=nr0#Cp<-(
zA$<&80n-=)F(%~!VPn4c*bXzL>9B&i*NiJ&oSjqX)3~?v6}8^!JWNXWP27F}Q1HWy
z^>wPkQAL50l%#>hm1?Br(HXEn&NGpPvkp$|@9&R;Z!s&|>1_dV7!Lyq)2*dMW-#g-
zIr2_kULF?yc#v@xQEJ$-%_F7=CsvAnS$!`T`ng4ryIGspJ!qoKp}&Z<5JsvW{n1x?
zJNy@WrZ)_8qNk{`nNiz~oyy1Aw@JT^B`7Lo#={WvT7mg`jtL)o;^fJ(8|v{I9~xjX
z-PV@*LK8hz@|j7z?clsb2;^-Heu9D~F`%3LdpCjz4+icX5~y7w(V!IgiIvzBqn3@g
zL6~R`66Xc|W7uqAU|n4tS>W=e>fY}R9C?#X*K^+(R>R*9Gl|FB4ReawyX@FLisc8b
z?l<})W(aqu9yC}#3e62{DEO<w>UFNG_QyUav>c#S+-_#|4h;=<XBP@XeEgAMjWu%0
z_8y!jA=mtCOJJ-e6z=6;+MKcB!&8?S!u)~d16i!lX$i?IXS%x(W~;W`RL0v_E#T+S
zX7>GSzd$Dj8%(_({v|iSQEt6Djm{5MtDq|2*r9xbUJ}oPc#+)psSPuB)`D|^*A`BR
z)vE!(&snfio)!srCk6?94ot%ep>y}{d!--2egYK0SR2AbKd=B8l}C<k)sln~T8hk*
z^M@@b3(SLy-~7dtgx|%0O6eIhBs^gl59~lpD1aA*h0}eZ)AHVO&;&NNhJ?~H&|G>z
zcy#EIa1<~Y7}_|K`5XvN*dZv;DA+gBsjok|w=*Jil-azp=@}V7*7;9}e1=OOVmO7m
zD+|8fphq{$R**5^M;#;LqAmXL0UzP1B~8GjMlJQd_E_m?X^D31P+lzZS)6RAAuSTN
zEI^8b6nZFg-KT@Bd1CtuHnLhOD`8j>K-Kq*g&l-aOX(DB7OtILVg^Hpio#ycIC0hb
z*LEkf3#n~DZoYFehA8L})d!2h?LtJNw~tTt4={NPxdI;R(TA$L%1L&NaIo#DethZ~
z4Q!Y5mbYaBotXH*VVMn^l6PYF($_WK%sv2(_wLE5Qsw=l<JQ*HWPudXMKFkuzo{w7
zdXBkQ)}G>I;@JT0E#9M`pOnay+0OuCErW6*E7nk<vo+8o!wl@uvEyT=K4lIOInK$^
zcPi0s0jE@vB2B%EBOy)UYj@X8yC7+euvAckomKmw%DsN?<l({gVRkr~8T4#ghOZRg
z@d8BxlYpjg%=DQ@TOWT=5FzXOsiGi~4~^*vih(ZOyQ>}?rmtVje$Hvfk(7Mp9u$rE
z)7%ougq++`PtU2dZwuR}FiF7gN<VJ6B^W1rjZ&H6^XC@h$2AT8XQJFCG_unJ5w9^Z
zEV6Qz&%<U%)%qYWIKw;8do&3JZ<C9wiD0Zb8@=xqG1_&}qKGytL!Lc?71T?lKt{N%
zOc|WhhbeeyC?Uh$Qo3BP^-WQKB01yMgh@RZqL}Q1e8XtuFvpA$6Co1bx0;%jA)@`d
zuV0yV&Y3yWfg#G;wYs~?8SRk^IZy-FZ#pAy$?yS=Bupp-nE7L(#zK?GfMp(H{vL_~
zCjL!toRb?N;Xn%}){+6?*4{ld0hOt$YGuJiD{Jd@t5!icf;85%iPUowj)==(&hIoh
zznV_s+pZm&aRT-w?iImxJP6*$zsRF#s)tNE;VcXLbsxAHF}qh}0VDA3A`zUu!HXyE
zQhBpN4=qw;>YoRF6!d;=djEwad~Gw^J(AaE2M!>RqV_Ks>^@p0nqax(O&A%;a>$Tk
zCg%tD?tOzCHr@ta+FB&l&Z|8Bh#(4K7jXH?m6=0&v%`YvgK|62at0XTvnb=nuYA>h
z&>q*(n}4u<CxytF#oJ)k2t6meyauZP<|4@kvbhn;j03bn^O)L&)g6K7Z)<4)xQ<`-
zuKr`D+1l>0I?DLy`IU9nUk*xGyuzvqRvr@wiGWd*P*4w+D~V#5uJ!MK^jwC#rH0H7
z_oYiOIgZf!Jjg+5MTcK&uzww`+QBQKVZ`dMx~ow`O_ZOSgZdpk1ZfPb3#uOUwn5EF
zgv*xN!jY04w-vZd+pjH(cJs8A{$2J98=F*)69Wm8J1SN)X(KzM7eaCYn}b1H#bQPH
zixdj0$Ie3$Mx104x<ohK$Fjtu_lX_Ma4@`JN^fpz%I*gSqFS;$DX&!3)Fw}TuC6E|
zyg(O$zk<~=st$DK_heplzb!p^yyCZ^3#7;N?=a$5Q023y0B;PjM$LJrQcXn#^FIuc
z<z!{$^;T?7?{xl$O+}Bni%|A30oxn5hk%ZZoGA@qaN*U>5F&eL+FDZ931(Ul%GgEd
z{rM$NQ+eMU8=JEza#e=nCJ4vBVzIC=ifiX>nWer4bd`AIsoVTQS+vQ=hxZPmia@P8
z{s4w9N`}e0!8jxI3CqDk0caK9AM=Es@3VRA7Oxf+%KdUFTW(V(ubedb>|9<hy`XH$
z^qTs5)2#yeZHDeqA~hOw20q)a$x>X#Zb~1r17SQlD8Ek_5=W5OdnS%4D(3E+iam6L
zvYnFccx9QFVNXSY<f<u4Y(N7xLG{o|`8FnZWc={o2eCF6jzN<K=Lkv#gq|V2Z$d(X
z-rPmGpd#2WM&<PP4GdVnynD36JOP$67P*&D{o8qz%(uMt+H2&z%MY{s{C;qu{ZMpY
zPnWT9_Uf6f|8o`CcxDhqV1k*Yg){R%Jm_Hrb2${63_Bkc7tdvV3QvG{n#rsGEHGv!
z9B<yR*aJ1{IjPIGW-xHD2e^mmM<PI}=MBcq6Ib2#7d)%b?82^QNsaTYSq~wyLLM6H
z*V@dye3a}?emsWsd+a{!EN|qQ=7sbRDybXcaA9Y9;+45WJaosgB#W$%^o3{1uwt)$
z;!fw51Hwy=e=T~f2|q|}lwg4Y0X@fFu(kA9wrpU}o|KM|2H9oj3x$AtkAWV@K7~AM
z+@$s^sH{vq)86ryV(7pD;Kp5h6$gpluD(pwLXf92ysPdC?*l~<FNMWEIr9j;apRul
z=60BRpM_-rzc=qNg3MY~xr+_z0Ven0pqzK_n-XYd;ml2^d|aua?eV83zESX{>$ybc
z@<d!RCw1Bt=rv20485PMw=2uLMtuEfHf(*Zt);(=h-=q9sF#dPppW?1caPrV$I{kb
z2qH$l%~c;i!Ys0kw=v%-+p~ZF9X@l<tBW`pt#HcV@(9#(3S_xaF2PWv_w6e_Y5NCS
zs{F@i8OZvLd3ok%knvEYG)e8=R%I2f$O3r;h&&<O+y4@(;AX(g(kwbq^|*hz_x$;S
z`OsaBWLzTgY1iLet<ROC_+~KNIpM*K)SUb-y^;+aRHRvLD)88;y3Bj!3KWRv&n>Fs
z=f2`W5R@q-@qr^_=Brv|USE`YCszLfDNiE6dD${V;#qAIRkQ+~ID10!Bd~^;uVRCG
zYcs!XxvexzM25~A$sqJ&-x1-T$8#I@i?H&Cd2#d0?H>kXK@gbK)1%h&TDr`>j<G+3
zz+2in|EQRzSvW&rgdq+IhP*(P!tf>J+Cs^Gqf{_CFnD2cWDdIm;Ew*#kCNfA>Jb^~
zY`p&33vN?bz*1fc%wNwXMMV!@RxolUF^jdP+zjF^6Ga%1G!0wR$Kov?^MiK@`Kzb<
z$(X70G-Sr;=o~OufB)*$%_i|-MXN0X+G6@nOL#~RPR>SPEGrqfefv#*1iljly=U*E
z?B2}{j-x!MFY;gDoU%__NpkEpO$}V+D9@=`I3683`TiV!xA@5kmpZ(s5VHi~0`o81
ztbxqO*&eUFT*cfH;DDJGJD~gZ+v>}ptvTteT@ud?W)cgRsG6{gRtVs>Cv>~WshTl+
zHWij2Jqiw{-s7G@tus|ULyg#6mffkTU*f4#$jMoz$<{aGInkmhur1WW*(BLv?%aEC
zSCfz-GnP_eBVnSxP`<Jaa~dv-Hk}eP!t4!g+|sqD9o`8`r_f)*8OPNQw({%Auc(^@
z{Yb{fIlJPhrzBHzW`vdfYa}A}FEGFH`;UCHYOe6M(4yMgKZTCaPqJggV&d(Lp@Xt=
z+}wG8-a^%Nbsep5MJf*s4W*OgexpQ$RC#y7GbKTOEGXRfFLv3#qwuv-R!+Wu1I#_v
zDh@LGjn)UxBUaw?CPUy{wxq7k&q^8<I7x<&$`RdWb(D}?hyyUR&KL`}vs42lAPYlu
zz&hKT`&uFX1GjMV>uGgf4_O?RQ?ai9?Vq8mtA5*skQA|eHb2}MZEf9~so*$rAyfh~
z{rU~nSsYyM4Y`)t;1ccqumP!qTrQrK-j}`7VD#u!$m|g+<m9Npn!MzI!AsnoP?3oJ
zDTjVEij-}OQj28+Gw=tw?%xFqGWvG_rhN52;X|6*cL3>-#!N!n?JoR3`}-T)CJ6Tw
z>NSf4<Nx?$GG&+VczWvlHFE`PbcELA4v-ou)w6aQqvUJ#gR<xHIKdPcVNaG#QthO8
z+i7pKaXYo2W6(<@Ga<DWTvVavT8X_%R#p}pnutf^H{jx&vfG^Moa!0x2mmu=KNPy2
zOAhX32@Xy#c6M~>MX~zePLcWRxXR>=esgaqHLJ0or&Gs{LU}uE7%`@f-eI`wAxukE
zRB~8~gg^z0s^|pOlnJqrC~$dY&W%(gY2Fo?v<a%MPxnSbJG^rFGTYghz?)B+H2Fi$
zUzFigi2G$8A|Gq{JlaD<h4IIZ1x|_be0t8(N;=E0?O^(f%Y!|wGg&H@%_CX8X3gNP
zf?8iOulHPr&1?c;I?auA*ed!c84*22_8-sPUwH1$9CFfy*|R_jU$kq+B|WpxLKs3u
zMlXjK1=~JfS61S>u&W#}lh=uz1475g;*<Ri{wlpCSPV)5jcJwnF8O{)b@x7oPRmAh
zI<DdSo=8gsP_EmhduwgGW;1)XuoT+Ta>Blxl^Bc*ySbPq(jjBdS@dp-VO(2t(<)Lb
zQ4ZvjR2(td*kI&X9NIrOG=L1C+G--^JJ>H6-e*U19j^hL=%e@CfJe#2Gd6C55;$tf
z{Uel@H!oi>8Pii_%GqGK*+Sp(E`w|S)69WhvP+&fP)m{^BM5Or%wzDA;2g|49lRKR
zK+D_Xaipb38kV)c6AYe|l*C#cWzCgObK~^xGrTnZ(NnzaFXXuC(F6caIA#`vF@O{=
zqF&Q3$S@4|1?lTOH|hg|9HdlbcTLG`Fakj?2Q75bB9dwrbh=)3hxK;hLj|5gUx6-W
zr@VeGTJ@ZWCA+0YU114s{z6S6TOFtpn<`nK^4g0ofUqEt#;8>h2l43K-QV+)gnd%%
zEy4Mrz6Xk0jE<gyoCe<HV3`1_)+1wMqRkNke=W(}6cg)Ln|-*B;(!RsZHHfu6bx*z
zSkvqDOFhA44b&E~BWVf4h!Ihf{qt5f6Y){Ya5N&7FJOy9HSddM51{u@QbHr4XSxXE
zIOI`B=Z>6fx;@8|ECHxV#YWG-p1m(vDCow7bkwuaLU1l@J0abG-EaogWTn?B#=X=V
zIAB2OkGgNvikDZx%@^tD>P!5RbQx(E38PG@q4&4LiX*vm+93O&P`rL!iB1YGGH`Wt
zH~5w?_95~1mSBbPMi4FvdMKt!Zz8oM5!?QG-hB>OET@D+E(AVm6eJ!fQcNdJ!b$WZ
zbs{f11zGn&u`A>krxw%VtcSpgS`6e5I7U~O-I(7HssP(Sjvgo@BPe+xo6<!<vII&3
zYA*b^&Fsci5bxiqNst&10IeW1lia`Y8hClt(mR9mATLKG0nNcOf6dSp@M+n_S6TTY
zef@*n+<<Efu>*msi+>W{0RluH6-*#gl!94<kvRc}?wR_T7a1)VwBo}UTG0n_$ANQs
z<%xH2T-YRAR9HwK>h|R}a14F{yiz&yaSmC4S2NU3_7xm4;~fW*YJ&`e;lhQ^<=kO}
z+Oqxn0h%Db6?}B~{1n5J5k3Y7+u<t--vXSLgK0K!b(nZ=c?~@b^ejMmpwJ-#yL_3A
zjSbBd@5%Jc8Oi@<AN)JjiiyA2#tgp0iNm?KpscQ5w@#tvlVE2=GeymwvF5$ZdUeFc
zSjT*Q5pTYeQh}0<*gg1ok#jQeP?k%9w5X;MPW9zWmzov6d^9+?UAI-Ct@y(ci+Gg}
zOTu;6%u!!w)wRzamtiXYL(au__z<IV)NQ)Di8{WR=V$gD^gVNx?&5uQ4IjR3s@!Ne
zX^s1ptkSIKm7xPy-QJh>W`E_a`p;vZ=sY=3h9eHLRS_FuMh`5xwesFHFjO#+0i&kw
zD~i_oZKR`%6MhT4nX6Z<=-jnyueTS5JMK4Dq;Y_^a)Y-*ZA!EzdUak&gatT*Kr&^-
z(~Nfop+zaCa~4c^;52xckV6^-D)UJ#&!^g)D%=SOnG$2ZNGuN?$tmHml38ejUry4(
z0%h{#Liq8Z2AmaKtKYtV51DNZj7j1zw-W#K?=xCqq<;SL1sfmJsb6XG(V~60c{Q>9
zxvm^sju{Tu7_i<kcTeBoCYV#uCSr?%?&k<XcuE&S-}u#4cY7+EH#5Q^-eSq{?f#jL
ziEQ6INga!vg&)+cSy>cQ`R*M6`y;>VWy5DEcy|?76#LshpOwX>M1H29Dwh|&_5xsK
zGJu;f@1O!r4x^38j<@1$`{>5Z<L1%^a;A|;fI5*ETZgUc-jdYPdf4loW2a2xe{%uw
znm+irHBY<s)W+pNbL=-k5XDxuP2X0-Y9-igyf58)YTVX_31aPy|MrjX2{F@G3vPA|
z*e2F_^Uwb@X9^$k#j4+QerqQs_VYiDM}@Bq9of74->&MfEByRj!dRts)17V)C4c%&
z!f$;UC4B8@x{cniziji>Ps7B*8^4YpV>9~KUnaI?fjVD{sx>M5=`Q~GeOYI?fEQm&
zjEnw$S%3ZS|Gl{XH=f+$+S(=`_O&n6^fnkce*~WE)zvvKTIa|#`uLJ*d5;L2b{ey-
zPZmMZ{^JiCrUl4Woc=UgMsEu@o@|BVV_s!l+saLL?S4I0zNa|?aW6$qb`bKZKRi6D
z$<d&Zy#@?uA*GX~$Q=BeS#z6Xh5M2vqTpbB16d#jhTLM+q9q9lFrVdBL@^||WF$Nu
z$@EWLf6Pk`96w%(H8b^+EnL)whBAj=PiW&?;dR)(JFgrfIh_qva0oU^<UT$J;}B?~
zdr3jm7S#H$-o9;$b05O$?sKWB2{uEh<_uX_7nI!;F$;Mls{<KLQFBaE3I{^yjX%ep
zhUxl%m;hm@iw1>TkOD~O-)1y@*8lZAYF26&oMY5}hZCaL5WH$=%E&?9-rguuF!&@8
zuxuPX^H7T2VZ*KvliM5xm*O5068ljQ($w*BGVfd6a!#h<*vMKvA}>_Rf#%MV*;IYZ
zLJ7jcCh7U}Ta_2HB}Qk=m<Mm`53c^RHGIIe3%|UeZGO_5Et)4TW>SYU2m?VzZt7ZE
z)Ah#Cf@ESEL~%m9*p_Rt)5(r%9`QYqe`7=?U0;s@V;}On_|034ufFyI$fgwE*jQaN
zXPPaeF^WfkdH=XqtvA1Y?(^$?=-ggBIOm05KQxsN4(^K=tBn}JF6W0OB^oniVv4}{
zpVLyc?g+Q5uxqUueqdS;Nl9GF{O%~%80{_2?t|d~)i*Qg<)xP!LhopPJv+s&+t26j
zrL`27*0Q)?_E`!A21gE4rg(5U0NAC4q=Q<fPpekFx18wywWw`koTltf%o<!>U;F7x
zC#1e)#V5kZ=xEvCoVIxPjwdC4ilc3JIw(r}wGB0P@?fH=B5gTuUJFxejAoQ_DJ)=b
z3PaDhkQ~Pm7nwCyJop26H1&Y5zWlTY$NL64$#*~ggXIudv}i|lV&!rz$=^rq<AX6F
zr_GS;SU&lgv+Rw9nh+<jX<PinDYclgh$F%AB`xAE$T*`^S<C(u_}BMn2Mb2QmMS-)
z22fA!-7DjA-8q@WO&`s33fOr3ciGu<=cXZtLsQQP&_t!Rddb!vzoeQ>6@vKWQRBa*
zpFVvX755ZXM7JD3+)}_dB^K*;52|CN_HlX$1QXbxbbZhbAj<-RkihYvI+K`a9Fwpw
z1j!~ZD9mkdcDMrr@>RsRY`RlMu|ZXd3&az{3|@GWIo+<!W&{Yd40L9+QQ$o6Zei0#
zug>kOYF<(Tu=hl;&wCy>ANs(07R95G`h0a3_ZGWqFb@7ye{HoLmEz}%;#)QsxL`z0
z$=AU5TrtW(9RS4n?aPN@(jt7dnFHcHc%DR!%YeZ*@L8b1#>PhEaFfi<fyoZbtzEqu
z*ZESG5U_BSctbl#4~d1=J4D#*T%c}gV31Y6Lo6t}ps-MIq{SNtW)1KPjSiz%xn8|y
z;=uJOagv(!Z1G=GvodF=?d}p9Uxtvh?(N05m?|}3@rXna^iZkGOcw=EVZaSq8bV3x
z`SU1a+0SD<Zx>$S)9vi?%Y_|}+&|bd%t-`}0oMd^g%WSu6jj_}0b-U>TG6KAN@l8*
z4Dpy2iN3+i^WN&QEj$DMla~Nc8I*CN<rVfysHnKm5OaX$)tLZTuVIG5r=!t8#ju*;
z?ahoSs-xA^Dyg$T*Vq#ddd0}A=j|psJ{~r8{Xs@YAg2h5gkdpWuJ|ipFf1)1NAQ>a
z5<xPk!0}c~5?^k>;azCiIU@f4IeZJ6E&d#_mq;YcUipBegqRp?U@oFhgxHOeM}^Pn
z>I!~{9xJ=DZr_weY;t110gr$cb!><yaL9~s6rgZONve@UuXkVm%SksjHWgD!?wo%y
z1I0&t{IwS^77&epm<7p&96NPt6LuZ^;*Twf_cROXEVx%)Wi%`>O02F%F-rnrruf&{
z1@@&brstsgdl4~sGP^?rnhS$?_8)nAGSu?;%f|u>3$o-!Kq$h6gTuI?LoF}8V|oGw
zpP#LVi{?8y=oIUy)p_Sm%}wPbjluP$3HE(6G#f;IXcOz1nh*fQw;W1K6EuAoNq}H5
z(o>O6Ev{xd&+CA7!)wa*Dp~dk@n(!>mai24=Xhz>h;mxNd;IvgRe4((egI!k%j3Zl
zW1bLifzA#1mtgta))T@8Sp}ectj`9Pf-OY#iZB-yHO~Yegr&=u=V|Vob{wfAHf(7e
zEO_(S+nVsM%$&*WM0&|%nHyVNe@(>3LLRQSGWI+OhhZOG3bU`W2a{*a@FI@leM8@@
z)Z;EtwV>rkM#F^2yK+8(2W>uqE25x+lMN-_QBex&KHp52&k)VGS#Y=noulXU_xCT!
z@{7yGtH9RtMdmyc6Ranc*`7FZs-l!O43Lf;+35EMg-c>0<c=wzB*be1PvgWwkRu%(
zT#>@C<Z*Xrf?s}~Vgrju)&^V;huH%ZK^uY__A)#P&D>P%K+lm3e5@00KL|02oLGXF
zTKS%ex+dOl@Z20_Ep_bbpx3O&SdaBF=$8mtCr+Qfp}Dj0HPQfqL<CAuT%4AaBzfvZ
z!|EDN1yIDxxvvy5b~|nS=`J?bwI_bWuDZQY6X$(MI=ID6Q3@xaqS;_E-k3328^4Zt
z?#R>Rz>Py2MDxic>Pu7Gdj4I_(crCbFW&C_R*ClF+*-mUmtbjO!J-rhQ9B-D1PkMA
zF&~!aO=U((a_jK0<Xu&jpiq2h>NtOXCZ-y=%P`{r3+Nh!kkX4~&b%0$n~fX4gYeXo
zoIk)K;&t^`);cha*+sKJ);V_$_lJOuGZWT}xI$BVQNY*1=@b{(ukx_Xl(Yu!!9WuJ
zSU~7lAOi4Rd;>~Knu*Ve+QB*3Po9<hDHSVzp30fZ61{gHR@c<b>Euic+#VucVw&vv
zOcFsKvzfXv2co0(7G4ztzQyKbU3?T_XUmprRG)o^+v5TpsI-z#0CkGUPrA6=qZ>L-
zG|8t<4S#p)Kv>x34PB|CFo*(Sz;(5AHft2V0+Y~AlD4oA#P6;w`=wVJW-;7e-f^tk
zbZjv3{^8rVfWK5`;fRENpd?I6YfH<XBZ96iM91?kRe4(1Gl3%+ZA0%MFs}>EA(U_`
zQ;3OVA7qO)Q^5e)yE=-cgv@FlenVHSC|z!N_U}C_|NHYP;a1pID?F}Tp-0@J#^7%3
ziHKkm><_!5N=89d#ZPGeSy4m<tV=$AT{)i;h5Ir@nhUEM77lu|di82(O%r&Sxc3zn
zvK+75)NTmnZxe{(4GI>eG9!q`H-ra7l~MAnU$@%Wg9kIwkCT5d+a@@cju&S2?;Z_9
zJIsehk#DeDDg0A#4w2#j=ILK8e29F2eyc-sc;|m$VXnE``*2z(d=Ic_?lDKjr`s>j
z*_Fz9!G*Wi#!x*`HYX%ZbeY$2TR4mE7A<;wW!-Y|Es7&Yekv=w<}!+PVPti}A>1&E
zP}2+2>vs&)Y~7%OSe=Vv_`}c^i89M;**@p<`Q;W82v7Fj=xoW3${HF|1UPpF`EACL
zJ=_j-V7^$8w-<LppN>`8gwpsclLT8^&eW3oD!oN7GB&C?I&nJX{&70vger96@e_<r
z;T7O@w~<v*BaMt+T))26JV6*9aae&sU@veONh;)A$c<Ho>Z1akfZq~BS6eG-$yvT9
z@`Khw95tZU;hsH7nv5InFbxgU^Uj*GXzr??oKXl7=Ih0f^vsriXIMqQr4+6Qy%k6C
zk>{oBybXMIx<doQnXAl8QM#-9)loke=2!hp#FT1!95@DH6Xca*Nuq~#KortdHraQS
zlx3A2qk!qNXH%Tg1*wi4`2tuJu>8%NMLw?Q*m43exb6O;9?EPv*n}@GiSo#i3ZP<6
z3>$$F_)iCFy-6Zvp|^s*mx{=AKUUrRBGa|o?L`<q;C;AZ!`N?MQcvaZ(okujIm2@R
zdEE6$-NNlm`#j(J3l7pMB$X<8;6bEz*Y4j>;XH4gz+E0UPRO@ZK$G`soH%o)(kl&J
z*IgDUL>7=WnYLWtwkSUEHS|-=3<erb-no|DII!ggAr_}A!wC^ooI{*$C>uz9N~#RE
zP$8WIL*2eTt!z1j47_A^&KPSLYx|WB=}&acbgTs~Uf_;YWP|13)>tGRJGK^9LfO2R
z-=*hY)vP{lG}(t4mrsOR*`{m1+<vjnKC`+1i|20m=0rt;pqpX~BE(#cz4?pWeBLsw
zgy}_dl;NS<Kl?1wH4rWJJ?g5ex(sGG)~uC2ci{s0lOhBw)#9g553i5VlkYCK@-l@q
zg*vR5BR<W;e`ucv;1=_P`B|FcN`cn3b@)5SO*|m_3=ndpbx5bnUL4kSAqNu7VILaI
zSUcXUy1ZO@&>$^Tmp++CDHn;%>jrd(7x3s&29UJxL;gC1%qliHP!N-~!K9ydh$_Uo
zBwY{_J3|c|{QRtj!K-r_8Jk#<Y>&5Vx$-m?8+I{jij9eJ|G_6^Hz6SO-EVAiLa+%+
zKfu6yg{f)#m?Dg@-+v1cJ0s?M<ktu&Ca%O`Ff-2l;5l__w+;4!aX45zP6o6XiJeIU
z;o(m1?$0>1m|qxNPqs@Eu*X=vaB8R_yC-bxNO<7J(XK#8Ay~D*kVq5>8Ij@*_82cH
z_+`%V0Uzg^NoLa;|F!!Ey}j9G?XK;`2ZlyPM*a@rfj2!qekIldyh++d5151ME`M&Y
z^kE{dkdGfed>KHhr6RlMc8)uQWk@?SS27AO3a~4=*kbbJk!-O8>rRWCPrt-{rn@H}
zGn7q(k3d5J3m%_!q`hFDa1p6;Y8Hkb{)AhK>6?CUYP>n$z!7f^N3JwCzX3jy?^4Uf
zfZ7HeT+dLHx}T{#-1Jo|R$O9i5B&pYo53YpLlk;z`~o#@-h5Wf)Y&Oy`FzI8$>=L-
zhv>cdRjlz4fE>~X^}W12FARQCZ~|(92@<Zw-RsVl3J5w!5)wEwTaJx1U!@a*`xqyf
zG8UZy8c8j!d%3x0=H`J@RH3xjaw~b!N+(@3cfD}_Jk94)H@E1R7;e`(BWc~37Um&D
z>VJ`4Hg2RyL(a(bU^4hK8{asM-uW8p>Vo|z8A@b20|r%cGCn9>-p!nP`~iT$`GwcS
z;Y0O~o^#5c#>pN&Gn_XDSga`*%0cc7kT*^_)HCz;;U~qHxHadKlc!Tb>gdo~-YhMh
zXJ!^)p+cF6^Rg179Z27>G1=ly)nKYbx_HkgB~DX@ay__f2xe^3BD~E?Qx{t^-F_lD
z1(z@ggg|1v6u1oGQOB^*yXBkC^ODj7;)d;h?i|J12_1USX@AlMb!9AG1*)oSK)S<9
zYwDz~Mj3*-fLzO+;M1gE)XYpJ{xYuW)?b(H(AL-h@;CU^paw(M!eOV@XPX%chNSQH
zDd*4A^tn%&BDsCHw|=8|+#Nxe%>;^;qGs>XW`}ba5;f8H8W{<8OD!#5Uob?X+`O2Y
z+O=D^;Uh=p1!ZC7$gL}3UkHYUPf@^sr-fi&^>lqe4VZe+DQP26;Kopj0w7>hQqpGu
z!**Uu3<+n`G@C2|a-<G|)W>MDC&;^Vvdt$!4US>!;aaSesBb@#+sPq(faS$09X36G
zlwES?4l4Db@b1|Y&l6<GM0!k3PA;aDMGMQSpg<=g6X~1Q@&hj#Q>}wWe%&*UnN1s?
z-r?t4-IxSqc_*d5ej*@0mMxDTt4guS&mHLA+FJPibfox(QP3%s=xNLt66nP7=S-2Y
zxPI(au1`FXzkj?>;X+LS4u6Hrmg+!~IqYnP2&{y}shVY*+3TwNW}l_Iq~J63ZPpWP
zIOQ27*U<Z6V-hY-2bYqX3M<<`Px`w@Y3BEdhH)>L>$9=fsqsoTr-?sz2EPf&!WOjw
z-TVCvg$c;MUsq$5!1sTfEc^w*8^7$)hXN(&ptqjKPe1I(Kp{A1MYmr=0n*%fVr<*p
zUOj?-Dba*-G+g%d&$m+eL0gPwk=7J8yed2UYb!2BH<PXNOCc-NvO&TqVxqNyyzb8>
zije$GoiBC#*XRG+6}8$>A^KH`g0egQ<0EXgkbLrU*&tlkRRv*i(PMngia&n=M)^-E
zQJLH?V-^0haiVaO<JAUs@BfdRET*L8_}f2!kY6H)$*4Xj+v%S}93G1M-!9?*p@-6T
z%YAd6up8_Ag$rJ3j<ZGtIysJrDsXANRcbtUywpNXS<X8d@|4iWCUtV~$yS#QMB;(n
zsmicnJFYGC$=+*p7M+bXn1GcPg!B&uJ)LA{&zrZ2=pP#^-@LVXOG}$yjF(<46-{m)
z>wBNHc`vasxzj;YvV4V}QO&F`K2KhpL&`!VVg=(8evtKuS>e|)9085r)y?eYmW%(r
z-FGMQ_{aNyd%Bdo0`SED;ftP~E$kbo@71RPg`0>aHm+@ag2M8e%-QXIzDBmcn+DtV
z8vGZuG0O<VWT3cUwl#ov^D?Ki&IZO0Am8jcbJ~tv_RExIEDdK|LE+Q;_rgjaq9L0F
zw%n=o^Zj5QhmajH1?&Ve6V86*qqf~80@r~8p8q&wmuxa=k{T;XhOOCr#`iEAZlN3#
zBFFLhs2_drTnb*6LH1;Kp$5e~O%aA#FIK<5_qLuAj+6wQ3iriwHF1;a|GoIneT44l
z+S_|`Ffs%h2bQJvqjQHyaf)#_jmE))&%vm%rw20-C{4x1#R;z#9#!bYqZF)mVdBxC
zTd3RzYbh@;_jAs+XCeVF3N#J54o({+dx#@`NjKZh>TJ6f92&ZA?OH4m@f)DfSkEBz
zNu>Gu^-Totw$|^<)%RE_O0mP#&tM@&QA`THH8!%n4@Yi&{WO71H}O%~dj*-7HQrPY
zlsJskVaN$f`yi`iwQkGr@u_ZHS3VqB3WH8o6&v?`$E9ubet-VrMaZPi)MQ|1(0aZ!
zG@vnQxxL})qQBje5MJS|p4EP*Z&%g{q|%o!4<#j~FMV{<-`}5<P9h@iqN^*obt{Qm
zOHax8-ru6x=(X>oaWXp^0K4g%7^eq|L@o6ej&tTjg@<E!nMs+*9#OwR(#Rk9KM)`M
zLTrZYK4|)iP6gp5(gv<EPF6%W6d4<v&LLUQR|N3Dki^d_=F6GO*IRRWsg|*hi}cE8
zzp_<ni?Qsuwbf{0eD7G?qLG4?*uOug!UsAyP1iv4SK!*Do)3TlAXc-~_n0T(hfkF3
zJ5u}4e@|GNe~h}SBru=VgDwh6i>v`3szD|3;f1d=+2=x*CnwP|Su{NxgT#<Y&)&$$
z?{C9pAH4=2pt4X2w`em_G2h5AY2F2oeU~nI(}F%#!I|?%&C|Mjw(~62(7b2N%SLX`
z;cZJwLbrj;N%F(T9&J&DuVwo71xpyBq~y%NrMJZEb-Qw^To^=+)7Qt$@QZ;o+)%+w
zlH!M_{^QfMeJ&i>UEyCLwRIDx`NeX!d_Y|U$N&i;VUrC_Z@yZgho>gx1D=|r&q?oi
z*?j*ZP!n&;TP)7_I5dB7ZCpk*E!dGmQl?e{CL13r{5j2Ya~d$7rk`Kig5JV3fYZ&b
z4Uda!n>;eK&9RIri@+la3u|mqUg_@s2Ng_uy3ZYDt+4}S17WgLyGkq7_<j85FY&Kf
ze${UtsqJgr1j%e(Vt`+>gnKZ{4WFH}#p}fV$p|zPTub?y-%J0^1?bW8!GY42a^}n1
z2bF!zUh(&rJUG@86CQnSVf4Ozn`WvY`9t~gJxu^(n0vL&F@+k5$Jy!Q$H(BP6P%+I
z<+Ey49k3q8fPQTjJKN+MP6>Y*xQ)#XGD^w$#X<j#jal}>XY9%th+Qt6D5Y>Dvp%5Q
z5V*o$u_PN;V~oTXE3<p+1P_z91MlaNBY}~WV(4lpf_`8@*DC8+;75_exeYb&V4_R^
z$>b7#CJj#JsDvI-g=TlmDk~~x&6$&Gm&BL|V4$qE?5}}Wa&q{c$~y0Kni*I*AkkEh
zes4vSB(wPlfTi>)z~}&8S=x5JSxnafCOg<1^O(+`?EjR=7MMe9H9xm#j;B$7(Y*>w
zqM_2HL5>d>NAWK4>}YTy4)H%w^MIygNsIWnu!Hz>4mx6ysP3OrzkjO^Vs;i&1UUp3
z9b9Ufs};?u(HDf~tR6d_cX#-3VR}iixFDs^i94XZAef<fOw$UvD<ej<R(IH`J88~5
zek4#I|8{VQS&_^Dm~Z0O(;{YROA{Jf%LfFh-&mB2=r+YLgNdEtMmKcP;O-|+N_?*e
zPlabTasK@IjBtBs1@z2JDY<|DRb{1`vT|K%xa<ILJ~oO8*idxmU!V0VHKjAJ`e?jv
z0W@`^=Nkwc*Dnrycc^AScq1_ZqFazf^PXYtGXFDiYV1P@^s}IIxyPbaXxIfVz!!9&
zZz?J}S1MqbP3#24EbB4-Zqe=AhU|!>x27&96K2x#@FOX9ySJRUSy>0ikBS$pYyzxO
z7DR)N0SK}(5q7FP0!Cg?vTRLj{ZmpUDFEE<uEIwRnPCXNU~tpJb0LIzo(>@4oys{V
z-ptHsv~j5{=Ff?ov~SGNnQ>nC%i*jpSfJ3WSNVqz87&VAA3R`J?FW8A8uBl}Auovq
z3*-s>d@w`<uH(A|uI0LQW3;s9COexwkt!kQaf_5Pd64V{uCJ?mhM<Q{g80?xE-R7!
zp`aM#*p6(@{DILI?$a13`Qoxni-hGQNpZ>Y<$Z_JMAR_(W7I?Y!sCXXPN0Tf7S8-_
z#W0Bc00#6F>=_#mDzbik+UJ30H*;R#&&nC^)Tz_*rh1?|FW!>cS~+ad7sm}=1{D(6
z5f(7KNU{P1a3}?W<89Zj_lmD+3VW)^Ney4Wex*NXXu#&TA5)di?P;59YHAQU*7E<p
ze981}89Q)5fbvSt3d4Dd7=h5oB)uVh18z)w7K{8QD-{&mFu+0ek4Hv6KrO-MuQw2&
zFirPa*I2f0fz+-X0It85$pe<X-LO@d_z-!OPX4gRWWmkvv{PI;=!dqJ78}M%{}@*D
zD07{06=LnWmA(Cb)(s39qK6!uA;9<Vlg!Kn=hYo0u;Y-sgTfqn@RmuT9-F(qmE`4B
zQfcsHTt@A4TfplN3zxf2?*@6oq=A`tTt+#gWU~^eCmS|=11Dh!$P-1uw~TfX3$NCe
zjm^)Ku=A#)GB)1KwGq%6F2;@D_@=x(75)NN$~;zK?va|cb<Nl60yQIP7N4x;UZGxP
z)?5wVhdY_8>v_sJTB~L?16~Vzdq%jafKI22b3p_I<KF)L-+%m=>72VA^g(bVA35^O
z_mLx!MDrXt8kBD47oRh?p>NH6JJ;EfW?)*ouKy`V+K$l#DBS;ume0yc&dAqbi!pT*
zuZpggRvNrWi|f6MJ8ipWVP!?fha9q$up|E4Z(u4|A3r^_z{tVj8H|PQK{Mf;Vd~20
zg$Q??GXf%{k7p?ofFDae4&XFNUZ8j0G9%~Egl+V`oV~j*l7>hVtb6p=^#HH|8%i9k
z3kuDKRMr!bgc;K^lq%*8iMAezUpE|VgIi2%951h4!W+R$#`n;CBmH@TY)=s8^zMz)
z6$p$8JCB527;PLsX1Qprr^Xr1<2c}F+_^mpdcuL=Ii+`vSrUSZQ!Ki8^r(TS52uom
z96@uS&eGjkS$?2_C&iYIuCJ*{PD!c#!30FWDy+oj?Z>@VVZealu_X+@ryVp93VJ}w
zSUA^8O4qp%u8UHFL5H3+qagf2rze<GrvYqzami%4@K^R!atmNd^6Z$F69;dzNf9>)
zptaITvEYhbB_$o%%fWI2w)J{@U*e?!=b|j86hfT-r-yE!lYqUSp67rc11#1(R;3r0
zD{PR;AVx5cB|30u21|=*J{m`M@KyopV=DmEjt}pm6`A=8ULISSQZdv9r4M*e8l}XR
zZGqLy154%z!jVMjgCp$W5yj9M`xq`zdNO>&4y9z)qJpK+S^&c<Dl2b0DG1SMQ49hY
z<4I;i%ffn(Wqucyl?rCwfZBk1mR45N7zcwy{SZ>J<5qv%xX}J%x|f;)sH{Q%%5UaC
zQz(H=h)iK*+$WW=#>Ym5nj7*ckQL-Ft_y0VNjU4>^dV+(rxD0JOJBbVVQ!!k*bbGP
z(mKIX4#X0YRMf$PyA}w%0LEb#;^y<1ap}7R0)q6BAIF{oo;iOHB`B{UuMA_izc57Q
zANCYF;B`(6CCTFj1^Z%R+H$)1XN{9iD3jFC(7=8F6)Wp{_FT#O8D4OV;n$Sj=6J3i
zd!WDt@bUh$XAX2<G@bcjgMgy-kgL-As7>9kjafBwZ7O?=`GRka5xUV=IU>qloIE;p
z=zzs2)%-1XO_Xl9Yt>x*tdn8;e`5)a-F^@^EGL8<Wp>pc_gX7vldkMb17u@7K`1Dl
zOvOZ@`G;W!M+zydoZAyV%d}~y>2R6Vg9RprJY;r2)+Fcfn3yvVo6xJ=#bJ_3Fqs_@
zD?)xVrEuOp7{nvfN9x85=-c-q=KZKfduLy6jr~i1#FUO|<c6l?hjo<1tm0-fF|wm^
z-y%VkPCq}z83Z8n`~GFPRaZV7tRYaRA<~EnX?m7CI%!MCGjHZYbWo&lMkh{m#b^We
z|Ioxhd3At5?d3IU>7Y+ce(_RgXB`7w64ZKwfkD~pIRVH5C`km3kF@mt$B)@_!J*Db
z|37S<c|ebOzy6aXiIR}5lA;ts2<_4)ZI;Pe5|XWkNR~DvZHkbg6=j5?lq@YGOB6L^
zYqLeD5J}7Lb?3~?bDr}%f6OyyX4Ln4-=EKWxvuMdy|3Wb=}khV_VY6=dHR&?f|E#$
zJb0R&muEf^!)XU$mWh29<gE)&5HyehAwW6%BV~g+xpr_%mVnbQ;Ol`}e3p)(WL^C7
zvZH`-df@2Xv+A~GTmVpk<t{EJZ&cYICj8j4G7=Ous!`}p1X+Z49_YcSDB2I<QM5e4
zksfb<UWMc?Ss5AM-hDs9sbum-T*kA`IBTm4J^>2|0z9&uoDRY;SswY&Oyvj;DOU75
ze;W8q66(7c{q5fHOMHDI$Mi!+%weI2=EX5O!F<OIZ|yy|;>=m0LK*9Vz?wN1J_;k1
zC|`(+WIWWw(8K9-$(B$%KrIviwja!LlxH2*@&gVZI_(?R1B)D#76%S6wR6x!87x;5
za)JN&>eXZSR$#(8xRaM+f|F|&=lo;a4ytoT0qEqR_TlXsES=@&!P(;xO$m(g3wph3
zcMd3iA<Ny|_Evhp79oW=uz!CYwlefp?@b?o^%6A@?ek#Ju57rps8dV+>fJkaRArg#
z9i^qiIXQ@sc$hdkaM2-+cwv_=U#@?aSx+3`(PQ1gUf?0RUJaP|`plc&xY<k?AY<zt
z$!jGFBZ_nR-58BGH+vB+JUkky>Dc&`IImIQ@uMdMnkKSx>G7>w$*WK2=H}AX@>kG$
zgh#WmnjJQ*%X&3xsb0N%$7n6h=UW5mhON6wr%WF!tkqliR@F2~dO=X*UHSh1K!)wJ
z=r0ZagyKh)PWVFupu!1j{wh0QK&;kM|D>dm6(jps&cZ?*jV6n9;hkdivKD=UrxbQp
zC`VAN1-5@>^a2QB-t5_IG6cM56$OPBlg-mfx;!@m96x~?j{y!y8l)>bJKE2lIU}sG
zpnT=vAj1gA%i7VF%}#oBONd|s%#4^r0stnpvCodz&)UNaPu8$l2ONuN4L@8nda;_K
z_tvd}yLTrT1XIm8I2<PLW@R;V{`$$vGW)YzVPtP<=~%8Z42Zq`Qz!>?IlGrKjzLFE
zR{;~6tC8!Z#Wo^+r(BUyQEqUZpI%I39XlgBR2JYIS5KZ4-^>yT#x>;n_Qh7Ao*Inr
zh5C|vdihA68C3w<3GeEJCM=J*FqeyGGRBUOWGj*uF#1o&vKzO@@4|@l>sG&@pxabQ
z4O8g=Q6MmbYLXR&riK!RIfFlwlXnIN_RP$fG<otbr4j}l+)L^DGlLWr4X|i|=adaX
zjGr{?4;;Sr2M4j{lkT96BCvO0fVdYh`TNo&=?HVKA7ev>WB)8R6&4{{>>n{uUOsMT
zco_O$D)k4h+R72EA{e%4OP{{@MJtbkH7E442Juf*$Z=j1qPidx0bb&^*p`!DnBjlJ
z;o4ca4AZ1a7UiO~!LHuJ!|2#e8Y9M1Y?LERVpQQjIQ7I;$|7p?{NV#zuJHXxdECu{
z*d~_U!e0n0R9#)w5^DEerr-rTyY%~O$uQ=qVB>bx>quQ^nvV*Q>7?yc=&c)>#sUx|
z0aH*3>Mrh5r_K>eVw(SU8cx(t^={A1XfHL`<pJwR$wx<!Z}wvG`M0s#Hmlsn&E(p)
zOUyxGL(_83P)UY)9af|6#i(G=AOcjJ8*60OKf5@KKtZxfHtRZdEVv5E=^a%c%>bdP
zL`|G7m*lzlg(1^+?91&|y|5lo6P2RiL_V)326y(pf8*j+9cQR{V_z0Kr)3X{ySTnG
z>`0ESfg7DRPnnxkqrRu`CEg+TVK1RpDgPrn-g+{W0ZtRbLPkR+U`LvUAsOogiyjgb
zCz;kP|A)-nBiF0h;Dt(briDfHks|;N3B_A<mtY{pcm}7G;dx1G@-kg2AC3-OR{ss?
z0cu8CGDpgaJ9qvhze27MsL-y>W-9&Lw=rsJhDHfUG0<TGZO>Q_tbpqk$SoO$(u*Fx
z!5Nc_?5Von-<1X$$Fo*cw%ZGaKPWYcR&Oc7JKkmuKey;o&8t_(aX{<T(vZa+(chx$
zBbzYAw}{oljuW)C%UFO2@?x3@k{*RuvbOe`7ugIMdcfv!Om6<X#!?tU+1YDP491V8
z&!j6qid6mR(dYailR>R)<QvE8lIoQLmPPr=58+FJ_W6yRT((631xPp}BFxz)15Rn;
zOR#!WQc|lB!~;Q|*?z)Y7tdQJQFNbDmLim(5K3I}gEHfQi<qcUr>24One-(kC51t~
z?=vC?8+z<c%@Os}LM?Ru{P?9-t?3Ef<brrYxY}#9&IOl3%88ni{YV$W@Kf>e@gX}<
zsL?xCUB<jRG9zPRggI^>Y;H9ko$k0-umIt%6Y~2}c5pk^t{weUof?CoHgXucQDM!B
z;|>laNfbS>$C4#6hDy2hI%GXxUy&=l^EV$wY`|+{EP$d15%z8XDRev46NT+D(u&qf
zGJ;y4WkNSaSyj&9EUWS|8`6v6V5v%YLR@IA$&(9LYe+Q>y<0g{ct%Js-xS9x%FFNR
z7(2(-)@j{3>l5~PWOX14nG?(LqJI+>GjV$Pr-kQ~6~YIw;ALC0JMb?;{e+cR@eD%u
zBPS;ZihlUWkx|<+s%HC7S7{IH+v|^isI^vuK9F#w<qt&8;FVEZJ-uuZjxY3B9>_7u
zMj*HXkO$!qWEGqTjjvDPWr0c{Gr0nT`}N!PzvXNC)9!4XKR+5b9Jl?H@5Zwh^5h6i
zTprZP`C1{EUhQa=*Hd$4t>$L88D{riHY(85a+Z`Mnz09qAGwBDM48J3G~pDH1Nj26
z<8w#@>b!8<doLRqEYx={kN|^obabpfIfIpQg9jrOLuN_+%26zvD1I(8Gt=KcpJY$h
zwJYpdX5BCciiNMwf2S0sUP6{YX@%eeQAxnLchqahW?SB|N8l921^q6LAcI0_X{KK3
zCN;Dy+$O)E+MObF5_P<)>IwFS_G#t#M)XMnGoaDpr0}7GC!cxw7{&V&^bU4?zXQuf
zTb(piYQARveESj_!OehJTsh^4+UjaQ16RaqBv|0RP74vnDy^TR(R<7uMrvfvETeMC
zkX)-Pws)CPbGG7h@>MxU*dAQfZP<HcHG&1=(!Hz+6gw9T-}U`9zyoM5l@l5xzGXt}
z;A?V0-9(LO^N{l~#J+pCpqa4~S*9gV(?TRluHX3B*4?%IEwvd9DjfF4J769Z5yV|&
zP1k-eoMC1L*#Lj_z3%aPx*CwE{C>bmY(5pT0BfaSq`9(`97GhlENr?snRb~=zkVTQ
zA3+Lu_;5MM&o$-SZ@)~NI+Y&!&-S;ciHSdNz2~$O>CpNiA>#8;qLOFHeZqss@lZDC
z__=eHO>*Ntf2gf(`2M{<`zgtd2Fx!rn@*cf5-p(sEh{OBWNb}3aU$MvDGf6(x^Xp`
zruCMJRf)#}2ib%FkiYE{g#s-42m?6>4^p!2fPF$%fliT*3UUMgqdct?L?dYN=oDwp
z)Zkux-*668;=lrY3kYl16oTx+Ybl%gs4y#uWA1PgfhoZ6r~BlbcSu33Nt8rV&Q8v%
z&>6M2><+C!^h4kR^5;qN$tjwI=~Hrzi85$mFGYRU+q5vao}Z}gqbiGflOxEVK|}|_
z0vSZSqp<`Fr*34Fv3Tfa_D*;J&G16$J<z*fB<5%b*?o_K)pO8%#M#S8Pfwono`SKl
z|L+@Z4HSY<C*t~m=_WS|@H1$o!kiu7&5uS#`acatOy1Z%wQ=?7t5;v393tEr8!PMR
z$e(x=+b_s2n@nO5VV<6rw#v;dUqgL-kJ)^XN}rBd@wO<y4v_nXQa^pCI?LB<Xq=uq
zfTPDuv8Lvb@h%cb?WTId!>(n@g;oohEtYQvm(M+a-m(3mT}z9lihxd;o7<vbVROgl
z&&ER)d3=-Cl>2)B$^9bm6Ian)Q;aYdt}<dojYU0IjB*F!uKD3m%!+K$p3v~g$q5{=
zx5l=M`MediT)HJ;UgScA4rBLZH}o!x4c60xRj*U-N#Wm#Wqy0q@#U|HMGi<%D$Ii~
zwtO-VnS^GK*$WA2>F?|>yRzj1iW0z}+b-wbRj9Sd9B3uk1$h*?eol^ow*xyt+&amz
zjMcX5B7T$)lMO!V`tNvW!%t)o?eQB5R$O>6<cji%xF8$gczjxrPq&ZU%9>AG+kN~j
zEKj*Kx8^CY-zppQW1Ie<k8E25)Y6+WCHjW5;O&9Hhc}=60Lo_Pu3f0}5f3>yIBcvh
zijIw4&!Q{w#BA@TQLq@rbMfsNz2r*P={|=Im8j_%PxZp3XZiB@C70nGctDgda+2L<
z)a2(I6GQPQWY7&!xZNxB#!T`PVT10%-p&rwH`6nxnltlzk}yG35fh!TKSds*3(v1?
z_fnw|6+9wnxwM=N@tHF>d8ZJ>1JqejB+nrRDnuC6YB6Vy#-u+!zJLD|2#KDHGNf#I
z)kxDCl33zbM58~W%ojO28Z5ghH9i`djpoBoqf@>&y*_6mG;bu?{pKoA+aUH(vqa<m
zGo1VE`*gY4QUxWz@#6)Z0{Z($CZ1k>MWcVPClk6|y9Q7s5fgD-p?bx<jMYjXo@LrJ
zs|P%K^oUDnX<<RrTV1z#5pfd5I?V$rp@W$FT-}`?yK&Q|n}vlP<|^x4UCS@53_pHc
z<-N6k$LYAZ)MbUetMv!C7G%}O91`Fu<Ub%2WIBN_Kr{fU#K{9pfW!&NlaP>TUZas_
zu7W@gymKJe;{CA7w#RCR4>>g3|2weYSLq04CVeast_ry)^4g7KcNM?I3<*Q1_(Dg_
zh(Ph4K6{4i#&A{Di5ONAJ2w^gkl)RMc)4hA*`NopcbRCQ^yisD+m0SJ>M2{I(M9Pm
zliYv%3V;gH<bD3AhlTKVlwn=;o=tgITD35F3mLTJ-B+RmQKjzPJNW-T5@Mt~f=OcQ
zk0$d)EH_8D#^3`QW*!vIB%}>qB#0kSw^U`fPd8sSW}7ZX7)&kCn6*&r9y;{f_rjzH
z+84>Pn*9ZJ8plU9!kmJlzA~pU*!b#Xk~B@#aFm%1k{wwP-kCt?J$eLT3BV!e@=L6L
zs3!}d!;B^c9Nnn?)^AqL^PS7O@1Q$H!p3(33pTypr>(%8f?1b5JwEyhf<@g~p7lB}
zz-E|;86VB|xep}xPb<4zPZc=GJ3SS3^smhO9#-m_{FXX7;`S@RPDoM=DQv((jN>&~
zAzpuf^rAt7LVC63e~vQOL>Bz)8TA2YpFjd`NZ0g0?lL$gFE%173KNX?M`rO4SJP5J
zZ8Q%{&&&+mxzpUjf{opdxCLlzUPSohJU^&<3#40jZA5JGN-g<X!yUS^sQn3ZTfu<a
ziyw2wA(2hIRkv-{@BngR%7bAAL=N>-AY}zW-EPa4!Py<Y`+E1zo!A)cGgsj!ldY;Z
zNS^s$vhaq#1>vlT<&h!dlTr92F*c1(gkIlO;soFZ_RS=FdS%EIvKY9}#jOErNj#4m
zbOji8%6r9W)`?wqGTSh5^QT3`A?_Ds9CBZNeU(jDBsDDZ(#|>?7G`a4A8Fnn*~UWt
z<0#9;>8^bSEx5$VL&kUELf?DiqtGXy3OHZ@qJ;dO>L5oU=yG<|*(Fzxuwio6o3GRn
zXeFpG67tf3q;`)t=*=Pqjz8Hb_Rt|jt22@LkB?4CO2QUsxbCyKC_pF}8?rR|NIDsa
zMF$|h)2Dx8U0W^n<>i?INI8ftjti-P;zW6+WOxDGgyB%Lo|2Lf;uuVUMME~2Jaw9{
z`H1vM!h{NGVdeTpH#&{rBTw1EyKCgq{J_Txn63G4aX8yxCZ~cQNCf9v;B?%e{g)mp
z4J(wc6nCt<LV4XPnP<an(QI?`J+~a3n=@UjHO>e_2vkH2;jpdm?rX*X@h!mpiS`1N
zX73_TL=FtKXlhC=mLg;?8iRmgE<b}t621BAk|s{8u=M+SHNBG65$zsrPi5uhv(Tti
zPg*i!|G=R`&oEu8q4D#?v`;^d-`Sr2w-(?FMh<!jrSG^jpTOQoModoL8vfmNMCvP>
zv0pVCr7y}RK8b`6c;E4sDbk2Mr#%ka9fj}(#Oc$~wwV%<J02SQNHGK{h5_h2u7Hdx
zfYB2;lrt6FRDndVZ2f-rR-4A}ql2#OT8TiqYV_Z#y4;-Mf~xc=ZEcBEa_rh-Cfq1+
zfO$CbL_grw+Oa<YMIt-3@8pW=M-vbu96Kghr+}8nm;or-&Ypb%u>%TBctkzDtDsjd
zD_6ekzWa^M0uElZm4c3Y6(qr~%U$r#J#s`)A&~eWV$NQ2&>3<crkRNxYH+(@Bs~5<
z$~c%Vj9#E*&~AIF(B6KBUfU%tc0H9mMbT|zWR&;p*<~KeZ5Pgc^6Aq|KC;@I4JAD{
z?_DuI8d@0LEiDW9CMuWYEt}Yj%A3yjasLg<2~?6C3ZcpgHLXV5A}qbj?^{t7;f2Eo
zx2p2%<|$KOf!ou{aomB@04|XCR6FW5n6Fv6GH`0xre3-bsZS?P(TcJpC&+EtlYZ&a
z76J}ZZE}#Sy{n%g1%);(q2w+=;ef(^Wv&Jcjf{_8L&G55UgV@jYmRIq+YE`vWfH~N
zVR3>w3M}qQ3_1lWi0uJECN*4AoJ)4CrNPCu3tn*Nmnl2?Rrl=dp2v<EBS;12&TZlu
zC+qpp1i`A}mN<AY9)>l$Siwh?KwppBPMK(BSs5#2L9FO7hdq1~zWWSN(~H!lT|-U5
zK~RWi2q4k11ZE%rPcY5mfKe*LRpifV;q0rb;#>1`=H^8hMH3uA3h%xC9p9L#fc(UE
zjJxsLxN>#qixAEO!15LTyiHI+zFbFE>-LDlw_TXQ<9YTTq+LrGZ603Zr4j=bO9HiR
z{j{ZUm3HM}ys@IKkizzml$34X)pNb70voLD+X@q}|K@8RGCNoF-{Y$;9N%<~FI_5|
zy=CO()mj5}Mjg2Aa<ia-!45#AM0unto}L+S?TmCsS$;h7VI!0Y@1254Fse5<cjth(
zyBn(ayqC7~q=ARKd+ieaB~85hf&!DWm7Zv2fa;Vr7&(Sqy|}t)6loE<u7`9GqxjfD
z;sHGcB#-yUk}rG>`}SRi1G1uGc%TK1@qhu;saY^u#|(U8?!K;xaG?3cb24ja)NL2m
zT?&pvKoEQmM##9uY(ws}$z}{-bH<`wJ9i5AmoSN}P*)d~$Y)Nfny!HVPFat2F!txT
zx4)Qp(4KiT8aqI1><p+L7&za){VLjdWHU@?l$Or4vMN}%$<uS9+e=}d!o@|U!hHc_
zr?_?_isHLg=e+c=*w*Dl3welQ4G2k4%pX54*3De%IsrdC+XBEdq0eSQyt6ah8LabO
zI8s`U#$&)$6qt0sy?C_<LYhyZtt)%@P<j7tJmiQDMz@duvTfn@tH`b*Mxg=mayE+a
zVzP>s-0Ks|=3$7bYZ$<qiXO#%?@Tr%>$odLm~Zs($TKKL8_?FR<ftjwhq|UFR+tzy
z=pyz<-Y6*5_lK>P7z^t{`_VGK$`R%jwi!kTx#Pe#-Mp8Lur`05JqsL!a*6=}Pm(YI
zDxkPfDd~9R=jMtu=@_<kAp5r6|CuvcqU8x>>9tjTP@e@xMt+tjaJQC?b&(HMKa-GP
ztQ^6f+~0+Pp1uc8aF|e)mkdohbqbxzlIm&e2spK2s8tYEVVCsn-9$!Jp=PP=xKPwf
z@E*u%gt59OF(rFS2{iNO%z1us?cnyop!N7vxN5K9ENydBTlDT{f20lHKRg+Z$qzP=
zG2iMfrZCLSh!C`Qt(k`QleyFgU@2TGyN(|uF8T^KU?Jdb`SAl9Wi!A5iRR{3nT8+R
z%7#w2x0k&)Zj6jXNwG}rBg%~mPK<{id5(UXuZ&a(L8L@ww+@H5LOJ2~nD}e(bNEYx
zgCZLLU{}7mn<eO}dZ%|>wqRxnBWw;Da@X(QQSILB5OdLzN8<su`GNcf@TWhRCF5^-
zu5cV??O%a(TQJ1L?5gPAJ>+vd!@)qw<9jfo6dXKQ%gGn<A07D&(@kwTQGy8nXLDmB
zxdOI>`ICkqw+2saN|r8-|KpE^#2|78Nfb5xo~81v%(`>ud|KK-)Snbrc3+eNuL~$F
z%`dyOaI0v%V`5^0BjU}H5}A7@d(GH)uS<`F;Yq>@HAZ<39$ew(HWj#l*^R29wlwan
z)C&JBk7eN0jmb<=P&2`5z}%#qIl~Yv_9=t1$~%qXA`F$7vBb>&(&|Uc$!lZ|kW{ju
zNZX~NmyP%e3#1dOi_xR6I_3EzsG`RJ(gp@y&#j_}`8Djr>bdD%)eCRj5F{1I*dS-%
z%<|VB&+2y#&Uh1<3Jhew`Ef+4IE<6~@Cl;>zRmyvE<@%jVe;ehS)c&<ikt_M6)>C1
zo5$Y2KO?*YC5}UH(JFy~3w%D4OV>*AbY|#`exgfPaVDBgOic+<_i;YBcTb?itVV!s
zP!Uob05(uvY3tAD$#1H!Sj>Q{y$2Ft-Yta3hc|CVEXp!e%3>_+&*P^~t$M8Dpr!^i
zLw--JK6TsWGZGLa3k=$!$%0W>h2WGWWkb|GdTp!bEhSe!uBcF0f89*F2A^4`bp-vd
zR}c7O`iF=^hs=hjhe8kl(^0XJ{|LYyo}M=f4PdOPH(2;!q<0kJV$-MR>f2NSeE2`K
zDCn)mE=ZT~nWM1ynK=ffaX;4*9)emlt2To%d}){_Y<`B(Z=TW42c)8in@BG}P+d=P
zL+eUk%<Ckv#ZAPXgQ#<P$8N0CnEdM7{zWo-#DnyQ=#p7dJM`1H;XM&yqfYHJU;qkc
zoegiKVt&h6GJ=E1B=6(;b<Bf9m62P3XJJ6dLOh%#TxZ04vAXXgR0j5_wB*DU04HKS
zyhP~tR&)j&KN>gy^9`Ffo9UTB%F#xHGVfWZM>{|^iCb8VvjO5n(?nQwVn^VvUH$s^
zS580o_+ar{NA_8gb%?^ms29aAA5RYa51)jp%ZMF(Cco&YNX5RoqGAcNLxAxh^oya!
z5lcXgqxJ!G(gv#|v8{ccHBL`&an}5B>m)p|ab>%G>sHn9dt73{FM~phx5g%4WGwtW
z(gdnYrlc{3d-3Ax>486H9$WBk<J7$=Jb?UO7n`d+bZ8%kd^K-C!i47ITYY7HeLc8J
z8p}E8D{8iHB)8$V%pMWgx<d#K$RMD4v6vpBR{{Yg;~IWE>LvIyPv0#y4sjku7;FyL
zkWfRh#?K7*pZsT6w_!M3q*EW^C$OW6pv<R3u#)@C3s97SHnci?2ndY@eLc6mz)zpe
z2{EJag5S37N<@Smh`MbN7vvN64-kP^*K5$+j2*k)#bqPsD7+*1>V)tlx1Sw38-{c*
z)IE8;Z1joa+3eitJ4<<){rH1v%2DwNCU(hlwEL*4N-j1zc}v$UIxr+Ua6|9=sm1lW
z3&IO`994Y3wf=4I*y1x89Z&B+Sy`VEv--^1tB-zOt*C$VhB_Y--pPkFhoIH8KEU2t
zugeM+b5>HJP|8S1N}gSqX$`Q#9ugE!)%m-0hEOlwgybjQ<gUL$_lfr#Ir`wfedUBd
z&NMzm*jQ(;ea0QnBqGckH$C2#mI`TT*!61Q0Q#{>Ys%fRlOuDejT*)1T2ZV)C1$X2
z_}Hb*88wmBLS!eBc?6L(I}f_55y=R3F|3GE%Alu(L=o7krFcpbkZ<0+NF+p<1(oF6
zbOf@CU4{I0$nu^kS-cZ2U**btCoNifKup4?SUJ#fJ3I)TBv-7<rDG2DBF^imv38(4
zcMS$$rv*S{0Zf%p6Kxz%71jHLx{QpB)5-0a5!T4fuBOb&%$z)7{#Vps4s#!YQh~D2
zFVNA>?~!;0IEj7N+S?1(vc;3yIz_*O&<I?~LwfW2^^BezrK=P?wCNEMeY7UAyB%4M
z@9Qn#gIs4qE@y#Og7^fzCNE{$S@&V&y1%L2HDX6`4}T?8QP5-XT61BTNR2pyVvohA
zsLb&R&mO$3Zk~ice)RZN5hPjZLt(NF4L`ZPXnS|zy5#43>B3Pr@fvW>=^-KEkh4Rt
zci_u6Z>Zijv${F(oEau_{6DbYOuRB0A0BRl<6*Sb2+Ro^8;gDmghV6XMMM|{#*qJM
z%kZ=d3%gH2@Zj|y>!UVo+op?H8|xJ`LP{aAq}a=sw-UE;Ias~9<<ZcpxBEm?M0yyC
zcK%Q6Kv7%Sj)C4G#3)2;xbKc<G#^m`IW8US0WiPaTW8udK33edb162|hoCt0YGD23
zq6w2Gfh(;+d!#j)u@|@wL3ns+!^o;SM29HC0Z0P9bI(^`Were9C538^3T0kKuJ^zw
z%eAXkAs=J2!d(I+O#u&BAWmUTpFIoS+jmeXHIXOYFz}Mtz!NlM+Ppbw7w*^FS!k-M
zxpHq=z2gpj#)6>7u!$?vCx83?J!i|8n|JTlaiE2dh|LDr7-K+gQKH=lF^C@+G)De3
zSxc+r@nZuJ4`R*NcN2q5?i3dz<7EfNvYUzL+5f@<&wKZ1JD0!FLna_Ba;>ZD8Z9`E
zFsMVjO~P8Csh}~Y?4#grgf=ry9xk7Lg$<xc_NHN`NZ{jF*`2c!55SJS@VVp;f-@yJ
zfmso4G7%O<H8@|g%Z%8EY!~g<Z~4lVzZ_VH4jS~7^7F-uj{tu)HL}Q{*>g2wzfq~}
zsWK=lbd%%`Ru@!JDImtZ?A54Tnv{tJ*;@Uoos`)MTwZz55g9ryd6sK0S`_kW1pO#O
zzbE+pP+E{m>`ZZTQmWH;N#9v&lWUoWKmq4ch_^h*eYOK(+^M_0WuvLVQZYf5h9^ju
z=|IZVS$uZPv0^fcB>Y3d!p3iJ5*(Kp#OBi=BYD&_cXtIh3A8I-e?XkqoKYF9!GVO}
z%9i$&(jT_}HXLB(Adi$BW!WGQ1}-6m4sUFldlk!hSEB5-z38-teGha`{%N<1s)P}5
zP+D3&s&wM0FITCKZ^4OF%GIeGzT@o_e<j`wI0FBatRfPA8RUZsmOzvw6+N)NNB?}t
z&~@Bh91i%?d_Mk5t{MML4CMo?IspseJAt4my{M`WWgk~Q)G?ftP9X6gB$!Q&7;*CA
z#r`R0_L<Wo=`x0}v6h`OaM=1-s9ZYN&Zpw?)z#N`7)<>5>Xi$f6ND`BJC7Cc{_JYT
zj^O0R4+HBY40ehsbukx_^%ef7%0|{Vve~8!bh}losn+BfGCR#x;5P^K>xZ#2ILNoJ
zU#)&Ks{LYk?F1)+^hdBS%jkEtDm;dO0~D8P8hxa(H%}Tem%GMO!lMD4Yj1<03|q1M
zO_crGvT3x4&w_+)`t+3F5+V;rXO*)zi95uWrLq%DmrU!2UYvi+e*;F#ePQe&C3E@c
z3AyZYs{Qc6q~FlGiH2F^VYmUxc!a?qF03Ky<eVqXm?WY%8&X0?r`hLz*@Gl5K0|J_
z7Su!}b9`uJgUZUwo6oo@ON{3S;Nv`Rp7?@q)3nv(EGeM)ba)&jSMlVSyv>{{?XQGj
zmXFQJp?W=1vCTCt$H!kuqP!IOH!6)iQ(JvHeoLw313^&;trYWru~!eVZRguJLI`|3
z)LxP6-EJDw_*#{gV%>HZflMWhZNb|DadNchTK|mXs-vC-g2B(U<>J+Gw9Y`WMm3G=
zJs-TY`Qi9e?8+ff?C9vz4nxPaAenDzxi<0Sj+LWxjm71?i3LuzpzgSs#22?5%k)2F
z^eeu0hS`QnWf9dzpWxP<_Di!>8Z(O?ceHrtOa4y?{`Y@!!)J<E)+lDK?Ray<?o=6x
zX7v2?Vh%y^D(!!4x&CbWfBeYK0G{h;!+)O>^UmgXGnwK|$ivAn07^f@mr1m#WI0V7
z_Rrb+`-u7M6FE@O5fJ*hUd`UeCnq+xk}V2gPSMfxdDc0bb6)2J=xD0`n;`zq6Mu=t
zskEOCY8U%HeE)4;1h=akl7vuA%g4Ln+QDZ%5IbYgMciS=-$(j?eyxaX^W(mpZO6);
z9oxDYn!h3e(*NYNc=Okhs;c9@D0CG5SkeAtLGDQ7|NfR_E7fryy8dU@`sa}usCQ8d
z@_D#B@UPwfagqM{t-g`+-~Rg%bpA`f*aJKVgH_kByZxW1+L;|Kq<;QKmi*`U?aQ^X
z<dMgwS1--@KMz;<$#E*XxBvU=|Kl@Nja20f*gS1Weft0XCbqKI_5aDr|NcG^m4^L7
zR2aF|%VF*Rd8$I#PzzeB*cm?l``0#G^f0t&-9Je;Wzzq7ox(3TP>?G9pTFpz-`;v$
zc-Iz#73K~86`20(CtEs~cmFqP{l~xDVJ{RD$9qYi?)7(l@xOk7@EUW1MWQSPFHxE&
z?8Y%Q@OiwxeeQr^5)T<PptL2>0-yQJeX?|E$L1bZ*4E4utB)A*hJKRy#MrTF{z_DQ
zNVloxTUvii@K@^CHn9EkNG4vGnWXqc1N*ix`GFjpD%C0GR8)>LByi`q2Ah8$U-Mnz
z(Ht7yHg0`6vqG<5<KTHZKE4sL(5R@E>t!39ofC-c3?=90I?<!>W5@{xuXKL~t~%e*
zwpU4FypGOcM&>XJCc#ieBT|=P(DeK(mcwA{qOJXv>VukrRu>q%<9*ny#0LV6R&lkb
z8*moVF{7l?4vRlKiY_30L*AQ#B^yFr8U&v=@eS&KpOIV}Atc0JeAnS{gOCKEm7kY4
zjIlGsR*Dv~n>{`CeA=Ib2BIYi4V~ran8SWP$1_9P9ZK_0cZiGfarg%m-jo7#5+)`T
zI;DhjpX-U&w%jG<!q38`161%G*+2rq?c-U9I3tXi;f))iX9}FO_#UJ%gX1bY8f&_t
z`4tbKEM#{?^NPXO$NqZ~s?I5K#2t+q3$qKE&w+ho9pdVYJtodD^k6==wk6UlOc=SK
zzobT*ZEKs0VTA03i$A5e=ue%x02jGT$vIPx>1%1Bk0<3#2I1-0tAgJx1yWAiw`XS;
zUoL<0#7D$J7b_AXeN@y5b{!PH^pUc__<=DrgXO0ZP}nd+KrVnAF*yFFW0<36s{Q{w
z&yFR+3Elea(|YwO$E=a>U{pH~a^gVueYanMnqzXp4DajHidDrJYCDw#L^gMKy;na6
zT9Ze?z!;g;=k58NSEqSVG@&@F@d3r>x~^M?^tRw-qk*rA_(aS=pXK-%_!%~LQ5hFy
z*-JuVPe{m7<)A)d=%(=D`g!hyLC4Ig23LCgeK8xx3K=3NIjub?p?9xdG!2-f80hJ>
z#d=kA6iuMuWZmeEyu2=|jU85hw2tnEW}j_s#XJxS!S;jQQ=cC&jz{MKgWWzrwUOk8
z@1o9>DL(QRx;i>oERxKAb~P8Ko*{h1#KnzgYu(NAOZw-W8O-9G`5bBP`22;63xtfp
zb0p)RVGTN7C$zs_ei~uX)vc2c6!=Uj?>IF$()>68<=I7->`Cg1`wHfa5{CRBA%2dv
ztYHTvN*m563lfGRvg^LDfHspG%33<;Tb`=V`x#w&cKsD48ZPu9!qu<!5HsSsP^w`@
zE-xh>YWfqtl357GlIVsrV`iPO=idm^OMEE!NN||-i>K)8SI`;KIlv<?TsU*Y{v1zL
zHp|u5j~zXlySbLW3kayWS*Pv>@GQtRMJ!Db4Cdi6>{e>wTfirx(Vp+q9DB^h%8F`c
z1>!8M${s!9TXuZV?|6GoM(iCwk=c5@wh*MAI~UtH-{*{qsmv?74q$LD5LX0_dxG^A
z3zdf;x`2YY6J5sBS8lPqT;yOhDry1d1Z8C=C+tU#7y+sd6bvrs@M0{-;=>2JQ;G;$
z&|{xRXN~q(;>2@Jssj0u^n#R=U0-;%B&y3<a;kB1W3iW_;@CECs~#QG6CdR6E=D%M
zyB~OZdQvH!wp7bn#GMpStn51Qu}(_7tC5Us5Sw*=@aTZgSzxqfswvOg%q&SdjVf6E
zNxr#?J!>r}DZ#%KBN?#W?(Q!0(YR94HKpX_Oy^NiPqCV1J0ztnjm*;}wbDkRJUKiX
zC}(-e@Ey7@qeLFSUGXS@4j4D)X~~&%jJ7}{$;qQ)CD`#-WNRx!ZkwsdQgotlLv(fP
zmN|b2jOjqha|yIuU+EnQ<ctf(<DjrG@~~+lCES&t-k4_5Vxc#nEt|E}KVgL)%o#Aw
z$9M0#44w{MMX*9rP4(-LxmT#}nj3}@+*wC6ZOOf=4Cz73Z|+tYGUV&$&!WTHRvh5m
zvJ`-U8NZBuwS)vj<Hg9-c*UnqMUNMMaMw`sERL(b2l)LLFEWffXWqOWbt7xnSO0r=
zzsLy3*KIXV2y|Lj)_Khufk&eg{@&E|0taq@J#`%nQGuQj-zOFQl{^P=*BM6E5IYd4
zxWcqGpsrR{MF(6BnTRLZ(d<%9qSmL2ECRrzm?wMOO%D)ybRzYM6WxqtlnfZ@6O2L;
zl7qFuyl#e$6$Uf!-xt4-O;gVt26_NV2??x~Fza5!Rv2E&{rh7kPK+{Fp*@F0L}JU{
z5?u|Ao<=g`qiGzWK0Hn)rByt>e&^16ROD6h68;=8XxJ)@gn7t_A<S)Ty1(CJHG->x
zEfEdo2Ve^TO4tc~j~Wwe>-!;}d!(0;2ms$OXKc{{-ht#}F!xoR9b=k!P;o+>oZN9b
zqHZOi@+iR66@N9fpb>vPe29D&{(3P3xd&bcs7K1*N}``6_0+z5$3>t!nPqLQEI|zF
zCok^`0toW!;_{XF561Io9fTHxLo5R6Ldo!}?}72AZ*FhjF{hlqgx|~biNpN)#D)0_
z1qVk2HXTr9T)*1oDVg2g(s=+$xXd$JbNN-&-&z1nq`}QOf%G+GbuJ!%Q~T;NcFb@U
z5bx-0U)QCf_-CXbK0`rKk)XkVY-uOk!f0eDoeGX0n9rejV&=_*!MI0r|KK;7%$UIx
z9i~~#SkRgL;Ir`KVRx>eQFGOqdW>DyTX3m^K12hA)Cfk35UVqKbg!uCPP=O8J&7uX
zISPbQpjC9p45}K}^?VcwQ9*X+YT<WxA~_kT|31SV%n}6L<vdaoxVk0-rPDp}UxG-&
zZ~>439OA_xwII|wsq0dA;wjgZ3yAsRh!Gc2bn!fSg4mfR79aav^!!|M#AA9p$`c9-
z>>WV+P|OfEJHnKWXYN@L1jbC9-pWsc93y40*pVA-fS`HrI`rFMeT36pzozu?{bc?b
zqrRlg6H<=~8)+#jh~flv4)rI-TnJ|=KLV3xI*S<z0+vOWxO}KvRua*9c-V(P+flJ-
zUHjV9M2=w8ozsgS@rKW@EPw~Kiio(hgn8rdkYWG<a+7%=;m}zM3P45lIY3%GMpD5q
zEL1S0YHC{R>MF8cSIkJCH-t`xp??@SRHfh-Y|OSKkn?s_RKyl<rkzC=fz53WiGc4#
zbIRYq@e*X^3g1z30Oe8~fdv%-1l_tN5t0Y~RsU+7apfF{ndjM_8s;<Gk<u_p#z0vL
z1IN@(cvCTa2W~rILMh@?P%@mdIf;nxMd}qFtt)-;qF2QfJ~HZG*7)&KKm=H#I$`Qr
z7&g~ctEK=PNr^)}VGJp~y9o6Ty*H<p78d3SJs)u;sWm+Afh!-ns%_Qs<pO1jK_Y<$
zVt(Vs3Gz~@-mmNGPV<Zs6M?H6etcQUwsBC7b0FBWW_?8c>9jUDqoHBQ-(5uW6rt?S
zOrN$d7~qM-S@^P%=@N$Kfdv2u(CI9^^t&q3d^tH`+<_|Qfh-*WUWr^$;go}F1NJ~B
z^9&GOGw6;nb#J!{W?zA6204b)Gb6*s2DF_z7wU`?e&DA!OZoUiA?&?-tH%$8We5Ai
zy{!qdhzoxXAXP<WBgz2~Pcb73R={XLF^O?h<@q!!0;0)83AifzdMNCJ`;V@vszO8i
zYqXvsn}<gD<G*pxJQx^A`KvQ|@_>w0h&Zs=V3sFk$<?Qol^lX-Sn04ZK+_Lg5n}u{
zGBLt0NE(WChFakv@S$lP{p<$W8!U>V87(*~%us=0!ibxogSv=u@T$lcpl^|p_DI;E
zlDBTX3}(o|2@0~H#`-mz3Niy}$~*|n&iqh=*(&398LxuCv$W(_4e&EOJaP3rw(lPH
z5S^9-P0MQ)d<{PvC)FEjL7<YA_)17fy46}Sr^vj%xR@B%$nOo-g5%iR#g@A8@UflN
z9M{~dg#^Lq+}DN+uF|J4?f>?zBFkeq;Fx#-#D)$yFU{Q)9i8&>a<<L?Xnbh~ygO$O
z=#<OSrHxRCK%F3^Xc(dlm6+BUudBO_HjGhL<Ow8|{(bu7IcaebNopi`-oDNdwh{FT
z$U}cuTw2<<YV?>f=q0*M6${9N3#IrK(33Asw(!=UU-t|(#S?^t0L#3kv1SJA<$=sm
zOy}YQe*C!HfC1fCd^1tTyxpB7M*7AC6Nq`w-n~!HFArv6CjyLQb=P}H=(%cjd?r*~
zDABpW@ME0fi>ax+3#zi>Teng#Two~U`pZWC70v9DB}<(4(Besk7xt8p7&3LEgj5=r
z9b0=v#aINytY4*(fKEX^BIqp_dR+94eo<Ix_G@D(Cp)gEU(|5QM@o@7uj1Agc>80=
zylYn|D>31%*<3`K4E#*U#SoP-$;vE`u5)kjQenqf2aQZ&A(Cf42how|2W3E4NaV5Y
zW1UorAcu_{8OR`r`XDn1@<99vYEZANX6(5=tw=3stGBnVo*qw1Sj9p2!JuTzxk9FD
z*j>vyKqTr|J|KR(<?=i16#zG5CG={1Bjy%kVq>Lu{~#21VsTOYS-j`5oQSq!j!Uc4
z24oj31(o@xO&4k388&%y|JYVulambda2}gCJ7%sMTL1VZF@?y1@5R#IYEt5fr%x}O
zJ-h4i%YaWv5aD9bU13FPY;4S766@BDk*3os3IhjXzrk|k^}HV*0p=!fEQGif#W6z_
z6+6ykOqzO({Qaq>MtSVmVnFHZ*U61TDFt7g3+&`r@Ta}(?{7>z1<t4E5_%)Hsj8~(
z>a^5gG~l*dDK4~Jf#<1917c$p8w!z?R6wD<Es9P|N(x+I_o=qltF@VRrF{t_=B=9q
zpnLNt0SlNjC+qTMW|$}t;K6Vqdh}Q>$`aW11@;Y8e#n@Z_q<Fzpw{ZsC!(LmJj8sy
zuNjNM8f7WHoePjS7SGI{uY`AHff#B?2#IBB<&60XLZ-PhE^J!t)%$N$rge^h@GLws
zSmHtDj-U4m3dDkMP?qE0c~oyJquyy~vDDS+x@6d!aO+mV&71!7CmyqgFr9{E3~dP&
zf9{Yla~jSOShS1djFz0tMOKn9PJBRL!*f6&@#6V&`U|#QMp<&1#GcG!8vu0}s1KQn
zbFyt)E7yp4tSBQRlA_9LG~Uyjw{N>!>|Uik$X|&o#6#e#dFd{}YB95N$M6Vq#;Yh*
zD7^^LL@1|0k}Bgw9#>ZSe0(~Q8wqlON{2csRa8jQ{r|vTPRxh~g9t*cK!#$zuSdvP
zJ_n`Q;#8+DfG%j!4@+LC*x3YC_7h1C^$+p`E^hKck;mjE^j8g-u~R=F;z80!i@`jc
zWbfYM6K+5saQPW2pv<D=N|-4nCB6(uAauOG{wEBI+nWqk$2H93i?H=fy?gh-Lx%<|
zsKf7+zlCNIHn+IAh#AR9?uw-BOGsc33>|3<Os2j*BW&k5Y?MT($>ux+>|yL3HTc_U
zky+$(c3DA)P{P9QkqKdw%Bf)RaRcwRIjZvjI)<{v)m5nUo<CoddQFR&h$BaY<;T?1
zzyMTj&|SY=27>5D0FdAs<<GN1ZeYKD8S5+c<I<ud)yIwN<6ueQ1)a%_<|F*lHsG}m
zM4!&!5m`<-!r`~y5L2Bxa|T^Vw-JphvcghR;-AitbqKfk{yaN|I&&poR8~qa2sKgW
zqOs)wV$s)Tk4X*P3xpw$ole{@Y5Il@7XkvhcJJQ3^l=%ELX;)65bEkdPimZI?DpKF
zI&vhl^wsWJES(hW$xaXM!t-7-d-gIXC*SMUm<Blz7`&V1G=@B_%zfk?Cm4&06oGe9
zoWou+0MGbZSxad9-X^iA0um?DmtsoTfoyD?PgtY$6_SXK4h68xfB|MF?E8qJVtdX=
z0}3EMoBQyQox9{0T=BvbBK7j+X)+19smw=bGgAkN26`r9LXX116AzGkzCX{&>JZ)L
zL_!R3-EY59N?e4hQ_cN4UI$?YFg%kF&_lVG+0{qVX7GelMgGBT;@DrKonhX2V#x9h
z3=~tgaH*FV8#|)~LU~s80^6I@iHX;5+{hrEP+h{sR8++L@yFIzxB75V8h)RKikH#&
zQqLJ=5ggzs<~ZwQ-JI6XchOnkp=^{iXy{NuDU3nw$yciP5u)epxQf2C!G5Whyvz70
zBxJa9vQcGZfrP(^nKK1+$q+hi9xHF2`mN}r6d(^T5&uDg8~RcSha|PJW5dJ3!0I42
zp?cP@TPH38qnB$5ZMzzT&?^ug4Pze^sF;_4cR1xHJ#gjssjK(!dc6q2_?k5#CdxE=
zhzB6qDxhQoug{9$GjL*%+;2i9!5?<ozSBA>Gd;ch>C;~V2VolLz&SHwA(@W<l*K^^
z`cQ!}-2ys8RfNnTJ}!;}!@s3{n7>t1H}G%FeuuRH6^4G)*VP@uSZU!)QW?WwxKie(
z5b8f5Qxg>x1v){|B6{IH`5Z=)VN#;O`LoaY91aT?CI+_<uh5Cpq7UfX_vh<Fj$GH0
zcWZ2H!ifXOH9|tH9314m`bU^=!(@uil(i@%&%7Iae+1&#4AA{IvYWlv1;P(41`x#2
zYlq}@?ob0I%ySkAvrd{Y+0@_R9?zSK#pL4(LupbyCNA>kjZ~VD<{)bLJH?+3k?<#j
z2sXR{d05!gpsz|+U*r9ZJ{YMqtXuEiVd#|7-mk=OgT%68h4_eIPAn!-41y6vLig+u
zF<+&P2gzYZInmA7+RC_<v>#Mq=?2k~Pl|SGWmEypA*pfI!7lThm4Mj1xxFB6ylu8e
z-SIP50SW?;!1O9BJDWYv%h#+a!oZ)@3jaN~Ny1-c<VYp~eP0K>^E5Lc|Li+>5EuKL
z_LkKsVYob`NDegs7k`gvf@j33nIHOF(c&ZgXwIJ1vsIMuzPN=c<7J)a1g8+AyG68M
zB$;UJSkztEDKPSf|3OnZh@Y70Xa?<Yl~!8w8Sk;DPf2U|9peYmA0T{_dE5!kHgS)N
z0vPku95?Xn<m6grr}=e;p<sibK4E>g4d?2BJQhdO&ybp|9@hw#A&)o#P!&W%p=Chl
z?nu?PC}+pe=0!x8xalG0D&!5G2i}!iwr&j=wp+=Z=*MQ@-hn^$wg%x*&-3Hg5$l;G
z>-v78zP<t~WiB+jKTcc1vhJft*7X<_#9%n1D%RG$%OA{Aj=-D>w;o@0+|aIFzWfJT
zuaP6q&A(vk;84y5x@GNj6Yb$}+E9dRxeDvYN5gzBgR7vEMb0JXMHR=tVUm)(o`3y%
zp3V{FAb?B2GEfB2N+9Bro84|O+s7;lucNxAMs#sR(+18_!<J>shA+4Wro~altB23Q
z-9ws2O)2V^Duft+Q7uXOYWA3S6BEO&g$a$k(@gH+-nyCV?4Y@c4v*GsWP~|Q5bYJC
zhlV8}Ayi+J^z?>qU(8SB=>r3tf1_$Dqrzq3kTMIQXt2Y?kNF{}VWh%4X38dJd?Crv
zJ-lorzEC;12Hw7RuiK=#sg}qaB;DYNSdhj#AXNfR>ns_upwLh@aV(%V*w?0(K!PVX
z5m6dGe<l<UJu}nW8x@Pv;K9$nUKPA5fjuF0Z{6C1pq72D)P;4m;$g!mQuCbCU@&Ng
zM8lC{O!aC|Dj$J0Ye<V1xcD)cY>+Li;-^d*IC`Y6-#>w8L1*BZWx#yg_fL2ie&V7s
z!Yq9(xy$Ke&=BOG;NYHzFHs3EpqS~|6WHqKg&`DDn3zrw4*(aR!Zeqoqhjf{jkK49
zWZDZN>>O{>umDJ!n@e~V_}!kGs_^W|6MUxN-~EFvRP52g2opy4j(B1ivGH2-P>biK
zrKpo`-n*waLw16E2)CS$nsuaO7iBdNUXx>R*8S4d<mv8?La}RV$_k&TYjnp`@f4le
zuZ=1sjcup2CDfDz;e?B)20lA^;X*0NDK^%JHUc2SY$6+24qdo#AuzCe`D#hcQG8wy
zCeD#le<~nu+#${R#tbL7w&toR=q@+afKvek{ak;bfY3@(pkAYz{_^dcsfHJ99iBBZ
z5@P&PjEq^aCL83kYSnE_$H$KK;d#c*7$|j<5=*vkUlwwgOga`}h_@9T2fOA^oKSTO
z5&aDY1{i|~4Js;>s42@GE^iv0+Q_B$pTt<xOCruVc_dTA+%9xW_=;$R&qfi3l+>_m
zEBA$?;;eO;(3?=|-SC{=0+5cuKt}(*#*-}3R^i}78T<0pD_xHou_()K;|&>Sy=3<d
zup#cGQaXg3dO#ky!Jgn?@UDf|w*8=*dT@F1rQdJdzYjMj9gs)j9;?(kxc1BQ=g)~Q
zv>VHZI#UgRdQe7CHaqQUv$K$@87ws2&z>QX_D>MCxPqlV<Kt9fiC4GZJZP+%#&N<(
zs7_WY$b=gk85MQIISmlG>uL+)82u7TFR<CTA{;k|51&p4hk4)g=R>llGhs1RM~A~e
z#3cO1g@bdBRa3*5&XiKaE!!okfV3>|c1(Bkcmy<ISv7m^pr&YGD6CjbCMw=LAP=+Q
zr<XU6?H#!A@}{+D-DN`MBvl!oz{C@$^=*`P3jO+d0zH9)GGOX|o`@pcT}jC?3olBw
zv2`$f&z^k|5yT+cm?N@_K2m^z?Yw>cT9A?wjq3K)*4G;#G^SQP{ZiO+AH8WSQESD<
z02mL$aLBWfBUy#(YhY(P+ZvNoN-qErKSRbH`kekEQQCJYq#U&@*m}wzt#|`a@X<Q#
z+h>ch+MZsUz?eC-)Ebobk3@${V5THCNu4j2P`A7?q5uwuY9S?3{z?g*ZE)dBwyflN
z`@p19RZ*mIT6xsy+)CW2s`&pp1&D*B#@Kp{j~;>-M&V0<SB`s9iLcK;5($H0(ElA@
zOp)u50TE`->gd3pQ&Llx!$s>~_2vzlNRwm6MpgUa4;**=m|<(%zyX$%+|{`fj1BWt
znBb4yQ-^Rci$)*g+)!oUNCZmVEmA(baKfxOsu#26A{>uBdt`p12lI+sz~Y37K6*_0
zQpv&TFdlM&*Z$__B^pkWNSlI1(R0oB)z#w?h2nt548bq+O;F6;-b}0NMzOUO$Xm$+
zLW`h-9v7T<Q%ymSgQLV*|9#`di=h%v@jyv<9i6sTP3{iwiz|B{+flO2B!6XzNMx$m
zAOXH^H0^oO2=WyImrzYz0_DYZLtH5%u@g^-){Mw31OU7@E-7$mHV!@u@_sETz=#Q?
zgRg*SaQ3M($OruNM2jmxh76d_-KIZ&yy)>8A)eh8L3Ty&{)H}b{%|L*KB<c?oNKN?
z*9ESXvYZ<J=$FS`GZc|4^e}gZ>rj7>`S&s;4f0aEV`B|qS9B-y7qy3csJN@WH8+9J
z;a|6q9egC@?XLVU$c>(^?$Kk%1R*wVuTEV+$ROYWG=%=O(>wb_>AU0S@SnuG=}TiH
zCm!+n84w5WOuo}%Iya}U-@bv+QL_VQfqEJ$@mqdUuBvHE?)nUnK+nX};r@tr=`d3r
zx986nyutEvi7OM}@@N_XP+_{kB0+^F?i##6#NFSr=AFf188MDaNoi@<N9{m4saxWK
zUE<@HG8|_$0@E|z+j2fZ(XofLQ@kAVwuC=R$Lh<|rh{VMySLV|dz`Hr@tniy+BH6s
ztzA^jcIb{uO0*_S__8o@4RcCF35s(<dh!6K+=4NH;Sp536Vj00JN>q8^Jdmq;4Uz2
z&=)DAeGq8u^LnE^2xt@M)V+JjJUAw6B9W!xh$_GtcK&&n9<v>+gI-fZf)CO5hZer%
zYvLF^KkxqGou?R?(g~;fVn5!K;$mr&oeJn1iM`57^XtW@HgFhdyta6GIXEhTIbFCQ
zAXkCcG4~!EbzW(6E(4`JF3On0WBWt$GG594FWiGceX@7NNxLzCedti3v%s>Va*Xr5
zHasYJ?_O%j`KtI?F+-bQ?amZvcGwA9H9^e&vXKfFC@gok?$oL8tEznSoR}40lSF9$
z6^MJ4mHmT*XVNsh$PM4o)8=pag<ou^vTI9Xcu2@|mi&4?jX!aMRWB@3@l#<XMyaX?
zO+RUlU(9GQzFd$#{1d$74<CF+^RTgKqYzpb=@Vqo>akHs7+Bb_Vfx6|{1bGL#4j?t
zH+-sFMVAd!0{E01rZggYFrmOBT22)3F_*>Cb(5(D(~>Ndp=#?PmJfi9{F_`3Gfry_
z4aytLYYn#=LBWDqC-faf?T(Y9Hf{9ugc?h@@MC?(J;D$`Aq6PieDk-D3lV1UJnHJU
zVgpK)S1+yP<%1^k5$H&?rfc9?ZZUIa$IwX3KkNxPhS*Z6C8L16DaqC8a^u;fM|4jr
zqekt`bHaaszRk_aiQc|2d*+vge|3bZ07f1*@VVyeYlxh3_3FBi<%VZU2;MH^2PRLX
z4nw$X8;Q%pKvmY{+02|tW#4ze02>>d*v5FFKE2|1CMs85B>0A~!<Ig~u&{emB4jhw
zD26fEF0K&QIMTR|vuF5VyO}J^fF@o&-21$|YJ-CXP9Nx=0fg?{y!i$VEe{wpi?*w6
zf24fKk!6Kp;OLr;*K|jXlKl9MJA^|Vm@grXr@@ZgMHg1|8WogR(S<|-984HgkM#16
zHBwEZyDJ}`3hf6OyYcp#J2o<6Bxb5gY3fz%P*E%RuDlE+aP3<Axtw;4JOvoX-rhK=
z6mlOni;;bYHm@$}FpFeh%#k4WP;Rm7x#7!~2}9$3etw*+B_<>GgI2Kg9cTtq1Uza2
zk?HlvehK&0f{bh&(ww{X4(vK6Pl#mSzpuyKWP4xhQ<^PrAsV?8R4M!w`jr04(o*t^
zCvOQD<m602p-VZ&k?AV|p(kd0yxyF<RHKe^HCd|Mj{`=we-IgfUi@H0L>_B)?%%&g
zHcE9G$AMwKC{ZOWBm@_={&4e)Papf;rg`K)!kbR=-e7$lj4<fx#Z}$QhqnX@ObIl(
zFa>dR$_5m}Vb)<QHHU<nYS2ACcu<XAA4DAm|KR{;E&}vU3qwaZOZspG=fi2B;Aa0b
z+o_4RROy0{b3uCTxyS-e3=<AuA^o7GH*JDkTye4kv2o+quO@B7m>q_QW5Srr2TFQU
z;<xnloVPnolu;Km&gM90j$E?=POl&fAY&J-P4oIsgZx1?!6{)BgZs;F=rgqT_4^8n
za#sNg4wsQ2;4RNED0UbwBlniigKwy4V<3F@A)KWdb6)r3kH$cJVW&mvV88(2ASPN(
zo~wMQTe~)Ac+jaiOdOByAG~~w|CJqWgIZtl-;Eo`%p9XC^j8VrV;jX>euMJFwX?fX
zeyYO<o*4d4Ol}R7GDTuaSELY*LEp4Naa(UL++JzfddS>aau*&c9(0^oK9Bo&9heNU
z3v3Ea(~mEaS*K6m{p&C4%-KtpC>$;UK_Ev^|H9zI%To^{Uguy=)Yf)T^&n+%W?5iS
zqPD2A=K7!|s~Iw*9axy<J`7LOzy87~;OD`4#MG}14Kn@u@neI7f(9xovf2^gE{i!}
zzAoWwfTlwOrU)_%I6h~oi<+WlsK^QkQAZO9sx_a{%q)<vwP(+*4TI8_|E&d}3z;+O
zufoEWFn2{->nZkKo2S~|BSw&;fg-G}DS8N{U8hwe&0X#6Y`<VZ%l5)m;sK3sRXx_M
z(X1^d`kHKrkN?QDMLdw;nkyaAg6Iucz)9MeNbkMUovTRm49gOy5@Rgh-s2x6UqNUV
z6)Yz>PSDqH7o-}i3b{|dXFf~M7nU6gyC`XIQ0o`DjvB%u6dG=ES|WUNF48d|c}KY+
za85Asu#x2O6G1^eCOD~2?S>4U2E39g3_nG<A7n*Vi4PEm5qdg|EkcxT5jU{xW%mpf
z1DyI7<XS{cf=pR2Hpy{Bg+T)TMasf3yDSNRDIYzDq{p?HDI;??&zU~GE8FX9Ybg){
z#BLGFYBljrMcY+@6o_ecc3GY})kCZ)G$`oDA1WR!qH})%C#<!)w|)96rK6fpwZYk4
zT;Qr+!DiA4c<IK3hLXa!xXQbI4V-OFFd?_XuK-yCovr*ZL#h7&hw$cWD(s_RQxye8
zk^JL05#l>z@pyrCourrE!y#BtU;qC5cFErt@vvFw5KCA3!4FN?Cyb1T48dUx(IQ|m
zCNa)ed+2~vQhDbN?pU88O9hF)3p_ouT$i%5sYy#*wNv$)#zqtvssY!HQdb9FJ!qZu
z_|c;n9S>u^<@4tNV?(@J$Iq4o&;(3SQjG+|VVlcF6J!Z|?pz<S3|Xc)5m+^#1woPr
zf=JJc9(BT5E0)rcAc6858XKulV7+{=4#q_YZaV|6kadp%0oMt*hPEQ}Zd)ox@Mi@<
z$De-=>esK^B3W>E&VI)}74fajRJAzX9I=%w`-<EOw3>sft!-jv2D;EygTPl$3Hd;)
ztaQGgP5TuUnjP_Z&J;BJ(xaQ^L)9qV_2p*NdmN2fry6tkFdHCNa8OJWus%ETITAa0
z3JR(^?jgw|`K5L`!cWnE;nr(2&>yak_>p5^CX6aLZ+r^HEIwqSPmYjMU^L*2l*XCj
zRdV3ed#Et-J2#_biqmh$Ddb>zv~IT0RCZd~v)kzWZhbZ%!<b;QD*DaE{aMZ;*{+_O
z={bIxoHI9#mJpw;_=sr3Bgxbn0DeaqL@Fpao}KM&IkfQRO`2*7W82>v>eKUbbA1Uq
zpm2cWV;F>Egb}Xg{D{LJ>*}U?zCVCv8%BRHcz)K?WnP6_I@8MW5sB>l==1%hOpdO|
za7H{T7&o)X52-%WTqy$r_QJuifTb2O1kaEd!z)*saSxVa-MX`+iCY(`QA93=>^R-R
zK_wOA)9Z|D_x}BVM0yQ;{*mJJ`==LO^$5#{)kkw1Mf~j&yBxiy8kFb12W@ZvU_?fG
zt96_kY)3^MiH`2!Z%5mXqm^HeHuwfU96}H9h>$!dt`g(*q<H!ycpkrH4RRpH<Z%DF
zNjc9fL4r1b3Q-7x%xHUkc2o=EWI*h308s^ii$nJD_3l~?<FIsmeK$LGqrcKEIiV5+
zYDc{Xz><=(hPPJd)%|>fAQV}0RaF14WEE_A1wD|5M;fXvTsR^lvHX#(o7!!)&uUj!
z9dI+8(qJ9iT3Z1g6|p~@GzlTV&F8+k*RNlIfI3;mvcKggLspD7<cX8y1oPPK?QzlV
z`-IaY7>SY%=*f2PHih9jEqc^W)~DIqw*q9L9akY{>h^i90e773JnzCIxuYFhELssL
z$Y`#G?Iu;u?!Oz4W_Vbh3oTCY?sqNI!%DRWeMD_VJ%|G!L$}_^4QR%BK2(Z;WWKx1
zYjyOl##fL0M`IfzM)dA;*YQhr{UJc|fJ;w4m!~b`2S82{?3FAhsCD;O;w4j>X0tA$
zVK?ax!{kZh$3q3-0C}dvJ8sjk^sf^B92=aSsvEt)xH$X`{YC|m!a&o)ZzjI~@Ija9
zWfs8m@shl9f!JS9+ZtqaxCUU?>C)mX_iCt6!pr<7sXd3Y$!(a?s;h7L^nA*^m(u7Y
z?%)5`(9rxbv(n*Xvg_iLM{z;}Y5yhs;)qgjs6QJ{xyZ@u>3=US{^ESqMrhIb*ENgf
zJ+LAYc2J<cqH6_;tle!PX2gw2W8LA9-kZODm|r#Ieu#9pE7Ohom*TrL@06C7R#kPi
z2h|Eim~0SeFiuAyk%U$fKDqH#O$|QD;(d}%&KcPDWm=>cd_h6M&M$Seo@HS9f2zV6
zvXFAT-W6QP1}>0oIKU4QbVB`C(-YoY+Hz1uyy8Bcx)YFFb#>asi>6m!`_1&3IWw5)
zH%#oJEVpCMgGp9NTn$J5`*%QV@Va5c;z@Btx|7F`1H@5*vguQW2CU!kXsaDf@1stf
zU{dL>&xjyt(jc@WGuDf<6L%V=F{aFF@xr{kG^TR3hsvE+VGn3@erQu~r-8M<bkct)
zED0vzZT*f`Dl|In8(IMq<uuF$pFD}C^0BiUr>fdbQ$EeI1`wS)>%Vyy+JVv^u?#tv
zl%%4`TfA7*j-^Le@X3%I6gF2jAb9~Hr>N~2L#8Yvqlq(l=AY5vv_7BQOjXI0fhQ&e
zP%TrBvCGqgas)(ZS70Fi`*-s4;+bjNKJ}QjPs`U+927sp256_k0dA^z(7yw|vCHT<
zb5-DWCQl}gHgV`7AT5X4S+v%j%kkf6=A?_@r|aTtT_PG#CXzkH#KfGJEqk!8Xu+(n
zt;I8I==EpMo_#V=j8*2}zQsHoN0UpXOW_ZMUXtmId=obsZYgL+oldvY3bVh-2Iy7L
zAC?X`4~P-g--!AtjUFxdNS7$v$|ipNkM_4-m@oRdt-UOhZWW0OpeTG)4{2$$kzqLY
znH=peBV(xAo%hCVfXp}2sz6qOK8k@|;&Rf-leoO#J}ol)FW4fGpvO=PY#?J?7#2rn
zOE3)NxLHaPoWzS;zptaekBe(yO~r~&GM&oqUY}EZqrKszI5CWeMGxFgz$#?qm^~zD
za6wQh{Fy_>0cqb(CSC=rGlmRjk8l^6jUbn1EV|38Mz2=jkNF$q0(u%|kKkWx_Gc};
zE@zDUC-dMthI}ATn5IQXy1$;*OOV_lFa$WH52PS|G~@;VMRxWA#^(aBBRCobaM~P4
zs1%0e_U;{@S<fR!+?&Q)qYpoYDIEOL+;zYUSOov4;j&>8vQWUtiT0(+sYJ!wpCb05
zAVt%h@0<pim^-ysg4G%9#>i5Efh*zl>Gjx*fEy)&8Kc@}Vk8U^MIx;}^bxVG#A-@z
z7VWRHl2ROo>Mt52qoy;KZ=U~(&TM(<c(B{h&|?!;_Lk^>l}1UJ%Z2#x^gNN2M8>U0
zYXw#v_rq30*z9B1B&u-W$PvlUjSN60v`v~Yp|8qPdf%fDOVKZqT5cW3`fH7=tFYvV
z&Wq2C3>&9L%=viBvro-A*<}O$K}ydt5Ss=DKJ+`Jc{&dXf0TGnP`m`>`IgKUIyN=6
z+V}4<pt*)fm%L$UDB>^}nw%+6g<BiI19$iD7pilwxOhDh&sQ@3O5k05D5dSI5zBQ-
zo#rCL``S*O%y*((^E;(GW=z<(Cfu)<-JHob091~YlZY{4h*}=StkkYaM@Rs*bGrFM
zeLczy7LZ=^^D_c&@>epHec9->!dH9Wyg^3$!oqqZ)q;0mBQQ81P}g=YE!{i+2z1e9
z*)sP0;>2CWIi^7j3=9NifwjZx^?}X?KB!sPkm^^jo~N(s>u!Lx$QHO~t~`4K=FY|C
z<LI@ILtJ_aWK#F;g>W5At@_>@Xta-tQp^7E?b|pQ-FqKvlT;e3yCuIU21a5B<H8Kg
z#3k^D5>Y|lzI};#rZ<ybLYd$kfSQ-8o?iq3hmKKQFEuBpk_Ehg?8lA`Ezh)@^{lLn
zQk@i*folX-t}<x`?4*MOEOKv2@!Z0q-3gDX2xAmv4g=;nnDupNZ=NT6k_SOGGNgAV
z4KRP79)M*$Jdcb=3sd=VQZSQURvi?CK6Z9_Q%(89gh8&i!{`b?YQ&_l5=ys}Bg{jB
zg1Q`ipkkF|eayIi0z=QpgNO7kynXxKt5*eoW>XA8{Uh9sUiG$Q-R==f1#<96ihO}x
z_dZGJ0u(4oc8Rz4{YU6Ze`e7-c~T2yBO3~+HQ^E_6w73v-h}80lo$CB4!S~vH)fBL
zIdB1LfIScLZ`^3QJ2nUD6&@WPFj=%UgtA;q3*`v->wK#Sh}hvwGaNsTGHe871MM^Z
zvJ^az5rB;tAue`AG$IsRD{KK6wkD{6HBnDceDTG7Pu#*YmmU!a7Loy_pIo0l)tDG$
zd!EKtg5cseH&FdF@SKOvb0qZGZck1ecE~uMAx(5hK+#`0471Ay-C9Hx+=MlATnaHB
z<o+aW2@4xHzI#YarH)L!@0wFNiGr3K#9E?vKmwGR^ON2Xo-#8Z^XAzB#YEWLxqtCl
z;4N5l&qP30b9+nOIVw<`_Cy=k;Hq#ALDUWB$!nhq3#2v<g5Kpq-Y2cXVv#5)lL2i2
zDVa9n=r7Ycj7pXE0=f*s)*bUldc&#>ESSf;2jc~J0iqXPy(84rBnn;(i!kRNTjkhx
zPDEJ82__dnj!4%S>_1tyTr!Y*OiGm!zd#zFXV+^?*D<ewL6u~Sc|7za$O0HapnMio
z;BywlMdFAX@|Qe7<4LGQW#!*l3h-#vcZk3SFI@}(==<!AWe$`xy7tcE{>_`>&aUu4
z9&B0Gn3u8-15LCDcgHbHL<7XtMO!N>y3E;Gnc+B8y+n0~A4n6hndv7d2l7clP2a(u
zGz3|Mxg07iz!B}&#rU9tO1tYEW!~c4xv_OJGtJFKrWawD6}7NPu7t#Yz1p4f3<8~G
z;(=oFSVEFJ9WGnh&}8FIJ%9ca$QHC_z>5MA!y81cfPfGCC*k@JDhq8Ip*;xo{8}_Y
zG<A><y`-hP3*0Fc1vW~w0zawo<B9_wFvq9KJAi*>u7v*q$p9UtVhqU2<B?NQBS8hI
zYao!LKNJt>BO}ApsQla{G7^Ts^*T#ig$|5Zp}C@q<M!0h`AAR<l|DSp(3m*Uvn7k@
zJ_QFdyd?<K_>5({QByKkG7z;SY_MP^GF07gA=*OJFS}sfnPDQaLq%3pR3O7;Stjx~
zL!~v(F5Y|eh^(>!wJ$#bG=U68u#7(6ACk?lP={FpR6C@&oE#sjCf+PP4Ux+zc@z^F
z`_{j!z8(mD!5O4AHf*z3JAlp%uoX20WqNvRN-wed>T-9Gs)EB)`CyDW|0mh535<p2
zLeL|>-@tU`(v>SI9`4<^(N964cP+F%5TJj*OxnG~)i&_5ygBM3=4X<F=+)_d{6=>r
zyrD*BZl<ZRvC9BmpZ25CX9ou40b(e&;a<WtKYt2d5y=5Q)#>BqjSznY^Rf2G^nRL<
znfV(B3^jF(-ZX|u&gev#vxtv#LURJBRhw)y*7x65rr4BrJ?F#?6d^Qsg0(I?7jNF&
zUHDRPYNL~4&V<+xP|_u;TZkZeH<WznnofeG)5W1)K6F{=byCnP;=%*@NuA~pcgo5R
z7%IgbiXVxH9(e!(5Xy%E98gp41d|Ua$T*(Fdc^N<VG^h|E-t^@UrJo?!2rt^W;Vs{
z78e7s06)K~uC~Kt3?!J0hfx6d1sET6iiB7`E~R8OXvm}soIN(GGkegr|GResK>n#o
z@n@yuid)X-WetN@)BApPE*o3cC;4F8cP1$*b7ir@#!M~mUQw288Anf4Ra2ASsrKeO
z6S4V%<z&xJb3xh;cB9S(jz_Blzu|Yol)(X(SWxLX-DO93IfZ8KNfRJ@?4-FdW~Qc?
zqB)@BDKI4gFo@P=cP&UU-~S9tEcQ&dEo9Seb4v?Da9!FAl_M}tA#rl4vGnh?sD^kC
z)UtisHeovD%)71F3Nl^57dG1GhV+ry8A=!s_{47-PRlte(FQ*H{ex!=6M7qMZMl27
z5RSGMS6m+`^J7R|z(*h}TF;!Ro5&d^p|SX6aU#%TX^00brPg3+)WnI~TbsvCo!>p?
z3kn;83hUsfEAGAF?9<lt7&UR~k?AMwkqpsA!j$oZA?CKw@$pPBdj*4x)954N&j>ZI
z4MktPyx+HJF!wa;5`BKNw`Yr3Hb|yc0iy%&=nrFJXxq&c6&0PT*=)y6;DAwL_jL@X
zcBqQbpw>KlR-sRy#xqOUGKoj}1-e`kdS2c*J{wsRWAL8@AYKkqFvtWDwb>v1T%}Ex
zW4SFzyb-}<AS@-HfwrS-U-#tvjoY`?nU?wMtWumWl3{*3FBnr6dwVuKqMt?A&FKU^
zVZ;bPv(wgdBD_8;yx5=Qs<FYt13P0{L%9?L+MasbTX4aU_v!_9M-r!bdI`-<IYWr2
zt5ZrH=o$>2{b=Z)h#{1fjc3ewP1Z?Swa>6&G;c<5%`jVT+enMe$rz34a;JuS44Qpr
z`GyV4Llcd+lDyOk?h*FZ;7xI6gnH&5Sk@*~EYu5&uZY}aBy1zG3t9Y--XjTB+#_m-
zH*Y}q#Uq~~dlMu<PEJ)^AK>{uEG@FPcmCv<g@rZFljxCpE9xJG;9lGi@Q_iwMT<VX
zex1R~T2VfV#7X-@{SMVdjG|Ja74j`u#xsI3K?H@fc?&oLj5iXmG{<m|%tcx5@wm#c
zO^V^kOB+_wt^w6DS%WBow*(AGW+ag`R#hoYwMJbYZ3V=LVQbeXw-7+GU5`0=egOtw
z(l?Jl7|}J4ay82CLQdj45=e#)J;un|5M3|Sc#YV`ad`|Yt*xx!H=Z&@4$Gn$y7tNW
z*VGO`sdxioB;9p>34Ibx1;QuWMT?3SXg$)GD*oF7!Y|ejI|ZMa8UdH=_yv?HcODOC
zGLF}X>XErR=89-lw#6`9$MLGD=v^TDYrI(~0iBdeM?Ye!UrDKo`OVqdHrUf3QH4Yy
zhi=8Nl1T*47WzF<OA-n3;{VZgCSW!1?fP#uQ&I^@QK^K`ge00188T;VHK0w%92!=G
zRAiPil`?O(k|AuhBFY>>nVMwQAVbmc|NQLpzUMvX`XASI&gI=!tKabbKHulL@B6tQ
zJlL_h!jZ7UYvIwf@6h22$rq;slN^+CpIM>LrzwGvdva+Oa_Zm;r0$lMU-&v$DRM&6
z1WGtMNCIYameIu<vth&0tnR;?SArQ}T4!+}OjM`7_>VtExw~gG2ZnhC<cIJ9Otigc
ztCv#0;gLN}S1c;@z{i69uEe-EhkpuPZI`&HEqC}W<v(J#j%=r~efwFZ4hMIp8UASy
zUvnhp`_#0e?B}lQk4*9Jlw7)QdBvW;LJvHx{kih*0}ZQN2W+pod|=6shT-?@KV*+9
zShMLz=7^N4tN=1~{F)#qHi0kSxr1a7qMR$q#aJD!)!4Be=s&ScW=C;vT#eY1gAmOt
zJp@0$p~qfJnMx_z=#)i%z=oo4j`uSy<O(5ydIU}CoQI@TJAjTfHP2v;oMZZ)#D|)Y
zN0eljaCaW7&4LP>2MBOLF())D1_hb7eV{j4?siPAiu;b6fK-*>j0FV+QAdOd8^cja
zrP7FF*hdbWed#RhEulSXI%326=z%vh1*>fqG&LrmKKI7U9_!&D*M46r8ObYfJiku*
z{7PCR*@a~br6Pj;^@4(wq08r?&C=Ij#PKlrjB+Hq3S3T5ZG-g{<c>fD7*6d%LL>Pg
zipryuptj57y|Wh8df4FtwSEfr6%h{aa`WNme+|r}?#syc)Z&>!lw8Oe!9y(5tc%=C
z?=oHDLk$fpxk7>rz@M~qB})Y*Bxw)(Okq!d^989lXtn@J-Zvuj8IwJM(Mab=H|e!e
zZ%n-D&w7WpsRL>t2JzOYmaEpy!)U9cipsBs`}Rm7%)9KlU5$W@uDt_2zuqP*L#ziR
zM69i<gZ$(4c5_oqDq*p~kPskQ&s0_D;P=*%ol}<a3E9v5+Zv__goWiu9oR1RkVRHj
zlf;z~LyLgam;r_%CwT%MneeX!7y7wz%eOW%l0Uhg;{!=*>o@tN8~hduRsKDxy_`hD
z<`#m73Jwc~VukS}H~{f0Dx+(cSPVb|Lb<|LFLpdsTUTHP9UUsin}l&n_Yr;jo@o1^
zuB|T{!GVvpbo8P^)-pl?`UUaU<x?dfH6FCiy!-f(EaVpXUivgIFL#q2d6jr#@x)2+
z;O6RS0%xiTydLsoi}CVaa*}zT^okQCFq0y#ImWKcxMATB{ZRkB&+gl&n6nE)$A%>f
zz&o)g^Ix}&P_Rpjx{6OC7#xzd0Ma^P+$;}}@G^3wQrKha9_k9!>~P=D(d}YoTx1Mo
zG$hK+PkYHsuPj>{dvVr)ZSH}sKkNLW+t=Z-D5SdN24R?I?iy{p<EFf<AP6Fk^CEy=
z=uRPkA|3=H5`A$Su-oJC#CGzsyGCD6G9=wF*`W~Nsb7=+=)JYhSczJX_7fd)M)Dt@
zy=a@sKkKWLNwGkWPyTS>by|ykey*sQKBAVXE6d$dku$rc`%Dq*6{Jdc4;AmZ>5s_+
zM0}?>7tgNy$JLUvfBe`zLtQ<z>n7UNx5#XlP8+Jek};{6!E++>7Zv~R8OF}xar(;K
z)6bt6$e;Y>)lS>vZ~Q>$<0r$R9~iR+!)=P6w7yrAw^KKYtKEZYq+3;|jPW+QYCCSa
zs7E^;q|>SR>C+46&Q%<~>ord54U5LT1JbdgT2-}2G!#7oQ2zF<;%L5pS!5siCu%VU
zd+$Q-mM!=$Ih<J<X#RvWpXXMlvrx;G#m+S*kGb(B$VN9u@4ckMn;;whQLHz?RO{q=
zx$_kxy(1TYFEiu<;#_3^ekYlGrZi9*Ecdvb`A%AzwA#B$KK7_v9<h6cEkAYz?_mdh
znLlUe9L|)U@eL1U&S~-(hA`3^6|it2&1T{AO;oJ?-q}ykVmgVJm10Woz`=W63_JLK
zuoGXIHQ)l&TKz|wiCa!}2$C+T@c8$taFCZ*mzZVB=;!_#FP_I(<VpaS@P3l^p5ukC
zHIn?ck)~J6^ju1EPAivBugp8XN?H5AR+NLhzO1^4uPV>&EGpD&yXJQO$`!rfl{A!I
zRa$WMlE|qG%3RD2y7#PBzAe*9T_ln5kE<9XQU3Q&{<Ab45*vFCR>DjIL6Zrs@XQ$D
zLJ)%pwh;iDXbO<g6APF+%pw09^^lwNck_monuCAXN5U0Z1pWQ`!-x3k$67}&h}reO
zzg|A9tGvEP^W{zX>d(<~lZ<nqyKUC(V_;xGRu9U}X}mvWz`wNs<U??5jJsTkrvbtO
zUhU^4BAfia;`41Cl$poFenDNsAw?e+k<mf#S6hcFwO`8Yv;X+z`ojGx$TTT6`)7KQ
zPQ#NS9xo^R0Gy++5_%W?{FZ~|!@W_znf7c|QhnVvs}sGC0J?9=%gtdTU|-cE1mkUo
zft78`??w-D{?~K=ucs#;HdJ=2aci}DTUz_y6xK*$E8rz(2x$bIv(VZT>HO5Y*vaeD
zl8p|aB#1EEFCC9=ma%X9>~cSE&5LpTpWoVSC_J)_lJ(b}{^vjZ*ZoOrH*<60KQtmg
zNB!qL3!&!sM<TqVg%4<CWO)6@YWuGhBV2joOAU!xeeDRRjL_e!=wEm9?~l}NWNFq9
zl<m?*<zHVathWFDT<$R8zF&@1KHu?oi2IL6|IcNFX$T*1m0tBV_-Cd5_s{;ba959%
zIg_9JOF8fR|GNEu-Q_?h;RDKEUS|LCd;jBdn`@L=y{mf~l#KWvm-g?EG`b2O=qgg#
zxc>kDn9B5oy;IXm{<+fsahJ-%2MonNng9OM|FO#IF8>bfq0!=B|9*7;eha_1XIBFv
zzqh=ZS(pFgF|Gc+J+`O^_WVEY^7mr!kho6R>28Erm_B-DjwyI6#iz|0u>0=3D(^4B
zc3Q3)@*2TS-ff*6w-Pu3vhc-bm5W=LT_PM$WjXkSI!@49XD^m@eL&?&4Y2IRq}j9S
za#3tc9DNvi?#1QR0#=A&zY2!Svj$8nUvBOuJFwon#rY9PKTt0vA?$PP6-L-$rLh36
zVDJuF9_aIf0Nm!DA0#%{ri8@6lISR%(|S%mK8+|!CwHE>`JAS7nrXc6q8qoGmgr4C
z8P!%Kk2IWYgTBwu(BVnR1Ya6YLg-kYJzH<XHBn1tkPSJ&=J<Hh^Peh@qVCR{WV+M)
zN(+ucIM<?)(Tw}Le1n|pgMS3qBZBKB<BqCm-J6&7YjuaFpUSVBkG8o?pz9Hx={js3
zOi2~XKDO!|ns}UF^f$RLA~_pbx|rCLm~sMwVo50NT{2W4PwkKX>{`-Bn;Z})>czc(
zwKS+U9zitQr_Xx=HF3$yJHT2PS_a<1u5SwslrAg3-KH&zgKcr~EGE1`U!jtmwHPf5
z3QM|)GTTY?-O=|DUl~<QOYQwdJ$`$!jWKC>+ohkU&NlZk?(V^jbv^`#!9x|k$edva
zGSZ-O_pC1<GYmovrL7GX6=0bGWOaY;eVMzyu7iur7B+l+K=VH9s63LbC>j%icffEV
zoidg&-W7#72|Ud|8Jugw2MziLYfgGzGB~2;Tdqw++B+f^kRHzUCgb*HBWn^Q{ZDj9
zgm^)IfHYFK<J=_i?ktUF23SlCiq-K~ha*u2XTBPs6M-HQ+ih~IVT{EflORX&azvj+
zz$I_TJz4CxLB9~K1g-3?Z|-()zuwUEnSIM!PC4=kYH`YECHsSn_XQF}2Eut?u&G-X
ztIQ!12g*yAFQa9m^dDwpgOG?NZ?a<zCIam`nH)QQoMEKBxut<JuIUeW)q;u}5E~ch
z8k*ht?(l=UMF-$+cnL63Ix_<}mZ{H4KZREP2La)y{2L$Nca_|(?$Wulo_!cICnk;^
zy9i>7e4br4?kL)aJm?qxBOOvaH{76HA3%!mn+5G4)*XTz;Puc6TEMw4L1buwJ~}4Z
z7js@%e7w8@`)RK|N&(B0#b)V!#5&4r3M_?r&wx<KXA$L_{|tV2PBm%AO@FYf5}c*^
zN>EF$m8S8U%F(p`fQeAO`<9`^WkMo_K+kYRpYWEEy#auGj0iz0pUz!joQBi&sTzId
zhc8}W@6jJ`IxgzBMBMZH)3?;eU=YyARu&cv9QpA6z2gLW<8bN4aYdL9PZI;Lq^xhZ
zbz9N`fVxl(vU!fReVcwZ-~m@lh8|;?2M&r<CN(|Xic$?ae*WCKOKo%&qnJ35fFLT$
z6@AXeC3-<#R^m$gC>bb9-0-mP!P^<%ORRr@9X4D;A&ONng4lg9Z@e=+%OdqDLwSP$
zeu$8mGqjLy^s*&J;w<3|2aoGB=}1y?a?{VBVKio$?&#n>EK;9jleLB9BB)?E*Uu-f
zF80B!4>B3*pEM3Of~j{o>SlMv<|O>gUKphD0~Ic+3XOE@-|dHF;f$|tqn0G^2|Ih&
zYo)nJqj9frhAfdaZN%A1s0gs?q!`V&f1IHgT~NiPDkv$@Q)oq{b@?`W3wSz!M&SZF
z4T!969n$({*+mX}qB3Lw+A(I^As11@InT@tb1GJ+FvFS(4_AQl`EK~ffD`>QDZt6u
znL-1^kH|rPkmBpZ8uH*yG%G9;i^Xf!3{5>Dk`gulsc=9Uq|x{Y(}nl>#YJJh7Rnd7
z#HKAhQdp?8iL1102jJlobUp)nKT2JIZa5My338inF^$La6+uk9&`<zG1X_jF%NSZf
znI`oB(jp8nFJeV1Sq?K-c%mF4$R4;UUKAnCTV3u;@ZXsK<vfglmf}D#d0P==gNg_d
zHudbajlMCj+>;un={x+Egl3`u;OTMg%*q8)7_ggVOGi24g#Hk11_l-H-@_$K=VbvF
zj95@?iYf>ULq%mH31sbni3nn@teuMs55*m57G870*aj+&(ozO~eYu=cweFuek#K27
z4Q=*F%@#98a>r`+{-1w-WC0SqcroEA{pOi#^X1^w5GCALa9B1HlBZ7@@0HF*@Nxw^
zG%~_{uUGHhO2eY+LYqb&#q^GSL|X-P4zK`OUe04ZEHIFpVWP#jZ9~JfBS$dZ0a}Gs
zr*{L>FR(kRe10>X9<*Z!*YE2qd+#_a4(zC7j*4i&Gv=@|(F!0$+z~&Op2Jq1#JwEl
zX4q8Kl0vjmXcdB#nQ~!hZl1w@$EJy{9PlS`E4t}W8iA$vD{i+LaRw14(U&hN$#CR+
zV(I1OMYMinAV>@kgnl(>EgDY{2V+lh?;i3oxksb0AtdI6XPx62G1;)R6ql^yP&W)N
z2!-C>wd*krw9wO0i&UJCuXi^BZ>5>7b8fOQaUnVR`i&cv8!MMxB&lZ?;0|cRnwAXl
zRE|Vd&Eq{18VdOecuWsWc6eKuorNULbl2#+g@q-p-&kTzHL~4Cdy9L-O1Bu2HT852
z%xHGV&ZHipx2gEalgg}z@4s?X;~@-?=NDqR`!;sgxGsML&TH*D=SP|;9N*ut8N4>m
zTn;=!Cbr755g7Lin5A$878cU4gndy}o|e0xSv|-s9W4>}mWQ94|LIQ-NF1VYN~$Q3
zHEm)mF=Yh2ozgLI68i=BXw`P@=#nYu+0HAX?W=s8%UZA@NMb+;rCNQ;Qgvm{3}WCl
zFJ|wKG~CA2QJ&yX2Fp^iz_dPj`j#V#%AD~X-A06DBTitCt7oQ7JPt?r1o8fpCxW8|
zMpGu4J$>6X2J$j8G7w=4&aNfZ*70eu6TEafash&_#dL2o7}K^zUs^33^O!Qgg7JpU
z6XCSv=`X-u>ew+RE1@IiYt$XL!Y4DiARNw=Wy6Jnj^16}xeoXaAtG2<&*5u9*f3ON
z|6N#;LO&yBOrD<xnfo^?T9P&*a76C0y)6up8D?RY`s~|M!9NFK80$9I>Z7{+nzq&}
z)bNN;Bp=%EAD6qVIv(RCV8-)lrGej(_dt*%r^v8U{&+pyQC9iZ0lPJtIy&^A#Lkxg
zT8nWBbGYaNgg?xW)zJ31GcOA<f8v1Iv?c|>3I=)Ht_UJ4#ID1Fd?RQa_9E&_dOXZ+
zW|`r+&iq7yXD1g0{srvY%U$6Ak-L>sw6ZCpHKifgZbZ~lsz3G~$1u<21s+Cc&TQxK
z4X%?S^Pocp5)!bhdEtp6a!-`KTlM7ssqh%DMDk>jnDm=`!zciRFhO_dL>%ydkzF6W
zc{7jhdb;5e!%?Y{eEzDPoRB7H57C{`Ifw=mauXnd)${e;HYN|Ch~<~Xc#VkE=kAc7
zu=m@3jQfry_vFb;f)d^GmUYD&dmkg4u&<!sQ98S;w(-)7v(z>Kx?(N%IK^0TE{Or&
z>U5T3yDN53oSC|yv6ErlBcay2AH8#oiQrQRD~(7i{clGFN_)V3p2&@XD=m{lSOyT@
z$g5iJtZH6<%Qw>tkOOL-RXGQ_BWL<ee@o9pNR`5VeLqEFLhONb)epVuB}`JsJFDZk
zxy)juJ|D+*lAM8KHTr@+A(sFKX2h<!t)}Bv9NDm@`T~?2zM<c>X<xe^A?Zd%t-jum
zoElj4Mi#ad)D%oQ;Tr^LO>i(+j+QHpj^x=$@o^2He&^U4yfX*b7)%-gD(D{@>&NBS
zRjY5KyAN+|qE0eC5b2*)O13X}V9>U&KCJa+yf`K$R;a}J4#02oMD4}^Mqb~$e}8pQ
z5Vlh|VJf)20lnmxq1?h-31X^e$Z?V|Mnn-I7;dI<x{wSQKUYS)*sbWlw*C4uFgzqG
zXdl=h55w)T;xW*SldEwJ9Q^#zBW5RlV9`WfSRQ0f<0~73iQzo8`pySUalFjHBMq9Y
ze7d(~vfz7(`hDf<)g9-2vHx*ex^=tLLDj1r{jSK_I+9CY_wr30N3Wq5D+8dEcgBj9
zaa3>JiaN{hZLtvbN_SG!P-M`QkE|M?aj34^#_M<!;Wys)4_!l713hEw2l+|mci*N;
z<P-<CB^{^FWF6H<d>Y29Y(czMXgfp;>HKz;;z@;^<~Zfw3ckS@RBkd>d}7Ok0zQ|<
zydyQV>#^lp1+7{%N@FrHh7L?=gk1R1ZXlf`9O-TemV*c1D=d_mDT+@cMzd6=dU^(}
zUft8hPu6=--RcY&7|4OPb-jP(wjs#^UslUL5@0QO6i}MrlQqm{e@t2c7FYOsUhu-Q
z5Pg9kQ;IlMIOm%W#4Iry<18PhCx8#hC47niuF6qFzSlU@U&|Fp2C<Ez**5ABwLm)#
zZp0{PKj;}%)3ep;-hEj4py&4kE0;{~Qk2U1<_DE^Aci@y2u${p6vZlKg?9{#H3ohp
z&m^qCK(J*S7tvhxh#7Zi%81moo)JD**rE~HhnXSXpoF5bGUio&$xTZAwB@s83HdXG
zMZK9tq2im17^;v?)Jr*E=qX)Ho3!a8@L3pE^gX*y_hNY{i0Yq8J~!3i{t!fLBDM(Z
z)XV_dj!4j<%h(RARv1vl)=M8Q&%LUet0Q9QJ5#Bc4wsqlmB1cEhl{r1y7w7yH1cA&
zFbo6~E<e0FB2Uva9<m#O%tCTR{xr6`(RD0o>{|XOQtXrTI~-C!DTtWq&Y)QAICpW>
zX+#DnlmOq!iZ=v&-!x@|vE(FfBkoR4l_WfkM}Cu;C;yoi2(?CEBd?@$b~y|xW79w!
zYMJLnIa|L`t6x+2_{ecb;RQU%Deh}V)llsdofbbk+h^FY?sCz$tC?aW*!56y>TDe@
zGZYhox2HSK87UL{73LoIuS@9IBc6MmjBkxY6%7SQBrWfl2aZg%Vcvj>Y5KP|-JGT^
z29)90F*4rcfU)8^rr)v>X*leD-#T(wDF`Hsx4GIa@_G&oJ^_f_*KR4p??`qD7zhx^
zymBv>Xvm8$O(ujo52;L_cpT6LmVJ+fAL5XQ`g%<RJnmF4<AZ>Yy~iY}cj@wd^<OGV
ze;{#l5vv3G*eToCfA5{T;Ub4UihFX1s@b2&V5UtYOXv-8HE^Ik!`Oft=-H#BfN#Yg
zi}1soT&m07{rY_@SkUtJt=ojNXU;6+oTHU9`0hSF$?HPaqcSi{FXOU(z9!}K;^*h_
z{@EPfEg4{=w=phpSX@C=NP~oNyN3=%U#mc4_6LkG$IzEAUr3vPjPz`qhKZxv-VcOM
zLe=*y#rVy_z0kQOz^_Yw-Sy2xHGK)KAv)pO1Gglj$x#?^FU;vZP|-9j^&0}^VXMdC
zWd`*$GXRJK)gGl4)M78UO?>zYwPM+Eg|J`CHS{&(xNx`>Su=}`*C~+hktS38Se$9+
z`T&9eOD3eT+V`u!FM;*tD8XX^1Nc!4cpNSBa4()j%o%4aliSFV9TyM0RaMVKUHZ(B
zrq7#a(mLRD_~FJOaJE>70%M^Z{FyjYC!|&M$YCb7PZTS6xTV})2FerX%=zoLOV&`|
zd}SKlP{&c2Fg}LD#KdGU{}D|*s=2o6)eaKlslR^8%=DERL>=qlfgT&-*7ZYq<vF$Z
zQj+A{NSV|!Qpt6K$&R>`Y5L>o&0q^+PK4G_q0;l~K>5E35<{tI`49DP>KRkbF-E^C
z#Aa)aR?F0zbuHsZ$~bQ2nNjm9XXHx{pxZM*V6wNfX*|7AjZ{~Sjpa=xJr{LOa9c-1
zP2uVBh-|~ULgosVG6)<1iN1Z)d*PwHrGTjuR8V9{6yWNf%XAM-Y0he8oAN?Hu}ImY
zbnDCJ3T{KF{>W1}5+Ej3-+tH6xMtt-8;5)(QTS^+Pz{~!CgTt6OH7OzsAGCTrnjIA
zg+P**jbISz_3M8uTqsvyjtUVCM|r<g!=!E71UP_7jt>Ff;Rx7#-Kr4k2!nS#b7<qI
zE&J7b(<d?n)~=J#&tqi6G$ejM$*gjASe|7^3%n~OGoB)&7a00dXOKtY8O06DhO!6>
zj)u7G2E`tmpzQE;oIYoc+Sh3yGL+`O{bR$YPVI8w8SR`rc8;vzM<09o#`V!^zg6(i
zhLD!e{Y?HMG&8<?hb0H~GW21Ddk<~`M5hacKiy2l#UV(Uo*3yQd?zJBi$O%pS!}m!
z^r>UV^mp8pRgzPGkEb6G6rZgFr}ZTBuZzmdUm5l4C6^zCN*PTQdcvMAy7e!&$!0oh
zcIrfoXzFpke)BnnoVi)0{7SA(w!c!Tv}H9n$D@HGrOiUdL)9)2@)Lt2s+Xu&Bo5D?
z3p3y8P@_9}lTLYku)g(mLTa5E$1B+##~!WO=#fLgRKs`5?-`z-LYvCap=)mK>?1zd
zO-BcNaJk__I0npLu*hJSy&}MCIY`loa3CRf3wc9#bEdsYguXkAiM`DA5C++rZG+QI
zX@`T+k*e0de@_X>aHrPWnoi;$<BT-fqB#9v0f497hTbt5b7YR;CPZok<j|Otk5M|W
zY|^AoVK#tQWZ?XxLr69kLH2_~rmC-9$3vSz{E#nK%`8XG9=0%zmqYylWJj|lBTqlh
z{E(kIDOLCgwxkHw-`&^5(vR^r&j34m<^oh=8eE136P8t8R<!q;M4Ko`oVhWFA<=jC
z3}QZPAdf;Y7O`z0&+Rd2!A=Ac2c0+M^y>@K^025#n-UFrsBFR{U>Q&U+aWE_*`zFv
znbW6txOb(hV1j;!^E+{W!`Oqu-B~=3$<cr~Y&0+h$}#)aM!Cj*0{cyBNZp;C-AJ}?
zzH)TA0%I!c$pOj7(K%rx4yB%QhiZ?s^|w?)a5c&e%j`m0j}s```sCZyOsNI`Krxi-
z{6nsG7?fPdm0LVBM#oppA2@ZOyQk?+ARV@2YbVWpCulxENGDVClVqWfRFh;GAsNbM
z5I1p60cb1DfG7ZQ9q6T=d79a9FyZ$0ZI{hP(mTiNr?Z_jQt1!-cM9=oA<c}*6U=p!
zljHVJB9;N`;GZEV%iqXohCF=w6y_Z*JsOy@q9TXG6G_P>1%Y-h63?c(3THAYoAdIC
zGG1{Muq<=pvDA4PN+^K7)q4|8yX$wD_ldB{3ZWQPDpdkF;quseG;TWRs{^*vF23qb
zq%Y?eNVBM$%)Y|_p*Ym|IJ7IiS5=R@#;H?)Ak|b66!l8o2Ab@^3A}sf&fkbWqG_V3
zHXE*iW7E7W_}3ycLgXRiG3Mwa_8`qFLT_WBy-!vtyNs$4Wt;Y^Ah`xhWXgkFj^VP;
z&C|zkNdZ7L*&JED>>@7@tr-O|_)?Eq2Z`3mgxFBP85|!(h+mD3LIjg;Ua9MW@x73=
zeR2Z3EqL`~e8_HNR^y1@b{n6f+jRmR$z7TDZD6;Y2<2uoff&l#+MHWW{~!l4xhC7=
zOH}`gjfyuCFD!mJ<J^K>bX)SoByBiZf2DPpL<Jc)5iDZSC5BLuJCL5Di^gRI3=u`s
z9^@M2zje#3q;>o3);wgX;6s#el5D&318Y?JeM4HnKQhaIhC9-d2(Tl-Kqw&y-%KyL
z&SRm+BB}Ws!`P7VwnwsD+<D`5c0cGe!r#5ND^a#AWcFA|5YB7({DC1Nu$*?%%K{ZM
z-FCRAkm7nsYJ4n{DLRN#UO6EbX|Vv9B-18i5^fLAlB#-2ZYpW=O<GOO+bb46ry-eS
zw@%5K8>O&hjRO2KxwO}(RplGJd<X9pf*rL5b6M$x5^dk<Vu(s`1%M}MAfe2`Me1+q
zIQbOSiZ@ndMWd7>84621&K!=1DCr4;fOJSo>E^=KB;1mnMS)7mc0bulN#B0uhhh}D
zD_5<OrR_!-{)zD{+G(8cyV4J=q{Q;4#<-VcaSibx#R=U);v{Tx=`Q(W)6}YwNA2*^
zX9_P_B<=xN3(2cHt8+SBV<kaR+`G3J!l0AM7;_ZR;jMNDh7;BSazlo^WFr!S-+DWj
zi<CMwq6p-1vo3gg6s>!0mR5rNP|4I!^i^MKguh$uw(edzRM4n3DmPXK*^tO`A`?M5
zK?{y8=(3THdaGrx-T#^G?K3$nJibHjnV9X0huoZ;Fi6=5aYo%G&9+Lu1EmMxj#V1$
zh;DEj%p8Xlnn~PWL3?S(eMCyidqcU*P<Ex0whn!I@X1`E7XZx^hk()<(c(IGA$NhC
zl&mL&y^W%_=_w8qw)m9+uW@LKUtYiX^<TaK{-6wyQtU37sep=H#B9d3ljmN%*aUDR
zscaXY#z%kzf${4Jt1Rt#G_<FuXECLc4rfvO7zh1X;N_)f=0YhjPjDt(lvG=+vIq-V
z)4nvw@K2yTe~12B1#b_6Ks{TK(4A&BMI*%$8J|!rk9oHFz)9d^lx$E9e1vXAeW^Mp
z5^Wb8z|*}`xFD82FxwAGn&AGPo`Ikvd>@r5({FDf%f#yi<jotu&e}QHSApkXs6p9Q
zsdt?c1VSi2zI{lrkCrR41E3ISKSueMzIdUUI1?9d@HDm^?ULbTxvXPUWNcoRK-93(
zv<Csq2oTkrj))T4$;r=DXQ~c}aKRKE-RIV=MG%n+H$3#;mfJV|Fe4=JlMFMGJ%9YS
z`fWc`WKq{5nuCmZ_Y@@OExvSI7~<k}ZLPz-rb~ArF0E!8bM_$Chn#~z5zKAvrnEoS
zhC{(PEHMa<EOxF7U|lfuOmFx1O!^qeuK^)zOS7P){lP8y#cW`L5_rf4j1rPQ!;Rqa
z7Z)EdYeySt!p4ouArP&t_t6VVX5265#ti2PXF++vrnx9u5-WbKC|}Y_LG(H$jz<yP
zy5V-UFbm?!+Lg$48QVL2&6h(m_nr0CC2u#wgTe$7ch|6G5VDXFOZ$zZwj>#;tn}54
zi(XU}I9Tu)!N$}<U;I`p)^I7)At2>IG>P*OI`!8I<_V1Jg@6ZX97n!GG#XW9|G-!K
zM^0&Rade6ix-H%fOD6lLlDB~}g2gN#9Kpi?k+ZGsmlip!cG=*}Q}(^WhGq>>t0%Px
zA(TChlRit#1&=i^z2C;4*QvOe$dh}Gwg@8SZLEhmB#VnzQ0EeT9zT7m6lKFRgV1ES
zVN_p4_>Se)(6mr!>~Yz|&aMym8Ekdnv?*5riTFsvlI5~;ath7Oy_E5=8pcsi3}uJ^
z)3wR!#P2<#O0zNCmg$k(wmkssCo!hLr(p&3h0KpePa$Zr-P;PWHOEs}{&GA;6>v6Y
zEfo0mR=P>8f=@V$;f;4sE*gdwU*03BsSaXE_N>M95MX6QRKP=lR$?n;pd^B<yT5lP
z-Sh{2?A*1h-v>p9?o6e6!wW0FA?kPW!UYDwXR&Z59T{^mtYvN69Pv;`*?<ykTAWZ1
zczApS0%=s0+!n$S2C!T^C{lfRXLmUbi@N6>oBfzZBY=`DKdE<=Ls(rW*9Sxsk`TCD
zx?4`NG^K%FZ}Jw!!EQo7n;=g@|0Ak>5~ZcmCa=*LC(wYsBX1(M;~2yvryIv0H>?n^
zIA;Ll915yTXEj%0L@9rsJW*7eoH~pNHFz7$#G?yMG&+1uP15o!Oi}<M_B7jl8>;IY
zCo^vPFquRPjya(Ro2nlWPgZFckA-dn3O1^8f*>oulqnby5hC@eJTyRjnDo6I0VL#v
zbpj1TkmN^>h);vgBLN{e2*acr>w5*vVU;1EB%ubiCCt*fPP8L0=A^^}h7cWlPTf3#
z4Nn=1ZSg|DYA%(wP3DJiu1H2&Xt|aK4n9yQbEPWCCgiq5kh`BbY&jjWLP<b7n7O&S
zUv79TMxw7tYI#$z8^NeH!$-{~A1-*hVcb!_4r0q>q7z@OeRsB(S2oSTATv<M0DXid
z0ea`p)vJaGQ@1Lc#uG_|WBKvpLG*PTITEu4VZ&t_<skS7vLs|Yb{c20Xk{brsV{j$
z;mrnRfznXHx*V~(W)|&ag3#gVTPoe)2NpYSQYmDR=~`M|l^toI%v5${=EK<uh&G5s
z;Bu@WkO>|jErc5B-`GN+g8<Udl4#*s*->}L$gCqILxD1JhzypGK;p1m=@P7SOmY}E
zcyGenb$K50j+nS8_6i0$Z)<MAEoT(nRHJs7_|#9}Mo56Eqaj-%((B%)g#R_?ip~oK
z2!*;{#+9{E4ilW)x&~NLF@u>^9Ii%I=ndo3FKC!*{!7x+ndcTvA=<JMc$;KdFj<m&
zcE>bgdvZTu_vEw@*Ny^>SoqyA?bolN+j}$}aFjcDp5^wq3R<YQ=nT5WdcAgyuW+V6
zj)I8BBN|Ht>W8y~YKWZ&B)svWt<s*qsA@PX>1m=(W^SgJbQE{-i)3a1ihg9O-rgyE
zIUpQDLQpi)cJ)cA%s&B6WFcN=20WL=^*TC6fSkv~+@R9pEFd)Fe0U?g<)b$-8HgJP
z+aDa|5M)+?CFZG}446nrXKP2j4L65)YT;pCUss2n=pq&#)M(i`0YqfOpH5Ac=60u;
zl)DBv1<OxjkV6|XLMQ?hRV|San22uSin%6CXV1t8f~6o{lJl|Es7j#dIAP$$8uiCG
zyyHviCXY~G@Gbmi^)jBxaZK@yjI7y)oE!3vo>~e^*RmjJfJJnnVDgrJ43Iv3<bsPA
z&zU{Dzo$l64pUj^QWNqI(mE`J<S!|5_)<r+c1jL+Ztb*{p2~9^t5nLME~}5fYEAK5
zk~HQGkA|`1WFk-PwVB>(q<Q@C;q@F(=Tc2ar$0c}%Mp<`dcL_f<u4<o)!MgTz=gor
zT;AVNSy_Ad+Orfs=hGs(+{6`uT8)aGC(rO6eix?-hY14_JoMEmq*yM$ZH|lhB-|9L
z1o&>+`bl;m1A*iZPe^yeBe!AA336@UG^ZlL1&tb*HkU77mSrsAaQO7{a@QBul&SpP
zf8IR$8)xGZBbAo(oeslrV5SuYu$?dk00Lpgw(od4yZG6&we&N}$wkpmB=ldC*s+Vi
zR5{shDEY{qabYJJC>FU**xB$cPpU+c&>nacD_oyzF@k;I67$IWz({RLun0;&7DtWg
z+dNIKN2J3R=hSFAM!<jx@A#5pCNAiPc1@+pUMLtyQnz+<eZa#&yF$Ijd~2$!4`ipv
z6`*E?jwHMyPoGwbI7u>df>%%BH}{rScz7G-OCKEYVq@J$jiM6^e;=|wuwPUhEAaCO
zjvEfwvUo9e6?7r4!L5Ug@5{G1M*Uh@&4h<ypS^r4_=uqe;iu4Z^q=zq>A>8@i*tZo
zsohCNfJMkXI6yhO+5g+zjnv<EJ3Al7M_{(ddQP7Fl;LwtDhn0>YYP!>rKk~m(1ufs
zi70eGJbnC_Ucb{Ek!)%h0~UFSSHtRiEJE#W-3UC0@SheJ+pYcTPDq|HV=c4ogL@v+
zReMWmL?TD{gtQ<JMWuoM9JoH87c#R`_<r9hl6t+ZpF}5$N!vMlIGreCOAgzIO)Y;k
zYrqhD`!cd(;uwdHgS*Pv&n!&#3F}HB+PZO>!<|?*CM3sW#xBt>>C%Q%I{uD0AkJN|
zpl?j?R%eF_Gp`IWLN=O9%J#IC@2DLe2bch8owvS`*H_m$&)TINSrIB%lY9EN6k??V
zGKP1!vWFr9$d*J1nnSd#gZo$z3pRyCOsD8INth}kOUX7<x^-;MoH=mSL{GkqvG9Z?
zVH+`}fnKyJQ%Je`6|H#=m%>ZR4Qb+yFayn;X1Xw=OQ7pwYju4!hA8F|wdhUF7)JU|
z8Lp$PZ8rVPYnl=yyA&!d>Cz|KU{#PZY_(clG8`B+5?}$SiClkliRtN4OEy+lRz}*3
zW0c3iM}ih`8k1Rnqm<vY=9fWYQbAQjV?Rjx%i(RUtH<vbJ-<;AgpJ+l^mGomn3t`<
zLHs)M58t;-QFzfUFzv5d$=kMxX56k`M$*%ma}L0o&5pbg`ji&}4M0+g=$SK=OpLUG
z2SKLInc$YXQ?Qcf2XahaqaRWzX=D*_nEPck1piHsZ+UtpDUbGOhR8zr5GLV}%9w)`
zu!<8N1q2Wr%-651e3(<hDu^IZ_Kn4lP|J{o|IEsllO0s<AstW5N5bMuGMhRK(}<=o
zt{80xtR#veV!_mVEiEwcZ2+#5unM_wLFr7oXk$yCfw<w}<4*qbsxcnp%gd|p(~M6f
zk=$Y?(+dDRiZpoFxKlZVB{+D1(~R~3);fT*(6pgH&vK$cCID&y*nu%2<a%9Rj-B`z
zeRb|8aiF)F><5fDs@93p3b8C~6<(!bg;M%6-ZcRX&**uLzy}e>Tt<&x0BFW;RnRJ7
zHG`Jm#<)K*QE`>#fZe~|Kk8kc6z`x97)QWjfD_LYC=Q!5I-luv=a!A}Ut<0LMpTQ*
zc(55UBVk*G=~d35cd$X$IvwOoSUt;EuH1z!^M=2uB1bP-GBD$lFh#N7MI-`IOHflF
zeqs^hTySIB9(NqYYU$mBks+HQ;}x8Y*TUtKGjR&ad->XpC>u*{3)!`<_}By%?VDP=
z)N_)4K-)8LxiYc65ns9CYxC3GR;GQ~5${ARJDPQLm$>&PNRY1rg%J#rE&LR-N8=XV
zRJFxk{z;$jYp^4U?YfH+LjPb~wXR)WMGza@*uX&W7a}_jej{p&PYYPL?iWQQ%z<k0
zD(T^WjIeiX*q~&i26T7)_|g?CW@U)!;uUER!r+FLNAM%gj@f5pVQG1WoB@>}wJZyZ
zbxZb#_6yvZuS^6vV#SgXq6)$6RJrCVE581etj7}IK+*vDPT(}dOikUvoNclcyfRBa
z3EfI>^!xPrBOoBStu?g#1r3voab&kHMi>GSwauLqaKFt`#^Iu|GceUXxgG{fB_qGl
zBy`AFBTZ&QF~l*z*Y^t)Mn-4l5QRf8*f8QagkGwyqs=@E_3el1j-$_>B$_vxxzJZ9
z0Zo{E<Otap>;d|-8h`2ofR&%`T9N~r-?97PO#^+e&{PMR!TOyuhf`q}@F8i@xpOOF
z14udn|M50jyViES6V^O$|I}h6B}5S9f7SCRuU_37;z}RC_9|oSt>z<-^SK($f)h_%
zp_8x*5DeZ}t^43Rj~;c(m-=OuhBwy><C$Jr$GI3nB>{U8r6V$40g01)vuZepfgNmC
zyz?Yvf~j#@ItDm!{(>#~T?i&^;=D#TAq~7mb%&fRyXhy3M`0dP7GP<#p0jYuUzN;I
zBQklz`fsHfK5|9<oz#tBWdaJY#faLW;nhxW*s3uS;~P;8FRi6hNyMm$EiETXw$-!^
zHD8NeC~+BxvhTcAO3P$F{s2o+Murs-@Pa9XTVE<F2P(@uk=?)>d&<dcWU#F1Nd$~8
z$rai4s72HO_Q#^3=9UI^H-Ec&dL@!^bV4Y?ndbRN(4bn;?F|DBWW#$3djC+>Ht%+3
zT~w62VO<t=JhU~}zGMF>-rlv0sm#5irmC91*~?@{6LuPGR;gx|*GcXal1L~Q!ma4Q
z!jQrOs*rRa@I(E)0SDr<XFBR@Ag+BwLaA9un@hb@2w0fm5I6a}My(AdrL=A1S71!_
z^X?^&7U*EJ&Y%TwyQFAd8_=_&<0BsjdwY9#?+-2@sQP_Xl@&55Zbp1*H;3<l0X2Mr
z_gC`Pc?`p(j5I-CfavNM_}SmmL=uDVgP^~;y!mp@WAnbdJ}@K~-w`I4*;(L8^traS
z<Le204<6b*w^yK__WH5Lu18c}34I4-OB4j0iFtO6>mVy(#=}HUPuiGGlE=);#9w)K
zv$L!_!(VTU23k;iiM~zFnIITn06WXOPvN(H_|TU@v#(!AU-<KNeK6St8%C1k4v#zT
z1%)+Axrq{E1ew$~_yR-c6qJO?xRXi6X8y5gQNm55-1UzowGbCPHuPjqoXihL{EhL+
zFIXAElZ&B7$tJ;{gzSScWmFy7r>w*`!yAn29+JKbT??OnwsYLdi7rTKu3r~bUxH8?
zlQQDv<HwzI?|@fhsKb3C&%qQ#@)JG1U{nYj3M)k>L9Zo^W9yxu2&I(?`-iV%^tBJX
zIXU9hM7u2ofGW>9gdt&5SBQ28pwq=j31<`Y7pb`nrRCTpK#?$k9>^@%N{uPtp$t-F
z?#Zfj$Ag}Kg@;Oi&b3S?TT5NjEPlzU;b4$_)1Tg~yI_ZtC-1bM#xX({V5C0TCD;H@
z3Tb>^>O9M2WZF#q?yR9fAO&!zp%AeZ0+bJ&kruWj6QmayW{|c<WL%*y@47FMigE~X
zjEa2cg7`&@U(3wg2Addkdi~tS#gRAtX$iy$f`iF-QxOzEULc2RUa@gTnt3AW-G$Ut
znVG%3Vnm%BjvhIG{t3fpv_Ed{X7z?&*l2Ne#Ov;B@P{Og<VkmMI^^4wyQ@6NhRuwM
zW7vv!>VtF2ZrPQuEAJ&H`Q*Wnwid|0!4!~Gh|r`Yj{C#<8AK%4O(Ivf`UoowUs|~Z
zdfavTg8=D}Xi{Y;H8Lwo8{SM=3Kp{?IVL0Z8K(_Fz_#a%<)Fx`?ZE;eF9Zdao7JW0
z5?CO%6WPp!&4~gqVfDcZf(o9wZ~;}9{1rb-5~*!K@zSh(HiWV9TnbgfHW^ml>C>R4
zl)`{uRh^G2$$yy12x@~JH-W&3UcoOrog7Xr2|W#H<<May7(~yj+~T9g(5jj1JJyGi
zFJa$9Zs4`6ME}eDTB<!3h2+?GAQ|bg_O+!OZ~8MTQl@GRYz*dU;<jpb4vPx|82Am@
z2pm+=vllIvTWgJ)pI62vGkI0pbxXlIO!bf<&&y?~bx3F^Di7Md;c+s~*9ZR%%%Z+>
z7Bj3lj&M&LV}inG2An9se3E0Q_%zfVa7D7yW=N0j2c^L(I(I$k4d!I>8)JXF5;}8J
zv?jxKrdG`w@B<JRF$Wzh24VeacNP#i&b!kq7$~Li>ZwB!=0MaEGV(H@QUF$pYderr
zz3o?t!II%N<#ApSUVC}Ay?Xiag~8X~8>ksh)m!gGqX#Yj(j|M#`pOrIO(?4S_FaI9
zkN!LvvwCE(EZZAfdJ1xUgPOq(=_d{zL=~~(;h|B~)|^-)gr#NL_#H0{1Vp&v2nunj
zs@I#^Gx?}2xOcKkK;|1M1HIY_BLBw%x;NiY@aJSNce9$OoNd{9&=%4MB8qis3jrYb
zuq@EF$wDoyxOW_{g|8t-Gl_`4=9-4u`7BI6Lr9dZ8RNM1($&*_b4aZ@eE3samPGZ-
zDJS!X+?z+rt`9g`fz840WH&1}W;AhR9zJ*wV~EJ36ByM8@JyOR(nt@?atg@4yV~p8
ztMYQLMz@3hNb+P-Svt%9?L&F~CwJUq^ekW7{jhVc>T8zNdE9Mv@LBS1h3(c;3Eiwr
z^z~(|ju`H^3EU~U+e<S}zi&D3`@*8<-)jxNloHoTy{IDL3Fy{|h%hZnP9U{8d-f~Q
z|JUVaQD6zwATX8NChdAMoiW)RLSFrBYVzrFmFNUs#=U?&=ADU1TyC?E*BkX7N31Bl
zOVk-$8Y|#c)TDhF!+TDeRQ2ex5Gi+90>7L)_ZT;&B_5j$8g_T0DG7fL{!E+*S+c9q
zLtc77bTK+H@d?tb)@A+6TDCeJWRkB3%MT>=v?Alsam^8(bJ164#sb5b$-@jYes&o+
zN3|RjPX1Mug{9uHTR&2ku}Z005dAPu1Qaj--8zS!fv^4^ig$<lau&Ie1EI>nmq4L%
zo1yX-wjkAtY(g2QI#_;kGOfA3>}D(k1s9f;G6MvwS@B{tbkOLu0dLY7^nsra&NGQ~
zu_gB^GJ8p7&bDbxutx#U7P))p4#{5Kq_sp4iT1gS3@~eCrn57BuOFL`KJ}zm#plln
z)nw>!vX<r|nXVxe-2`2ZDTo~n{V3cy1siIy`jOhrRTnISF1~=}5G9syXu0&hI)B`#
zQ4bzIl<gWzoDH_rNm(SdE;)?r59}X>KF68jAq~-f!aJcL;Z&YTMfbIFd>RuIi2SVC
z>z(SOLLRn_mmcm}G@eX5e$%G>ozuaXP@_Bk0B90^Hx2}N=7^n1II60vuU{~sZ-pm{
z_zag|rNy#j^@1padNyTT>MC`s8&o&5W`$5CCB2KgR)LqNplgCyD(`U+hKZ$yZU?~C
zVVK-P`}j1BG^7@<n5G9e-Z3C_@LoNfH>{UgTz?Nzh90aBs<$MIUIqrD++FZ*qUGCj
z?`Zms)iD>%(x#?kdFrC_rNDjtkty6D9C5j`wCfrSa{SG;*&~A5e$WD~B7ennx5E=L
zkdc?q@V6|5ewjYKl*f!>q<cO)@*YRwG3EZVvNIUS9^3;#CS!)=E@jIq4X=|~1`ke^
zar@@Yif@Nx<UX;=FK$APXHExO*RJ-M?3&~$wp506s7?iKG&B1Iy;oW~D*b_Aq%yf)
zR4u2t(cOqvOL0F26k-Mjc_B2BTZVhi1JDD&b;%vU$q&-&pkJ4;7&ieuUEPd1Xb6JW
ztsB3`depm*Fq<Y!=1591W!Mfv1o)fE<$|hU)-p;VB%Hc7?`6JxE-LbDUg4yEC@oF)
zSPe~c%DOqux_5itQuOlWfP#^LAZ-`hjsAJ$Zsr?tWY;$IP<<w2_kf(bQ$Up9(UKan
zwL{~Dvftz5UrM@V^a$N;taxB7Wo0HD233V>a7yeh#ZKxG-Vp*4qjmy1amWzD{3}E^
z1cIdVAG}TV)T_}55hDPe_K|CG!ID_TtlfyGl{P$K83<#1?4M=|PP>$TY@0BWp{)^G
zp(~9{2Mk!eaN)+Gt$9N>Aq{2h7BD6kPo5FGMO*a-IuD==Dq*GXp*i6jfg^4g7NW^|
zab?{!i5DtxzO4sPD1UbEo<>VWR9<%IufgK`gfa_q0ytqj_vIFvM%=Ie-1OjU(cye(
zKa`wkCK-%;{Z2{PS=-c!tvE5KW>B##VJ12X2n0cD8=?|~4({?!uti;TbmBXBGO)=z
zF}UetL*;dqpqH3R336rdYnXv0#}@)%kKJd3nN~4U!$}^uh4E>}lHz-*PbQ3QSiio)
z)i8B0J4A7EEc&0R?qHzdi8ioqpoJ4BTK4TbS|)9Yf{$k5cV~N&B8WZ^TA9_+N4rLB
zET$Mkt(HJrkiLF-?{PgM++<6&%&jTV8OCgbi$}()Ynxt?1c0DLY<qlRY8h2q#7~*>
zKmcp$$VNg`%Sd_mT4=Uj_@$gay=9aYfgQGxV!xeskMgv6D8PA#2x>po*3c-ij1v^0
z4(Sa~YrbVNsTIJfbc+<wj6MG2cZ+A_g$b{NY$V2t^HyrVY-cjm+?Q#lGtLG~ASEE0
z0`b#BLUUT^w+~aAccPwDc&?^ii~kD{2A*A?rB&K8|Iz~BQ^yp^+uhJd>gs}@RHOPQ
zQDqztv@mcEure-f-qNYfGaZxUV?J#NTXyjUmn$>SGNj>lYy2Z3I9E%80FV>nt!nS$
zB768JH_5amP-RpuK0hR~30yBcE#)G$;=3}%h&wIeXmT0NM-^37HHpkAJt4m<v%o;)
z!e}4MS(Jq^hZ))#3NmwKq}H@mF%vwIkc+*_;GLwp_`Zny!F}8!)5lMTb}MFR{~pbN
zM((OgMCNGZOeo8FO+nIF*{jq%KhQ<6G_Ma>1pkTvLS_>ubje$NV*D8jH3S;~@*vOR
zAHzbzuY!XF_gT7T%|)16ybKuxCGWn9WB@yG(UwQDom+OMI280qDnQXepGycpXYjYQ
z+({~t`XqmQ1~1Z4e+oN|u!A->9bGr^pTM<e>Dk6T5E}}nY1Bn&;{ZQ(F#@ilcW*vs
zFsg@kLWok<bcgIxY~pC7jE{>eef}J=p{V^qco={=$^~(E#|dA_WI!;f<_eyF6Ys}<
zLH^lot9f^LQsS&qs3Ga5=?t=<)aGGH^}E$>rR=~xOt3}<?UwDg(|$K)p{)Fu%d0-8
zJ$lcX7P8TtX?zrL6+_ZuW0f;BgqcmVvLRYT8&~JZ4(^cxbS}BirIRuPk%1!7#6>2|
zRNlC63MY4pqRcBAn%7(JxOwvQ>9&Wp<eMnCk%dasIR35{6e+Hoz`4L+A4$V0(1g}^
zZldOa6uyE2a{Ty#OiGk$mISVX;@~`>XOJe%y7@zLa-DtRL<Yp{PYf>kRB9#qW*zc}
zc?XTg&cEs7RG1sd?yKxQOjN$*PH8!4>u@p>=k)Sjpolyt!O+ejU;e5Ul(`#m?&;Ir
zfQU+KN#%kT%x)f}Td8kmp{^XYbr;<_auw-~mv(b?uYh3Pj#9h?2M05QY3v^B_xJ7F
zv~2oJH+uq;M)0GNjcwX7WFOVi0n{EOxl)J8`~rYSj;XgglRB(7{-;ruEyJj0F?iRj
zl}|b*s3oFI6owgl-e<cL$RUr}u?m|l*4WLV6^ELJ9wD^G?3$rP>Jw;su<^s_9ZXJf
ze%vS{q!695UB-h;j;<w5B{7n7Thow!0K|$$yD_t7HM7=Rx@Dl6D>s`V%v<#Tcwe*O
z)Omq~hj9rk$>7TUt|-QN=L?fW2%szA1+X;N@^YcV1MvnNBk)s~zAqaX(WP~N3P?MI
zAo;em{s`7g_G=&Uk|M?;ie>GPRq+n#-H19pLVp76Ot-Rw#XQxmMlgKS$Bh%F)A0vY
z*r7u_&*%*s{C4Ys(XnFHH8iGQTxRT9acy;0diu5d_s4?*gQ7Z&l}oxqYi-1M4cTdn
zBo;{Cugd5~8^5U!CPAh=6Ro<(#zS}Moi&fipf9NQ0DhGAJ*4am9Q=!oLO^62vo%T2
z<=!9%#Yc|V&uPafzmh$b>%R6A`Uz=C?S(2EWhrwI?>rbVb;*hq)*0@CcE2sxw^VTy
zi6OZXPd1QZD5~yHUA3b$%5cb%E>fH7U2>1k&FpErLNEa%&y|Z=-u=*`mbU!rWr)_K
zb7_*x;J)MIZ}B4**V>m~9XWpd5^hmn{9cmYZdLI?MCdXPkvya0c=Dvnr`bGF#5Kd2
zz?hV58V|TBjAL?f@u%2rneLm>@@2LWQ2*8E&%4K_mj<4f@z|6Wfba{T9(QvAa6go)
zt=wjjs9jtrHfMt!<?Jc#D(>I3w;c}wS40FN#0BwtkQBj<^wTWJLmJVy@fg|G4jIzc
zs8~HW_8pd>7`HeSf5a!)cK^MKAY$q}Otn|vS5zC6dKQTXvg}o`_pRgJz>FLjlPs%x
z+p%y!j?x=;AdniN2t<XV%gQPXDz|FaLPejrHFmF9ToDSNIIIw$jvgJ)a-$D7Tk^4N
zVc%W1#OB$vu-REhMT!=qpv+zA4*6w7X9<xT`zAC8AnSE<KTc)mH`>|nQMB{|r+nPj
zCem<*d4)rre<#Vn%#1LUvVD8xz@9}b9aiGE)X}S@+)C9L2AaKh^Xc`XhYxk~_4GGf
z19u9>8Vy1hhxek;PNw0eW)|7g^|t})j6yXmG_u^fCEIm??BTqWe<fzJBxV#BGBe9i
zBl}4|mv1;BT5QBTF`=Obl0-V5)-X^*rJz~7PsU?x-?okaocH|e_tOg5$IfMCb&oby
zd}Bd+MiPg{P~qzev}JTNg3VaWIQ6AW^bQV^>}B&6rCqWIaAO~jJuGdZoG70b1732{
zAalv9^uei;-V_gqQD?$$Z)lyz#VafCL}AKcN(|TtCGE^-JD*m2?J{8}^CXRpMJA$*
z@tm*}0n#U3qvaX8BY1MIzU#f=s%E+=%S<qM0FS1`Yv`QS)H+R|R~p*Ru72e+!Dx2+
zeE02968T>7@gh&HJMp3?(!ObtNy}G>u6@|EOaG4vk?+zL%BrSjNW?PvQzonS>vv3S
z*w=mBHPs!pv+lQict1?8*S*THFF8ls%KNN6(XSalpK*_mFCVwx@UlhV;B^2H;7isz
zcgxDWXRZFoHKcZ3;N#<X=X3l<kcNeD{#bKikq8TJ7?iW#eT>#on#Kn&d1dy{7Vz_*
zoCJUY^{~me&V9TtH>-Tu%mh0x29cS00G#o@!M2pt9>aR0biuKOWa+VY;PevXL^I86
zhFxQgDQ!fzD+pT%LON@N;x__IKn|JUMq`!SslWxH>*o)Gm;Up}5j-f>)zxLX4?^(9
z{9PLxuk6*3<4Td4bjkz=+n7l`y2RmtgkF`di6wr14aic2MZ&h>Mp;~m=C^>63JVKG
za*81jBJpXd|Mm?P#h<vbacCEQ=wAG>dt5$RQ++#Vn|gpi!-oEK9%j9I3DYf)PphF;
zDLw4b6=w$O>$pSX_l!B#n8jaV7ElOE94)`>cr8<sPgXqh(u(7(@+mX6Hj5YLlFk9q
zae5(IcA}$5-tXYgrEm*oGa1xf0^uC+=10*%XTyF64gWarY811hE1(aer*~z!Z7|w&
zwNU<olCfJ=vV-kjQJ;|f>i6np<zJ{?UmAkwGB`N9&gBwkB+`i$^OkM{F-3-k>XjGK
zGO$Lo(`X<KHW|kt8DeF852I&K6&q7J#Hs98F`IdQ3>I)B+&~C<n=uV_z%2s7KXvLW
z2HwXy(rW(9P_v<_87drH5{#TvbNVrR6abd|jn`pmfb?8EF2yaKr?%xq@1Z~^PLEV|
ztd%FH=B*b5N1zo!$*LiHv1CMHafRaUXN><gWP1P>_W%%y`vD6U2z(efK^rRWb~9d7
zL|;|DQ2+A93x9uq#g0A9EZc8;=#-k1^C~Y-^mSM3`q{oV0p`>xMfE1(KF-6KBFQ?2
zAL098t2z3LA8O|2iw!6E50BNE<fN^-i_x0r5KqJ3E==&@JaTc#r#teW@oGk2nqs~_
zH`Qd)F#=p*G9aMsaw9ZH$J!f2tTK`qF8w8a-O%LJ$B@oa6i_Vjl-ui?@83&quc89}
zYmX}!rzY7KQI#1Y)MvR!{;*x4FU@IMg8#!Yr$(W-!v4Z$#m&}-11!9{k>u3iut*?y
zdnb7Zu?xf=rfyQ`IxQ_N2%dH?ZtB{uh&|!gt`FL7Rb3lT!hP_aO$)xNtgwLuwua{<
z?$_y5G6mXoY2=Jv?JCa4=GWQmy*q#*f6Uy?*3{Vc!Px)7v+>}E<Zoa`1)yUUE{Px*
zl$LxSgCN0jC}`G)4V2zXb~ltLe3yA{sCjKNQwzI{3q`HhOpN6qzI*egLBr$$yDwvb
zVS1A%m;Y@uhk>I}m$ipYHe8;e6$eH(`d5hF@U@c<y)JVynwM4T{}U|H(D3WkgMu&>
zbO`arlgU{wx0=ScqV49^DG?Z+4E}%kK>%wI;Bx?e(s%FfC(LtTX_t4t?;4PNk~QPM
zi<=W$z2T9O%^@_Q*1;Ps0#<7G?yi40jz~#KOoT)g6yrGMbJ}Z6-x!<EVi434J2W%?
z5PA)QQc12=6jQLZR}7mwW757Z%JL+ENJ4l~;*olH)ab}WS{kumcH5<_(og6uQ5w#o
z1wDH_T*_I5SzV4MaVMbFKoaFf``pq6=H|6m!4S<j`><x^kte~;TsF!5Hsc?NM&sbv
zXhgrUs!I)b?W(Kgtux#ZL@Vx_&9*`$2UqXsGn`X;A+hkZcXQVqHLgY=Cs(d)c{|Y}
zNlCDQC5u4J=6FQMTr4Hv<c(<FYT!(xInVUELU;3Sre7s8y;X9K*>tGq+}@Os;Mfgu
z&`eWHrlKVqsr9=^`e^=?!L}z0XYGs4=jC%Snd_f5)fC#MNtDWCu~Xl5>$~?WW1a_l
z1ENCCXV<aVNgKb8ze?C8(WL<kRIGgd1cEtxh?PfJp`M=P=}GM<^liJwsCmxo)4%_E
z<6>S_<bAcz@O?+q(kyvRG<ac$e3M4NUcI6=+07d8w4h+a+Qr_77<uMOt^zxpm6>@k
z%n;I#rx=W$4>jr4L<vLD2=Q9u&$#cS>!3#U;4~6_`rx;?rStpG1@BA96Ki$p(*9)@
z;b%N61B)PIW7k9bQlnM7jH3Q^l%Fzn>IhQ3L2oXU7@K^|a+=vv{1MoOb;5h(W+~2z
zjj)(PLilZvPo@_P7rHJqHAr(skL{Gsm2AJ3@%R&y)B#Vv{M@Pp6!*Hew)XXF5NP?u
z%7x>L9cH@t7G<wkwoI@!MwC^UAG1d-W}EavFM`LqGmvA%Bu?JvXXb7!e#9t~JybXV
zOHv2MWPvG4w;o5#0Y^>@p*jMcAJDt^d<?LvtBuceE3B&LGr$1+|7Y1As$B${`czt)
zFVdsp0y@6ab93#dSkg$OFwB@r0ik;8vm?CAz`?`tKx8D(xL6!20S?F!RgMl5pTaw{
z{gz6yn%jVG<Hj+#W7MU&9`%X~FT1ODe+ovY&HoXT3k^)`t&Pk6K;?yQh$aljW5}C0
zPOvSK+2sKM$k1OZbijqx0F9*8q@$C!Zw=;EV3m7P@9YF4#p<(^iBY+}SPek=#+n{t
z6qRUj`x~3}Jha}ruM}=SpvzE+lI<(Q`Efq+`d^#qEwQ58Vw;+qOC_LR+|!M(zfBQQ
zOEBNjCS@=UAikfwX-1qD6!6F^YIEBLj5z%3#NS3P(6HfcEk8g-#fwD?P0>2wg|LmT
z{4-}R(Jn#p3(|wN7x!ke_}Zp|s^Nq<m{K~<0@5q3R|u_1k);QFhBf-2dE!9|MDe*J
z{BzLKrF>6kTTz$H{VH81RXChUNEk~AlyX0uM1`c%(NN)0HuX5ithnR_gAD)rYx5_~
z?%LW|nru{#fNU3=-+B4+%5NRhGKyh{WojtY(k>DMI}k`#;(+3Z*x|NvLBxiU2|By>
z>=`}pruq(gopVB<)_)QlAo#>@=i!CoWUTf<H#RmOIvNY&qpdE>b{gv2eePH=kwzW7
zM~-!xs~81b-yTICicN(4qp$d{f^R`<h6HRu<)LFv50-NATm_(GqOFSg#jfh=MPxcR
zYo@s8REjblFiN;Xd;!eI!Gjgh)f}-w<}@~+Vh|DrFRxyqKk3%JJ2JTS&w3x+Ktt+l
z)KpNPi(VKj&dg?TFvWCt+ZD$^i0JzQ0X)`;Q^6O^+x%E2qLFP&;b6aG@4%)(y&?Xp
zoa0y-|A@fbQeV)M;ihZxneEcW?Q{I(ZH-hWZC9OUqB;jZqcr5w`<+vZbRTxc>!d(L
z?9(;1-+28eSHNh{_Br{K>4GycP&rzAEM@SUmyDF#=0ZZI*`<r(!ikHt;_{ky1gXl0
zU*{Yu0h4&V@0^1^L%)!x9(fReu(mulV$Tv93kf$Y^~;ynq22|N#T}-opV10An)Omr
za<T6T8aHCy_dw5Wy$mxs)e5KkdhWxZXcBeDv^nU!#a0*Dv#C|i{pr_0@<e}RXJvWB
z^GIVbjS!juvZvVD?ysq?UitQ(9`B9S>iJ?OwfoQrS--{$HXf=YGN=1?%}xtgycj~M
z27G`(d|}c_zxML7w)=Z@>xSC)G58V5%jhA+b-|3ks2Q7VIT!HPFhRu#=K-Dq*;s{o
zit?Nfx!zh7igT!I$qB&g#5JQsb+5UXd+Q4k%So}T7G{7tmi~o&-60QQV!FP*zNO{%
zI~~!?AnztmM~qa`RpGQY%ZEM8+oR|$zTd=w8=aNO4vhS3!uPgMnjrb^b>DCJX0|p~
zb!1#shR)}A?;1(cC(gJ3Z9U(v`Kr)DFm!10&xNpvM1ElaFtu)&Cq*y(8YhpleBX>!
zf*L!+v#)OlC)-)F5#@in_%f}Gw@tqWXdddl^EUHad`B^O9s3_{HqNH~fZeq4F`B^w
zDhRo?O2;WRlyWRT`l>f=oz&2G;J~sBA7>7kLq%@ey!6#+%JQYKBOe&P_Nz8WE(go;
z9d?W-OiAhZOvqAD<{ReDVfs4xD`e>8%Y7;@=W{u%wjfgvZ*P0fxLeV&`H0{RowNo$
zdm01mSQxn)uJ2ntKrR$K5;;`t@g@E-%EjZ{LtQQfIXg#rP6%PK`j1liIvI41l1s6J
zjuvgHB_+Xt2&f21F|iUu%jsE`gHE`j*^dp7(YNfzY@UPX^y%*_Dh}2+;gf%wV>DKD
z05S{Co*(qup;<afp@D0kQKwJ5B5$Hb`PLu#3pazs2?>8peMD?NZxY_=(36ZFxLPB2
z@DvJ+jnmDh!jBh8XruZ>vjQ`Oj@P4XWi~8W5O4sp7Q)A0Cr&&&KB+e~pGL0_ph8Gd
z{Q?6|7InVm9p0kg<_p2OxySI)owMTH&GPPSS#fF~CO|$uG%T)Y%xYM*T^K71YhJ{6
z@Opf;B+bumIAG;RM~_hRRGKB&wG#f>Qyn@aP$ungJkUH^Rx>OT+s_|hGn{)+D<(QU
zU)P_PZw$%F$c(O8kYcySsWPiHusodx3<yE57k2RMHnT`mtyfx0w8EOIyP}RhU#qDi
zA4z5;<X$x|=w=7$@uw0tT$SbHL^qwX_wW-r+c8ycm_gKL`@MEmFEchd|B;av<bsG;
z+^3Wq8ZH%dva+(rs;mw^$Psz&>w%=IXLz%LrRBA&nOdb5$#-A?%EH_B7nX#K$YrMM
z%a^k`6+txVK49+cIMc#gw|Gk?Mn+q=SZ=aIal^dj$Zw^C<5^+)R3A5PfU#x*w6l<a
zJBt1DItqhru(|-upwHLk$smd|lEBL=-pg)|Ma4SazGdgWePdpa397cCsnmRL$C!7q
z?tv%(Nr*ozWPZu2+E*`m>VP~MYq1(+>b&ycW2COf*F7j2LaquB(!NLSrPZ|quu(a3
zWYxPOg9WZc0Xi;G8BUm>vEkZ9r06I^65KvAJZj~hkuQxgb`LBVm>xYx<W@!h6$GNS
z-wo9h#eH@22;N8WWTkcN+jnQuXm|HQ7#R97iqbq=z|)9fupTv~StFP2$~DzQ@C}p5
zIm!_9S^m~r9c03tWIwyhxK^%;ZVI1$??yqvwKFf+?uR`taV7y#;QMZSiPu7n?=fkT
zFm=_blUC4G`M*8UzOZMW-@W^p--F<cc50HE6wA4znaG^<)Nou9jZ6m9r+;MEiyg>s
zx_4RZdct$Yj7yAu;ZmWDPE_|N>HwTksB&;!119{gJKDozHF|Z7MF{CTR?y%AAaaa}
zF&M#7$Slk4FM{1*8<R10?l%<yd+aBj&{OUq<b*!gVvq$=VXI#+KCdOo_c7N-nof=-
z){?JTZljA7gKa=>3c@Mu3WWq^#R*DpYZU>3Vu%0*Bd8O$p7YTKa&oS}KL$5i8y{iz
z#I~O9N7Okn@ILPvcAlgH6z=+!LUaHmenE9iVs=kJmvcU_G!6INN8{}$w4~Dufx{-2
zIN6sjZC~TVaZ6K6fb|}>KZ(ilNjCw-^TM)uz*_gtqWo}l%maEwk%#$XoE?29VBQw<
z?r75l&4IuD@LJ!c0!lt>p(L%960eJyR}ruqNGL2!tYmvl8RZ-$CRC$fA8Mq4At(JC
zATz`ZTPv#_1yy;&6b6ftl5&}XYYc6tNQGG@lxiCHNAbqVItl;4=ZrQ|nG$34-dSeW
zDuj%W0?tOrDG8P?{txd|)$>G9eK6`|h*&D&uUl_m{l}i|&OW6OcIdU|{#z{lpCU=P
zb}g#!{MMGzbshE%QH-)kwISa=L&EZ5jZ(#tGFA`mC*Z5!KRoW|wN@AwvSJ0TJ@Sv9
zkRKC5Zi2KkNghaSvaVXHW~aG8QJkb|?b@Nm38SiWafzl^87jcXR+#Haf#f++o8pF5
zRrq%k<S3UndE&$mM5JZQEZ_Gwd|}i~&vF*+ob*QR8@?{_=Mk&qF-)TYs^m_6MH}zG
zMMg%Jf$w1+31RQLyu8P-Vc6oM8$YPcC@wtkA&8t*zSGR<KRYH*9K3cdEF#6vsdKVr
zI3w~!Ab$u$irWo8uKX$YTWwhxu=|g)@ZQD-8u~K5Gg(5A&`sz3`W%v0)zeTwd)H-h
zl@q$eoyzj^)Z@o5(qvmPT@^JnXEUq@{5Cc>?O)zu8&igwp)DUV;uV!H7{iM`8okHR
z(}1Gmuw~ais1Z5x_gKyqLdla;dvkMhl?Md<A?J3K60+vwM~_2V|1b(vxOJfpjf_Gg
zohG@>+uZH-D{KL}cV9Sf9yTm=YaV-^1;jv7O+aO3Aa&{`x7mGyaWh?WT6%hP*ndSF
z!pWhexIDva75~md+p$GUceApZ8ij?R$XZ##1Z%2(n8s#q1~KgDP$gskv0<3ipi{&n
zvXx;LqgLsvjm+-xGHd>L_BT6{<SV!J=R$ls%G;P(`+B!`81py;k$CX91OI3n54NLq
z;OWWf3@!CpuwYMOqFdc|-BFV3zC@mmiJ`(W&6$s5Ai0m++EJ{6qi*UZ0)b0^=9E9D
zMl4h%S*)x)gNfmZWu5lkWtf;kC(Vo+XBS^SLFdqkeN#c{D3!?mK_H|hg>M^>Er@PC
z2bvb&!m8;s(jZ&gwNw&8mqaTDoL~GBuFoM<5d8cje<a~RG6=GU7fp0RsZi%Vdv^7*
z;4**4kP%@d*3o;KNtM71w>wQp&J)vaI3~&52V#`?r@zlwiLNjV=*Em4OXbO0?dYfB
zb)8cGJwO@t;hKvu5rhN;5yJ3F7+WW^y?4Vv$OS&WwycdK%5o2$Ixu|Ab=NxbjutL`
z(BaT5Ucb5OsFtGG-Ax+}m%`~$&rysst?_VT#r1~k!`xFp%X=Cv9`@(J0(c6pf3l}1
z_5|Ge&o6TQuS@2xtFur}G<VQg3rsAhsLHS#&5-X><viXpRR<QSKm(kizD)6f6}L0P
zGt;po?DevXZ0>Gk4+(DFE&bgYrm=B{xvBD}>nk}#F)_5Y-4o(H%Hp6Aa;s@FPDWue
zGJ08~TpY2{sCoS7ZhAORjv?bm9Rs8nMAJ^b?^qmHh$QIt83QNGmermQ%bsX9-4fRY
zQkv}-2afVyCNr;r`2v~?)Fy2)4BzFBPZ!9t(6u~h&^d~^b~^^QTdz^GkC3g?ts4Ww
zEQbu~>VOZ#z!_(cv4COp^@Ae2_qDl<Ad|}UuhXZO;5vY2F)&cKTendrK8TruwzB`}
zN7yr_b%vQU$sn<oNI_aLW7Bkma5Xi5p{L*&c=HA$q241>?&B7gmd3N^1zK-w`4bR1
zvOWuSg2sg8`)?V=qOR5jtx*!z$G?7|kw7(oLd!XXY=^XHDe3O^-1Ua%IG+$(pJkJR
z$OCSbZ<5K!W&;ux+Xd7h`VX;5az?dAT8RYE?Ow`LI>_G`CAjtSa5d~Us(xU};?EBc
zZ=|6Dg#6&6#NE4l+68BDOu@NEt6dYDOG|b&K7V>)2}TCvBQvRGImrHBduRTRb>8-I
zBukW~ED2egR3vRG36Z5u+N4CwD5jFSlonZ%ORKFJ8YMA>rbQ(*$x^hCX`#lnSu&$d
zmKLOVUf=0Co_X&3p8w!^<~ZgD;c{Ky&*$9U=lgu0{JAWzVYV|Fxd%exE9e^)^s_->
z>;GU#k@RYP32dbRpc_JrUMi209b2Cvp2UoeD#1gLgVBI9*J9(M(4<246Fa?g^QQ8;
zlQEvmP5Aiw4y1lgRY4w%L;!*vRm}$Etu4}|di_M+9rtBB@=65T;;hOvM<op8#hUeN
z+7KWFKS^1MOt|k~Y;3u=^KULy?&wdMh4Kuiibe_se}!eM$n-`}>4vmTcE~WPIjY0J
ztem)WV#?lHL@xmQVy^z=9B)7FAR67=b2qXHFt@4A6?j@EMb4cIfF%+5M=E~}jtcoL
zco+?}@I&iJBdQ<tYTrQf)~<ObFB-_=*|B~IU*$&>n}T?w@dWb!?8@cRS8|Q7L3bh^
zWDvM>g7Q=b7;2b$*r(kS^2RNv=SC=YCfs-q{wWNqaPJlR^@}_qD?5knHoDB!^WgM1
zFbxJlmB1P`aFb?P#H*Uxftp+8;%}iZFYzbT3HI|DciN?#KY#zm4J6FhLasA1^wU<~
zi}6jyB_M%Aed#*C_FX58Jcd!4e>+=4-y(B#pr!Yz^mN&-$0;i%e@#Vei|wQa7y_ie
z7cVq*bxF+*aqjInUosIMGr%!iA4GRz^D7-plWp|S8uz5PLnjq}=g7j(Qo+xe_2I%J
zW*|0n0^LE?gN%}RLvxFdq13uUN!VIcY!QF>@Dlm~%r6Z;_AY9GL_Z(iT_LxV9B<_W
zkST$fMEXL5-}NL(9<dMwpleAqzaE0cP;X71e1+ks$X&Z)M}6k#*5@N;75{3JyVZAL
zHtVq>{i%_Zl;X(9INNBg3xK8=F1>k5A_NymMH*X!U@SAeRaGS_Tjigt_wfEp5tUk2
z!)$G7w9o?}t#BsnZwj@ZX1|;+(8+s26OTZl6?RnOz}@CsQB@;{PLh9aq7SC{mt+Y`
zN@=^=8WrId!0E!|e}>meqX!qnPHkv{97_CrMde_g4PF%w9Z~+83X@S#TsfT|&BS(!
zJ!Wx2E2ZaYsa~Zjg2SjC5~>q;-o?1i#I+IaR+6Td_tJ!o#Kp1pRE&TyB=PV&?ObMM
zj|TXm2%|)75hj|>Xdzg@daiXvo0}e~VNfi#2Dt>fg3XXPM(pHlQ+CAS+daJDv^2vH
zbInxymvMFzNCp5Yd)mrJ*3Ugl<T(qOg((Scn1ML5WbU;|PPL1bZDR8#XX0E4qjMPY
zBh@yL`Sdt>Cb9(hz@jT91P_+h3d(<ss_!RzWoi8OtYSSE504+OT$!AhBC+BaCII+D
ztCB-$8OZV*soB9<MTJ~%>?`(;#6@q$f0!izQb)mm*>@W^qnDeMBrMHRP|9HPp|8$F
zkq{vtKIAI2x3%G5^}<EIz9xyP47}1bdO=nR2b>~=`mvhWpY0PA>7g6jLe(s&;=?<p
zr>dppa^kd?u_}{}cUO&raz|iWIMdo`i+4gE^(Afq(?l3i*a$%}NaceM&a7GCzDj4*
za_KRW+t<k|YOY5F!hE!XxE^Y|(zwI04M>sT2FD&c<lLYfH&U86apdq}_A@wniqfx#
z8HU3V#JANtZpGsG%wN|sg>-#1^-Y6-2GR1W?ILauWi>WLA))ecX7!qn<RHawhaWbr
zx_1wzI|6f6DYiQ)NoWDH@YmUScSNANU$GvV%jh}V80n7o*%#GGAM^xQ4w0MiCBFdC
z$;yfap;=kkxm`2BnfwdCP?bve*8##f*_Ix3Vr~9hFRzjBk0@-)|MaoxG9FtX*YZDQ
z7B|k=Y-MrDcdXwy+`Y?(hLzpoAz18PNf`I2R1v`+{=9G`rlb56(lS!5&mK)vj=!~U
z&mLF=G@RF-UKKv@0Yw_T1*pFJbtZij58h!8_jF>QAC#EZoQlSG!tP~?boUV#E?&eS
zUvrWmcHn$TB!~@ztBt`F2bp_^A|ZvK349~!&~HRtf;5q(wd3&{D=olBX!JQ|)yo7n
zlW>6ZOpul9pF-k;&OEiy)nlU7ncU7WHTAe5YnGf^oI8sa@Pc+`=+Fvcr=#KzuNcR;
z$Z$JA-j45^$CxE-L$W&N7T41>b@Z+0t+cthUXS=TuLB$VXAFTnrC?K&mb<Z0X|Jb!
z?v@iIWf%Fex=+GW9=A;C4CrjTQ$~>ar?VZ`c%CPfHC(_<Et2EkNFVL1fzRtj8}*X9
zPQXs<DVBeb!K9xYFeg4vJJPcrv=ep;<tpiA9oQj$NoU-eM2NsaTXzm98nB*m75D=K
z6i-Pib-!^QWTnasG<%r$b92Oh$|P*4P0T7?PT9-WOXRMYqd9LmRP_S0`@AxACoHF`
zvU2AGZ8)CH8v-E4ONLeWP_EpDufBmL33z`F?^mKkajq-40Wu*t^`hh)mOG-~N6IT~
zi;g(}N{m2aVcGlfr<R@eDqIT3W#PgE&1-ZPHv|T<UrcZM0}8IOqedN?wArkqTWz2z
z^S={N2;@0&^QoGNLLu|NyJ{9dzC-@S!vjId!CJWc?j9bL%WkrbTyD%1;+%Zs%+)t=
z)r5!QnBHkec_t%%57oa-fsIyTZr;aX%5qrqg0oBMaFq~t=8RwCJgKd7yK*%pHMCA#
z@g!mvKC=B~<th*fO0$O1vX@K9iTFj@3sb(luf!0T>{!8e5XNNM7O2KDOZ6KqrLr<V
zdKpvD3PBAn;>SBQW`~-Zs_8HB@?s_7EvU>zL(Jy^zt$OSt4%2oq&Cbq^}R<Gl+9$D
z>$M@@Q%mtYsg8#Xx92IV?0E~EWkE|aAt9GCj5iH(>)>MNrmR#n=!#E;me&3g2))oJ
zQQxv>irmh%JTlm{k^OW~Fc5AONEXKk?Z<VMA?s&~z3HH1a$(=wySp$zO7K8>%wYdC
z$fuYK>pghj&Cp%^pZ>zgWKF$D#ib2GGyzg;ztB?-Smj%Fe@8$<UVi>|Y>`qv%iP|_
zq{`lWpLBtV<bd6e`;P4BpFG|_nZpMbxw-pB&MLA_3Ms*J(?N%Pf~W~&{>RGq1Dm%V
zQm0MNa+=w*nYM@mt%eMN9+>UE?f}cfJa(FaaXptnmB3kVIy&XgquW76mA9?^Oaypm
zE;}n&CopW-D<TdJBvMuA7z~vEv_qoE>N*t_FJR_XpslId@%n6`;Ke}{xJRloi(1`^
zb%-eO@f&H_0qdV1_~GIzL8*XGDy&ynw{8b!lM@n{aU5_2poSeIo?zJs&I$@YQc`A~
zzc8okSR3ErJ!Q0s2^!Hgm6h*6fJizF<F{pPgJ1bg%L+k_0=gc39a5Ty%3&8OXn8(7
zVbZdnlA1&b2^XL&dea9OWT~h)4V^VdC8^>}W@abJd5<V2j$Gr_804t=Yb<c6WTxZV
zHA7}a$?>s@!Y?0@7$a9X6cp@Sx>zAptpW^<L$^W_`g6JC*0F2;gcnEvh<ZOzH+mtX
zl>mW!A1ZL)!PZOK+Vd`6jd~*Mf9`5p7u_AQd<t|tItU&;!Aq{C340DC`m$qllec#Y
zM?|`Zp*n}QbP9_7OdyB16M(&A7Uh?@Dpn6=(N6E&X9nLI_Rx)@CMIG~Qeo4=oNz|&
z2&;6a@H2x^6rub48~@HV?E2DP!^jJJ>@czg9v&{w)}5bDz1rN=6wJ4g1?v99`F;8L
zn5?0!ynOMK>k(2+rNA*kqz_n&F0o_72k|VpMDM|*pb;{K%@yW@(`7qWV0`g#iVOn?
z!j@BY^*>pZY6NMLt+`}wyvHI{P5ryqZ3yq2F7_{czLPVOcP(tDr7Cc!kaxj0!uC1+
zZsXtczH#p`wq@;OQXjeOB4LmgqCX+?zO&ONBS6xLFmhTxK1tnVoKVhQ=yTE0cK`qp
zUt8koSvpDau>KpcR!ESz%8cd_w=zt_aAJHLi36?zzzF+6M_O8T5Y+Ifs=iyzH+nKX
zdhlQa^E)qJQcKPJGK?vBwo2W9JpC_WX`}I|jQu4kG(FpOM?WzQw+{^D5RSI;<Z0p1
zl>yCLDYq+`4isW{G%J=3?Lyj<jno6j1X<~_A_poze+Ehnc`eBaBjfx&qRYUA#!8n?
z$5QokUO+PFp~y6Oy|@jo6w=+f3hvciy>F?&0PW5r!jCwa_5<6sW38-&A`w;zgHW-x
zbu;pf$i9&%#Rh34(_P%DPc(Q1WNq4S5hViAw2z`9i7d$i+dz${s=KFabZWv}*rPb2
z%7P1r14IEKC(l7~)UwV3nBrz;X#d{<d!Durg(SZlk<Hu4tY~W8-j0bbU$Np?bZl;1
zR0-ivC`fgu>ZOTj+{Yfy+$B9H3*ZO2-_>WXmX{CL*JqpMyr0B7cb~%X6!vsaLJUYC
zoY>lu%c-st?JcZ=0|KHnVZ!fS@6byi1bOh6sG5is#QxZVZ`@Snd+g>CH688kU2``X
zTiNZ9x`{v78yzj4a3Ac)x!g?<D!`jehP+LC*5KXXtW-vVG_|$0wX}v=DaR%y4c~G`
z&KG&fHAsKcR`@j|-p61<T#<$YbAn7zjL4Qi@HCe|v1j&XXE#k7shTK>Jta*t>h{7m
zhv6nBLNZc%Y1U$k=kGf6?<Cv}wu-;?Q%Hfw=Yw{B-Z5G1#hjH6Xxe)2vgx5X%k9=j
zzjPXG_D}$>L*2~Hs&%`wLxJXniz7;!H(pvIvs2&Vc=t)qdV(A$hlfNlunFR`>a_K(
zPck>x9v+wJv0_D<bVqI4-mJKZbKNAyC7DWveYWo#I&WHfrLjizC#Sv3#wGRLC3`9S
zPUF<!*_xO3kEff4o<pFEQ5)3QW!npCr4w$RHCF;QK9iAQiB#u7letA|IYHTHuk`XC
z9DQTOIrq>5#opNqe*GBS<vojA>`{KeL!-8`x_aoChKB|QL6XNJ6lKy%6YY&qAdE=+
zU^GO0E%wPAWE>Vp>fD!qDf*>hmcm$r=bBb>Kh{<4$(^id;<VaY*&Cg&oyDtT^&5KM
zPw7xVi#BnF53Zu&hC`p*D=i3g!vV@+<7`m2G3qD2cC7LxmV{&$w9WpVY7;|%-9jaM
z(S4xGusxAeKgzf!%uuaG<Hw~Lj)rE#V(cGn9=fyYkz0^vCn;B9^<JkrrM*_>LD9H-
z1zk2&&B|X7N!EH2b|>3ur18iju1UF>na-;lmVEAVnyI|Cn+k~LZCzudqbM;mz$l_r
zJfgM0MOQrAD*uu}>5zbeVMTT8jS7E@(Rw*S)p}aP&t)qu22Js*A3fMWRpEg<{>@v}
zK!2v2Mr>Hr6Ah)7AS(++mluO<;y!&FA#0p(UB6}bldu6sr);B2G&(i(Mr$ettTP(2
z+pz6faj<4ZLG=n}Kc@Du1L!&of8%fr+Dm)UH|NQUMDIaq0HyoQx>wr2nDQ`5RVWWz
z`!tT{x-+Eh4q8xE{;_FMO3#7p0v98itym~YJ^SE&Tl4-5k-g9p;}QO6BeTJT_MruR
zI|jSm@?X?fC05h%w7+~;&v8@HmMhDy$>5J*$2&cfXXZx>=<!^Qp<52kUHJ4gDoHA0
zkG9nGbCk%}JhSKmL-!8hnh)z<J$Tz&U1hiN*|FK%-X^BVNt)aA8s}1UJ=saRtr?5b
zjYc{617bf|GuXrOa#fLL$8T~ePEV3EisdUQuQ1FEpDB+<E6td`uV~@!5_2=A`EEUX
z)=hC5*Irz5{_3C_6-mo}!$g|}As&?}*K6jO6gH=lWD}v=Up-LRw0n+Gx5kgtGXk34
zyb<W)Kqrr~qi;NiJ~lJiY61dzV<nlhWGV~_=-cXZX%{Vf>;ldAhRgy8=ZCQNxAcEi
z$Heq(nbsp|Vy>x3+5=~-+IU@4-%m;zzTyl!n$YY(LCcZq#^ZvVgj#2+)9t$T<OYP6
z1*bh8Jeue&_730mCQm?w8*|WsQ%f$<oG4n2veKT#O^UhSH*h{O{f|)5$V_##>{;FW
zRr`)4&}`lTvJ=D;9KPkKxHHA>Bh(XzskKiZ;Thghr6CU_kxs*f|4uJ*{rS`>5!)DF
zrXTI@?()C&ixNo+>|>-zV%9wF-0N^vu4k__&>Gz<3??=?`B`;!RHe+VwYKS%)K+M*
zSEtV&tTMVSZg7d$<0BH5?H=b>%6C*9d=f|(6s6v^2$ZevL!WoPedgt-(+|iSgsIDO
zU<T?h{lkMxfzU{ij#>st-HvxTs%`zdjFi0*+h*T9xpbksv78J6R`%(pt@mDvj*UHq
z!|dwpR8v<^wRs?OyJq14vxMQ<2T^=<zIgs!uv+Wok$n?aBd>FX%b%KBPkIM|)p+)I
z1zi(^f9t)*&reuu$CF`69W{c-RA~RCt1#{g^V$`3BasI*$Cr_Khir&yy)4r{*wa#G
zC!9KhfViT)bdyX%m3PU~uhCj{&5RwR#_nsGEf?w^MRSANbAMjy0Oy!uZ`O8GUtc?Q
z3bIA5{oE4y{tTm)l|7>LMeBlXhrO(iJH%ZLi7hI$p(FfJtax3F;UlF#P+7TU{zJpZ
zg=2bpn}lz!AdRpu6R1nD8Ra*Yk;0L7Ae#s~VJy2k78*}lGTV1%>WlSion9vE$&~>a
z7^d3MQ73LaIuiX8!nLD=L*21x|9b{7oUE;_1z7Z(O<qfG_-?C_>1v{)C4Gc!a=OVX
zWUtn;ADiq#dpi9Re(Ju^-^9!eN;PcwjbI^`pvq)hoYq+`xDZjS-}n4JqdV7cA&Bds
zL9d&e;gor*j90HRD6TufCAvQ64Aa7NlJBpaF=X`Q$xm6NzTLfc#=btv*Lp0dKnm5?
zXK6d7SKdnMIlbYksJE1Ev~1-0%n(jvy5jZvq5F=!DBLfh=nCiY;z98LexLKYbMJL%
zyi(W^TA;F&g%R&N{VtFAGIHL)3pRAu*(-^-<-;#M3t3R`_Drr}!?+>6uRmtUvA}XO
zN(kEh#1ltROI2MOcuw?G{qi4cN9azQDs^AQCf0r8x{d*=Hd0O!@_Ld+q0%uDU%wCq
zNexxq+%cr2&%gZh*Dpdv80QZM23ha=pP&Exr*x7D^Ew6c=l<h0`58SOKK}9Nk+b#x
z_aFQE%QoU~U^9vR?N0sod-(e`d3R2Z5)R8>=GD#p_jk%q-K`TWt1d}-_}?Gk?_d7^
zk17BErzsutf9KM6uZ^{wGUez2jeoFfy|Cs`8y}w&l=1ZL3KpdP(D_J~ZsxZwcK>9r
zEk{&3#@p8eSe<<SPsZ+4JIT<T9dl=&zW?&dv;J&_#B;;{v}_604r?s*b8wEr4}JdC
z&-`Vk1rr3PIAQtie{(`#zd0LE6mqmF{P;h-!!Z9@wLKCU(UXsEDAzl|EVqQS!z}wV
IcHZIt1<WLawg3PC

literal 0
HcmV?d00001

diff --git a/assets/index-9620d214-B8uh0R2i.js b/assets/index-9620d214-BlfbO5wW.js
similarity index 96%
rename from assets/index-9620d214-B8uh0R2i.js
rename to assets/index-9620d214-BlfbO5wW.js
index b13dc90..3391d72 100644
--- a/assets/index-9620d214-B8uh0R2i.js
+++ b/assets/index-9620d214-BlfbO5wW.js
@@ -1 +1 @@
-import{q as N,G as A}from"./graph-T5JS4vfK.js";import{m as $,l as q}from"./layout-DUYLy6Ue.js";import{c as H}from"./clone-CI3kFeqi.js";import{i as V,u as U,s as W,a as _,b as z,g as D,p as O,c as K,d as Q,e as Y,f as Z,h as J,j as p}from"./edges-5962ec63-B19hLEst.js";import{l as s,c as T,q as S,h as L}from"./mermaid.core-ChLYKTZm.js";import{c as I}from"./createText-4a4f35c9-BuT3nXUz.js";function m(e){var t={options:{directed:e.isDirected(),multigraph:e.isMultigraph(),compound:e.isCompound()},nodes:tt(e),edges:et(e)};return N(e.graph())||(t.value=H(e.graph())),t}function tt(e){return $(e.nodes(),function(t){var n=e.node(t),r=e.parent(t),i={v:t};return N(n)||(i.value=n),N(r)||(i.parent=r),i})}function et(e){return $(e.edges(),function(t){var n=e.edge(t),r={v:t.v,w:t.w};return N(t.name)||(r.name=t.name),N(n)||(r.value=n),r})}let l={},g={},R={};const nt=()=>{g={},R={},l={}},B=(e,t)=>(s.trace("In isDescendant",t," ",e," = ",g[t].includes(e)),!!g[t].includes(e)),it=(e,t)=>(s.info("Descendants of ",t," is ",g[t]),s.info("Edge is ",e),e.v===t||e.w===t?!1:g[t]?g[t].includes(e.v)||B(e.v,t)||B(e.w,t)||g[t].includes(e.w):(s.debug("Tilt, ",t,",not in descendants"),!1)),P=(e,t,n,r)=>{s.warn("Copying children of ",e,"root",r,"data",t.node(e),r);const i=t.children(e)||[];e!==r&&i.push(e),s.warn("Copying (nodes) clusterId",e,"nodes",i),i.forEach(a=>{if(t.children(a).length>0)P(a,t,n,r);else{const d=t.node(a);s.info("cp ",a," to ",r," with parent ",e),n.setNode(a,d),r!==t.parent(a)&&(s.warn("Setting parent",a,t.parent(a)),n.setParent(a,t.parent(a))),e!==r&&a!==e?(s.debug("Setting parent",a,e),n.setParent(a,e)):(s.info("In copy ",e,"root",r,"data",t.node(e),r),s.debug("Not Setting parent for node=",a,"cluster!==rootId",e!==r,"node!==clusterId",a!==e));const u=t.edges(a);s.debug("Copying Edges",u),u.forEach(f=>{s.info("Edge",f);const h=t.edge(f.v,f.w,f.name);s.info("Edge data",h,r);try{it(f,r)?(s.info("Copying as ",f.v,f.w,h,f.name),n.setEdge(f.v,f.w,h,f.name),s.info("newGraph edges ",n.edges(),n.edge(n.edges()[0]))):s.info("Skipping copy of edge ",f.v,"-->",f.w," rootId: ",r," clusterId:",e)}catch(w){s.error(w)}})}s.debug("Removing node",a),t.removeNode(a)})},k=(e,t)=>{const n=t.children(e);let r=[...n];for(const i of n)R[i]=e,r=[...r,...k(i,t)];return r},C=(e,t)=>{s.trace("Searching",e);const n=t.children(e);if(s.trace("Searching children of id ",e,n),n.length<1)return s.trace("This is a valid node",e),e;for(const r of n){const i=C(r,t);if(i)return s.trace("Found replacement for",e," => ",i),i}},X=e=>!l[e]||!l[e].externalConnections?e:l[e]?l[e].id:e,st=(e,t)=>{if(!e||t>10){s.debug("Opting out, no graph ");return}else s.debug("Opting in, graph ");e.nodes().forEach(function(n){e.children(n).length>0&&(s.warn("Cluster identified",n," Replacement id in edges: ",C(n,e)),g[n]=k(n,e),l[n]={id:C(n,e),clusterData:e.node(n)})}),e.nodes().forEach(function(n){const r=e.children(n),i=e.edges();r.length>0?(s.debug("Cluster identified",n,g),i.forEach(a=>{if(a.v!==n&&a.w!==n){const d=B(a.v,n),u=B(a.w,n);d^u&&(s.warn("Edge: ",a," leaves cluster ",n),s.warn("Descendants of XXX ",n,": ",g[n]),l[n].externalConnections=!0)}})):s.debug("Not a cluster ",n,g)});for(let n of Object.keys(l)){const r=l[n].id,i=e.parent(r);i!==n&&l[i]&&!l[i].externalConnections&&(l[n].id=i)}e.edges().forEach(function(n){const r=e.edge(n);s.warn("Edge "+n.v+" -> "+n.w+": "+JSON.stringify(n)),s.warn("Edge "+n.v+" -> "+n.w+": "+JSON.stringify(e.edge(n)));let i=n.v,a=n.w;if(s.warn("Fix XXX",l,"ids:",n.v,n.w,"Translating: ",l[n.v]," --- ",l[n.w]),l[n.v]&&l[n.w]&&l[n.v]===l[n.w]){s.warn("Fixing and trixing link to self - removing XXX",n.v,n.w,n.name),s.warn("Fixing and trixing - removing XXX",n.v,n.w,n.name),i=X(n.v),a=X(n.w),e.removeEdge(n.v,n.w,n.name);const d=n.w+"---"+n.v;e.setNode(d,{domId:d,id:d,labelStyle:"",labelText:r.label,padding:0,shape:"labelRect",style:""});const u=structuredClone(r),f=structuredClone(r);u.label="",u.arrowTypeEnd="none",f.label="",u.fromCluster=n.v,f.toCluster=n.v,e.setEdge(i,d,u,n.name+"-cyclic-special"),e.setEdge(d,a,f,n.name+"-cyclic-special")}else if(l[n.v]||l[n.w]){if(s.warn("Fixing and trixing - removing XXX",n.v,n.w,n.name),i=X(n.v),a=X(n.w),e.removeEdge(n.v,n.w,n.name),i!==n.v){const d=e.parent(i);l[d].externalConnections=!0,r.fromCluster=n.v}if(a!==n.w){const d=e.parent(a);l[d].externalConnections=!0,r.toCluster=n.w}s.warn("Fix Replacing with XXX",i,a,n.name),e.setEdge(i,a,r,n.name)}}),s.warn("Adjusted Graph",m(e)),F(e,0),s.trace(l)},F=(e,t)=>{if(s.warn("extractor - ",t,m(e),e.children("D")),t>10){s.error("Bailing out");return}let n=e.nodes(),r=!1;for(const i of n){const a=e.children(i);r=r||a.length>0}if(!r){s.debug("Done, no node has children",e.nodes());return}s.debug("Nodes = ",n,t);for(const i of n)if(s.debug("Extracting node",i,l,l[i]&&!l[i].externalConnections,!e.parent(i),e.node(i),e.children("D")," Depth ",t),!l[i])s.debug("Not a cluster",i,t);else if(!l[i].externalConnections&&e.children(i)&&e.children(i).length>0){s.warn("Cluster without external connections, without a parent and with children",i,t);let d=e.graph().rankdir==="TB"?"LR":"TB";l[i]&&l[i].clusterData&&l[i].clusterData.dir&&(d=l[i].clusterData.dir,s.warn("Fixing dir",l[i].clusterData.dir,d));const u=new A({multigraph:!0,compound:!0}).setGraph({rankdir:d,nodesep:50,ranksep:50,marginx:8,marginy:8}).setDefaultEdgeLabel(function(){return{}});s.warn("Old graph before copy",m(e)),P(i,e,u,i),e.setNode(i,{clusterNode:!0,id:i,clusterData:l[i].clusterData,labelText:l[i].labelText,graph:u}),s.warn("New graph after copy node: (",i,")",m(u)),s.debug("Old graph after copy",m(e))}else s.warn("Cluster ** ",i," **not meeting the criteria !externalConnections:",!l[i].externalConnections," no parent: ",!e.parent(i)," children ",e.children(i)&&e.children(i).length>0,e.children("D"),t),s.debug(l);n=e.nodes(),s.warn("New list of nodes",n);for(const i of n){const a=e.node(i);s.warn(" Now next level",i,a),a.clusterNode&&F(a.graph,t+1)}},G=(e,t)=>{if(t.length===0)return[];let n=Object.assign(t);return t.forEach(r=>{const i=e.children(r),a=G(e,i);n=[...n,...a]}),n},rt=e=>G(e,e.children()),at=(e,t)=>{s.info("Creating subgraph rect for ",t.id,t);const n=T(),r=e.insert("g").attr("class","cluster"+(t.class?" "+t.class:"")).attr("id",t.id),i=r.insert("rect",":first-child"),a=S(n.flowchart.htmlLabels),d=r.insert("g").attr("class","cluster-label"),u=t.labelType==="markdown"?I(d,t.labelText,{style:t.labelStyle,useHtmlLabels:a}):d.node().appendChild(J(t.labelText,t.labelStyle,void 0,!0));let f=u.getBBox();if(S(n.flowchart.htmlLabels)){const c=u.children[0],o=L(u);f=c.getBoundingClientRect(),o.attr("width",f.width),o.attr("height",f.height)}const h=0*t.padding,w=h/2,x=t.width<=f.width+h?f.width+h:t.width;t.width<=f.width+h?t.diff=(f.width-t.width)/2-t.padding/2:t.diff=-t.padding/2,s.trace("Data ",t,JSON.stringify(t)),i.attr("style",t.style).attr("rx",t.rx).attr("ry",t.ry).attr("x",t.x-x/2).attr("y",t.y-t.height/2-w).attr("width",x).attr("height",t.height+h);const{subGraphTitleTopMargin:v}=D(n);a?d.attr("transform",`translate(${t.x-f.width/2}, ${t.y-t.height/2+v})`):d.attr("transform",`translate(${t.x}, ${t.y-t.height/2+v})`);const y=i.node().getBBox();return t.width=y.width,t.height=y.height,t.intersect=function(c){return p(t,c)},r},ct=(e,t)=>{const n=e.insert("g").attr("class","note-cluster").attr("id",t.id),r=n.insert("rect",":first-child"),i=0*t.padding,a=i/2;r.attr("rx",t.rx).attr("ry",t.ry).attr("x",t.x-t.width/2-a).attr("y",t.y-t.height/2-a).attr("width",t.width+i).attr("height",t.height+i).attr("fill","none");const d=r.node().getBBox();return t.width=d.width,t.height=d.height,t.intersect=function(u){return p(t,u)},n},ot=(e,t)=>{const n=T(),r=e.insert("g").attr("class",t.classes).attr("id",t.id),i=r.insert("rect",":first-child"),a=r.insert("g").attr("class","cluster-label"),d=r.append("rect"),u=a.node().appendChild(J(t.labelText,t.labelStyle,void 0,!0));let f=u.getBBox();if(S(n.flowchart.htmlLabels)){const c=u.children[0],o=L(u);f=c.getBoundingClientRect(),o.attr("width",f.width),o.attr("height",f.height)}f=u.getBBox();const h=0*t.padding,w=h/2,x=t.width<=f.width+t.padding?f.width+t.padding:t.width;t.width<=f.width+t.padding?t.diff=(f.width+t.padding*0-t.width)/2:t.diff=-t.padding/2,i.attr("class","outer").attr("x",t.x-x/2-w).attr("y",t.y-t.height/2-w).attr("width",x+h).attr("height",t.height+h),d.attr("class","inner").attr("x",t.x-x/2-w).attr("y",t.y-t.height/2-w+f.height-1).attr("width",x+h).attr("height",t.height+h-f.height-3);const{subGraphTitleTopMargin:v}=D(n);a.attr("transform",`translate(${t.x-f.width/2}, ${t.y-t.height/2-t.padding/3+(S(n.flowchart.htmlLabels)?5:3)+v})`);const y=i.node().getBBox();return t.height=y.height,t.intersect=function(c){return p(t,c)},r},lt=(e,t)=>{const n=e.insert("g").attr("class",t.classes).attr("id",t.id),r=n.insert("rect",":first-child"),i=0*t.padding,a=i/2;r.attr("class","divider").attr("x",t.x-t.width/2-a).attr("y",t.y-t.height/2).attr("width",t.width+i).attr("height",t.height+i);const d=r.node().getBBox();return t.width=d.width,t.height=d.height,t.diff=-t.padding/2,t.intersect=function(u){return p(t,u)},n},ft={rect:at,roundedWithTitle:ot,noteGroup:ct,divider:lt};let j={};const dt=(e,t)=>{s.trace("Inserting cluster");const n=t.shape||"rect";j[t.id]=ft[n](e,t)},ut=()=>{j={}},M=async(e,t,n,r,i,a)=>{s.info("Graph in recursive render: XXX",m(t),i);const d=t.graph().rankdir;s.trace("Dir in recursive render - dir:",d);const u=e.insert("g").attr("class","root");t.nodes()?s.info("Recursive render XXX",t.nodes()):s.info("No nodes found for",t),t.edges().length>0&&s.trace("Recursive edges",t.edge(t.edges()[0]));const f=u.insert("g").attr("class","clusters"),h=u.insert("g").attr("class","edgePaths"),w=u.insert("g").attr("class","edgeLabels"),x=u.insert("g").attr("class","nodes");await Promise.all(t.nodes().map(async function(c){const o=t.node(c);if(i!==void 0){const b=JSON.parse(JSON.stringify(i.clusterData));s.info("Setting data for cluster XXX (",c,") ",b,i),t.setNode(i.id,b),t.parent(c)||(s.trace("Setting parent",c,i.id),t.setParent(c,i.id,b))}if(s.info("(Insert) Node XXX"+c+": "+JSON.stringify(t.node(c))),o&&o.clusterNode){s.info("Cluster identified",c,o.width,t.node(c));const b=await M(x,o.graph,n,r,t.node(c),a),E=b.elem;U(o,E),o.diff=b.diff||0,s.info("Node bounds (abc123)",c,o,o.width,o.x,o.y),W(E,o),s.warn("Recursive render complete ",E,o)}else t.children(c).length>0?(s.info("Cluster - the non recursive path XXX",c,o.id,o,t),s.info(C(o.id,t)),l[o.id]={id:C(o.id,t),node:o}):(s.info("Node - the non recursive path",c,o.id,o),await _(x,t.node(c),d))})),t.edges().forEach(function(c){const o=t.edge(c.v,c.w,c.name);s.info("Edge "+c.v+" -> "+c.w+": "+JSON.stringify(c)),s.info("Edge "+c.v+" -> "+c.w+": ",c," ",JSON.stringify(t.edge(c))),s.info("Fix",l,"ids:",c.v,c.w,"Translating: ",l[c.v],l[c.w]),z(w,o)}),t.edges().forEach(function(c){s.info("Edge "+c.v+" -> "+c.w+": "+JSON.stringify(c))}),s.info("#############################################"),s.info("###                Layout                 ###"),s.info("#############################################"),s.info(t),q(t),s.info("Graph after layout:",m(t));let v=0;const{subGraphTitleTotalMargin:y}=D(a);return rt(t).forEach(function(c){const o=t.node(c);s.info("Position "+c+": "+JSON.stringify(t.node(c))),s.info("Position "+c+": ("+o.x,","+o.y,") width: ",o.width," height: ",o.height),o&&o.clusterNode?(o.y+=y,O(o)):t.children(c).length>0?(o.height+=y,dt(f,o),l[o.id].node=o):(o.y+=y/2,O(o))}),t.edges().forEach(function(c){const o=t.edge(c);s.info("Edge "+c.v+" -> "+c.w+": "+JSON.stringify(o),o),o.points.forEach(E=>E.y+=y/2);const b=K(h,c,o,l,n,t,r);Q(o,b)}),t.nodes().forEach(function(c){const o=t.node(c);s.info(c,o.type,o.diff),o.type==="group"&&(v=o.diff)}),{elem:u,diff:v}},bt=async(e,t,n,r,i)=>{V(e,n,r,i),Y(),Z(),ut(),nt(),s.warn("Graph at first:",JSON.stringify(m(t))),st(t),s.warn("Graph after:",JSON.stringify(m(t)));const a=T();await M(e,t,r,i,void 0,a)};export{bt as r};
+import{q as N,G as A}from"./graph-B1296pfd.js";import{m as $,l as q}from"./layout-qMafh1ee.js";import{c as H}from"./clone-C3EvpqoY.js";import{i as V,u as U,s as W,a as _,b as z,g as D,p as O,c as K,d as Q,e as Y,f as Z,h as J,j as p}from"./edges-5962ec63-ApWhby2b.js";import{l as s,c as T,q as S,h as L}from"./mermaid.core-DNo_7Q2B.js";import{c as I}from"./createText-4a4f35c9-CISzj231.js";function m(e){var t={options:{directed:e.isDirected(),multigraph:e.isMultigraph(),compound:e.isCompound()},nodes:tt(e),edges:et(e)};return N(e.graph())||(t.value=H(e.graph())),t}function tt(e){return $(e.nodes(),function(t){var n=e.node(t),r=e.parent(t),i={v:t};return N(n)||(i.value=n),N(r)||(i.parent=r),i})}function et(e){return $(e.edges(),function(t){var n=e.edge(t),r={v:t.v,w:t.w};return N(t.name)||(r.name=t.name),N(n)||(r.value=n),r})}let l={},g={},R={};const nt=()=>{g={},R={},l={}},B=(e,t)=>(s.trace("In isDescendant",t," ",e," = ",g[t].includes(e)),!!g[t].includes(e)),it=(e,t)=>(s.info("Descendants of ",t," is ",g[t]),s.info("Edge is ",e),e.v===t||e.w===t?!1:g[t]?g[t].includes(e.v)||B(e.v,t)||B(e.w,t)||g[t].includes(e.w):(s.debug("Tilt, ",t,",not in descendants"),!1)),P=(e,t,n,r)=>{s.warn("Copying children of ",e,"root",r,"data",t.node(e),r);const i=t.children(e)||[];e!==r&&i.push(e),s.warn("Copying (nodes) clusterId",e,"nodes",i),i.forEach(a=>{if(t.children(a).length>0)P(a,t,n,r);else{const d=t.node(a);s.info("cp ",a," to ",r," with parent ",e),n.setNode(a,d),r!==t.parent(a)&&(s.warn("Setting parent",a,t.parent(a)),n.setParent(a,t.parent(a))),e!==r&&a!==e?(s.debug("Setting parent",a,e),n.setParent(a,e)):(s.info("In copy ",e,"root",r,"data",t.node(e),r),s.debug("Not Setting parent for node=",a,"cluster!==rootId",e!==r,"node!==clusterId",a!==e));const u=t.edges(a);s.debug("Copying Edges",u),u.forEach(f=>{s.info("Edge",f);const h=t.edge(f.v,f.w,f.name);s.info("Edge data",h,r);try{it(f,r)?(s.info("Copying as ",f.v,f.w,h,f.name),n.setEdge(f.v,f.w,h,f.name),s.info("newGraph edges ",n.edges(),n.edge(n.edges()[0]))):s.info("Skipping copy of edge ",f.v,"-->",f.w," rootId: ",r," clusterId:",e)}catch(w){s.error(w)}})}s.debug("Removing node",a),t.removeNode(a)})},k=(e,t)=>{const n=t.children(e);let r=[...n];for(const i of n)R[i]=e,r=[...r,...k(i,t)];return r},C=(e,t)=>{s.trace("Searching",e);const n=t.children(e);if(s.trace("Searching children of id ",e,n),n.length<1)return s.trace("This is a valid node",e),e;for(const r of n){const i=C(r,t);if(i)return s.trace("Found replacement for",e," => ",i),i}},X=e=>!l[e]||!l[e].externalConnections?e:l[e]?l[e].id:e,st=(e,t)=>{if(!e||t>10){s.debug("Opting out, no graph ");return}else s.debug("Opting in, graph ");e.nodes().forEach(function(n){e.children(n).length>0&&(s.warn("Cluster identified",n," Replacement id in edges: ",C(n,e)),g[n]=k(n,e),l[n]={id:C(n,e),clusterData:e.node(n)})}),e.nodes().forEach(function(n){const r=e.children(n),i=e.edges();r.length>0?(s.debug("Cluster identified",n,g),i.forEach(a=>{if(a.v!==n&&a.w!==n){const d=B(a.v,n),u=B(a.w,n);d^u&&(s.warn("Edge: ",a," leaves cluster ",n),s.warn("Descendants of XXX ",n,": ",g[n]),l[n].externalConnections=!0)}})):s.debug("Not a cluster ",n,g)});for(let n of Object.keys(l)){const r=l[n].id,i=e.parent(r);i!==n&&l[i]&&!l[i].externalConnections&&(l[n].id=i)}e.edges().forEach(function(n){const r=e.edge(n);s.warn("Edge "+n.v+" -> "+n.w+": "+JSON.stringify(n)),s.warn("Edge "+n.v+" -> "+n.w+": "+JSON.stringify(e.edge(n)));let i=n.v,a=n.w;if(s.warn("Fix XXX",l,"ids:",n.v,n.w,"Translating: ",l[n.v]," --- ",l[n.w]),l[n.v]&&l[n.w]&&l[n.v]===l[n.w]){s.warn("Fixing and trixing link to self - removing XXX",n.v,n.w,n.name),s.warn("Fixing and trixing - removing XXX",n.v,n.w,n.name),i=X(n.v),a=X(n.w),e.removeEdge(n.v,n.w,n.name);const d=n.w+"---"+n.v;e.setNode(d,{domId:d,id:d,labelStyle:"",labelText:r.label,padding:0,shape:"labelRect",style:""});const u=structuredClone(r),f=structuredClone(r);u.label="",u.arrowTypeEnd="none",f.label="",u.fromCluster=n.v,f.toCluster=n.v,e.setEdge(i,d,u,n.name+"-cyclic-special"),e.setEdge(d,a,f,n.name+"-cyclic-special")}else if(l[n.v]||l[n.w]){if(s.warn("Fixing and trixing - removing XXX",n.v,n.w,n.name),i=X(n.v),a=X(n.w),e.removeEdge(n.v,n.w,n.name),i!==n.v){const d=e.parent(i);l[d].externalConnections=!0,r.fromCluster=n.v}if(a!==n.w){const d=e.parent(a);l[d].externalConnections=!0,r.toCluster=n.w}s.warn("Fix Replacing with XXX",i,a,n.name),e.setEdge(i,a,r,n.name)}}),s.warn("Adjusted Graph",m(e)),F(e,0),s.trace(l)},F=(e,t)=>{if(s.warn("extractor - ",t,m(e),e.children("D")),t>10){s.error("Bailing out");return}let n=e.nodes(),r=!1;for(const i of n){const a=e.children(i);r=r||a.length>0}if(!r){s.debug("Done, no node has children",e.nodes());return}s.debug("Nodes = ",n,t);for(const i of n)if(s.debug("Extracting node",i,l,l[i]&&!l[i].externalConnections,!e.parent(i),e.node(i),e.children("D")," Depth ",t),!l[i])s.debug("Not a cluster",i,t);else if(!l[i].externalConnections&&e.children(i)&&e.children(i).length>0){s.warn("Cluster without external connections, without a parent and with children",i,t);let d=e.graph().rankdir==="TB"?"LR":"TB";l[i]&&l[i].clusterData&&l[i].clusterData.dir&&(d=l[i].clusterData.dir,s.warn("Fixing dir",l[i].clusterData.dir,d));const u=new A({multigraph:!0,compound:!0}).setGraph({rankdir:d,nodesep:50,ranksep:50,marginx:8,marginy:8}).setDefaultEdgeLabel(function(){return{}});s.warn("Old graph before copy",m(e)),P(i,e,u,i),e.setNode(i,{clusterNode:!0,id:i,clusterData:l[i].clusterData,labelText:l[i].labelText,graph:u}),s.warn("New graph after copy node: (",i,")",m(u)),s.debug("Old graph after copy",m(e))}else s.warn("Cluster ** ",i," **not meeting the criteria !externalConnections:",!l[i].externalConnections," no parent: ",!e.parent(i)," children ",e.children(i)&&e.children(i).length>0,e.children("D"),t),s.debug(l);n=e.nodes(),s.warn("New list of nodes",n);for(const i of n){const a=e.node(i);s.warn(" Now next level",i,a),a.clusterNode&&F(a.graph,t+1)}},G=(e,t)=>{if(t.length===0)return[];let n=Object.assign(t);return t.forEach(r=>{const i=e.children(r),a=G(e,i);n=[...n,...a]}),n},rt=e=>G(e,e.children()),at=(e,t)=>{s.info("Creating subgraph rect for ",t.id,t);const n=T(),r=e.insert("g").attr("class","cluster"+(t.class?" "+t.class:"")).attr("id",t.id),i=r.insert("rect",":first-child"),a=S(n.flowchart.htmlLabels),d=r.insert("g").attr("class","cluster-label"),u=t.labelType==="markdown"?I(d,t.labelText,{style:t.labelStyle,useHtmlLabels:a}):d.node().appendChild(J(t.labelText,t.labelStyle,void 0,!0));let f=u.getBBox();if(S(n.flowchart.htmlLabels)){const c=u.children[0],o=L(u);f=c.getBoundingClientRect(),o.attr("width",f.width),o.attr("height",f.height)}const h=0*t.padding,w=h/2,x=t.width<=f.width+h?f.width+h:t.width;t.width<=f.width+h?t.diff=(f.width-t.width)/2-t.padding/2:t.diff=-t.padding/2,s.trace("Data ",t,JSON.stringify(t)),i.attr("style",t.style).attr("rx",t.rx).attr("ry",t.ry).attr("x",t.x-x/2).attr("y",t.y-t.height/2-w).attr("width",x).attr("height",t.height+h);const{subGraphTitleTopMargin:v}=D(n);a?d.attr("transform",`translate(${t.x-f.width/2}, ${t.y-t.height/2+v})`):d.attr("transform",`translate(${t.x}, ${t.y-t.height/2+v})`);const y=i.node().getBBox();return t.width=y.width,t.height=y.height,t.intersect=function(c){return p(t,c)},r},ct=(e,t)=>{const n=e.insert("g").attr("class","note-cluster").attr("id",t.id),r=n.insert("rect",":first-child"),i=0*t.padding,a=i/2;r.attr("rx",t.rx).attr("ry",t.ry).attr("x",t.x-t.width/2-a).attr("y",t.y-t.height/2-a).attr("width",t.width+i).attr("height",t.height+i).attr("fill","none");const d=r.node().getBBox();return t.width=d.width,t.height=d.height,t.intersect=function(u){return p(t,u)},n},ot=(e,t)=>{const n=T(),r=e.insert("g").attr("class",t.classes).attr("id",t.id),i=r.insert("rect",":first-child"),a=r.insert("g").attr("class","cluster-label"),d=r.append("rect"),u=a.node().appendChild(J(t.labelText,t.labelStyle,void 0,!0));let f=u.getBBox();if(S(n.flowchart.htmlLabels)){const c=u.children[0],o=L(u);f=c.getBoundingClientRect(),o.attr("width",f.width),o.attr("height",f.height)}f=u.getBBox();const h=0*t.padding,w=h/2,x=t.width<=f.width+t.padding?f.width+t.padding:t.width;t.width<=f.width+t.padding?t.diff=(f.width+t.padding*0-t.width)/2:t.diff=-t.padding/2,i.attr("class","outer").attr("x",t.x-x/2-w).attr("y",t.y-t.height/2-w).attr("width",x+h).attr("height",t.height+h),d.attr("class","inner").attr("x",t.x-x/2-w).attr("y",t.y-t.height/2-w+f.height-1).attr("width",x+h).attr("height",t.height+h-f.height-3);const{subGraphTitleTopMargin:v}=D(n);a.attr("transform",`translate(${t.x-f.width/2}, ${t.y-t.height/2-t.padding/3+(S(n.flowchart.htmlLabels)?5:3)+v})`);const y=i.node().getBBox();return t.height=y.height,t.intersect=function(c){return p(t,c)},r},lt=(e,t)=>{const n=e.insert("g").attr("class",t.classes).attr("id",t.id),r=n.insert("rect",":first-child"),i=0*t.padding,a=i/2;r.attr("class","divider").attr("x",t.x-t.width/2-a).attr("y",t.y-t.height/2).attr("width",t.width+i).attr("height",t.height+i);const d=r.node().getBBox();return t.width=d.width,t.height=d.height,t.diff=-t.padding/2,t.intersect=function(u){return p(t,u)},n},ft={rect:at,roundedWithTitle:ot,noteGroup:ct,divider:lt};let j={};const dt=(e,t)=>{s.trace("Inserting cluster");const n=t.shape||"rect";j[t.id]=ft[n](e,t)},ut=()=>{j={}},M=async(e,t,n,r,i,a)=>{s.info("Graph in recursive render: XXX",m(t),i);const d=t.graph().rankdir;s.trace("Dir in recursive render - dir:",d);const u=e.insert("g").attr("class","root");t.nodes()?s.info("Recursive render XXX",t.nodes()):s.info("No nodes found for",t),t.edges().length>0&&s.trace("Recursive edges",t.edge(t.edges()[0]));const f=u.insert("g").attr("class","clusters"),h=u.insert("g").attr("class","edgePaths"),w=u.insert("g").attr("class","edgeLabels"),x=u.insert("g").attr("class","nodes");await Promise.all(t.nodes().map(async function(c){const o=t.node(c);if(i!==void 0){const b=JSON.parse(JSON.stringify(i.clusterData));s.info("Setting data for cluster XXX (",c,") ",b,i),t.setNode(i.id,b),t.parent(c)||(s.trace("Setting parent",c,i.id),t.setParent(c,i.id,b))}if(s.info("(Insert) Node XXX"+c+": "+JSON.stringify(t.node(c))),o&&o.clusterNode){s.info("Cluster identified",c,o.width,t.node(c));const b=await M(x,o.graph,n,r,t.node(c),a),E=b.elem;U(o,E),o.diff=b.diff||0,s.info("Node bounds (abc123)",c,o,o.width,o.x,o.y),W(E,o),s.warn("Recursive render complete ",E,o)}else t.children(c).length>0?(s.info("Cluster - the non recursive path XXX",c,o.id,o,t),s.info(C(o.id,t)),l[o.id]={id:C(o.id,t),node:o}):(s.info("Node - the non recursive path",c,o.id,o),await _(x,t.node(c),d))})),t.edges().forEach(function(c){const o=t.edge(c.v,c.w,c.name);s.info("Edge "+c.v+" -> "+c.w+": "+JSON.stringify(c)),s.info("Edge "+c.v+" -> "+c.w+": ",c," ",JSON.stringify(t.edge(c))),s.info("Fix",l,"ids:",c.v,c.w,"Translating: ",l[c.v],l[c.w]),z(w,o)}),t.edges().forEach(function(c){s.info("Edge "+c.v+" -> "+c.w+": "+JSON.stringify(c))}),s.info("#############################################"),s.info("###                Layout                 ###"),s.info("#############################################"),s.info(t),q(t),s.info("Graph after layout:",m(t));let v=0;const{subGraphTitleTotalMargin:y}=D(a);return rt(t).forEach(function(c){const o=t.node(c);s.info("Position "+c+": "+JSON.stringify(t.node(c))),s.info("Position "+c+": ("+o.x,","+o.y,") width: ",o.width," height: ",o.height),o&&o.clusterNode?(o.y+=y,O(o)):t.children(c).length>0?(o.height+=y,dt(f,o),l[o.id].node=o):(o.y+=y/2,O(o))}),t.edges().forEach(function(c){const o=t.edge(c);s.info("Edge "+c.v+" -> "+c.w+": "+JSON.stringify(o),o),o.points.forEach(E=>E.y+=y/2);const b=K(h,c,o,l,n,t,r);Q(o,b)}),t.nodes().forEach(function(c){const o=t.node(c);s.info(c,o.type,o.diff),o.type==="group"&&(v=o.diff)}),{elem:u,diff:v}},bt=async(e,t,n,r,i)=>{V(e,n,r,i),Y(),Z(),ut(),nt(),s.warn("Graph at first:",JSON.stringify(m(t))),st(t),s.warn("Graph after:",JSON.stringify(m(t)));const a=T();await M(e,t,r,i,void 0,a)};export{bt as r};
diff --git a/assets/index.html-CZDJXbd3.js b/assets/index.html-B1eL3fl0.js
similarity index 94%
rename from assets/index.html-CZDJXbd3.js
rename to assets/index.html-B1eL3fl0.js
index b48e1e6..d000ba6 100644
--- a/assets/index.html-CZDJXbd3.js
+++ b/assets/index.html-B1eL3fl0.js
@@ -1 +1 @@
-import{_ as e,o as t,c as o}from"./app-B69Gl_S-.js";const a={};function r(n,c){return t(),o("div")}const l=e(a,[["render",r],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/category/%E6%95%B0%E5%AD%A6/","title":"数学 分类","lang":"zh-CN","frontmatter":{"title":"数学 分类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"数学","key":"category"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/category/%E6%95%B0%E5%AD%A6/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"数学 分类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"数学 分类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as o}from"./app-B4LGNJZ0.js";const a={};function r(n,c){return t(),o("div")}const l=e(a,[["render",r],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/category/%E6%95%B0%E5%AD%A6/","title":"数学 分类","lang":"zh-CN","frontmatter":{"title":"数学 分类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"数学","key":"category"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/category/%E6%95%B0%E5%AD%A6/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"数学 分类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"数学 分类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-B7IKPS0E.js b/assets/index.html-BCqj2PVi.js
similarity index 94%
rename from assets/index.html-B7IKPS0E.js
rename to assets/index.html-BCqj2PVi.js
index 2a48601..c33ba23 100644
--- a/assets/index.html-B7IKPS0E.js
+++ b/assets/index.html-BCqj2PVi.js
@@ -1 +1 @@
-import{_ as t,o as e,c as o}from"./app-B69Gl_S-.js";const a={};function l(r,n){return e(),o("div")}const c=t(a,[["render",l],["__file","index.html.vue"]]),s=JSON.parse('{"path":"/category/build-tools/","title":"build-tools 分类","lang":"zh-CN","frontmatter":{"title":"build-tools 分类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"build-tools","key":"category"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/category/build-tools/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"build-tools 分类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"build-tools 分类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{c as comp,s as data};
+import{_ as t,o as e,c as o}from"./app-B4LGNJZ0.js";const a={};function l(r,n){return e(),o("div")}const c=t(a,[["render",l],["__file","index.html.vue"]]),s=JSON.parse('{"path":"/category/build-tools/","title":"build-tools 分类","lang":"zh-CN","frontmatter":{"title":"build-tools 分类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"build-tools","key":"category"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/category/build-tools/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"build-tools 分类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"build-tools 分类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{c as comp,s as data};
diff --git a/assets/index.html-0LHdE1Bw.js b/assets/index.html-BFj2MrdQ.js
similarity index 94%
rename from assets/index.html-0LHdE1Bw.js
rename to assets/index.html-BFj2MrdQ.js
index 218d007..5e14773 100644
--- a/assets/index.html-0LHdE1Bw.js
+++ b/assets/index.html-BFj2MrdQ.js
@@ -1 +1 @@
-import{_ as e,o as t,c as a}from"./app-B69Gl_S-.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E7%AE%80%E5%8D%95%E5%8C%96/","title":"标签: 简单化","lang":"zh-CN","frontmatter":{"title":"标签: 简单化","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"简单化","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E7%AE%80%E5%8D%95%E5%8C%96/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 简单化"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 简单化\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as a}from"./app-B4LGNJZ0.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E7%AE%80%E5%8D%95%E5%8C%96/","title":"标签: 简单化","lang":"zh-CN","frontmatter":{"title":"标签: 简单化","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"简单化","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E7%AE%80%E5%8D%95%E5%8C%96/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 简单化"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 简单化\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-BlxatHgv.js b/assets/index.html-BJX9B5Ij.js
similarity index 94%
rename from assets/index.html-BlxatHgv.js
rename to assets/index.html-BJX9B5Ij.js
index 0a2ed38..9d7f8a7 100644
--- a/assets/index.html-BlxatHgv.js
+++ b/assets/index.html-BJX9B5Ij.js
@@ -1 +1 @@
-import{_ as e,o as t,c as a}from"./app-B69Gl_S-.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/","title":"标签: 交给子类","lang":"zh-CN","frontmatter":{"title":"标签: 交给子类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"交给子类","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 交给子类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 交给子类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as a}from"./app-B4LGNJZ0.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/","title":"标签: 交给子类","lang":"zh-CN","frontmatter":{"title":"标签: 交给子类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"交给子类","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 交给子类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 交给子类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-Bb8RnxYT.js b/assets/index.html-BOaWfYA8.js
similarity index 93%
rename from assets/index.html-Bb8RnxYT.js
rename to assets/index.html-BOaWfYA8.js
index 81143ef..a3bbeea 100644
--- a/assets/index.html-Bb8RnxYT.js
+++ b/assets/index.html-BOaWfYA8.js
@@ -1 +1 @@
-import{_ as e,o as t,c as n}from"./app-B69Gl_S-.js";const o={};function a(i,r){return t(),n("div")}const p=e(o,[["render",a],["__file","index.html.vue"]]),c=JSON.parse('{"path":"/timeline/","title":"时间轴","lang":"zh-CN","frontmatter":{"title":"时间轴","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"type","key":"timeline"},"layout":"Timeline","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/timeline/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"时间轴"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"时间轴\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{p as comp,c as data};
+import{_ as e,o as t,c as n}from"./app-B4LGNJZ0.js";const o={};function a(i,r){return t(),n("div")}const p=e(o,[["render",a],["__file","index.html.vue"]]),c=JSON.parse('{"path":"/timeline/","title":"时间轴","lang":"zh-CN","frontmatter":{"title":"时间轴","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"type","key":"timeline"},"layout":"Timeline","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/timeline/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"时间轴"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"时间轴\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{p as comp,c as data};
diff --git a/assets/index.html-DRlrhC7d.js b/assets/index.html-BgifGsNR.js
similarity index 94%
rename from assets/index.html-DRlrhC7d.js
rename to assets/index.html-BgifGsNR.js
index 1d1a053..96bc7a0 100644
--- a/assets/index.html-DRlrhC7d.js
+++ b/assets/index.html-BgifGsNR.js
@@ -1 +1 @@
-import{_ as e,o as t,c as o}from"./app-B69Gl_S-.js";const r={};function a(c,n){return t(),o("div")}const l=e(r,[["render",a],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/category/docker/","title":"docker 分类","lang":"zh-CN","frontmatter":{"title":"docker 分类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"docker","key":"category"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/category/docker/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"docker 分类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"docker 分类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as o}from"./app-B4LGNJZ0.js";const r={};function a(c,n){return t(),o("div")}const l=e(r,[["render",a],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/category/docker/","title":"docker 分类","lang":"zh-CN","frontmatter":{"title":"docker 分类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"docker","key":"category"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/category/docker/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"docker 分类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"docker 分类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-BjAw7f-F.js b/assets/index.html-BjAw7f-F.js
deleted file mode 100644
index c92f686..0000000
--- a/assets/index.html-BjAw7f-F.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as e,o as t,c as o,a as n}from"./app-B69Gl_S-.js";const r={};function a(c,p){return t(),o("div",null,[n(" https://theme-hope.vuejs.press/zh/guide/ ")])}const i=e(r,[["render",a],["__file","index.html.vue"]]),h=JSON.parse('{"path":"/","title":"主页","lang":"zh-CN","frontmatter":{"home":true,"layout":"BlogHome","icon":"home","title":"主页","author":"King-sj","heroText":"KSJ","bgImage":"/bg-2.png","heroFullScreen":true,"archive":true,"tagline":"Talking is cheap, show me your code.","copyright":"MIT 许可证","projects":[{"icon":"project","name":"自动机","desc":"自动机","link":"https://Automaton.bupt.online"}],"gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"主页"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"King-sj"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"主页\\"}"]]},"headers":[],"readingTime":{"minutes":0.18,"words":53},"filePathRelative":"README.md","excerpt":"<!-- https://theme-hope.vuejs.press/zh/guide/ -->\\n"}');export{i as comp,h as data};
diff --git a/assets/index.html-BjDh3PHW.js b/assets/index.html-BjDh3PHW.js
deleted file mode 100644
index 4728453..0000000
--- a/assets/index.html-BjDh3PHW.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as n,r,o as s,c,d as p,b as e}from"./app-B69Gl_S-.js";const i={},l=e("h1",{id:"项目",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#项目"},[e("span",null,"项目")])],-1),d=e("p",null,"这里是你参与或开发的项目介绍和进展。",-1);function h(t,m){const o=r("BlogPosts");return s(),c("div",null,[l,d,p(o,{pages:t.$site.pages,filter:a=>a.path.startsWith("/projects/")},null,8,["pages","filter"])])}const g=n(i,[["render",h],["__file","index.html.vue"]]),_=JSON.parse('{"path":"/projects/","title":"项目","lang":"zh-CN","frontmatter":{"layout":"Layout","title":"项目","date":"2024-10-18T00:00:00.000Z","description":"项目 这里是你参与或开发的项目介绍和进展。","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/projects/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"项目"}],["meta",{"property":"og:description","content":"项目 这里是你参与或开发的项目介绍和进展。"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:published_time","content":"2024-10-18T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"项目\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-10-18T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.12,"words":36},"filePathRelative":"projects/index.md","localizedDate":"2024年10月18日","excerpt":"\\n<p>这里是你参与或开发的项目介绍和进展。</p>\\n","autoDesc":true}');export{g as comp,_ as data};
diff --git a/assets/index.html-C8X5E5_U.js b/assets/index.html-BjeRhPA4.js
similarity index 94%
rename from assets/index.html-C8X5E5_U.js
rename to assets/index.html-BjeRhPA4.js
index 8f60487..f9bc679 100644
--- a/assets/index.html-C8X5E5_U.js
+++ b/assets/index.html-BjeRhPA4.js
@@ -1 +1 @@
-import{_ as e,o as t,c as o}from"./app-B69Gl_S-.js";const a={};function r(n,c){return t(),o("div")}const l=e(a,[["render",r],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/category/%E9%A3%8E%E6%A0%BC/","title":"风格 分类","lang":"zh-CN","frontmatter":{"title":"风格 分类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"风格","key":"category"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/category/%E9%A3%8E%E6%A0%BC/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"风格 分类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"风格 分类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as o}from"./app-B4LGNJZ0.js";const a={};function r(n,c){return t(),o("div")}const l=e(a,[["render",r],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/category/%E9%A3%8E%E6%A0%BC/","title":"风格 分类","lang":"zh-CN","frontmatter":{"title":"风格 分类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"风格","key":"category"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/category/%E9%A3%8E%E6%A0%BC/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"风格 分类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"风格 分类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-CXhg3e64.js b/assets/index.html-BlsqD0oa.js
similarity index 96%
rename from assets/index.html-CXhg3e64.js
rename to assets/index.html-BlsqD0oa.js
index fe81267..5930239 100644
--- a/assets/index.html-CXhg3e64.js
+++ b/assets/index.html-BlsqD0oa.js
@@ -1 +1 @@
-import{_ as e,o,c as n,b as t}from"./app-B69Gl_S-.js";const r={},m=t("h1",{id:"html-转-md-工具",tabindex:"-1"},[t("a",{class:"header-anchor",href:"#html-转-md-工具"},[t("span",null,"html 转 md 工具")])],-1),i=t("ul",null,[t("li",null,"https://github.com/mixmark-io/turndown"),t("li",null,"https://github.com/aaronsw/html2text")],-1),a=[m,i];function l(h,s){return o(),n("div",null,a)}const p=e(r,[["render",l],["__file","index.html.vue"]]),d=JSON.parse('{"path":"/resources/html2md/","title":"html 转 md 工具","lang":"zh-CN","frontmatter":{"description":"html 转 md 工具 https://github.com/mixmark-io/turndown https://github.com/aaronsw/html2text","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/resources/html2md/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"html 转 md 工具"}],["meta",{"property":"og:description","content":"html 转 md 工具 https://github.com/mixmark-io/turndown https://github.com/aaronsw/html2text"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"html 转 md 工具\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.03,"words":10},"filePathRelative":"resources/html2md/index.md","excerpt":"\\n<ul>\\n<li>https://github.com/mixmark-io/turndown</li>\\n<li>https://github.com/aaronsw/html2text</li>\\n</ul>\\n","autoDesc":true}');export{p as comp,d as data};
+import{_ as e,o,c as n,b as t}from"./app-B4LGNJZ0.js";const r={},m=t("h1",{id:"html-转-md-工具",tabindex:"-1"},[t("a",{class:"header-anchor",href:"#html-转-md-工具"},[t("span",null,"html 转 md 工具")])],-1),i=t("ul",null,[t("li",null,"https://github.com/mixmark-io/turndown"),t("li",null,"https://github.com/aaronsw/html2text")],-1),a=[m,i];function l(h,s){return o(),n("div",null,a)}const p=e(r,[["render",l],["__file","index.html.vue"]]),d=JSON.parse('{"path":"/resources/html2md/","title":"html 转 md 工具","lang":"zh-CN","frontmatter":{"description":"html 转 md 工具 https://github.com/mixmark-io/turndown https://github.com/aaronsw/html2text","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/resources/html2md/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"html 转 md 工具"}],["meta",{"property":"og:description","content":"html 转 md 工具 https://github.com/mixmark-io/turndown https://github.com/aaronsw/html2text"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"html 转 md 工具\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.03,"words":10},"filePathRelative":"resources/html2md/index.md","excerpt":"\\n<ul>\\n<li>https://github.com/mixmark-io/turndown</li>\\n<li>https://github.com/aaronsw/html2text</li>\\n</ul>\\n","autoDesc":true}');export{p as comp,d as data};
diff --git a/assets/index.html-Bq7J9cN0.js b/assets/index.html-Bq7J9cN0.js
new file mode 100644
index 0000000..d5a9c86
--- /dev/null
+++ b/assets/index.html-Bq7J9cN0.js
@@ -0,0 +1 @@
+import{_ as e,o as t,c as o,a as n}from"./app-B4LGNJZ0.js";const r={};function a(c,p){return t(),o("div",null,[n(" https://theme-hope.vuejs.press/zh/guide/ ")])}const s=e(r,[["render",a],["__file","index.html.vue"]]),h=JSON.parse('{"path":"/","title":"主页","lang":"zh-CN","frontmatter":{"home":true,"layout":"BlogHome","icon":"home","title":"主页","author":"King-sj","heroText":"KSJ","bgImage":"/bg-2.png","heroFullScreen":true,"archive":true,"tagline":"Talking is cheap, show me your code.","copyright":"MIT 许可证","projects":[{"icon":"project","name":"自动机","desc":"自动机","link":"https://Automaton.bupt.online"},{"icon":"project","name":"智能车循迹","desc":"北京邮电大学创新创业智能车循迹python版","link":"https://github.com/king-sj/carrobot"}],"gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"主页"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"King-sj"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"主页\\"}"]]},"headers":[],"readingTime":{"minutes":0.28,"words":83},"filePathRelative":"README.md","excerpt":"<!-- https://theme-hope.vuejs.press/zh/guide/ -->\\n"}');export{s as comp,h as data};
diff --git a/assets/index.html-CLOegCHC.js b/assets/index.html-BwXv95cV.js
similarity index 94%
rename from assets/index.html-CLOegCHC.js
rename to assets/index.html-BwXv95cV.js
index 3506051..1c5d386 100644
--- a/assets/index.html-CLOegCHC.js
+++ b/assets/index.html-BwXv95cV.js
@@ -1 +1 @@
-import{_ as e,o as t,c as a}from"./app-B69Gl_S-.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/","title":"标签: 公理系统","lang":"zh-CN","frontmatter":{"title":"标签: 公理系统","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"公理系统","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 公理系统"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 公理系统\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as a}from"./app-B4LGNJZ0.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/","title":"标签: 公理系统","lang":"zh-CN","frontmatter":{"title":"标签: 公理系统","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"公理系统","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 公理系统"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 公理系统\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-BtJnl_OK.js b/assets/index.html-C9AeqWIc.js
similarity index 96%
rename from assets/index.html-BtJnl_OK.js
rename to assets/index.html-C9AeqWIc.js
index 671baf6..a1fddb1 100644
--- a/assets/index.html-BtJnl_OK.js
+++ b/assets/index.html-C9AeqWIc.js
@@ -1 +1 @@
-import{_ as i,r as e,o as l,c,d as o,b as t}from"./app-B69Gl_S-.js";const p={},d=t("h1",{id:"教程",tabindex:"-1"},[t("a",{class:"header-anchor",href:"#教程"},[t("span",null,"教程")])],-1),m=t("p",null,"这里是所有详细的教程和指南。",-1);function h(a,u){const n=e("BlogPosts"),r=e("Catalog");return l(),c("div",null,[d,m,o(n,{pages:a.$site.pages,filter:s=>s.path.startsWith("/tutorials/")},null,8,["pages","filter"]),o(r)])}const _=i(p,[["render",h],["__file","index.html.vue"]]),y=JSON.parse('{"path":"/tutorials/","title":"教程","lang":"zh-CN","frontmatter":{"layout":"Layout","title":"教程","date":"2024-10-18T00:00:00.000Z","description":"教程 这里是所有详细的教程和指南。","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tutorials/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"教程"}],["meta",{"property":"og:description","content":"教程 这里是所有详细的教程和指南。"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:published_time","content":"2024-10-18T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"教程\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-10-18T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.12,"words":35},"filePathRelative":"tutorials/index.md","localizedDate":"2024年10月18日","excerpt":"\\n<p>这里是所有详细的教程和指南。</p>\\n","autoDesc":true}');export{_ as comp,y as data};
+import{_ as i,r as e,o as l,c,d as o,b as t}from"./app-B4LGNJZ0.js";const p={},d=t("h1",{id:"教程",tabindex:"-1"},[t("a",{class:"header-anchor",href:"#教程"},[t("span",null,"教程")])],-1),m=t("p",null,"这里是所有详细的教程和指南。",-1);function h(a,u){const n=e("BlogPosts"),r=e("Catalog");return l(),c("div",null,[d,m,o(n,{pages:a.$site.pages,filter:s=>s.path.startsWith("/tutorials/")},null,8,["pages","filter"]),o(r)])}const _=i(p,[["render",h],["__file","index.html.vue"]]),y=JSON.parse('{"path":"/tutorials/","title":"教程","lang":"zh-CN","frontmatter":{"layout":"Layout","title":"教程","date":"2024-10-18T00:00:00.000Z","description":"教程 这里是所有详细的教程和指南。","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tutorials/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"教程"}],["meta",{"property":"og:description","content":"教程 这里是所有详细的教程和指南。"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:published_time","content":"2024-10-18T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"教程\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-10-18T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.12,"words":35},"filePathRelative":"tutorials/index.md","localizedDate":"2024年10月18日","excerpt":"\\n<p>这里是所有详细的教程和指南。</p>\\n","autoDesc":true}');export{_ as comp,y as data};
diff --git a/assets/index.html-BK-iNYKv.js b/assets/index.html-CE6ffKsf.js
similarity index 93%
rename from assets/index.html-BK-iNYKv.js
rename to assets/index.html-CE6ffKsf.js
index 7645e47..502ec6f 100644
--- a/assets/index.html-BK-iNYKv.js
+++ b/assets/index.html-CE6ffKsf.js
@@ -1 +1 @@
-import{_ as e,o as t,c as o}from"./app-B69Gl_S-.js";const a={};function r(n,c){return t(),o("div")}const p=e(a,[["render",r],["__file","index.html.vue"]]),l=JSON.parse('{"path":"/category/cicd/","title":"CI/CD 分类","lang":"zh-CN","frontmatter":{"title":"CI/CD 分类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"CI/CD","key":"category"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/category/cicd/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"CI/CD 分类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"CI/CD 分类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{p as comp,l as data};
+import{_ as e,o as t,c as o}from"./app-B4LGNJZ0.js";const a={};function r(n,c){return t(),o("div")}const p=e(a,[["render",r],["__file","index.html.vue"]]),l=JSON.parse('{"path":"/category/cicd/","title":"CI/CD 分类","lang":"zh-CN","frontmatter":{"title":"CI/CD 分类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"CI/CD","key":"category"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/category/cicd/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"CI/CD 分类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"CI/CD 分类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{p as comp,l as data};
diff --git a/assets/index.html-ZxSgoRoh.js b/assets/index.html-CL479cux.js
similarity index 94%
rename from assets/index.html-ZxSgoRoh.js
rename to assets/index.html-CL479cux.js
index dfb704e..fb453fc 100644
--- a/assets/index.html-ZxSgoRoh.js
+++ b/assets/index.html-CL479cux.js
@@ -1 +1 @@
-import{_ as e,o as t,c as o}from"./app-B69Gl_S-.js";const a={};function r(n,c){return t(),o("div")}const l=e(a,[["render",r],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/category/%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86/","title":"编译原理 分类","lang":"zh-CN","frontmatter":{"title":"编译原理 分类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"编译原理","key":"category"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/category/%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"编译原理 分类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"编译原理 分类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as o}from"./app-B4LGNJZ0.js";const a={};function r(n,c){return t(),o("div")}const l=e(a,[["render",r],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/category/%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86/","title":"编译原理 分类","lang":"zh-CN","frontmatter":{"title":"编译原理 分类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"编译原理","key":"category"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/category/%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"编译原理 分类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"编译原理 分类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-B3D_5fpm.js b/assets/index.html-COyA9Sec.js
similarity index 94%
rename from assets/index.html-B3D_5fpm.js
rename to assets/index.html-COyA9Sec.js
index f9a9694..341de9d 100644
--- a/assets/index.html-B3D_5fpm.js
+++ b/assets/index.html-COyA9Sec.js
@@ -1 +1 @@
-import{_ as e,o as t,c as a}from"./app-B69Gl_S-.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/","title":"标签: 管理状态","lang":"zh-CN","frontmatter":{"title":"标签: 管理状态","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"管理状态","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 管理状态"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 管理状态\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as a}from"./app-B4LGNJZ0.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/","title":"标签: 管理状态","lang":"zh-CN","frontmatter":{"title":"标签: 管理状态","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"管理状态","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 管理状态"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 管理状态\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-DDeLtmuh.js b/assets/index.html-CVNN5Fwq.js
similarity index 93%
rename from assets/index.html-DDeLtmuh.js
rename to assets/index.html-CVNN5Fwq.js
index 2dca782..3b77e55 100644
--- a/assets/index.html-DDeLtmuh.js
+++ b/assets/index.html-CVNN5Fwq.js
@@ -1 +1 @@
-import{_ as e,o as t,c as n}from"./app-B69Gl_S-.js";const o={};function a(r,i){return t(),n("div")}const p=e(o,[["render",a],["__file","index.html.vue"]]),l=JSON.parse('{"path":"/category/nginx/","title":"nginx 分类","lang":"zh-CN","frontmatter":{"title":"nginx 分类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"nginx","key":"category"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/category/nginx/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"nginx 分类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"nginx 分类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{p as comp,l as data};
+import{_ as e,o as t,c as n}from"./app-B4LGNJZ0.js";const o={};function a(r,i){return t(),n("div")}const p=e(o,[["render",a],["__file","index.html.vue"]]),l=JSON.parse('{"path":"/category/nginx/","title":"nginx 分类","lang":"zh-CN","frontmatter":{"title":"nginx 分类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"nginx","key":"category"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/category/nginx/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"nginx 分类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"nginx 分类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{p as comp,l as data};
diff --git a/assets/index.html-DzsdPiFk.js b/assets/index.html-CYOJa5u_.js
similarity index 94%
rename from assets/index.html-DzsdPiFk.js
rename to assets/index.html-CYOJa5u_.js
index f18a4a6..7624aaa 100644
--- a/assets/index.html-DzsdPiFk.js
+++ b/assets/index.html-CYOJa5u_.js
@@ -1 +1 @@
-import{_ as e,o as t,c as a}from"./app-B69Gl_S-.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/","title":"标签: 设计模式","lang":"zh-CN","frontmatter":{"title":"标签: 设计模式","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"设计模式","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 设计模式"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 设计模式\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as a}from"./app-B4LGNJZ0.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/","title":"标签: 设计模式","lang":"zh-CN","frontmatter":{"title":"标签: 设计模式","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"设计模式","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 设计模式"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 设计模式\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-CdwZ1P48.js b/assets/index.html-CdwZ1P48.js
new file mode 100644
index 0000000..8569936
--- /dev/null
+++ b/assets/index.html-CdwZ1P48.js
@@ -0,0 +1 @@
+import{_ as c,r as t,o as i,c as l,d as o,b as e}from"./app-B4LGNJZ0.js";const p={},d=e("h1",{id:"随笔",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#随笔"},[e("span",null,"随笔")])],-1),m=e("p",null,"这里是所有个人感想、生活记录等非技术类文章。",-1);function h(a,g){const n=t("BlogPosts"),s=t("Catalog");return i(),l("div",null,[d,m,o(n,{pages:a.$site.pages,filter:r=>r.path.startsWith("/essays/")},null,8,["pages","filter"]),o(s)])}const _=c(p,[["render",h],["__file","index.html.vue"]]),y=JSON.parse('{"path":"/essays/","title":"随笔","lang":"zh-CN","frontmatter":{"layout":"Layout","title":"随笔","date":"2024-10-18T00:00:00.000Z","description":"随笔 这里是所有个人感想、生活记录等非技术类文章。","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/essays/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"随笔"}],["meta",{"property":"og:description","content":"随笔 这里是所有个人感想、生活记录等非技术类文章。"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:published_time","content":"2024-10-18T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"随笔\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-10-18T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.13,"words":40},"filePathRelative":"essays/index.md","localizedDate":"2024年10月18日","excerpt":"\\n<p>这里是所有个人感想、生活记录等非技术类文章。</p>\\n","autoDesc":true}');export{_ as comp,y as data};
diff --git a/assets/index.html-Dakgazin.js b/assets/index.html-CqYdKjYM.js
similarity index 93%
rename from assets/index.html-Dakgazin.js
rename to assets/index.html-CqYdKjYM.js
index 089aaad..0c87338 100644
--- a/assets/index.html-Dakgazin.js
+++ b/assets/index.html-CqYdKjYM.js
@@ -1 +1 @@
-import{_ as i,r as t,o as s,c as l,d as o,b as e}from"./app-B69Gl_S-.js";const p={},d=e("h1",{id:"技术",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#技术"},[e("span",null,"技术")])],-1),h=e("p",null,"这里是所有与技术相关的文章，包括编程、工具使用、技术分享等内容。",-1);function m(a,g){const n=t("BlogHome"),r=t("Catalog");return s(),l("div",null,[d,h,o(n,{pages:a.$site.pages,filter:c=>c.path.startsWith("/tech/")},null,8,["pages","filter"]),o(r)])}const _=i(p,[["render",m],["__file","index.html.vue"]]),y=JSON.parse('{"path":"/tech/","title":"技术","lang":"zh-CN","frontmatter":{"layout":"Layout","title":"技术","date":"2024-10-18T00:00:00.000Z","description":"技术 这里是所有与技术相关的文章，包括编程、工具使用、技术分享等内容。","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"技术"}],["meta",{"property":"og:description","content":"技术 这里是所有与技术相关的文章，包括编程、工具使用、技术分享等内容。"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:published_time","content":"2024-10-18T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"技术\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-10-18T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.16,"words":49},"filePathRelative":"tech/index.md","localizedDate":"2024年10月18日","excerpt":"\\n<p>这里是所有与技术相关的文章，包括编程、工具使用、技术分享等内容。</p>\\n","autoDesc":true}');export{_ as comp,y as data};
+import{_ as i,r as t,o as s,c as l,d as o,b as e}from"./app-B4LGNJZ0.js";const p={},d=e("h1",{id:"技术",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#技术"},[e("span",null,"技术")])],-1),h=e("p",null,"这里是所有与技术相关的文章，包括编程、工具使用、技术分享等内容。",-1);function m(a,g){const n=t("BlogHome"),r=t("Catalog");return s(),l("div",null,[d,h,o(n,{pages:a.$site.pages,filter:c=>c.path.startsWith("/tech/")},null,8,["pages","filter"]),o(r)])}const _=i(p,[["render",m],["__file","index.html.vue"]]),y=JSON.parse('{"path":"/tech/","title":"技术","lang":"zh-CN","frontmatter":{"layout":"Layout","title":"技术","date":"2024-10-18T00:00:00.000Z","description":"技术 这里是所有与技术相关的文章，包括编程、工具使用、技术分享等内容。","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"技术"}],["meta",{"property":"og:description","content":"技术 这里是所有与技术相关的文章，包括编程、工具使用、技术分享等内容。"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:published_time","content":"2024-10-18T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"技术\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-10-18T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.16,"words":49},"filePathRelative":"tech/index.md","localizedDate":"2024年10月18日","excerpt":"\\n<p>这里是所有与技术相关的文章，包括编程、工具使用、技术分享等内容。</p>\\n","autoDesc":true}');export{_ as comp,y as data};
diff --git a/assets/index.html-B2T3kUK3.js b/assets/index.html-CryaZFG_.js
similarity index 95%
rename from assets/index.html-B2T3kUK3.js
rename to assets/index.html-CryaZFG_.js
index 1c3fe14..52a7bb0 100644
--- a/assets/index.html-B2T3kUK3.js
+++ b/assets/index.html-CryaZFG_.js
@@ -1 +1 @@
-import{_ as e,o as t,c as a}from"./app-B69Gl_S-.js";const o={};function n(r,E){return t(),a("div")}const p=e(o,[["render",n],["__file","index.html.vue"]]),l=JSON.parse('{"path":"/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/","title":"标签: 访问数据结构并处理数据","lang":"zh-CN","frontmatter":{"title":"标签: 访问数据结构并处理数据","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"访问数据结构并处理数据","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 访问数据结构并处理数据"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 访问数据结构并处理数据\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{p as comp,l as data};
+import{_ as e,o as t,c as a}from"./app-B4LGNJZ0.js";const o={};function n(r,E){return t(),a("div")}const p=e(o,[["render",n],["__file","index.html.vue"]]),l=JSON.parse('{"path":"/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/","title":"标签: 访问数据结构并处理数据","lang":"zh-CN","frontmatter":{"title":"标签: 访问数据结构并处理数据","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"访问数据结构并处理数据","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 访问数据结构并处理数据"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 访问数据结构并处理数据\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{p as comp,l as data};
diff --git a/assets/index.html-BZLD09T1.js b/assets/index.html-Cw9y1ZOg.js
similarity index 94%
rename from assets/index.html-BZLD09T1.js
rename to assets/index.html-Cw9y1ZOg.js
index 3f486bd..f4db8a1 100644
--- a/assets/index.html-BZLD09T1.js
+++ b/assets/index.html-Cw9y1ZOg.js
@@ -1 +1 @@
-import{_ as e,o as t,c as a}from"./app-B69Gl_S-.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/","title":"标签: 生成实例","lang":"zh-CN","frontmatter":{"title":"标签: 生成实例","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"生成实例","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 生成实例"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 生成实例\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as a}from"./app-B4LGNJZ0.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/","title":"标签: 生成实例","lang":"zh-CN","frontmatter":{"title":"标签: 生成实例","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"生成实例","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 生成实例"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 生成实例\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-DDn6tClc.js b/assets/index.html-CzSwk-A5.js
similarity index 94%
rename from assets/index.html-DDn6tClc.js
rename to assets/index.html-CzSwk-A5.js
index 7757a3b..56516a6 100644
--- a/assets/index.html-DDn6tClc.js
+++ b/assets/index.html-CzSwk-A5.js
@@ -1 +1 @@
-import{_ as e,o as t,c as a}from"./app-B69Gl_S-.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E9%83%A8%E7%BD%B2/","title":"标签: 部署","lang":"zh-CN","frontmatter":{"title":"标签: 部署","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"部署","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E9%83%A8%E7%BD%B2/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 部署"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 部署\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as a}from"./app-B4LGNJZ0.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E9%83%A8%E7%BD%B2/","title":"标签: 部署","lang":"zh-CN","frontmatter":{"title":"标签: 部署","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"部署","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E9%83%A8%E7%BD%B2/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 部署"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 部署\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-BKjCcFT0.js b/assets/index.html-D8p9fsJ8.js
similarity index 93%
rename from assets/index.html-BKjCcFT0.js
rename to assets/index.html-D8p9fsJ8.js
index 9afb2e8..cd9a9c8 100644
--- a/assets/index.html-BKjCcFT0.js
+++ b/assets/index.html-D8p9fsJ8.js
@@ -1 +1 @@
-import{_ as t,o as e,c as n}from"./app-B69Gl_S-.js";const o={};function a(r,c){return e(),n("div")}const p=t(o,[["render",a],["__file","index.html.vue"]]),l=JSON.parse('{"path":"/tag/modint/","title":"标签: MODInt","lang":"zh-CN","frontmatter":{"title":"标签: MODInt","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"MODInt","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/modint/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: MODInt"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: MODInt\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{p as comp,l as data};
+import{_ as t,o as e,c as n}from"./app-B4LGNJZ0.js";const o={};function a(r,c){return e(),n("div")}const p=t(o,[["render",a],["__file","index.html.vue"]]),l=JSON.parse('{"path":"/tag/modint/","title":"标签: MODInt","lang":"zh-CN","frontmatter":{"title":"标签: MODInt","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"MODInt","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/modint/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: MODInt"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: MODInt\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{p as comp,l as data};
diff --git a/assets/index.html-VMxXqaQ8.js b/assets/index.html-DCZKDe-x.js
similarity index 94%
rename from assets/index.html-VMxXqaQ8.js
rename to assets/index.html-DCZKDe-x.js
index 084d831..b48d5a0 100644
--- a/assets/index.html-VMxXqaQ8.js
+++ b/assets/index.html-DCZKDe-x.js
@@ -1 +1 @@
-import{_ as e,o as t,c as a}from"./app-B69Gl_S-.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/","title":"标签: 解释器","lang":"zh-CN","frontmatter":{"title":"标签: 解释器","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"解释器","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 解释器"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 解释器\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as a}from"./app-B4LGNJZ0.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/","title":"标签: 解释器","lang":"zh-CN","frontmatter":{"title":"标签: 解释器","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"解释器","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 解释器"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 解释器\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-DeH2SCB3.js b/assets/index.html-DERlmHfl.js
similarity index 93%
rename from assets/index.html-DeH2SCB3.js
rename to assets/index.html-DERlmHfl.js
index 4565389..c197280 100644
--- a/assets/index.html-DeH2SCB3.js
+++ b/assets/index.html-DERlmHfl.js
@@ -1 +1 @@
-import{_ as e,o as t,c as o}from"./app-B69Gl_S-.js";const a={};function n(r,c){return t(),o("div")}const p=e(a,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/article/","title":"文章","lang":"zh-CN","frontmatter":{"title":"文章","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"type","key":"article"},"layout":"BlogType","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/article/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"文章"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"文章\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{p as comp,i as data};
+import{_ as e,o as t,c as o}from"./app-B4LGNJZ0.js";const a={};function n(r,c){return t(),o("div")}const p=e(a,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/article/","title":"文章","lang":"zh-CN","frontmatter":{"title":"文章","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"type","key":"article"},"layout":"BlogType","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/article/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"文章"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"文章\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{p as comp,i as data};
diff --git a/assets/index.html-BXtqeyHq.js b/assets/index.html-DOXbY5aY.js
similarity index 93%
rename from assets/index.html-BXtqeyHq.js
rename to assets/index.html-DOXbY5aY.js
index 9d425d4..af490bd 100644
--- a/assets/index.html-BXtqeyHq.js
+++ b/assets/index.html-DOXbY5aY.js
@@ -1 +1 @@
-import{_ as e,o as t,c as o}from"./app-B69Gl_S-.js";const a={};function r(n,c){return t(),o("div")}const p=e(a,[["render",r],["__file","index.html.vue"]]),l=JSON.parse('{"path":"/category/oi/","title":"OI 分类","lang":"zh-CN","frontmatter":{"title":"OI 分类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"OI","key":"category"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/category/oi/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"OI 分类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"OI 分类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{p as comp,l as data};
+import{_ as e,o as t,c as o}from"./app-B4LGNJZ0.js";const a={};function r(n,c){return t(),o("div")}const p=e(a,[["render",r],["__file","index.html.vue"]]),l=JSON.parse('{"path":"/category/oi/","title":"OI 分类","lang":"zh-CN","frontmatter":{"title":"OI 分类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"OI","key":"category"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/category/oi/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"OI 分类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"OI 分类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{p as comp,l as data};
diff --git a/assets/index.html-B71I-yvI.js b/assets/index.html-DOZrz5tX.js
similarity index 94%
rename from assets/index.html-B71I-yvI.js
rename to assets/index.html-DOZrz5tX.js
index b90bd92..07847d8 100644
--- a/assets/index.html-B71I-yvI.js
+++ b/assets/index.html-DOZrz5tX.js
@@ -1 +1 @@
-import{_ as e,o as t,c as o}from"./app-B69Gl_S-.js";const a={};function r(n,c){return t(),o("div")}const l=e(a,[["render",r],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/category/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/","title":"设计模式 分类","lang":"zh-CN","frontmatter":{"title":"设计模式 分类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"设计模式","key":"category"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/category/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"设计模式 分类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"设计模式 分类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as o}from"./app-B4LGNJZ0.js";const a={};function r(n,c){return t(),o("div")}const l=e(a,[["render",r],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/category/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/","title":"设计模式 分类","lang":"zh-CN","frontmatter":{"title":"设计模式 分类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"设计模式","key":"category"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/category/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"设计模式 分类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"设计模式 分类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-DR-PJoSN.js b/assets/index.html-DW1c3ODz.js
similarity index 93%
rename from assets/index.html-DR-PJoSN.js
rename to assets/index.html-DW1c3ODz.js
index 1fcdc35..8b1d5ba 100644
--- a/assets/index.html-DR-PJoSN.js
+++ b/assets/index.html-DW1c3ODz.js
@@ -1 +1 @@
-import{_ as e,o as t,c as a}from"./app-B69Gl_S-.js";const o={};function n(r,c){return t(),a("div")}const p=e(o,[["render",n],["__file","index.html.vue"]]),l=JSON.parse('{"path":"/tag/cicd/","title":"标签: CI/CD","lang":"zh-CN","frontmatter":{"title":"标签: CI/CD","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"CI/CD","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/cicd/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: CI/CD"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: CI/CD\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{p as comp,l as data};
+import{_ as e,o as t,c as a}from"./app-B4LGNJZ0.js";const o={};function n(r,c){return t(),a("div")}const p=e(o,[["render",n],["__file","index.html.vue"]]),l=JSON.parse('{"path":"/tag/cicd/","title":"标签: CI/CD","lang":"zh-CN","frontmatter":{"title":"标签: CI/CD","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"CI/CD","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/cicd/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: CI/CD"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: CI/CD\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{p as comp,l as data};
diff --git a/assets/index.html-CcgdDCiF.js b/assets/index.html-DYx5t_sy.js
similarity index 94%
rename from assets/index.html-CcgdDCiF.js
rename to assets/index.html-DYx5t_sy.js
index b78507d..8cf4f77 100644
--- a/assets/index.html-CcgdDCiF.js
+++ b/assets/index.html-DYx5t_sy.js
@@ -1 +1 @@
-import{_ as e,o as t,c as a}from"./app-B69Gl_S-.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/","title":"标签: 整体的替换算法","lang":"zh-CN","frontmatter":{"title":"标签: 整体的替换算法","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"整体的替换算法","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 整体的替换算法"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 整体的替换算法\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as a}from"./app-B4LGNJZ0.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/","title":"标签: 整体的替换算法","lang":"zh-CN","frontmatter":{"title":"标签: 整体的替换算法","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"整体的替换算法","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 整体的替换算法"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 整体的替换算法\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-D2pTqZFy.js b/assets/index.html-DeNCk-ye.js
similarity index 93%
rename from assets/index.html-D2pTqZFy.js
rename to assets/index.html-DeNCk-ye.js
index 677c169..9ce78af 100644
--- a/assets/index.html-D2pTqZFy.js
+++ b/assets/index.html-DeNCk-ye.js
@@ -1 +1 @@
-import{_ as e,o as t,c as o}from"./app-B69Gl_S-.js";const a={};function n(r,l){return t(),o("div")}const c=e(a,[["render",n],["__file","index.html.vue"]]),p=JSON.parse('{"path":"/tag/mobile/","title":"标签: mobile","lang":"zh-CN","frontmatter":{"title":"标签: mobile","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"mobile","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/mobile/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: mobile"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: mobile\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{c as comp,p as data};
+import{_ as e,o as t,c as o}from"./app-B4LGNJZ0.js";const a={};function n(r,l){return t(),o("div")}const c=e(a,[["render",n],["__file","index.html.vue"]]),p=JSON.parse('{"path":"/tag/mobile/","title":"标签: mobile","lang":"zh-CN","frontmatter":{"title":"标签: mobile","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"mobile","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/mobile/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: mobile"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: mobile\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{c as comp,p as data};
diff --git a/assets/index.html-BSJr7qwh.js b/assets/index.html-DhCS_0vf.js
similarity index 94%
rename from assets/index.html-BSJr7qwh.js
rename to assets/index.html-DhCS_0vf.js
index a27dde0..209d043 100644
--- a/assets/index.html-BSJr7qwh.js
+++ b/assets/index.html-DhCS_0vf.js
@@ -1 +1 @@
-import{_ as e,o as t,c as o}from"./app-B69Gl_S-.js";const a={};function r(n,c){return t(),o("div")}const l=e(a,[["render",r],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/category/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/","title":"奇技淫巧 分类","lang":"zh-CN","frontmatter":{"title":"奇技淫巧 分类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"奇技淫巧","key":"category"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/category/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"奇技淫巧 分类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"奇技淫巧 分类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as o}from"./app-B4LGNJZ0.js";const a={};function r(n,c){return t(),o("div")}const l=e(a,[["render",r],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/category/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/","title":"奇技淫巧 分类","lang":"zh-CN","frontmatter":{"title":"奇技淫巧 分类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"奇技淫巧","key":"category"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/category/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"奇技淫巧 分类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"奇技淫巧 分类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-B5GIg4Ij.js b/assets/index.html-Dj_dWWjR.js
similarity index 95%
rename from assets/index.html-B5GIg4Ij.js
rename to assets/index.html-Dj_dWWjR.js
index 250cc39..ff2f02d 100644
--- a/assets/index.html-B5GIg4Ij.js
+++ b/assets/index.html-Dj_dWWjR.js
@@ -1 +1 @@
-import{_ as a,r,o,c,a as s,b as e,e as t,d as i}from"./app-B69Gl_S-.js";const p={},l=e("p",null,"面向对象三大特性：封装、继承、多态。 设计模式需遵循面向对象的设计原则，由于笔者不太喜欢java, 并嫌弃cpp中没有interface, 遂使用ts作为实现语言(我才不用rust呢 😃 )",-1),d=e("p",null,"本专栏源码大部分参考自参考资料[1]",-1),h={href:"https://github.com/King-sj/DesignPatterns",target:"_blank",rel:"noopener noreferrer"},m=e("h1",{id:"参考资料",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#参考资料"},[e("span",null,"参考资料")])],-1),u=e("p",null,[t("[1] 结城浩. "),e("em",null,"图解设计模式"),t(". 杨文轩译. 北京: 人民邮电出版社, 2017.")],-1);function g(_,y){const n=r("ExternalLinkIcon");return o(),c("div",null,[l,s(" more "),d,e("p",null,[e("a",h,[t("教程源码示例"),i(n)])]),m,u])}const x=a(p,[["render",g],["__file","index.html.vue"]]),b=JSON.parse('{"path":"/tech/DesignPatterns/","title":"设计模式","lang":"zh-CN","frontmatter":{"title":"设计模式","date":"2024-10-21T00:00:00.000Z","category":["设计模式"],"tag":["设计模式","typescript"],"prev":null,"next":"./DesignPrinciples","description":"面向对象三大特性：封装、继承、多态。 设计模式需遵循面向对象的设计原则，由于笔者不太喜欢java, 并嫌弃cpp中没有interface, 遂使用ts作为实现语言(我才不用rust呢 😃 )","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/DesignPatterns/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"设计模式"}],["meta",{"property":"og:description","content":"面向对象三大特性：封装、继承、多态。 设计模式需遵循面向对象的设计原则，由于笔者不太喜欢java, 并嫌弃cpp中没有interface, 遂使用ts作为实现语言(我才不用rust呢 😃 )"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"设计模式"}],["meta",{"property":"article:tag","content":"typescript"}],["meta",{"property":"article:published_time","content":"2024-10-21T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"设计模式\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-10-21T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.48,"words":144},"filePathRelative":"tech/DesignPatterns/index.md","localizedDate":"2024年10月21日","excerpt":"<p>面向对象三大特性：封装、继承、多态。 设计模式需遵循面向对象的设计原则，由于笔者不太喜欢java, 并嫌弃cpp中没有interface, 遂使用ts作为实现语言(我才不用rust呢 😃 )</p>\\n","autoDesc":true}');export{x as comp,b as data};
+import{_ as a,r,o,c,a as s,b as e,e as t,d as i}from"./app-B4LGNJZ0.js";const p={},l=e("p",null,"面向对象三大特性：封装、继承、多态。 设计模式需遵循面向对象的设计原则，由于笔者不太喜欢java, 并嫌弃cpp中没有interface, 遂使用ts作为实现语言(我才不用rust呢 😃 )",-1),d=e("p",null,"本专栏源码大部分参考自参考资料[1]",-1),h={href:"https://github.com/King-sj/DesignPatterns",target:"_blank",rel:"noopener noreferrer"},m=e("h1",{id:"参考资料",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#参考资料"},[e("span",null,"参考资料")])],-1),u=e("p",null,[t("[1] 结城浩. "),e("em",null,"图解设计模式"),t(". 杨文轩译. 北京: 人民邮电出版社, 2017.")],-1);function g(_,y){const n=r("ExternalLinkIcon");return o(),c("div",null,[l,s(" more "),d,e("p",null,[e("a",h,[t("教程源码示例"),i(n)])]),m,u])}const x=a(p,[["render",g],["__file","index.html.vue"]]),b=JSON.parse('{"path":"/tech/DesignPatterns/","title":"设计模式","lang":"zh-CN","frontmatter":{"title":"设计模式","date":"2024-10-21T00:00:00.000Z","category":["设计模式"],"tag":["设计模式","typescript"],"prev":null,"next":"./DesignPrinciples","description":"面向对象三大特性：封装、继承、多态。 设计模式需遵循面向对象的设计原则，由于笔者不太喜欢java, 并嫌弃cpp中没有interface, 遂使用ts作为实现语言(我才不用rust呢 😃 )","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/DesignPatterns/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"设计模式"}],["meta",{"property":"og:description","content":"面向对象三大特性：封装、继承、多态。 设计模式需遵循面向对象的设计原则，由于笔者不太喜欢java, 并嫌弃cpp中没有interface, 遂使用ts作为实现语言(我才不用rust呢 😃 )"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"设计模式"}],["meta",{"property":"article:tag","content":"typescript"}],["meta",{"property":"article:published_time","content":"2024-10-21T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"设计模式\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-10-21T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.48,"words":144},"filePathRelative":"tech/DesignPatterns/index.md","localizedDate":"2024年10月21日","excerpt":"<p>面向对象三大特性：封装、继承、多态。 设计模式需遵循面向对象的设计原则，由于笔者不太喜欢java, 并嫌弃cpp中没有interface, 遂使用ts作为实现语言(我才不用rust呢 😃 )</p>\\n","autoDesc":true}');export{x as comp,b as data};
diff --git a/assets/index.html-BHNGjpbb.js b/assets/index.html-DklcXGYl.js
similarity index 95%
rename from assets/index.html-BHNGjpbb.js
rename to assets/index.html-DklcXGYl.js
index cbe68ad..e400ab9 100644
--- a/assets/index.html-BHNGjpbb.js
+++ b/assets/index.html-DklcXGYl.js
@@ -1 +1 @@
-import{_ as e,o as t,c as a}from"./app-B69Gl_S-.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/","title":"标签: 容器与内容的一致性","lang":"zh-CN","frontmatter":{"title":"标签: 容器与内容的一致性","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"容器与内容的一致性","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 容器与内容的一致性"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 容器与内容的一致性\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as a}from"./app-B4LGNJZ0.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/","title":"标签: 容器与内容的一致性","lang":"zh-CN","frontmatter":{"title":"标签: 容器与内容的一致性","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"容器与内容的一致性","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 容器与内容的一致性"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 容器与内容的一致性\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-Dh_a7h_3.js b/assets/index.html-DottIbHL.js
similarity index 93%
rename from assets/index.html-Dh_a7h_3.js
rename to assets/index.html-DottIbHL.js
index cb80e34..884932c 100644
--- a/assets/index.html-Dh_a7h_3.js
+++ b/assets/index.html-DottIbHL.js
@@ -1 +1 @@
-import{_ as e,o as t,c as o}from"./app-B69Gl_S-.js";const a={};function n(r,p){return t(),o("div")}const s=e(a,[["render",n],["__file","index.html.vue"]]),l=JSON.parse('{"path":"/star/","title":"星标","lang":"zh-CN","frontmatter":{"title":"星标","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"type","key":"star"},"layout":"BlogType","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/star/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"星标"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"星标\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{s as comp,l as data};
+import{_ as e,o as t,c as o}from"./app-B4LGNJZ0.js";const a={};function n(r,p){return t(),o("div")}const s=e(a,[["render",n],["__file","index.html.vue"]]),l=JSON.parse('{"path":"/star/","title":"星标","lang":"zh-CN","frontmatter":{"title":"星标","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"type","key":"star"},"layout":"BlogType","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/star/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"星标"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"星标\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{s as comp,l as data};
diff --git a/assets/index.html-CGsa9ffM.js b/assets/index.html-Dpy8imS-.js
similarity index 94%
rename from assets/index.html-CGsa9ffM.js
rename to assets/index.html-Dpy8imS-.js
index 25190d2..dece954 100644
--- a/assets/index.html-CGsa9ffM.js
+++ b/assets/index.html-Dpy8imS-.js
@@ -1 +1 @@
-import{_ as e,o as t,c as a}from"./app-B69Gl_S-.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/","title":"标签: 分开考虑","lang":"zh-CN","frontmatter":{"title":"标签: 分开考虑","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"分开考虑","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 分开考虑"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 分开考虑\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as a}from"./app-B4LGNJZ0.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/","title":"标签: 分开考虑","lang":"zh-CN","frontmatter":{"title":"标签: 分开考虑","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"分开考虑","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 分开考虑"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 分开考虑\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-Dv6rE_pN.js b/assets/index.html-DtPJaw_H.js
similarity index 98%
rename from assets/index.html-Dv6rE_pN.js
rename to assets/index.html-DtPJaw_H.js
index 9731b5d..aa19164 100644
--- a/assets/index.html-Dv6rE_pN.js
+++ b/assets/index.html-DtPJaw_H.js
@@ -1 +1 @@
-import{_ as i,r as n,o as c,c as p,a as h,b as e,e as o,d as t}from"./app-B69Gl_S-.js";const u={},d=e("h1",{id:"资源",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#资源"},[e("span",null,"资源")])],-1),_=e("p",null,"这里是推荐的书籍、网站、工具等资源。",-1),m={href:"https://github.com/",target:"_blank",rel:"noopener noreferrer"},g={href:"https://zh.z-lib.gs/",target:"_blank",rel:"noopener noreferrer"},b={href:"https://v2.vuepress.vuejs.org/zh/",target:"_blank",rel:"noopener noreferrer"},f={href:"https://plantuml.com/zh/",target:"_blank",rel:"noopener noreferrer"},y={href:"https://github.com/ikatyang/emoji-cheat-sheet",target:"_blank",rel:"noopener noreferrer"},k={href:"https://www.sci-hub.st/",target:"_blank",rel:"noopener noreferrer"},x={href:"https://libgen.mx/",target:"_blank",rel:"noopener noreferrer"};function v(a,j){const r=n("ExternalLinkIcon"),s=n("BlogPosts");return c(),p("div",null,[d,_,h(" more "),e("ul",null,[e("li",null,[e("a",m,[o("github - 世界上最大的代码托管平台"),t(r)])]),e("li",null,[e("a",g,[o("Z-Library – 世界上最大的电子图书馆。自由访问知识和文化。"),t(r)])]),e("li",null,[e("a",b,[o("Vuepress - 我的博客构建库"),t(r)])]),e("li",null,[e("a",f,[o("plantUML - 一个通用性很强的工具，可以快速、直接地创建各种图表"),t(r)])]),e("li",null,[e("a",y,[o("emoji-cheat-sheet - A markdown version emoji cheat sheet"),t(r)])]),e("li",null,[e("a",k,[o("Sci-hub —— 当今科学界最具争议性的项目。Sci-hub的目标是 免费并且不受限制地 提供所有科学知识。"),t(r)])]),e("li",null,[e("a",x,[o("Lib.Genesis —— Part of Library Genesis. ex libgen.io, libgen.org"),t(r)])])]),t(s,{pages:a.$site.pages,filter:l=>l.path.startsWith("/resources/")},null,8,["pages","filter"])])}const L=i(u,[["render",v],["__file","index.html.vue"]]),N=JSON.parse('{"path":"/resources/","title":"资源","lang":"zh-CN","frontmatter":{"layout":"Layout","title":"资源","date":"2024-10-18T00:00:00.000Z","description":"这里是推荐的书籍、网站、工具等资源。","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/resources/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"资源"}],["meta",{"property":"og:description","content":"这里是推荐的书籍、网站、工具等资源。"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:published_time","content":"2024-10-18T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"资源\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-10-18T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.58,"words":175},"filePathRelative":"resources/index.md","localizedDate":"2024年10月18日","excerpt":"\\n<p>这里是推荐的书籍、网站、工具等资源。</p>\\n","autoDesc":true}');export{L as comp,N as data};
+import{_ as i,r as n,o as c,c as p,a as h,b as e,e as o,d as t}from"./app-B4LGNJZ0.js";const u={},d=e("h1",{id:"资源",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#资源"},[e("span",null,"资源")])],-1),_=e("p",null,"这里是推荐的书籍、网站、工具等资源。",-1),m={href:"https://github.com/",target:"_blank",rel:"noopener noreferrer"},g={href:"https://zh.z-lib.gs/",target:"_blank",rel:"noopener noreferrer"},b={href:"https://v2.vuepress.vuejs.org/zh/",target:"_blank",rel:"noopener noreferrer"},f={href:"https://plantuml.com/zh/",target:"_blank",rel:"noopener noreferrer"},y={href:"https://github.com/ikatyang/emoji-cheat-sheet",target:"_blank",rel:"noopener noreferrer"},k={href:"https://www.sci-hub.st/",target:"_blank",rel:"noopener noreferrer"},x={href:"https://libgen.mx/",target:"_blank",rel:"noopener noreferrer"};function v(a,j){const r=n("ExternalLinkIcon"),s=n("BlogPosts");return c(),p("div",null,[d,_,h(" more "),e("ul",null,[e("li",null,[e("a",m,[o("github - 世界上最大的代码托管平台"),t(r)])]),e("li",null,[e("a",g,[o("Z-Library – 世界上最大的电子图书馆。自由访问知识和文化。"),t(r)])]),e("li",null,[e("a",b,[o("Vuepress - 我的博客构建库"),t(r)])]),e("li",null,[e("a",f,[o("plantUML - 一个通用性很强的工具，可以快速、直接地创建各种图表"),t(r)])]),e("li",null,[e("a",y,[o("emoji-cheat-sheet - A markdown version emoji cheat sheet"),t(r)])]),e("li",null,[e("a",k,[o("Sci-hub —— 当今科学界最具争议性的项目。Sci-hub的目标是 免费并且不受限制地 提供所有科学知识。"),t(r)])]),e("li",null,[e("a",x,[o("Lib.Genesis —— Part of Library Genesis. ex libgen.io, libgen.org"),t(r)])])]),t(s,{pages:a.$site.pages,filter:l=>l.path.startsWith("/resources/")},null,8,["pages","filter"])])}const L=i(u,[["render",v],["__file","index.html.vue"]]),N=JSON.parse('{"path":"/resources/","title":"资源","lang":"zh-CN","frontmatter":{"layout":"Layout","title":"资源","date":"2024-10-18T00:00:00.000Z","description":"这里是推荐的书籍、网站、工具等资源。","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/resources/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"资源"}],["meta",{"property":"og:description","content":"这里是推荐的书籍、网站、工具等资源。"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:published_time","content":"2024-10-18T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"资源\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-10-18T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.58,"words":175},"filePathRelative":"resources/index.md","localizedDate":"2024年10月18日","excerpt":"\\n<p>这里是推荐的书籍、网站、工具等资源。</p>\\n","autoDesc":true}');export{L as comp,N as data};
diff --git a/assets/index.html-BLuB_Eoc.js b/assets/index.html-DwPUACaS.js
similarity index 94%
rename from assets/index.html-BLuB_Eoc.js
rename to assets/index.html-DwPUACaS.js
index c273aa4..d49b83c 100644
--- a/assets/index.html-BLuB_Eoc.js
+++ b/assets/index.html-DwPUACaS.js
@@ -1 +1 @@
-import{_ as e,o as t,c as a}from"./app-B69Gl_S-.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E9%A3%8E%E6%A0%BC/","title":"标签: 风格","lang":"zh-CN","frontmatter":{"title":"标签: 风格","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"风格","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E9%A3%8E%E6%A0%BC/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 风格"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 风格\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as a}from"./app-B4LGNJZ0.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E9%A3%8E%E6%A0%BC/","title":"标签: 风格","lang":"zh-CN","frontmatter":{"title":"标签: 风格","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"风格","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E9%A3%8E%E6%A0%BC/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 风格"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 风格\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-DzJoMr4P.js b/assets/index.html-DzJoMr4P.js
deleted file mode 100644
index bb53ad3..0000000
--- a/assets/index.html-DzJoMr4P.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as s,r as n,o as r,c as i,d as c,b as e}from"./app-B69Gl_S-.js";const p={},l=e("h1",{id:"随笔",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#随笔"},[e("span",null,"随笔")])],-1),d=e("p",null,"这里是所有个人感想、生活记录等非技术类文章。",-1);function h(t,m){const o=n("BlogPosts");return r(),i("div",null,[l,d,c(o,{pages:t.$site.pages,filter:a=>a.path.startsWith("/essays/")},null,8,["pages","filter"])])}const g=s(p,[["render",h],["__file","index.html.vue"]]),_=JSON.parse('{"path":"/essays/","title":"随笔","lang":"zh-CN","frontmatter":{"layout":"Layout","title":"随笔","date":"2024-10-18T00:00:00.000Z","description":"随笔 这里是所有个人感想、生活记录等非技术类文章。","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/essays/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"随笔"}],["meta",{"property":"og:description","content":"随笔 这里是所有个人感想、生活记录等非技术类文章。"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:published_time","content":"2024-10-18T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"随笔\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-10-18T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.13,"words":39},"filePathRelative":"essays/index.md","localizedDate":"2024年10月18日","excerpt":"\\n<p>这里是所有个人感想、生活记录等非技术类文章。</p>\\n","autoDesc":true}');export{g as comp,_ as data};
diff --git a/assets/index.html-ayClYbZ3.js b/assets/index.html-F61LMFJS.js
similarity index 94%
rename from assets/index.html-ayClYbZ3.js
rename to assets/index.html-F61LMFJS.js
index ff88ce3..6f36ca9 100644
--- a/assets/index.html-ayClYbZ3.js
+++ b/assets/index.html-F61LMFJS.js
@@ -1 +1 @@
-import{_ as e,o as t,c as a}from"./app-B69Gl_S-.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/","title":"标签: 避免浪费","lang":"zh-CN","frontmatter":{"title":"标签: 避免浪费","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"避免浪费","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 避免浪费"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 避免浪费\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as a}from"./app-B4LGNJZ0.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/","title":"标签: 避免浪费","lang":"zh-CN","frontmatter":{"title":"标签: 避免浪费","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"避免浪费","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 避免浪费"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 避免浪费\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-CRzs15I0.js b/assets/index.html-JQfnAIea.js
similarity index 94%
rename from assets/index.html-CRzs15I0.js
rename to assets/index.html-JQfnAIea.js
index c687e14..72b580e 100644
--- a/assets/index.html-CRzs15I0.js
+++ b/assets/index.html-JQfnAIea.js
@@ -1 +1 @@
-import{_ as e,o as t,c as a}from"./app-B69Gl_S-.js";const o={};function r(p,n){return t(),a("div")}const i=e(o,[["render",r],["__file","index.html.vue"]]),l=JSON.parse('{"path":"/tag/typescript/","title":"标签: TypeScript","lang":"zh-CN","frontmatter":{"title":"标签: TypeScript","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"TypeScript","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/typescript/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: TypeScript"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: TypeScript\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{i as comp,l as data};
+import{_ as e,o as t,c as a}from"./app-B4LGNJZ0.js";const o={};function r(p,n){return t(),a("div")}const i=e(o,[["render",r],["__file","index.html.vue"]]),l=JSON.parse('{"path":"/tag/typescript/","title":"标签: TypeScript","lang":"zh-CN","frontmatter":{"title":"标签: TypeScript","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"TypeScript","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/typescript/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: TypeScript"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: TypeScript\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{i as comp,l as data};
diff --git a/assets/index.html-kOhwCTdr.js b/assets/index.html-NUfXNLwU.js
similarity index 94%
rename from assets/index.html-kOhwCTdr.js
rename to assets/index.html-NUfXNLwU.js
index 7316dc4..9e7cda2 100644
--- a/assets/index.html-kOhwCTdr.js
+++ b/assets/index.html-NUfXNLwU.js
@@ -1 +1 @@
-import{_ as e,o as t,c as a}from"./app-B69Gl_S-.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/","title":"标签: 工厂方法","lang":"zh-CN","frontmatter":{"title":"标签: 工厂方法","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"工厂方法","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 工厂方法"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 工厂方法\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as a}from"./app-B4LGNJZ0.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/","title":"标签: 工厂方法","lang":"zh-CN","frontmatter":{"title":"标签: 工厂方法","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"工厂方法","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 工厂方法"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 工厂方法\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-BvZSJ2r-.js b/assets/index.html-SMm58lXr.js
similarity index 93%
rename from assets/index.html-BvZSJ2r-.js
rename to assets/index.html-SMm58lXr.js
index 75cbb51..784d6dd 100644
--- a/assets/index.html-BvZSJ2r-.js
+++ b/assets/index.html-SMm58lXr.js
@@ -1 +1 @@
-import{_ as e,o as t,c as o}from"./app-B69Gl_S-.js";const a={};function r(n,c){return t(),o("div")}const l=e(a,[["render",r],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/docker/","title":"标签: docker","lang":"zh-CN","frontmatter":{"title":"标签: docker","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"docker","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/docker/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: docker"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: docker\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as o}from"./app-B4LGNJZ0.js";const a={};function r(n,c){return t(),o("div")}const l=e(a,[["render",r],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/docker/","title":"标签: docker","lang":"zh-CN","frontmatter":{"title":"标签: docker","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"docker","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/docker/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: docker"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: docker\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-Ak5uwHrg.js b/assets/index.html-SwHQd6yQ.js
similarity index 94%
rename from assets/index.html-Ak5uwHrg.js
rename to assets/index.html-SwHQd6yQ.js
index a325129..2994e32 100644
--- a/assets/index.html-Ak5uwHrg.js
+++ b/assets/index.html-SwHQd6yQ.js
@@ -1 +1 @@
-import{_ as t,r as o,o as i,c as n,d as a}from"./app-B69Gl_S-.js";const r={};function l(p,c){const e=o("Catalog");return i(),n("div",null,[a(e)])}const m=t(r,[["render",l],["__file","index.html.vue"]]),g=JSON.parse('{"path":"/tech/designASimpileCCompiler/","title":"Design ASimpile CCompiler","lang":"zh-CN","frontmatter":{"title":"Design ASimpile CCompiler","article":false,"feed":false,"sitemap":false,"gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/designASimpileCCompiler/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"Design ASimpile CCompiler"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"Design ASimpile CCompiler\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":1},"filePathRelative":null,"excerpt":""}');export{m as comp,g as data};
+import{_ as t,r as o,o as i,c as n,d as a}from"./app-B4LGNJZ0.js";const r={};function l(p,c){const e=o("Catalog");return i(),n("div",null,[a(e)])}const m=t(r,[["render",l],["__file","index.html.vue"]]),g=JSON.parse('{"path":"/tech/designASimpileCCompiler/","title":"Design ASimpile CCompiler","lang":"zh-CN","frontmatter":{"title":"Design ASimpile CCompiler","article":false,"feed":false,"sitemap":false,"gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/designASimpileCCompiler/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"Design ASimpile CCompiler"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"Design ASimpile CCompiler\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":1},"filePathRelative":null,"excerpt":""}');export{m as comp,g as data};
diff --git a/assets/index.html-CO8-8uSt.js b/assets/index.html-TRJ6qSMT.js
similarity index 93%
rename from assets/index.html-CO8-8uSt.js
rename to assets/index.html-TRJ6qSMT.js
index bf7e267..925c5d7 100644
--- a/assets/index.html-CO8-8uSt.js
+++ b/assets/index.html-TRJ6qSMT.js
@@ -1 +1 @@
-import{_ as e,o as t,c as o}from"./app-B69Gl_S-.js";const a={};function r(n,c){return t(),o("div")}const l=e(a,[["render",r],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/category/","title":"分类","lang":"zh-CN","frontmatter":{"title":"分类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","key":"category"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/category/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"分类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"分类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as o}from"./app-B4LGNJZ0.js";const a={};function r(n,c){return t(),o("div")}const l=e(a,[["render",r],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/category/","title":"分类","lang":"zh-CN","frontmatter":{"title":"分类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","key":"category"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/category/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"分类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"分类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-UrkKwESw.js b/assets/index.html-ZzlVKqB8.js
similarity index 94%
rename from assets/index.html-UrkKwESw.js
rename to assets/index.html-ZzlVKqB8.js
index 64ebfdd..b552e10 100644
--- a/assets/index.html-UrkKwESw.js
+++ b/assets/index.html-ZzlVKqB8.js
@@ -1 +1 @@
-import{_ as t,o as e,c as o}from"./app-B69Gl_S-.js";const n={};function a(r,p){return e(),o("div")}const l=t(n,[["render",a],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/category/python/","title":"python 分类","lang":"zh-CN","frontmatter":{"title":"python 分类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"python","key":"category"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/category/python/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"python 分类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"python 分类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as t,o as e,c as o}from"./app-B4LGNJZ0.js";const n={};function a(r,p){return e(),o("div")}const l=t(n,[["render",a],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/category/python/","title":"python 分类","lang":"zh-CN","frontmatter":{"title":"python 分类","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"python","key":"category"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/category/python/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"python 分类"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"python 分类\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-BNAyU6dK.js b/assets/index.html-auYNF0Cp.js
similarity index 94%
rename from assets/index.html-BNAyU6dK.js
rename to assets/index.html-auYNF0Cp.js
index 1ba344d..da0e055 100644
--- a/assets/index.html-BNAyU6dK.js
+++ b/assets/index.html-auYNF0Cp.js
@@ -1 +1 @@
-import{_ as e,o as t,c as a}from"./app-B69Gl_S-.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E7%BC%96%E8%AF%91%E5%99%A8/","title":"标签: 编译器","lang":"zh-CN","frontmatter":{"title":"标签: 编译器","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"编译器","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E7%BC%96%E8%AF%91%E5%99%A8/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 编译器"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 编译器\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as a}from"./app-B4LGNJZ0.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E7%BC%96%E8%AF%91%E5%99%A8/","title":"标签: 编译器","lang":"zh-CN","frontmatter":{"title":"标签: 编译器","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"编译器","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E7%BC%96%E8%AF%91%E5%99%A8/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 编译器"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 编译器\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-DZYdDCPP.js b/assets/index.html-hPg6lxSo.js
similarity index 94%
rename from assets/index.html-DZYdDCPP.js
rename to assets/index.html-hPg6lxSo.js
index 48e4832..f2a6f25 100644
--- a/assets/index.html-DZYdDCPP.js
+++ b/assets/index.html-hPg6lxSo.js
@@ -1 +1 @@
-import{_ as e,o as t,c as a}from"./app-B69Gl_S-.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E6%BF%80%E6%B4%BB/","title":"标签: 激活","lang":"zh-CN","frontmatter":{"title":"标签: 激活","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"激活","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E6%BF%80%E6%B4%BB/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 激活"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 激活\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as a}from"./app-B4LGNJZ0.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E6%BF%80%E6%B4%BB/","title":"标签: 激活","lang":"zh-CN","frontmatter":{"title":"标签: 激活","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"激活","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E6%BF%80%E6%B4%BB/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 激活"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 激活\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-QNuKjuoZ.js b/assets/index.html-i5A_pLCb.js
similarity index 94%
rename from assets/index.html-QNuKjuoZ.js
rename to assets/index.html-i5A_pLCb.js
index 750f69a..174ff58 100644
--- a/assets/index.html-QNuKjuoZ.js
+++ b/assets/index.html-i5A_pLCb.js
@@ -1 +1 @@
-import{_ as e,o as t,c as a}from"./app-B69Gl_S-.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/","title":"标签: 推卸责任","lang":"zh-CN","frontmatter":{"title":"标签: 推卸责任","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"推卸责任","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 推卸责任"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 推卸责任\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as a}from"./app-B4LGNJZ0.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/","title":"标签: 推卸责任","lang":"zh-CN","frontmatter":{"title":"标签: 推卸责任","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"推卸责任","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 推卸责任"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 推卸责任\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-jwKIpsPi.js b/assets/index.html-jwKIpsPi.js
new file mode 100644
index 0000000..5e611ea
--- /dev/null
+++ b/assets/index.html-jwKIpsPi.js
@@ -0,0 +1 @@
+import{_ as c,r as e,o as p,c as i,d as o,b as t}from"./app-B4LGNJZ0.js";const l={},d=t("h1",{id:"项目",tabindex:"-1"},[t("a",{class:"header-anchor",href:"#项目"},[t("span",null,"项目")])],-1),m=t("p",null,"这里是你参与或开发的项目介绍和进展。",-1);function h(a,g){const n=e("BlogPosts"),r=e("Catalog");return p(),i("div",null,[d,m,o(n,{pages:a.$site.pages,filter:s=>s.path.startsWith("/projects/")},null,8,["pages","filter"]),o(r)])}const _=c(l,[["render",h],["__file","index.html.vue"]]),y=JSON.parse('{"path":"/projects/","title":"项目","lang":"zh-CN","frontmatter":{"layout":"Layout","title":"项目","date":"2024-10-18T00:00:00.000Z","description":"项目 这里是你参与或开发的项目介绍和进展。","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/projects/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"项目"}],["meta",{"property":"og:description","content":"项目 这里是你参与或开发的项目介绍和进展。"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:published_time","content":"2024-10-18T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"项目\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-10-18T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.12,"words":37},"filePathRelative":"projects/index.md","localizedDate":"2024年10月18日","excerpt":"\\n<p>这里是你参与或开发的项目介绍和进展。</p>\\n","autoDesc":true}');export{_ as comp,y as data};
diff --git a/assets/index.html-bipylPNF.js b/assets/index.html-mplfcIL_.js
similarity index 93%
rename from assets/index.html-bipylPNF.js
rename to assets/index.html-mplfcIL_.js
index d709649..4338e40 100644
--- a/assets/index.html-bipylPNF.js
+++ b/assets/index.html-mplfcIL_.js
@@ -1 +1 @@
-import{_ as e,o as t,c as o}from"./app-B69Gl_S-.js";const a={};function n(r,c){return t(),o("div")}const l=e(a,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/","title":"标签","lang":"zh-CN","frontmatter":{"title":"标签","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as o}from"./app-B4LGNJZ0.js";const a={};function n(r,c){return t(),o("div")}const l=e(a,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/","title":"标签","lang":"zh-CN","frontmatter":{"title":"标签","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-CSRSsNOG.js b/assets/index.html-rivgPJ9m.js
similarity index 94%
rename from assets/index.html-CSRSsNOG.js
rename to assets/index.html-rivgPJ9m.js
index e365454..9223d91 100644
--- a/assets/index.html-CSRSsNOG.js
+++ b/assets/index.html-rivgPJ9m.js
@@ -1 +1 @@
-import{_ as e,o as t,c as a}from"./app-B69Gl_S-.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/","title":"标签: 踩坑记录","lang":"zh-CN","frontmatter":{"title":"标签: 踩坑记录","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"踩坑记录","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 踩坑记录"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 踩坑记录\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as a}from"./app-B4LGNJZ0.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/","title":"标签: 踩坑记录","lang":"zh-CN","frontmatter":{"title":"标签: 踩坑记录","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"踩坑记录","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 踩坑记录"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 踩坑记录\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-BpjUVtkj.js b/assets/index.html-y8ELyp0v.js
similarity index 93%
rename from assets/index.html-BpjUVtkj.js
rename to assets/index.html-y8ELyp0v.js
index f58c7d5..a097313 100644
--- a/assets/index.html-BpjUVtkj.js
+++ b/assets/index.html-y8ELyp0v.js
@@ -1 +1 @@
-import{_ as e,o as t,c as a}from"./app-B69Gl_S-.js";const o={};function n(c,r){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/c/","title":"标签: c","lang":"zh-CN","frontmatter":{"title":"标签: c","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"c","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/c/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: c"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: c\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as a}from"./app-B4LGNJZ0.js";const o={};function n(c,r){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/c/","title":"标签: c","lang":"zh-CN","frontmatter":{"title":"标签: c","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"c","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/c/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: c"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: c\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-9q-r5JHT.js b/assets/index.html-yUxPRBBH.js
similarity index 94%
rename from assets/index.html-9q-r5JHT.js
rename to assets/index.html-yUxPRBBH.js
index 36eda50..3843325 100644
--- a/assets/index.html-9q-r5JHT.js
+++ b/assets/index.html-yUxPRBBH.js
@@ -1 +1 @@
-import{_ as e,o as t,c as a}from"./app-B69Gl_S-.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/","title":"标签: 用类实现","lang":"zh-CN","frontmatter":{"title":"标签: 用类实现","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"用类实现","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 用类实现"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 用类实现\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
+import{_ as e,o as t,c as a}from"./app-B4LGNJZ0.js";const o={};function n(r,c){return t(),a("div")}const l=e(o,[["render",n],["__file","index.html.vue"]]),i=JSON.parse('{"path":"/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/","title":"标签: 用类实现","lang":"zh-CN","frontmatter":{"title":"标签: 用类实现","dir":{"index":false},"index":false,"feed":false,"sitemap":false,"blog":{"type":"category","name":"用类实现","key":"tag"},"layout":"BlogCategory","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"标签: 用类实现"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"标签: 用类实现\\"}"]]},"headers":[],"readingTime":{"minutes":0,"words":0},"filePathRelative":null,"excerpt":""}');export{l as comp,i as data};
diff --git a/assets/index.html-ybZqFA4D.js b/assets/index.html-ybZqFA4D.js
new file mode 100644
index 0000000..285271d
--- /dev/null
+++ b/assets/index.html-ybZqFA4D.js
@@ -0,0 +1 @@
+import{_ as t,o,c as n,b as e}from"./app-B4LGNJZ0.js";const r={},a=e("ul",null,[e("li",null,"anltr.grammar"),e("li",null,"bison/yacc"),e("li",null,"flex")],-1),l=[a];function i(c,s){return o(),n("div",null,l)}const m=t(r,[["render",i],["__file","index.html.vue"]]),d=JSON.parse('{"path":"/resources/compile/","title":"编译原理相关","lang":"zh-CN","frontmatter":{"date":"2024-11-06T00:00:00.000Z","title":"编译原理相关","description":"anltr.grammar bison/yacc flex","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/resources/compile/"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"编译原理相关"}],["meta",{"property":"og:description","content":"anltr.grammar bison/yacc flex"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:published_time","content":"2024-11-06T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"编译原理相关\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-11-06T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.05,"words":14},"filePathRelative":"resources/compile/index.md","localizedDate":"2024年11月6日","excerpt":"<ul>\\n<li>anltr.grammar</li>\\n<li>bison/yacc</li>\\n<li>flex</li>\\n</ul>\\n","autoDesc":true}');export{m as comp,d as data};
diff --git a/assets/infoDiagram-f86e0131-BJ_tgdHe.js b/assets/infoDiagram-f86e0131-BvySRD9D.js
similarity index 98%
rename from assets/infoDiagram-f86e0131-BJ_tgdHe.js
rename to assets/infoDiagram-f86e0131-BvySRD9D.js
index 3672851..337abcb 100644
--- a/assets/infoDiagram-f86e0131-BJ_tgdHe.js
+++ b/assets/infoDiagram-f86e0131-BvySRD9D.js
@@ -1,4 +1,4 @@
-import{l as Y,aJ as D,i as M}from"./mermaid.core-ChLYKTZm.js";import"./app-B69Gl_S-.js";var O=function(){var a=function(u,t,e,n){for(e=e||{},n=u.length;n--;e[u[n]]=t);return e},f=[6,9,10],m={trace:function(){},yy:{},symbols_:{error:2,start:3,info:4,document:5,EOF:6,line:7,statement:8,NL:9,showInfo:10,$accept:0,$end:1},terminals_:{2:"error",4:"info",6:"EOF",9:"NL",10:"showInfo"},productions_:[0,[3,3],[5,0],[5,2],[7,1],[7,1],[8,1]],performAction:function(t,e,n,s,r,i,d){switch(i.length-1,r){case 1:return s;case 4:break;case 6:s.setInfo(!0);break}},table:[{3:1,4:[1,2]},{1:[3]},a(f,[2,2],{5:3}),{6:[1,4],7:5,8:6,9:[1,7],10:[1,8]},{1:[2,1]},a(f,[2,3]),a(f,[2,4]),a(f,[2,5]),a(f,[2,6])],defaultActions:{4:[2,1]},parseError:function(t,e){if(e.recoverable)this.trace(t);else{var n=new Error(t);throw n.hash=e,n}},parse:function(t){var e=this,n=[0],s=[],r=[null],i=[],d=this.table,P="",v=0,L=0,N=2,T=1,R=i.slice.call(arguments,1),o=Object.create(this.lexer),p={yy:{}};for(var E in this.yy)Object.prototype.hasOwnProperty.call(this.yy,E)&&(p.yy[E]=this.yy[E]);o.setInput(t,p.yy),p.yy.lexer=o,p.yy.parser=this,typeof o.yylloc>"u"&&(o.yylloc={});var I=o.yylloc;i.push(I);var z=o.options&&o.options.ranges;typeof p.yy.parseError=="function"?this.parseError=p.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function U(){var y;return y=s.pop()||o.lex()||T,typeof y!="number"&&(y instanceof Array&&(s=y,y=s.pop()),y=e.symbols_[y]||y),y}for(var l,g,h,w,_={},b,c,F,S;;){if(g=n[n.length-1],this.defaultActions[g]?h=this.defaultActions[g]:((l===null||typeof l>"u")&&(l=U()),h=d[g]&&d[g][l]),typeof h>"u"||!h.length||!h[0]){var A="";S=[];for(b in d[g])this.terminals_[b]&&b>N&&S.push("'"+this.terminals_[b]+"'");o.showPosition?A="Parse error on line "+(v+1)+`:
+import{l as Y,aJ as D,i as M}from"./mermaid.core-DNo_7Q2B.js";import"./app-B4LGNJZ0.js";var O=function(){var a=function(u,t,e,n){for(e=e||{},n=u.length;n--;e[u[n]]=t);return e},f=[6,9,10],m={trace:function(){},yy:{},symbols_:{error:2,start:3,info:4,document:5,EOF:6,line:7,statement:8,NL:9,showInfo:10,$accept:0,$end:1},terminals_:{2:"error",4:"info",6:"EOF",9:"NL",10:"showInfo"},productions_:[0,[3,3],[5,0],[5,2],[7,1],[7,1],[8,1]],performAction:function(t,e,n,s,r,i,d){switch(i.length-1,r){case 1:return s;case 4:break;case 6:s.setInfo(!0);break}},table:[{3:1,4:[1,2]},{1:[3]},a(f,[2,2],{5:3}),{6:[1,4],7:5,8:6,9:[1,7],10:[1,8]},{1:[2,1]},a(f,[2,3]),a(f,[2,4]),a(f,[2,5]),a(f,[2,6])],defaultActions:{4:[2,1]},parseError:function(t,e){if(e.recoverable)this.trace(t);else{var n=new Error(t);throw n.hash=e,n}},parse:function(t){var e=this,n=[0],s=[],r=[null],i=[],d=this.table,P="",v=0,L=0,N=2,T=1,R=i.slice.call(arguments,1),o=Object.create(this.lexer),p={yy:{}};for(var E in this.yy)Object.prototype.hasOwnProperty.call(this.yy,E)&&(p.yy[E]=this.yy[E]);o.setInput(t,p.yy),p.yy.lexer=o,p.yy.parser=this,typeof o.yylloc>"u"&&(o.yylloc={});var I=o.yylloc;i.push(I);var z=o.options&&o.options.ranges;typeof p.yy.parseError=="function"?this.parseError=p.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function U(){var y;return y=s.pop()||o.lex()||T,typeof y!="number"&&(y instanceof Array&&(s=y,y=s.pop()),y=e.symbols_[y]||y),y}for(var l,g,h,w,_={},b,c,F,S;;){if(g=n[n.length-1],this.defaultActions[g]?h=this.defaultActions[g]:((l===null||typeof l>"u")&&(l=U()),h=d[g]&&d[g][l]),typeof h>"u"||!h.length||!h[0]){var A="";S=[];for(b in d[g])this.terminals_[b]&&b>N&&S.push("'"+this.terminals_[b]+"'");o.showPosition?A="Parse error on line "+(v+1)+`:
 `+o.showPosition()+`
 Expecting `+S.join(", ")+", got '"+(this.terminals_[l]||l)+"'":A="Parse error on line "+(v+1)+": Unexpected "+(l==T?"end of input":"'"+(this.terminals_[l]||l)+"'"),this.parseError(A,{text:o.match,token:this.terminals_[l]||l,line:o.yylineno,loc:I,expected:S})}if(h[0]instanceof Array&&h.length>1)throw new Error("Parse Error: multiple actions possible at state: "+g+", token: "+l);switch(h[0]){case 1:n.push(l),r.push(o.yytext),i.push(o.yylloc),n.push(h[1]),l=null,L=o.yyleng,P=o.yytext,v=o.yylineno,I=o.yylloc;break;case 2:if(c=this.productions_[h[1]][1],_.$=r[r.length-c],_._$={first_line:i[i.length-(c||1)].first_line,last_line:i[i.length-1].last_line,first_column:i[i.length-(c||1)].first_column,last_column:i[i.length-1].last_column},z&&(_._$.range=[i[i.length-(c||1)].range[0],i[i.length-1].range[1]]),w=this.performAction.apply(_,[P,L,v,p.yy,h[1],r,i].concat(R)),typeof w<"u")return w;c&&(n=n.slice(0,-1*c*2),r=r.slice(0,-1*c),i=i.slice(0,-1*c)),n.push(this.productions_[h[1]][0]),r.push(_.$),i.push(_._$),F=d[n[n.length-2]][n[n.length-1]],n.push(F);break;case 3:return!0}}return!0}},k=function(){var u={EOF:1,parseError:function(e,n){if(this.yy.parser)this.yy.parser.parseError(e,n);else throw new Error(e)},setInput:function(t,e){return this.yy=e||this.yy||{},this._input=t,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var t=this._input[0];this.yytext+=t,this.yyleng++,this.offset++,this.match+=t,this.matched+=t;var e=t.match(/(?:\r\n?|\n).*/g);return e?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),t},unput:function(t){var e=t.length,n=t.split(/(?:\r\n?|\n)/g);this._input=t+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-e),this.offset-=e;var s=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),n.length-1&&(this.yylineno-=n.length-1);var r=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:n?(n.length===s.length?this.yylloc.first_column:0)+s[s.length-n.length].length-n[0].length:this.yylloc.first_column-e},this.options.ranges&&(this.yylloc.range=[r[0],r[0]+this.yyleng-e]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){if(this.options.backtrack_lexer)this._backtrack=!0;else return this.parseError("Lexical error on line "+(this.yylineno+1)+`. You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).
 `+this.showPosition(),{text:"",token:null,line:this.yylineno});return this},less:function(t){this.unput(this.match.slice(t))},pastInput:function(){var t=this.matched.substr(0,this.matched.length-this.match.length);return(t.length>20?"...":"")+t.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var t=this.match;return t.length<20&&(t+=this._input.substr(0,20-t.length)),(t.substr(0,20)+(t.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var t=this.pastInput(),e=new Array(t.length+1).join("-");return t+this.upcomingInput()+`
diff --git a/assets/interpreter.html-CansycaD.js b/assets/interpreter.html-DfDQyPSV.js
similarity index 99%
rename from assets/interpreter.html-CansycaD.js
rename to assets/interpreter.html-DfDQyPSV.js
index 35f3bd6..0792eed 100644
--- a/assets/interpreter.html-CansycaD.js
+++ b/assets/interpreter.html-DfDQyPSV.js
@@ -1,4 +1,4 @@
-import{_ as p,r as e,o,c,b as n,e as s,d as i,f as a}from"./app-B69Gl_S-.js";const l={},u=a('<h2 id="为什么使用此模式" tabindex="-1"><a class="header-anchor" href="#为什么使用此模式"><span>为什么使用此模式</span></a></h2><p>解释器模式（Interpreter Pattern）是一种行为设计模式，它定义了一种语言的文法表示，并定义一个解释器来解释该语言中的句子。使用解释器模式的原因包括：</p><ol><li><strong>简化语法解析</strong>：通过定义文法规则，可以轻松解析和执行特定的语言或指令集。</li><li><strong>可扩展性</strong>：可以轻松添加新的语法规则或指令，而无需修改现有代码。</li><li><strong>代码复用</strong>：通过将不同的语法规则封装在不同的类中，可以提高代码的复用性和可维护性。</li></ol><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2>',4),r={href:"https://bupt.online/tech/designASimpileCCompiler/0.html",target:"_blank",rel:"noopener noreferrer"},k=a(`<div class="language-text line-numbers-mode" data-ext="text" data-title="text"><pre class="language-text"><code>&lt;program&gt; ::= program &lt;command list&gt;
+import{_ as p,r as e,o,c,b as n,e as s,d as i,f as a}from"./app-B4LGNJZ0.js";const l={},u=a('<h2 id="为什么使用此模式" tabindex="-1"><a class="header-anchor" href="#为什么使用此模式"><span>为什么使用此模式</span></a></h2><p>解释器模式（Interpreter Pattern）是一种行为设计模式，它定义了一种语言的文法表示，并定义一个解释器来解释该语言中的句子。使用解释器模式的原因包括：</p><ol><li><strong>简化语法解析</strong>：通过定义文法规则，可以轻松解析和执行特定的语言或指令集。</li><li><strong>可扩展性</strong>：可以轻松添加新的语法规则或指令，而无需修改现有代码。</li><li><strong>代码复用</strong>：通过将不同的语法规则封装在不同的类中，可以提高代码的复用性和可维护性。</li></ol><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2>',4),r={href:"https://bupt.online/tech/designASimpileCCompiler/0.html",target:"_blank",rel:"noopener noreferrer"},k=a(`<div class="language-text line-numbers-mode" data-ext="text" data-title="text"><pre class="language-text"><code>&lt;program&gt; ::= program &lt;command list&gt;
 &lt;command list&gt; ::= &lt;command&gt;* end
 &lt;command&gt; ::= &lt;repeat command&gt; | &lt;primitive command&gt;
 &lt;repeat command&gt; ::= repeat &lt;number&gt; &lt;command list&gt;
diff --git a/assets/intro.html-CEHYbhC9.js b/assets/intro.html-DcelwrZW.js
similarity index 97%
rename from assets/intro.html-CEHYbhC9.js
rename to assets/intro.html-DcelwrZW.js
index e232dfa..c59dedd 100644
--- a/assets/intro.html-CEHYbhC9.js
+++ b/assets/intro.html-DcelwrZW.js
@@ -1 +1 @@
-import{_ as o,o as n,c as r,a as e,b as t}from"./app-B69Gl_S-.js";const a={},c=t("h1",{id:"介绍页",tabindex:"-1"},[t("a",{class:"header-anchor",href:"#介绍页"},[t("span",null,"介绍页")])],-1),i=t("p",null,"一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。",-1);function p(s,l){return n(),r("div",null,[c,i,e(" # LOGO 设计理念 "),e(" 使用“KSJ”三个字母的抽象化设计。字母“K”和“J”可以设计成镜像对称，中间的“S”则像一条流畅的线条将两者连接起来，代表博客内容的连贯性和深度。整个LOGO采用深海蓝为主色调，象征智慧和深度，辅以银色或白色，增加科技感和现代感。 ")])}const d=o(a,[["render",p],["__file","intro.html.vue"]]),h=JSON.parse('{"path":"/intro.html","title":"介绍页","lang":"zh-CN","frontmatter":{"icon":"circle-info","archive":true,"sticky":true,"home":true,"portfolio":true,"titles":"student","date":"2023-07-08T00:00:00.000Z","description":"介绍页 一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/intro.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"介绍页"}],["meta",{"property":"og:description","content":"介绍页 一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:published_time","content":"2023-07-08T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"介绍页\\",\\"description\\":\\"介绍页 一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。\\"}"]]},"headers":[],"readingTime":{"minutes":0.56,"words":167},"filePathRelative":"intro.md","localizedDate":"2023年7月8日","excerpt":"\\n<p>一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</p>\\n<!-- # LOGO 设计理念 -->\\n<!-- 使用“KSJ”三个字母的抽象化设计。字母“K”和“J”可以设计成镜像对称，中间的“S”则像一条流畅的线条将两者连接起来，代表博客内容的连贯性和深度。整个LOGO采用深海蓝为主色调，象征智慧和深度，辅以银色或白色，增加科技感和现代感。 -->\\n","autoDesc":true}');export{d as comp,h as data};
+import{_ as o,o as n,c as r,a as e,b as t}from"./app-B4LGNJZ0.js";const a={},c=t("h1",{id:"介绍页",tabindex:"-1"},[t("a",{class:"header-anchor",href:"#介绍页"},[t("span",null,"介绍页")])],-1),i=t("p",null,"一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。",-1);function p(s,l){return n(),r("div",null,[c,i,e(" # LOGO 设计理念 "),e(" 使用“KSJ”三个字母的抽象化设计。字母“K”和“J”可以设计成镜像对称，中间的“S”则像一条流畅的线条将两者连接起来，代表博客内容的连贯性和深度。整个LOGO采用深海蓝为主色调，象征智慧和深度，辅以银色或白色，增加科技感和现代感。 ")])}const d=o(a,[["render",p],["__file","intro.html.vue"]]),h=JSON.parse('{"path":"/intro.html","title":"介绍页","lang":"zh-CN","frontmatter":{"icon":"circle-info","archive":true,"sticky":true,"home":true,"portfolio":true,"titles":"student","date":"2023-07-08T00:00:00.000Z","description":"介绍页 一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/intro.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"介绍页"}],["meta",{"property":"og:description","content":"介绍页 一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。"}],["meta",{"property":"og:type","content":"website"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:published_time","content":"2023-07-08T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"WebPage\\",\\"name\\":\\"介绍页\\",\\"description\\":\\"介绍页 一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。\\"}"]]},"headers":[],"readingTime":{"minutes":0.56,"words":167},"filePathRelative":"intro.md","localizedDate":"2023年7月8日","excerpt":"\\n<p>一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</p>\\n<!-- # LOGO 设计理念 -->\\n<!-- 使用“KSJ”三个字母的抽象化设计。字母“K”和“J”可以设计成镜像对称，中间的“S”则像一条流畅的线条将两者连接起来，代表博客内容的连贯性和深度。整个LOGO采用深海蓝为主色调，象征智慧和深度，辅以银色或白色，增加科技感和现代感。 -->\\n","autoDesc":true}');export{d as comp,h as data};
diff --git a/assets/iterator.html-USsHv5Pr.js b/assets/iterator.html-9EjNXcsT.js
similarity index 99%
rename from assets/iterator.html-USsHv5Pr.js
rename to assets/iterator.html-9EjNXcsT.js
index 0389cec..4f8d83f 100644
--- a/assets/iterator.html-USsHv5Pr.js
+++ b/assets/iterator.html-9EjNXcsT.js
@@ -1,4 +1,4 @@
-import{_ as n,o as s,c as a,f as t}from"./app-B69Gl_S-.js";const p={},e=t(`<h2 id="为什么要使用迭代器模式" tabindex="-1"><a class="header-anchor" href="#为什么要使用迭代器模式"><span>为什么要使用迭代器模式</span></a></h2><p>迭代器模式提供了一种方法来顺序访问集合中的元素，而无需暴露其底层表示。使用迭代器模式有以下几个优点：</p><ol><li><strong>简化代码</strong>：迭代器模式将遍历逻辑封装在迭代器对象中，使得客户端代码更加简洁和易读。</li><li><strong>解耦集合和遍历</strong>：集合对象和遍历算法分离，增加了代码的灵活性和可维护性。可以在不修改集合对象的情况下，改变遍历算法。</li><li><strong>统一接口</strong>：通过实现统一的迭代器接口，不同类型的集合可以使用相同的遍历方式，增强了代码的可扩展性。</li><li><strong>支持多种遍历方式</strong>：可以根据需要实现不同的迭代器，以支持多种遍历方式，如正向遍历、反向遍历、过滤遍历等。</li></ol><p>通过使用迭代器模式，我们可以更好地管理和操作集合数据，提高代码的可读性和可维护性。</p><h2 id="typescript-实现迭代器模式" tabindex="-1"><a class="header-anchor" href="#typescript-实现迭代器模式"><span>TypeScript 实现迭代器模式</span></a></h2><p>在本节中，我们将展示如何使用 TypeScript 实现迭代器模式。迭代器模式是一种行为设计模式，它允许顺序访问集合中的元素，而无需暴露其底层表示。</p><h3 id="代码示例" tabindex="-1"><a class="header-anchor" href="#代码示例"><span>代码示例</span></a></h3><p>以下是实现迭代器模式的 TypeScript 代码示例：</p><img src="https://www.plantuml.com/plantuml/svg/ZL8nRiCm3Dpz2evE2tr0KzAjG96bOz51iHbPY4KP4bEaAFhtYh8Ts-ZGRjBnxdWKjKzi8bzzNpbYZ6VJ83pdW-4GuQi2UEnCEkADwvs6KmWz6XAK9iZGP_LThSG7QoDQmpYgtUGbtDbN14rlKeAd42w5fyXur90uEhAYiyZ738bi0ZUYrmxxCpW_zEYHE2rjYriEUacwCD_U1SX2ra1NVy8usKlnmBMZ5czpQJTgX6660QcLMorkOo7NFu9h9uSN9CkTH5oC_vwtHBy_yMg46RjFK9Xw4Gc-YVlVzImxKUfXMQ-69c96gz-nb0ghlcLDMsYV7oV_cXy0" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// aggregate.ts</span>
+import{_ as n,o as s,c as a,f as t}from"./app-B4LGNJZ0.js";const p={},e=t(`<h2 id="为什么要使用迭代器模式" tabindex="-1"><a class="header-anchor" href="#为什么要使用迭代器模式"><span>为什么要使用迭代器模式</span></a></h2><p>迭代器模式提供了一种方法来顺序访问集合中的元素，而无需暴露其底层表示。使用迭代器模式有以下几个优点：</p><ol><li><strong>简化代码</strong>：迭代器模式将遍历逻辑封装在迭代器对象中，使得客户端代码更加简洁和易读。</li><li><strong>解耦集合和遍历</strong>：集合对象和遍历算法分离，增加了代码的灵活性和可维护性。可以在不修改集合对象的情况下，改变遍历算法。</li><li><strong>统一接口</strong>：通过实现统一的迭代器接口，不同类型的集合可以使用相同的遍历方式，增强了代码的可扩展性。</li><li><strong>支持多种遍历方式</strong>：可以根据需要实现不同的迭代器，以支持多种遍历方式，如正向遍历、反向遍历、过滤遍历等。</li></ol><p>通过使用迭代器模式，我们可以更好地管理和操作集合数据，提高代码的可读性和可维护性。</p><h2 id="typescript-实现迭代器模式" tabindex="-1"><a class="header-anchor" href="#typescript-实现迭代器模式"><span>TypeScript 实现迭代器模式</span></a></h2><p>在本节中，我们将展示如何使用 TypeScript 实现迭代器模式。迭代器模式是一种行为设计模式，它允许顺序访问集合中的元素，而无需暴露其底层表示。</p><h3 id="代码示例" tabindex="-1"><a class="header-anchor" href="#代码示例"><span>代码示例</span></a></h3><p>以下是实现迭代器模式的 TypeScript 代码示例：</p><img src="https://www.plantuml.com/plantuml/svg/ZL8nRiCm3Dpz2evE2tr0KzAjG96bOz51iHbPY4KP4bEaAFhtYh8Ts-ZGRjBnxdWKjKzi8bzzNpbYZ6VJ83pdW-4GuQi2UEnCEkADwvs6KmWz6XAK9iZGP_LThSG7QoDQmpYgtUGbtDbN14rlKeAd42w5fyXur90uEhAYiyZ738bi0ZUYrmxxCpW_zEYHE2rjYriEUacwCD_U1SX2ra1NVy8usKlnmBMZ5czpQJTgX6660QcLMorkOo7NFu9h9uSN9CkTH5oC_vwtHBy_yMg46RjFK9Xw4Gc-YVlVzImxKUfXMQ-69c96gz-nb0ghlcLDMsYV7oV_cXy0" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// aggregate.ts</span>
 <span class="token keyword">import</span> <span class="token punctuation">{</span> Iterator <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&#39;./iterator&#39;</span><span class="token punctuation">;</span>
 <span class="token keyword">export</span> <span class="token keyword">interface</span> <span class="token class-name">Aggregate</span> <span class="token punctuation">{</span>
   <span class="token function">iterator</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">:</span> Iterator<span class="token punctuation">;</span>
diff --git a/assets/journeyDiagram-de0d04b7-DXj0d_vq.js b/assets/journeyDiagram-de0d04b7-bCIGoTun.js
similarity index 98%
rename from assets/journeyDiagram-de0d04b7-DXj0d_vq.js
rename to assets/journeyDiagram-de0d04b7-bCIGoTun.js
index 30153eb..6f7bb51 100644
--- a/assets/journeyDiagram-de0d04b7-DXj0d_vq.js
+++ b/assets/journeyDiagram-de0d04b7-bCIGoTun.js
@@ -1,4 +1,4 @@
-import{c as A,x as yt,y as ft,s as dt,g as pt,b as gt,a as mt,A as xt,h as W,i as kt}from"./mermaid.core-ChLYKTZm.js";import{d as _t,f as bt,a as vt,g as it}from"./svgDrawCommon-9d162435-DXbPg0E8.js";import{a as Q}from"./arc-BCmLGSVu.js";import"./app-B69Gl_S-.js";import"./path-CbwjOpE9.js";var G=function(){var t=function(p,s,r,a){for(r=r||{},a=p.length;a--;r[p[a]]=s);return r},e=[6,8,10,11,12,14,16,17,18],i=[1,9],l=[1,10],n=[1,11],h=[1,12],c=[1,13],f=[1,14],y={trace:function(){},yy:{},symbols_:{error:2,start:3,journey:4,document:5,EOF:6,line:7,SPACE:8,statement:9,NEWLINE:10,title:11,acc_title:12,acc_title_value:13,acc_descr:14,acc_descr_value:15,acc_descr_multiline_value:16,section:17,taskName:18,taskData:19,$accept:0,$end:1},terminals_:{2:"error",4:"journey",6:"EOF",8:"SPACE",10:"NEWLINE",11:"title",12:"acc_title",13:"acc_title_value",14:"acc_descr",15:"acc_descr_value",16:"acc_descr_multiline_value",17:"section",18:"taskName",19:"taskData"},productions_:[0,[3,3],[5,0],[5,2],[7,2],[7,1],[7,1],[7,1],[9,1],[9,2],[9,2],[9,1],[9,1],[9,2]],performAction:function(s,r,a,u,d,o,w){var k=o.length-1;switch(d){case 1:return o[k-1];case 2:this.$=[];break;case 3:o[k-1].push(o[k]),this.$=o[k-1];break;case 4:case 5:this.$=o[k];break;case 6:case 7:this.$=[];break;case 8:u.setDiagramTitle(o[k].substr(6)),this.$=o[k].substr(6);break;case 9:this.$=o[k].trim(),u.setAccTitle(this.$);break;case 10:case 11:this.$=o[k].trim(),u.setAccDescription(this.$);break;case 12:u.addSection(o[k].substr(8)),this.$=o[k].substr(8);break;case 13:u.addTask(o[k-1],o[k]),this.$="task";break}},table:[{3:1,4:[1,2]},{1:[3]},t(e,[2,2],{5:3}),{6:[1,4],7:5,8:[1,6],9:7,10:[1,8],11:i,12:l,14:n,16:h,17:c,18:f},t(e,[2,7],{1:[2,1]}),t(e,[2,3]),{9:15,11:i,12:l,14:n,16:h,17:c,18:f},t(e,[2,5]),t(e,[2,6]),t(e,[2,8]),{13:[1,16]},{15:[1,17]},t(e,[2,11]),t(e,[2,12]),{19:[1,18]},t(e,[2,4]),t(e,[2,9]),t(e,[2,10]),t(e,[2,13])],defaultActions:{},parseError:function(s,r){if(r.recoverable)this.trace(s);else{var a=new Error(s);throw a.hash=r,a}},parse:function(s){var r=this,a=[0],u=[],d=[null],o=[],w=this.table,k="",R=0,Z=0,lt=2,J=1,ct=o.slice.call(arguments,1),x=Object.create(this.lexer),S={yy:{}};for(var z in this.yy)Object.prototype.hasOwnProperty.call(this.yy,z)&&(S.yy[z]=this.yy[z]);x.setInput(s,S.yy),S.yy.lexer=x,S.yy.parser=this,typeof x.yylloc>"u"&&(x.yylloc={});var Y=x.yylloc;o.push(Y);var ht=x.options&&x.options.ranges;typeof S.yy.parseError=="function"?this.parseError=S.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function ut(){var T;return T=u.pop()||x.lex()||J,typeof T!="number"&&(T instanceof Array&&(u=T,T=u.pop()),T=r.symbols_[T]||T),T}for(var _,E,b,O,I={},N,$,K,B;;){if(E=a[a.length-1],this.defaultActions[E]?b=this.defaultActions[E]:((_===null||typeof _>"u")&&(_=ut()),b=w[E]&&w[E][_]),typeof b>"u"||!b.length||!b[0]){var q="";B=[];for(N in w[E])this.terminals_[N]&&N>lt&&B.push("'"+this.terminals_[N]+"'");x.showPosition?q="Parse error on line "+(R+1)+`:
+import{c as A,x as yt,y as ft,s as dt,g as pt,b as gt,a as mt,A as xt,h as W,i as kt}from"./mermaid.core-DNo_7Q2B.js";import{d as _t,f as bt,a as vt,g as it}from"./svgDrawCommon-9d162435-DBc9TLjw.js";import{a as Q}from"./arc-DWlpCdAw.js";import"./app-B4LGNJZ0.js";import"./path-CbwjOpE9.js";var G=function(){var t=function(p,s,r,a){for(r=r||{},a=p.length;a--;r[p[a]]=s);return r},e=[6,8,10,11,12,14,16,17,18],i=[1,9],l=[1,10],n=[1,11],h=[1,12],c=[1,13],f=[1,14],y={trace:function(){},yy:{},symbols_:{error:2,start:3,journey:4,document:5,EOF:6,line:7,SPACE:8,statement:9,NEWLINE:10,title:11,acc_title:12,acc_title_value:13,acc_descr:14,acc_descr_value:15,acc_descr_multiline_value:16,section:17,taskName:18,taskData:19,$accept:0,$end:1},terminals_:{2:"error",4:"journey",6:"EOF",8:"SPACE",10:"NEWLINE",11:"title",12:"acc_title",13:"acc_title_value",14:"acc_descr",15:"acc_descr_value",16:"acc_descr_multiline_value",17:"section",18:"taskName",19:"taskData"},productions_:[0,[3,3],[5,0],[5,2],[7,2],[7,1],[7,1],[7,1],[9,1],[9,2],[9,2],[9,1],[9,1],[9,2]],performAction:function(s,r,a,u,d,o,w){var k=o.length-1;switch(d){case 1:return o[k-1];case 2:this.$=[];break;case 3:o[k-1].push(o[k]),this.$=o[k-1];break;case 4:case 5:this.$=o[k];break;case 6:case 7:this.$=[];break;case 8:u.setDiagramTitle(o[k].substr(6)),this.$=o[k].substr(6);break;case 9:this.$=o[k].trim(),u.setAccTitle(this.$);break;case 10:case 11:this.$=o[k].trim(),u.setAccDescription(this.$);break;case 12:u.addSection(o[k].substr(8)),this.$=o[k].substr(8);break;case 13:u.addTask(o[k-1],o[k]),this.$="task";break}},table:[{3:1,4:[1,2]},{1:[3]},t(e,[2,2],{5:3}),{6:[1,4],7:5,8:[1,6],9:7,10:[1,8],11:i,12:l,14:n,16:h,17:c,18:f},t(e,[2,7],{1:[2,1]}),t(e,[2,3]),{9:15,11:i,12:l,14:n,16:h,17:c,18:f},t(e,[2,5]),t(e,[2,6]),t(e,[2,8]),{13:[1,16]},{15:[1,17]},t(e,[2,11]),t(e,[2,12]),{19:[1,18]},t(e,[2,4]),t(e,[2,9]),t(e,[2,10]),t(e,[2,13])],defaultActions:{},parseError:function(s,r){if(r.recoverable)this.trace(s);else{var a=new Error(s);throw a.hash=r,a}},parse:function(s){var r=this,a=[0],u=[],d=[null],o=[],w=this.table,k="",R=0,Z=0,lt=2,J=1,ct=o.slice.call(arguments,1),x=Object.create(this.lexer),S={yy:{}};for(var z in this.yy)Object.prototype.hasOwnProperty.call(this.yy,z)&&(S.yy[z]=this.yy[z]);x.setInput(s,S.yy),S.yy.lexer=x,S.yy.parser=this,typeof x.yylloc>"u"&&(x.yylloc={});var Y=x.yylloc;o.push(Y);var ht=x.options&&x.options.ranges;typeof S.yy.parseError=="function"?this.parseError=S.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function ut(){var T;return T=u.pop()||x.lex()||J,typeof T!="number"&&(T instanceof Array&&(u=T,T=u.pop()),T=r.symbols_[T]||T),T}for(var _,E,b,O,I={},N,$,K,B;;){if(E=a[a.length-1],this.defaultActions[E]?b=this.defaultActions[E]:((_===null||typeof _>"u")&&(_=ut()),b=w[E]&&w[E][_]),typeof b>"u"||!b.length||!b[0]){var q="";B=[];for(N in w[E])this.terminals_[N]&&N>lt&&B.push("'"+this.terminals_[N]+"'");x.showPosition?q="Parse error on line "+(R+1)+`:
 `+x.showPosition()+`
 Expecting `+B.join(", ")+", got '"+(this.terminals_[_]||_)+"'":q="Parse error on line "+(R+1)+": Unexpected "+(_==J?"end of input":"'"+(this.terminals_[_]||_)+"'"),this.parseError(q,{text:x.match,token:this.terminals_[_]||_,line:x.yylineno,loc:Y,expected:B})}if(b[0]instanceof Array&&b.length>1)throw new Error("Parse Error: multiple actions possible at state: "+E+", token: "+_);switch(b[0]){case 1:a.push(_),d.push(x.yytext),o.push(x.yylloc),a.push(b[1]),_=null,Z=x.yyleng,k=x.yytext,R=x.yylineno,Y=x.yylloc;break;case 2:if($=this.productions_[b[1]][1],I.$=d[d.length-$],I._$={first_line:o[o.length-($||1)].first_line,last_line:o[o.length-1].last_line,first_column:o[o.length-($||1)].first_column,last_column:o[o.length-1].last_column},ht&&(I._$.range=[o[o.length-($||1)].range[0],o[o.length-1].range[1]]),O=this.performAction.apply(I,[k,Z,R,S.yy,b[1],d,o].concat(ct)),typeof O<"u")return O;$&&(a=a.slice(0,-1*$*2),d=d.slice(0,-1*$),o=o.slice(0,-1*$)),a.push(this.productions_[b[1]][0]),d.push(I.$),o.push(I._$),K=w[a[a.length-2]][a[a.length-1]],a.push(K);break;case 3:return!0}}return!0}},m=function(){var p={EOF:1,parseError:function(r,a){if(this.yy.parser)this.yy.parser.parseError(r,a);else throw new Error(r)},setInput:function(s,r){return this.yy=r||this.yy||{},this._input=s,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var s=this._input[0];this.yytext+=s,this.yyleng++,this.offset++,this.match+=s,this.matched+=s;var r=s.match(/(?:\r\n?|\n).*/g);return r?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),s},unput:function(s){var r=s.length,a=s.split(/(?:\r\n?|\n)/g);this._input=s+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-r),this.offset-=r;var u=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),a.length-1&&(this.yylineno-=a.length-1);var d=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:a?(a.length===u.length?this.yylloc.first_column:0)+u[u.length-a.length].length-a[0].length:this.yylloc.first_column-r},this.options.ranges&&(this.yylloc.range=[d[0],d[0]+this.yyleng-r]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){if(this.options.backtrack_lexer)this._backtrack=!0;else return this.parseError("Lexical error on line "+(this.yylineno+1)+`. You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).
 `+this.showPosition(),{text:"",token:null,line:this.yylineno});return this},less:function(s){this.unput(this.match.slice(s))},pastInput:function(){var s=this.matched.substr(0,this.matched.length-this.match.length);return(s.length>20?"...":"")+s.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var s=this.match;return s.length<20&&(s+=this._input.substr(0,20-s.length)),(s.substr(0,20)+(s.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var s=this.pastInput(),r=new Array(s.length+1).join("-");return s+this.upcomingInput()+`
diff --git a/assets/layout-DUYLy6Ue.js b/assets/layout-qMafh1ee.js
similarity index 99%
rename from assets/layout-DUYLy6Ue.js
rename to assets/layout-qMafh1ee.js
index 24bf0da..feb5bcb 100644
--- a/assets/layout-DUYLy6Ue.js
+++ b/assets/layout-qMafh1ee.js
@@ -1 +1 @@
-import{i as F,b as gn,a as zn,c as L,k as Xn,d as Un,e as Hn,g as P,j as xn,l as En,m as kn,t as jn,n as yn,o as Kn,p as Jn,f as s,G as x,h as w,q as g,r as M,v as y,s as Y}from"./graph-T5JS4vfK.js";import{R as A,ag as Qn,ah as Zn,a6 as Nn,ai as B,K as Ln,_ as ne,E as _n,D as K,a4 as ee,aj as re,a3 as J,a2 as te,Y as Cn,Q as ie,a8 as ae,ak as H}from"./mermaid.core-ChLYKTZm.js";var oe=/\s/;function ue(n){for(var e=n.length;e--&&oe.test(n.charAt(e)););return e}var de=/^\s+/;function fe(n){return n&&n.slice(0,ue(n)+1).replace(de,"")}var un=NaN,se=/^[-+]0x[0-9a-f]+$/i,ce=/^0b[01]+$/i,he=/^0o[0-7]+$/i,le=parseInt;function ve(n){if(typeof n=="number")return n;if(F(n))return un;if(A(n)){var e=typeof n.valueOf=="function"?n.valueOf():n;n=A(e)?e+"":e}if(typeof n!="string")return n===0?n:+n;n=fe(n);var r=ce.test(n);return r||he.test(n)?le(n.slice(2),r?2:8):se.test(n)?un:+n}var dn=1/0,pe=17976931348623157e292;function S(n){if(!n)return n===0?n:0;if(n=ve(n),n===dn||n===-dn){var e=n<0?-1:1;return e*pe}return n===n?n:0}function we(n){var e=S(n),r=e%1;return e===e?r?e-r:e:0}function _(n){var e=n==null?0:n.length;return e?gn(n):[]}function me(n){return Qn(Zn(n,void 0,_),n+"")}var be=1,ge=4;function xe(n){return zn(n,be|ge)}var In=Object.prototype,Ee=In.hasOwnProperty,ke=Nn(function(n,e){n=Object(n);var r=-1,t=e.length,i=t>2?e[2]:void 0;for(i&&B(e[0],e[1],i)&&(t=1);++r<t;)for(var o=e[r],a=Ln(o),u=-1,d=a.length;++u<d;){var f=a[u],c=n[f];(c===void 0||ne(c,In[f])&&!Ee.call(n,f))&&(n[f]=o[f])}return n});function G(n){var e=n==null?0:n.length;return e?n[e-1]:void 0}function ye(n){return function(e,r,t){var i=Object(e);if(!_n(e)){var o=L(r);e=Xn(e),r=function(u){return o(i[u],u,i)}}var a=n(e,r,t);return a>-1?i[o?e[a]:a]:void 0}}var Ne=Math.max;function Le(n,e,r){var t=n==null?0:n.length;if(!t)return-1;var i=r==null?0:we(r);return i<0&&(i=Ne(t+i,0)),Un(n,L(e),i)}var Q=ye(Le);function Rn(n,e){var r=-1,t=_n(n)?Array(n.length):[];return Hn(n,function(i,o,a){t[++r]=e(i,o,a)}),t}function m(n,e){var r=K(n)?P:Rn;return r(n,L(e))}function _e(n,e){return n==null?n:ee(n,xn(e),Ln)}function Ce(n,e){return n&&En(n,xn(e))}function Ie(n,e){return n>e}function Tn(n,e){return n<e}function D(n,e){var r={};return e=L(e),En(n,function(t,i,o){re(r,i,e(t,i,o))}),r}function Z(n,e,r){for(var t=-1,i=n.length;++t<i;){var o=n[t],a=e(o);if(a!=null&&(u===void 0?a===a&&!F(a):r(a,u)))var u=a,d=o}return d}function E(n){return n&&n.length?Z(n,J,Ie):void 0}function R(n){return n&&n.length?Z(n,J,Tn):void 0}function nn(n,e){return n&&n.length?Z(n,L(e),Tn):void 0}function Re(n,e,r,t){if(!A(n))return n;e=kn(e,n);for(var i=-1,o=e.length,a=o-1,u=n;u!=null&&++i<o;){var d=jn(e[i]),f=r;if(d==="__proto__"||d==="constructor"||d==="prototype")return n;if(i!=a){var c=u[d];f=void 0,f===void 0&&(f=A(c)?c:te(e[i+1])?[]:{})}Cn(u,d,f),u=u[d]}return n}function Te(n,e,r){for(var t=-1,i=e.length,o={};++t<i;){var a=e[t],u=yn(n,a);r(u,a)&&Re(o,kn(a,n),u)}return o}function Me(n,e){var r=n.length;for(n.sort(e);r--;)n[r]=n[r].value;return n}function Oe(n,e){if(n!==e){var r=n!==void 0,t=n===null,i=n===n,o=F(n),a=e!==void 0,u=e===null,d=e===e,f=F(e);if(!u&&!f&&!o&&n>e||o&&a&&d&&!u&&!f||t&&a&&d||!r&&d||!i)return 1;if(!t&&!o&&!f&&n<e||f&&r&&i&&!t&&!o||u&&r&&i||!a&&i||!d)return-1}return 0}function Pe(n,e,r){for(var t=-1,i=n.criteria,o=e.criteria,a=i.length,u=r.length;++t<a;){var d=Oe(i[t],o[t]);if(d){if(t>=u)return d;var f=r[t];return d*(f=="desc"?-1:1)}}return n.index-e.index}function Se(n,e,r){e.length?e=P(e,function(o){return K(o)?function(a){return yn(a,o.length===1?o[0]:o)}:o}):e=[J];var t=-1;e=P(e,ie(L));var i=Rn(n,function(o,a,u){var d=P(e,function(f){return f(o)});return{criteria:d,index:++t,value:o}});return Me(i,function(o,a){return Pe(o,a,r)})}function Fe(n,e){return Te(n,e,function(r,t){return Kn(n,t)})}var V=me(function(n,e){return n==null?{}:Fe(n,e)}),Ae=Math.ceil,Be=Math.max;function Ge(n,e,r,t){for(var i=-1,o=Be(Ae((e-n)/(r||1)),0),a=Array(o);o--;)a[++i]=n,n+=r;return a}function Ve(n){return function(e,r,t){return t&&typeof t!="number"&&B(e,r,t)&&(r=t=void 0),e=S(e),r===void 0?(r=e,e=0):r=S(r),t=t===void 0?e<r?1:-1:S(t),Ge(e,r,t)}}var N=Ve(),O=Nn(function(n,e){if(n==null)return[];var r=e.length;return r>1&&B(n,e[0],e[1])?e=[]:r>2&&B(e[0],e[1],e[2])&&(e=[e[0]]),Se(n,gn(e),[])}),Ye=0;function en(n){var e=++Ye;return Jn(n)+e}function De(n,e,r){for(var t=-1,i=n.length,o=e.length,a={};++t<i;){var u=t<o?e[t]:void 0;r(a,n[t],u)}return a}function $e(n,e){return De(n||[],e||[],Cn)}class qe{constructor(){var e={};e._next=e._prev=e,this._sentinel=e}dequeue(){var e=this._sentinel,r=e._prev;if(r!==e)return fn(r),r}enqueue(e){var r=this._sentinel;e._prev&&e._next&&fn(e),e._next=r._next,r._next._prev=e,r._next=e,e._prev=r}toString(){for(var e=[],r=this._sentinel,t=r._prev;t!==r;)e.push(JSON.stringify(t,We)),t=t._prev;return"["+e.join(", ")+"]"}}function fn(n){n._prev._next=n._next,n._next._prev=n._prev,delete n._next,delete n._prev}function We(n,e){if(n!=="_next"&&n!=="_prev")return e}var ze=ae(1);function Xe(n,e){if(n.nodeCount()<=1)return[];var r=He(n,e||ze),t=Ue(r.graph,r.buckets,r.zeroIdx);return _(m(t,function(i){return n.outEdges(i.v,i.w)}))}function Ue(n,e,r){for(var t=[],i=e[e.length-1],o=e[0],a;n.nodeCount();){for(;a=o.dequeue();)q(n,e,r,a);for(;a=i.dequeue();)q(n,e,r,a);if(n.nodeCount()){for(var u=e.length-2;u>0;--u)if(a=e[u].dequeue(),a){t=t.concat(q(n,e,r,a,!0));break}}}return t}function q(n,e,r,t,i){var o=i?[]:void 0;return s(n.inEdges(t.v),function(a){var u=n.edge(a),d=n.node(a.v);i&&o.push({v:a.v,w:a.w}),d.out-=u,j(e,r,d)}),s(n.outEdges(t.v),function(a){var u=n.edge(a),d=a.w,f=n.node(d);f.in-=u,j(e,r,f)}),n.removeNode(t.v),o}function He(n,e){var r=new x,t=0,i=0;s(n.nodes(),function(u){r.setNode(u,{v:u,in:0,out:0})}),s(n.edges(),function(u){var d=r.edge(u.v,u.w)||0,f=e(u),c=d+f;r.setEdge(u.v,u.w,c),i=Math.max(i,r.node(u.v).out+=f),t=Math.max(t,r.node(u.w).in+=f)});var o=N(i+t+3).map(function(){return new qe}),a=t+1;return s(r.nodes(),function(u){j(o,a,r.node(u))}),{graph:r,buckets:o,zeroIdx:a}}function j(n,e,r){r.out?r.in?n[r.out-r.in+e].enqueue(r):n[n.length-1].enqueue(r):n[0].enqueue(r)}function je(n){var e=n.graph().acyclicer==="greedy"?Xe(n,r(n)):Ke(n);s(e,function(t){var i=n.edge(t);n.removeEdge(t),i.forwardName=t.name,i.reversed=!0,n.setEdge(t.w,t.v,i,en("rev"))});function r(t){return function(i){return t.edge(i).weight}}}function Ke(n){var e=[],r={},t={};function i(o){w(t,o)||(t[o]=!0,r[o]=!0,s(n.outEdges(o),function(a){w(r,a.w)?e.push(a):i(a.w)}),delete r[o])}return s(n.nodes(),i),e}function Je(n){s(n.edges(),function(e){var r=n.edge(e);if(r.reversed){n.removeEdge(e);var t=r.forwardName;delete r.reversed,delete r.forwardName,n.setEdge(e.w,e.v,r,t)}})}function C(n,e,r,t){var i;do i=en(t);while(n.hasNode(i));return r.dummy=e,n.setNode(i,r),i}function Qe(n){var e=new x().setGraph(n.graph());return s(n.nodes(),function(r){e.setNode(r,n.node(r))}),s(n.edges(),function(r){var t=e.edge(r.v,r.w)||{weight:0,minlen:1},i=n.edge(r);e.setEdge(r.v,r.w,{weight:t.weight+i.weight,minlen:Math.max(t.minlen,i.minlen)})}),e}function Mn(n){var e=new x({multigraph:n.isMultigraph()}).setGraph(n.graph());return s(n.nodes(),function(r){n.children(r).length||e.setNode(r,n.node(r))}),s(n.edges(),function(r){e.setEdge(r,n.edge(r))}),e}function sn(n,e){var r=n.x,t=n.y,i=e.x-r,o=e.y-t,a=n.width/2,u=n.height/2;if(!i&&!o)throw new Error("Not possible to find intersection inside of the rectangle");var d,f;return Math.abs(o)*a>Math.abs(i)*u?(o<0&&(u=-u),d=u*i/o,f=u):(i<0&&(a=-a),d=a,f=a*o/i),{x:r+d,y:t+f}}function $(n){var e=m(N(On(n)+1),function(){return[]});return s(n.nodes(),function(r){var t=n.node(r),i=t.rank;g(i)||(e[i][t.order]=r)}),e}function Ze(n){var e=R(m(n.nodes(),function(r){return n.node(r).rank}));s(n.nodes(),function(r){var t=n.node(r);w(t,"rank")&&(t.rank-=e)})}function nr(n){var e=R(m(n.nodes(),function(o){return n.node(o).rank})),r=[];s(n.nodes(),function(o){var a=n.node(o).rank-e;r[a]||(r[a]=[]),r[a].push(o)});var t=0,i=n.graph().nodeRankFactor;s(r,function(o,a){g(o)&&a%i!==0?--t:t&&s(o,function(u){n.node(u).rank+=t})})}function cn(n,e,r,t){var i={width:0,height:0};return arguments.length>=4&&(i.rank=r,i.order=t),C(n,"border",i,e)}function On(n){return E(m(n.nodes(),function(e){var r=n.node(e).rank;if(!g(r))return r}))}function er(n,e){var r={lhs:[],rhs:[]};return s(n,function(t){e(t)?r.lhs.push(t):r.rhs.push(t)}),r}function rr(n,e){return e()}function tr(n){function e(r){var t=n.children(r),i=n.node(r);if(t.length&&s(t,e),w(i,"minRank")){i.borderLeft=[],i.borderRight=[];for(var o=i.minRank,a=i.maxRank+1;o<a;++o)hn(n,"borderLeft","_bl",r,i,o),hn(n,"borderRight","_br",r,i,o)}}s(n.children(),e)}function hn(n,e,r,t,i,o){var a={width:0,height:0,rank:o,borderType:e},u=i[e][o-1],d=C(n,"border",a,r);i[e][o]=d,n.setParent(d,t),u&&n.setEdge(u,d,{weight:1})}function ir(n){var e=n.graph().rankdir.toLowerCase();(e==="lr"||e==="rl")&&Pn(n)}function ar(n){var e=n.graph().rankdir.toLowerCase();(e==="bt"||e==="rl")&&or(n),(e==="lr"||e==="rl")&&(ur(n),Pn(n))}function Pn(n){s(n.nodes(),function(e){ln(n.node(e))}),s(n.edges(),function(e){ln(n.edge(e))})}function ln(n){var e=n.width;n.width=n.height,n.height=e}function or(n){s(n.nodes(),function(e){W(n.node(e))}),s(n.edges(),function(e){var r=n.edge(e);s(r.points,W),w(r,"y")&&W(r)})}function W(n){n.y=-n.y}function ur(n){s(n.nodes(),function(e){z(n.node(e))}),s(n.edges(),function(e){var r=n.edge(e);s(r.points,z),w(r,"x")&&z(r)})}function z(n){var e=n.x;n.x=n.y,n.y=e}function dr(n){n.graph().dummyChains=[],s(n.edges(),function(e){fr(n,e)})}function fr(n,e){var r=e.v,t=n.node(r).rank,i=e.w,o=n.node(i).rank,a=e.name,u=n.edge(e),d=u.labelRank;if(o!==t+1){n.removeEdge(e);var f,c,h;for(h=0,++t;t<o;++h,++t)u.points=[],c={width:0,height:0,edgeLabel:u,edgeObj:e,rank:t},f=C(n,"edge",c,"_d"),t===d&&(c.width=u.width,c.height=u.height,c.dummy="edge-label",c.labelpos=u.labelpos),n.setEdge(r,f,{weight:u.weight},a),h===0&&n.graph().dummyChains.push(f),r=f;n.setEdge(r,i,{weight:u.weight},a)}}function sr(n){s(n.graph().dummyChains,function(e){var r=n.node(e),t=r.edgeLabel,i;for(n.setEdge(r.edgeObj,t);r.dummy;)i=n.successors(e)[0],n.removeNode(e),t.points.push({x:r.x,y:r.y}),r.dummy==="edge-label"&&(t.x=r.x,t.y=r.y,t.width=r.width,t.height=r.height),e=i,r=n.node(e)})}function rn(n){var e={};function r(t){var i=n.node(t);if(w(e,t))return i.rank;e[t]=!0;var o=R(m(n.outEdges(t),function(a){return r(a.w)-n.edge(a).minlen}));return(o===Number.POSITIVE_INFINITY||o===void 0||o===null)&&(o=0),i.rank=o}s(n.sources(),r)}function T(n,e){return n.node(e.w).rank-n.node(e.v).rank-n.edge(e).minlen}function Sn(n){var e=new x({directed:!1}),r=n.nodes()[0],t=n.nodeCount();e.setNode(r,{});for(var i,o;cr(e,n)<t;)i=hr(e,n),o=e.hasNode(i.v)?T(n,i):-T(n,i),lr(e,n,o);return e}function cr(n,e){function r(t){s(e.nodeEdges(t),function(i){var o=i.v,a=t===o?i.w:o;!n.hasNode(a)&&!T(e,i)&&(n.setNode(a,{}),n.setEdge(t,a,{}),r(a))})}return s(n.nodes(),r),n.nodeCount()}function hr(n,e){return nn(e.edges(),function(r){if(n.hasNode(r.v)!==n.hasNode(r.w))return T(e,r)})}function lr(n,e,r){s(n.nodes(),function(t){e.node(t).rank+=r})}function vr(){}vr.prototype=new Error;function Fn(n,e,r){K(e)||(e=[e]);var t=(n.isDirected()?n.successors:n.neighbors).bind(n),i=[],o={};return s(e,function(a){if(!n.hasNode(a))throw new Error("Graph does not have node: "+a);An(n,a,r==="post",o,t,i)}),i}function An(n,e,r,t,i,o){w(t,e)||(t[e]=!0,r||o.push(e),s(i(e),function(a){An(n,a,r,t,i,o)}),r&&o.push(e))}function pr(n,e){return Fn(n,e,"post")}function wr(n,e){return Fn(n,e,"pre")}k.initLowLimValues=an;k.initCutValues=tn;k.calcCutValue=Bn;k.leaveEdge=Vn;k.enterEdge=Yn;k.exchangeEdges=Dn;function k(n){n=Qe(n),rn(n);var e=Sn(n);an(e),tn(e,n);for(var r,t;r=Vn(e);)t=Yn(e,n,r),Dn(e,n,r,t)}function tn(n,e){var r=pr(n,n.nodes());r=r.slice(0,r.length-1),s(r,function(t){mr(n,e,t)})}function mr(n,e,r){var t=n.node(r),i=t.parent;n.edge(r,i).cutvalue=Bn(n,e,r)}function Bn(n,e,r){var t=n.node(r),i=t.parent,o=!0,a=e.edge(r,i),u=0;return a||(o=!1,a=e.edge(i,r)),u=a.weight,s(e.nodeEdges(r),function(d){var f=d.v===r,c=f?d.w:d.v;if(c!==i){var h=f===o,l=e.edge(d).weight;if(u+=h?l:-l,gr(n,r,c)){var v=n.edge(r,c).cutvalue;u+=h?-v:v}}}),u}function an(n,e){arguments.length<2&&(e=n.nodes()[0]),Gn(n,{},1,e)}function Gn(n,e,r,t,i){var o=r,a=n.node(t);return e[t]=!0,s(n.neighbors(t),function(u){w(e,u)||(r=Gn(n,e,r,u,t))}),a.low=o,a.lim=r++,i?a.parent=i:delete a.parent,r}function Vn(n){return Q(n.edges(),function(e){return n.edge(e).cutvalue<0})}function Yn(n,e,r){var t=r.v,i=r.w;e.hasEdge(t,i)||(t=r.w,i=r.v);var o=n.node(t),a=n.node(i),u=o,d=!1;o.lim>a.lim&&(u=a,d=!0);var f=M(e.edges(),function(c){return d===vn(n,n.node(c.v),u)&&d!==vn(n,n.node(c.w),u)});return nn(f,function(c){return T(e,c)})}function Dn(n,e,r,t){var i=r.v,o=r.w;n.removeEdge(i,o),n.setEdge(t.v,t.w,{}),an(n),tn(n,e),br(n,e)}function br(n,e){var r=Q(n.nodes(),function(i){return!e.node(i).parent}),t=wr(n,r);t=t.slice(1),s(t,function(i){var o=n.node(i).parent,a=e.edge(i,o),u=!1;a||(a=e.edge(o,i),u=!0),e.node(i).rank=e.node(o).rank+(u?a.minlen:-a.minlen)})}function gr(n,e,r){return n.hasEdge(e,r)}function vn(n,e,r){return r.low<=e.lim&&e.lim<=r.lim}function xr(n){switch(n.graph().ranker){case"network-simplex":pn(n);break;case"tight-tree":kr(n);break;case"longest-path":Er(n);break;default:pn(n)}}var Er=rn;function kr(n){rn(n),Sn(n)}function pn(n){k(n)}function yr(n){var e=C(n,"root",{},"_root"),r=Nr(n),t=E(y(r))-1,i=2*t+1;n.graph().nestingRoot=e,s(n.edges(),function(a){n.edge(a).minlen*=i});var o=Lr(n)+1;s(n.children(),function(a){$n(n,e,i,o,t,r,a)}),n.graph().nodeRankFactor=i}function $n(n,e,r,t,i,o,a){var u=n.children(a);if(!u.length){a!==e&&n.setEdge(e,a,{weight:0,minlen:r});return}var d=cn(n,"_bt"),f=cn(n,"_bb"),c=n.node(a);n.setParent(d,a),c.borderTop=d,n.setParent(f,a),c.borderBottom=f,s(u,function(h){$n(n,e,r,t,i,o,h);var l=n.node(h),v=l.borderTop?l.borderTop:h,p=l.borderBottom?l.borderBottom:h,b=l.borderTop?t:2*t,I=v!==p?1:i-o[a]+1;n.setEdge(d,v,{weight:b,minlen:I,nestingEdge:!0}),n.setEdge(p,f,{weight:b,minlen:I,nestingEdge:!0})}),n.parent(a)||n.setEdge(e,d,{weight:0,minlen:i+o[a]})}function Nr(n){var e={};function r(t,i){var o=n.children(t);o&&o.length&&s(o,function(a){r(a,i+1)}),e[t]=i}return s(n.children(),function(t){r(t,1)}),e}function Lr(n){return Y(n.edges(),function(e,r){return e+n.edge(r).weight},0)}function _r(n){var e=n.graph();n.removeNode(e.nestingRoot),delete e.nestingRoot,s(n.edges(),function(r){var t=n.edge(r);t.nestingEdge&&n.removeEdge(r)})}function Cr(n,e,r){var t={},i;s(r,function(o){for(var a=n.parent(o),u,d;a;){if(u=n.parent(a),u?(d=t[u],t[u]=a):(d=i,i=a),d&&d!==a){e.setEdge(d,a);return}a=u}})}function Ir(n,e,r){var t=Rr(n),i=new x({compound:!0}).setGraph({root:t}).setDefaultNodeLabel(function(o){return n.node(o)});return s(n.nodes(),function(o){var a=n.node(o),u=n.parent(o);(a.rank===e||a.minRank<=e&&e<=a.maxRank)&&(i.setNode(o),i.setParent(o,u||t),s(n[r](o),function(d){var f=d.v===o?d.w:d.v,c=i.edge(f,o),h=g(c)?0:c.weight;i.setEdge(f,o,{weight:n.edge(d).weight+h})}),w(a,"minRank")&&i.setNode(o,{borderLeft:a.borderLeft[e],borderRight:a.borderRight[e]}))}),i}function Rr(n){for(var e;n.hasNode(e=en("_root")););return e}function Tr(n,e){for(var r=0,t=1;t<e.length;++t)r+=Mr(n,e[t-1],e[t]);return r}function Mr(n,e,r){for(var t=$e(r,m(r,function(f,c){return c})),i=_(m(e,function(f){return O(m(n.outEdges(f),function(c){return{pos:t[c.w],weight:n.edge(c).weight}}),"pos")})),o=1;o<r.length;)o<<=1;var a=2*o-1;o-=1;var u=m(new Array(a),function(){return 0}),d=0;return s(i.forEach(function(f){var c=f.pos+o;u[c]+=f.weight;for(var h=0;c>0;)c%2&&(h+=u[c+1]),c=c-1>>1,u[c]+=f.weight;d+=f.weight*h})),d}function Or(n){var e={},r=M(n.nodes(),function(u){return!n.children(u).length}),t=E(m(r,function(u){return n.node(u).rank})),i=m(N(t+1),function(){return[]});function o(u){if(!w(e,u)){e[u]=!0;var d=n.node(u);i[d.rank].push(u),s(n.successors(u),o)}}var a=O(r,function(u){return n.node(u).rank});return s(a,o),i}function Pr(n,e){return m(e,function(r){var t=n.inEdges(r);if(t.length){var i=Y(t,function(o,a){var u=n.edge(a),d=n.node(a.v);return{sum:o.sum+u.weight*d.order,weight:o.weight+u.weight}},{sum:0,weight:0});return{v:r,barycenter:i.sum/i.weight,weight:i.weight}}else return{v:r}})}function Sr(n,e){var r={};s(n,function(i,o){var a=r[i.v]={indegree:0,in:[],out:[],vs:[i.v],i:o};g(i.barycenter)||(a.barycenter=i.barycenter,a.weight=i.weight)}),s(e.edges(),function(i){var o=r[i.v],a=r[i.w];!g(o)&&!g(a)&&(a.indegree++,o.out.push(r[i.w]))});var t=M(r,function(i){return!i.indegree});return Fr(t)}function Fr(n){var e=[];function r(o){return function(a){a.merged||(g(a.barycenter)||g(o.barycenter)||a.barycenter>=o.barycenter)&&Ar(o,a)}}function t(o){return function(a){a.in.push(o),--a.indegree===0&&n.push(a)}}for(;n.length;){var i=n.pop();e.push(i),s(i.in.reverse(),r(i)),s(i.out,t(i))}return m(M(e,function(o){return!o.merged}),function(o){return V(o,["vs","i","barycenter","weight"])})}function Ar(n,e){var r=0,t=0;n.weight&&(r+=n.barycenter*n.weight,t+=n.weight),e.weight&&(r+=e.barycenter*e.weight,t+=e.weight),n.vs=e.vs.concat(n.vs),n.barycenter=r/t,n.weight=t,n.i=Math.min(e.i,n.i),e.merged=!0}function Br(n,e){var r=er(n,function(c){return w(c,"barycenter")}),t=r.lhs,i=O(r.rhs,function(c){return-c.i}),o=[],a=0,u=0,d=0;t.sort(Gr(!!e)),d=wn(o,i,d),s(t,function(c){d+=c.vs.length,o.push(c.vs),a+=c.barycenter*c.weight,u+=c.weight,d=wn(o,i,d)});var f={vs:_(o)};return u&&(f.barycenter=a/u,f.weight=u),f}function wn(n,e,r){for(var t;e.length&&(t=G(e)).i<=r;)e.pop(),n.push(t.vs),r++;return r}function Gr(n){return function(e,r){return e.barycenter<r.barycenter?-1:e.barycenter>r.barycenter?1:n?r.i-e.i:e.i-r.i}}function qn(n,e,r,t){var i=n.children(e),o=n.node(e),a=o?o.borderLeft:void 0,u=o?o.borderRight:void 0,d={};a&&(i=M(i,function(p){return p!==a&&p!==u}));var f=Pr(n,i);s(f,function(p){if(n.children(p.v).length){var b=qn(n,p.v,r,t);d[p.v]=b,w(b,"barycenter")&&Yr(p,b)}});var c=Sr(f,r);Vr(c,d);var h=Br(c,t);if(a&&(h.vs=_([a,h.vs,u]),n.predecessors(a).length)){var l=n.node(n.predecessors(a)[0]),v=n.node(n.predecessors(u)[0]);w(h,"barycenter")||(h.barycenter=0,h.weight=0),h.barycenter=(h.barycenter*h.weight+l.order+v.order)/(h.weight+2),h.weight+=2}return h}function Vr(n,e){s(n,function(r){r.vs=_(r.vs.map(function(t){return e[t]?e[t].vs:t}))})}function Yr(n,e){g(n.barycenter)?(n.barycenter=e.barycenter,n.weight=e.weight):(n.barycenter=(n.barycenter*n.weight+e.barycenter*e.weight)/(n.weight+e.weight),n.weight+=e.weight)}function Dr(n){var e=On(n),r=mn(n,N(1,e+1),"inEdges"),t=mn(n,N(e-1,-1,-1),"outEdges"),i=Or(n);bn(n,i);for(var o=Number.POSITIVE_INFINITY,a,u=0,d=0;d<4;++u,++d){$r(u%2?r:t,u%4>=2),i=$(n);var f=Tr(n,i);f<o&&(d=0,a=xe(i),o=f)}bn(n,a)}function mn(n,e,r){return m(e,function(t){return Ir(n,t,r)})}function $r(n,e){var r=new x;s(n,function(t){var i=t.graph().root,o=qn(t,i,r,e);s(o.vs,function(a,u){t.node(a).order=u}),Cr(t,r,o.vs)})}function bn(n,e){s(e,function(r){s(r,function(t,i){n.node(t).order=i})})}function qr(n){var e=zr(n);s(n.graph().dummyChains,function(r){for(var t=n.node(r),i=t.edgeObj,o=Wr(n,e,i.v,i.w),a=o.path,u=o.lca,d=0,f=a[d],c=!0;r!==i.w;){if(t=n.node(r),c){for(;(f=a[d])!==u&&n.node(f).maxRank<t.rank;)d++;f===u&&(c=!1)}if(!c){for(;d<a.length-1&&n.node(f=a[d+1]).minRank<=t.rank;)d++;f=a[d]}n.setParent(r,f),r=n.successors(r)[0]}})}function Wr(n,e,r,t){var i=[],o=[],a=Math.min(e[r].low,e[t].low),u=Math.max(e[r].lim,e[t].lim),d,f;d=r;do d=n.parent(d),i.push(d);while(d&&(e[d].low>a||u>e[d].lim));for(f=d,d=t;(d=n.parent(d))!==f;)o.push(d);return{path:i.concat(o.reverse()),lca:f}}function zr(n){var e={},r=0;function t(i){var o=r;s(n.children(i),t),e[i]={low:o,lim:r++}}return s(n.children(),t),e}function Xr(n,e){var r={};function t(i,o){var a=0,u=0,d=i.length,f=G(o);return s(o,function(c,h){var l=Hr(n,c),v=l?n.node(l).order:d;(l||c===f)&&(s(o.slice(u,h+1),function(p){s(n.predecessors(p),function(b){var I=n.node(b),on=I.order;(on<a||v<on)&&!(I.dummy&&n.node(p).dummy)&&Wn(r,b,p)})}),u=h+1,a=v)}),o}return Y(e,t),r}function Ur(n,e){var r={};function t(o,a,u,d,f){var c;s(N(a,u),function(h){c=o[h],n.node(c).dummy&&s(n.predecessors(c),function(l){var v=n.node(l);v.dummy&&(v.order<d||v.order>f)&&Wn(r,l,c)})})}function i(o,a){var u=-1,d,f=0;return s(a,function(c,h){if(n.node(c).dummy==="border"){var l=n.predecessors(c);l.length&&(d=n.node(l[0]).order,t(a,f,h,u,d),f=h,u=d)}t(a,f,a.length,d,o.length)}),a}return Y(e,i),r}function Hr(n,e){if(n.node(e).dummy)return Q(n.predecessors(e),function(r){return n.node(r).dummy})}function Wn(n,e,r){if(e>r){var t=e;e=r,r=t}var i=n[e];i||(n[e]=i={}),i[r]=!0}function jr(n,e,r){if(e>r){var t=e;e=r,r=t}return w(n[e],r)}function Kr(n,e,r,t){var i={},o={},a={};return s(e,function(u){s(u,function(d,f){i[d]=d,o[d]=d,a[d]=f})}),s(e,function(u){var d=-1;s(u,function(f){var c=t(f);if(c.length){c=O(c,function(b){return a[b]});for(var h=(c.length-1)/2,l=Math.floor(h),v=Math.ceil(h);l<=v;++l){var p=c[l];o[f]===f&&d<a[p]&&!jr(r,f,p)&&(o[p]=f,o[f]=i[f]=i[p],d=a[p])}}})}),{root:i,align:o}}function Jr(n,e,r,t,i){var o={},a=Qr(n,e,r,i),u=i?"borderLeft":"borderRight";function d(h,l){for(var v=a.nodes(),p=v.pop(),b={};p;)b[p]?h(p):(b[p]=!0,v.push(p),v=v.concat(l(p))),p=v.pop()}function f(h){o[h]=a.inEdges(h).reduce(function(l,v){return Math.max(l,o[v.v]+a.edge(v))},0)}function c(h){var l=a.outEdges(h).reduce(function(p,b){return Math.min(p,o[b.w]-a.edge(b))},Number.POSITIVE_INFINITY),v=n.node(h);l!==Number.POSITIVE_INFINITY&&v.borderType!==u&&(o[h]=Math.max(o[h],l))}return d(f,a.predecessors.bind(a)),d(c,a.successors.bind(a)),s(t,function(h){o[h]=o[r[h]]}),o}function Qr(n,e,r,t){var i=new x,o=n.graph(),a=tt(o.nodesep,o.edgesep,t);return s(e,function(u){var d;s(u,function(f){var c=r[f];if(i.setNode(c),d){var h=r[d],l=i.edge(h,c);i.setEdge(h,c,Math.max(a(n,f,d),l||0))}d=f})}),i}function Zr(n,e){return nn(y(e),function(r){var t=Number.NEGATIVE_INFINITY,i=Number.POSITIVE_INFINITY;return _e(r,function(o,a){var u=it(n,a)/2;t=Math.max(o+u,t),i=Math.min(o-u,i)}),t-i})}function nt(n,e){var r=y(e),t=R(r),i=E(r);s(["u","d"],function(o){s(["l","r"],function(a){var u=o+a,d=n[u],f;if(d!==e){var c=y(d);f=a==="l"?t-R(c):i-E(c),f&&(n[u]=D(d,function(h){return h+f}))}})})}function et(n,e){return D(n.ul,function(r,t){if(e)return n[e.toLowerCase()][t];var i=O(m(n,t));return(i[1]+i[2])/2})}function rt(n){var e=$(n),r=H(Xr(n,e),Ur(n,e)),t={},i;s(["u","d"],function(a){i=a==="u"?e:y(e).reverse(),s(["l","r"],function(u){u==="r"&&(i=m(i,function(h){return y(h).reverse()}));var d=(a==="u"?n.predecessors:n.successors).bind(n),f=Kr(n,i,r,d),c=Jr(n,i,f.root,f.align,u==="r");u==="r"&&(c=D(c,function(h){return-h})),t[a+u]=c})});var o=Zr(n,t);return nt(t,o),et(t,n.graph().align)}function tt(n,e,r){return function(t,i,o){var a=t.node(i),u=t.node(o),d=0,f;if(d+=a.width/2,w(a,"labelpos"))switch(a.labelpos.toLowerCase()){case"l":f=-a.width/2;break;case"r":f=a.width/2;break}if(f&&(d+=r?f:-f),f=0,d+=(a.dummy?e:n)/2,d+=(u.dummy?e:n)/2,d+=u.width/2,w(u,"labelpos"))switch(u.labelpos.toLowerCase()){case"l":f=u.width/2;break;case"r":f=-u.width/2;break}return f&&(d+=r?f:-f),f=0,d}}function it(n,e){return n.node(e).width}function at(n){n=Mn(n),ot(n),Ce(rt(n),function(e,r){n.node(r).x=e})}function ot(n){var e=$(n),r=n.graph().ranksep,t=0;s(e,function(i){var o=E(m(i,function(a){return n.node(a).height}));s(i,function(a){n.node(a).y=t+o/2}),t+=o+r})}function Ot(n,e){var r=rr;r("layout",function(){var t=r("  buildLayoutGraph",function(){return mt(n)});r("  runLayout",function(){ut(t,r)}),r("  updateInputGraph",function(){dt(n,t)})})}function ut(n,e){e("    makeSpaceForEdgeLabels",function(){bt(n)}),e("    removeSelfEdges",function(){Ct(n)}),e("    acyclic",function(){je(n)}),e("    nestingGraph.run",function(){yr(n)}),e("    rank",function(){xr(Mn(n))}),e("    injectEdgeLabelProxies",function(){gt(n)}),e("    removeEmptyRanks",function(){nr(n)}),e("    nestingGraph.cleanup",function(){_r(n)}),e("    normalizeRanks",function(){Ze(n)}),e("    assignRankMinMax",function(){xt(n)}),e("    removeEdgeLabelProxies",function(){Et(n)}),e("    normalize.run",function(){dr(n)}),e("    parentDummyChains",function(){qr(n)}),e("    addBorderSegments",function(){tr(n)}),e("    order",function(){Dr(n)}),e("    insertSelfEdges",function(){It(n)}),e("    adjustCoordinateSystem",function(){ir(n)}),e("    position",function(){at(n)}),e("    positionSelfEdges",function(){Rt(n)}),e("    removeBorderNodes",function(){_t(n)}),e("    normalize.undo",function(){sr(n)}),e("    fixupEdgeLabelCoords",function(){Nt(n)}),e("    undoCoordinateSystem",function(){ar(n)}),e("    translateGraph",function(){kt(n)}),e("    assignNodeIntersects",function(){yt(n)}),e("    reversePoints",function(){Lt(n)}),e("    acyclic.undo",function(){Je(n)})}function dt(n,e){s(n.nodes(),function(r){var t=n.node(r),i=e.node(r);t&&(t.x=i.x,t.y=i.y,e.children(r).length&&(t.width=i.width,t.height=i.height))}),s(n.edges(),function(r){var t=n.edge(r),i=e.edge(r);t.points=i.points,w(i,"x")&&(t.x=i.x,t.y=i.y)}),n.graph().width=e.graph().width,n.graph().height=e.graph().height}var ft=["nodesep","edgesep","ranksep","marginx","marginy"],st={ranksep:50,edgesep:20,nodesep:50,rankdir:"tb"},ct=["acyclicer","ranker","rankdir","align"],ht=["width","height"],lt={width:0,height:0},vt=["minlen","weight","width","height","labeloffset"],pt={minlen:1,weight:1,width:0,height:0,labeloffset:10,labelpos:"r"},wt=["labelpos"];function mt(n){var e=new x({multigraph:!0,compound:!0}),r=U(n.graph());return e.setGraph(H({},st,X(r,ft),V(r,ct))),s(n.nodes(),function(t){var i=U(n.node(t));e.setNode(t,ke(X(i,ht),lt)),e.setParent(t,n.parent(t))}),s(n.edges(),function(t){var i=U(n.edge(t));e.setEdge(t,H({},pt,X(i,vt),V(i,wt)))}),e}function bt(n){var e=n.graph();e.ranksep/=2,s(n.edges(),function(r){var t=n.edge(r);t.minlen*=2,t.labelpos.toLowerCase()!=="c"&&(e.rankdir==="TB"||e.rankdir==="BT"?t.width+=t.labeloffset:t.height+=t.labeloffset)})}function gt(n){s(n.edges(),function(e){var r=n.edge(e);if(r.width&&r.height){var t=n.node(e.v),i=n.node(e.w),o={rank:(i.rank-t.rank)/2+t.rank,e};C(n,"edge-proxy",o,"_ep")}})}function xt(n){var e=0;s(n.nodes(),function(r){var t=n.node(r);t.borderTop&&(t.minRank=n.node(t.borderTop).rank,t.maxRank=n.node(t.borderBottom).rank,e=E(e,t.maxRank))}),n.graph().maxRank=e}function Et(n){s(n.nodes(),function(e){var r=n.node(e);r.dummy==="edge-proxy"&&(n.edge(r.e).labelRank=r.rank,n.removeNode(e))})}function kt(n){var e=Number.POSITIVE_INFINITY,r=0,t=Number.POSITIVE_INFINITY,i=0,o=n.graph(),a=o.marginx||0,u=o.marginy||0;function d(f){var c=f.x,h=f.y,l=f.width,v=f.height;e=Math.min(e,c-l/2),r=Math.max(r,c+l/2),t=Math.min(t,h-v/2),i=Math.max(i,h+v/2)}s(n.nodes(),function(f){d(n.node(f))}),s(n.edges(),function(f){var c=n.edge(f);w(c,"x")&&d(c)}),e-=a,t-=u,s(n.nodes(),function(f){var c=n.node(f);c.x-=e,c.y-=t}),s(n.edges(),function(f){var c=n.edge(f);s(c.points,function(h){h.x-=e,h.y-=t}),w(c,"x")&&(c.x-=e),w(c,"y")&&(c.y-=t)}),o.width=r-e+a,o.height=i-t+u}function yt(n){s(n.edges(),function(e){var r=n.edge(e),t=n.node(e.v),i=n.node(e.w),o,a;r.points?(o=r.points[0],a=r.points[r.points.length-1]):(r.points=[],o=i,a=t),r.points.unshift(sn(t,o)),r.points.push(sn(i,a))})}function Nt(n){s(n.edges(),function(e){var r=n.edge(e);if(w(r,"x"))switch((r.labelpos==="l"||r.labelpos==="r")&&(r.width-=r.labeloffset),r.labelpos){case"l":r.x-=r.width/2+r.labeloffset;break;case"r":r.x+=r.width/2+r.labeloffset;break}})}function Lt(n){s(n.edges(),function(e){var r=n.edge(e);r.reversed&&r.points.reverse()})}function _t(n){s(n.nodes(),function(e){if(n.children(e).length){var r=n.node(e),t=n.node(r.borderTop),i=n.node(r.borderBottom),o=n.node(G(r.borderLeft)),a=n.node(G(r.borderRight));r.width=Math.abs(a.x-o.x),r.height=Math.abs(i.y-t.y),r.x=o.x+r.width/2,r.y=t.y+r.height/2}}),s(n.nodes(),function(e){n.node(e).dummy==="border"&&n.removeNode(e)})}function Ct(n){s(n.edges(),function(e){if(e.v===e.w){var r=n.node(e.v);r.selfEdges||(r.selfEdges=[]),r.selfEdges.push({e,label:n.edge(e)}),n.removeEdge(e)}})}function It(n){var e=$(n);s(e,function(r){var t=0;s(r,function(i,o){var a=n.node(i);a.order=o+t,s(a.selfEdges,function(u){C(n,"selfedge",{width:u.label.width,height:u.label.height,rank:a.rank,order:o+ ++t,e:u.e,label:u.label},"_se")}),delete a.selfEdges})})}function Rt(n){s(n.nodes(),function(e){var r=n.node(e);if(r.dummy==="selfedge"){var t=n.node(r.e.v),i=t.x+t.width/2,o=t.y,a=r.x-i,u=t.height/2;n.setEdge(r.e,r.label),n.removeNode(e),r.label.points=[{x:i+2*a/3,y:o-u},{x:i+5*a/6,y:o-u},{x:i+a,y:o},{x:i+5*a/6,y:o+u},{x:i+2*a/3,y:o+u}],r.label.x=r.x,r.label.y=r.y}})}function X(n,e){return D(V(n,e),Number)}function U(n){var e={};return s(n,function(r,t){e[t.toLowerCase()]=r}),e}export{ke as d,Ot as l,m,V as p,N as r,en as u};
+import{i as F,b as gn,a as zn,c as L,k as Xn,d as Un,e as Hn,g as P,j as xn,l as En,m as kn,t as jn,n as yn,o as Kn,p as Jn,f as s,G as x,h as w,q as g,r as M,v as y,s as Y}from"./graph-B1296pfd.js";import{R as A,ag as Qn,ah as Zn,a6 as Nn,ai as B,K as Ln,_ as ne,E as _n,D as K,a4 as ee,aj as re,a3 as J,a2 as te,Y as Cn,Q as ie,a8 as ae,ak as H}from"./mermaid.core-DNo_7Q2B.js";var oe=/\s/;function ue(n){for(var e=n.length;e--&&oe.test(n.charAt(e)););return e}var de=/^\s+/;function fe(n){return n&&n.slice(0,ue(n)+1).replace(de,"")}var un=NaN,se=/^[-+]0x[0-9a-f]+$/i,ce=/^0b[01]+$/i,he=/^0o[0-7]+$/i,le=parseInt;function ve(n){if(typeof n=="number")return n;if(F(n))return un;if(A(n)){var e=typeof n.valueOf=="function"?n.valueOf():n;n=A(e)?e+"":e}if(typeof n!="string")return n===0?n:+n;n=fe(n);var r=ce.test(n);return r||he.test(n)?le(n.slice(2),r?2:8):se.test(n)?un:+n}var dn=1/0,pe=17976931348623157e292;function S(n){if(!n)return n===0?n:0;if(n=ve(n),n===dn||n===-dn){var e=n<0?-1:1;return e*pe}return n===n?n:0}function we(n){var e=S(n),r=e%1;return e===e?r?e-r:e:0}function _(n){var e=n==null?0:n.length;return e?gn(n):[]}function me(n){return Qn(Zn(n,void 0,_),n+"")}var be=1,ge=4;function xe(n){return zn(n,be|ge)}var In=Object.prototype,Ee=In.hasOwnProperty,ke=Nn(function(n,e){n=Object(n);var r=-1,t=e.length,i=t>2?e[2]:void 0;for(i&&B(e[0],e[1],i)&&(t=1);++r<t;)for(var o=e[r],a=Ln(o),u=-1,d=a.length;++u<d;){var f=a[u],c=n[f];(c===void 0||ne(c,In[f])&&!Ee.call(n,f))&&(n[f]=o[f])}return n});function G(n){var e=n==null?0:n.length;return e?n[e-1]:void 0}function ye(n){return function(e,r,t){var i=Object(e);if(!_n(e)){var o=L(r);e=Xn(e),r=function(u){return o(i[u],u,i)}}var a=n(e,r,t);return a>-1?i[o?e[a]:a]:void 0}}var Ne=Math.max;function Le(n,e,r){var t=n==null?0:n.length;if(!t)return-1;var i=r==null?0:we(r);return i<0&&(i=Ne(t+i,0)),Un(n,L(e),i)}var Q=ye(Le);function Rn(n,e){var r=-1,t=_n(n)?Array(n.length):[];return Hn(n,function(i,o,a){t[++r]=e(i,o,a)}),t}function m(n,e){var r=K(n)?P:Rn;return r(n,L(e))}function _e(n,e){return n==null?n:ee(n,xn(e),Ln)}function Ce(n,e){return n&&En(n,xn(e))}function Ie(n,e){return n>e}function Tn(n,e){return n<e}function D(n,e){var r={};return e=L(e),En(n,function(t,i,o){re(r,i,e(t,i,o))}),r}function Z(n,e,r){for(var t=-1,i=n.length;++t<i;){var o=n[t],a=e(o);if(a!=null&&(u===void 0?a===a&&!F(a):r(a,u)))var u=a,d=o}return d}function E(n){return n&&n.length?Z(n,J,Ie):void 0}function R(n){return n&&n.length?Z(n,J,Tn):void 0}function nn(n,e){return n&&n.length?Z(n,L(e),Tn):void 0}function Re(n,e,r,t){if(!A(n))return n;e=kn(e,n);for(var i=-1,o=e.length,a=o-1,u=n;u!=null&&++i<o;){var d=jn(e[i]),f=r;if(d==="__proto__"||d==="constructor"||d==="prototype")return n;if(i!=a){var c=u[d];f=void 0,f===void 0&&(f=A(c)?c:te(e[i+1])?[]:{})}Cn(u,d,f),u=u[d]}return n}function Te(n,e,r){for(var t=-1,i=e.length,o={};++t<i;){var a=e[t],u=yn(n,a);r(u,a)&&Re(o,kn(a,n),u)}return o}function Me(n,e){var r=n.length;for(n.sort(e);r--;)n[r]=n[r].value;return n}function Oe(n,e){if(n!==e){var r=n!==void 0,t=n===null,i=n===n,o=F(n),a=e!==void 0,u=e===null,d=e===e,f=F(e);if(!u&&!f&&!o&&n>e||o&&a&&d&&!u&&!f||t&&a&&d||!r&&d||!i)return 1;if(!t&&!o&&!f&&n<e||f&&r&&i&&!t&&!o||u&&r&&i||!a&&i||!d)return-1}return 0}function Pe(n,e,r){for(var t=-1,i=n.criteria,o=e.criteria,a=i.length,u=r.length;++t<a;){var d=Oe(i[t],o[t]);if(d){if(t>=u)return d;var f=r[t];return d*(f=="desc"?-1:1)}}return n.index-e.index}function Se(n,e,r){e.length?e=P(e,function(o){return K(o)?function(a){return yn(a,o.length===1?o[0]:o)}:o}):e=[J];var t=-1;e=P(e,ie(L));var i=Rn(n,function(o,a,u){var d=P(e,function(f){return f(o)});return{criteria:d,index:++t,value:o}});return Me(i,function(o,a){return Pe(o,a,r)})}function Fe(n,e){return Te(n,e,function(r,t){return Kn(n,t)})}var V=me(function(n,e){return n==null?{}:Fe(n,e)}),Ae=Math.ceil,Be=Math.max;function Ge(n,e,r,t){for(var i=-1,o=Be(Ae((e-n)/(r||1)),0),a=Array(o);o--;)a[++i]=n,n+=r;return a}function Ve(n){return function(e,r,t){return t&&typeof t!="number"&&B(e,r,t)&&(r=t=void 0),e=S(e),r===void 0?(r=e,e=0):r=S(r),t=t===void 0?e<r?1:-1:S(t),Ge(e,r,t)}}var N=Ve(),O=Nn(function(n,e){if(n==null)return[];var r=e.length;return r>1&&B(n,e[0],e[1])?e=[]:r>2&&B(e[0],e[1],e[2])&&(e=[e[0]]),Se(n,gn(e),[])}),Ye=0;function en(n){var e=++Ye;return Jn(n)+e}function De(n,e,r){for(var t=-1,i=n.length,o=e.length,a={};++t<i;){var u=t<o?e[t]:void 0;r(a,n[t],u)}return a}function $e(n,e){return De(n||[],e||[],Cn)}class qe{constructor(){var e={};e._next=e._prev=e,this._sentinel=e}dequeue(){var e=this._sentinel,r=e._prev;if(r!==e)return fn(r),r}enqueue(e){var r=this._sentinel;e._prev&&e._next&&fn(e),e._next=r._next,r._next._prev=e,r._next=e,e._prev=r}toString(){for(var e=[],r=this._sentinel,t=r._prev;t!==r;)e.push(JSON.stringify(t,We)),t=t._prev;return"["+e.join(", ")+"]"}}function fn(n){n._prev._next=n._next,n._next._prev=n._prev,delete n._next,delete n._prev}function We(n,e){if(n!=="_next"&&n!=="_prev")return e}var ze=ae(1);function Xe(n,e){if(n.nodeCount()<=1)return[];var r=He(n,e||ze),t=Ue(r.graph,r.buckets,r.zeroIdx);return _(m(t,function(i){return n.outEdges(i.v,i.w)}))}function Ue(n,e,r){for(var t=[],i=e[e.length-1],o=e[0],a;n.nodeCount();){for(;a=o.dequeue();)q(n,e,r,a);for(;a=i.dequeue();)q(n,e,r,a);if(n.nodeCount()){for(var u=e.length-2;u>0;--u)if(a=e[u].dequeue(),a){t=t.concat(q(n,e,r,a,!0));break}}}return t}function q(n,e,r,t,i){var o=i?[]:void 0;return s(n.inEdges(t.v),function(a){var u=n.edge(a),d=n.node(a.v);i&&o.push({v:a.v,w:a.w}),d.out-=u,j(e,r,d)}),s(n.outEdges(t.v),function(a){var u=n.edge(a),d=a.w,f=n.node(d);f.in-=u,j(e,r,f)}),n.removeNode(t.v),o}function He(n,e){var r=new x,t=0,i=0;s(n.nodes(),function(u){r.setNode(u,{v:u,in:0,out:0})}),s(n.edges(),function(u){var d=r.edge(u.v,u.w)||0,f=e(u),c=d+f;r.setEdge(u.v,u.w,c),i=Math.max(i,r.node(u.v).out+=f),t=Math.max(t,r.node(u.w).in+=f)});var o=N(i+t+3).map(function(){return new qe}),a=t+1;return s(r.nodes(),function(u){j(o,a,r.node(u))}),{graph:r,buckets:o,zeroIdx:a}}function j(n,e,r){r.out?r.in?n[r.out-r.in+e].enqueue(r):n[n.length-1].enqueue(r):n[0].enqueue(r)}function je(n){var e=n.graph().acyclicer==="greedy"?Xe(n,r(n)):Ke(n);s(e,function(t){var i=n.edge(t);n.removeEdge(t),i.forwardName=t.name,i.reversed=!0,n.setEdge(t.w,t.v,i,en("rev"))});function r(t){return function(i){return t.edge(i).weight}}}function Ke(n){var e=[],r={},t={};function i(o){w(t,o)||(t[o]=!0,r[o]=!0,s(n.outEdges(o),function(a){w(r,a.w)?e.push(a):i(a.w)}),delete r[o])}return s(n.nodes(),i),e}function Je(n){s(n.edges(),function(e){var r=n.edge(e);if(r.reversed){n.removeEdge(e);var t=r.forwardName;delete r.reversed,delete r.forwardName,n.setEdge(e.w,e.v,r,t)}})}function C(n,e,r,t){var i;do i=en(t);while(n.hasNode(i));return r.dummy=e,n.setNode(i,r),i}function Qe(n){var e=new x().setGraph(n.graph());return s(n.nodes(),function(r){e.setNode(r,n.node(r))}),s(n.edges(),function(r){var t=e.edge(r.v,r.w)||{weight:0,minlen:1},i=n.edge(r);e.setEdge(r.v,r.w,{weight:t.weight+i.weight,minlen:Math.max(t.minlen,i.minlen)})}),e}function Mn(n){var e=new x({multigraph:n.isMultigraph()}).setGraph(n.graph());return s(n.nodes(),function(r){n.children(r).length||e.setNode(r,n.node(r))}),s(n.edges(),function(r){e.setEdge(r,n.edge(r))}),e}function sn(n,e){var r=n.x,t=n.y,i=e.x-r,o=e.y-t,a=n.width/2,u=n.height/2;if(!i&&!o)throw new Error("Not possible to find intersection inside of the rectangle");var d,f;return Math.abs(o)*a>Math.abs(i)*u?(o<0&&(u=-u),d=u*i/o,f=u):(i<0&&(a=-a),d=a,f=a*o/i),{x:r+d,y:t+f}}function $(n){var e=m(N(On(n)+1),function(){return[]});return s(n.nodes(),function(r){var t=n.node(r),i=t.rank;g(i)||(e[i][t.order]=r)}),e}function Ze(n){var e=R(m(n.nodes(),function(r){return n.node(r).rank}));s(n.nodes(),function(r){var t=n.node(r);w(t,"rank")&&(t.rank-=e)})}function nr(n){var e=R(m(n.nodes(),function(o){return n.node(o).rank})),r=[];s(n.nodes(),function(o){var a=n.node(o).rank-e;r[a]||(r[a]=[]),r[a].push(o)});var t=0,i=n.graph().nodeRankFactor;s(r,function(o,a){g(o)&&a%i!==0?--t:t&&s(o,function(u){n.node(u).rank+=t})})}function cn(n,e,r,t){var i={width:0,height:0};return arguments.length>=4&&(i.rank=r,i.order=t),C(n,"border",i,e)}function On(n){return E(m(n.nodes(),function(e){var r=n.node(e).rank;if(!g(r))return r}))}function er(n,e){var r={lhs:[],rhs:[]};return s(n,function(t){e(t)?r.lhs.push(t):r.rhs.push(t)}),r}function rr(n,e){return e()}function tr(n){function e(r){var t=n.children(r),i=n.node(r);if(t.length&&s(t,e),w(i,"minRank")){i.borderLeft=[],i.borderRight=[];for(var o=i.minRank,a=i.maxRank+1;o<a;++o)hn(n,"borderLeft","_bl",r,i,o),hn(n,"borderRight","_br",r,i,o)}}s(n.children(),e)}function hn(n,e,r,t,i,o){var a={width:0,height:0,rank:o,borderType:e},u=i[e][o-1],d=C(n,"border",a,r);i[e][o]=d,n.setParent(d,t),u&&n.setEdge(u,d,{weight:1})}function ir(n){var e=n.graph().rankdir.toLowerCase();(e==="lr"||e==="rl")&&Pn(n)}function ar(n){var e=n.graph().rankdir.toLowerCase();(e==="bt"||e==="rl")&&or(n),(e==="lr"||e==="rl")&&(ur(n),Pn(n))}function Pn(n){s(n.nodes(),function(e){ln(n.node(e))}),s(n.edges(),function(e){ln(n.edge(e))})}function ln(n){var e=n.width;n.width=n.height,n.height=e}function or(n){s(n.nodes(),function(e){W(n.node(e))}),s(n.edges(),function(e){var r=n.edge(e);s(r.points,W),w(r,"y")&&W(r)})}function W(n){n.y=-n.y}function ur(n){s(n.nodes(),function(e){z(n.node(e))}),s(n.edges(),function(e){var r=n.edge(e);s(r.points,z),w(r,"x")&&z(r)})}function z(n){var e=n.x;n.x=n.y,n.y=e}function dr(n){n.graph().dummyChains=[],s(n.edges(),function(e){fr(n,e)})}function fr(n,e){var r=e.v,t=n.node(r).rank,i=e.w,o=n.node(i).rank,a=e.name,u=n.edge(e),d=u.labelRank;if(o!==t+1){n.removeEdge(e);var f,c,h;for(h=0,++t;t<o;++h,++t)u.points=[],c={width:0,height:0,edgeLabel:u,edgeObj:e,rank:t},f=C(n,"edge",c,"_d"),t===d&&(c.width=u.width,c.height=u.height,c.dummy="edge-label",c.labelpos=u.labelpos),n.setEdge(r,f,{weight:u.weight},a),h===0&&n.graph().dummyChains.push(f),r=f;n.setEdge(r,i,{weight:u.weight},a)}}function sr(n){s(n.graph().dummyChains,function(e){var r=n.node(e),t=r.edgeLabel,i;for(n.setEdge(r.edgeObj,t);r.dummy;)i=n.successors(e)[0],n.removeNode(e),t.points.push({x:r.x,y:r.y}),r.dummy==="edge-label"&&(t.x=r.x,t.y=r.y,t.width=r.width,t.height=r.height),e=i,r=n.node(e)})}function rn(n){var e={};function r(t){var i=n.node(t);if(w(e,t))return i.rank;e[t]=!0;var o=R(m(n.outEdges(t),function(a){return r(a.w)-n.edge(a).minlen}));return(o===Number.POSITIVE_INFINITY||o===void 0||o===null)&&(o=0),i.rank=o}s(n.sources(),r)}function T(n,e){return n.node(e.w).rank-n.node(e.v).rank-n.edge(e).minlen}function Sn(n){var e=new x({directed:!1}),r=n.nodes()[0],t=n.nodeCount();e.setNode(r,{});for(var i,o;cr(e,n)<t;)i=hr(e,n),o=e.hasNode(i.v)?T(n,i):-T(n,i),lr(e,n,o);return e}function cr(n,e){function r(t){s(e.nodeEdges(t),function(i){var o=i.v,a=t===o?i.w:o;!n.hasNode(a)&&!T(e,i)&&(n.setNode(a,{}),n.setEdge(t,a,{}),r(a))})}return s(n.nodes(),r),n.nodeCount()}function hr(n,e){return nn(e.edges(),function(r){if(n.hasNode(r.v)!==n.hasNode(r.w))return T(e,r)})}function lr(n,e,r){s(n.nodes(),function(t){e.node(t).rank+=r})}function vr(){}vr.prototype=new Error;function Fn(n,e,r){K(e)||(e=[e]);var t=(n.isDirected()?n.successors:n.neighbors).bind(n),i=[],o={};return s(e,function(a){if(!n.hasNode(a))throw new Error("Graph does not have node: "+a);An(n,a,r==="post",o,t,i)}),i}function An(n,e,r,t,i,o){w(t,e)||(t[e]=!0,r||o.push(e),s(i(e),function(a){An(n,a,r,t,i,o)}),r&&o.push(e))}function pr(n,e){return Fn(n,e,"post")}function wr(n,e){return Fn(n,e,"pre")}k.initLowLimValues=an;k.initCutValues=tn;k.calcCutValue=Bn;k.leaveEdge=Vn;k.enterEdge=Yn;k.exchangeEdges=Dn;function k(n){n=Qe(n),rn(n);var e=Sn(n);an(e),tn(e,n);for(var r,t;r=Vn(e);)t=Yn(e,n,r),Dn(e,n,r,t)}function tn(n,e){var r=pr(n,n.nodes());r=r.slice(0,r.length-1),s(r,function(t){mr(n,e,t)})}function mr(n,e,r){var t=n.node(r),i=t.parent;n.edge(r,i).cutvalue=Bn(n,e,r)}function Bn(n,e,r){var t=n.node(r),i=t.parent,o=!0,a=e.edge(r,i),u=0;return a||(o=!1,a=e.edge(i,r)),u=a.weight,s(e.nodeEdges(r),function(d){var f=d.v===r,c=f?d.w:d.v;if(c!==i){var h=f===o,l=e.edge(d).weight;if(u+=h?l:-l,gr(n,r,c)){var v=n.edge(r,c).cutvalue;u+=h?-v:v}}}),u}function an(n,e){arguments.length<2&&(e=n.nodes()[0]),Gn(n,{},1,e)}function Gn(n,e,r,t,i){var o=r,a=n.node(t);return e[t]=!0,s(n.neighbors(t),function(u){w(e,u)||(r=Gn(n,e,r,u,t))}),a.low=o,a.lim=r++,i?a.parent=i:delete a.parent,r}function Vn(n){return Q(n.edges(),function(e){return n.edge(e).cutvalue<0})}function Yn(n,e,r){var t=r.v,i=r.w;e.hasEdge(t,i)||(t=r.w,i=r.v);var o=n.node(t),a=n.node(i),u=o,d=!1;o.lim>a.lim&&(u=a,d=!0);var f=M(e.edges(),function(c){return d===vn(n,n.node(c.v),u)&&d!==vn(n,n.node(c.w),u)});return nn(f,function(c){return T(e,c)})}function Dn(n,e,r,t){var i=r.v,o=r.w;n.removeEdge(i,o),n.setEdge(t.v,t.w,{}),an(n),tn(n,e),br(n,e)}function br(n,e){var r=Q(n.nodes(),function(i){return!e.node(i).parent}),t=wr(n,r);t=t.slice(1),s(t,function(i){var o=n.node(i).parent,a=e.edge(i,o),u=!1;a||(a=e.edge(o,i),u=!0),e.node(i).rank=e.node(o).rank+(u?a.minlen:-a.minlen)})}function gr(n,e,r){return n.hasEdge(e,r)}function vn(n,e,r){return r.low<=e.lim&&e.lim<=r.lim}function xr(n){switch(n.graph().ranker){case"network-simplex":pn(n);break;case"tight-tree":kr(n);break;case"longest-path":Er(n);break;default:pn(n)}}var Er=rn;function kr(n){rn(n),Sn(n)}function pn(n){k(n)}function yr(n){var e=C(n,"root",{},"_root"),r=Nr(n),t=E(y(r))-1,i=2*t+1;n.graph().nestingRoot=e,s(n.edges(),function(a){n.edge(a).minlen*=i});var o=Lr(n)+1;s(n.children(),function(a){$n(n,e,i,o,t,r,a)}),n.graph().nodeRankFactor=i}function $n(n,e,r,t,i,o,a){var u=n.children(a);if(!u.length){a!==e&&n.setEdge(e,a,{weight:0,minlen:r});return}var d=cn(n,"_bt"),f=cn(n,"_bb"),c=n.node(a);n.setParent(d,a),c.borderTop=d,n.setParent(f,a),c.borderBottom=f,s(u,function(h){$n(n,e,r,t,i,o,h);var l=n.node(h),v=l.borderTop?l.borderTop:h,p=l.borderBottom?l.borderBottom:h,b=l.borderTop?t:2*t,I=v!==p?1:i-o[a]+1;n.setEdge(d,v,{weight:b,minlen:I,nestingEdge:!0}),n.setEdge(p,f,{weight:b,minlen:I,nestingEdge:!0})}),n.parent(a)||n.setEdge(e,d,{weight:0,minlen:i+o[a]})}function Nr(n){var e={};function r(t,i){var o=n.children(t);o&&o.length&&s(o,function(a){r(a,i+1)}),e[t]=i}return s(n.children(),function(t){r(t,1)}),e}function Lr(n){return Y(n.edges(),function(e,r){return e+n.edge(r).weight},0)}function _r(n){var e=n.graph();n.removeNode(e.nestingRoot),delete e.nestingRoot,s(n.edges(),function(r){var t=n.edge(r);t.nestingEdge&&n.removeEdge(r)})}function Cr(n,e,r){var t={},i;s(r,function(o){for(var a=n.parent(o),u,d;a;){if(u=n.parent(a),u?(d=t[u],t[u]=a):(d=i,i=a),d&&d!==a){e.setEdge(d,a);return}a=u}})}function Ir(n,e,r){var t=Rr(n),i=new x({compound:!0}).setGraph({root:t}).setDefaultNodeLabel(function(o){return n.node(o)});return s(n.nodes(),function(o){var a=n.node(o),u=n.parent(o);(a.rank===e||a.minRank<=e&&e<=a.maxRank)&&(i.setNode(o),i.setParent(o,u||t),s(n[r](o),function(d){var f=d.v===o?d.w:d.v,c=i.edge(f,o),h=g(c)?0:c.weight;i.setEdge(f,o,{weight:n.edge(d).weight+h})}),w(a,"minRank")&&i.setNode(o,{borderLeft:a.borderLeft[e],borderRight:a.borderRight[e]}))}),i}function Rr(n){for(var e;n.hasNode(e=en("_root")););return e}function Tr(n,e){for(var r=0,t=1;t<e.length;++t)r+=Mr(n,e[t-1],e[t]);return r}function Mr(n,e,r){for(var t=$e(r,m(r,function(f,c){return c})),i=_(m(e,function(f){return O(m(n.outEdges(f),function(c){return{pos:t[c.w],weight:n.edge(c).weight}}),"pos")})),o=1;o<r.length;)o<<=1;var a=2*o-1;o-=1;var u=m(new Array(a),function(){return 0}),d=0;return s(i.forEach(function(f){var c=f.pos+o;u[c]+=f.weight;for(var h=0;c>0;)c%2&&(h+=u[c+1]),c=c-1>>1,u[c]+=f.weight;d+=f.weight*h})),d}function Or(n){var e={},r=M(n.nodes(),function(u){return!n.children(u).length}),t=E(m(r,function(u){return n.node(u).rank})),i=m(N(t+1),function(){return[]});function o(u){if(!w(e,u)){e[u]=!0;var d=n.node(u);i[d.rank].push(u),s(n.successors(u),o)}}var a=O(r,function(u){return n.node(u).rank});return s(a,o),i}function Pr(n,e){return m(e,function(r){var t=n.inEdges(r);if(t.length){var i=Y(t,function(o,a){var u=n.edge(a),d=n.node(a.v);return{sum:o.sum+u.weight*d.order,weight:o.weight+u.weight}},{sum:0,weight:0});return{v:r,barycenter:i.sum/i.weight,weight:i.weight}}else return{v:r}})}function Sr(n,e){var r={};s(n,function(i,o){var a=r[i.v]={indegree:0,in:[],out:[],vs:[i.v],i:o};g(i.barycenter)||(a.barycenter=i.barycenter,a.weight=i.weight)}),s(e.edges(),function(i){var o=r[i.v],a=r[i.w];!g(o)&&!g(a)&&(a.indegree++,o.out.push(r[i.w]))});var t=M(r,function(i){return!i.indegree});return Fr(t)}function Fr(n){var e=[];function r(o){return function(a){a.merged||(g(a.barycenter)||g(o.barycenter)||a.barycenter>=o.barycenter)&&Ar(o,a)}}function t(o){return function(a){a.in.push(o),--a.indegree===0&&n.push(a)}}for(;n.length;){var i=n.pop();e.push(i),s(i.in.reverse(),r(i)),s(i.out,t(i))}return m(M(e,function(o){return!o.merged}),function(o){return V(o,["vs","i","barycenter","weight"])})}function Ar(n,e){var r=0,t=0;n.weight&&(r+=n.barycenter*n.weight,t+=n.weight),e.weight&&(r+=e.barycenter*e.weight,t+=e.weight),n.vs=e.vs.concat(n.vs),n.barycenter=r/t,n.weight=t,n.i=Math.min(e.i,n.i),e.merged=!0}function Br(n,e){var r=er(n,function(c){return w(c,"barycenter")}),t=r.lhs,i=O(r.rhs,function(c){return-c.i}),o=[],a=0,u=0,d=0;t.sort(Gr(!!e)),d=wn(o,i,d),s(t,function(c){d+=c.vs.length,o.push(c.vs),a+=c.barycenter*c.weight,u+=c.weight,d=wn(o,i,d)});var f={vs:_(o)};return u&&(f.barycenter=a/u,f.weight=u),f}function wn(n,e,r){for(var t;e.length&&(t=G(e)).i<=r;)e.pop(),n.push(t.vs),r++;return r}function Gr(n){return function(e,r){return e.barycenter<r.barycenter?-1:e.barycenter>r.barycenter?1:n?r.i-e.i:e.i-r.i}}function qn(n,e,r,t){var i=n.children(e),o=n.node(e),a=o?o.borderLeft:void 0,u=o?o.borderRight:void 0,d={};a&&(i=M(i,function(p){return p!==a&&p!==u}));var f=Pr(n,i);s(f,function(p){if(n.children(p.v).length){var b=qn(n,p.v,r,t);d[p.v]=b,w(b,"barycenter")&&Yr(p,b)}});var c=Sr(f,r);Vr(c,d);var h=Br(c,t);if(a&&(h.vs=_([a,h.vs,u]),n.predecessors(a).length)){var l=n.node(n.predecessors(a)[0]),v=n.node(n.predecessors(u)[0]);w(h,"barycenter")||(h.barycenter=0,h.weight=0),h.barycenter=(h.barycenter*h.weight+l.order+v.order)/(h.weight+2),h.weight+=2}return h}function Vr(n,e){s(n,function(r){r.vs=_(r.vs.map(function(t){return e[t]?e[t].vs:t}))})}function Yr(n,e){g(n.barycenter)?(n.barycenter=e.barycenter,n.weight=e.weight):(n.barycenter=(n.barycenter*n.weight+e.barycenter*e.weight)/(n.weight+e.weight),n.weight+=e.weight)}function Dr(n){var e=On(n),r=mn(n,N(1,e+1),"inEdges"),t=mn(n,N(e-1,-1,-1),"outEdges"),i=Or(n);bn(n,i);for(var o=Number.POSITIVE_INFINITY,a,u=0,d=0;d<4;++u,++d){$r(u%2?r:t,u%4>=2),i=$(n);var f=Tr(n,i);f<o&&(d=0,a=xe(i),o=f)}bn(n,a)}function mn(n,e,r){return m(e,function(t){return Ir(n,t,r)})}function $r(n,e){var r=new x;s(n,function(t){var i=t.graph().root,o=qn(t,i,r,e);s(o.vs,function(a,u){t.node(a).order=u}),Cr(t,r,o.vs)})}function bn(n,e){s(e,function(r){s(r,function(t,i){n.node(t).order=i})})}function qr(n){var e=zr(n);s(n.graph().dummyChains,function(r){for(var t=n.node(r),i=t.edgeObj,o=Wr(n,e,i.v,i.w),a=o.path,u=o.lca,d=0,f=a[d],c=!0;r!==i.w;){if(t=n.node(r),c){for(;(f=a[d])!==u&&n.node(f).maxRank<t.rank;)d++;f===u&&(c=!1)}if(!c){for(;d<a.length-1&&n.node(f=a[d+1]).minRank<=t.rank;)d++;f=a[d]}n.setParent(r,f),r=n.successors(r)[0]}})}function Wr(n,e,r,t){var i=[],o=[],a=Math.min(e[r].low,e[t].low),u=Math.max(e[r].lim,e[t].lim),d,f;d=r;do d=n.parent(d),i.push(d);while(d&&(e[d].low>a||u>e[d].lim));for(f=d,d=t;(d=n.parent(d))!==f;)o.push(d);return{path:i.concat(o.reverse()),lca:f}}function zr(n){var e={},r=0;function t(i){var o=r;s(n.children(i),t),e[i]={low:o,lim:r++}}return s(n.children(),t),e}function Xr(n,e){var r={};function t(i,o){var a=0,u=0,d=i.length,f=G(o);return s(o,function(c,h){var l=Hr(n,c),v=l?n.node(l).order:d;(l||c===f)&&(s(o.slice(u,h+1),function(p){s(n.predecessors(p),function(b){var I=n.node(b),on=I.order;(on<a||v<on)&&!(I.dummy&&n.node(p).dummy)&&Wn(r,b,p)})}),u=h+1,a=v)}),o}return Y(e,t),r}function Ur(n,e){var r={};function t(o,a,u,d,f){var c;s(N(a,u),function(h){c=o[h],n.node(c).dummy&&s(n.predecessors(c),function(l){var v=n.node(l);v.dummy&&(v.order<d||v.order>f)&&Wn(r,l,c)})})}function i(o,a){var u=-1,d,f=0;return s(a,function(c,h){if(n.node(c).dummy==="border"){var l=n.predecessors(c);l.length&&(d=n.node(l[0]).order,t(a,f,h,u,d),f=h,u=d)}t(a,f,a.length,d,o.length)}),a}return Y(e,i),r}function Hr(n,e){if(n.node(e).dummy)return Q(n.predecessors(e),function(r){return n.node(r).dummy})}function Wn(n,e,r){if(e>r){var t=e;e=r,r=t}var i=n[e];i||(n[e]=i={}),i[r]=!0}function jr(n,e,r){if(e>r){var t=e;e=r,r=t}return w(n[e],r)}function Kr(n,e,r,t){var i={},o={},a={};return s(e,function(u){s(u,function(d,f){i[d]=d,o[d]=d,a[d]=f})}),s(e,function(u){var d=-1;s(u,function(f){var c=t(f);if(c.length){c=O(c,function(b){return a[b]});for(var h=(c.length-1)/2,l=Math.floor(h),v=Math.ceil(h);l<=v;++l){var p=c[l];o[f]===f&&d<a[p]&&!jr(r,f,p)&&(o[p]=f,o[f]=i[f]=i[p],d=a[p])}}})}),{root:i,align:o}}function Jr(n,e,r,t,i){var o={},a=Qr(n,e,r,i),u=i?"borderLeft":"borderRight";function d(h,l){for(var v=a.nodes(),p=v.pop(),b={};p;)b[p]?h(p):(b[p]=!0,v.push(p),v=v.concat(l(p))),p=v.pop()}function f(h){o[h]=a.inEdges(h).reduce(function(l,v){return Math.max(l,o[v.v]+a.edge(v))},0)}function c(h){var l=a.outEdges(h).reduce(function(p,b){return Math.min(p,o[b.w]-a.edge(b))},Number.POSITIVE_INFINITY),v=n.node(h);l!==Number.POSITIVE_INFINITY&&v.borderType!==u&&(o[h]=Math.max(o[h],l))}return d(f,a.predecessors.bind(a)),d(c,a.successors.bind(a)),s(t,function(h){o[h]=o[r[h]]}),o}function Qr(n,e,r,t){var i=new x,o=n.graph(),a=tt(o.nodesep,o.edgesep,t);return s(e,function(u){var d;s(u,function(f){var c=r[f];if(i.setNode(c),d){var h=r[d],l=i.edge(h,c);i.setEdge(h,c,Math.max(a(n,f,d),l||0))}d=f})}),i}function Zr(n,e){return nn(y(e),function(r){var t=Number.NEGATIVE_INFINITY,i=Number.POSITIVE_INFINITY;return _e(r,function(o,a){var u=it(n,a)/2;t=Math.max(o+u,t),i=Math.min(o-u,i)}),t-i})}function nt(n,e){var r=y(e),t=R(r),i=E(r);s(["u","d"],function(o){s(["l","r"],function(a){var u=o+a,d=n[u],f;if(d!==e){var c=y(d);f=a==="l"?t-R(c):i-E(c),f&&(n[u]=D(d,function(h){return h+f}))}})})}function et(n,e){return D(n.ul,function(r,t){if(e)return n[e.toLowerCase()][t];var i=O(m(n,t));return(i[1]+i[2])/2})}function rt(n){var e=$(n),r=H(Xr(n,e),Ur(n,e)),t={},i;s(["u","d"],function(a){i=a==="u"?e:y(e).reverse(),s(["l","r"],function(u){u==="r"&&(i=m(i,function(h){return y(h).reverse()}));var d=(a==="u"?n.predecessors:n.successors).bind(n),f=Kr(n,i,r,d),c=Jr(n,i,f.root,f.align,u==="r");u==="r"&&(c=D(c,function(h){return-h})),t[a+u]=c})});var o=Zr(n,t);return nt(t,o),et(t,n.graph().align)}function tt(n,e,r){return function(t,i,o){var a=t.node(i),u=t.node(o),d=0,f;if(d+=a.width/2,w(a,"labelpos"))switch(a.labelpos.toLowerCase()){case"l":f=-a.width/2;break;case"r":f=a.width/2;break}if(f&&(d+=r?f:-f),f=0,d+=(a.dummy?e:n)/2,d+=(u.dummy?e:n)/2,d+=u.width/2,w(u,"labelpos"))switch(u.labelpos.toLowerCase()){case"l":f=u.width/2;break;case"r":f=-u.width/2;break}return f&&(d+=r?f:-f),f=0,d}}function it(n,e){return n.node(e).width}function at(n){n=Mn(n),ot(n),Ce(rt(n),function(e,r){n.node(r).x=e})}function ot(n){var e=$(n),r=n.graph().ranksep,t=0;s(e,function(i){var o=E(m(i,function(a){return n.node(a).height}));s(i,function(a){n.node(a).y=t+o/2}),t+=o+r})}function Ot(n,e){var r=rr;r("layout",function(){var t=r("  buildLayoutGraph",function(){return mt(n)});r("  runLayout",function(){ut(t,r)}),r("  updateInputGraph",function(){dt(n,t)})})}function ut(n,e){e("    makeSpaceForEdgeLabels",function(){bt(n)}),e("    removeSelfEdges",function(){Ct(n)}),e("    acyclic",function(){je(n)}),e("    nestingGraph.run",function(){yr(n)}),e("    rank",function(){xr(Mn(n))}),e("    injectEdgeLabelProxies",function(){gt(n)}),e("    removeEmptyRanks",function(){nr(n)}),e("    nestingGraph.cleanup",function(){_r(n)}),e("    normalizeRanks",function(){Ze(n)}),e("    assignRankMinMax",function(){xt(n)}),e("    removeEdgeLabelProxies",function(){Et(n)}),e("    normalize.run",function(){dr(n)}),e("    parentDummyChains",function(){qr(n)}),e("    addBorderSegments",function(){tr(n)}),e("    order",function(){Dr(n)}),e("    insertSelfEdges",function(){It(n)}),e("    adjustCoordinateSystem",function(){ir(n)}),e("    position",function(){at(n)}),e("    positionSelfEdges",function(){Rt(n)}),e("    removeBorderNodes",function(){_t(n)}),e("    normalize.undo",function(){sr(n)}),e("    fixupEdgeLabelCoords",function(){Nt(n)}),e("    undoCoordinateSystem",function(){ar(n)}),e("    translateGraph",function(){kt(n)}),e("    assignNodeIntersects",function(){yt(n)}),e("    reversePoints",function(){Lt(n)}),e("    acyclic.undo",function(){Je(n)})}function dt(n,e){s(n.nodes(),function(r){var t=n.node(r),i=e.node(r);t&&(t.x=i.x,t.y=i.y,e.children(r).length&&(t.width=i.width,t.height=i.height))}),s(n.edges(),function(r){var t=n.edge(r),i=e.edge(r);t.points=i.points,w(i,"x")&&(t.x=i.x,t.y=i.y)}),n.graph().width=e.graph().width,n.graph().height=e.graph().height}var ft=["nodesep","edgesep","ranksep","marginx","marginy"],st={ranksep:50,edgesep:20,nodesep:50,rankdir:"tb"},ct=["acyclicer","ranker","rankdir","align"],ht=["width","height"],lt={width:0,height:0},vt=["minlen","weight","width","height","labeloffset"],pt={minlen:1,weight:1,width:0,height:0,labeloffset:10,labelpos:"r"},wt=["labelpos"];function mt(n){var e=new x({multigraph:!0,compound:!0}),r=U(n.graph());return e.setGraph(H({},st,X(r,ft),V(r,ct))),s(n.nodes(),function(t){var i=U(n.node(t));e.setNode(t,ke(X(i,ht),lt)),e.setParent(t,n.parent(t))}),s(n.edges(),function(t){var i=U(n.edge(t));e.setEdge(t,H({},pt,X(i,vt),V(i,wt)))}),e}function bt(n){var e=n.graph();e.ranksep/=2,s(n.edges(),function(r){var t=n.edge(r);t.minlen*=2,t.labelpos.toLowerCase()!=="c"&&(e.rankdir==="TB"||e.rankdir==="BT"?t.width+=t.labeloffset:t.height+=t.labeloffset)})}function gt(n){s(n.edges(),function(e){var r=n.edge(e);if(r.width&&r.height){var t=n.node(e.v),i=n.node(e.w),o={rank:(i.rank-t.rank)/2+t.rank,e};C(n,"edge-proxy",o,"_ep")}})}function xt(n){var e=0;s(n.nodes(),function(r){var t=n.node(r);t.borderTop&&(t.minRank=n.node(t.borderTop).rank,t.maxRank=n.node(t.borderBottom).rank,e=E(e,t.maxRank))}),n.graph().maxRank=e}function Et(n){s(n.nodes(),function(e){var r=n.node(e);r.dummy==="edge-proxy"&&(n.edge(r.e).labelRank=r.rank,n.removeNode(e))})}function kt(n){var e=Number.POSITIVE_INFINITY,r=0,t=Number.POSITIVE_INFINITY,i=0,o=n.graph(),a=o.marginx||0,u=o.marginy||0;function d(f){var c=f.x,h=f.y,l=f.width,v=f.height;e=Math.min(e,c-l/2),r=Math.max(r,c+l/2),t=Math.min(t,h-v/2),i=Math.max(i,h+v/2)}s(n.nodes(),function(f){d(n.node(f))}),s(n.edges(),function(f){var c=n.edge(f);w(c,"x")&&d(c)}),e-=a,t-=u,s(n.nodes(),function(f){var c=n.node(f);c.x-=e,c.y-=t}),s(n.edges(),function(f){var c=n.edge(f);s(c.points,function(h){h.x-=e,h.y-=t}),w(c,"x")&&(c.x-=e),w(c,"y")&&(c.y-=t)}),o.width=r-e+a,o.height=i-t+u}function yt(n){s(n.edges(),function(e){var r=n.edge(e),t=n.node(e.v),i=n.node(e.w),o,a;r.points?(o=r.points[0],a=r.points[r.points.length-1]):(r.points=[],o=i,a=t),r.points.unshift(sn(t,o)),r.points.push(sn(i,a))})}function Nt(n){s(n.edges(),function(e){var r=n.edge(e);if(w(r,"x"))switch((r.labelpos==="l"||r.labelpos==="r")&&(r.width-=r.labeloffset),r.labelpos){case"l":r.x-=r.width/2+r.labeloffset;break;case"r":r.x+=r.width/2+r.labeloffset;break}})}function Lt(n){s(n.edges(),function(e){var r=n.edge(e);r.reversed&&r.points.reverse()})}function _t(n){s(n.nodes(),function(e){if(n.children(e).length){var r=n.node(e),t=n.node(r.borderTop),i=n.node(r.borderBottom),o=n.node(G(r.borderLeft)),a=n.node(G(r.borderRight));r.width=Math.abs(a.x-o.x),r.height=Math.abs(i.y-t.y),r.x=o.x+r.width/2,r.y=t.y+r.height/2}}),s(n.nodes(),function(e){n.node(e).dummy==="border"&&n.removeNode(e)})}function Ct(n){s(n.edges(),function(e){if(e.v===e.w){var r=n.node(e.v);r.selfEdges||(r.selfEdges=[]),r.selfEdges.push({e,label:n.edge(e)}),n.removeEdge(e)}})}function It(n){var e=$(n);s(e,function(r){var t=0;s(r,function(i,o){var a=n.node(i);a.order=o+t,s(a.selfEdges,function(u){C(n,"selfedge",{width:u.label.width,height:u.label.height,rank:a.rank,order:o+ ++t,e:u.e,label:u.label},"_se")}),delete a.selfEdges})})}function Rt(n){s(n.nodes(),function(e){var r=n.node(e);if(r.dummy==="selfedge"){var t=n.node(r.e.v),i=t.x+t.width/2,o=t.y,a=r.x-i,u=t.height/2;n.setEdge(r.e,r.label),n.removeNode(e),r.label.points=[{x:i+2*a/3,y:o-u},{x:i+5*a/6,y:o-u},{x:i+a,y:o},{x:i+5*a/6,y:o+u},{x:i+2*a/3,y:o+u}],r.label.x=r.x,r.label.y=r.y}})}function X(n,e){return D(V(n,e),Number)}function U(n){var e={};return s(n,function(r,t){e[t.toLowerCase()]=r}),e}export{ke as d,Ot as l,m,V as p,N as r,en as u};
diff --git a/assets/line-D0jG_HZ-.js b/assets/line-BqHmcuby.js
similarity index 93%
rename from assets/line-D0jG_HZ-.js
rename to assets/line-BqHmcuby.js
index 463f7b8..e286ed4 100644
--- a/assets/line-D0jG_HZ-.js
+++ b/assets/line-BqHmcuby.js
@@ -1 +1 @@
-import{a as h}from"./array-BKyUJesY.js";import{w as d,c as o}from"./path-CbwjOpE9.js";import{o as v}from"./mermaid.core-ChLYKTZm.js";function w(t){return t[0]}function b(t){return t[1]}function P(t,u){var s=o(!0),i=null,l=v,r=null,m=d(e);t=typeof t=="function"?t:t===void 0?w:o(t),u=typeof u=="function"?u:u===void 0?b:o(u);function e(n){var f,g=(n=h(n)).length,p,c=!1,a;for(i==null&&(r=l(a=m())),f=0;f<=g;++f)!(f<g&&s(p=n[f],f,n))===c&&((c=!c)?r.lineStart():r.lineEnd()),c&&r.point(+t(p,f,n),+u(p,f,n));if(a)return r=null,a+""||null}return e.x=function(n){return arguments.length?(t=typeof n=="function"?n:o(+n),e):t},e.y=function(n){return arguments.length?(u=typeof n=="function"?n:o(+n),e):u},e.defined=function(n){return arguments.length?(s=typeof n=="function"?n:o(!!n),e):s},e.curve=function(n){return arguments.length?(l=n,i!=null&&(r=l(i)),e):l},e.context=function(n){return arguments.length?(n==null?i=r=null:r=l(i=n),e):i},e}export{P as l};
+import{a as h}from"./array-BKyUJesY.js";import{w as d,c as o}from"./path-CbwjOpE9.js";import{o as v}from"./mermaid.core-DNo_7Q2B.js";function w(t){return t[0]}function b(t){return t[1]}function P(t,u){var s=o(!0),i=null,l=v,r=null,m=d(e);t=typeof t=="function"?t:t===void 0?w:o(t),u=typeof u=="function"?u:u===void 0?b:o(u);function e(n){var f,g=(n=h(n)).length,p,c=!1,a;for(i==null&&(r=l(a=m())),f=0;f<=g;++f)!(f<g&&s(p=n[f],f,n))===c&&((c=!c)?r.lineStart():r.lineEnd()),c&&r.point(+t(p,f,n),+u(p,f,n));if(a)return r=null,a+""||null}return e.x=function(n){return arguments.length?(t=typeof n=="function"?n:o(+n),e):t},e.y=function(n){return arguments.length?(u=typeof n=="function"?n:o(+n),e):u},e.defined=function(n){return arguments.length?(s=typeof n=="function"?n:o(!!n),e):s},e.curve=function(n){return arguments.length?(l=n,i!=null&&(r=l(i)),e):l},e.context=function(n){return arguments.length?(n==null?i=r=null:r=l(i=n),e):i},e}export{P as l};
diff --git a/assets/linear-CRQH6hcv.js b/assets/linear-Cb1OAgs3.js
similarity index 99%
rename from assets/linear-CRQH6hcv.js
rename to assets/linear-Cb1OAgs3.js
index 17ce8c5..19e2acd 100644
--- a/assets/linear-CRQH6hcv.js
+++ b/assets/linear-Cb1OAgs3.js
@@ -1 +1 @@
-import{aE as un,aF as T,aG as H,aH as U,aI as fn}from"./mermaid.core-ChLYKTZm.js";import{i as cn}from"./init-Gi6I4Gst.js";function $(n,t){return n==null||t==null?NaN:n<t?-1:n>t?1:n>=t?0:NaN}function hn(n,t){return n==null||t==null?NaN:t<n?-1:t>n?1:t>=n?0:NaN}function _(n){let t,e,r;n.length!==2?(t=$,e=(u,c)=>$(n(u),c),r=(u,c)=>n(u)-c):(t=n===$||n===hn?n:mn,e=n,r=n);function i(u,c,o=0,s=u.length){if(o<s){if(t(c,c)!==0)return s;do{const h=o+s>>>1;e(u[h],c)<0?o=h+1:s=h}while(o<s)}return o}function f(u,c,o=0,s=u.length){if(o<s){if(t(c,c)!==0)return s;do{const h=o+s>>>1;e(u[h],c)<=0?o=h+1:s=h}while(o<s)}return o}function a(u,c,o=0,s=u.length){const h=i(u,c,o,s-1);return h>o&&r(u[h-1],c)>-r(u[h],c)?h-1:h}return{left:i,center:a,right:f}}function mn(){return 0}function ln(n){return n===null?NaN:+n}const sn=_($),dn=sn.right;_(ln).center;const gn=Math.sqrt(50),yn=Math.sqrt(10),Mn=Math.sqrt(2);function E(n,t,e){const r=(t-n)/Math.max(0,e),i=Math.floor(Math.log10(r)),f=r/Math.pow(10,i),a=f>=gn?10:f>=yn?5:f>=Mn?2:1;let u,c,o;return i<0?(o=Math.pow(10,-i)/a,u=Math.round(n*o),c=Math.round(t*o),u/o<n&&++u,c/o>t&&--c,o=-o):(o=Math.pow(10,i)*a,u=Math.round(n/o),c=Math.round(t/o),u*o<n&&++u,c*o>t&&--c),c<u&&.5<=e&&e<2?E(n,t,e*2):[u,c,o]}function pn(n,t,e){if(t=+t,n=+n,e=+e,!(e>0))return[];if(n===t)return[n];const r=t<n,[i,f,a]=r?E(t,n,e):E(n,t,e);if(!(f>=i))return[];const u=f-i+1,c=new Array(u);if(r)if(a<0)for(let o=0;o<u;++o)c[o]=(f-o)/-a;else for(let o=0;o<u;++o)c[o]=(f-o)*a;else if(a<0)for(let o=0;o<u;++o)c[o]=(i+o)/-a;else for(let o=0;o<u;++o)c[o]=(i+o)*a;return c}function L(n,t,e){return t=+t,n=+n,e=+e,E(n,t,e)[2]}function wn(n,t,e){t=+t,n=+n,e=+e;const r=t<n,i=r?L(t,n,e):L(n,t,e);return(r?-1:1)*(i<0?1/-i:i)}function Nn(n,t){t||(t=[]);var e=n?Math.min(t.length,n.length):0,r=t.slice(),i;return function(f){for(i=0;i<e;++i)r[i]=n[i]*(1-f)+t[i]*f;return r}}function kn(n){return ArrayBuffer.isView(n)&&!(n instanceof DataView)}function xn(n,t){var e=t?t.length:0,r=n?Math.min(e,n.length):0,i=new Array(r),f=new Array(e),a;for(a=0;a<r;++a)i[a]=C(n[a],t[a]);for(;a<e;++a)f[a]=t[a];return function(u){for(a=0;a<r;++a)f[a]=i[a](u);return f}}function An(n,t){var e=new Date;return n=+n,t=+t,function(r){return e.setTime(n*(1-r)+t*r),e}}function vn(n,t){var e={},r={},i;(n===null||typeof n!="object")&&(n={}),(t===null||typeof t!="object")&&(t={});for(i in t)i in n?e[i]=C(n[i],t[i]):r[i]=t[i];return function(f){for(i in e)r[i]=e[i](f);return r}}function C(n,t){var e=typeof t,r;return t==null||e==="boolean"?un(t):(e==="number"?T:e==="string"?(r=H(t))?(t=r,U):fn:t instanceof H?U:t instanceof Date?An:kn(t)?Nn:Array.isArray(t)?xn:typeof t.valueOf!="function"&&typeof t.toString!="function"||isNaN(t)?vn:T)(n,t)}function Sn(n,t){return n=+n,t=+t,function(e){return Math.round(n*(1-e)+t*e)}}function bn(n){return Math.abs(n=Math.round(n))>=1e21?n.toLocaleString("en").replace(/,/g,""):n.toString(10)}function R(n,t){if((e=(n=t?n.toExponential(t-1):n.toExponential()).indexOf("e"))<0)return null;var e,r=n.slice(0,e);return[r.length>1?r[0]+r.slice(2):r,+n.slice(e+1)]}function v(n){return n=R(Math.abs(n)),n?n[1]:NaN}function jn(n,t){return function(e,r){for(var i=e.length,f=[],a=0,u=n[0],c=0;i>0&&u>0&&(c+u+1>r&&(u=Math.max(1,r-c)),f.push(e.substring(i-=u,i+u)),!((c+=u+1)>r));)u=n[a=(a+1)%n.length];return f.reverse().join(t)}}function Pn(n){return function(t){return t.replace(/[0-9]/g,function(e){return n[+e]})}}var zn=/^(?:(.)?([<>=^]))?([+\-( ])?([$#])?(0)?(\d+)?(,)?(\.\d+)?(~)?([a-z%])?$/i;function D(n){if(!(t=zn.exec(n)))throw new Error("invalid format: "+n);var t;return new G({fill:t[1],align:t[2],sign:t[3],symbol:t[4],zero:t[5],width:t[6],comma:t[7],precision:t[8]&&t[8].slice(1),trim:t[9],type:t[10]})}D.prototype=G.prototype;function G(n){this.fill=n.fill===void 0?" ":n.fill+"",this.align=n.align===void 0?">":n.align+"",this.sign=n.sign===void 0?"-":n.sign+"",this.symbol=n.symbol===void 0?"":n.symbol+"",this.zero=!!n.zero,this.width=n.width===void 0?void 0:+n.width,this.comma=!!n.comma,this.precision=n.precision===void 0?void 0:+n.precision,this.trim=!!n.trim,this.type=n.type===void 0?"":n.type+""}G.prototype.toString=function(){return this.fill+this.align+this.sign+this.symbol+(this.zero?"0":"")+(this.width===void 0?"":Math.max(1,this.width|0))+(this.comma?",":"")+(this.precision===void 0?"":"."+Math.max(0,this.precision|0))+(this.trim?"~":"")+this.type};function Fn(n){n:for(var t=n.length,e=1,r=-1,i;e<t;++e)switch(n[e]){case".":r=i=e;break;case"0":r===0&&(r=e),i=e;break;default:if(!+n[e])break n;r>0&&(r=0);break}return r>0?n.slice(0,r)+n.slice(i+1):n}var nn;function $n(n,t){var e=R(n,t);if(!e)return n+"";var r=e[0],i=e[1],f=i-(nn=Math.max(-8,Math.min(8,Math.floor(i/3)))*3)+1,a=r.length;return f===a?r:f>a?r+new Array(f-a+1).join("0"):f>0?r.slice(0,f)+"."+r.slice(f):"0."+new Array(1-f).join("0")+R(n,Math.max(0,t+f-1))[0]}function Y(n,t){var e=R(n,t);if(!e)return n+"";var r=e[0],i=e[1];return i<0?"0."+new Array(-i).join("0")+r:r.length>i+1?r.slice(0,i+1)+"."+r.slice(i+1):r+new Array(i-r.length+2).join("0")}const Z={"%":(n,t)=>(n*100).toFixed(t),b:n=>Math.round(n).toString(2),c:n=>n+"",d:bn,e:(n,t)=>n.toExponential(t),f:(n,t)=>n.toFixed(t),g:(n,t)=>n.toPrecision(t),o:n=>Math.round(n).toString(8),p:(n,t)=>Y(n*100,t),r:Y,s:$n,X:n=>Math.round(n).toString(16).toUpperCase(),x:n=>Math.round(n).toString(16)};function J(n){return n}var K=Array.prototype.map,Q=["y","z","a","f","p","n","µ","m","","k","M","G","T","P","E","Z","Y"];function En(n){var t=n.grouping===void 0||n.thousands===void 0?J:jn(K.call(n.grouping,Number),n.thousands+""),e=n.currency===void 0?"":n.currency[0]+"",r=n.currency===void 0?"":n.currency[1]+"",i=n.decimal===void 0?".":n.decimal+"",f=n.numerals===void 0?J:Pn(K.call(n.numerals,String)),a=n.percent===void 0?"%":n.percent+"",u=n.minus===void 0?"−":n.minus+"",c=n.nan===void 0?"NaN":n.nan+"";function o(h){h=D(h);var l=h.fill,p=h.align,y=h.sign,S=h.symbol,k=h.zero,b=h.width,I=h.comma,w=h.precision,B=h.trim,d=h.type;d==="n"?(I=!0,d="g"):Z[d]||(w===void 0&&(w=12),B=!0,d="g"),(k||l==="0"&&p==="=")&&(k=!0,l="0",p="=");var en=S==="$"?e:S==="#"&&/[boxX]/.test(d)?"0"+d.toLowerCase():"",on=S==="$"?r:/[%p]/.test(d)?a:"",O=Z[d],an=/[defgprs%]/.test(d);w=w===void 0?6:/[gprs]/.test(d)?Math.max(1,Math.min(21,w)):Math.max(0,Math.min(20,w));function V(m){var N=en,g=on,x,X,j;if(d==="c")g=O(m)+g,m="";else{m=+m;var P=m<0||1/m<0;if(m=isNaN(m)?c:O(Math.abs(m),w),B&&(m=Fn(m)),P&&+m==0&&y!=="+"&&(P=!1),N=(P?y==="("?y:u:y==="-"||y==="("?"":y)+N,g=(d==="s"?Q[8+nn/3]:"")+g+(P&&y==="("?")":""),an){for(x=-1,X=m.length;++x<X;)if(j=m.charCodeAt(x),48>j||j>57){g=(j===46?i+m.slice(x+1):m.slice(x))+g,m=m.slice(0,x);break}}}I&&!k&&(m=t(m,1/0));var z=N.length+m.length+g.length,M=z<b?new Array(b-z+1).join(l):"";switch(I&&k&&(m=t(M+m,M.length?b-g.length:1/0),M=""),p){case"<":m=N+m+g+M;break;case"=":m=N+M+m+g;break;case"^":m=M.slice(0,z=M.length>>1)+N+m+g+M.slice(z);break;default:m=M+N+m+g;break}return f(m)}return V.toString=function(){return h+""},V}function s(h,l){var p=o((h=D(h),h.type="f",h)),y=Math.max(-8,Math.min(8,Math.floor(v(l)/3)))*3,S=Math.pow(10,-y),k=Q[8+y/3];return function(b){return p(S*b)+k}}return{format:o,formatPrefix:s}}var F,tn,rn;Rn({thousands:",",grouping:[3],currency:["$",""]});function Rn(n){return F=En(n),tn=F.format,rn=F.formatPrefix,F}function Dn(n){return Math.max(0,-v(Math.abs(n)))}function In(n,t){return Math.max(0,Math.max(-8,Math.min(8,Math.floor(v(t)/3)))*3-v(Math.abs(n)))}function Tn(n,t){return n=Math.abs(n),t=Math.abs(t)-n,Math.max(0,v(t)-v(n))+1}function Ln(n){return function(){return n}}function qn(n){return+n}var W=[0,1];function A(n){return n}function q(n,t){return(t-=n=+n)?function(e){return(e-n)/t}:Ln(isNaN(t)?NaN:.5)}function Cn(n,t){var e;return n>t&&(e=n,n=t,t=e),function(r){return Math.max(n,Math.min(t,r))}}function Gn(n,t,e){var r=n[0],i=n[1],f=t[0],a=t[1];return i<r?(r=q(i,r),f=e(a,f)):(r=q(r,i),f=e(f,a)),function(u){return f(r(u))}}function Bn(n,t,e){var r=Math.min(n.length,t.length)-1,i=new Array(r),f=new Array(r),a=-1;for(n[r]<n[0]&&(n=n.slice().reverse(),t=t.slice().reverse());++a<r;)i[a]=q(n[a],n[a+1]),f[a]=e(t[a],t[a+1]);return function(u){var c=dn(n,u,1,r)-1;return f[c](i[c](u))}}function On(n,t){return t.domain(n.domain()).range(n.range()).interpolate(n.interpolate()).clamp(n.clamp()).unknown(n.unknown())}function Vn(){var n=W,t=W,e=C,r,i,f,a=A,u,c,o;function s(){var l=Math.min(n.length,t.length);return a!==A&&(a=Cn(n[0],n[l-1])),u=l>2?Bn:Gn,c=o=null,h}function h(l){return l==null||isNaN(l=+l)?f:(c||(c=u(n.map(r),t,e)))(r(a(l)))}return h.invert=function(l){return a(i((o||(o=u(t,n.map(r),T)))(l)))},h.domain=function(l){return arguments.length?(n=Array.from(l,qn),s()):n.slice()},h.range=function(l){return arguments.length?(t=Array.from(l),s()):t.slice()},h.rangeRound=function(l){return t=Array.from(l),e=Sn,s()},h.clamp=function(l){return arguments.length?(a=l?!0:A,s()):a!==A},h.interpolate=function(l){return arguments.length?(e=l,s()):e},h.unknown=function(l){return arguments.length?(f=l,h):f},function(l,p){return r=l,i=p,s()}}function Xn(){return Vn()(A,A)}function Hn(n,t,e,r){var i=wn(n,t,e),f;switch(r=D(r??",f"),r.type){case"s":{var a=Math.max(Math.abs(n),Math.abs(t));return r.precision==null&&!isNaN(f=In(i,a))&&(r.precision=f),rn(r,a)}case"":case"e":case"g":case"p":case"r":{r.precision==null&&!isNaN(f=Tn(i,Math.max(Math.abs(n),Math.abs(t))))&&(r.precision=f-(r.type==="e"));break}case"f":case"%":{r.precision==null&&!isNaN(f=Dn(i))&&(r.precision=f-(r.type==="%")*2);break}}return tn(r)}function Un(n){var t=n.domain;return n.ticks=function(e){var r=t();return pn(r[0],r[r.length-1],e??10)},n.tickFormat=function(e,r){var i=t();return Hn(i[0],i[i.length-1],e??10,r)},n.nice=function(e){e==null&&(e=10);var r=t(),i=0,f=r.length-1,a=r[i],u=r[f],c,o,s=10;for(u<a&&(o=a,a=u,u=o,o=i,i=f,f=o);s-- >0;){if(o=L(a,u,e),o===c)return r[i]=a,r[f]=u,t(r);if(o>0)a=Math.floor(a/o)*o,u=Math.ceil(u/o)*o;else if(o<0)a=Math.ceil(a*o)/o,u=Math.floor(u*o)/o;else break;c=o}return n},n}function Yn(){var n=Xn();return n.copy=function(){return On(n,Yn())},cn.apply(n,arguments),Un(n)}export{On as a,_ as b,Xn as c,Yn as l,wn as t};
+import{aE as un,aF as T,aG as H,aH as U,aI as fn}from"./mermaid.core-DNo_7Q2B.js";import{i as cn}from"./init-Gi6I4Gst.js";function $(n,t){return n==null||t==null?NaN:n<t?-1:n>t?1:n>=t?0:NaN}function hn(n,t){return n==null||t==null?NaN:t<n?-1:t>n?1:t>=n?0:NaN}function _(n){let t,e,r;n.length!==2?(t=$,e=(u,c)=>$(n(u),c),r=(u,c)=>n(u)-c):(t=n===$||n===hn?n:mn,e=n,r=n);function i(u,c,o=0,s=u.length){if(o<s){if(t(c,c)!==0)return s;do{const h=o+s>>>1;e(u[h],c)<0?o=h+1:s=h}while(o<s)}return o}function f(u,c,o=0,s=u.length){if(o<s){if(t(c,c)!==0)return s;do{const h=o+s>>>1;e(u[h],c)<=0?o=h+1:s=h}while(o<s)}return o}function a(u,c,o=0,s=u.length){const h=i(u,c,o,s-1);return h>o&&r(u[h-1],c)>-r(u[h],c)?h-1:h}return{left:i,center:a,right:f}}function mn(){return 0}function ln(n){return n===null?NaN:+n}const sn=_($),dn=sn.right;_(ln).center;const gn=Math.sqrt(50),yn=Math.sqrt(10),Mn=Math.sqrt(2);function E(n,t,e){const r=(t-n)/Math.max(0,e),i=Math.floor(Math.log10(r)),f=r/Math.pow(10,i),a=f>=gn?10:f>=yn?5:f>=Mn?2:1;let u,c,o;return i<0?(o=Math.pow(10,-i)/a,u=Math.round(n*o),c=Math.round(t*o),u/o<n&&++u,c/o>t&&--c,o=-o):(o=Math.pow(10,i)*a,u=Math.round(n/o),c=Math.round(t/o),u*o<n&&++u,c*o>t&&--c),c<u&&.5<=e&&e<2?E(n,t,e*2):[u,c,o]}function pn(n,t,e){if(t=+t,n=+n,e=+e,!(e>0))return[];if(n===t)return[n];const r=t<n,[i,f,a]=r?E(t,n,e):E(n,t,e);if(!(f>=i))return[];const u=f-i+1,c=new Array(u);if(r)if(a<0)for(let o=0;o<u;++o)c[o]=(f-o)/-a;else for(let o=0;o<u;++o)c[o]=(f-o)*a;else if(a<0)for(let o=0;o<u;++o)c[o]=(i+o)/-a;else for(let o=0;o<u;++o)c[o]=(i+o)*a;return c}function L(n,t,e){return t=+t,n=+n,e=+e,E(n,t,e)[2]}function wn(n,t,e){t=+t,n=+n,e=+e;const r=t<n,i=r?L(t,n,e):L(n,t,e);return(r?-1:1)*(i<0?1/-i:i)}function Nn(n,t){t||(t=[]);var e=n?Math.min(t.length,n.length):0,r=t.slice(),i;return function(f){for(i=0;i<e;++i)r[i]=n[i]*(1-f)+t[i]*f;return r}}function kn(n){return ArrayBuffer.isView(n)&&!(n instanceof DataView)}function xn(n,t){var e=t?t.length:0,r=n?Math.min(e,n.length):0,i=new Array(r),f=new Array(e),a;for(a=0;a<r;++a)i[a]=C(n[a],t[a]);for(;a<e;++a)f[a]=t[a];return function(u){for(a=0;a<r;++a)f[a]=i[a](u);return f}}function An(n,t){var e=new Date;return n=+n,t=+t,function(r){return e.setTime(n*(1-r)+t*r),e}}function vn(n,t){var e={},r={},i;(n===null||typeof n!="object")&&(n={}),(t===null||typeof t!="object")&&(t={});for(i in t)i in n?e[i]=C(n[i],t[i]):r[i]=t[i];return function(f){for(i in e)r[i]=e[i](f);return r}}function C(n,t){var e=typeof t,r;return t==null||e==="boolean"?un(t):(e==="number"?T:e==="string"?(r=H(t))?(t=r,U):fn:t instanceof H?U:t instanceof Date?An:kn(t)?Nn:Array.isArray(t)?xn:typeof t.valueOf!="function"&&typeof t.toString!="function"||isNaN(t)?vn:T)(n,t)}function Sn(n,t){return n=+n,t=+t,function(e){return Math.round(n*(1-e)+t*e)}}function bn(n){return Math.abs(n=Math.round(n))>=1e21?n.toLocaleString("en").replace(/,/g,""):n.toString(10)}function R(n,t){if((e=(n=t?n.toExponential(t-1):n.toExponential()).indexOf("e"))<0)return null;var e,r=n.slice(0,e);return[r.length>1?r[0]+r.slice(2):r,+n.slice(e+1)]}function v(n){return n=R(Math.abs(n)),n?n[1]:NaN}function jn(n,t){return function(e,r){for(var i=e.length,f=[],a=0,u=n[0],c=0;i>0&&u>0&&(c+u+1>r&&(u=Math.max(1,r-c)),f.push(e.substring(i-=u,i+u)),!((c+=u+1)>r));)u=n[a=(a+1)%n.length];return f.reverse().join(t)}}function Pn(n){return function(t){return t.replace(/[0-9]/g,function(e){return n[+e]})}}var zn=/^(?:(.)?([<>=^]))?([+\-( ])?([$#])?(0)?(\d+)?(,)?(\.\d+)?(~)?([a-z%])?$/i;function D(n){if(!(t=zn.exec(n)))throw new Error("invalid format: "+n);var t;return new G({fill:t[1],align:t[2],sign:t[3],symbol:t[4],zero:t[5],width:t[6],comma:t[7],precision:t[8]&&t[8].slice(1),trim:t[9],type:t[10]})}D.prototype=G.prototype;function G(n){this.fill=n.fill===void 0?" ":n.fill+"",this.align=n.align===void 0?">":n.align+"",this.sign=n.sign===void 0?"-":n.sign+"",this.symbol=n.symbol===void 0?"":n.symbol+"",this.zero=!!n.zero,this.width=n.width===void 0?void 0:+n.width,this.comma=!!n.comma,this.precision=n.precision===void 0?void 0:+n.precision,this.trim=!!n.trim,this.type=n.type===void 0?"":n.type+""}G.prototype.toString=function(){return this.fill+this.align+this.sign+this.symbol+(this.zero?"0":"")+(this.width===void 0?"":Math.max(1,this.width|0))+(this.comma?",":"")+(this.precision===void 0?"":"."+Math.max(0,this.precision|0))+(this.trim?"~":"")+this.type};function Fn(n){n:for(var t=n.length,e=1,r=-1,i;e<t;++e)switch(n[e]){case".":r=i=e;break;case"0":r===0&&(r=e),i=e;break;default:if(!+n[e])break n;r>0&&(r=0);break}return r>0?n.slice(0,r)+n.slice(i+1):n}var nn;function $n(n,t){var e=R(n,t);if(!e)return n+"";var r=e[0],i=e[1],f=i-(nn=Math.max(-8,Math.min(8,Math.floor(i/3)))*3)+1,a=r.length;return f===a?r:f>a?r+new Array(f-a+1).join("0"):f>0?r.slice(0,f)+"."+r.slice(f):"0."+new Array(1-f).join("0")+R(n,Math.max(0,t+f-1))[0]}function Y(n,t){var e=R(n,t);if(!e)return n+"";var r=e[0],i=e[1];return i<0?"0."+new Array(-i).join("0")+r:r.length>i+1?r.slice(0,i+1)+"."+r.slice(i+1):r+new Array(i-r.length+2).join("0")}const Z={"%":(n,t)=>(n*100).toFixed(t),b:n=>Math.round(n).toString(2),c:n=>n+"",d:bn,e:(n,t)=>n.toExponential(t),f:(n,t)=>n.toFixed(t),g:(n,t)=>n.toPrecision(t),o:n=>Math.round(n).toString(8),p:(n,t)=>Y(n*100,t),r:Y,s:$n,X:n=>Math.round(n).toString(16).toUpperCase(),x:n=>Math.round(n).toString(16)};function J(n){return n}var K=Array.prototype.map,Q=["y","z","a","f","p","n","µ","m","","k","M","G","T","P","E","Z","Y"];function En(n){var t=n.grouping===void 0||n.thousands===void 0?J:jn(K.call(n.grouping,Number),n.thousands+""),e=n.currency===void 0?"":n.currency[0]+"",r=n.currency===void 0?"":n.currency[1]+"",i=n.decimal===void 0?".":n.decimal+"",f=n.numerals===void 0?J:Pn(K.call(n.numerals,String)),a=n.percent===void 0?"%":n.percent+"",u=n.minus===void 0?"−":n.minus+"",c=n.nan===void 0?"NaN":n.nan+"";function o(h){h=D(h);var l=h.fill,p=h.align,y=h.sign,S=h.symbol,k=h.zero,b=h.width,I=h.comma,w=h.precision,B=h.trim,d=h.type;d==="n"?(I=!0,d="g"):Z[d]||(w===void 0&&(w=12),B=!0,d="g"),(k||l==="0"&&p==="=")&&(k=!0,l="0",p="=");var en=S==="$"?e:S==="#"&&/[boxX]/.test(d)?"0"+d.toLowerCase():"",on=S==="$"?r:/[%p]/.test(d)?a:"",O=Z[d],an=/[defgprs%]/.test(d);w=w===void 0?6:/[gprs]/.test(d)?Math.max(1,Math.min(21,w)):Math.max(0,Math.min(20,w));function V(m){var N=en,g=on,x,X,j;if(d==="c")g=O(m)+g,m="";else{m=+m;var P=m<0||1/m<0;if(m=isNaN(m)?c:O(Math.abs(m),w),B&&(m=Fn(m)),P&&+m==0&&y!=="+"&&(P=!1),N=(P?y==="("?y:u:y==="-"||y==="("?"":y)+N,g=(d==="s"?Q[8+nn/3]:"")+g+(P&&y==="("?")":""),an){for(x=-1,X=m.length;++x<X;)if(j=m.charCodeAt(x),48>j||j>57){g=(j===46?i+m.slice(x+1):m.slice(x))+g,m=m.slice(0,x);break}}}I&&!k&&(m=t(m,1/0));var z=N.length+m.length+g.length,M=z<b?new Array(b-z+1).join(l):"";switch(I&&k&&(m=t(M+m,M.length?b-g.length:1/0),M=""),p){case"<":m=N+m+g+M;break;case"=":m=N+M+m+g;break;case"^":m=M.slice(0,z=M.length>>1)+N+m+g+M.slice(z);break;default:m=M+N+m+g;break}return f(m)}return V.toString=function(){return h+""},V}function s(h,l){var p=o((h=D(h),h.type="f",h)),y=Math.max(-8,Math.min(8,Math.floor(v(l)/3)))*3,S=Math.pow(10,-y),k=Q[8+y/3];return function(b){return p(S*b)+k}}return{format:o,formatPrefix:s}}var F,tn,rn;Rn({thousands:",",grouping:[3],currency:["$",""]});function Rn(n){return F=En(n),tn=F.format,rn=F.formatPrefix,F}function Dn(n){return Math.max(0,-v(Math.abs(n)))}function In(n,t){return Math.max(0,Math.max(-8,Math.min(8,Math.floor(v(t)/3)))*3-v(Math.abs(n)))}function Tn(n,t){return n=Math.abs(n),t=Math.abs(t)-n,Math.max(0,v(t)-v(n))+1}function Ln(n){return function(){return n}}function qn(n){return+n}var W=[0,1];function A(n){return n}function q(n,t){return(t-=n=+n)?function(e){return(e-n)/t}:Ln(isNaN(t)?NaN:.5)}function Cn(n,t){var e;return n>t&&(e=n,n=t,t=e),function(r){return Math.max(n,Math.min(t,r))}}function Gn(n,t,e){var r=n[0],i=n[1],f=t[0],a=t[1];return i<r?(r=q(i,r),f=e(a,f)):(r=q(r,i),f=e(f,a)),function(u){return f(r(u))}}function Bn(n,t,e){var r=Math.min(n.length,t.length)-1,i=new Array(r),f=new Array(r),a=-1;for(n[r]<n[0]&&(n=n.slice().reverse(),t=t.slice().reverse());++a<r;)i[a]=q(n[a],n[a+1]),f[a]=e(t[a],t[a+1]);return function(u){var c=dn(n,u,1,r)-1;return f[c](i[c](u))}}function On(n,t){return t.domain(n.domain()).range(n.range()).interpolate(n.interpolate()).clamp(n.clamp()).unknown(n.unknown())}function Vn(){var n=W,t=W,e=C,r,i,f,a=A,u,c,o;function s(){var l=Math.min(n.length,t.length);return a!==A&&(a=Cn(n[0],n[l-1])),u=l>2?Bn:Gn,c=o=null,h}function h(l){return l==null||isNaN(l=+l)?f:(c||(c=u(n.map(r),t,e)))(r(a(l)))}return h.invert=function(l){return a(i((o||(o=u(t,n.map(r),T)))(l)))},h.domain=function(l){return arguments.length?(n=Array.from(l,qn),s()):n.slice()},h.range=function(l){return arguments.length?(t=Array.from(l),s()):t.slice()},h.rangeRound=function(l){return t=Array.from(l),e=Sn,s()},h.clamp=function(l){return arguments.length?(a=l?!0:A,s()):a!==A},h.interpolate=function(l){return arguments.length?(e=l,s()):e},h.unknown=function(l){return arguments.length?(f=l,h):f},function(l,p){return r=l,i=p,s()}}function Xn(){return Vn()(A,A)}function Hn(n,t,e,r){var i=wn(n,t,e),f;switch(r=D(r??",f"),r.type){case"s":{var a=Math.max(Math.abs(n),Math.abs(t));return r.precision==null&&!isNaN(f=In(i,a))&&(r.precision=f),rn(r,a)}case"":case"e":case"g":case"p":case"r":{r.precision==null&&!isNaN(f=Tn(i,Math.max(Math.abs(n),Math.abs(t))))&&(r.precision=f-(r.type==="e"));break}case"f":case"%":{r.precision==null&&!isNaN(f=Dn(i))&&(r.precision=f-(r.type==="%")*2);break}}return tn(r)}function Un(n){var t=n.domain;return n.ticks=function(e){var r=t();return pn(r[0],r[r.length-1],e??10)},n.tickFormat=function(e,r){var i=t();return Hn(i[0],i[i.length-1],e??10,r)},n.nice=function(e){e==null&&(e=10);var r=t(),i=0,f=r.length-1,a=r[i],u=r[f],c,o,s=10;for(u<a&&(o=a,a=u,u=o,o=i,i=f,f=o);s-- >0;){if(o=L(a,u,e),o===c)return r[i]=a,r[f]=u,t(r);if(o>0)a=Math.floor(a/o)*o,u=Math.ceil(u/o)*o;else if(o<0)a=Math.ceil(a*o)/o,u=Math.floor(u*o)/o;else break;c=o}return n},n}function Yn(){var n=Xn();return n.copy=function(){return On(n,Yn())},cn.apply(n,arguments),Un(n)}export{On as a,_ as b,Xn as c,Yn as l,wn as t};
diff --git a/assets/mailserver.html-DITZCknd.js b/assets/mailserver.html-DO5Xbwgi.js
similarity index 99%
rename from assets/mailserver.html-DITZCknd.js
rename to assets/mailserver.html-DO5Xbwgi.js
index 62be574..6af9d52 100644
--- a/assets/mailserver.html-DITZCknd.js
+++ b/assets/mailserver.html-DO5Xbwgi.js
@@ -1,4 +1,4 @@
-import{_ as n,o as s,c as a,f as t}from"./app-B69Gl_S-.js";const e="/assets/image-BdPl4tjs.png",p={},o=t(`<p>参见:</p><ul><li>https://docker-mailserver.github.io/docker-mailserver/latest/</li><li>https://blog.csdn.net/qq_25866579/article/details/140717115</li><li>https://zhuanlan.zhihu.com/p/609639797</li></ul><p>值得注意的是docker-mailserver 并不支持通过ui注册/修改等操作， 当可以自行实现（后端通过shell命令即可</p><h2 id="使用python-发送示例" tabindex="-1"><a class="header-anchor" href="#使用python-发送示例"><span>使用python 发送示例</span></a></h2><div class="language-python line-numbers-mode" data-ext="py" data-title="py"><pre class="language-python"><code><span class="token keyword">import</span> smtplib
+import{_ as n,o as s,c as a,f as t}from"./app-B4LGNJZ0.js";const e="/assets/image-BdPl4tjs.png",p={},o=t(`<p>参见:</p><ul><li>https://docker-mailserver.github.io/docker-mailserver/latest/</li><li>https://blog.csdn.net/qq_25866579/article/details/140717115</li><li>https://zhuanlan.zhihu.com/p/609639797</li></ul><p>值得注意的是docker-mailserver 并不支持通过ui注册/修改等操作， 当可以自行实现（后端通过shell命令即可</p><h2 id="使用python-发送示例" tabindex="-1"><a class="header-anchor" href="#使用python-发送示例"><span>使用python 发送示例</span></a></h2><div class="language-python line-numbers-mode" data-ext="py" data-title="py"><pre class="language-python"><code><span class="token keyword">import</span> smtplib
 <span class="token keyword">from</span> email<span class="token punctuation">.</span>mime<span class="token punctuation">.</span>text <span class="token keyword">import</span> MIMEText
 <span class="token keyword">from</span> email<span class="token punctuation">.</span>mime<span class="token punctuation">.</span>multipart <span class="token keyword">import</span> MIMEMultipart
 <span class="token keyword">from</span> email<span class="token punctuation">.</span>utils <span class="token keyword">import</span> formatdate
diff --git a/assets/mediator.html-RBFBa63Z.js b/assets/mediator.html-C5vte2nl.js
similarity index 99%
rename from assets/mediator.html-RBFBa63Z.js
rename to assets/mediator.html-C5vte2nl.js
index 776434a..d3466a0 100644
--- a/assets/mediator.html-RBFBa63Z.js
+++ b/assets/mediator.html-C5vte2nl.js
@@ -1,4 +1,4 @@
-import{_ as a,r as e,o as t,c as p,a as o,b as n,e as i,d as c,f as l}from"./app-B69Gl_S-.js";const u={},r=n("h2",{id:"为什么使用此类",tabindex:"-1"},[n("a",{class:"header-anchor",href:"#为什么使用此类"},[n("span",null,"为什么使用此类")])],-1),d=n("p",null,"请大家想象一下一个乱糟糟的开发小组的工作状态。小组中的 10 个成员虽然一起协同工作，但是意见难以统一，总是互相指挥，导致工作进度始终滞后。不仅如此，他们还十分在意编码细节，经常为此争执不下。",-1),k=n("p",null,"这时，我们就需要一个中立的仲裁者站出来说：“各位，请大家将情况报告给我，我来负责仲裁。我会从团队整体出发进行考虑，然后下达指示，但我不会评价大家的工作细节。”这样，当出现争执时大家就会找仲裁者进行商量，仲裁者会负责统一大家的意见。",-1),m=n("p",null,"最后，整个团队的交流过程就变为了组员向仲裁者报告，仲裁者向组员下达指示。组员之间不再相互询问和相互指示。",-1),v=n("h2",{id:"示例代码",tabindex:"-1"},[n("a",{class:"header-anchor",href:"#示例代码"},[n("span",null,"示例代码")])],-1),b={href:"https://github.com/RefactoringGuru/design-patterns-typescript/blob/main/src/Mediator/RealWorld/index.ts",target:"_blank",rel:"noopener noreferrer"},g=l(`<img src="https://www.plantuml.com/plantuml/svg/hP6z3e8m4CVtFiMD6847wE17d1sTZCC9fzP0Ite7YL7VtQA2YeEBqwNNN_h_w8m5lTHbeOmLyZlC29QK6nJduQm0njQ9sPqY9fkJr-2sHyea1ch8YWOMR-m-XWfFXSDyscr66XfdSdLLAYkG6LPCtODOKeU5Sr8-vNGlt58j7xsZCNo3evRqb95fQ4dCkAUeVCoXaG1MzROmVFW1zeuN1vHvLNsqaTJ15kjxclNcB_NSYqcIoIlzK3XDBs-tFJ_4T5-GcWKtuKzl" alt=""><img src="https://www.plantuml.com/plantuml/svg/fPF1ReCm44Jl_egzaKhfeN3ZKALAUmkdfX-mc0sicXZBNXhnztK0jIIA40gtbJppFDwHDrxGINCwAjHIE_Zov5v6SpoQ4sM3bZLRD0BR2kNDsemAng1GghF2y-ljIGgc5ZwqgyWtkTUESugUr8teuki0ANmEAZObxBYin8IfnyTByV4r_htMFJXP2awkmHaApLg9RV8Z-ofQGxH5qHMU9yDdv3sM18uqyGyLaBUNHwGmc2VYtRDsCV_DCtOyollHmZSNarNUk_ElqXHwmcEP1--CzaQHz_Kfd2s9t1CUQMXmRiWKuRlz0W00" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token doc-comment comment">/**
+import{_ as a,r as e,o as t,c as p,a as o,b as n,e as i,d as c,f as l}from"./app-B4LGNJZ0.js";const u={},r=n("h2",{id:"为什么使用此类",tabindex:"-1"},[n("a",{class:"header-anchor",href:"#为什么使用此类"},[n("span",null,"为什么使用此类")])],-1),d=n("p",null,"请大家想象一下一个乱糟糟的开发小组的工作状态。小组中的 10 个成员虽然一起协同工作，但是意见难以统一，总是互相指挥，导致工作进度始终滞后。不仅如此，他们还十分在意编码细节，经常为此争执不下。",-1),k=n("p",null,"这时，我们就需要一个中立的仲裁者站出来说：“各位，请大家将情况报告给我，我来负责仲裁。我会从团队整体出发进行考虑，然后下达指示，但我不会评价大家的工作细节。”这样，当出现争执时大家就会找仲裁者进行商量，仲裁者会负责统一大家的意见。",-1),m=n("p",null,"最后，整个团队的交流过程就变为了组员向仲裁者报告，仲裁者向组员下达指示。组员之间不再相互询问和相互指示。",-1),v=n("h2",{id:"示例代码",tabindex:"-1"},[n("a",{class:"header-anchor",href:"#示例代码"},[n("span",null,"示例代码")])],-1),b={href:"https://github.com/RefactoringGuru/design-patterns-typescript/blob/main/src/Mediator/RealWorld/index.ts",target:"_blank",rel:"noopener noreferrer"},g=l(`<img src="https://www.plantuml.com/plantuml/svg/hP6z3e8m4CVtFiMD6847wE17d1sTZCC9fzP0Ite7YL7VtQA2YeEBqwNNN_h_w8m5lTHbeOmLyZlC29QK6nJduQm0njQ9sPqY9fkJr-2sHyea1ch8YWOMR-m-XWfFXSDyscr66XfdSdLLAYkG6LPCtODOKeU5Sr8-vNGlt58j7xsZCNo3evRqb95fQ4dCkAUeVCoXaG1MzROmVFW1zeuN1vHvLNsqaTJ15kjxclNcB_NSYqcIoIlzK3XDBs-tFJ_4T5-GcWKtuKzl" alt=""><img src="https://www.plantuml.com/plantuml/svg/fPF1ReCm44Jl_egzaKhfeN3ZKALAUmkdfX-mc0sicXZBNXhnztK0jIIA40gtbJppFDwHDrxGINCwAjHIE_Zov5v6SpoQ4sM3bZLRD0BR2kNDsemAng1GghF2y-ljIGgc5ZwqgyWtkTUESugUr8teuki0ANmEAZObxBYin8IfnyTByV4r_htMFJXP2awkmHaApLg9RV8Z-ofQGxH5qHMU9yDdv3sM18uqyGyLaBUNHwGmc2VYtRDsCV_DCtOyollHmZSNarNUk_ElqXHwmcEP1--CzaQHz_Kfd2s9t1CUQMXmRiWKuRlz0W00" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token doc-comment comment">/**
  * EN: Real World Example for the Mediator design pattern
  *
  * Need: To have a messaging application to notify groups of people. Users
diff --git a/assets/memento.html-CbbBldep.js b/assets/memento.html-Dw4vFzUb.js
similarity index 99%
rename from assets/memento.html-CbbBldep.js
rename to assets/memento.html-Dw4vFzUb.js
index f1494b9..84b65ab 100644
--- a/assets/memento.html-CbbBldep.js
+++ b/assets/memento.html-Dw4vFzUb.js
@@ -1,4 +1,4 @@
-import{_ as n,o as s,c as a,f as t}from"./app-B69Gl_S-.js";const p={},e=t(`<h2 id="为什么使用-memento-模式" tabindex="-1"><a class="header-anchor" href="#为什么使用-memento-模式"><span>为什么使用 Memento 模式</span></a></h2><p>Memento 模式的主要目的是在不破坏封装性的前提下，捕获和恢复对象的内部状态。它在以下情况下特别有用：</p><ul><li>需要保存和恢复对象的多个状态。</li><li>需要在对象状态变化时进行撤销操作。</li><li>需要在不暴露对象实现细节的情况下保存对象状态。</li></ul><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><p>在这个示例中，我们使用了 Memento 模式来管理 <code>Gamer</code> 对象的状态。Memento 模式允许我们在不暴露对象实现细节的情况下保存和恢复对象的状态。以下是示例代码：</p><img src="https://www.plantuml.com/plantuml/svg/bP0z3i8m38Ntdi8ZAEe5650dc3en8eQqCLMb9f5i5maXxav-sXA9YId9i_FyFJSiccIsKzLFcXdEsYB1gmAemNg7pmEusNP8IRdJF0eVW8L6DrnlGLGmeBInSxSlUXLqA55v-D6aTq-e1LkqwCJ7od9DHK8MJrlLvdFhANt4NzBqQ94v4bgWE4MwGdvNIwZ59SLIFx7KNx6qCNbE-hJ-AG5N4lwY1Ci0atTRrySjUeFEXDr_0000" alt=""><img src="https://www.plantuml.com/plantuml/svg/VP1D2W8n38NtFKMMTU45kf01GLTpY3fzoi0qXJH5lBrrgbBmPvD7tal8HuQiNhJ4nVX9az1-cS5gcj1sHqSV8OvEKBinQzEvay0hHiGwdFhyQJbYNEbVxaCuI9dLdX-rcsW4ZWHQX5yBvfDCa2lu6o8s_NRh0XqJusP_X2j8hka03lKbTm00" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// gamer.ts</span>
+import{_ as n,o as s,c as a,f as t}from"./app-B4LGNJZ0.js";const p={},e=t(`<h2 id="为什么使用-memento-模式" tabindex="-1"><a class="header-anchor" href="#为什么使用-memento-模式"><span>为什么使用 Memento 模式</span></a></h2><p>Memento 模式的主要目的是在不破坏封装性的前提下，捕获和恢复对象的内部状态。它在以下情况下特别有用：</p><ul><li>需要保存和恢复对象的多个状态。</li><li>需要在对象状态变化时进行撤销操作。</li><li>需要在不暴露对象实现细节的情况下保存对象状态。</li></ul><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><p>在这个示例中，我们使用了 Memento 模式来管理 <code>Gamer</code> 对象的状态。Memento 模式允许我们在不暴露对象实现细节的情况下保存和恢复对象的状态。以下是示例代码：</p><img src="https://www.plantuml.com/plantuml/svg/bP0z3i8m38Ntdi8ZAEe5650dc3en8eQqCLMb9f5i5maXxav-sXA9YId9i_FyFJSiccIsKzLFcXdEsYB1gmAemNg7pmEusNP8IRdJF0eVW8L6DrnlGLGmeBInSxSlUXLqA55v-D6aTq-e1LkqwCJ7od9DHK8MJrlLvdFhANt4NzBqQ94v4bgWE4MwGdvNIwZ59SLIFx7KNx6qCNbE-hJ-AG5N4lwY1Ci0atTRrySjUeFEXDr_0000" alt=""><img src="https://www.plantuml.com/plantuml/svg/VP1D2W8n38NtFKMMTU45kf01GLTpY3fzoi0qXJH5lBrrgbBmPvD7tal8HuQiNhJ4nVX9az1-cS5gcj1sHqSV8OvEKBinQzEvay0hHiGwdFhyQJbYNEbVxaCuI9dLdX-rcsW4ZWHQX5yBvfDCa2lu6o8s_NRh0XqJusP_X2j8hka03lKbTm00" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// gamer.ts</span>
 <span class="token keyword">import</span> <span class="token punctuation">{</span> Memento <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&#39;./memento&#39;</span><span class="token punctuation">;</span>
 <span class="token keyword">export</span> <span class="token keyword">class</span> <span class="token class-name">Gamer</span> <span class="token punctuation">{</span>
   <span class="token keyword">private</span> money<span class="token operator">:</span> <span class="token builtin">number</span><span class="token punctuation">;</span>
diff --git a/assets/mermaid.core-ChLYKTZm.js b/assets/mermaid.core-DNo_7Q2B.js
similarity index 98%
rename from assets/mermaid.core-ChLYKTZm.js
rename to assets/mermaid.core-DNo_7Q2B.js
index d612a08..801a9a3 100644
--- a/assets/mermaid.core-ChLYKTZm.js
+++ b/assets/mermaid.core-DNo_7Q2B.js
@@ -1,5 +1,5 @@
-const __vite__fileDeps=["assets/c4Diagram-dc8f04df-CiA8sQW3.js","assets/svgDrawCommon-9d162435-DXbPg0E8.js","assets/app-B69Gl_S-.js","assets/flowDiagram-622f9fc1-C8iBq7aS.js","assets/flowDb-0da60e67-C3mEtQas.js","assets/graph-T5JS4vfK.js","assets/layout-DUYLy6Ue.js","assets/styles-422bd1c9-CXxGUMW8.js","assets/index-9620d214-B8uh0R2i.js","assets/clone-CI3kFeqi.js","assets/edges-5962ec63-B19hLEst.js","assets/createText-4a4f35c9-BuT3nXUz.js","assets/line-D0jG_HZ-.js","assets/array-BKyUJesY.js","assets/path-CbwjOpE9.js","assets/channel-DJsAcM5I.js","assets/flowDiagram-v2-a33b4996-BVubizbB.js","assets/erDiagram-51d2b61e-BxYe-GEp.js","assets/gitGraphDiagram-23af1bdb-BuC3CTB9.js","assets/ganttDiagram-a649f789-B8bnTgqC.js","assets/linear-CRQH6hcv.js","assets/init-Gi6I4Gst.js","assets/infoDiagram-f86e0131-BJ_tgdHe.js","assets/pieDiagram-31d824a1-CV6f6fQ6.js","assets/arc-BCmLGSVu.js","assets/ordinal-Cboi1Yqb.js","assets/quadrantDiagram-a712a7d9-Bu83u7Zz.js","assets/xychartDiagram-4a8b8217-CYu3f7i9.js","assets/requirementDiagram-eb878fee-DPiNb9b5.js","assets/sequenceDiagram-66748113-MIUFy2Oj.js","assets/classDiagram-8298e144-w121JOWu.js","assets/styles-e2b9d258-TYWOaoPC.js","assets/classDiagram-v2-296fb1cd-BmyNy9b3.js","assets/stateDiagram-35d39939-BlCBJSJX.js","assets/styles-de3becd0-Bjk-EQ8n.js","assets/stateDiagram-v2-6c43c13a-CtOdsXqX.js","assets/journeyDiagram-de0d04b7-DXj0d_vq.js","assets/flowchart-elk-definition-930acc39-Q-ihdrlR.js","assets/timeline-definition-6eaa3543-BApSUGyX.js","assets/mindmap-definition-b08d3ac4-DYSC8IDG.js","assets/sankeyDiagram-c599f8ec-BGnWqC27.js","assets/Tableau10-B-NsZVaP.js","assets/blockDiagram-a8a0820c-1CGnBiz2.js"],__vite__mapDeps=i=>i.map(i=>__vite__fileDeps[i]);
-import{M as K}from"./app-B69Gl_S-.js";function yh(t){for(var e=[],i=1;i<arguments.length;i++)e[i-1]=arguments[i];var r=Array.from(typeof t=="string"?[t]:t);r[r.length-1]=r[r.length-1].replace(/\r?\n([\t ]*)$/,"");var n=r.reduce(function(a,l){var h=l.match(/\n([\t ]+|(?!\s).)/g);return h?a.concat(h.map(function(u){var f,c;return(c=(f=u.match(/[\t ]/g))===null||f===void 0?void 0:f.length)!==null&&c!==void 0?c:0})):a},[]);if(n.length){var o=new RegExp(`
+const __vite__fileDeps=["assets/c4Diagram-dc8f04df-DWstOjwk.js","assets/svgDrawCommon-9d162435-DBc9TLjw.js","assets/app-B4LGNJZ0.js","assets/flowDiagram-622f9fc1-BpT3eoaF.js","assets/flowDb-0da60e67-XaXEQp9e.js","assets/graph-B1296pfd.js","assets/layout-qMafh1ee.js","assets/styles-422bd1c9-CFsDtXUv.js","assets/index-9620d214-BlfbO5wW.js","assets/clone-C3EvpqoY.js","assets/edges-5962ec63-ApWhby2b.js","assets/createText-4a4f35c9-CISzj231.js","assets/line-BqHmcuby.js","assets/array-BKyUJesY.js","assets/path-CbwjOpE9.js","assets/channel-yU22lAlC.js","assets/flowDiagram-v2-a33b4996-BQrZXIe9.js","assets/erDiagram-51d2b61e-D5StoYmd.js","assets/gitGraphDiagram-23af1bdb-Dd7cNN9F.js","assets/ganttDiagram-a649f789-B7dFucT2.js","assets/linear-Cb1OAgs3.js","assets/init-Gi6I4Gst.js","assets/infoDiagram-f86e0131-BvySRD9D.js","assets/pieDiagram-31d824a1-BIcjeA1S.js","assets/arc-DWlpCdAw.js","assets/ordinal-Cboi1Yqb.js","assets/quadrantDiagram-a712a7d9-CNklQ4II.js","assets/xychartDiagram-4a8b8217-DS1INfpk.js","assets/requirementDiagram-eb878fee-OFUpKWxv.js","assets/sequenceDiagram-66748113-sH_v1_cD.js","assets/classDiagram-8298e144-DKojaSxZ.js","assets/styles-e2b9d258-CoUUuHq5.js","assets/classDiagram-v2-296fb1cd-DTrZkQpq.js","assets/stateDiagram-35d39939-D7FEhrYs.js","assets/styles-de3becd0-D7QN2-IT.js","assets/stateDiagram-v2-6c43c13a-C7zU9Dfv.js","assets/journeyDiagram-de0d04b7-bCIGoTun.js","assets/flowchart-elk-definition-930acc39-D2d6YT5I.js","assets/timeline-definition-6eaa3543-CYqJxmAu.js","assets/mindmap-definition-b08d3ac4-CtqZ8Vgk.js","assets/sankeyDiagram-c599f8ec-Ss3oz1oB.js","assets/Tableau10-B-NsZVaP.js","assets/blockDiagram-a8a0820c-DvOSxzpN.js"],__vite__mapDeps=i=>i.map(i=>__vite__fileDeps[i]);
+import{M as K}from"./app-B4LGNJZ0.js";function yh(t){for(var e=[],i=1;i<arguments.length;i++)e[i-1]=arguments[i];var r=Array.from(typeof t=="string"?[t]:t);r[r.length-1]=r[r.length-1].replace(/\r?\n([\t ]*)$/,"");var n=r.reduce(function(a,l){var h=l.match(/\n([\t ]+|(?!\s).)/g);return h?a.concat(h.map(function(u){var f,c;return(c=(f=u.match(/[\t ]/g))===null||f===void 0?void 0:f.length)!==null&&c!==void 0?c:0})):a},[]);if(n.length){var o=new RegExp(`
 [	 ]{`+Math.min.apply(Math,n)+"}","g");r=r.map(function(a){return a.replace(o,`
 `)})}r[0]=r[0].replace(/^\r?\n/,"");var s=r[0];return e.forEach(function(a,l){var h=s.match(/(?:^|\n)( *)$/),u=h?h[1]:"",f=a;typeof a=="string"&&a.includes(`
 `)&&(f=String(a).split(`
@@ -11,7 +11,7 @@ import{M as K}from"./app-B69Gl_S-.js";function yh(t){for(var e=[],i=1;i<argument
             </div>
           `:`<div>${r}</div>`).join("").replace(Tn,(r,n)=>i.renderToString(n,{throwOnError:!0,displayMode:!0,output:ks()?"mathml":"htmlAndMathml"}).replace(/\n/g," ").replace(/<annotation.*<\/annotation>/g,""))},jn={getRows:Im,sanitizeText:Ci,sanitizeTextOrArray:Nm,hasBreaks:Rm,splitBreaks:Pm,lineBreakRegex:wi,removeScript:el,getUrl:zm,evaluate:rl,getMax:Wm,getMin:Hm},ut=(t,e)=>e?g(t,{s:-40,l:10}):g(t,{s:-40,l:-10}),Lr="#ffffff",Fr="#f2f2f2";let Vm=class{constructor(){this.background="#f4f4f4",this.primaryColor="#fff4dd",this.noteBkgColor="#fff5ad",this.noteTextColor="#333",this.THEME_COLOR_LIMIT=12,this.fontFamily='"trebuchet ms", verdana, arial, sans-serif',this.fontSize="16px"}updateColors(){var e,i,r,n,o,s,a,l,h,u,f;if(this.primaryTextColor=this.primaryTextColor||(this.darkMode?"#eee":"#333"),this.secondaryColor=this.secondaryColor||g(this.primaryColor,{h:-120}),this.tertiaryColor=this.tertiaryColor||g(this.primaryColor,{h:180,l:5}),this.primaryBorderColor=this.primaryBorderColor||ut(this.primaryColor,this.darkMode),this.secondaryBorderColor=this.secondaryBorderColor||ut(this.secondaryColor,this.darkMode),this.tertiaryBorderColor=this.tertiaryBorderColor||ut(this.tertiaryColor,this.darkMode),this.noteBorderColor=this.noteBorderColor||ut(this.noteBkgColor,this.darkMode),this.noteBkgColor=this.noteBkgColor||"#fff5ad",this.noteTextColor=this.noteTextColor||"#333",this.secondaryTextColor=this.secondaryTextColor||C(this.secondaryColor),this.tertiaryTextColor=this.tertiaryTextColor||C(this.tertiaryColor),this.lineColor=this.lineColor||C(this.background),this.arrowheadColor=this.arrowheadColor||C(this.background),this.textColor=this.textColor||this.primaryTextColor,this.border2=this.border2||this.tertiaryBorderColor,this.nodeBkg=this.nodeBkg||this.primaryColor,this.mainBkg=this.mainBkg||this.primaryColor,this.nodeBorder=this.nodeBorder||this.primaryBorderColor,this.clusterBkg=this.clusterBkg||this.tertiaryColor,this.clusterBorder=this.clusterBorder||this.tertiaryBorderColor,this.defaultLinkColor=this.defaultLinkColor||this.lineColor,this.titleColor=this.titleColor||this.tertiaryTextColor,this.edgeLabelBackground=this.edgeLabelBackground||(this.darkMode?O(this.secondaryColor,30):this.secondaryColor),this.nodeTextColor=this.nodeTextColor||this.primaryTextColor,this.actorBorder=this.actorBorder||this.primaryBorderColor,this.actorBkg=this.actorBkg||this.mainBkg,this.actorTextColor=this.actorTextColor||this.primaryTextColor,this.actorLineColor=this.actorLineColor||"grey",this.labelBoxBkgColor=this.labelBoxBkgColor||this.actorBkg,this.signalColor=this.signalColor||this.textColor,this.signalTextColor=this.signalTextColor||this.textColor,this.labelBoxBorderColor=this.labelBoxBorderColor||this.actorBorder,this.labelTextColor=this.labelTextColor||this.actorTextColor,this.loopTextColor=this.loopTextColor||this.actorTextColor,this.activationBorderColor=this.activationBorderColor||O(this.secondaryColor,10),this.activationBkgColor=this.activationBkgColor||this.secondaryColor,this.sequenceNumberColor=this.sequenceNumberColor||C(this.lineColor),this.sectionBkgColor=this.sectionBkgColor||this.tertiaryColor,this.altSectionBkgColor=this.altSectionBkgColor||"white",this.sectionBkgColor=this.sectionBkgColor||this.secondaryColor,this.sectionBkgColor2=this.sectionBkgColor2||this.primaryColor,this.excludeBkgColor=this.excludeBkgColor||"#eeeeee",this.taskBorderColor=this.taskBorderColor||this.primaryBorderColor,this.taskBkgColor=this.taskBkgColor||this.primaryColor,this.activeTaskBorderColor=this.activeTaskBorderColor||this.primaryColor,this.activeTaskBkgColor=this.activeTaskBkgColor||A(this.primaryColor,23),this.gridColor=this.gridColor||"lightgrey",this.doneTaskBkgColor=this.doneTaskBkgColor||"lightgrey",this.doneTaskBorderColor=this.doneTaskBorderColor||"grey",this.critBorderColor=this.critBorderColor||"#ff8888",this.critBkgColor=this.critBkgColor||"red",this.todayLineColor=this.todayLineColor||"red",this.taskTextColor=this.taskTextColor||this.textColor,this.taskTextOutsideColor=this.taskTextOutsideColor||this.textColor,this.taskTextLightColor=this.taskTextLightColor||this.textColor,this.taskTextColor=this.taskTextColor||this.primaryTextColor,this.taskTextDarkColor=this.taskTextDarkColor||this.textColor,this.taskTextClickableColor=this.taskTextClickableColor||"#003163",this.personBorder=this.personBorder||this.primaryBorderColor,this.personBkg=this.personBkg||this.mainBkg,this.transitionColor=this.transitionColor||this.lineColor,this.transitionLabelColor=this.transitionLabelColor||this.textColor,this.stateLabelColor=this.stateLabelColor||this.stateBkg||this.primaryTextColor,this.stateBkg=this.stateBkg||this.mainBkg,this.labelBackgroundColor=this.labelBackgroundColor||this.stateBkg,this.compositeBackground=this.compositeBackground||this.background||this.tertiaryColor,this.altBackground=this.altBackground||this.tertiaryColor,this.compositeTitleBackground=this.compositeTitleBackground||this.mainBkg,this.compositeBorder=this.compositeBorder||this.nodeBorder,this.innerEndBackground=this.nodeBorder,this.errorBkgColor=this.errorBkgColor||this.tertiaryColor,this.errorTextColor=this.errorTextColor||this.tertiaryTextColor,this.transitionColor=this.transitionColor||this.lineColor,this.specialStateColor=this.lineColor,this.cScale0=this.cScale0||this.primaryColor,this.cScale1=this.cScale1||this.secondaryColor,this.cScale2=this.cScale2||this.tertiaryColor,this.cScale3=this.cScale3||g(this.primaryColor,{h:30}),this.cScale4=this.cScale4||g(this.primaryColor,{h:60}),this.cScale5=this.cScale5||g(this.primaryColor,{h:90}),this.cScale6=this.cScale6||g(this.primaryColor,{h:120}),this.cScale7=this.cScale7||g(this.primaryColor,{h:150}),this.cScale8=this.cScale8||g(this.primaryColor,{h:210,l:150}),this.cScale9=this.cScale9||g(this.primaryColor,{h:270}),this.cScale10=this.cScale10||g(this.primaryColor,{h:300}),this.cScale11=this.cScale11||g(this.primaryColor,{h:330}),this.darkMode)for(let p=0;p<this.THEME_COLOR_LIMIT;p++)this["cScale"+p]=O(this["cScale"+p],75);else for(let p=0;p<this.THEME_COLOR_LIMIT;p++)this["cScale"+p]=O(this["cScale"+p],25);for(let p=0;p<this.THEME_COLOR_LIMIT;p++)this["cScaleInv"+p]=this["cScaleInv"+p]||C(this["cScale"+p]);for(let p=0;p<this.THEME_COLOR_LIMIT;p++)this.darkMode?this["cScalePeer"+p]=this["cScalePeer"+p]||A(this["cScale"+p],10):this["cScalePeer"+p]=this["cScalePeer"+p]||O(this["cScale"+p],10);this.scaleLabelColor=this.scaleLabelColor||this.labelTextColor;for(let p=0;p<this.THEME_COLOR_LIMIT;p++)this["cScaleLabel"+p]=this["cScaleLabel"+p]||this.scaleLabelColor;const c=this.darkMode?-4:-1;for(let p=0;p<5;p++)this["surface"+p]=this["surface"+p]||g(this.mainBkg,{h:180,s:-15,l:c*(5+p*3)}),this["surfacePeer"+p]=this["surfacePeer"+p]||g(this.mainBkg,{h:180,s:-15,l:c*(8+p*3)});this.classText=this.classText||this.textColor,this.fillType0=this.fillType0||this.primaryColor,this.fillType1=this.fillType1||this.secondaryColor,this.fillType2=this.fillType2||g(this.primaryColor,{h:64}),this.fillType3=this.fillType3||g(this.secondaryColor,{h:64}),this.fillType4=this.fillType4||g(this.primaryColor,{h:-64}),this.fillType5=this.fillType5||g(this.secondaryColor,{h:-64}),this.fillType6=this.fillType6||g(this.primaryColor,{h:128}),this.fillType7=this.fillType7||g(this.secondaryColor,{h:128}),this.pie1=this.pie1||this.primaryColor,this.pie2=this.pie2||this.secondaryColor,this.pie3=this.pie3||this.tertiaryColor,this.pie4=this.pie4||g(this.primaryColor,{l:-10}),this.pie5=this.pie5||g(this.secondaryColor,{l:-10}),this.pie6=this.pie6||g(this.tertiaryColor,{l:-10}),this.pie7=this.pie7||g(this.primaryColor,{h:60,l:-10}),this.pie8=this.pie8||g(this.primaryColor,{h:-60,l:-10}),this.pie9=this.pie9||g(this.primaryColor,{h:120,l:0}),this.pie10=this.pie10||g(this.primaryColor,{h:60,l:-20}),this.pie11=this.pie11||g(this.primaryColor,{h:-60,l:-20}),this.pie12=this.pie12||g(this.primaryColor,{h:120,l:-10}),this.pieTitleTextSize=this.pieTitleTextSize||"25px",this.pieTitleTextColor=this.pieTitleTextColor||this.taskTextDarkColor,this.pieSectionTextSize=this.pieSectionTextSize||"17px",this.pieSectionTextColor=this.pieSectionTextColor||this.textColor,this.pieLegendTextSize=this.pieLegendTextSize||"17px",this.pieLegendTextColor=this.pieLegendTextColor||this.taskTextDarkColor,this.pieStrokeColor=this.pieStrokeColor||"black",this.pieStrokeWidth=this.pieStrokeWidth||"2px",this.pieOuterStrokeWidth=this.pieOuterStrokeWidth||"2px",this.pieOuterStrokeColor=this.pieOuterStrokeColor||"black",this.pieOpacity=this.pieOpacity||"0.7",this.quadrant1Fill=this.quadrant1Fill||this.primaryColor,this.quadrant2Fill=this.quadrant2Fill||g(this.primaryColor,{r:5,g:5,b:5}),this.quadrant3Fill=this.quadrant3Fill||g(this.primaryColor,{r:10,g:10,b:10}),this.quadrant4Fill=this.quadrant4Fill||g(this.primaryColor,{r:15,g:15,b:15}),this.quadrant1TextFill=this.quadrant1TextFill||this.primaryTextColor,this.quadrant2TextFill=this.quadrant2TextFill||g(this.primaryTextColor,{r:-5,g:-5,b:-5}),this.quadrant3TextFill=this.quadrant3TextFill||g(this.primaryTextColor,{r:-10,g:-10,b:-10}),this.quadrant4TextFill=this.quadrant4TextFill||g(this.primaryTextColor,{r:-15,g:-15,b:-15}),this.quadrantPointFill=this.quadrantPointFill||vi(this.quadrant1Fill)?A(this.quadrant1Fill):O(this.quadrant1Fill),this.quadrantPointTextFill=this.quadrantPointTextFill||this.primaryTextColor,this.quadrantXAxisTextFill=this.quadrantXAxisTextFill||this.primaryTextColor,this.quadrantYAxisTextFill=this.quadrantYAxisTextFill||this.primaryTextColor,this.quadrantInternalBorderStrokeFill=this.quadrantInternalBorderStrokeFill||this.primaryBorderColor,this.quadrantExternalBorderStrokeFill=this.quadrantExternalBorderStrokeFill||this.primaryBorderColor,this.quadrantTitleFill=this.quadrantTitleFill||this.primaryTextColor,this.xyChart={backgroundColor:((e=this.xyChart)==null?void 0:e.backgroundColor)||this.background,titleColor:((i=this.xyChart)==null?void 0:i.titleColor)||this.primaryTextColor,xAxisTitleColor:((r=this.xyChart)==null?void 0:r.xAxisTitleColor)||this.primaryTextColor,xAxisLabelColor:((n=this.xyChart)==null?void 0:n.xAxisLabelColor)||this.primaryTextColor,xAxisTickColor:((o=this.xyChart)==null?void 0:o.xAxisTickColor)||this.primaryTextColor,xAxisLineColor:((s=this.xyChart)==null?void 0:s.xAxisLineColor)||this.primaryTextColor,yAxisTitleColor:((a=this.xyChart)==null?void 0:a.yAxisTitleColor)||this.primaryTextColor,yAxisLabelColor:((l=this.xyChart)==null?void 0:l.yAxisLabelColor)||this.primaryTextColor,yAxisTickColor:((h=this.xyChart)==null?void 0:h.yAxisTickColor)||this.primaryTextColor,yAxisLineColor:((u=this.xyChart)==null?void 0:u.yAxisLineColor)||this.primaryTextColor,plotColorPalette:((f=this.xyChart)==null?void 0:f.plotColorPalette)||"#FFF4DD,#FFD8B1,#FFA07A,#ECEFF1,#D6DBDF,#C3E0A8,#FFB6A4,#FFD74D,#738FA7,#FFFFF0"},this.requirementBackground=this.requirementBackground||this.primaryColor,this.requirementBorderColor=this.requirementBorderColor||this.primaryBorderColor,this.requirementBorderSize=this.requirementBorderSize||"1",this.requirementTextColor=this.requirementTextColor||this.primaryTextColor,this.relationColor=this.relationColor||this.lineColor,this.relationLabelBackground=this.relationLabelBackground||(this.darkMode?O(this.secondaryColor,30):this.secondaryColor),this.relationLabelColor=this.relationLabelColor||this.actorTextColor,this.git0=this.git0||this.primaryColor,this.git1=this.git1||this.secondaryColor,this.git2=this.git2||this.tertiaryColor,this.git3=this.git3||g(this.primaryColor,{h:-30}),this.git4=this.git4||g(this.primaryColor,{h:-60}),this.git5=this.git5||g(this.primaryColor,{h:-90}),this.git6=this.git6||g(this.primaryColor,{h:60}),this.git7=this.git7||g(this.primaryColor,{h:120}),this.darkMode?(this.git0=A(this.git0,25),this.git1=A(this.git1,25),this.git2=A(this.git2,25),this.git3=A(this.git3,25),this.git4=A(this.git4,25),this.git5=A(this.git5,25),this.git6=A(this.git6,25),this.git7=A(this.git7,25)):(this.git0=O(this.git0,25),this.git1=O(this.git1,25),this.git2=O(this.git2,25),this.git3=O(this.git3,25),this.git4=O(this.git4,25),this.git5=O(this.git5,25),this.git6=O(this.git6,25),this.git7=O(this.git7,25)),this.gitInv0=this.gitInv0||C(this.git0),this.gitInv1=this.gitInv1||C(this.git1),this.gitInv2=this.gitInv2||C(this.git2),this.gitInv3=this.gitInv3||C(this.git3),this.gitInv4=this.gitInv4||C(this.git4),this.gitInv5=this.gitInv5||C(this.git5),this.gitInv6=this.gitInv6||C(this.git6),this.gitInv7=this.gitInv7||C(this.git7),this.branchLabelColor=this.branchLabelColor||(this.darkMode?"black":this.labelTextColor),this.gitBranchLabel0=this.gitBranchLabel0||this.branchLabelColor,this.gitBranchLabel1=this.gitBranchLabel1||this.branchLabelColor,this.gitBranchLabel2=this.gitBranchLabel2||this.branchLabelColor,this.gitBranchLabel3=this.gitBranchLabel3||this.branchLabelColor,this.gitBranchLabel4=this.gitBranchLabel4||this.branchLabelColor,this.gitBranchLabel5=this.gitBranchLabel5||this.branchLabelColor,this.gitBranchLabel6=this.gitBranchLabel6||this.branchLabelColor,this.gitBranchLabel7=this.gitBranchLabel7||this.branchLabelColor,this.tagLabelColor=this.tagLabelColor||this.primaryTextColor,this.tagLabelBackground=this.tagLabelBackground||this.primaryColor,this.tagLabelBorder=this.tagBorder||this.primaryBorderColor,this.tagLabelFontSize=this.tagLabelFontSize||"10px",this.commitLabelColor=this.commitLabelColor||this.secondaryTextColor,this.commitLabelBackground=this.commitLabelBackground||this.secondaryColor,this.commitLabelFontSize=this.commitLabelFontSize||"10px",this.attributeBackgroundColorOdd=this.attributeBackgroundColorOdd||Lr,this.attributeBackgroundColorEven=this.attributeBackgroundColorEven||Fr}calculate(e){if(typeof e!="object"){this.updateColors();return}const i=Object.keys(e);i.forEach(r=>{this[r]=e[r]}),this.updateColors(),i.forEach(r=>{this[r]=e[r]})}};const Gm=t=>{const e=new Vm;return e.calculate(t),e};let Xm=class{constructor(){this.background="#333",this.primaryColor="#1f2020",this.secondaryColor=A(this.primaryColor,16),this.tertiaryColor=g(this.primaryColor,{h:-160}),this.primaryBorderColor=C(this.background),this.secondaryBorderColor=ut(this.secondaryColor,this.darkMode),this.tertiaryBorderColor=ut(this.tertiaryColor,this.darkMode),this.primaryTextColor=C(this.primaryColor),this.secondaryTextColor=C(this.secondaryColor),this.tertiaryTextColor=C(this.tertiaryColor),this.lineColor=C(this.background),this.textColor=C(this.background),this.mainBkg="#1f2020",this.secondBkg="calculated",this.mainContrastColor="lightgrey",this.darkTextColor=A(C("#323D47"),10),this.lineColor="calculated",this.border1="#81B1DB",this.border2=si(255,255,255,.25),this.arrowheadColor="calculated",this.fontFamily='"trebuchet ms", verdana, arial, sans-serif',this.fontSize="16px",this.labelBackground="#181818",this.textColor="#ccc",this.THEME_COLOR_LIMIT=12,this.nodeBkg="calculated",this.nodeBorder="calculated",this.clusterBkg="calculated",this.clusterBorder="calculated",this.defaultLinkColor="calculated",this.titleColor="#F9FFFE",this.edgeLabelBackground="calculated",this.actorBorder="calculated",this.actorBkg="calculated",this.actorTextColor="calculated",this.actorLineColor="calculated",this.signalColor="calculated",this.signalTextColor="calculated",this.labelBoxBkgColor="calculated",this.labelBoxBorderColor="calculated",this.labelTextColor="calculated",this.loopTextColor="calculated",this.noteBorderColor="calculated",this.noteBkgColor="#fff5ad",this.noteTextColor="calculated",this.activationBorderColor="calculated",this.activationBkgColor="calculated",this.sequenceNumberColor="black",this.sectionBkgColor=O("#EAE8D9",30),this.altSectionBkgColor="calculated",this.sectionBkgColor2="#EAE8D9",this.excludeBkgColor=O(this.sectionBkgColor,10),this.taskBorderColor=si(255,255,255,70),this.taskBkgColor="calculated",this.taskTextColor="calculated",this.taskTextLightColor="calculated",this.taskTextOutsideColor="calculated",this.taskTextClickableColor="#003163",this.activeTaskBorderColor=si(255,255,255,50),this.activeTaskBkgColor="#81B1DB",this.gridColor="calculated",this.doneTaskBkgColor="calculated",this.doneTaskBorderColor="grey",this.critBorderColor="#E83737",this.critBkgColor="#E83737",this.taskTextDarkColor="calculated",this.todayLineColor="#DB5757",this.personBorder=this.primaryBorderColor,this.personBkg=this.mainBkg,this.labelColor="calculated",this.errorBkgColor="#a44141",this.errorTextColor="#ddd"}updateColors(){var e,i,r,n,o,s,a,l,h,u,f;this.secondBkg=A(this.mainBkg,16),this.lineColor=this.mainContrastColor,this.arrowheadColor=this.mainContrastColor,this.nodeBkg=this.mainBkg,this.nodeBorder=this.border1,this.clusterBkg=this.secondBkg,this.clusterBorder=this.border2,this.defaultLinkColor=this.lineColor,this.edgeLabelBackground=A(this.labelBackground,25),this.actorBorder=this.border1,this.actorBkg=this.mainBkg,this.actorTextColor=this.mainContrastColor,this.actorLineColor=this.mainContrastColor,this.signalColor=this.mainContrastColor,this.signalTextColor=this.mainContrastColor,this.labelBoxBkgColor=this.actorBkg,this.labelBoxBorderColor=this.actorBorder,this.labelTextColor=this.mainContrastColor,this.loopTextColor=this.mainContrastColor,this.noteBorderColor=this.secondaryBorderColor,this.noteBkgColor=this.secondBkg,this.noteTextColor=this.secondaryTextColor,this.activationBorderColor=this.border1,this.activationBkgColor=this.secondBkg,this.altSectionBkgColor=this.background,this.taskBkgColor=A(this.mainBkg,23),this.taskTextColor=this.darkTextColor,this.taskTextLightColor=this.mainContrastColor,this.taskTextOutsideColor=this.taskTextLightColor,this.gridColor=this.mainContrastColor,this.doneTaskBkgColor=this.mainContrastColor,this.taskTextDarkColor=this.darkTextColor,this.transitionColor=this.transitionColor||this.lineColor,this.transitionLabelColor=this.transitionLabelColor||this.textColor,this.stateLabelColor=this.stateLabelColor||this.stateBkg||this.primaryTextColor,this.stateBkg=this.stateBkg||this.mainBkg,this.labelBackgroundColor=this.labelBackgroundColor||this.stateBkg,this.compositeBackground=this.compositeBackground||this.background||this.tertiaryColor,this.altBackground=this.altBackground||"#555",this.compositeTitleBackground=this.compositeTitleBackground||this.mainBkg,this.compositeBorder=this.compositeBorder||this.nodeBorder,this.innerEndBackground=this.primaryBorderColor,this.specialStateColor="#f4f4f4",this.errorBkgColor=this.errorBkgColor||this.tertiaryColor,this.errorTextColor=this.errorTextColor||this.tertiaryTextColor,this.fillType0=this.primaryColor,this.fillType1=this.secondaryColor,this.fillType2=g(this.primaryColor,{h:64}),this.fillType3=g(this.secondaryColor,{h:64}),this.fillType4=g(this.primaryColor,{h:-64}),this.fillType5=g(this.secondaryColor,{h:-64}),this.fillType6=g(this.primaryColor,{h:128}),this.fillType7=g(this.secondaryColor,{h:128}),this.cScale1=this.cScale1||"#0b0000",this.cScale2=this.cScale2||"#4d1037",this.cScale3=this.cScale3||"#3f5258",this.cScale4=this.cScale4||"#4f2f1b",this.cScale5=this.cScale5||"#6e0a0a",this.cScale6=this.cScale6||"#3b0048",this.cScale7=this.cScale7||"#995a01",this.cScale8=this.cScale8||"#154706",this.cScale9=this.cScale9||"#161722",this.cScale10=this.cScale10||"#00296f",this.cScale11=this.cScale11||"#01629c",this.cScale12=this.cScale12||"#010029",this.cScale0=this.cScale0||this.primaryColor,this.cScale1=this.cScale1||this.secondaryColor,this.cScale2=this.cScale2||this.tertiaryColor,this.cScale3=this.cScale3||g(this.primaryColor,{h:30}),this.cScale4=this.cScale4||g(this.primaryColor,{h:60}),this.cScale5=this.cScale5||g(this.primaryColor,{h:90}),this.cScale6=this.cScale6||g(this.primaryColor,{h:120}),this.cScale7=this.cScale7||g(this.primaryColor,{h:150}),this.cScale8=this.cScale8||g(this.primaryColor,{h:210}),this.cScale9=this.cScale9||g(this.primaryColor,{h:270}),this.cScale10=this.cScale10||g(this.primaryColor,{h:300}),this.cScale11=this.cScale11||g(this.primaryColor,{h:330});for(let c=0;c<this.THEME_COLOR_LIMIT;c++)this["cScaleInv"+c]=this["cScaleInv"+c]||C(this["cScale"+c]);for(let c=0;c<this.THEME_COLOR_LIMIT;c++)this["cScalePeer"+c]=this["cScalePeer"+c]||A(this["cScale"+c],10);for(let c=0;c<5;c++)this["surface"+c]=this["surface"+c]||g(this.mainBkg,{h:30,s:-30,l:-(-10+c*4)}),this["surfacePeer"+c]=this["surfacePeer"+c]||g(this.mainBkg,{h:30,s:-30,l:-(-7+c*4)});this.scaleLabelColor=this.scaleLabelColor||(this.darkMode?"black":this.labelTextColor);for(let c=0;c<this.THEME_COLOR_LIMIT;c++)this["cScaleLabel"+c]=this["cScaleLabel"+c]||this.scaleLabelColor;for(let c=0;c<this.THEME_COLOR_LIMIT;c++)this["pie"+c]=this["cScale"+c];this.pieTitleTextSize=this.pieTitleTextSize||"25px",this.pieTitleTextColor=this.pieTitleTextColor||this.taskTextDarkColor,this.pieSectionTextSize=this.pieSectionTextSize||"17px",this.pieSectionTextColor=this.pieSectionTextColor||this.textColor,this.pieLegendTextSize=this.pieLegendTextSize||"17px",this.pieLegendTextColor=this.pieLegendTextColor||this.taskTextDarkColor,this.pieStrokeColor=this.pieStrokeColor||"black",this.pieStrokeWidth=this.pieStrokeWidth||"2px",this.pieOuterStrokeWidth=this.pieOuterStrokeWidth||"2px",this.pieOuterStrokeColor=this.pieOuterStrokeColor||"black",this.pieOpacity=this.pieOpacity||"0.7",this.quadrant1Fill=this.quadrant1Fill||this.primaryColor,this.quadrant2Fill=this.quadrant2Fill||g(this.primaryColor,{r:5,g:5,b:5}),this.quadrant3Fill=this.quadrant3Fill||g(this.primaryColor,{r:10,g:10,b:10}),this.quadrant4Fill=this.quadrant4Fill||g(this.primaryColor,{r:15,g:15,b:15}),this.quadrant1TextFill=this.quadrant1TextFill||this.primaryTextColor,this.quadrant2TextFill=this.quadrant2TextFill||g(this.primaryTextColor,{r:-5,g:-5,b:-5}),this.quadrant3TextFill=this.quadrant3TextFill||g(this.primaryTextColor,{r:-10,g:-10,b:-10}),this.quadrant4TextFill=this.quadrant4TextFill||g(this.primaryTextColor,{r:-15,g:-15,b:-15}),this.quadrantPointFill=this.quadrantPointFill||vi(this.quadrant1Fill)?A(this.quadrant1Fill):O(this.quadrant1Fill),this.quadrantPointTextFill=this.quadrantPointTextFill||this.primaryTextColor,this.quadrantXAxisTextFill=this.quadrantXAxisTextFill||this.primaryTextColor,this.quadrantYAxisTextFill=this.quadrantYAxisTextFill||this.primaryTextColor,this.quadrantInternalBorderStrokeFill=this.quadrantInternalBorderStrokeFill||this.primaryBorderColor,this.quadrantExternalBorderStrokeFill=this.quadrantExternalBorderStrokeFill||this.primaryBorderColor,this.quadrantTitleFill=this.quadrantTitleFill||this.primaryTextColor,this.xyChart={backgroundColor:((e=this.xyChart)==null?void 0:e.backgroundColor)||this.background,titleColor:((i=this.xyChart)==null?void 0:i.titleColor)||this.primaryTextColor,xAxisTitleColor:((r=this.xyChart)==null?void 0:r.xAxisTitleColor)||this.primaryTextColor,xAxisLabelColor:((n=this.xyChart)==null?void 0:n.xAxisLabelColor)||this.primaryTextColor,xAxisTickColor:((o=this.xyChart)==null?void 0:o.xAxisTickColor)||this.primaryTextColor,xAxisLineColor:((s=this.xyChart)==null?void 0:s.xAxisLineColor)||this.primaryTextColor,yAxisTitleColor:((a=this.xyChart)==null?void 0:a.yAxisTitleColor)||this.primaryTextColor,yAxisLabelColor:((l=this.xyChart)==null?void 0:l.yAxisLabelColor)||this.primaryTextColor,yAxisTickColor:((h=this.xyChart)==null?void 0:h.yAxisTickColor)||this.primaryTextColor,yAxisLineColor:((u=this.xyChart)==null?void 0:u.yAxisLineColor)||this.primaryTextColor,plotColorPalette:((f=this.xyChart)==null?void 0:f.plotColorPalette)||"#3498db,#2ecc71,#e74c3c,#f1c40f,#bdc3c7,#ffffff,#34495e,#9b59b6,#1abc9c,#e67e22"},this.classText=this.primaryTextColor,this.requirementBackground=this.requirementBackground||this.primaryColor,this.requirementBorderColor=this.requirementBorderColor||this.primaryBorderColor,this.requirementBorderSize=this.requirementBorderSize||"1",this.requirementTextColor=this.requirementTextColor||this.primaryTextColor,this.relationColor=this.relationColor||this.lineColor,this.relationLabelBackground=this.relationLabelBackground||(this.darkMode?O(this.secondaryColor,30):this.secondaryColor),this.relationLabelColor=this.relationLabelColor||this.actorTextColor,this.git0=A(this.secondaryColor,20),this.git1=A(this.pie2||this.secondaryColor,20),this.git2=A(this.pie3||this.tertiaryColor,20),this.git3=A(this.pie4||g(this.primaryColor,{h:-30}),20),this.git4=A(this.pie5||g(this.primaryColor,{h:-60}),20),this.git5=A(this.pie6||g(this.primaryColor,{h:-90}),10),this.git6=A(this.pie7||g(this.primaryColor,{h:60}),10),this.git7=A(this.pie8||g(this.primaryColor,{h:120}),20),this.gitInv0=this.gitInv0||C(this.git0),this.gitInv1=this.gitInv1||C(this.git1),this.gitInv2=this.gitInv2||C(this.git2),this.gitInv3=this.gitInv3||C(this.git3),this.gitInv4=this.gitInv4||C(this.git4),this.gitInv5=this.gitInv5||C(this.git5),this.gitInv6=this.gitInv6||C(this.git6),this.gitInv7=this.gitInv7||C(this.git7),this.gitBranchLabel0=this.gitBranchLabel0||C(this.labelTextColor),this.gitBranchLabel1=this.gitBranchLabel1||this.labelTextColor,this.gitBranchLabel2=this.gitBranchLabel2||this.labelTextColor,this.gitBranchLabel3=this.gitBranchLabel3||C(this.labelTextColor),this.gitBranchLabel4=this.gitBranchLabel4||this.labelTextColor,this.gitBranchLabel5=this.gitBranchLabel5||this.labelTextColor,this.gitBranchLabel6=this.gitBranchLabel6||this.labelTextColor,this.gitBranchLabel7=this.gitBranchLabel7||this.labelTextColor,this.tagLabelColor=this.tagLabelColor||this.primaryTextColor,this.tagLabelBackground=this.tagLabelBackground||this.primaryColor,this.tagLabelBorder=this.tagBorder||this.primaryBorderColor,this.tagLabelFontSize=this.tagLabelFontSize||"10px",this.commitLabelColor=this.commitLabelColor||this.secondaryTextColor,this.commitLabelBackground=this.commitLabelBackground||this.secondaryColor,this.commitLabelFontSize=this.commitLabelFontSize||"10px",this.attributeBackgroundColorOdd=this.attributeBackgroundColorOdd||A(this.background,12),this.attributeBackgroundColorEven=this.attributeBackgroundColorEven||A(this.background,2)}calculate(e){if(typeof e!="object"){this.updateColors();return}const i=Object.keys(e);i.forEach(r=>{this[r]=e[r]}),this.updateColors(),i.forEach(r=>{this[r]=e[r]})}};const Km=t=>{const e=new Xm;return e.calculate(t),e};let Zm=class{constructor(){this.background="#f4f4f4",this.primaryColor="#ECECFF",this.secondaryColor=g(this.primaryColor,{h:120}),this.secondaryColor="#ffffde",this.tertiaryColor=g(this.primaryColor,{h:-160}),this.primaryBorderColor=ut(this.primaryColor,this.darkMode),this.secondaryBorderColor=ut(this.secondaryColor,this.darkMode),this.tertiaryBorderColor=ut(this.tertiaryColor,this.darkMode),this.primaryTextColor=C(this.primaryColor),this.secondaryTextColor=C(this.secondaryColor),this.tertiaryTextColor=C(this.tertiaryColor),this.lineColor=C(this.background),this.textColor=C(this.background),this.background="white",this.mainBkg="#ECECFF",this.secondBkg="#ffffde",this.lineColor="#333333",this.border1="#9370DB",this.border2="#aaaa33",this.arrowheadColor="#333333",this.fontFamily='"trebuchet ms", verdana, arial, sans-serif',this.fontSize="16px",this.labelBackground="#e8e8e8",this.textColor="#333",this.THEME_COLOR_LIMIT=12,this.nodeBkg="calculated",this.nodeBorder="calculated",this.clusterBkg="calculated",this.clusterBorder="calculated",this.defaultLinkColor="calculated",this.titleColor="calculated",this.edgeLabelBackground="calculated",this.actorBorder="calculated",this.actorBkg="calculated",this.actorTextColor="black",this.actorLineColor="grey",this.signalColor="calculated",this.signalTextColor="calculated",this.labelBoxBkgColor="calculated",this.labelBoxBorderColor="calculated",this.labelTextColor="calculated",this.loopTextColor="calculated",this.noteBorderColor="calculated",this.noteBkgColor="#fff5ad",this.noteTextColor="calculated",this.activationBorderColor="#666",this.activationBkgColor="#f4f4f4",this.sequenceNumberColor="white",this.sectionBkgColor="calculated",this.altSectionBkgColor="calculated",this.sectionBkgColor2="calculated",this.excludeBkgColor="#eeeeee",this.taskBorderColor="calculated",this.taskBkgColor="calculated",this.taskTextLightColor="calculated",this.taskTextColor=this.taskTextLightColor,this.taskTextDarkColor="calculated",this.taskTextOutsideColor=this.taskTextDarkColor,this.taskTextClickableColor="calculated",this.activeTaskBorderColor="calculated",this.activeTaskBkgColor="calculated",this.gridColor="calculated",this.doneTaskBkgColor="calculated",this.doneTaskBorderColor="calculated",this.critBorderColor="calculated",this.critBkgColor="calculated",this.todayLineColor="calculated",this.sectionBkgColor=si(102,102,255,.49),this.altSectionBkgColor="white",this.sectionBkgColor2="#fff400",this.taskBorderColor="#534fbc",this.taskBkgColor="#8a90dd",this.taskTextLightColor="white",this.taskTextColor="calculated",this.taskTextDarkColor="black",this.taskTextOutsideColor="calculated",this.taskTextClickableColor="#003163",this.activeTaskBorderColor="#534fbc",this.activeTaskBkgColor="#bfc7ff",this.gridColor="lightgrey",this.doneTaskBkgColor="lightgrey",this.doneTaskBorderColor="grey",this.critBorderColor="#ff8888",this.critBkgColor="red",this.todayLineColor="red",this.personBorder=this.primaryBorderColor,this.personBkg=this.mainBkg,this.labelColor="black",this.errorBkgColor="#552222",this.errorTextColor="#552222",this.updateColors()}updateColors(){var e,i,r,n,o,s,a,l,h,u,f;this.cScale0=this.cScale0||this.primaryColor,this.cScale1=this.cScale1||this.secondaryColor,this.cScale2=this.cScale2||this.tertiaryColor,this.cScale3=this.cScale3||g(this.primaryColor,{h:30}),this.cScale4=this.cScale4||g(this.primaryColor,{h:60}),this.cScale5=this.cScale5||g(this.primaryColor,{h:90}),this.cScale6=this.cScale6||g(this.primaryColor,{h:120}),this.cScale7=this.cScale7||g(this.primaryColor,{h:150}),this.cScale8=this.cScale8||g(this.primaryColor,{h:210}),this.cScale9=this.cScale9||g(this.primaryColor,{h:270}),this.cScale10=this.cScale10||g(this.primaryColor,{h:300}),this.cScale11=this.cScale11||g(this.primaryColor,{h:330}),this.cScalePeer1=this.cScalePeer1||O(this.secondaryColor,45),this.cScalePeer2=this.cScalePeer2||O(this.tertiaryColor,40);for(let c=0;c<this.THEME_COLOR_LIMIT;c++)this["cScale"+c]=O(this["cScale"+c],10),this["cScalePeer"+c]=this["cScalePeer"+c]||O(this["cScale"+c],25);for(let c=0;c<this.THEME_COLOR_LIMIT;c++)this["cScaleInv"+c]=this["cScaleInv"+c]||g(this["cScale"+c],{h:180});for(let c=0;c<5;c++)this["surface"+c]=this["surface"+c]||g(this.mainBkg,{h:30,l:-(5+c*5)}),this["surfacePeer"+c]=this["surfacePeer"+c]||g(this.mainBkg,{h:30,l:-(7+c*5)});if(this.scaleLabelColor=this.scaleLabelColor!=="calculated"&&this.scaleLabelColor?this.scaleLabelColor:this.labelTextColor,this.labelTextColor!=="calculated"){this.cScaleLabel0=this.cScaleLabel0||C(this.labelTextColor),this.cScaleLabel3=this.cScaleLabel3||C(this.labelTextColor);for(let c=0;c<this.THEME_COLOR_LIMIT;c++)this["cScaleLabel"+c]=this["cScaleLabel"+c]||this.labelTextColor}this.nodeBkg=this.mainBkg,this.nodeBorder=this.border1,this.clusterBkg=this.secondBkg,this.clusterBorder=this.border2,this.defaultLinkColor=this.lineColor,this.titleColor=this.textColor,this.edgeLabelBackground=this.labelBackground,this.actorBorder=A(this.border1,23),this.actorBkg=this.mainBkg,this.labelBoxBkgColor=this.actorBkg,this.signalColor=this.textColor,this.signalTextColor=this.textColor,this.labelBoxBorderColor=this.actorBorder,this.labelTextColor=this.actorTextColor,this.loopTextColor=this.actorTextColor,this.noteBorderColor=this.border2,this.noteTextColor=this.actorTextColor,this.taskTextColor=this.taskTextLightColor,this.taskTextOutsideColor=this.taskTextDarkColor,this.transitionColor=this.transitionColor||this.lineColor,this.transitionLabelColor=this.transitionLabelColor||this.textColor,this.stateLabelColor=this.stateLabelColor||this.stateBkg||this.primaryTextColor,this.stateBkg=this.stateBkg||this.mainBkg,this.labelBackgroundColor=this.labelBackgroundColor||this.stateBkg,this.compositeBackground=this.compositeBackground||this.background||this.tertiaryColor,this.altBackground=this.altBackground||"#f0f0f0",this.compositeTitleBackground=this.compositeTitleBackground||this.mainBkg,this.compositeBorder=this.compositeBorder||this.nodeBorder,this.innerEndBackground=this.nodeBorder,this.specialStateColor=this.lineColor,this.errorBkgColor=this.errorBkgColor||this.tertiaryColor,this.errorTextColor=this.errorTextColor||this.tertiaryTextColor,this.transitionColor=this.transitionColor||this.lineColor,this.classText=this.primaryTextColor,this.fillType0=this.primaryColor,this.fillType1=this.secondaryColor,this.fillType2=g(this.primaryColor,{h:64}),this.fillType3=g(this.secondaryColor,{h:64}),this.fillType4=g(this.primaryColor,{h:-64}),this.fillType5=g(this.secondaryColor,{h:-64}),this.fillType6=g(this.primaryColor,{h:128}),this.fillType7=g(this.secondaryColor,{h:128}),this.pie1=this.pie1||this.primaryColor,this.pie2=this.pie2||this.secondaryColor,this.pie3=this.pie3||g(this.tertiaryColor,{l:-40}),this.pie4=this.pie4||g(this.primaryColor,{l:-10}),this.pie5=this.pie5||g(this.secondaryColor,{l:-30}),this.pie6=this.pie6||g(this.tertiaryColor,{l:-20}),this.pie7=this.pie7||g(this.primaryColor,{h:60,l:-20}),this.pie8=this.pie8||g(this.primaryColor,{h:-60,l:-40}),this.pie9=this.pie9||g(this.primaryColor,{h:120,l:-40}),this.pie10=this.pie10||g(this.primaryColor,{h:60,l:-40}),this.pie11=this.pie11||g(this.primaryColor,{h:-90,l:-40}),this.pie12=this.pie12||g(this.primaryColor,{h:120,l:-30}),this.pieTitleTextSize=this.pieTitleTextSize||"25px",this.pieTitleTextColor=this.pieTitleTextColor||this.taskTextDarkColor,this.pieSectionTextSize=this.pieSectionTextSize||"17px",this.pieSectionTextColor=this.pieSectionTextColor||this.textColor,this.pieLegendTextSize=this.pieLegendTextSize||"17px",this.pieLegendTextColor=this.pieLegendTextColor||this.taskTextDarkColor,this.pieStrokeColor=this.pieStrokeColor||"black",this.pieStrokeWidth=this.pieStrokeWidth||"2px",this.pieOuterStrokeWidth=this.pieOuterStrokeWidth||"2px",this.pieOuterStrokeColor=this.pieOuterStrokeColor||"black",this.pieOpacity=this.pieOpacity||"0.7",this.quadrant1Fill=this.quadrant1Fill||this.primaryColor,this.quadrant2Fill=this.quadrant2Fill||g(this.primaryColor,{r:5,g:5,b:5}),this.quadrant3Fill=this.quadrant3Fill||g(this.primaryColor,{r:10,g:10,b:10}),this.quadrant4Fill=this.quadrant4Fill||g(this.primaryColor,{r:15,g:15,b:15}),this.quadrant1TextFill=this.quadrant1TextFill||this.primaryTextColor,this.quadrant2TextFill=this.quadrant2TextFill||g(this.primaryTextColor,{r:-5,g:-5,b:-5}),this.quadrant3TextFill=this.quadrant3TextFill||g(this.primaryTextColor,{r:-10,g:-10,b:-10}),this.quadrant4TextFill=this.quadrant4TextFill||g(this.primaryTextColor,{r:-15,g:-15,b:-15}),this.quadrantPointFill=this.quadrantPointFill||vi(this.quadrant1Fill)?A(this.quadrant1Fill):O(this.quadrant1Fill),this.quadrantPointTextFill=this.quadrantPointTextFill||this.primaryTextColor,this.quadrantXAxisTextFill=this.quadrantXAxisTextFill||this.primaryTextColor,this.quadrantYAxisTextFill=this.quadrantYAxisTextFill||this.primaryTextColor,this.quadrantInternalBorderStrokeFill=this.quadrantInternalBorderStrokeFill||this.primaryBorderColor,this.quadrantExternalBorderStrokeFill=this.quadrantExternalBorderStrokeFill||this.primaryBorderColor,this.quadrantTitleFill=this.quadrantTitleFill||this.primaryTextColor,this.xyChart={backgroundColor:((e=this.xyChart)==null?void 0:e.backgroundColor)||this.background,titleColor:((i=this.xyChart)==null?void 0:i.titleColor)||this.primaryTextColor,xAxisTitleColor:((r=this.xyChart)==null?void 0:r.xAxisTitleColor)||this.primaryTextColor,xAxisLabelColor:((n=this.xyChart)==null?void 0:n.xAxisLabelColor)||this.primaryTextColor,xAxisTickColor:((o=this.xyChart)==null?void 0:o.xAxisTickColor)||this.primaryTextColor,xAxisLineColor:((s=this.xyChart)==null?void 0:s.xAxisLineColor)||this.primaryTextColor,yAxisTitleColor:((a=this.xyChart)==null?void 0:a.yAxisTitleColor)||this.primaryTextColor,yAxisLabelColor:((l=this.xyChart)==null?void 0:l.yAxisLabelColor)||this.primaryTextColor,yAxisTickColor:((h=this.xyChart)==null?void 0:h.yAxisTickColor)||this.primaryTextColor,yAxisLineColor:((u=this.xyChart)==null?void 0:u.yAxisLineColor)||this.primaryTextColor,plotColorPalette:((f=this.xyChart)==null?void 0:f.plotColorPalette)||"#ECECFF,#8493A6,#FFC3A0,#DCDDE1,#B8E994,#D1A36F,#C3CDE6,#FFB6C1,#496078,#F8F3E3"},this.requirementBackground=this.requirementBackground||this.primaryColor,this.requirementBorderColor=this.requirementBorderColor||this.primaryBorderColor,this.requirementBorderSize=this.requirementBorderSize||"1",this.requirementTextColor=this.requirementTextColor||this.primaryTextColor,this.relationColor=this.relationColor||this.lineColor,this.relationLabelBackground=this.relationLabelBackground||this.labelBackground,this.relationLabelColor=this.relationLabelColor||this.actorTextColor,this.git0=this.git0||this.primaryColor,this.git1=this.git1||this.secondaryColor,this.git2=this.git2||this.tertiaryColor,this.git3=this.git3||g(this.primaryColor,{h:-30}),this.git4=this.git4||g(this.primaryColor,{h:-60}),this.git5=this.git5||g(this.primaryColor,{h:-90}),this.git6=this.git6||g(this.primaryColor,{h:60}),this.git7=this.git7||g(this.primaryColor,{h:120}),this.darkMode?(this.git0=A(this.git0,25),this.git1=A(this.git1,25),this.git2=A(this.git2,25),this.git3=A(this.git3,25),this.git4=A(this.git4,25),this.git5=A(this.git5,25),this.git6=A(this.git6,25),this.git7=A(this.git7,25)):(this.git0=O(this.git0,25),this.git1=O(this.git1,25),this.git2=O(this.git2,25),this.git3=O(this.git3,25),this.git4=O(this.git4,25),this.git5=O(this.git5,25),this.git6=O(this.git6,25),this.git7=O(this.git7,25)),this.gitInv0=this.gitInv0||O(C(this.git0),25),this.gitInv1=this.gitInv1||C(this.git1),this.gitInv2=this.gitInv2||C(this.git2),this.gitInv3=this.gitInv3||C(this.git3),this.gitInv4=this.gitInv4||C(this.git4),this.gitInv5=this.gitInv5||C(this.git5),this.gitInv6=this.gitInv6||C(this.git6),this.gitInv7=this.gitInv7||C(this.git7),this.gitBranchLabel0=this.gitBranchLabel0||C(this.labelTextColor),this.gitBranchLabel1=this.gitBranchLabel1||this.labelTextColor,this.gitBranchLabel2=this.gitBranchLabel2||this.labelTextColor,this.gitBranchLabel3=this.gitBranchLabel3||C(this.labelTextColor),this.gitBranchLabel4=this.gitBranchLabel4||this.labelTextColor,this.gitBranchLabel5=this.gitBranchLabel5||this.labelTextColor,this.gitBranchLabel6=this.gitBranchLabel6||this.labelTextColor,this.gitBranchLabel7=this.gitBranchLabel7||this.labelTextColor,this.tagLabelColor=this.tagLabelColor||this.primaryTextColor,this.tagLabelBackground=this.tagLabelBackground||this.primaryColor,this.tagLabelBorder=this.tagBorder||this.primaryBorderColor,this.tagLabelFontSize=this.tagLabelFontSize||"10px",this.commitLabelColor=this.commitLabelColor||this.secondaryTextColor,this.commitLabelBackground=this.commitLabelBackground||this.secondaryColor,this.commitLabelFontSize=this.commitLabelFontSize||"10px",this.attributeBackgroundColorOdd=this.attributeBackgroundColorOdd||Lr,this.attributeBackgroundColorEven=this.attributeBackgroundColorEven||Fr}calculate(e){if(typeof e!="object"){this.updateColors();return}const i=Object.keys(e);i.forEach(r=>{this[r]=e[r]}),this.updateColors(),i.forEach(r=>{this[r]=e[r]})}};const Jm=t=>{const e=new Zm;return e.calculate(t),e};let Qm=class{constructor(){this.background="#f4f4f4",this.primaryColor="#cde498",this.secondaryColor="#cdffb2",this.background="white",this.mainBkg="#cde498",this.secondBkg="#cdffb2",this.lineColor="green",this.border1="#13540c",this.border2="#6eaa49",this.arrowheadColor="green",this.fontFamily='"trebuchet ms", verdana, arial, sans-serif',this.fontSize="16px",this.tertiaryColor=A("#cde498",10),this.primaryBorderColor=ut(this.primaryColor,this.darkMode),this.secondaryBorderColor=ut(this.secondaryColor,this.darkMode),this.tertiaryBorderColor=ut(this.tertiaryColor,this.darkMode),this.primaryTextColor=C(this.primaryColor),this.secondaryTextColor=C(this.secondaryColor),this.tertiaryTextColor=C(this.primaryColor),this.lineColor=C(this.background),this.textColor=C(this.background),this.THEME_COLOR_LIMIT=12,this.nodeBkg="calculated",this.nodeBorder="calculated",this.clusterBkg="calculated",this.clusterBorder="calculated",this.defaultLinkColor="calculated",this.titleColor="#333",this.edgeLabelBackground="#e8e8e8",this.actorBorder="calculated",this.actorBkg="calculated",this.actorTextColor="black",this.actorLineColor="grey",this.signalColor="#333",this.signalTextColor="#333",this.labelBoxBkgColor="calculated",this.labelBoxBorderColor="#326932",this.labelTextColor="calculated",this.loopTextColor="calculated",this.noteBorderColor="calculated",this.noteBkgColor="#fff5ad",this.noteTextColor="calculated",this.activationBorderColor="#666",this.activationBkgColor="#f4f4f4",this.sequenceNumberColor="white",this.sectionBkgColor="#6eaa49",this.altSectionBkgColor="white",this.sectionBkgColor2="#6eaa49",this.excludeBkgColor="#eeeeee",this.taskBorderColor="calculated",this.taskBkgColor="#487e3a",this.taskTextLightColor="white",this.taskTextColor="calculated",this.taskTextDarkColor="black",this.taskTextOutsideColor="calculated",this.taskTextClickableColor="#003163",this.activeTaskBorderColor="calculated",this.activeTaskBkgColor="calculated",this.gridColor="lightgrey",this.doneTaskBkgColor="lightgrey",this.doneTaskBorderColor="grey",this.critBorderColor="#ff8888",this.critBkgColor="red",this.todayLineColor="red",this.personBorder=this.primaryBorderColor,this.personBkg=this.mainBkg,this.labelColor="black",this.errorBkgColor="#552222",this.errorTextColor="#552222"}updateColors(){var e,i,r,n,o,s,a,l,h,u,f;this.actorBorder=O(this.mainBkg,20),this.actorBkg=this.mainBkg,this.labelBoxBkgColor=this.actorBkg,this.labelTextColor=this.actorTextColor,this.loopTextColor=this.actorTextColor,this.noteBorderColor=this.border2,this.noteTextColor=this.actorTextColor,this.cScale0=this.cScale0||this.primaryColor,this.cScale1=this.cScale1||this.secondaryColor,this.cScale2=this.cScale2||this.tertiaryColor,this.cScale3=this.cScale3||g(this.primaryColor,{h:30}),this.cScale4=this.cScale4||g(this.primaryColor,{h:60}),this.cScale5=this.cScale5||g(this.primaryColor,{h:90}),this.cScale6=this.cScale6||g(this.primaryColor,{h:120}),this.cScale7=this.cScale7||g(this.primaryColor,{h:150}),this.cScale8=this.cScale8||g(this.primaryColor,{h:210}),this.cScale9=this.cScale9||g(this.primaryColor,{h:270}),this.cScale10=this.cScale10||g(this.primaryColor,{h:300}),this.cScale11=this.cScale11||g(this.primaryColor,{h:330}),this.cScalePeer1=this.cScalePeer1||O(this.secondaryColor,45),this.cScalePeer2=this.cScalePeer2||O(this.tertiaryColor,40);for(let c=0;c<this.THEME_COLOR_LIMIT;c++)this["cScale"+c]=O(this["cScale"+c],10),this["cScalePeer"+c]=this["cScalePeer"+c]||O(this["cScale"+c],25);for(let c=0;c<this.THEME_COLOR_LIMIT;c++)this["cScaleInv"+c]=this["cScaleInv"+c]||g(this["cScale"+c],{h:180});this.scaleLabelColor=this.scaleLabelColor!=="calculated"&&this.scaleLabelColor?this.scaleLabelColor:this.labelTextColor;for(let c=0;c<this.THEME_COLOR_LIMIT;c++)this["cScaleLabel"+c]=this["cScaleLabel"+c]||this.scaleLabelColor;for(let c=0;c<5;c++)this["surface"+c]=this["surface"+c]||g(this.mainBkg,{h:30,s:-30,l:-(5+c*5)}),this["surfacePeer"+c]=this["surfacePeer"+c]||g(this.mainBkg,{h:30,s:-30,l:-(8+c*5)});this.nodeBkg=this.mainBkg,this.nodeBorder=this.border1,this.clusterBkg=this.secondBkg,this.clusterBorder=this.border2,this.defaultLinkColor=this.lineColor,this.taskBorderColor=this.border1,this.taskTextColor=this.taskTextLightColor,this.taskTextOutsideColor=this.taskTextDarkColor,this.activeTaskBorderColor=this.taskBorderColor,this.activeTaskBkgColor=this.mainBkg,this.transitionColor=this.transitionColor||this.lineColor,this.transitionLabelColor=this.transitionLabelColor||this.textColor,this.stateLabelColor=this.stateLabelColor||this.stateBkg||this.primaryTextColor,this.stateBkg=this.stateBkg||this.mainBkg,this.labelBackgroundColor=this.labelBackgroundColor||this.stateBkg,this.compositeBackground=this.compositeBackground||this.background||this.tertiaryColor,this.altBackground=this.altBackground||"#f0f0f0",this.compositeTitleBackground=this.compositeTitleBackground||this.mainBkg,this.compositeBorder=this.compositeBorder||this.nodeBorder,this.innerEndBackground=this.primaryBorderColor,this.specialStateColor=this.lineColor,this.errorBkgColor=this.errorBkgColor||this.tertiaryColor,this.errorTextColor=this.errorTextColor||this.tertiaryTextColor,this.transitionColor=this.transitionColor||this.lineColor,this.classText=this.primaryTextColor,this.fillType0=this.primaryColor,this.fillType1=this.secondaryColor,this.fillType2=g(this.primaryColor,{h:64}),this.fillType3=g(this.secondaryColor,{h:64}),this.fillType4=g(this.primaryColor,{h:-64}),this.fillType5=g(this.secondaryColor,{h:-64}),this.fillType6=g(this.primaryColor,{h:128}),this.fillType7=g(this.secondaryColor,{h:128}),this.pie1=this.pie1||this.primaryColor,this.pie2=this.pie2||this.secondaryColor,this.pie3=this.pie3||this.tertiaryColor,this.pie4=this.pie4||g(this.primaryColor,{l:-30}),this.pie5=this.pie5||g(this.secondaryColor,{l:-30}),this.pie6=this.pie6||g(this.tertiaryColor,{h:40,l:-40}),this.pie7=this.pie7||g(this.primaryColor,{h:60,l:-10}),this.pie8=this.pie8||g(this.primaryColor,{h:-60,l:-10}),this.pie9=this.pie9||g(this.primaryColor,{h:120,l:0}),this.pie10=this.pie10||g(this.primaryColor,{h:60,l:-50}),this.pie11=this.pie11||g(this.primaryColor,{h:-60,l:-50}),this.pie12=this.pie12||g(this.primaryColor,{h:120,l:-50}),this.pieTitleTextSize=this.pieTitleTextSize||"25px",this.pieTitleTextColor=this.pieTitleTextColor||this.taskTextDarkColor,this.pieSectionTextSize=this.pieSectionTextSize||"17px",this.pieSectionTextColor=this.pieSectionTextColor||this.textColor,this.pieLegendTextSize=this.pieLegendTextSize||"17px",this.pieLegendTextColor=this.pieLegendTextColor||this.taskTextDarkColor,this.pieStrokeColor=this.pieStrokeColor||"black",this.pieStrokeWidth=this.pieStrokeWidth||"2px",this.pieOuterStrokeWidth=this.pieOuterStrokeWidth||"2px",this.pieOuterStrokeColor=this.pieOuterStrokeColor||"black",this.pieOpacity=this.pieOpacity||"0.7",this.quadrant1Fill=this.quadrant1Fill||this.primaryColor,this.quadrant2Fill=this.quadrant2Fill||g(this.primaryColor,{r:5,g:5,b:5}),this.quadrant3Fill=this.quadrant3Fill||g(this.primaryColor,{r:10,g:10,b:10}),this.quadrant4Fill=this.quadrant4Fill||g(this.primaryColor,{r:15,g:15,b:15}),this.quadrant1TextFill=this.quadrant1TextFill||this.primaryTextColor,this.quadrant2TextFill=this.quadrant2TextFill||g(this.primaryTextColor,{r:-5,g:-5,b:-5}),this.quadrant3TextFill=this.quadrant3TextFill||g(this.primaryTextColor,{r:-10,g:-10,b:-10}),this.quadrant4TextFill=this.quadrant4TextFill||g(this.primaryTextColor,{r:-15,g:-15,b:-15}),this.quadrantPointFill=this.quadrantPointFill||vi(this.quadrant1Fill)?A(this.quadrant1Fill):O(this.quadrant1Fill),this.quadrantPointTextFill=this.quadrantPointTextFill||this.primaryTextColor,this.quadrantXAxisTextFill=this.quadrantXAxisTextFill||this.primaryTextColor,this.quadrantYAxisTextFill=this.quadrantYAxisTextFill||this.primaryTextColor,this.quadrantInternalBorderStrokeFill=this.quadrantInternalBorderStrokeFill||this.primaryBorderColor,this.quadrantExternalBorderStrokeFill=this.quadrantExternalBorderStrokeFill||this.primaryBorderColor,this.quadrantTitleFill=this.quadrantTitleFill||this.primaryTextColor,this.xyChart={backgroundColor:((e=this.xyChart)==null?void 0:e.backgroundColor)||this.background,titleColor:((i=this.xyChart)==null?void 0:i.titleColor)||this.primaryTextColor,xAxisTitleColor:((r=this.xyChart)==null?void 0:r.xAxisTitleColor)||this.primaryTextColor,xAxisLabelColor:((n=this.xyChart)==null?void 0:n.xAxisLabelColor)||this.primaryTextColor,xAxisTickColor:((o=this.xyChart)==null?void 0:o.xAxisTickColor)||this.primaryTextColor,xAxisLineColor:((s=this.xyChart)==null?void 0:s.xAxisLineColor)||this.primaryTextColor,yAxisTitleColor:((a=this.xyChart)==null?void 0:a.yAxisTitleColor)||this.primaryTextColor,yAxisLabelColor:((l=this.xyChart)==null?void 0:l.yAxisLabelColor)||this.primaryTextColor,yAxisTickColor:((h=this.xyChart)==null?void 0:h.yAxisTickColor)||this.primaryTextColor,yAxisLineColor:((u=this.xyChart)==null?void 0:u.yAxisLineColor)||this.primaryTextColor,plotColorPalette:((f=this.xyChart)==null?void 0:f.plotColorPalette)||"#CDE498,#FF6B6B,#A0D2DB,#D7BDE2,#F0F0F0,#FFC3A0,#7FD8BE,#FF9A8B,#FAF3E0,#FFF176"},this.requirementBackground=this.requirementBackground||this.primaryColor,this.requirementBorderColor=this.requirementBorderColor||this.primaryBorderColor,this.requirementBorderSize=this.requirementBorderSize||"1",this.requirementTextColor=this.requirementTextColor||this.primaryTextColor,this.relationColor=this.relationColor||this.lineColor,this.relationLabelBackground=this.relationLabelBackground||this.edgeLabelBackground,this.relationLabelColor=this.relationLabelColor||this.actorTextColor,this.git0=this.git0||this.primaryColor,this.git1=this.git1||this.secondaryColor,this.git2=this.git2||this.tertiaryColor,this.git3=this.git3||g(this.primaryColor,{h:-30}),this.git4=this.git4||g(this.primaryColor,{h:-60}),this.git5=this.git5||g(this.primaryColor,{h:-90}),this.git6=this.git6||g(this.primaryColor,{h:60}),this.git7=this.git7||g(this.primaryColor,{h:120}),this.darkMode?(this.git0=A(this.git0,25),this.git1=A(this.git1,25),this.git2=A(this.git2,25),this.git3=A(this.git3,25),this.git4=A(this.git4,25),this.git5=A(this.git5,25),this.git6=A(this.git6,25),this.git7=A(this.git7,25)):(this.git0=O(this.git0,25),this.git1=O(this.git1,25),this.git2=O(this.git2,25),this.git3=O(this.git3,25),this.git4=O(this.git4,25),this.git5=O(this.git5,25),this.git6=O(this.git6,25),this.git7=O(this.git7,25)),this.gitInv0=this.gitInv0||C(this.git0),this.gitInv1=this.gitInv1||C(this.git1),this.gitInv2=this.gitInv2||C(this.git2),this.gitInv3=this.gitInv3||C(this.git3),this.gitInv4=this.gitInv4||C(this.git4),this.gitInv5=this.gitInv5||C(this.git5),this.gitInv6=this.gitInv6||C(this.git6),this.gitInv7=this.gitInv7||C(this.git7),this.gitBranchLabel0=this.gitBranchLabel0||C(this.labelTextColor),this.gitBranchLabel1=this.gitBranchLabel1||this.labelTextColor,this.gitBranchLabel2=this.gitBranchLabel2||this.labelTextColor,this.gitBranchLabel3=this.gitBranchLabel3||C(this.labelTextColor),this.gitBranchLabel4=this.gitBranchLabel4||this.labelTextColor,this.gitBranchLabel5=this.gitBranchLabel5||this.labelTextColor,this.gitBranchLabel6=this.gitBranchLabel6||this.labelTextColor,this.gitBranchLabel7=this.gitBranchLabel7||this.labelTextColor,this.tagLabelColor=this.tagLabelColor||this.primaryTextColor,this.tagLabelBackground=this.tagLabelBackground||this.primaryColor,this.tagLabelBorder=this.tagBorder||this.primaryBorderColor,this.tagLabelFontSize=this.tagLabelFontSize||"10px",this.commitLabelColor=this.commitLabelColor||this.secondaryTextColor,this.commitLabelBackground=this.commitLabelBackground||this.secondaryColor,this.commitLabelFontSize=this.commitLabelFontSize||"10px",this.attributeBackgroundColorOdd=this.attributeBackgroundColorOdd||Lr,this.attributeBackgroundColorEven=this.attributeBackgroundColorEven||Fr}calculate(e){if(typeof e!="object"){this.updateColors();return}const i=Object.keys(e);i.forEach(r=>{this[r]=e[r]}),this.updateColors(),i.forEach(r=>{this[r]=e[r]})}};const t0=t=>{const e=new Qm;return e.calculate(t),e};class e0{constructor(){this.primaryColor="#eee",this.contrast="#707070",this.secondaryColor=A(this.contrast,55),this.background="#ffffff",this.tertiaryColor=g(this.primaryColor,{h:-160}),this.primaryBorderColor=ut(this.primaryColor,this.darkMode),this.secondaryBorderColor=ut(this.secondaryColor,this.darkMode),this.tertiaryBorderColor=ut(this.tertiaryColor,this.darkMode),this.primaryTextColor=C(this.primaryColor),this.secondaryTextColor=C(this.secondaryColor),this.tertiaryTextColor=C(this.tertiaryColor),this.lineColor=C(this.background),this.textColor=C(this.background),this.mainBkg="#eee",this.secondBkg="calculated",this.lineColor="#666",this.border1="#999",this.border2="calculated",this.note="#ffa",this.text="#333",this.critical="#d42",this.done="#bbb",this.arrowheadColor="#333333",this.fontFamily='"trebuchet ms", verdana, arial, sans-serif',this.fontSize="16px",this.THEME_COLOR_LIMIT=12,this.nodeBkg="calculated",this.nodeBorder="calculated",this.clusterBkg="calculated",this.clusterBorder="calculated",this.defaultLinkColor="calculated",this.titleColor="calculated",this.edgeLabelBackground="white",this.actorBorder="calculated",this.actorBkg="calculated",this.actorTextColor="calculated",this.actorLineColor="calculated",this.signalColor="calculated",this.signalTextColor="calculated",this.labelBoxBkgColor="calculated",this.labelBoxBorderColor="calculated",this.labelTextColor="calculated",this.loopTextColor="calculated",this.noteBorderColor="calculated",this.noteBkgColor="calculated",this.noteTextColor="calculated",this.activationBorderColor="#666",this.activationBkgColor="#f4f4f4",this.sequenceNumberColor="white",this.sectionBkgColor="calculated",this.altSectionBkgColor="white",this.sectionBkgColor2="calculated",this.excludeBkgColor="#eeeeee",this.taskBorderColor="calculated",this.taskBkgColor="calculated",this.taskTextLightColor="white",this.taskTextColor="calculated",this.taskTextDarkColor="calculated",this.taskTextOutsideColor="calculated",this.taskTextClickableColor="#003163",this.activeTaskBorderColor="calculated",this.activeTaskBkgColor="calculated",this.gridColor="calculated",this.doneTaskBkgColor="calculated",this.doneTaskBorderColor="calculated",this.critBkgColor="calculated",this.critBorderColor="calculated",this.todayLineColor="calculated",this.personBorder=this.primaryBorderColor,this.personBkg=this.mainBkg,this.labelColor="black",this.errorBkgColor="#552222",this.errorTextColor="#552222"}updateColors(){var e,i,r,n,o,s,a,l,h,u,f;this.secondBkg=A(this.contrast,55),this.border2=this.contrast,this.actorBorder=A(this.border1,23),this.actorBkg=this.mainBkg,this.actorTextColor=this.text,this.actorLineColor=this.lineColor,this.signalColor=this.text,this.signalTextColor=this.text,this.labelBoxBkgColor=this.actorBkg,this.labelBoxBorderColor=this.actorBorder,this.labelTextColor=this.text,this.loopTextColor=this.text,this.noteBorderColor="#999",this.noteBkgColor="#666",this.noteTextColor="#fff",this.cScale0=this.cScale0||"#555",this.cScale1=this.cScale1||"#F4F4F4",this.cScale2=this.cScale2||"#555",this.cScale3=this.cScale3||"#BBB",this.cScale4=this.cScale4||"#777",this.cScale5=this.cScale5||"#999",this.cScale6=this.cScale6||"#DDD",this.cScale7=this.cScale7||"#FFF",this.cScale8=this.cScale8||"#DDD",this.cScale9=this.cScale9||"#BBB",this.cScale10=this.cScale10||"#999",this.cScale11=this.cScale11||"#777";for(let c=0;c<this.THEME_COLOR_LIMIT;c++)this["cScaleInv"+c]=this["cScaleInv"+c]||C(this["cScale"+c]);for(let c=0;c<this.THEME_COLOR_LIMIT;c++)this.darkMode?this["cScalePeer"+c]=this["cScalePeer"+c]||A(this["cScale"+c],10):this["cScalePeer"+c]=this["cScalePeer"+c]||O(this["cScale"+c],10);this.scaleLabelColor=this.scaleLabelColor||(this.darkMode?"black":this.labelTextColor),this.cScaleLabel0=this.cScaleLabel0||this.cScale1,this.cScaleLabel2=this.cScaleLabel2||this.cScale1;for(let c=0;c<this.THEME_COLOR_LIMIT;c++)this["cScaleLabel"+c]=this["cScaleLabel"+c]||this.scaleLabelColor;for(let c=0;c<5;c++)this["surface"+c]=this["surface"+c]||g(this.mainBkg,{l:-(5+c*5)}),this["surfacePeer"+c]=this["surfacePeer"+c]||g(this.mainBkg,{l:-(8+c*5)});this.nodeBkg=this.mainBkg,this.nodeBorder=this.border1,this.clusterBkg=this.secondBkg,this.clusterBorder=this.border2,this.defaultLinkColor=this.lineColor,this.titleColor=this.text,this.sectionBkgColor=A(this.contrast,30),this.sectionBkgColor2=A(this.contrast,30),this.taskBorderColor=O(this.contrast,10),this.taskBkgColor=this.contrast,this.taskTextColor=this.taskTextLightColor,this.taskTextDarkColor=this.text,this.taskTextOutsideColor=this.taskTextDarkColor,this.activeTaskBorderColor=this.taskBorderColor,this.activeTaskBkgColor=this.mainBkg,this.gridColor=A(this.border1,30),this.doneTaskBkgColor=this.done,this.doneTaskBorderColor=this.lineColor,this.critBkgColor=this.critical,this.critBorderColor=O(this.critBkgColor,10),this.todayLineColor=this.critBkgColor,this.transitionColor=this.transitionColor||"#000",this.transitionLabelColor=this.transitionLabelColor||this.textColor,this.stateLabelColor=this.stateLabelColor||this.stateBkg||this.primaryTextColor,this.stateBkg=this.stateBkg||this.mainBkg,this.labelBackgroundColor=this.labelBackgroundColor||this.stateBkg,this.compositeBackground=this.compositeBackground||this.background||this.tertiaryColor,this.altBackground=this.altBackground||"#f4f4f4",this.compositeTitleBackground=this.compositeTitleBackground||this.mainBkg,this.stateBorder=this.stateBorder||"#000",this.innerEndBackground=this.primaryBorderColor,this.specialStateColor="#222",this.errorBkgColor=this.errorBkgColor||this.tertiaryColor,this.errorTextColor=this.errorTextColor||this.tertiaryTextColor,this.classText=this.primaryTextColor,this.fillType0=this.primaryColor,this.fillType1=this.secondaryColor,this.fillType2=g(this.primaryColor,{h:64}),this.fillType3=g(this.secondaryColor,{h:64}),this.fillType4=g(this.primaryColor,{h:-64}),this.fillType5=g(this.secondaryColor,{h:-64}),this.fillType6=g(this.primaryColor,{h:128}),this.fillType7=g(this.secondaryColor,{h:128});for(let c=0;c<this.THEME_COLOR_LIMIT;c++)this["pie"+c]=this["cScale"+c];this.pie12=this.pie0,this.pieTitleTextSize=this.pieTitleTextSize||"25px",this.pieTitleTextColor=this.pieTitleTextColor||this.taskTextDarkColor,this.pieSectionTextSize=this.pieSectionTextSize||"17px",this.pieSectionTextColor=this.pieSectionTextColor||this.textColor,this.pieLegendTextSize=this.pieLegendTextSize||"17px",this.pieLegendTextColor=this.pieLegendTextColor||this.taskTextDarkColor,this.pieStrokeColor=this.pieStrokeColor||"black",this.pieStrokeWidth=this.pieStrokeWidth||"2px",this.pieOuterStrokeWidth=this.pieOuterStrokeWidth||"2px",this.pieOuterStrokeColor=this.pieOuterStrokeColor||"black",this.pieOpacity=this.pieOpacity||"0.7",this.quadrant1Fill=this.quadrant1Fill||this.primaryColor,this.quadrant2Fill=this.quadrant2Fill||g(this.primaryColor,{r:5,g:5,b:5}),this.quadrant3Fill=this.quadrant3Fill||g(this.primaryColor,{r:10,g:10,b:10}),this.quadrant4Fill=this.quadrant4Fill||g(this.primaryColor,{r:15,g:15,b:15}),this.quadrant1TextFill=this.quadrant1TextFill||this.primaryTextColor,this.quadrant2TextFill=this.quadrant2TextFill||g(this.primaryTextColor,{r:-5,g:-5,b:-5}),this.quadrant3TextFill=this.quadrant3TextFill||g(this.primaryTextColor,{r:-10,g:-10,b:-10}),this.quadrant4TextFill=this.quadrant4TextFill||g(this.primaryTextColor,{r:-15,g:-15,b:-15}),this.quadrantPointFill=this.quadrantPointFill||vi(this.quadrant1Fill)?A(this.quadrant1Fill):O(this.quadrant1Fill),this.quadrantPointTextFill=this.quadrantPointTextFill||this.primaryTextColor,this.quadrantXAxisTextFill=this.quadrantXAxisTextFill||this.primaryTextColor,this.quadrantYAxisTextFill=this.quadrantYAxisTextFill||this.primaryTextColor,this.quadrantInternalBorderStrokeFill=this.quadrantInternalBorderStrokeFill||this.primaryBorderColor,this.quadrantExternalBorderStrokeFill=this.quadrantExternalBorderStrokeFill||this.primaryBorderColor,this.quadrantTitleFill=this.quadrantTitleFill||this.primaryTextColor,this.xyChart={backgroundColor:((e=this.xyChart)==null?void 0:e.backgroundColor)||this.background,titleColor:((i=this.xyChart)==null?void 0:i.titleColor)||this.primaryTextColor,xAxisTitleColor:((r=this.xyChart)==null?void 0:r.xAxisTitleColor)||this.primaryTextColor,xAxisLabelColor:((n=this.xyChart)==null?void 0:n.xAxisLabelColor)||this.primaryTextColor,xAxisTickColor:((o=this.xyChart)==null?void 0:o.xAxisTickColor)||this.primaryTextColor,xAxisLineColor:((s=this.xyChart)==null?void 0:s.xAxisLineColor)||this.primaryTextColor,yAxisTitleColor:((a=this.xyChart)==null?void 0:a.yAxisTitleColor)||this.primaryTextColor,yAxisLabelColor:((l=this.xyChart)==null?void 0:l.yAxisLabelColor)||this.primaryTextColor,yAxisTickColor:((h=this.xyChart)==null?void 0:h.yAxisTickColor)||this.primaryTextColor,yAxisLineColor:((u=this.xyChart)==null?void 0:u.yAxisLineColor)||this.primaryTextColor,plotColorPalette:((f=this.xyChart)==null?void 0:f.plotColorPalette)||"#EEE,#6BB8E4,#8ACB88,#C7ACD6,#E8DCC2,#FFB2A8,#FFF380,#7E8D91,#FFD8B1,#FAF3E0"},this.requirementBackground=this.requirementBackground||this.primaryColor,this.requirementBorderColor=this.requirementBorderColor||this.primaryBorderColor,this.requirementBorderSize=this.requirementBorderSize||"1",this.requirementTextColor=this.requirementTextColor||this.primaryTextColor,this.relationColor=this.relationColor||this.lineColor,this.relationLabelBackground=this.relationLabelBackground||this.edgeLabelBackground,this.relationLabelColor=this.relationLabelColor||this.actorTextColor,this.git0=O(this.pie1,25)||this.primaryColor,this.git1=this.pie2||this.secondaryColor,this.git2=this.pie3||this.tertiaryColor,this.git3=this.pie4||g(this.primaryColor,{h:-30}),this.git4=this.pie5||g(this.primaryColor,{h:-60}),this.git5=this.pie6||g(this.primaryColor,{h:-90}),this.git6=this.pie7||g(this.primaryColor,{h:60}),this.git7=this.pie8||g(this.primaryColor,{h:120}),this.gitInv0=this.gitInv0||C(this.git0),this.gitInv1=this.gitInv1||C(this.git1),this.gitInv2=this.gitInv2||C(this.git2),this.gitInv3=this.gitInv3||C(this.git3),this.gitInv4=this.gitInv4||C(this.git4),this.gitInv5=this.gitInv5||C(this.git5),this.gitInv6=this.gitInv6||C(this.git6),this.gitInv7=this.gitInv7||C(this.git7),this.branchLabelColor=this.branchLabelColor||this.labelTextColor,this.gitBranchLabel0=this.branchLabelColor,this.gitBranchLabel1="white",this.gitBranchLabel2=this.branchLabelColor,this.gitBranchLabel3="white",this.gitBranchLabel4=this.branchLabelColor,this.gitBranchLabel5=this.branchLabelColor,this.gitBranchLabel6=this.branchLabelColor,this.gitBranchLabel7=this.branchLabelColor,this.tagLabelColor=this.tagLabelColor||this.primaryTextColor,this.tagLabelBackground=this.tagLabelBackground||this.primaryColor,this.tagLabelBorder=this.tagBorder||this.primaryBorderColor,this.tagLabelFontSize=this.tagLabelFontSize||"10px",this.commitLabelColor=this.commitLabelColor||this.secondaryTextColor,this.commitLabelBackground=this.commitLabelBackground||this.secondaryColor,this.commitLabelFontSize=this.commitLabelFontSize||"10px",this.attributeBackgroundColorOdd=this.attributeBackgroundColorOdd||Lr,this.attributeBackgroundColorEven=this.attributeBackgroundColorEven||Fr}calculate(e){if(typeof e!="object"){this.updateColors();return}const i=Object.keys(e);i.forEach(r=>{this[r]=e[r]}),this.updateColors(),i.forEach(r=>{this[r]=e[r]})}}const i0=t=>{const e=new e0;return e.calculate(t),e},Xt={base:{getThemeVariables:Gm},dark:{getThemeVariables:Km},default:{getThemeVariables:Jm},forest:{getThemeVariables:t0},neutral:{getThemeVariables:i0}},Vt={flowchart:{useMaxWidth:!0,titleTopMargin:25,subGraphTitleMargin:{top:0,bottom:0},diagramPadding:8,htmlLabels:!0,nodeSpacing:50,rankSpacing:50,curve:"basis",padding:15,defaultRenderer:"dagre-wrapper",wrappingWidth:200},sequence:{useMaxWidth:!0,hideUnusedParticipants:!1,activationWidth:10,diagramMarginX:50,diagramMarginY:10,actorMargin:50,width:150,height:65,boxMargin:10,boxTextMargin:5,noteMargin:10,messageMargin:35,messageAlign:"center",mirrorActors:!0,forceMenus:!1,bottomMarginAdj:1,rightAngles:!1,showSequenceNumbers:!1,actorFontSize:14,actorFontFamily:'"Open Sans", sans-serif',actorFontWeight:400,noteFontSize:14,noteFontFamily:'"trebuchet ms", verdana, arial, sans-serif',noteFontWeight:400,noteAlign:"center",messageFontSize:16,messageFontFamily:'"trebuchet ms", verdana, arial, sans-serif',messageFontWeight:400,wrap:!1,wrapPadding:10,labelBoxWidth:50,labelBoxHeight:20},gantt:{useMaxWidth:!0,titleTopMargin:25,barHeight:20,barGap:4,topPadding:50,rightPadding:75,leftPadding:75,gridLineStartPadding:35,fontSize:11,sectionFontSize:11,numberSectionStyles:4,axisFormat:"%Y-%m-%d",topAxis:!1,displayMode:"",weekday:"sunday"},journey:{useMaxWidth:!0,diagramMarginX:50,diagramMarginY:10,leftMargin:150,width:150,height:50,boxMargin:10,boxTextMargin:5,noteMargin:10,messageMargin:35,messageAlign:"center",bottomMarginAdj:1,rightAngles:!1,taskFontSize:14,taskFontFamily:'"Open Sans", sans-serif',taskMargin:50,activationWidth:10,textPlacement:"fo",actorColours:["#8FBC8F","#7CFC00","#00FFFF","#20B2AA","#B0E0E6","#FFFFE0"],sectionFills:["#191970","#8B008B","#4B0082","#2F4F4F","#800000","#8B4513","#00008B"],sectionColours:["#fff"]},class:{useMaxWidth:!0,titleTopMargin:25,arrowMarkerAbsolute:!1,dividerMargin:10,padding:5,textHeight:10,defaultRenderer:"dagre-wrapper",htmlLabels:!1},state:{useMaxWidth:!0,titleTopMargin:25,dividerMargin:10,sizeUnit:5,padding:8,textHeight:10,titleShift:-15,noteMargin:10,forkWidth:70,forkHeight:7,miniPadding:2,fontSizeFactor:5.02,fontSize:24,labelHeight:16,edgeLengthFactor:"20",compositTitleSize:35,radius:5,defaultRenderer:"dagre-wrapper"},er:{useMaxWidth:!0,titleTopMargin:25,diagramPadding:20,layoutDirection:"TB",minEntityWidth:100,minEntityHeight:75,entityPadding:15,stroke:"gray",fill:"honeydew",fontSize:12},pie:{useMaxWidth:!0,textPosition:.75},quadrantChart:{useMaxWidth:!0,chartWidth:500,chartHeight:500,titleFontSize:20,titlePadding:10,quadrantPadding:5,xAxisLabelPadding:5,yAxisLabelPadding:5,xAxisLabelFontSize:16,yAxisLabelFontSize:16,quadrantLabelFontSize:16,quadrantTextTopPadding:5,pointTextPadding:5,pointLabelFontSize:12,pointRadius:5,xAxisPosition:"top",yAxisPosition:"left",quadrantInternalBorderStrokeWidth:1,quadrantExternalBorderStrokeWidth:2},xyChart:{useMaxWidth:!0,width:700,height:500,titleFontSize:20,titlePadding:10,showTitle:!0,xAxis:{$ref:"#/$defs/XYChartAxisConfig",showLabel:!0,labelFontSize:14,labelPadding:5,showTitle:!0,titleFontSize:16,titlePadding:5,showTick:!0,tickLength:5,tickWidth:2,showAxisLine:!0,axisLineWidth:2},yAxis:{$ref:"#/$defs/XYChartAxisConfig",showLabel:!0,labelFontSize:14,labelPadding:5,showTitle:!0,titleFontSize:16,titlePadding:5,showTick:!0,tickLength:5,tickWidth:2,showAxisLine:!0,axisLineWidth:2},chartOrientation:"vertical",plotReservedSpacePercent:50},requirement:{useMaxWidth:!0,rect_fill:"#f9f9f9",text_color:"#333",rect_border_size:"0.5px",rect_border_color:"#bbb",rect_min_width:200,rect_min_height:200,fontSize:14,rect_padding:10,line_height:20},mindmap:{useMaxWidth:!0,padding:10,maxNodeWidth:200},timeline:{useMaxWidth:!0,diagramMarginX:50,diagramMarginY:10,leftMargin:150,width:150,height:50,boxMargin:10,boxTextMargin:5,noteMargin:10,messageMargin:35,messageAlign:"center",bottomMarginAdj:1,rightAngles:!1,taskFontSize:14,taskFontFamily:'"Open Sans", sans-serif',taskMargin:50,activationWidth:10,textPlacement:"fo",actorColours:["#8FBC8F","#7CFC00","#00FFFF","#20B2AA","#B0E0E6","#FFFFE0"],sectionFills:["#191970","#8B008B","#4B0082","#2F4F4F","#800000","#8B4513","#00008B"],sectionColours:["#fff"],disableMulticolor:!1},gitGraph:{useMaxWidth:!0,titleTopMargin:25,diagramPadding:8,nodeLabel:{width:75,height:100,x:-25,y:0},mainBranchName:"main",mainBranchOrder:0,showCommitLabel:!0,showBranches:!0,rotateCommitLabel:!0,parallelCommits:!1,arrowMarkerAbsolute:!1},c4:{useMaxWidth:!0,diagramMarginX:50,diagramMarginY:10,c4ShapeMargin:50,c4ShapePadding:20,width:216,height:60,boxMargin:10,c4ShapeInRow:4,nextLinePaddingX:0,c4BoundaryInRow:2,personFontSize:14,personFontFamily:'"Open Sans", sans-serif',personFontWeight:"normal",external_personFontSize:14,external_personFontFamily:'"Open Sans", sans-serif',external_personFontWeight:"normal",systemFontSize:14,systemFontFamily:'"Open Sans", sans-serif',systemFontWeight:"normal",external_systemFontSize:14,external_systemFontFamily:'"Open Sans", sans-serif',external_systemFontWeight:"normal",system_dbFontSize:14,system_dbFontFamily:'"Open Sans", sans-serif',system_dbFontWeight:"normal",external_system_dbFontSize:14,external_system_dbFontFamily:'"Open Sans", sans-serif',external_system_dbFontWeight:"normal",system_queueFontSize:14,system_queueFontFamily:'"Open Sans", sans-serif',system_queueFontWeight:"normal",external_system_queueFontSize:14,external_system_queueFontFamily:'"Open Sans", sans-serif',external_system_queueFontWeight:"normal",boundaryFontSize:14,boundaryFontFamily:'"Open Sans", sans-serif',boundaryFontWeight:"normal",messageFontSize:12,messageFontFamily:'"Open Sans", sans-serif',messageFontWeight:"normal",containerFontSize:14,containerFontFamily:'"Open Sans", sans-serif',containerFontWeight:"normal",external_containerFontSize:14,external_containerFontFamily:'"Open Sans", sans-serif',external_containerFontWeight:"normal",container_dbFontSize:14,container_dbFontFamily:'"Open Sans", sans-serif',container_dbFontWeight:"normal",external_container_dbFontSize:14,external_container_dbFontFamily:'"Open Sans", sans-serif',external_container_dbFontWeight:"normal",container_queueFontSize:14,container_queueFontFamily:'"Open Sans", sans-serif',container_queueFontWeight:"normal",external_container_queueFontSize:14,external_container_queueFontFamily:'"Open Sans", sans-serif',external_container_queueFontWeight:"normal",componentFontSize:14,componentFontFamily:'"Open Sans", sans-serif',componentFontWeight:"normal",external_componentFontSize:14,external_componentFontFamily:'"Open Sans", sans-serif',external_componentFontWeight:"normal",component_dbFontSize:14,component_dbFontFamily:'"Open Sans", sans-serif',component_dbFontWeight:"normal",external_component_dbFontSize:14,external_component_dbFontFamily:'"Open Sans", sans-serif',external_component_dbFontWeight:"normal",component_queueFontSize:14,component_queueFontFamily:'"Open Sans", sans-serif',component_queueFontWeight:"normal",external_component_queueFontSize:14,external_component_queueFontFamily:'"Open Sans", sans-serif',external_component_queueFontWeight:"normal",wrap:!0,wrapPadding:10,person_bg_color:"#08427B",person_border_color:"#073B6F",external_person_bg_color:"#686868",external_person_border_color:"#8A8A8A",system_bg_color:"#1168BD",system_border_color:"#3C7FC0",system_db_bg_color:"#1168BD",system_db_border_color:"#3C7FC0",system_queue_bg_color:"#1168BD",system_queue_border_color:"#3C7FC0",external_system_bg_color:"#999999",external_system_border_color:"#8A8A8A",external_system_db_bg_color:"#999999",external_system_db_border_color:"#8A8A8A",external_system_queue_bg_color:"#999999",external_system_queue_border_color:"#8A8A8A",container_bg_color:"#438DD5",container_border_color:"#3C7FC0",container_db_bg_color:"#438DD5",container_db_border_color:"#3C7FC0",container_queue_bg_color:"#438DD5",container_queue_border_color:"#3C7FC0",external_container_bg_color:"#B3B3B3",external_container_border_color:"#A6A6A6",external_container_db_bg_color:"#B3B3B3",external_container_db_border_color:"#A6A6A6",external_container_queue_bg_color:"#B3B3B3",external_container_queue_border_color:"#A6A6A6",component_bg_color:"#85BBF0",component_border_color:"#78A8D8",component_db_bg_color:"#85BBF0",component_db_border_color:"#78A8D8",component_queue_bg_color:"#85BBF0",component_queue_border_color:"#78A8D8",external_component_bg_color:"#CCCCCC",external_component_border_color:"#BFBFBF",external_component_db_bg_color:"#CCCCCC",external_component_db_border_color:"#BFBFBF",external_component_queue_bg_color:"#CCCCCC",external_component_queue_border_color:"#BFBFBF"},sankey:{useMaxWidth:!0,width:600,height:400,linkColor:"gradient",nodeAlignment:"justify",showValues:!0,prefix:"",suffix:""},block:{useMaxWidth:!0,padding:8},theme:"default",maxTextSize:5e4,maxEdges:500,darkMode:!1,fontFamily:'"trebuchet ms", verdana, arial, sans-serif;',logLevel:5,securityLevel:"strict",startOnLoad:!0,arrowMarkerAbsolute:!1,secure:["secure","securityLevel","startOnLoad","maxTextSize","maxEdges"],legacyMathML:!1,deterministicIds:!1,fontSize:16},nl={...Vt,deterministicIDSeed:void 0,themeCSS:void 0,themeVariables:Xt.default.getThemeVariables(),sequence:{...Vt.sequence,messageFont:function(){return{fontFamily:this.messageFontFamily,fontSize:this.messageFontSize,fontWeight:this.messageFontWeight}},noteFont:function(){return{fontFamily:this.noteFontFamily,fontSize:this.noteFontSize,fontWeight:this.noteFontWeight}},actorFont:function(){return{fontFamily:this.actorFontFamily,fontSize:this.actorFontSize,fontWeight:this.actorFontWeight}}},gantt:{...Vt.gantt,tickInterval:void 0,useWidth:void 0},c4:{...Vt.c4,useWidth:void 0,personFont:function(){return{fontFamily:this.personFontFamily,fontSize:this.personFontSize,fontWeight:this.personFontWeight}},external_personFont:function(){return{fontFamily:this.external_personFontFamily,fontSize:this.external_personFontSize,fontWeight:this.external_personFontWeight}},systemFont:function(){return{fontFamily:this.systemFontFamily,fontSize:this.systemFontSize,fontWeight:this.systemFontWeight}},external_systemFont:function(){return{fontFamily:this.external_systemFontFamily,fontSize:this.external_systemFontSize,fontWeight:this.external_systemFontWeight}},system_dbFont:function(){return{fontFamily:this.system_dbFontFamily,fontSize:this.system_dbFontSize,fontWeight:this.system_dbFontWeight}},external_system_dbFont:function(){return{fontFamily:this.external_system_dbFontFamily,fontSize:this.external_system_dbFontSize,fontWeight:this.external_system_dbFontWeight}},system_queueFont:function(){return{fontFamily:this.system_queueFontFamily,fontSize:this.system_queueFontSize,fontWeight:this.system_queueFontWeight}},external_system_queueFont:function(){return{fontFamily:this.external_system_queueFontFamily,fontSize:this.external_system_queueFontSize,fontWeight:this.external_system_queueFontWeight}},containerFont:function(){return{fontFamily:this.containerFontFamily,fontSize:this.containerFontSize,fontWeight:this.containerFontWeight}},external_containerFont:function(){return{fontFamily:this.external_containerFontFamily,fontSize:this.external_containerFontSize,fontWeight:this.external_containerFontWeight}},container_dbFont:function(){return{fontFamily:this.container_dbFontFamily,fontSize:this.container_dbFontSize,fontWeight:this.container_dbFontWeight}},external_container_dbFont:function(){return{fontFamily:this.external_container_dbFontFamily,fontSize:this.external_container_dbFontSize,fontWeight:this.external_container_dbFontWeight}},container_queueFont:function(){return{fontFamily:this.container_queueFontFamily,fontSize:this.container_queueFontSize,fontWeight:this.container_queueFontWeight}},external_container_queueFont:function(){return{fontFamily:this.external_container_queueFontFamily,fontSize:this.external_container_queueFontSize,fontWeight:this.external_container_queueFontWeight}},componentFont:function(){return{fontFamily:this.componentFontFamily,fontSize:this.componentFontSize,fontWeight:this.componentFontWeight}},external_componentFont:function(){return{fontFamily:this.external_componentFontFamily,fontSize:this.external_componentFontSize,fontWeight:this.external_componentFontWeight}},component_dbFont:function(){return{fontFamily:this.component_dbFontFamily,fontSize:this.component_dbFontSize,fontWeight:this.component_dbFontWeight}},external_component_dbFont:function(){return{fontFamily:this.external_component_dbFontFamily,fontSize:this.external_component_dbFontSize,fontWeight:this.external_component_dbFontWeight}},component_queueFont:function(){return{fontFamily:this.component_queueFontFamily,fontSize:this.component_queueFontSize,fontWeight:this.component_queueFontWeight}},external_component_queueFont:function(){return{fontFamily:this.external_component_queueFontFamily,fontSize:this.external_component_queueFontSize,fontWeight:this.external_component_queueFontWeight}},boundaryFont:function(){return{fontFamily:this.boundaryFontFamily,fontSize:this.boundaryFontSize,fontWeight:this.boundaryFontWeight}},messageFont:function(){return{fontFamily:this.messageFontFamily,fontSize:this.messageFontSize,fontWeight:this.messageFontWeight}}},pie:{...Vt.pie,useWidth:984},xyChart:{...Vt.xyChart,useWidth:void 0},requirement:{...Vt.requirement,useWidth:void 0},gitGraph:{...Vt.gitGraph,useMaxWidth:!1},sankey:{...Vt.sankey,useMaxWidth:!1}},ol=(t,e="")=>Object.keys(t).reduce((i,r)=>Array.isArray(t[r])?i:typeof t[r]=="object"&&t[r]!==null?[...i,e+r,...ol(t[r],"")]:[...i,e+r],[]),r0=new Set(ol(nl,"")),n0=nl,ar=t=>{if(E.debug("sanitizeDirective called with",t),!(typeof t!="object"||t==null)){if(Array.isArray(t)){t.forEach(e=>ar(e));return}for(const e of Object.keys(t)){if(E.debug("Checking key",e),e.startsWith("__")||e.includes("proto")||e.includes("constr")||!r0.has(e)||t[e]==null){E.debug("sanitize deleting key: ",e),delete t[e];continue}if(typeof t[e]=="object"){E.debug("sanitizing object",e),ar(t[e]);continue}const i=["themeCSS","fontFamily","altFontFamily"];for(const r of i)e.includes(r)&&(E.debug("sanitizing css option",e),t[e]=o0(t[e]))}if(t.themeVariables)for(const e of Object.keys(t.themeVariables)){const i=t.themeVariables[e];i!=null&&i.match&&!i.match(/^[\d "#%(),.;A-Za-z]+$/)&&(t.themeVariables[e]="")}E.debug("After sanitization",t)}},o0=t=>{let e=0,i=0;for(const r of t){if(e<i)return"{ /* ERROR: Unbalanced CSS */ }";r==="{"?e++:r==="}"&&i++}return e!==i?"{ /* ERROR: Unbalanced CSS */ }":t},sl=/^-{3}\s*[\n\r](.*?)[\n\r]-{3}\s*[\n\r]+/s,li=/%{2}{\s*(?:(\w+)\s*:|(\w+))\s*(?:(\w+)|((?:(?!}%{2}).|\r?\n)*))?\s*(?:}%{2})?/gi,s0=/\s*%%.*\n/gm;class al extends Error{constructor(e){super(e),this.name="UnknownDiagramError"}}const Re={},Er=function(t,e){t=t.replace(sl,"").replace(li,"").replace(s0,`
 `);for(const[i,{detector:r}]of Object.entries(Re))if(r(t,e))return i;throw new al(`No diagram type detected matching given configuration for text: ${t}`)},ll=(...t)=>{for(const{id:e,detector:i,loader:r}of t)hl(e,i,r)},hl=(t,e,i)=>{Re[t]?E.error(`Detector with key ${t} already exists`):Re[t]={detector:e,loader:i},E.debug(`Detector with key ${t} added${i?" with loader":""}`)},a0=t=>Re[t].loader,vn=(t,e,{depth:i=2,clobber:r=!1}={})=>{const n={depth:i,clobber:r};return Array.isArray(e)&&!Array.isArray(t)?(e.forEach(o=>vn(t,o,n)),t):Array.isArray(e)&&Array.isArray(t)?(e.forEach(o=>{t.includes(o)||t.push(o)}),t):t===void 0||i<=0?t!=null&&typeof t=="object"&&typeof e=="object"?Object.assign(t,e):e:(e!==void 0&&typeof t=="object"&&typeof e=="object"&&Object.keys(e).forEach(o=>{typeof e[o]=="object"&&(t[o]===void 0||typeof t[o]=="object")?(t[o]===void 0&&(t[o]=Array.isArray(e[o])?[]:{}),t[o]=vn(t[o],e[o],{depth:i-1,clobber:r})):(r||typeof t[o]!="object"&&typeof e[o]!="object")&&(t[o]=e[o])}),t)},st=vn,l0="​",h0={curveBasis:zf,curveBasisClosed:Wf,curveBasisOpen:Hf,curveBumpX:Pf,curveBumpY:qf,curveBundle:jf,curveCardinalClosed:Yf,curveCardinalOpen:Vf,curveCardinal:Uf,curveCatmullRomClosed:Xf,curveCatmullRomOpen:Kf,curveCatmullRom:Gf,curveLinear:Rf,curveLinearClosed:Zf,curveMonotoneX:Jf,curveMonotoneY:Qf,curveNatural:td,curveStep:ed,curveStepAfter:rd,curveStepBefore:id},c0=/\s*(?:(\w+)(?=:):|(\w+))\s*(?:(\w+)|((?:(?!}%{2}).|\r?\n)*))?\s*(?:}%{2})?/gi,u0=function(t,e){const i=cl(t,/(?:init\b)|(?:initialize\b)/);let r={};if(Array.isArray(i)){const s=i.map(a=>a.args);ar(s),r=st(r,[...s])}else r=i.args;if(!r)return;let n=Er(t,e);const o="config";return r[o]!==void 0&&(n==="flowchart-v2"&&(n="flowchart"),r[n]=r[o],delete r[o]),r},cl=function(t,e=null){try{const i=new RegExp(`[%]{2}(?![{]${c0.source})(?=[}][%]{2}).*
-`,"ig");t=t.trim().replace(i,"").replace(/'/gm,'"'),E.debug(`Detecting diagram directive${e!==null?" type:"+e:""} based on the text:${t}`);let r;const n=[];for(;(r=li.exec(t))!==null;)if(r.index===li.lastIndex&&li.lastIndex++,r&&!e||e&&r[1]&&r[1].match(e)||e&&r[2]&&r[2].match(e)){const o=r[1]?r[1]:r[2],s=r[3]?r[3].trim():r[4]?JSON.parse(r[4].trim()):null;n.push({type:o,args:s})}return n.length===0?{type:t,args:null}:n.length===1?n[0]:n}catch(i){return E.error(`ERROR: ${i.message} - Unable to parse directive type: '${e}' based on the text: '${t}'`),{type:void 0,args:null}}},f0=function(t){return t.replace(li,"")},d0=function(t,e){for(const[i,r]of e.entries())if(r.match(t))return i;return-1};function p0(t,e){if(!t)return e;const i=`curve${t.charAt(0).toUpperCase()+t.slice(1)}`;return h0[i]??e}function g0(t,e){const i=t.trim();if(i)return e.securityLevel!=="loose"?Hs.sanitizeUrl(i):i}const m0=(t,...e)=>{const i=t.split("."),r=i.length-1,n=i[r];let o=window;for(let s=0;s<r;s++)if(o=o[i[s]],!o){E.error(`Function name: ${t} not found in window`);return}o[n](...e)};function ul(t,e){return!t||!e?0:Math.sqrt(Math.pow(e.x-t.x,2)+Math.pow(e.y-t.y,2))}function _0(t){let e,i=0;t.forEach(n=>{i+=ul(n,e),e=n});const r=i/2;return Un(t,r)}function y0(t){return t.length===1?t[0]:_0(t)}const ws=(t,e=2)=>{const i=Math.pow(10,e);return Math.round(t*i)/i},Un=(t,e)=>{let i,r=e;for(const n of t){if(i){const o=ul(n,i);if(o<r)r-=o;else{const s=r/o;if(s<=0)return i;if(s>=1)return{x:n.x,y:n.y};if(s>0&&s<1)return{x:ws((1-s)*i.x+s*n.x,5),y:ws((1-s)*i.y+s*n.y,5)}}}i=n}throw new Error("Could not find a suitable point for the given distance")},C0=(t,e,i)=>{E.info(`our points ${JSON.stringify(e)}`),e[0]!==i&&(e=e.reverse());const n=Un(e,25),o=t?10:5,s=Math.atan2(e[0].y-n.y,e[0].x-n.x),a={x:0,y:0};return a.x=Math.sin(s)*o+(e[0].x+n.x)/2,a.y=-Math.cos(s)*o+(e[0].y+n.y)/2,a};function x0(t,e,i){const r=structuredClone(i);E.info("our points",r),e!=="start_left"&&e!=="start_right"&&r.reverse();const n=25+t,o=Un(r,n),s=10+t*.5,a=Math.atan2(r[0].y-o.y,r[0].x-o.x),l={x:0,y:0};return e==="start_left"?(l.x=Math.sin(a+Math.PI)*s+(r[0].x+o.x)/2,l.y=-Math.cos(a+Math.PI)*s+(r[0].y+o.y)/2):e==="end_right"?(l.x=Math.sin(a-Math.PI)*s+(r[0].x+o.x)/2-5,l.y=-Math.cos(a-Math.PI)*s+(r[0].y+o.y)/2-5):e==="end_left"?(l.x=Math.sin(a)*s+(r[0].x+o.x)/2-5,l.y=-Math.cos(a)*s+(r[0].y+o.y)/2-5):(l.x=Math.sin(a)*s+(r[0].x+o.x)/2,l.y=-Math.cos(a)*s+(r[0].y+o.y)/2),l}function b0(t){let e="",i="";for(const r of t)r!==void 0&&(r.startsWith("color:")||r.startsWith("text-align:")?i=i+r+";":e=e+r+";");return{style:e,labelStyle:i}}let Bs=0;const T0=()=>(Bs++,"id-"+Math.random().toString(36).substr(2,12)+"-"+Bs);function v0(t){let e="";const i="0123456789abcdef",r=i.length;for(let n=0;n<t;n++)e+=i.charAt(Math.floor(Math.random()*r));return e}const k0=t=>v0(t.length),S0=function(){return{x:0,y:0,fill:void 0,anchor:"start",style:"#666",width:100,height:100,textMargin:0,rx:0,ry:0,valign:void 0,text:""}},w0=function(t,e){const i=e.text.replace(jn.lineBreakRegex," "),[,r]=Vn(e.fontSize),n=t.append("text");n.attr("x",e.x),n.attr("y",e.y),n.style("text-anchor",e.anchor),n.style("font-family",e.fontFamily),n.style("font-size",r),n.style("font-weight",e.fontWeight),n.attr("fill",e.fill),e.class!==void 0&&n.attr("class",e.class);const o=n.append("tspan");return o.attr("x",e.x+e.textMargin*2),o.attr("fill",e.fill),o.text(i),n},B0=ki((t,e,i)=>{if(!t||(i=Object.assign({fontSize:12,fontWeight:400,fontFamily:"Arial",joinWith:"<br/>"},i),jn.lineBreakRegex.test(t)))return t;const r=t.split(" "),n=[];let o="";return r.forEach((s,a)=>{const l=lr(`${s} `,i),h=lr(o,i);if(l>e){const{hyphenatedStrings:c,remainingWord:p}=A0(s,e,"-",i);n.push(o,...c),o=p}else h+l>=e?(n.push(o),o=s):o=[o,s].filter(Boolean).join(" ");a+1===r.length&&n.push(o)}),n.filter(s=>s!=="").join(i.joinWith)},(t,e,i)=>`${t}${e}${i.fontSize}${i.fontWeight}${i.fontFamily}${i.joinWith}`),A0=ki((t,e,i="-",r)=>{r=Object.assign({fontSize:12,fontWeight:400,fontFamily:"Arial",margin:0},r);const n=[...t],o=[];let s="";return n.forEach((a,l)=>{const h=`${s}${a}`;if(lr(h,r)>=e){const f=l+1,c=n.length===f,p=`${h}${i}`;o.push(c?h:p),s=""}else s=h}),{hyphenatedStrings:o,remainingWord:s}},(t,e,i="-",r)=>`${t}${e}${i}${r.fontSize}${r.fontWeight}${r.fontFamily}`);function L0(t,e){return Yn(t,e).height}function lr(t,e){return Yn(t,e).width}const Yn=ki((t,e)=>{const{fontSize:i=12,fontFamily:r="Arial",fontWeight:n=400}=e;if(!t)return{width:0,height:0};const[,o]=Vn(i),s=["sans-serif",r],a=t.split(jn.lineBreakRegex),l=[],h=Tt("body");if(!h.remove)return{width:0,height:0,lineHeight:0};const u=h.append("svg");for(const c of s){let p=0;const _={width:0,height:0,lineHeight:0};for(const b of a){const k=S0();k.text=b||l0;const P=w0(u,k).style("font-size",o).style("font-weight",n).style("font-family",c),v=(P._groups||P)[0][0].getBBox();if(v.width===0&&v.height===0)throw new Error("svg element not in render tree");_.width=Math.round(Math.max(_.width,v.width)),p=Math.round(v.height),_.height+=p,_.lineHeight=Math.round(Math.max(_.lineHeight,p))}l.push(_)}u.remove();const f=isNaN(l[1].height)||isNaN(l[1].width)||isNaN(l[1].lineHeight)||l[0].height>l[1].height&&l[0].width>l[1].width&&l[0].lineHeight>l[1].lineHeight?0:1;return l[f]},(t,e)=>`${t}${e.fontSize}${e.fontWeight}${e.fontFamily}`);class F0{constructor(e=!1,i){this.count=0,this.count=i?i.length:0,this.next=e?()=>this.count++:()=>Date.now()}}let Ri;const E0=function(t){return Ri=Ri||document.createElement("div"),t=escape(t).replace(/%26/g,"&").replace(/%23/g,"#").replace(/%3B/g,";"),Ri.innerHTML=t,unescape(Ri.textContent)};function fl(t){return"str"in t}const O0=(t,e,i,r)=>{var n;if(!r)return;const o=(n=t.node())==null?void 0:n.getBBox();o&&t.append("text").text(r).attr("x",o.x+o.width/2).attr("y",-i).attr("class",e)},Vn=t=>{if(typeof t=="number")return[t,t+"px"];const e=parseInt(t??"",10);return Number.isNaN(e)?[void 0,void 0]:t===String(e)?[e,t+"px"]:[e,t]};function dl(t,e){return rm({},t,e)}const hi={assignWithDepth:st,wrapLabel:B0,calculateTextHeight:L0,calculateTextWidth:lr,calculateTextDimensions:Yn,cleanAndMerge:dl,detectInit:u0,detectDirective:cl,isSubstringInArray:d0,interpolateToCurve:p0,calcLabelPosition:y0,calcCardinalityPosition:C0,calcTerminalLabelPosition:x0,formatUrl:g0,getStylesFromArray:b0,generateId:T0,random:k0,runFunc:m0,entityDecode:E0,insertTitle:O0,parseFontSize:Vn,InitIDGenerator:F0},M0=function(t){let e=t;return e=e.replace(/style.*:\S*#.*;/g,function(i){return i.substring(0,i.length-1)}),e=e.replace(/classDef.*:\S*#.*;/g,function(i){return i.substring(0,i.length-1)}),e=e.replace(/#\w+;/g,function(i){const r=i.substring(1,i.length-1);return/^\+?\d+$/.test(r)?"fl°°"+r+"¶ß":"fl°"+r+"¶ß"}),e},I0=function(t){return t.replace(/fl°°/g,"&#").replace(/fl°/g,"&").replace(/¶ß/g,";")},As="10.9.2",Pe=Object.freeze(n0);let pt=st({},Pe),pl,qe=[],ci=st({},Pe);const Or=(t,e)=>{let i=st({},t),r={};for(const n of e)_l(n),r=st(r,n);if(i=st(i,r),r.theme&&r.theme in Xt){const n=st({},pl),o=st(n.themeVariables||{},r.themeVariables);i.theme&&i.theme in Xt&&(i.themeVariables=Xt[i.theme].getThemeVariables(o))}return ci=i,yl(ci),ci},$0=t=>(pt=st({},Pe),pt=st(pt,t),t.theme&&Xt[t.theme]&&(pt.themeVariables=Xt[t.theme].getThemeVariables(t.themeVariables)),Or(pt,qe),pt),D0=t=>{pl=st({},t)},N0=t=>(pt=st(pt,t),Or(pt,qe),pt),gl=()=>st({},pt),ml=t=>(yl(t),st(ci,t),qt()),qt=()=>st({},ci),_l=t=>{t&&(["secure",...pt.secure??[]].forEach(e=>{Object.hasOwn(t,e)&&(E.debug(`Denied attempt to modify a secure key ${e}`,t[e]),delete t[e])}),Object.keys(t).forEach(e=>{e.startsWith("__")&&delete t[e]}),Object.keys(t).forEach(e=>{typeof t[e]=="string"&&(t[e].includes("<")||t[e].includes(">")||t[e].includes("url(data:"))&&delete t[e],typeof t[e]=="object"&&_l(t[e])}))},R0=t=>{ar(t),t.fontFamily&&(!t.themeVariables||!t.themeVariables.fontFamily)&&(t.themeVariables={fontFamily:t.fontFamily}),qe.push(t),Or(pt,qe)},hr=(t=pt)=>{qe=[],Or(t,qe)},P0={LAZY_LOAD_DEPRECATED:"The configuration options lazyLoadedDiagrams and loadExternalDiagramsAtStartup are deprecated. Please use registerExternalDiagrams instead."},Ls={},q0=t=>{Ls[t]||(E.warn(P0[t]),Ls[t]=!0)},yl=t=>{t&&(t.lazyLoadedDiagrams||t.loadExternalDiagramsAtStartup)&&q0("LAZY_LOAD_DEPRECATED")},Cl="c4",z0=t=>/^\s*C4Context|C4Container|C4Component|C4Dynamic|C4Deployment/.test(t),W0=async()=>{const{diagram:t}=await K(()=>import("./c4Diagram-dc8f04df-CiA8sQW3.js"),__vite__mapDeps([0,1,2]));return{id:Cl,diagram:t}},H0={id:Cl,detector:z0,loader:W0},j0=H0,xl="flowchart",U0=(t,e)=>{var i,r;return((i=e==null?void 0:e.flowchart)==null?void 0:i.defaultRenderer)==="dagre-wrapper"||((r=e==null?void 0:e.flowchart)==null?void 0:r.defaultRenderer)==="elk"?!1:/^\s*graph/.test(t)},Y0=async()=>{const{diagram:t}=await K(()=>import("./flowDiagram-622f9fc1-C8iBq7aS.js"),__vite__mapDeps([3,4,5,6,7,8,9,10,11,12,13,14,15,2]));return{id:xl,diagram:t}},V0={id:xl,detector:U0,loader:Y0},G0=V0,bl="flowchart-v2",X0=(t,e)=>{var i,r,n;return((i=e==null?void 0:e.flowchart)==null?void 0:i.defaultRenderer)==="dagre-d3"||((r=e==null?void 0:e.flowchart)==null?void 0:r.defaultRenderer)==="elk"?!1:/^\s*graph/.test(t)&&((n=e==null?void 0:e.flowchart)==null?void 0:n.defaultRenderer)==="dagre-wrapper"?!0:/^\s*flowchart/.test(t)},K0=async()=>{const{diagram:t}=await K(()=>import("./flowDiagram-v2-a33b4996-BVubizbB.js"),__vite__mapDeps([16,4,7,5,8,6,9,10,11,12,13,14,15,2]));return{id:bl,diagram:t}},Z0={id:bl,detector:X0,loader:K0},J0=Z0,Tl="er",Q0=t=>/^\s*erDiagram/.test(t),t_=async()=>{const{diagram:t}=await K(()=>import("./erDiagram-51d2b61e-BxYe-GEp.js"),__vite__mapDeps([17,5,6,12,13,14,2]));return{id:Tl,diagram:t}},e_={id:Tl,detector:Q0,loader:t_},i_=e_,vl="gitGraph",r_=t=>/^\s*gitGraph/.test(t),n_=async()=>{const{diagram:t}=await K(()=>import("./gitGraphDiagram-23af1bdb-BuC3CTB9.js"),__vite__mapDeps([18,2]));return{id:vl,diagram:t}},o_={id:vl,detector:r_,loader:n_},s_=o_,kl="gantt",a_=t=>/^\s*gantt/.test(t),l_=async()=>{const{diagram:t}=await K(()=>import("./ganttDiagram-a649f789-B8bnTgqC.js"),__vite__mapDeps([19,20,21,2]));return{id:kl,diagram:t}},h_={id:kl,detector:a_,loader:l_},c_=h_,Sl="info",u_=t=>/^\s*info/.test(t),f_=async()=>{const{diagram:t}=await K(()=>import("./infoDiagram-f86e0131-BJ_tgdHe.js"),__vite__mapDeps([22,2]));return{id:Sl,diagram:t}},d_={id:Sl,detector:u_,loader:f_},wl="pie",p_=t=>/^\s*pie/.test(t),g_=async()=>{const{diagram:t}=await K(()=>import("./pieDiagram-31d824a1-CV6f6fQ6.js"),__vite__mapDeps([23,24,14,25,21,13,2]));return{id:wl,diagram:t}},m_={id:wl,detector:p_,loader:g_},Bl="quadrantChart",__=t=>/^\s*quadrantChart/.test(t),y_=async()=>{const{diagram:t}=await K(()=>import("./quadrantDiagram-a712a7d9-Bu83u7Zz.js"),__vite__mapDeps([26,20,21,2]));return{id:Bl,diagram:t}},C_={id:Bl,detector:__,loader:y_},x_=C_,Al="xychart",b_=t=>/^\s*xychart-beta/.test(t),T_=async()=>{const{diagram:t}=await K(()=>import("./xychartDiagram-4a8b8217-CYu3f7i9.js"),__vite__mapDeps([27,11,21,25,20,12,13,14,2]));return{id:Al,diagram:t}},v_={id:Al,detector:b_,loader:T_},k_=v_,Ll="requirement",S_=t=>/^\s*requirement(Diagram)?/.test(t),w_=async()=>{const{diagram:t}=await K(()=>import("./requirementDiagram-eb878fee-DPiNb9b5.js"),__vite__mapDeps([28,5,6,12,13,14,2]));return{id:Ll,diagram:t}},B_={id:Ll,detector:S_,loader:w_},A_=B_,Fl="sequence",L_=t=>/^\s*sequenceDiagram/.test(t),F_=async()=>{const{diagram:t}=await K(()=>import("./sequenceDiagram-66748113-MIUFy2Oj.js"),__vite__mapDeps([29,1,2]));return{id:Fl,diagram:t}},E_={id:Fl,detector:L_,loader:F_},O_=E_,El="class",M_=(t,e)=>{var i;return((i=e==null?void 0:e.class)==null?void 0:i.defaultRenderer)==="dagre-wrapper"?!1:/^\s*classDiagram/.test(t)},I_=async()=>{const{diagram:t}=await K(()=>import("./classDiagram-8298e144-w121JOWu.js"),__vite__mapDeps([30,31,5,6,12,13,14,2]));return{id:El,diagram:t}},$_={id:El,detector:M_,loader:I_},D_=$_,Ol="classDiagram",N_=(t,e)=>{var i;return/^\s*classDiagram/.test(t)&&((i=e==null?void 0:e.class)==null?void 0:i.defaultRenderer)==="dagre-wrapper"?!0:/^\s*classDiagram-v2/.test(t)},R_=async()=>{const{diagram:t}=await K(()=>import("./classDiagram-v2-296fb1cd-BmyNy9b3.js"),__vite__mapDeps([32,31,5,8,6,9,10,11,12,13,14,2]));return{id:Ol,diagram:t}},P_={id:Ol,detector:N_,loader:R_},q_=P_,Ml="state",z_=(t,e)=>{var i;return((i=e==null?void 0:e.state)==null?void 0:i.defaultRenderer)==="dagre-wrapper"?!1:/^\s*stateDiagram/.test(t)},W_=async()=>{const{diagram:t}=await K(()=>import("./stateDiagram-35d39939-BlCBJSJX.js"),__vite__mapDeps([33,34,5,6,12,13,14,2]));return{id:Ml,diagram:t}},H_={id:Ml,detector:z_,loader:W_},j_=H_,Il="stateDiagram",U_=(t,e)=>{var i;return!!(/^\s*stateDiagram-v2/.test(t)||/^\s*stateDiagram/.test(t)&&((i=e==null?void 0:e.state)==null?void 0:i.defaultRenderer)==="dagre-wrapper")},Y_=async()=>{const{diagram:t}=await K(()=>import("./stateDiagram-v2-6c43c13a-CtOdsXqX.js"),__vite__mapDeps([35,34,5,8,6,9,10,11,12,13,14,2]));return{id:Il,diagram:t}},V_={id:Il,detector:U_,loader:Y_},G_=V_,$l="journey",X_=t=>/^\s*journey/.test(t),K_=async()=>{const{diagram:t}=await K(()=>import("./journeyDiagram-de0d04b7-DXj0d_vq.js"),__vite__mapDeps([36,1,24,14,2]));return{id:$l,diagram:t}},Z_={id:$l,detector:X_,loader:K_},J_=Z_,Q_=function(t,e){for(let i of e)t.attr(i[0],i[1])},ty=function(t,e,i){let r=new Map;return i?(r.set("width","100%"),r.set("style",`max-width: ${e}px;`)):(r.set("height",t),r.set("width",e)),r},Dl=function(t,e,i,r){const n=ty(e,i,r);Q_(t,n)},ey=function(t,e,i,r){const n=e.node().getBBox(),o=n.width,s=n.height;E.info(`SVG bounds: ${o}x${s}`,n);let a=0,l=0;E.info(`Graph bounds: ${a}x${l}`,t),a=o+i*2,l=s+i*2,E.info(`Calculated bounds: ${a}x${l}`),Dl(e,l,a,r);const h=`${n.x-i} ${n.y-i} ${n.width+2*i} ${n.height+2*i}`;e.attr("viewBox",h)},Vi={},iy=(t,e,i)=>{let r="";return t in Vi&&Vi[t]?r=Vi[t](i):E.warn(`No theme found for ${t}`),` & {
+`,"ig");t=t.trim().replace(i,"").replace(/'/gm,'"'),E.debug(`Detecting diagram directive${e!==null?" type:"+e:""} based on the text:${t}`);let r;const n=[];for(;(r=li.exec(t))!==null;)if(r.index===li.lastIndex&&li.lastIndex++,r&&!e||e&&r[1]&&r[1].match(e)||e&&r[2]&&r[2].match(e)){const o=r[1]?r[1]:r[2],s=r[3]?r[3].trim():r[4]?JSON.parse(r[4].trim()):null;n.push({type:o,args:s})}return n.length===0?{type:t,args:null}:n.length===1?n[0]:n}catch(i){return E.error(`ERROR: ${i.message} - Unable to parse directive type: '${e}' based on the text: '${t}'`),{type:void 0,args:null}}},f0=function(t){return t.replace(li,"")},d0=function(t,e){for(const[i,r]of e.entries())if(r.match(t))return i;return-1};function p0(t,e){if(!t)return e;const i=`curve${t.charAt(0).toUpperCase()+t.slice(1)}`;return h0[i]??e}function g0(t,e){const i=t.trim();if(i)return e.securityLevel!=="loose"?Hs.sanitizeUrl(i):i}const m0=(t,...e)=>{const i=t.split("."),r=i.length-1,n=i[r];let o=window;for(let s=0;s<r;s++)if(o=o[i[s]],!o){E.error(`Function name: ${t} not found in window`);return}o[n](...e)};function ul(t,e){return!t||!e?0:Math.sqrt(Math.pow(e.x-t.x,2)+Math.pow(e.y-t.y,2))}function _0(t){let e,i=0;t.forEach(n=>{i+=ul(n,e),e=n});const r=i/2;return Un(t,r)}function y0(t){return t.length===1?t[0]:_0(t)}const ws=(t,e=2)=>{const i=Math.pow(10,e);return Math.round(t*i)/i},Un=(t,e)=>{let i,r=e;for(const n of t){if(i){const o=ul(n,i);if(o<r)r-=o;else{const s=r/o;if(s<=0)return i;if(s>=1)return{x:n.x,y:n.y};if(s>0&&s<1)return{x:ws((1-s)*i.x+s*n.x,5),y:ws((1-s)*i.y+s*n.y,5)}}}i=n}throw new Error("Could not find a suitable point for the given distance")},C0=(t,e,i)=>{E.info(`our points ${JSON.stringify(e)}`),e[0]!==i&&(e=e.reverse());const n=Un(e,25),o=t?10:5,s=Math.atan2(e[0].y-n.y,e[0].x-n.x),a={x:0,y:0};return a.x=Math.sin(s)*o+(e[0].x+n.x)/2,a.y=-Math.cos(s)*o+(e[0].y+n.y)/2,a};function x0(t,e,i){const r=structuredClone(i);E.info("our points",r),e!=="start_left"&&e!=="start_right"&&r.reverse();const n=25+t,o=Un(r,n),s=10+t*.5,a=Math.atan2(r[0].y-o.y,r[0].x-o.x),l={x:0,y:0};return e==="start_left"?(l.x=Math.sin(a+Math.PI)*s+(r[0].x+o.x)/2,l.y=-Math.cos(a+Math.PI)*s+(r[0].y+o.y)/2):e==="end_right"?(l.x=Math.sin(a-Math.PI)*s+(r[0].x+o.x)/2-5,l.y=-Math.cos(a-Math.PI)*s+(r[0].y+o.y)/2-5):e==="end_left"?(l.x=Math.sin(a)*s+(r[0].x+o.x)/2-5,l.y=-Math.cos(a)*s+(r[0].y+o.y)/2-5):(l.x=Math.sin(a)*s+(r[0].x+o.x)/2,l.y=-Math.cos(a)*s+(r[0].y+o.y)/2),l}function b0(t){let e="",i="";for(const r of t)r!==void 0&&(r.startsWith("color:")||r.startsWith("text-align:")?i=i+r+";":e=e+r+";");return{style:e,labelStyle:i}}let Bs=0;const T0=()=>(Bs++,"id-"+Math.random().toString(36).substr(2,12)+"-"+Bs);function v0(t){let e="";const i="0123456789abcdef",r=i.length;for(let n=0;n<t;n++)e+=i.charAt(Math.floor(Math.random()*r));return e}const k0=t=>v0(t.length),S0=function(){return{x:0,y:0,fill:void 0,anchor:"start",style:"#666",width:100,height:100,textMargin:0,rx:0,ry:0,valign:void 0,text:""}},w0=function(t,e){const i=e.text.replace(jn.lineBreakRegex," "),[,r]=Vn(e.fontSize),n=t.append("text");n.attr("x",e.x),n.attr("y",e.y),n.style("text-anchor",e.anchor),n.style("font-family",e.fontFamily),n.style("font-size",r),n.style("font-weight",e.fontWeight),n.attr("fill",e.fill),e.class!==void 0&&n.attr("class",e.class);const o=n.append("tspan");return o.attr("x",e.x+e.textMargin*2),o.attr("fill",e.fill),o.text(i),n},B0=ki((t,e,i)=>{if(!t||(i=Object.assign({fontSize:12,fontWeight:400,fontFamily:"Arial",joinWith:"<br/>"},i),jn.lineBreakRegex.test(t)))return t;const r=t.split(" "),n=[];let o="";return r.forEach((s,a)=>{const l=lr(`${s} `,i),h=lr(o,i);if(l>e){const{hyphenatedStrings:c,remainingWord:p}=A0(s,e,"-",i);n.push(o,...c),o=p}else h+l>=e?(n.push(o),o=s):o=[o,s].filter(Boolean).join(" ");a+1===r.length&&n.push(o)}),n.filter(s=>s!=="").join(i.joinWith)},(t,e,i)=>`${t}${e}${i.fontSize}${i.fontWeight}${i.fontFamily}${i.joinWith}`),A0=ki((t,e,i="-",r)=>{r=Object.assign({fontSize:12,fontWeight:400,fontFamily:"Arial",margin:0},r);const n=[...t],o=[];let s="";return n.forEach((a,l)=>{const h=`${s}${a}`;if(lr(h,r)>=e){const f=l+1,c=n.length===f,p=`${h}${i}`;o.push(c?h:p),s=""}else s=h}),{hyphenatedStrings:o,remainingWord:s}},(t,e,i="-",r)=>`${t}${e}${i}${r.fontSize}${r.fontWeight}${r.fontFamily}`);function L0(t,e){return Yn(t,e).height}function lr(t,e){return Yn(t,e).width}const Yn=ki((t,e)=>{const{fontSize:i=12,fontFamily:r="Arial",fontWeight:n=400}=e;if(!t)return{width:0,height:0};const[,o]=Vn(i),s=["sans-serif",r],a=t.split(jn.lineBreakRegex),l=[],h=Tt("body");if(!h.remove)return{width:0,height:0,lineHeight:0};const u=h.append("svg");for(const c of s){let p=0;const _={width:0,height:0,lineHeight:0};for(const b of a){const k=S0();k.text=b||l0;const P=w0(u,k).style("font-size",o).style("font-weight",n).style("font-family",c),v=(P._groups||P)[0][0].getBBox();if(v.width===0&&v.height===0)throw new Error("svg element not in render tree");_.width=Math.round(Math.max(_.width,v.width)),p=Math.round(v.height),_.height+=p,_.lineHeight=Math.round(Math.max(_.lineHeight,p))}l.push(_)}u.remove();const f=isNaN(l[1].height)||isNaN(l[1].width)||isNaN(l[1].lineHeight)||l[0].height>l[1].height&&l[0].width>l[1].width&&l[0].lineHeight>l[1].lineHeight?0:1;return l[f]},(t,e)=>`${t}${e.fontSize}${e.fontWeight}${e.fontFamily}`);class F0{constructor(e=!1,i){this.count=0,this.count=i?i.length:0,this.next=e?()=>this.count++:()=>Date.now()}}let Ri;const E0=function(t){return Ri=Ri||document.createElement("div"),t=escape(t).replace(/%26/g,"&").replace(/%23/g,"#").replace(/%3B/g,";"),Ri.innerHTML=t,unescape(Ri.textContent)};function fl(t){return"str"in t}const O0=(t,e,i,r)=>{var n;if(!r)return;const o=(n=t.node())==null?void 0:n.getBBox();o&&t.append("text").text(r).attr("x",o.x+o.width/2).attr("y",-i).attr("class",e)},Vn=t=>{if(typeof t=="number")return[t,t+"px"];const e=parseInt(t??"",10);return Number.isNaN(e)?[void 0,void 0]:t===String(e)?[e,t+"px"]:[e,t]};function dl(t,e){return rm({},t,e)}const hi={assignWithDepth:st,wrapLabel:B0,calculateTextHeight:L0,calculateTextWidth:lr,calculateTextDimensions:Yn,cleanAndMerge:dl,detectInit:u0,detectDirective:cl,isSubstringInArray:d0,interpolateToCurve:p0,calcLabelPosition:y0,calcCardinalityPosition:C0,calcTerminalLabelPosition:x0,formatUrl:g0,getStylesFromArray:b0,generateId:T0,random:k0,runFunc:m0,entityDecode:E0,insertTitle:O0,parseFontSize:Vn,InitIDGenerator:F0},M0=function(t){let e=t;return e=e.replace(/style.*:\S*#.*;/g,function(i){return i.substring(0,i.length-1)}),e=e.replace(/classDef.*:\S*#.*;/g,function(i){return i.substring(0,i.length-1)}),e=e.replace(/#\w+;/g,function(i){const r=i.substring(1,i.length-1);return/^\+?\d+$/.test(r)?"fl°°"+r+"¶ß":"fl°"+r+"¶ß"}),e},I0=function(t){return t.replace(/fl°°/g,"&#").replace(/fl°/g,"&").replace(/¶ß/g,";")},As="10.9.2",Pe=Object.freeze(n0);let pt=st({},Pe),pl,qe=[],ci=st({},Pe);const Or=(t,e)=>{let i=st({},t),r={};for(const n of e)_l(n),r=st(r,n);if(i=st(i,r),r.theme&&r.theme in Xt){const n=st({},pl),o=st(n.themeVariables||{},r.themeVariables);i.theme&&i.theme in Xt&&(i.themeVariables=Xt[i.theme].getThemeVariables(o))}return ci=i,yl(ci),ci},$0=t=>(pt=st({},Pe),pt=st(pt,t),t.theme&&Xt[t.theme]&&(pt.themeVariables=Xt[t.theme].getThemeVariables(t.themeVariables)),Or(pt,qe),pt),D0=t=>{pl=st({},t)},N0=t=>(pt=st(pt,t),Or(pt,qe),pt),gl=()=>st({},pt),ml=t=>(yl(t),st(ci,t),qt()),qt=()=>st({},ci),_l=t=>{t&&(["secure",...pt.secure??[]].forEach(e=>{Object.hasOwn(t,e)&&(E.debug(`Denied attempt to modify a secure key ${e}`,t[e]),delete t[e])}),Object.keys(t).forEach(e=>{e.startsWith("__")&&delete t[e]}),Object.keys(t).forEach(e=>{typeof t[e]=="string"&&(t[e].includes("<")||t[e].includes(">")||t[e].includes("url(data:"))&&delete t[e],typeof t[e]=="object"&&_l(t[e])}))},R0=t=>{ar(t),t.fontFamily&&(!t.themeVariables||!t.themeVariables.fontFamily)&&(t.themeVariables={fontFamily:t.fontFamily}),qe.push(t),Or(pt,qe)},hr=(t=pt)=>{qe=[],Or(t,qe)},P0={LAZY_LOAD_DEPRECATED:"The configuration options lazyLoadedDiagrams and loadExternalDiagramsAtStartup are deprecated. Please use registerExternalDiagrams instead."},Ls={},q0=t=>{Ls[t]||(E.warn(P0[t]),Ls[t]=!0)},yl=t=>{t&&(t.lazyLoadedDiagrams||t.loadExternalDiagramsAtStartup)&&q0("LAZY_LOAD_DEPRECATED")},Cl="c4",z0=t=>/^\s*C4Context|C4Container|C4Component|C4Dynamic|C4Deployment/.test(t),W0=async()=>{const{diagram:t}=await K(()=>import("./c4Diagram-dc8f04df-DWstOjwk.js"),__vite__mapDeps([0,1,2]));return{id:Cl,diagram:t}},H0={id:Cl,detector:z0,loader:W0},j0=H0,xl="flowchart",U0=(t,e)=>{var i,r;return((i=e==null?void 0:e.flowchart)==null?void 0:i.defaultRenderer)==="dagre-wrapper"||((r=e==null?void 0:e.flowchart)==null?void 0:r.defaultRenderer)==="elk"?!1:/^\s*graph/.test(t)},Y0=async()=>{const{diagram:t}=await K(()=>import("./flowDiagram-622f9fc1-BpT3eoaF.js"),__vite__mapDeps([3,4,5,6,7,8,9,10,11,12,13,14,15,2]));return{id:xl,diagram:t}},V0={id:xl,detector:U0,loader:Y0},G0=V0,bl="flowchart-v2",X0=(t,e)=>{var i,r,n;return((i=e==null?void 0:e.flowchart)==null?void 0:i.defaultRenderer)==="dagre-d3"||((r=e==null?void 0:e.flowchart)==null?void 0:r.defaultRenderer)==="elk"?!1:/^\s*graph/.test(t)&&((n=e==null?void 0:e.flowchart)==null?void 0:n.defaultRenderer)==="dagre-wrapper"?!0:/^\s*flowchart/.test(t)},K0=async()=>{const{diagram:t}=await K(()=>import("./flowDiagram-v2-a33b4996-BQrZXIe9.js"),__vite__mapDeps([16,4,7,5,8,6,9,10,11,12,13,14,15,2]));return{id:bl,diagram:t}},Z0={id:bl,detector:X0,loader:K0},J0=Z0,Tl="er",Q0=t=>/^\s*erDiagram/.test(t),t_=async()=>{const{diagram:t}=await K(()=>import("./erDiagram-51d2b61e-D5StoYmd.js"),__vite__mapDeps([17,5,6,12,13,14,2]));return{id:Tl,diagram:t}},e_={id:Tl,detector:Q0,loader:t_},i_=e_,vl="gitGraph",r_=t=>/^\s*gitGraph/.test(t),n_=async()=>{const{diagram:t}=await K(()=>import("./gitGraphDiagram-23af1bdb-Dd7cNN9F.js"),__vite__mapDeps([18,2]));return{id:vl,diagram:t}},o_={id:vl,detector:r_,loader:n_},s_=o_,kl="gantt",a_=t=>/^\s*gantt/.test(t),l_=async()=>{const{diagram:t}=await K(()=>import("./ganttDiagram-a649f789-B7dFucT2.js"),__vite__mapDeps([19,20,21,2]));return{id:kl,diagram:t}},h_={id:kl,detector:a_,loader:l_},c_=h_,Sl="info",u_=t=>/^\s*info/.test(t),f_=async()=>{const{diagram:t}=await K(()=>import("./infoDiagram-f86e0131-BvySRD9D.js"),__vite__mapDeps([22,2]));return{id:Sl,diagram:t}},d_={id:Sl,detector:u_,loader:f_},wl="pie",p_=t=>/^\s*pie/.test(t),g_=async()=>{const{diagram:t}=await K(()=>import("./pieDiagram-31d824a1-BIcjeA1S.js"),__vite__mapDeps([23,24,14,25,21,13,2]));return{id:wl,diagram:t}},m_={id:wl,detector:p_,loader:g_},Bl="quadrantChart",__=t=>/^\s*quadrantChart/.test(t),y_=async()=>{const{diagram:t}=await K(()=>import("./quadrantDiagram-a712a7d9-CNklQ4II.js"),__vite__mapDeps([26,20,21,2]));return{id:Bl,diagram:t}},C_={id:Bl,detector:__,loader:y_},x_=C_,Al="xychart",b_=t=>/^\s*xychart-beta/.test(t),T_=async()=>{const{diagram:t}=await K(()=>import("./xychartDiagram-4a8b8217-DS1INfpk.js"),__vite__mapDeps([27,11,21,25,20,12,13,14,2]));return{id:Al,diagram:t}},v_={id:Al,detector:b_,loader:T_},k_=v_,Ll="requirement",S_=t=>/^\s*requirement(Diagram)?/.test(t),w_=async()=>{const{diagram:t}=await K(()=>import("./requirementDiagram-eb878fee-OFUpKWxv.js"),__vite__mapDeps([28,5,6,12,13,14,2]));return{id:Ll,diagram:t}},B_={id:Ll,detector:S_,loader:w_},A_=B_,Fl="sequence",L_=t=>/^\s*sequenceDiagram/.test(t),F_=async()=>{const{diagram:t}=await K(()=>import("./sequenceDiagram-66748113-sH_v1_cD.js"),__vite__mapDeps([29,1,2]));return{id:Fl,diagram:t}},E_={id:Fl,detector:L_,loader:F_},O_=E_,El="class",M_=(t,e)=>{var i;return((i=e==null?void 0:e.class)==null?void 0:i.defaultRenderer)==="dagre-wrapper"?!1:/^\s*classDiagram/.test(t)},I_=async()=>{const{diagram:t}=await K(()=>import("./classDiagram-8298e144-DKojaSxZ.js"),__vite__mapDeps([30,31,5,6,12,13,14,2]));return{id:El,diagram:t}},$_={id:El,detector:M_,loader:I_},D_=$_,Ol="classDiagram",N_=(t,e)=>{var i;return/^\s*classDiagram/.test(t)&&((i=e==null?void 0:e.class)==null?void 0:i.defaultRenderer)==="dagre-wrapper"?!0:/^\s*classDiagram-v2/.test(t)},R_=async()=>{const{diagram:t}=await K(()=>import("./classDiagram-v2-296fb1cd-DTrZkQpq.js"),__vite__mapDeps([32,31,5,8,6,9,10,11,12,13,14,2]));return{id:Ol,diagram:t}},P_={id:Ol,detector:N_,loader:R_},q_=P_,Ml="state",z_=(t,e)=>{var i;return((i=e==null?void 0:e.state)==null?void 0:i.defaultRenderer)==="dagre-wrapper"?!1:/^\s*stateDiagram/.test(t)},W_=async()=>{const{diagram:t}=await K(()=>import("./stateDiagram-35d39939-D7FEhrYs.js"),__vite__mapDeps([33,34,5,6,12,13,14,2]));return{id:Ml,diagram:t}},H_={id:Ml,detector:z_,loader:W_},j_=H_,Il="stateDiagram",U_=(t,e)=>{var i;return!!(/^\s*stateDiagram-v2/.test(t)||/^\s*stateDiagram/.test(t)&&((i=e==null?void 0:e.state)==null?void 0:i.defaultRenderer)==="dagre-wrapper")},Y_=async()=>{const{diagram:t}=await K(()=>import("./stateDiagram-v2-6c43c13a-C7zU9Dfv.js"),__vite__mapDeps([35,34,5,8,6,9,10,11,12,13,14,2]));return{id:Il,diagram:t}},V_={id:Il,detector:U_,loader:Y_},G_=V_,$l="journey",X_=t=>/^\s*journey/.test(t),K_=async()=>{const{diagram:t}=await K(()=>import("./journeyDiagram-de0d04b7-bCIGoTun.js"),__vite__mapDeps([36,1,24,14,2]));return{id:$l,diagram:t}},Z_={id:$l,detector:X_,loader:K_},J_=Z_,Q_=function(t,e){for(let i of e)t.attr(i[0],i[1])},ty=function(t,e,i){let r=new Map;return i?(r.set("width","100%"),r.set("style",`max-width: ${e}px;`)):(r.set("height",t),r.set("width",e)),r},Dl=function(t,e,i,r){const n=ty(e,i,r);Q_(t,n)},ey=function(t,e,i,r){const n=e.node().getBBox(),o=n.width,s=n.height;E.info(`SVG bounds: ${o}x${s}`,n);let a=0,l=0;E.info(`Graph bounds: ${a}x${l}`,t),a=o+i*2,l=s+i*2,E.info(`Calculated bounds: ${a}x${l}`),Dl(e,l,a,r);const h=`${n.x-i} ${n.y-i} ${n.width+2*i} ${n.height+2*i}`;e.attr("viewBox",h)},Vi={},iy=(t,e,i)=>{let r="";return t in Vi&&Vi[t]?r=Vi[t](i):E.warn(`No theme found for ${t}`),` & {
     font-family: ${i.fontFamily};
     font-size: ${i.fontSize};
     fill: ${i.textColor}
@@ -62,7 +62,7 @@ import{M as K}from"./app-B69Gl_S-.js";function yh(t){for(var e=[],i=1;i<argument
   ${e}
 `},ry=(t,e)=>{e!==void 0&&(Vi[t]=e)},ny=iy;let Gn="",Xn="",Kn="";const Zn=t=>Ci(t,qt()),oy=()=>{Gn="",Kn="",Xn=""},sy=t=>{Gn=Zn(t).replace(/^\s+/g,"")},ay=()=>Gn,ly=t=>{Kn=Zn(t).replace(/\n\s+/g,`
 `)},hy=()=>Kn,cy=t=>{Xn=Zn(t)},uy=()=>Xn,fy=Object.freeze(Object.defineProperty({__proto__:null,clear:oy,getAccDescription:hy,getAccTitle:ay,getDiagramTitle:uy,setAccDescription:ly,setAccTitle:sy,setDiagramTitle:cy},Symbol.toStringTag,{value:"Module"})),dy=E,py=Hn,Jn=qt,Rb=ml,Pb=Pe,gy=t=>Ci(t,Jn()),my=ey,_y=()=>fy,cr={},ur=(t,e,i)=>{var r;if(cr[t])throw new Error(`Diagram ${t} already registered.`);cr[t]=e,i&&hl(t,i),ry(t,e.styles),(r=e.injectUtils)==null||r.call(e,dy,py,Jn,gy,my,_y(),()=>{})},Qn=t=>{if(t in cr)return cr[t];throw new yy(t)};class yy extends Error{constructor(e){super(`Diagram ${e} not found.`)}}const Cy=t=>{var e;const{securityLevel:i}=Jn();let r=Tt("body");if(i==="sandbox"){const s=((e=Tt(`#i${t}`).node())==null?void 0:e.contentDocument)??document;r=Tt(s.body)}return r.select(`#${t}`)},xy=(t,e,i)=>{E.debug(`rendering svg for syntax error
-`);const r=Cy(e),n=r.append("g");r.attr("viewBox","0 0 2412 512"),Dl(r,100,512,!0),n.append("path").attr("class","error-icon").attr("d","m411.313,123.313c6.25-6.25 6.25-16.375 0-22.625s-16.375-6.25-22.625,0l-32,32-9.375,9.375-20.688-20.688c-12.484-12.5-32.766-12.5-45.25,0l-16,16c-1.261,1.261-2.304,2.648-3.31,4.051-21.739-8.561-45.324-13.426-70.065-13.426-105.867,0-192,86.133-192,192s86.133,192 192,192 192-86.133 192-192c0-24.741-4.864-48.327-13.426-70.065 1.402-1.007 2.79-2.049 4.051-3.31l16-16c12.5-12.492 12.5-32.758 0-45.25l-20.688-20.688 9.375-9.375 32.001-31.999zm-219.313,100.687c-52.938,0-96,43.063-96,96 0,8.836-7.164,16-16,16s-16-7.164-16-16c0-70.578 57.422-128 128-128 8.836,0 16,7.164 16,16s-7.164,16-16,16z"),n.append("path").attr("class","error-icon").attr("d","m459.02,148.98c-6.25-6.25-16.375-6.25-22.625,0s-6.25,16.375 0,22.625l16,16c3.125,3.125 7.219,4.688 11.313,4.688 4.094,0 8.188-1.563 11.313-4.688 6.25-6.25 6.25-16.375 0-22.625l-16.001-16z"),n.append("path").attr("class","error-icon").attr("d","m340.395,75.605c3.125,3.125 7.219,4.688 11.313,4.688 4.094,0 8.188-1.563 11.313-4.688 6.25-6.25 6.25-16.375 0-22.625l-16-16c-6.25-6.25-16.375-6.25-22.625,0s-6.25,16.375 0,22.625l15.999,16z"),n.append("path").attr("class","error-icon").attr("d","m400,64c8.844,0 16-7.164 16-16v-32c0-8.836-7.156-16-16-16-8.844,0-16,7.164-16,16v32c0,8.836 7.156,16 16,16z"),n.append("path").attr("class","error-icon").attr("d","m496,96.586h-32c-8.844,0-16,7.164-16,16 0,8.836 7.156,16 16,16h32c8.844,0 16-7.164 16-16 0-8.836-7.156-16-16-16z"),n.append("path").attr("class","error-icon").attr("d","m436.98,75.605c3.125,3.125 7.219,4.688 11.313,4.688 4.094,0 8.188-1.563 11.313-4.688l32-32c6.25-6.25 6.25-16.375 0-22.625s-16.375-6.25-22.625,0l-32,32c-6.251,6.25-6.251,16.375-0.001,22.625z"),n.append("text").attr("class","error-text").attr("x",1440).attr("y",250).attr("font-size","150px").style("text-anchor","middle").text("Syntax error in text"),n.append("text").attr("class","error-text").attr("x",1250).attr("y",400).attr("font-size","100px").style("text-anchor","middle").text(`mermaid version ${i}`)},Nl={draw:xy},by=Nl,Ty={db:{},renderer:Nl,parser:{parser:{yy:{}},parse:()=>{}}},vy=Ty,Rl="flowchart-elk",ky=(t,e)=>{var i;return!!(/^\s*flowchart-elk/.test(t)||/^\s*flowchart|graph/.test(t)&&((i=e==null?void 0:e.flowchart)==null?void 0:i.defaultRenderer)==="elk")},Sy=async()=>{const{diagram:t}=await K(()=>import("./flowchart-elk-definition-930acc39-Q-ihdrlR.js"),__vite__mapDeps([37,4,10,11,12,13,14,2]));return{id:Rl,diagram:t}},wy={id:Rl,detector:ky,loader:Sy},By=wy,Pl="timeline",Ay=t=>/^\s*timeline/.test(t),Ly=async()=>{const{diagram:t}=await K(()=>import("./timeline-definition-6eaa3543-BApSUGyX.js"),__vite__mapDeps([38,24,14,2]));return{id:Pl,diagram:t}},Fy={id:Pl,detector:Ay,loader:Ly},Ey=Fy,ql="mindmap",Oy=t=>/^\s*mindmap/.test(t),My=async()=>{const{diagram:t}=await K(()=>import("./mindmap-definition-b08d3ac4-DYSC8IDG.js"),__vite__mapDeps([39,11,2]));return{id:ql,diagram:t}},Iy={id:ql,detector:Oy,loader:My},$y=Iy,zl="sankey",Dy=t=>/^\s*sankey-beta/.test(t),Ny=async()=>{const{diagram:t}=await K(()=>import("./sankeyDiagram-c599f8ec-BGnWqC27.js"),__vite__mapDeps([40,25,21,41,2]));return{id:zl,diagram:t}},Ry={id:zl,detector:Dy,loader:Ny},Py=Ry,Wl="block",qy=t=>/^\s*block-beta/.test(t),zy=async()=>{const{diagram:t}=await K(()=>import("./blockDiagram-a8a0820c-1CGnBiz2.js"),__vite__mapDeps([42,9,5,10,11,12,13,14,25,21,15,41,2]));return{id:Wl,diagram:t}},Wy={id:Wl,detector:qy,loader:zy},Hy=Wy;let Fs=!1;const to=()=>{Fs||(Fs=!0,ur("error",vy,t=>t.toLowerCase().trim()==="error"),ur("---",{db:{clear:()=>{}},styles:{},renderer:{draw:()=>{}},parser:{parser:{yy:{}},parse:()=>{throw new Error("Diagrams beginning with --- are not valid. If you were trying to use a YAML front-matter, please ensure that you've correctly opened and closed the YAML front-matter with un-indented `---` blocks")}},init:()=>null},t=>t.toLowerCase().trimStart().startsWith("---")),ll(j0,q_,D_,i_,c_,d_,m_,A_,O_,By,J0,G0,$y,Ey,s_,G_,j_,J_,x_,Py,k_,Hy))};class Hl{constructor(e,i={}){this.text=e,this.metadata=i,this.type="graph",this.text=M0(e),this.text+=`
+`);const r=Cy(e),n=r.append("g");r.attr("viewBox","0 0 2412 512"),Dl(r,100,512,!0),n.append("path").attr("class","error-icon").attr("d","m411.313,123.313c6.25-6.25 6.25-16.375 0-22.625s-16.375-6.25-22.625,0l-32,32-9.375,9.375-20.688-20.688c-12.484-12.5-32.766-12.5-45.25,0l-16,16c-1.261,1.261-2.304,2.648-3.31,4.051-21.739-8.561-45.324-13.426-70.065-13.426-105.867,0-192,86.133-192,192s86.133,192 192,192 192-86.133 192-192c0-24.741-4.864-48.327-13.426-70.065 1.402-1.007 2.79-2.049 4.051-3.31l16-16c12.5-12.492 12.5-32.758 0-45.25l-20.688-20.688 9.375-9.375 32.001-31.999zm-219.313,100.687c-52.938,0-96,43.063-96,96 0,8.836-7.164,16-16,16s-16-7.164-16-16c0-70.578 57.422-128 128-128 8.836,0 16,7.164 16,16s-7.164,16-16,16z"),n.append("path").attr("class","error-icon").attr("d","m459.02,148.98c-6.25-6.25-16.375-6.25-22.625,0s-6.25,16.375 0,22.625l16,16c3.125,3.125 7.219,4.688 11.313,4.688 4.094,0 8.188-1.563 11.313-4.688 6.25-6.25 6.25-16.375 0-22.625l-16.001-16z"),n.append("path").attr("class","error-icon").attr("d","m340.395,75.605c3.125,3.125 7.219,4.688 11.313,4.688 4.094,0 8.188-1.563 11.313-4.688 6.25-6.25 6.25-16.375 0-22.625l-16-16c-6.25-6.25-16.375-6.25-22.625,0s-6.25,16.375 0,22.625l15.999,16z"),n.append("path").attr("class","error-icon").attr("d","m400,64c8.844,0 16-7.164 16-16v-32c0-8.836-7.156-16-16-16-8.844,0-16,7.164-16,16v32c0,8.836 7.156,16 16,16z"),n.append("path").attr("class","error-icon").attr("d","m496,96.586h-32c-8.844,0-16,7.164-16,16 0,8.836 7.156,16 16,16h32c8.844,0 16-7.164 16-16 0-8.836-7.156-16-16-16z"),n.append("path").attr("class","error-icon").attr("d","m436.98,75.605c3.125,3.125 7.219,4.688 11.313,4.688 4.094,0 8.188-1.563 11.313-4.688l32-32c6.25-6.25 6.25-16.375 0-22.625s-16.375-6.25-22.625,0l-32,32c-6.251,6.25-6.251,16.375-0.001,22.625z"),n.append("text").attr("class","error-text").attr("x",1440).attr("y",250).attr("font-size","150px").style("text-anchor","middle").text("Syntax error in text"),n.append("text").attr("class","error-text").attr("x",1250).attr("y",400).attr("font-size","100px").style("text-anchor","middle").text(`mermaid version ${i}`)},Nl={draw:xy},by=Nl,Ty={db:{},renderer:Nl,parser:{parser:{yy:{}},parse:()=>{}}},vy=Ty,Rl="flowchart-elk",ky=(t,e)=>{var i;return!!(/^\s*flowchart-elk/.test(t)||/^\s*flowchart|graph/.test(t)&&((i=e==null?void 0:e.flowchart)==null?void 0:i.defaultRenderer)==="elk")},Sy=async()=>{const{diagram:t}=await K(()=>import("./flowchart-elk-definition-930acc39-D2d6YT5I.js"),__vite__mapDeps([37,4,10,11,12,13,14,2]));return{id:Rl,diagram:t}},wy={id:Rl,detector:ky,loader:Sy},By=wy,Pl="timeline",Ay=t=>/^\s*timeline/.test(t),Ly=async()=>{const{diagram:t}=await K(()=>import("./timeline-definition-6eaa3543-CYqJxmAu.js"),__vite__mapDeps([38,24,14,2]));return{id:Pl,diagram:t}},Fy={id:Pl,detector:Ay,loader:Ly},Ey=Fy,ql="mindmap",Oy=t=>/^\s*mindmap/.test(t),My=async()=>{const{diagram:t}=await K(()=>import("./mindmap-definition-b08d3ac4-CtqZ8Vgk.js"),__vite__mapDeps([39,11,2]));return{id:ql,diagram:t}},Iy={id:ql,detector:Oy,loader:My},$y=Iy,zl="sankey",Dy=t=>/^\s*sankey-beta/.test(t),Ny=async()=>{const{diagram:t}=await K(()=>import("./sankeyDiagram-c599f8ec-Ss3oz1oB.js"),__vite__mapDeps([40,25,21,41,2]));return{id:zl,diagram:t}},Ry={id:zl,detector:Dy,loader:Ny},Py=Ry,Wl="block",qy=t=>/^\s*block-beta/.test(t),zy=async()=>{const{diagram:t}=await K(()=>import("./blockDiagram-a8a0820c-DvOSxzpN.js"),__vite__mapDeps([42,9,5,10,11,12,13,14,25,21,15,41,2]));return{id:Wl,diagram:t}},Wy={id:Wl,detector:qy,loader:zy},Hy=Wy;let Fs=!1;const to=()=>{Fs||(Fs=!0,ur("error",vy,t=>t.toLowerCase().trim()==="error"),ur("---",{db:{clear:()=>{}},styles:{},renderer:{draw:()=>{}},parser:{parser:{yy:{}},parse:()=>{throw new Error("Diagrams beginning with --- are not valid. If you were trying to use a YAML front-matter, please ensure that you've correctly opened and closed the YAML front-matter with un-indented `---` blocks")}},init:()=>null},t=>t.toLowerCase().trimStart().startsWith("---")),ll(j0,q_,D_,i_,c_,d_,m_,A_,O_,By,J0,G0,$y,Ey,s_,G_,j_,J_,x_,Py,k_,Hy))};class Hl{constructor(e,i={}){this.text=e,this.metadata=i,this.type="graph",this.text=M0(e),this.text+=`
 `;const r=qt();try{this.type=Er(e,r)}catch(o){this.type="error",this.detectError=o}const n=Qn(this.type);E.debug("Type "+this.type),this.db=n.db,this.renderer=n.renderer,this.parser=n.parser,this.parser.parser.yy=this.db,this.init=n.init,this.parse()}parse(){var e,i,r,n,o;if(this.detectError)throw this.detectError;(i=(e=this.db).clear)==null||i.call(e);const s=qt();(r=this.init)==null||r.call(this,s),this.metadata.title&&((o=(n=this.db).setDiagramTitle)==null||o.call(n,this.metadata.title)),this.parser.parse(this.text)}async render(e,i){await this.renderer.draw(this.text,e,i,this)}getParser(){return this.parser}getType(){return this.type}}const jy=async(t,e={})=>{const i=Er(t,qt());try{Qn(i)}catch{const n=a0(i);if(!n)throw new al(`Diagram ${i} not found.`);const{id:o,diagram:s}=await n();ur(o,s)}return new Hl(t,e)};let Es=[];const Uy=()=>{Es.forEach(t=>{t()}),Es=[]},Yy="graphics-document document";function Vy(t,e){t.attr("role",Yy),e!==""&&t.attr("aria-roledescription",e)}function Gy(t,e,i,r){if(t.insert!==void 0){if(i){const n=`chart-desc-${r}`;t.attr("aria-describedby",n),t.insert("desc",":first-child").attr("id",n).text(i)}if(e){const n=`chart-title-${r}`;t.attr("aria-labelledby",n),t.insert("title",":first-child").attr("id",n).text(e)}}}const Xy=t=>t.replace(/^\s*%%(?!{)[^\n]+\n?/gm,"").trimStart();/*! js-yaml 4.1.0 https://github.com/nodeca/js-yaml @license MIT */function jl(t){return typeof t>"u"||t===null}function Ky(t){return typeof t=="object"&&t!==null}function Zy(t){return Array.isArray(t)?t:jl(t)?[]:[t]}function Jy(t,e){var i,r,n,o;if(e)for(o=Object.keys(e),i=0,r=o.length;i<r;i+=1)n=o[i],t[n]=e[n];return t}function Qy(t,e){var i="",r;for(r=0;r<e;r+=1)i+=t;return i}function tC(t){return t===0&&Number.NEGATIVE_INFINITY===1/t}var eC=jl,iC=Ky,rC=Zy,nC=Qy,oC=tC,sC=Jy,ct={isNothing:eC,isObject:iC,toArray:rC,repeat:nC,isNegativeZero:oC,extend:sC};function Ul(t,e){var i="",r=t.reason||"(unknown reason)";return t.mark?(t.mark.name&&(i+='in "'+t.mark.name+'" '),i+="("+(t.mark.line+1)+":"+(t.mark.column+1)+")",!e&&t.mark.snippet&&(i+=`
 
 `+t.mark.snippet),r+" "+i):r}function xi(t,e){Error.call(this),this.name="YAMLException",this.reason=t,this.mark=e,this.message=Ul(this,!1),Error.captureStackTrace?Error.captureStackTrace(this,this.constructor):this.stack=new Error().stack||""}xi.prototype=Object.create(Error.prototype);xi.prototype.constructor=xi;xi.prototype.toString=function(e){return this.name+": "+Ul(this,e)};var Gt=xi;function Qr(t,e,i,r,n){var o="",s="",a=Math.floor(n/2)-1;return r-e>a&&(o=" ... ",e=r-a+o.length),i-r>a&&(s=" ...",i=r+a-s.length),{str:o+t.slice(e,i).replace(/\t/g,"→")+s,pos:r-e+o.length}}function tn(t,e){return ct.repeat(" ",e-t.length)+t}function aC(t,e){if(e=Object.create(e||null),!t.buffer)return null;e.maxLength||(e.maxLength=79),typeof e.indent!="number"&&(e.indent=1),typeof e.linesBefore!="number"&&(e.linesBefore=3),typeof e.linesAfter!="number"&&(e.linesAfter=2);for(var i=/\r?\n|\r|\0/g,r=[0],n=[],o,s=-1;o=i.exec(t.buffer);)n.push(o.index),r.push(o.index+o[0].length),t.position<=o.index&&s<0&&(s=r.length-2);s<0&&(s=r.length-1);var a="",l,h,u=Math.min(t.line+e.linesAfter,n.length).toString().length,f=e.maxLength-(e.indent+u+3);for(l=1;l<=e.linesBefore&&!(s-l<0);l++)h=Qr(t.buffer,r[s-l],n[s-l],t.position-(r[s]-r[s-l]),f),a=ct.repeat(" ",e.indent)+tn((t.line-l+1).toString(),u)+" | "+h.str+`
diff --git a/assets/mindmap-definition-b08d3ac4-DYSC8IDG.js b/assets/mindmap-definition-b08d3ac4-CtqZ8Vgk.js
similarity index 99%
rename from assets/mindmap-definition-b08d3ac4-DYSC8IDG.js
rename to assets/mindmap-definition-b08d3ac4-CtqZ8Vgk.js
index fb6c93f..380c567 100644
--- a/assets/mindmap-definition-b08d3ac4-DYSC8IDG.js
+++ b/assets/mindmap-definition-b08d3ac4-CtqZ8Vgk.js
@@ -1,4 +1,4 @@
-import{aB as hi,aC as rl,l as Er,c as ci,aJ as al,u as nl,aL as ja,d as en,h as il,b5 as sl,b6 as ol,b7 as ul,aN as ll}from"./mermaid.core-ChLYKTZm.js";import{c as fl}from"./createText-4a4f35c9-BuT3nXUz.js";import"./app-B69Gl_S-.js";function Xe(t){"@babel/helpers - typeof";return Xe=typeof Symbol=="function"&&typeof Symbol.iterator=="symbol"?function(e){return typeof e}:function(e){return e&&typeof Symbol=="function"&&e.constructor===Symbol&&e!==Symbol.prototype?"symbol":typeof e},Xe(t)}function vi(t,e){if(!(t instanceof e))throw new TypeError("Cannot call a class as a function")}function hl(t,e){for(var r=0;r<e.length;r++){var a=e[r];a.enumerable=a.enumerable||!1,a.configurable=!0,"value"in a&&(a.writable=!0),Object.defineProperty(t,a.key,a)}}function di(t,e,r){return e&&hl(t.prototype,e),Object.defineProperty(t,"prototype",{writable:!1}),t}function ao(t,e,r){return e in t?Object.defineProperty(t,e,{value:r,enumerable:!0,configurable:!0,writable:!0}):t[e]=r,t}function St(t,e){return cl(t)||vl(t,e)||no(t,e)||dl()}function cl(t){if(Array.isArray(t))return t}function vl(t,e){var r=t==null?null:typeof Symbol<"u"&&t[Symbol.iterator]||t["@@iterator"];if(r!=null){var a=[],n=!0,i=!1,s,o;try{for(r=r.call(t);!(n=(s=r.next()).done)&&(a.push(s.value),!(e&&a.length===e));n=!0);}catch(u){i=!0,o=u}finally{try{!n&&r.return!=null&&r.return()}finally{if(i)throw o}}return a}}function no(t,e){if(t){if(typeof t=="string")return $i(t,e);var r=Object.prototype.toString.call(t).slice(8,-1);if(r==="Object"&&t.constructor&&(r=t.constructor.name),r==="Map"||r==="Set")return Array.from(t);if(r==="Arguments"||/^(?:Ui|I)nt(?:8|16|32)(?:Clamped)?Array$/.test(r))return $i(t,e)}}function $i(t,e){(e==null||e>t.length)&&(e=t.length);for(var r=0,a=new Array(e);r<e;r++)a[r]=t[r];return a}function dl(){throw new TypeError(`Invalid attempt to destructure non-iterable instance.
+import{aB as hi,aC as rl,l as Er,c as ci,aJ as al,u as nl,aL as ja,d as en,h as il,b5 as sl,b6 as ol,b7 as ul,aN as ll}from"./mermaid.core-DNo_7Q2B.js";import{c as fl}from"./createText-4a4f35c9-CISzj231.js";import"./app-B4LGNJZ0.js";function Xe(t){"@babel/helpers - typeof";return Xe=typeof Symbol=="function"&&typeof Symbol.iterator=="symbol"?function(e){return typeof e}:function(e){return e&&typeof Symbol=="function"&&e.constructor===Symbol&&e!==Symbol.prototype?"symbol":typeof e},Xe(t)}function vi(t,e){if(!(t instanceof e))throw new TypeError("Cannot call a class as a function")}function hl(t,e){for(var r=0;r<e.length;r++){var a=e[r];a.enumerable=a.enumerable||!1,a.configurable=!0,"value"in a&&(a.writable=!0),Object.defineProperty(t,a.key,a)}}function di(t,e,r){return e&&hl(t.prototype,e),Object.defineProperty(t,"prototype",{writable:!1}),t}function ao(t,e,r){return e in t?Object.defineProperty(t,e,{value:r,enumerable:!0,configurable:!0,writable:!0}):t[e]=r,t}function St(t,e){return cl(t)||vl(t,e)||no(t,e)||dl()}function cl(t){if(Array.isArray(t))return t}function vl(t,e){var r=t==null?null:typeof Symbol<"u"&&t[Symbol.iterator]||t["@@iterator"];if(r!=null){var a=[],n=!0,i=!1,s,o;try{for(r=r.call(t);!(n=(s=r.next()).done)&&(a.push(s.value),!(e&&a.length===e));n=!0);}catch(u){i=!0,o=u}finally{try{!n&&r.return!=null&&r.return()}finally{if(i)throw o}}return a}}function no(t,e){if(t){if(typeof t=="string")return $i(t,e);var r=Object.prototype.toString.call(t).slice(8,-1);if(r==="Object"&&t.constructor&&(r=t.constructor.name),r==="Map"||r==="Set")return Array.from(t);if(r==="Arguments"||/^(?:Ui|I)nt(?:8|16|32)(?:Clamped)?Array$/.test(r))return $i(t,e)}}function $i(t,e){(e==null||e>t.length)&&(e=t.length);for(var r=0,a=new Array(e);r<e;r++)a[r]=t[r];return a}function dl(){throw new TypeError(`Invalid attempt to destructure non-iterable instance.
 In order to be iterable, non-array objects must have a [Symbol.iterator]() method.`)}function io(t,e){var r=typeof Symbol<"u"&&t[Symbol.iterator]||t["@@iterator"];if(!r){if(Array.isArray(t)||(r=no(t))||e){r&&(t=r);var a=0,n=function(){};return{s:n,n:function(){return a>=t.length?{done:!0}:{done:!1,value:t[a++]}},e:function(u){throw u},f:n}}throw new TypeError(`Invalid attempt to iterate non-iterable instance.
 In order to be iterable, non-array objects must have a [Symbol.iterator]() method.`)}var i=!0,s=!1,o;return{s:function(){r=r.call(t)},n:function(){var u=r.next();return i=u.done,u},e:function(u){s=!0,o=u},f:function(){try{!i&&r.return!=null&&r.return()}finally{if(s)throw o}}}}var Ye=typeof window>"u"?null:window,Yi=Ye?Ye.navigator:null;Ye&&Ye.document;var gl=Xe(""),so=Xe({}),pl=Xe(function(){}),yl=typeof HTMLElement>"u"?"undefined":Xe(HTMLElement),xa=function(e){return e&&e.instanceString&&Ge(e.instanceString)?e.instanceString():null},de=function(e){return e!=null&&Xe(e)==gl},Ge=function(e){return e!=null&&Xe(e)===pl},Re=function(e){return!pt(e)&&(Array.isArray?Array.isArray(e):e!=null&&e instanceof Array)},Ce=function(e){return e!=null&&Xe(e)===so&&!Re(e)&&e.constructor===Object},ml=function(e){return e!=null&&Xe(e)===so},ie=function(e){return e!=null&&Xe(e)===Xe(1)&&!isNaN(e)},bl=function(e){return ie(e)&&Math.floor(e)===e},tn=function(e){if(yl!=="undefined")return e!=null&&e instanceof HTMLElement},pt=function(e){return Ta(e)||oo(e)},Ta=function(e){return xa(e)==="collection"&&e._private.single},oo=function(e){return xa(e)==="collection"&&!e._private.single},gi=function(e){return xa(e)==="core"},uo=function(e){return xa(e)==="stylesheet"},El=function(e){return xa(e)==="event"},jt=function(e){return e==null?!0:!!(e===""||e.match(/^\s+$/))},wl=function(e){return typeof HTMLElement>"u"?!1:e instanceof HTMLElement},xl=function(e){return Ce(e)&&ie(e.x1)&&ie(e.x2)&&ie(e.y1)&&ie(e.y2)},Tl=function(e){return ml(e)&&Ge(e.then)},Cl=function(){return Yi&&Yi.userAgent.match(/msie|trident|edge/i)},ha=function(e,r){r||(r=function(){if(arguments.length===1)return arguments[0];if(arguments.length===0)return"undefined";for(var i=[],s=0;s<arguments.length;s++)i.push(arguments[s]);return i.join("$")});var a=function n(){var i=this,s=arguments,o,u=r.apply(i,s),l=n.cache;return(o=l[u])||(o=l[u]=e.apply(i,s)),o};return a.cache={},a},pi=ha(function(t){return t.replace(/([A-Z])/g,function(e){return"-"+e.toLowerCase()})}),vn=ha(function(t){return t.replace(/(-\w)/g,function(e){return e[1].toUpperCase()})}),lo=ha(function(t,e){return t+e[0].toUpperCase()+e.substring(1)},function(t,e){return t+"$"+e}),_i=function(e){return jt(e)?e:e.charAt(0).toUpperCase()+e.substring(1)},He="(?:[-+]?(?:(?:\\d+|\\d*\\.\\d+)(?:[Ee][+-]?\\d+)?))",Dl="rgb[a]?\\(("+He+"[%]?)\\s*,\\s*("+He+"[%]?)\\s*,\\s*("+He+"[%]?)(?:\\s*,\\s*("+He+"))?\\)",Sl="rgb[a]?\\((?:"+He+"[%]?)\\s*,\\s*(?:"+He+"[%]?)\\s*,\\s*(?:"+He+"[%]?)(?:\\s*,\\s*(?:"+He+"))?\\)",Ll="hsl[a]?\\(("+He+")\\s*,\\s*("+He+"[%])\\s*,\\s*("+He+"[%])(?:\\s*,\\s*("+He+"))?\\)",Al="hsl[a]?\\((?:"+He+")\\s*,\\s*(?:"+He+"[%])\\s*,\\s*(?:"+He+"[%])(?:\\s*,\\s*(?:"+He+"))?\\)",Ol="\\#[0-9a-fA-F]{3}",Nl="\\#[0-9a-fA-F]{6}",fo=function(e,r){return e<r?-1:e>r?1:0},Il=function(e,r){return-1*fo(e,r)},be=Object.assign!=null?Object.assign.bind(Object):function(t){for(var e=arguments,r=1;r<e.length;r++){var a=e[r];if(a!=null)for(var n=Object.keys(a),i=0;i<n.length;i++){var s=n[i];t[s]=a[s]}}return t},Ml=function(e){if(!(!(e.length===4||e.length===7)||e[0]!=="#")){var r=e.length===4,a,n,i,s=16;return r?(a=parseInt(e[1]+e[1],s),n=parseInt(e[2]+e[2],s),i=parseInt(e[3]+e[3],s)):(a=parseInt(e[1]+e[2],s),n=parseInt(e[3]+e[4],s),i=parseInt(e[5]+e[6],s)),[a,n,i]}},Rl=function(e){var r,a,n,i,s,o,u,l;function f(v,p,g){return g<0&&(g+=1),g>1&&(g-=1),g<1/6?v+(p-v)*6*g:g<1/2?p:g<2/3?v+(p-v)*(2/3-g)*6:v}var h=new RegExp("^"+Ll+"$").exec(e);if(h){if(a=parseInt(h[1]),a<0?a=(360- -1*a%360)%360:a>360&&(a=a%360),a/=360,n=parseFloat(h[2]),n<0||n>100||(n=n/100,i=parseFloat(h[3]),i<0||i>100)||(i=i/100,s=h[4],s!==void 0&&(s=parseFloat(s),s<0||s>1)))return;if(n===0)o=u=l=Math.round(i*255);else{var d=i<.5?i*(1+n):i+n-i*n,c=2*i-d;o=Math.round(255*f(c,d,a+1/3)),u=Math.round(255*f(c,d,a)),l=Math.round(255*f(c,d,a-1/3))}r=[o,u,l,s]}return r},kl=function(e){var r,a=new RegExp("^"+Dl+"$").exec(e);if(a){r=[];for(var n=[],i=1;i<=3;i++){var s=a[i];if(s[s.length-1]==="%"&&(n[i]=!0),s=parseFloat(s),n[i]&&(s=s/100*255),s<0||s>255)return;r.push(Math.floor(s))}var o=n[1]||n[2]||n[3],u=n[1]&&n[2]&&n[3];if(o&&!u)return;var l=a[4];if(l!==void 0){if(l=parseFloat(l),l<0||l>1)return;r.push(l)}}return r},Pl=function(e){return Fl[e.toLowerCase()]},Bl=function(e){return(Re(e)?e:null)||Pl(e)||Ml(e)||kl(e)||Rl(e)},Fl={transparent:[0,0,0,0],aliceblue:[240,248,255],antiquewhite:[250,235,215],aqua:[0,255,255],aquamarine:[127,255,212],azure:[240,255,255],beige:[245,245,220],bisque:[255,228,196],black:[0,0,0],blanchedalmond:[255,235,205],blue:[0,0,255],blueviolet:[138,43,226],brown:[165,42,42],burlywood:[222,184,135],cadetblue:[95,158,160],chartreuse:[127,255,0],chocolate:[210,105,30],coral:[255,127,80],cornflowerblue:[100,149,237],cornsilk:[255,248,220],crimson:[220,20,60],cyan:[0,255,255],darkblue:[0,0,139],darkcyan:[0,139,139],darkgoldenrod:[184,134,11],darkgray:[169,169,169],darkgreen:[0,100,0],darkgrey:[169,169,169],darkkhaki:[189,183,107],darkmagenta:[139,0,139],darkolivegreen:[85,107,47],darkorange:[255,140,0],darkorchid:[153,50,204],darkred:[139,0,0],darksalmon:[233,150,122],darkseagreen:[143,188,143],darkslateblue:[72,61,139],darkslategray:[47,79,79],darkslategrey:[47,79,79],darkturquoise:[0,206,209],darkviolet:[148,0,211],deeppink:[255,20,147],deepskyblue:[0,191,255],dimgray:[105,105,105],dimgrey:[105,105,105],dodgerblue:[30,144,255],firebrick:[178,34,34],floralwhite:[255,250,240],forestgreen:[34,139,34],fuchsia:[255,0,255],gainsboro:[220,220,220],ghostwhite:[248,248,255],gold:[255,215,0],goldenrod:[218,165,32],gray:[128,128,128],grey:[128,128,128],green:[0,128,0],greenyellow:[173,255,47],honeydew:[240,255,240],hotpink:[255,105,180],indianred:[205,92,92],indigo:[75,0,130],ivory:[255,255,240],khaki:[240,230,140],lavender:[230,230,250],lavenderblush:[255,240,245],lawngreen:[124,252,0],lemonchiffon:[255,250,205],lightblue:[173,216,230],lightcoral:[240,128,128],lightcyan:[224,255,255],lightgoldenrodyellow:[250,250,210],lightgray:[211,211,211],lightgreen:[144,238,144],lightgrey:[211,211,211],lightpink:[255,182,193],lightsalmon:[255,160,122],lightseagreen:[32,178,170],lightskyblue:[135,206,250],lightslategray:[119,136,153],lightslategrey:[119,136,153],lightsteelblue:[176,196,222],lightyellow:[255,255,224],lime:[0,255,0],limegreen:[50,205,50],linen:[250,240,230],magenta:[255,0,255],maroon:[128,0,0],mediumaquamarine:[102,205,170],mediumblue:[0,0,205],mediumorchid:[186,85,211],mediumpurple:[147,112,219],mediumseagreen:[60,179,113],mediumslateblue:[123,104,238],mediumspringgreen:[0,250,154],mediumturquoise:[72,209,204],mediumvioletred:[199,21,133],midnightblue:[25,25,112],mintcream:[245,255,250],mistyrose:[255,228,225],moccasin:[255,228,181],navajowhite:[255,222,173],navy:[0,0,128],oldlace:[253,245,230],olive:[128,128,0],olivedrab:[107,142,35],orange:[255,165,0],orangered:[255,69,0],orchid:[218,112,214],palegoldenrod:[238,232,170],palegreen:[152,251,152],paleturquoise:[175,238,238],palevioletred:[219,112,147],papayawhip:[255,239,213],peachpuff:[255,218,185],peru:[205,133,63],pink:[255,192,203],plum:[221,160,221],powderblue:[176,224,230],purple:[128,0,128],red:[255,0,0],rosybrown:[188,143,143],royalblue:[65,105,225],saddlebrown:[139,69,19],salmon:[250,128,114],sandybrown:[244,164,96],seagreen:[46,139,87],seashell:[255,245,238],sienna:[160,82,45],silver:[192,192,192],skyblue:[135,206,235],slateblue:[106,90,205],slategray:[112,128,144],slategrey:[112,128,144],snow:[255,250,250],springgreen:[0,255,127],steelblue:[70,130,180],tan:[210,180,140],teal:[0,128,128],thistle:[216,191,216],tomato:[255,99,71],turquoise:[64,224,208],violet:[238,130,238],wheat:[245,222,179],white:[255,255,255],whitesmoke:[245,245,245],yellow:[255,255,0],yellowgreen:[154,205,50]},ho=function(e){for(var r=e.map,a=e.keys,n=a.length,i=0;i<n;i++){var s=a[i];if(Ce(s))throw Error("Tried to set map with object key");i<a.length-1?(r[s]==null&&(r[s]={}),r=r[s]):r[s]=e.value}},co=function(e){for(var r=e.map,a=e.keys,n=a.length,i=0;i<n;i++){var s=a[i];if(Ce(s))throw Error("Tried to get map with object key");if(r=r[s],r==null)return r}return r};function Gl(t){var e=typeof t;return t!=null&&(e=="object"||e=="function")}var vr=Gl,na=typeof globalThis<"u"?globalThis:typeof window<"u"?window:typeof global<"u"?global:typeof self<"u"?self:{};function zl(t,e){return e={exports:{}},t(e,e.exports),e.exports}var Vl=typeof na=="object"&&na&&na.Object===Object&&na,Ul=Vl,$l=typeof self=="object"&&self&&self.Object===Object&&self,Yl=Ul||$l||Function("return this")(),dn=Yl,_l=function(){return dn.Date.now()},Rn=_l,Hl=/\s/;function Xl(t){for(var e=t.length;e--&&Hl.test(t.charAt(e)););return e}var ql=Xl,Wl=/^\s+/;function Kl(t){return t&&t.slice(0,ql(t)+1).replace(Wl,"")}var Zl=Kl,Ql=dn.Symbol,Fr=Ql,vo=Object.prototype,Jl=vo.hasOwnProperty,jl=vo.toString,jr=Fr?Fr.toStringTag:void 0;function ef(t){var e=Jl.call(t,jr),r=t[jr];try{t[jr]=void 0;var a=!0}catch{}var n=jl.call(t);return a&&(e?t[jr]=r:delete t[jr]),n}var tf=ef,rf=Object.prototype,af=rf.toString;function nf(t){return af.call(t)}var sf=nf,of="[object Null]",uf="[object Undefined]",Hi=Fr?Fr.toStringTag:void 0;function lf(t){return t==null?t===void 0?uf:of:Hi&&Hi in Object(t)?tf(t):sf(t)}var go=lf;function ff(t){return t!=null&&typeof t=="object"}var hf=ff,cf="[object Symbol]";function vf(t){return typeof t=="symbol"||hf(t)&&go(t)==cf}var Ca=vf,Xi=NaN,df=/^[-+]0x[0-9a-f]+$/i,gf=/^0b[01]+$/i,pf=/^0o[0-7]+$/i,yf=parseInt;function mf(t){if(typeof t=="number")return t;if(Ca(t))return Xi;if(vr(t)){var e=typeof t.valueOf=="function"?t.valueOf():t;t=vr(e)?e+"":e}if(typeof t!="string")return t===0?t:+t;t=Zl(t);var r=gf.test(t);return r||pf.test(t)?yf(t.slice(2),r?2:8):df.test(t)?Xi:+t}var qi=mf,bf="Expected a function",Ef=Math.max,wf=Math.min;function xf(t,e,r){var a,n,i,s,o,u,l=0,f=!1,h=!1,d=!0;if(typeof t!="function")throw new TypeError(bf);e=qi(e)||0,vr(r)&&(f=!!r.leading,h="maxWait"in r,i=h?Ef(qi(r.maxWait)||0,e):i,d="trailing"in r?!!r.trailing:d);function c(S){var E=a,w=n;return a=n=void 0,l=S,s=t.apply(w,E),s}function v(S){return l=S,o=setTimeout(y,e),f?c(S):s}function p(S){var E=S-u,w=S-l,x=e-E;return h?wf(x,i-w):x}function g(S){var E=S-u,w=S-l;return u===void 0||E>=e||E<0||h&&w>=i}function y(){var S=Rn();if(g(S))return b(S);o=setTimeout(y,p(S))}function b(S){return o=void 0,d&&a?c(S):(a=n=void 0,s)}function m(){o!==void 0&&clearTimeout(o),l=0,a=u=n=o=void 0}function T(){return o===void 0?s:b(Rn())}function C(){var S=Rn(),E=g(S);if(a=arguments,n=this,u=S,E){if(o===void 0)return v(u);if(h)return clearTimeout(o),o=setTimeout(y,e),c(u)}return o===void 0&&(o=setTimeout(y,e)),s}return C.cancel=m,C.flush=T,C}var gn=xf,kn=Ye?Ye.performance:null,po=kn&&kn.now?function(){return kn.now()}:function(){return Date.now()},Tf=function(){if(Ye){if(Ye.requestAnimationFrame)return function(t){Ye.requestAnimationFrame(t)};if(Ye.mozRequestAnimationFrame)return function(t){Ye.mozRequestAnimationFrame(t)};if(Ye.webkitRequestAnimationFrame)return function(t){Ye.webkitRequestAnimationFrame(t)};if(Ye.msRequestAnimationFrame)return function(t){Ye.msRequestAnimationFrame(t)}}return function(t){t&&setTimeout(function(){t(po())},1e3/60)}}(),rn=function(e){return Tf(e)},$t=po,Nr=9261,yo=65599,ia=5381,mo=function(e){for(var r=arguments.length>1&&arguments[1]!==void 0?arguments[1]:Nr,a=r,n;n=e.next(),!n.done;)a=a*yo+n.value|0;return a},ca=function(e){var r=arguments.length>1&&arguments[1]!==void 0?arguments[1]:Nr;return r*yo+e|0},va=function(e){var r=arguments.length>1&&arguments[1]!==void 0?arguments[1]:ia;return(r<<5)+r+e|0},Cf=function(e,r){return e*2097152+r},qt=function(e){return e[0]*2097152+e[1]},Ma=function(e,r){return[ca(e[0],r[0]),va(e[1],r[1])]},Df=function(e,r){var a={value:0,done:!1},n=0,i=e.length,s={next:function(){return n<i?a.value=e[n++]:a.done=!0,a}};return mo(s,r)},dr=function(e,r){var a={value:0,done:!1},n=0,i=e.length,s={next:function(){return n<i?a.value=e.charCodeAt(n++):a.done=!0,a}};return mo(s,r)},bo=function(){return Sf(arguments)},Sf=function(e){for(var r,a=0;a<e.length;a++){var n=e[a];a===0?r=dr(n):r=dr(n,r)}return r},Wi=!0,Lf=console.warn!=null,Af=console.trace!=null,yi=Number.MAX_SAFE_INTEGER||9007199254740991,Eo=function(){return!0},an=function(){return!1},Ki=function(){return 0},mi=function(){},ze=function(e){throw new Error(e)},wo=function(e){if(e!==void 0)Wi=!!e;else return Wi},Ne=function(e){wo()&&(Lf?console.warn(e):(console.log(e),Af&&console.trace()))},Of=function(e){return be({},e)},Pt=function(e){return e==null?e:Re(e)?e.slice():Ce(e)?Of(e):e},Nf=function(e){return e.slice()},xo=function(e,r){for(r=e="";e++<36;r+=e*51&52?(e^15?8^Math.random()*(e^20?16:4):4).toString(16):"-");return r},If={},To=function(){return If},tt=function(e){var r=Object.keys(e);return function(a){for(var n={},i=0;i<r.length;i++){var s=r[i],o=a==null?void 0:a[s];n[s]=o===void 0?e[s]:o}return n}},er=function(e,r,a){for(var n=e.length-1;n>=0;n--)e[n]===r&&e.splice(n,1)},bi=function(e){e.splice(0,e.length)},Mf=function(e,r){for(var a=0;a<r.length;a++){var n=r[a];e.push(n)}},At=function(e,r,a){return a&&(r=lo(a,r)),e[r]},Kt=function(e,r,a,n){a&&(r=lo(a,r)),e[r]=n},Rf=function(){function t(){vi(this,t),this._obj={}}return di(t,[{key:"set",value:function(r,a){return this._obj[r]=a,this}},{key:"delete",value:function(r){return this._obj[r]=void 0,this}},{key:"clear",value:function(){this._obj={}}},{key:"has",value:function(r){return this._obj[r]!==void 0}},{key:"get",value:function(r){return this._obj[r]}}]),t}(),Bt=typeof Map<"u"?Map:Rf,kf="undefined",Pf=function(){function t(e){if(vi(this,t),this._obj=Object.create(null),this.size=0,e!=null){var r;e.instanceString!=null&&e.instanceString()===this.instanceString()?r=e.toArray():r=e;for(var a=0;a<r.length;a++)this.add(r[a])}}return di(t,[{key:"instanceString",value:function(){return"set"}},{key:"add",value:function(r){var a=this._obj;a[r]!==1&&(a[r]=1,this.size++)}},{key:"delete",value:function(r){var a=this._obj;a[r]===1&&(a[r]=0,this.size--)}},{key:"clear",value:function(){this._obj=Object.create(null)}},{key:"has",value:function(r){return this._obj[r]===1}},{key:"toArray",value:function(){var r=this;return Object.keys(this._obj).filter(function(a){return r.has(a)})}},{key:"forEach",value:function(r,a){return this.toArray().forEach(r,a)}}]),t}(),Ur=(typeof Set>"u"?"undefined":Xe(Set))!==kf?Set:Pf,pn=function(e,r){var a=arguments.length>2&&arguments[2]!==void 0?arguments[2]:!0;if(e===void 0||r===void 0||!gi(e)){ze("An element must have a core reference and parameters set");return}var n=r.group;if(n==null&&(r.data&&r.data.source!=null&&r.data.target!=null?n="edges":n="nodes"),n!=="nodes"&&n!=="edges"){ze("An element must be of type `nodes` or `edges`; you specified `"+n+"`");return}this.length=1,this[0]=this;var i=this._private={cy:e,single:!0,data:r.data||{},position:r.position||{x:0,y:0},autoWidth:void 0,autoHeight:void 0,autoPadding:void 0,compoundBoundsClean:!1,listeners:[],group:n,style:{},rstyle:{},styleCxts:[],styleKeys:{},removed:!0,selected:!!r.selected,selectable:r.selectable===void 0?!0:!!r.selectable,locked:!!r.locked,grabbed:!1,grabbable:r.grabbable===void 0?!0:!!r.grabbable,pannable:r.pannable===void 0?n==="edges":!!r.pannable,active:!1,classes:new Ur,animation:{current:[],queue:[]},rscratch:{},scratch:r.scratch||{},edges:[],children:[],parent:r.parent&&r.parent.isNode()?r.parent:null,traversalCache:{},backgrounding:!1,bbCache:null,bbCacheShift:{x:0,y:0},bodyBounds:null,overlayBounds:null,labelBounds:{all:null,source:null,target:null,main:null},arrowBounds:{source:null,target:null,"mid-source":null,"mid-target":null}};if(i.position.x==null&&(i.position.x=0),i.position.y==null&&(i.position.y=0),r.renderedPosition){var s=r.renderedPosition,o=e.pan(),u=e.zoom();i.position={x:(s.x-o.x)/u,y:(s.y-o.y)/u}}var l=[];Re(r.classes)?l=r.classes:de(r.classes)&&(l=r.classes.split(/\s+/));for(var f=0,h=l.length;f<h;f++){var d=l[f];!d||d===""||i.classes.add(d)}this.createEmitter();var c=r.style||r.css;c&&(Ne("Setting a `style` bypass at element creation should be done only when absolutely necessary.  Try to use the stylesheet instead."),this.style(c)),(a===void 0||a)&&this.restore()},Zi=function(e){return e={bfs:e.bfs||!e.dfs,dfs:e.dfs||!e.bfs},function(a,n,i){var s;Ce(a)&&!pt(a)&&(s=a,a=s.roots||s.root,n=s.visit,i=s.directed),i=arguments.length===2&&!Ge(n)?n:i,n=Ge(n)?n:function(){};for(var o=this._private.cy,u=a=de(a)?this.filter(a):a,l=[],f=[],h={},d={},c={},v=0,p,g=this.byGroup(),y=g.nodes,b=g.edges,m=0;m<u.length;m++){var T=u[m],C=T.id();T.isNode()&&(l.unshift(T),e.bfs&&(c[C]=!0,f.push(T)),d[C]=0)}for(var S=function(){var N=e.bfs?l.shift():l.pop(),O=N.id();if(e.dfs){if(c[O])return"continue";c[O]=!0,f.push(N)}var M=d[O],R=h[O],k=R!=null?R.source():null,P=R!=null?R.target():null,B=R==null?void 0:N.same(k)?P[0]:k[0],z=void 0;if(z=n(N,R,B,v++,M),z===!0)return p=N,"break";if(z===!1)return"break";for(var G=N.connectedEdges().filter(function(K){return(!i||K.source().same(N))&&b.has(K)}),F=0;F<G.length;F++){var U=G[F],Y=U.connectedNodes().filter(function(K){return!K.same(N)&&y.has(K)}),W=Y.id();Y.length!==0&&!c[W]&&(Y=Y[0],l.push(Y),e.bfs&&(c[W]=!0,f.push(Y)),h[W]=U,d[W]=d[O]+1)}};l.length!==0;){var E=S();if(E!=="continue"&&E==="break")break}for(var w=o.collection(),x=0;x<f.length;x++){var D=f[x],L=h[D.id()];L!=null&&w.push(L),w.push(D)}return{path:o.collection(w),found:o.collection(p)}}},da={breadthFirstSearch:Zi({bfs:!0}),depthFirstSearch:Zi({dfs:!0})};da.bfs=da.breadthFirstSearch;da.dfs=da.depthFirstSearch;var Bf=zl(function(t,e){(function(){var r,a,n,i,s,o,u,l,f,h,d,c,v,p,g;n=Math.floor,h=Math.min,a=function(y,b){return y<b?-1:y>b?1:0},f=function(y,b,m,T,C){var S;if(m==null&&(m=0),C==null&&(C=a),m<0)throw new Error("lo must be non-negative");for(T==null&&(T=y.length);m<T;)S=n((m+T)/2),C(b,y[S])<0?T=S:m=S+1;return[].splice.apply(y,[m,m-m].concat(b)),b},o=function(y,b,m){return m==null&&(m=a),y.push(b),p(y,0,y.length-1,m)},s=function(y,b){var m,T;return b==null&&(b=a),m=y.pop(),y.length?(T=y[0],y[0]=m,g(y,0,b)):T=m,T},l=function(y,b,m){var T;return m==null&&(m=a),T=y[0],y[0]=b,g(y,0,m),T},u=function(y,b,m){var T;return m==null&&(m=a),y.length&&m(y[0],b)<0&&(T=[y[0],b],b=T[0],y[0]=T[1],g(y,0,m)),b},i=function(y,b){var m,T,C,S,E,w;for(b==null&&(b=a),S=(function(){w=[];for(var x=0,D=n(y.length/2);0<=D?x<D:x>D;0<=D?x++:x--)w.push(x);return w}).apply(this).reverse(),E=[],T=0,C=S.length;T<C;T++)m=S[T],E.push(g(y,m,b));return E},v=function(y,b,m){var T;if(m==null&&(m=a),T=y.indexOf(b),T!==-1)return p(y,0,T,m),g(y,T,m)},d=function(y,b,m){var T,C,S,E,w;if(m==null&&(m=a),C=y.slice(0,b),!C.length)return C;for(i(C,m),w=y.slice(b),S=0,E=w.length;S<E;S++)T=w[S],u(C,T,m);return C.sort(m).reverse()},c=function(y,b,m){var T,C,S,E,w,x,D,L,A;if(m==null&&(m=a),b*10<=y.length){if(S=y.slice(0,b).sort(m),!S.length)return S;for(C=S[S.length-1],D=y.slice(b),E=0,x=D.length;E<x;E++)T=D[E],m(T,C)<0&&(f(S,T,0,null,m),S.pop(),C=S[S.length-1]);return S}for(i(y,m),A=[],w=0,L=h(b,y.length);0<=L?w<L:w>L;0<=L?++w:--w)A.push(s(y,m));return A},p=function(y,b,m,T){var C,S,E;for(T==null&&(T=a),C=y[m];m>b;){if(E=m-1>>1,S=y[E],T(C,S)<0){y[m]=S,m=E;continue}break}return y[m]=C},g=function(y,b,m){var T,C,S,E,w;for(m==null&&(m=a),C=y.length,w=b,S=y[b],T=2*b+1;T<C;)E=T+1,E<C&&!(m(y[T],y[E])<0)&&(T=E),y[b]=y[T],b=T,T=2*b+1;return y[b]=S,p(y,w,b,m)},r=function(){y.push=o,y.pop=s,y.replace=l,y.pushpop=u,y.heapify=i,y.updateItem=v,y.nlargest=d,y.nsmallest=c;function y(b){this.cmp=b??a,this.nodes=[]}return y.prototype.push=function(b){return o(this.nodes,b,this.cmp)},y.prototype.pop=function(){return s(this.nodes,this.cmp)},y.prototype.peek=function(){return this.nodes[0]},y.prototype.contains=function(b){return this.nodes.indexOf(b)!==-1},y.prototype.replace=function(b){return l(this.nodes,b,this.cmp)},y.prototype.pushpop=function(b){return u(this.nodes,b,this.cmp)},y.prototype.heapify=function(){return i(this.nodes,this.cmp)},y.prototype.updateItem=function(b){return v(this.nodes,b,this.cmp)},y.prototype.clear=function(){return this.nodes=[]},y.prototype.empty=function(){return this.nodes.length===0},y.prototype.size=function(){return this.nodes.length},y.prototype.clone=function(){var b;return b=new y,b.nodes=this.nodes.slice(0),b},y.prototype.toArray=function(){return this.nodes.slice(0)},y.prototype.insert=y.prototype.push,y.prototype.top=y.prototype.peek,y.prototype.front=y.prototype.peek,y.prototype.has=y.prototype.contains,y.prototype.copy=y.prototype.clone,y}(),function(y,b){return t.exports=b()}(this,function(){return r})}).call(na)}),Da=Bf,Ff=tt({root:null,weight:function(e){return 1},directed:!1}),Gf={dijkstra:function(e){if(!Ce(e)){var r=arguments;e={root:r[0],weight:r[1],directed:r[2]}}var a=Ff(e),n=a.root,i=a.weight,s=a.directed,o=this,u=i,l=de(n)?this.filter(n)[0]:n[0],f={},h={},d={},c=this.byGroup(),v=c.nodes,p=c.edges;p.unmergeBy(function(M){return M.isLoop()});for(var g=function(R){return f[R.id()]},y=function(R,k){f[R.id()]=k,b.updateItem(R)},b=new Da(function(M,R){return g(M)-g(R)}),m=0;m<v.length;m++){var T=v[m];f[T.id()]=T.same(l)?0:1/0,b.push(T)}for(var C=function(R,k){for(var P=(s?R.edgesTo(k):R.edgesWith(k)).intersect(p),B=1/0,z,G=0;G<P.length;G++){var F=P[G],U=u(F);(U<B||!z)&&(B=U,z=F)}return{edge:z,dist:B}};b.size()>0;){var S=b.pop(),E=g(S),w=S.id();if(d[w]=E,E!==1/0)for(var x=S.neighborhood().intersect(v),D=0;D<x.length;D++){var L=x[D],A=L.id(),N=C(S,L),O=E+N.dist;O<g(L)&&(y(L,O),h[A]={node:S,edge:N.edge})}}return{distanceTo:function(R){var k=de(R)?v.filter(R)[0]:R[0];return d[k.id()]},pathTo:function(R){var k=de(R)?v.filter(R)[0]:R[0],P=[],B=k,z=B.id();if(k.length>0)for(P.unshift(k);h[z];){var G=h[z];P.unshift(G.edge),P.unshift(G.node),B=G.node,z=B.id()}return o.spawn(P)}}}},zf={kruskal:function(e){e=e||function(m){return 1};for(var r=this.byGroup(),a=r.nodes,n=r.edges,i=a.length,s=new Array(i),o=a,u=function(T){for(var C=0;C<s.length;C++){var S=s[C];if(S.has(T))return C}},l=0;l<i;l++)s[l]=this.spawn(a[l]);for(var f=n.sort(function(m,T){return e(m)-e(T)}),h=0;h<f.length;h++){var d=f[h],c=d.source()[0],v=d.target()[0],p=u(c),g=u(v),y=s[p],b=s[g];p!==g&&(o.merge(d),y.merge(b),s.splice(g,1))}return o}},Vf=tt({root:null,goal:null,weight:function(e){return 1},heuristic:function(e){return 0},directed:!1}),Uf={aStar:function(e){var r=this.cy(),a=Vf(e),n=a.root,i=a.goal,s=a.heuristic,o=a.directed,u=a.weight;n=r.collection(n)[0],i=r.collection(i)[0];var l=n.id(),f=i.id(),h={},d={},c={},v=new Da(function(z,G){return d[z.id()]-d[G.id()]}),p=new Ur,g={},y={},b=function(G,F){v.push(G),p.add(F)},m,T,C=function(){m=v.pop(),T=m.id(),p.delete(T)},S=function(G){return p.has(G)};b(n,l),h[l]=0,d[l]=s(n);for(var E=0;v.size()>0;){if(C(),E++,T===f){for(var w=[],x=i,D=f,L=y[D];w.unshift(x),L!=null&&w.unshift(L),x=g[D],x!=null;)D=x.id(),L=y[D];return{found:!0,distance:h[T],path:this.spawn(w),steps:E}}c[T]=!0;for(var A=m._private.edges,N=0;N<A.length;N++){var O=A[N];if(this.hasElementWithId(O.id())&&!(o&&O.data("source")!==T)){var M=O.source(),R=O.target(),k=M.id()!==T?M:R,P=k.id();if(this.hasElementWithId(P)&&!c[P]){var B=h[T]+u(O);if(!S(P)){h[P]=B,d[P]=B+s(k),b(k,P),g[P]=m,y[P]=O;continue}B<h[P]&&(h[P]=B,d[P]=B+s(k),g[P]=m,y[P]=O)}}}}return{found:!1,distance:void 0,path:void 0,steps:E}}},$f=tt({weight:function(e){return 1},directed:!1}),Yf={floydWarshall:function(e){for(var r=this.cy(),a=$f(e),n=a.weight,i=a.directed,s=n,o=this.byGroup(),u=o.nodes,l=o.edges,f=u.length,h=f*f,d=function(U){return u.indexOf(U)},c=function(U){return u[U]},v=new Array(h),p=0;p<h;p++){var g=p%f,y=(p-g)/f;y===g?v[p]=0:v[p]=1/0}for(var b=new Array(h),m=new Array(h),T=0;T<l.length;T++){var C=l[T],S=C.source()[0],E=C.target()[0];if(S!==E){var w=d(S),x=d(E),D=w*f+x,L=s(C);if(v[D]>L&&(v[D]=L,b[D]=x,m[D]=C),!i){var A=x*f+w;!i&&v[A]>L&&(v[A]=L,b[A]=w,m[A]=C)}}}for(var N=0;N<f;N++)for(var O=0;O<f;O++)for(var M=O*f+N,R=0;R<f;R++){var k=O*f+R,P=N*f+R;v[M]+v[P]<v[k]&&(v[k]=v[M]+v[P],b[k]=b[M])}var B=function(U){return(de(U)?r.filter(U):U)[0]},z=function(U){return d(B(U))},G={distance:function(U,Y){var W=z(U),K=z(Y);return v[W*f+K]},path:function(U,Y){var W=z(U),K=z(Y),j=c(W);if(W===K)return j.collection();if(b[W*f+K]==null)return r.collection();var _=r.collection(),V=W,H;for(_.merge(j);W!==K;)V=W,W=b[W*f+K],H=m[V*f+W],_.merge(H),_.merge(c(W));return _}};return G}},_f=tt({weight:function(e){return 1},directed:!1,root:null}),Hf={bellmanFord:function(e){var r=this,a=_f(e),n=a.weight,i=a.directed,s=a.root,o=n,u=this,l=this.cy(),f=this.byGroup(),h=f.edges,d=f.nodes,c=d.length,v=new Bt,p=!1,g=[];s=l.collection(s)[0],h.unmergeBy(function(ve){return ve.isLoop()});for(var y=h.length,b=function(fe){var pe=v.get(fe.id());return pe||(pe={},v.set(fe.id(),pe)),pe},m=function(fe){return(de(fe)?l.$(fe):fe)[0]},T=function(fe){return b(m(fe)).dist},C=function(fe){for(var pe=arguments.length>1&&arguments[1]!==void 0?arguments[1]:s,Ae=m(fe),xe=[],we=Ae;;){if(we==null)return r.spawn();var De=b(we),ee=De.edge,I=De.pred;if(xe.unshift(we[0]),we.same(pe)&&xe.length>0)break;ee!=null&&xe.unshift(ee),we=I}return u.spawn(xe)},S=0;S<c;S++){var E=d[S],w=b(E);E.same(s)?w.dist=0:w.dist=1/0,w.pred=null,w.edge=null}for(var x=!1,D=function(fe,pe,Ae,xe,we,De){var ee=xe.dist+De;ee<we.dist&&!Ae.same(xe.edge)&&(we.dist=ee,we.pred=fe,we.edge=Ae,x=!0)},L=1;L<c;L++){x=!1;for(var A=0;A<y;A++){var N=h[A],O=N.source(),M=N.target(),R=o(N),k=b(O),P=b(M);D(O,M,N,k,P,R),i||D(M,O,N,P,k,R)}if(!x)break}if(x)for(var B=[],z=0;z<y;z++){var G=h[z],F=G.source(),U=G.target(),Y=o(G),W=b(F).dist,K=b(U).dist;if(W+Y<K||!i&&K+Y<W)if(p||(Ne("Graph contains a negative weight cycle for Bellman-Ford"),p=!0),e.findNegativeWeightCycles!==!1){var j=[];W+Y<K&&j.push(F),!i&&K+Y<W&&j.push(U);for(var _=j.length,V=0;V<_;V++){var H=j[V],Q=[H];Q.push(b(H).edge);for(var ne=b(H).pred;Q.indexOf(ne)===-1;)Q.push(ne),Q.push(b(ne).edge),ne=b(ne).pred;Q=Q.slice(Q.indexOf(ne));for(var ce=Q[0].id(),te=0,se=2;se<Q.length;se+=2)Q[se].id()<ce&&(ce=Q[se].id(),te=se);Q=Q.slice(te).concat(Q.slice(0,te)),Q.push(Q[0]);var ue=Q.map(function(ve){return ve.id()}).join(",");B.indexOf(ue)===-1&&(g.push(u.spawn(Q)),B.push(ue))}}else break}return{distanceTo:T,pathTo:C,hasNegativeWeightCycle:p,negativeWeightCycles:g}}},Xf=Math.sqrt(2),qf=function(e,r,a){a.length===0&&ze("Karger-Stein must be run on a connected (sub)graph");for(var n=a[e],i=n[1],s=n[2],o=r[i],u=r[s],l=a,f=l.length-1;f>=0;f--){var h=l[f],d=h[1],c=h[2];(r[d]===o&&r[c]===u||r[d]===u&&r[c]===o)&&l.splice(f,1)}for(var v=0;v<l.length;v++){var p=l[v];p[1]===u?(l[v]=p.slice(),l[v][1]=o):p[2]===u&&(l[v]=p.slice(),l[v][2]=o)}for(var g=0;g<r.length;g++)r[g]===u&&(r[g]=o);return l},Pn=function(e,r,a,n){for(;a>n;){var i=Math.floor(Math.random()*r.length);r=qf(i,e,r),a--}return r},Wf={kargerStein:function(){var e=this,r=this.byGroup(),a=r.nodes,n=r.edges;n.unmergeBy(function(P){return P.isLoop()});var i=a.length,s=n.length,o=Math.ceil(Math.pow(Math.log(i)/Math.LN2,2)),u=Math.floor(i/Xf);if(i<2){ze("At least 2 nodes are required for Karger-Stein algorithm");return}for(var l=[],f=0;f<s;f++){var h=n[f];l.push([f,a.indexOf(h.source()),a.indexOf(h.target())])}for(var d=1/0,c=[],v=new Array(i),p=new Array(i),g=new Array(i),y=function(B,z){for(var G=0;G<i;G++)z[G]=B[G]},b=0;b<=o;b++){for(var m=0;m<i;m++)p[m]=m;var T=Pn(p,l.slice(),i,u),C=T.slice();y(p,g);var S=Pn(p,T,u,2),E=Pn(g,C,u,2);S.length<=E.length&&S.length<d?(d=S.length,c=S,y(p,v)):E.length<=S.length&&E.length<d&&(d=E.length,c=E,y(g,v))}for(var w=this.spawn(c.map(function(P){return n[P[0]]})),x=this.spawn(),D=this.spawn(),L=v[0],A=0;A<v.length;A++){var N=v[A],O=a[A];N===L?x.merge(O):D.merge(O)}var M=function(B){var z=e.spawn();return B.forEach(function(G){z.merge(G),G.connectedEdges().forEach(function(F){e.contains(F)&&!w.contains(F)&&z.merge(F)})}),z},R=[M(x),M(D)],k={cut:w,components:R,partition1:x,partition2:D};return k}},Kf=function(e){return{x:e.x,y:e.y}},yn=function(e,r,a){return{x:e.x*r+a.x,y:e.y*r+a.y}},Co=function(e,r,a){return{x:(e.x-a.x)/r,y:(e.y-a.y)/r}},Ir=function(e){return{x:e[0],y:e[1]}},Zf=function(e){for(var r=arguments.length>1&&arguments[1]!==void 0?arguments[1]:0,a=arguments.length>2&&arguments[2]!==void 0?arguments[2]:e.length,n=1/0,i=r;i<a;i++){var s=e[i];isFinite(s)&&(n=Math.min(s,n))}return n},Qf=function(e){for(var r=arguments.length>1&&arguments[1]!==void 0?arguments[1]:0,a=arguments.length>2&&arguments[2]!==void 0?arguments[2]:e.length,n=-1/0,i=r;i<a;i++){var s=e[i];isFinite(s)&&(n=Math.max(s,n))}return n},Jf=function(e){for(var r=arguments.length>1&&arguments[1]!==void 0?arguments[1]:0,a=arguments.length>2&&arguments[2]!==void 0?arguments[2]:e.length,n=0,i=0,s=r;s<a;s++){var o=e[s];isFinite(o)&&(n+=o,i++)}return n/i},jf=function(e){var r=arguments.length>1&&arguments[1]!==void 0?arguments[1]:0,a=arguments.length>2&&arguments[2]!==void 0?arguments[2]:e.length,n=arguments.length>3&&arguments[3]!==void 0?arguments[3]:!0,i=arguments.length>4&&arguments[4]!==void 0?arguments[4]:!0,s=arguments.length>5&&arguments[5]!==void 0?arguments[5]:!0;n?e=e.slice(r,a):(a<e.length&&e.splice(a,e.length-a),r>0&&e.splice(0,r));for(var o=0,u=e.length-1;u>=0;u--){var l=e[u];s?isFinite(l)||(e[u]=-1/0,o++):e.splice(u,1)}i&&e.sort(function(d,c){return d-c});var f=e.length,h=Math.floor(f/2);return f%2!==0?e[h+1+o]:(e[h-1+o]+e[h+o])/2},eh=function(e){return Math.PI*e/180},Ra=function(e,r){return Math.atan2(r,e)-Math.PI/2},Ei=Math.log2||function(t){return Math.log(t)/Math.log(2)},Do=function(e){return e>0?1:e<0?-1:0},gr=function(e,r){return Math.sqrt(ur(e,r))},ur=function(e,r){var a=r.x-e.x,n=r.y-e.y;return a*a+n*n},th=function(e){for(var r=e.length,a=0,n=0;n<r;n++)a+=e[n];for(var i=0;i<r;i++)e[i]=e[i]/a;return e},Ke=function(e,r,a,n){return(1-n)*(1-n)*e+2*(1-n)*n*r+n*n*a},Rr=function(e,r,a,n){return{x:Ke(e.x,r.x,a.x,n),y:Ke(e.y,r.y,a.y,n)}},rh=function(e,r,a,n){var i={x:r.x-e.x,y:r.y-e.y},s=gr(e,r),o={x:i.x/s,y:i.y/s};return a=a??0,n=n??a*s,{x:e.x+o.x*n,y:e.y+o.y*n}},ga=function(e,r,a){return Math.max(e,Math.min(a,r))},gt=function(e){if(e==null)return{x1:1/0,y1:1/0,x2:-1/0,y2:-1/0,w:0,h:0};if(e.x1!=null&&e.y1!=null){if(e.x2!=null&&e.y2!=null&&e.x2>=e.x1&&e.y2>=e.y1)return{x1:e.x1,y1:e.y1,x2:e.x2,y2:e.y2,w:e.x2-e.x1,h:e.y2-e.y1};if(e.w!=null&&e.h!=null&&e.w>=0&&e.h>=0)return{x1:e.x1,y1:e.y1,x2:e.x1+e.w,y2:e.y1+e.h,w:e.w,h:e.h}}},ah=function(e){return{x1:e.x1,x2:e.x2,w:e.w,y1:e.y1,y2:e.y2,h:e.h}},nh=function(e){e.x1=1/0,e.y1=1/0,e.x2=-1/0,e.y2=-1/0,e.w=0,e.h=0},ih=function(e,r,a){return{x1:e.x1+r,x2:e.x2+r,y1:e.y1+a,y2:e.y2+a,w:e.w,h:e.h}},So=function(e,r){e.x1=Math.min(e.x1,r.x1),e.x2=Math.max(e.x2,r.x2),e.w=e.x2-e.x1,e.y1=Math.min(e.y1,r.y1),e.y2=Math.max(e.y2,r.y2),e.h=e.y2-e.y1},sh=function(e,r,a){e.x1=Math.min(e.x1,r),e.x2=Math.max(e.x2,r),e.w=e.x2-e.x1,e.y1=Math.min(e.y1,a),e.y2=Math.max(e.y2,a),e.h=e.y2-e.y1},_a=function(e){var r=arguments.length>1&&arguments[1]!==void 0?arguments[1]:0;return e.x1-=r,e.x2+=r,e.y1-=r,e.y2+=r,e.w=e.x2-e.x1,e.h=e.y2-e.y1,e},Ha=function(e){var r=arguments.length>1&&arguments[1]!==void 0?arguments[1]:[0],a,n,i,s;if(r.length===1)a=n=i=s=r[0];else if(r.length===2)a=i=r[0],s=n=r[1];else if(r.length===4){var o=St(r,4);a=o[0],n=o[1],i=o[2],s=o[3]}return e.x1-=s,e.x2+=n,e.y1-=a,e.y2+=i,e.w=e.x2-e.x1,e.h=e.y2-e.y1,e},Qi=function(e,r){e.x1=r.x1,e.y1=r.y1,e.x2=r.x2,e.y2=r.y2,e.w=e.x2-e.x1,e.h=e.y2-e.y1},wi=function(e,r){return!(e.x1>r.x2||r.x1>e.x2||e.x2<r.x1||r.x2<e.x1||e.y2<r.y1||r.y2<e.y1||e.y1>r.y2||r.y1>e.y2)},Gr=function(e,r,a){return e.x1<=r&&r<=e.x2&&e.y1<=a&&a<=e.y2},oh=function(e,r){return Gr(e,r.x,r.y)},Lo=function(e,r){return Gr(e,r.x1,r.y1)&&Gr(e,r.x2,r.y2)},Ao=function(e,r,a,n,i,s,o){var u=arguments.length>7&&arguments[7]!==void 0?arguments[7]:"auto",l=u==="auto"?pr(i,s):u,f=i/2,h=s/2;l=Math.min(l,f,h);var d=l!==f,c=l!==h,v;if(d){var p=a-f+l-o,g=n-h-o,y=a+f-l+o,b=g;if(v=Zt(e,r,a,n,p,g,y,b,!1),v.length>0)return v}if(c){var m=a+f+o,T=n-h+l-o,C=m,S=n+h-l+o;if(v=Zt(e,r,a,n,m,T,C,S,!1),v.length>0)return v}if(d){var E=a-f+l-o,w=n+h+o,x=a+f-l+o,D=w;if(v=Zt(e,r,a,n,E,w,x,D,!1),v.length>0)return v}if(c){var L=a-f-o,A=n-h+l-o,N=L,O=n+h-l+o;if(v=Zt(e,r,a,n,L,A,N,O,!1),v.length>0)return v}var M;{var R=a-f+l,k=n-h+l;if(M=sa(e,r,a,n,R,k,l+o),M.length>0&&M[0]<=R&&M[1]<=k)return[M[0],M[1]]}{var P=a+f-l,B=n-h+l;if(M=sa(e,r,a,n,P,B,l+o),M.length>0&&M[0]>=P&&M[1]<=B)return[M[0],M[1]]}{var z=a+f-l,G=n+h-l;if(M=sa(e,r,a,n,z,G,l+o),M.length>0&&M[0]>=z&&M[1]>=G)return[M[0],M[1]]}{var F=a-f+l,U=n+h-l;if(M=sa(e,r,a,n,F,U,l+o),M.length>0&&M[0]<=F&&M[1]>=U)return[M[0],M[1]]}return[]},uh=function(e,r,a,n,i,s,o){var u=o,l=Math.min(a,i),f=Math.max(a,i),h=Math.min(n,s),d=Math.max(n,s);return l-u<=e&&e<=f+u&&h-u<=r&&r<=d+u},lh=function(e,r,a,n,i,s,o,u,l){var f={x1:Math.min(a,o,i)-l,x2:Math.max(a,o,i)+l,y1:Math.min(n,u,s)-l,y2:Math.max(n,u,s)+l};return!(e<f.x1||e>f.x2||r<f.y1||r>f.y2)},fh=function(e,r,a,n){a-=n;var i=r*r-4*e*a;if(i<0)return[];var s=Math.sqrt(i),o=2*e,u=(-r+s)/o,l=(-r-s)/o;return[u,l]},hh=function(e,r,a,n,i){var s=1e-5;e===0&&(e=s),r/=e,a/=e,n/=e;var o,u,l,f,h,d,c,v;if(u=(3*a-r*r)/9,l=-(27*n)+r*(9*a-2*(r*r)),l/=54,o=u*u*u+l*l,i[1]=0,c=r/3,o>0){h=l+Math.sqrt(o),h=h<0?-Math.pow(-h,1/3):Math.pow(h,1/3),d=l-Math.sqrt(o),d=d<0?-Math.pow(-d,1/3):Math.pow(d,1/3),i[0]=-c+h+d,c+=(h+d)/2,i[4]=i[2]=-c,c=Math.sqrt(3)*(-d+h)/2,i[3]=c,i[5]=-c;return}if(i[5]=i[3]=0,o===0){v=l<0?-Math.pow(-l,1/3):Math.pow(l,1/3),i[0]=-c+2*v,i[4]=i[2]=-(v+c);return}u=-u,f=u*u*u,f=Math.acos(l/Math.sqrt(f)),v=2*Math.sqrt(u),i[0]=-c+v*Math.cos(f/3),i[2]=-c+v*Math.cos((f+2*Math.PI)/3),i[4]=-c+v*Math.cos((f+4*Math.PI)/3)},ch=function(e,r,a,n,i,s,o,u){var l=1*a*a-4*a*i+2*a*o+4*i*i-4*i*o+o*o+n*n-4*n*s+2*n*u+4*s*s-4*s*u+u*u,f=1*9*a*i-3*a*a-3*a*o-6*i*i+3*i*o+9*n*s-3*n*n-3*n*u-6*s*s+3*s*u,h=1*3*a*a-6*a*i+a*o-a*e+2*i*i+2*i*e-o*e+3*n*n-6*n*s+n*u-n*r+2*s*s+2*s*r-u*r,d=1*a*i-a*a+a*e-i*e+n*s-n*n+n*r-s*r,c=[];hh(l,f,h,d,c);for(var v=1e-7,p=[],g=0;g<6;g+=2)Math.abs(c[g+1])<v&&c[g]>=0&&c[g]<=1&&p.push(c[g]);p.push(1),p.push(0);for(var y=-1,b,m,T,C=0;C<p.length;C++)b=Math.pow(1-p[C],2)*a+2*(1-p[C])*p[C]*i+p[C]*p[C]*o,m=Math.pow(1-p[C],2)*n+2*(1-p[C])*p[C]*s+p[C]*p[C]*u,T=Math.pow(b-e,2)+Math.pow(m-r,2),y>=0?T<y&&(y=T):y=T;return y},vh=function(e,r,a,n,i,s){var o=[e-a,r-n],u=[i-a,s-n],l=u[0]*u[0]+u[1]*u[1],f=o[0]*o[0]+o[1]*o[1],h=o[0]*u[0]+o[1]*u[1],d=h*h/l;return h<0?f:d>l?(e-i)*(e-i)+(r-s)*(r-s):f-d},dt=function(e,r,a){for(var n,i,s,o,u,l=0,f=0;f<a.length/2;f++)if(n=a[f*2],i=a[f*2+1],f+1<a.length/2?(s=a[(f+1)*2],o=a[(f+1)*2+1]):(s=a[(f+1-a.length/2)*2],o=a[(f+1-a.length/2)*2+1]),!(n==e&&s==e))if(n>=e&&e>=s||n<=e&&e<=s)u=(e-n)/(s-n)*(o-i)+i,u>r&&l++;else continue;return l%2!==0},Yt=function(e,r,a,n,i,s,o,u,l){var f=new Array(a.length),h;u[0]!=null?(h=Math.atan(u[1]/u[0]),u[0]<0?h=h+Math.PI/2:h=-h-Math.PI/2):h=u;for(var d=Math.cos(-h),c=Math.sin(-h),v=0;v<f.length/2;v++)f[v*2]=s/2*(a[v*2]*d-a[v*2+1]*c),f[v*2+1]=o/2*(a[v*2+1]*d+a[v*2]*c),f[v*2]+=n,f[v*2+1]+=i;var p;if(l>0){var g=sn(f,-l);p=nn(g)}else p=f;return dt(e,r,p)},dh=function(e,r,a,n,i,s,o,u){for(var l=new Array(a.length*2),f=0;f<u.length;f++){var h=u[f];l[f*4+0]=h.startX,l[f*4+1]=h.startY,l[f*4+2]=h.stopX,l[f*4+3]=h.stopY;var d=Math.pow(h.cx-e,2)+Math.pow(h.cy-r,2);if(d<=Math.pow(h.radius,2))return!0}return dt(e,r,l)},nn=function(e){for(var r=new Array(e.length/2),a,n,i,s,o,u,l,f,h=0;h<e.length/4;h++){a=e[h*4],n=e[h*4+1],i=e[h*4+2],s=e[h*4+3],h<e.length/4-1?(o=e[(h+1)*4],u=e[(h+1)*4+1],l=e[(h+1)*4+2],f=e[(h+1)*4+3]):(o=e[0],u=e[1],l=e[2],f=e[3]);var d=Zt(a,n,i,s,o,u,l,f,!0);r[h*2]=d[0],r[h*2+1]=d[1]}return r},sn=function(e,r){for(var a=new Array(e.length*2),n,i,s,o,u=0;u<e.length/2;u++){n=e[u*2],i=e[u*2+1],u<e.length/2-1?(s=e[(u+1)*2],o=e[(u+1)*2+1]):(s=e[0],o=e[1]);var l=o-i,f=-(s-n),h=Math.sqrt(l*l+f*f),d=l/h,c=f/h;a[u*4]=n+d*r,a[u*4+1]=i+c*r,a[u*4+2]=s+d*r,a[u*4+3]=o+c*r}return a},gh=function(e,r,a,n,i,s){var o=a-e,u=n-r;o/=i,u/=s;var l=Math.sqrt(o*o+u*u),f=l-1;if(f<0)return[];var h=f/l;return[(a-e)*h+e,(n-r)*h+r]},cr=function(e,r,a,n,i,s,o){return e-=i,r-=s,e/=a/2+o,r/=n/2+o,e*e+r*r<=1},sa=function(e,r,a,n,i,s,o){var u=[a-e,n-r],l=[e-i,r-s],f=u[0]*u[0]+u[1]*u[1],h=2*(l[0]*u[0]+l[1]*u[1]),d=l[0]*l[0]+l[1]*l[1]-o*o,c=h*h-4*f*d;if(c<0)return[];var v=(-h+Math.sqrt(c))/(2*f),p=(-h-Math.sqrt(c))/(2*f),g=Math.min(v,p),y=Math.max(v,p),b=[];if(g>=0&&g<=1&&b.push(g),y>=0&&y<=1&&b.push(y),b.length===0)return[];var m=b[0]*u[0]+e,T=b[0]*u[1]+r;if(b.length>1){if(b[0]==b[1])return[m,T];var C=b[1]*u[0]+e,S=b[1]*u[1]+r;return[m,T,C,S]}else return[m,T]},Bn=function(e,r,a){return r<=e&&e<=a||a<=e&&e<=r?e:e<=r&&r<=a||a<=r&&r<=e?r:a},Zt=function(e,r,a,n,i,s,o,u,l){var f=e-i,h=a-e,d=o-i,c=r-s,v=n-r,p=u-s,g=d*c-p*f,y=h*c-v*f,b=p*h-d*v;if(b!==0){var m=g/b,T=y/b,C=.001,S=0-C,E=1+C;return S<=m&&m<=E&&S<=T&&T<=E?[e+m*h,r+m*v]:l?[e+m*h,r+m*v]:[]}else return g===0||y===0?Bn(e,a,o)===o?[o,u]:Bn(e,a,i)===i?[i,s]:Bn(i,o,a)===a?[a,n]:[]:[]},pa=function(e,r,a,n,i,s,o,u){var l=[],f,h=new Array(a.length),d=!0;s==null&&(d=!1);var c;if(d){for(var v=0;v<h.length/2;v++)h[v*2]=a[v*2]*s+n,h[v*2+1]=a[v*2+1]*o+i;if(u>0){var p=sn(h,-u);c=nn(p)}else c=h}else c=a;for(var g,y,b,m,T=0;T<c.length/2;T++)g=c[T*2],y=c[T*2+1],T<c.length/2-1?(b=c[(T+1)*2],m=c[(T+1)*2+1]):(b=c[0],m=c[1]),f=Zt(e,r,n,i,g,y,b,m),f.length!==0&&l.push(f[0],f[1]);return l},ph=function(e,r,a,n,i,s,o,u,l){var f=[],h,d=new Array(a.length*2);l.forEach(function(b,m){m===0?(d[d.length-2]=b.startX,d[d.length-1]=b.startY):(d[m*4-2]=b.startX,d[m*4-1]=b.startY),d[m*4]=b.stopX,d[m*4+1]=b.stopY,h=sa(e,r,n,i,b.cx,b.cy,b.radius),h.length!==0&&f.push(h[0],h[1])});for(var c=0;c<d.length/4;c++)h=Zt(e,r,n,i,d[c*4],d[c*4+1],d[c*4+2],d[c*4+3],!1),h.length!==0&&f.push(h[0],h[1]);if(f.length>2){for(var v=[f[0],f[1]],p=Math.pow(v[0]-e,2)+Math.pow(v[1]-r,2),g=1;g<f.length/2;g++){var y=Math.pow(f[g*2]-e,2)+Math.pow(f[g*2+1]-r,2);y<=p&&(v[0]=f[g*2],v[1]=f[g*2+1],p=y)}return v}return f},ka=function(e,r,a){var n=[e[0]-r[0],e[1]-r[1]],i=Math.sqrt(n[0]*n[0]+n[1]*n[1]),s=(i-a)/i;return s<0&&(s=1e-5),[r[0]+s*n[0],r[1]+s*n[1]]},ht=function(e,r){var a=Wn(e,r);return a=Oo(a),a},Oo=function(e){for(var r,a,n=e.length/2,i=1/0,s=1/0,o=-1/0,u=-1/0,l=0;l<n;l++)r=e[2*l],a=e[2*l+1],i=Math.min(i,r),o=Math.max(o,r),s=Math.min(s,a),u=Math.max(u,a);for(var f=2/(o-i),h=2/(u-s),d=0;d<n;d++)r=e[2*d]=e[2*d]*f,a=e[2*d+1]=e[2*d+1]*h,i=Math.min(i,r),o=Math.max(o,r),s=Math.min(s,a),u=Math.max(u,a);if(s<-1)for(var c=0;c<n;c++)a=e[2*c+1]=e[2*c+1]+(-1-s);return e},Wn=function(e,r){var a=1/e*2*Math.PI,n=e%2===0?Math.PI/2+a/2:Math.PI/2;n+=r;for(var i=new Array(e*2),s,o=0;o<e;o++)s=o*a+n,i[2*o]=Math.cos(s),i[2*o+1]=Math.sin(-s);return i},pr=function(e,r){return Math.min(e/4,r/4,8)},No=function(e,r){return Math.min(e/10,r/10,8)},xi=function(){return 8},yh=function(e,r,a){return[e-2*r+a,2*(r-e),e]},Kn=function(e,r){return{heightOffset:Math.min(15,.05*r),widthOffset:Math.min(100,.25*e),ctrlPtOffsetPct:.05}},mh=tt({dampingFactor:.8,precision:1e-6,iterations:200,weight:function(e){return 1}}),bh={pageRank:function(e){for(var r=mh(e),a=r.dampingFactor,n=r.precision,i=r.iterations,s=r.weight,o=this._private.cy,u=this.byGroup(),l=u.nodes,f=u.edges,h=l.length,d=h*h,c=f.length,v=new Array(d),p=new Array(h),g=(1-a)/h,y=0;y<h;y++){for(var b=0;b<h;b++){var m=y*h+b;v[m]=0}p[y]=0}for(var T=0;T<c;T++){var C=f[T],S=C.data("source"),E=C.data("target");if(S!==E){var w=l.indexOfId(S),x=l.indexOfId(E),D=s(C),L=x*h+w;v[L]+=D,p[w]+=D}}for(var A=1/h+g,N=0;N<h;N++)if(p[N]===0)for(var O=0;O<h;O++){var M=O*h+N;v[M]=A}else for(var R=0;R<h;R++){var k=R*h+N;v[k]=v[k]/p[N]+g}for(var P=new Array(h),B=new Array(h),z,G=0;G<h;G++)P[G]=1;for(var F=0;F<i;F++){for(var U=0;U<h;U++)B[U]=0;for(var Y=0;Y<h;Y++)for(var W=0;W<h;W++){var K=Y*h+W;B[Y]+=v[K]*P[W]}th(B),z=P,P=B,B=z;for(var j=0,_=0;_<h;_++){var V=z[_]-P[_];j+=V*V}if(j<n)break}var H={rank:function(ne){return ne=o.collection(ne)[0],P[l.indexOf(ne)]}};return H}},Ji=tt({root:null,weight:function(e){return 1},directed:!1,alpha:0}),kr={degreeCentralityNormalized:function(e){e=Ji(e);var r=this.cy(),a=this.nodes(),n=a.length;if(e.directed){for(var f={},h={},d=0,c=0,v=0;v<n;v++){var p=a[v],g=p.id();e.root=p;var y=this.degreeCentrality(e);d<y.indegree&&(d=y.indegree),c<y.outdegree&&(c=y.outdegree),f[g]=y.indegree,h[g]=y.outdegree}return{indegree:function(m){return d==0?0:(de(m)&&(m=r.filter(m)),f[m.id()]/d)},outdegree:function(m){return c===0?0:(de(m)&&(m=r.filter(m)),h[m.id()]/c)}}}else{for(var i={},s=0,o=0;o<n;o++){var u=a[o];e.root=u;var l=this.degreeCentrality(e);s<l.degree&&(s=l.degree),i[u.id()]=l.degree}return{degree:function(m){return s===0?0:(de(m)&&(m=r.filter(m)),i[m.id()]/s)}}}},degreeCentrality:function(e){e=Ji(e);var r=this.cy(),a=this,n=e,i=n.root,s=n.weight,o=n.directed,u=n.alpha;if(i=r.collection(i)[0],o){for(var c=i.connectedEdges(),v=c.filter(function(S){return S.target().same(i)&&a.has(S)}),p=c.filter(function(S){return S.source().same(i)&&a.has(S)}),g=v.length,y=p.length,b=0,m=0,T=0;T<v.length;T++)b+=s(v[T]);for(var C=0;C<p.length;C++)m+=s(p[C]);return{indegree:Math.pow(g,1-u)*Math.pow(b,u),outdegree:Math.pow(y,1-u)*Math.pow(m,u)}}else{for(var l=i.connectedEdges().intersection(a),f=l.length,h=0,d=0;d<l.length;d++)h+=s(l[d]);return{degree:Math.pow(f,1-u)*Math.pow(h,u)}}}};kr.dc=kr.degreeCentrality;kr.dcn=kr.degreeCentralityNormalised=kr.degreeCentralityNormalized;var ji=tt({harmonic:!0,weight:function(){return 1},directed:!1,root:null}),Pr={closenessCentralityNormalized:function(e){for(var r=ji(e),a=r.harmonic,n=r.weight,i=r.directed,s=this.cy(),o={},u=0,l=this.nodes(),f=this.floydWarshall({weight:n,directed:i}),h=0;h<l.length;h++){for(var d=0,c=l[h],v=0;v<l.length;v++)if(h!==v){var p=f.distance(c,l[v]);a?d+=1/p:d+=p}a||(d=1/d),u<d&&(u=d),o[c.id()]=d}return{closeness:function(y){return u==0?0:(de(y)?y=s.filter(y)[0].id():y=y.id(),o[y]/u)}}},closenessCentrality:function(e){var r=ji(e),a=r.root,n=r.weight,i=r.directed,s=r.harmonic;a=this.filter(a)[0];for(var o=this.dijkstra({root:a,weight:n,directed:i}),u=0,l=this.nodes(),f=0;f<l.length;f++){var h=l[f];if(!h.same(a)){var d=o.distanceTo(h);s?u+=1/d:u+=d}}return s?u:1/u}};Pr.cc=Pr.closenessCentrality;Pr.ccn=Pr.closenessCentralityNormalised=Pr.closenessCentralityNormalized;var Eh=tt({weight:null,directed:!1}),Zn={betweennessCentrality:function(e){for(var r=Eh(e),a=r.directed,n=r.weight,i=n!=null,s=this.cy(),o=this.nodes(),u={},l={},f=0,h={set:function(m,T){l[m]=T,T>f&&(f=T)},get:function(m){return l[m]}},d=0;d<o.length;d++){var c=o[d],v=c.id();a?u[v]=c.outgoers().nodes():u[v]=c.openNeighborhood().nodes(),h.set(v,0)}for(var p=function(m){for(var T=o[m].id(),C=[],S={},E={},w={},x=new Da(function(W,K){return w[W]-w[K]}),D=0;D<o.length;D++){var L=o[D].id();S[L]=[],E[L]=0,w[L]=1/0}for(E[T]=1,w[T]=0,x.push(T);!x.empty();){var A=x.pop();if(C.push(A),i)for(var N=0;N<u[A].length;N++){var O=u[A][N],M=s.getElementById(A),R=void 0;M.edgesTo(O).length>0?R=M.edgesTo(O)[0]:R=O.edgesTo(M)[0];var k=n(R);O=O.id(),w[O]>w[A]+k&&(w[O]=w[A]+k,x.nodes.indexOf(O)<0?x.push(O):x.updateItem(O),E[O]=0,S[O]=[]),w[O]==w[A]+k&&(E[O]=E[O]+E[A],S[O].push(A))}else for(var P=0;P<u[A].length;P++){var B=u[A][P].id();w[B]==1/0&&(x.push(B),w[B]=w[A]+1),w[B]==w[A]+1&&(E[B]=E[B]+E[A],S[B].push(A))}}for(var z={},G=0;G<o.length;G++)z[o[G].id()]=0;for(;C.length>0;){for(var F=C.pop(),U=0;U<S[F].length;U++){var Y=S[F][U];z[Y]=z[Y]+E[Y]/E[F]*(1+z[F])}F!=o[m].id()&&h.set(F,h.get(F)+z[F])}},g=0;g<o.length;g++)p(g);var y={betweenness:function(m){var T=s.collection(m).id();return h.get(T)},betweennessNormalized:function(m){if(f==0)return 0;var T=s.collection(m).id();return h.get(T)/f}};return y.betweennessNormalised=y.betweennessNormalized,y}};Zn.bc=Zn.betweennessCentrality;var wh=tt({expandFactor:2,inflateFactor:2,multFactor:1,maxIterations:20,attributes:[function(t){return 1}]}),xh=function(e){return wh(e)},Th=function(e,r){for(var a=0,n=0;n<r.length;n++)a+=r[n](e);return a},Ch=function(e,r,a){for(var n=0;n<r;n++)e[n*r+n]=a},Io=function(e,r){for(var a,n=0;n<r;n++){a=0;for(var i=0;i<r;i++)a+=e[i*r+n];for(var s=0;s<r;s++)e[s*r+n]=e[s*r+n]/a}},Dh=function(e,r,a){for(var n=new Array(a*a),i=0;i<a;i++){for(var s=0;s<a;s++)n[i*a+s]=0;for(var o=0;o<a;o++)for(var u=0;u<a;u++)n[i*a+u]+=e[i*a+o]*r[o*a+u]}return n},Sh=function(e,r,a){for(var n=e.slice(0),i=1;i<a;i++)e=Dh(e,n,r);return e},Lh=function(e,r,a){for(var n=new Array(r*r),i=0;i<r*r;i++)n[i]=Math.pow(e[i],a);return Io(n,r),n},Ah=function(e,r,a,n){for(var i=0;i<a;i++){var s=Math.round(e[i]*Math.pow(10,n))/Math.pow(10,n),o=Math.round(r[i]*Math.pow(10,n))/Math.pow(10,n);if(s!==o)return!1}return!0},Oh=function(e,r,a,n){for(var i=[],s=0;s<r;s++){for(var o=[],u=0;u<r;u++)Math.round(e[s*r+u]*1e3)/1e3>0&&o.push(a[u]);o.length!==0&&i.push(n.collection(o))}return i},Nh=function(e,r){for(var a=0;a<e.length;a++)if(!r[a]||e[a].id()!==r[a].id())return!1;return!0},Ih=function(e){for(var r=0;r<e.length;r++)for(var a=0;a<e.length;a++)r!=a&&Nh(e[r],e[a])&&e.splice(a,1);return e},es=function(e){for(var r=this.nodes(),a=this.edges(),n=this.cy(),i=xh(e),s={},o=0;o<r.length;o++)s[r[o].id()]=o;for(var u=r.length,l=u*u,f=new Array(l),h,d=0;d<l;d++)f[d]=0;for(var c=0;c<a.length;c++){var v=a[c],p=s[v.source().id()],g=s[v.target().id()],y=Th(v,i.attributes);f[p*u+g]+=y,f[g*u+p]+=y}Ch(f,u,i.multFactor),Io(f,u);for(var b=!0,m=0;b&&m<i.maxIterations;)b=!1,h=Sh(f,u,i.expandFactor),f=Lh(h,u,i.inflateFactor),Ah(f,h,l,4)||(b=!0),m++;var T=Oh(f,u,r,n);return T=Ih(T),T},Mh={markovClustering:es,mcl:es},Rh=function(e){return e},Mo=function(e,r){return Math.abs(r-e)},ts=function(e,r,a){return e+Mo(r,a)},rs=function(e,r,a){return e+Math.pow(a-r,2)},kh=function(e){return Math.sqrt(e)},Ph=function(e,r,a){return Math.max(e,Mo(r,a))},ea=function(e,r,a,n,i){for(var s=arguments.length>5&&arguments[5]!==void 0?arguments[5]:Rh,o=n,u,l,f=0;f<e;f++)u=r(f),l=a(f),o=i(o,u,l);return s(o)},zr={euclidean:function(e,r,a){return e>=2?ea(e,r,a,0,rs,kh):ea(e,r,a,0,ts)},squaredEuclidean:function(e,r,a){return ea(e,r,a,0,rs)},manhattan:function(e,r,a){return ea(e,r,a,0,ts)},max:function(e,r,a){return ea(e,r,a,-1/0,Ph)}};zr["squared-euclidean"]=zr.squaredEuclidean;zr.squaredeuclidean=zr.squaredEuclidean;function mn(t,e,r,a,n,i){var s;return Ge(t)?s=t:s=zr[t]||zr.euclidean,e===0&&Ge(t)?s(n,i):s(e,r,a,n,i)}var Bh=tt({k:2,m:2,sensitivityThreshold:1e-4,distance:"euclidean",maxIterations:10,attributes:[],testMode:!1,testCentroids:null}),Ti=function(e){return Bh(e)},on=function(e,r,a,n,i){var s=i!=="kMedoids",o=s?function(h){return a[h]}:function(h){return n[h](a)},u=function(d){return n[d](r)},l=a,f=r;return mn(e,n.length,o,u,l,f)},Fn=function(e,r,a){for(var n=a.length,i=new Array(n),s=new Array(n),o=new Array(r),u=null,l=0;l<n;l++)i[l]=e.min(a[l]).value,s[l]=e.max(a[l]).value;for(var f=0;f<r;f++){u=[];for(var h=0;h<n;h++)u[h]=Math.random()*(s[h]-i[h])+i[h];o[f]=u}return o},Ro=function(e,r,a,n,i){for(var s=1/0,o=0,u=0;u<r.length;u++){var l=on(a,e,r[u],n,i);l<s&&(s=l,o=u)}return o},ko=function(e,r,a){for(var n=[],i=null,s=0;s<r.length;s++)i=r[s],a[i.id()]===e&&n.push(i);return n},Fh=function(e,r,a){return Math.abs(r-e)<=a},Gh=function(e,r,a){for(var n=0;n<e.length;n++)for(var i=0;i<e[n].length;i++){var s=Math.abs(e[n][i]-r[n][i]);if(s>a)return!1}return!0},zh=function(e,r,a){for(var n=0;n<a;n++)if(e===r[n])return!0;return!1},as=function(e,r){var a=new Array(r);if(e.length<50)for(var n=0;n<r;n++){for(var i=e[Math.floor(Math.random()*e.length)];zh(i,a,n);)i=e[Math.floor(Math.random()*e.length)];a[n]=i}else for(var s=0;s<r;s++)a[s]=e[Math.floor(Math.random()*e.length)];return a},ns=function(e,r,a){for(var n=0,i=0;i<r.length;i++)n+=on("manhattan",r[i],e,a,"kMedoids");return n},Vh=function(e){var r=this.cy(),a=this.nodes(),n=null,i=Ti(e),s=new Array(i.k),o={},u;i.testMode?typeof i.testCentroids=="number"?(i.testCentroids,u=Fn(a,i.k,i.attributes)):Xe(i.testCentroids)==="object"?u=i.testCentroids:u=Fn(a,i.k,i.attributes):u=Fn(a,i.k,i.attributes);for(var l=!0,f=0;l&&f<i.maxIterations;){for(var h=0;h<a.length;h++)n=a[h],o[n.id()]=Ro(n,u,i.distance,i.attributes,"kMeans");l=!1;for(var d=0;d<i.k;d++){var c=ko(d,a,o);if(c.length!==0){for(var v=i.attributes.length,p=u[d],g=new Array(v),y=new Array(v),b=0;b<v;b++){y[b]=0;for(var m=0;m<c.length;m++)n=c[m],y[b]+=i.attributes[b](n);g[b]=y[b]/c.length,Fh(g[b],p[b],i.sensitivityThreshold)||(l=!0)}u[d]=g,s[d]=r.collection(c)}}f++}return s},Uh=function(e){var r=this.cy(),a=this.nodes(),n=null,i=Ti(e),s=new Array(i.k),o,u={},l,f=new Array(i.k);i.testMode?typeof i.testCentroids=="number"||(Xe(i.testCentroids)==="object"?o=i.testCentroids:o=as(a,i.k)):o=as(a,i.k);for(var h=!0,d=0;h&&d<i.maxIterations;){for(var c=0;c<a.length;c++)n=a[c],u[n.id()]=Ro(n,o,i.distance,i.attributes,"kMedoids");h=!1;for(var v=0;v<o.length;v++){var p=ko(v,a,u);if(p.length!==0){f[v]=ns(o[v],p,i.attributes);for(var g=0;g<p.length;g++)l=ns(p[g],p,i.attributes),l<f[v]&&(f[v]=l,o[v]=p[g],h=!0);s[v]=r.collection(p)}}d++}return s},$h=function(e,r,a,n,i){for(var s,o,u=0;u<r.length;u++)for(var l=0;l<e.length;l++)n[u][l]=Math.pow(a[u][l],i.m);for(var f=0;f<e.length;f++)for(var h=0;h<i.attributes.length;h++){s=0,o=0;for(var d=0;d<r.length;d++)s+=n[d][f]*i.attributes[h](r[d]),o+=n[d][f];e[f][h]=s/o}},Yh=function(e,r,a,n,i){for(var s=0;s<e.length;s++)r[s]=e[s].slice();for(var o,u,l,f=2/(i.m-1),h=0;h<a.length;h++)for(var d=0;d<n.length;d++){o=0;for(var c=0;c<a.length;c++)u=on(i.distance,n[d],a[h],i.attributes,"cmeans"),l=on(i.distance,n[d],a[c],i.attributes,"cmeans"),o+=Math.pow(u/l,f);e[d][h]=1/o}},_h=function(e,r,a,n){for(var i=new Array(a.k),s=0;s<i.length;s++)i[s]=[];for(var o,u,l=0;l<r.length;l++){o=-1/0,u=-1;for(var f=0;f<r[0].length;f++)r[l][f]>o&&(o=r[l][f],u=f);i[u].push(e[l])}for(var h=0;h<i.length;h++)i[h]=n.collection(i[h]);return i},is=function(e){var r=this.cy(),a=this.nodes(),n=Ti(e),i,s,o,u,l;u=new Array(a.length);for(var f=0;f<a.length;f++)u[f]=new Array(n.k);o=new Array(a.length);for(var h=0;h<a.length;h++)o[h]=new Array(n.k);for(var d=0;d<a.length;d++){for(var c=0,v=0;v<n.k;v++)o[d][v]=Math.random(),c+=o[d][v];for(var p=0;p<n.k;p++)o[d][p]=o[d][p]/c}s=new Array(n.k);for(var g=0;g<n.k;g++)s[g]=new Array(n.attributes.length);l=new Array(a.length);for(var y=0;y<a.length;y++)l[y]=new Array(n.k);for(var b=!0,m=0;b&&m<n.maxIterations;)b=!1,$h(s,a,o,l,n),Yh(o,u,s,a,n),Gh(o,u,n.sensitivityThreshold)||(b=!0),m++;return i=_h(a,o,n,r),{clusters:i,degreeOfMembership:o}},Hh={kMeans:Vh,kMedoids:Uh,fuzzyCMeans:is,fcm:is},Xh=tt({distance:"euclidean",linkage:"min",mode:"threshold",threshold:1/0,addDendrogram:!1,dendrogramDepth:0,attributes:[]}),qh={single:"min",complete:"max"},Wh=function(e){var r=Xh(e),a=qh[r.linkage];return a!=null&&(r.linkage=a),r},ss=function(e,r,a,n,i){for(var s=0,o=1/0,u,l=i.attributes,f=function(x,D){return mn(i.distance,l.length,function(L){return l[L](x)},function(L){return l[L](D)},x,D)},h=0;h<e.length;h++){var d=e[h].key,c=a[d][n[d]];c<o&&(s=d,o=c)}if(i.mode==="threshold"&&o>=i.threshold||i.mode==="dendrogram"&&e.length===1)return!1;var v=r[s],p=r[n[s]],g;i.mode==="dendrogram"?g={left:v,right:p,key:v.key}:g={value:v.value.concat(p.value),key:v.key},e[v.index]=g,e.splice(p.index,1),r[v.key]=g;for(var y=0;y<e.length;y++){var b=e[y];v.key===b.key?u=1/0:i.linkage==="min"?(u=a[v.key][b.key],a[v.key][b.key]>a[p.key][b.key]&&(u=a[p.key][b.key])):i.linkage==="max"?(u=a[v.key][b.key],a[v.key][b.key]<a[p.key][b.key]&&(u=a[p.key][b.key])):i.linkage==="mean"?u=(a[v.key][b.key]*v.size+a[p.key][b.key]*p.size)/(v.size+p.size):i.mode==="dendrogram"?u=f(b.value,v.value):u=f(b.value[0],v.value[0]),a[v.key][b.key]=a[b.key][v.key]=u}for(var m=0;m<e.length;m++){var T=e[m].key;if(n[T]===v.key||n[T]===p.key){for(var C=T,S=0;S<e.length;S++){var E=e[S].key;a[T][E]<a[T][C]&&(C=E)}n[T]=C}e[m].index=m}return v.key=p.key=v.index=p.index=null,!0},Pa=function t(e,r,a){e&&(e.value?r.push(e.value):(e.left&&t(e.left,r),e.right&&t(e.right,r)))},Kh=function t(e,r){if(!e)return"";if(e.left&&e.right){var a=t(e.left,r),n=t(e.right,r),i=r.add({group:"nodes",data:{id:a+","+n}});return r.add({group:"edges",data:{source:a,target:i.id()}}),r.add({group:"edges",data:{source:n,target:i.id()}}),i.id()}else if(e.value)return e.value.id()},Zh=function t(e,r,a){if(!e)return[];var n=[],i=[],s=[];return r===0?(e.left&&Pa(e.left,n),e.right&&Pa(e.right,i),s=n.concat(i),[a.collection(s)]):r===1?e.value?[a.collection(e.value)]:(e.left&&Pa(e.left,n),e.right&&Pa(e.right,i),[a.collection(n),a.collection(i)]):e.value?[a.collection(e.value)]:(e.left&&(n=t(e.left,r-1,a)),e.right&&(i=t(e.right,r-1,a)),n.concat(i))},os=function(e){for(var r=this.cy(),a=this.nodes(),n=Wh(e),i=n.attributes,s=function(m,T){return mn(n.distance,i.length,function(C){return i[C](m)},function(C){return i[C](T)},m,T)},o=[],u=[],l=[],f=[],h=0;h<a.length;h++){var d={value:n.mode==="dendrogram"?a[h]:[a[h]],key:h,index:h};o[h]=d,f[h]=d,u[h]=[],l[h]=0}for(var c=0;c<o.length;c++)for(var v=0;v<=c;v++){var p=void 0;n.mode==="dendrogram"?p=c===v?1/0:s(o[c].value,o[v].value):p=c===v?1/0:s(o[c].value[0],o[v].value[0]),u[c][v]=p,u[v][c]=p,p<u[c][l[c]]&&(l[c]=v)}for(var g=ss(o,f,u,l,n);g;)g=ss(o,f,u,l,n);var y;return n.mode==="dendrogram"?(y=Zh(o[0],n.dendrogramDepth,r),n.addDendrogram&&Kh(o[0],r)):(y=new Array(o.length),o.forEach(function(b,m){b.key=b.index=null,y[m]=r.collection(b.value)})),y},Qh={hierarchicalClustering:os,hca:os},Jh=tt({distance:"euclidean",preference:"median",damping:.8,maxIterations:1e3,minIterations:100,attributes:[]}),jh=function(e){var r=e.damping,a=e.preference;.5<=r&&r<1||ze("Damping must range on [0.5, 1).  Got: ".concat(r));var n=["median","mean","min","max"];return n.some(function(i){return i===a})||ie(a)||ze("Preference must be one of [".concat(n.map(function(i){return"'".concat(i,"'")}).join(", "),"] or a number.  Got: ").concat(a)),Jh(e)},ec=function(e,r,a,n){var i=function(o,u){return n[u](o)};return-mn(e,n.length,function(s){return i(r,s)},function(s){return i(a,s)},r,a)},tc=function(e,r){var a=null;return r==="median"?a=jf(e):r==="mean"?a=Jf(e):r==="min"?a=Zf(e):r==="max"?a=Qf(e):a=r,a},rc=function(e,r,a){for(var n=[],i=0;i<e;i++)r[i*e+i]+a[i*e+i]>0&&n.push(i);return n},us=function(e,r,a){for(var n=[],i=0;i<e;i++){for(var s=-1,o=-1/0,u=0;u<a.length;u++){var l=a[u];r[i*e+l]>o&&(s=l,o=r[i*e+l])}s>0&&n.push(s)}for(var f=0;f<a.length;f++)n[a[f]]=a[f];return n},ac=function(e,r,a){for(var n=us(e,r,a),i=0;i<a.length;i++){for(var s=[],o=0;o<n.length;o++)n[o]===a[i]&&s.push(o);for(var u=-1,l=-1/0,f=0;f<s.length;f++){for(var h=0,d=0;d<s.length;d++)h+=r[s[d]*e+s[f]];h>l&&(u=f,l=h)}a[i]=s[u]}return n=us(e,r,a),n},ls=function(e){for(var r=this.cy(),a=this.nodes(),n=jh(e),i={},s=0;s<a.length;s++)i[a[s].id()]=s;var o,u,l,f,h,d;o=a.length,u=o*o,l=new Array(u);for(var c=0;c<u;c++)l[c]=-1/0;for(var v=0;v<o;v++)for(var p=0;p<o;p++)v!==p&&(l[v*o+p]=ec(n.distance,a[v],a[p],n.attributes));f=tc(l,n.preference);for(var g=0;g<o;g++)l[g*o+g]=f;h=new Array(u);for(var y=0;y<u;y++)h[y]=0;d=new Array(u);for(var b=0;b<u;b++)d[b]=0;for(var m=new Array(o),T=new Array(o),C=new Array(o),S=0;S<o;S++)m[S]=0,T[S]=0,C[S]=0;for(var E=new Array(o*n.minIterations),w=0;w<E.length;w++)E[w]=0;var x;for(x=0;x<n.maxIterations;x++){for(var D=0;D<o;D++){for(var L=-1/0,A=-1/0,N=-1,O=0,M=0;M<o;M++)m[M]=h[D*o+M],O=d[D*o+M]+l[D*o+M],O>=L?(A=L,L=O,N=M):O>A&&(A=O);for(var R=0;R<o;R++)h[D*o+R]=(1-n.damping)*(l[D*o+R]-L)+n.damping*m[R];h[D*o+N]=(1-n.damping)*(l[D*o+N]-A)+n.damping*m[N]}for(var k=0;k<o;k++){for(var P=0,B=0;B<o;B++)m[B]=d[B*o+k],T[B]=Math.max(0,h[B*o+k]),P+=T[B];P-=T[k],T[k]=h[k*o+k],P+=T[k];for(var z=0;z<o;z++)d[z*o+k]=(1-n.damping)*Math.min(0,P-T[z])+n.damping*m[z];d[k*o+k]=(1-n.damping)*(P-T[k])+n.damping*m[k]}for(var G=0,F=0;F<o;F++){var U=d[F*o+F]+h[F*o+F]>0?1:0;E[x%n.minIterations*o+F]=U,G+=U}if(G>0&&(x>=n.minIterations-1||x==n.maxIterations-1)){for(var Y=0,W=0;W<o;W++){C[W]=0;for(var K=0;K<n.minIterations;K++)C[W]+=E[K*o+W];(C[W]===0||C[W]===n.minIterations)&&Y++}if(Y===o)break}}for(var j=rc(o,h,d),_=ac(o,l,j),V={},H=0;H<j.length;H++)V[j[H]]=[];for(var Q=0;Q<a.length;Q++){var ne=i[a[Q].id()],ce=_[ne];ce!=null&&V[ce].push(a[Q])}for(var te=new Array(j.length),se=0;se<j.length;se++)te[se]=r.collection(V[j[se]]);return te},nc={affinityPropagation:ls,ap:ls},ic=tt({root:void 0,directed:!1}),sc={hierholzer:function(e){if(!Ce(e)){var r=arguments;e={root:r[0],directed:r[1]}}var a=ic(e),n=a.root,i=a.directed,s=this,o=!1,u,l,f;n&&(f=de(n)?this.filter(n)[0].id():n[0].id());var h={},d={};i?s.forEach(function(b){var m=b.id();if(b.isNode()){var T=b.indegree(!0),C=b.outdegree(!0),S=T-C,E=C-T;S==1?u?o=!0:u=m:E==1?l?o=!0:l=m:(E>1||S>1)&&(o=!0),h[m]=[],b.outgoers().forEach(function(w){w.isEdge()&&h[m].push(w.id())})}else d[m]=[void 0,b.target().id()]}):s.forEach(function(b){var m=b.id();if(b.isNode()){var T=b.degree(!0);T%2&&(u?l?o=!0:l=m:u=m),h[m]=[],b.connectedEdges().forEach(function(C){return h[m].push(C.id())})}else d[m]=[b.source().id(),b.target().id()]});var c={found:!1,trail:void 0};if(o)return c;if(l&&u)if(i){if(f&&l!=f)return c;f=l}else{if(f&&l!=f&&u!=f)return c;f||(f=l)}else f||(f=s[0].id());var v=function(m){for(var T=m,C=[m],S,E,w;h[T].length;)S=h[T].shift(),E=d[S][0],w=d[S][1],T!=w?(h[w]=h[w].filter(function(x){return x!=S}),T=w):!i&&T!=E&&(h[E]=h[E].filter(function(x){return x!=S}),T=E),C.unshift(S),C.unshift(T);return C},p=[],g=[];for(g=v(f);g.length!=1;)h[g[0]].length==0?(p.unshift(s.getElementById(g.shift())),p.unshift(s.getElementById(g.shift()))):g=v(g.shift()).concat(g);p.unshift(s.getElementById(g.shift()));for(var y in h)if(h[y].length)return c;return c.found=!0,c.trail=this.spawn(p,!0),c}},Ba=function(){var e=this,r={},a=0,n=0,i=[],s=[],o={},u=function(d,c){for(var v=s.length-1,p=[],g=e.spawn();s[v].x!=d||s[v].y!=c;)p.push(s.pop().edge),v--;p.push(s.pop().edge),p.forEach(function(y){var b=y.connectedNodes().intersection(e);g.merge(y),b.forEach(function(m){var T=m.id(),C=m.connectedEdges().intersection(e);g.merge(m),r[T].cutVertex?g.merge(C.filter(function(S){return S.isLoop()})):g.merge(C)})}),i.push(g)},l=function h(d,c,v){d===v&&(n+=1),r[c]={id:a,low:a++,cutVertex:!1};var p=e.getElementById(c).connectedEdges().intersection(e);if(p.size()===0)i.push(e.spawn(e.getElementById(c)));else{var g,y,b,m;p.forEach(function(T){g=T.source().id(),y=T.target().id(),b=g===c?y:g,b!==v&&(m=T.id(),o[m]||(o[m]=!0,s.push({x:c,y:b,edge:T})),b in r?r[c].low=Math.min(r[c].low,r[b].id):(h(d,b,c),r[c].low=Math.min(r[c].low,r[b].low),r[c].id<=r[b].low&&(r[c].cutVertex=!0,u(c,b))))})}};e.forEach(function(h){if(h.isNode()){var d=h.id();d in r||(n=0,l(d,d),r[d].cutVertex=n>1)}});var f=Object.keys(r).filter(function(h){return r[h].cutVertex}).map(function(h){return e.getElementById(h)});return{cut:e.spawn(f),components:i}},oc={hopcroftTarjanBiconnected:Ba,htbc:Ba,htb:Ba,hopcroftTarjanBiconnectedComponents:Ba},Fa=function(){var e=this,r={},a=0,n=[],i=[],s=e.spawn(e),o=function u(l){i.push(l),r[l]={index:a,low:a++,explored:!1};var f=e.getElementById(l).connectedEdges().intersection(e);if(f.forEach(function(p){var g=p.target().id();g!==l&&(g in r||u(g),r[g].explored||(r[l].low=Math.min(r[l].low,r[g].low)))}),r[l].index===r[l].low){for(var h=e.spawn();;){var d=i.pop();if(h.merge(e.getElementById(d)),r[d].low=r[l].index,r[d].explored=!0,d===l)break}var c=h.edgesWith(h),v=h.merge(c);n.push(v),s=s.difference(v)}};return e.forEach(function(u){if(u.isNode()){var l=u.id();l in r||o(l)}}),{cut:s,components:n}},uc={tarjanStronglyConnected:Fa,tsc:Fa,tscc:Fa,tarjanStronglyConnectedComponents:Fa},Po={};[da,Gf,zf,Uf,Yf,Hf,Wf,bh,kr,Pr,Zn,Mh,Hh,Qh,nc,sc,oc,uc].forEach(function(t){be(Po,t)});/*!
 Embeddable Minimum Strictly-Compliant Promises/A+ 1.1.1 Thenable
diff --git a/assets/modint.html-M2GwLZ2U.js b/assets/modint.html-DNrISIPe.js
similarity index 99%
rename from assets/modint.html-M2GwLZ2U.js
rename to assets/modint.html-DNrISIPe.js
index 8a8199a..8c576c3 100644
--- a/assets/modint.html-M2GwLZ2U.js
+++ b/assets/modint.html-DNrISIPe.js
@@ -1,4 +1,4 @@
-import{_ as e,o as a,c as s,a as o,b as n,e as t,f as p}from"./app-B69Gl_S-.js";const c={},l=n("h1",{id:"「泛型与-oi」modint",tabindex:"-1"},[n("a",{class:"header-anchor",href:"#「泛型与-oi」modint"},[n("span",null,"「泛型与 OI」modint")])],-1),i=n("p",null,"在 OI 中，有大量的题目要求对一些数字取模，这便是本文写作的背景。",-1),r=n("h2",{id:"背景介绍",tabindex:"-1"},[n("a",{class:"header-anchor",href:"#背景介绍"},[n("span",null,"背景介绍")])],-1),u=n("p",null,"这些题目要么是因为答案太大，不方便输出结果，例如许多计数 dp；要么是因为答案是浮点数，出题人不愿意写一个确定精度的 Special Judge，例如很多期望概率题；要么是因为这道题目直接考察了模的性质和运用，比如大量的 998244353 类的多项式题目。",-1),d=n("h2",{id:"过去的做法",tabindex:"-1"},[n("a",{class:"header-anchor",href:"#过去的做法"},[n("span",null,"过去的做法")])],-1),k={class:"MathJax",jax:"SVG",style:{position:"relative"}},Q={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.387ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 9452.9 1000","aria-hidden":"true"},T=p('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtext"><path data-c="1D68A" d="M126 306Q105 306 90 321T74 359Q74 439 211 439Q268 439 276 438Q343 426 383 390T430 306Q431 301 431 190V81Q446 79 465 78T492 76T509 72T521 60T524 38Q524 11 506 3Q502 1 466 1Q426 1 406 5T379 14T355 36L345 30Q284 -6 205 -6Q135 -6 92 39T48 141Q48 182 79 212T158 256T252 278T342 285H347V290Q347 315 325 335T267 362Q258 363 224 363Q189 363 185 362H179L178 358Q178 353 178 352T176 345T174 337T170 330T165 322T158 316T150 311T139 308T126 306ZM132 140Q132 115 157 93T224 70Q269 70 302 87T344 133Q346 139 347 175V211H339Q256 209 194 190T132 140Z"></path><path data-c="1D697" d="M89 431Q94 431 105 431T122 432Q173 432 173 399Q173 394 175 394Q176 394 190 404T233 425T298 436Q343 436 371 423Q411 402 423 365T436 265Q436 257 436 239T435 211V198V76H498Q512 67 516 60T520 38Q520 9 498 1H308Q286 9 286 32V38V45Q286 65 303 73Q309 76 329 76H351V188Q351 204 351 230T352 266Q352 321 341 341T288 361Q253 361 222 341T176 274L174 264L173 170V76H236Q250 67 254 60T258 38Q258 9 236 1H27Q4 8 4 38Q4 53 8 60T27 76H89V355H58L27 356Q4 363 4 393Q4 408 8 415T27 431H89Z" transform="translate(525,0)"></path><path data-c="1D69C" d="M72 317Q72 361 108 396T229 439Q231 439 245 439T268 440Q303 439 324 435T353 427T363 423L372 432Q380 440 397 440Q430 440 430 395Q430 390 430 380T429 366V335Q429 311 422 302T387 293Q364 293 355 300T346 316T343 336T325 353Q306 364 257 364Q209 364 178 351T147 317Q147 284 231 272Q327 256 357 247Q458 210 458 129V121Q458 74 413 34T271 -6Q246 -6 224 -3T189 5T165 14T150 22T144 26Q142 23 139 18T135 11T132 6T128 1T124 -2T119 -4T113 -5T104 -6Q84 -6 78 6T71 43Q71 48 71 60T72 79Q72 132 73 141T81 157Q90 166 115 166Q135 166 142 162T157 140Q168 108 191 90T260 70Q297 70 323 76T361 91T379 110T384 129Q384 157 346 171T247 195T165 212Q119 228 96 256T72 317Z" transform="translate(1050,0)"></path></g><g data-mml-node="mo" transform="translate(1852.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(2908.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3297.6,0)"><path data-c="1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></g><g data-mml-node="mo" transform="translate(4091.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5092,0)"><path data-c="1D466" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5804.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6804.4,0)"><path data-c="1D467" d="M347 338Q337 338 294 349T231 360Q211 360 197 356T174 346T162 335T155 324L153 320Q150 317 138 317Q117 317 117 325Q117 330 120 339Q133 378 163 406T229 440Q241 442 246 442Q271 442 291 425T329 392T367 375Q389 375 411 408T434 441Q435 442 449 442H462Q468 436 468 434Q468 430 463 420T449 399T432 377T418 358L411 349Q368 298 275 214T160 106L148 94L163 93Q185 93 227 82T290 71Q328 71 360 90T402 140Q406 149 409 151T424 153Q443 153 443 143Q443 138 442 134Q425 72 376 31T278 -11Q252 -11 232 6T193 40T155 57Q111 57 76 -3Q70 -11 59 -11H54H41Q35 -5 35 -2Q35 13 93 84Q132 129 225 214T340 322Q352 338 347 338Z"></path></g><g data-mml-node="mo" transform="translate(7269.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7880.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8880.9,0)"><path data-c="1D462" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),m=[T],v=n("mjx-assistive-mml",{unselectable:"on",display:"inline"},[n("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[n("mtext",{mathvariant:"monospace"},"ans"),n("mo",null,"="),n("mo",{stretchy:"false"},"("),n("mi",null,"x"),n("mo",null,"+"),n("mi",null,"y"),n("mo",null,"+"),n("mi",null,"z"),n("mo",{stretchy:"false"},")"),n("mo",null,"×"),n("mi",null,"u")])],-1),h=p(`<h3 id="第一种-直接取模" tabindex="-1"><a class="header-anchor" href="#第一种-直接取模"><span>第一种 直接取模</span></a></h3><p>这种方法是直接取模，简单直接，清晰明了。</p><div class="language-cpp line-numbers-mode" data-ext="cpp" data-title="cpp"><pre class="language-cpp"><code><span class="token keyword">constexpr</span> <span class="token keyword">int</span> p<span class="token operator">=</span><span class="token number">998244353</span><span class="token punctuation">;</span>
+import{_ as e,o as a,c as s,a as o,b as n,e as t,f as p}from"./app-B4LGNJZ0.js";const c={},l=n("h1",{id:"「泛型与-oi」modint",tabindex:"-1"},[n("a",{class:"header-anchor",href:"#「泛型与-oi」modint"},[n("span",null,"「泛型与 OI」modint")])],-1),i=n("p",null,"在 OI 中，有大量的题目要求对一些数字取模，这便是本文写作的背景。",-1),r=n("h2",{id:"背景介绍",tabindex:"-1"},[n("a",{class:"header-anchor",href:"#背景介绍"},[n("span",null,"背景介绍")])],-1),u=n("p",null,"这些题目要么是因为答案太大，不方便输出结果，例如许多计数 dp；要么是因为答案是浮点数，出题人不愿意写一个确定精度的 Special Judge，例如很多期望概率题；要么是因为这道题目直接考察了模的性质和运用，比如大量的 998244353 类的多项式题目。",-1),d=n("h2",{id:"过去的做法",tabindex:"-1"},[n("a",{class:"header-anchor",href:"#过去的做法"},[n("span",null,"过去的做法")])],-1),k={class:"MathJax",jax:"SVG",style:{position:"relative"}},Q={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.387ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 9452.9 1000","aria-hidden":"true"},T=p('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtext"><path data-c="1D68A" d="M126 306Q105 306 90 321T74 359Q74 439 211 439Q268 439 276 438Q343 426 383 390T430 306Q431 301 431 190V81Q446 79 465 78T492 76T509 72T521 60T524 38Q524 11 506 3Q502 1 466 1Q426 1 406 5T379 14T355 36L345 30Q284 -6 205 -6Q135 -6 92 39T48 141Q48 182 79 212T158 256T252 278T342 285H347V290Q347 315 325 335T267 362Q258 363 224 363Q189 363 185 362H179L178 358Q178 353 178 352T176 345T174 337T170 330T165 322T158 316T150 311T139 308T126 306ZM132 140Q132 115 157 93T224 70Q269 70 302 87T344 133Q346 139 347 175V211H339Q256 209 194 190T132 140Z"></path><path data-c="1D697" d="M89 431Q94 431 105 431T122 432Q173 432 173 399Q173 394 175 394Q176 394 190 404T233 425T298 436Q343 436 371 423Q411 402 423 365T436 265Q436 257 436 239T435 211V198V76H498Q512 67 516 60T520 38Q520 9 498 1H308Q286 9 286 32V38V45Q286 65 303 73Q309 76 329 76H351V188Q351 204 351 230T352 266Q352 321 341 341T288 361Q253 361 222 341T176 274L174 264L173 170V76H236Q250 67 254 60T258 38Q258 9 236 1H27Q4 8 4 38Q4 53 8 60T27 76H89V355H58L27 356Q4 363 4 393Q4 408 8 415T27 431H89Z" transform="translate(525,0)"></path><path data-c="1D69C" d="M72 317Q72 361 108 396T229 439Q231 439 245 439T268 440Q303 439 324 435T353 427T363 423L372 432Q380 440 397 440Q430 440 430 395Q430 390 430 380T429 366V335Q429 311 422 302T387 293Q364 293 355 300T346 316T343 336T325 353Q306 364 257 364Q209 364 178 351T147 317Q147 284 231 272Q327 256 357 247Q458 210 458 129V121Q458 74 413 34T271 -6Q246 -6 224 -3T189 5T165 14T150 22T144 26Q142 23 139 18T135 11T132 6T128 1T124 -2T119 -4T113 -5T104 -6Q84 -6 78 6T71 43Q71 48 71 60T72 79Q72 132 73 141T81 157Q90 166 115 166Q135 166 142 162T157 140Q168 108 191 90T260 70Q297 70 323 76T361 91T379 110T384 129Q384 157 346 171T247 195T165 212Q119 228 96 256T72 317Z" transform="translate(1050,0)"></path></g><g data-mml-node="mo" transform="translate(1852.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(2908.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3297.6,0)"><path data-c="1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></g><g data-mml-node="mo" transform="translate(4091.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5092,0)"><path data-c="1D466" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5804.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6804.4,0)"><path data-c="1D467" d="M347 338Q337 338 294 349T231 360Q211 360 197 356T174 346T162 335T155 324L153 320Q150 317 138 317Q117 317 117 325Q117 330 120 339Q133 378 163 406T229 440Q241 442 246 442Q271 442 291 425T329 392T367 375Q389 375 411 408T434 441Q435 442 449 442H462Q468 436 468 434Q468 430 463 420T449 399T432 377T418 358L411 349Q368 298 275 214T160 106L148 94L163 93Q185 93 227 82T290 71Q328 71 360 90T402 140Q406 149 409 151T424 153Q443 153 443 143Q443 138 442 134Q425 72 376 31T278 -11Q252 -11 232 6T193 40T155 57Q111 57 76 -3Q70 -11 59 -11H54H41Q35 -5 35 -2Q35 13 93 84Q132 129 225 214T340 322Q352 338 347 338Z"></path></g><g data-mml-node="mo" transform="translate(7269.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7880.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8880.9,0)"><path data-c="1D462" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),m=[T],v=n("mjx-assistive-mml",{unselectable:"on",display:"inline"},[n("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[n("mtext",{mathvariant:"monospace"},"ans"),n("mo",null,"="),n("mo",{stretchy:"false"},"("),n("mi",null,"x"),n("mo",null,"+"),n("mi",null,"y"),n("mo",null,"+"),n("mi",null,"z"),n("mo",{stretchy:"false"},")"),n("mo",null,"×"),n("mi",null,"u")])],-1),h=p(`<h3 id="第一种-直接取模" tabindex="-1"><a class="header-anchor" href="#第一种-直接取模"><span>第一种 直接取模</span></a></h3><p>这种方法是直接取模，简单直接，清晰明了。</p><div class="language-cpp line-numbers-mode" data-ext="cpp" data-title="cpp"><pre class="language-cpp"><code><span class="token keyword">constexpr</span> <span class="token keyword">int</span> p<span class="token operator">=</span><span class="token number">998244353</span><span class="token punctuation">;</span>
 
 <span class="token keyword">int</span> ans<span class="token operator">=</span><span class="token number">1ll</span><span class="token operator">*</span><span class="token punctuation">(</span><span class="token punctuation">(</span><span class="token punctuation">(</span>x<span class="token operator">+</span>y<span class="token punctuation">)</span><span class="token operator">%</span>p<span class="token operator">+</span>z<span class="token punctuation">)</span><span class="token operator">%</span>p<span class="token punctuation">)</span><span class="token operator">*</span>u<span class="token operator">%</span>p<span class="token punctuation">;</span>
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><p>但是这种方法有着严重的缺陷，一是容易忘记大括号，二是容易中间运算时搞错运算顺序、忘记取模，三是式子太长、括号太多、不易检验。</p><p>因此，不推荐运用这种方法。</p><h3 id="第二种-函数取模" tabindex="-1"><a class="header-anchor" href="#第二种-函数取模"><span>第二种 函数取模</span></a></h3><p>这种方法有效地解决了直接取模的忘记取模的漏洞。</p><div class="language-cpp line-numbers-mode" data-ext="cpp" data-title="cpp"><pre class="language-cpp"><code><span class="token keyword">constexpr</span> <span class="token keyword">int</span> p<span class="token operator">=</span><span class="token number">998244353</span><span class="token punctuation">;</span>
diff --git a/assets/observer.html-BvrPoU9w.js b/assets/observer.html-DCoBW7Y-.js
similarity index 99%
rename from assets/observer.html-BvrPoU9w.js
rename to assets/observer.html-DCoBW7Y-.js
index 9309b54..343fc36 100644
--- a/assets/observer.html-BvrPoU9w.js
+++ b/assets/observer.html-DCoBW7Y-.js
@@ -1,4 +1,4 @@
-import{_ as n,o as s,c as a,f as e}from"./app-B69Gl_S-.js";const t={},p=e(`<h2 id="为什么使用观察者模式" tabindex="-1"><a class="header-anchor" href="#为什么使用观察者模式"><span>为什么使用观察者模式</span></a></h2><p>观察者模式非常适合用于需要自动更新的场景。例如，在图形用户界面（GUI）应用程序中，当数据模型发生变化时，所有显示该数据的视图都需要自动更新。通过使用观察者模式，我们可以将这些视图注册为观察者，当数据模型发生变化时，它们会自动收到通知并更新显示。</p><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><p>在这个示例中，我们展示了如何使用观察者模式来管理状态变化。观察者模式定义了一种一对多的依赖关系，当一个对象的状态发生改变时，所有依赖于它的对象都会得到通知并自动更新。以下是 TypeScript 实现的代码示例：</p><img src="https://www.plantuml.com/plantuml/svg/jL912i8m4Bpd5JbMf1_eoOFWJS4VR9kn1fgaRBP54VzkDRQKua4GRyliC3CxoIOAiNIkKTOB-4GLzA6Cu1wiRqhhTTSQ4cGrF9WaSA7tdIl1kn5O5ReFrgYxKbH6OQf4Lmt5k2GcFJ9cDCZ2UoWcpr5i81eq47p7zK7iwJekOZPRrP2Kumdwr_I4SK7L3NVDqgVGMrjRcIgmhctWu2N-K4iItZ6rvty87ycRu9PbuoBmvlCZvAc7UH_VrxGK37a-dQ0sW-Vmcnu0" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// DigitObserver.ts</span>
+import{_ as n,o as s,c as a,f as e}from"./app-B4LGNJZ0.js";const t={},p=e(`<h2 id="为什么使用观察者模式" tabindex="-1"><a class="header-anchor" href="#为什么使用观察者模式"><span>为什么使用观察者模式</span></a></h2><p>观察者模式非常适合用于需要自动更新的场景。例如，在图形用户界面（GUI）应用程序中，当数据模型发生变化时，所有显示该数据的视图都需要自动更新。通过使用观察者模式，我们可以将这些视图注册为观察者，当数据模型发生变化时，它们会自动收到通知并更新显示。</p><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><p>在这个示例中，我们展示了如何使用观察者模式来管理状态变化。观察者模式定义了一种一对多的依赖关系，当一个对象的状态发生改变时，所有依赖于它的对象都会得到通知并自动更新。以下是 TypeScript 实现的代码示例：</p><img src="https://www.plantuml.com/plantuml/svg/jL912i8m4Bpd5JbMf1_eoOFWJS4VR9kn1fgaRBP54VzkDRQKua4GRyliC3CxoIOAiNIkKTOB-4GLzA6Cu1wiRqhhTTSQ4cGrF9WaSA7tdIl1kn5O5ReFrgYxKbH6OQf4Lmt5k2GcFJ9cDCZ2UoWcpr5i81eq47p7zK7iwJekOZPRrP2Kumdwr_I4SK7L3NVDqgVGMrjRcIgmhctWu2N-K4iItZ6rvty87ycRu9PbuoBmvlCZvAc7UH_VrxGK37a-dQ0sW-Vmcnu0" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// DigitObserver.ts</span>
 <span class="token keyword">import</span> <span class="token punctuation">{</span> NumberGenerator <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&#39;./numberGenerator&#39;</span><span class="token punctuation">;</span>
 <span class="token keyword">import</span> <span class="token punctuation">{</span> Observer <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&#39;./observer&#39;</span><span class="token punctuation">;</span>
 <span class="token keyword">export</span> <span class="token keyword">class</span> <span class="token class-name">DigitObserver</span> <span class="token keyword">implements</span> <span class="token class-name">Observer</span> <span class="token punctuation">{</span>
diff --git a/assets/pieDiagram-31d824a1-CV6f6fQ6.js b/assets/pieDiagram-31d824a1-BIcjeA1S.js
similarity index 98%
rename from assets/pieDiagram-31d824a1-CV6f6fQ6.js
rename to assets/pieDiagram-31d824a1-BIcjeA1S.js
index 6bcd3ef..fde9d52 100644
--- a/assets/pieDiagram-31d824a1-CV6f6fQ6.js
+++ b/assets/pieDiagram-31d824a1-BIcjeA1S.js
@@ -1,4 +1,4 @@
-import{aK as q,aL as at,x as lt,y as ot,s as ct,g as ht,b as ut,a as yt,A as ft,d as pt,c as et,l as it,aM as gt,aJ as dt,aN as mt,i as _t}from"./mermaid.core-ChLYKTZm.js";import{a as tt}from"./arc-BCmLGSVu.js";import{o as xt}from"./ordinal-Cboi1Yqb.js";import{a as kt}from"./array-BKyUJesY.js";import{c as F}from"./path-CbwjOpE9.js";import"./app-B69Gl_S-.js";import"./init-Gi6I4Gst.js";function vt(e,u){return u<e?-1:u>e?1:u>=e?0:NaN}function bt(e){return e}function St(){var e=bt,u=vt,$=null,p=F(0),g=F(q),A=F(0);function y(a){var l,d=(a=kt(a)).length,m,I,T=0,_=new Array(d),v=new Array(d),c=+p.apply(this,arguments),E=Math.min(q,Math.max(-q,g.apply(this,arguments)-c)),O,w=Math.min(Math.abs(E)/d,A.apply(this,arguments)),b=w*(E<0?-1:1),t;for(l=0;l<d;++l)(t=v[_[l]=l]=+e(a[l],l,a))>0&&(T+=t);for(u!=null?_.sort(function(i,n){return u(v[i],v[n])}):$!=null&&_.sort(function(i,n){return $(a[i],a[n])}),l=0,I=T?(E-d*b)/T:0;l<d;++l,c=O)m=_[l],t=v[m],O=c+(t>0?t*I:0)+b,v[m]={data:a[m],index:l,value:t,startAngle:c,endAngle:O,padAngle:w};return v}return y.value=function(a){return arguments.length?(e=typeof a=="function"?a:F(+a),y):e},y.sortValues=function(a){return arguments.length?(u=a,$=null,y):u},y.sort=function(a){return arguments.length?($=a,u=null,y):$},y.startAngle=function(a){return arguments.length?(p=typeof a=="function"?a:F(+a),y):p},y.endAngle=function(a){return arguments.length?(g=typeof a=="function"?a:F(+a),y):g},y.padAngle=function(a){return arguments.length?(A=typeof a=="function"?a:F(+a),y):A},y}var H=function(){var e=function(b,t,i,n){for(i=i||{},n=b.length;n--;i[b[n]]=t);return i},u=[1,3],$=[1,4],p=[1,5],g=[1,6],A=[1,10,12,14,16,18,19,20,21,22],y=[2,4],a=[1,5,10,12,14,16,18,19,20,21,22],l=[20,21,22],d=[2,7],m=[1,12],I=[1,13],T=[1,14],_=[1,15],v=[1,16],c=[1,17],E={trace:function(){},yy:{},symbols_:{error:2,start:3,eol:4,PIE:5,document:6,showData:7,line:8,statement:9,txt:10,value:11,title:12,title_value:13,acc_title:14,acc_title_value:15,acc_descr:16,acc_descr_value:17,acc_descr_multiline_value:18,section:19,NEWLINE:20,";":21,EOF:22,$accept:0,$end:1},terminals_:{2:"error",5:"PIE",7:"showData",10:"txt",11:"value",12:"title",13:"title_value",14:"acc_title",15:"acc_title_value",16:"acc_descr",17:"acc_descr_value",18:"acc_descr_multiline_value",19:"section",20:"NEWLINE",21:";",22:"EOF"},productions_:[0,[3,2],[3,2],[3,3],[6,0],[6,2],[8,2],[9,0],[9,2],[9,2],[9,2],[9,2],[9,1],[9,1],[4,1],[4,1],[4,1]],performAction:function(t,i,n,r,o,s,P){var x=s.length-1;switch(o){case 3:r.setShowData(!0);break;case 6:this.$=s[x-1];break;case 8:r.addSection(s[x-1],r.cleanupValue(s[x]));break;case 9:this.$=s[x].trim(),r.setDiagramTitle(this.$);break;case 10:this.$=s[x].trim(),r.setAccTitle(this.$);break;case 11:case 12:this.$=s[x].trim(),r.setAccDescription(this.$);break;case 13:r.addSection(s[x].substr(8)),this.$=s[x].substr(8);break}},table:[{3:1,4:2,5:u,20:$,21:p,22:g},{1:[3]},{3:7,4:2,5:u,20:$,21:p,22:g},e(A,y,{6:8,7:[1,9]}),e(a,[2,14]),e(a,[2,15]),e(a,[2,16]),{1:[2,1]},e(l,d,{8:10,9:11,1:[2,2],10:m,12:I,14:T,16:_,18:v,19:c}),e(A,y,{6:18}),e(A,[2,5]),{4:19,20:$,21:p,22:g},{11:[1,20]},{13:[1,21]},{15:[1,22]},{17:[1,23]},e(l,[2,12]),e(l,[2,13]),e(l,d,{8:10,9:11,1:[2,3],10:m,12:I,14:T,16:_,18:v,19:c}),e(A,[2,6]),e(l,[2,8]),e(l,[2,9]),e(l,[2,10]),e(l,[2,11])],defaultActions:{7:[2,1]},parseError:function(t,i){if(i.recoverable)this.trace(t);else{var n=new Error(t);throw n.hash=i,n}},parse:function(t){var i=this,n=[0],r=[],o=[null],s=[],P=this.table,x="",f=0,V=0,R=2,M=1,B=s.slice.call(arguments,1),h=Object.create(this.lexer),N={yy:{}};for(var Y in this.yy)Object.prototype.hasOwnProperty.call(this.yy,Y)&&(N.yy[Y]=this.yy[Y]);h.setInput(t,N.yy),N.yy.lexer=h,N.yy.parser=this,typeof h.yylloc>"u"&&(h.yylloc={});var J=h.yylloc;s.push(J);var st=h.options&&h.options.ranges;typeof N.yy.parseError=="function"?this.parseError=N.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function rt(){var C;return C=r.pop()||h.lex()||M,typeof C!="number"&&(C instanceof Array&&(r=C,C=r.pop()),C=i.symbols_[C]||C),C}for(var k,L,S,K,z={},j,D,X,W;;){if(L=n[n.length-1],this.defaultActions[L]?S=this.defaultActions[L]:((k===null||typeof k>"u")&&(k=rt()),S=P[L]&&P[L][k]),typeof S>"u"||!S.length||!S[0]){var Z="";W=[];for(j in P[L])this.terminals_[j]&&j>R&&W.push("'"+this.terminals_[j]+"'");h.showPosition?Z="Parse error on line "+(f+1)+`:
+import{aK as q,aL as at,x as lt,y as ot,s as ct,g as ht,b as ut,a as yt,A as ft,d as pt,c as et,l as it,aM as gt,aJ as dt,aN as mt,i as _t}from"./mermaid.core-DNo_7Q2B.js";import{a as tt}from"./arc-DWlpCdAw.js";import{o as xt}from"./ordinal-Cboi1Yqb.js";import{a as kt}from"./array-BKyUJesY.js";import{c as F}from"./path-CbwjOpE9.js";import"./app-B4LGNJZ0.js";import"./init-Gi6I4Gst.js";function vt(e,u){return u<e?-1:u>e?1:u>=e?0:NaN}function bt(e){return e}function St(){var e=bt,u=vt,$=null,p=F(0),g=F(q),A=F(0);function y(a){var l,d=(a=kt(a)).length,m,I,T=0,_=new Array(d),v=new Array(d),c=+p.apply(this,arguments),E=Math.min(q,Math.max(-q,g.apply(this,arguments)-c)),O,w=Math.min(Math.abs(E)/d,A.apply(this,arguments)),b=w*(E<0?-1:1),t;for(l=0;l<d;++l)(t=v[_[l]=l]=+e(a[l],l,a))>0&&(T+=t);for(u!=null?_.sort(function(i,n){return u(v[i],v[n])}):$!=null&&_.sort(function(i,n){return $(a[i],a[n])}),l=0,I=T?(E-d*b)/T:0;l<d;++l,c=O)m=_[l],t=v[m],O=c+(t>0?t*I:0)+b,v[m]={data:a[m],index:l,value:t,startAngle:c,endAngle:O,padAngle:w};return v}return y.value=function(a){return arguments.length?(e=typeof a=="function"?a:F(+a),y):e},y.sortValues=function(a){return arguments.length?(u=a,$=null,y):u},y.sort=function(a){return arguments.length?($=a,u=null,y):$},y.startAngle=function(a){return arguments.length?(p=typeof a=="function"?a:F(+a),y):p},y.endAngle=function(a){return arguments.length?(g=typeof a=="function"?a:F(+a),y):g},y.padAngle=function(a){return arguments.length?(A=typeof a=="function"?a:F(+a),y):A},y}var H=function(){var e=function(b,t,i,n){for(i=i||{},n=b.length;n--;i[b[n]]=t);return i},u=[1,3],$=[1,4],p=[1,5],g=[1,6],A=[1,10,12,14,16,18,19,20,21,22],y=[2,4],a=[1,5,10,12,14,16,18,19,20,21,22],l=[20,21,22],d=[2,7],m=[1,12],I=[1,13],T=[1,14],_=[1,15],v=[1,16],c=[1,17],E={trace:function(){},yy:{},symbols_:{error:2,start:3,eol:4,PIE:5,document:6,showData:7,line:8,statement:9,txt:10,value:11,title:12,title_value:13,acc_title:14,acc_title_value:15,acc_descr:16,acc_descr_value:17,acc_descr_multiline_value:18,section:19,NEWLINE:20,";":21,EOF:22,$accept:0,$end:1},terminals_:{2:"error",5:"PIE",7:"showData",10:"txt",11:"value",12:"title",13:"title_value",14:"acc_title",15:"acc_title_value",16:"acc_descr",17:"acc_descr_value",18:"acc_descr_multiline_value",19:"section",20:"NEWLINE",21:";",22:"EOF"},productions_:[0,[3,2],[3,2],[3,3],[6,0],[6,2],[8,2],[9,0],[9,2],[9,2],[9,2],[9,2],[9,1],[9,1],[4,1],[4,1],[4,1]],performAction:function(t,i,n,r,o,s,P){var x=s.length-1;switch(o){case 3:r.setShowData(!0);break;case 6:this.$=s[x-1];break;case 8:r.addSection(s[x-1],r.cleanupValue(s[x]));break;case 9:this.$=s[x].trim(),r.setDiagramTitle(this.$);break;case 10:this.$=s[x].trim(),r.setAccTitle(this.$);break;case 11:case 12:this.$=s[x].trim(),r.setAccDescription(this.$);break;case 13:r.addSection(s[x].substr(8)),this.$=s[x].substr(8);break}},table:[{3:1,4:2,5:u,20:$,21:p,22:g},{1:[3]},{3:7,4:2,5:u,20:$,21:p,22:g},e(A,y,{6:8,7:[1,9]}),e(a,[2,14]),e(a,[2,15]),e(a,[2,16]),{1:[2,1]},e(l,d,{8:10,9:11,1:[2,2],10:m,12:I,14:T,16:_,18:v,19:c}),e(A,y,{6:18}),e(A,[2,5]),{4:19,20:$,21:p,22:g},{11:[1,20]},{13:[1,21]},{15:[1,22]},{17:[1,23]},e(l,[2,12]),e(l,[2,13]),e(l,d,{8:10,9:11,1:[2,3],10:m,12:I,14:T,16:_,18:v,19:c}),e(A,[2,6]),e(l,[2,8]),e(l,[2,9]),e(l,[2,10]),e(l,[2,11])],defaultActions:{7:[2,1]},parseError:function(t,i){if(i.recoverable)this.trace(t);else{var n=new Error(t);throw n.hash=i,n}},parse:function(t){var i=this,n=[0],r=[],o=[null],s=[],P=this.table,x="",f=0,V=0,R=2,M=1,B=s.slice.call(arguments,1),h=Object.create(this.lexer),N={yy:{}};for(var Y in this.yy)Object.prototype.hasOwnProperty.call(this.yy,Y)&&(N.yy[Y]=this.yy[Y]);h.setInput(t,N.yy),N.yy.lexer=h,N.yy.parser=this,typeof h.yylloc>"u"&&(h.yylloc={});var J=h.yylloc;s.push(J);var st=h.options&&h.options.ranges;typeof N.yy.parseError=="function"?this.parseError=N.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function rt(){var C;return C=r.pop()||h.lex()||M,typeof C!="number"&&(C instanceof Array&&(r=C,C=r.pop()),C=i.symbols_[C]||C),C}for(var k,L,S,K,z={},j,D,X,W;;){if(L=n[n.length-1],this.defaultActions[L]?S=this.defaultActions[L]:((k===null||typeof k>"u")&&(k=rt()),S=P[L]&&P[L][k]),typeof S>"u"||!S.length||!S[0]){var Z="";W=[];for(j in P[L])this.terminals_[j]&&j>R&&W.push("'"+this.terminals_[j]+"'");h.showPosition?Z="Parse error on line "+(f+1)+`:
 `+h.showPosition()+`
 Expecting `+W.join(", ")+", got '"+(this.terminals_[k]||k)+"'":Z="Parse error on line "+(f+1)+": Unexpected "+(k==M?"end of input":"'"+(this.terminals_[k]||k)+"'"),this.parseError(Z,{text:h.match,token:this.terminals_[k]||k,line:h.yylineno,loc:J,expected:W})}if(S[0]instanceof Array&&S.length>1)throw new Error("Parse Error: multiple actions possible at state: "+L+", token: "+k);switch(S[0]){case 1:n.push(k),o.push(h.yytext),s.push(h.yylloc),n.push(S[1]),k=null,V=h.yyleng,x=h.yytext,f=h.yylineno,J=h.yylloc;break;case 2:if(D=this.productions_[S[1]][1],z.$=o[o.length-D],z._$={first_line:s[s.length-(D||1)].first_line,last_line:s[s.length-1].last_line,first_column:s[s.length-(D||1)].first_column,last_column:s[s.length-1].last_column},st&&(z._$.range=[s[s.length-(D||1)].range[0],s[s.length-1].range[1]]),K=this.performAction.apply(z,[x,V,f,N.yy,S[1],o,s].concat(B)),typeof K<"u")return K;D&&(n=n.slice(0,-1*D*2),o=o.slice(0,-1*D),s=s.slice(0,-1*D)),n.push(this.productions_[S[1]][0]),o.push(z.$),s.push(z._$),X=P[n[n.length-2]][n[n.length-1]],n.push(X);break;case 3:return!0}}return!0}},O=function(){var b={EOF:1,parseError:function(i,n){if(this.yy.parser)this.yy.parser.parseError(i,n);else throw new Error(i)},setInput:function(t,i){return this.yy=i||this.yy||{},this._input=t,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var t=this._input[0];this.yytext+=t,this.yyleng++,this.offset++,this.match+=t,this.matched+=t;var i=t.match(/(?:\r\n?|\n).*/g);return i?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),t},unput:function(t){var i=t.length,n=t.split(/(?:\r\n?|\n)/g);this._input=t+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-i),this.offset-=i;var r=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),n.length-1&&(this.yylineno-=n.length-1);var o=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:n?(n.length===r.length?this.yylloc.first_column:0)+r[r.length-n.length].length-n[0].length:this.yylloc.first_column-i},this.options.ranges&&(this.yylloc.range=[o[0],o[0]+this.yyleng-i]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){if(this.options.backtrack_lexer)this._backtrack=!0;else return this.parseError("Lexical error on line "+(this.yylineno+1)+`. You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).
 `+this.showPosition(),{text:"",token:null,line:this.yylineno});return this},less:function(t){this.unput(this.match.slice(t))},pastInput:function(){var t=this.matched.substr(0,this.matched.length-this.match.length);return(t.length>20?"...":"")+t.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var t=this.match;return t.length<20&&(t+=this._input.substr(0,20-t.length)),(t.substr(0,20)+(t.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var t=this.pastInput(),i=new Array(t.length+1).join("-");return t+this.upcomingInput()+`
diff --git a/assets/prototype.html-Boe-0El2.js b/assets/prototype.html-Be3THUal.js
similarity index 99%
rename from assets/prototype.html-Boe-0El2.js
rename to assets/prototype.html-Be3THUal.js
index 9f26bed..527c2a6 100644
--- a/assets/prototype.html-Boe-0El2.js
+++ b/assets/prototype.html-Be3THUal.js
@@ -1,4 +1,4 @@
-import{_ as s,o as a,c as t,a as p,b as n,f as e}from"./app-B69Gl_S-.js";const o={},c=n("h2",{id:"为什么要使用-prototype-模式",tabindex:"-1"},[n("a",{class:"header-anchor",href:"#为什么要使用-prototype-模式"},[n("span",null,"为什么要使用 Prototype 模式")])],-1),l=n("p",null,"Prototype 模式是一种创建型设计模式，它允许你复制现有对象而无需使代码依赖它们所属的类。使用 Prototype 模式可以：",-1),i=n("ul",null,[n("li",null,"避免重复初始化对象的复杂过程。"),n("li",null,"提高性能，特别是在创建对象代价较高时。"),n("li",null,"简化代码，使得对象的创建更加灵活。"),n("li",null,"对象种类繁多，无法将它们整合到一个类中"),n("li",null,"难以根据类生成实例"),n("li",null,"解耦框架与生成的实例")],-1),u=e(`<h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/fP5FQm913CNlyoboN6dN3p2K8lKi2CMJU0WpwJeuPaeown-itxtZsYqhdiJhuvVtNfA9PfJSRgC9d4c-q17C9VdMPJWPW9TMgL8Bdra2DoCBknJyHNT2c6aQ4rDLvByPSpR6HLI56J8s99r9hUkqTwXauGJB3HqjQEUtie1yXFF5KAW9MYfKZ5lgWLVubfHJXzs5tv2ZZXdaasefy94ErmgUN79hb9uVxAQFxhPWJn83qvpuwjx6vxtxix_zZCU3-hVwCDhqDwxhz_-dMIZ9PaBiorD_0G00" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// main.ts</span>
+import{_ as s,o as a,c as t,a as p,b as n,f as e}from"./app-B4LGNJZ0.js";const o={},c=n("h2",{id:"为什么要使用-prototype-模式",tabindex:"-1"},[n("a",{class:"header-anchor",href:"#为什么要使用-prototype-模式"},[n("span",null,"为什么要使用 Prototype 模式")])],-1),l=n("p",null,"Prototype 模式是一种创建型设计模式，它允许你复制现有对象而无需使代码依赖它们所属的类。使用 Prototype 模式可以：",-1),i=n("ul",null,[n("li",null,"避免重复初始化对象的复杂过程。"),n("li",null,"提高性能，特别是在创建对象代价较高时。"),n("li",null,"简化代码，使得对象的创建更加灵活。"),n("li",null,"对象种类繁多，无法将它们整合到一个类中"),n("li",null,"难以根据类生成实例"),n("li",null,"解耦框架与生成的实例")],-1),u=e(`<h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/fP5FQm913CNlyoboN6dN3p2K8lKi2CMJU0WpwJeuPaeown-itxtZsYqhdiJhuvVtNfA9PfJSRgC9d4c-q17C9VdMPJWPW9TMgL8Bdra2DoCBknJyHNT2c6aQ4rDLvByPSpR6HLI56J8s99r9hUkqTwXauGJB3HqjQEUtie1yXFF5KAW9MYfKZ5lgWLVubfHJXzs5tv2ZZXdaasefy94ErmgUN79hb9uVxAQFxhPWJn83qvpuwjx6vxtxix_zZCU3-hVwCDhqDwxhz_-dMIZ9PaBiorD_0G00" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// main.ts</span>
 <span class="token keyword">import</span> <span class="token punctuation">{</span> Manager <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&#39;./manager&#39;</span><span class="token punctuation">;</span>
 <span class="token keyword">import</span> <span class="token punctuation">{</span> UnderlinePen <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&#39;./underlinePen&#39;</span><span class="token punctuation">;</span>
 <span class="token keyword">import</span> <span class="token punctuation">{</span> MessageBox <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&#39;./messageBox&#39;</span><span class="token punctuation">;</span>
diff --git a/assets/proxy.html-CSHBH0Xk.js b/assets/proxy.html-DydmfTHY.js
similarity index 99%
rename from assets/proxy.html-CSHBH0Xk.js
rename to assets/proxy.html-DydmfTHY.js
index 715daa2..c7b3b06 100644
--- a/assets/proxy.html-CSHBH0Xk.js
+++ b/assets/proxy.html-DydmfTHY.js
@@ -1,4 +1,4 @@
-import{_ as s,o as a,c as t,a as p,b as n,f as e}from"./app-B69Gl_S-.js";const o={},c=n("h2",{id:"为什么使用代理模式",tabindex:"-1"},[n("a",{class:"header-anchor",href:"#为什么使用代理模式"},[n("span",null,"为什么使用代理模式")])],-1),i=n("p",null,'在面向对象编程中，“本人”和“代理人”都是对象。如果“本人”对象太忙了．有些工作无法自己亲自完成，就将其交给“代理人"对象负责。',-1),l=e(`<p>Proxy 模式用于为某对象提供一个代理，以控制对该对象的访问。主要有以下几个优点：</p><ul><li>延迟实例化：代理对象可以在需要时才创建实际对象，节省资源。</li><li>控制访问：可以在代理中加入额外的逻辑来控制对实际对象的访问。</li><li>远程代理：可以用于访问远程对象。</li></ul><h2 id="实例代码" tabindex="-1"><a class="header-anchor" href="#实例代码"><span>实例代码</span></a></h2><p>为了让 PrinterProxy 类与 Printer 类具有一致性，我们定义了 Printable 接口。示例程序的前提是&quot;生成 Printer 类的实例&quot;这一处理需要花费很多时间。为了在程序中体现这一点，我们在 Printer 类的构造了数中调用了 heavyJob 方法，让它干一些“重活”（虽说是重活，也不过是让程序睡眠 5 秒钟）。</p><img src="https://www.plantuml.com/plantuml/svg/nP9D2eCm48NtESKibP8BP55STr6yGjIf3UH7Cb5gI-_U6BIecz95wIQ4cVTctaTIK90-z4OpPGFwYwmHIX_lij883mPm0CAGIkZFqc1cuo60GYorkO31gIR9sgqiNpIfsKsTB1RspYTZjPP4C7j1cKwZGHje5uJ3UdEQEdksaNwVUSfoHJcC9rTbXjfFJALtj_4BC0uUfHQBVOsQHls3TqgaxicoC6xe7EV7zniAw0bPWRQ9F-i5" alt=""><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuKfCBialKd3EoKpDA-62K0gwTWe1HPbv9Qb50KNv5PLM2iMf9L01lyJSL0qbf_ma9KsGrioon99K5CLSo1nCaufI4tCogr8rC7NZqcYba9TQ3kF0h4v99Lvx0OYXeVHaxuAdI_U-tzFpPCUqvrDx7ZSq0Ss1Aa9Hdv6QM5RfbP-aeVHixUAdSrOydpB_MSS4gFJpMIrFryrxigzR0-WGJQmcG7twT5tFarrjG6kGbK02s4h1rjPM0MW0Y8x9mtGPDlzX2a72so4rBmKOaG00" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// main.ts</span>
+import{_ as s,o as a,c as t,a as p,b as n,f as e}from"./app-B4LGNJZ0.js";const o={},c=n("h2",{id:"为什么使用代理模式",tabindex:"-1"},[n("a",{class:"header-anchor",href:"#为什么使用代理模式"},[n("span",null,"为什么使用代理模式")])],-1),i=n("p",null,'在面向对象编程中，“本人”和“代理人”都是对象。如果“本人”对象太忙了．有些工作无法自己亲自完成，就将其交给“代理人"对象负责。',-1),l=e(`<p>Proxy 模式用于为某对象提供一个代理，以控制对该对象的访问。主要有以下几个优点：</p><ul><li>延迟实例化：代理对象可以在需要时才创建实际对象，节省资源。</li><li>控制访问：可以在代理中加入额外的逻辑来控制对实际对象的访问。</li><li>远程代理：可以用于访问远程对象。</li></ul><h2 id="实例代码" tabindex="-1"><a class="header-anchor" href="#实例代码"><span>实例代码</span></a></h2><p>为了让 PrinterProxy 类与 Printer 类具有一致性，我们定义了 Printable 接口。示例程序的前提是&quot;生成 Printer 类的实例&quot;这一处理需要花费很多时间。为了在程序中体现这一点，我们在 Printer 类的构造了数中调用了 heavyJob 方法，让它干一些“重活”（虽说是重活，也不过是让程序睡眠 5 秒钟）。</p><img src="https://www.plantuml.com/plantuml/svg/nP9D2eCm48NtESKibP8BP55STr6yGjIf3UH7Cb5gI-_U6BIecz95wIQ4cVTctaTIK90-z4OpPGFwYwmHIX_lij883mPm0CAGIkZFqc1cuo60GYorkO31gIR9sgqiNpIfsKsTB1RspYTZjPP4C7j1cKwZGHje5uJ3UdEQEdksaNwVUSfoHJcC9rTbXjfFJALtj_4BC0uUfHQBVOsQHls3TqgaxicoC6xe7EV7zniAw0bPWRQ9F-i5" alt=""><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuKfCBialKd3EoKpDA-62K0gwTWe1HPbv9Qb50KNv5PLM2iMf9L01lyJSL0qbf_ma9KsGrioon99K5CLSo1nCaufI4tCogr8rC7NZqcYba9TQ3kF0h4v99Lvx0OYXeVHaxuAdI_U-tzFpPCUqvrDx7ZSq0Ss1Aa9Hdv6QM5RfbP-aeVHixUAdSrOydpB_MSS4gFJpMIrFryrxigzR0-WGJQmcG7twT5tFarrjG6kGbK02s4h1rjPM0MW0Y8x9mtGPDlzX2a72so4rBmKOaG00" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// main.ts</span>
 <span class="token keyword">import</span> <span class="token punctuation">{</span> Printable <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&#39;./printable&#39;</span><span class="token punctuation">;</span>
 <span class="token keyword">import</span> <span class="token punctuation">{</span> PrinterProxy <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&#39;./printerProxy&#39;</span><span class="token punctuation">;</span>
 <span class="token keyword">let</span> p<span class="token operator">:</span> Printable <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">PrinterProxy</span><span class="token punctuation">(</span><span class="token string">&#39;Alice&#39;</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
diff --git a/assets/python_requrements.html-Va55tBYB.js b/assets/python_requrements.html-D_iboyN4.js
similarity index 97%
rename from assets/python_requrements.html-Va55tBYB.js
rename to assets/python_requrements.html-D_iboyN4.js
index 422ea1c..160aa6f 100644
--- a/assets/python_requrements.html-Va55tBYB.js
+++ b/assets/python_requrements.html-D_iboyN4.js
@@ -1 +1 @@
-import{_ as r,o as n,c as o,b as e,e as t}from"./app-B69Gl_S-.js";const i={},p=e("p",null,[t("Python 生成 "),e("code",null,"requirements"),t("有两种方式")],-1),l=e("ul",null,[e("li",null,[e("code",null,"pip list --format=freeze > requirements.txt"),t(" (推荐做法)")]),e("li",null,[e("code",null,"pip freeze > requirements.txt"),t(" (不推荐，会带有本地路径)")])],-1),s=[p,l];function c(a,m){return n(),o("div",null,s)}const h=r(i,[["render",c],["__file","python_requrements.html.vue"]]),d=JSON.parse('{"path":"/tech/python_requrements.html","title":"python requirements.txt","lang":"zh-CN","frontmatter":{"title":"python requirements.txt","date":"2024-10-29T00:00:00.000Z","category":["python"],"tag":["踩坑记录"],"description":"Python 生成 requirements有两种方式 pip list --format=freeze > requirements.txt (推荐做法) pip freeze > requirements.txt (不推荐，会带有本地路径)","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/python_requrements.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"python requirements.txt"}],["meta",{"property":"og:description","content":"Python 生成 requirements有两种方式 pip list --format=freeze > requirements.txt (推荐做法) pip freeze > requirements.txt (不推荐，会带有本地路径)"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"踩坑记录"}],["meta",{"property":"article:published_time","content":"2024-10-29T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"python requirements.txt\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-10-29T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.15,"words":45},"filePathRelative":"tech/python_requrements.md","localizedDate":"2024年10月29日","excerpt":"<p>Python 生成 <code>requirements</code>有两种方式</p>\\n<ul>\\n<li><code>pip list --format=freeze &gt; requirements.txt</code> (推荐做法)</li>\\n<li><code>pip freeze &gt; requirements.txt</code> (不推荐，会带有本地路径)</li>\\n</ul>\\n","autoDesc":true}');export{h as comp,d as data};
+import{_ as r,o as n,c as o,b as e,e as t}from"./app-B4LGNJZ0.js";const i={},p=e("p",null,[t("Python 生成 "),e("code",null,"requirements"),t("有两种方式")],-1),l=e("ul",null,[e("li",null,[e("code",null,"pip list --format=freeze > requirements.txt"),t(" (推荐做法)")]),e("li",null,[e("code",null,"pip freeze > requirements.txt"),t(" (不推荐，会带有本地路径)")])],-1),s=[p,l];function c(a,m){return n(),o("div",null,s)}const h=r(i,[["render",c],["__file","python_requrements.html.vue"]]),d=JSON.parse('{"path":"/tech/python_requrements.html","title":"python requirements.txt","lang":"zh-CN","frontmatter":{"title":"python requirements.txt","date":"2024-10-29T00:00:00.000Z","category":["python"],"tag":["踩坑记录"],"description":"Python 生成 requirements有两种方式 pip list --format=freeze > requirements.txt (推荐做法) pip freeze > requirements.txt (不推荐，会带有本地路径)","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/python_requrements.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"python requirements.txt"}],["meta",{"property":"og:description","content":"Python 生成 requirements有两种方式 pip list --format=freeze > requirements.txt (推荐做法) pip freeze > requirements.txt (不推荐，会带有本地路径)"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"踩坑记录"}],["meta",{"property":"article:published_time","content":"2024-10-29T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"python requirements.txt\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-10-29T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.15,"words":45},"filePathRelative":"tech/python_requrements.md","localizedDate":"2024年10月29日","excerpt":"<p>Python 生成 <code>requirements</code>有两种方式</p>\\n<ul>\\n<li><code>pip list --format=freeze &gt; requirements.txt</code> (推荐做法)</li>\\n<li><code>pip freeze &gt; requirements.txt</code> (不推荐，会带有本地路径)</li>\\n</ul>\\n","autoDesc":true}');export{h as comp,d as data};
diff --git a/assets/quadrantDiagram-a712a7d9-Bu83u7Zz.js b/assets/quadrantDiagram-a712a7d9-CNklQ4II.js
similarity index 99%
rename from assets/quadrantDiagram-a712a7d9-Bu83u7Zz.js
rename to assets/quadrantDiagram-a712a7d9-CNklQ4II.js
index 01fd558..47994e5 100644
--- a/assets/quadrantDiagram-a712a7d9-Bu83u7Zz.js
+++ b/assets/quadrantDiagram-a712a7d9-CNklQ4II.js
@@ -1,4 +1,4 @@
-import{a_ as vt,c as yt,aL as D,l as ot,s as Lt,g as Ct,x as zt,y as bt,a as Et,b as Dt,A as It,h as gt,i as Bt,d as wt}from"./mermaid.core-ChLYKTZm.js";import{l as mt}from"./linear-CRQH6hcv.js";import"./app-B69Gl_S-.js";import"./init-Gi6I4Gst.js";var pt=function(){var e=function(K,n,r,l){for(r=r||{},l=K.length;l--;r[K[l]]=n);return r},s=[1,3],h=[1,4],x=[1,5],f=[1,6],d=[1,7],c=[1,5,13,15,17,19,20,25,27,28,29,30,31,32,33,34,37,38,40,41,42,43,44,45,46,47,48,49,50],g=[1,5,6,13,15,17,19,20,25,27,28,29,30,31,32,33,34,37,38,40,41,42,43,44,45,46,47,48,49,50],i=[32,33,34],y=[2,7],p=[1,13],B=[1,17],N=[1,18],V=[1,19],I=[1,20],b=[1,21],M=[1,22],X=[1,23],C=[1,24],it=[1,25],at=[1,26],nt=[1,27],U=[1,30],Q=[1,31],T=[1,32],m=[1,33],_=[1,34],t=[1,35],A=[1,36],S=[1,37],k=[1,38],F=[1,39],P=[1,40],v=[1,41],L=[1,42],O=[1,57],Y=[1,58],z=[5,22,26,32,33,34,40,41,42,43,44,45,46,47,48,49,50,51],ht={trace:function(){},yy:{},symbols_:{error:2,start:3,eol:4,SPACE:5,QUADRANT:6,document:7,line:8,statement:9,axisDetails:10,quadrantDetails:11,points:12,title:13,title_value:14,acc_title:15,acc_title_value:16,acc_descr:17,acc_descr_value:18,acc_descr_multiline_value:19,section:20,text:21,point_start:22,point_x:23,point_y:24,"X-AXIS":25,"AXIS-TEXT-DELIMITER":26,"Y-AXIS":27,QUADRANT_1:28,QUADRANT_2:29,QUADRANT_3:30,QUADRANT_4:31,NEWLINE:32,SEMI:33,EOF:34,alphaNumToken:35,textNoTagsToken:36,STR:37,MD_STR:38,alphaNum:39,PUNCTUATION:40,AMP:41,NUM:42,ALPHA:43,COMMA:44,PLUS:45,EQUALS:46,MULT:47,DOT:48,BRKT:49,UNDERSCORE:50,MINUS:51,$accept:0,$end:1},terminals_:{2:"error",5:"SPACE",6:"QUADRANT",13:"title",14:"title_value",15:"acc_title",16:"acc_title_value",17:"acc_descr",18:"acc_descr_value",19:"acc_descr_multiline_value",20:"section",22:"point_start",23:"point_x",24:"point_y",25:"X-AXIS",26:"AXIS-TEXT-DELIMITER",27:"Y-AXIS",28:"QUADRANT_1",29:"QUADRANT_2",30:"QUADRANT_3",31:"QUADRANT_4",32:"NEWLINE",33:"SEMI",34:"EOF",37:"STR",38:"MD_STR",40:"PUNCTUATION",41:"AMP",42:"NUM",43:"ALPHA",44:"COMMA",45:"PLUS",46:"EQUALS",47:"MULT",48:"DOT",49:"BRKT",50:"UNDERSCORE",51:"MINUS"},productions_:[0,[3,2],[3,2],[3,2],[7,0],[7,2],[8,2],[9,0],[9,2],[9,1],[9,1],[9,1],[9,2],[9,2],[9,2],[9,1],[9,1],[12,4],[10,4],[10,3],[10,2],[10,4],[10,3],[10,2],[11,2],[11,2],[11,2],[11,2],[4,1],[4,1],[4,1],[21,1],[21,2],[21,1],[21,1],[39,1],[39,2],[35,1],[35,1],[35,1],[35,1],[35,1],[35,1],[35,1],[35,1],[35,1],[35,1],[35,1],[36,1],[36,1],[36,1]],performAction:function(n,r,l,o,q,a,et){var u=a.length-1;switch(q){case 12:this.$=a[u].trim(),o.setDiagramTitle(this.$);break;case 13:this.$=a[u].trim(),o.setAccTitle(this.$);break;case 14:case 15:this.$=a[u].trim(),o.setAccDescription(this.$);break;case 16:o.addSection(a[u].substr(8)),this.$=a[u].substr(8);break;case 17:o.addPoint(a[u-3],a[u-1],a[u]);break;case 18:o.setXAxisLeftText(a[u-2]),o.setXAxisRightText(a[u]);break;case 19:a[u-1].text+=" ⟶ ",o.setXAxisLeftText(a[u-1]);break;case 20:o.setXAxisLeftText(a[u]);break;case 21:o.setYAxisBottomText(a[u-2]),o.setYAxisTopText(a[u]);break;case 22:a[u-1].text+=" ⟶ ",o.setYAxisBottomText(a[u-1]);break;case 23:o.setYAxisBottomText(a[u]);break;case 24:o.setQuadrant1Text(a[u]);break;case 25:o.setQuadrant2Text(a[u]);break;case 26:o.setQuadrant3Text(a[u]);break;case 27:o.setQuadrant4Text(a[u]);break;case 31:this.$={text:a[u],type:"text"};break;case 32:this.$={text:a[u-1].text+""+a[u],type:a[u-1].type};break;case 33:this.$={text:a[u],type:"text"};break;case 34:this.$={text:a[u],type:"markdown"};break;case 35:this.$=a[u];break;case 36:this.$=a[u-1]+""+a[u];break}},table:[{3:1,4:2,5:s,6:h,32:x,33:f,34:d},{1:[3]},{3:8,4:2,5:s,6:h,32:x,33:f,34:d},{3:9,4:2,5:s,6:h,32:x,33:f,34:d},e(c,[2,4],{7:10}),e(g,[2,28]),e(g,[2,29]),e(g,[2,30]),{1:[2,1]},{1:[2,2]},e(i,y,{8:11,9:12,10:14,11:15,12:16,21:28,35:29,1:[2,3],5:p,13:B,15:N,17:V,19:I,20:b,25:M,27:X,28:C,29:it,30:at,31:nt,37:U,38:Q,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L}),e(c,[2,5]),{4:43,32:x,33:f,34:d},e(i,y,{10:14,11:15,12:16,21:28,35:29,9:44,5:p,13:B,15:N,17:V,19:I,20:b,25:M,27:X,28:C,29:it,30:at,31:nt,37:U,38:Q,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L}),e(i,[2,9]),e(i,[2,10]),e(i,[2,11]),{14:[1,45]},{16:[1,46]},{18:[1,47]},e(i,[2,15]),e(i,[2,16]),{21:48,35:29,37:U,38:Q,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L},{21:49,35:29,37:U,38:Q,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L},{21:50,35:29,37:U,38:Q,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L},{21:51,35:29,37:U,38:Q,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L},{21:52,35:29,37:U,38:Q,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L},{21:53,35:29,37:U,38:Q,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L},{5:O,22:[1,54],35:56,36:55,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L,51:Y},e(z,[2,31]),e(z,[2,33]),e(z,[2,34]),e(z,[2,37]),e(z,[2,38]),e(z,[2,39]),e(z,[2,40]),e(z,[2,41]),e(z,[2,42]),e(z,[2,43]),e(z,[2,44]),e(z,[2,45]),e(z,[2,46]),e(z,[2,47]),e(c,[2,6]),e(i,[2,8]),e(i,[2,12]),e(i,[2,13]),e(i,[2,14]),e(i,[2,20],{36:55,35:56,5:O,26:[1,59],40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L,51:Y}),e(i,[2,23],{36:55,35:56,5:O,26:[1,60],40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L,51:Y}),e(i,[2,24],{36:55,35:56,5:O,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L,51:Y}),e(i,[2,25],{36:55,35:56,5:O,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L,51:Y}),e(i,[2,26],{36:55,35:56,5:O,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L,51:Y}),e(i,[2,27],{36:55,35:56,5:O,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L,51:Y}),{23:[1,61]},e(z,[2,32]),e(z,[2,48]),e(z,[2,49]),e(z,[2,50]),e(i,[2,19],{35:29,21:62,37:U,38:Q,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L}),e(i,[2,22],{35:29,21:63,37:U,38:Q,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L}),{24:[1,64]},e(i,[2,18],{36:55,35:56,5:O,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L,51:Y}),e(i,[2,21],{36:55,35:56,5:O,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L,51:Y}),e(i,[2,17])],defaultActions:{8:[2,1],9:[2,2]},parseError:function(n,r){if(r.recoverable)this.trace(n);else{var l=new Error(n);throw l.hash=r,l}},parse:function(n){var r=this,l=[0],o=[],q=[null],a=[],et=this.table,u="",st=0,qt=0,St=2,Tt=1,kt=a.slice.call(arguments,1),E=Object.create(this.lexer),Z={yy:{}};for(var dt in this.yy)Object.prototype.hasOwnProperty.call(this.yy,dt)&&(Z.yy[dt]=this.yy[dt]);E.setInput(n,Z.yy),Z.yy.lexer=E,Z.yy.parser=this,typeof E.yylloc>"u"&&(E.yylloc={});var ut=E.yylloc;a.push(ut);var Ft=E.options&&E.options.ranges;typeof Z.yy.parseError=="function"?this.parseError=Z.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function Pt(){var j;return j=o.pop()||E.lex()||Tt,typeof j!="number"&&(j instanceof Array&&(o=j,j=o.pop()),j=r.symbols_[j]||j),j}for(var W,J,H,xt,tt={},rt,$,_t,lt;;){if(J=l[l.length-1],this.defaultActions[J]?H=this.defaultActions[J]:((W===null||typeof W>"u")&&(W=Pt()),H=et[J]&&et[J][W]),typeof H>"u"||!H.length||!H[0]){var ft="";lt=[];for(rt in et[J])this.terminals_[rt]&&rt>St&&lt.push("'"+this.terminals_[rt]+"'");E.showPosition?ft="Parse error on line "+(st+1)+`:
+import{a_ as vt,c as yt,aL as D,l as ot,s as Lt,g as Ct,x as zt,y as bt,a as Et,b as Dt,A as It,h as gt,i as Bt,d as wt}from"./mermaid.core-DNo_7Q2B.js";import{l as mt}from"./linear-Cb1OAgs3.js";import"./app-B4LGNJZ0.js";import"./init-Gi6I4Gst.js";var pt=function(){var e=function(K,n,r,l){for(r=r||{},l=K.length;l--;r[K[l]]=n);return r},s=[1,3],h=[1,4],x=[1,5],f=[1,6],d=[1,7],c=[1,5,13,15,17,19,20,25,27,28,29,30,31,32,33,34,37,38,40,41,42,43,44,45,46,47,48,49,50],g=[1,5,6,13,15,17,19,20,25,27,28,29,30,31,32,33,34,37,38,40,41,42,43,44,45,46,47,48,49,50],i=[32,33,34],y=[2,7],p=[1,13],B=[1,17],N=[1,18],V=[1,19],I=[1,20],b=[1,21],M=[1,22],X=[1,23],C=[1,24],it=[1,25],at=[1,26],nt=[1,27],U=[1,30],Q=[1,31],T=[1,32],m=[1,33],_=[1,34],t=[1,35],A=[1,36],S=[1,37],k=[1,38],F=[1,39],P=[1,40],v=[1,41],L=[1,42],O=[1,57],Y=[1,58],z=[5,22,26,32,33,34,40,41,42,43,44,45,46,47,48,49,50,51],ht={trace:function(){},yy:{},symbols_:{error:2,start:3,eol:4,SPACE:5,QUADRANT:6,document:7,line:8,statement:9,axisDetails:10,quadrantDetails:11,points:12,title:13,title_value:14,acc_title:15,acc_title_value:16,acc_descr:17,acc_descr_value:18,acc_descr_multiline_value:19,section:20,text:21,point_start:22,point_x:23,point_y:24,"X-AXIS":25,"AXIS-TEXT-DELIMITER":26,"Y-AXIS":27,QUADRANT_1:28,QUADRANT_2:29,QUADRANT_3:30,QUADRANT_4:31,NEWLINE:32,SEMI:33,EOF:34,alphaNumToken:35,textNoTagsToken:36,STR:37,MD_STR:38,alphaNum:39,PUNCTUATION:40,AMP:41,NUM:42,ALPHA:43,COMMA:44,PLUS:45,EQUALS:46,MULT:47,DOT:48,BRKT:49,UNDERSCORE:50,MINUS:51,$accept:0,$end:1},terminals_:{2:"error",5:"SPACE",6:"QUADRANT",13:"title",14:"title_value",15:"acc_title",16:"acc_title_value",17:"acc_descr",18:"acc_descr_value",19:"acc_descr_multiline_value",20:"section",22:"point_start",23:"point_x",24:"point_y",25:"X-AXIS",26:"AXIS-TEXT-DELIMITER",27:"Y-AXIS",28:"QUADRANT_1",29:"QUADRANT_2",30:"QUADRANT_3",31:"QUADRANT_4",32:"NEWLINE",33:"SEMI",34:"EOF",37:"STR",38:"MD_STR",40:"PUNCTUATION",41:"AMP",42:"NUM",43:"ALPHA",44:"COMMA",45:"PLUS",46:"EQUALS",47:"MULT",48:"DOT",49:"BRKT",50:"UNDERSCORE",51:"MINUS"},productions_:[0,[3,2],[3,2],[3,2],[7,0],[7,2],[8,2],[9,0],[9,2],[9,1],[9,1],[9,1],[9,2],[9,2],[9,2],[9,1],[9,1],[12,4],[10,4],[10,3],[10,2],[10,4],[10,3],[10,2],[11,2],[11,2],[11,2],[11,2],[4,1],[4,1],[4,1],[21,1],[21,2],[21,1],[21,1],[39,1],[39,2],[35,1],[35,1],[35,1],[35,1],[35,1],[35,1],[35,1],[35,1],[35,1],[35,1],[35,1],[36,1],[36,1],[36,1]],performAction:function(n,r,l,o,q,a,et){var u=a.length-1;switch(q){case 12:this.$=a[u].trim(),o.setDiagramTitle(this.$);break;case 13:this.$=a[u].trim(),o.setAccTitle(this.$);break;case 14:case 15:this.$=a[u].trim(),o.setAccDescription(this.$);break;case 16:o.addSection(a[u].substr(8)),this.$=a[u].substr(8);break;case 17:o.addPoint(a[u-3],a[u-1],a[u]);break;case 18:o.setXAxisLeftText(a[u-2]),o.setXAxisRightText(a[u]);break;case 19:a[u-1].text+=" ⟶ ",o.setXAxisLeftText(a[u-1]);break;case 20:o.setXAxisLeftText(a[u]);break;case 21:o.setYAxisBottomText(a[u-2]),o.setYAxisTopText(a[u]);break;case 22:a[u-1].text+=" ⟶ ",o.setYAxisBottomText(a[u-1]);break;case 23:o.setYAxisBottomText(a[u]);break;case 24:o.setQuadrant1Text(a[u]);break;case 25:o.setQuadrant2Text(a[u]);break;case 26:o.setQuadrant3Text(a[u]);break;case 27:o.setQuadrant4Text(a[u]);break;case 31:this.$={text:a[u],type:"text"};break;case 32:this.$={text:a[u-1].text+""+a[u],type:a[u-1].type};break;case 33:this.$={text:a[u],type:"text"};break;case 34:this.$={text:a[u],type:"markdown"};break;case 35:this.$=a[u];break;case 36:this.$=a[u-1]+""+a[u];break}},table:[{3:1,4:2,5:s,6:h,32:x,33:f,34:d},{1:[3]},{3:8,4:2,5:s,6:h,32:x,33:f,34:d},{3:9,4:2,5:s,6:h,32:x,33:f,34:d},e(c,[2,4],{7:10}),e(g,[2,28]),e(g,[2,29]),e(g,[2,30]),{1:[2,1]},{1:[2,2]},e(i,y,{8:11,9:12,10:14,11:15,12:16,21:28,35:29,1:[2,3],5:p,13:B,15:N,17:V,19:I,20:b,25:M,27:X,28:C,29:it,30:at,31:nt,37:U,38:Q,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L}),e(c,[2,5]),{4:43,32:x,33:f,34:d},e(i,y,{10:14,11:15,12:16,21:28,35:29,9:44,5:p,13:B,15:N,17:V,19:I,20:b,25:M,27:X,28:C,29:it,30:at,31:nt,37:U,38:Q,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L}),e(i,[2,9]),e(i,[2,10]),e(i,[2,11]),{14:[1,45]},{16:[1,46]},{18:[1,47]},e(i,[2,15]),e(i,[2,16]),{21:48,35:29,37:U,38:Q,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L},{21:49,35:29,37:U,38:Q,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L},{21:50,35:29,37:U,38:Q,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L},{21:51,35:29,37:U,38:Q,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L},{21:52,35:29,37:U,38:Q,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L},{21:53,35:29,37:U,38:Q,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L},{5:O,22:[1,54],35:56,36:55,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L,51:Y},e(z,[2,31]),e(z,[2,33]),e(z,[2,34]),e(z,[2,37]),e(z,[2,38]),e(z,[2,39]),e(z,[2,40]),e(z,[2,41]),e(z,[2,42]),e(z,[2,43]),e(z,[2,44]),e(z,[2,45]),e(z,[2,46]),e(z,[2,47]),e(c,[2,6]),e(i,[2,8]),e(i,[2,12]),e(i,[2,13]),e(i,[2,14]),e(i,[2,20],{36:55,35:56,5:O,26:[1,59],40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L,51:Y}),e(i,[2,23],{36:55,35:56,5:O,26:[1,60],40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L,51:Y}),e(i,[2,24],{36:55,35:56,5:O,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L,51:Y}),e(i,[2,25],{36:55,35:56,5:O,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L,51:Y}),e(i,[2,26],{36:55,35:56,5:O,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L,51:Y}),e(i,[2,27],{36:55,35:56,5:O,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L,51:Y}),{23:[1,61]},e(z,[2,32]),e(z,[2,48]),e(z,[2,49]),e(z,[2,50]),e(i,[2,19],{35:29,21:62,37:U,38:Q,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L}),e(i,[2,22],{35:29,21:63,37:U,38:Q,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L}),{24:[1,64]},e(i,[2,18],{36:55,35:56,5:O,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L,51:Y}),e(i,[2,21],{36:55,35:56,5:O,40:T,41:m,42:_,43:t,44:A,45:S,46:k,47:F,48:P,49:v,50:L,51:Y}),e(i,[2,17])],defaultActions:{8:[2,1],9:[2,2]},parseError:function(n,r){if(r.recoverable)this.trace(n);else{var l=new Error(n);throw l.hash=r,l}},parse:function(n){var r=this,l=[0],o=[],q=[null],a=[],et=this.table,u="",st=0,qt=0,St=2,Tt=1,kt=a.slice.call(arguments,1),E=Object.create(this.lexer),Z={yy:{}};for(var dt in this.yy)Object.prototype.hasOwnProperty.call(this.yy,dt)&&(Z.yy[dt]=this.yy[dt]);E.setInput(n,Z.yy),Z.yy.lexer=E,Z.yy.parser=this,typeof E.yylloc>"u"&&(E.yylloc={});var ut=E.yylloc;a.push(ut);var Ft=E.options&&E.options.ranges;typeof Z.yy.parseError=="function"?this.parseError=Z.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function Pt(){var j;return j=o.pop()||E.lex()||Tt,typeof j!="number"&&(j instanceof Array&&(o=j,j=o.pop()),j=r.symbols_[j]||j),j}for(var W,J,H,xt,tt={},rt,$,_t,lt;;){if(J=l[l.length-1],this.defaultActions[J]?H=this.defaultActions[J]:((W===null||typeof W>"u")&&(W=Pt()),H=et[J]&&et[J][W]),typeof H>"u"||!H.length||!H[0]){var ft="";lt=[];for(rt in et[J])this.terminals_[rt]&&rt>St&&lt.push("'"+this.terminals_[rt]+"'");E.showPosition?ft="Parse error on line "+(st+1)+`:
 `+E.showPosition()+`
 Expecting `+lt.join(", ")+", got '"+(this.terminals_[W]||W)+"'":ft="Parse error on line "+(st+1)+": Unexpected "+(W==Tt?"end of input":"'"+(this.terminals_[W]||W)+"'"),this.parseError(ft,{text:E.match,token:this.terminals_[W]||W,line:E.yylineno,loc:ut,expected:lt})}if(H[0]instanceof Array&&H.length>1)throw new Error("Parse Error: multiple actions possible at state: "+J+", token: "+W);switch(H[0]){case 1:l.push(W),q.push(E.yytext),a.push(E.yylloc),l.push(H[1]),W=null,qt=E.yyleng,u=E.yytext,st=E.yylineno,ut=E.yylloc;break;case 2:if($=this.productions_[H[1]][1],tt.$=q[q.length-$],tt._$={first_line:a[a.length-($||1)].first_line,last_line:a[a.length-1].last_line,first_column:a[a.length-($||1)].first_column,last_column:a[a.length-1].last_column},Ft&&(tt._$.range=[a[a.length-($||1)].range[0],a[a.length-1].range[1]]),xt=this.performAction.apply(tt,[u,qt,st,Z.yy,H[1],q,a].concat(kt)),typeof xt<"u")return xt;$&&(l=l.slice(0,-1*$*2),q=q.slice(0,-1*$),a=a.slice(0,-1*$)),l.push(this.productions_[H[1]][0]),q.push(tt.$),a.push(tt._$),_t=et[l[l.length-2]][l[l.length-1]],l.push(_t);break;case 3:return!0}}return!0}},At=function(){var K={EOF:1,parseError:function(r,l){if(this.yy.parser)this.yy.parser.parseError(r,l);else throw new Error(r)},setInput:function(n,r){return this.yy=r||this.yy||{},this._input=n,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var n=this._input[0];this.yytext+=n,this.yyleng++,this.offset++,this.match+=n,this.matched+=n;var r=n.match(/(?:\r\n?|\n).*/g);return r?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),n},unput:function(n){var r=n.length,l=n.split(/(?:\r\n?|\n)/g);this._input=n+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-r),this.offset-=r;var o=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),l.length-1&&(this.yylineno-=l.length-1);var q=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:l?(l.length===o.length?this.yylloc.first_column:0)+o[o.length-l.length].length-l[0].length:this.yylloc.first_column-r},this.options.ranges&&(this.yylloc.range=[q[0],q[0]+this.yyleng-r]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){if(this.options.backtrack_lexer)this._backtrack=!0;else return this.parseError("Lexical error on line "+(this.yylineno+1)+`. You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).
 `+this.showPosition(),{text:"",token:null,line:this.yylineno});return this},less:function(n){this.unput(this.match.slice(n))},pastInput:function(){var n=this.matched.substr(0,this.matched.length-this.match.length);return(n.length>20?"...":"")+n.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var n=this.match;return n.length<20&&(n+=this._input.substr(0,20-n.length)),(n.substr(0,20)+(n.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var n=this.pastInput(),r=new Array(n.length+1).join("-");return n+this.upcomingInput()+`
diff --git a/assets/requirementDiagram-eb878fee-DPiNb9b5.js b/assets/requirementDiagram-eb878fee-OFUpKWxv.js
similarity index 98%
rename from assets/requirementDiagram-eb878fee-DPiNb9b5.js
rename to assets/requirementDiagram-eb878fee-OFUpKWxv.js
index c5f9f08..4efea54 100644
--- a/assets/requirementDiagram-eb878fee-DPiNb9b5.js
+++ b/assets/requirementDiagram-eb878fee-OFUpKWxv.js
@@ -1,4 +1,4 @@
-import{c as Te,s as Ce,g as Fe,b as Me,a as De,l as Ne,A as Pe,h as oe,i as Ye,j as ke}from"./mermaid.core-ChLYKTZm.js";import{G as Ue}from"./graph-T5JS4vfK.js";import{l as Be}from"./layout-DUYLy6Ue.js";import{l as Qe}from"./line-D0jG_HZ-.js";import"./app-B69Gl_S-.js";import"./array-BKyUJesY.js";import"./path-CbwjOpE9.js";var ce=function(){var e=function(V,i,n,a){for(n=n||{},a=V.length;a--;n[V[a]]=i);return n},t=[1,3],l=[1,4],c=[1,5],u=[1,6],d=[5,6,8,9,11,13,31,32,33,34,35,36,44,62,63],p=[1,18],h=[2,7],o=[1,22],g=[1,23],R=[1,24],A=[1,25],T=[1,26],N=[1,27],v=[1,20],k=[1,28],x=[1,29],F=[62,63],de=[5,8,9,11,13,31,32,33,34,35,36,44,51,53,62,63],pe=[1,47],fe=[1,48],ye=[1,49],_e=[1,50],ge=[1,51],Ee=[1,52],Re=[1,53],O=[53,54],M=[1,64],D=[1,60],P=[1,61],Y=[1,62],U=[1,63],B=[1,65],j=[1,69],z=[1,70],X=[1,67],J=[1,68],m=[5,8,9,11,13,31,32,33,34,35,36,44,62,63],ie={trace:function(){},yy:{},symbols_:{error:2,start:3,directive:4,NEWLINE:5,RD:6,diagram:7,EOF:8,acc_title:9,acc_title_value:10,acc_descr:11,acc_descr_value:12,acc_descr_multiline_value:13,requirementDef:14,elementDef:15,relationshipDef:16,requirementType:17,requirementName:18,STRUCT_START:19,requirementBody:20,ID:21,COLONSEP:22,id:23,TEXT:24,text:25,RISK:26,riskLevel:27,VERIFYMTHD:28,verifyType:29,STRUCT_STOP:30,REQUIREMENT:31,FUNCTIONAL_REQUIREMENT:32,INTERFACE_REQUIREMENT:33,PERFORMANCE_REQUIREMENT:34,PHYSICAL_REQUIREMENT:35,DESIGN_CONSTRAINT:36,LOW_RISK:37,MED_RISK:38,HIGH_RISK:39,VERIFY_ANALYSIS:40,VERIFY_DEMONSTRATION:41,VERIFY_INSPECTION:42,VERIFY_TEST:43,ELEMENT:44,elementName:45,elementBody:46,TYPE:47,type:48,DOCREF:49,ref:50,END_ARROW_L:51,relationship:52,LINE:53,END_ARROW_R:54,CONTAINS:55,COPIES:56,DERIVES:57,SATISFIES:58,VERIFIES:59,REFINES:60,TRACES:61,unqString:62,qString:63,$accept:0,$end:1},terminals_:{2:"error",5:"NEWLINE",6:"RD",8:"EOF",9:"acc_title",10:"acc_title_value",11:"acc_descr",12:"acc_descr_value",13:"acc_descr_multiline_value",19:"STRUCT_START",21:"ID",22:"COLONSEP",24:"TEXT",26:"RISK",28:"VERIFYMTHD",30:"STRUCT_STOP",31:"REQUIREMENT",32:"FUNCTIONAL_REQUIREMENT",33:"INTERFACE_REQUIREMENT",34:"PERFORMANCE_REQUIREMENT",35:"PHYSICAL_REQUIREMENT",36:"DESIGN_CONSTRAINT",37:"LOW_RISK",38:"MED_RISK",39:"HIGH_RISK",40:"VERIFY_ANALYSIS",41:"VERIFY_DEMONSTRATION",42:"VERIFY_INSPECTION",43:"VERIFY_TEST",44:"ELEMENT",47:"TYPE",49:"DOCREF",51:"END_ARROW_L",53:"LINE",54:"END_ARROW_R",55:"CONTAINS",56:"COPIES",57:"DERIVES",58:"SATISFIES",59:"VERIFIES",60:"REFINES",61:"TRACES",62:"unqString",63:"qString"},productions_:[0,[3,3],[3,2],[3,4],[4,2],[4,2],[4,1],[7,0],[7,2],[7,2],[7,2],[7,2],[7,2],[14,5],[20,5],[20,5],[20,5],[20,5],[20,2],[20,1],[17,1],[17,1],[17,1],[17,1],[17,1],[17,1],[27,1],[27,1],[27,1],[29,1],[29,1],[29,1],[29,1],[15,5],[46,5],[46,5],[46,2],[46,1],[16,5],[16,5],[52,1],[52,1],[52,1],[52,1],[52,1],[52,1],[52,1],[18,1],[18,1],[23,1],[23,1],[25,1],[25,1],[45,1],[45,1],[48,1],[48,1],[50,1],[50,1]],performAction:function(i,n,a,r,f,s,W){var _=s.length-1;switch(f){case 4:this.$=s[_].trim(),r.setAccTitle(this.$);break;case 5:case 6:this.$=s[_].trim(),r.setAccDescription(this.$);break;case 7:this.$=[];break;case 13:r.addRequirement(s[_-3],s[_-4]);break;case 14:r.setNewReqId(s[_-2]);break;case 15:r.setNewReqText(s[_-2]);break;case 16:r.setNewReqRisk(s[_-2]);break;case 17:r.setNewReqVerifyMethod(s[_-2]);break;case 20:this.$=r.RequirementType.REQUIREMENT;break;case 21:this.$=r.RequirementType.FUNCTIONAL_REQUIREMENT;break;case 22:this.$=r.RequirementType.INTERFACE_REQUIREMENT;break;case 23:this.$=r.RequirementType.PERFORMANCE_REQUIREMENT;break;case 24:this.$=r.RequirementType.PHYSICAL_REQUIREMENT;break;case 25:this.$=r.RequirementType.DESIGN_CONSTRAINT;break;case 26:this.$=r.RiskLevel.LOW_RISK;break;case 27:this.$=r.RiskLevel.MED_RISK;break;case 28:this.$=r.RiskLevel.HIGH_RISK;break;case 29:this.$=r.VerifyType.VERIFY_ANALYSIS;break;case 30:this.$=r.VerifyType.VERIFY_DEMONSTRATION;break;case 31:this.$=r.VerifyType.VERIFY_INSPECTION;break;case 32:this.$=r.VerifyType.VERIFY_TEST;break;case 33:r.addElement(s[_-3]);break;case 34:r.setNewElementType(s[_-2]);break;case 35:r.setNewElementDocRef(s[_-2]);break;case 38:r.addRelationship(s[_-2],s[_],s[_-4]);break;case 39:r.addRelationship(s[_-2],s[_-4],s[_]);break;case 40:this.$=r.Relationships.CONTAINS;break;case 41:this.$=r.Relationships.COPIES;break;case 42:this.$=r.Relationships.DERIVES;break;case 43:this.$=r.Relationships.SATISFIES;break;case 44:this.$=r.Relationships.VERIFIES;break;case 45:this.$=r.Relationships.REFINES;break;case 46:this.$=r.Relationships.TRACES;break}},table:[{3:1,4:2,6:t,9:l,11:c,13:u},{1:[3]},{3:8,4:2,5:[1,7],6:t,9:l,11:c,13:u},{5:[1,9]},{10:[1,10]},{12:[1,11]},e(d,[2,6]),{3:12,4:2,6:t,9:l,11:c,13:u},{1:[2,2]},{4:17,5:p,7:13,8:h,9:l,11:c,13:u,14:14,15:15,16:16,17:19,23:21,31:o,32:g,33:R,34:A,35:T,36:N,44:v,62:k,63:x},e(d,[2,4]),e(d,[2,5]),{1:[2,1]},{8:[1,30]},{4:17,5:p,7:31,8:h,9:l,11:c,13:u,14:14,15:15,16:16,17:19,23:21,31:o,32:g,33:R,34:A,35:T,36:N,44:v,62:k,63:x},{4:17,5:p,7:32,8:h,9:l,11:c,13:u,14:14,15:15,16:16,17:19,23:21,31:o,32:g,33:R,34:A,35:T,36:N,44:v,62:k,63:x},{4:17,5:p,7:33,8:h,9:l,11:c,13:u,14:14,15:15,16:16,17:19,23:21,31:o,32:g,33:R,34:A,35:T,36:N,44:v,62:k,63:x},{4:17,5:p,7:34,8:h,9:l,11:c,13:u,14:14,15:15,16:16,17:19,23:21,31:o,32:g,33:R,34:A,35:T,36:N,44:v,62:k,63:x},{4:17,5:p,7:35,8:h,9:l,11:c,13:u,14:14,15:15,16:16,17:19,23:21,31:o,32:g,33:R,34:A,35:T,36:N,44:v,62:k,63:x},{18:36,62:[1,37],63:[1,38]},{45:39,62:[1,40],63:[1,41]},{51:[1,42],53:[1,43]},e(F,[2,20]),e(F,[2,21]),e(F,[2,22]),e(F,[2,23]),e(F,[2,24]),e(F,[2,25]),e(de,[2,49]),e(de,[2,50]),{1:[2,3]},{8:[2,8]},{8:[2,9]},{8:[2,10]},{8:[2,11]},{8:[2,12]},{19:[1,44]},{19:[2,47]},{19:[2,48]},{19:[1,45]},{19:[2,53]},{19:[2,54]},{52:46,55:pe,56:fe,57:ye,58:_e,59:ge,60:Ee,61:Re},{52:54,55:pe,56:fe,57:ye,58:_e,59:ge,60:Ee,61:Re},{5:[1,55]},{5:[1,56]},{53:[1,57]},e(O,[2,40]),e(O,[2,41]),e(O,[2,42]),e(O,[2,43]),e(O,[2,44]),e(O,[2,45]),e(O,[2,46]),{54:[1,58]},{5:M,20:59,21:D,24:P,26:Y,28:U,30:B},{5:j,30:z,46:66,47:X,49:J},{23:71,62:k,63:x},{23:72,62:k,63:x},e(m,[2,13]),{22:[1,73]},{22:[1,74]},{22:[1,75]},{22:[1,76]},{5:M,20:77,21:D,24:P,26:Y,28:U,30:B},e(m,[2,19]),e(m,[2,33]),{22:[1,78]},{22:[1,79]},{5:j,30:z,46:80,47:X,49:J},e(m,[2,37]),e(m,[2,38]),e(m,[2,39]),{23:81,62:k,63:x},{25:82,62:[1,83],63:[1,84]},{27:85,37:[1,86],38:[1,87],39:[1,88]},{29:89,40:[1,90],41:[1,91],42:[1,92],43:[1,93]},e(m,[2,18]),{48:94,62:[1,95],63:[1,96]},{50:97,62:[1,98],63:[1,99]},e(m,[2,36]),{5:[1,100]},{5:[1,101]},{5:[2,51]},{5:[2,52]},{5:[1,102]},{5:[2,26]},{5:[2,27]},{5:[2,28]},{5:[1,103]},{5:[2,29]},{5:[2,30]},{5:[2,31]},{5:[2,32]},{5:[1,104]},{5:[2,55]},{5:[2,56]},{5:[1,105]},{5:[2,57]},{5:[2,58]},{5:M,20:106,21:D,24:P,26:Y,28:U,30:B},{5:M,20:107,21:D,24:P,26:Y,28:U,30:B},{5:M,20:108,21:D,24:P,26:Y,28:U,30:B},{5:M,20:109,21:D,24:P,26:Y,28:U,30:B},{5:j,30:z,46:110,47:X,49:J},{5:j,30:z,46:111,47:X,49:J},e(m,[2,14]),e(m,[2,15]),e(m,[2,16]),e(m,[2,17]),e(m,[2,34]),e(m,[2,35])],defaultActions:{8:[2,2],12:[2,1],30:[2,3],31:[2,8],32:[2,9],33:[2,10],34:[2,11],35:[2,12],37:[2,47],38:[2,48],40:[2,53],41:[2,54],83:[2,51],84:[2,52],86:[2,26],87:[2,27],88:[2,28],90:[2,29],91:[2,30],92:[2,31],93:[2,32],95:[2,55],96:[2,56],98:[2,57],99:[2,58]},parseError:function(i,n){if(n.recoverable)this.trace(i);else{var a=new Error(i);throw a.hash=n,a}},parse:function(i){var n=this,a=[0],r=[],f=[null],s=[],W=this.table,_="",Z=0,me=0,Ve=2,Ie=1,qe=s.slice.call(arguments,1),E=Object.create(this.lexer),L={yy:{}};for(var ne in this.yy)Object.prototype.hasOwnProperty.call(this.yy,ne)&&(L.yy[ne]=this.yy[ne]);E.setInput(i,L.yy),L.yy.lexer=E,L.yy.parser=this,typeof E.yylloc>"u"&&(E.yylloc={});var se=E.yylloc;s.push(se);var Oe=E.options&&E.options.ranges;typeof L.yy.parseError=="function"?this.parseError=L.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function Le(){var $;return $=r.pop()||E.lex()||Ie,typeof $!="number"&&($ instanceof Array&&(r=$,$=r.pop()),$=n.symbols_[$]||$),$}for(var I,C,S,ae,Q={},ee,w,be,te;;){if(C=a[a.length-1],this.defaultActions[C]?S=this.defaultActions[C]:((I===null||typeof I>"u")&&(I=Le()),S=W[C]&&W[C][I]),typeof S>"u"||!S.length||!S[0]){var le="";te=[];for(ee in W[C])this.terminals_[ee]&&ee>Ve&&te.push("'"+this.terminals_[ee]+"'");E.showPosition?le="Parse error on line "+(Z+1)+`:
+import{c as Te,s as Ce,g as Fe,b as Me,a as De,l as Ne,A as Pe,h as oe,i as Ye,j as ke}from"./mermaid.core-DNo_7Q2B.js";import{G as Ue}from"./graph-B1296pfd.js";import{l as Be}from"./layout-qMafh1ee.js";import{l as Qe}from"./line-BqHmcuby.js";import"./app-B4LGNJZ0.js";import"./array-BKyUJesY.js";import"./path-CbwjOpE9.js";var ce=function(){var e=function(V,i,n,a){for(n=n||{},a=V.length;a--;n[V[a]]=i);return n},t=[1,3],l=[1,4],c=[1,5],u=[1,6],d=[5,6,8,9,11,13,31,32,33,34,35,36,44,62,63],p=[1,18],h=[2,7],o=[1,22],g=[1,23],R=[1,24],A=[1,25],T=[1,26],N=[1,27],v=[1,20],k=[1,28],x=[1,29],F=[62,63],de=[5,8,9,11,13,31,32,33,34,35,36,44,51,53,62,63],pe=[1,47],fe=[1,48],ye=[1,49],_e=[1,50],ge=[1,51],Ee=[1,52],Re=[1,53],O=[53,54],M=[1,64],D=[1,60],P=[1,61],Y=[1,62],U=[1,63],B=[1,65],j=[1,69],z=[1,70],X=[1,67],J=[1,68],m=[5,8,9,11,13,31,32,33,34,35,36,44,62,63],ie={trace:function(){},yy:{},symbols_:{error:2,start:3,directive:4,NEWLINE:5,RD:6,diagram:7,EOF:8,acc_title:9,acc_title_value:10,acc_descr:11,acc_descr_value:12,acc_descr_multiline_value:13,requirementDef:14,elementDef:15,relationshipDef:16,requirementType:17,requirementName:18,STRUCT_START:19,requirementBody:20,ID:21,COLONSEP:22,id:23,TEXT:24,text:25,RISK:26,riskLevel:27,VERIFYMTHD:28,verifyType:29,STRUCT_STOP:30,REQUIREMENT:31,FUNCTIONAL_REQUIREMENT:32,INTERFACE_REQUIREMENT:33,PERFORMANCE_REQUIREMENT:34,PHYSICAL_REQUIREMENT:35,DESIGN_CONSTRAINT:36,LOW_RISK:37,MED_RISK:38,HIGH_RISK:39,VERIFY_ANALYSIS:40,VERIFY_DEMONSTRATION:41,VERIFY_INSPECTION:42,VERIFY_TEST:43,ELEMENT:44,elementName:45,elementBody:46,TYPE:47,type:48,DOCREF:49,ref:50,END_ARROW_L:51,relationship:52,LINE:53,END_ARROW_R:54,CONTAINS:55,COPIES:56,DERIVES:57,SATISFIES:58,VERIFIES:59,REFINES:60,TRACES:61,unqString:62,qString:63,$accept:0,$end:1},terminals_:{2:"error",5:"NEWLINE",6:"RD",8:"EOF",9:"acc_title",10:"acc_title_value",11:"acc_descr",12:"acc_descr_value",13:"acc_descr_multiline_value",19:"STRUCT_START",21:"ID",22:"COLONSEP",24:"TEXT",26:"RISK",28:"VERIFYMTHD",30:"STRUCT_STOP",31:"REQUIREMENT",32:"FUNCTIONAL_REQUIREMENT",33:"INTERFACE_REQUIREMENT",34:"PERFORMANCE_REQUIREMENT",35:"PHYSICAL_REQUIREMENT",36:"DESIGN_CONSTRAINT",37:"LOW_RISK",38:"MED_RISK",39:"HIGH_RISK",40:"VERIFY_ANALYSIS",41:"VERIFY_DEMONSTRATION",42:"VERIFY_INSPECTION",43:"VERIFY_TEST",44:"ELEMENT",47:"TYPE",49:"DOCREF",51:"END_ARROW_L",53:"LINE",54:"END_ARROW_R",55:"CONTAINS",56:"COPIES",57:"DERIVES",58:"SATISFIES",59:"VERIFIES",60:"REFINES",61:"TRACES",62:"unqString",63:"qString"},productions_:[0,[3,3],[3,2],[3,4],[4,2],[4,2],[4,1],[7,0],[7,2],[7,2],[7,2],[7,2],[7,2],[14,5],[20,5],[20,5],[20,5],[20,5],[20,2],[20,1],[17,1],[17,1],[17,1],[17,1],[17,1],[17,1],[27,1],[27,1],[27,1],[29,1],[29,1],[29,1],[29,1],[15,5],[46,5],[46,5],[46,2],[46,1],[16,5],[16,5],[52,1],[52,1],[52,1],[52,1],[52,1],[52,1],[52,1],[18,1],[18,1],[23,1],[23,1],[25,1],[25,1],[45,1],[45,1],[48,1],[48,1],[50,1],[50,1]],performAction:function(i,n,a,r,f,s,W){var _=s.length-1;switch(f){case 4:this.$=s[_].trim(),r.setAccTitle(this.$);break;case 5:case 6:this.$=s[_].trim(),r.setAccDescription(this.$);break;case 7:this.$=[];break;case 13:r.addRequirement(s[_-3],s[_-4]);break;case 14:r.setNewReqId(s[_-2]);break;case 15:r.setNewReqText(s[_-2]);break;case 16:r.setNewReqRisk(s[_-2]);break;case 17:r.setNewReqVerifyMethod(s[_-2]);break;case 20:this.$=r.RequirementType.REQUIREMENT;break;case 21:this.$=r.RequirementType.FUNCTIONAL_REQUIREMENT;break;case 22:this.$=r.RequirementType.INTERFACE_REQUIREMENT;break;case 23:this.$=r.RequirementType.PERFORMANCE_REQUIREMENT;break;case 24:this.$=r.RequirementType.PHYSICAL_REQUIREMENT;break;case 25:this.$=r.RequirementType.DESIGN_CONSTRAINT;break;case 26:this.$=r.RiskLevel.LOW_RISK;break;case 27:this.$=r.RiskLevel.MED_RISK;break;case 28:this.$=r.RiskLevel.HIGH_RISK;break;case 29:this.$=r.VerifyType.VERIFY_ANALYSIS;break;case 30:this.$=r.VerifyType.VERIFY_DEMONSTRATION;break;case 31:this.$=r.VerifyType.VERIFY_INSPECTION;break;case 32:this.$=r.VerifyType.VERIFY_TEST;break;case 33:r.addElement(s[_-3]);break;case 34:r.setNewElementType(s[_-2]);break;case 35:r.setNewElementDocRef(s[_-2]);break;case 38:r.addRelationship(s[_-2],s[_],s[_-4]);break;case 39:r.addRelationship(s[_-2],s[_-4],s[_]);break;case 40:this.$=r.Relationships.CONTAINS;break;case 41:this.$=r.Relationships.COPIES;break;case 42:this.$=r.Relationships.DERIVES;break;case 43:this.$=r.Relationships.SATISFIES;break;case 44:this.$=r.Relationships.VERIFIES;break;case 45:this.$=r.Relationships.REFINES;break;case 46:this.$=r.Relationships.TRACES;break}},table:[{3:1,4:2,6:t,9:l,11:c,13:u},{1:[3]},{3:8,4:2,5:[1,7],6:t,9:l,11:c,13:u},{5:[1,9]},{10:[1,10]},{12:[1,11]},e(d,[2,6]),{3:12,4:2,6:t,9:l,11:c,13:u},{1:[2,2]},{4:17,5:p,7:13,8:h,9:l,11:c,13:u,14:14,15:15,16:16,17:19,23:21,31:o,32:g,33:R,34:A,35:T,36:N,44:v,62:k,63:x},e(d,[2,4]),e(d,[2,5]),{1:[2,1]},{8:[1,30]},{4:17,5:p,7:31,8:h,9:l,11:c,13:u,14:14,15:15,16:16,17:19,23:21,31:o,32:g,33:R,34:A,35:T,36:N,44:v,62:k,63:x},{4:17,5:p,7:32,8:h,9:l,11:c,13:u,14:14,15:15,16:16,17:19,23:21,31:o,32:g,33:R,34:A,35:T,36:N,44:v,62:k,63:x},{4:17,5:p,7:33,8:h,9:l,11:c,13:u,14:14,15:15,16:16,17:19,23:21,31:o,32:g,33:R,34:A,35:T,36:N,44:v,62:k,63:x},{4:17,5:p,7:34,8:h,9:l,11:c,13:u,14:14,15:15,16:16,17:19,23:21,31:o,32:g,33:R,34:A,35:T,36:N,44:v,62:k,63:x},{4:17,5:p,7:35,8:h,9:l,11:c,13:u,14:14,15:15,16:16,17:19,23:21,31:o,32:g,33:R,34:A,35:T,36:N,44:v,62:k,63:x},{18:36,62:[1,37],63:[1,38]},{45:39,62:[1,40],63:[1,41]},{51:[1,42],53:[1,43]},e(F,[2,20]),e(F,[2,21]),e(F,[2,22]),e(F,[2,23]),e(F,[2,24]),e(F,[2,25]),e(de,[2,49]),e(de,[2,50]),{1:[2,3]},{8:[2,8]},{8:[2,9]},{8:[2,10]},{8:[2,11]},{8:[2,12]},{19:[1,44]},{19:[2,47]},{19:[2,48]},{19:[1,45]},{19:[2,53]},{19:[2,54]},{52:46,55:pe,56:fe,57:ye,58:_e,59:ge,60:Ee,61:Re},{52:54,55:pe,56:fe,57:ye,58:_e,59:ge,60:Ee,61:Re},{5:[1,55]},{5:[1,56]},{53:[1,57]},e(O,[2,40]),e(O,[2,41]),e(O,[2,42]),e(O,[2,43]),e(O,[2,44]),e(O,[2,45]),e(O,[2,46]),{54:[1,58]},{5:M,20:59,21:D,24:P,26:Y,28:U,30:B},{5:j,30:z,46:66,47:X,49:J},{23:71,62:k,63:x},{23:72,62:k,63:x},e(m,[2,13]),{22:[1,73]},{22:[1,74]},{22:[1,75]},{22:[1,76]},{5:M,20:77,21:D,24:P,26:Y,28:U,30:B},e(m,[2,19]),e(m,[2,33]),{22:[1,78]},{22:[1,79]},{5:j,30:z,46:80,47:X,49:J},e(m,[2,37]),e(m,[2,38]),e(m,[2,39]),{23:81,62:k,63:x},{25:82,62:[1,83],63:[1,84]},{27:85,37:[1,86],38:[1,87],39:[1,88]},{29:89,40:[1,90],41:[1,91],42:[1,92],43:[1,93]},e(m,[2,18]),{48:94,62:[1,95],63:[1,96]},{50:97,62:[1,98],63:[1,99]},e(m,[2,36]),{5:[1,100]},{5:[1,101]},{5:[2,51]},{5:[2,52]},{5:[1,102]},{5:[2,26]},{5:[2,27]},{5:[2,28]},{5:[1,103]},{5:[2,29]},{5:[2,30]},{5:[2,31]},{5:[2,32]},{5:[1,104]},{5:[2,55]},{5:[2,56]},{5:[1,105]},{5:[2,57]},{5:[2,58]},{5:M,20:106,21:D,24:P,26:Y,28:U,30:B},{5:M,20:107,21:D,24:P,26:Y,28:U,30:B},{5:M,20:108,21:D,24:P,26:Y,28:U,30:B},{5:M,20:109,21:D,24:P,26:Y,28:U,30:B},{5:j,30:z,46:110,47:X,49:J},{5:j,30:z,46:111,47:X,49:J},e(m,[2,14]),e(m,[2,15]),e(m,[2,16]),e(m,[2,17]),e(m,[2,34]),e(m,[2,35])],defaultActions:{8:[2,2],12:[2,1],30:[2,3],31:[2,8],32:[2,9],33:[2,10],34:[2,11],35:[2,12],37:[2,47],38:[2,48],40:[2,53],41:[2,54],83:[2,51],84:[2,52],86:[2,26],87:[2,27],88:[2,28],90:[2,29],91:[2,30],92:[2,31],93:[2,32],95:[2,55],96:[2,56],98:[2,57],99:[2,58]},parseError:function(i,n){if(n.recoverable)this.trace(i);else{var a=new Error(i);throw a.hash=n,a}},parse:function(i){var n=this,a=[0],r=[],f=[null],s=[],W=this.table,_="",Z=0,me=0,Ve=2,Ie=1,qe=s.slice.call(arguments,1),E=Object.create(this.lexer),L={yy:{}};for(var ne in this.yy)Object.prototype.hasOwnProperty.call(this.yy,ne)&&(L.yy[ne]=this.yy[ne]);E.setInput(i,L.yy),L.yy.lexer=E,L.yy.parser=this,typeof E.yylloc>"u"&&(E.yylloc={});var se=E.yylloc;s.push(se);var Oe=E.options&&E.options.ranges;typeof L.yy.parseError=="function"?this.parseError=L.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function Le(){var $;return $=r.pop()||E.lex()||Ie,typeof $!="number"&&($ instanceof Array&&(r=$,$=r.pop()),$=n.symbols_[$]||$),$}for(var I,C,S,ae,Q={},ee,w,be,te;;){if(C=a[a.length-1],this.defaultActions[C]?S=this.defaultActions[C]:((I===null||typeof I>"u")&&(I=Le()),S=W[C]&&W[C][I]),typeof S>"u"||!S.length||!S[0]){var le="";te=[];for(ee in W[C])this.terminals_[ee]&&ee>Ve&&te.push("'"+this.terminals_[ee]+"'");E.showPosition?le="Parse error on line "+(Z+1)+`:
 `+E.showPosition()+`
 Expecting `+te.join(", ")+", got '"+(this.terminals_[I]||I)+"'":le="Parse error on line "+(Z+1)+": Unexpected "+(I==Ie?"end of input":"'"+(this.terminals_[I]||I)+"'"),this.parseError(le,{text:E.match,token:this.terminals_[I]||I,line:E.yylineno,loc:se,expected:te})}if(S[0]instanceof Array&&S.length>1)throw new Error("Parse Error: multiple actions possible at state: "+C+", token: "+I);switch(S[0]){case 1:a.push(I),f.push(E.yytext),s.push(E.yylloc),a.push(S[1]),I=null,me=E.yyleng,_=E.yytext,Z=E.yylineno,se=E.yylloc;break;case 2:if(w=this.productions_[S[1]][1],Q.$=f[f.length-w],Q._$={first_line:s[s.length-(w||1)].first_line,last_line:s[s.length-1].last_line,first_column:s[s.length-(w||1)].first_column,last_column:s[s.length-1].last_column},Oe&&(Q._$.range=[s[s.length-(w||1)].range[0],s[s.length-1].range[1]]),ae=this.performAction.apply(Q,[_,me,Z,L.yy,S[1],f,s].concat(qe)),typeof ae<"u")return ae;w&&(a=a.slice(0,-1*w*2),f=f.slice(0,-1*w),s=s.slice(0,-1*w)),a.push(this.productions_[S[1]][0]),f.push(Q.$),s.push(Q._$),be=W[a[a.length-2]][a[a.length-1]],a.push(be);break;case 3:return!0}}return!0}},$e=function(){var V={EOF:1,parseError:function(n,a){if(this.yy.parser)this.yy.parser.parseError(n,a);else throw new Error(n)},setInput:function(i,n){return this.yy=n||this.yy||{},this._input=i,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var i=this._input[0];this.yytext+=i,this.yyleng++,this.offset++,this.match+=i,this.matched+=i;var n=i.match(/(?:\r\n?|\n).*/g);return n?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),i},unput:function(i){var n=i.length,a=i.split(/(?:\r\n?|\n)/g);this._input=i+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-n),this.offset-=n;var r=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),a.length-1&&(this.yylineno-=a.length-1);var f=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:a?(a.length===r.length?this.yylloc.first_column:0)+r[r.length-a.length].length-a[0].length:this.yylloc.first_column-n},this.options.ranges&&(this.yylloc.range=[f[0],f[0]+this.yyleng-n]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){if(this.options.backtrack_lexer)this._backtrack=!0;else return this.parseError("Lexical error on line "+(this.yylineno+1)+`. You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).
 `+this.showPosition(),{text:"",token:null,line:this.yylineno});return this},less:function(i){this.unput(this.match.slice(i))},pastInput:function(){var i=this.matched.substr(0,this.matched.length-this.match.length);return(i.length>20?"...":"")+i.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var i=this.match;return i.length<20&&(i+=this._input.substr(0,20-i.length)),(i.substr(0,20)+(i.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var i=this.pastInput(),n=new Array(i.length+1).join("-");return i+this.upcomingInput()+`
diff --git a/assets/sankeyDiagram-c599f8ec-BGnWqC27.js b/assets/sankeyDiagram-c599f8ec-Ss3oz1oB.js
similarity index 99%
rename from assets/sankeyDiagram-c599f8ec-BGnWqC27.js
rename to assets/sankeyDiagram-c599f8ec-Ss3oz1oB.js
index 5fc2bb7..4a3383a 100644
--- a/assets/sankeyDiagram-c599f8ec-BGnWqC27.js
+++ b/assets/sankeyDiagram-c599f8ec-Ss3oz1oB.js
@@ -1,4 +1,4 @@
-import{c as rt,g as mt,s as kt,a as _t,b as xt,y as vt,x as bt,A as wt,j as St,v as Lt,h as G,u as Et}from"./mermaid.core-ChLYKTZm.js";import{o as At}from"./ordinal-Cboi1Yqb.js";import{s as Tt}from"./Tableau10-B-NsZVaP.js";import"./app-B69Gl_S-.js";import"./init-Gi6I4Gst.js";function ot(t,n){let s;if(n===void 0)for(const a of t)a!=null&&(s<a||s===void 0&&a>=a)&&(s=a);else{let a=-1;for(let u of t)(u=n(u,++a,t))!=null&&(s<u||s===void 0&&u>=u)&&(s=u)}return s}function yt(t,n){let s;if(n===void 0)for(const a of t)a!=null&&(s>a||s===void 0&&a>=a)&&(s=a);else{let a=-1;for(let u of t)(u=n(u,++a,t))!=null&&(s>u||s===void 0&&u>=u)&&(s=u)}return s}function Z(t,n){let s=0;if(n===void 0)for(let a of t)(a=+a)&&(s+=a);else{let a=-1;for(let u of t)(u=+n(u,++a,t))&&(s+=u)}return s}function Mt(t){return t.target.depth}function Nt(t){return t.depth}function Pt(t,n){return n-1-t.height}function dt(t,n){return t.sourceLinks.length?t.depth:n-1}function Ct(t){return t.targetLinks.length?t.depth:t.sourceLinks.length?yt(t.sourceLinks,Mt)-1:0}function Y(t){return function(){return t}}function lt(t,n){return H(t.source,n.source)||t.index-n.index}function at(t,n){return H(t.target,n.target)||t.index-n.index}function H(t,n){return t.y0-n.y0}function J(t){return t.value}function It(t){return t.index}function $t(t){return t.nodes}function Ot(t){return t.links}function ct(t,n){const s=t.get(n);if(!s)throw new Error("missing: "+n);return s}function ut({nodes:t}){for(const n of t){let s=n.y0,a=s;for(const u of n.sourceLinks)u.y0=s+u.width/2,s+=u.width;for(const u of n.targetLinks)u.y1=a+u.width/2,a+=u.width}}function jt(){let t=0,n=0,s=1,a=1,u=24,_=8,g,p=It,i=dt,o,c,m=$t,b=Ot,y=6;function x(){const e={nodes:m.apply(null,arguments),links:b.apply(null,arguments)};return E(e),L(e),A(e),N(e),S(e),ut(e),e}x.update=function(e){return ut(e),e},x.nodeId=function(e){return arguments.length?(p=typeof e=="function"?e:Y(e),x):p},x.nodeAlign=function(e){return arguments.length?(i=typeof e=="function"?e:Y(e),x):i},x.nodeSort=function(e){return arguments.length?(o=e,x):o},x.nodeWidth=function(e){return arguments.length?(u=+e,x):u},x.nodePadding=function(e){return arguments.length?(_=g=+e,x):_},x.nodes=function(e){return arguments.length?(m=typeof e=="function"?e:Y(e),x):m},x.links=function(e){return arguments.length?(b=typeof e=="function"?e:Y(e),x):b},x.linkSort=function(e){return arguments.length?(c=e,x):c},x.size=function(e){return arguments.length?(t=n=0,s=+e[0],a=+e[1],x):[s-t,a-n]},x.extent=function(e){return arguments.length?(t=+e[0][0],s=+e[1][0],n=+e[0][1],a=+e[1][1],x):[[t,n],[s,a]]},x.iterations=function(e){return arguments.length?(y=+e,x):y};function E({nodes:e,links:f}){for(const[h,r]of e.entries())r.index=h,r.sourceLinks=[],r.targetLinks=[];const l=new Map(e.map((h,r)=>[p(h,r,e),h]));for(const[h,r]of f.entries()){r.index=h;let{source:k,target:v}=r;typeof k!="object"&&(k=r.source=ct(l,k)),typeof v!="object"&&(v=r.target=ct(l,v)),k.sourceLinks.push(r),v.targetLinks.push(r)}if(c!=null)for(const{sourceLinks:h,targetLinks:r}of e)h.sort(c),r.sort(c)}function L({nodes:e}){for(const f of e)f.value=f.fixedValue===void 0?Math.max(Z(f.sourceLinks,J),Z(f.targetLinks,J)):f.fixedValue}function A({nodes:e}){const f=e.length;let l=new Set(e),h=new Set,r=0;for(;l.size;){for(const k of l){k.depth=r;for(const{target:v}of k.sourceLinks)h.add(v)}if(++r>f)throw new Error("circular link");l=h,h=new Set}}function N({nodes:e}){const f=e.length;let l=new Set(e),h=new Set,r=0;for(;l.size;){for(const k of l){k.height=r;for(const{source:v}of k.targetLinks)h.add(v)}if(++r>f)throw new Error("circular link");l=h,h=new Set}}function I({nodes:e}){const f=ot(e,r=>r.depth)+1,l=(s-t-u)/(f-1),h=new Array(f);for(const r of e){const k=Math.max(0,Math.min(f-1,Math.floor(i.call(null,r,f))));r.layer=k,r.x0=t+k*l,r.x1=r.x0+u,h[k]?h[k].push(r):h[k]=[r]}if(o)for(const r of h)r.sort(o);return h}function j(e){const f=yt(e,l=>(a-n-(l.length-1)*g)/Z(l,J));for(const l of e){let h=n;for(const r of l){r.y0=h,r.y1=h+r.value*f,h=r.y1+g;for(const k of r.sourceLinks)k.width=k.value*f}h=(a-h+g)/(l.length+1);for(let r=0;r<l.length;++r){const k=l[r];k.y0+=h*(r+1),k.y1+=h*(r+1)}$(l)}}function S(e){const f=I(e);g=Math.min(_,(a-n)/(ot(f,l=>l.length)-1)),j(f);for(let l=0;l<y;++l){const h=Math.pow(.99,l),r=Math.max(1-h,(l+1)/y);O(f,h,r),M(f,h,r)}}function M(e,f,l){for(let h=1,r=e.length;h<r;++h){const k=e[h];for(const v of k){let R=0,z=0;for(const{source:W,value:K}of v.targetLinks){let F=K*(v.layer-W.layer);R+=T(W,v)*F,z+=F}if(!(z>0))continue;let U=(R/z-v.y0)*f;v.y0+=U,v.y1+=U,w(v)}o===void 0&&k.sort(H),P(k,l)}}function O(e,f,l){for(let h=e.length,r=h-2;r>=0;--r){const k=e[r];for(const v of k){let R=0,z=0;for(const{target:W,value:K}of v.sourceLinks){let F=K*(W.layer-v.layer);R+=V(v,W)*F,z+=F}if(!(z>0))continue;let U=(R/z-v.y0)*f;v.y0+=U,v.y1+=U,w(v)}o===void 0&&k.sort(H),P(k,l)}}function P(e,f){const l=e.length>>1,h=e[l];d(e,h.y0-g,l-1,f),C(e,h.y1+g,l+1,f),d(e,a,e.length-1,f),C(e,n,0,f)}function C(e,f,l,h){for(;l<e.length;++l){const r=e[l],k=(f-r.y0)*h;k>1e-6&&(r.y0+=k,r.y1+=k),f=r.y1+g}}function d(e,f,l,h){for(;l>=0;--l){const r=e[l],k=(r.y1-f)*h;k>1e-6&&(r.y0-=k,r.y1-=k),f=r.y0-g}}function w({sourceLinks:e,targetLinks:f}){if(c===void 0){for(const{source:{sourceLinks:l}}of f)l.sort(at);for(const{target:{targetLinks:l}}of e)l.sort(lt)}}function $(e){if(c===void 0)for(const{sourceLinks:f,targetLinks:l}of e)f.sort(at),l.sort(lt)}function T(e,f){let l=e.y0-(e.sourceLinks.length-1)*g/2;for(const{target:h,width:r}of e.sourceLinks){if(h===f)break;l+=r+g}for(const{source:h,width:r}of f.targetLinks){if(h===e)break;l-=r}return l}function V(e,f){let l=f.y0-(f.targetLinks.length-1)*g/2;for(const{source:h,width:r}of f.targetLinks){if(h===e)break;l+=r+g}for(const{target:h,width:r}of e.sourceLinks){if(h===f)break;l-=r}return l}return x}var tt=Math.PI,et=2*tt,D=1e-6,zt=et-D;function nt(){this._x0=this._y0=this._x1=this._y1=null,this._=""}function gt(){return new nt}nt.prototype=gt.prototype={constructor:nt,moveTo:function(t,n){this._+="M"+(this._x0=this._x1=+t)+","+(this._y0=this._y1=+n)},closePath:function(){this._x1!==null&&(this._x1=this._x0,this._y1=this._y0,this._+="Z")},lineTo:function(t,n){this._+="L"+(this._x1=+t)+","+(this._y1=+n)},quadraticCurveTo:function(t,n,s,a){this._+="Q"+ +t+","+ +n+","+(this._x1=+s)+","+(this._y1=+a)},bezierCurveTo:function(t,n,s,a,u,_){this._+="C"+ +t+","+ +n+","+ +s+","+ +a+","+(this._x1=+u)+","+(this._y1=+_)},arcTo:function(t,n,s,a,u){t=+t,n=+n,s=+s,a=+a,u=+u;var _=this._x1,g=this._y1,p=s-t,i=a-n,o=_-t,c=g-n,m=o*o+c*c;if(u<0)throw new Error("negative radius: "+u);if(this._x1===null)this._+="M"+(this._x1=t)+","+(this._y1=n);else if(m>D)if(!(Math.abs(c*p-i*o)>D)||!u)this._+="L"+(this._x1=t)+","+(this._y1=n);else{var b=s-_,y=a-g,x=p*p+i*i,E=b*b+y*y,L=Math.sqrt(x),A=Math.sqrt(m),N=u*Math.tan((tt-Math.acos((x+m-E)/(2*L*A)))/2),I=N/A,j=N/L;Math.abs(I-1)>D&&(this._+="L"+(t+I*o)+","+(n+I*c)),this._+="A"+u+","+u+",0,0,"+ +(c*b>o*y)+","+(this._x1=t+j*p)+","+(this._y1=n+j*i)}},arc:function(t,n,s,a,u,_){t=+t,n=+n,s=+s,_=!!_;var g=s*Math.cos(a),p=s*Math.sin(a),i=t+g,o=n+p,c=1^_,m=_?a-u:u-a;if(s<0)throw new Error("negative radius: "+s);this._x1===null?this._+="M"+i+","+o:(Math.abs(this._x1-i)>D||Math.abs(this._y1-o)>D)&&(this._+="L"+i+","+o),s&&(m<0&&(m=m%et+et),m>zt?this._+="A"+s+","+s+",0,1,"+c+","+(t-g)+","+(n-p)+"A"+s+","+s+",0,1,"+c+","+(this._x1=i)+","+(this._y1=o):m>D&&(this._+="A"+s+","+s+",0,"+ +(m>=tt)+","+c+","+(this._x1=t+s*Math.cos(u))+","+(this._y1=n+s*Math.sin(u))))},rect:function(t,n,s,a){this._+="M"+(this._x0=this._x1=+t)+","+(this._y0=this._y1=+n)+"h"+ +s+"v"+ +a+"h"+-s+"Z"},toString:function(){return this._}};function ht(t){return function(){return t}}function Dt(t){return t[0]}function Bt(t){return t[1]}var Vt=Array.prototype.slice;function Rt(t){return t.source}function Ut(t){return t.target}function Wt(t){var n=Rt,s=Ut,a=Dt,u=Bt,_=null;function g(){var p,i=Vt.call(arguments),o=n.apply(this,i),c=s.apply(this,i);if(_||(_=p=gt()),t(_,+a.apply(this,(i[0]=o,i)),+u.apply(this,i),+a.apply(this,(i[0]=c,i)),+u.apply(this,i)),p)return _=null,p+""||null}return g.source=function(p){return arguments.length?(n=p,g):n},g.target=function(p){return arguments.length?(s=p,g):s},g.x=function(p){return arguments.length?(a=typeof p=="function"?p:ht(+p),g):a},g.y=function(p){return arguments.length?(u=typeof p=="function"?p:ht(+p),g):u},g.context=function(p){return arguments.length?(_=p??null,g):_},g}function Ft(t,n,s,a,u){t.moveTo(n,s),t.bezierCurveTo(n=(n+a)/2,s,n,u,a,u)}function Gt(){return Wt(Ft)}function Yt(t){return[t.source.x1,t.y0]}function Ht(t){return[t.target.x0,t.y1]}function Xt(){return Gt().source(Yt).target(Ht)}var it=function(){var t=function(p,i,o,c){for(o=o||{},c=p.length;c--;o[p[c]]=i);return o},n=[1,9],s=[1,10],a=[1,5,10,12],u={trace:function(){},yy:{},symbols_:{error:2,start:3,SANKEY:4,NEWLINE:5,csv:6,opt_eof:7,record:8,csv_tail:9,EOF:10,"field[source]":11,COMMA:12,"field[target]":13,"field[value]":14,field:15,escaped:16,non_escaped:17,DQUOTE:18,ESCAPED_TEXT:19,NON_ESCAPED_TEXT:20,$accept:0,$end:1},terminals_:{2:"error",4:"SANKEY",5:"NEWLINE",10:"EOF",11:"field[source]",12:"COMMA",13:"field[target]",14:"field[value]",18:"DQUOTE",19:"ESCAPED_TEXT",20:"NON_ESCAPED_TEXT"},productions_:[0,[3,4],[6,2],[9,2],[9,0],[7,1],[7,0],[8,5],[15,1],[15,1],[16,3],[17,1]],performAction:function(i,o,c,m,b,y,x){var E=y.length-1;switch(b){case 7:const L=m.findOrCreateNode(y[E-4].trim().replaceAll('""','"')),A=m.findOrCreateNode(y[E-2].trim().replaceAll('""','"')),N=parseFloat(y[E].trim());m.addLink(L,A,N);break;case 8:case 9:case 11:this.$=y[E];break;case 10:this.$=y[E-1];break}},table:[{3:1,4:[1,2]},{1:[3]},{5:[1,3]},{6:4,8:5,15:6,16:7,17:8,18:n,20:s},{1:[2,6],7:11,10:[1,12]},t(s,[2,4],{9:13,5:[1,14]}),{12:[1,15]},t(a,[2,8]),t(a,[2,9]),{19:[1,16]},t(a,[2,11]),{1:[2,1]},{1:[2,5]},t(s,[2,2]),{6:17,8:5,15:6,16:7,17:8,18:n,20:s},{15:18,16:7,17:8,18:n,20:s},{18:[1,19]},t(s,[2,3]),{12:[1,20]},t(a,[2,10]),{15:21,16:7,17:8,18:n,20:s},t([1,5,10],[2,7])],defaultActions:{11:[2,1],12:[2,5]},parseError:function(i,o){if(o.recoverable)this.trace(i);else{var c=new Error(i);throw c.hash=o,c}},parse:function(i){var o=this,c=[0],m=[],b=[null],y=[],x=this.table,E="",L=0,A=0,N=2,I=1,j=y.slice.call(arguments,1),S=Object.create(this.lexer),M={yy:{}};for(var O in this.yy)Object.prototype.hasOwnProperty.call(this.yy,O)&&(M.yy[O]=this.yy[O]);S.setInput(i,M.yy),M.yy.lexer=S,M.yy.parser=this,typeof S.yylloc>"u"&&(S.yylloc={});var P=S.yylloc;y.push(P);var C=S.options&&S.options.ranges;typeof M.yy.parseError=="function"?this.parseError=M.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function d(){var v;return v=m.pop()||S.lex()||I,typeof v!="number"&&(v instanceof Array&&(m=v,v=m.pop()),v=o.symbols_[v]||v),v}for(var w,$,T,V,e={},f,l,h,r;;){if($=c[c.length-1],this.defaultActions[$]?T=this.defaultActions[$]:((w===null||typeof w>"u")&&(w=d()),T=x[$]&&x[$][w]),typeof T>"u"||!T.length||!T[0]){var k="";r=[];for(f in x[$])this.terminals_[f]&&f>N&&r.push("'"+this.terminals_[f]+"'");S.showPosition?k="Parse error on line "+(L+1)+`:
+import{c as rt,g as mt,s as kt,a as _t,b as xt,y as vt,x as bt,A as wt,j as St,v as Lt,h as G,u as Et}from"./mermaid.core-DNo_7Q2B.js";import{o as At}from"./ordinal-Cboi1Yqb.js";import{s as Tt}from"./Tableau10-B-NsZVaP.js";import"./app-B4LGNJZ0.js";import"./init-Gi6I4Gst.js";function ot(t,n){let s;if(n===void 0)for(const a of t)a!=null&&(s<a||s===void 0&&a>=a)&&(s=a);else{let a=-1;for(let u of t)(u=n(u,++a,t))!=null&&(s<u||s===void 0&&u>=u)&&(s=u)}return s}function yt(t,n){let s;if(n===void 0)for(const a of t)a!=null&&(s>a||s===void 0&&a>=a)&&(s=a);else{let a=-1;for(let u of t)(u=n(u,++a,t))!=null&&(s>u||s===void 0&&u>=u)&&(s=u)}return s}function Z(t,n){let s=0;if(n===void 0)for(let a of t)(a=+a)&&(s+=a);else{let a=-1;for(let u of t)(u=+n(u,++a,t))&&(s+=u)}return s}function Mt(t){return t.target.depth}function Nt(t){return t.depth}function Pt(t,n){return n-1-t.height}function dt(t,n){return t.sourceLinks.length?t.depth:n-1}function Ct(t){return t.targetLinks.length?t.depth:t.sourceLinks.length?yt(t.sourceLinks,Mt)-1:0}function Y(t){return function(){return t}}function lt(t,n){return H(t.source,n.source)||t.index-n.index}function at(t,n){return H(t.target,n.target)||t.index-n.index}function H(t,n){return t.y0-n.y0}function J(t){return t.value}function It(t){return t.index}function $t(t){return t.nodes}function Ot(t){return t.links}function ct(t,n){const s=t.get(n);if(!s)throw new Error("missing: "+n);return s}function ut({nodes:t}){for(const n of t){let s=n.y0,a=s;for(const u of n.sourceLinks)u.y0=s+u.width/2,s+=u.width;for(const u of n.targetLinks)u.y1=a+u.width/2,a+=u.width}}function jt(){let t=0,n=0,s=1,a=1,u=24,_=8,g,p=It,i=dt,o,c,m=$t,b=Ot,y=6;function x(){const e={nodes:m.apply(null,arguments),links:b.apply(null,arguments)};return E(e),L(e),A(e),N(e),S(e),ut(e),e}x.update=function(e){return ut(e),e},x.nodeId=function(e){return arguments.length?(p=typeof e=="function"?e:Y(e),x):p},x.nodeAlign=function(e){return arguments.length?(i=typeof e=="function"?e:Y(e),x):i},x.nodeSort=function(e){return arguments.length?(o=e,x):o},x.nodeWidth=function(e){return arguments.length?(u=+e,x):u},x.nodePadding=function(e){return arguments.length?(_=g=+e,x):_},x.nodes=function(e){return arguments.length?(m=typeof e=="function"?e:Y(e),x):m},x.links=function(e){return arguments.length?(b=typeof e=="function"?e:Y(e),x):b},x.linkSort=function(e){return arguments.length?(c=e,x):c},x.size=function(e){return arguments.length?(t=n=0,s=+e[0],a=+e[1],x):[s-t,a-n]},x.extent=function(e){return arguments.length?(t=+e[0][0],s=+e[1][0],n=+e[0][1],a=+e[1][1],x):[[t,n],[s,a]]},x.iterations=function(e){return arguments.length?(y=+e,x):y};function E({nodes:e,links:f}){for(const[h,r]of e.entries())r.index=h,r.sourceLinks=[],r.targetLinks=[];const l=new Map(e.map((h,r)=>[p(h,r,e),h]));for(const[h,r]of f.entries()){r.index=h;let{source:k,target:v}=r;typeof k!="object"&&(k=r.source=ct(l,k)),typeof v!="object"&&(v=r.target=ct(l,v)),k.sourceLinks.push(r),v.targetLinks.push(r)}if(c!=null)for(const{sourceLinks:h,targetLinks:r}of e)h.sort(c),r.sort(c)}function L({nodes:e}){for(const f of e)f.value=f.fixedValue===void 0?Math.max(Z(f.sourceLinks,J),Z(f.targetLinks,J)):f.fixedValue}function A({nodes:e}){const f=e.length;let l=new Set(e),h=new Set,r=0;for(;l.size;){for(const k of l){k.depth=r;for(const{target:v}of k.sourceLinks)h.add(v)}if(++r>f)throw new Error("circular link");l=h,h=new Set}}function N({nodes:e}){const f=e.length;let l=new Set(e),h=new Set,r=0;for(;l.size;){for(const k of l){k.height=r;for(const{source:v}of k.targetLinks)h.add(v)}if(++r>f)throw new Error("circular link");l=h,h=new Set}}function I({nodes:e}){const f=ot(e,r=>r.depth)+1,l=(s-t-u)/(f-1),h=new Array(f);for(const r of e){const k=Math.max(0,Math.min(f-1,Math.floor(i.call(null,r,f))));r.layer=k,r.x0=t+k*l,r.x1=r.x0+u,h[k]?h[k].push(r):h[k]=[r]}if(o)for(const r of h)r.sort(o);return h}function j(e){const f=yt(e,l=>(a-n-(l.length-1)*g)/Z(l,J));for(const l of e){let h=n;for(const r of l){r.y0=h,r.y1=h+r.value*f,h=r.y1+g;for(const k of r.sourceLinks)k.width=k.value*f}h=(a-h+g)/(l.length+1);for(let r=0;r<l.length;++r){const k=l[r];k.y0+=h*(r+1),k.y1+=h*(r+1)}$(l)}}function S(e){const f=I(e);g=Math.min(_,(a-n)/(ot(f,l=>l.length)-1)),j(f);for(let l=0;l<y;++l){const h=Math.pow(.99,l),r=Math.max(1-h,(l+1)/y);O(f,h,r),M(f,h,r)}}function M(e,f,l){for(let h=1,r=e.length;h<r;++h){const k=e[h];for(const v of k){let R=0,z=0;for(const{source:W,value:K}of v.targetLinks){let F=K*(v.layer-W.layer);R+=T(W,v)*F,z+=F}if(!(z>0))continue;let U=(R/z-v.y0)*f;v.y0+=U,v.y1+=U,w(v)}o===void 0&&k.sort(H),P(k,l)}}function O(e,f,l){for(let h=e.length,r=h-2;r>=0;--r){const k=e[r];for(const v of k){let R=0,z=0;for(const{target:W,value:K}of v.sourceLinks){let F=K*(W.layer-v.layer);R+=V(v,W)*F,z+=F}if(!(z>0))continue;let U=(R/z-v.y0)*f;v.y0+=U,v.y1+=U,w(v)}o===void 0&&k.sort(H),P(k,l)}}function P(e,f){const l=e.length>>1,h=e[l];d(e,h.y0-g,l-1,f),C(e,h.y1+g,l+1,f),d(e,a,e.length-1,f),C(e,n,0,f)}function C(e,f,l,h){for(;l<e.length;++l){const r=e[l],k=(f-r.y0)*h;k>1e-6&&(r.y0+=k,r.y1+=k),f=r.y1+g}}function d(e,f,l,h){for(;l>=0;--l){const r=e[l],k=(r.y1-f)*h;k>1e-6&&(r.y0-=k,r.y1-=k),f=r.y0-g}}function w({sourceLinks:e,targetLinks:f}){if(c===void 0){for(const{source:{sourceLinks:l}}of f)l.sort(at);for(const{target:{targetLinks:l}}of e)l.sort(lt)}}function $(e){if(c===void 0)for(const{sourceLinks:f,targetLinks:l}of e)f.sort(at),l.sort(lt)}function T(e,f){let l=e.y0-(e.sourceLinks.length-1)*g/2;for(const{target:h,width:r}of e.sourceLinks){if(h===f)break;l+=r+g}for(const{source:h,width:r}of f.targetLinks){if(h===e)break;l-=r}return l}function V(e,f){let l=f.y0-(f.targetLinks.length-1)*g/2;for(const{source:h,width:r}of f.targetLinks){if(h===e)break;l+=r+g}for(const{target:h,width:r}of e.sourceLinks){if(h===f)break;l-=r}return l}return x}var tt=Math.PI,et=2*tt,D=1e-6,zt=et-D;function nt(){this._x0=this._y0=this._x1=this._y1=null,this._=""}function gt(){return new nt}nt.prototype=gt.prototype={constructor:nt,moveTo:function(t,n){this._+="M"+(this._x0=this._x1=+t)+","+(this._y0=this._y1=+n)},closePath:function(){this._x1!==null&&(this._x1=this._x0,this._y1=this._y0,this._+="Z")},lineTo:function(t,n){this._+="L"+(this._x1=+t)+","+(this._y1=+n)},quadraticCurveTo:function(t,n,s,a){this._+="Q"+ +t+","+ +n+","+(this._x1=+s)+","+(this._y1=+a)},bezierCurveTo:function(t,n,s,a,u,_){this._+="C"+ +t+","+ +n+","+ +s+","+ +a+","+(this._x1=+u)+","+(this._y1=+_)},arcTo:function(t,n,s,a,u){t=+t,n=+n,s=+s,a=+a,u=+u;var _=this._x1,g=this._y1,p=s-t,i=a-n,o=_-t,c=g-n,m=o*o+c*c;if(u<0)throw new Error("negative radius: "+u);if(this._x1===null)this._+="M"+(this._x1=t)+","+(this._y1=n);else if(m>D)if(!(Math.abs(c*p-i*o)>D)||!u)this._+="L"+(this._x1=t)+","+(this._y1=n);else{var b=s-_,y=a-g,x=p*p+i*i,E=b*b+y*y,L=Math.sqrt(x),A=Math.sqrt(m),N=u*Math.tan((tt-Math.acos((x+m-E)/(2*L*A)))/2),I=N/A,j=N/L;Math.abs(I-1)>D&&(this._+="L"+(t+I*o)+","+(n+I*c)),this._+="A"+u+","+u+",0,0,"+ +(c*b>o*y)+","+(this._x1=t+j*p)+","+(this._y1=n+j*i)}},arc:function(t,n,s,a,u,_){t=+t,n=+n,s=+s,_=!!_;var g=s*Math.cos(a),p=s*Math.sin(a),i=t+g,o=n+p,c=1^_,m=_?a-u:u-a;if(s<0)throw new Error("negative radius: "+s);this._x1===null?this._+="M"+i+","+o:(Math.abs(this._x1-i)>D||Math.abs(this._y1-o)>D)&&(this._+="L"+i+","+o),s&&(m<0&&(m=m%et+et),m>zt?this._+="A"+s+","+s+",0,1,"+c+","+(t-g)+","+(n-p)+"A"+s+","+s+",0,1,"+c+","+(this._x1=i)+","+(this._y1=o):m>D&&(this._+="A"+s+","+s+",0,"+ +(m>=tt)+","+c+","+(this._x1=t+s*Math.cos(u))+","+(this._y1=n+s*Math.sin(u))))},rect:function(t,n,s,a){this._+="M"+(this._x0=this._x1=+t)+","+(this._y0=this._y1=+n)+"h"+ +s+"v"+ +a+"h"+-s+"Z"},toString:function(){return this._}};function ht(t){return function(){return t}}function Dt(t){return t[0]}function Bt(t){return t[1]}var Vt=Array.prototype.slice;function Rt(t){return t.source}function Ut(t){return t.target}function Wt(t){var n=Rt,s=Ut,a=Dt,u=Bt,_=null;function g(){var p,i=Vt.call(arguments),o=n.apply(this,i),c=s.apply(this,i);if(_||(_=p=gt()),t(_,+a.apply(this,(i[0]=o,i)),+u.apply(this,i),+a.apply(this,(i[0]=c,i)),+u.apply(this,i)),p)return _=null,p+""||null}return g.source=function(p){return arguments.length?(n=p,g):n},g.target=function(p){return arguments.length?(s=p,g):s},g.x=function(p){return arguments.length?(a=typeof p=="function"?p:ht(+p),g):a},g.y=function(p){return arguments.length?(u=typeof p=="function"?p:ht(+p),g):u},g.context=function(p){return arguments.length?(_=p??null,g):_},g}function Ft(t,n,s,a,u){t.moveTo(n,s),t.bezierCurveTo(n=(n+a)/2,s,n,u,a,u)}function Gt(){return Wt(Ft)}function Yt(t){return[t.source.x1,t.y0]}function Ht(t){return[t.target.x0,t.y1]}function Xt(){return Gt().source(Yt).target(Ht)}var it=function(){var t=function(p,i,o,c){for(o=o||{},c=p.length;c--;o[p[c]]=i);return o},n=[1,9],s=[1,10],a=[1,5,10,12],u={trace:function(){},yy:{},symbols_:{error:2,start:3,SANKEY:4,NEWLINE:5,csv:6,opt_eof:7,record:8,csv_tail:9,EOF:10,"field[source]":11,COMMA:12,"field[target]":13,"field[value]":14,field:15,escaped:16,non_escaped:17,DQUOTE:18,ESCAPED_TEXT:19,NON_ESCAPED_TEXT:20,$accept:0,$end:1},terminals_:{2:"error",4:"SANKEY",5:"NEWLINE",10:"EOF",11:"field[source]",12:"COMMA",13:"field[target]",14:"field[value]",18:"DQUOTE",19:"ESCAPED_TEXT",20:"NON_ESCAPED_TEXT"},productions_:[0,[3,4],[6,2],[9,2],[9,0],[7,1],[7,0],[8,5],[15,1],[15,1],[16,3],[17,1]],performAction:function(i,o,c,m,b,y,x){var E=y.length-1;switch(b){case 7:const L=m.findOrCreateNode(y[E-4].trim().replaceAll('""','"')),A=m.findOrCreateNode(y[E-2].trim().replaceAll('""','"')),N=parseFloat(y[E].trim());m.addLink(L,A,N);break;case 8:case 9:case 11:this.$=y[E];break;case 10:this.$=y[E-1];break}},table:[{3:1,4:[1,2]},{1:[3]},{5:[1,3]},{6:4,8:5,15:6,16:7,17:8,18:n,20:s},{1:[2,6],7:11,10:[1,12]},t(s,[2,4],{9:13,5:[1,14]}),{12:[1,15]},t(a,[2,8]),t(a,[2,9]),{19:[1,16]},t(a,[2,11]),{1:[2,1]},{1:[2,5]},t(s,[2,2]),{6:17,8:5,15:6,16:7,17:8,18:n,20:s},{15:18,16:7,17:8,18:n,20:s},{18:[1,19]},t(s,[2,3]),{12:[1,20]},t(a,[2,10]),{15:21,16:7,17:8,18:n,20:s},t([1,5,10],[2,7])],defaultActions:{11:[2,1],12:[2,5]},parseError:function(i,o){if(o.recoverable)this.trace(i);else{var c=new Error(i);throw c.hash=o,c}},parse:function(i){var o=this,c=[0],m=[],b=[null],y=[],x=this.table,E="",L=0,A=0,N=2,I=1,j=y.slice.call(arguments,1),S=Object.create(this.lexer),M={yy:{}};for(var O in this.yy)Object.prototype.hasOwnProperty.call(this.yy,O)&&(M.yy[O]=this.yy[O]);S.setInput(i,M.yy),M.yy.lexer=S,M.yy.parser=this,typeof S.yylloc>"u"&&(S.yylloc={});var P=S.yylloc;y.push(P);var C=S.options&&S.options.ranges;typeof M.yy.parseError=="function"?this.parseError=M.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function d(){var v;return v=m.pop()||S.lex()||I,typeof v!="number"&&(v instanceof Array&&(m=v,v=m.pop()),v=o.symbols_[v]||v),v}for(var w,$,T,V,e={},f,l,h,r;;){if($=c[c.length-1],this.defaultActions[$]?T=this.defaultActions[$]:((w===null||typeof w>"u")&&(w=d()),T=x[$]&&x[$][w]),typeof T>"u"||!T.length||!T[0]){var k="";r=[];for(f in x[$])this.terminals_[f]&&f>N&&r.push("'"+this.terminals_[f]+"'");S.showPosition?k="Parse error on line "+(L+1)+`:
 `+S.showPosition()+`
 Expecting `+r.join(", ")+", got '"+(this.terminals_[w]||w)+"'":k="Parse error on line "+(L+1)+": Unexpected "+(w==I?"end of input":"'"+(this.terminals_[w]||w)+"'"),this.parseError(k,{text:S.match,token:this.terminals_[w]||w,line:S.yylineno,loc:P,expected:r})}if(T[0]instanceof Array&&T.length>1)throw new Error("Parse Error: multiple actions possible at state: "+$+", token: "+w);switch(T[0]){case 1:c.push(w),b.push(S.yytext),y.push(S.yylloc),c.push(T[1]),w=null,A=S.yyleng,E=S.yytext,L=S.yylineno,P=S.yylloc;break;case 2:if(l=this.productions_[T[1]][1],e.$=b[b.length-l],e._$={first_line:y[y.length-(l||1)].first_line,last_line:y[y.length-1].last_line,first_column:y[y.length-(l||1)].first_column,last_column:y[y.length-1].last_column},C&&(e._$.range=[y[y.length-(l||1)].range[0],y[y.length-1].range[1]]),V=this.performAction.apply(e,[E,A,L,M.yy,T[1],b,y].concat(j)),typeof V<"u")return V;l&&(c=c.slice(0,-1*l*2),b=b.slice(0,-1*l),y=y.slice(0,-1*l)),c.push(this.productions_[T[1]][0]),b.push(e.$),y.push(e._$),h=x[c[c.length-2]][c[c.length-1]],c.push(h);break;case 3:return!0}}return!0}},_=function(){var p={EOF:1,parseError:function(o,c){if(this.yy.parser)this.yy.parser.parseError(o,c);else throw new Error(o)},setInput:function(i,o){return this.yy=o||this.yy||{},this._input=i,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var i=this._input[0];this.yytext+=i,this.yyleng++,this.offset++,this.match+=i,this.matched+=i;var o=i.match(/(?:\r\n?|\n).*/g);return o?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),i},unput:function(i){var o=i.length,c=i.split(/(?:\r\n?|\n)/g);this._input=i+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-o),this.offset-=o;var m=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),c.length-1&&(this.yylineno-=c.length-1);var b=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:c?(c.length===m.length?this.yylloc.first_column:0)+m[m.length-c.length].length-c[0].length:this.yylloc.first_column-o},this.options.ranges&&(this.yylloc.range=[b[0],b[0]+this.yyleng-o]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){if(this.options.backtrack_lexer)this._backtrack=!0;else return this.parseError("Lexical error on line "+(this.yylineno+1)+`. You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).
 `+this.showPosition(),{text:"",token:null,line:this.yylineno});return this},less:function(i){this.unput(this.match.slice(i))},pastInput:function(){var i=this.matched.substr(0,this.matched.length-this.match.length);return(i.length>20?"...":"")+i.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var i=this.match;return i.length<20&&(i+=this._input.substr(0,20-i.length)),(i.substr(0,20)+(i.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var i=this.pastInput(),o=new Array(i.length+1).join("-");return i+this.upcomingInput()+`
diff --git a/assets/sequenceDiagram-66748113-MIUFy2Oj.js b/assets/sequenceDiagram-66748113-sH_v1_cD.js
similarity index 99%
rename from assets/sequenceDiagram-66748113-MIUFy2Oj.js
rename to assets/sequenceDiagram-66748113-sH_v1_cD.js
index d866807..4027862 100644
--- a/assets/sequenceDiagram-66748113-MIUFy2Oj.js
+++ b/assets/sequenceDiagram-66748113-sH_v1_cD.js
@@ -1,4 +1,4 @@
-import{g as we,y as ve,x as _e,c as st,s as $t,b as ke,a as Pe,A as Le,l as X,d as At,j as v,e as Ie,h as Lt,i as Ae,z as B,b0 as nt,b1 as wt,m as te,r as ee,a$ as Bt,aN as se,b2 as Ne}from"./mermaid.core-ChLYKTZm.js";import{d as Se,a as Me,g as Nt,b as zt,c as Re,e as Ce}from"./svgDrawCommon-9d162435-DXbPg0E8.js";import"./app-B69Gl_S-.js";var Yt=function(){var t=function(dt,w,k,L){for(k=k||{},L=dt.length;L--;k[dt[L]]=w);return k},e=[1,2],c=[1,3],s=[1,4],i=[2,4],a=[1,9],o=[1,11],l=[1,13],p=[1,14],r=[1,16],x=[1,17],T=[1,18],u=[1,24],g=[1,25],m=[1,26],_=[1,27],I=[1,28],V=[1,29],S=[1,30],O=[1,31],R=[1,32],q=[1,33],z=[1,34],J=[1,35],$=[1,36],H=[1,37],U=[1,38],F=[1,39],W=[1,41],Z=[1,42],K=[1,43],Q=[1,44],tt=[1,45],N=[1,46],y=[1,4,5,13,14,16,18,21,23,29,30,31,33,35,36,37,38,39,41,43,44,46,47,48,49,50,52,53,54,59,60,61,62,70],P=[4,5,16,50,52,53],j=[4,5,13,14,16,18,21,23,29,30,31,33,35,36,37,38,39,41,43,44,46,50,52,53,54,59,60,61,62,70],rt=[4,5,13,14,16,18,21,23,29,30,31,33,35,36,37,38,39,41,43,44,46,49,50,52,53,54,59,60,61,62,70],A=[4,5,13,14,16,18,21,23,29,30,31,33,35,36,37,38,39,41,43,44,46,48,50,52,53,54,59,60,61,62,70],Gt=[4,5,13,14,16,18,21,23,29,30,31,33,35,36,37,38,39,41,43,44,46,47,50,52,53,54,59,60,61,62,70],ht=[68,69,70],ot=[1,120],Mt={trace:function(){},yy:{},symbols_:{error:2,start:3,SPACE:4,NEWLINE:5,SD:6,document:7,line:8,statement:9,box_section:10,box_line:11,participant_statement:12,create:13,box:14,restOfLine:15,end:16,signal:17,autonumber:18,NUM:19,off:20,activate:21,actor:22,deactivate:23,note_statement:24,links_statement:25,link_statement:26,properties_statement:27,details_statement:28,title:29,legacy_title:30,acc_title:31,acc_title_value:32,acc_descr:33,acc_descr_value:34,acc_descr_multiline_value:35,loop:36,rect:37,opt:38,alt:39,else_sections:40,par:41,par_sections:42,par_over:43,critical:44,option_sections:45,break:46,option:47,and:48,else:49,participant:50,AS:51,participant_actor:52,destroy:53,note:54,placement:55,text2:56,over:57,actor_pair:58,links:59,link:60,properties:61,details:62,spaceList:63,",":64,left_of:65,right_of:66,signaltype:67,"+":68,"-":69,ACTOR:70,SOLID_OPEN_ARROW:71,DOTTED_OPEN_ARROW:72,SOLID_ARROW:73,DOTTED_ARROW:74,SOLID_CROSS:75,DOTTED_CROSS:76,SOLID_POINT:77,DOTTED_POINT:78,TXT:79,$accept:0,$end:1},terminals_:{2:"error",4:"SPACE",5:"NEWLINE",6:"SD",13:"create",14:"box",15:"restOfLine",16:"end",18:"autonumber",19:"NUM",20:"off",21:"activate",23:"deactivate",29:"title",30:"legacy_title",31:"acc_title",32:"acc_title_value",33:"acc_descr",34:"acc_descr_value",35:"acc_descr_multiline_value",36:"loop",37:"rect",38:"opt",39:"alt",41:"par",43:"par_over",44:"critical",46:"break",47:"option",48:"and",49:"else",50:"participant",51:"AS",52:"participant_actor",53:"destroy",54:"note",57:"over",59:"links",60:"link",61:"properties",62:"details",64:",",65:"left_of",66:"right_of",68:"+",69:"-",70:"ACTOR",71:"SOLID_OPEN_ARROW",72:"DOTTED_OPEN_ARROW",73:"SOLID_ARROW",74:"DOTTED_ARROW",75:"SOLID_CROSS",76:"DOTTED_CROSS",77:"SOLID_POINT",78:"DOTTED_POINT",79:"TXT"},productions_:[0,[3,2],[3,2],[3,2],[7,0],[7,2],[8,2],[8,1],[8,1],[10,0],[10,2],[11,2],[11,1],[11,1],[9,1],[9,2],[9,4],[9,2],[9,4],[9,3],[9,3],[9,2],[9,3],[9,3],[9,2],[9,2],[9,2],[9,2],[9,2],[9,1],[9,1],[9,2],[9,2],[9,1],[9,4],[9,4],[9,4],[9,4],[9,4],[9,4],[9,4],[9,4],[45,1],[45,4],[42,1],[42,4],[40,1],[40,4],[12,5],[12,3],[12,5],[12,3],[12,3],[24,4],[24,4],[25,3],[26,3],[27,3],[28,3],[63,2],[63,1],[58,3],[58,1],[55,1],[55,1],[17,5],[17,5],[17,4],[22,1],[67,1],[67,1],[67,1],[67,1],[67,1],[67,1],[67,1],[67,1],[56,1]],performAction:function(w,k,L,b,M,h,Et){var d=h.length-1;switch(M){case 3:return b.apply(h[d]),h[d];case 4:case 9:this.$=[];break;case 5:case 10:h[d-1].push(h[d]),this.$=h[d-1];break;case 6:case 7:case 11:case 12:this.$=h[d];break;case 8:case 13:this.$=[];break;case 15:h[d].type="createParticipant",this.$=h[d];break;case 16:h[d-1].unshift({type:"boxStart",boxData:b.parseBoxData(h[d-2])}),h[d-1].push({type:"boxEnd",boxText:h[d-2]}),this.$=h[d-1];break;case 18:this.$={type:"sequenceIndex",sequenceIndex:Number(h[d-2]),sequenceIndexStep:Number(h[d-1]),sequenceVisible:!0,signalType:b.LINETYPE.AUTONUMBER};break;case 19:this.$={type:"sequenceIndex",sequenceIndex:Number(h[d-1]),sequenceIndexStep:1,sequenceVisible:!0,signalType:b.LINETYPE.AUTONUMBER};break;case 20:this.$={type:"sequenceIndex",sequenceVisible:!1,signalType:b.LINETYPE.AUTONUMBER};break;case 21:this.$={type:"sequenceIndex",sequenceVisible:!0,signalType:b.LINETYPE.AUTONUMBER};break;case 22:this.$={type:"activeStart",signalType:b.LINETYPE.ACTIVE_START,actor:h[d-1]};break;case 23:this.$={type:"activeEnd",signalType:b.LINETYPE.ACTIVE_END,actor:h[d-1]};break;case 29:b.setDiagramTitle(h[d].substring(6)),this.$=h[d].substring(6);break;case 30:b.setDiagramTitle(h[d].substring(7)),this.$=h[d].substring(7);break;case 31:this.$=h[d].trim(),b.setAccTitle(this.$);break;case 32:case 33:this.$=h[d].trim(),b.setAccDescription(this.$);break;case 34:h[d-1].unshift({type:"loopStart",loopText:b.parseMessage(h[d-2]),signalType:b.LINETYPE.LOOP_START}),h[d-1].push({type:"loopEnd",loopText:h[d-2],signalType:b.LINETYPE.LOOP_END}),this.$=h[d-1];break;case 35:h[d-1].unshift({type:"rectStart",color:b.parseMessage(h[d-2]),signalType:b.LINETYPE.RECT_START}),h[d-1].push({type:"rectEnd",color:b.parseMessage(h[d-2]),signalType:b.LINETYPE.RECT_END}),this.$=h[d-1];break;case 36:h[d-1].unshift({type:"optStart",optText:b.parseMessage(h[d-2]),signalType:b.LINETYPE.OPT_START}),h[d-1].push({type:"optEnd",optText:b.parseMessage(h[d-2]),signalType:b.LINETYPE.OPT_END}),this.$=h[d-1];break;case 37:h[d-1].unshift({type:"altStart",altText:b.parseMessage(h[d-2]),signalType:b.LINETYPE.ALT_START}),h[d-1].push({type:"altEnd",signalType:b.LINETYPE.ALT_END}),this.$=h[d-1];break;case 38:h[d-1].unshift({type:"parStart",parText:b.parseMessage(h[d-2]),signalType:b.LINETYPE.PAR_START}),h[d-1].push({type:"parEnd",signalType:b.LINETYPE.PAR_END}),this.$=h[d-1];break;case 39:h[d-1].unshift({type:"parStart",parText:b.parseMessage(h[d-2]),signalType:b.LINETYPE.PAR_OVER_START}),h[d-1].push({type:"parEnd",signalType:b.LINETYPE.PAR_END}),this.$=h[d-1];break;case 40:h[d-1].unshift({type:"criticalStart",criticalText:b.parseMessage(h[d-2]),signalType:b.LINETYPE.CRITICAL_START}),h[d-1].push({type:"criticalEnd",signalType:b.LINETYPE.CRITICAL_END}),this.$=h[d-1];break;case 41:h[d-1].unshift({type:"breakStart",breakText:b.parseMessage(h[d-2]),signalType:b.LINETYPE.BREAK_START}),h[d-1].push({type:"breakEnd",optText:b.parseMessage(h[d-2]),signalType:b.LINETYPE.BREAK_END}),this.$=h[d-1];break;case 43:this.$=h[d-3].concat([{type:"option",optionText:b.parseMessage(h[d-1]),signalType:b.LINETYPE.CRITICAL_OPTION},h[d]]);break;case 45:this.$=h[d-3].concat([{type:"and",parText:b.parseMessage(h[d-1]),signalType:b.LINETYPE.PAR_AND},h[d]]);break;case 47:this.$=h[d-3].concat([{type:"else",altText:b.parseMessage(h[d-1]),signalType:b.LINETYPE.ALT_ELSE},h[d]]);break;case 48:h[d-3].draw="participant",h[d-3].type="addParticipant",h[d-3].description=b.parseMessage(h[d-1]),this.$=h[d-3];break;case 49:h[d-1].draw="participant",h[d-1].type="addParticipant",this.$=h[d-1];break;case 50:h[d-3].draw="actor",h[d-3].type="addParticipant",h[d-3].description=b.parseMessage(h[d-1]),this.$=h[d-3];break;case 51:h[d-1].draw="actor",h[d-1].type="addParticipant",this.$=h[d-1];break;case 52:h[d-1].type="destroyParticipant",this.$=h[d-1];break;case 53:this.$=[h[d-1],{type:"addNote",placement:h[d-2],actor:h[d-1].actor,text:h[d]}];break;case 54:h[d-2]=[].concat(h[d-1],h[d-1]).slice(0,2),h[d-2][0]=h[d-2][0].actor,h[d-2][1]=h[d-2][1].actor,this.$=[h[d-1],{type:"addNote",placement:b.PLACEMENT.OVER,actor:h[d-2].slice(0,2),text:h[d]}];break;case 55:this.$=[h[d-1],{type:"addLinks",actor:h[d-1].actor,text:h[d]}];break;case 56:this.$=[h[d-1],{type:"addALink",actor:h[d-1].actor,text:h[d]}];break;case 57:this.$=[h[d-1],{type:"addProperties",actor:h[d-1].actor,text:h[d]}];break;case 58:this.$=[h[d-1],{type:"addDetails",actor:h[d-1].actor,text:h[d]}];break;case 61:this.$=[h[d-2],h[d]];break;case 62:this.$=h[d];break;case 63:this.$=b.PLACEMENT.LEFTOF;break;case 64:this.$=b.PLACEMENT.RIGHTOF;break;case 65:this.$=[h[d-4],h[d-1],{type:"addMessage",from:h[d-4].actor,to:h[d-1].actor,signalType:h[d-3],msg:h[d],activate:!0},{type:"activeStart",signalType:b.LINETYPE.ACTIVE_START,actor:h[d-1]}];break;case 66:this.$=[h[d-4],h[d-1],{type:"addMessage",from:h[d-4].actor,to:h[d-1].actor,signalType:h[d-3],msg:h[d]},{type:"activeEnd",signalType:b.LINETYPE.ACTIVE_END,actor:h[d-4]}];break;case 67:this.$=[h[d-3],h[d-1],{type:"addMessage",from:h[d-3].actor,to:h[d-1].actor,signalType:h[d-2],msg:h[d]}];break;case 68:this.$={type:"addParticipant",actor:h[d]};break;case 69:this.$=b.LINETYPE.SOLID_OPEN;break;case 70:this.$=b.LINETYPE.DOTTED_OPEN;break;case 71:this.$=b.LINETYPE.SOLID;break;case 72:this.$=b.LINETYPE.DOTTED;break;case 73:this.$=b.LINETYPE.SOLID_CROSS;break;case 74:this.$=b.LINETYPE.DOTTED_CROSS;break;case 75:this.$=b.LINETYPE.SOLID_POINT;break;case 76:this.$=b.LINETYPE.DOTTED_POINT;break;case 77:this.$=b.parseMessage(h[d].trim().substring(1));break}},table:[{3:1,4:e,5:c,6:s},{1:[3]},{3:5,4:e,5:c,6:s},{3:6,4:e,5:c,6:s},t([1,4,5,13,14,18,21,23,29,30,31,33,35,36,37,38,39,41,43,44,46,50,52,53,54,59,60,61,62,70],i,{7:7}),{1:[2,1]},{1:[2,2]},{1:[2,3],4:a,5:o,8:8,9:10,12:12,13:l,14:p,17:15,18:r,21:x,22:40,23:T,24:19,25:20,26:21,27:22,28:23,29:u,30:g,31:m,33:_,35:I,36:V,37:S,38:O,39:R,41:q,43:z,44:J,46:$,50:H,52:U,53:F,54:W,59:Z,60:K,61:Q,62:tt,70:N},t(y,[2,5]),{9:47,12:12,13:l,14:p,17:15,18:r,21:x,22:40,23:T,24:19,25:20,26:21,27:22,28:23,29:u,30:g,31:m,33:_,35:I,36:V,37:S,38:O,39:R,41:q,43:z,44:J,46:$,50:H,52:U,53:F,54:W,59:Z,60:K,61:Q,62:tt,70:N},t(y,[2,7]),t(y,[2,8]),t(y,[2,14]),{12:48,50:H,52:U,53:F},{15:[1,49]},{5:[1,50]},{5:[1,53],19:[1,51],20:[1,52]},{22:54,70:N},{22:55,70:N},{5:[1,56]},{5:[1,57]},{5:[1,58]},{5:[1,59]},{5:[1,60]},t(y,[2,29]),t(y,[2,30]),{32:[1,61]},{34:[1,62]},t(y,[2,33]),{15:[1,63]},{15:[1,64]},{15:[1,65]},{15:[1,66]},{15:[1,67]},{15:[1,68]},{15:[1,69]},{15:[1,70]},{22:71,70:N},{22:72,70:N},{22:73,70:N},{67:74,71:[1,75],72:[1,76],73:[1,77],74:[1,78],75:[1,79],76:[1,80],77:[1,81],78:[1,82]},{55:83,57:[1,84],65:[1,85],66:[1,86]},{22:87,70:N},{22:88,70:N},{22:89,70:N},{22:90,70:N},t([5,51,64,71,72,73,74,75,76,77,78,79],[2,68]),t(y,[2,6]),t(y,[2,15]),t(P,[2,9],{10:91}),t(y,[2,17]),{5:[1,93],19:[1,92]},{5:[1,94]},t(y,[2,21]),{5:[1,95]},{5:[1,96]},t(y,[2,24]),t(y,[2,25]),t(y,[2,26]),t(y,[2,27]),t(y,[2,28]),t(y,[2,31]),t(y,[2,32]),t(j,i,{7:97}),t(j,i,{7:98}),t(j,i,{7:99}),t(rt,i,{40:100,7:101}),t(A,i,{42:102,7:103}),t(A,i,{7:103,42:104}),t(Gt,i,{45:105,7:106}),t(j,i,{7:107}),{5:[1,109],51:[1,108]},{5:[1,111],51:[1,110]},{5:[1,112]},{22:115,68:[1,113],69:[1,114],70:N},t(ht,[2,69]),t(ht,[2,70]),t(ht,[2,71]),t(ht,[2,72]),t(ht,[2,73]),t(ht,[2,74]),t(ht,[2,75]),t(ht,[2,76]),{22:116,70:N},{22:118,58:117,70:N},{70:[2,63]},{70:[2,64]},{56:119,79:ot},{56:121,79:ot},{56:122,79:ot},{56:123,79:ot},{4:[1,126],5:[1,128],11:125,12:127,16:[1,124],50:H,52:U,53:F},{5:[1,129]},t(y,[2,19]),t(y,[2,20]),t(y,[2,22]),t(y,[2,23]),{4:a,5:o,8:8,9:10,12:12,13:l,14:p,16:[1,130],17:15,18:r,21:x,22:40,23:T,24:19,25:20,26:21,27:22,28:23,29:u,30:g,31:m,33:_,35:I,36:V,37:S,38:O,39:R,41:q,43:z,44:J,46:$,50:H,52:U,53:F,54:W,59:Z,60:K,61:Q,62:tt,70:N},{4:a,5:o,8:8,9:10,12:12,13:l,14:p,16:[1,131],17:15,18:r,21:x,22:40,23:T,24:19,25:20,26:21,27:22,28:23,29:u,30:g,31:m,33:_,35:I,36:V,37:S,38:O,39:R,41:q,43:z,44:J,46:$,50:H,52:U,53:F,54:W,59:Z,60:K,61:Q,62:tt,70:N},{4:a,5:o,8:8,9:10,12:12,13:l,14:p,16:[1,132],17:15,18:r,21:x,22:40,23:T,24:19,25:20,26:21,27:22,28:23,29:u,30:g,31:m,33:_,35:I,36:V,37:S,38:O,39:R,41:q,43:z,44:J,46:$,50:H,52:U,53:F,54:W,59:Z,60:K,61:Q,62:tt,70:N},{16:[1,133]},{4:a,5:o,8:8,9:10,12:12,13:l,14:p,16:[2,46],17:15,18:r,21:x,22:40,23:T,24:19,25:20,26:21,27:22,28:23,29:u,30:g,31:m,33:_,35:I,36:V,37:S,38:O,39:R,41:q,43:z,44:J,46:$,49:[1,134],50:H,52:U,53:F,54:W,59:Z,60:K,61:Q,62:tt,70:N},{16:[1,135]},{4:a,5:o,8:8,9:10,12:12,13:l,14:p,16:[2,44],17:15,18:r,21:x,22:40,23:T,24:19,25:20,26:21,27:22,28:23,29:u,30:g,31:m,33:_,35:I,36:V,37:S,38:O,39:R,41:q,43:z,44:J,46:$,48:[1,136],50:H,52:U,53:F,54:W,59:Z,60:K,61:Q,62:tt,70:N},{16:[1,137]},{16:[1,138]},{4:a,5:o,8:8,9:10,12:12,13:l,14:p,16:[2,42],17:15,18:r,21:x,22:40,23:T,24:19,25:20,26:21,27:22,28:23,29:u,30:g,31:m,33:_,35:I,36:V,37:S,38:O,39:R,41:q,43:z,44:J,46:$,47:[1,139],50:H,52:U,53:F,54:W,59:Z,60:K,61:Q,62:tt,70:N},{4:a,5:o,8:8,9:10,12:12,13:l,14:p,16:[1,140],17:15,18:r,21:x,22:40,23:T,24:19,25:20,26:21,27:22,28:23,29:u,30:g,31:m,33:_,35:I,36:V,37:S,38:O,39:R,41:q,43:z,44:J,46:$,50:H,52:U,53:F,54:W,59:Z,60:K,61:Q,62:tt,70:N},{15:[1,141]},t(y,[2,49]),{15:[1,142]},t(y,[2,51]),t(y,[2,52]),{22:143,70:N},{22:144,70:N},{56:145,79:ot},{56:146,79:ot},{56:147,79:ot},{64:[1,148],79:[2,62]},{5:[2,55]},{5:[2,77]},{5:[2,56]},{5:[2,57]},{5:[2,58]},t(y,[2,16]),t(P,[2,10]),{12:149,50:H,52:U,53:F},t(P,[2,12]),t(P,[2,13]),t(y,[2,18]),t(y,[2,34]),t(y,[2,35]),t(y,[2,36]),t(y,[2,37]),{15:[1,150]},t(y,[2,38]),{15:[1,151]},t(y,[2,39]),t(y,[2,40]),{15:[1,152]},t(y,[2,41]),{5:[1,153]},{5:[1,154]},{56:155,79:ot},{56:156,79:ot},{5:[2,67]},{5:[2,53]},{5:[2,54]},{22:157,70:N},t(P,[2,11]),t(rt,i,{7:101,40:158}),t(A,i,{7:103,42:159}),t(Gt,i,{7:106,45:160}),t(y,[2,48]),t(y,[2,50]),{5:[2,65]},{5:[2,66]},{79:[2,61]},{16:[2,47]},{16:[2,45]},{16:[2,43]}],defaultActions:{5:[2,1],6:[2,2],85:[2,63],86:[2,64],119:[2,55],120:[2,77],121:[2,56],122:[2,57],123:[2,58],145:[2,67],146:[2,53],147:[2,54],155:[2,65],156:[2,66],157:[2,61],158:[2,47],159:[2,45],160:[2,43]},parseError:function(w,k){if(k.recoverable)this.trace(w);else{var L=new Error(w);throw L.hash=k,L}},parse:function(w){var k=this,L=[0],b=[],M=[null],h=[],Et=this.table,d="",_t=0,Xt=0,Te=2,Jt=1,be=h.slice.call(arguments,1),Y=Object.create(this.lexer),pt={yy:{}};for(var Ct in this.yy)Object.prototype.hasOwnProperty.call(this.yy,Ct)&&(pt.yy[Ct]=this.yy[Ct]);Y.setInput(w,pt.yy),pt.yy.lexer=Y,pt.yy.parser=this,typeof Y.yylloc>"u"&&(Y.yylloc={});var Dt=Y.yylloc;h.push(Dt);var Ee=Y.options&&Y.options.ranges;typeof pt.yy.parseError=="function"?this.parseError=pt.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function me(){var lt;return lt=b.pop()||Y.lex()||Jt,typeof lt!="number"&&(lt instanceof Array&&(b=lt,lt=b.pop()),lt=k.symbols_[lt]||lt),lt}for(var G,ut,et,Vt,yt={},kt,ct,Zt,Pt;;){if(ut=L[L.length-1],this.defaultActions[ut]?et=this.defaultActions[ut]:((G===null||typeof G>"u")&&(G=me()),et=Et[ut]&&Et[ut][G]),typeof et>"u"||!et.length||!et[0]){var Ot="";Pt=[];for(kt in Et[ut])this.terminals_[kt]&&kt>Te&&Pt.push("'"+this.terminals_[kt]+"'");Y.showPosition?Ot="Parse error on line "+(_t+1)+`:
+import{g as we,y as ve,x as _e,c as st,s as $t,b as ke,a as Pe,A as Le,l as X,d as At,j as v,e as Ie,h as Lt,i as Ae,z as B,b0 as nt,b1 as wt,m as te,r as ee,a$ as Bt,aN as se,b2 as Ne}from"./mermaid.core-DNo_7Q2B.js";import{d as Se,a as Me,g as Nt,b as zt,c as Re,e as Ce}from"./svgDrawCommon-9d162435-DBc9TLjw.js";import"./app-B4LGNJZ0.js";var Yt=function(){var t=function(dt,w,k,L){for(k=k||{},L=dt.length;L--;k[dt[L]]=w);return k},e=[1,2],c=[1,3],s=[1,4],i=[2,4],a=[1,9],o=[1,11],l=[1,13],p=[1,14],r=[1,16],x=[1,17],T=[1,18],u=[1,24],g=[1,25],m=[1,26],_=[1,27],I=[1,28],V=[1,29],S=[1,30],O=[1,31],R=[1,32],q=[1,33],z=[1,34],J=[1,35],$=[1,36],H=[1,37],U=[1,38],F=[1,39],W=[1,41],Z=[1,42],K=[1,43],Q=[1,44],tt=[1,45],N=[1,46],y=[1,4,5,13,14,16,18,21,23,29,30,31,33,35,36,37,38,39,41,43,44,46,47,48,49,50,52,53,54,59,60,61,62,70],P=[4,5,16,50,52,53],j=[4,5,13,14,16,18,21,23,29,30,31,33,35,36,37,38,39,41,43,44,46,50,52,53,54,59,60,61,62,70],rt=[4,5,13,14,16,18,21,23,29,30,31,33,35,36,37,38,39,41,43,44,46,49,50,52,53,54,59,60,61,62,70],A=[4,5,13,14,16,18,21,23,29,30,31,33,35,36,37,38,39,41,43,44,46,48,50,52,53,54,59,60,61,62,70],Gt=[4,5,13,14,16,18,21,23,29,30,31,33,35,36,37,38,39,41,43,44,46,47,50,52,53,54,59,60,61,62,70],ht=[68,69,70],ot=[1,120],Mt={trace:function(){},yy:{},symbols_:{error:2,start:3,SPACE:4,NEWLINE:5,SD:6,document:7,line:8,statement:9,box_section:10,box_line:11,participant_statement:12,create:13,box:14,restOfLine:15,end:16,signal:17,autonumber:18,NUM:19,off:20,activate:21,actor:22,deactivate:23,note_statement:24,links_statement:25,link_statement:26,properties_statement:27,details_statement:28,title:29,legacy_title:30,acc_title:31,acc_title_value:32,acc_descr:33,acc_descr_value:34,acc_descr_multiline_value:35,loop:36,rect:37,opt:38,alt:39,else_sections:40,par:41,par_sections:42,par_over:43,critical:44,option_sections:45,break:46,option:47,and:48,else:49,participant:50,AS:51,participant_actor:52,destroy:53,note:54,placement:55,text2:56,over:57,actor_pair:58,links:59,link:60,properties:61,details:62,spaceList:63,",":64,left_of:65,right_of:66,signaltype:67,"+":68,"-":69,ACTOR:70,SOLID_OPEN_ARROW:71,DOTTED_OPEN_ARROW:72,SOLID_ARROW:73,DOTTED_ARROW:74,SOLID_CROSS:75,DOTTED_CROSS:76,SOLID_POINT:77,DOTTED_POINT:78,TXT:79,$accept:0,$end:1},terminals_:{2:"error",4:"SPACE",5:"NEWLINE",6:"SD",13:"create",14:"box",15:"restOfLine",16:"end",18:"autonumber",19:"NUM",20:"off",21:"activate",23:"deactivate",29:"title",30:"legacy_title",31:"acc_title",32:"acc_title_value",33:"acc_descr",34:"acc_descr_value",35:"acc_descr_multiline_value",36:"loop",37:"rect",38:"opt",39:"alt",41:"par",43:"par_over",44:"critical",46:"break",47:"option",48:"and",49:"else",50:"participant",51:"AS",52:"participant_actor",53:"destroy",54:"note",57:"over",59:"links",60:"link",61:"properties",62:"details",64:",",65:"left_of",66:"right_of",68:"+",69:"-",70:"ACTOR",71:"SOLID_OPEN_ARROW",72:"DOTTED_OPEN_ARROW",73:"SOLID_ARROW",74:"DOTTED_ARROW",75:"SOLID_CROSS",76:"DOTTED_CROSS",77:"SOLID_POINT",78:"DOTTED_POINT",79:"TXT"},productions_:[0,[3,2],[3,2],[3,2],[7,0],[7,2],[8,2],[8,1],[8,1],[10,0],[10,2],[11,2],[11,1],[11,1],[9,1],[9,2],[9,4],[9,2],[9,4],[9,3],[9,3],[9,2],[9,3],[9,3],[9,2],[9,2],[9,2],[9,2],[9,2],[9,1],[9,1],[9,2],[9,2],[9,1],[9,4],[9,4],[9,4],[9,4],[9,4],[9,4],[9,4],[9,4],[45,1],[45,4],[42,1],[42,4],[40,1],[40,4],[12,5],[12,3],[12,5],[12,3],[12,3],[24,4],[24,4],[25,3],[26,3],[27,3],[28,3],[63,2],[63,1],[58,3],[58,1],[55,1],[55,1],[17,5],[17,5],[17,4],[22,1],[67,1],[67,1],[67,1],[67,1],[67,1],[67,1],[67,1],[67,1],[56,1]],performAction:function(w,k,L,b,M,h,Et){var d=h.length-1;switch(M){case 3:return b.apply(h[d]),h[d];case 4:case 9:this.$=[];break;case 5:case 10:h[d-1].push(h[d]),this.$=h[d-1];break;case 6:case 7:case 11:case 12:this.$=h[d];break;case 8:case 13:this.$=[];break;case 15:h[d].type="createParticipant",this.$=h[d];break;case 16:h[d-1].unshift({type:"boxStart",boxData:b.parseBoxData(h[d-2])}),h[d-1].push({type:"boxEnd",boxText:h[d-2]}),this.$=h[d-1];break;case 18:this.$={type:"sequenceIndex",sequenceIndex:Number(h[d-2]),sequenceIndexStep:Number(h[d-1]),sequenceVisible:!0,signalType:b.LINETYPE.AUTONUMBER};break;case 19:this.$={type:"sequenceIndex",sequenceIndex:Number(h[d-1]),sequenceIndexStep:1,sequenceVisible:!0,signalType:b.LINETYPE.AUTONUMBER};break;case 20:this.$={type:"sequenceIndex",sequenceVisible:!1,signalType:b.LINETYPE.AUTONUMBER};break;case 21:this.$={type:"sequenceIndex",sequenceVisible:!0,signalType:b.LINETYPE.AUTONUMBER};break;case 22:this.$={type:"activeStart",signalType:b.LINETYPE.ACTIVE_START,actor:h[d-1]};break;case 23:this.$={type:"activeEnd",signalType:b.LINETYPE.ACTIVE_END,actor:h[d-1]};break;case 29:b.setDiagramTitle(h[d].substring(6)),this.$=h[d].substring(6);break;case 30:b.setDiagramTitle(h[d].substring(7)),this.$=h[d].substring(7);break;case 31:this.$=h[d].trim(),b.setAccTitle(this.$);break;case 32:case 33:this.$=h[d].trim(),b.setAccDescription(this.$);break;case 34:h[d-1].unshift({type:"loopStart",loopText:b.parseMessage(h[d-2]),signalType:b.LINETYPE.LOOP_START}),h[d-1].push({type:"loopEnd",loopText:h[d-2],signalType:b.LINETYPE.LOOP_END}),this.$=h[d-1];break;case 35:h[d-1].unshift({type:"rectStart",color:b.parseMessage(h[d-2]),signalType:b.LINETYPE.RECT_START}),h[d-1].push({type:"rectEnd",color:b.parseMessage(h[d-2]),signalType:b.LINETYPE.RECT_END}),this.$=h[d-1];break;case 36:h[d-1].unshift({type:"optStart",optText:b.parseMessage(h[d-2]),signalType:b.LINETYPE.OPT_START}),h[d-1].push({type:"optEnd",optText:b.parseMessage(h[d-2]),signalType:b.LINETYPE.OPT_END}),this.$=h[d-1];break;case 37:h[d-1].unshift({type:"altStart",altText:b.parseMessage(h[d-2]),signalType:b.LINETYPE.ALT_START}),h[d-1].push({type:"altEnd",signalType:b.LINETYPE.ALT_END}),this.$=h[d-1];break;case 38:h[d-1].unshift({type:"parStart",parText:b.parseMessage(h[d-2]),signalType:b.LINETYPE.PAR_START}),h[d-1].push({type:"parEnd",signalType:b.LINETYPE.PAR_END}),this.$=h[d-1];break;case 39:h[d-1].unshift({type:"parStart",parText:b.parseMessage(h[d-2]),signalType:b.LINETYPE.PAR_OVER_START}),h[d-1].push({type:"parEnd",signalType:b.LINETYPE.PAR_END}),this.$=h[d-1];break;case 40:h[d-1].unshift({type:"criticalStart",criticalText:b.parseMessage(h[d-2]),signalType:b.LINETYPE.CRITICAL_START}),h[d-1].push({type:"criticalEnd",signalType:b.LINETYPE.CRITICAL_END}),this.$=h[d-1];break;case 41:h[d-1].unshift({type:"breakStart",breakText:b.parseMessage(h[d-2]),signalType:b.LINETYPE.BREAK_START}),h[d-1].push({type:"breakEnd",optText:b.parseMessage(h[d-2]),signalType:b.LINETYPE.BREAK_END}),this.$=h[d-1];break;case 43:this.$=h[d-3].concat([{type:"option",optionText:b.parseMessage(h[d-1]),signalType:b.LINETYPE.CRITICAL_OPTION},h[d]]);break;case 45:this.$=h[d-3].concat([{type:"and",parText:b.parseMessage(h[d-1]),signalType:b.LINETYPE.PAR_AND},h[d]]);break;case 47:this.$=h[d-3].concat([{type:"else",altText:b.parseMessage(h[d-1]),signalType:b.LINETYPE.ALT_ELSE},h[d]]);break;case 48:h[d-3].draw="participant",h[d-3].type="addParticipant",h[d-3].description=b.parseMessage(h[d-1]),this.$=h[d-3];break;case 49:h[d-1].draw="participant",h[d-1].type="addParticipant",this.$=h[d-1];break;case 50:h[d-3].draw="actor",h[d-3].type="addParticipant",h[d-3].description=b.parseMessage(h[d-1]),this.$=h[d-3];break;case 51:h[d-1].draw="actor",h[d-1].type="addParticipant",this.$=h[d-1];break;case 52:h[d-1].type="destroyParticipant",this.$=h[d-1];break;case 53:this.$=[h[d-1],{type:"addNote",placement:h[d-2],actor:h[d-1].actor,text:h[d]}];break;case 54:h[d-2]=[].concat(h[d-1],h[d-1]).slice(0,2),h[d-2][0]=h[d-2][0].actor,h[d-2][1]=h[d-2][1].actor,this.$=[h[d-1],{type:"addNote",placement:b.PLACEMENT.OVER,actor:h[d-2].slice(0,2),text:h[d]}];break;case 55:this.$=[h[d-1],{type:"addLinks",actor:h[d-1].actor,text:h[d]}];break;case 56:this.$=[h[d-1],{type:"addALink",actor:h[d-1].actor,text:h[d]}];break;case 57:this.$=[h[d-1],{type:"addProperties",actor:h[d-1].actor,text:h[d]}];break;case 58:this.$=[h[d-1],{type:"addDetails",actor:h[d-1].actor,text:h[d]}];break;case 61:this.$=[h[d-2],h[d]];break;case 62:this.$=h[d];break;case 63:this.$=b.PLACEMENT.LEFTOF;break;case 64:this.$=b.PLACEMENT.RIGHTOF;break;case 65:this.$=[h[d-4],h[d-1],{type:"addMessage",from:h[d-4].actor,to:h[d-1].actor,signalType:h[d-3],msg:h[d],activate:!0},{type:"activeStart",signalType:b.LINETYPE.ACTIVE_START,actor:h[d-1]}];break;case 66:this.$=[h[d-4],h[d-1],{type:"addMessage",from:h[d-4].actor,to:h[d-1].actor,signalType:h[d-3],msg:h[d]},{type:"activeEnd",signalType:b.LINETYPE.ACTIVE_END,actor:h[d-4]}];break;case 67:this.$=[h[d-3],h[d-1],{type:"addMessage",from:h[d-3].actor,to:h[d-1].actor,signalType:h[d-2],msg:h[d]}];break;case 68:this.$={type:"addParticipant",actor:h[d]};break;case 69:this.$=b.LINETYPE.SOLID_OPEN;break;case 70:this.$=b.LINETYPE.DOTTED_OPEN;break;case 71:this.$=b.LINETYPE.SOLID;break;case 72:this.$=b.LINETYPE.DOTTED;break;case 73:this.$=b.LINETYPE.SOLID_CROSS;break;case 74:this.$=b.LINETYPE.DOTTED_CROSS;break;case 75:this.$=b.LINETYPE.SOLID_POINT;break;case 76:this.$=b.LINETYPE.DOTTED_POINT;break;case 77:this.$=b.parseMessage(h[d].trim().substring(1));break}},table:[{3:1,4:e,5:c,6:s},{1:[3]},{3:5,4:e,5:c,6:s},{3:6,4:e,5:c,6:s},t([1,4,5,13,14,18,21,23,29,30,31,33,35,36,37,38,39,41,43,44,46,50,52,53,54,59,60,61,62,70],i,{7:7}),{1:[2,1]},{1:[2,2]},{1:[2,3],4:a,5:o,8:8,9:10,12:12,13:l,14:p,17:15,18:r,21:x,22:40,23:T,24:19,25:20,26:21,27:22,28:23,29:u,30:g,31:m,33:_,35:I,36:V,37:S,38:O,39:R,41:q,43:z,44:J,46:$,50:H,52:U,53:F,54:W,59:Z,60:K,61:Q,62:tt,70:N},t(y,[2,5]),{9:47,12:12,13:l,14:p,17:15,18:r,21:x,22:40,23:T,24:19,25:20,26:21,27:22,28:23,29:u,30:g,31:m,33:_,35:I,36:V,37:S,38:O,39:R,41:q,43:z,44:J,46:$,50:H,52:U,53:F,54:W,59:Z,60:K,61:Q,62:tt,70:N},t(y,[2,7]),t(y,[2,8]),t(y,[2,14]),{12:48,50:H,52:U,53:F},{15:[1,49]},{5:[1,50]},{5:[1,53],19:[1,51],20:[1,52]},{22:54,70:N},{22:55,70:N},{5:[1,56]},{5:[1,57]},{5:[1,58]},{5:[1,59]},{5:[1,60]},t(y,[2,29]),t(y,[2,30]),{32:[1,61]},{34:[1,62]},t(y,[2,33]),{15:[1,63]},{15:[1,64]},{15:[1,65]},{15:[1,66]},{15:[1,67]},{15:[1,68]},{15:[1,69]},{15:[1,70]},{22:71,70:N},{22:72,70:N},{22:73,70:N},{67:74,71:[1,75],72:[1,76],73:[1,77],74:[1,78],75:[1,79],76:[1,80],77:[1,81],78:[1,82]},{55:83,57:[1,84],65:[1,85],66:[1,86]},{22:87,70:N},{22:88,70:N},{22:89,70:N},{22:90,70:N},t([5,51,64,71,72,73,74,75,76,77,78,79],[2,68]),t(y,[2,6]),t(y,[2,15]),t(P,[2,9],{10:91}),t(y,[2,17]),{5:[1,93],19:[1,92]},{5:[1,94]},t(y,[2,21]),{5:[1,95]},{5:[1,96]},t(y,[2,24]),t(y,[2,25]),t(y,[2,26]),t(y,[2,27]),t(y,[2,28]),t(y,[2,31]),t(y,[2,32]),t(j,i,{7:97}),t(j,i,{7:98}),t(j,i,{7:99}),t(rt,i,{40:100,7:101}),t(A,i,{42:102,7:103}),t(A,i,{7:103,42:104}),t(Gt,i,{45:105,7:106}),t(j,i,{7:107}),{5:[1,109],51:[1,108]},{5:[1,111],51:[1,110]},{5:[1,112]},{22:115,68:[1,113],69:[1,114],70:N},t(ht,[2,69]),t(ht,[2,70]),t(ht,[2,71]),t(ht,[2,72]),t(ht,[2,73]),t(ht,[2,74]),t(ht,[2,75]),t(ht,[2,76]),{22:116,70:N},{22:118,58:117,70:N},{70:[2,63]},{70:[2,64]},{56:119,79:ot},{56:121,79:ot},{56:122,79:ot},{56:123,79:ot},{4:[1,126],5:[1,128],11:125,12:127,16:[1,124],50:H,52:U,53:F},{5:[1,129]},t(y,[2,19]),t(y,[2,20]),t(y,[2,22]),t(y,[2,23]),{4:a,5:o,8:8,9:10,12:12,13:l,14:p,16:[1,130],17:15,18:r,21:x,22:40,23:T,24:19,25:20,26:21,27:22,28:23,29:u,30:g,31:m,33:_,35:I,36:V,37:S,38:O,39:R,41:q,43:z,44:J,46:$,50:H,52:U,53:F,54:W,59:Z,60:K,61:Q,62:tt,70:N},{4:a,5:o,8:8,9:10,12:12,13:l,14:p,16:[1,131],17:15,18:r,21:x,22:40,23:T,24:19,25:20,26:21,27:22,28:23,29:u,30:g,31:m,33:_,35:I,36:V,37:S,38:O,39:R,41:q,43:z,44:J,46:$,50:H,52:U,53:F,54:W,59:Z,60:K,61:Q,62:tt,70:N},{4:a,5:o,8:8,9:10,12:12,13:l,14:p,16:[1,132],17:15,18:r,21:x,22:40,23:T,24:19,25:20,26:21,27:22,28:23,29:u,30:g,31:m,33:_,35:I,36:V,37:S,38:O,39:R,41:q,43:z,44:J,46:$,50:H,52:U,53:F,54:W,59:Z,60:K,61:Q,62:tt,70:N},{16:[1,133]},{4:a,5:o,8:8,9:10,12:12,13:l,14:p,16:[2,46],17:15,18:r,21:x,22:40,23:T,24:19,25:20,26:21,27:22,28:23,29:u,30:g,31:m,33:_,35:I,36:V,37:S,38:O,39:R,41:q,43:z,44:J,46:$,49:[1,134],50:H,52:U,53:F,54:W,59:Z,60:K,61:Q,62:tt,70:N},{16:[1,135]},{4:a,5:o,8:8,9:10,12:12,13:l,14:p,16:[2,44],17:15,18:r,21:x,22:40,23:T,24:19,25:20,26:21,27:22,28:23,29:u,30:g,31:m,33:_,35:I,36:V,37:S,38:O,39:R,41:q,43:z,44:J,46:$,48:[1,136],50:H,52:U,53:F,54:W,59:Z,60:K,61:Q,62:tt,70:N},{16:[1,137]},{16:[1,138]},{4:a,5:o,8:8,9:10,12:12,13:l,14:p,16:[2,42],17:15,18:r,21:x,22:40,23:T,24:19,25:20,26:21,27:22,28:23,29:u,30:g,31:m,33:_,35:I,36:V,37:S,38:O,39:R,41:q,43:z,44:J,46:$,47:[1,139],50:H,52:U,53:F,54:W,59:Z,60:K,61:Q,62:tt,70:N},{4:a,5:o,8:8,9:10,12:12,13:l,14:p,16:[1,140],17:15,18:r,21:x,22:40,23:T,24:19,25:20,26:21,27:22,28:23,29:u,30:g,31:m,33:_,35:I,36:V,37:S,38:O,39:R,41:q,43:z,44:J,46:$,50:H,52:U,53:F,54:W,59:Z,60:K,61:Q,62:tt,70:N},{15:[1,141]},t(y,[2,49]),{15:[1,142]},t(y,[2,51]),t(y,[2,52]),{22:143,70:N},{22:144,70:N},{56:145,79:ot},{56:146,79:ot},{56:147,79:ot},{64:[1,148],79:[2,62]},{5:[2,55]},{5:[2,77]},{5:[2,56]},{5:[2,57]},{5:[2,58]},t(y,[2,16]),t(P,[2,10]),{12:149,50:H,52:U,53:F},t(P,[2,12]),t(P,[2,13]),t(y,[2,18]),t(y,[2,34]),t(y,[2,35]),t(y,[2,36]),t(y,[2,37]),{15:[1,150]},t(y,[2,38]),{15:[1,151]},t(y,[2,39]),t(y,[2,40]),{15:[1,152]},t(y,[2,41]),{5:[1,153]},{5:[1,154]},{56:155,79:ot},{56:156,79:ot},{5:[2,67]},{5:[2,53]},{5:[2,54]},{22:157,70:N},t(P,[2,11]),t(rt,i,{7:101,40:158}),t(A,i,{7:103,42:159}),t(Gt,i,{7:106,45:160}),t(y,[2,48]),t(y,[2,50]),{5:[2,65]},{5:[2,66]},{79:[2,61]},{16:[2,47]},{16:[2,45]},{16:[2,43]}],defaultActions:{5:[2,1],6:[2,2],85:[2,63],86:[2,64],119:[2,55],120:[2,77],121:[2,56],122:[2,57],123:[2,58],145:[2,67],146:[2,53],147:[2,54],155:[2,65],156:[2,66],157:[2,61],158:[2,47],159:[2,45],160:[2,43]},parseError:function(w,k){if(k.recoverable)this.trace(w);else{var L=new Error(w);throw L.hash=k,L}},parse:function(w){var k=this,L=[0],b=[],M=[null],h=[],Et=this.table,d="",_t=0,Xt=0,Te=2,Jt=1,be=h.slice.call(arguments,1),Y=Object.create(this.lexer),pt={yy:{}};for(var Ct in this.yy)Object.prototype.hasOwnProperty.call(this.yy,Ct)&&(pt.yy[Ct]=this.yy[Ct]);Y.setInput(w,pt.yy),pt.yy.lexer=Y,pt.yy.parser=this,typeof Y.yylloc>"u"&&(Y.yylloc={});var Dt=Y.yylloc;h.push(Dt);var Ee=Y.options&&Y.options.ranges;typeof pt.yy.parseError=="function"?this.parseError=pt.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function me(){var lt;return lt=b.pop()||Y.lex()||Jt,typeof lt!="number"&&(lt instanceof Array&&(b=lt,lt=b.pop()),lt=k.symbols_[lt]||lt),lt}for(var G,ut,et,Vt,yt={},kt,ct,Zt,Pt;;){if(ut=L[L.length-1],this.defaultActions[ut]?et=this.defaultActions[ut]:((G===null||typeof G>"u")&&(G=me()),et=Et[ut]&&Et[ut][G]),typeof et>"u"||!et.length||!et[0]){var Ot="";Pt=[];for(kt in Et[ut])this.terminals_[kt]&&kt>Te&&Pt.push("'"+this.terminals_[kt]+"'");Y.showPosition?Ot="Parse error on line "+(_t+1)+`:
 `+Y.showPosition()+`
 Expecting `+Pt.join(", ")+", got '"+(this.terminals_[G]||G)+"'":Ot="Parse error on line "+(_t+1)+": Unexpected "+(G==Jt?"end of input":"'"+(this.terminals_[G]||G)+"'"),this.parseError(Ot,{text:Y.match,token:this.terminals_[G]||G,line:Y.yylineno,loc:Dt,expected:Pt})}if(et[0]instanceof Array&&et.length>1)throw new Error("Parse Error: multiple actions possible at state: "+ut+", token: "+G);switch(et[0]){case 1:L.push(G),M.push(Y.yytext),h.push(Y.yylloc),L.push(et[1]),G=null,Xt=Y.yyleng,d=Y.yytext,_t=Y.yylineno,Dt=Y.yylloc;break;case 2:if(ct=this.productions_[et[1]][1],yt.$=M[M.length-ct],yt._$={first_line:h[h.length-(ct||1)].first_line,last_line:h[h.length-1].last_line,first_column:h[h.length-(ct||1)].first_column,last_column:h[h.length-1].last_column},Ee&&(yt._$.range=[h[h.length-(ct||1)].range[0],h[h.length-1].range[1]]),Vt=this.performAction.apply(yt,[d,Xt,_t,pt.yy,et[1],M,h].concat(be)),typeof Vt<"u")return Vt;ct&&(L=L.slice(0,-1*ct*2),M=M.slice(0,-1*ct),h=h.slice(0,-1*ct)),L.push(this.productions_[et[1]][0]),M.push(yt.$),h.push(yt._$),Zt=Et[L[L.length-2]][L[L.length-1]],L.push(Zt);break;case 3:return!0}}return!0}},ye=function(){var dt={EOF:1,parseError:function(k,L){if(this.yy.parser)this.yy.parser.parseError(k,L);else throw new Error(k)},setInput:function(w,k){return this.yy=k||this.yy||{},this._input=w,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var w=this._input[0];this.yytext+=w,this.yyleng++,this.offset++,this.match+=w,this.matched+=w;var k=w.match(/(?:\r\n?|\n).*/g);return k?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),w},unput:function(w){var k=w.length,L=w.split(/(?:\r\n?|\n)/g);this._input=w+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-k),this.offset-=k;var b=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),L.length-1&&(this.yylineno-=L.length-1);var M=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:L?(L.length===b.length?this.yylloc.first_column:0)+b[b.length-L.length].length-L[0].length:this.yylloc.first_column-k},this.options.ranges&&(this.yylloc.range=[M[0],M[0]+this.yyleng-k]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){if(this.options.backtrack_lexer)this._backtrack=!0;else return this.parseError("Lexical error on line "+(this.yylineno+1)+`. You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).
 `+this.showPosition(),{text:"",token:null,line:this.yylineno});return this},less:function(w){this.unput(this.match.slice(w))},pastInput:function(){var w=this.matched.substr(0,this.matched.length-this.match.length);return(w.length>20?"...":"")+w.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var w=this.match;return w.length<20&&(w+=this._input.substr(0,20-w.length)),(w.substr(0,20)+(w.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var w=this.pastInput(),k=new Array(w.length+1).join("-");return w+this.upcomingInput()+`
diff --git a/assets/singleton.html-Pzh1ZzrO.js b/assets/singleton.html-CJylCsqx.js
similarity index 99%
rename from assets/singleton.html-Pzh1ZzrO.js
rename to assets/singleton.html-CJylCsqx.js
index 054317c..fa9ccfb 100644
--- a/assets/singleton.html-Pzh1ZzrO.js
+++ b/assets/singleton.html-CJylCsqx.js
@@ -1,4 +1,4 @@
-import{_ as s,o as a,c as t,a as e,b as n,f as p}from"./app-B69Gl_S-.js";const o={},c=n("h2",{id:"为什么要使用-singleton-模式",tabindex:"-1"},[n("a",{class:"header-anchor",href:"#为什么要使用-singleton-模式"},[n("span",null,"为什么要使用 Singleton 模式")])],-1),l=n("p",null,"Singleton 模式确保一个类只有一个实例，并提供一个全局访问点。它常用于需要控制资源访问的场景，例如数据库连接、日志记录器等。通过 Singleton 模式，可以避免创建多个实例带来的资源浪费和不一致性问题。",-1),i=p(`<h3 id="总结" tabindex="-1"><a class="header-anchor" href="#总结"><span>总结:</span></a></h3><ul><li>想确保任何情况下都绝对只有 1 个实例</li><li>想在程序上表现出“只存在一个实例”</li></ul><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/JOun2iCm34LtdK9ZGl05F9IicNi2LnR1uCXWoLFetMjAmDw4tl-Vjwk5QktAG3ceuZl9cTcAu0s83ZksH9Ya7qBiHs369mlNO1oFw57QzU7wnrHwhpQoKfUrVxPHiEEPNDPvz0im59nxJK8UcxB2pXAxxmy0" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// main.ts</span>
+import{_ as s,o as a,c as t,a as e,b as n,f as p}from"./app-B4LGNJZ0.js";const o={},c=n("h2",{id:"为什么要使用-singleton-模式",tabindex:"-1"},[n("a",{class:"header-anchor",href:"#为什么要使用-singleton-模式"},[n("span",null,"为什么要使用 Singleton 模式")])],-1),l=n("p",null,"Singleton 模式确保一个类只有一个实例，并提供一个全局访问点。它常用于需要控制资源访问的场景，例如数据库连接、日志记录器等。通过 Singleton 模式，可以避免创建多个实例带来的资源浪费和不一致性问题。",-1),i=p(`<h3 id="总结" tabindex="-1"><a class="header-anchor" href="#总结"><span>总结:</span></a></h3><ul><li>想确保任何情况下都绝对只有 1 个实例</li><li>想在程序上表现出“只存在一个实例”</li></ul><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/JOun2iCm34LtdK9ZGl05F9IicNi2LnR1uCXWoLFetMjAmDw4tl-Vjwk5QktAG3ceuZl9cTcAu0s83ZksH9Ya7qBiHs369mlNO1oFw57QzU7wnrHwhpQoKfUrVxPHiEEPNDPvz0im59nxJK8UcxB2pXAxxmy0" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// main.ts</span>
 <span class="token keyword">import</span> <span class="token punctuation">{</span> Singleton <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&#39;./singleton&#39;</span><span class="token punctuation">;</span>
 <span class="token keyword">const</span> singleton1 <span class="token operator">=</span> Singleton<span class="token punctuation">.</span><span class="token function">getInstance</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
 <span class="token keyword">const</span> singleton2 <span class="token operator">=</span> Singleton<span class="token punctuation">.</span><span class="token function">getInstance</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
diff --git a/assets/state.html-DsXXtCU9.js b/assets/state.html-D0BJywlY.js
similarity index 99%
rename from assets/state.html-DsXXtCU9.js
rename to assets/state.html-D0BJywlY.js
index de7d9e6..6a3d7cb 100644
--- a/assets/state.html-DsXXtCU9.js
+++ b/assets/state.html-D0BJywlY.js
@@ -1,4 +1,4 @@
-import{_ as n,o as s,c as a,f as t}from"./app-B69Gl_S-.js";const p={},e=t(`<h2 id="为什么使用-state-模式" tabindex="-1"><a class="header-anchor" href="#为什么使用-state-模式"><span>为什么使用 State 模式</span></a></h2><p>State 模式允许对象在其内部状态改变时改变其行为。它将与状态相关的行为封装在独立的类中，使得状态转换变得清晰且易于管理。使用 State 模式可以避免大量的条件语句，使代码更加简洁和可维护。</p><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/vPJ1JeGm48RlF4MFaCeBS5g3CJ4nneJi0zGoMnhRZca7inlZkzi2AnXnqRCN0fq_q--VydSNI7ZghScq8_078O7L65-FnDuonW9GRL0-vntslcAkjq_WYugzecvZMNR2AMX84EGXFIisV2mKmfW6PEyrdMf8U-Gsg8e5yjgfMUT1ec_lKQsLtxC5th310DVYo2P7uEfCViNMQLlS1_YcNjQlZV3sekAnG_TpZmWgZGY1tOZJoAdjYm4RZOSHF75p1NJduhoSXBoOHXRNozWs6kybeS-B9FohGxvbaMzxv5iceuIm6GueqOz7DLj_qAgZ_sg-4GUuzS9-yJwrIExBPKfIius0yUs4yTz6Z5_CsEVyLkQrCf_vZpzV5rYMawqTk3PUAHy0" alt=""><img src="https://www.plantuml.com/plantuml/svg/XP513e8m44NtFKMNcEW5M1YCngKn8HvWKaRQ21tI3edUNce50X7S_l_cpIIJUGR7RLq9K4nEtZmwqNIHKQO1opA7EvuTr3X9J_3A6NWQNaofESOYUEHkFuwdqYCVArAFH5FhDc9e0jRxKbbGX1HPnYTlPQHxOEPK6co9doOPry_aOx6e_t5kGLsOhAe2y1KjA0uLk7fT4f5rpLMJ_NDBH0PDXhRelle6" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// context.ts</span>
+import{_ as n,o as s,c as a,f as t}from"./app-B4LGNJZ0.js";const p={},e=t(`<h2 id="为什么使用-state-模式" tabindex="-1"><a class="header-anchor" href="#为什么使用-state-模式"><span>为什么使用 State 模式</span></a></h2><p>State 模式允许对象在其内部状态改变时改变其行为。它将与状态相关的行为封装在独立的类中，使得状态转换变得清晰且易于管理。使用 State 模式可以避免大量的条件语句，使代码更加简洁和可维护。</p><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/vPJ1JeGm48RlF4MFaCeBS5g3CJ4nneJi0zGoMnhRZca7inlZkzi2AnXnqRCN0fq_q--VydSNI7ZghScq8_078O7L65-FnDuonW9GRL0-vntslcAkjq_WYugzecvZMNR2AMX84EGXFIisV2mKmfW6PEyrdMf8U-Gsg8e5yjgfMUT1ec_lKQsLtxC5th310DVYo2P7uEfCViNMQLlS1_YcNjQlZV3sekAnG_TpZmWgZGY1tOZJoAdjYm4RZOSHF75p1NJduhoSXBoOHXRNozWs6kybeS-B9FohGxvbaMzxv5iceuIm6GueqOz7DLj_qAgZ_sg-4GUuzS9-yJwrIExBPKfIius0yUs4yTz6Z5_CsEVyLkQrCf_vZpzV5rYMawqTk3PUAHy0" alt=""><img src="https://www.plantuml.com/plantuml/svg/XP513e8m44NtFKMNcEW5M1YCngKn8HvWKaRQ21tI3edUNce50X7S_l_cpIIJUGR7RLq9K4nEtZmwqNIHKQO1opA7EvuTr3X9J_3A6NWQNaofESOYUEHkFuwdqYCVArAFH5FhDc9e0jRxKbbGX1HPnYTlPQHxOEPK6co9doOPry_aOx6e_t5kGLsOhAe2y1KjA0uLk7fT4f5rpLMJ_NDBH0PDXhRelle6" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// context.ts</span>
 <span class="token keyword">import</span> <span class="token punctuation">{</span> State <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&#39;./state&#39;</span><span class="token punctuation">;</span>
 <span class="token keyword">export</span> <span class="token keyword">interface</span> <span class="token class-name">Context</span> <span class="token punctuation">{</span>
   <span class="token function">setClock</span><span class="token punctuation">(</span>hour<span class="token operator">:</span> <span class="token builtin">number</span><span class="token punctuation">)</span><span class="token operator">:</span> <span class="token keyword">void</span><span class="token punctuation">;</span>
diff --git a/assets/stateDiagram-35d39939-BlCBJSJX.js b/assets/stateDiagram-35d39939-D7FEhrYs.js
similarity index 97%
rename from assets/stateDiagram-35d39939-BlCBJSJX.js
rename to assets/stateDiagram-35d39939-D7FEhrYs.js
index b95abb6..a8131fb 100644
--- a/assets/stateDiagram-35d39939-BlCBJSJX.js
+++ b/assets/stateDiagram-35d39939-D7FEhrYs.js
@@ -1 +1 @@
-import{p as P,d as N,s as W}from"./styles-de3becd0-Bjk-EQ8n.js";import{c as t,h as H,l as b,i as R,j as T,ao as v,z as U}from"./mermaid.core-ChLYKTZm.js";import{G as C}from"./graph-T5JS4vfK.js";import{l as F}from"./layout-DUYLy6Ue.js";import{l as $}from"./line-D0jG_HZ-.js";import"./app-B69Gl_S-.js";import"./array-BKyUJesY.js";import"./path-CbwjOpE9.js";const O=e=>e.append("circle").attr("class","start-state").attr("r",t().state.sizeUnit).attr("cx",t().state.padding+t().state.sizeUnit).attr("cy",t().state.padding+t().state.sizeUnit),X=e=>e.append("line").style("stroke","grey").style("stroke-dasharray","3").attr("x1",t().state.textHeight).attr("class","divider").attr("x2",t().state.textHeight*2).attr("y1",0).attr("y2",0),J=(e,i)=>{const o=e.append("text").attr("x",2*t().state.padding).attr("y",t().state.textHeight+2*t().state.padding).attr("font-size",t().state.fontSize).attr("class","state-title").text(i.id),c=o.node().getBBox();return e.insert("rect",":first-child").attr("x",t().state.padding).attr("y",t().state.padding).attr("width",c.width+2*t().state.padding).attr("height",c.height+2*t().state.padding).attr("rx",t().state.radius),o},Y=(e,i)=>{const o=function(l,m,w){const E=l.append("tspan").attr("x",2*t().state.padding).text(m);w||E.attr("dy",t().state.textHeight)},s=e.append("text").attr("x",2*t().state.padding).attr("y",t().state.textHeight+1.3*t().state.padding).attr("font-size",t().state.fontSize).attr("class","state-title").text(i.descriptions[0]).node().getBBox(),g=s.height,p=e.append("text").attr("x",t().state.padding).attr("y",g+t().state.padding*.4+t().state.dividerMargin+t().state.textHeight).attr("class","state-description");let a=!0,r=!0;i.descriptions.forEach(function(l){a||(o(p,l,r),r=!1),a=!1});const y=e.append("line").attr("x1",t().state.padding).attr("y1",t().state.padding+g+t().state.dividerMargin/2).attr("y2",t().state.padding+g+t().state.dividerMargin/2).attr("class","descr-divider"),x=p.node().getBBox(),d=Math.max(x.width,s.width);return y.attr("x2",d+3*t().state.padding),e.insert("rect",":first-child").attr("x",t().state.padding).attr("y",t().state.padding).attr("width",d+2*t().state.padding).attr("height",x.height+g+2*t().state.padding).attr("rx",t().state.radius),e},I=(e,i,o)=>{const c=t().state.padding,s=2*t().state.padding,g=e.node().getBBox(),p=g.width,a=g.x,r=e.append("text").attr("x",0).attr("y",t().state.titleShift).attr("font-size",t().state.fontSize).attr("class","state-title").text(i.id),x=r.node().getBBox().width+s;let d=Math.max(x,p);d===p&&(d=d+s);let l;const m=e.node().getBBox();i.doc,l=a-c,x>p&&(l=(p-d)/2+c),Math.abs(a-m.x)<c&&x>p&&(l=a-(x-p)/2);const w=1-t().state.textHeight;return e.insert("rect",":first-child").attr("x",l).attr("y",w).attr("class",o?"alt-composit":"composit").attr("width",d).attr("height",m.height+t().state.textHeight+t().state.titleShift+1).attr("rx","0"),r.attr("x",l+c),x<=p&&r.attr("x",a+(d-s)/2-x/2+c),e.insert("rect",":first-child").attr("x",l).attr("y",t().state.titleShift-t().state.textHeight-t().state.padding).attr("width",d).attr("height",t().state.textHeight*3).attr("rx",t().state.radius),e.insert("rect",":first-child").attr("x",l).attr("y",t().state.titleShift-t().state.textHeight-t().state.padding).attr("width",d).attr("height",m.height+3+2*t().state.textHeight).attr("rx",t().state.radius),e},_=e=>(e.append("circle").attr("class","end-state-outer").attr("r",t().state.sizeUnit+t().state.miniPadding).attr("cx",t().state.padding+t().state.sizeUnit+t().state.miniPadding).attr("cy",t().state.padding+t().state.sizeUnit+t().state.miniPadding),e.append("circle").attr("class","end-state-inner").attr("r",t().state.sizeUnit).attr("cx",t().state.padding+t().state.sizeUnit+2).attr("cy",t().state.padding+t().state.sizeUnit+2)),q=(e,i)=>{let o=t().state.forkWidth,c=t().state.forkHeight;if(i.parentId){let s=o;o=c,c=s}return e.append("rect").style("stroke","black").style("fill","black").attr("width",o).attr("height",c).attr("x",t().state.padding).attr("y",t().state.padding)},Z=(e,i,o,c)=>{let s=0;const g=c.append("text");g.style("text-anchor","start"),g.attr("class","noteText");let p=e.replace(/\r\n/g,"<br/>");p=p.replace(/\n/g,"<br/>");const a=p.split(T.lineBreakRegex);let r=1.25*t().state.noteMargin;for(const y of a){const x=y.trim();if(x.length>0){const d=g.append("tspan");if(d.text(x),r===0){const l=d.node().getBBox();r+=l.height}s+=r,d.attr("x",i+t().state.noteMargin),d.attr("y",o+s+1.25*t().state.noteMargin)}}return{textWidth:g.node().getBBox().width,textHeight:s}},j=(e,i)=>{i.attr("class","state-note");const o=i.append("rect").attr("x",0).attr("y",t().state.padding),c=i.append("g"),{textWidth:s,textHeight:g}=Z(e,0,0,c);return o.attr("height",g+2*t().state.noteMargin),o.attr("width",s+t().state.noteMargin*2),o},L=function(e,i){const o=i.id,c={id:o,label:i.id,width:0,height:0},s=e.append("g").attr("id",o).attr("class","stateGroup");i.type==="start"&&O(s),i.type==="end"&&_(s),(i.type==="fork"||i.type==="join")&&q(s,i),i.type==="note"&&j(i.note.text,s),i.type==="divider"&&X(s),i.type==="default"&&i.descriptions.length===0&&J(s,i),i.type==="default"&&i.descriptions.length>0&&Y(s,i);const g=s.node().getBBox();return c.width=g.width+2*t().state.padding,c.height=g.height+2*t().state.padding,c};let G=0;const K=function(e,i,o){const c=function(r){switch(r){case N.relationType.AGGREGATION:return"aggregation";case N.relationType.EXTENSION:return"extension";case N.relationType.COMPOSITION:return"composition";case N.relationType.DEPENDENCY:return"dependency"}};i.points=i.points.filter(r=>!Number.isNaN(r.y));const s=i.points,g=$().x(function(r){return r.x}).y(function(r){return r.y}).curve(v),p=e.append("path").attr("d",g(s)).attr("id","edge"+G).attr("class","transition");let a="";if(t().state.arrowMarkerAbsolute&&(a=window.location.protocol+"//"+window.location.host+window.location.pathname+window.location.search,a=a.replace(/\(/g,"\\("),a=a.replace(/\)/g,"\\)")),p.attr("marker-end","url("+a+"#"+c(N.relationType.DEPENDENCY)+"End)"),o.title!==void 0){const r=e.append("g").attr("class","stateLabel"),{x:y,y:x}=U.calcLabelPosition(i.points),d=T.getRows(o.title);let l=0;const m=[];let w=0,E=0;for(let u=0;u<=d.length;u++){const h=r.append("text").attr("text-anchor","middle").text(d[u]).attr("x",y).attr("y",x+l),f=h.node().getBBox();w=Math.max(w,f.width),E=Math.min(E,f.x),b.info(f.x,y,x+l),l===0&&(l=h.node().getBBox().height,b.info("Title height",l,x)),m.push(h)}let k=l*d.length;if(d.length>1){const u=(d.length-1)*l*.5;m.forEach((h,f)=>h.attr("y",x+f*l-u)),k=l*d.length}const n=r.node().getBBox();r.insert("rect",":first-child").attr("class","box").attr("x",y-w/2-t().state.padding/2).attr("y",x-k/2-t().state.padding/2-3.5).attr("width",w+t().state.padding).attr("height",k+t().state.padding),b.info(n)}G++};let B;const z={},Q=function(){},V=function(e){e.append("defs").append("marker").attr("id","dependencyEnd").attr("refX",19).attr("refY",7).attr("markerWidth",20).attr("markerHeight",28).attr("orient","auto").append("path").attr("d","M 19,7 L9,13 L14,7 L9,1 Z")},D=function(e,i,o,c){B=t().state;const s=t().securityLevel;let g;s==="sandbox"&&(g=H("#i"+i));const p=s==="sandbox"?H(g.nodes()[0].contentDocument.body):H("body"),a=s==="sandbox"?g.nodes()[0].contentDocument:document;b.debug("Rendering diagram "+e);const r=p.select(`[id='${i}']`);V(r);const y=c.db.getRootDoc();A(y,r,void 0,!1,p,a,c);const x=B.padding,d=r.node().getBBox(),l=d.width+x*2,m=d.height+x*2,w=l*1.75;R(r,m,w,B.useMaxWidth),r.attr("viewBox",`${d.x-B.padding}  ${d.y-B.padding} `+l+" "+m)},tt=e=>e?e.length*B.fontSizeFactor:1,A=(e,i,o,c,s,g,p)=>{const a=new C({compound:!0,multigraph:!0});let r,y=!0;for(r=0;r<e.length;r++)if(e[r].stmt==="relation"){y=!1;break}o?a.setGraph({rankdir:"LR",multigraph:!0,compound:!0,ranker:"tight-tree",ranksep:y?1:B.edgeLengthFactor,nodeSep:y?1:50,isMultiGraph:!0}):a.setGraph({rankdir:"TB",multigraph:!0,compound:!0,ranksep:y?1:B.edgeLengthFactor,nodeSep:y?1:50,ranker:"tight-tree",isMultiGraph:!0}),a.setDefaultEdgeLabel(function(){return{}}),p.db.extract(e);const x=p.db.getStates(),d=p.db.getRelations(),l=Object.keys(x);for(const n of l){const u=x[n];o&&(u.parentId=o);let h;if(u.doc){let f=i.append("g").attr("id",u.id).attr("class","stateGroup");h=A(u.doc,f,u.id,!c,s,g,p);{f=I(f,u,c);let S=f.node().getBBox();h.width=S.width,h.height=S.height+B.padding/2,z[u.id]={y:B.compositTitleSize}}}else h=L(i,u);if(u.note){const f={descriptions:[],id:u.id+"-note",note:u.note,type:"note"},S=L(i,f);u.note.position==="left of"?(a.setNode(h.id+"-note",S),a.setNode(h.id,h)):(a.setNode(h.id,h),a.setNode(h.id+"-note",S)),a.setParent(h.id,h.id+"-group"),a.setParent(h.id+"-note",h.id+"-group")}else a.setNode(h.id,h)}b.debug("Count=",a.nodeCount(),a);let m=0;d.forEach(function(n){m++,b.debug("Setting edge",n),a.setEdge(n.id1,n.id2,{relation:n,width:tt(n.title),height:B.labelHeight*T.getRows(n.title).length,labelpos:"c"},"id"+m)}),F(a),b.debug("Graph after layout",a.nodes());const w=i.node();a.nodes().forEach(function(n){n!==void 0&&a.node(n)!==void 0?(b.warn("Node "+n+": "+JSON.stringify(a.node(n))),s.select("#"+w.id+" #"+n).attr("transform","translate("+(a.node(n).x-a.node(n).width/2)+","+(a.node(n).y+(z[n]?z[n].y:0)-a.node(n).height/2)+" )"),s.select("#"+w.id+" #"+n).attr("data-x-shift",a.node(n).x-a.node(n).width/2),g.querySelectorAll("#"+w.id+" #"+n+" .divider").forEach(h=>{const f=h.parentElement;let S=0,M=0;f&&(f.parentElement&&(S=f.parentElement.getBBox().width),M=parseInt(f.getAttribute("data-x-shift"),10),Number.isNaN(M)&&(M=0)),h.setAttribute("x1",0-M+8),h.setAttribute("x2",S-M-8)})):b.debug("No Node "+n+": "+JSON.stringify(a.node(n)))});let E=w.getBBox();a.edges().forEach(function(n){n!==void 0&&a.edge(n)!==void 0&&(b.debug("Edge "+n.v+" -> "+n.w+": "+JSON.stringify(a.edge(n))),K(i,a.edge(n),a.edge(n).relation))}),E=w.getBBox();const k={id:o||"root",label:o||"root",width:0,height:0};return k.width=E.width+2*B.padding,k.height=E.height+2*B.padding,b.debug("Doc rendered",k,a),k},et={setConf:Q,draw:D},lt={parser:P,db:N,renderer:et,styles:W,init:e=>{e.state||(e.state={}),e.state.arrowMarkerAbsolute=e.arrowMarkerAbsolute,N.clear()}};export{lt as diagram};
+import{p as P,d as N,s as W}from"./styles-de3becd0-D7QN2-IT.js";import{c as t,h as H,l as b,i as R,j as T,ao as v,z as U}from"./mermaid.core-DNo_7Q2B.js";import{G as C}from"./graph-B1296pfd.js";import{l as F}from"./layout-qMafh1ee.js";import{l as $}from"./line-BqHmcuby.js";import"./app-B4LGNJZ0.js";import"./array-BKyUJesY.js";import"./path-CbwjOpE9.js";const O=e=>e.append("circle").attr("class","start-state").attr("r",t().state.sizeUnit).attr("cx",t().state.padding+t().state.sizeUnit).attr("cy",t().state.padding+t().state.sizeUnit),X=e=>e.append("line").style("stroke","grey").style("stroke-dasharray","3").attr("x1",t().state.textHeight).attr("class","divider").attr("x2",t().state.textHeight*2).attr("y1",0).attr("y2",0),J=(e,i)=>{const o=e.append("text").attr("x",2*t().state.padding).attr("y",t().state.textHeight+2*t().state.padding).attr("font-size",t().state.fontSize).attr("class","state-title").text(i.id),c=o.node().getBBox();return e.insert("rect",":first-child").attr("x",t().state.padding).attr("y",t().state.padding).attr("width",c.width+2*t().state.padding).attr("height",c.height+2*t().state.padding).attr("rx",t().state.radius),o},Y=(e,i)=>{const o=function(l,m,w){const E=l.append("tspan").attr("x",2*t().state.padding).text(m);w||E.attr("dy",t().state.textHeight)},s=e.append("text").attr("x",2*t().state.padding).attr("y",t().state.textHeight+1.3*t().state.padding).attr("font-size",t().state.fontSize).attr("class","state-title").text(i.descriptions[0]).node().getBBox(),g=s.height,p=e.append("text").attr("x",t().state.padding).attr("y",g+t().state.padding*.4+t().state.dividerMargin+t().state.textHeight).attr("class","state-description");let a=!0,r=!0;i.descriptions.forEach(function(l){a||(o(p,l,r),r=!1),a=!1});const y=e.append("line").attr("x1",t().state.padding).attr("y1",t().state.padding+g+t().state.dividerMargin/2).attr("y2",t().state.padding+g+t().state.dividerMargin/2).attr("class","descr-divider"),x=p.node().getBBox(),d=Math.max(x.width,s.width);return y.attr("x2",d+3*t().state.padding),e.insert("rect",":first-child").attr("x",t().state.padding).attr("y",t().state.padding).attr("width",d+2*t().state.padding).attr("height",x.height+g+2*t().state.padding).attr("rx",t().state.radius),e},I=(e,i,o)=>{const c=t().state.padding,s=2*t().state.padding,g=e.node().getBBox(),p=g.width,a=g.x,r=e.append("text").attr("x",0).attr("y",t().state.titleShift).attr("font-size",t().state.fontSize).attr("class","state-title").text(i.id),x=r.node().getBBox().width+s;let d=Math.max(x,p);d===p&&(d=d+s);let l;const m=e.node().getBBox();i.doc,l=a-c,x>p&&(l=(p-d)/2+c),Math.abs(a-m.x)<c&&x>p&&(l=a-(x-p)/2);const w=1-t().state.textHeight;return e.insert("rect",":first-child").attr("x",l).attr("y",w).attr("class",o?"alt-composit":"composit").attr("width",d).attr("height",m.height+t().state.textHeight+t().state.titleShift+1).attr("rx","0"),r.attr("x",l+c),x<=p&&r.attr("x",a+(d-s)/2-x/2+c),e.insert("rect",":first-child").attr("x",l).attr("y",t().state.titleShift-t().state.textHeight-t().state.padding).attr("width",d).attr("height",t().state.textHeight*3).attr("rx",t().state.radius),e.insert("rect",":first-child").attr("x",l).attr("y",t().state.titleShift-t().state.textHeight-t().state.padding).attr("width",d).attr("height",m.height+3+2*t().state.textHeight).attr("rx",t().state.radius),e},_=e=>(e.append("circle").attr("class","end-state-outer").attr("r",t().state.sizeUnit+t().state.miniPadding).attr("cx",t().state.padding+t().state.sizeUnit+t().state.miniPadding).attr("cy",t().state.padding+t().state.sizeUnit+t().state.miniPadding),e.append("circle").attr("class","end-state-inner").attr("r",t().state.sizeUnit).attr("cx",t().state.padding+t().state.sizeUnit+2).attr("cy",t().state.padding+t().state.sizeUnit+2)),q=(e,i)=>{let o=t().state.forkWidth,c=t().state.forkHeight;if(i.parentId){let s=o;o=c,c=s}return e.append("rect").style("stroke","black").style("fill","black").attr("width",o).attr("height",c).attr("x",t().state.padding).attr("y",t().state.padding)},Z=(e,i,o,c)=>{let s=0;const g=c.append("text");g.style("text-anchor","start"),g.attr("class","noteText");let p=e.replace(/\r\n/g,"<br/>");p=p.replace(/\n/g,"<br/>");const a=p.split(T.lineBreakRegex);let r=1.25*t().state.noteMargin;for(const y of a){const x=y.trim();if(x.length>0){const d=g.append("tspan");if(d.text(x),r===0){const l=d.node().getBBox();r+=l.height}s+=r,d.attr("x",i+t().state.noteMargin),d.attr("y",o+s+1.25*t().state.noteMargin)}}return{textWidth:g.node().getBBox().width,textHeight:s}},j=(e,i)=>{i.attr("class","state-note");const o=i.append("rect").attr("x",0).attr("y",t().state.padding),c=i.append("g"),{textWidth:s,textHeight:g}=Z(e,0,0,c);return o.attr("height",g+2*t().state.noteMargin),o.attr("width",s+t().state.noteMargin*2),o},L=function(e,i){const o=i.id,c={id:o,label:i.id,width:0,height:0},s=e.append("g").attr("id",o).attr("class","stateGroup");i.type==="start"&&O(s),i.type==="end"&&_(s),(i.type==="fork"||i.type==="join")&&q(s,i),i.type==="note"&&j(i.note.text,s),i.type==="divider"&&X(s),i.type==="default"&&i.descriptions.length===0&&J(s,i),i.type==="default"&&i.descriptions.length>0&&Y(s,i);const g=s.node().getBBox();return c.width=g.width+2*t().state.padding,c.height=g.height+2*t().state.padding,c};let G=0;const K=function(e,i,o){const c=function(r){switch(r){case N.relationType.AGGREGATION:return"aggregation";case N.relationType.EXTENSION:return"extension";case N.relationType.COMPOSITION:return"composition";case N.relationType.DEPENDENCY:return"dependency"}};i.points=i.points.filter(r=>!Number.isNaN(r.y));const s=i.points,g=$().x(function(r){return r.x}).y(function(r){return r.y}).curve(v),p=e.append("path").attr("d",g(s)).attr("id","edge"+G).attr("class","transition");let a="";if(t().state.arrowMarkerAbsolute&&(a=window.location.protocol+"//"+window.location.host+window.location.pathname+window.location.search,a=a.replace(/\(/g,"\\("),a=a.replace(/\)/g,"\\)")),p.attr("marker-end","url("+a+"#"+c(N.relationType.DEPENDENCY)+"End)"),o.title!==void 0){const r=e.append("g").attr("class","stateLabel"),{x:y,y:x}=U.calcLabelPosition(i.points),d=T.getRows(o.title);let l=0;const m=[];let w=0,E=0;for(let u=0;u<=d.length;u++){const h=r.append("text").attr("text-anchor","middle").text(d[u]).attr("x",y).attr("y",x+l),f=h.node().getBBox();w=Math.max(w,f.width),E=Math.min(E,f.x),b.info(f.x,y,x+l),l===0&&(l=h.node().getBBox().height,b.info("Title height",l,x)),m.push(h)}let k=l*d.length;if(d.length>1){const u=(d.length-1)*l*.5;m.forEach((h,f)=>h.attr("y",x+f*l-u)),k=l*d.length}const n=r.node().getBBox();r.insert("rect",":first-child").attr("class","box").attr("x",y-w/2-t().state.padding/2).attr("y",x-k/2-t().state.padding/2-3.5).attr("width",w+t().state.padding).attr("height",k+t().state.padding),b.info(n)}G++};let B;const z={},Q=function(){},V=function(e){e.append("defs").append("marker").attr("id","dependencyEnd").attr("refX",19).attr("refY",7).attr("markerWidth",20).attr("markerHeight",28).attr("orient","auto").append("path").attr("d","M 19,7 L9,13 L14,7 L9,1 Z")},D=function(e,i,o,c){B=t().state;const s=t().securityLevel;let g;s==="sandbox"&&(g=H("#i"+i));const p=s==="sandbox"?H(g.nodes()[0].contentDocument.body):H("body"),a=s==="sandbox"?g.nodes()[0].contentDocument:document;b.debug("Rendering diagram "+e);const r=p.select(`[id='${i}']`);V(r);const y=c.db.getRootDoc();A(y,r,void 0,!1,p,a,c);const x=B.padding,d=r.node().getBBox(),l=d.width+x*2,m=d.height+x*2,w=l*1.75;R(r,m,w,B.useMaxWidth),r.attr("viewBox",`${d.x-B.padding}  ${d.y-B.padding} `+l+" "+m)},tt=e=>e?e.length*B.fontSizeFactor:1,A=(e,i,o,c,s,g,p)=>{const a=new C({compound:!0,multigraph:!0});let r,y=!0;for(r=0;r<e.length;r++)if(e[r].stmt==="relation"){y=!1;break}o?a.setGraph({rankdir:"LR",multigraph:!0,compound:!0,ranker:"tight-tree",ranksep:y?1:B.edgeLengthFactor,nodeSep:y?1:50,isMultiGraph:!0}):a.setGraph({rankdir:"TB",multigraph:!0,compound:!0,ranksep:y?1:B.edgeLengthFactor,nodeSep:y?1:50,ranker:"tight-tree",isMultiGraph:!0}),a.setDefaultEdgeLabel(function(){return{}}),p.db.extract(e);const x=p.db.getStates(),d=p.db.getRelations(),l=Object.keys(x);for(const n of l){const u=x[n];o&&(u.parentId=o);let h;if(u.doc){let f=i.append("g").attr("id",u.id).attr("class","stateGroup");h=A(u.doc,f,u.id,!c,s,g,p);{f=I(f,u,c);let S=f.node().getBBox();h.width=S.width,h.height=S.height+B.padding/2,z[u.id]={y:B.compositTitleSize}}}else h=L(i,u);if(u.note){const f={descriptions:[],id:u.id+"-note",note:u.note,type:"note"},S=L(i,f);u.note.position==="left of"?(a.setNode(h.id+"-note",S),a.setNode(h.id,h)):(a.setNode(h.id,h),a.setNode(h.id+"-note",S)),a.setParent(h.id,h.id+"-group"),a.setParent(h.id+"-note",h.id+"-group")}else a.setNode(h.id,h)}b.debug("Count=",a.nodeCount(),a);let m=0;d.forEach(function(n){m++,b.debug("Setting edge",n),a.setEdge(n.id1,n.id2,{relation:n,width:tt(n.title),height:B.labelHeight*T.getRows(n.title).length,labelpos:"c"},"id"+m)}),F(a),b.debug("Graph after layout",a.nodes());const w=i.node();a.nodes().forEach(function(n){n!==void 0&&a.node(n)!==void 0?(b.warn("Node "+n+": "+JSON.stringify(a.node(n))),s.select("#"+w.id+" #"+n).attr("transform","translate("+(a.node(n).x-a.node(n).width/2)+","+(a.node(n).y+(z[n]?z[n].y:0)-a.node(n).height/2)+" )"),s.select("#"+w.id+" #"+n).attr("data-x-shift",a.node(n).x-a.node(n).width/2),g.querySelectorAll("#"+w.id+" #"+n+" .divider").forEach(h=>{const f=h.parentElement;let S=0,M=0;f&&(f.parentElement&&(S=f.parentElement.getBBox().width),M=parseInt(f.getAttribute("data-x-shift"),10),Number.isNaN(M)&&(M=0)),h.setAttribute("x1",0-M+8),h.setAttribute("x2",S-M-8)})):b.debug("No Node "+n+": "+JSON.stringify(a.node(n)))});let E=w.getBBox();a.edges().forEach(function(n){n!==void 0&&a.edge(n)!==void 0&&(b.debug("Edge "+n.v+" -> "+n.w+": "+JSON.stringify(a.edge(n))),K(i,a.edge(n),a.edge(n).relation))}),E=w.getBBox();const k={id:o||"root",label:o||"root",width:0,height:0};return k.width=E.width+2*B.padding,k.height=E.height+2*B.padding,b.debug("Doc rendered",k,a),k},et={setConf:Q,draw:D},lt={parser:P,db:N,renderer:et,styles:W,init:e=>{e.state||(e.state={}),e.state.arrowMarkerAbsolute=e.arrowMarkerAbsolute,N.clear()}};export{lt as diagram};
diff --git a/assets/stateDiagram-v2-6c43c13a-CtOdsXqX.js b/assets/stateDiagram-v2-6c43c13a-C7zU9Dfv.js
similarity index 90%
rename from assets/stateDiagram-v2-6c43c13a-CtOdsXqX.js
rename to assets/stateDiagram-v2-6c43c13a-C7zU9Dfv.js
index c1c6053..9e58fd2 100644
--- a/assets/stateDiagram-v2-6c43c13a-CtOdsXqX.js
+++ b/assets/stateDiagram-v2-6c43c13a-C7zU9Dfv.js
@@ -1 +1 @@
-import{p as J,d as B,s as Q,D as H,a as X,S as Z,b as F,c as I}from"./styles-de3becd0-Bjk-EQ8n.js";import{G as tt}from"./graph-T5JS4vfK.js";import{l as E,c as g,h as x,z as et,i as ot,j as w}from"./mermaid.core-ChLYKTZm.js";import{r as st}from"./index-9620d214-B8uh0R2i.js";import"./layout-DUYLy6Ue.js";import"./app-B69Gl_S-.js";import"./clone-CI3kFeqi.js";import"./edges-5962ec63-B19hLEst.js";import"./createText-4a4f35c9-BuT3nXUz.js";import"./line-D0jG_HZ-.js";import"./array-BKyUJesY.js";import"./path-CbwjOpE9.js";const h="rect",C="rectWithTitle",nt="start",it="end",ct="divider",rt="roundedWithTitle",lt="note",at="noteGroup",_="statediagram",dt="state",Et=`${_}-${dt}`,U="transition",St="note",Tt="note-edge",pt=`${U} ${Tt}`,_t=`${_}-${St}`,ut="cluster",Dt=`${_}-${ut}`,bt="cluster-alt",ft=`${_}-${bt}`,V="parent",Y="note",At="state",N="----",ht=`${N}${Y}`,M=`${N}${V}`,m="fill:none",z="fill: #333",W="c",j="text",q="normal";let y={},d=0;const yt=function(t){const n=Object.keys(t);for(const e of n)t[e]},gt=function(t,n){return n.db.extract(n.db.getRootDocV2()),n.db.getClasses()};function $t(t){return t==null?"":t.classes?t.classes.join(" "):""}function R(t="",n=0,e="",i=N){const c=e!==null&&e.length>0?`${i}${e}`:"";return`${At}-${t}${c}-${n}`}const A=(t,n,e,i,c,r)=>{const o=e.id,u=$t(i[o]);if(o!=="root"){let T=h;e.start===!0&&(T=nt),e.start===!1&&(T=it),e.type!==H&&(T=e.type),y[o]||(y[o]={id:o,shape:T,description:w.sanitizeText(o,g()),classes:`${u} ${Et}`});const s=y[o];e.description&&(Array.isArray(s.description)?(s.shape=C,s.description.push(e.description)):s.description.length>0?(s.shape=C,s.description===o?s.description=[e.description]:s.description=[s.description,e.description]):(s.shape=h,s.description=e.description),s.description=w.sanitizeTextOrArray(s.description,g())),s.description.length===1&&s.shape===C&&(s.shape=h),!s.type&&e.doc&&(E.info("Setting cluster for ",o,G(e)),s.type="group",s.dir=G(e),s.shape=e.type===X?ct:rt,s.classes=s.classes+" "+Dt+" "+(r?ft:""));const p={labelStyle:"",shape:s.shape,labelText:s.description,classes:s.classes,style:"",id:o,dir:s.dir,domId:R(o,d),type:s.type,padding:15};if(p.centerLabel=!0,e.note){const l={labelStyle:"",shape:lt,labelText:e.note.text,classes:_t,style:"",id:o+ht+"-"+d,domId:R(o,d,Y),type:s.type,padding:15},a={labelStyle:"",shape:at,labelText:e.note.text,classes:s.classes,style:"",id:o+M,domId:R(o,d,V),type:"group",padding:0};d++;const D=o+M;t.setNode(D,a),t.setNode(l.id,l),t.setNode(o,p),t.setParent(o,D),t.setParent(l.id,D);let S=o,b=l.id;e.note.position==="left of"&&(S=l.id,b=o),t.setEdge(S,b,{arrowhead:"none",arrowType:"",style:m,labelStyle:"",classes:pt,arrowheadStyle:z,labelpos:W,labelType:j,thickness:q})}else t.setNode(o,p)}n&&n.id!=="root"&&(E.trace("Setting node ",o," to be child of its parent ",n.id),t.setParent(o,n.id)),e.doc&&(E.trace("Adding nodes children "),xt(t,e,e.doc,i,c,!r))},xt=(t,n,e,i,c,r)=>{E.trace("items",e),e.forEach(o=>{switch(o.stmt){case F:A(t,n,o,i,c,r);break;case H:A(t,n,o,i,c,r);break;case Z:{A(t,n,o.state1,i,c,r),A(t,n,o.state2,i,c,r);const u={id:"edge"+d,arrowhead:"normal",arrowTypeEnd:"arrow_barb",style:m,labelStyle:"",label:w.sanitizeText(o.description,g()),arrowheadStyle:z,labelpos:W,labelType:j,thickness:q,classes:U};t.setEdge(o.state1.id,o.state2.id,u,d),d++}break}})},G=(t,n=I)=>{let e=n;if(t.doc)for(let i=0;i<t.doc.length;i++){const c=t.doc[i];c.stmt==="dir"&&(e=c.value)}return e},Ct=async function(t,n,e,i){E.info("Drawing state diagram (v2)",n),y={},i.db.getDirection();const{securityLevel:c,state:r}=g(),o=r.nodeSpacing||50,u=r.rankSpacing||50;E.info(i.db.getRootDocV2()),i.db.extract(i.db.getRootDocV2()),E.info(i.db.getRootDocV2());const T=i.db.getStates(),s=new tt({multigraph:!0,compound:!0}).setGraph({rankdir:G(i.db.getRootDocV2()),nodesep:o,ranksep:u,marginx:8,marginy:8}).setDefaultEdgeLabel(function(){return{}});A(s,void 0,i.db.getRootDocV2(),T,i.db,!0);let p;c==="sandbox"&&(p=x("#i"+n));const l=c==="sandbox"?x(p.nodes()[0].contentDocument.body):x("body"),a=l.select(`[id="${n}"]`),D=l.select("#"+n+" g");await st(D,s,["barb"],_,n);const S=8;et.insertTitle(a,"statediagramTitleText",r.titleTopMargin,i.db.getDiagramTitle());const b=a.node().getBBox(),L=b.width+S*2,P=b.height+S*2;a.attr("class",_);const O=a.node().getBBox();ot(a,P,L,r.useMaxWidth);const k=`${O.x-S} ${O.y-S} ${L} ${P}`;E.debug(`viewBox ${k}`),a.attr("viewBox",k);const K=document.querySelectorAll('[id="'+n+'"] .edgeLabel .label');for(const $ of K){const v=$.getBBox(),f=document.createElementNS("http://www.w3.org/2000/svg",h);f.setAttribute("rx",0),f.setAttribute("ry",0),f.setAttribute("width",v.width),f.setAttribute("height",v.height),$.insertBefore(f,$.firstChild)}},Rt={setConf:yt,getClasses:gt,draw:Ct},Vt={parser:J,db:B,renderer:Rt,styles:Q,init:t=>{t.state||(t.state={}),t.state.arrowMarkerAbsolute=t.arrowMarkerAbsolute,B.clear()}};export{Vt as diagram};
+import{p as J,d as B,s as Q,D as H,a as X,S as Z,b as F,c as I}from"./styles-de3becd0-D7QN2-IT.js";import{G as tt}from"./graph-B1296pfd.js";import{l as E,c as g,h as x,z as et,i as ot,j as w}from"./mermaid.core-DNo_7Q2B.js";import{r as st}from"./index-9620d214-BlfbO5wW.js";import"./layout-qMafh1ee.js";import"./app-B4LGNJZ0.js";import"./clone-C3EvpqoY.js";import"./edges-5962ec63-ApWhby2b.js";import"./createText-4a4f35c9-CISzj231.js";import"./line-BqHmcuby.js";import"./array-BKyUJesY.js";import"./path-CbwjOpE9.js";const h="rect",C="rectWithTitle",nt="start",it="end",ct="divider",rt="roundedWithTitle",lt="note",at="noteGroup",_="statediagram",dt="state",Et=`${_}-${dt}`,U="transition",St="note",Tt="note-edge",pt=`${U} ${Tt}`,_t=`${_}-${St}`,ut="cluster",Dt=`${_}-${ut}`,bt="cluster-alt",ft=`${_}-${bt}`,V="parent",Y="note",At="state",N="----",ht=`${N}${Y}`,M=`${N}${V}`,m="fill:none",z="fill: #333",W="c",j="text",q="normal";let y={},d=0;const yt=function(t){const n=Object.keys(t);for(const e of n)t[e]},gt=function(t,n){return n.db.extract(n.db.getRootDocV2()),n.db.getClasses()};function $t(t){return t==null?"":t.classes?t.classes.join(" "):""}function R(t="",n=0,e="",i=N){const c=e!==null&&e.length>0?`${i}${e}`:"";return`${At}-${t}${c}-${n}`}const A=(t,n,e,i,c,r)=>{const o=e.id,u=$t(i[o]);if(o!=="root"){let T=h;e.start===!0&&(T=nt),e.start===!1&&(T=it),e.type!==H&&(T=e.type),y[o]||(y[o]={id:o,shape:T,description:w.sanitizeText(o,g()),classes:`${u} ${Et}`});const s=y[o];e.description&&(Array.isArray(s.description)?(s.shape=C,s.description.push(e.description)):s.description.length>0?(s.shape=C,s.description===o?s.description=[e.description]:s.description=[s.description,e.description]):(s.shape=h,s.description=e.description),s.description=w.sanitizeTextOrArray(s.description,g())),s.description.length===1&&s.shape===C&&(s.shape=h),!s.type&&e.doc&&(E.info("Setting cluster for ",o,G(e)),s.type="group",s.dir=G(e),s.shape=e.type===X?ct:rt,s.classes=s.classes+" "+Dt+" "+(r?ft:""));const p={labelStyle:"",shape:s.shape,labelText:s.description,classes:s.classes,style:"",id:o,dir:s.dir,domId:R(o,d),type:s.type,padding:15};if(p.centerLabel=!0,e.note){const l={labelStyle:"",shape:lt,labelText:e.note.text,classes:_t,style:"",id:o+ht+"-"+d,domId:R(o,d,Y),type:s.type,padding:15},a={labelStyle:"",shape:at,labelText:e.note.text,classes:s.classes,style:"",id:o+M,domId:R(o,d,V),type:"group",padding:0};d++;const D=o+M;t.setNode(D,a),t.setNode(l.id,l),t.setNode(o,p),t.setParent(o,D),t.setParent(l.id,D);let S=o,b=l.id;e.note.position==="left of"&&(S=l.id,b=o),t.setEdge(S,b,{arrowhead:"none",arrowType:"",style:m,labelStyle:"",classes:pt,arrowheadStyle:z,labelpos:W,labelType:j,thickness:q})}else t.setNode(o,p)}n&&n.id!=="root"&&(E.trace("Setting node ",o," to be child of its parent ",n.id),t.setParent(o,n.id)),e.doc&&(E.trace("Adding nodes children "),xt(t,e,e.doc,i,c,!r))},xt=(t,n,e,i,c,r)=>{E.trace("items",e),e.forEach(o=>{switch(o.stmt){case F:A(t,n,o,i,c,r);break;case H:A(t,n,o,i,c,r);break;case Z:{A(t,n,o.state1,i,c,r),A(t,n,o.state2,i,c,r);const u={id:"edge"+d,arrowhead:"normal",arrowTypeEnd:"arrow_barb",style:m,labelStyle:"",label:w.sanitizeText(o.description,g()),arrowheadStyle:z,labelpos:W,labelType:j,thickness:q,classes:U};t.setEdge(o.state1.id,o.state2.id,u,d),d++}break}})},G=(t,n=I)=>{let e=n;if(t.doc)for(let i=0;i<t.doc.length;i++){const c=t.doc[i];c.stmt==="dir"&&(e=c.value)}return e},Ct=async function(t,n,e,i){E.info("Drawing state diagram (v2)",n),y={},i.db.getDirection();const{securityLevel:c,state:r}=g(),o=r.nodeSpacing||50,u=r.rankSpacing||50;E.info(i.db.getRootDocV2()),i.db.extract(i.db.getRootDocV2()),E.info(i.db.getRootDocV2());const T=i.db.getStates(),s=new tt({multigraph:!0,compound:!0}).setGraph({rankdir:G(i.db.getRootDocV2()),nodesep:o,ranksep:u,marginx:8,marginy:8}).setDefaultEdgeLabel(function(){return{}});A(s,void 0,i.db.getRootDocV2(),T,i.db,!0);let p;c==="sandbox"&&(p=x("#i"+n));const l=c==="sandbox"?x(p.nodes()[0].contentDocument.body):x("body"),a=l.select(`[id="${n}"]`),D=l.select("#"+n+" g");await st(D,s,["barb"],_,n);const S=8;et.insertTitle(a,"statediagramTitleText",r.titleTopMargin,i.db.getDiagramTitle());const b=a.node().getBBox(),L=b.width+S*2,P=b.height+S*2;a.attr("class",_);const O=a.node().getBBox();ot(a,P,L,r.useMaxWidth);const k=`${O.x-S} ${O.y-S} ${L} ${P}`;E.debug(`viewBox ${k}`),a.attr("viewBox",k);const K=document.querySelectorAll('[id="'+n+'"] .edgeLabel .label');for(const $ of K){const v=$.getBBox(),f=document.createElementNS("http://www.w3.org/2000/svg",h);f.setAttribute("rx",0),f.setAttribute("ry",0),f.setAttribute("width",v.width),f.setAttribute("height",v.height),$.insertBefore(f,$.firstChild)}},Rt={setConf:yt,getClasses:gt,draw:Ct},Vt={parser:J,db:B,renderer:Rt,styles:Q,init:t=>{t.state||(t.state={}),t.state.arrowMarkerAbsolute=t.arrowMarkerAbsolute,B.clear()}};export{Vt as diagram};
diff --git "a/assets/steam\346\250\241\347\273\204\345\274\200\345\217\221.html-DQKsmuFu.js" "b/assets/steam\346\250\241\347\273\204\345\274\200\345\217\221.html-BnsNbJlM.js"
similarity index 98%
rename from "assets/steam\346\250\241\347\273\204\345\274\200\345\217\221.html-DQKsmuFu.js"
rename to "assets/steam\346\250\241\347\273\204\345\274\200\345\217\221.html-BnsNbJlM.js"
index 40c7896..c557edb 100644
--- "a/assets/steam\346\250\241\347\273\204\345\274\200\345\217\221.html-DQKsmuFu.js"
+++ "b/assets/steam\346\250\241\347\273\204\345\274\200\345\217\221.html-BnsNbJlM.js"
@@ -1 +1 @@
-import{_ as o,r as a,o as i,c as l,b as e,e as n,d as r}from"./app-B69Gl_S-.js";const s={},p=e("p",null,"This is the content of the game plugin post.",-1),h={href:"https://github.com/BepInEx/BepInEx",target:"_blank",rel:"noopener noreferrer"},c={href:"https://github.com/Perfare/AssetStudio",target:"_blank",rel:"noopener noreferrer"},m={href:"https://github.com/dnSpy/dnSpy",target:"_blank",rel:"noopener noreferrer"},d={href:"https://github.com/pardeike/Harmony",target:"_blank",rel:"noopener noreferrer"},u={href:"https://github.com/sinai-dev/UnityExplorer",target:"_blank",rel:"noopener noreferrer"},g=e("div",{class:"hint-container info"},[e("p",{class:"hint-container-title"},"相关信息"),e("p",null,"TODO")],-1);function _(f,y){const t=a("ExternalLinkIcon");return i(),l("div",null,[p,e("ul",null,[e("li",null,[e("a",h,[n("BepInEx"),r(t)])]),e("li",null,[e("a",c,[n("AssetStudioAssetStudio"),r(t)])]),e("li",null,[e("a",m,[n("dnSpy"),r(t)])]),e("li",null,[e("a",d,[n("Harmony"),r(t)])]),e("li",null,[e("a",u,[n("UnityExplorer"),r(t)])])]),g])}const E=o(s,[["render",_],["__file","steam模组开发.html.vue"]]),x=JSON.parse('{"path":"/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html","title":"Game Plugin","lang":"zh-CN","frontmatter":{"title":"Game Plugin","date":"2024-09-09T00:00:00.000Z","draft":false,"description":"This is the content of the game plugin post. BepInEx AssetStudioAssetStudio dnSpy Harmony UnityExplorer 相关信息 TODO","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"Game Plugin"}],["meta",{"property":"og:description","content":"This is the content of the game plugin post. BepInEx AssetStudioAssetStudio dnSpy Harmony UnityExplorer 相关信息 TODO"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:published_time","content":"2024-09-09T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"Game Plugin\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-09-09T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.12,"words":36},"filePathRelative":"tech/steam模组开发.md","localizedDate":"2024年9月9日","excerpt":"<p>This is the content of the game plugin post.</p>\\n<ul>\\n<li><a href=\\"https://github.com/BepInEx/BepInEx\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">BepInEx</a></li>\\n<li><a href=\\"https://github.com/Perfare/AssetStudio\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">AssetStudioAssetStudio</a></li>\\n<li><a href=\\"https://github.com/dnSpy/dnSpy\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">dnSpy</a></li>\\n<li><a href=\\"https://github.com/pardeike/Harmony\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">Harmony</a></li>\\n<li><a href=\\"https://github.com/sinai-dev/UnityExplorer\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">UnityExplorer</a></li>\\n</ul>","autoDesc":true}');export{E as comp,x as data};
+import{_ as o,r as a,o as i,c as l,b as e,e as n,d as r}from"./app-B4LGNJZ0.js";const s={},p=e("p",null,"This is the content of the game plugin post.",-1),h={href:"https://github.com/BepInEx/BepInEx",target:"_blank",rel:"noopener noreferrer"},c={href:"https://github.com/Perfare/AssetStudio",target:"_blank",rel:"noopener noreferrer"},m={href:"https://github.com/dnSpy/dnSpy",target:"_blank",rel:"noopener noreferrer"},d={href:"https://github.com/pardeike/Harmony",target:"_blank",rel:"noopener noreferrer"},u={href:"https://github.com/sinai-dev/UnityExplorer",target:"_blank",rel:"noopener noreferrer"},g=e("div",{class:"hint-container info"},[e("p",{class:"hint-container-title"},"相关信息"),e("p",null,"TODO")],-1);function _(f,y){const t=a("ExternalLinkIcon");return i(),l("div",null,[p,e("ul",null,[e("li",null,[e("a",h,[n("BepInEx"),r(t)])]),e("li",null,[e("a",c,[n("AssetStudioAssetStudio"),r(t)])]),e("li",null,[e("a",m,[n("dnSpy"),r(t)])]),e("li",null,[e("a",d,[n("Harmony"),r(t)])]),e("li",null,[e("a",u,[n("UnityExplorer"),r(t)])])]),g])}const E=o(s,[["render",_],["__file","steam模组开发.html.vue"]]),x=JSON.parse('{"path":"/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html","title":"Game Plugin","lang":"zh-CN","frontmatter":{"title":"Game Plugin","date":"2024-09-09T00:00:00.000Z","draft":false,"description":"This is the content of the game plugin post. BepInEx AssetStudioAssetStudio dnSpy Harmony UnityExplorer 相关信息 TODO","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"Game Plugin"}],["meta",{"property":"og:description","content":"This is the content of the game plugin post. BepInEx AssetStudioAssetStudio dnSpy Harmony UnityExplorer 相关信息 TODO"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:published_time","content":"2024-09-09T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"Game Plugin\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-09-09T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.12,"words":36},"filePathRelative":"tech/steam模组开发.md","localizedDate":"2024年9月9日","excerpt":"<p>This is the content of the game plugin post.</p>\\n<ul>\\n<li><a href=\\"https://github.com/BepInEx/BepInEx\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">BepInEx</a></li>\\n<li><a href=\\"https://github.com/Perfare/AssetStudio\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">AssetStudioAssetStudio</a></li>\\n<li><a href=\\"https://github.com/dnSpy/dnSpy\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">dnSpy</a></li>\\n<li><a href=\\"https://github.com/pardeike/Harmony\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">Harmony</a></li>\\n<li><a href=\\"https://github.com/sinai-dev/UnityExplorer\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">UnityExplorer</a></li>\\n</ul>","autoDesc":true}');export{E as comp,x as data};
diff --git a/assets/strategy.html-Cprd53d9.js b/assets/strategy.html-BeQd57Ga.js
similarity index 99%
rename from assets/strategy.html-Cprd53d9.js
rename to assets/strategy.html-BeQd57Ga.js
index 6df8bea..7231ad5 100644
--- a/assets/strategy.html-Cprd53d9.js
+++ b/assets/strategy.html-BeQd57Ga.js
@@ -1,4 +1,4 @@
-import{_ as n,o as s,c as a,f as t}from"./app-B69Gl_S-.js";const p={},e=t(`<h2 id="使用此设计模式的理由" tabindex="-1"><a class="header-anchor" href="#使用此设计模式的理由"><span>使用此设计模式的理由</span></a></h2><p>在这个示例程序中，我们使用了策略模式（Strategy Pattern）来实现不同的猜拳策略。策略模式的主要优点包括：</p><ol><li><strong>易于扩展</strong>：可以很容易地添加新的策略，而不需要修改现有的代码。</li><li><strong>提高代码的可读性和可维护性</strong>：将不同的算法封装在独立的类中，使得代码更加清晰。</li><li><strong>减少重复代码</strong>：通过使用策略模式，可以避免在多个地方重复相同的算法逻辑。</li></ol><h2 id="示例程序" tabindex="-1"><a class="header-anchor" href="#示例程序"><span>示例程序</span></a></h2><p>下面我们来看一段使用了 strategy 模式的示例程序。这段示例程序的功能是让电脑玩“猜拳&quot;游戏。</p><p>我们考虑了两种猜拳的策略。第一种策略是“如果这局猜拳获胜，那么下一局也出一样的手势&quot; (WinningStrategy), 这是一种稍微有些笨的策略；另外一种策略是“根据上一局的手势从概率上计算出下一局的手势&quot;（ ProbStrategy ）。</p><img src="https://www.plantuml.com/plantuml/svg/fLFBRiCW4BpxApWwYlW1dnBrqDmQAKrpY78WziP6jQ7YuTIg-kzTm2PswpwaNX3C3iFiWvKsJ1dRr4bUCwt9Xec2l2M4K88HmtDI8P9v_7WQuu8re3CyAIxAFkIuJwos42xuBGQMmvqIZCFJETuYx3sTwvrHKfIW7f6QLY64ZBEKDJ3Hamx0dd-WK7BXPML6CM6RCoX_syYTTvukXXoIzoG1PDmi-KBSx_UutcqUSDskrux5XG5rOJaGr606oiupbqJ0QqXmd8msjkZIAnVH6qPRoGid5Qf-u4AWWwY6CY0A7UL3GwvIJDDxKT1kOdl-vM2hvFcNvuVN-iR5MbAIMwL0cFbWnRMHgXkmuydFognJwWPaPvkqQWVwj6b_IQHc7QX-XDsCnlQ6sGqPPJ6tK5akScc5cHYlfOQlQ8cIdz5loewgwU3FdPtW180MfepveRpDewGq_D2CM0r9R1YbSeptDN1ef8J82lkAd_q3" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// hand.ts</span>
+import{_ as n,o as s,c as a,f as t}from"./app-B4LGNJZ0.js";const p={},e=t(`<h2 id="使用此设计模式的理由" tabindex="-1"><a class="header-anchor" href="#使用此设计模式的理由"><span>使用此设计模式的理由</span></a></h2><p>在这个示例程序中，我们使用了策略模式（Strategy Pattern）来实现不同的猜拳策略。策略模式的主要优点包括：</p><ol><li><strong>易于扩展</strong>：可以很容易地添加新的策略，而不需要修改现有的代码。</li><li><strong>提高代码的可读性和可维护性</strong>：将不同的算法封装在独立的类中，使得代码更加清晰。</li><li><strong>减少重复代码</strong>：通过使用策略模式，可以避免在多个地方重复相同的算法逻辑。</li></ol><h2 id="示例程序" tabindex="-1"><a class="header-anchor" href="#示例程序"><span>示例程序</span></a></h2><p>下面我们来看一段使用了 strategy 模式的示例程序。这段示例程序的功能是让电脑玩“猜拳&quot;游戏。</p><p>我们考虑了两种猜拳的策略。第一种策略是“如果这局猜拳获胜，那么下一局也出一样的手势&quot; (WinningStrategy), 这是一种稍微有些笨的策略；另外一种策略是“根据上一局的手势从概率上计算出下一局的手势&quot;（ ProbStrategy ）。</p><img src="https://www.plantuml.com/plantuml/svg/fLFBRiCW4BpxApWwYlW1dnBrqDmQAKrpY78WziP6jQ7YuTIg-kzTm2PswpwaNX3C3iFiWvKsJ1dRr4bUCwt9Xec2l2M4K88HmtDI8P9v_7WQuu8re3CyAIxAFkIuJwos42xuBGQMmvqIZCFJETuYx3sTwvrHKfIW7f6QLY64ZBEKDJ3Hamx0dd-WK7BXPML6CM6RCoX_syYTTvukXXoIzoG1PDmi-KBSx_UutcqUSDskrux5XG5rOJaGr606oiupbqJ0QqXmd8msjkZIAnVH6qPRoGid5Qf-u4AWWwY6CY0A7UL3GwvIJDDxKT1kOdl-vM2hvFcNvuVN-iR5MbAIMwL0cFbWnRMHgXkmuydFognJwWPaPvkqQWVwj6b_IQHc7QX-XDsCnlQ6sGqPPJ6tK5akScc5cHYlfOQlQ8cIdz5loewgwU3FdPtW180MfepveRpDewGq_D2CM0r9R1YbSeptDN1ef8J82lkAd_q3" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// hand.ts</span>
 <span class="token keyword">export</span> <span class="token keyword">enum</span> HandValue <span class="token punctuation">{</span>
   <span class="token constant">GUU</span> <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">,</span>
   <span class="token constant">CHO</span> <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">,</span>
diff --git a/assets/style.html-CXxr9xzn.js b/assets/style.html-4qtN5eOW.js
similarity index 98%
rename from assets/style.html-CXxr9xzn.js
rename to assets/style.html-4qtN5eOW.js
index 7991c84..df0a8db 100644
--- a/assets/style.html-CXxr9xzn.js
+++ b/assets/style.html-4qtN5eOW.js
@@ -1,4 +1,4 @@
-import{_ as e,o as t,c as i,f as n}from"./app-B69Gl_S-.js";const a={},o=n(`<h1 id="风格统一" tabindex="-1"><a class="header-anchor" href="#风格统一"><span>风格统一</span></a></h1><p>如何实现风格统一？ 可以使用*.editorconfig*文件来实现风格统一。</p><ol><li>安装EditorConfig插件 (部分IDE默认直接支持)</li><li>在项目根目录下创建.editorconfig文件，并添加以下内容：</li></ol><div class="language-text line-numbers-mode" data-ext="text" data-title="text"><pre class="language-text"><code>root = true
+import{_ as e,o as t,c as i,f as n}from"./app-B4LGNJZ0.js";const a={},o=n(`<h1 id="风格统一" tabindex="-1"><a class="header-anchor" href="#风格统一"><span>风格统一</span></a></h1><p>如何实现风格统一？ 可以使用*.editorconfig*文件来实现风格统一。</p><ol><li>安装EditorConfig插件 (部分IDE默认直接支持)</li><li>在项目根目录下创建.editorconfig文件，并添加以下内容：</li></ol><div class="language-text line-numbers-mode" data-ext="text" data-title="text"><pre class="language-text"><code>root = true
 [*]
 indent_style = space
 tab_width = 2
diff --git a/assets/styles-422bd1c9-CXxGUMW8.js b/assets/styles-422bd1c9-CFsDtXUv.js
similarity index 98%
rename from assets/styles-422bd1c9-CXxGUMW8.js
rename to assets/styles-422bd1c9-CFsDtXUv.js
index ae81c14..22d35c5 100644
--- a/assets/styles-422bd1c9-CXxGUMW8.js
+++ b/assets/styles-422bd1c9-CFsDtXUv.js
@@ -1,4 +1,4 @@
-import{G as R}from"./graph-T5JS4vfK.js";import{ab as z,ac as F,ad as j,ae as U,a9 as H,p as A,l as g,q as K,c as S,j as G,r as q,t as E,o as L,h as C,z as W,u as X,af as J}from"./mermaid.core-ChLYKTZm.js";import{r as Q}from"./index-9620d214-B8uh0R2i.js";import{c as Y}from"./channel-DJsAcM5I.js";function Z(e){return typeof e=="string"?new z([document.querySelectorAll(e)],[document.documentElement]):new z([j(e)],F)}function pe(e,l){return!!e.children(l).length}function be(e){return N(e.v)+":"+N(e.w)+":"+N(e.name)}var O=/:/g;function N(e){return e?String(e).replace(O,"\\:"):""}function ee(e,l){l&&e.attr("style",l)}function fe(e,l,c){l&&e.attr("class",l).attr("class",c+" "+e.attr("class"))}function ue(e,l){var c=l.graph();if(U(c)){var a=c.transition;if(H(a))return a(e)}return e}function te(e,l){var c=e.append("foreignObject").attr("width","100000"),a=c.append("xhtml:div");a.attr("xmlns","http://www.w3.org/1999/xhtml");var i=l.label;switch(typeof i){case"function":a.insert(i);break;case"object":a.insert(function(){return i});break;default:a.html(i)}ee(a,l.labelStyle),a.style("display","inline-block"),a.style("white-space","nowrap");var d=a.node().getBoundingClientRect();return c.attr("width",d.width).attr("height",d.height),c}const P={},re=function(e){const l=Object.keys(e);for(const c of l)P[c]=e[c]},V=async function(e,l,c,a,i,d){const u=a.select(`[id="${c}"]`),n=Object.keys(e);for(const p of n){const r=e[p];let y="default";r.classes.length>0&&(y=r.classes.join(" ")),y=y+" flowchart-label";const w=A(r.styles);let t=r.text!==void 0?r.text:r.id,s;if(g.info("vertex",r,r.labelType),r.labelType==="markdown")g.info("vertex",r,r.labelType);else if(K(S().flowchart.htmlLabels))s=te(u,{label:t}).node(),s.parentNode.removeChild(s);else{const k=i.createElementNS("http://www.w3.org/2000/svg","text");k.setAttribute("style",w.labelStyle.replace("color:","fill:"));const _=t.split(G.lineBreakRegex);for(const $ of _){const v=i.createElementNS("http://www.w3.org/2000/svg","tspan");v.setAttributeNS("http://www.w3.org/XML/1998/namespace","xml:space","preserve"),v.setAttribute("dy","1em"),v.setAttribute("x","1"),v.textContent=$,k.appendChild(v)}s=k}let b=0,o="";switch(r.type){case"round":b=5,o="rect";break;case"square":o="rect";break;case"diamond":o="question";break;case"hexagon":o="hexagon";break;case"odd":o="rect_left_inv_arrow";break;case"lean_right":o="lean_right";break;case"lean_left":o="lean_left";break;case"trapezoid":o="trapezoid";break;case"inv_trapezoid":o="inv_trapezoid";break;case"odd_right":o="rect_left_inv_arrow";break;case"circle":o="circle";break;case"ellipse":o="ellipse";break;case"stadium":o="stadium";break;case"subroutine":o="subroutine";break;case"cylinder":o="cylinder";break;case"group":o="rect";break;case"doublecircle":o="doublecircle";break;default:o="rect"}const T=await q(t,S());l.setNode(r.id,{labelStyle:w.labelStyle,shape:o,labelText:T,labelType:r.labelType,rx:b,ry:b,class:y,style:w.style,id:r.id,link:r.link,linkTarget:r.linkTarget,tooltip:d.db.getTooltip(r.id)||"",domId:d.db.lookUpDomId(r.id),haveCallback:r.haveCallback,width:r.type==="group"?500:void 0,dir:r.dir,type:r.type,props:r.props,padding:S().flowchart.padding}),g.info("setNode",{labelStyle:w.labelStyle,labelType:r.labelType,shape:o,labelText:T,rx:b,ry:b,class:y,style:w.style,id:r.id,domId:d.db.lookUpDomId(r.id),width:r.type==="group"?500:void 0,type:r.type,dir:r.dir,props:r.props,padding:S().flowchart.padding})}},M=async function(e,l,c){g.info("abc78 edges = ",e);let a=0,i={},d,u;if(e.defaultStyle!==void 0){const n=A(e.defaultStyle);d=n.style,u=n.labelStyle}for(const n of e){a++;const p="L-"+n.start+"-"+n.end;i[p]===void 0?(i[p]=0,g.info("abc78 new entry",p,i[p])):(i[p]++,g.info("abc78 new entry",p,i[p]));let r=p+"-"+i[p];g.info("abc78 new link id to be used is",p,r,i[p]);const y="LS-"+n.start,w="LE-"+n.end,t={style:"",labelStyle:""};switch(t.minlen=n.length||1,n.type==="arrow_open"?t.arrowhead="none":t.arrowhead="normal",t.arrowTypeStart="arrow_open",t.arrowTypeEnd="arrow_open",n.type){case"double_arrow_cross":t.arrowTypeStart="arrow_cross";case"arrow_cross":t.arrowTypeEnd="arrow_cross";break;case"double_arrow_point":t.arrowTypeStart="arrow_point";case"arrow_point":t.arrowTypeEnd="arrow_point";break;case"double_arrow_circle":t.arrowTypeStart="arrow_circle";case"arrow_circle":t.arrowTypeEnd="arrow_circle";break}let s="",b="";switch(n.stroke){case"normal":s="fill:none;",d!==void 0&&(s=d),u!==void 0&&(b=u),t.thickness="normal",t.pattern="solid";break;case"dotted":t.thickness="normal",t.pattern="dotted",t.style="fill:none;stroke-width:2px;stroke-dasharray:3;";break;case"thick":t.thickness="thick",t.pattern="solid",t.style="stroke-width: 3.5px;fill:none;";break;case"invisible":t.thickness="invisible",t.pattern="solid",t.style="stroke-width: 0;fill:none;";break}if(n.style!==void 0){const o=A(n.style);s=o.style,b=o.labelStyle}t.style=t.style+=s,t.labelStyle=t.labelStyle+=b,n.interpolate!==void 0?t.curve=E(n.interpolate,L):e.defaultInterpolate!==void 0?t.curve=E(e.defaultInterpolate,L):t.curve=E(P.curve,L),n.text===void 0?n.style!==void 0&&(t.arrowheadStyle="fill: #333"):(t.arrowheadStyle="fill: #333",t.labelpos="c"),t.labelType=n.labelType,t.label=await q(n.text.replace(G.lineBreakRegex,`
+import{G as R}from"./graph-B1296pfd.js";import{ab as z,ac as F,ad as j,ae as U,a9 as H,p as A,l as g,q as K,c as S,j as G,r as q,t as E,o as L,h as C,z as W,u as X,af as J}from"./mermaid.core-DNo_7Q2B.js";import{r as Q}from"./index-9620d214-BlfbO5wW.js";import{c as Y}from"./channel-yU22lAlC.js";function Z(e){return typeof e=="string"?new z([document.querySelectorAll(e)],[document.documentElement]):new z([j(e)],F)}function pe(e,l){return!!e.children(l).length}function be(e){return N(e.v)+":"+N(e.w)+":"+N(e.name)}var O=/:/g;function N(e){return e?String(e).replace(O,"\\:"):""}function ee(e,l){l&&e.attr("style",l)}function fe(e,l,c){l&&e.attr("class",l).attr("class",c+" "+e.attr("class"))}function ue(e,l){var c=l.graph();if(U(c)){var a=c.transition;if(H(a))return a(e)}return e}function te(e,l){var c=e.append("foreignObject").attr("width","100000"),a=c.append("xhtml:div");a.attr("xmlns","http://www.w3.org/1999/xhtml");var i=l.label;switch(typeof i){case"function":a.insert(i);break;case"object":a.insert(function(){return i});break;default:a.html(i)}ee(a,l.labelStyle),a.style("display","inline-block"),a.style("white-space","nowrap");var d=a.node().getBoundingClientRect();return c.attr("width",d.width).attr("height",d.height),c}const P={},re=function(e){const l=Object.keys(e);for(const c of l)P[c]=e[c]},V=async function(e,l,c,a,i,d){const u=a.select(`[id="${c}"]`),n=Object.keys(e);for(const p of n){const r=e[p];let y="default";r.classes.length>0&&(y=r.classes.join(" ")),y=y+" flowchart-label";const w=A(r.styles);let t=r.text!==void 0?r.text:r.id,s;if(g.info("vertex",r,r.labelType),r.labelType==="markdown")g.info("vertex",r,r.labelType);else if(K(S().flowchart.htmlLabels))s=te(u,{label:t}).node(),s.parentNode.removeChild(s);else{const k=i.createElementNS("http://www.w3.org/2000/svg","text");k.setAttribute("style",w.labelStyle.replace("color:","fill:"));const _=t.split(G.lineBreakRegex);for(const $ of _){const v=i.createElementNS("http://www.w3.org/2000/svg","tspan");v.setAttributeNS("http://www.w3.org/XML/1998/namespace","xml:space","preserve"),v.setAttribute("dy","1em"),v.setAttribute("x","1"),v.textContent=$,k.appendChild(v)}s=k}let b=0,o="";switch(r.type){case"round":b=5,o="rect";break;case"square":o="rect";break;case"diamond":o="question";break;case"hexagon":o="hexagon";break;case"odd":o="rect_left_inv_arrow";break;case"lean_right":o="lean_right";break;case"lean_left":o="lean_left";break;case"trapezoid":o="trapezoid";break;case"inv_trapezoid":o="inv_trapezoid";break;case"odd_right":o="rect_left_inv_arrow";break;case"circle":o="circle";break;case"ellipse":o="ellipse";break;case"stadium":o="stadium";break;case"subroutine":o="subroutine";break;case"cylinder":o="cylinder";break;case"group":o="rect";break;case"doublecircle":o="doublecircle";break;default:o="rect"}const T=await q(t,S());l.setNode(r.id,{labelStyle:w.labelStyle,shape:o,labelText:T,labelType:r.labelType,rx:b,ry:b,class:y,style:w.style,id:r.id,link:r.link,linkTarget:r.linkTarget,tooltip:d.db.getTooltip(r.id)||"",domId:d.db.lookUpDomId(r.id),haveCallback:r.haveCallback,width:r.type==="group"?500:void 0,dir:r.dir,type:r.type,props:r.props,padding:S().flowchart.padding}),g.info("setNode",{labelStyle:w.labelStyle,labelType:r.labelType,shape:o,labelText:T,rx:b,ry:b,class:y,style:w.style,id:r.id,domId:d.db.lookUpDomId(r.id),width:r.type==="group"?500:void 0,type:r.type,dir:r.dir,props:r.props,padding:S().flowchart.padding})}},M=async function(e,l,c){g.info("abc78 edges = ",e);let a=0,i={},d,u;if(e.defaultStyle!==void 0){const n=A(e.defaultStyle);d=n.style,u=n.labelStyle}for(const n of e){a++;const p="L-"+n.start+"-"+n.end;i[p]===void 0?(i[p]=0,g.info("abc78 new entry",p,i[p])):(i[p]++,g.info("abc78 new entry",p,i[p]));let r=p+"-"+i[p];g.info("abc78 new link id to be used is",p,r,i[p]);const y="LS-"+n.start,w="LE-"+n.end,t={style:"",labelStyle:""};switch(t.minlen=n.length||1,n.type==="arrow_open"?t.arrowhead="none":t.arrowhead="normal",t.arrowTypeStart="arrow_open",t.arrowTypeEnd="arrow_open",n.type){case"double_arrow_cross":t.arrowTypeStart="arrow_cross";case"arrow_cross":t.arrowTypeEnd="arrow_cross";break;case"double_arrow_point":t.arrowTypeStart="arrow_point";case"arrow_point":t.arrowTypeEnd="arrow_point";break;case"double_arrow_circle":t.arrowTypeStart="arrow_circle";case"arrow_circle":t.arrowTypeEnd="arrow_circle";break}let s="",b="";switch(n.stroke){case"normal":s="fill:none;",d!==void 0&&(s=d),u!==void 0&&(b=u),t.thickness="normal",t.pattern="solid";break;case"dotted":t.thickness="normal",t.pattern="dotted",t.style="fill:none;stroke-width:2px;stroke-dasharray:3;";break;case"thick":t.thickness="thick",t.pattern="solid",t.style="stroke-width: 3.5px;fill:none;";break;case"invisible":t.thickness="invisible",t.pattern="solid",t.style="stroke-width: 0;fill:none;";break}if(n.style!==void 0){const o=A(n.style);s=o.style,b=o.labelStyle}t.style=t.style+=s,t.labelStyle=t.labelStyle+=b,n.interpolate!==void 0?t.curve=E(n.interpolate,L):e.defaultInterpolate!==void 0?t.curve=E(e.defaultInterpolate,L):t.curve=E(P.curve,L),n.text===void 0?n.style!==void 0&&(t.arrowheadStyle="fill: #333"):(t.arrowheadStyle="fill: #333",t.labelpos="c"),t.labelType=n.labelType,t.label=await q(n.text.replace(G.lineBreakRegex,`
 `),S()),n.style===void 0&&(t.style=t.style||"stroke: #333; stroke-width: 1.5px;fill:none;"),t.labelStyle=t.labelStyle.replace("color:","fill:"),t.id=r,t.classes="flowchart-link "+y+" "+w,l.setEdge(n.start,n.end,t,a)}},le=function(e,l){return l.db.getClasses()},ae=async function(e,l,c,a){g.info("Drawing flowchart");let i=a.db.getDirection();i===void 0&&(i="TD");const{securityLevel:d,flowchart:u}=S(),n=u.nodeSpacing||50,p=u.rankSpacing||50;let r;d==="sandbox"&&(r=C("#i"+l));const y=d==="sandbox"?C(r.nodes()[0].contentDocument.body):C("body"),w=d==="sandbox"?r.nodes()[0].contentDocument:document,t=new R({multigraph:!0,compound:!0}).setGraph({rankdir:i,nodesep:n,ranksep:p,marginx:0,marginy:0}).setDefaultEdgeLabel(function(){return{}});let s;const b=a.db.getSubGraphs();g.info("Subgraphs - ",b);for(let f=b.length-1;f>=0;f--)s=b[f],g.info("Subgraph - ",s),a.db.addVertex(s.id,{text:s.title,type:s.labelType},"group",void 0,s.classes,s.dir);const o=a.db.getVertices(),T=a.db.getEdges();g.info("Edges",T);let k=0;for(k=b.length-1;k>=0;k--){s=b[k],Z("cluster").append("text");for(let f=0;f<s.nodes.length;f++)g.info("Setting up subgraphs",s.nodes[f],s.id),t.setParent(s.nodes[f],s.id)}await V(o,t,l,y,w,a),await M(T,t);const _=y.select(`[id="${l}"]`),$=y.select("#"+l+" g");if(await Q($,t,["point","circle","cross"],"flowchart",l),W.insertTitle(_,"flowchartTitleText",u.titleTopMargin,a.db.getDiagramTitle()),X(t,_,u.diagramPadding,u.useMaxWidth),a.db.indexNodes("subGraph"+k),!u.htmlLabels){const f=w.querySelectorAll('[id="'+l+'"] .edgeLabel .label');for(const x of f){const m=x.getBBox(),h=w.createElementNS("http://www.w3.org/2000/svg","rect");h.setAttribute("rx",0),h.setAttribute("ry",0),h.setAttribute("width",m.width),h.setAttribute("height",m.height),x.insertBefore(h,x.firstChild)}}Object.keys(o).forEach(function(f){const x=o[f];if(x.link){const m=C("#"+l+' [id="'+f+'"]');if(m){const h=w.createElementNS("http://www.w3.org/2000/svg","a");h.setAttributeNS("http://www.w3.org/2000/svg","class",x.classes.join(" ")),h.setAttributeNS("http://www.w3.org/2000/svg","href",x.link),h.setAttributeNS("http://www.w3.org/2000/svg","rel","noopener"),d==="sandbox"?h.setAttributeNS("http://www.w3.org/2000/svg","target","_top"):x.linkTarget&&h.setAttributeNS("http://www.w3.org/2000/svg","target",x.linkTarget);const B=m.insert(function(){return h},":first-child"),I=m.select(".label-container");I&&B.append(function(){return I.node()});const D=m.select(".label");D&&B.append(function(){return D.node()})}}})},we={setConf:re,addVertices:V,addEdges:M,getClasses:le,draw:ae},oe=(e,l)=>{const c=Y,a=c(e,"r"),i=c(e,"g"),d=c(e,"b");return J(a,i,d,l)},ne=e=>`.label {
     font-family: ${e.fontFamily};
     color: ${e.nodeTextColor||e.textColor};
diff --git a/assets/styles-de3becd0-Bjk-EQ8n.js b/assets/styles-de3becd0-D7QN2-IT.js
similarity index 99%
rename from assets/styles-de3becd0-Bjk-EQ8n.js
rename to assets/styles-de3becd0-D7QN2-IT.js
index 5347aaa..dde6c9a 100644
--- a/assets/styles-de3becd0-Bjk-EQ8n.js
+++ b/assets/styles-de3becd0-D7QN2-IT.js
@@ -1,4 +1,4 @@
-import{c as Y,g as Ut,s as zt,a as Mt,b as Ht,x as Xt,y as Kt,l as D,j as ot,A as Wt,b3 as Jt}from"./mermaid.core-ChLYKTZm.js";var gt=function(){var t=function(C,r,n,i){for(n=n||{},i=C.length;i--;n[C[i]]=r);return n},s=[1,2],a=[1,3],h=[1,4],f=[2,4],d=[1,9],y=[1,11],k=[1,15],u=[1,16],E=[1,17],T=[1,18],R=[1,30],G=[1,19],j=[1,20],U=[1,21],z=[1,22],M=[1,23],H=[1,25],X=[1,26],K=[1,27],W=[1,28],J=[1,29],q=[1,32],Q=[1,33],Z=[1,34],tt=[1,35],w=[1,31],c=[1,4,5,15,16,18,20,21,23,24,25,26,27,28,32,34,36,37,41,44,45,46,47,50],et=[1,4,5,13,14,15,16,18,20,21,23,24,25,26,27,28,32,34,36,37,41,44,45,46,47,50],Dt=[4,5,15,16,18,20,21,23,24,25,26,27,28,32,34,36,37,41,44,45,46,47,50],ht={trace:function(){},yy:{},symbols_:{error:2,start:3,SPACE:4,NL:5,SD:6,document:7,line:8,statement:9,classDefStatement:10,cssClassStatement:11,idStatement:12,DESCR:13,"-->":14,HIDE_EMPTY:15,scale:16,WIDTH:17,COMPOSIT_STATE:18,STRUCT_START:19,STRUCT_STOP:20,STATE_DESCR:21,AS:22,ID:23,FORK:24,JOIN:25,CHOICE:26,CONCURRENT:27,note:28,notePosition:29,NOTE_TEXT:30,direction:31,acc_title:32,acc_title_value:33,acc_descr:34,acc_descr_value:35,acc_descr_multiline_value:36,classDef:37,CLASSDEF_ID:38,CLASSDEF_STYLEOPTS:39,DEFAULT:40,class:41,CLASSENTITY_IDS:42,STYLECLASS:43,direction_tb:44,direction_bt:45,direction_rl:46,direction_lr:47,eol:48,";":49,EDGE_STATE:50,STYLE_SEPARATOR:51,left_of:52,right_of:53,$accept:0,$end:1},terminals_:{2:"error",4:"SPACE",5:"NL",6:"SD",13:"DESCR",14:"-->",15:"HIDE_EMPTY",16:"scale",17:"WIDTH",18:"COMPOSIT_STATE",19:"STRUCT_START",20:"STRUCT_STOP",21:"STATE_DESCR",22:"AS",23:"ID",24:"FORK",25:"JOIN",26:"CHOICE",27:"CONCURRENT",28:"note",30:"NOTE_TEXT",32:"acc_title",33:"acc_title_value",34:"acc_descr",35:"acc_descr_value",36:"acc_descr_multiline_value",37:"classDef",38:"CLASSDEF_ID",39:"CLASSDEF_STYLEOPTS",40:"DEFAULT",41:"class",42:"CLASSENTITY_IDS",43:"STYLECLASS",44:"direction_tb",45:"direction_bt",46:"direction_rl",47:"direction_lr",49:";",50:"EDGE_STATE",51:"STYLE_SEPARATOR",52:"left_of",53:"right_of"},productions_:[0,[3,2],[3,2],[3,2],[7,0],[7,2],[8,2],[8,1],[8,1],[9,1],[9,1],[9,1],[9,2],[9,3],[9,4],[9,1],[9,2],[9,1],[9,4],[9,3],[9,6],[9,1],[9,1],[9,1],[9,1],[9,4],[9,4],[9,1],[9,2],[9,2],[9,1],[10,3],[10,3],[11,3],[31,1],[31,1],[31,1],[31,1],[48,1],[48,1],[12,1],[12,1],[12,3],[12,3],[29,1],[29,1]],performAction:function(r,n,i,o,p,e,$){var l=e.length-1;switch(p){case 3:return o.setRootDoc(e[l]),e[l];case 4:this.$=[];break;case 5:e[l]!="nl"&&(e[l-1].push(e[l]),this.$=e[l-1]);break;case 6:case 7:this.$=e[l];break;case 8:this.$="nl";break;case 11:this.$=e[l];break;case 12:const B=e[l-1];B.description=o.trimColon(e[l]),this.$=B;break;case 13:this.$={stmt:"relation",state1:e[l-2],state2:e[l]};break;case 14:const ft=o.trimColon(e[l]);this.$={stmt:"relation",state1:e[l-3],state2:e[l-1],description:ft};break;case 18:this.$={stmt:"state",id:e[l-3],type:"default",description:"",doc:e[l-1]};break;case 19:var A=e[l],O=e[l-2].trim();if(e[l].match(":")){var st=e[l].split(":");A=st[0],O=[O,st[1]]}this.$={stmt:"state",id:A,type:"default",description:O};break;case 20:this.$={stmt:"state",id:e[l-3],type:"default",description:e[l-5],doc:e[l-1]};break;case 21:this.$={stmt:"state",id:e[l],type:"fork"};break;case 22:this.$={stmt:"state",id:e[l],type:"join"};break;case 23:this.$={stmt:"state",id:e[l],type:"choice"};break;case 24:this.$={stmt:"state",id:o.getDividerId(),type:"divider"};break;case 25:this.$={stmt:"state",id:e[l-1].trim(),note:{position:e[l-2].trim(),text:e[l].trim()}};break;case 28:this.$=e[l].trim(),o.setAccTitle(this.$);break;case 29:case 30:this.$=e[l].trim(),o.setAccDescription(this.$);break;case 31:case 32:this.$={stmt:"classDef",id:e[l-1].trim(),classes:e[l].trim()};break;case 33:this.$={stmt:"applyClass",id:e[l-1].trim(),styleClass:e[l].trim()};break;case 34:o.setDirection("TB"),this.$={stmt:"dir",value:"TB"};break;case 35:o.setDirection("BT"),this.$={stmt:"dir",value:"BT"};break;case 36:o.setDirection("RL"),this.$={stmt:"dir",value:"RL"};break;case 37:o.setDirection("LR"),this.$={stmt:"dir",value:"LR"};break;case 40:case 41:this.$={stmt:"state",id:e[l].trim(),type:"default",description:""};break;case 42:this.$={stmt:"state",id:e[l-2].trim(),classes:[e[l].trim()],type:"default",description:""};break;case 43:this.$={stmt:"state",id:e[l-2].trim(),classes:[e[l].trim()],type:"default",description:""};break}},table:[{3:1,4:s,5:a,6:h},{1:[3]},{3:5,4:s,5:a,6:h},{3:6,4:s,5:a,6:h},t([1,4,5,15,16,18,21,23,24,25,26,27,28,32,34,36,37,41,44,45,46,47,50],f,{7:7}),{1:[2,1]},{1:[2,2]},{1:[2,3],4:d,5:y,8:8,9:10,10:12,11:13,12:14,15:k,16:u,18:E,21:T,23:R,24:G,25:j,26:U,27:z,28:M,31:24,32:H,34:X,36:K,37:W,41:J,44:q,45:Q,46:Z,47:tt,50:w},t(c,[2,5]),{9:36,10:12,11:13,12:14,15:k,16:u,18:E,21:T,23:R,24:G,25:j,26:U,27:z,28:M,31:24,32:H,34:X,36:K,37:W,41:J,44:q,45:Q,46:Z,47:tt,50:w},t(c,[2,7]),t(c,[2,8]),t(c,[2,9]),t(c,[2,10]),t(c,[2,11],{13:[1,37],14:[1,38]}),t(c,[2,15]),{17:[1,39]},t(c,[2,17],{19:[1,40]}),{22:[1,41]},t(c,[2,21]),t(c,[2,22]),t(c,[2,23]),t(c,[2,24]),{29:42,30:[1,43],52:[1,44],53:[1,45]},t(c,[2,27]),{33:[1,46]},{35:[1,47]},t(c,[2,30]),{38:[1,48],40:[1,49]},{42:[1,50]},t(et,[2,40],{51:[1,51]}),t(et,[2,41],{51:[1,52]}),t(c,[2,34]),t(c,[2,35]),t(c,[2,36]),t(c,[2,37]),t(c,[2,6]),t(c,[2,12]),{12:53,23:R,50:w},t(c,[2,16]),t(Dt,f,{7:54}),{23:[1,55]},{23:[1,56]},{22:[1,57]},{23:[2,44]},{23:[2,45]},t(c,[2,28]),t(c,[2,29]),{39:[1,58]},{39:[1,59]},{43:[1,60]},{23:[1,61]},{23:[1,62]},t(c,[2,13],{13:[1,63]}),{4:d,5:y,8:8,9:10,10:12,11:13,12:14,15:k,16:u,18:E,20:[1,64],21:T,23:R,24:G,25:j,26:U,27:z,28:M,31:24,32:H,34:X,36:K,37:W,41:J,44:q,45:Q,46:Z,47:tt,50:w},t(c,[2,19],{19:[1,65]}),{30:[1,66]},{23:[1,67]},t(c,[2,31]),t(c,[2,32]),t(c,[2,33]),t(et,[2,42]),t(et,[2,43]),t(c,[2,14]),t(c,[2,18]),t(Dt,f,{7:68}),t(c,[2,25]),t(c,[2,26]),{4:d,5:y,8:8,9:10,10:12,11:13,12:14,15:k,16:u,18:E,20:[1,69],21:T,23:R,24:G,25:j,26:U,27:z,28:M,31:24,32:H,34:X,36:K,37:W,41:J,44:q,45:Q,46:Z,47:tt,50:w},t(c,[2,20])],defaultActions:{5:[2,1],6:[2,2],44:[2,44],45:[2,45]},parseError:function(r,n){if(n.recoverable)this.trace(r);else{var i=new Error(r);throw i.hash=n,i}},parse:function(r){var n=this,i=[0],o=[],p=[null],e=[],$=this.table,l="",A=0,O=0,st=2,B=1,ft=e.slice.call(arguments,1),S=Object.create(this.lexer),v={yy:{}};for(var dt in this.yy)Object.prototype.hasOwnProperty.call(this.yy,dt)&&(v.yy[dt]=this.yy[dt]);S.setInput(r,v.yy),v.yy.lexer=S,v.yy.parser=this,typeof S.yylloc>"u"&&(S.yylloc={});var yt=S.yylloc;e.push(yt);var Gt=S.options&&S.options.ranges;typeof v.yy.parseError=="function"?this.parseError=v.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function jt(){var x;return x=o.pop()||S.lex()||B,typeof x!="number"&&(x instanceof Array&&(o=x,x=o.pop()),x=n.symbols_[x]||x),x}for(var _,L,m,pt,N={},it,b,Ct,rt;;){if(L=i[i.length-1],this.defaultActions[L]?m=this.defaultActions[L]:((_===null||typeof _>"u")&&(_=jt()),m=$[L]&&$[L][_]),typeof m>"u"||!m.length||!m[0]){var St="";rt=[];for(it in $[L])this.terminals_[it]&&it>st&&rt.push("'"+this.terminals_[it]+"'");S.showPosition?St="Parse error on line "+(A+1)+`:
+import{c as Y,g as Ut,s as zt,a as Mt,b as Ht,x as Xt,y as Kt,l as D,j as ot,A as Wt,b3 as Jt}from"./mermaid.core-DNo_7Q2B.js";var gt=function(){var t=function(C,r,n,i){for(n=n||{},i=C.length;i--;n[C[i]]=r);return n},s=[1,2],a=[1,3],h=[1,4],f=[2,4],d=[1,9],y=[1,11],k=[1,15],u=[1,16],E=[1,17],T=[1,18],R=[1,30],G=[1,19],j=[1,20],U=[1,21],z=[1,22],M=[1,23],H=[1,25],X=[1,26],K=[1,27],W=[1,28],J=[1,29],q=[1,32],Q=[1,33],Z=[1,34],tt=[1,35],w=[1,31],c=[1,4,5,15,16,18,20,21,23,24,25,26,27,28,32,34,36,37,41,44,45,46,47,50],et=[1,4,5,13,14,15,16,18,20,21,23,24,25,26,27,28,32,34,36,37,41,44,45,46,47,50],Dt=[4,5,15,16,18,20,21,23,24,25,26,27,28,32,34,36,37,41,44,45,46,47,50],ht={trace:function(){},yy:{},symbols_:{error:2,start:3,SPACE:4,NL:5,SD:6,document:7,line:8,statement:9,classDefStatement:10,cssClassStatement:11,idStatement:12,DESCR:13,"-->":14,HIDE_EMPTY:15,scale:16,WIDTH:17,COMPOSIT_STATE:18,STRUCT_START:19,STRUCT_STOP:20,STATE_DESCR:21,AS:22,ID:23,FORK:24,JOIN:25,CHOICE:26,CONCURRENT:27,note:28,notePosition:29,NOTE_TEXT:30,direction:31,acc_title:32,acc_title_value:33,acc_descr:34,acc_descr_value:35,acc_descr_multiline_value:36,classDef:37,CLASSDEF_ID:38,CLASSDEF_STYLEOPTS:39,DEFAULT:40,class:41,CLASSENTITY_IDS:42,STYLECLASS:43,direction_tb:44,direction_bt:45,direction_rl:46,direction_lr:47,eol:48,";":49,EDGE_STATE:50,STYLE_SEPARATOR:51,left_of:52,right_of:53,$accept:0,$end:1},terminals_:{2:"error",4:"SPACE",5:"NL",6:"SD",13:"DESCR",14:"-->",15:"HIDE_EMPTY",16:"scale",17:"WIDTH",18:"COMPOSIT_STATE",19:"STRUCT_START",20:"STRUCT_STOP",21:"STATE_DESCR",22:"AS",23:"ID",24:"FORK",25:"JOIN",26:"CHOICE",27:"CONCURRENT",28:"note",30:"NOTE_TEXT",32:"acc_title",33:"acc_title_value",34:"acc_descr",35:"acc_descr_value",36:"acc_descr_multiline_value",37:"classDef",38:"CLASSDEF_ID",39:"CLASSDEF_STYLEOPTS",40:"DEFAULT",41:"class",42:"CLASSENTITY_IDS",43:"STYLECLASS",44:"direction_tb",45:"direction_bt",46:"direction_rl",47:"direction_lr",49:";",50:"EDGE_STATE",51:"STYLE_SEPARATOR",52:"left_of",53:"right_of"},productions_:[0,[3,2],[3,2],[3,2],[7,0],[7,2],[8,2],[8,1],[8,1],[9,1],[9,1],[9,1],[9,2],[9,3],[9,4],[9,1],[9,2],[9,1],[9,4],[9,3],[9,6],[9,1],[9,1],[9,1],[9,1],[9,4],[9,4],[9,1],[9,2],[9,2],[9,1],[10,3],[10,3],[11,3],[31,1],[31,1],[31,1],[31,1],[48,1],[48,1],[12,1],[12,1],[12,3],[12,3],[29,1],[29,1]],performAction:function(r,n,i,o,p,e,$){var l=e.length-1;switch(p){case 3:return o.setRootDoc(e[l]),e[l];case 4:this.$=[];break;case 5:e[l]!="nl"&&(e[l-1].push(e[l]),this.$=e[l-1]);break;case 6:case 7:this.$=e[l];break;case 8:this.$="nl";break;case 11:this.$=e[l];break;case 12:const B=e[l-1];B.description=o.trimColon(e[l]),this.$=B;break;case 13:this.$={stmt:"relation",state1:e[l-2],state2:e[l]};break;case 14:const ft=o.trimColon(e[l]);this.$={stmt:"relation",state1:e[l-3],state2:e[l-1],description:ft};break;case 18:this.$={stmt:"state",id:e[l-3],type:"default",description:"",doc:e[l-1]};break;case 19:var A=e[l],O=e[l-2].trim();if(e[l].match(":")){var st=e[l].split(":");A=st[0],O=[O,st[1]]}this.$={stmt:"state",id:A,type:"default",description:O};break;case 20:this.$={stmt:"state",id:e[l-3],type:"default",description:e[l-5],doc:e[l-1]};break;case 21:this.$={stmt:"state",id:e[l],type:"fork"};break;case 22:this.$={stmt:"state",id:e[l],type:"join"};break;case 23:this.$={stmt:"state",id:e[l],type:"choice"};break;case 24:this.$={stmt:"state",id:o.getDividerId(),type:"divider"};break;case 25:this.$={stmt:"state",id:e[l-1].trim(),note:{position:e[l-2].trim(),text:e[l].trim()}};break;case 28:this.$=e[l].trim(),o.setAccTitle(this.$);break;case 29:case 30:this.$=e[l].trim(),o.setAccDescription(this.$);break;case 31:case 32:this.$={stmt:"classDef",id:e[l-1].trim(),classes:e[l].trim()};break;case 33:this.$={stmt:"applyClass",id:e[l-1].trim(),styleClass:e[l].trim()};break;case 34:o.setDirection("TB"),this.$={stmt:"dir",value:"TB"};break;case 35:o.setDirection("BT"),this.$={stmt:"dir",value:"BT"};break;case 36:o.setDirection("RL"),this.$={stmt:"dir",value:"RL"};break;case 37:o.setDirection("LR"),this.$={stmt:"dir",value:"LR"};break;case 40:case 41:this.$={stmt:"state",id:e[l].trim(),type:"default",description:""};break;case 42:this.$={stmt:"state",id:e[l-2].trim(),classes:[e[l].trim()],type:"default",description:""};break;case 43:this.$={stmt:"state",id:e[l-2].trim(),classes:[e[l].trim()],type:"default",description:""};break}},table:[{3:1,4:s,5:a,6:h},{1:[3]},{3:5,4:s,5:a,6:h},{3:6,4:s,5:a,6:h},t([1,4,5,15,16,18,21,23,24,25,26,27,28,32,34,36,37,41,44,45,46,47,50],f,{7:7}),{1:[2,1]},{1:[2,2]},{1:[2,3],4:d,5:y,8:8,9:10,10:12,11:13,12:14,15:k,16:u,18:E,21:T,23:R,24:G,25:j,26:U,27:z,28:M,31:24,32:H,34:X,36:K,37:W,41:J,44:q,45:Q,46:Z,47:tt,50:w},t(c,[2,5]),{9:36,10:12,11:13,12:14,15:k,16:u,18:E,21:T,23:R,24:G,25:j,26:U,27:z,28:M,31:24,32:H,34:X,36:K,37:W,41:J,44:q,45:Q,46:Z,47:tt,50:w},t(c,[2,7]),t(c,[2,8]),t(c,[2,9]),t(c,[2,10]),t(c,[2,11],{13:[1,37],14:[1,38]}),t(c,[2,15]),{17:[1,39]},t(c,[2,17],{19:[1,40]}),{22:[1,41]},t(c,[2,21]),t(c,[2,22]),t(c,[2,23]),t(c,[2,24]),{29:42,30:[1,43],52:[1,44],53:[1,45]},t(c,[2,27]),{33:[1,46]},{35:[1,47]},t(c,[2,30]),{38:[1,48],40:[1,49]},{42:[1,50]},t(et,[2,40],{51:[1,51]}),t(et,[2,41],{51:[1,52]}),t(c,[2,34]),t(c,[2,35]),t(c,[2,36]),t(c,[2,37]),t(c,[2,6]),t(c,[2,12]),{12:53,23:R,50:w},t(c,[2,16]),t(Dt,f,{7:54}),{23:[1,55]},{23:[1,56]},{22:[1,57]},{23:[2,44]},{23:[2,45]},t(c,[2,28]),t(c,[2,29]),{39:[1,58]},{39:[1,59]},{43:[1,60]},{23:[1,61]},{23:[1,62]},t(c,[2,13],{13:[1,63]}),{4:d,5:y,8:8,9:10,10:12,11:13,12:14,15:k,16:u,18:E,20:[1,64],21:T,23:R,24:G,25:j,26:U,27:z,28:M,31:24,32:H,34:X,36:K,37:W,41:J,44:q,45:Q,46:Z,47:tt,50:w},t(c,[2,19],{19:[1,65]}),{30:[1,66]},{23:[1,67]},t(c,[2,31]),t(c,[2,32]),t(c,[2,33]),t(et,[2,42]),t(et,[2,43]),t(c,[2,14]),t(c,[2,18]),t(Dt,f,{7:68}),t(c,[2,25]),t(c,[2,26]),{4:d,5:y,8:8,9:10,10:12,11:13,12:14,15:k,16:u,18:E,20:[1,69],21:T,23:R,24:G,25:j,26:U,27:z,28:M,31:24,32:H,34:X,36:K,37:W,41:J,44:q,45:Q,46:Z,47:tt,50:w},t(c,[2,20])],defaultActions:{5:[2,1],6:[2,2],44:[2,44],45:[2,45]},parseError:function(r,n){if(n.recoverable)this.trace(r);else{var i=new Error(r);throw i.hash=n,i}},parse:function(r){var n=this,i=[0],o=[],p=[null],e=[],$=this.table,l="",A=0,O=0,st=2,B=1,ft=e.slice.call(arguments,1),S=Object.create(this.lexer),v={yy:{}};for(var dt in this.yy)Object.prototype.hasOwnProperty.call(this.yy,dt)&&(v.yy[dt]=this.yy[dt]);S.setInput(r,v.yy),v.yy.lexer=S,v.yy.parser=this,typeof S.yylloc>"u"&&(S.yylloc={});var yt=S.yylloc;e.push(yt);var Gt=S.options&&S.options.ranges;typeof v.yy.parseError=="function"?this.parseError=v.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function jt(){var x;return x=o.pop()||S.lex()||B,typeof x!="number"&&(x instanceof Array&&(o=x,x=o.pop()),x=n.symbols_[x]||x),x}for(var _,L,m,pt,N={},it,b,Ct,rt;;){if(L=i[i.length-1],this.defaultActions[L]?m=this.defaultActions[L]:((_===null||typeof _>"u")&&(_=jt()),m=$[L]&&$[L][_]),typeof m>"u"||!m.length||!m[0]){var St="";rt=[];for(it in $[L])this.terminals_[it]&&it>st&&rt.push("'"+this.terminals_[it]+"'");S.showPosition?St="Parse error on line "+(A+1)+`:
 `+S.showPosition()+`
 Expecting `+rt.join(", ")+", got '"+(this.terminals_[_]||_)+"'":St="Parse error on line "+(A+1)+": Unexpected "+(_==B?"end of input":"'"+(this.terminals_[_]||_)+"'"),this.parseError(St,{text:S.match,token:this.terminals_[_]||_,line:S.yylineno,loc:yt,expected:rt})}if(m[0]instanceof Array&&m.length>1)throw new Error("Parse Error: multiple actions possible at state: "+L+", token: "+_);switch(m[0]){case 1:i.push(_),p.push(S.yytext),e.push(S.yylloc),i.push(m[1]),_=null,O=S.yyleng,l=S.yytext,A=S.yylineno,yt=S.yylloc;break;case 2:if(b=this.productions_[m[1]][1],N.$=p[p.length-b],N._$={first_line:e[e.length-(b||1)].first_line,last_line:e[e.length-1].last_line,first_column:e[e.length-(b||1)].first_column,last_column:e[e.length-1].last_column},Gt&&(N._$.range=[e[e.length-(b||1)].range[0],e[e.length-1].range[1]]),pt=this.performAction.apply(N,[l,O,A,v.yy,m[1],p,e].concat(ft)),typeof pt<"u")return pt;b&&(i=i.slice(0,-1*b*2),p=p.slice(0,-1*b),e=e.slice(0,-1*b)),i.push(this.productions_[m[1]][0]),p.push(N.$),e.push(N._$),Ct=$[i[i.length-2]][i[i.length-1]],i.push(Ct);break;case 3:return!0}}return!0}},Yt=function(){var C={EOF:1,parseError:function(n,i){if(this.yy.parser)this.yy.parser.parseError(n,i);else throw new Error(n)},setInput:function(r,n){return this.yy=n||this.yy||{},this._input=r,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var r=this._input[0];this.yytext+=r,this.yyleng++,this.offset++,this.match+=r,this.matched+=r;var n=r.match(/(?:\r\n?|\n).*/g);return n?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),r},unput:function(r){var n=r.length,i=r.split(/(?:\r\n?|\n)/g);this._input=r+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-n),this.offset-=n;var o=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),i.length-1&&(this.yylineno-=i.length-1);var p=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:i?(i.length===o.length?this.yylloc.first_column:0)+o[o.length-i.length].length-i[0].length:this.yylloc.first_column-n},this.options.ranges&&(this.yylloc.range=[p[0],p[0]+this.yyleng-n]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){if(this.options.backtrack_lexer)this._backtrack=!0;else return this.parseError("Lexical error on line "+(this.yylineno+1)+`. You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).
 `+this.showPosition(),{text:"",token:null,line:this.yylineno});return this},less:function(r){this.unput(this.match.slice(r))},pastInput:function(){var r=this.matched.substr(0,this.matched.length-this.match.length);return(r.length>20?"...":"")+r.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var r=this.match;return r.length<20&&(r+=this._input.substr(0,20-r.length)),(r.substr(0,20)+(r.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var r=this.pastInput(),n=new Array(r.length+1).join("-");return r+this.upcomingInput()+`
diff --git a/assets/styles-e2b9d258-TYWOaoPC.js b/assets/styles-e2b9d258-CoUUuHq5.js
similarity index 99%
rename from assets/styles-e2b9d258-TYWOaoPC.js
rename to assets/styles-e2b9d258-CoUUuHq5.js
index 3d31d0f..cc6c6a6 100644
--- a/assets/styles-e2b9d258-TYWOaoPC.js
+++ b/assets/styles-e2b9d258-CoUUuHq5.js
@@ -1,4 +1,4 @@
-import{s as ut,g as rt,a as at,b as lt,c as F,x as ct,y as ot,j as v,A as ht,l as At,z as We,h as z,d as pt,ar as Re}from"./mermaid.core-ChLYKTZm.js";var Ve=function(){var e=function(x,u,a,h){for(a=a||{},h=x.length;h--;a[x[h]]=u);return a},i=[1,17],r=[1,18],l=[1,19],o=[1,39],A=[1,40],g=[1,25],D=[1,23],B=[1,24],_=[1,31],fe=[1,32],de=[1,33],Ee=[1,34],Ce=[1,35],me=[1,36],be=[1,26],ge=[1,27],ke=[1,28],Te=[1,29],d=[1,43],Fe=[1,30],E=[1,42],C=[1,44],m=[1,41],k=[1,45],ye=[1,9],c=[1,8,9],Y=[1,56],j=[1,57],Q=[1,58],X=[1,59],H=[1,60],De=[1,61],Be=[1,62],W=[1,8,9,39],Ge=[1,74],M=[1,8,9,12,13,21,37,39,42,59,60,61,62,63,64,65,70,72],q=[1,8,9,12,13,19,21,37,39,42,46,59,60,61,62,63,64,65,70,72,74,80,95,97,98],J=[13,74,80,95,97,98],G=[13,64,65,74,80,95,97,98],Ue=[13,59,60,61,62,63,74,80,95,97,98],_e=[1,93],Z=[1,110],$=[1,108],ee=[1,102],te=[1,103],se=[1,104],ie=[1,105],ne=[1,106],ue=[1,107],re=[1,109],Se=[1,8,9,37,39,42],ae=[1,8,9,21],ze=[1,8,9,78],S=[1,8,9,21,73,74,78,80,81,82,83,84,85],Ne={trace:function(){},yy:{},symbols_:{error:2,start:3,mermaidDoc:4,statements:5,graphConfig:6,CLASS_DIAGRAM:7,NEWLINE:8,EOF:9,statement:10,classLabel:11,SQS:12,STR:13,SQE:14,namespaceName:15,alphaNumToken:16,className:17,classLiteralName:18,GENERICTYPE:19,relationStatement:20,LABEL:21,namespaceStatement:22,classStatement:23,memberStatement:24,annotationStatement:25,clickStatement:26,styleStatement:27,cssClassStatement:28,noteStatement:29,direction:30,acc_title:31,acc_title_value:32,acc_descr:33,acc_descr_value:34,acc_descr_multiline_value:35,namespaceIdentifier:36,STRUCT_START:37,classStatements:38,STRUCT_STOP:39,NAMESPACE:40,classIdentifier:41,STYLE_SEPARATOR:42,members:43,CLASS:44,ANNOTATION_START:45,ANNOTATION_END:46,MEMBER:47,SEPARATOR:48,relation:49,NOTE_FOR:50,noteText:51,NOTE:52,direction_tb:53,direction_bt:54,direction_rl:55,direction_lr:56,relationType:57,lineType:58,AGGREGATION:59,EXTENSION:60,COMPOSITION:61,DEPENDENCY:62,LOLLIPOP:63,LINE:64,DOTTED_LINE:65,CALLBACK:66,LINK:67,LINK_TARGET:68,CLICK:69,CALLBACK_NAME:70,CALLBACK_ARGS:71,HREF:72,STYLE:73,ALPHA:74,stylesOpt:75,CSSCLASS:76,style:77,COMMA:78,styleComponent:79,NUM:80,COLON:81,UNIT:82,SPACE:83,BRKT:84,PCT:85,commentToken:86,textToken:87,graphCodeTokens:88,textNoTagsToken:89,TAGSTART:90,TAGEND:91,"==":92,"--":93,DEFAULT:94,MINUS:95,keywords:96,UNICODE_TEXT:97,BQUOTE_STR:98,$accept:0,$end:1},terminals_:{2:"error",7:"CLASS_DIAGRAM",8:"NEWLINE",9:"EOF",12:"SQS",13:"STR",14:"SQE",19:"GENERICTYPE",21:"LABEL",31:"acc_title",32:"acc_title_value",33:"acc_descr",34:"acc_descr_value",35:"acc_descr_multiline_value",37:"STRUCT_START",39:"STRUCT_STOP",40:"NAMESPACE",42:"STYLE_SEPARATOR",44:"CLASS",45:"ANNOTATION_START",46:"ANNOTATION_END",47:"MEMBER",48:"SEPARATOR",50:"NOTE_FOR",52:"NOTE",53:"direction_tb",54:"direction_bt",55:"direction_rl",56:"direction_lr",59:"AGGREGATION",60:"EXTENSION",61:"COMPOSITION",62:"DEPENDENCY",63:"LOLLIPOP",64:"LINE",65:"DOTTED_LINE",66:"CALLBACK",67:"LINK",68:"LINK_TARGET",69:"CLICK",70:"CALLBACK_NAME",71:"CALLBACK_ARGS",72:"HREF",73:"STYLE",74:"ALPHA",76:"CSSCLASS",78:"COMMA",80:"NUM",81:"COLON",82:"UNIT",83:"SPACE",84:"BRKT",85:"PCT",88:"graphCodeTokens",90:"TAGSTART",91:"TAGEND",92:"==",93:"--",94:"DEFAULT",95:"MINUS",96:"keywords",97:"UNICODE_TEXT",98:"BQUOTE_STR"},productions_:[0,[3,1],[3,1],[4,1],[6,4],[5,1],[5,2],[5,3],[11,3],[15,1],[15,2],[17,1],[17,1],[17,2],[17,2],[17,2],[10,1],[10,2],[10,1],[10,1],[10,1],[10,1],[10,1],[10,1],[10,1],[10,1],[10,1],[10,2],[10,2],[10,1],[22,4],[22,5],[36,2],[38,1],[38,2],[38,3],[23,1],[23,3],[23,4],[23,6],[41,2],[41,3],[25,4],[43,1],[43,2],[24,1],[24,2],[24,1],[24,1],[20,3],[20,4],[20,4],[20,5],[29,3],[29,2],[30,1],[30,1],[30,1],[30,1],[49,3],[49,2],[49,2],[49,1],[57,1],[57,1],[57,1],[57,1],[57,1],[58,1],[58,1],[26,3],[26,4],[26,3],[26,4],[26,4],[26,5],[26,3],[26,4],[26,4],[26,5],[26,4],[26,5],[26,5],[26,6],[27,3],[28,3],[75,1],[75,3],[77,1],[77,2],[79,1],[79,1],[79,1],[79,1],[79,1],[79,1],[79,1],[79,1],[79,1],[86,1],[86,1],[87,1],[87,1],[87,1],[87,1],[87,1],[87,1],[87,1],[89,1],[89,1],[89,1],[89,1],[16,1],[16,1],[16,1],[16,1],[18,1],[51,1]],performAction:function(u,a,h,n,f,t,U){var s=t.length-1;switch(f){case 8:this.$=t[s-1];break;case 9:case 11:case 12:this.$=t[s];break;case 10:case 13:this.$=t[s-1]+t[s];break;case 14:case 15:this.$=t[s-1]+"~"+t[s]+"~";break;case 16:n.addRelation(t[s]);break;case 17:t[s-1].title=n.cleanupLabel(t[s]),n.addRelation(t[s-1]);break;case 27:this.$=t[s].trim(),n.setAccTitle(this.$);break;case 28:case 29:this.$=t[s].trim(),n.setAccDescription(this.$);break;case 30:n.addClassesToNamespace(t[s-3],t[s-1]);break;case 31:n.addClassesToNamespace(t[s-4],t[s-1]);break;case 32:this.$=t[s],n.addNamespace(t[s]);break;case 33:this.$=[t[s]];break;case 34:this.$=[t[s-1]];break;case 35:t[s].unshift(t[s-2]),this.$=t[s];break;case 37:n.setCssClass(t[s-2],t[s]);break;case 38:n.addMembers(t[s-3],t[s-1]);break;case 39:n.setCssClass(t[s-5],t[s-3]),n.addMembers(t[s-5],t[s-1]);break;case 40:this.$=t[s],n.addClass(t[s]);break;case 41:this.$=t[s-1],n.addClass(t[s-1]),n.setClassLabel(t[s-1],t[s]);break;case 42:n.addAnnotation(t[s],t[s-2]);break;case 43:this.$=[t[s]];break;case 44:t[s].push(t[s-1]),this.$=t[s];break;case 45:break;case 46:n.addMember(t[s-1],n.cleanupLabel(t[s]));break;case 47:break;case 48:break;case 49:this.$={id1:t[s-2],id2:t[s],relation:t[s-1],relationTitle1:"none",relationTitle2:"none"};break;case 50:this.$={id1:t[s-3],id2:t[s],relation:t[s-1],relationTitle1:t[s-2],relationTitle2:"none"};break;case 51:this.$={id1:t[s-3],id2:t[s],relation:t[s-2],relationTitle1:"none",relationTitle2:t[s-1]};break;case 52:this.$={id1:t[s-4],id2:t[s],relation:t[s-2],relationTitle1:t[s-3],relationTitle2:t[s-1]};break;case 53:n.addNote(t[s],t[s-1]);break;case 54:n.addNote(t[s]);break;case 55:n.setDirection("TB");break;case 56:n.setDirection("BT");break;case 57:n.setDirection("RL");break;case 58:n.setDirection("LR");break;case 59:this.$={type1:t[s-2],type2:t[s],lineType:t[s-1]};break;case 60:this.$={type1:"none",type2:t[s],lineType:t[s-1]};break;case 61:this.$={type1:t[s-1],type2:"none",lineType:t[s]};break;case 62:this.$={type1:"none",type2:"none",lineType:t[s]};break;case 63:this.$=n.relationType.AGGREGATION;break;case 64:this.$=n.relationType.EXTENSION;break;case 65:this.$=n.relationType.COMPOSITION;break;case 66:this.$=n.relationType.DEPENDENCY;break;case 67:this.$=n.relationType.LOLLIPOP;break;case 68:this.$=n.lineType.LINE;break;case 69:this.$=n.lineType.DOTTED_LINE;break;case 70:case 76:this.$=t[s-2],n.setClickEvent(t[s-1],t[s]);break;case 71:case 77:this.$=t[s-3],n.setClickEvent(t[s-2],t[s-1]),n.setTooltip(t[s-2],t[s]);break;case 72:this.$=t[s-2],n.setLink(t[s-1],t[s]);break;case 73:this.$=t[s-3],n.setLink(t[s-2],t[s-1],t[s]);break;case 74:this.$=t[s-3],n.setLink(t[s-2],t[s-1]),n.setTooltip(t[s-2],t[s]);break;case 75:this.$=t[s-4],n.setLink(t[s-3],t[s-2],t[s]),n.setTooltip(t[s-3],t[s-1]);break;case 78:this.$=t[s-3],n.setClickEvent(t[s-2],t[s-1],t[s]);break;case 79:this.$=t[s-4],n.setClickEvent(t[s-3],t[s-2],t[s-1]),n.setTooltip(t[s-3],t[s]);break;case 80:this.$=t[s-3],n.setLink(t[s-2],t[s]);break;case 81:this.$=t[s-4],n.setLink(t[s-3],t[s-1],t[s]);break;case 82:this.$=t[s-4],n.setLink(t[s-3],t[s-1]),n.setTooltip(t[s-3],t[s]);break;case 83:this.$=t[s-5],n.setLink(t[s-4],t[s-2],t[s]),n.setTooltip(t[s-4],t[s-1]);break;case 84:this.$=t[s-2],n.setCssStyle(t[s-1],t[s]);break;case 85:n.setCssClass(t[s-1],t[s]);break;case 86:this.$=[t[s]];break;case 87:t[s-2].push(t[s]),this.$=t[s-2];break;case 89:this.$=t[s-1]+t[s];break}},table:[{3:1,4:2,5:3,6:4,7:[1,6],10:5,16:37,17:20,18:38,20:7,22:8,23:9,24:10,25:11,26:12,27:13,28:14,29:15,30:16,31:i,33:r,35:l,36:21,40:o,41:22,44:A,45:g,47:D,48:B,50:_,52:fe,53:de,54:Ee,55:Ce,56:me,66:be,67:ge,69:ke,73:Te,74:d,76:Fe,80:E,95:C,97:m,98:k},{1:[3]},{1:[2,1]},{1:[2,2]},{1:[2,3]},e(ye,[2,5],{8:[1,46]}),{8:[1,47]},e(c,[2,16],{21:[1,48]}),e(c,[2,18]),e(c,[2,19]),e(c,[2,20]),e(c,[2,21]),e(c,[2,22]),e(c,[2,23]),e(c,[2,24]),e(c,[2,25]),e(c,[2,26]),{32:[1,49]},{34:[1,50]},e(c,[2,29]),e(c,[2,45],{49:51,57:54,58:55,13:[1,52],21:[1,53],59:Y,60:j,61:Q,62:X,63:H,64:De,65:Be}),{37:[1,63]},e(W,[2,36],{37:[1,65],42:[1,64]}),e(c,[2,47]),e(c,[2,48]),{16:66,74:d,80:E,95:C,97:m},{16:37,17:67,18:38,74:d,80:E,95:C,97:m,98:k},{16:37,17:68,18:38,74:d,80:E,95:C,97:m,98:k},{16:37,17:69,18:38,74:d,80:E,95:C,97:m,98:k},{74:[1,70]},{13:[1,71]},{16:37,17:72,18:38,74:d,80:E,95:C,97:m,98:k},{13:Ge,51:73},e(c,[2,55]),e(c,[2,56]),e(c,[2,57]),e(c,[2,58]),e(M,[2,11],{16:37,18:38,17:75,19:[1,76],74:d,80:E,95:C,97:m,98:k}),e(M,[2,12],{19:[1,77]}),{15:78,16:79,74:d,80:E,95:C,97:m},{16:37,17:80,18:38,74:d,80:E,95:C,97:m,98:k},e(q,[2,112]),e(q,[2,113]),e(q,[2,114]),e(q,[2,115]),e([1,8,9,12,13,19,21,37,39,42,59,60,61,62,63,64,65,70,72],[2,116]),e(ye,[2,6],{10:5,20:7,22:8,23:9,24:10,25:11,26:12,27:13,28:14,29:15,30:16,17:20,36:21,41:22,16:37,18:38,5:81,31:i,33:r,35:l,40:o,44:A,45:g,47:D,48:B,50:_,52:fe,53:de,54:Ee,55:Ce,56:me,66:be,67:ge,69:ke,73:Te,74:d,76:Fe,80:E,95:C,97:m,98:k}),{5:82,10:5,16:37,17:20,18:38,20:7,22:8,23:9,24:10,25:11,26:12,27:13,28:14,29:15,30:16,31:i,33:r,35:l,36:21,40:o,41:22,44:A,45:g,47:D,48:B,50:_,52:fe,53:de,54:Ee,55:Ce,56:me,66:be,67:ge,69:ke,73:Te,74:d,76:Fe,80:E,95:C,97:m,98:k},e(c,[2,17]),e(c,[2,27]),e(c,[2,28]),{13:[1,84],16:37,17:83,18:38,74:d,80:E,95:C,97:m,98:k},{49:85,57:54,58:55,59:Y,60:j,61:Q,62:X,63:H,64:De,65:Be},e(c,[2,46]),{58:86,64:De,65:Be},e(J,[2,62],{57:87,59:Y,60:j,61:Q,62:X,63:H}),e(G,[2,63]),e(G,[2,64]),e(G,[2,65]),e(G,[2,66]),e(G,[2,67]),e(Ue,[2,68]),e(Ue,[2,69]),{8:[1,89],23:90,38:88,41:22,44:A},{16:91,74:d,80:E,95:C,97:m},{43:92,47:_e},{46:[1,94]},{13:[1,95]},{13:[1,96]},{70:[1,97],72:[1,98]},{21:Z,73:$,74:ee,75:99,77:100,79:101,80:te,81:se,82:ie,83:ne,84:ue,85:re},{74:[1,111]},{13:Ge,51:112},e(c,[2,54]),e(c,[2,117]),e(M,[2,13]),e(M,[2,14]),e(M,[2,15]),{37:[2,32]},{15:113,16:79,37:[2,9],74:d,80:E,95:C,97:m},e(Se,[2,40],{11:114,12:[1,115]}),e(ye,[2,7]),{9:[1,116]},e(ae,[2,49]),{16:37,17:117,18:38,74:d,80:E,95:C,97:m,98:k},{13:[1,119],16:37,17:118,18:38,74:d,80:E,95:C,97:m,98:k},e(J,[2,61],{57:120,59:Y,60:j,61:Q,62:X,63:H}),e(J,[2,60]),{39:[1,121]},{23:90,38:122,41:22,44:A},{8:[1,123],39:[2,33]},e(W,[2,37],{37:[1,124]}),{39:[1,125]},{39:[2,43],43:126,47:_e},{16:37,17:127,18:38,74:d,80:E,95:C,97:m,98:k},e(c,[2,70],{13:[1,128]}),e(c,[2,72],{13:[1,130],68:[1,129]}),e(c,[2,76],{13:[1,131],71:[1,132]}),{13:[1,133]},e(c,[2,84],{78:[1,134]}),e(ze,[2,86],{79:135,21:Z,73:$,74:ee,80:te,81:se,82:ie,83:ne,84:ue,85:re}),e(S,[2,88]),e(S,[2,90]),e(S,[2,91]),e(S,[2,92]),e(S,[2,93]),e(S,[2,94]),e(S,[2,95]),e(S,[2,96]),e(S,[2,97]),e(S,[2,98]),e(c,[2,85]),e(c,[2,53]),{37:[2,10]},e(Se,[2,41]),{13:[1,136]},{1:[2,4]},e(ae,[2,51]),e(ae,[2,50]),{16:37,17:137,18:38,74:d,80:E,95:C,97:m,98:k},e(J,[2,59]),e(c,[2,30]),{39:[1,138]},{23:90,38:139,39:[2,34],41:22,44:A},{43:140,47:_e},e(W,[2,38]),{39:[2,44]},e(c,[2,42]),e(c,[2,71]),e(c,[2,73]),e(c,[2,74],{68:[1,141]}),e(c,[2,77]),e(c,[2,78],{13:[1,142]}),e(c,[2,80],{13:[1,144],68:[1,143]}),{21:Z,73:$,74:ee,77:145,79:101,80:te,81:se,82:ie,83:ne,84:ue,85:re},e(S,[2,89]),{14:[1,146]},e(ae,[2,52]),e(c,[2,31]),{39:[2,35]},{39:[1,147]},e(c,[2,75]),e(c,[2,79]),e(c,[2,81]),e(c,[2,82],{68:[1,148]}),e(ze,[2,87],{79:135,21:Z,73:$,74:ee,80:te,81:se,82:ie,83:ne,84:ue,85:re}),e(Se,[2,8]),e(W,[2,39]),e(c,[2,83])],defaultActions:{2:[2,1],3:[2,2],4:[2,3],78:[2,32],113:[2,10],116:[2,4],126:[2,44],139:[2,35]},parseError:function(u,a){if(a.recoverable)this.trace(u);else{var h=new Error(u);throw h.hash=a,h}},parse:function(u){var a=this,h=[0],n=[],f=[null],t=[],U=this.table,s="",le=0,Ke=0,tt=2,Ye=1,st=t.slice.call(arguments,1),b=Object.create(this.lexer),I={yy:{}};for(var ve in this.yy)Object.prototype.hasOwnProperty.call(this.yy,ve)&&(I.yy[ve]=this.yy[ve]);b.setInput(u,I.yy),I.yy.lexer=b,I.yy.parser=this,typeof b.yylloc>"u"&&(b.yylloc={});var xe=b.yylloc;t.push(xe);var it=b.options&&b.options.ranges;typeof I.yy.parseError=="function"?this.parseError=I.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function nt(){var L;return L=n.pop()||b.lex()||Ye,typeof L!="number"&&(L instanceof Array&&(n=L,L=n.pop()),L=a.symbols_[L]||L),L}for(var T,R,y,Oe,P={},ce,N,je,oe;;){if(R=h[h.length-1],this.defaultActions[R]?y=this.defaultActions[R]:((T===null||typeof T>"u")&&(T=nt()),y=U[R]&&U[R][T]),typeof y>"u"||!y.length||!y[0]){var Ie="";oe=[];for(ce in U[R])this.terminals_[ce]&&ce>tt&&oe.push("'"+this.terminals_[ce]+"'");b.showPosition?Ie="Parse error on line "+(le+1)+`:
+import{s as ut,g as rt,a as at,b as lt,c as F,x as ct,y as ot,j as v,A as ht,l as At,z as We,h as z,d as pt,ar as Re}from"./mermaid.core-DNo_7Q2B.js";var Ve=function(){var e=function(x,u,a,h){for(a=a||{},h=x.length;h--;a[x[h]]=u);return a},i=[1,17],r=[1,18],l=[1,19],o=[1,39],A=[1,40],g=[1,25],D=[1,23],B=[1,24],_=[1,31],fe=[1,32],de=[1,33],Ee=[1,34],Ce=[1,35],me=[1,36],be=[1,26],ge=[1,27],ke=[1,28],Te=[1,29],d=[1,43],Fe=[1,30],E=[1,42],C=[1,44],m=[1,41],k=[1,45],ye=[1,9],c=[1,8,9],Y=[1,56],j=[1,57],Q=[1,58],X=[1,59],H=[1,60],De=[1,61],Be=[1,62],W=[1,8,9,39],Ge=[1,74],M=[1,8,9,12,13,21,37,39,42,59,60,61,62,63,64,65,70,72],q=[1,8,9,12,13,19,21,37,39,42,46,59,60,61,62,63,64,65,70,72,74,80,95,97,98],J=[13,74,80,95,97,98],G=[13,64,65,74,80,95,97,98],Ue=[13,59,60,61,62,63,74,80,95,97,98],_e=[1,93],Z=[1,110],$=[1,108],ee=[1,102],te=[1,103],se=[1,104],ie=[1,105],ne=[1,106],ue=[1,107],re=[1,109],Se=[1,8,9,37,39,42],ae=[1,8,9,21],ze=[1,8,9,78],S=[1,8,9,21,73,74,78,80,81,82,83,84,85],Ne={trace:function(){},yy:{},symbols_:{error:2,start:3,mermaidDoc:4,statements:5,graphConfig:6,CLASS_DIAGRAM:7,NEWLINE:8,EOF:9,statement:10,classLabel:11,SQS:12,STR:13,SQE:14,namespaceName:15,alphaNumToken:16,className:17,classLiteralName:18,GENERICTYPE:19,relationStatement:20,LABEL:21,namespaceStatement:22,classStatement:23,memberStatement:24,annotationStatement:25,clickStatement:26,styleStatement:27,cssClassStatement:28,noteStatement:29,direction:30,acc_title:31,acc_title_value:32,acc_descr:33,acc_descr_value:34,acc_descr_multiline_value:35,namespaceIdentifier:36,STRUCT_START:37,classStatements:38,STRUCT_STOP:39,NAMESPACE:40,classIdentifier:41,STYLE_SEPARATOR:42,members:43,CLASS:44,ANNOTATION_START:45,ANNOTATION_END:46,MEMBER:47,SEPARATOR:48,relation:49,NOTE_FOR:50,noteText:51,NOTE:52,direction_tb:53,direction_bt:54,direction_rl:55,direction_lr:56,relationType:57,lineType:58,AGGREGATION:59,EXTENSION:60,COMPOSITION:61,DEPENDENCY:62,LOLLIPOP:63,LINE:64,DOTTED_LINE:65,CALLBACK:66,LINK:67,LINK_TARGET:68,CLICK:69,CALLBACK_NAME:70,CALLBACK_ARGS:71,HREF:72,STYLE:73,ALPHA:74,stylesOpt:75,CSSCLASS:76,style:77,COMMA:78,styleComponent:79,NUM:80,COLON:81,UNIT:82,SPACE:83,BRKT:84,PCT:85,commentToken:86,textToken:87,graphCodeTokens:88,textNoTagsToken:89,TAGSTART:90,TAGEND:91,"==":92,"--":93,DEFAULT:94,MINUS:95,keywords:96,UNICODE_TEXT:97,BQUOTE_STR:98,$accept:0,$end:1},terminals_:{2:"error",7:"CLASS_DIAGRAM",8:"NEWLINE",9:"EOF",12:"SQS",13:"STR",14:"SQE",19:"GENERICTYPE",21:"LABEL",31:"acc_title",32:"acc_title_value",33:"acc_descr",34:"acc_descr_value",35:"acc_descr_multiline_value",37:"STRUCT_START",39:"STRUCT_STOP",40:"NAMESPACE",42:"STYLE_SEPARATOR",44:"CLASS",45:"ANNOTATION_START",46:"ANNOTATION_END",47:"MEMBER",48:"SEPARATOR",50:"NOTE_FOR",52:"NOTE",53:"direction_tb",54:"direction_bt",55:"direction_rl",56:"direction_lr",59:"AGGREGATION",60:"EXTENSION",61:"COMPOSITION",62:"DEPENDENCY",63:"LOLLIPOP",64:"LINE",65:"DOTTED_LINE",66:"CALLBACK",67:"LINK",68:"LINK_TARGET",69:"CLICK",70:"CALLBACK_NAME",71:"CALLBACK_ARGS",72:"HREF",73:"STYLE",74:"ALPHA",76:"CSSCLASS",78:"COMMA",80:"NUM",81:"COLON",82:"UNIT",83:"SPACE",84:"BRKT",85:"PCT",88:"graphCodeTokens",90:"TAGSTART",91:"TAGEND",92:"==",93:"--",94:"DEFAULT",95:"MINUS",96:"keywords",97:"UNICODE_TEXT",98:"BQUOTE_STR"},productions_:[0,[3,1],[3,1],[4,1],[6,4],[5,1],[5,2],[5,3],[11,3],[15,1],[15,2],[17,1],[17,1],[17,2],[17,2],[17,2],[10,1],[10,2],[10,1],[10,1],[10,1],[10,1],[10,1],[10,1],[10,1],[10,1],[10,1],[10,2],[10,2],[10,1],[22,4],[22,5],[36,2],[38,1],[38,2],[38,3],[23,1],[23,3],[23,4],[23,6],[41,2],[41,3],[25,4],[43,1],[43,2],[24,1],[24,2],[24,1],[24,1],[20,3],[20,4],[20,4],[20,5],[29,3],[29,2],[30,1],[30,1],[30,1],[30,1],[49,3],[49,2],[49,2],[49,1],[57,1],[57,1],[57,1],[57,1],[57,1],[58,1],[58,1],[26,3],[26,4],[26,3],[26,4],[26,4],[26,5],[26,3],[26,4],[26,4],[26,5],[26,4],[26,5],[26,5],[26,6],[27,3],[28,3],[75,1],[75,3],[77,1],[77,2],[79,1],[79,1],[79,1],[79,1],[79,1],[79,1],[79,1],[79,1],[79,1],[86,1],[86,1],[87,1],[87,1],[87,1],[87,1],[87,1],[87,1],[87,1],[89,1],[89,1],[89,1],[89,1],[16,1],[16,1],[16,1],[16,1],[18,1],[51,1]],performAction:function(u,a,h,n,f,t,U){var s=t.length-1;switch(f){case 8:this.$=t[s-1];break;case 9:case 11:case 12:this.$=t[s];break;case 10:case 13:this.$=t[s-1]+t[s];break;case 14:case 15:this.$=t[s-1]+"~"+t[s]+"~";break;case 16:n.addRelation(t[s]);break;case 17:t[s-1].title=n.cleanupLabel(t[s]),n.addRelation(t[s-1]);break;case 27:this.$=t[s].trim(),n.setAccTitle(this.$);break;case 28:case 29:this.$=t[s].trim(),n.setAccDescription(this.$);break;case 30:n.addClassesToNamespace(t[s-3],t[s-1]);break;case 31:n.addClassesToNamespace(t[s-4],t[s-1]);break;case 32:this.$=t[s],n.addNamespace(t[s]);break;case 33:this.$=[t[s]];break;case 34:this.$=[t[s-1]];break;case 35:t[s].unshift(t[s-2]),this.$=t[s];break;case 37:n.setCssClass(t[s-2],t[s]);break;case 38:n.addMembers(t[s-3],t[s-1]);break;case 39:n.setCssClass(t[s-5],t[s-3]),n.addMembers(t[s-5],t[s-1]);break;case 40:this.$=t[s],n.addClass(t[s]);break;case 41:this.$=t[s-1],n.addClass(t[s-1]),n.setClassLabel(t[s-1],t[s]);break;case 42:n.addAnnotation(t[s],t[s-2]);break;case 43:this.$=[t[s]];break;case 44:t[s].push(t[s-1]),this.$=t[s];break;case 45:break;case 46:n.addMember(t[s-1],n.cleanupLabel(t[s]));break;case 47:break;case 48:break;case 49:this.$={id1:t[s-2],id2:t[s],relation:t[s-1],relationTitle1:"none",relationTitle2:"none"};break;case 50:this.$={id1:t[s-3],id2:t[s],relation:t[s-1],relationTitle1:t[s-2],relationTitle2:"none"};break;case 51:this.$={id1:t[s-3],id2:t[s],relation:t[s-2],relationTitle1:"none",relationTitle2:t[s-1]};break;case 52:this.$={id1:t[s-4],id2:t[s],relation:t[s-2],relationTitle1:t[s-3],relationTitle2:t[s-1]};break;case 53:n.addNote(t[s],t[s-1]);break;case 54:n.addNote(t[s]);break;case 55:n.setDirection("TB");break;case 56:n.setDirection("BT");break;case 57:n.setDirection("RL");break;case 58:n.setDirection("LR");break;case 59:this.$={type1:t[s-2],type2:t[s],lineType:t[s-1]};break;case 60:this.$={type1:"none",type2:t[s],lineType:t[s-1]};break;case 61:this.$={type1:t[s-1],type2:"none",lineType:t[s]};break;case 62:this.$={type1:"none",type2:"none",lineType:t[s]};break;case 63:this.$=n.relationType.AGGREGATION;break;case 64:this.$=n.relationType.EXTENSION;break;case 65:this.$=n.relationType.COMPOSITION;break;case 66:this.$=n.relationType.DEPENDENCY;break;case 67:this.$=n.relationType.LOLLIPOP;break;case 68:this.$=n.lineType.LINE;break;case 69:this.$=n.lineType.DOTTED_LINE;break;case 70:case 76:this.$=t[s-2],n.setClickEvent(t[s-1],t[s]);break;case 71:case 77:this.$=t[s-3],n.setClickEvent(t[s-2],t[s-1]),n.setTooltip(t[s-2],t[s]);break;case 72:this.$=t[s-2],n.setLink(t[s-1],t[s]);break;case 73:this.$=t[s-3],n.setLink(t[s-2],t[s-1],t[s]);break;case 74:this.$=t[s-3],n.setLink(t[s-2],t[s-1]),n.setTooltip(t[s-2],t[s]);break;case 75:this.$=t[s-4],n.setLink(t[s-3],t[s-2],t[s]),n.setTooltip(t[s-3],t[s-1]);break;case 78:this.$=t[s-3],n.setClickEvent(t[s-2],t[s-1],t[s]);break;case 79:this.$=t[s-4],n.setClickEvent(t[s-3],t[s-2],t[s-1]),n.setTooltip(t[s-3],t[s]);break;case 80:this.$=t[s-3],n.setLink(t[s-2],t[s]);break;case 81:this.$=t[s-4],n.setLink(t[s-3],t[s-1],t[s]);break;case 82:this.$=t[s-4],n.setLink(t[s-3],t[s-1]),n.setTooltip(t[s-3],t[s]);break;case 83:this.$=t[s-5],n.setLink(t[s-4],t[s-2],t[s]),n.setTooltip(t[s-4],t[s-1]);break;case 84:this.$=t[s-2],n.setCssStyle(t[s-1],t[s]);break;case 85:n.setCssClass(t[s-1],t[s]);break;case 86:this.$=[t[s]];break;case 87:t[s-2].push(t[s]),this.$=t[s-2];break;case 89:this.$=t[s-1]+t[s];break}},table:[{3:1,4:2,5:3,6:4,7:[1,6],10:5,16:37,17:20,18:38,20:7,22:8,23:9,24:10,25:11,26:12,27:13,28:14,29:15,30:16,31:i,33:r,35:l,36:21,40:o,41:22,44:A,45:g,47:D,48:B,50:_,52:fe,53:de,54:Ee,55:Ce,56:me,66:be,67:ge,69:ke,73:Te,74:d,76:Fe,80:E,95:C,97:m,98:k},{1:[3]},{1:[2,1]},{1:[2,2]},{1:[2,3]},e(ye,[2,5],{8:[1,46]}),{8:[1,47]},e(c,[2,16],{21:[1,48]}),e(c,[2,18]),e(c,[2,19]),e(c,[2,20]),e(c,[2,21]),e(c,[2,22]),e(c,[2,23]),e(c,[2,24]),e(c,[2,25]),e(c,[2,26]),{32:[1,49]},{34:[1,50]},e(c,[2,29]),e(c,[2,45],{49:51,57:54,58:55,13:[1,52],21:[1,53],59:Y,60:j,61:Q,62:X,63:H,64:De,65:Be}),{37:[1,63]},e(W,[2,36],{37:[1,65],42:[1,64]}),e(c,[2,47]),e(c,[2,48]),{16:66,74:d,80:E,95:C,97:m},{16:37,17:67,18:38,74:d,80:E,95:C,97:m,98:k},{16:37,17:68,18:38,74:d,80:E,95:C,97:m,98:k},{16:37,17:69,18:38,74:d,80:E,95:C,97:m,98:k},{74:[1,70]},{13:[1,71]},{16:37,17:72,18:38,74:d,80:E,95:C,97:m,98:k},{13:Ge,51:73},e(c,[2,55]),e(c,[2,56]),e(c,[2,57]),e(c,[2,58]),e(M,[2,11],{16:37,18:38,17:75,19:[1,76],74:d,80:E,95:C,97:m,98:k}),e(M,[2,12],{19:[1,77]}),{15:78,16:79,74:d,80:E,95:C,97:m},{16:37,17:80,18:38,74:d,80:E,95:C,97:m,98:k},e(q,[2,112]),e(q,[2,113]),e(q,[2,114]),e(q,[2,115]),e([1,8,9,12,13,19,21,37,39,42,59,60,61,62,63,64,65,70,72],[2,116]),e(ye,[2,6],{10:5,20:7,22:8,23:9,24:10,25:11,26:12,27:13,28:14,29:15,30:16,17:20,36:21,41:22,16:37,18:38,5:81,31:i,33:r,35:l,40:o,44:A,45:g,47:D,48:B,50:_,52:fe,53:de,54:Ee,55:Ce,56:me,66:be,67:ge,69:ke,73:Te,74:d,76:Fe,80:E,95:C,97:m,98:k}),{5:82,10:5,16:37,17:20,18:38,20:7,22:8,23:9,24:10,25:11,26:12,27:13,28:14,29:15,30:16,31:i,33:r,35:l,36:21,40:o,41:22,44:A,45:g,47:D,48:B,50:_,52:fe,53:de,54:Ee,55:Ce,56:me,66:be,67:ge,69:ke,73:Te,74:d,76:Fe,80:E,95:C,97:m,98:k},e(c,[2,17]),e(c,[2,27]),e(c,[2,28]),{13:[1,84],16:37,17:83,18:38,74:d,80:E,95:C,97:m,98:k},{49:85,57:54,58:55,59:Y,60:j,61:Q,62:X,63:H,64:De,65:Be},e(c,[2,46]),{58:86,64:De,65:Be},e(J,[2,62],{57:87,59:Y,60:j,61:Q,62:X,63:H}),e(G,[2,63]),e(G,[2,64]),e(G,[2,65]),e(G,[2,66]),e(G,[2,67]),e(Ue,[2,68]),e(Ue,[2,69]),{8:[1,89],23:90,38:88,41:22,44:A},{16:91,74:d,80:E,95:C,97:m},{43:92,47:_e},{46:[1,94]},{13:[1,95]},{13:[1,96]},{70:[1,97],72:[1,98]},{21:Z,73:$,74:ee,75:99,77:100,79:101,80:te,81:se,82:ie,83:ne,84:ue,85:re},{74:[1,111]},{13:Ge,51:112},e(c,[2,54]),e(c,[2,117]),e(M,[2,13]),e(M,[2,14]),e(M,[2,15]),{37:[2,32]},{15:113,16:79,37:[2,9],74:d,80:E,95:C,97:m},e(Se,[2,40],{11:114,12:[1,115]}),e(ye,[2,7]),{9:[1,116]},e(ae,[2,49]),{16:37,17:117,18:38,74:d,80:E,95:C,97:m,98:k},{13:[1,119],16:37,17:118,18:38,74:d,80:E,95:C,97:m,98:k},e(J,[2,61],{57:120,59:Y,60:j,61:Q,62:X,63:H}),e(J,[2,60]),{39:[1,121]},{23:90,38:122,41:22,44:A},{8:[1,123],39:[2,33]},e(W,[2,37],{37:[1,124]}),{39:[1,125]},{39:[2,43],43:126,47:_e},{16:37,17:127,18:38,74:d,80:E,95:C,97:m,98:k},e(c,[2,70],{13:[1,128]}),e(c,[2,72],{13:[1,130],68:[1,129]}),e(c,[2,76],{13:[1,131],71:[1,132]}),{13:[1,133]},e(c,[2,84],{78:[1,134]}),e(ze,[2,86],{79:135,21:Z,73:$,74:ee,80:te,81:se,82:ie,83:ne,84:ue,85:re}),e(S,[2,88]),e(S,[2,90]),e(S,[2,91]),e(S,[2,92]),e(S,[2,93]),e(S,[2,94]),e(S,[2,95]),e(S,[2,96]),e(S,[2,97]),e(S,[2,98]),e(c,[2,85]),e(c,[2,53]),{37:[2,10]},e(Se,[2,41]),{13:[1,136]},{1:[2,4]},e(ae,[2,51]),e(ae,[2,50]),{16:37,17:137,18:38,74:d,80:E,95:C,97:m,98:k},e(J,[2,59]),e(c,[2,30]),{39:[1,138]},{23:90,38:139,39:[2,34],41:22,44:A},{43:140,47:_e},e(W,[2,38]),{39:[2,44]},e(c,[2,42]),e(c,[2,71]),e(c,[2,73]),e(c,[2,74],{68:[1,141]}),e(c,[2,77]),e(c,[2,78],{13:[1,142]}),e(c,[2,80],{13:[1,144],68:[1,143]}),{21:Z,73:$,74:ee,77:145,79:101,80:te,81:se,82:ie,83:ne,84:ue,85:re},e(S,[2,89]),{14:[1,146]},e(ae,[2,52]),e(c,[2,31]),{39:[2,35]},{39:[1,147]},e(c,[2,75]),e(c,[2,79]),e(c,[2,81]),e(c,[2,82],{68:[1,148]}),e(ze,[2,87],{79:135,21:Z,73:$,74:ee,80:te,81:se,82:ie,83:ne,84:ue,85:re}),e(Se,[2,8]),e(W,[2,39]),e(c,[2,83])],defaultActions:{2:[2,1],3:[2,2],4:[2,3],78:[2,32],113:[2,10],116:[2,4],126:[2,44],139:[2,35]},parseError:function(u,a){if(a.recoverable)this.trace(u);else{var h=new Error(u);throw h.hash=a,h}},parse:function(u){var a=this,h=[0],n=[],f=[null],t=[],U=this.table,s="",le=0,Ke=0,tt=2,Ye=1,st=t.slice.call(arguments,1),b=Object.create(this.lexer),I={yy:{}};for(var ve in this.yy)Object.prototype.hasOwnProperty.call(this.yy,ve)&&(I.yy[ve]=this.yy[ve]);b.setInput(u,I.yy),I.yy.lexer=b,I.yy.parser=this,typeof b.yylloc>"u"&&(b.yylloc={});var xe=b.yylloc;t.push(xe);var it=b.options&&b.options.ranges;typeof I.yy.parseError=="function"?this.parseError=I.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function nt(){var L;return L=n.pop()||b.lex()||Ye,typeof L!="number"&&(L instanceof Array&&(n=L,L=n.pop()),L=a.symbols_[L]||L),L}for(var T,R,y,Oe,P={},ce,N,je,oe;;){if(R=h[h.length-1],this.defaultActions[R]?y=this.defaultActions[R]:((T===null||typeof T>"u")&&(T=nt()),y=U[R]&&U[R][T]),typeof y>"u"||!y.length||!y[0]){var Ie="";oe=[];for(ce in U[R])this.terminals_[ce]&&ce>tt&&oe.push("'"+this.terminals_[ce]+"'");b.showPosition?Ie="Parse error on line "+(le+1)+`:
 `+b.showPosition()+`
 Expecting `+oe.join(", ")+", got '"+(this.terminals_[T]||T)+"'":Ie="Parse error on line "+(le+1)+": Unexpected "+(T==Ye?"end of input":"'"+(this.terminals_[T]||T)+"'"),this.parseError(Ie,{text:b.match,token:this.terminals_[T]||T,line:b.yylineno,loc:xe,expected:oe})}if(y[0]instanceof Array&&y.length>1)throw new Error("Parse Error: multiple actions possible at state: "+R+", token: "+T);switch(y[0]){case 1:h.push(T),f.push(b.yytext),t.push(b.yylloc),h.push(y[1]),T=null,Ke=b.yyleng,s=b.yytext,le=b.yylineno,xe=b.yylloc;break;case 2:if(N=this.productions_[y[1]][1],P.$=f[f.length-N],P._$={first_line:t[t.length-(N||1)].first_line,last_line:t[t.length-1].last_line,first_column:t[t.length-(N||1)].first_column,last_column:t[t.length-1].last_column},it&&(P._$.range=[t[t.length-(N||1)].range[0],t[t.length-1].range[1]]),Oe=this.performAction.apply(P,[s,Ke,le,I.yy,y[1],f,t].concat(st)),typeof Oe<"u")return Oe;N&&(h=h.slice(0,-1*N*2),f=f.slice(0,-1*N),t=t.slice(0,-1*N)),h.push(this.productions_[y[1]][0]),f.push(P.$),t.push(P._$),je=U[h[h.length-2]][h[h.length-1]],h.push(je);break;case 3:return!0}}return!0}},et=function(){var x={EOF:1,parseError:function(a,h){if(this.yy.parser)this.yy.parser.parseError(a,h);else throw new Error(a)},setInput:function(u,a){return this.yy=a||this.yy||{},this._input=u,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var u=this._input[0];this.yytext+=u,this.yyleng++,this.offset++,this.match+=u,this.matched+=u;var a=u.match(/(?:\r\n?|\n).*/g);return a?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),u},unput:function(u){var a=u.length,h=u.split(/(?:\r\n?|\n)/g);this._input=u+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-a),this.offset-=a;var n=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),h.length-1&&(this.yylineno-=h.length-1);var f=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:h?(h.length===n.length?this.yylloc.first_column:0)+n[n.length-h.length].length-h[0].length:this.yylloc.first_column-a},this.options.ranges&&(this.yylloc.range=[f[0],f[0]+this.yyleng-a]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){if(this.options.backtrack_lexer)this._backtrack=!0;else return this.parseError("Lexical error on line "+(this.yylineno+1)+`. You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).
 `+this.showPosition(),{text:"",token:null,line:this.yylineno});return this},less:function(u){this.unput(this.match.slice(u))},pastInput:function(){var u=this.matched.substr(0,this.matched.length-this.match.length);return(u.length>20?"...":"")+u.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var u=this.match;return u.length<20&&(u+=this._input.substr(0,20-u.length)),(u.substr(0,20)+(u.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var u=this.pastInput(),a=new Array(u.length+1).join("-");return u+this.upcomingInput()+`
diff --git a/assets/svgDrawCommon-9d162435-DXbPg0E8.js b/assets/svgDrawCommon-9d162435-DBc9TLjw.js
similarity index 95%
rename from assets/svgDrawCommon-9d162435-DXbPg0E8.js
rename to assets/svgDrawCommon-9d162435-DBc9TLjw.js
index b0a2c42..6f8a560 100644
--- a/assets/svgDrawCommon-9d162435-DXbPg0E8.js
+++ b/assets/svgDrawCommon-9d162435-DBc9TLjw.js
@@ -1 +1 @@
-import{n as o,m as i}from"./mermaid.core-ChLYKTZm.js";const l=(s,t)=>{const e=s.append("rect");if(e.attr("x",t.x),e.attr("y",t.y),e.attr("fill",t.fill),e.attr("stroke",t.stroke),e.attr("width",t.width),e.attr("height",t.height),t.name&&e.attr("name",t.name),t.rx!==void 0&&e.attr("rx",t.rx),t.ry!==void 0&&e.attr("ry",t.ry),t.attrs!==void 0)for(const r in t.attrs)e.attr(r,t.attrs[r]);return t.class!==void 0&&e.attr("class",t.class),e},x=(s,t)=>{const e={x:t.startx,y:t.starty,width:t.stopx-t.startx,height:t.stopy-t.starty,fill:t.fill,stroke:t.stroke,class:"rect"};l(s,e).lower()},d=(s,t)=>{const e=t.text.replace(o," "),r=s.append("text");r.attr("x",t.x),r.attr("y",t.y),r.attr("class","legend"),r.style("text-anchor",t.anchor),t.class!==void 0&&r.attr("class",t.class);const n=r.append("tspan");return n.attr("x",t.x+t.textMargin*2),n.text(e),r},h=(s,t,e,r)=>{const n=s.append("image");n.attr("x",t),n.attr("y",e);const a=i.sanitizeUrl(r);n.attr("xlink:href",a)},y=(s,t,e,r)=>{const n=s.append("use");n.attr("x",t),n.attr("y",e);const a=i.sanitizeUrl(r);n.attr("xlink:href",`#${a}`)},g=()=>({x:0,y:0,width:100,height:100,fill:"#EDF2AE",stroke:"#666",anchor:"start",rx:0,ry:0}),m=()=>({x:0,y:0,width:100,height:100,"text-anchor":"start",style:"#666",textMargin:0,rx:0,ry:0,tspan:!0});export{x as a,m as b,y as c,l as d,h as e,d as f,g};
+import{n as o,m as i}from"./mermaid.core-DNo_7Q2B.js";const l=(s,t)=>{const e=s.append("rect");if(e.attr("x",t.x),e.attr("y",t.y),e.attr("fill",t.fill),e.attr("stroke",t.stroke),e.attr("width",t.width),e.attr("height",t.height),t.name&&e.attr("name",t.name),t.rx!==void 0&&e.attr("rx",t.rx),t.ry!==void 0&&e.attr("ry",t.ry),t.attrs!==void 0)for(const r in t.attrs)e.attr(r,t.attrs[r]);return t.class!==void 0&&e.attr("class",t.class),e},x=(s,t)=>{const e={x:t.startx,y:t.starty,width:t.stopx-t.startx,height:t.stopy-t.starty,fill:t.fill,stroke:t.stroke,class:"rect"};l(s,e).lower()},d=(s,t)=>{const e=t.text.replace(o," "),r=s.append("text");r.attr("x",t.x),r.attr("y",t.y),r.attr("class","legend"),r.style("text-anchor",t.anchor),t.class!==void 0&&r.attr("class",t.class);const n=r.append("tspan");return n.attr("x",t.x+t.textMargin*2),n.text(e),r},h=(s,t,e,r)=>{const n=s.append("image");n.attr("x",t),n.attr("y",e);const a=i.sanitizeUrl(r);n.attr("xlink:href",a)},y=(s,t,e,r)=>{const n=s.append("use");n.attr("x",t),n.attr("y",e);const a=i.sanitizeUrl(r);n.attr("xlink:href",`#${a}`)},g=()=>({x:0,y:0,width:100,height:100,fill:"#EDF2AE",stroke:"#666",anchor:"start",rx:0,ry:0}),m=()=>({x:0,y:0,width:100,height:100,"text-anchor":"start",style:"#666",textMargin:0,rx:0,ry:0,tspan:!0});export{x as a,m as b,y as c,l as d,h as e,d as f,g};
diff --git a/assets/template_method.html-Do5aF6Sl.js b/assets/template_method.html-B7oRZ-kS.js
similarity index 99%
rename from assets/template_method.html-Do5aF6Sl.js
rename to assets/template_method.html-B7oRZ-kS.js
index 868ee25..c6f41af 100644
--- a/assets/template_method.html-Do5aF6Sl.js
+++ b/assets/template_method.html-B7oRZ-kS.js
@@ -1,4 +1,4 @@
-import{_ as n,o as s,c as a,a as t,b as p,f as e}from"./app-B69Gl_S-.js";const o={},c=p("p",null,"在父类中定义处理流程的框架，在子类中实现具体处理。Template Method 模式的主要目的是为了定义一个算法的骨架，而将一些步骤的具体实现延迟到子类中。通过这种方式，子类可以在不改变算法结构的情况下，重新定义算法中的某些步骤。",-1),l=e(`<h2 id="为什么要使用-template-method-模式" tabindex="-1"><a class="header-anchor" href="#为什么要使用-template-method-模式"><span>为什么要使用 Template Method 模式？</span></a></h2><ol><li><strong>代码复用</strong>：将通用的算法结构放在父类中，避免重复代码。</li><li><strong>灵活性</strong>：允许子类实现具体的步骤，增加了灵活性。</li><li><strong>控制反转</strong>：父类控制算法的执行流程，子类只需关注具体步骤的实现。</li></ol><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/dP513i8W44Ntd68IDpI42pGkQdJfpXDG89Q4GWEqngXt5wbHgBfnENy-__qCZG_CXR7NYBK-ECO3SCsyXyrpt2a_Q7Q62m8W8EO9LpLCLecehS0EqXJ2u9G9XSArzVAbt12Q6TkEkJoV0kzgY5nbZWcN6V1xLQNT0ai-iEGNzf1IId1CpiWKJag423HZtqgNmefNEFF_MUT1IPwzCaN9vUNNLqhpItmt5FLG8us8dte7" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// abstractDisplay.ts</span>
+import{_ as n,o as s,c as a,a as t,b as p,f as e}from"./app-B4LGNJZ0.js";const o={},c=p("p",null,"在父类中定义处理流程的框架，在子类中实现具体处理。Template Method 模式的主要目的是为了定义一个算法的骨架，而将一些步骤的具体实现延迟到子类中。通过这种方式，子类可以在不改变算法结构的情况下，重新定义算法中的某些步骤。",-1),l=e(`<h2 id="为什么要使用-template-method-模式" tabindex="-1"><a class="header-anchor" href="#为什么要使用-template-method-模式"><span>为什么要使用 Template Method 模式？</span></a></h2><ol><li><strong>代码复用</strong>：将通用的算法结构放在父类中，避免重复代码。</li><li><strong>灵活性</strong>：允许子类实现具体的步骤，增加了灵活性。</li><li><strong>控制反转</strong>：父类控制算法的执行流程，子类只需关注具体步骤的实现。</li></ol><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/dP513i8W44Ntd68IDpI42pGkQdJfpXDG89Q4GWEqngXt5wbHgBfnENy-__qCZG_CXR7NYBK-ECO3SCsyXyrpt2a_Q7Q62m8W8EO9LpLCLecehS0EqXJ2u9G9XSArzVAbt12Q6TkEkJoV0kzgY5nbZWcN6V1xLQNT0ai-iEGNzf1IId1CpiWKJag423HZtqgNmefNEFF_MUT1IPwzCaN9vUNNLqhpItmt5FLG8us8dte7" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// abstractDisplay.ts</span>
 <span class="token keyword">export</span> <span class="token keyword">abstract</span> <span class="token keyword">class</span> <span class="token class-name">AbstractDisplay</span> <span class="token punctuation">{</span>
   <span class="token keyword">protected</span> <span class="token keyword">abstract</span> <span class="token function">open</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">:</span> <span class="token keyword">void</span><span class="token punctuation">;</span>
   <span class="token keyword">protected</span> <span class="token keyword">abstract</span> <span class="token function">print</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">:</span> <span class="token keyword">void</span><span class="token punctuation">;</span>
diff --git "a/assets/tensorflow\350\270\251\345\235\221.html-BAaphJ4H.js" "b/assets/tensorflow\350\270\251\345\235\221.html-CtBHw7dX.js"
similarity index 97%
rename from "assets/tensorflow\350\270\251\345\235\221.html-BAaphJ4H.js"
rename to "assets/tensorflow\350\270\251\345\235\221.html-CtBHw7dX.js"
index 87eae76..68d09a5 100644
--- "a/assets/tensorflow\350\270\251\345\235\221.html-BAaphJ4H.js"
+++ "b/assets/tensorflow\350\270\251\345\235\221.html-CtBHw7dX.js"
@@ -1 +1 @@
-import{_ as o,o as r,c as n,a as l,b as t,e}from"./app-B69Gl_S-.js";const s={},c=t("p",null,[t("strong",null,"Pytorch 用于快速原型验证（学术研究）， TensorFlow 用于工业生产部署")],-1),a=t("p",null,[e("近日使用 TensorFlow 完成图像去噪任务，然而速度太慢，于是寻求 GPU 资源进行加速。本以为 TensorFlow 2 能轻松使用 GPU（当然需要配置相关驱动），谁知 TensorFlow 高版本（>=2.10.0）不再支持 Windows，而 Pytorch 仍然支持。最终 "),t("s",null,"选择了 Pytorch 进行实验"),e(" 寻得了Linux GPU 环境（感谢lucky&agicy）。")],-1),i=t("p",null,"此外，Pytorch 的动态计算图机制使得调试和开发更加灵活，适合快速迭代和原型验证。而 TensorFlow 虽然在工业部署中表现出色，但其静态计算图机制在开发过程中略显繁琐。综合考虑，决定以后在学术研究和快速原型验证阶段使用 Pytorch，而在工业生产部署阶段方才使用 TensorFlow（当然得是Linux环境）。",-1);function p(h,m){return r(),n("div",null,[c,l(" more "),a,i])}const u=o(s,[["render",p],["__file","tensorflow踩坑.html.vue"]]),y=JSON.parse('{"path":"/tech/tensorflow%E8%B8%A9%E5%9D%91.html","title":"tensorflow 踩坑记录","lang":"zh-CN","frontmatter":{"date":"2024-11-01T00:00:00.000Z","title":"tensorflow 踩坑记录","description":"Pytorch 用于快速原型验证（学术研究）， TensorFlow 用于工业生产部署","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/tensorflow%E8%B8%A9%E5%9D%91.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"tensorflow 踩坑记录"}],["meta",{"property":"og:description","content":"Pytorch 用于快速原型验证（学术研究）， TensorFlow 用于工业生产部署"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:published_time","content":"2024-11-01T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"tensorflow 踩坑记录\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-11-01T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.79,"words":236},"filePathRelative":"tech/tensorflow踩坑.md","localizedDate":"2024年11月1日","excerpt":"<p><strong>Pytorch 用于快速原型验证（学术研究）， TensorFlow 用于工业生产部署</strong></p>\\n","autoDesc":true}');export{u as comp,y as data};
+import{_ as o,o as r,c as n,a as l,b as t,e}from"./app-B4LGNJZ0.js";const s={},c=t("p",null,[t("strong",null,"Pytorch 用于快速原型验证（学术研究）， TensorFlow 用于工业生产部署")],-1),a=t("p",null,[e("近日使用 TensorFlow 完成图像去噪任务，然而速度太慢，于是寻求 GPU 资源进行加速。本以为 TensorFlow 2 能轻松使用 GPU（当然需要配置相关驱动），谁知 TensorFlow 高版本（>=2.10.0）不再支持 Windows，而 Pytorch 仍然支持。最终 "),t("s",null,"选择了 Pytorch 进行实验"),e(" 寻得了Linux GPU 环境（感谢lucky&agicy）。")],-1),i=t("p",null,"此外，Pytorch 的动态计算图机制使得调试和开发更加灵活，适合快速迭代和原型验证。而 TensorFlow 虽然在工业部署中表现出色，但其静态计算图机制在开发过程中略显繁琐。综合考虑，决定以后在学术研究和快速原型验证阶段使用 Pytorch，而在工业生产部署阶段方才使用 TensorFlow（当然得是Linux环境）。",-1);function p(h,m){return r(),n("div",null,[c,l(" more "),a,i])}const u=o(s,[["render",p],["__file","tensorflow踩坑.html.vue"]]),y=JSON.parse('{"path":"/tech/tensorflow%E8%B8%A9%E5%9D%91.html","title":"tensorflow 踩坑记录","lang":"zh-CN","frontmatter":{"date":"2024-11-01T00:00:00.000Z","title":"tensorflow 踩坑记录","description":"Pytorch 用于快速原型验证（学术研究）， TensorFlow 用于工业生产部署","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/tensorflow%E8%B8%A9%E5%9D%91.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"tensorflow 踩坑记录"}],["meta",{"property":"og:description","content":"Pytorch 用于快速原型验证（学术研究）， TensorFlow 用于工业生产部署"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:published_time","content":"2024-11-01T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"tensorflow 踩坑记录\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-11-01T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.79,"words":236},"filePathRelative":"tech/tensorflow踩坑.md","localizedDate":"2024年11月1日","excerpt":"<p><strong>Pytorch 用于快速原型验证（学术研究）， TensorFlow 用于工业生产部署</strong></p>\\n","autoDesc":true}');export{u as comp,y as data};
diff --git a/assets/timeline-definition-6eaa3543-BApSUGyX.js b/assets/timeline-definition-6eaa3543-CYqJxmAu.js
similarity index 99%
rename from assets/timeline-definition-6eaa3543-BApSUGyX.js
rename to assets/timeline-definition-6eaa3543-CYqJxmAu.js
index d79eab6..3513633 100644
--- a/assets/timeline-definition-6eaa3543-BApSUGyX.js
+++ b/assets/timeline-definition-6eaa3543-CYqJxmAu.js
@@ -1,4 +1,4 @@
-import{b4 as ft,A as gt,c as mt,l as E,h as G,u as xt,b5 as bt,b6 as _t,b7 as kt}from"./mermaid.core-ChLYKTZm.js";import{a as D}from"./arc-BCmLGSVu.js";import"./app-B69Gl_S-.js";import"./path-CbwjOpE9.js";var K=function(){var n=function(g,i,r,c){for(r=r||{},c=g.length;c--;r[g[c]]=i);return r},t=[6,8,10,11,12,14,16,17,20,21],e=[1,9],a=[1,10],s=[1,11],h=[1,12],l=[1,13],p=[1,16],y=[1,17],f={trace:function(){},yy:{},symbols_:{error:2,start:3,timeline:4,document:5,EOF:6,line:7,SPACE:8,statement:9,NEWLINE:10,title:11,acc_title:12,acc_title_value:13,acc_descr:14,acc_descr_value:15,acc_descr_multiline_value:16,section:17,period_statement:18,event_statement:19,period:20,event:21,$accept:0,$end:1},terminals_:{2:"error",4:"timeline",6:"EOF",8:"SPACE",10:"NEWLINE",11:"title",12:"acc_title",13:"acc_title_value",14:"acc_descr",15:"acc_descr_value",16:"acc_descr_multiline_value",17:"section",20:"period",21:"event"},productions_:[0,[3,3],[5,0],[5,2],[7,2],[7,1],[7,1],[7,1],[9,1],[9,2],[9,2],[9,1],[9,1],[9,1],[9,1],[18,1],[19,1]],performAction:function(i,r,c,d,u,o,$){var x=o.length-1;switch(u){case 1:return o[x-1];case 2:this.$=[];break;case 3:o[x-1].push(o[x]),this.$=o[x-1];break;case 4:case 5:this.$=o[x];break;case 6:case 7:this.$=[];break;case 8:d.getCommonDb().setDiagramTitle(o[x].substr(6)),this.$=o[x].substr(6);break;case 9:this.$=o[x].trim(),d.getCommonDb().setAccTitle(this.$);break;case 10:case 11:this.$=o[x].trim(),d.getCommonDb().setAccDescription(this.$);break;case 12:d.addSection(o[x].substr(8)),this.$=o[x].substr(8);break;case 15:d.addTask(o[x],0,""),this.$=o[x];break;case 16:d.addEvent(o[x].substr(2)),this.$=o[x];break}},table:[{3:1,4:[1,2]},{1:[3]},n(t,[2,2],{5:3}),{6:[1,4],7:5,8:[1,6],9:7,10:[1,8],11:e,12:a,14:s,16:h,17:l,18:14,19:15,20:p,21:y},n(t,[2,7],{1:[2,1]}),n(t,[2,3]),{9:18,11:e,12:a,14:s,16:h,17:l,18:14,19:15,20:p,21:y},n(t,[2,5]),n(t,[2,6]),n(t,[2,8]),{13:[1,19]},{15:[1,20]},n(t,[2,11]),n(t,[2,12]),n(t,[2,13]),n(t,[2,14]),n(t,[2,15]),n(t,[2,16]),n(t,[2,4]),n(t,[2,9]),n(t,[2,10])],defaultActions:{},parseError:function(i,r){if(r.recoverable)this.trace(i);else{var c=new Error(i);throw c.hash=r,c}},parse:function(i){var r=this,c=[0],d=[],u=[null],o=[],$=this.table,x="",T=0,W=0,C=2,A=1,B=o.slice.call(arguments,1),k=Object.create(this.lexer),w={yy:{}};for(var v in this.yy)Object.prototype.hasOwnProperty.call(this.yy,v)&&(w.yy[v]=this.yy[v]);k.setInput(i,w.yy),w.yy.lexer=k,w.yy.parser=this,typeof k.yylloc>"u"&&(k.yylloc={});var I=k.yylloc;o.push(I);var P=k.options&&k.options.ranges;typeof w.yy.parseError=="function"?this.parseError=w.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function z(){var M;return M=d.pop()||k.lex()||A,typeof M!="number"&&(M instanceof Array&&(d=M,M=d.pop()),M=r.symbols_[M]||M),M}for(var _,L,S,Z,R={},O,N,Y,j;;){if(L=c[c.length-1],this.defaultActions[L]?S=this.defaultActions[L]:((_===null||typeof _>"u")&&(_=z()),S=$[L]&&$[L][_]),typeof S>"u"||!S.length||!S[0]){var J="";j=[];for(O in $[L])this.terminals_[O]&&O>C&&j.push("'"+this.terminals_[O]+"'");k.showPosition?J="Parse error on line "+(T+1)+`:
+import{b4 as ft,A as gt,c as mt,l as E,h as G,u as xt,b5 as bt,b6 as _t,b7 as kt}from"./mermaid.core-DNo_7Q2B.js";import{a as D}from"./arc-DWlpCdAw.js";import"./app-B4LGNJZ0.js";import"./path-CbwjOpE9.js";var K=function(){var n=function(g,i,r,c){for(r=r||{},c=g.length;c--;r[g[c]]=i);return r},t=[6,8,10,11,12,14,16,17,20,21],e=[1,9],a=[1,10],s=[1,11],h=[1,12],l=[1,13],p=[1,16],y=[1,17],f={trace:function(){},yy:{},symbols_:{error:2,start:3,timeline:4,document:5,EOF:6,line:7,SPACE:8,statement:9,NEWLINE:10,title:11,acc_title:12,acc_title_value:13,acc_descr:14,acc_descr_value:15,acc_descr_multiline_value:16,section:17,period_statement:18,event_statement:19,period:20,event:21,$accept:0,$end:1},terminals_:{2:"error",4:"timeline",6:"EOF",8:"SPACE",10:"NEWLINE",11:"title",12:"acc_title",13:"acc_title_value",14:"acc_descr",15:"acc_descr_value",16:"acc_descr_multiline_value",17:"section",20:"period",21:"event"},productions_:[0,[3,3],[5,0],[5,2],[7,2],[7,1],[7,1],[7,1],[9,1],[9,2],[9,2],[9,1],[9,1],[9,1],[9,1],[18,1],[19,1]],performAction:function(i,r,c,d,u,o,$){var x=o.length-1;switch(u){case 1:return o[x-1];case 2:this.$=[];break;case 3:o[x-1].push(o[x]),this.$=o[x-1];break;case 4:case 5:this.$=o[x];break;case 6:case 7:this.$=[];break;case 8:d.getCommonDb().setDiagramTitle(o[x].substr(6)),this.$=o[x].substr(6);break;case 9:this.$=o[x].trim(),d.getCommonDb().setAccTitle(this.$);break;case 10:case 11:this.$=o[x].trim(),d.getCommonDb().setAccDescription(this.$);break;case 12:d.addSection(o[x].substr(8)),this.$=o[x].substr(8);break;case 15:d.addTask(o[x],0,""),this.$=o[x];break;case 16:d.addEvent(o[x].substr(2)),this.$=o[x];break}},table:[{3:1,4:[1,2]},{1:[3]},n(t,[2,2],{5:3}),{6:[1,4],7:5,8:[1,6],9:7,10:[1,8],11:e,12:a,14:s,16:h,17:l,18:14,19:15,20:p,21:y},n(t,[2,7],{1:[2,1]}),n(t,[2,3]),{9:18,11:e,12:a,14:s,16:h,17:l,18:14,19:15,20:p,21:y},n(t,[2,5]),n(t,[2,6]),n(t,[2,8]),{13:[1,19]},{15:[1,20]},n(t,[2,11]),n(t,[2,12]),n(t,[2,13]),n(t,[2,14]),n(t,[2,15]),n(t,[2,16]),n(t,[2,4]),n(t,[2,9]),n(t,[2,10])],defaultActions:{},parseError:function(i,r){if(r.recoverable)this.trace(i);else{var c=new Error(i);throw c.hash=r,c}},parse:function(i){var r=this,c=[0],d=[],u=[null],o=[],$=this.table,x="",T=0,W=0,C=2,A=1,B=o.slice.call(arguments,1),k=Object.create(this.lexer),w={yy:{}};for(var v in this.yy)Object.prototype.hasOwnProperty.call(this.yy,v)&&(w.yy[v]=this.yy[v]);k.setInput(i,w.yy),w.yy.lexer=k,w.yy.parser=this,typeof k.yylloc>"u"&&(k.yylloc={});var I=k.yylloc;o.push(I);var P=k.options&&k.options.ranges;typeof w.yy.parseError=="function"?this.parseError=w.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function z(){var M;return M=d.pop()||k.lex()||A,typeof M!="number"&&(M instanceof Array&&(d=M,M=d.pop()),M=r.symbols_[M]||M),M}for(var _,L,S,Z,R={},O,N,Y,j;;){if(L=c[c.length-1],this.defaultActions[L]?S=this.defaultActions[L]:((_===null||typeof _>"u")&&(_=z()),S=$[L]&&$[L][_]),typeof S>"u"||!S.length||!S[0]){var J="";j=[];for(O in $[L])this.terminals_[O]&&O>C&&j.push("'"+this.terminals_[O]+"'");k.showPosition?J="Parse error on line "+(T+1)+`:
 `+k.showPosition()+`
 Expecting `+j.join(", ")+", got '"+(this.terminals_[_]||_)+"'":J="Parse error on line "+(T+1)+": Unexpected "+(_==A?"end of input":"'"+(this.terminals_[_]||_)+"'"),this.parseError(J,{text:k.match,token:this.terminals_[_]||_,line:k.yylineno,loc:I,expected:j})}if(S[0]instanceof Array&&S.length>1)throw new Error("Parse Error: multiple actions possible at state: "+L+", token: "+_);switch(S[0]){case 1:c.push(_),u.push(k.yytext),o.push(k.yylloc),c.push(S[1]),_=null,W=k.yyleng,x=k.yytext,T=k.yylineno,I=k.yylloc;break;case 2:if(N=this.productions_[S[1]][1],R.$=u[u.length-N],R._$={first_line:o[o.length-(N||1)].first_line,last_line:o[o.length-1].last_line,first_column:o[o.length-(N||1)].first_column,last_column:o[o.length-1].last_column},P&&(R._$.range=[o[o.length-(N||1)].range[0],o[o.length-1].range[1]]),Z=this.performAction.apply(R,[x,W,T,w.yy,S[1],u,o].concat(B)),typeof Z<"u")return Z;N&&(c=c.slice(0,-1*N*2),u=u.slice(0,-1*N),o=o.slice(0,-1*N)),c.push(this.productions_[S[1]][0]),u.push(R.$),o.push(R._$),Y=$[c[c.length-2]][c[c.length-1]],c.push(Y);break;case 3:return!0}}return!0}},b=function(){var g={EOF:1,parseError:function(r,c){if(this.yy.parser)this.yy.parser.parseError(r,c);else throw new Error(r)},setInput:function(i,r){return this.yy=r||this.yy||{},this._input=i,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var i=this._input[0];this.yytext+=i,this.yyleng++,this.offset++,this.match+=i,this.matched+=i;var r=i.match(/(?:\r\n?|\n).*/g);return r?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),i},unput:function(i){var r=i.length,c=i.split(/(?:\r\n?|\n)/g);this._input=i+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-r),this.offset-=r;var d=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),c.length-1&&(this.yylineno-=c.length-1);var u=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:c?(c.length===d.length?this.yylloc.first_column:0)+d[d.length-c.length].length-c[0].length:this.yylloc.first_column-r},this.options.ranges&&(this.yylloc.range=[u[0],u[0]+this.yyleng-r]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){if(this.options.backtrack_lexer)this._backtrack=!0;else return this.parseError("Lexical error on line "+(this.yylineno+1)+`. You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).
 `+this.showPosition(),{text:"",token:null,line:this.yylineno});return this},less:function(i){this.unput(this.match.slice(i))},pastInput:function(){var i=this.matched.substr(0,this.matched.length-this.match.length);return(i.length>20?"...":"")+i.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var i=this.match;return i.length<20&&(i+=this._input.substr(0,20-i.length)),(i.substr(0,20)+(i.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var i=this.pastInput(),r=new Array(i.length+1).join("-");return i+this.upcomingInput()+`
diff --git "a/assets/typora\346\277\200\346\264\273.html-BuwKOD8g.js" "b/assets/typora\346\277\200\346\264\273.html-DUOLfN6Y.js"
similarity index 98%
rename from "assets/typora\346\277\200\346\264\273.html-BuwKOD8g.js"
rename to "assets/typora\346\277\200\346\264\273.html-DUOLfN6Y.js"
index 45420eb..86750a9 100644
--- "a/assets/typora\346\277\200\346\264\273.html-BuwKOD8g.js"
+++ "b/assets/typora\346\277\200\346\264\273.html-DUOLfN6Y.js"
@@ -1 +1 @@
-import{_ as a,r as n,o as p,c as l,b as e,e as t,d as r,a as i,f as c}from"./app-B69Gl_S-.js";const s={},d=e("h1",{id:"typora-简介",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#typora-简介"},[e("span",null,"Typora 简介")])],-1),h=e("p",null,"Typora 是一款简洁高效的 Markdown 编辑器，支持实时预览和多种导出格式，适用于编写笔记、文档和博客等。",-1),y=e("h1",{id:"安装教程",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#安装教程"},[e("span",null,"安装教程")])],-1),_={href:"https://typora.io",target:"_blank",rel:"noopener noreferrer"},u={href:"https://typoraio.cn",target:"_blank",rel:"noopener noreferrer"},m={href:"https://pan.baidu.com/share/init?surl=gga2OZ732Xvig1QKn52NHQ",target:"_blank",rel:"noopener noreferrer"},g=c('<ol><li><p>一路点击“下一步”进行安装。<strong>将下载的工具解压后得到的两个 exe 文件（license-gen.exe 和 node_inject.exe）复制到 Typora 安装目录下</strong>（默认为 <code>C:\\Program Files\\Typora\\</code>）。</p></li><li><p>以管理员身份在 Typora 安装路径打开 PowerShell。</p></li><li><p>输入 <code>node_inject.exe</code> 并回车，等待提示 &quot;done!&quot;。</p></li><li><p>输入 <code>license-gen.exe</code> 并回车，等待显示序列号。</p></li><li><p>启动 Typora，输入任意邮箱和刚才生成的序列号到激活窗口，并点击激活。</p></li></ol><h1 id="结语" tabindex="-1"><a class="header-anchor" href="#结语"><span>结语</span></a></h1><p>通过上述步骤，您可以免费安装并使用 Typora，但如有条件还请支持正版。</p>',3);function T(f,x){const o=n("ExternalLinkIcon");return p(),l("div",null,[d,h,y,e("ul",null,[e("li",null,[e("a",_,[t("Typora 官网"),r(o)])]),e("li",null,[e("a",u,[t("Typora 中文官网"),r(o)])])]),i(" TODO: 添加自己的静态服务 "),e("ul",null,[e("li",null,[t("工具下载："),e("a",m,[t("百度网盘，密码：dcqe"),r(o)])])]),g])}const k=a(s,[["render",T],["__file","typora激活.html.vue"]]),B=JSON.parse('{"path":"/tutorials/typora%E6%BF%80%E6%B4%BB.html","title":"Typora激活教程","lang":"zh-CN","frontmatter":{"title":"Typora激活教程","date":"2024-10-21T00:00:00.000Z","tags":["激活"],"description":"Typora 简介 Typora 是一款简洁高效的 Markdown 编辑器，支持实时预览和多种导出格式，适用于编写笔记、文档和博客等。 安装教程 Typora 官网 Typora 中文官网 工具下载：百度网盘，密码：dcqe 一路点击“下一步”进行安装。将下载的工具解压后得到的两个 exe 文件（license-gen.exe 和 node_inje...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tutorials/typora%E6%BF%80%E6%B4%BB.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"Typora激活教程"}],["meta",{"property":"og:description","content":"Typora 简介 Typora 是一款简洁高效的 Markdown 编辑器，支持实时预览和多种导出格式，适用于编写笔记、文档和博客等。 安装教程 Typora 官网 Typora 中文官网 工具下载：百度网盘，密码：dcqe 一路点击“下一步”进行安装。将下载的工具解压后得到的两个 exe 文件（license-gen.exe 和 node_inje..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"激活"}],["meta",{"property":"article:published_time","content":"2024-10-21T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"Typora激活教程\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-10-21T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.82,"words":247},"filePathRelative":"tutorials/typora激活.md","localizedDate":"2024年10月21日","excerpt":"\\n<p>Typora 是一款简洁高效的 Markdown 编辑器，支持实时预览和多种导出格式，适用于编写笔记、文档和博客等。</p>\\n<h1>安装教程</h1>\\n<ul>\\n<li><a href=\\"https://typora.io\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">Typora 官网</a></li>\\n<li><a href=\\"https://typoraio.cn\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">Typora 中文官网</a></li>\\n</ul>\\n<!-- TODO: 添加自己的静态服务 -->","autoDesc":true}');export{k as comp,B as data};
+import{_ as a,r as n,o as p,c as l,b as e,e as t,d as r,a as i,f as c}from"./app-B4LGNJZ0.js";const s={},d=e("h1",{id:"typora-简介",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#typora-简介"},[e("span",null,"Typora 简介")])],-1),h=e("p",null,"Typora 是一款简洁高效的 Markdown 编辑器，支持实时预览和多种导出格式，适用于编写笔记、文档和博客等。",-1),y=e("h1",{id:"安装教程",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#安装教程"},[e("span",null,"安装教程")])],-1),_={href:"https://typora.io",target:"_blank",rel:"noopener noreferrer"},u={href:"https://typoraio.cn",target:"_blank",rel:"noopener noreferrer"},m={href:"https://pan.baidu.com/share/init?surl=gga2OZ732Xvig1QKn52NHQ",target:"_blank",rel:"noopener noreferrer"},g=c('<ol><li><p>一路点击“下一步”进行安装。<strong>将下载的工具解压后得到的两个 exe 文件（license-gen.exe 和 node_inject.exe）复制到 Typora 安装目录下</strong>（默认为 <code>C:\\Program Files\\Typora\\</code>）。</p></li><li><p>以管理员身份在 Typora 安装路径打开 PowerShell。</p></li><li><p>输入 <code>node_inject.exe</code> 并回车，等待提示 &quot;done!&quot;。</p></li><li><p>输入 <code>license-gen.exe</code> 并回车，等待显示序列号。</p></li><li><p>启动 Typora，输入任意邮箱和刚才生成的序列号到激活窗口，并点击激活。</p></li></ol><h1 id="结语" tabindex="-1"><a class="header-anchor" href="#结语"><span>结语</span></a></h1><p>通过上述步骤，您可以免费安装并使用 Typora，但如有条件还请支持正版。</p>',3);function T(f,x){const o=n("ExternalLinkIcon");return p(),l("div",null,[d,h,y,e("ul",null,[e("li",null,[e("a",_,[t("Typora 官网"),r(o)])]),e("li",null,[e("a",u,[t("Typora 中文官网"),r(o)])])]),i(" TODO: 添加自己的静态服务 "),e("ul",null,[e("li",null,[t("工具下载："),e("a",m,[t("百度网盘，密码：dcqe"),r(o)])])]),g])}const k=a(s,[["render",T],["__file","typora激活.html.vue"]]),B=JSON.parse('{"path":"/tutorials/typora%E6%BF%80%E6%B4%BB.html","title":"Typora激活教程","lang":"zh-CN","frontmatter":{"title":"Typora激活教程","date":"2024-10-21T00:00:00.000Z","tags":["激活"],"description":"Typora 简介 Typora 是一款简洁高效的 Markdown 编辑器，支持实时预览和多种导出格式，适用于编写笔记、文档和博客等。 安装教程 Typora 官网 Typora 中文官网 工具下载：百度网盘，密码：dcqe 一路点击“下一步”进行安装。将下载的工具解压后得到的两个 exe 文件（license-gen.exe 和 node_inje...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tutorials/typora%E6%BF%80%E6%B4%BB.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"Typora激活教程"}],["meta",{"property":"og:description","content":"Typora 简介 Typora 是一款简洁高效的 Markdown 编辑器，支持实时预览和多种导出格式，适用于编写笔记、文档和博客等。 安装教程 Typora 官网 Typora 中文官网 工具下载：百度网盘，密码：dcqe 一路点击“下一步”进行安装。将下载的工具解压后得到的两个 exe 文件（license-gen.exe 和 node_inje..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"激活"}],["meta",{"property":"article:published_time","content":"2024-10-21T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"Typora激活教程\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-10-21T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.82,"words":247},"filePathRelative":"tutorials/typora激活.md","localizedDate":"2024年10月21日","excerpt":"\\n<p>Typora 是一款简洁高效的 Markdown 编辑器，支持实时预览和多种导出格式，适用于编写笔记、文档和博客等。</p>\\n<h1>安装教程</h1>\\n<ul>\\n<li><a href=\\"https://typora.io\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">Typora 官网</a></li>\\n<li><a href=\\"https://typoraio.cn\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">Typora 中文官网</a></li>\\n</ul>\\n<!-- TODO: 添加自己的静态服务 -->","autoDesc":true}');export{k as comp,B as data};
diff --git a/assets/visitor.html-C6V612X1.js b/assets/visitor.html-DaIekGHb.js
similarity index 99%
rename from assets/visitor.html-C6V612X1.js
rename to assets/visitor.html-DaIekGHb.js
index 90f7b44..d84538e 100644
--- a/assets/visitor.html-C6V612X1.js
+++ b/assets/visitor.html-DaIekGHb.js
@@ -1,4 +1,4 @@
-import{_ as n,o as s,c as a,a as t,b as p,f as o}from"./app-B69Gl_S-.js";const e={},c=p("p",null,"在 Visitor 模式中，数据结构与处理被分离开来。我们编写一个表示“访问者”的类来访问数据结构中的元素，并把对各元素的处理交给访问者类。这样，当需要增加新的处理时，我们只需要编写新的访问者，然后让数据结构可以接受访问者的访问即可。",-1),i=o(`<h3 id="为什么使用-visitor-模式" tabindex="-1"><a class="header-anchor" href="#为什么使用-visitor-模式"><span>为什么使用 Visitor 模式？</span></a></h3><ol><li><strong>分离关注点</strong>：将数据结构与操作分离，使得代码更清晰、更易维护。</li><li><strong>增加新操作更容易</strong>：只需添加新的访问者类，而不需要修改现有的数据结构。</li><li><strong>符合开闭原则</strong>：对扩展开放，对修改关闭。</li></ol><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/fPCnRiCm34LtdOAZWq8Ny51aQ3eLNG9aAJeeCXiGiEH0eeCcGUzUIh9JkqEQe9E5J_7nVq9UHZQ1UzSgyepXmrY4LOiEFSDP0JmOQt7FrO4YSHTgs9J3eeP3HutwKifi8mTZ6MnhOeILvt04Slj2YNFS3ldLEAoaNxh8xmPnJQSi-jvjCUJ1JLDXOjK5kHY-gKPYrOYBQXJVtfFCtJepv_I_4nJZpzGYu2UZRyOKoRBsudV2qr6iJetU4Ub69qyKq4hXU8kTXi9i2V_Qy6NobItV_IA62-K1vBRVO-VnNoZos3CkOChGjWz123dvJyQhvB90hHylf1fA43KAgLYkILlIr596ow_n3G00" alt=""><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuKfCBialKd3EoKpDA-62K0gwTWekcKMf89bA1Ik5n9GK3Q1mKQMLWYk8qiIbBZavjQ14eoopE1CeOgKG1c5eSY4K0NNuP1QNG6M0Ui2AqKn7Le5cHMP9Qb4YaAs1PgXRPaugFXUW6GbLZiroXzIy562u0000" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// directory.ts</span>
+import{_ as n,o as s,c as a,a as t,b as p,f as o}from"./app-B4LGNJZ0.js";const e={},c=p("p",null,"在 Visitor 模式中，数据结构与处理被分离开来。我们编写一个表示“访问者”的类来访问数据结构中的元素，并把对各元素的处理交给访问者类。这样，当需要增加新的处理时，我们只需要编写新的访问者，然后让数据结构可以接受访问者的访问即可。",-1),i=o(`<h3 id="为什么使用-visitor-模式" tabindex="-1"><a class="header-anchor" href="#为什么使用-visitor-模式"><span>为什么使用 Visitor 模式？</span></a></h3><ol><li><strong>分离关注点</strong>：将数据结构与操作分离，使得代码更清晰、更易维护。</li><li><strong>增加新操作更容易</strong>：只需添加新的访问者类，而不需要修改现有的数据结构。</li><li><strong>符合开闭原则</strong>：对扩展开放，对修改关闭。</li></ol><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/fPCnRiCm34LtdOAZWq8Ny51aQ3eLNG9aAJeeCXiGiEH0eeCcGUzUIh9JkqEQe9E5J_7nVq9UHZQ1UzSgyepXmrY4LOiEFSDP0JmOQt7FrO4YSHTgs9J3eeP3HutwKifi8mTZ6MnhOeILvt04Slj2YNFS3ldLEAoaNxh8xmPnJQSi-jvjCUJ1JLDXOjK5kHY-gKPYrOYBQXJVtfFCtJepv_I_4nJZpzGYu2UZRyOKoRBsudV2qr6iJetU4Ub69qyKq4hXU8kTXi9i2V_Qy6NobItV_IA62-K1vBRVO-VnNoZos3CkOChGjWz123dvJyQhvB90hHylf1fA43KAgLYkILlIr596ow_n3G00" alt=""><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuKfCBialKd3EoKpDA-62K0gwTWekcKMf89bA1Ik5n9GK3Q1mKQMLWYk8qiIbBZavjQ14eoopE1CeOgKG1c5eSY4K0NNuP1QNG6M0Ui2AqKn7Le5cHMP9Qb4YaAs1PgXRPaugFXUW6GbLZiroXzIy562u0000" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// directory.ts</span>
 <span class="token keyword">import</span> <span class="token punctuation">{</span> Entry <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&#39;./entry&#39;</span><span class="token punctuation">;</span>
 <span class="token keyword">import</span> <span class="token punctuation">{</span> Visitor <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&#39;./visitor&#39;</span><span class="token punctuation">;</span>
 <span class="token keyword">export</span> <span class="token keyword">class</span> <span class="token class-name">Directory</span> <span class="token keyword">extends</span> <span class="token class-name">Entry</span> <span class="token punctuation">{</span>
diff --git "a/assets/vsocde\346\217\222\344\273\266\345\274\200\345\217\221\345\260\217\350\256\260.html-DtdCKw5q.js" "b/assets/vsocde\346\217\222\344\273\266\345\274\200\345\217\221\345\260\217\350\256\260.html-BytDpa8J.js"
similarity index 97%
rename from "assets/vsocde\346\217\222\344\273\266\345\274\200\345\217\221\345\260\217\350\256\260.html-DtdCKw5q.js"
rename to "assets/vsocde\346\217\222\344\273\266\345\274\200\345\217\221\345\260\217\350\256\260.html-BytDpa8J.js"
index 79962ce..ae4d0e7 100644
--- "a/assets/vsocde\346\217\222\344\273\266\345\274\200\345\217\221\345\260\217\350\256\260.html-DtdCKw5q.js"
+++ "b/assets/vsocde\346\217\222\344\273\266\345\274\200\345\217\221\345\260\217\350\256\260.html-BytDpa8J.js"
@@ -1 +1 @@
-import{_ as e,o as t,c as i,f as o}from"./app-B69Gl_S-.js";const n={},c=o('<h1 id="vscode-plugin" tabindex="-1"><a class="header-anchor" href="#vscode-plugin"><span>vscode plugin</span></a></h1><p>// TODO https://code.visualstudio.com/api/get-started/your-first-extension</p><h1 id="tips" tabindex="-1"><a class="header-anchor" href="#tips"><span>tips</span></a></h1><ul><li>若activate function执行时间过长，会导致<code>Activating extension &#39;undefined_publisher.kcodetime&#39; failed: AggregateError.</code>, 从而启动失败</li><li>若deactivate function执行时间超过5s, 会被强行终止，导致插件无法正常退出。</li><li>关闭vscode 不会触发onDidCloseTextDocument事件</li></ul>',4),s=[c];function a(r,d){return t(),i("div",null,s)}const l=e(n,[["render",a],["__file","vsocde插件开发小记.html.vue"]]),u=JSON.parse(`{"path":"/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html","title":"vscode plugin","lang":"zh-CN","frontmatter":{"description":"vscode plugin // TODO https://code.visualstudio.com/api/get-started/your-first-extension tips 若activate function执行时间过长，会导致Activating extension 'undefined_publisher.kcodetime' fa...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"vscode plugin"}],["meta",{"property":"og:description","content":"vscode plugin // TODO https://code.visualstudio.com/api/get-started/your-first-extension tips 若activate function执行时间过长，会导致Activating extension 'undefined_publisher.kcodetime' fa..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"vscode plugin\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.23,"words":69},"filePathRelative":"tech/vsocde插件开发小记.md","excerpt":"\\n<p>// TODO\\nhttps://code.visualstudio.com/api/get-started/your-first-extension</p>\\n<h1>tips</h1>\\n<ul>\\n<li>若activate function执行时间过长，会导致<code>Activating extension 'undefined_publisher.kcodetime' failed: AggregateError.</code>, 从而启动失败</li>\\n<li>若deactivate function执行时间超过5s, 会被强行终止，导致插件无法正常退出。</li>\\n<li>关闭vscode 不会触发onDidCloseTextDocument事件</li>\\n</ul>","autoDesc":true}`);export{l as comp,u as data};
+import{_ as e,o as t,c as i,f as o}from"./app-B4LGNJZ0.js";const n={},c=o('<h1 id="vscode-plugin" tabindex="-1"><a class="header-anchor" href="#vscode-plugin"><span>vscode plugin</span></a></h1><p>// TODO https://code.visualstudio.com/api/get-started/your-first-extension</p><h1 id="tips" tabindex="-1"><a class="header-anchor" href="#tips"><span>tips</span></a></h1><ul><li>若activate function执行时间过长，会导致<code>Activating extension &#39;undefined_publisher.kcodetime&#39; failed: AggregateError.</code>, 从而启动失败</li><li>若deactivate function执行时间超过5s, 会被强行终止，导致插件无法正常退出。</li><li>关闭vscode 不会触发onDidCloseTextDocument事件</li></ul>',4),s=[c];function a(r,d){return t(),i("div",null,s)}const l=e(n,[["render",a],["__file","vsocde插件开发小记.html.vue"]]),u=JSON.parse(`{"path":"/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html","title":"vscode plugin","lang":"zh-CN","frontmatter":{"description":"vscode plugin // TODO https://code.visualstudio.com/api/get-started/your-first-extension tips 若activate function执行时间过长，会导致Activating extension 'undefined_publisher.kcodetime' fa...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"vscode plugin"}],["meta",{"property":"og:description","content":"vscode plugin // TODO https://code.visualstudio.com/api/get-started/your-first-extension tips 若activate function执行时间过长，会导致Activating extension 'undefined_publisher.kcodetime' fa..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"vscode plugin\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.23,"words":69},"filePathRelative":"tech/vsocde插件开发小记.md","excerpt":"\\n<p>// TODO\\nhttps://code.visualstudio.com/api/get-started/your-first-extension</p>\\n<h1>tips</h1>\\n<ul>\\n<li>若activate function执行时间过长，会导致<code>Activating extension 'undefined_publisher.kcodetime' failed: AggregateError.</code>, 从而启动失败</li>\\n<li>若deactivate function执行时间超过5s, 会被强行终止，导致插件无法正常退出。</li>\\n<li>关闭vscode 不会触发onDidCloseTextDocument事件</li>\\n</ul>","autoDesc":true}`);export{l as comp,u as data};
diff --git a/assets/xychartDiagram-4a8b8217-CYu3f7i9.js b/assets/xychartDiagram-4a8b8217-DS1INfpk.js
similarity index 99%
rename from assets/xychartDiagram-4a8b8217-CYu3f7i9.js
rename to assets/xychartDiagram-4a8b8217-DS1INfpk.js
index aa5d554..0b58b5a 100644
--- a/assets/xychartDiagram-4a8b8217-CYu3f7i9.js
+++ b/assets/xychartDiagram-4a8b8217-DS1INfpk.js
@@ -1,4 +1,4 @@
-import{a_ as zt,a$ as ot,aM as wt,aL as Ft,s as Nt,g as Xt,x as Yt,y as St,a as Ht,b as $t,A as Ut,l as _t,aJ as qt,i as jt,d as Gt}from"./mermaid.core-ChLYKTZm.js";import{a as Qt}from"./createText-4a4f35c9-BuT3nXUz.js";import{i as Kt}from"./init-Gi6I4Gst.js";import{o as Jt}from"./ordinal-Cboi1Yqb.js";import{l as ft}from"./linear-CRQH6hcv.js";import{l as pt}from"./line-D0jG_HZ-.js";import"./app-B69Gl_S-.js";import"./array-BKyUJesY.js";import"./path-CbwjOpE9.js";function Zt(e,t,i){e=+e,t=+t,i=(n=arguments.length)<2?(t=e,e=0,1):n<3?1:+i;for(var s=-1,n=Math.max(0,Math.ceil((t-e)/i))|0,o=new Array(n);++s<n;)o[s]=e+s*i;return o}function st(){var e=Jt().unknown(void 0),t=e.domain,i=e.range,s=0,n=1,o,c,f=!1,d=0,R=0,C=.5;delete e.unknown;function A(){var m=t().length,T=n<s,S=T?n:s,P=T?s:n;o=(P-S)/Math.max(1,m-d+R*2),f&&(o=Math.floor(o)),S+=(P-S-o*(m-d))*C,c=o*(1-d),f&&(S=Math.round(S),c=Math.round(c));var p=Zt(m).map(function(_){return S+o*_});return i(T?p.reverse():p)}return e.domain=function(m){return arguments.length?(t(m),A()):t()},e.range=function(m){return arguments.length?([s,n]=m,s=+s,n=+n,A()):[s,n]},e.rangeRound=function(m){return[s,n]=m,s=+s,n=+n,f=!0,A()},e.bandwidth=function(){return c},e.step=function(){return o},e.round=function(m){return arguments.length?(f=!!m,A()):f},e.padding=function(m){return arguments.length?(d=Math.min(1,R=+m),A()):d},e.paddingInner=function(m){return arguments.length?(d=Math.min(1,m),A()):d},e.paddingOuter=function(m){return arguments.length?(R=+m,A()):R},e.align=function(m){return arguments.length?(C=Math.max(0,Math.min(1,m)),A()):C},e.copy=function(){return st(t(),[s,n]).round(f).paddingInner(d).paddingOuter(R).align(C)},Kt.apply(A(),arguments)}var nt=function(){var e=function(V,r,l,u){for(l=l||{},u=V.length;u--;l[V[u]]=r);return l},t=[1,10,12,14,16,18,19,21,23],i=[2,6],s=[1,3],n=[1,5],o=[1,6],c=[1,7],f=[1,5,10,12,14,16,18,19,21,23,34,35,36],d=[1,25],R=[1,26],C=[1,28],A=[1,29],m=[1,30],T=[1,31],S=[1,32],P=[1,33],p=[1,34],_=[1,35],h=[1,36],L=[1,37],z=[1,43],lt=[1,42],ct=[1,47],$=[1,50],w=[1,10,12,14,16,18,19,21,23,34,35,36],Q=[1,10,12,14,16,18,19,21,23,24,26,27,28,34,35,36],E=[1,10,12,14,16,18,19,21,23,24,26,27,28,34,35,36,41,42,43,44,45,46,47,48,49,50],ut=[1,64],K={trace:function(){},yy:{},symbols_:{error:2,start:3,eol:4,XYCHART:5,chartConfig:6,document:7,CHART_ORIENTATION:8,statement:9,title:10,text:11,X_AXIS:12,parseXAxis:13,Y_AXIS:14,parseYAxis:15,LINE:16,plotData:17,BAR:18,acc_title:19,acc_title_value:20,acc_descr:21,acc_descr_value:22,acc_descr_multiline_value:23,SQUARE_BRACES_START:24,commaSeparatedNumbers:25,SQUARE_BRACES_END:26,NUMBER_WITH_DECIMAL:27,COMMA:28,xAxisData:29,bandData:30,ARROW_DELIMITER:31,commaSeparatedTexts:32,yAxisData:33,NEWLINE:34,SEMI:35,EOF:36,alphaNum:37,STR:38,MD_STR:39,alphaNumToken:40,AMP:41,NUM:42,ALPHA:43,PLUS:44,EQUALS:45,MULT:46,DOT:47,BRKT:48,MINUS:49,UNDERSCORE:50,$accept:0,$end:1},terminals_:{2:"error",5:"XYCHART",8:"CHART_ORIENTATION",10:"title",12:"X_AXIS",14:"Y_AXIS",16:"LINE",18:"BAR",19:"acc_title",20:"acc_title_value",21:"acc_descr",22:"acc_descr_value",23:"acc_descr_multiline_value",24:"SQUARE_BRACES_START",26:"SQUARE_BRACES_END",27:"NUMBER_WITH_DECIMAL",28:"COMMA",31:"ARROW_DELIMITER",34:"NEWLINE",35:"SEMI",36:"EOF",38:"STR",39:"MD_STR",41:"AMP",42:"NUM",43:"ALPHA",44:"PLUS",45:"EQUALS",46:"MULT",47:"DOT",48:"BRKT",49:"MINUS",50:"UNDERSCORE"},productions_:[0,[3,2],[3,3],[3,2],[3,1],[6,1],[7,0],[7,2],[9,2],[9,2],[9,2],[9,2],[9,2],[9,3],[9,2],[9,3],[9,2],[9,2],[9,1],[17,3],[25,3],[25,1],[13,1],[13,2],[13,1],[29,1],[29,3],[30,3],[32,3],[32,1],[15,1],[15,2],[15,1],[33,3],[4,1],[4,1],[4,1],[11,1],[11,1],[11,1],[37,1],[37,2],[40,1],[40,1],[40,1],[40,1],[40,1],[40,1],[40,1],[40,1],[40,1],[40,1]],performAction:function(r,l,u,g,b,a,F){var x=a.length-1;switch(b){case 5:g.setOrientation(a[x]);break;case 9:g.setDiagramTitle(a[x].text.trim());break;case 12:g.setLineData({text:"",type:"text"},a[x]);break;case 13:g.setLineData(a[x-1],a[x]);break;case 14:g.setBarData({text:"",type:"text"},a[x]);break;case 15:g.setBarData(a[x-1],a[x]);break;case 16:this.$=a[x].trim(),g.setAccTitle(this.$);break;case 17:case 18:this.$=a[x].trim(),g.setAccDescription(this.$);break;case 19:this.$=a[x-1];break;case 20:this.$=[Number(a[x-2]),...a[x]];break;case 21:this.$=[Number(a[x])];break;case 22:g.setXAxisTitle(a[x]);break;case 23:g.setXAxisTitle(a[x-1]);break;case 24:g.setXAxisTitle({type:"text",text:""});break;case 25:g.setXAxisBand(a[x]);break;case 26:g.setXAxisRangeData(Number(a[x-2]),Number(a[x]));break;case 27:this.$=a[x-1];break;case 28:this.$=[a[x-2],...a[x]];break;case 29:this.$=[a[x]];break;case 30:g.setYAxisTitle(a[x]);break;case 31:g.setYAxisTitle(a[x-1]);break;case 32:g.setYAxisTitle({type:"text",text:""});break;case 33:g.setYAxisRangeData(Number(a[x-2]),Number(a[x]));break;case 37:this.$={text:a[x],type:"text"};break;case 38:this.$={text:a[x],type:"text"};break;case 39:this.$={text:a[x],type:"markdown"};break;case 40:this.$=a[x];break;case 41:this.$=a[x-1]+""+a[x];break}},table:[e(t,i,{3:1,4:2,7:4,5:s,34:n,35:o,36:c}),{1:[3]},e(t,i,{4:2,7:4,3:8,5:s,34:n,35:o,36:c}),e(t,i,{4:2,7:4,6:9,3:10,5:s,8:[1,11],34:n,35:o,36:c}),{1:[2,4],9:12,10:[1,13],12:[1,14],14:[1,15],16:[1,16],18:[1,17],19:[1,18],21:[1,19],23:[1,20]},e(f,[2,34]),e(f,[2,35]),e(f,[2,36]),{1:[2,1]},e(t,i,{4:2,7:4,3:21,5:s,34:n,35:o,36:c}),{1:[2,3]},e(f,[2,5]),e(t,[2,7],{4:22,34:n,35:o,36:c}),{11:23,37:24,38:d,39:R,40:27,41:C,42:A,43:m,44:T,45:S,46:P,47:p,48:_,49:h,50:L},{11:39,13:38,24:z,27:lt,29:40,30:41,37:24,38:d,39:R,40:27,41:C,42:A,43:m,44:T,45:S,46:P,47:p,48:_,49:h,50:L},{11:45,15:44,27:ct,33:46,37:24,38:d,39:R,40:27,41:C,42:A,43:m,44:T,45:S,46:P,47:p,48:_,49:h,50:L},{11:49,17:48,24:$,37:24,38:d,39:R,40:27,41:C,42:A,43:m,44:T,45:S,46:P,47:p,48:_,49:h,50:L},{11:52,17:51,24:$,37:24,38:d,39:R,40:27,41:C,42:A,43:m,44:T,45:S,46:P,47:p,48:_,49:h,50:L},{20:[1,53]},{22:[1,54]},e(w,[2,18]),{1:[2,2]},e(w,[2,8]),e(w,[2,9]),e(Q,[2,37],{40:55,41:C,42:A,43:m,44:T,45:S,46:P,47:p,48:_,49:h,50:L}),e(Q,[2,38]),e(Q,[2,39]),e(E,[2,40]),e(E,[2,42]),e(E,[2,43]),e(E,[2,44]),e(E,[2,45]),e(E,[2,46]),e(E,[2,47]),e(E,[2,48]),e(E,[2,49]),e(E,[2,50]),e(E,[2,51]),e(w,[2,10]),e(w,[2,22],{30:41,29:56,24:z,27:lt}),e(w,[2,24]),e(w,[2,25]),{31:[1,57]},{11:59,32:58,37:24,38:d,39:R,40:27,41:C,42:A,43:m,44:T,45:S,46:P,47:p,48:_,49:h,50:L},e(w,[2,11]),e(w,[2,30],{33:60,27:ct}),e(w,[2,32]),{31:[1,61]},e(w,[2,12]),{17:62,24:$},{25:63,27:ut},e(w,[2,14]),{17:65,24:$},e(w,[2,16]),e(w,[2,17]),e(E,[2,41]),e(w,[2,23]),{27:[1,66]},{26:[1,67]},{26:[2,29],28:[1,68]},e(w,[2,31]),{27:[1,69]},e(w,[2,13]),{26:[1,70]},{26:[2,21],28:[1,71]},e(w,[2,15]),e(w,[2,26]),e(w,[2,27]),{11:59,32:72,37:24,38:d,39:R,40:27,41:C,42:A,43:m,44:T,45:S,46:P,47:p,48:_,49:h,50:L},e(w,[2,33]),e(w,[2,19]),{25:73,27:ut},{26:[2,28]},{26:[2,20]}],defaultActions:{8:[2,1],10:[2,3],21:[2,2],72:[2,28],73:[2,20]},parseError:function(r,l){if(l.recoverable)this.trace(r);else{var u=new Error(r);throw u.hash=l,u}},parse:function(r){var l=this,u=[0],g=[],b=[null],a=[],F=this.table,x="",U=0,gt=0,Vt=2,xt=1,Bt=a.slice.call(arguments,1),k=Object.create(this.lexer),B={yy:{}};for(var Z in this.yy)Object.prototype.hasOwnProperty.call(this.yy,Z)&&(B.yy[Z]=this.yy[Z]);k.setInput(r,B.yy),B.yy.lexer=k,B.yy.parser=this,typeof k.yylloc>"u"&&(k.yylloc={});var tt=k.yylloc;a.push(tt);var Wt=k.options&&k.options.ranges;typeof B.yy.parseError=="function"?this.parseError=B.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function Ot(){var I;return I=g.pop()||k.lex()||xt,typeof I!="number"&&(I instanceof Array&&(g=I,I=g.pop()),I=l.symbols_[I]||I),I}for(var D,W,v,it,O={},q,M,dt,j;;){if(W=u[u.length-1],this.defaultActions[W]?v=this.defaultActions[W]:((D===null||typeof D>"u")&&(D=Ot()),v=F[W]&&F[W][D]),typeof v>"u"||!v.length||!v[0]){var et="";j=[];for(q in F[W])this.terminals_[q]&&q>Vt&&j.push("'"+this.terminals_[q]+"'");k.showPosition?et="Parse error on line "+(U+1)+`:
+import{a_ as zt,a$ as ot,aM as wt,aL as Ft,s as Nt,g as Xt,x as Yt,y as St,a as Ht,b as $t,A as Ut,l as _t,aJ as qt,i as jt,d as Gt}from"./mermaid.core-DNo_7Q2B.js";import{a as Qt}from"./createText-4a4f35c9-CISzj231.js";import{i as Kt}from"./init-Gi6I4Gst.js";import{o as Jt}from"./ordinal-Cboi1Yqb.js";import{l as ft}from"./linear-Cb1OAgs3.js";import{l as pt}from"./line-BqHmcuby.js";import"./app-B4LGNJZ0.js";import"./array-BKyUJesY.js";import"./path-CbwjOpE9.js";function Zt(e,t,i){e=+e,t=+t,i=(n=arguments.length)<2?(t=e,e=0,1):n<3?1:+i;for(var s=-1,n=Math.max(0,Math.ceil((t-e)/i))|0,o=new Array(n);++s<n;)o[s]=e+s*i;return o}function st(){var e=Jt().unknown(void 0),t=e.domain,i=e.range,s=0,n=1,o,c,f=!1,d=0,R=0,C=.5;delete e.unknown;function A(){var m=t().length,T=n<s,S=T?n:s,P=T?s:n;o=(P-S)/Math.max(1,m-d+R*2),f&&(o=Math.floor(o)),S+=(P-S-o*(m-d))*C,c=o*(1-d),f&&(S=Math.round(S),c=Math.round(c));var p=Zt(m).map(function(_){return S+o*_});return i(T?p.reverse():p)}return e.domain=function(m){return arguments.length?(t(m),A()):t()},e.range=function(m){return arguments.length?([s,n]=m,s=+s,n=+n,A()):[s,n]},e.rangeRound=function(m){return[s,n]=m,s=+s,n=+n,f=!0,A()},e.bandwidth=function(){return c},e.step=function(){return o},e.round=function(m){return arguments.length?(f=!!m,A()):f},e.padding=function(m){return arguments.length?(d=Math.min(1,R=+m),A()):d},e.paddingInner=function(m){return arguments.length?(d=Math.min(1,m),A()):d},e.paddingOuter=function(m){return arguments.length?(R=+m,A()):R},e.align=function(m){return arguments.length?(C=Math.max(0,Math.min(1,m)),A()):C},e.copy=function(){return st(t(),[s,n]).round(f).paddingInner(d).paddingOuter(R).align(C)},Kt.apply(A(),arguments)}var nt=function(){var e=function(V,r,l,u){for(l=l||{},u=V.length;u--;l[V[u]]=r);return l},t=[1,10,12,14,16,18,19,21,23],i=[2,6],s=[1,3],n=[1,5],o=[1,6],c=[1,7],f=[1,5,10,12,14,16,18,19,21,23,34,35,36],d=[1,25],R=[1,26],C=[1,28],A=[1,29],m=[1,30],T=[1,31],S=[1,32],P=[1,33],p=[1,34],_=[1,35],h=[1,36],L=[1,37],z=[1,43],lt=[1,42],ct=[1,47],$=[1,50],w=[1,10,12,14,16,18,19,21,23,34,35,36],Q=[1,10,12,14,16,18,19,21,23,24,26,27,28,34,35,36],E=[1,10,12,14,16,18,19,21,23,24,26,27,28,34,35,36,41,42,43,44,45,46,47,48,49,50],ut=[1,64],K={trace:function(){},yy:{},symbols_:{error:2,start:3,eol:4,XYCHART:5,chartConfig:6,document:7,CHART_ORIENTATION:8,statement:9,title:10,text:11,X_AXIS:12,parseXAxis:13,Y_AXIS:14,parseYAxis:15,LINE:16,plotData:17,BAR:18,acc_title:19,acc_title_value:20,acc_descr:21,acc_descr_value:22,acc_descr_multiline_value:23,SQUARE_BRACES_START:24,commaSeparatedNumbers:25,SQUARE_BRACES_END:26,NUMBER_WITH_DECIMAL:27,COMMA:28,xAxisData:29,bandData:30,ARROW_DELIMITER:31,commaSeparatedTexts:32,yAxisData:33,NEWLINE:34,SEMI:35,EOF:36,alphaNum:37,STR:38,MD_STR:39,alphaNumToken:40,AMP:41,NUM:42,ALPHA:43,PLUS:44,EQUALS:45,MULT:46,DOT:47,BRKT:48,MINUS:49,UNDERSCORE:50,$accept:0,$end:1},terminals_:{2:"error",5:"XYCHART",8:"CHART_ORIENTATION",10:"title",12:"X_AXIS",14:"Y_AXIS",16:"LINE",18:"BAR",19:"acc_title",20:"acc_title_value",21:"acc_descr",22:"acc_descr_value",23:"acc_descr_multiline_value",24:"SQUARE_BRACES_START",26:"SQUARE_BRACES_END",27:"NUMBER_WITH_DECIMAL",28:"COMMA",31:"ARROW_DELIMITER",34:"NEWLINE",35:"SEMI",36:"EOF",38:"STR",39:"MD_STR",41:"AMP",42:"NUM",43:"ALPHA",44:"PLUS",45:"EQUALS",46:"MULT",47:"DOT",48:"BRKT",49:"MINUS",50:"UNDERSCORE"},productions_:[0,[3,2],[3,3],[3,2],[3,1],[6,1],[7,0],[7,2],[9,2],[9,2],[9,2],[9,2],[9,2],[9,3],[9,2],[9,3],[9,2],[9,2],[9,1],[17,3],[25,3],[25,1],[13,1],[13,2],[13,1],[29,1],[29,3],[30,3],[32,3],[32,1],[15,1],[15,2],[15,1],[33,3],[4,1],[4,1],[4,1],[11,1],[11,1],[11,1],[37,1],[37,2],[40,1],[40,1],[40,1],[40,1],[40,1],[40,1],[40,1],[40,1],[40,1],[40,1]],performAction:function(r,l,u,g,b,a,F){var x=a.length-1;switch(b){case 5:g.setOrientation(a[x]);break;case 9:g.setDiagramTitle(a[x].text.trim());break;case 12:g.setLineData({text:"",type:"text"},a[x]);break;case 13:g.setLineData(a[x-1],a[x]);break;case 14:g.setBarData({text:"",type:"text"},a[x]);break;case 15:g.setBarData(a[x-1],a[x]);break;case 16:this.$=a[x].trim(),g.setAccTitle(this.$);break;case 17:case 18:this.$=a[x].trim(),g.setAccDescription(this.$);break;case 19:this.$=a[x-1];break;case 20:this.$=[Number(a[x-2]),...a[x]];break;case 21:this.$=[Number(a[x])];break;case 22:g.setXAxisTitle(a[x]);break;case 23:g.setXAxisTitle(a[x-1]);break;case 24:g.setXAxisTitle({type:"text",text:""});break;case 25:g.setXAxisBand(a[x]);break;case 26:g.setXAxisRangeData(Number(a[x-2]),Number(a[x]));break;case 27:this.$=a[x-1];break;case 28:this.$=[a[x-2],...a[x]];break;case 29:this.$=[a[x]];break;case 30:g.setYAxisTitle(a[x]);break;case 31:g.setYAxisTitle(a[x-1]);break;case 32:g.setYAxisTitle({type:"text",text:""});break;case 33:g.setYAxisRangeData(Number(a[x-2]),Number(a[x]));break;case 37:this.$={text:a[x],type:"text"};break;case 38:this.$={text:a[x],type:"text"};break;case 39:this.$={text:a[x],type:"markdown"};break;case 40:this.$=a[x];break;case 41:this.$=a[x-1]+""+a[x];break}},table:[e(t,i,{3:1,4:2,7:4,5:s,34:n,35:o,36:c}),{1:[3]},e(t,i,{4:2,7:4,3:8,5:s,34:n,35:o,36:c}),e(t,i,{4:2,7:4,6:9,3:10,5:s,8:[1,11],34:n,35:o,36:c}),{1:[2,4],9:12,10:[1,13],12:[1,14],14:[1,15],16:[1,16],18:[1,17],19:[1,18],21:[1,19],23:[1,20]},e(f,[2,34]),e(f,[2,35]),e(f,[2,36]),{1:[2,1]},e(t,i,{4:2,7:4,3:21,5:s,34:n,35:o,36:c}),{1:[2,3]},e(f,[2,5]),e(t,[2,7],{4:22,34:n,35:o,36:c}),{11:23,37:24,38:d,39:R,40:27,41:C,42:A,43:m,44:T,45:S,46:P,47:p,48:_,49:h,50:L},{11:39,13:38,24:z,27:lt,29:40,30:41,37:24,38:d,39:R,40:27,41:C,42:A,43:m,44:T,45:S,46:P,47:p,48:_,49:h,50:L},{11:45,15:44,27:ct,33:46,37:24,38:d,39:R,40:27,41:C,42:A,43:m,44:T,45:S,46:P,47:p,48:_,49:h,50:L},{11:49,17:48,24:$,37:24,38:d,39:R,40:27,41:C,42:A,43:m,44:T,45:S,46:P,47:p,48:_,49:h,50:L},{11:52,17:51,24:$,37:24,38:d,39:R,40:27,41:C,42:A,43:m,44:T,45:S,46:P,47:p,48:_,49:h,50:L},{20:[1,53]},{22:[1,54]},e(w,[2,18]),{1:[2,2]},e(w,[2,8]),e(w,[2,9]),e(Q,[2,37],{40:55,41:C,42:A,43:m,44:T,45:S,46:P,47:p,48:_,49:h,50:L}),e(Q,[2,38]),e(Q,[2,39]),e(E,[2,40]),e(E,[2,42]),e(E,[2,43]),e(E,[2,44]),e(E,[2,45]),e(E,[2,46]),e(E,[2,47]),e(E,[2,48]),e(E,[2,49]),e(E,[2,50]),e(E,[2,51]),e(w,[2,10]),e(w,[2,22],{30:41,29:56,24:z,27:lt}),e(w,[2,24]),e(w,[2,25]),{31:[1,57]},{11:59,32:58,37:24,38:d,39:R,40:27,41:C,42:A,43:m,44:T,45:S,46:P,47:p,48:_,49:h,50:L},e(w,[2,11]),e(w,[2,30],{33:60,27:ct}),e(w,[2,32]),{31:[1,61]},e(w,[2,12]),{17:62,24:$},{25:63,27:ut},e(w,[2,14]),{17:65,24:$},e(w,[2,16]),e(w,[2,17]),e(E,[2,41]),e(w,[2,23]),{27:[1,66]},{26:[1,67]},{26:[2,29],28:[1,68]},e(w,[2,31]),{27:[1,69]},e(w,[2,13]),{26:[1,70]},{26:[2,21],28:[1,71]},e(w,[2,15]),e(w,[2,26]),e(w,[2,27]),{11:59,32:72,37:24,38:d,39:R,40:27,41:C,42:A,43:m,44:T,45:S,46:P,47:p,48:_,49:h,50:L},e(w,[2,33]),e(w,[2,19]),{25:73,27:ut},{26:[2,28]},{26:[2,20]}],defaultActions:{8:[2,1],10:[2,3],21:[2,2],72:[2,28],73:[2,20]},parseError:function(r,l){if(l.recoverable)this.trace(r);else{var u=new Error(r);throw u.hash=l,u}},parse:function(r){var l=this,u=[0],g=[],b=[null],a=[],F=this.table,x="",U=0,gt=0,Vt=2,xt=1,Bt=a.slice.call(arguments,1),k=Object.create(this.lexer),B={yy:{}};for(var Z in this.yy)Object.prototype.hasOwnProperty.call(this.yy,Z)&&(B.yy[Z]=this.yy[Z]);k.setInput(r,B.yy),B.yy.lexer=k,B.yy.parser=this,typeof k.yylloc>"u"&&(k.yylloc={});var tt=k.yylloc;a.push(tt);var Wt=k.options&&k.options.ranges;typeof B.yy.parseError=="function"?this.parseError=B.yy.parseError:this.parseError=Object.getPrototypeOf(this).parseError;function Ot(){var I;return I=g.pop()||k.lex()||xt,typeof I!="number"&&(I instanceof Array&&(g=I,I=g.pop()),I=l.symbols_[I]||I),I}for(var D,W,v,it,O={},q,M,dt,j;;){if(W=u[u.length-1],this.defaultActions[W]?v=this.defaultActions[W]:((D===null||typeof D>"u")&&(D=Ot()),v=F[W]&&F[W][D]),typeof v>"u"||!v.length||!v[0]){var et="";j=[];for(q in F[W])this.terminals_[q]&&q>Vt&&j.push("'"+this.terminals_[q]+"'");k.showPosition?et="Parse error on line "+(U+1)+`:
 `+k.showPosition()+`
 Expecting `+j.join(", ")+", got '"+(this.terminals_[D]||D)+"'":et="Parse error on line "+(U+1)+": Unexpected "+(D==xt?"end of input":"'"+(this.terminals_[D]||D)+"'"),this.parseError(et,{text:k.match,token:this.terminals_[D]||D,line:k.yylineno,loc:tt,expected:j})}if(v[0]instanceof Array&&v.length>1)throw new Error("Parse Error: multiple actions possible at state: "+W+", token: "+D);switch(v[0]){case 1:u.push(D),b.push(k.yytext),a.push(k.yylloc),u.push(v[1]),D=null,gt=k.yyleng,x=k.yytext,U=k.yylineno,tt=k.yylloc;break;case 2:if(M=this.productions_[v[1]][1],O.$=b[b.length-M],O._$={first_line:a[a.length-(M||1)].first_line,last_line:a[a.length-1].last_line,first_column:a[a.length-(M||1)].first_column,last_column:a[a.length-1].last_column},Wt&&(O._$.range=[a[a.length-(M||1)].range[0],a[a.length-1].range[1]]),it=this.performAction.apply(O,[x,gt,U,B.yy,v[1],b,a].concat(Bt)),typeof it<"u")return it;M&&(u=u.slice(0,-1*M*2),b=b.slice(0,-1*M),a=a.slice(0,-1*M)),u.push(this.productions_[v[1]][0]),b.push(O.$),a.push(O._$),dt=F[u[u.length-2]][u[u.length-1]],u.push(dt);break;case 3:return!0}}return!0}},It=function(){var V={EOF:1,parseError:function(l,u){if(this.yy.parser)this.yy.parser.parseError(l,u);else throw new Error(l)},setInput:function(r,l){return this.yy=l||this.yy||{},this._input=r,this._more=this._backtrack=this.done=!1,this.yylineno=this.yyleng=0,this.yytext=this.matched=this.match="",this.conditionStack=["INITIAL"],this.yylloc={first_line:1,first_column:0,last_line:1,last_column:0},this.options.ranges&&(this.yylloc.range=[0,0]),this.offset=0,this},input:function(){var r=this._input[0];this.yytext+=r,this.yyleng++,this.offset++,this.match+=r,this.matched+=r;var l=r.match(/(?:\r\n?|\n).*/g);return l?(this.yylineno++,this.yylloc.last_line++):this.yylloc.last_column++,this.options.ranges&&this.yylloc.range[1]++,this._input=this._input.slice(1),r},unput:function(r){var l=r.length,u=r.split(/(?:\r\n?|\n)/g);this._input=r+this._input,this.yytext=this.yytext.substr(0,this.yytext.length-l),this.offset-=l;var g=this.match.split(/(?:\r\n?|\n)/g);this.match=this.match.substr(0,this.match.length-1),this.matched=this.matched.substr(0,this.matched.length-1),u.length-1&&(this.yylineno-=u.length-1);var b=this.yylloc.range;return this.yylloc={first_line:this.yylloc.first_line,last_line:this.yylineno+1,first_column:this.yylloc.first_column,last_column:u?(u.length===g.length?this.yylloc.first_column:0)+g[g.length-u.length].length-u[0].length:this.yylloc.first_column-l},this.options.ranges&&(this.yylloc.range=[b[0],b[0]+this.yyleng-l]),this.yyleng=this.yytext.length,this},more:function(){return this._more=!0,this},reject:function(){if(this.options.backtrack_lexer)this._backtrack=!0;else return this.parseError("Lexical error on line "+(this.yylineno+1)+`. You can only invoke reject() in the lexer when the lexer is of the backtracking persuasion (options.backtrack_lexer = true).
 `+this.showPosition(),{text:"",token:null,line:this.yylineno});return this},less:function(r){this.unput(this.match.slice(r))},pastInput:function(){var r=this.matched.substr(0,this.matched.length-this.match.length);return(r.length>20?"...":"")+r.substr(-20).replace(/\n/g,"")},upcomingInput:function(){var r=this.match;return r.length<20&&(r+=this._input.substr(0,20-r.length)),(r.substr(0,20)+(r.length>20?"...":"")).replace(/\n/g,"")},showPosition:function(){var r=this.pastInput(),l=new Array(r.length+1).join("-");return r+this.upcomingInput()+`
diff --git "a/assets/\343\200\214\347\256\227\346\234\257\345\205\254\347\220\206\347\263\273\347\273\237 1\343\200\215\350\207\252\347\204\266\346\225\260.html-CtzEDcR8.js" "b/assets/\343\200\214\347\256\227\346\234\257\345\205\254\347\220\206\347\263\273\347\273\237 1\343\200\215\350\207\252\347\204\266\346\225\260.html-NHamcIiY.js"
similarity index 99%
rename from "assets/\343\200\214\347\256\227\346\234\257\345\205\254\347\220\206\347\263\273\347\273\237 1\343\200\215\350\207\252\347\204\266\346\225\260.html-CtzEDcR8.js"
rename to "assets/\343\200\214\347\256\227\346\234\257\345\205\254\347\220\206\347\263\273\347\273\237 1\343\200\215\350\207\252\347\204\266\346\225\260.html-NHamcIiY.js"
index 8bad911..a9b5a96 100644
--- "a/assets/\343\200\214\347\256\227\346\234\257\345\205\254\347\220\206\347\263\273\347\273\237 1\343\200\215\350\207\252\347\204\266\346\225\260.html-CtzEDcR8.js"	
+++ "b/assets/\343\200\214\347\256\227\346\234\257\345\205\254\347\220\206\347\263\273\347\273\237 1\343\200\215\350\207\252\347\204\266\346\225\260.html-NHamcIiY.js"	
@@ -1 +1 @@
-import{_ as n,o as t,c as T,a as l,b as Q,e as a,f as m}from"./app-B69Gl_S-.js";const e={},s=Q("h1",{id:"「算术公理系统-1」自然数",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#「算术公理系统-1」自然数"},[Q("span",null,"「算术公理系统 1」自然数")])],-1),o=Q("p",null,[a("假设存在一个算数系统的模型满足 Peano 公理，即假定 Peano 公理相容，在此承认次假设的基础之上，我们即可建立如今最常用的"),Q("strong",null,"算术公理系统"),a("。"),Q("strong",null,"自然数的定义"),a("则是构建此算术公理系统的第一步。")],-1),r=Q("h2",{id:"自然数的定义",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#自然数的定义"},[Q("span",null,"自然数的定义")])],-1),d=Q("p",null,"先介绍 Peano 公理，共有五条：",-1),h={class:"MathJax",jax:"SVG",style:{position:"relative"}},i={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 500 688","aria-hidden":"true"},g=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"30",d:"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"})])])],-1),H=[g],L=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0")])],-1),c={class:"MathJax",jax:"SVG",style:{position:"relative"}},p={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.271ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2772 1000","aria-hidden":"true"},f=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2383,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),M=[f],u=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")])],-1),x={class:"MathJax",jax:"SVG",style:{position:"relative"}},Z={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},V=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),w=[V],_=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),v={class:"MathJax",jax:"SVG",style:{position:"relative"}},y={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 500 688","aria-hidden":"true"},D=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"30",d:"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"})])])],-1),b=[D],j=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0")])],-1),B=Q("li",null,[Q("p",null,"不同的自然数后继不同；")],-1),k={class:"MathJax",jax:"SVG",style:{position:"relative"}},C={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.256ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 1881 1000","aria-hidden":"true"},z=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mo" transform="translate(503,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(892,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1492,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),S=[z],J=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"p"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")])],-1),G={class:"MathJax",jax:"SVG",style:{position:"relative"}},A={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},E=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),F=[E],O=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),R={class:"MathJax",jax:"SVG",style:{position:"relative"}},P={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.029ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 1781 1000","aria-hidden":"true"},X=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mo" transform="translate(503,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(892,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(1392,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),N=[X],K=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"p"),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")")])],-1),I={class:"MathJax",jax:"SVG",style:{position:"relative"}},q={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.256ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 1881 1000","aria-hidden":"true"},U=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mo" transform="translate(503,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(892,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1492,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),W=[U],Y=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"p"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")])],-1),$={class:"MathJax",jax:"SVG",style:{position:"relative"}},Q1={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.17ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4053 1000","aria-hidden":"true"},a1=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mo" transform="translate(503,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(892,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2286,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(2675,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3275,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3664,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),t1=[a1],T1=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"p"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")")])],-1),m1={class:"MathJax",jax:"SVG",style:{position:"relative"}},n1={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},l1=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),e1=[l1],s1=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),o1={class:"MathJax",jax:"SVG",style:{position:"relative"}},r1={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.256ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 1881 1000","aria-hidden":"true"},d1=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mo" transform="translate(503,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(892,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1492,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),h1=[d1],i1=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"p"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")])],-1),g1=Q("p",null,"这样就定义了自然数，自然数这个新的数学对象因我们的假设而确立。",-1),H1=Q("h2",{id:"自然数的加法运算",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#自然数的加法运算"},[Q("span",null,"自然数的加法运算")])],-1),L1=Q("p",null,[a("自然数中最重要的运算当然是"),Q("strong",null,"加法"),a("。")],-1),c1=Q("h3",{id:"加法的定义",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#加法的定义"},[Q("span",null,"加法的定义")])],-1),p1=Q("p",null,"定义加法的运算规则：",-1),f1={class:"MathJax",jax:"SVG",style:{position:"relative"}},M1={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},u1=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),x1=[u1],Z1=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),V1={class:"MathJax",jax:"SVG",style:{position:"relative"}},w1={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.254ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2322.4 748","aria-hidden":"true"},_1=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),v1=[_1],y1=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),D1={class:"MathJax",jax:"SVG",style:{position:"relative"}},b1={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},j1=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),B1=[j1],k1=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),C1={class:"MathJax",jax:"SVG",style:{position:"relative"}},z1={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.629ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 4256 748","aria-hidden":"true"},S1=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3656,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),J1=[S1],G1=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"n")])],-1),A1={class:"MathJax",jax:"SVG",style:{position:"relative"}},E1={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.35ex",height:"1.439ex",role:"img",focusable:"false",viewBox:"0 -442 1922.7 636","aria-hidden":"true"},F1=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),O1=[F1],R1=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"m")])],-1),P1={class:"MathJax",jax:"SVG",style:{position:"relative"}},X1={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.064ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 11078.4 1000","aria-hidden":"true"},N1=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7989,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9089.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10089.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10689.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),K1=[N1],I1=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")])],-1),q1=Q("p",null,"下面我们需要证明对于任意两个自然数，都可以进行加法运算，也就是说，我们需要证明加法结果的存在性和唯一性。",-1),U1=Q("h4",{id:"加法结果的存在性",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#加法结果的存在性"},[Q("span",null,"加法结果的存在性")])],-1),W1={class:"MathJax",jax:"SVG",style:{position:"relative"}},Y1={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},$1=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),Q3=[$1],a3=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),t3={class:"MathJax",jax:"SVG",style:{position:"relative"}},T3={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},m3=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),n3=[m3],l3=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),e3={class:"MathJax",jax:"SVG",style:{position:"relative"}},s3={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 2700.4 665","aria-hidden":"true"},o3=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),r3=[o3],d3=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),h3={class:"MathJax",jax:"SVG",style:{position:"relative"}},i3={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 2700.4 665","aria-hidden":"true"},g3=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),H3=[g3],L3=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),c3={class:"MathJax",jax:"SVG",style:{position:"relative"}},p3={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},f3=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),M3=[f3],u3=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),x3={class:"MathJax",jax:"SVG",style:{position:"relative"}},Z3={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.629ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 4256 748","aria-hidden":"true"},V3=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3656,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),w3=[V3],_3=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"n")])],-1),v3={class:"MathJax",jax:"SVG",style:{position:"relative"}},y3={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.254ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2322.4 748","aria-hidden":"true"},D3=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),b3=[D3],j3=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),B3={class:"MathJax",jax:"SVG",style:{position:"relative"}},k3={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.177ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2288.3 1000","aria-hidden":"true"},C3=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(1399.3,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(1899.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),z3=[C3],S3=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")")])],-1),J3={class:"MathJax",jax:"SVG",style:{position:"relative"}},G3={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.986ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 878 453","aria-hidden":"true"},A3=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45A",d:"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"})])])],-1),E3=[A3],F3=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m")])],-1),O3={class:"MathJax",jax:"SVG",style:{position:"relative"}},R3={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 2700.4 665","aria-hidden":"true"},P3=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),X3=[P3],N3=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),K3={class:"MathJax",jax:"SVG",style:{position:"relative"}},I3={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.9ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3050 1000","aria-hidden":"true"},q3=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),U3=[q3],W3=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),Y3={class:"MathJax",jax:"SVG",style:{position:"relative"}},$3={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.024ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4872.4 1000","aria-hidden":"true"},Q2=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2883.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),a2=[Q2],t2=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")])],-1),T2={class:"MathJax",jax:"SVG",style:{position:"relative"}},m2={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.064ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 11078.4 1000","aria-hidden":"true"},n2=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7989,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9089.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10089.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10689.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),l2=[n2],e2=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")])],-1),s2={class:"MathJax",jax:"SVG",style:{position:"relative"}},o2={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.024ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4872.4 1000","aria-hidden":"true"},r2=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),d2=[r2],h2=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),i2={class:"MathJax",jax:"SVG",style:{position:"relative"}},g2={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 2700.4 665","aria-hidden":"true"},H2=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),L2=[H2],c2=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),p2={class:"MathJax",jax:"SVG",style:{position:"relative"}},f2={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.024ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4872.4 1000","aria-hidden":"true"},M2=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),u2=[M2],x2=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),Z2={class:"MathJax",jax:"SVG",style:{position:"relative"}},V2={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},w2=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),_2=[w2],v2=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),y2={class:"MathJax",jax:"SVG",style:{position:"relative"}},D2={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.946ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4838.3 1000","aria-hidden":"true"},b2=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2793.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3182.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4060.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4449.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),j2=[b2],B2=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")")])],-1),k2={class:"MathJax",jax:"SVG",style:{position:"relative"}},C2={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},z2=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),S2=[z2],J2=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),G2={class:"MathJax",jax:"SVG",style:{position:"relative"}},A2={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.986ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 878 453","aria-hidden":"true"},E2=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45A",d:"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"})])])],-1),F2=[E2],O2=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m")])],-1),R2={class:"MathJax",jax:"SVG",style:{position:"relative"}},P2={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},X2=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),N2=[X2],K2=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),I2={class:"MathJax",jax:"SVG",style:{position:"relative"}},q2={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 2700.4 665","aria-hidden":"true"},U2=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),W2=[U2],Y2=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),$2={class:"MathJax",jax:"SVG",style:{position:"relative"}},Q4={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},a4=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),t4=[a4],T4=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),m4={class:"MathJax",jax:"SVG",style:{position:"relative"}},n4={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.35ex",height:"1.439ex",role:"img",focusable:"false",viewBox:"0 -442 1922.7 636","aria-hidden":"true"},l4=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),e4=[l4],s4=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"m")])],-1),o4={class:"MathJax",jax:"SVG",style:{position:"relative"}},r4={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 2700.4 665","aria-hidden":"true"},d4=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),h4=[d4],i4=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),g4=Q("h4",{id:"加法结果的唯一性",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#加法结果的唯一性"},[Q("span",null,"加法结果的唯一性")])],-1),H4={class:"MathJax",jax:"SVG",style:{position:"relative"}},L4={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},c4=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),p4=[c4],f4=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),M4={class:"MathJax",jax:"SVG",style:{position:"relative"}},u4={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},x4=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Z4=[x4],V4=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),w4={class:"MathJax",jax:"SVG",style:{position:"relative"}},_4={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 2700.4 665","aria-hidden":"true"},v4=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),y4=[v4],D4=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),b4={class:"MathJax",jax:"SVG",style:{position:"relative"}},j4={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 2700.4 665","aria-hidden":"true"},B4=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),k4=[B4],C4=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),z4={class:"MathJax",jax:"SVG",style:{position:"relative"}},S4={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},J4=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),G4=[J4],A4=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),E4={class:"MathJax",jax:"SVG",style:{position:"relative"}},F4={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.629ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 4256 748","aria-hidden":"true"},O4=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3656,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),R4=[O4],P4=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"n")])],-1),X4={class:"MathJax",jax:"SVG",style:{position:"relative"}},N4={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.254ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2322.4 748","aria-hidden":"true"},K4=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),I4=[K4],q4=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),U4={class:"MathJax",jax:"SVG",style:{position:"relative"}},W4={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Y4=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),$4=[Y4],Q5=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),a5={class:"MathJax",jax:"SVG",style:{position:"relative"}},t5={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.177ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2288.3 1000","aria-hidden":"true"},T5=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(1399.3,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(1899.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),m5=[T5],n5=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")")])],-1),l5={class:"MathJax",jax:"SVG",style:{position:"relative"}},e5={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.986ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 878 453","aria-hidden":"true"},s5=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45A",d:"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"})])])],-1),o5=[s5],r5=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m")])],-1),d5={class:"MathJax",jax:"SVG",style:{position:"relative"}},h5={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 2700.4 665","aria-hidden":"true"},i5=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),g5=[i5],H5=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),L5={class:"MathJax",jax:"SVG",style:{position:"relative"}},c5={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.9ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3050 1000","aria-hidden":"true"},p5=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),f5=[p5],M5=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),u5={class:"MathJax",jax:"SVG",style:{position:"relative"}},x5={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.024ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4872.4 1000","aria-hidden":"true"},Z5=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2883.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),V5=[Z5],w5=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")])],-1),_5={class:"MathJax",jax:"SVG",style:{position:"relative"}},v5={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.064ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 11078.4 1000","aria-hidden":"true"},y5=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7989,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9089.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10089.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10689.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),D5=[y5],b5=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")])],-1),j5={class:"MathJax",jax:"SVG",style:{position:"relative"}},B5={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.024ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4872.4 1000","aria-hidden":"true"},k5=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),C5=[k5],z5=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),S5={class:"MathJax",jax:"SVG",style:{position:"relative"}},J5={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 2700.4 665","aria-hidden":"true"},G5=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),A5=[G5],E5=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),F5={class:"MathJax",jax:"SVG",style:{position:"relative"}},O5={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.024ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4872.4 1000","aria-hidden":"true"},R5=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),P5=[R5],X5=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),N5={class:"MathJax",jax:"SVG",style:{position:"relative"}},K5={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},I5=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),q5=[I5],U5=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),W5={class:"MathJax",jax:"SVG",style:{position:"relative"}},Y5={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.946ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4838.3 1000","aria-hidden":"true"},$5=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2793.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3182.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4060.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4449.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Q6=[$5],a6=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")")])],-1),t6={class:"MathJax",jax:"SVG",style:{position:"relative"}},T6={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},m6=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),n6=[m6],l6=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),e6={class:"MathJax",jax:"SVG",style:{position:"relative"}},s6={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.986ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 878 453","aria-hidden":"true"},o6=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45A",d:"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"})])])],-1),r6=[o6],d6=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m")])],-1),h6={class:"MathJax",jax:"SVG",style:{position:"relative"}},i6={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},g6=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),H6=[g6],L6=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),c6={class:"MathJax",jax:"SVG",style:{position:"relative"}},p6={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 2700.4 665","aria-hidden":"true"},f6=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),M6=[f6],u6=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),x6={class:"MathJax",jax:"SVG",style:{position:"relative"}},Z6={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},V6=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),w6=[V6],_6=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),v6={class:"MathJax",jax:"SVG",style:{position:"relative"}},y6={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.35ex",height:"1.439ex",role:"img",focusable:"false",viewBox:"0 -442 1922.7 636","aria-hidden":"true"},D6=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),b6=[D6],j6=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"m")])],-1),B6={class:"MathJax",jax:"SVG",style:{position:"relative"}},k6={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 2700.4 665","aria-hidden":"true"},C6=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),z6=[C6],S6=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),J6=Q("h3",{id:"加法的性质",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#加法的性质"},[Q("span",null,"加法的性质")])],-1),G6=Q("p",null,"在明确证明了自然数加法运算的良好性质，即任意两个自然数都可以进行加法运算，且加法运算的结果存在且唯一之后，我们终于可以对自然数加法的性质进行进一步的探索。",-1),A6=Q("h4",{id:"加法交换律",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#加法交换律"},[Q("span",null,"加法交换律")])],-1),E6={class:"MathJax",jax:"SVG",style:{position:"relative"}},F6={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.35ex",height:"1.439ex",role:"img",focusable:"false",viewBox:"0 -442 1922.7 636","aria-hidden":"true"},O6=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),R6=[O6],P6=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"m")])],-1),X6={class:"MathJax",jax:"SVG",style:{position:"relative"}},N6={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.236ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 6734.4 665","aria-hidden":"true"},K6=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),I6=[K6],q6=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),U6=Q("p",null,"直接证明比较困难，考虑从加法运算的定义下手，即先证明加法的两条运算规则符合交换律。",-1),W6={class:"MathJax",jax:"SVG",style:{position:"relative"}},Y6={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"17.9ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 7912 748","aria-hidden":"true"},$6=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3656,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4533.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5589.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6411.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(7412,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),Q7=[$6],a7=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"+"),Q("mn",null,"0")])],-1),t7={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},T7={style:{"vertical-align":"-2.036ex"},xmlns:"http://www.w3.org/2000/svg",width:"37.243ex",height:"5.204ex",role:"img",focusable:"false",viewBox:"0 -1400 16461.4 2300","aria-hidden":"true"},m7=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,650)"><g data-mml-node="mtd"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(1722.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g><g data-mml-node="mtd" transform="translate(2222.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(1833.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(8778.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-650)"><g data-mml-node="mtd" transform="translate(2222.4,0)"></g><g data-mml-node="mtd" transform="translate(2222.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2055.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(3056,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(3556,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(8778.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g></g></g></g>',1),n7=[m7],l7=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mn",null,"0"),Q("mo",null,"+"),Q("mn",null,"0")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])])])])],-1),e7={class:"MathJax",jax:"SVG",style:{position:"relative"}},s7={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},o7=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),r7=[o7],d7=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),h7={class:"MathJax",jax:"SVG",style:{position:"relative"}},i7={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"17.9ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 7912 748","aria-hidden":"true"},g7=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3656,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4533.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5589.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6411.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(7412,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),H7=[g7],L7=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"+"),Q("mn",null,"0")])],-1),c7={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},p7={style:{"vertical-align":"-3.507ex"},xmlns:"http://www.w3.org/2000/svg",width:"47.524ex",height:"8.145ex",role:"img",focusable:"false",viewBox:"0 -2050 21005.4 3600","aria-hidden":"true"},f7=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3116.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3505.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4105.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3716.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(4105.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13322.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(4494.4,0)"></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3938.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(4939,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(5439,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5828,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(15916.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(877.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1933.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2755.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(3756,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(4494.4,0)"></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3716.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4327.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(5328,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(5828,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13322.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),M7=[f7],u7=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"+"),Q("mn",null,"0")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])])])])],-1),x7={class:"MathJax",jax:"SVG",style:{position:"relative"}},Z7={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"17.9ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 7912 748","aria-hidden":"true"},V7=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3656,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4533.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5589.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6411.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(7412,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),w7=[V7],_7=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"+"),Q("mn",null,"0")])],-1),v7={class:"MathJax",jax:"SVG",style:{position:"relative"}},y7={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},D7=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),b7=[D7],j7=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),B7={class:"MathJax",jax:"SVG",style:{position:"relative"}},k7={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"39.105ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 17284.4 1000","aria-hidden":"true"},C7=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7989,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9089.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10089.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10689.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(11356.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(12412,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(13806,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(14195,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(15073,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(15684.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(16684.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),z7=[C7],S7=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),J7={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},G7={style:{"vertical-align":"-3.507ex"},xmlns:"http://www.w3.org/2000/svg",width:"47.524ex",height:"8.145ex",role:"img",focusable:"false",viewBox:"0 -2050 21005.4 3600","aria-hidden":"true"},A7=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3116.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3505.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4105.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3716.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(4105.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13322.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(4494.4,0)"></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(3116.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(3838.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4839,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5439,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5828,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13322.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(4494.4,0)"></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(3116.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(3616.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4227.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5228,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mstyle" transform="translate(5828,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13322.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),E7=[A7],F7=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])])])])],-1),O7={class:"MathJax",jax:"SVG",style:{position:"relative"}},R7={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.986ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 878 453","aria-hidden":"true"},P7=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45A",d:"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"})])])],-1),X7=[P7],N7=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m")])],-1),K7={class:"MathJax",jax:"SVG",style:{position:"relative"}},I7={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"39.105ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 17284.4 1000","aria-hidden":"true"},q7=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7989,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9089.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10089.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10689.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(11356.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(12412,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(13806,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(14195,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(15073,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(15684.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(16684.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),U7=[q7],W7=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),Y7={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},$7={style:{"vertical-align":"-4.977ex"},xmlns:"http://www.w3.org/2000/svg",width:"68.629ex",height:"11.086ex",role:"img",focusable:"false",viewBox:"0 -2700 30333.9 4900","aria-hidden":"true"},Q0=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1950)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(5666.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6055.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6655.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4216.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5217,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6611,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7000,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7989,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(8378,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(22650.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,650)"><g data-mml-node="mtd" transform="translate(7044.4,0)"></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4510.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4899.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5999.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7000,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7989,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(8378,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18422.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7989,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9089.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10089.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10689.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-650)"><g data-mml-node="mtd" transform="translate(7044.4,0)"></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4510.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4899.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5777.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6388.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7389,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7989,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(8378,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18422.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2883.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7989,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(8867,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(9478.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10478.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1950)"><g data-mml-node="mtd" transform="translate(7044.4,0)"></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4510.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4899.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5777.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6166.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6777.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7778,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mstyle" transform="translate(8378,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(22650.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),a0=[Q0],t0=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])])])])],-1),T0={class:"MathJax",jax:"SVG",style:{position:"relative"}},m0={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"39.105ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 17284.4 1000","aria-hidden":"true"},n0=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7989,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9089.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10089.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10689.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(11356.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(12412,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(13806,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(14195,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(15073,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(15684.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(16684.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),l0=[n0],e0=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),s0={class:"MathJax",jax:"SVG",style:{position:"relative"}},o0={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.35ex",height:"1.439ex",role:"img",focusable:"false",viewBox:"0 -442 1922.7 636","aria-hidden":"true"},r0=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),d0=[r0],h0=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"m")])],-1),i0=Q("strong",null,"加法运算规则 Ⅱ",-1),g0={class:"MathJax",jax:"SVG",style:{position:"relative"}},H0={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.236ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 6734.4 665","aria-hidden":"true"},L0=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),c0=[L0],p0=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),f0={class:"MathJax",jax:"SVG",style:{position:"relative"}},M0={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"14.784ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 6534.4 748","aria-hidden":"true"},u0=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2878.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3934,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5034.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(6034.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),x0=[u0],Z0=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"+"),Q("mn",null,"0")])],-1),V0={class:"MathJax",jax:"SVG",style:{position:"relative"}},w0={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},_0=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),v0=[_0],y0=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),D0={class:"MathJax",jax:"SVG",style:{position:"relative"}},b0={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.236ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 6734.4 665","aria-hidden":"true"},j0=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),B0=[j0],k0=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),C0={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},z0={style:{"vertical-align":"-3.507ex"},xmlns:"http://www.w3.org/2000/svg",width:"49.234ex",height:"8.145ex",role:"img",focusable:"false",viewBox:"0 -2050 21761.4 3600","aria-hidden":"true"},S0=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2383,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(2994.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3994.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3938.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4939,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5817,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(6206,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14078.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(4872.4,0)"></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4216.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5217,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5817,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(6206,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14194,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(4872.4,0)"></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2433.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3434,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4828,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5217,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5817,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(6206,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14078.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),J0=[S0],G0=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"m")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])])])])],-1),A0={class:"MathJax",jax:"SVG",style:{position:"relative"}},E0={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.236ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 6734.4 665","aria-hidden":"true"},F0=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),O0=[F0],R0=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),P0={class:"MathJax",jax:"SVG",style:{position:"relative"}},X0={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.35ex",height:"1.439ex",role:"img",focusable:"false",viewBox:"0 -442 1922.7 636","aria-hidden":"true"},N0=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),K0=[N0],I0=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"m")])],-1),q0=Q("h4",{id:"加法结合律",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#加法结合律"},[Q("span",null,"加法结合律")])],-1),U0={class:"MathJax",jax:"SVG",style:{position:"relative"}},W0={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.159ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 2280.3 888","aria-hidden":"true"},Y0=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),$0=[Y0],Q8=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b"),Q("mo",null,","),Q("mi",null,"c")])],-1),a8={class:"MathJax",jax:"SVG",style:{position:"relative"}},t8={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"23.894ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10561.3 1000","aria-hidden":"true"},T8=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5947.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6698.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(7698.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8739.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9739.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(10172.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),m8=[T8],n8=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),l8={class:"MathJax",jax:"SVG",style:{position:"relative"}},e8={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.128ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2266.6 748","aria-hidden":"true"},s8=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),o8=[s8],r8=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])],-1),d8={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},h8={style:{"vertical-align":"-4.977ex"},xmlns:"http://www.w3.org/2000/svg",width:"48.216ex",height:"11.086ex",role:"img",focusable:"false",viewBox:"0 -2700 21311.3 4900","aria-hidden":"true"},i8=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1950)"><g data-mml-node="mtd"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g><g data-mml-node="mtd" transform="translate(4613.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(1333.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2473.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3474,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(3903,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4514.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(5514.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(6014.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18211.8,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,650)"><g data-mml-node="mtd" transform="translate(4613.9,0)"></g><g data-mml-node="mtd" transform="translate(4613.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3085,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(3514,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13628.3,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-650)"><g data-mml-node="mtd" transform="translate(4613.9,0)"></g><g data-mml-node="mtd" transform="translate(4613.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(3085,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3474,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4125.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(5125.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(5625.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(6014.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13628.3,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1950)"><g data-mml-node="mtd" transform="translate(4613.9,0)"></g><g data-mml-node="mtd" transform="translate(4613.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(3085,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3474,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4125.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5125.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5558.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5947.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18211.8,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g></g></g></g>',1),g8=[i8],H8=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"c")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])])])])])],-1),L8={class:"MathJax",jax:"SVG",style:{position:"relative"}},c8={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.98ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 433 453","aria-hidden":"true"},p8=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D450",d:"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"})])])],-1),f8=[p8],M8=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c")])],-1),u8={class:"MathJax",jax:"SVG",style:{position:"relative"}},x8={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"23.894ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10561.3 1000","aria-hidden":"true"},Z8=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5947.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6698.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(7698.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8739.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9739.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(10172.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),V8=[Z8],w8=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),_8={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},v8={style:{"vertical-align":"-4.977ex"},xmlns:"http://www.w3.org/2000/svg",width:"66.289ex",height:"11.086ex",role:"img",focusable:"false",viewBox:"0 -2700 29299.7 4900","aria-hidden":"true"},y8=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1950)"><g data-mml-node="mtd"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(5574.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5963.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6396.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(6785.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mo" transform="translate(3116.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3505.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4256.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5257,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(5686,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6297.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7297.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(7730.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(8119.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(21616.7,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,650)"><g data-mml-node="mtd" transform="translate(6785.9,0)"></g><g data-mml-node="mtd" transform="translate(6785.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(3867.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(4868,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5257,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(5908.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6908.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(7341.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7730.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(8119.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(17905.3,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5947.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6698.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(7698.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8739.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9739.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(10172.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-650)"><g data-mml-node="mtd" transform="translate(6785.9,0)"></g><g data-mml-node="mtd" transform="translate(6785.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3085,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4479,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4868,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(5519.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6519.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6952.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(7341.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(21616.7,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1950)"><g data-mml-node="mtd" transform="translate(6785.9,0)"></g><g data-mml-node="mtd" transform="translate(6785.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(3085,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3474,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4125.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5125.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6519.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6908.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(7341.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7730.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(8119.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(21616.7,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),D8=[y8],b8=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])])])])],-1),j8={class:"MathJax",jax:"SVG",style:{position:"relative"}},B8={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"23.894ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10561.3 1000","aria-hidden":"true"},k8=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5947.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6698.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(7698.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8739.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9739.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(10172.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),C8=[k8],z8=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),S8={class:"MathJax",jax:"SVG",style:{position:"relative"}},J8={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.159ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 2280.3 888","aria-hidden":"true"},G8=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),A8=[G8],E8=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b"),Q("mo",null,","),Q("mi",null,"c")])],-1),F8=Q("h4",{id:"加法消去律",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#加法消去律"},[Q("span",null,"加法消去律")])],-1),O8={class:"MathJax",jax:"SVG",style:{position:"relative"}},R8={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.159ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 2280.3 888","aria-hidden":"true"},P8=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),X8=[P8],N8=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b"),Q("mo",null,","),Q("mi",null,"c")])],-1),K8={class:"MathJax",jax:"SVG",style:{position:"relative"}},I8={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.379ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 9449.6 776","aria-hidden":"true"},q8=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5880.2,0)"><path data-c="21D4" d="M308 524Q318 526 323 526Q340 526 340 514Q340 507 336 499Q326 476 314 454T292 417T274 391T260 374L255 368Q255 367 500 367Q744 367 744 368L739 374Q734 379 726 390T707 416T685 453T663 499Q658 511 658 515Q658 525 680 525Q687 524 690 523T695 519T701 507Q766 359 902 287Q921 276 939 269T961 259T966 250Q966 246 965 244T960 240T949 236T930 228T902 213Q763 137 701 -7Q697 -16 695 -19T690 -23T680 -25Q658 -25 658 -15Q658 -11 663 1Q673 24 685 46T707 83T725 109T739 126L744 132Q744 133 500 133Q255 133 255 132L260 126Q265 121 273 110T292 84T314 47T336 1Q341 -11 341 -15Q341 -25 319 -25Q312 -24 309 -23T304 -19T298 -7Q233 141 97 213Q83 221 70 227T51 235T41 239T35 243T34 250T35 256T40 261T51 265T70 273T97 287Q235 363 299 509Q305 522 308 524ZM792 319L783 327H216Q183 294 120 256L110 250L120 244Q173 212 207 181L216 173H783L792 181Q826 212 879 244L889 250L879 256Q826 288 792 319Z"></path></g><g data-mml-node="mi" transform="translate(7158,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7964.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9020.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),U8=[q8],W8=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},"⇔"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),Y8={class:"MathJax",jax:"SVG",style:{position:"relative"}},$8={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.379ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 9449.6 776","aria-hidden":"true"},Q9=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(3847.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4598.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5598.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6309.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(7365.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8016.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9016.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),a9=[Q9],t9=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c")])],-1),T9={class:"MathJax",jax:"SVG",style:{position:"relative"}},m9={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.128ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2266.6 748","aria-hidden":"true"},n9=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),l9=[n9],e9=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])],-1),s9={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},o9={style:{"vertical-align":"-6.448ex"},xmlns:"http://www.w3.org/2000/svg",width:"37.223ex",height:"14.027ex",role:"img",focusable:"false",viewBox:"0 -3350 16452.4 6200","aria-hidden":"true"},r9=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,2600)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g><g data-mml-node="mtd" transform="translate(2184.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(3085,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(3585,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13352.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd" transform="translate(2184.4,0)"></g><g data-mml-node="mtd" transform="translate(2184.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mstyle" transform="translate(1862.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(8769.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(2184.4,0)"></g><g data-mml-node="mtd" transform="translate(2184.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(1762.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13327.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(2184.4,0)"></g><g data-mml-node="mtd" transform="translate(2184.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(2985,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(3485,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(8769.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-2600)"><g data-mml-node="mtd" transform="translate(2184.4,0)"></g><g data-mml-node="mtd" transform="translate(2184.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mstyle" transform="translate(3418,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13352.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g></g></g></g>',1),d9=[r9],h9=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])])])])])],-1),i9={class:"MathJax",jax:"SVG",style:{position:"relative"}},g9={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.98ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 433 453","aria-hidden":"true"},H9=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D450",d:"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"})])])],-1),L9=[H9],c9=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c")])],-1),p9={class:"MathJax",jax:"SVG",style:{position:"relative"}},f9={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.379ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 9449.6 776","aria-hidden":"true"},M9=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(3847.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4598.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5598.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6309.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(7365.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8016.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9016.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),u9=[M9],x9=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c")])],-1),Z9={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},V9={style:{"vertical-align":"-3.507ex"},xmlns:"http://www.w3.org/2000/svg",width:"52.781ex",height:"8.145ex",role:"img",focusable:"false",viewBox:"0 -2050 23329 3600","aria-hidden":"true"},w9=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(3867.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4868,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5301,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5690,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(15646,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(3767.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5590,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13046.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(3847.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4598.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5598.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6309.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(7365.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8016.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9016.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5590,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(15646,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),_9=[w9],v9=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])])])])],-1),y9={class:"MathJax",jax:"SVG",style:{position:"relative"}},D9={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"47.402ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 20951.6 1000","aria-hidden":"true"},b9=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(3847.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4598.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5598.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6309.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(7365.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8016.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9016.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9727.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(11005.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(11756.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(12756.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(14150.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(14539.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(14972.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(15639.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(16695.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(17346.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(18346.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(19740.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(20129.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(20562.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),j9=[b9],B9=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),k9={class:"MathJax",jax:"SVG",style:{position:"relative"}},C9={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.379ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 9449.6 776","aria-hidden":"true"},z9=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(3847.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4598.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5598.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6309.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(7365.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8016.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9016.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),S9=[z9],J9=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c")])],-1),G9={class:"MathJax",jax:"SVG",style:{position:"relative"}},A9={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.159ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 2280.3 888","aria-hidden":"true"},E9=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),F9=[E9],O9=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b"),Q("mo",null,","),Q("mi",null,"c")])],-1),R9={class:"MathJax",jax:"SVG",style:{position:"relative"}},P9={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.379ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 9449.6 776","aria-hidden":"true"},X9=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5880.2,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(7158,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7964.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9020.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),N9=[X9],K9=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),I9={class:"MathJax",jax:"SVG",style:{position:"relative"}},q9={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.128ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2266.6 748","aria-hidden":"true"},U9=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),W9=[U9],Y9=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])],-1),$9={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},QQ={style:{"vertical-align":"-6.448ex"},xmlns:"http://www.w3.org/2000/svg",width:"33.477ex",height:"14.027ex",role:"img",focusable:"false",viewBox:"0 -3350 14797 6200","aria-hidden":"true"},aQ=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,2600)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g></g><g data-mml-node="mtd" transform="translate(529,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(3085,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(3585,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(7114,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd" transform="translate(529,0)"></g><g data-mml-node="mtd" transform="translate(529,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3085,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mstyle" transform="translate(3518,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(11697.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(529,0)"></g><g data-mml-node="mtd" transform="translate(529,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mstyle" transform="translate(3418,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(8361.6,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(529,0)"></g><g data-mml-node="mtd" transform="translate(529,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(2985,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(3485,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(11697.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-2600)"><g data-mml-node="mtd" transform="translate(529,0)"></g><g data-mml-node="mtd" transform="translate(529,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(1762.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(7114,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g></g></g></g>',1),tQ=[aQ],TQ=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"a")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])])])])],-1),mQ={class:"MathJax",jax:"SVG",style:{position:"relative"}},nQ={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.98ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 433 453","aria-hidden":"true"},lQ=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D450",d:"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"})])])],-1),eQ=[lQ],sQ=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c")])],-1),oQ={class:"MathJax",jax:"SVG",style:{position:"relative"}},rQ={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.379ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 9449.6 776","aria-hidden":"true"},dQ=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5880.2,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(7158,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7964.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9020.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),hQ=[dQ],iQ=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),gQ={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},HQ={style:{"vertical-align":"-4.977ex"},xmlns:"http://www.w3.org/2000/svg",width:"52.554ex",height:"11.086ex",role:"img",focusable:"false",viewBox:"0 -2700 23229 4900","aria-hidden":"true"},LQ=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1950)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5590,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18396,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">已</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">知</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">条</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">件</text></g></g></g><g data-mml-node="mtr" transform="translate(0,650)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2534.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(3767.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5590,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(15546,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-650)"><g data-mml-node="mtd" transform="translate(2172,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mstyle" transform="translate(3418,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(16615,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><path data-c="50" d="M130 622Q123 629 119 631T103 634T60 637H27V683H214Q237 683 276 683T331 684Q419 684 471 671T567 616Q624 563 624 489Q624 421 573 372T451 307Q429 302 328 301H234V181Q234 62 237 58Q245 47 304 46H337V0H326Q305 3 182 3Q47 3 38 0H27V46H60Q102 47 111 49T130 61V622ZM507 488Q507 514 506 528T500 564T483 597T450 620T397 635Q385 637 307 637H286Q237 637 234 628Q231 624 231 483V342H302H339Q390 342 423 349T481 382Q507 411 507 488Z"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(681,0)"></path><path data-c="61" d="M137 305T115 305T78 320T63 359Q63 394 97 421T218 448Q291 448 336 416T396 340Q401 326 401 309T402 194V124Q402 76 407 58T428 40Q443 40 448 56T453 109V145H493V106Q492 66 490 59Q481 29 455 12T400 -6T353 12T329 54V58L327 55Q325 52 322 49T314 40T302 29T287 17T269 6T247 -2T221 -8T190 -11Q130 -11 82 20T34 107Q34 128 41 147T68 188T116 225T194 253T304 268H318V290Q318 324 312 340Q290 411 215 411Q197 411 181 410T156 406T148 403Q170 388 170 359Q170 334 154 320ZM126 106Q126 75 150 51T209 26Q247 26 276 49T315 109Q317 116 318 175Q318 233 317 233Q309 233 296 232T251 223T193 203T147 166T126 106Z" transform="translate(1125,0)"></path><path data-c="6E" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z" transform="translate(1625,0)"></path><path data-c="6F" d="M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z" transform="translate(2181,0)"></path><path data-c="20" d="" transform="translate(2681,0)"></path><text data-variant="normal" transform="translate(2931,0) scale(1,-1)" font-size="884px" font-family="serif">公</text><text data-variant="normal" transform="translate(3931,0) scale(1,-1)" font-size="884px" font-family="serif">理</text><path data-c="20" d="" transform="translate(4931,0)"></path><text data-variant="normal" transform="translate(5181,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅳ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1950)"><g data-mml-node="mtd" transform="translate(3827.4,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(1762.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(12946.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5880.2,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(7158,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7964.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9020.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></g></g></g></g>',1),cQ=[LQ],pQ=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"已知条件")])]),Q("mtr",null,[Q("mtd",null,[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd",null,[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"Peano 公理 Ⅳ")])]),Q("mtr",null,[Q("mtd",null,[Q("mi",null,"a")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])])])])])],-1),fQ={class:"MathJax",jax:"SVG",style:{position:"relative"}},MQ={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"47.402ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 20951.6 1000","aria-hidden":"true"},uQ=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(10224.2,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(11502,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(12253.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(13253.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(13964.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(15020,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(15671.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(16671.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(17382.2,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(18660,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(19466.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(20522.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),xQ=[uQ],ZQ=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),VQ={class:"MathJax",jax:"SVG",style:{position:"relative"}},wQ={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.379ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 9449.6 776","aria-hidden":"true"},_Q=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5880.2,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(7158,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7964.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9020.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),vQ=[_Q],yQ=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),DQ={class:"MathJax",jax:"SVG",style:{position:"relative"}},bQ={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.159ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 2280.3 888","aria-hidden":"true"},jQ=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),BQ=[jQ],kQ=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b"),Q("mo",null,","),Q("mi",null,"c")])],-1),CQ={class:"MathJax",jax:"SVG",style:{position:"relative"}},zQ={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.379ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 9449.6 776","aria-hidden":"true"},SQ=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5880.2,0)"><path data-c="21D4" d="M308 524Q318 526 323 526Q340 526 340 514Q340 507 336 499Q326 476 314 454T292 417T274 391T260 374L255 368Q255 367 500 367Q744 367 744 368L739 374Q734 379 726 390T707 416T685 453T663 499Q658 511 658 515Q658 525 680 525Q687 524 690 523T695 519T701 507Q766 359 902 287Q921 276 939 269T961 259T966 250Q966 246 965 244T960 240T949 236T930 228T902 213Q763 137 701 -7Q697 -16 695 -19T690 -23T680 -25Q658 -25 658 -15Q658 -11 663 1Q673 24 685 46T707 83T725 109T739 126L744 132Q744 133 500 133Q255 133 255 132L260 126Q265 121 273 110T292 84T314 47T336 1Q341 -11 341 -15Q341 -25 319 -25Q312 -24 309 -23T304 -19T298 -7Q233 141 97 213Q83 221 70 227T51 235T41 239T35 243T34 250T35 256T40 261T51 265T70 273T97 287Q235 363 299 509Q305 522 308 524ZM792 319L783 327H216Q183 294 120 256L110 250L120 244Q173 212 207 181L216 173H783L792 181Q826 212 879 244L889 250L879 256Q826 288 792 319Z"></path></g><g data-mml-node="mi" transform="translate(7158,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7964.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9020.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),JQ=[SQ],GQ=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},"⇔"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),AQ={class:"MathJax",jax:"SVG",style:{position:"relative"}},EQ={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.159ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 2280.3 888","aria-hidden":"true"},FQ=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),OQ=[FQ],RQ=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b"),Q("mo",null,","),Q("mi",null,"c")])],-1),PQ=Q("h2",{id:"自然数的序",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#自然数的序"},[Q("span",null,"自然数的序")])],-1),XQ=Q("p",null,"自然数的序为两个自然数的关系。",-1),NQ=Q("h3",{id:"序的定义",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#序的定义"},[Q("span",null,"序的定义")])],-1),KQ={class:"MathJax",jax:"SVG",style:{position:"relative"}},IQ={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.361ex",height:"1.751ex",role:"img",focusable:"false",viewBox:"0 -636 2811.6 774","aria-hidden":"true"},qQ=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(877.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1933.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),UQ=[qQ],WQ=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"≤"),Q("mi",null,"m")])],-1),YQ={class:"MathJax",jax:"SVG",style:{position:"relative"}},$Q={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.294ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 572 453","aria-hidden":"true"},Qa=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D465",d:"M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"})])])],-1),aa=[Qa],ta=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"x")])],-1),Ta={class:"MathJax",jax:"SVG",style:{position:"relative"}},ma={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.421ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 4606 665","aria-hidden":"true"},na=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(877.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1933.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3033.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></g></g></g>',1),la=[na],ea=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"x")])],-1),sa={class:"MathJax",jax:"SVG",style:{position:"relative"}},oa={style:{"vertical-align":"-0.09ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.361ex",height:"1.312ex",role:"img",focusable:"false",viewBox:"0 -540 2811.6 580","aria-hidden":"true"},ra=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(877.8,0)"><path data-c="3C" d="M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z"></path></g><g data-mml-node="mi" transform="translate(1933.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),da=[ra],ha=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"<"),Q("mi",null,"m")])],-1),ia={class:"MathJax",jax:"SVG",style:{position:"relative"}},ga={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.361ex",height:"1.751ex",role:"img",focusable:"false",viewBox:"0 -636 2811.6 774","aria-hidden":"true"},Ha=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(877.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1933.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),La=[Ha],ca=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"≤"),Q("mi",null,"m")])],-1),pa={class:"MathJax",jax:"SVG",style:{position:"relative"}},fa={style:{"vertical-align":"-0.486ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.361ex",height:"2.106ex",role:"img",focusable:"false",viewBox:"0 -716 2811.6 931","aria-hidden":"true"},Ma=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(877.8,0)"><path data-c="2260" d="M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z"></path></g><g data-mml-node="mi" transform="translate(1933.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),ua=[Ma],xa=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"≠"),Q("mi",null,"m")])],-1),Za=Q("p",null,"自然数的序是全序关系，它应该具有反对称性、传递性和完全性。",-1),Va=Q("h3",{id:"正自然数",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#正自然数"},[Q("span",null,"正自然数")])],-1),wa=Q("p",null,"在考察序的性质之前，我们预先准备以方便证明。",-1),_a={class:"MathJax",jax:"SVG",style:{position:"relative"}},va={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 500 688","aria-hidden":"true"},ya=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"30",d:"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"})])])],-1),Da=[ya],ba=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0")])],-1),ja=Q("h4",{id:"正自然数的性质",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#正自然数的性质"},[Q("span",null,"正自然数的性质")])],-1),Ba={class:"MathJax",jax:"SVG",style:{position:"relative"}},ka={style:{"vertical-align":"-0.023ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.197ex",height:"1.02ex",role:"img",focusable:"false",viewBox:"0 -441 529 451","aria-hidden":"true"},Ca=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D44E",d:"M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"})])])],-1),za=[Ca],Sa=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a")])],-1),Ja={class:"MathJax",jax:"SVG",style:{position:"relative"}},Ga={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.971ex",height:"1.595ex",role:"img",focusable:"false",viewBox:"0 -694 429 705","aria-hidden":"true"},Aa=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D44F",d:"M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"})])])],-1),Ea=[Aa],Fa=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b")])],-1),Oa={class:"MathJax",jax:"SVG",style:{position:"relative"}},Ra={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.933ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 2180.4 776","aria-hidden":"true"},Pa=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),Xa=[Pa],Na=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b")])],-1),Ka={class:"MathJax",jax:"SVG",style:{position:"relative"}},Ia={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.119ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 2262.6 776","aria-hidden":"true"},qa=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1762.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),Ua=[qa],Wa=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"="),Q("mn",null,"0")])],-1),Ya={class:"MathJax",jax:"SVG",style:{position:"relative"}},$a={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.308ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 4114 748","aria-hidden":"true"},Qt=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(1751.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2529.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3585,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g></g></g>',1),at=[Qt],tt=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mo",null,"="),Q("mi",null,"a")])],-1),Tt={class:"MathJax",jax:"SVG",style:{position:"relative"}},mt={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.971ex",height:"1.595ex",role:"img",focusable:"false",viewBox:"0 -694 429 705","aria-hidden":"true"},nt=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D44F",d:"M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"})])])],-1),lt=[nt],et=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b")])],-1),st={class:"MathJax",jax:"SVG",style:{position:"relative"}},ot={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.933ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 2180.4 776","aria-hidden":"true"},rt=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),dt=[rt],ht=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b")])],-1),it={class:"MathJax",jax:"SVG",style:{position:"relative"}},gt={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.711ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10038.4 1000","aria-hidden":"true"},Ht=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(3963.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4630.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5686,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7080,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7469,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(8220.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9220.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(9649.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Lt=[Ht],ct=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")")])],-1),pt={class:"MathJax",jax:"SVG",style:{position:"relative"}},ft={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.847ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4352.4 1000","aria-hidden":"true"},Mt=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2534.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(3963.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),ut=[Mt],xt=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")")])],-1),Zt={class:"MathJax",jax:"SVG",style:{position:"relative"}},Vt={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.847ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4352.4 1000","aria-hidden":"true"},wt=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(3963.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),_t=[wt],vt=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")")])],-1),yt=Q("p",null,"根据 Peano 公理 Ⅴ，正自然数与自然数相加为正自然数。",-1),Dt=Q("h3",{id:"序的反对称性",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#序的反对称性"},[Q("span",null,"序的反对称性")])],-1),bt={class:"MathJax",jax:"SVG",style:{position:"relative"}},jt={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 832","aria-hidden":"true"},Bt=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),kt=[Bt],Ct=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≤"),Q("mi",null,"b")])],-1),zt={class:"MathJax",jax:"SVG",style:{position:"relative"}},St={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 832","aria-hidden":"true"},Jt=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g></g></g>',1),Gt=[Jt],At=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"≤"),Q("mi",null,"a")])],-1),Et={class:"MathJax",jax:"SVG",style:{position:"relative"}},Ft={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 776","aria-hidden":"true"},Ot=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),Rt=[Ot],Pt=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),Xt={class:"MathJax",jax:"SVG",style:{position:"relative"}},Nt={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 832","aria-hidden":"true"},Kt=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),It=[Kt],qt=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≤"),Q("mi",null,"b")])],-1),Ut={class:"MathJax",jax:"SVG",style:{position:"relative"}},Wt={style:{"vertical-align":"-0.339ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.924ex",height:"1.91ex",role:"img",focusable:"false",viewBox:"0 -694 4828.6 844","aria-hidden":"true"},Yt=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(3514,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g></g></g>',1),$t=[Yt],QT=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"1")])])],-1),aT={class:"MathJax",jax:"SVG",style:{position:"relative"}},tT={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 832","aria-hidden":"true"},TT=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g></g></g>',1),mT=[TT],nT=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"≤"),Q("mi",null,"a")])],-1),lT={class:"MathJax",jax:"SVG",style:{position:"relative"}},eT={style:{"vertical-align":"-0.339ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.924ex",height:"1.91ex",role:"img",focusable:"false",viewBox:"0 -694 4828.6 844","aria-hidden":"true"},sT=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(3514,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g></g></g>',1),oT=[sT],rT=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"2")])])],-1),dT={class:"MathJax",jax:"SVG",style:{position:"relative"}},hT={style:{"vertical-align":"-0.339ex"},xmlns:"http://www.w3.org/2000/svg",width:"34.729ex",height:"1.91ex",role:"img",focusable:"false",viewBox:"0 -694 15350.1 844","aria-hidden":"true"},iT=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2529.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3585,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4391.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5447.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6098.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(7099,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g><g data-mml-node="mo" transform="translate(8691.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9747.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(10498.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(11498.6,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g><g data-mml-node="mo" transform="translate(13035.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(14035.6,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g></g></g>',1),gT=[iT],HT=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"2")]),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"1")]),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"2")])])],-1),LT={class:"MathJax",jax:"SVG",style:{position:"relative"}},cT={style:{"vertical-align":"-0.339ex"},xmlns:"http://www.w3.org/2000/svg",width:"12.862ex",height:"1.846ex",role:"img",focusable:"false",viewBox:"0 -666 5685.1 816","aria-hidden":"true"},pT=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g><g data-mml-node="mo" transform="translate(1536.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(2537,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g><g data-mml-node="mo" transform="translate(4129.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(5185.1,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),fT=[pT],MT=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"1")]),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"2")]),Q("mo",null,"="),Q("mn",null,"0")])],-1),uT={class:"MathJax",jax:"SVG",style:{position:"relative"}},xT={style:{"vertical-align":"-0.339ex"},xmlns:"http://www.w3.org/2000/svg",width:"13.114ex",height:"1.846ex",role:"img",focusable:"false",viewBox:"0 -666 5796.2 816","aria-hidden":"true"},ZT=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g><g data-mml-node="mo" transform="translate(1592.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="msub" transform="translate(2648.1,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g><g data-mml-node="mo" transform="translate(4240.4,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(5296.2,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),VT=[ZT],wT=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"1")]),Q("mo",null,"="),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"2")]),Q("mo",null,"="),Q("mn",null,"0")])],-1),_T={class:"MathJax",jax:"SVG",style:{position:"relative"}},vT={style:{"vertical-align":"-0.339ex"},xmlns:"http://www.w3.org/2000/svg",width:"23.249ex",height:"1.91ex",role:"img",focusable:"false",viewBox:"0 -694 10276.1 844","aria-hidden":"true"},yT=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2613.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(3614,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(4391.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5447.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6198.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(7199,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g><g data-mml-node="mo" transform="translate(8791.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9847.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),DT=[yT],bT=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"1")]),Q("mo",null,"="),Q("mi",null,"b")])],-1),jT=Q("h3",{id:"序的传递性",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#序的传递性"},[Q("span",null,"序的传递性")])],-1),BT={class:"MathJax",jax:"SVG",style:{position:"relative"}},kT={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 832","aria-hidden":"true"},CT=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),zT=[CT],ST=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≤"),Q("mi",null,"b")])],-1),JT={class:"MathJax",jax:"SVG",style:{position:"relative"}},GT={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.967ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2195.6 832","aria-hidden":"true"},AT=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),ET=[AT],FT=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"≤"),Q("mi",null,"c")])],-1),OT={class:"MathJax",jax:"SVG",style:{position:"relative"}},RT={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.194ex",height:"1.751ex",role:"img",focusable:"false",viewBox:"0 -636 2295.6 774","aria-hidden":"true"},PT=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),XT=[PT],NT=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≤"),Q("mi",null,"c")])],-1),KT={class:"MathJax",jax:"SVG",style:{position:"relative"}},IT={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 832","aria-hidden":"true"},qT=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),UT=[qT],WT=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≤"),Q("mi",null,"b")])],-1),YT={class:"MathJax",jax:"SVG",style:{position:"relative"}},$T={style:{"vertical-align":"-0.339ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.924ex",height:"1.91ex",role:"img",focusable:"false",viewBox:"0 -694 4828.6 844","aria-hidden":"true"},Qm=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(3514,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g></g></g>',1),am=[Qm],tm=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"1")])])],-1),Tm={class:"MathJax",jax:"SVG",style:{position:"relative"}},mm={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.967ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2195.6 832","aria-hidden":"true"},nm=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),lm=[nm],em=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"≤"),Q("mi",null,"c")])],-1),sm={class:"MathJax",jax:"SVG",style:{position:"relative"}},om={style:{"vertical-align":"-0.339ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.707ex",height:"1.91ex",role:"img",focusable:"false",viewBox:"0 -694 4732.6 844","aria-hidden":"true"},rm=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1766.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2417.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(3418,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g></g></g>',1),dm=[rm],hm=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"2")])])],-1),im={class:"MathJax",jax:"SVG",style:{position:"relative"}},gm={style:{"vertical-align":"-0.339ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.714ex",height:"1.658ex",role:"img",focusable:"false",viewBox:"0 -583 3851.6 733","aria-hidden":"true"},Hm=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g><g data-mml-node="mo" transform="translate(1536.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(2537,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g></g></g>',1),Lm=[Hm],cm=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"1")]),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"2")])])],-1),pm={class:"MathJax",jax:"SVG",style:{position:"relative"}},fm={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"45.615ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 20161.7 1000","aria-hidden":"true"},Mm=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1766.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2417.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(3418,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g><g data-mml-node="mo" transform="translate(5010.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(6066.1,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6455.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7206.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(8206.6,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g><g data-mml-node="mo" transform="translate(9521.1,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(10132.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(11132.6,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g><g data-mml-node="mo" transform="translate(12724.9,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(13780.7,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(14531.9,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(15532.1,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="msub" transform="translate(15921.1,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g><g data-mml-node="mo" transform="translate(17457.9,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(18458.1,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g><g data-mml-node="mo" transform="translate(19772.7,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),um=[Mm],xm=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"2")]),Q("mo",null,"="),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"1")]),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"2")]),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mo",{stretchy:"false"},"("),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"1")]),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"2")]),Q("mo",{stretchy:"false"},")")])],-1),Zm={class:"MathJax",jax:"SVG",style:{position:"relative"}},Vm={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.194ex",height:"1.751ex",role:"img",focusable:"false",viewBox:"0 -636 2295.6 774","aria-hidden":"true"},wm=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),_m=[wm],vm=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≤"),Q("mi",null,"c")])],-1),ym=Q("h3",{id:"序的完全性",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#序的完全性"},[Q("span",null,"序的完全性")])],-1),Dm={class:"MathJax",jax:"SVG",style:{position:"relative"}},bm={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"3.173ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 1402.7 888","aria-hidden":"true"},jm=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),Bm=[jm],km=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b")])],-1),Cm={class:"MathJax",jax:"SVG",style:{position:"relative"}},zm={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"3.173ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 1402.7 888","aria-hidden":"true"},Sm=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),Jm=[Sm],Gm=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b")])],-1),Am={class:"MathJax",jax:"SVG",style:{position:"relative"}},Em={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.119ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 2262.6 776","aria-hidden":"true"},Fm=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1762.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),Om=[Fm],Rm=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"="),Q("mn",null,"0")])],-1),Pm={class:"MathJax",jax:"SVG",style:{position:"relative"}},Xm={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"17.258ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 7628 776","aria-hidden":"true"},Nm=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1862.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2584.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3585,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4391.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5447.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6098.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7099,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g></g></g>',1),Km=[Nm],Im=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"a")])],-1),qm={class:"MathJax",jax:"SVG",style:{position:"relative"}},Um={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 832","aria-hidden":"true"},Wm=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),Ym=[Wm],$m=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≤"),Q("mi",null,"b")])],-1),Qn={class:"MathJax",jax:"SVG",style:{position:"relative"}},an={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.971ex",height:"1.595ex",role:"img",focusable:"false",viewBox:"0 -694 429 705","aria-hidden":"true"},tn=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D44F",d:"M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"})])])],-1),Tn=[tn],mn=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b")])],-1),nn={class:"MathJax",jax:"SVG",style:{position:"relative"}},ln={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 776","aria-hidden":"true"},en=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),sn=[en],on=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),rn={class:"MathJax",jax:"SVG",style:{position:"relative"}},dn={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"18.91ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 8358 1000","aria-hidden":"true"},hn=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2212,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(2878.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3934.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4685.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5686,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7080,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(7469,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(7969,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),gn=[hn],Hn=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")")])],-1),Ln={class:"MathJax",jax:"SVG",style:{position:"relative"}},cn={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.099ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4463.6 1000","aria-hidden":"true"},pn=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3C" d="M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3256.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3645.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4074.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),fn=[pn],Mn=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"<"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")")])],-1),un={class:"MathJax",jax:"SVG",style:{position:"relative"}},xn={style:{"vertical-align":"-0.09ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.661ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 734","aria-hidden":"true"},Zn=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3C" d="M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),Vn=[Zn],wn=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"<"),Q("mi",null,"b")])],-1),_n={class:"MathJax",jax:"SVG",style:{position:"relative"}},vn={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"36.234ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 16015.4 1000","aria-hidden":"true"},yn=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2212,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(2878.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3934.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4585.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5586,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6980,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(7369,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(7869,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(8535.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9591.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(10242.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(11243,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(12343.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(13343.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(14737.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(15126.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(15626.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Dn=[yn],bn=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")")])],-1),jn={class:"MathJax",jax:"SVG",style:{position:"relative"}},Bn={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.099ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4463.6 1000","aria-hidden":"true"},kn=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3C" d="M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3256.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3645.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4074.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Cn=[kn],zn=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"<"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")")])],-1),Sn={class:"MathJax",jax:"SVG",style:{position:"relative"}},Jn={style:{"vertical-align":"-0.09ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.661ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 734","aria-hidden":"true"},Gn=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3E" d="M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),An=[Gn],En=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,">"),Q("mi",null,"b")])],-1),Fn={class:"MathJax",jax:"SVG",style:{position:"relative"}},On={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.099ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4463.6 1000","aria-hidden":"true"},Rn=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2265" d="M83 616Q83 624 89 630T99 636Q107 636 253 568T543 431T687 361Q694 356 694 346T687 331Q685 329 395 192L107 56H101Q83 58 83 76Q83 77 83 79Q82 86 98 95Q117 105 248 167Q326 204 378 228L626 346L360 472Q291 505 200 548Q112 589 98 597T83 616ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3256.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3645.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4074.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Pn=[Rn],Xn=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≥"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")")])],-1),Nn={class:"MathJax",jax:"SVG",style:{position:"relative"}},Kn={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"3.173ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 1402.7 888","aria-hidden":"true"},In=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),qn=[In],Un=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b")])],-1),Wn=Q("h3",{id:"加法保序性",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#加法保序性"},[Q("span",null,"加法保序性")])],-1),Yn={class:"MathJax",jax:"SVG",style:{position:"relative"}},$n={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 832","aria-hidden":"true"},Ql=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),al=[Ql],tl=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≤"),Q("mi",null,"b")])],-1),Tl={class:"MathJax",jax:"SVG",style:{position:"relative"}},ml={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"12.675ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 5602.4 832","aria-hidden":"true"},nl=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),ll=[nl],el=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"≤"),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c")])],-1),sl={class:"MathJax",jax:"SVG",style:{position:"relative"}},ol={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 832","aria-hidden":"true"},rl=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),dl=[rl],hl=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≤"),Q("mi",null,"b")])],-1),il={class:"MathJax",jax:"SVG",style:{position:"relative"}},gl={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 4392 776","aria-hidden":"true"},Hl=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3514,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Ll=[Hl],cl=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"m")])],-1),pl={class:"MathJax",jax:"SVG",style:{position:"relative"}},fl={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"46.371ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 20495.8 1000","aria-hidden":"true"},Ml=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(651.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1651.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2362.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(3418,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3807,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4558.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5558.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6436.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7047.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(8047.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(8758.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9814.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(10565.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(11565.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(12666.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(13666.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(14377.1,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(15432.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(15821.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(16573.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(17573.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(18006.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(18617.6,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(19617.8,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),ul=[Ml],xl=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"m")])],-1),Zl={class:"MathJax",jax:"SVG",style:{position:"relative"}},Vl={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"12.675ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 5602.4 832","aria-hidden":"true"},wl=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),_l=[wl],vl=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"≤"),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c")])],-1),yl=Q("h2",{id:"自然数的乘法运算",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#自然数的乘法运算"},[Q("span",null,"自然数的乘法运算")])],-1),Dl=Q("p",null,"自然数的乘法也十分重要。",-1),bl=Q("h3",{id:"乘法的定义",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#乘法的定义"},[Q("span",null,"乘法的定义")])],-1),jl=Q("p",null,"定义乘法的运算规则：",-1),Bl={class:"MathJax",jax:"SVG",style:{position:"relative"}},kl={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Cl=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),zl=[Cl],Sl=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),Jl={class:"MathJax",jax:"SVG",style:{position:"relative"}},Gl={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.254ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 2322.4 688","aria-hidden":"true"},Al=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),El=[Al],Fl=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),Ol={class:"MathJax",jax:"SVG",style:{position:"relative"}},Rl={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 500 688","aria-hidden":"true"},Pl=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"30",d:"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"})])])],-1),Xl=[Pl],Nl=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0")])],-1),Kl={class:"MathJax",jax:"SVG",style:{position:"relative"}},Il={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.403ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 4156 748","aria-hidden":"true"},ql=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(3656,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),Ul=[ql],Wl=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"="),Q("mn",null,"0")])],-1),Yl={class:"MathJax",jax:"SVG",style:{position:"relative"}},$l={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.35ex",height:"1.439ex",role:"img",focusable:"false",viewBox:"0 -442 1922.7 636","aria-hidden":"true"},Qe=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),ae=[Qe],te=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"m")])],-1),Te={class:"MathJax",jax:"SVG",style:{position:"relative"}},me={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"24.274ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10728.9 1000","aria-hidden":"true"},ne=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7306.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8306.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9128.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10128.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),le=[ne],ee=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),se=Q("p",null,"下面我们需要证明对于任意两个自然数，都可以进行乘法运算，也就是说，我们需要证明乘法结果的存在性和唯一性。",-1),oe=Q("h4",{id:"乘法结果的存在性",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#乘法结果的存在性"},[Q("span",null,"乘法结果的存在性")])],-1),re={class:"MathJax",jax:"SVG",style:{position:"relative"}},de={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},he=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),ie=[he],ge=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),He={class:"MathJax",jax:"SVG",style:{position:"relative"}},Le={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},ce=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),pe=[ce],fe=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),Me={class:"MathJax",jax:"SVG",style:{position:"relative"}},ue={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.136ex",role:"img",focusable:"false",viewBox:"0 -491 2700.4 502","aria-hidden":"true"},xe=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Ze=[xe],Ve=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),we={class:"MathJax",jax:"SVG",style:{position:"relative"}},_e={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.136ex",role:"img",focusable:"false",viewBox:"0 -491 2700.4 502","aria-hidden":"true"},ve=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),ye=[ve],De=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),be={class:"MathJax",jax:"SVG",style:{position:"relative"}},je={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Be=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),ke=[Be],Ce=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),ze={class:"MathJax",jax:"SVG",style:{position:"relative"}},Se={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.403ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 4156 748","aria-hidden":"true"},Je=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(3656,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),Ge=[Je],Ae=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"="),Q("mn",null,"0")])],-1),Ee={class:"MathJax",jax:"SVG",style:{position:"relative"}},Fe={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.254ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 2322.4 688","aria-hidden":"true"},Oe=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Re=[Oe],Pe=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),Xe={class:"MathJax",jax:"SVG",style:{position:"relative"}},Ne={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.177ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2288.3 1000","aria-hidden":"true"},Ke=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(1399.3,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(1899.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Ie=[Ke],qe=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")")])],-1),Ue={class:"MathJax",jax:"SVG",style:{position:"relative"}},We={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Ye=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),$e=[Ye],Qs=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),as={class:"MathJax",jax:"SVG",style:{position:"relative"}},ts={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.136ex",role:"img",focusable:"false",viewBox:"0 -491 2700.4 502","aria-hidden":"true"},Ts=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),ms=[Ts],ns=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),ls={class:"MathJax",jax:"SVG",style:{position:"relative"}},es={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.233ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 4522.9 665","aria-hidden":"true"},ss=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2922.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3922.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),os=[ss],rs=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),ds={class:"MathJax",jax:"SVG",style:{position:"relative"}},hs={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"24.274ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10728.9 1000","aria-hidden":"true"},is=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7306.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8306.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9128.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10128.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),gs=[is],Hs=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),Ls={class:"MathJax",jax:"SVG",style:{position:"relative"}},cs={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.024ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4872.4 1000","aria-hidden":"true"},ps=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),fs=[ps],Ms=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),us={class:"MathJax",jax:"SVG",style:{position:"relative"}},xs={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.136ex",role:"img",focusable:"false",viewBox:"0 -491 2700.4 502","aria-hidden":"true"},Zs=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Vs=[Zs],ws=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),_s={class:"MathJax",jax:"SVG",style:{position:"relative"}},vs={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.024ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4872.4 1000","aria-hidden":"true"},ys=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Ds=[ys],bs=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),js={class:"MathJax",jax:"SVG",style:{position:"relative"}},Bs={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},ks=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Cs=[ks],zs=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),Ss={class:"MathJax",jax:"SVG",style:{position:"relative"}},Js={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.946ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4838.3 1000","aria-hidden":"true"},Gs=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2793.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3182.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4060.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4449.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),As=[Gs],Es=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")")])],-1),Fs={class:"MathJax",jax:"SVG",style:{position:"relative"}},Os={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},Rs=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Ps=[Rs],Xs=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),Ns={class:"MathJax",jax:"SVG",style:{position:"relative"}},Ks={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.986ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 878 453","aria-hidden":"true"},Is=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45A",d:"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"})])])],-1),qs=[Is],Us=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m")])],-1),Ws={class:"MathJax",jax:"SVG",style:{position:"relative"}},Ys={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},$s=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Qo=[$s],ao=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),to={class:"MathJax",jax:"SVG",style:{position:"relative"}},To={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.136ex",role:"img",focusable:"false",viewBox:"0 -491 2700.4 502","aria-hidden":"true"},mo=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),no=[mo],lo=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),eo={class:"MathJax",jax:"SVG",style:{position:"relative"}},so={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},oo=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),ro=[oo],ho=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),io={class:"MathJax",jax:"SVG",style:{position:"relative"}},go={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.35ex",height:"1.439ex",role:"img",focusable:"false",viewBox:"0 -442 1922.7 636","aria-hidden":"true"},Ho=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Lo=[Ho],co=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"m")])],-1),po={class:"MathJax",jax:"SVG",style:{position:"relative"}},fo={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.136ex",role:"img",focusable:"false",viewBox:"0 -491 2700.4 502","aria-hidden":"true"},Mo=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),uo=[Mo],xo=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),Zo=Q("h4",{id:"乘法结果的唯一性",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#乘法结果的唯一性"},[Q("span",null,"乘法结果的唯一性")])],-1),Vo={class:"MathJax",jax:"SVG",style:{position:"relative"}},wo={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},_o=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),vo=[_o],yo=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),Do={class:"MathJax",jax:"SVG",style:{position:"relative"}},bo={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},jo=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Bo=[jo],ko=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),Co={class:"MathJax",jax:"SVG",style:{position:"relative"}},zo={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.136ex",role:"img",focusable:"false",viewBox:"0 -491 2700.4 502","aria-hidden":"true"},So=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Jo=[So],Go=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),Ao={class:"MathJax",jax:"SVG",style:{position:"relative"}},Eo={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.136ex",role:"img",focusable:"false",viewBox:"0 -491 2700.4 502","aria-hidden":"true"},Fo=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Oo=[Fo],Ro=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),Po={class:"MathJax",jax:"SVG",style:{position:"relative"}},Xo={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},No=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),Ko=[No],Io=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),qo={class:"MathJax",jax:"SVG",style:{position:"relative"}},Uo={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.403ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 4156 748","aria-hidden":"true"},Wo=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(3656,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),Yo=[Wo],$o=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"="),Q("mn",null,"0")])],-1),Qr={class:"MathJax",jax:"SVG",style:{position:"relative"}},ar={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.254ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 2322.4 688","aria-hidden":"true"},tr=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Tr=[tr],mr=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),nr={class:"MathJax",jax:"SVG",style:{position:"relative"}},lr={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 500 688","aria-hidden":"true"},er=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"30",d:"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"})])])],-1),sr=[er],or=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0")])],-1),rr={class:"MathJax",jax:"SVG",style:{position:"relative"}},dr={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.177ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2288.3 1000","aria-hidden":"true"},hr=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(1399.3,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(1899.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),ir=[hr],gr=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")")])],-1),Hr={class:"MathJax",jax:"SVG",style:{position:"relative"}},Lr={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.986ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 878 453","aria-hidden":"true"},cr=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45A",d:"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"})])])],-1),pr=[cr],fr=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m")])],-1),Mr={class:"MathJax",jax:"SVG",style:{position:"relative"}},ur={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.136ex",role:"img",focusable:"false",viewBox:"0 -491 2700.4 502","aria-hidden":"true"},xr=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Zr=[xr],Vr=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),wr={class:"MathJax",jax:"SVG",style:{position:"relative"}},_r={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.233ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 4522.9 665","aria-hidden":"true"},vr=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2922.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3922.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),yr=[vr],Dr=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),br={class:"MathJax",jax:"SVG",style:{position:"relative"}},jr={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"24.274ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10728.9 1000","aria-hidden":"true"},Br=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7306.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8306.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9128.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10128.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),kr=[Br],Cr=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),zr={class:"MathJax",jax:"SVG",style:{position:"relative"}},Sr={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.024ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4872.4 1000","aria-hidden":"true"},Jr=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Gr=[Jr],Ar=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),Er={class:"MathJax",jax:"SVG",style:{position:"relative"}},Fr={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.136ex",role:"img",focusable:"false",viewBox:"0 -491 2700.4 502","aria-hidden":"true"},Or=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Rr=[Or],Pr=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),Xr={class:"MathJax",jax:"SVG",style:{position:"relative"}},Nr={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.024ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4872.4 1000","aria-hidden":"true"},Kr=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Ir=[Kr],qr=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),Ur={class:"MathJax",jax:"SVG",style:{position:"relative"}},Wr={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},Yr=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),$r=[Yr],Qd=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),ad={class:"MathJax",jax:"SVG",style:{position:"relative"}},td={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.946ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4838.3 1000","aria-hidden":"true"},Td=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2793.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3182.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4060.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4449.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),md=[Td],nd=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")")])],-1),ld={class:"MathJax",jax:"SVG",style:{position:"relative"}},ed={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},sd=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),od=[sd],rd=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),dd={class:"MathJax",jax:"SVG",style:{position:"relative"}},hd={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.986ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 878 453","aria-hidden":"true"},id=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45A",d:"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"})])])],-1),gd=[id],Hd=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m")])],-1),Ld={class:"MathJax",jax:"SVG",style:{position:"relative"}},cd={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},pd=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),fd=[pd],Md=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),ud={class:"MathJax",jax:"SVG",style:{position:"relative"}},xd={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.136ex",role:"img",focusable:"false",viewBox:"0 -491 2700.4 502","aria-hidden":"true"},Zd=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Vd=[Zd],wd=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),_d={class:"MathJax",jax:"SVG",style:{position:"relative"}},vd={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},yd=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),Dd=[yd],bd=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),jd={class:"MathJax",jax:"SVG",style:{position:"relative"}},Bd={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.35ex",height:"1.439ex",role:"img",focusable:"false",viewBox:"0 -442 1922.7 636","aria-hidden":"true"},kd=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Cd=[kd],zd=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"m")])],-1),Sd={class:"MathJax",jax:"SVG",style:{position:"relative"}},Jd={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.136ex",role:"img",focusable:"false",viewBox:"0 -491 2700.4 502","aria-hidden":"true"},Gd=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Ad=[Gd],Ed=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),Fd=Q("h3",{id:"乘法的性质",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#乘法的性质"},[Q("span",null,"乘法的性质")])],-1),Od=Q("p",null,"在明确证明了自然数乘法运算的良好性质，即任意两个自然数都可以进行乘法运算，且乘法运算的结果存在且唯一之后，我们终于可以对自然数乘法的性质进行进一步的探索。",-1),Rd=Q("h4",{id:"乘法交换律",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#乘法交换律"},[Q("span",null,"乘法交换律")])],-1),Pd={class:"MathJax",jax:"SVG",style:{position:"relative"}},Xd={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.35ex",height:"1.439ex",role:"img",focusable:"false",viewBox:"0 -442 1922.7 636","aria-hidden":"true"},Nd=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Kd=[Nd],Id=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"m")])],-1),qd={class:"MathJax",jax:"SVG",style:{position:"relative"}},Ud={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.236ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 6734.4 665","aria-hidden":"true"},Wd=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Yd=[Wd],$d=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),Qh=Q("p",null,"直接证明比较困难，考虑从乘法运算的定义下手，即先证明乘法的两条运算规则符合交换律。",-1),ah={class:"MathJax",jax:"SVG",style:{position:"relative"}},th={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"17.674ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 7812 748","aria-hidden":"true"},Th=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(3656,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(4433.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5489.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6311.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(7312,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),mh=[Th],nh=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mn",null,"0")])],-1),lh={class:"MathJax",jax:"SVG",style:{position:"relative"}},eh={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"17.222ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 7612 748","aria-hidden":"true"},sh=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(1722.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2500.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(3556,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(4333.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(5389.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(6111.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(7112,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),oh=[sh],rh=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"×"),Q("mn",null,"0"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"×"),Q("mn",null,"0")])],-1),dh={class:"MathJax",jax:"SVG",style:{position:"relative"}},hh={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},ih=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),gh=[ih],Hh=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),Lh={class:"MathJax",jax:"SVG",style:{position:"relative"}},ch={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"17.674ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 7812 748","aria-hidden":"true"},ph=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(3656,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(4433.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5489.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6311.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(7312,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),fh=[ph],Mh=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mn",null,"0")])],-1),uh={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},xh={style:{"vertical-align":"-4.977ex"},xmlns:"http://www.w3.org/2000/svg",width:"47.524ex",height:"11.086ex",role:"img",focusable:"false",viewBox:"0 -2700 21005.4 4900","aria-hidden":"true"},Zh=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1950)"><g data-mml-node="mtd"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3116.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3505.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4105.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(1833.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13322.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,650)"><g data-mml-node="mtd" transform="translate(4494.4,0)"></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2155.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(3156,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(3656,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(16016.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(777.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1833.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2655.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(3656,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-650)"><g data-mml-node="mtd" transform="translate(4494.4,0)"></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2155.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(3156,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(3878.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(4878.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(5378.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13322.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1950)"><g data-mml-node="mtd" transform="translate(4494.4,0)"></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3716.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4327.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(5328,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(5828,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13322.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),Vh=[Zh],wh=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mn",null,"0"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mn",null,"0")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mn",null,"0"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])])])])],-1),_h={class:"MathJax",jax:"SVG",style:{position:"relative"}},vh={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"17.674ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 7812 748","aria-hidden":"true"},yh=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(3656,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(4433.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5489.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6311.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(7312,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),Dh=[yh],bh=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mn",null,"0")])],-1),jh={class:"MathJax",jax:"SVG",style:{position:"relative"}},Bh={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},kh=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),Ch=[kh],zh=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),Sh={class:"MathJax",jax:"SVG",style:{position:"relative"}},Jh={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"24.902ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 11006.9 1000","aria-hidden":"true"},Gh=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7306.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8306.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9128.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10128.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Ah=[Gh],Eh=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m")])],-1),Fh={class:"MathJax",jax:"SVG",style:{position:"relative"}},Oh={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.135ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2711.6 748","aria-hidden":"true"},Rh=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1155.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(2211.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),Ph=[Rh],Xh=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"="),Q("mn",null,"0")])],-1),Nh={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},Kh={style:{"vertical-align":"-6.448ex"},xmlns:"http://www.w3.org/2000/svg",width:"49.072ex",height:"14.027ex",role:"img",focusable:"false",viewBox:"0 -3350 21689.9 6200","aria-hidden":"true"},Ih=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,2600)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2055.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3056,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4450,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4839,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5439,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5828,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18145.3,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1155.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(2211.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd" transform="translate(4872.4,0)"></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(1833.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14006.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(4872.4,0)"></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2055.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3056,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mstyle" transform="translate(3656,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14006.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(4872.4,0)"></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2055.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3056,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3878.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(4878.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(5378.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14006.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-2600)"><g data-mml-node="mtd" transform="translate(4872.4,0)"></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2433.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3434,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4256.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5256.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mstyle" transform="translate(6134.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18145.3,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1155.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(2211.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g></g></g></g>',1),qh=[Ih],Uh=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"m"),Q("mo",null,"="),Q("mn",null,"0")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"m"),Q("mo",null,"="),Q("mn",null,"0")])])])])])],-1),Wh={class:"MathJax",jax:"SVG",style:{position:"relative"}},Yh={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.986ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 878 453","aria-hidden":"true"},$h=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45A",d:"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"})])])],-1),Qi=[$h],ai=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m")])],-1),ti={class:"MathJax",jax:"SVG",style:{position:"relative"}},Ti={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"24.902ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 11006.9 1000","aria-hidden":"true"},mi=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7306.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8306.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9128.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10128.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),ni=[mi],li=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m")])],-1),ei={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},si={style:{"vertical-align":"-6.448ex"},xmlns:"http://www.w3.org/2000/svg",width:"63.814ex",height:"14.027ex",role:"img",focusable:"false",viewBox:"0 -3350 28205.9 6200","aria-hidden":"true"},oi=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,2600)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(5666.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6055.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6655.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2433.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3434,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4828,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5217,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5817,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6428.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7428.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8822.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9211.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9811.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(10200.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(20522.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd" transform="translate(7044.4,0)"></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2433.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3434,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4256.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5256.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6356.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7356.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8750.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9139.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9739.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(10128.9,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(22572,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2922.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3922.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(7044.4,0)"></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2433.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3434,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4256.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5256.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6650.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7039.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7917.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(8528.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9528.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mstyle" transform="translate(10128.9,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(20522.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(7044.4,0)"></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2433.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3434,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4256.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5256.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6078.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7078.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8472.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8861.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9739.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(10128.9,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(22372.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">交</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">换</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">律</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-2600)"><g data-mml-node="mtd" transform="translate(7044.4,0)"></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3994.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4605.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5606,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6428.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7428.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8822.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9211.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10089.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(10478.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(20522.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),ri=[oi],di=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法交换律")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])])])])],-1),hi={class:"MathJax",jax:"SVG",style:{position:"relative"}},ii={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"24.902ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 11006.9 1000","aria-hidden":"true"},gi=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7306.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8306.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9128.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10128.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Hi=[gi],Li=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m")])],-1),ci={class:"MathJax",jax:"SVG",style:{position:"relative"}},pi={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.35ex",height:"1.439ex",role:"img",focusable:"false",viewBox:"0 -442 1922.7 636","aria-hidden":"true"},fi=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Mi=[fi],ui=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"m")])],-1),xi=Q("strong",null,"乘法运算规则 Ⅱ",-1),Zi={class:"MathJax",jax:"SVG",style:{position:"relative"}},Vi={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.236ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 6734.4 665","aria-hidden":"true"},wi=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),_i=[wi],vi=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),yi={class:"MathJax",jax:"SVG",style:{position:"relative"}},Di={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.506ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2433.6 748","aria-hidden":"true"},bi=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(877.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1933.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),ji=[bi],Bi=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"="),Q("mn",null,"0")])],-1),ki={class:"MathJax",jax:"SVG",style:{position:"relative"}},Ci={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"14.784ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 6534.4 748","aria-hidden":"true"},zi=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2878.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3934,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5034.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(6034.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),Si=[zi],Ji=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mn",null,"0")])],-1),Gi={class:"MathJax",jax:"SVG",style:{position:"relative"}},Ai={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Ei=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),Fi=[Ei],Oi=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),Ri={class:"MathJax",jax:"SVG",style:{position:"relative"}},Pi={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.236ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 6734.4 665","aria-hidden":"true"},Xi=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Ni=[Xi],Ki=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),Ii={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},qi={style:{"vertical-align":"-3.507ex"},xmlns:"http://www.w3.org/2000/svg",width:"49.234ex",height:"8.145ex",role:"img",focusable:"false",viewBox:"0 -2050 21761.4 3600","aria-hidden":"true"},Ui=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2383,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(2994.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3994.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2155.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3156,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4256.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5256.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mstyle" transform="translate(6134.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14078.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(4872.4,0)"></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2433.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3434,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4256.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5256.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mstyle" transform="translate(6134.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14194,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(4872.4,0)"></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2433.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3434,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4828,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5217,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5817,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(6206,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14078.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),Wi=[Ui],Yi=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"m")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])])])])],-1),$i={class:"MathJax",jax:"SVG",style:{position:"relative"}},Qg={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.236ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 6734.4 665","aria-hidden":"true"},ag=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),tg=[ag],Tg=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),mg={class:"MathJax",jax:"SVG",style:{position:"relative"}},ng={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.35ex",height:"1.439ex",role:"img",focusable:"false",viewBox:"0 -442 1922.7 636","aria-hidden":"true"},lg=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),eg=[lg],sg=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"m")])],-1),og=Q("h4",{id:"乘法分配律",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#乘法分配律"},[Q("span",null,"乘法分配律")])],-1),rg={class:"MathJax",jax:"SVG",style:{position:"relative"}},dg={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.537ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 2447.3 888","aria-hidden":"true"},hg=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),ig=[hg],gg=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b"),Q("mo",null,","),Q("mi",null,"n")])],-1),Hg={class:"MathJax",jax:"SVG",style:{position:"relative"}},Lg={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.013ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 11939.8 1000","aria-hidden":"true"},cg=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(1822.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(2211.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2962.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3962.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4391.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5058.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6114.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6936.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7936.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(8688.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9688.3,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10510.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(11510.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),pg=[cg],fg=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"b")])],-1),Mg={class:"MathJax",jax:"SVG",style:{position:"relative"}},ug={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.506ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2433.6 748","aria-hidden":"true"},xg=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(877.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1933.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),Zg=[xg],Vg=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"="),Q("mn",null,"0")])],-1),wg={class:"MathJax",jax:"SVG",style:{position:"relative"}},_g={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"68.558ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 30302.7 1000","aria-hidden":"true"},vg=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(1822.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(2211.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2962.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3962.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4391.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5058.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(6114.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(6836.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(7836.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8225.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(8977.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9977.3,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(10406.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(11073.1,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(12128.9,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(12906.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(13962.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(14684.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(15684.9,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(16462.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(17518.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(18240.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(19240.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(19992.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(20992.3,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(21714.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(22714.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(23421.6,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(24477.3,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(25299.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(26299.8,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(27051,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(28051.2,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(28873.4,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(29873.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),yg=[vg],Dg=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"b")])],-1),bg={class:"MathJax",jax:"SVG",style:{position:"relative"}},jg={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Bg=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),kg=[Bg],Cg=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),zg={class:"MathJax",jax:"SVG",style:{position:"relative"}},Sg={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.013ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 11939.8 1000","aria-hidden":"true"},Jg=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(1822.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(2211.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2962.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3962.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4391.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5058.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6114.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6936.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7936.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(8688.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9688.3,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10510.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(11510.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),Gg=[Jg],Ag=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"b")])],-1),Eg={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},Fg={style:{"vertical-align":"-7.919ex"},xmlns:"http://www.w3.org/2000/svg",width:"78.831ex",height:"16.968ex",role:"img",focusable:"false",viewBox:"0 -4000 34843.4 7500","aria-hidden":"true"},Og=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,3250)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2383,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(2994.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(3994.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4383.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(5134.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6134.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6563.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(6952.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2155.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(3156,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3545,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4296.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5296.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(5725.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6336.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(7336.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7725.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(8477.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9477.3,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(9906.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(10295.3,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(27160.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,1950)"><g data-mml-node="mtd" transform="translate(6952.9,0)"></g><g data-mml-node="mtd" transform="translate(6952.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2155.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3156,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(3907.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4907.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5729.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(6729.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(7381.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(8381.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8770.3,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(9521.6,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10521.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(10950.8,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(11339.8,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(22070.7,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(1822.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(2211.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2962.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3962.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4391.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5058.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6114.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6936.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7936.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(8688.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9688.3,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10510.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(11510.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,650)"><g data-mml-node="mtd" transform="translate(6952.9,0)"></g><g data-mml-node="mtd" transform="translate(6952.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2155.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3156,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(3907.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4907.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5729.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(6729.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(7381.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(8381.3,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(9132.6,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10132.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(10561.8,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(29010.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">结</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">合</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">律</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-650)"><g data-mml-node="mtd" transform="translate(6952.9,0)"></g><g data-mml-node="mtd" transform="translate(6952.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2155.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3156,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(3907.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4907.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(5658.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6658.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7481.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8481.3,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(9132.6,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10132.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(10561.8,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(29010.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">交</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">换</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">律</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1950)"><g data-mml-node="mtd" transform="translate(6952.9,0)"></g><g data-mml-node="mtd" transform="translate(6952.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(1333.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2544.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3545,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4296.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5296.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(5825.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6436.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(7436.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7825.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(8648.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(9648.3,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(10299.6,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(11299.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(11728.8,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(12117.8,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(29010.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">结</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">合</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">律</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-3250)"><g data-mml-node="mtd" transform="translate(6952.9,0)"></g><g data-mml-node="mtd" transform="translate(6952.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3716.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4327.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5328,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6079.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7079.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8473.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8862.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9462.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(10073.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(11073.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(11502.9,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(27160.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),Rg=[Og],Pg=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",null,"+"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"n"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"b")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法结合律")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法交换律")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"a"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法结合律")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])])])])],-1),Xg={class:"MathJax",jax:"SVG",style:{position:"relative"}},Ng={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.013ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 11939.8 1000","aria-hidden":"true"},Kg=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(1822.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(2211.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2962.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3962.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4391.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5058.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6114.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6936.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7936.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(8688.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9688.3,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10510.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(11510.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),Ig=[Kg],qg=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"b")])],-1),Ug={class:"MathJax",jax:"SVG",style:{position:"relative"}},Wg={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.537ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 2447.3 888","aria-hidden":"true"},Yg=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1573.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(2018.3,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),$g=[Yg],QH=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b")])],-1),aH=Q("h4",{id:"乘法结合律",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#乘法结合律"},[Q("span",null,"乘法结合律")])],-1),tH={class:"MathJax",jax:"SVG",style:{position:"relative"}},TH={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.159ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 2280.3 888","aria-hidden":"true"},mH=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),nH=[mH],lH=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b"),Q("mo",null,","),Q("mi",null,"c")])],-1),eH={class:"MathJax",jax:"SVG",style:{position:"relative"}},sH={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"23.894ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10561.3 1000","aria-hidden":"true"},oH=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5947.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6698.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(7698.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8739.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(9739.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(10172.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),rH=[oH],dH=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),hH={class:"MathJax",jax:"SVG",style:{position:"relative"}},iH={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.128ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2266.6 748","aria-hidden":"true"},gH=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),HH=[gH],LH=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])],-1),cH={class:"MathJax",jax:"SVG",style:{position:"relative"}},pH={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"63.368ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 28008.8 1000","aria-hidden":"true"},fH=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(5947.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6336.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7087.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8516.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(9128.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(10128.3,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(10906.1,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(11961.9,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(12739.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(13795.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(14546.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(15546.9,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(16324.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(17380.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(18131.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(19131.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(19520.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(20172.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(21172.3,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(21672.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(22339.1,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(23394.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(24146.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(25146.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(25535.3,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(26186.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(27186.8,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(27619.8,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),MH=[fH],uH=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",null,"="),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mn",null,"0"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mn",null,"0"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"×"),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),xH={class:"MathJax",jax:"SVG",style:{position:"relative"}},ZH={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.98ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 433 453","aria-hidden":"true"},VH=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D450",d:"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"})])])],-1),wH=[VH],_H=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c")])],-1),vH={class:"MathJax",jax:"SVG",style:{position:"relative"}},yH={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"23.894ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10561.3 1000","aria-hidden":"true"},DH=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5947.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6698.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(7698.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8739.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(9739.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(10172.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),bH=[DH],jH=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),BH={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},kH={style:{"vertical-align":"-4.977ex"},xmlns:"http://www.w3.org/2000/svg",width:"69.074ex",height:"11.086ex",role:"img",focusable:"false",viewBox:"0 -2700 30530.6 4900","aria-hidden":"true"},CH=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1950)"><g data-mml-node="mtd"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(5574.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5963.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6396.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(6785.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(1333.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2473.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3474,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(3903,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4514.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5514.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6169.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7169.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7921.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8921.3,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(9350.3,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(22847.6,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,650)"><g data-mml-node="mtd" transform="translate(6785.9,0)"></g><g data-mml-node="mtd" transform="translate(6785.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(3085,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3474,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4125.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5125.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5558.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6169.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7169.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7921.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8921.3,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(9350.3,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(19136.2,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5947.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6698.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(7698.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8739.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(9739.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(10172.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-650)"><g data-mml-node="mtd" transform="translate(6785.9,0)"></g><g data-mml-node="mtd" transform="translate(6785.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(3085,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3474,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4125.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5125.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5780.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6780.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(7209.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(7598.9,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(24697.6,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">分</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">配</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">律</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1950)"><g data-mml-node="mtd" transform="translate(6785.9,0)"></g><g data-mml-node="mtd" transform="translate(6785.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(3085,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3474,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4125.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5125.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6519.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6908.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(7341.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7730.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(8119.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(22847.6,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),zH=[CH],SH=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",null,"+"),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法分配律")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])])])])],-1),JH={class:"MathJax",jax:"SVG",style:{position:"relative"}},GH={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"23.894ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10561.3 1000","aria-hidden":"true"},AH=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5947.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6698.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(7698.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8739.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(9739.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(10172.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),EH=[AH],FH=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),OH={class:"MathJax",jax:"SVG",style:{position:"relative"}},RH={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.159ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 2280.3 888","aria-hidden":"true"},PH=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),XH=[PH],NH=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b"),Q("mo",null,","),Q("mi",null,"c")])],-1),KH=Q("h4",{id:"乘法消去律",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#乘法消去律"},[Q("span",null,"乘法消去律")])],-1),IH={class:"MathJax",jax:"SVG",style:{position:"relative"}},qH={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"3.173ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 1402.7 888","aria-hidden":"true"},UH=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),WH=[UH],YH=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b")])],-1),$H={class:"MathJax",jax:"SVG",style:{position:"relative"}},QL={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.98ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 433 453","aria-hidden":"true"},aL=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D450",d:"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"})])])],-1),tL=[aL],TL=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c")])],-1),mL={class:"MathJax",jax:"SVG",style:{position:"relative"}},nL={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"31.207ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 13793.6 1000","aria-hidden":"true"},lL=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(10224.2,0)"><path data-c="21D4" d="M308 524Q318 526 323 526Q340 526 340 514Q340 507 336 499Q326 476 314 454T292 417T274 391T260 374L255 368Q255 367 500 367Q744 367 744 368L739 374Q734 379 726 390T707 416T685 453T663 499Q658 511 658 515Q658 525 680 525Q687 524 690 523T695 519T701 507Q766 359 902 287Q921 276 939 269T961 259T966 250Q966 246 965 244T960 240T949 236T930 228T902 213Q763 137 701 -7Q697 -16 695 -19T690 -23T680 -25Q658 -25 658 -15Q658 -11 663 1Q673 24 685 46T707 83T725 109T739 126L744 132Q744 133 500 133Q255 133 255 132L260 126Q265 121 273 110T292 84T314 47T336 1Q341 -11 341 -15Q341 -25 319 -25Q312 -24 309 -23T304 -19T298 -7Q233 141 97 213Q83 221 70 227T51 235T41 239T35 243T34 250T35 256T40 261T51 265T70 273T97 287Q235 363 299 509Q305 522 308 524ZM792 319L783 327H216Q183 294 120 256L110 250L120 244Q173 212 207 181L216 173H783L792 181Q826 212 879 244L889 250L879 256Q826 288 792 319Z"></path></g><g data-mml-node="mi" transform="translate(11502,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(12308.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(13364.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),eL=[lL],sL=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},"⇔"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),oL={class:"MathJax",jax:"SVG",style:{position:"relative"}},rL={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"31.207ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 13793.6 1000","aria-hidden":"true"},dL=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(3847.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4598.3,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5598.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6992.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7381.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(7814.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(8481.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9537.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(10188.3,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(11188.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(12582.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(12971.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(13404.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),hL=[dL],iL=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),gL={class:"MathJax",jax:"SVG",style:{position:"relative"}},HL={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.128ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2266.6 748","aria-hidden":"true"},LL=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),cL=[LL],pL=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])],-1),fL={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},ML={style:{"vertical-align":"-12.33ex"},xmlns:"http://www.w3.org/2000/svg",width:"47.051ex",height:"25.792ex",role:"img",focusable:"false",viewBox:"0 -5950 20796.4 11400","aria-hidden":"true"},uL=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,5200)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3085,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4479,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(4868,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(5368,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5757,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(17696.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,3900)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(3085,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(3807.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4807.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mstyle" transform="translate(5336.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13113.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,2600)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2055.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3056,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mstyle" transform="translate(3585,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13113.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mstyle" transform="translate(1862.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13113.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(1762.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(17671.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2055.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3056,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(3485,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13113.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-2600)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(2985,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(3707.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4707.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(5136.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13113.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-3900)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(4768,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(5268,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5657,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13113.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-5200)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5590,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(17696.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g></g></g></g>',1),xL=[uL],ZL=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"a"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"a"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])])])])])],-1),VL={class:"MathJax",jax:"SVG",style:{position:"relative"}},wL={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.98ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 433 453","aria-hidden":"true"},_L=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D450",d:"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"})])])],-1),vL=[_L],yL=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c")])],-1),DL={class:"MathJax",jax:"SVG",style:{position:"relative"}},bL={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.503ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 9946.4 1000","aria-hidden":"true"},jL=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),BL=[jL],kL=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),CL={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},zL={style:{"vertical-align":"-3.507ex"},xmlns:"http://www.w3.org/2000/svg",width:"72.085ex",height:"8.145ex",role:"img",focusable:"false",viewBox:"0 -2050 31861.4 3600","aria-hidden":"true"},SL=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4928.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5317.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5750.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6139.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(6528.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3085,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4479,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4868,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5301,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5912.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6912.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mstyle" transform="translate(7441.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(24178.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(6528.4,0)"></g><g data-mml-node="mtd" transform="translate(6528.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5812.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6812.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(7241.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(17290.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mrow" transform="translate(833,0)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g><g data-mml-node="mtext" transform="translate(2291.6,0)"><path data-c="A0" d=""></path><text data-variant="normal" transform="translate(250,0) scale(1,-1)" font-size="884px" font-family="serif">且</text><path data-c="A0" d="" transform="translate(1250,0)"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(3791.6,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(6528.4,0)"></g><g data-mml-node="mtd" transform="translate(6528.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6162,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6551,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6984,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7373,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(7762,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(24178.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),JL=[SL],GL=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"a"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",null,[Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")]),Q("mtext",null," 且 "),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])])])])],-1),AL={class:"MathJax",jax:"SVG",style:{position:"relative"}},EL={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"67.058ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 29639.6 1000","aria-hidden":"true"},FL=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(3847.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4598.3,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5598.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6992.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7381.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(7814.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(8481.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9537.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(10188.3,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(11188.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(12582.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(12971.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(13404.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(14071.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(15349.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(16100.3,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(17100.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(18494.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(18883.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(20277.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(20666.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(21099.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(21488.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(22155.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(23211.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(23862.3,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(24862.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(26256.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(26645.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(28039.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(28428.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(28861.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(29250.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),OL=[FL],RL=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")")])],-1),PL={class:"MathJax",jax:"SVG",style:{position:"relative"}},XL={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"31.207ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 13793.6 1000","aria-hidden":"true"},NL=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(3847.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4598.3,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5598.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6992.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7381.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(7814.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(8481.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9537.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(10188.3,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(11188.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(12582.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(12971.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(13404.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),KL=[NL],IL=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),qL={class:"MathJax",jax:"SVG",style:{position:"relative"}},UL={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.159ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 2280.3 888","aria-hidden":"true"},WL=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),YL=[WL],$L=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b"),Q("mo",null,","),Q("mi",null,"c")])],-1),Qc={class:"MathJax",jax:"SVG",style:{position:"relative"}},ac={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"31.207ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 13793.6 1000","aria-hidden":"true"},tc=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(10224.2,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(11502,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(12308.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(13364.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),Tc=[tc],mc=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),nc={class:"MathJax",jax:"SVG",style:{position:"relative"}},lc={style:{"vertical-align":"-0.486ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"2.106ex",role:"img",focusable:"false",viewBox:"0 -716 2291.6 931","aria-hidden":"true"},ec=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2260" d="M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),sc=[ec],oc=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≠"),Q("mi",null,"b")])],-1),rc={class:"MathJax",jax:"SVG",style:{position:"relative"}},dc={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 4392 776","aria-hidden":"true"},hc=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3514,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),ic=[hc],gc=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"m")])],-1),Hc={class:"MathJax",jax:"SVG",style:{position:"relative"}},Lc={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 4392 776","aria-hidden":"true"},cc=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3514,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),pc=[cc],fc=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"m")])],-1),Mc={class:"MathJax",jax:"SVG",style:{position:"relative"}},uc={style:{"vertical-align":"-0.486ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.135ex",height:"2.106ex",role:"img",focusable:"false",viewBox:"0 -716 2711.6 931","aria-hidden":"true"},xc=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1155.8,0)"><path data-c="2260" d="M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z"></path></g><g data-mml-node="mn" transform="translate(2211.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),Zc=[xc],Vc=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"≠"),Q("mn",null,"0")])],-1),wc={class:"MathJax",jax:"SVG",style:{position:"relative"}},_c={style:{"vertical-align":"-0.486ex"},xmlns:"http://www.w3.org/2000/svg",width:"17.077ex",height:"2.106ex",role:"img",focusable:"false",viewBox:"0 -716 7548.2 931","aria-hidden":"true"},vc=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3514,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4392,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(4836.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5992.4,0)"><path data-c="2260" d="M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z"></path></g><g data-mml-node="mn" transform="translate(7048.2,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),yc=[vc],Dc=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,","),Q("mi",null,"m"),Q("mo",null,"≠"),Q("mn",null,"0")])],-1),bc={class:"MathJax",jax:"SVG",style:{position:"relative"}},jc={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.042ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4438.6 1000","aria-hidden":"true"},Bc=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2216,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(2882.8,0)"><path data-c="2260" d="M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z"></path></g><g data-mml-node="mn" transform="translate(3938.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),kc=[Bc],Cc=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"≠"),Q("mn",null,"0")])],-1),zc={class:"MathJax",jax:"SVG",style:{position:"relative"}},Sc={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.98ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 433 453","aria-hidden":"true"},Jc=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D450",d:"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"})])])],-1),Gc=[Jc],Ac=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c")])],-1),Ec={class:"MathJax",jax:"SVG",style:{position:"relative"}},Fc={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.294ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 572 453","aria-hidden":"true"},Oc=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D465",d:"M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"})])])],-1),Rc=[Oc],Pc=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"x")])],-1),Xc={class:"MathJax",jax:"SVG",style:{position:"relative"}},Nc={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.205ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4510.6 1000","aria-hidden":"true"},Kc=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></g><g data-mml-node="mo" transform="translate(2355,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3021.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4077.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),Ic=[Kc],qc=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"x"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"c")])],-1),Uc={class:"MathJax",jax:"SVG",style:{position:"relative"}},Wc={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.2ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4508.6 1000","aria-hidden":"true"},Yc=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="70" d="M36 -148H50Q89 -148 97 -134V-126Q97 -119 97 -107T97 -77T98 -38T98 6T98 55T98 106Q98 140 98 177T98 243T98 296T97 335T97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 61 434T98 436Q115 437 135 438T165 441T176 442H179V416L180 390L188 397Q247 441 326 441Q407 441 464 377T522 216Q522 115 457 52T310 -11Q242 -11 190 33L182 40V-45V-101Q182 -128 184 -134T195 -145Q216 -148 244 -148H260V-194H252L228 -193Q205 -192 178 -192T140 -191Q37 -191 28 -194H20V-148H36ZM424 218Q424 292 390 347T305 402Q234 402 182 337V98Q222 26 294 26Q345 26 384 80T424 218Z"></path><path data-c="72" d="M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z" transform="translate(556,0)"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(948,0)"></path></g><g data-mml-node="mo" transform="translate(1392,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1781,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2214,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(2880.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3936.6,0)"><path data-c="1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></g></g></g>',1),$c=[Yc],Qp=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"pre"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"x")])],-1),ap={class:"MathJax",jax:"SVG",style:{position:"relative"}},tp={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.503ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 9946.4 1000","aria-hidden":"true"},Tp=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),mp=[Tp],np=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),lp={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},ep={style:{"vertical-align":"-9.389ex"},xmlns:"http://www.w3.org/2000/svg",width:"69.571ex",height:"19.91ex",role:"img",focusable:"false",viewBox:"0 -4650 30750.4 8800","aria-hidden":"true"},sp=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,3900)"><g data-mml-node="mtd" transform="translate(5827.9,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(10184.3,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5590,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(25917.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">已</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">知</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">条</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">件</text></g></g></g><g data-mml-node="mtr" transform="translate(0,2600)"><g data-mml-node="mtd" transform="translate(3049.4,0)"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1040.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2040.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2918.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3529.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4529.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(5923.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6312.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6745.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(10184.3,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5590,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(25525.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3514,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(651.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1651.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3045.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3434.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3867.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4478.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5478.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6579.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7579.3,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8973.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9362.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9795.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(10184.3,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5590,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18917.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">交</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">换</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">律</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">、</text><text data-variant="normal" transform="translate(6000,0) scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(7000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(8000,0) scale(1,-1)" font-size="884px" font-family="serif">分</text><text data-variant="normal" transform="translate(9000,0) scale(1,-1)" font-size="884px" font-family="serif">配</text><text data-variant="normal" transform="translate(10000,0) scale(1,-1)" font-size="884px" font-family="serif">律</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(5478.9,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4316.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(10184.3,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(1833.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(24917.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">消</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">去</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">律</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(5550.4,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2755.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3755.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mtd" transform="translate(10184.3,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(1833.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(23067.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-2600)"><g data-mml-node="mtd" transform="translate(1208.4,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2755.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3755.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(5149.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5538.9,0)"><path data-c="70" d="M36 -148H50Q89 -148 97 -134V-126Q97 -119 97 -107T97 -77T98 -38T98 6T98 55T98 106Q98 140 98 177T98 243T98 296T97 335T97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 61 434T98 436Q115 437 135 438T165 441T176 442H179V416L180 390L188 397Q247 441 326 441Q407 441 464 377T522 216Q522 115 457 52T310 -11Q242 -11 190 33L182 40V-45V-101Q182 -128 184 -134T195 -145Q216 -148 244 -148H260V-194H252L228 -193Q205 -192 178 -192T140 -191Q37 -191 28 -194H20V-148H36ZM424 218Q424 292 390 347T305 402Q234 402 182 337V98Q222 26 294 26Q345 26 384 80T424 218Z"></path><path data-c="72" d="M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z" transform="translate(556,0)"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(948,0)"></path></g><g data-mml-node="mo" transform="translate(6930.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7319.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(8197.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(8586.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(10184.3,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(1833.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18774.3,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mrow" transform="translate(833,0)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1155.8,0)"><path data-c="2260" d="M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z"></path></g><g data-mml-node="mn" transform="translate(2211.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g><g data-mml-node="mtext" transform="translate(2711.6,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">、</text></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(3711.6,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1155.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(2211.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3605.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3994.6,0)"><path data-c="70" d="M36 -148H50Q89 -148 97 -134V-126Q97 -119 97 -107T97 -77T98 -38T98 6T98 55T98 106Q98 140 98 177T98 243T98 296T97 335T97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 61 434T98 436Q115 437 135 438T165 441T176 442H179V416L180 390L188 397Q247 441 326 441Q407 441 464 377T522 216Q522 115 457 52T310 -11Q242 -11 190 33L182 40V-45V-101Q182 -128 184 -134T195 -145Q216 -148 244 -148H260V-194H252L228 -193Q205 -192 178 -192T140 -191Q37 -191 28 -194H20V-148H36ZM424 218Q424 292 390 347T305 402Q234 402 182 337V98Q222 26 294 26Q345 26 384 80T424 218Z"></path><path data-c="72" d="M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z" transform="translate(556,0)"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(948,0)"></path></g><g data-mml-node="mo" transform="translate(5386.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5775.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6653.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7042.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-3900)"><g data-mml-node="mtd" transform="translate(1208.4,0)"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2883.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4538.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5538.9,0)"><path data-c="70" d="M36 -148H50Q89 -148 97 -134V-126Q97 -119 97 -107T97 -77T98 -38T98 6T98 55T98 106Q98 140 98 177T98 243T98 296T97 335T97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 61 434T98 436Q115 437 135 438T165 441T176 442H179V416L180 390L188 397Q247 441 326 441Q407 441 464 377T522 216Q522 115 457 52T310 -11Q242 -11 190 33L182 40V-45V-101Q182 -128 184 -134T195 -145Q216 -148 244 -148H260V-194H252L228 -193Q205 -192 178 -192T140 -191Q37 -191 28 -194H20V-148H36ZM424 218Q424 292 390 347T305 402Q234 402 182 337V98Q222 26 294 26Q345 26 384 80T424 218Z"></path><path data-c="72" d="M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z" transform="translate(556,0)"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(948,0)"></path></g><g data-mml-node="mo" transform="translate(6930.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7319.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(8197.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(8586.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(10184.3,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(1833.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(23067.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),op=[sp],rp=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"已知条件")])]),Q("mtr",null,[Q("mtd",null,[Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"m")])])]),Q("mtr",null,[Q("mtd",null,[Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法交换律、乘法分配律")])]),Q("mtr",null,[Q("mtd",null,[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法消去律")])]),Q("mtr",null,[Q("mtd",null,[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",null,"+"),Q("mi",null,"m")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd",null,[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"pre"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",null,[Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"m"),Q("mo",null,"≠"),Q("mn",null,"0")]),Q("mtext",null,"、"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"pre"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")")])])])]),Q("mtr",null,[Q("mtd",null,[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",null,"+"),Q("mi",null,"pre"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])])])])],-1),dp={class:"MathJax",jax:"SVG",style:{position:"relative"}},hp={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 500 688","aria-hidden":"true"},ip=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"30",d:"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"})])])],-1),gp=[ip],Hp=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0")])],-1),Lp={class:"MathJax",jax:"SVG",style:{position:"relative"}},cp={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.393ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 6803.9 1000","aria-hidden":"true"},pp=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2755.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3755.9,0)"><path data-c="70" d="M36 -148H50Q89 -148 97 -134V-126Q97 -119 97 -107T97 -77T98 -38T98 6T98 55T98 106Q98 140 98 177T98 243T98 296T97 335T97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 61 434T98 436Q115 437 135 438T165 441T176 442H179V416L180 390L188 397Q247 441 326 441Q407 441 464 377T522 216Q522 115 457 52T310 -11Q242 -11 190 33L182 40V-45V-101Q182 -128 184 -134T195 -145Q216 -148 244 -148H260V-194H252L228 -193Q205 -192 178 -192T140 -191Q37 -191 28 -194H20V-148H36ZM424 218Q424 292 390 347T305 402Q234 402 182 337V98Q222 26 294 26Q345 26 384 80T424 218Z"></path><path data-c="72" d="M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z" transform="translate(556,0)"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(948,0)"></path></g><g data-mml-node="mo" transform="translate(5147.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5536.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6414.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),fp=[pp],Mp=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",null,"+"),Q("mi",null,"pre"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),up={class:"MathJax",jax:"SVG",style:{position:"relative"}},xp={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"31.207ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 13793.6 1000","aria-hidden":"true"},Zp=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(10224.2,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(11502,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(12308.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(13364.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),Vp=[Zp],wp=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),_p={class:"MathJax",jax:"SVG",style:{position:"relative"}},vp={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"31.207ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 13793.6 1000","aria-hidden":"true"},yp=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(10224.2,0)"><path data-c="21D4" d="M308 524Q318 526 323 526Q340 526 340 514Q340 507 336 499Q326 476 314 454T292 417T274 391T260 374L255 368Q255 367 500 367Q744 367 744 368L739 374Q734 379 726 390T707 416T685 453T663 499Q658 511 658 515Q658 525 680 525Q687 524 690 523T695 519T701 507Q766 359 902 287Q921 276 939 269T961 259T966 250Q966 246 965 244T960 240T949 236T930 228T902 213Q763 137 701 -7Q697 -16 695 -19T690 -23T680 -25Q658 -25 658 -15Q658 -11 663 1Q673 24 685 46T707 83T725 109T739 126L744 132Q744 133 500 133Q255 133 255 132L260 126Q265 121 273 110T292 84T314 47T336 1Q341 -11 341 -15Q341 -25 319 -25Q312 -24 309 -23T304 -19T298 -7Q233 141 97 213Q83 221 70 227T51 235T41 239T35 243T34 250T35 256T40 261T51 265T70 273T97 287Q235 363 299 509Q305 522 308 524ZM792 319L783 327H216Q183 294 120 256L110 250L120 244Q173 212 207 181L216 173H783L792 181Q826 212 879 244L889 250L879 256Q826 288 792 319Z"></path></g><g data-mml-node="mi" transform="translate(11502,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(12308.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(13364.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),Dp=[yp],bp=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},"⇔"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),jp={class:"MathJax",jax:"SVG",style:{position:"relative"}},Bp={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.159ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 2280.3 888","aria-hidden":"true"},kp=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),Cp=[kp],zp=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b"),Q("mo",null,","),Q("mi",null,"c")])],-1),Sp=Q("h2",{id:"peano-公理的合理性",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#peano-公理的合理性"},[Q("span",null,"Peano 公理的合理性")])],-1),Jp=Q("p",null,"通过上述步骤，我们成功地由 Peano 公理构建出了一个自然数代数系统。但 Peano 公理自身任有待研究。从上述步骤中我们看出 Peano 公理每一条公理都被使用过，少了任何一条都不足以构建出上述的自然数系统，这究竟是为什么呢？",-1),Gp=Q("p",null,"下面我将阐述为什么每条公理都是必须的，通过举反例的方式。研究 Peano 公理自然不能从 Peano 公理系统内出发，我们将借助另一个公理系统——图论。",-1),Ap=Q("h3",{id:"乘法保序性",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#乘法保序性"},[Q("span",null,"乘法保序性")])],-1),Ep={class:"MathJax",jax:"SVG",style:{position:"relative"}},Fp={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 832","aria-hidden":"true"},Op=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),Rp=[Op],Pp=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≤"),Q("mi",null,"b")])],-1),Xp={class:"MathJax",jax:"SVG",style:{position:"relative"}},Np={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.503ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 9946.4 1000","aria-hidden":"true"},Kp=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Ip=[Kp],qp=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"≤"),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),Up={class:"MathJax",jax:"SVG",style:{position:"relative"}},Wp={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 832","aria-hidden":"true"},Yp=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),$p=[Yp],Qf=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≤"),Q("mi",null,"b")])],-1),af={class:"MathJax",jax:"SVG",style:{position:"relative"}},tf={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 4392 776","aria-hidden":"true"},Tf=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3514,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),mf=[Tf],nf=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"m")])],-1),lf={class:"MathJax",jax:"SVG",style:{position:"relative"}},ef={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"55.3ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 24442.8 1000","aria-hidden":"true"},sf=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(651.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1651.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3045.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3434.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3867.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4534.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(5590,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5979,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6730.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7730.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(8608.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(9219.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(10219.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(11613.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(12002.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(12435.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(13102.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(14158.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(14909.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(15909.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(17303.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(17692.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(18125.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(18737.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(19737.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(20837.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(21837.8,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(23231.8,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(23620.8,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(24053.8,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),of=[sf],rf=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),df={class:"MathJax",jax:"SVG",style:{position:"relative"}},hf={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.503ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 9946.4 1000","aria-hidden":"true"},gf=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Hf=[gf],Lf=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"≤"),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),cf=Q("h3",{id:"乘法消去保序性",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#乘法消去保序性"},[Q("span",null,"乘法消去保序性")])],-1),pf={class:"MathJax",jax:"SVG",style:{position:"relative"}},ff={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.503ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 9946.4 1000","aria-hidden":"true"},Mf=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),uf=[Mf],xf=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"≤"),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),Zf={class:"MathJax",jax:"SVG",style:{position:"relative"}},Vf={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 832","aria-hidden":"true"},wf=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),_f=[wf],vf=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≤"),Q("mi",null,"b")])],-1),yf={class:"MathJax",jax:"SVG",style:{position:"relative"}},Df={style:{"vertical-align":"-0.09ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.661ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 734","aria-hidden":"true"},bf=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3E" d="M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),jf=[bf],Bf=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,">"),Q("mi",null,"b")])],-1),kf={class:"MathJax",jax:"SVG",style:{position:"relative"}},Cf={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.986ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 878 453","aria-hidden":"true"},zf=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45A",d:"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"})])])],-1),Sf=[zf],Jf=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m")])],-1),Gf={class:"MathJax",jax:"SVG",style:{position:"relative"}},Af={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 4392 776","aria-hidden":"true"},Ef=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3514,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Ff=[Ef],Of=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"m")])],-1),Rf={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},Pf={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"55.074ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 24342.8 1000","aria-hidden":"true"},Xf=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(5690,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6079,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6730.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7730.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(8608.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(9219.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(10219.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(11613.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(12002.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(12435.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(13102.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(14158.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(14809.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(15809.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(17203.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(17592.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(18025.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(18637.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(19637.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(20737.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(21737.8,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(23131.8,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(23520.8,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(23953.8,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Nf=[Xf],Kf=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),If={class:"MathJax",jax:"SVG",style:{position:"relative"}},qf={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.503ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 9946.4 1000","aria-hidden":"true"},Uf=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(651.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1651.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3045.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3434.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3867.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4534.2,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(5590,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Wf=[Uf],Yf=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"≤"),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),$f={class:"MathJax",jax:"SVG",style:{position:"relative"}},QM={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.503ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 9946.4 1000","aria-hidden":"true"},aM=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),tM=[aM],TM=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),mM={class:"MathJax",jax:"SVG",style:{position:"relative"}},nM={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 776","aria-hidden":"true"},lM=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),eM=[lM],sM=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),oM={class:"MathJax",jax:"SVG",style:{position:"relative"}},rM={style:{"vertical-align":"-0.09ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.661ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 734","aria-hidden":"true"},dM=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3E" d="M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),hM=[dM],iM=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,">"),Q("mi",null,"b")])],-1),gM=Q("h3",{id:"用图论阐述-peano-系统",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#用图论阐述-peano-系统"},[Q("span",null,"用图论阐述 Peano 系统")])],-1),HM={class:"MathJax",jax:"SVG",style:{position:"relative"}},LM={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"7.78ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3438.7 1000","aria-hidden":"true"},cM=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mi"><path data-c="47" d="M56 342Q56 428 89 500T174 615T283 681T391 705Q394 705 400 705T408 704Q499 704 569 636L582 624L612 663Q639 700 643 704Q644 704 647 704T653 705H657Q660 705 666 699V419L660 413H626Q620 419 619 430Q610 512 571 572T476 651Q457 658 426 658Q401 658 376 654T316 633T254 592T205 519T177 411Q173 369 173 335Q173 259 192 201T238 111T302 58T370 31T431 24Q478 24 513 45T559 100Q562 110 562 160V212Q561 213 557 216T551 220T542 223T526 225T502 226T463 227H437V273H449L609 270Q715 270 727 273H735V227H721Q674 227 668 215Q666 211 666 108V6Q660 0 657 0Q653 0 639 10Q617 25 600 42L587 54Q571 27 524 3T406 -22Q317 -22 238 22T108 151T56 342Z"></path></g></g><g data-mml-node="mo" transform="translate(785,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(1174,0)"><g data-mml-node="mi"><path data-c="56" d="M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z"></path></g></g><g data-mml-node="mo" transform="translate(1924,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(2368.7,0)"><g data-mml-node="mi"><path data-c="45" d="M128 619Q121 626 117 628T101 631T58 634H25V680H597V676Q599 670 611 560T625 444V440H585V444Q584 447 582 465Q578 500 570 526T553 571T528 601T498 619T457 629T411 633T353 634Q266 634 251 633T233 622Q233 622 233 621Q232 619 232 497V376H286Q359 378 377 385Q413 401 416 469Q416 471 416 473V493H456V213H416V233Q415 268 408 288T383 317T349 328T297 330Q290 330 286 330H232V196V114Q232 57 237 52Q243 47 289 47H340H391Q428 47 452 50T505 62T552 92T584 146Q594 172 599 200T607 247T612 270V273H652V270Q651 267 632 137T610 3V0H25V46H58Q100 47 109 49T128 61V619Z"></path></g></g><g data-mml-node="mo" transform="translate(3049.7,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),pM=[cM],fM=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",{mathvariant:"normal"},"G")]),Q("mo",{stretchy:"false"},"("),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",{mathvariant:"normal"},"V")]),Q("mo",null,","),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",{mathvariant:"normal"},"E")]),Q("mo",{stretchy:"false"},")")])],-1),MM={class:"MathJax",jax:"SVG",style:{position:"relative"}},uM={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 500 688","aria-hidden":"true"},xM=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"30",d:"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"})])])],-1),ZM=[xM],VM=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0")])],-1),wM={class:"MathJax",jax:"SVG",style:{position:"relative"}},_M={style:{"vertical-align":"-0.375ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.548ex",height:"1.92ex",role:"img",focusable:"false",viewBox:"0 -683 2894.1 848.6","aria-hidden":"true"},vM=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path></g><g data-mml-node="mn" transform="translate(518,-150) scale(0.707)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g><g data-mml-node="mo" transform="translate(1199.3,0)"><path data-c="2208" d="M84 250Q84 372 166 450T360 539Q361 539 377 539T419 540T469 540H568Q583 532 583 520Q583 511 570 501L466 500Q355 499 329 494Q280 482 242 458T183 409T147 354T129 306T124 272V270H568Q583 262 583 250T568 230H124V228Q124 207 134 177T167 112T231 48T328 7Q355 1 466 0H570Q583 -10 583 -20Q583 -32 568 -40H471Q464 -40 446 -40T417 -41Q262 -41 172 45Q84 127 84 250Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(2144.1,0)"><g data-mml-node="mi"><path data-c="56" d="M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z"></path></g></g></g></g>',1),yM=[vM],DM=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"v"),Q("mn",null,"0")]),Q("mo",null,"∈"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",{mathvariant:"normal"},"V")])])],-1),bM={class:"MathJax",jax:"SVG",style:{position:"relative"}},jM={style:{"vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.507ex",role:"img",focusable:"false",viewBox:"0 -666 500 666","aria-hidden":"true"},BM=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"31",d:"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"})])])],-1),kM=[BM],CM=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"1")])],-1),zM={class:"MathJax",jax:"SVG",style:{position:"relative"}},SM={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"14.139ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 6249.6 1000","aria-hidden":"true"},JM=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="6F" d="M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(500,0)"></path><path data-c="74" d="M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z" transform="translate(1056,0)"></path><path data-c="44" d="M130 622Q123 629 119 631T103 634T60 637H27V683H228Q399 682 419 682T461 676Q504 667 546 641T626 573T685 470T708 336Q708 210 634 116T442 3Q429 1 228 0H27V46H60Q102 47 111 49T130 61V622ZM593 338Q593 439 571 501T493 602Q439 637 355 637H322H294Q238 637 234 628Q231 624 231 344Q231 62 232 59Q233 49 248 48T339 46H350Q456 46 515 95Q561 133 577 191T593 338Z" transform="translate(1445,0)"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(2209,0)"></path><path data-c="67" d="M329 409Q373 453 429 453Q459 453 472 434T485 396Q485 382 476 371T449 360Q416 360 412 390Q410 404 415 411Q415 412 416 414V415Q388 412 363 393Q355 388 355 386Q355 385 359 381T368 369T379 351T388 325T392 292Q392 230 343 187T222 143Q172 143 123 171Q112 153 112 133Q112 98 138 81Q147 75 155 75T227 73Q311 72 335 67Q396 58 431 26Q470 -13 470 -72Q470 -139 392 -175Q332 -206 250 -206Q167 -206 107 -175Q29 -140 29 -75Q29 -39 50 -15T92 18L103 24Q67 55 67 108Q67 155 96 193Q52 237 52 292Q52 355 102 398T223 442Q274 442 318 416L329 409ZM299 343Q294 371 273 387T221 404Q192 404 171 388T145 343Q142 326 142 292Q142 248 149 227T179 192Q196 182 222 182Q244 182 260 189T283 207T294 227T299 242Q302 258 302 292T299 343ZM403 -75Q403 -50 389 -34T348 -11T299 -2T245 0H218Q151 0 138 -6Q118 -15 107 -34T95 -74Q95 -84 101 -97T122 -127T170 -155T250 -167Q319 -167 361 -139T403 -75Z" transform="translate(2653,0)"></path></g><g data-mml-node="mo" transform="translate(3153,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3542,0)"><path data-c="1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path></g><g data-mml-node="mo" transform="translate(4027,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4693.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(5749.6,0)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g></g>',1),GM=[JM],AM=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"outDeg"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"v"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mn",null,"1")])],-1),EM={class:"MathJax",jax:"SVG",style:{position:"relative"}},FM={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 500 688","aria-hidden":"true"},OM=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"30",d:"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"})])])],-1),RM=[OM],PM=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0")])],-1),XM={class:"MathJax",jax:"SVG",style:{position:"relative"}},NM={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 500 688","aria-hidden":"true"},KM=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"30",d:"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"})])])],-1),IM=[KM],qM=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0")])],-1),UM={class:"MathJax",jax:"SVG",style:{position:"relative"}},WM={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"13.745ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 6075.1 1000","aria-hidden":"true"},YM=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="69" d="M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z"></path><path data-c="6E" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z" transform="translate(278,0)"></path><path data-c="44" d="M130 622Q123 629 119 631T103 634T60 637H27V683H228Q399 682 419 682T461 676Q504 667 546 641T626 573T685 470T708 336Q708 210 634 116T442 3Q429 1 228 0H27V46H60Q102 47 111 49T130 61V622ZM593 338Q593 439 571 501T493 602Q439 637 355 637H322H294Q238 637 234 628Q231 624 231 344Q231 62 232 59Q233 49 248 48T339 46H350Q456 46 515 95Q561 133 577 191T593 338Z" transform="translate(834,0)"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(1598,0)"></path><path data-c="67" d="M329 409Q373 453 429 453Q459 453 472 434T485 396Q485 382 476 371T449 360Q416 360 412 390Q410 404 415 411Q415 412 416 414V415Q388 412 363 393Q355 388 355 386Q355 385 359 381T368 369T379 351T388 325T392 292Q392 230 343 187T222 143Q172 143 123 171Q112 153 112 133Q112 98 138 81Q147 75 155 75T227 73Q311 72 335 67Q396 58 431 26Q470 -13 470 -72Q470 -139 392 -175Q332 -206 250 -206Q167 -206 107 -175Q29 -140 29 -75Q29 -39 50 -15T92 18L103 24Q67 55 67 108Q67 155 96 193Q52 237 52 292Q52 355 102 398T223 442Q274 442 318 416L329 409ZM299 343Q294 371 273 387T221 404Q192 404 171 388T145 343Q142 326 142 292Q142 248 149 227T179 192Q196 182 222 182Q244 182 260 189T283 207T294 227T299 242Q302 258 302 292T299 343ZM403 -75Q403 -50 389 -34T348 -11T299 -2T245 0H218Q151 0 138 -6Q118 -15 107 -34T95 -74Q95 -84 101 -97T122 -127T170 -155T250 -167Q319 -167 361 -139T403 -75Z" transform="translate(2042,0)"></path></g><g data-mml-node="mo" transform="translate(2542,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="msub" transform="translate(2931,0)"><g data-mml-node="mi"><path data-c="1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path></g><g data-mml-node="mn" transform="translate(518,-150) scale(0.707)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g><g data-mml-node="mo" transform="translate(3852.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4519.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(5575.1,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),$M=[YM],Qu=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"inDeg"),Q("mo",{stretchy:"false"},"("),Q("msub",null,[Q("mi",null,"v"),Q("mn",null,"0")]),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mn",null,"0")])],-1),au={class:"MathJax",jax:"SVG",style:{position:"relative"}},tu={style:{"vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.507ex",role:"img",focusable:"false",viewBox:"0 -666 500 666","aria-hidden":"true"},Tu=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"31",d:"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"})])])],-1),mu=[Tu],nu=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"1")])],-1),lu={class:"MathJax",jax:"SVG",style:{position:"relative"}},eu={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"12.757ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 5638.6 1000","aria-hidden":"true"},su=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="69" d="M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z"></path><path data-c="6E" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z" transform="translate(278,0)"></path><path data-c="44" d="M130 622Q123 629 119 631T103 634T60 637H27V683H228Q399 682 419 682T461 676Q504 667 546 641T626 573T685 470T708 336Q708 210 634 116T442 3Q429 1 228 0H27V46H60Q102 47 111 49T130 61V622ZM593 338Q593 439 571 501T493 602Q439 637 355 637H322H294Q238 637 234 628Q231 624 231 344Q231 62 232 59Q233 49 248 48T339 46H350Q456 46 515 95Q561 133 577 191T593 338Z" transform="translate(834,0)"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(1598,0)"></path><path data-c="67" d="M329 409Q373 453 429 453Q459 453 472 434T485 396Q485 382 476 371T449 360Q416 360 412 390Q410 404 415 411Q415 412 416 414V415Q388 412 363 393Q355 388 355 386Q355 385 359 381T368 369T379 351T388 325T392 292Q392 230 343 187T222 143Q172 143 123 171Q112 153 112 133Q112 98 138 81Q147 75 155 75T227 73Q311 72 335 67Q396 58 431 26Q470 -13 470 -72Q470 -139 392 -175Q332 -206 250 -206Q167 -206 107 -175Q29 -140 29 -75Q29 -39 50 -15T92 18L103 24Q67 55 67 108Q67 155 96 193Q52 237 52 292Q52 355 102 398T223 442Q274 442 318 416L329 409ZM299 343Q294 371 273 387T221 404Q192 404 171 388T145 343Q142 326 142 292Q142 248 149 227T179 192Q196 182 222 182Q244 182 260 189T283 207T294 227T299 242Q302 258 302 292T299 343ZM403 -75Q403 -50 389 -34T348 -11T299 -2T245 0H218Q151 0 138 -6Q118 -15 107 -34T95 -74Q95 -84 101 -97T122 -127T170 -155T250 -167Q319 -167 361 -139T403 -75Z" transform="translate(2042,0)"></path></g><g data-mml-node="mo" transform="translate(2542,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(2931,0)"><path data-c="1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path></g><g data-mml-node="mo" transform="translate(3416,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4082.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mn" transform="translate(5138.6,0)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g></g>',1),ou=[su],ru=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"inDeg"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"v"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"≤"),Q("mn",null,"1")])],-1),du={class:"MathJax",jax:"SVG",style:{position:"relative"}},hu={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 500 688","aria-hidden":"true"},iu=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"30",d:"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"})])])],-1),gu=[iu],Hu=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0")])],-1),Lu={class:"MathJax",jax:"SVG",style:{position:"relative"}},cu={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.157ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4931.3 1000","aria-hidden":"true"},pu=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="2203" d="M56 661T56 674T70 694H487Q497 686 500 679V15Q497 10 487 1L279 0H70Q56 7 56 20T70 40H460V327H84Q70 334 70 347T84 367H460V654H70Q56 661 56 674Z"></path></g><g data-mml-node="mi" transform="translate(722.7,0)"><path data-c="70" d="M36 -148H50Q89 -148 97 -134V-126Q97 -119 97 -107T97 -77T98 -38T98 6T98 55T98 106Q98 140 98 177T98 243T98 296T97 335T97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 61 434T98 436Q115 437 135 438T165 441T176 442H179V416L180 390L188 397Q247 441 326 441Q407 441 464 377T522 216Q522 115 457 52T310 -11Q242 -11 190 33L182 40V-45V-101Q182 -128 184 -134T195 -145Q216 -148 244 -148H260V-194H252L228 -193Q205 -192 178 -192T140 -191Q37 -191 28 -194H20V-148H36ZM424 218Q424 292 390 347T305 402Q234 402 182 337V98Q222 26 294 26Q345 26 384 80T424 218Z"></path><path data-c="61" d="M137 305T115 305T78 320T63 359Q63 394 97 421T218 448Q291 448 336 416T396 340Q401 326 401 309T402 194V124Q402 76 407 58T428 40Q443 40 448 56T453 109V145H493V106Q492 66 490 59Q481 29 455 12T400 -6T353 12T329 54V58L327 55Q325 52 322 49T314 40T302 29T287 17T269 6T247 -2T221 -8T190 -11Q130 -11 82 20T34 107Q34 128 41 147T68 188T116 225T194 253T304 268H318V290Q318 324 312 340Q290 411 215 411Q197 411 181 410T156 406T148 403Q170 388 170 359Q170 334 154 320ZM126 106Q126 75 150 51T209 26Q247 26 276 49T315 109Q317 116 318 175Q318 233 317 233Q309 233 296 232T251 223T193 203T147 166T126 106Z" transform="translate(556,0)"></path><path data-c="74" d="M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z" transform="translate(1056,0)"></path><path data-c="68" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z" transform="translate(1445,0)"></path></g><g data-mml-node="mo" transform="translate(2723.7,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(3112.7,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(3612.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(4057.3,0)"><path data-c="1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path></g><g data-mml-node="mo" transform="translate(4542.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),fu=[pu],Mu=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",{mathvariant:"normal"},"∃"),Q("mi",null,"path"),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",null,","),Q("mi",null,"v"),Q("mo",{stretchy:"false"},")")])],-1),uu=Q("p",null,[a("下面我们试着通过"),Q("strong",null,"删除公理"),a("的方法来寻找反例。")],-1),xu=Q("h4",{id:"peano-公理-i",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#peano-公理-i"},[Q("span",null,"Peano 公理 Ⅰ")])],-1),Zu={class:"MathJax",jax:"SVG",style:{position:"relative"}},Vu={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 500 688","aria-hidden":"true"},wu=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"30",d:"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"})])])],-1),_u=[wu],vu=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0")])],-1),yu=Q("h4",{id:"peano-公理-ii",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#peano-公理-ii"},[Q("span",null,"Peano 公理 Ⅱ")])],-1),Du=Q("p",null,"若去除，则对点的出度无规定，可以构造出菊花图自然数系统。",-1),bu=Q("h4",{id:"peano-公理-iii",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#peano-公理-iii"},[Q("span",null,"Peano 公理 Ⅲ")])],-1),ju={class:"MathJax",jax:"SVG",style:{position:"relative"}},Bu={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 500 688","aria-hidden":"true"},ku=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"30",d:"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"})])])],-1),Cu=[ku],zu=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0")])],-1),Su=Q("h4",{id:"peano-公理-iv",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#peano-公理-iv"},[Q("span",null,"Peano 公理 Ⅳ")])],-1),Ju={class:"MathJax",jax:"SVG",style:{position:"relative"}},Gu={style:{"vertical-align":"-0.489ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.17ex",height:"1.489ex",role:"img",focusable:"false",viewBox:"0 -442 517 658","aria-hidden":"true"},Au=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D70C",d:"M58 -216Q25 -216 23 -186Q23 -176 73 26T127 234Q143 289 182 341Q252 427 341 441Q343 441 349 441T359 442Q432 442 471 394T510 276Q510 219 486 165T425 74T345 13T266 -10H255H248Q197 -10 165 35L160 41L133 -71Q108 -168 104 -181T92 -202Q76 -216 58 -216ZM424 322Q424 359 407 382T357 405Q322 405 287 376T231 300Q217 269 193 170L176 102Q193 26 260 26Q298 26 334 62Q367 92 389 158T418 266T424 322Z"})])])],-1),Eu=[Au],Fu=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"ρ")])],-1),Ou=Q("h4",{id:"peano-公理-v",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#peano-公理-v"},[Q("span",null,"Peano 公理 Ⅴ")])],-1),Ru=Q("p",null,"若去除，则对连通性无要求，可以构造出分段状自然数系统。",-1);function Pu(Xu,Nu){return t(),T("div",null,[s,o,l(" more "),r,d,Q("ol",null,[Q("li",null,[Q("p",null,[Q("mjx-container",h,[(t(),T("svg",i,H)),L]),a(" 是自然数；")])]),Q("li",null,[Q("p",null,[a("任何自然数的后继存在且唯一，下文用 "),Q("mjx-container",c,[(t(),T("svg",p,M)),u]),a(" 表示 "),Q("mjx-container",x,[(t(),T("svg",Z,w)),_]),a(" 的后继；")])]),Q("li",null,[Q("p",null,[Q("mjx-container",v,[(t(),T("svg",y,b)),j]),a(" 不是任何自然数的后继；")])]),B,Q("li",null,[Q("p",null,[Q("mjx-container",k,[(t(),T("svg",C,S)),J]),a(" 是关于自然数 "),Q("mjx-container",G,[(t(),T("svg",A,F)),O]),a(" 的一个命题，且满足两个条件：")]),Q("ul",null,[Q("li",null,[Q("mjx-container",R,[(t(),T("svg",P,N)),K]),a(" 是真命题；")]),Q("li",null,[a("由 "),Q("mjx-container",I,[(t(),T("svg",q,W)),Y]),a(" 为真命题可以推理出 "),Q("mjx-container",$,[(t(),T("svg",Q1,t1)),T1]),a(" 为真命题。")])]),Q("p",null,[a("则有，对于任意自然数 "),Q("mjx-container",m1,[(t(),T("svg",n1,e1)),s1]),a("，"),Q("mjx-container",o1,[(t(),T("svg",r1,h1)),i1]),a(" 为真命题。")])])]),g1,H1,L1,c1,p1,Q("ol",null,[Q("li",null,[a("若 "),Q("mjx-container",f1,[(t(),T("svg",M1,x1)),Z1]),a(" 是自然数，则 "),Q("mjx-container",V1,[(t(),T("svg",w1,v1)),y1]),a(" 的运算结果为 "),Q("mjx-container",D1,[(t(),T("svg",b1,B1)),k1]),a("，即 "),Q("mjx-container",C1,[(t(),T("svg",z1,J1)),G1]),a("；")]),Q("li",null,[a("若 "),Q("mjx-container",A1,[(t(),T("svg",E1,O1)),R1]),a(" 都是自然数，则 "),Q("mjx-container",P1,[(t(),T("svg",X1,K1)),I1]),a("。")])]),q1,U1,Q("p",null,[Q("mjx-container",W1,[(t(),T("svg",Y1,Q3)),a3]),a(" 是任意自然数，记 "),Q("mjx-container",t3,[(t(),T("svg",T3,n3)),l3]),a(" 表示 "),Q("mjx-container",e3,[(t(),T("svg",s3,r3)),d3]),a(" 是否是自然数，即 "),Q("mjx-container",h3,[(t(),T("svg",i3,H3)),L3]),a(" 是否存在。")]),Q("p",null,[Q("mjx-container",c3,[(t(),T("svg",p3,M3)),u3]),a(" 是自然数，由加法运算规则 Ⅰ 有 "),Q("mjx-container",x3,[(t(),T("svg",Z3,w3)),_3]),a("，进而有 "),Q("mjx-container",v3,[(t(),T("svg",y3,b3)),j3]),a(" 是自然数； "),Q("strong",null,[a("即 "),Q("mjx-container",B3,[(t(),T("svg",k3,z3)),S3]),a(" 得证。")])]),Q("p",null,[Q("mjx-container",J3,[(t(),T("svg",G3,E3)),F3]),a(" 和 "),Q("mjx-container",O3,[(t(),T("svg",R3,X3)),N3]),a(" 是自然数，由 Peano 公理 Ⅱ 有 "),Q("mjx-container",K3,[(t(),T("svg",I3,U3)),W3]),a(" 和 "),Q("mjx-container",Y3,[(t(),T("svg",$3,a2)),t2]),a(" 是自然数； 根据加法运算规则 Ⅱ 有 "),Q("mjx-container",T2,[(t(),T("svg",m2,l2)),e2]),a("，进有 "),Q("mjx-container",s2,[(t(),T("svg",o2,d2)),h2]),a(" 是自然数； 综上所述，若 "),Q("mjx-container",i2,[(t(),T("svg",g2,L2)),c2]),a(" 是自然数，则 "),Q("mjx-container",p2,[(t(),T("svg",f2,u2)),x2]),a(" 也是自然数； "),Q("strong",null,[a("即由 "),Q("mjx-container",Z2,[(t(),T("svg",V2,_2)),v2]),a(" 为真命题可以推出 "),Q("mjx-container",y2,[(t(),T("svg",D2,j2)),B2]),a(" 为真命题。")])]),Q("p",null,[a("由 "),Q("mjx-container",k2,[(t(),T("svg",C2,S2)),J2]),a(" 的性质和 Peano 公理 Ⅴ 有，对于任意自然数 "),Q("mjx-container",G2,[(t(),T("svg",A2,F2)),O2]),a("，"),Q("mjx-container",R2,[(t(),T("svg",P2,N2)),K2]),a(" 成立，即 "),Q("mjx-container",I2,[(t(),T("svg",q2,W2)),Y2]),a(" 是自然数，再根据 "),Q("mjx-container",$2,[(t(),T("svg",Q4,t4)),T4]),a(" 的任意性，得出对于任意自然数 "),Q("mjx-container",m4,[(t(),T("svg",n4,e4)),s4]),a("，"),Q("mjx-container",o4,[(t(),T("svg",r4,h4)),i4]),a(" 都是自然数。")]),g4,Q("p",null,[Q("mjx-container",H4,[(t(),T("svg",L4,p4)),f4]),a(" 是任意自然数，记 "),Q("mjx-container",M4,[(t(),T("svg",u4,Z4)),V4]),a(" 表示 "),Q("mjx-container",w4,[(t(),T("svg",_4,y4)),D4]),a(" 是否唯一，即 "),Q("mjx-container",b4,[(t(),T("svg",j4,k4)),C4]),a(" 的结果是否唯一。")]),Q("p",null,[Q("mjx-container",z4,[(t(),T("svg",S4,G4)),A4]),a(" 是自然数，由加法运算规则 Ⅰ 有 "),Q("mjx-container",E4,[(t(),T("svg",F4,R4)),P4]),a("，进而 "),Q("mjx-container",X4,[(t(),T("svg",N4,I4)),q4]),a(" 是唯一的，就是 "),Q("mjx-container",U4,[(t(),T("svg",W4,$4)),Q5]),a("； "),Q("strong",null,[a("即 "),Q("mjx-container",a5,[(t(),T("svg",t5,m5)),n5]),a(" 得证。")])]),Q("p",null,[Q("mjx-container",l5,[(t(),T("svg",e5,o5)),r5]),a(" 是自然数，"),Q("mjx-container",d5,[(t(),T("svg",h5,g5)),H5]),a(" 是唯一的，由 Peano 公理 Ⅱ 有 "),Q("mjx-container",L5,[(t(),T("svg",c5,f5)),M5]),a(" 是自然数且 "),Q("mjx-container",u5,[(t(),T("svg",x5,V5)),w5]),a(" 唯一； 根据加法运算规则 Ⅱ 有 "),Q("mjx-container",_5,[(t(),T("svg",v5,D5)),b5]),a("，进有 "),Q("mjx-container",j5,[(t(),T("svg",B5,C5)),z5]),a(" 唯一； 综上所述，若 "),Q("mjx-container",S5,[(t(),T("svg",J5,A5)),E5]),a(" 唯一，则 "),Q("mjx-container",F5,[(t(),T("svg",O5,P5)),X5]),a(" 也唯一； "),Q("strong",null,[a("即由 "),Q("mjx-container",N5,[(t(),T("svg",K5,q5)),U5]),a(" 为真命题可以推出 "),Q("mjx-container",W5,[(t(),T("svg",Y5,Q6)),a6]),a(" 为真命题。")])]),Q("p",null,[a("由 "),Q("mjx-container",t6,[(t(),T("svg",T6,n6)),l6]),a(" 的性质和 Peano 公理 Ⅴ 有，对于任意自然数 "),Q("mjx-container",e6,[(t(),T("svg",s6,r6)),d6]),a("，"),Q("mjx-container",h6,[(t(),T("svg",i6,H6)),L6]),a(" 成立，即 "),Q("mjx-container",c6,[(t(),T("svg",p6,M6)),u6]),a(" 唯一，再根据 "),Q("mjx-container",x6,[(t(),T("svg",Z6,w6)),_6]),a(" 的任意性，得出对于任意自然数 "),Q("mjx-container",v6,[(t(),T("svg",y6,b6)),j6]),a("，"),Q("mjx-container",B6,[(t(),T("svg",k6,z6)),S6]),a(" 都是唯一的。")]),J6,G6,A6,Q("p",null,[a("下面证明加法交换律，即对于任意自然数 "),Q("mjx-container",E6,[(t(),T("svg",F6,R6)),P6]),a("，有 "),Q("mjx-container",X6,[(t(),T("svg",N6,I6)),q6]),a("。")]),U6,Q("p",null,[a("试证 "),Q("mjx-container",W6,[(t(),T("svg",Y6,Q7)),a7]),a("，首先有")]),Q("mjx-container",t7,[(t(),T("svg",T7,n7)),l7]),Q("p",null,[a("进而当 "),Q("mjx-container",e7,[(t(),T("svg",s7,r7)),d7]),a(" 是自然数且 "),Q("mjx-container",h7,[(t(),T("svg",i7,H7)),L7]),a(" 时有")]),Q("mjx-container",c7,[(t(),T("svg",p7,M7)),u7]),Q("p",null,[a("根据 Peano 公理 Ⅴ，得知 "),Q("mjx-container",x7,[(t(),T("svg",Z7,w7)),_7]),a(" 对任意自然数 "),Q("mjx-container",v7,[(t(),T("svg",y7,b7)),j7]),a(" 成立。")]),Q("p",null,[a("试证 "),Q("mjx-container",B7,[(t(),T("svg",k7,z7)),S7]),a("，首先有")]),Q("mjx-container",J7,[(t(),T("svg",G7,E7)),F7]),Q("p",null,[a("进而当 "),Q("mjx-container",O7,[(t(),T("svg",R7,X7)),N7]),a(" 是自然数且 "),Q("mjx-container",K7,[(t(),T("svg",I7,U7)),W7]),a(" 时有")]),Q("mjx-container",Y7,[(t(),T("svg",$7,a0)),t0]),Q("p",null,[a("根据 Peano 公理 Ⅴ，得知 "),Q("mjx-container",T0,[(t(),T("svg",m0,l0)),e0]),a(" 对任意自然数 "),Q("mjx-container",s0,[(t(),T("svg",o0,d0)),h0]),a(" 成立，将其称为新的"),i0,a("。")]),Q("p",null,[a("证明了加法运算规则的交换律之后，试证加法交换律 "),Q("mjx-container",g0,[(t(),T("svg",H0,c0)),p0]),a("，首先由加法运算规则 Ⅰ 有 "),Q("mjx-container",f0,[(t(),T("svg",M0,x0)),Z0]),a("，进而当 "),Q("mjx-container",V0,[(t(),T("svg",w0,v0)),y0]),a(" 是自然数且 "),Q("mjx-container",D0,[(t(),T("svg",b0,B0)),k0]),a(" 时，有")]),Q("mjx-container",C0,[(t(),T("svg",z0,J0)),G0]),Q("p",null,[a("根据 Peano 公理 Ⅴ，得知 "),Q("mjx-container",A0,[(t(),T("svg",E0,O0)),R0]),a(" 对任意自然数 "),Q("mjx-container",P0,[(t(),T("svg",X0,K0)),I0]),a(" 成立，即加法交换律成立。")]),q0,Q("p",null,[a("下面证明加法结合律，即对于任意自然数 "),Q("mjx-container",U0,[(t(),T("svg",W0,$0)),Q8]),a("，有 "),Q("mjx-container",a8,[(t(),T("svg",t8,m8)),n8]),a("。")]),Q("p",null,[a("首先当 "),Q("mjx-container",l8,[(t(),T("svg",e8,o8)),r8]),a(" 时，有")]),Q("mjx-container",d8,[(t(),T("svg",h8,g8)),H8]),Q("p",null,[a("进而当 "),Q("mjx-container",L8,[(t(),T("svg",c8,f8)),M8]),a(" 为自然数且 "),Q("mjx-container",u8,[(t(),T("svg",x8,V8)),w8]),a(" 时有")]),Q("mjx-container",_8,[(t(),T("svg",v8,D8)),b8]),Q("p",null,[a("根据 Peano 公理 Ⅴ，得知 "),Q("mjx-container",j8,[(t(),T("svg",B8,C8)),z8]),a(" 对任意自然数 "),Q("mjx-container",S8,[(t(),T("svg",J8,A8)),E8]),a(" 成立，即加法结合律成立。")]),F8,Q("p",null,[a("下面证明加法消去律，即对于任意自然数 "),Q("mjx-container",O8,[(t(),T("svg",R8,X8)),N8]),a("，有 "),Q("mjx-container",K8,[(t(),T("svg",I8,U8)),W8]),a("。")]),Q("p",null,[a("试证 "),Q("mjx-container",Y8,[(t(),T("svg",$8,a9)),t9]),a("。")]),Q("p",null,[a("首先当 "),Q("mjx-container",T9,[(t(),T("svg",m9,l9)),e9]),a(" 时有")]),Q("mjx-container",s9,[(t(),T("svg",o9,d9)),h9]),Q("p",null,[a("进而当 "),Q("mjx-container",i9,[(t(),T("svg",g9,L9)),c9]),a(" 为自然数且 "),Q("mjx-container",p9,[(t(),T("svg",f9,u9)),x9]),a(" 时有")]),Q("mjx-container",Z9,[(t(),T("svg",V9,_9)),v9]),Q("p",null,[a("即 "),Q("mjx-container",y9,[(t(),T("svg",D9,j9)),B9]),a("，根据 Peano 公理 Ⅴ，得知 "),Q("mjx-container",k9,[(t(),T("svg",C9,S9)),J9]),a(" 对任意自然数 "),Q("mjx-container",G9,[(t(),T("svg",A9,F9)),O9]),a(" 成立。")]),Q("p",null,[a("试证 "),Q("mjx-container",R9,[(t(),T("svg",P9,N9)),K9]),a("。")]),Q("p",null,[a("首先当 "),Q("mjx-container",I9,[(t(),T("svg",q9,W9)),Y9]),a(" 时有")]),Q("mjx-container",$9,[(t(),T("svg",QQ,tQ)),TQ]),Q("p",null,[a("进而当 "),Q("mjx-container",mQ,[(t(),T("svg",nQ,eQ)),sQ]),a(" 为自然数且 "),Q("mjx-container",oQ,[(t(),T("svg",rQ,hQ)),iQ]),a(" 时有")]),Q("mjx-container",gQ,[(t(),T("svg",HQ,cQ)),pQ]),Q("p",null,[a("即 "),Q("mjx-container",fQ,[(t(),T("svg",MQ,xQ)),ZQ]),a("，根据 Peano 公理 Ⅴ，得知 "),Q("mjx-container",VQ,[(t(),T("svg",wQ,vQ)),yQ]),a(" 对任意自然数 "),Q("mjx-container",DQ,[(t(),T("svg",bQ,BQ)),kQ]),a(" 成立。")]),Q("p",null,[a("综上所述，加法消去律 "),Q("mjx-container",CQ,[(t(),T("svg",zQ,JQ)),GQ]),a("，对任意自然数 "),Q("mjx-container",AQ,[(t(),T("svg",EQ,OQ)),RQ]),a(" 成立。")]),PQ,XQ,NQ,Q("p",null,[a("定义自然数的序即定义 "),Q("mjx-container",KQ,[(t(),T("svg",IQ,UQ)),WQ]),a(" 当且仅当存在自然数 "),Q("mjx-container",YQ,[(t(),T("svg",$Q,aa)),ta]),a(" 满足 "),Q("mjx-container",Ta,[(t(),T("svg",ma,la)),ea]),a("。定义 "),Q("mjx-container",sa,[(t(),T("svg",oa,da)),ha]),a(" 当且仅当 "),Q("mjx-container",ia,[(t(),T("svg",ga,La)),ca]),a(" 且 "),Q("mjx-container",pa,[(t(),T("svg",fa,ua)),xa]),a("。")]),Za,Va,wa,Q("p",null,[a("定义正自然数为非 "),Q("mjx-container",_a,[(t(),T("svg",va,Da)),ba]),a(" 自然数。")]),ja,Q("p",null,[a("正自然数与自然数相加为正自然数，即对于正自然数 "),Q("mjx-container",Ba,[(t(),T("svg",ka,za)),Sa]),a("，其与自然数 "),Q("mjx-container",Ja,[(t(),T("svg",Ga,Ea)),Fa]),a(" 的和 "),Q("mjx-container",Oa,[(t(),T("svg",Ra,Xa)),Na]),a(" 为正自然数。")]),Q("p",null,[a("首先，当 "),Q("mjx-container",Ka,[(t(),T("svg",Ia,Ua)),Wa]),a(" 时，"),Q("mjx-container",Ya,[(t(),T("svg",$a,at)),tt]),a(" 为正自然数。")]),Q("p",null,[a("进而当 "),Q("mjx-container",Tt,[(t(),T("svg",mt,lt)),et]),a(" 为自然数且 "),Q("mjx-container",st,[(t(),T("svg",ot,dt)),ht]),a(" 为正自然数时有 "),Q("mjx-container",it,[(t(),T("svg",gt,Lt)),ct]),a("，根据 Peano 公理 Ⅲ，"),Q("mjx-container",pt,[(t(),T("svg",ft,ut)),xt]),a(" 为正自然数，进而 "),Q("mjx-container",Zt,[(t(),T("svg",Vt,_t)),vt]),a(" 为正自然数。")]),yt,Dt,Q("p",null,[a("若 "),Q("mjx-container",bt,[(t(),T("svg",jt,kt)),Ct]),a(" 且 "),Q("mjx-container",zt,[(t(),T("svg",St,Gt)),At]),a("，则 "),Q("mjx-container",Et,[(t(),T("svg",Ft,Rt)),Pt]),a("。")]),Q("p",null,[a("由 "),Q("mjx-container",Xt,[(t(),T("svg",Nt,It)),qt]),a(" 有 "),Q("mjx-container",Ut,[(t(),T("svg",Wt,$t)),QT]),a("，由 "),Q("mjx-container",aT,[(t(),T("svg",tT,mT)),nT]),a(" 有 "),Q("mjx-container",lT,[(t(),T("svg",eT,oT)),rT]),a("。")]),Q("p",null,[a("因此 "),Q("mjx-container",dT,[(t(),T("svg",hT,gT)),HT]),a("，由加法消去律得到 "),Q("mjx-container",LT,[(t(),T("svg",cT,fT)),MT]),a("，根据正自然数的性质得出 "),Q("mjx-container",uT,[(t(),T("svg",xT,VT)),wT]),a("，因此 "),Q("mjx-container",_T,[(t(),T("svg",vT,DT)),bT]),a("。")]),jT,Q("p",null,[a("若 "),Q("mjx-container",BT,[(t(),T("svg",kT,zT)),ST]),a(" 且 "),Q("mjx-container",JT,[(t(),T("svg",GT,ET)),FT]),a("，则 "),Q("mjx-container",OT,[(t(),T("svg",RT,XT)),NT]),a("。")]),Q("p",null,[a("由 "),Q("mjx-container",KT,[(t(),T("svg",IT,UT)),WT]),a(" 有 "),Q("mjx-container",YT,[(t(),T("svg",$T,am)),tm]),a("，由 "),Q("mjx-container",Tm,[(t(),T("svg",mm,lm)),em]),a(" 有 "),Q("mjx-container",sm,[(t(),T("svg",om,dm)),hm]),a("。")]),Q("p",null,[a("根据加法结果的存在性得到 "),Q("mjx-container",im,[(t(),T("svg",gm,Lm)),cm]),a(" 是自然数，根据加法结合律得出 "),Q("mjx-container",pm,[(t(),T("svg",fm,um)),xm]),a("，进而 "),Q("mjx-container",Zm,[(t(),T("svg",Vm,_m)),vm]),a("。")]),ym,Q("p",null,[a("任意两个自然数 "),Q("mjx-container",Dm,[(t(),T("svg",bm,Bm)),km]),a(" 都有序关系。")]),Q("p",null,[a("对于 "),Q("mjx-container",Cm,[(t(),T("svg",zm,Jm)),Gm]),a(" 两个自然数，当 "),Q("mjx-container",Am,[(t(),T("svg",Em,Om)),Rm]),a(" 时有 "),Q("mjx-container",Pm,[(t(),T("svg",Xm,Km)),Im]),a(" 所以 "),Q("mjx-container",qm,[(t(),T("svg",Um,Ym)),$m]),a("。")]),Q("p",null,[a("当 "),Q("mjx-container",Qn,[(t(),T("svg",an,Tn)),mn]),a(" 为自然数时。若 "),Q("mjx-container",nn,[(t(),T("svg",ln,sn)),on]),a("，则 "),Q("mjx-container",rn,[(t(),T("svg",dn,gn)),Hn]),a("，因此 "),Q("mjx-container",Ln,[(t(),T("svg",cn,fn)),Mn]),a("；若 "),Q("mjx-container",un,[(t(),T("svg",xn,Vn)),wn]),a("，则 "),Q("mjx-container",_n,[(t(),T("svg",vn,Dn)),bn]),a("，因此 "),Q("mjx-container",jn,[(t(),T("svg",Bn,Cn)),zn]),a("；若 "),Q("mjx-container",Sn,[(t(),T("svg",Jn,An)),En]),a("，则 "),Q("mjx-container",Fn,[(t(),T("svg",On,Pn)),Xn]),a("。")]),Q("p",null,[a("由 Peano 公理 Ⅴ 有任意两个自然数 "),Q("mjx-container",Nn,[(t(),T("svg",Kn,qn)),Un]),a(" 都有序关系。")]),Wn,Q("p",null,[a("若 "),Q("mjx-container",Yn,[(t(),T("svg",$n,al)),tl]),a("，则 "),Q("mjx-container",Tl,[(t(),T("svg",ml,ll)),el]),a("。")]),Q("p",null,[a("由 "),Q("mjx-container",sl,[(t(),T("svg",ol,dl)),hl]),a(" 有 "),Q("mjx-container",il,[(t(),T("svg",gl,Ll)),cl]),a("，进而 "),Q("mjx-container",pl,[(t(),T("svg",fl,ul)),xl]),a(" 因此 "),Q("mjx-container",Zl,[(t(),T("svg",Vl,_l)),vl]),a("。")]),yl,Dl,bl,jl,Q("ol",null,[Q("li",null,[a("若 "),Q("mjx-container",Bl,[(t(),T("svg",kl,zl)),Sl]),a(" 是自然数，则 "),Q("mjx-container",Jl,[(t(),T("svg",Gl,El)),Fl]),a(" 的运算结果为 "),Q("mjx-container",Ol,[(t(),T("svg",Rl,Xl)),Nl]),a("，即 "),Q("mjx-container",Kl,[(t(),T("svg",Il,Ul)),Wl]),a("；")]),Q("li",null,[a("若 "),Q("mjx-container",Yl,[(t(),T("svg",$l,ae)),te]),a(" 都是自然数，则 "),Q("mjx-container",Te,[(t(),T("svg",me,le)),ee]),a("。")])]),se,oe,Q("p",null,[Q("mjx-container",re,[(t(),T("svg",de,ie)),ge]),a(" 是任意自然数，记 "),Q("mjx-container",He,[(t(),T("svg",Le,pe)),fe]),a(" 表示 "),Q("mjx-container",Me,[(t(),T("svg",ue,Ze)),Ve]),a(" 是否是自然数，即 "),Q("mjx-container",we,[(t(),T("svg",_e,ye)),De]),a(" 是否存在。")]),Q("p",null,[Q("mjx-container",be,[(t(),T("svg",je,ke)),Ce]),a(" 是自然数，由乘法运算规则 Ⅰ 有 "),Q("mjx-container",ze,[(t(),T("svg",Se,Ge)),Ae]),a("，进而有 "),Q("mjx-container",Ee,[(t(),T("svg",Fe,Re)),Pe]),a(" 是自然数； "),Q("strong",null,[a("即 "),Q("mjx-container",Xe,[(t(),T("svg",Ne,Ie)),qe]),a(" 得证。")])]),Q("p",null,[Q("mjx-container",Ue,[(t(),T("svg",We,$e)),Qs]),a(" 和 "),Q("mjx-container",as,[(t(),T("svg",ts,ms)),ns]),a(" 是自然数，由加法结果的存在性有 "),Q("mjx-container",ls,[(t(),T("svg",es,os)),rs]),a(" 存在； 根据乘法运算规则 Ⅱ 有 "),Q("mjx-container",ds,[(t(),T("svg",hs,gs)),Hs]),a("，进有 "),Q("mjx-container",Ls,[(t(),T("svg",cs,fs)),Ms]),a(" 是自然数； 综上所述，若 "),Q("mjx-container",us,[(t(),T("svg",xs,Vs)),ws]),a(" 是自然数，则 "),Q("mjx-container",_s,[(t(),T("svg",vs,Ds)),bs]),a(" 也是自然数； "),Q("strong",null,[a("即由 "),Q("mjx-container",js,[(t(),T("svg",Bs,Cs)),zs]),a(" 为真命题可以推出 "),Q("mjx-container",Ss,[(t(),T("svg",Js,As)),Es]),a(" 为真命题。")])]),Q("p",null,[a("由 "),Q("mjx-container",Fs,[(t(),T("svg",Os,Ps)),Xs]),a(" 的性质和 Peano 公理 Ⅴ 有，对于任意自然数 "),Q("mjx-container",Ns,[(t(),T("svg",Ks,qs)),Us]),a("，"),Q("mjx-container",Ws,[(t(),T("svg",Ys,Qo)),ao]),a(" 成立，即 "),Q("mjx-container",to,[(t(),T("svg",To,no)),lo]),a(" 是自然数，再根据 "),Q("mjx-container",eo,[(t(),T("svg",so,ro)),ho]),a(" 的任意性，得出对于任意自然数 "),Q("mjx-container",io,[(t(),T("svg",go,Lo)),co]),a("，"),Q("mjx-container",po,[(t(),T("svg",fo,uo)),xo]),a(" 都是自然数。")]),Zo,Q("p",null,[Q("mjx-container",Vo,[(t(),T("svg",wo,vo)),yo]),a(" 是任意自然数，记 "),Q("mjx-container",Do,[(t(),T("svg",bo,Bo)),ko]),a(" 表示 "),Q("mjx-container",Co,[(t(),T("svg",zo,Jo)),Go]),a(" 是否唯一，即 "),Q("mjx-container",Ao,[(t(),T("svg",Eo,Oo)),Ro]),a(" 的结果是否唯一。")]),Q("p",null,[Q("mjx-container",Po,[(t(),T("svg",Xo,Ko)),Io]),a(" 是自然数，由乘法运算规则 Ⅰ 有 "),Q("mjx-container",qo,[(t(),T("svg",Uo,Yo)),$o]),a("，进而 "),Q("mjx-container",Qr,[(t(),T("svg",ar,Tr)),mr]),a(" 是唯一的，就是 "),Q("mjx-container",nr,[(t(),T("svg",lr,sr)),or]),a("； "),Q("strong",null,[a("即 "),Q("mjx-container",rr,[(t(),T("svg",dr,ir)),gr]),a(" 得证。")])]),Q("p",null,[Q("mjx-container",Hr,[(t(),T("svg",Lr,pr)),fr]),a(" 是自然数，"),Q("mjx-container",Mr,[(t(),T("svg",ur,Zr)),Vr]),a(" 是唯一的，由加法结果的唯一性有 "),Q("mjx-container",wr,[(t(),T("svg",_r,yr)),Dr]),a(" 唯一； 根据乘法运算规则 Ⅱ 有 "),Q("mjx-container",br,[(t(),T("svg",jr,kr)),Cr]),a("，进有 "),Q("mjx-container",zr,[(t(),T("svg",Sr,Gr)),Ar]),a(" 唯一； 综上所述，若 "),Q("mjx-container",Er,[(t(),T("svg",Fr,Rr)),Pr]),a(" 唯一，则 "),Q("mjx-container",Xr,[(t(),T("svg",Nr,Ir)),qr]),a(" 也唯一； "),Q("strong",null,[a("即由 "),Q("mjx-container",Ur,[(t(),T("svg",Wr,$r)),Qd]),a(" 为真命题可以推出 "),Q("mjx-container",ad,[(t(),T("svg",td,md)),nd]),a(" 为真命题。")])]),Q("p",null,[a("由 "),Q("mjx-container",ld,[(t(),T("svg",ed,od)),rd]),a(" 的性质和 Peano 公理 Ⅴ 有，对于任意自然数 "),Q("mjx-container",dd,[(t(),T("svg",hd,gd)),Hd]),a("，"),Q("mjx-container",Ld,[(t(),T("svg",cd,fd)),Md]),a(" 成立，即 "),Q("mjx-container",ud,[(t(),T("svg",xd,Vd)),wd]),a(" 唯一，再根据 "),Q("mjx-container",_d,[(t(),T("svg",vd,Dd)),bd]),a(" 的任意性，得出对于任意自然数 "),Q("mjx-container",jd,[(t(),T("svg",Bd,Cd)),zd]),a("，"),Q("mjx-container",Sd,[(t(),T("svg",Jd,Ad)),Ed]),a(" 都是唯一的。")]),Fd,Od,Rd,Q("p",null,[a("下面证明乘法交换律，即对于任意自然数 "),Q("mjx-container",Pd,[(t(),T("svg",Xd,Kd)),Id]),a("，有 "),Q("mjx-container",qd,[(t(),T("svg",Ud,Yd)),$d]),a("。")]),Qh,Q("p",null,[a("试证 "),Q("mjx-container",ah,[(t(),T("svg",th,mh)),nh]),a("。")]),Q("p",null,[a("首先有 "),Q("mjx-container",lh,[(t(),T("svg",eh,oh)),rh]),a("。")]),Q("p",null,[a("进而当 "),Q("mjx-container",dh,[(t(),T("svg",hh,gh)),Hh]),a(" 是自然数且 "),Q("mjx-container",Lh,[(t(),T("svg",ch,fh)),Mh]),a(" 时有")]),Q("mjx-container",uh,[(t(),T("svg",xh,Vh)),wh]),Q("p",null,[a("根据 Peano 公理 Ⅴ，得知 "),Q("mjx-container",_h,[(t(),T("svg",vh,Dh)),bh]),a(" 对任意自然数 "),Q("mjx-container",jh,[(t(),T("svg",Bh,Ch)),zh]),a(" 成立。")]),Q("p",null,[a("试证 "),Q("mjx-container",Sh,[(t(),T("svg",Jh,Ah)),Eh]),a("。")]),Q("p",null,[a("首先 "),Q("mjx-container",Fh,[(t(),T("svg",Oh,Ph)),Xh]),a(" 时有")]),Q("mjx-container",Nh,[(t(),T("svg",Kh,qh)),Uh]),Q("p",null,[a("进而当 "),Q("mjx-container",Wh,[(t(),T("svg",Yh,Qi)),ai]),a(" 是自然数且 "),Q("mjx-container",ti,[(t(),T("svg",Ti,ni)),li]),a(" 时有")]),Q("mjx-container",ei,[(t(),T("svg",si,ri)),di]),Q("p",null,[a("根据 Peano 公理 Ⅴ，得知 "),Q("mjx-container",hi,[(t(),T("svg",ii,Hi)),Li]),a(" 对任意自然数 "),Q("mjx-container",ci,[(t(),T("svg",pi,Mi)),ui]),a(" 成立，将其称为新的"),xi,a("。")]),Q("p",null,[a("证明了乘法运算规则的交换律之后，试证乘法交换律 "),Q("mjx-container",Zi,[(t(),T("svg",Vi,_i)),vi]),a("，首先当 "),Q("mjx-container",yi,[(t(),T("svg",Di,ji)),Bi]),a(" 时由乘法运算规则 Ⅰ 有 "),Q("mjx-container",ki,[(t(),T("svg",Ci,Si)),Ji]),a("。")]),Q("p",null,[a("进而当 "),Q("mjx-container",Gi,[(t(),T("svg",Ai,Fi)),Oi]),a(" 是自然数且 "),Q("mjx-container",Ri,[(t(),T("svg",Pi,Ni)),Ki]),a(" 时，有")]),Q("mjx-container",Ii,[(t(),T("svg",qi,Wi)),Yi]),Q("p",null,[a("根据 Peano 公理 Ⅴ，得知 "),Q("mjx-container",$i,[(t(),T("svg",Qg,tg)),Tg]),a(" 对任意自然数 "),Q("mjx-container",mg,[(t(),T("svg",ng,eg)),sg]),a(" 成立，即乘法交换律成立。")]),og,Q("p",null,[a("下面证明乘法分配律，即对于任意自然数 "),Q("mjx-container",rg,[(t(),T("svg",dg,ig)),gg]),a("，有 "),Q("mjx-container",Hg,[(t(),T("svg",Lg,pg)),fg]),a("。")]),Q("p",null,[a("首先当 "),Q("mjx-container",Mg,[(t(),T("svg",ug,Zg)),Vg]),a(" 时，"),Q("mjx-container",wg,[(t(),T("svg",_g,yg)),Dg]),a("，进而当 "),Q("mjx-container",bg,[(t(),T("svg",jg,kg)),Cg]),a(" 为自然数且 "),Q("mjx-container",zg,[(t(),T("svg",Sg,Gg)),Ag]),a(" 时有")]),Q("mjx-container",Eg,[(t(),T("svg",Fg,Rg)),Pg]),Q("p",null,[a("根据 Peano 公理 Ⅴ，得知 "),Q("mjx-container",Xg,[(t(),T("svg",Ng,Ig)),qg]),a(" 对任意自然数 "),Q("mjx-container",Ug,[(t(),T("svg",Wg,$g)),QH]),a(" 成立，即乘法分配律成立。")]),aH,Q("p",null,[a("下面证明乘法结合律，即对于任意自然数 "),Q("mjx-container",tH,[(t(),T("svg",TH,nH)),lH]),a("，有 "),Q("mjx-container",eH,[(t(),T("svg",sH,rH)),dH]),a("。")]),Q("p",null,[a("首先当 "),Q("mjx-container",hH,[(t(),T("svg",iH,HH)),LH]),a(" 时，有 "),Q("mjx-container",cH,[(t(),T("svg",pH,MH)),uH]),a("。")]),Q("p",null,[a("进而当 "),Q("mjx-container",xH,[(t(),T("svg",ZH,wH)),_H]),a(" 为自然数且 "),Q("mjx-container",vH,[(t(),T("svg",yH,bH)),jH]),a(" 时有")]),Q("mjx-container",BH,[(t(),T("svg",kH,zH)),SH]),Q("p",null,[a("根据 Peano 公理 Ⅴ，得知 "),Q("mjx-container",JH,[(t(),T("svg",GH,EH)),FH]),a(" 对任意自然数 "),Q("mjx-container",OH,[(t(),T("svg",RH,XH)),NH]),a(" 成立，即乘法结合律成立。")]),KH,Q("p",null,[a("下面证明乘法消去律，即对于任意自然数 "),Q("mjx-container",IH,[(t(),T("svg",qH,WH)),YH]),a(" 和 "),Q("mjx-container",$H,[(t(),T("svg",QL,tL)),TL]),a("，有 "),Q("mjx-container",mL,[(t(),T("svg",nL,eL)),sL]),a("。")]),Q("p",null,[a("试证 "),Q("mjx-container",oL,[(t(),T("svg",rL,hL)),iL]),a("。")]),Q("p",null,[a("首先当 "),Q("mjx-container",gL,[(t(),T("svg",HL,cL)),pL]),a(" 时有")]),Q("mjx-container",fL,[(t(),T("svg",ML,xL)),ZL]),Q("p",null,[a("进而当 "),Q("mjx-container",VL,[(t(),T("svg",wL,vL)),yL]),a(" 为自然数且 "),Q("mjx-container",DL,[(t(),T("svg",bL,BL)),kL]),a(" 时有")]),Q("mjx-container",CL,[(t(),T("svg",zL,JL)),GL]),Q("p",null,[a("即 "),Q("mjx-container",AL,[(t(),T("svg",EL,OL)),RL]),a("，根据 Peano 公理 Ⅴ，得知 "),Q("mjx-container",PL,[(t(),T("svg",XL,KL)),IL]),a(" 对任意自然数 "),Q("mjx-container",qL,[(t(),T("svg",UL,YL)),$L]),a(" 成立。")]),Q("p",null,[a("试证 "),Q("mjx-container",Qc,[(t(),T("svg",ac,Tc)),mc]),a("，采用反证法，假设 "),Q("mjx-container",nc,[(t(),T("svg",lc,sc)),oc]),a("，则由加法运算规则 Ⅱ 可知 "),Q("mjx-container",rc,[(t(),T("svg",dc,ic)),gc]),a(" 或 "),Q("mjx-container",Hc,[(t(),T("svg",Lc,pc)),fc]),a("，其中 "),Q("mjx-container",Mc,[(t(),T("svg",uc,Zc)),Vc]),a("，不妨设 "),Q("mjx-container",wc,[(t(),T("svg",_c,yc)),Dc]),a("。")]),Q("p",null,[a("由 Peano 公理 Ⅲ 有 "),Q("mjx-container",bc,[(t(),T("svg",jc,kc)),Cc]),a("。")]),Q("p",null,[a("由 Peano 公理 Ⅲ、Ⅳ 有，任意非零自然数 "),Q("mjx-container",zc,[(t(),T("svg",Sc,Gc)),Ac]),a(" 都有唯一的数 "),Q("mjx-container",Ec,[(t(),T("svg",Fc,Rc)),Pc]),a(" 满足 "),Q("mjx-container",Xc,[(t(),T("svg",Nc,Ic)),qc]),a("，不妨记作 "),Q("mjx-container",Uc,[(t(),T("svg",Wc,$c)),Qp]),a("。")]),Q("p",null,[a("若有 "),Q("mjx-container",ap,[(t(),T("svg",tp,mp)),np]),a("，则有")]),Q("mjx-container",lp,[(t(),T("svg",ep,op)),rp]),Q("p",null,[a("上述等式表明 "),Q("mjx-container",dp,[(t(),T("svg",hp,gp)),Hp]),a(" 是 "),Q("mjx-container",Lp,[(t(),T("svg",cp,fp)),Mp]),a(" 的后继，这违背了 Peano 公理 Ⅲ，由此知道假设不成立，即 "),Q("mjx-container",up,[(t(),T("svg",xp,Vp)),wp]),a("。")]),Q("p",null,[a("综上所述，乘法消去律 "),Q("mjx-container",_p,[(t(),T("svg",vp,Dp)),bp]),a("，对任意自然数 "),Q("mjx-container",jp,[(t(),T("svg",Bp,Cp)),zp]),a(" 成立。")]),Sp,Jp,Gp,Ap,Q("p",null,[a("若 "),Q("mjx-container",Ep,[(t(),T("svg",Fp,Rp)),Pp]),a("，则 "),Q("mjx-container",Xp,[(t(),T("svg",Np,Ip)),qp]),a("。")]),Q("p",null,[a("由 "),Q("mjx-container",Up,[(t(),T("svg",Wp,$p)),Qf]),a(" 有 "),Q("mjx-container",af,[(t(),T("svg",tf,mf)),nf]),a("，进而 "),Q("mjx-container",lf,[(t(),T("svg",ef,of)),rf]),a(" 因此 "),Q("mjx-container",df,[(t(),T("svg",hf,Hf)),Lf]),a("。")]),cf,Q("p",null,[a("若 "),Q("mjx-container",pf,[(t(),T("svg",ff,uf)),xf]),a("，则 "),Q("mjx-container",Zf,[(t(),T("svg",Vf,_f)),vf]),a("。")]),Q("p",null,[a("采用反证法，假设 "),Q("mjx-container",yf,[(t(),T("svg",Df,jf)),Bf]),a("，则存在正自然数 "),Q("mjx-container",kf,[(t(),T("svg",Cf,Sf)),Jf]),a(" 满足 "),Q("mjx-container",Gf,[(t(),T("svg",Af,Ff)),Of]),a("，有")]),Q("mjx-container",Rf,[(t(),T("svg",Pf,Nf)),Kf]),Q("p",null,[a("由此有 "),Q("mjx-container",If,[(t(),T("svg",qf,Wf)),Yf]),a("，根据序的反对称性有 "),Q("mjx-container",$f,[(t(),T("svg",QM,tM)),TM]),a("，根据乘法消去律有 "),Q("mjx-container",mM,[(t(),T("svg",nM,eM)),sM]),a("，这与 "),Q("mjx-container",oM,[(t(),T("svg",rM,hM)),iM]),a(" 的假设矛盾，因此假设不成立，即证明了乘法消去的保序性。")]),gM,Q("p",null,[a("自然数与有向图 "),Q("mjx-container",HM,[(t(),T("svg",LM,pM)),fM]),a(" 同构，这个图满足如下性质：")]),Q("ol",null,[Q("li",null,[a("存在点 "),Q("mjx-container",MM,[(t(),T("svg",uM,ZM)),VM]),a("，即 "),Q("mjx-container",wM,[(t(),T("svg",_M,yM)),DM]),a("；")]),Q("li",null,[a("所有点的出度为 "),Q("mjx-container",bM,[(t(),T("svg",jM,kM)),CM]),a("，即 "),Q("mjx-container",zM,[(t(),T("svg",SM,GM)),AM]),a("；")]),Q("li",null,[a("点 "),Q("mjx-container",EM,[(t(),T("svg",FM,RM)),PM]),a(" 入度为 "),Q("mjx-container",XM,[(t(),T("svg",NM,IM)),qM]),a("，即 "),Q("mjx-container",UM,[(t(),T("svg",WM,$M)),Qu]),a("；")]),Q("li",null,[a("任意点的入度小于等于 "),Q("mjx-container",au,[(t(),T("svg",tu,mu)),nu]),a("，即 "),Q("mjx-container",lu,[(t(),T("svg",eu,ou)),ru]),a("；")]),Q("li",null,[a("存在从 "),Q("mjx-container",du,[(t(),T("svg",hu,gu)),Hu]),a(" 到任意点的路径，即 "),Q("mjx-container",Lu,[(t(),T("svg",cu,fu)),Mu]),a("。")])]),uu,xu,Q("p",null,[a("若去除，则允许不存在 "),Q("mjx-container",Zu,[(t(),T("svg",Vu,_u)),vu]),a("，可以构造出空集自然数系统。")]),yu,Du,bu,Q("p",null,[a("若去除，则对 "),Q("mjx-container",ju,[(t(),T("svg",Bu,Cu)),zu]),a(" 的入度无规定，可以构造出环状自然数系统。")]),Su,Q("p",null,[a("若去除，则对一个数可以是多个数的后继，可以构造出 "),Q("mjx-container",Ju,[(t(),T("svg",Gu,Eu)),Fu]),a(" 状自然数系统。")]),Ou,Ru])}const Iu=n(e,[["render",Pu],["__file","「算术公理系统 1」自然数.html.vue"]]),qu=JSON.parse('{"path":"/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html","title":"「算术公理系统 1」自然数","lang":"zh-CN","frontmatter":{"lang":"zh-CN","date":"2023-07-09T00:00:00.000Z","category":["数学"],"tag":["公理系统"],"description":"假设存在一个算数系统的模型满足 Peano 公理，即假定 Peano 公理相容，在此承认次假设的基础之上，我们即可建立如今最常用的算术公理系统。自然数的定义则是构建此算术公理系统的第一步。","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"「算术公理系统 1」自然数"}],["meta",{"property":"og:description","content":"假设存在一个算数系统的模型满足 Peano 公理，即假定 Peano 公理相容，在此承认次假设的基础之上，我们即可建立如今最常用的算术公理系统。自然数的定义则是构建此算术公理系统的第一步。"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"公理系统"}],["meta",{"property":"article:published_time","content":"2023-07-09T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"「算术公理系统 1」自然数\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2023-07-09T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"自然数的定义","slug":"自然数的定义","link":"#自然数的定义","children":[]},{"level":2,"title":"自然数的加法运算","slug":"自然数的加法运算","link":"#自然数的加法运算","children":[{"level":3,"title":"加法的定义","slug":"加法的定义","link":"#加法的定义","children":[]},{"level":3,"title":"加法的性质","slug":"加法的性质","link":"#加法的性质","children":[]}]},{"level":2,"title":"自然数的序","slug":"自然数的序","link":"#自然数的序","children":[{"level":3,"title":"序的定义","slug":"序的定义","link":"#序的定义","children":[]},{"level":3,"title":"正自然数","slug":"正自然数","link":"#正自然数","children":[]},{"level":3,"title":"序的反对称性","slug":"序的反对称性","link":"#序的反对称性","children":[]},{"level":3,"title":"序的传递性","slug":"序的传递性","link":"#序的传递性","children":[]},{"level":3,"title":"序的完全性","slug":"序的完全性","link":"#序的完全性","children":[]},{"level":3,"title":"加法保序性","slug":"加法保序性","link":"#加法保序性","children":[]}]},{"level":2,"title":"自然数的乘法运算","slug":"自然数的乘法运算","link":"#自然数的乘法运算","children":[{"level":3,"title":"乘法的定义","slug":"乘法的定义","link":"#乘法的定义","children":[]},{"level":3,"title":"乘法的性质","slug":"乘法的性质","link":"#乘法的性质","children":[]}]},{"level":2,"title":"Peano 公理的合理性","slug":"peano-公理的合理性","link":"#peano-公理的合理性","children":[{"level":3,"title":"乘法保序性","slug":"乘法保序性","link":"#乘法保序性","children":[]},{"level":3,"title":"乘法消去保序性","slug":"乘法消去保序性","link":"#乘法消去保序性","children":[]},{"level":3,"title":"用图论阐述 Peano 系统","slug":"用图论阐述-peano-系统","link":"#用图论阐述-peano-系统","children":[]}]}],"readingTime":{"minutes":18.04,"words":5412},"filePathRelative":"tech/「算术公理系统 1」自然数.md","localizedDate":"2023年7月9日","excerpt":"\\n<p>假设存在一个算数系统的模型满足 Peano 公理，即假定 Peano 公理相容，在此承认次假设的基础之上，我们即可建立如今最常用的<strong>算术公理系统</strong>。<strong>自然数的定义</strong>则是构建此算术公理系统的第一步。</p>\\n","autoDesc":true}');export{Iu as comp,qu as data};
+import{_ as n,o as t,c as T,a as l,b as Q,e as a,f as m}from"./app-B4LGNJZ0.js";const e={},s=Q("h1",{id:"「算术公理系统-1」自然数",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#「算术公理系统-1」自然数"},[Q("span",null,"「算术公理系统 1」自然数")])],-1),o=Q("p",null,[a("假设存在一个算数系统的模型满足 Peano 公理，即假定 Peano 公理相容，在此承认次假设的基础之上，我们即可建立如今最常用的"),Q("strong",null,"算术公理系统"),a("。"),Q("strong",null,"自然数的定义"),a("则是构建此算术公理系统的第一步。")],-1),r=Q("h2",{id:"自然数的定义",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#自然数的定义"},[Q("span",null,"自然数的定义")])],-1),d=Q("p",null,"先介绍 Peano 公理，共有五条：",-1),h={class:"MathJax",jax:"SVG",style:{position:"relative"}},i={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 500 688","aria-hidden":"true"},g=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"30",d:"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"})])])],-1),H=[g],L=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0")])],-1),c={class:"MathJax",jax:"SVG",style:{position:"relative"}},p={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.271ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2772 1000","aria-hidden":"true"},f=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2383,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),M=[f],u=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")])],-1),x={class:"MathJax",jax:"SVG",style:{position:"relative"}},Z={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},V=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),w=[V],_=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),v={class:"MathJax",jax:"SVG",style:{position:"relative"}},y={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 500 688","aria-hidden":"true"},D=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"30",d:"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"})])])],-1),b=[D],j=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0")])],-1),B=Q("li",null,[Q("p",null,"不同的自然数后继不同；")],-1),k={class:"MathJax",jax:"SVG",style:{position:"relative"}},C={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.256ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 1881 1000","aria-hidden":"true"},z=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mo" transform="translate(503,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(892,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1492,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),S=[z],J=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"p"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")])],-1),G={class:"MathJax",jax:"SVG",style:{position:"relative"}},A={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},E=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),F=[E],O=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),R={class:"MathJax",jax:"SVG",style:{position:"relative"}},P={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.029ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 1781 1000","aria-hidden":"true"},X=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mo" transform="translate(503,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(892,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(1392,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),N=[X],K=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"p"),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")")])],-1),I={class:"MathJax",jax:"SVG",style:{position:"relative"}},q={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.256ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 1881 1000","aria-hidden":"true"},U=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mo" transform="translate(503,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(892,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1492,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),W=[U],Y=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"p"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")])],-1),$={class:"MathJax",jax:"SVG",style:{position:"relative"}},Q1={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.17ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4053 1000","aria-hidden":"true"},a1=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mo" transform="translate(503,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(892,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2286,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(2675,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3275,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3664,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),t1=[a1],T1=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"p"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")")])],-1),m1={class:"MathJax",jax:"SVG",style:{position:"relative"}},n1={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},l1=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),e1=[l1],s1=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),o1={class:"MathJax",jax:"SVG",style:{position:"relative"}},r1={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.256ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 1881 1000","aria-hidden":"true"},d1=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mo" transform="translate(503,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(892,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1492,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),h1=[d1],i1=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"p"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")])],-1),g1=Q("p",null,"这样就定义了自然数，自然数这个新的数学对象因我们的假设而确立。",-1),H1=Q("h2",{id:"自然数的加法运算",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#自然数的加法运算"},[Q("span",null,"自然数的加法运算")])],-1),L1=Q("p",null,[a("自然数中最重要的运算当然是"),Q("strong",null,"加法"),a("。")],-1),c1=Q("h3",{id:"加法的定义",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#加法的定义"},[Q("span",null,"加法的定义")])],-1),p1=Q("p",null,"定义加法的运算规则：",-1),f1={class:"MathJax",jax:"SVG",style:{position:"relative"}},M1={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},u1=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),x1=[u1],Z1=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),V1={class:"MathJax",jax:"SVG",style:{position:"relative"}},w1={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.254ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2322.4 748","aria-hidden":"true"},_1=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),v1=[_1],y1=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),D1={class:"MathJax",jax:"SVG",style:{position:"relative"}},b1={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},j1=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),B1=[j1],k1=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),C1={class:"MathJax",jax:"SVG",style:{position:"relative"}},z1={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.629ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 4256 748","aria-hidden":"true"},S1=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3656,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),J1=[S1],G1=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"n")])],-1),A1={class:"MathJax",jax:"SVG",style:{position:"relative"}},E1={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.35ex",height:"1.439ex",role:"img",focusable:"false",viewBox:"0 -442 1922.7 636","aria-hidden":"true"},F1=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),O1=[F1],R1=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"m")])],-1),P1={class:"MathJax",jax:"SVG",style:{position:"relative"}},X1={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.064ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 11078.4 1000","aria-hidden":"true"},N1=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7989,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9089.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10089.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10689.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),K1=[N1],I1=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")])],-1),q1=Q("p",null,"下面我们需要证明对于任意两个自然数，都可以进行加法运算，也就是说，我们需要证明加法结果的存在性和唯一性。",-1),U1=Q("h4",{id:"加法结果的存在性",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#加法结果的存在性"},[Q("span",null,"加法结果的存在性")])],-1),W1={class:"MathJax",jax:"SVG",style:{position:"relative"}},Y1={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},$1=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),Q3=[$1],a3=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),t3={class:"MathJax",jax:"SVG",style:{position:"relative"}},T3={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},m3=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),n3=[m3],l3=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),e3={class:"MathJax",jax:"SVG",style:{position:"relative"}},s3={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 2700.4 665","aria-hidden":"true"},o3=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),r3=[o3],d3=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),h3={class:"MathJax",jax:"SVG",style:{position:"relative"}},i3={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 2700.4 665","aria-hidden":"true"},g3=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),H3=[g3],L3=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),c3={class:"MathJax",jax:"SVG",style:{position:"relative"}},p3={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},f3=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),M3=[f3],u3=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),x3={class:"MathJax",jax:"SVG",style:{position:"relative"}},Z3={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.629ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 4256 748","aria-hidden":"true"},V3=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3656,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),w3=[V3],_3=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"n")])],-1),v3={class:"MathJax",jax:"SVG",style:{position:"relative"}},y3={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.254ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2322.4 748","aria-hidden":"true"},D3=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),b3=[D3],j3=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),B3={class:"MathJax",jax:"SVG",style:{position:"relative"}},k3={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.177ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2288.3 1000","aria-hidden":"true"},C3=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(1399.3,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(1899.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),z3=[C3],S3=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")")])],-1),J3={class:"MathJax",jax:"SVG",style:{position:"relative"}},G3={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.986ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 878 453","aria-hidden":"true"},A3=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45A",d:"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"})])])],-1),E3=[A3],F3=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m")])],-1),O3={class:"MathJax",jax:"SVG",style:{position:"relative"}},R3={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 2700.4 665","aria-hidden":"true"},P3=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),X3=[P3],N3=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),K3={class:"MathJax",jax:"SVG",style:{position:"relative"}},I3={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.9ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3050 1000","aria-hidden":"true"},q3=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),U3=[q3],W3=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),Y3={class:"MathJax",jax:"SVG",style:{position:"relative"}},$3={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.024ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4872.4 1000","aria-hidden":"true"},Q2=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2883.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),a2=[Q2],t2=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")])],-1),T2={class:"MathJax",jax:"SVG",style:{position:"relative"}},m2={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.064ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 11078.4 1000","aria-hidden":"true"},n2=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7989,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9089.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10089.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10689.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),l2=[n2],e2=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")])],-1),s2={class:"MathJax",jax:"SVG",style:{position:"relative"}},o2={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.024ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4872.4 1000","aria-hidden":"true"},r2=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),d2=[r2],h2=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),i2={class:"MathJax",jax:"SVG",style:{position:"relative"}},g2={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 2700.4 665","aria-hidden":"true"},H2=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),L2=[H2],c2=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),p2={class:"MathJax",jax:"SVG",style:{position:"relative"}},f2={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.024ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4872.4 1000","aria-hidden":"true"},M2=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),u2=[M2],x2=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),Z2={class:"MathJax",jax:"SVG",style:{position:"relative"}},V2={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},w2=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),_2=[w2],v2=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),y2={class:"MathJax",jax:"SVG",style:{position:"relative"}},D2={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.946ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4838.3 1000","aria-hidden":"true"},b2=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2793.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3182.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4060.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4449.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),j2=[b2],B2=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")")])],-1),k2={class:"MathJax",jax:"SVG",style:{position:"relative"}},C2={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},z2=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),S2=[z2],J2=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),G2={class:"MathJax",jax:"SVG",style:{position:"relative"}},A2={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.986ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 878 453","aria-hidden":"true"},E2=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45A",d:"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"})])])],-1),F2=[E2],O2=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m")])],-1),R2={class:"MathJax",jax:"SVG",style:{position:"relative"}},P2={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},X2=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),N2=[X2],K2=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),I2={class:"MathJax",jax:"SVG",style:{position:"relative"}},q2={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 2700.4 665","aria-hidden":"true"},U2=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),W2=[U2],Y2=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),$2={class:"MathJax",jax:"SVG",style:{position:"relative"}},Q4={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},a4=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),t4=[a4],T4=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),m4={class:"MathJax",jax:"SVG",style:{position:"relative"}},n4={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.35ex",height:"1.439ex",role:"img",focusable:"false",viewBox:"0 -442 1922.7 636","aria-hidden":"true"},l4=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),e4=[l4],s4=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"m")])],-1),o4={class:"MathJax",jax:"SVG",style:{position:"relative"}},r4={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 2700.4 665","aria-hidden":"true"},d4=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),h4=[d4],i4=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),g4=Q("h4",{id:"加法结果的唯一性",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#加法结果的唯一性"},[Q("span",null,"加法结果的唯一性")])],-1),H4={class:"MathJax",jax:"SVG",style:{position:"relative"}},L4={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},c4=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),p4=[c4],f4=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),M4={class:"MathJax",jax:"SVG",style:{position:"relative"}},u4={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},x4=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Z4=[x4],V4=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),w4={class:"MathJax",jax:"SVG",style:{position:"relative"}},_4={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 2700.4 665","aria-hidden":"true"},v4=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),y4=[v4],D4=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),b4={class:"MathJax",jax:"SVG",style:{position:"relative"}},j4={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 2700.4 665","aria-hidden":"true"},B4=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),k4=[B4],C4=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),z4={class:"MathJax",jax:"SVG",style:{position:"relative"}},S4={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},J4=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),G4=[J4],A4=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),E4={class:"MathJax",jax:"SVG",style:{position:"relative"}},F4={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.629ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 4256 748","aria-hidden":"true"},O4=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3656,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),R4=[O4],P4=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"n")])],-1),X4={class:"MathJax",jax:"SVG",style:{position:"relative"}},N4={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.254ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2322.4 748","aria-hidden":"true"},K4=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),I4=[K4],q4=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),U4={class:"MathJax",jax:"SVG",style:{position:"relative"}},W4={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Y4=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),$4=[Y4],Q5=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),a5={class:"MathJax",jax:"SVG",style:{position:"relative"}},t5={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.177ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2288.3 1000","aria-hidden":"true"},T5=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(1399.3,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(1899.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),m5=[T5],n5=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")")])],-1),l5={class:"MathJax",jax:"SVG",style:{position:"relative"}},e5={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.986ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 878 453","aria-hidden":"true"},s5=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45A",d:"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"})])])],-1),o5=[s5],r5=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m")])],-1),d5={class:"MathJax",jax:"SVG",style:{position:"relative"}},h5={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 2700.4 665","aria-hidden":"true"},i5=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),g5=[i5],H5=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),L5={class:"MathJax",jax:"SVG",style:{position:"relative"}},c5={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.9ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3050 1000","aria-hidden":"true"},p5=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),f5=[p5],M5=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),u5={class:"MathJax",jax:"SVG",style:{position:"relative"}},x5={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.024ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4872.4 1000","aria-hidden":"true"},Z5=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2883.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),V5=[Z5],w5=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")])],-1),_5={class:"MathJax",jax:"SVG",style:{position:"relative"}},v5={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.064ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 11078.4 1000","aria-hidden":"true"},y5=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7989,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9089.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10089.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10689.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),D5=[y5],b5=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")])],-1),j5={class:"MathJax",jax:"SVG",style:{position:"relative"}},B5={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.024ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4872.4 1000","aria-hidden":"true"},k5=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),C5=[k5],z5=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),S5={class:"MathJax",jax:"SVG",style:{position:"relative"}},J5={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 2700.4 665","aria-hidden":"true"},G5=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),A5=[G5],E5=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),F5={class:"MathJax",jax:"SVG",style:{position:"relative"}},O5={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.024ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4872.4 1000","aria-hidden":"true"},R5=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),P5=[R5],X5=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),N5={class:"MathJax",jax:"SVG",style:{position:"relative"}},K5={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},I5=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),q5=[I5],U5=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),W5={class:"MathJax",jax:"SVG",style:{position:"relative"}},Y5={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.946ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4838.3 1000","aria-hidden":"true"},$5=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2793.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3182.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4060.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4449.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Q6=[$5],a6=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")")])],-1),t6={class:"MathJax",jax:"SVG",style:{position:"relative"}},T6={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},m6=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),n6=[m6],l6=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),e6={class:"MathJax",jax:"SVG",style:{position:"relative"}},s6={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.986ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 878 453","aria-hidden":"true"},o6=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45A",d:"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"})])])],-1),r6=[o6],d6=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m")])],-1),h6={class:"MathJax",jax:"SVG",style:{position:"relative"}},i6={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},g6=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),H6=[g6],L6=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),c6={class:"MathJax",jax:"SVG",style:{position:"relative"}},p6={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 2700.4 665","aria-hidden":"true"},f6=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),M6=[f6],u6=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),x6={class:"MathJax",jax:"SVG",style:{position:"relative"}},Z6={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},V6=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),w6=[V6],_6=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),v6={class:"MathJax",jax:"SVG",style:{position:"relative"}},y6={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.35ex",height:"1.439ex",role:"img",focusable:"false",viewBox:"0 -442 1922.7 636","aria-hidden":"true"},D6=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),b6=[D6],j6=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"m")])],-1),B6={class:"MathJax",jax:"SVG",style:{position:"relative"}},k6={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 2700.4 665","aria-hidden":"true"},C6=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),z6=[C6],S6=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),J6=Q("h3",{id:"加法的性质",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#加法的性质"},[Q("span",null,"加法的性质")])],-1),G6=Q("p",null,"在明确证明了自然数加法运算的良好性质，即任意两个自然数都可以进行加法运算，且加法运算的结果存在且唯一之后，我们终于可以对自然数加法的性质进行进一步的探索。",-1),A6=Q("h4",{id:"加法交换律",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#加法交换律"},[Q("span",null,"加法交换律")])],-1),E6={class:"MathJax",jax:"SVG",style:{position:"relative"}},F6={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.35ex",height:"1.439ex",role:"img",focusable:"false",viewBox:"0 -442 1922.7 636","aria-hidden":"true"},O6=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),R6=[O6],P6=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"m")])],-1),X6={class:"MathJax",jax:"SVG",style:{position:"relative"}},N6={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.236ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 6734.4 665","aria-hidden":"true"},K6=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),I6=[K6],q6=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),U6=Q("p",null,"直接证明比较困难，考虑从加法运算的定义下手，即先证明加法的两条运算规则符合交换律。",-1),W6={class:"MathJax",jax:"SVG",style:{position:"relative"}},Y6={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"17.9ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 7912 748","aria-hidden":"true"},$6=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3656,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4533.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5589.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6411.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(7412,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),Q7=[$6],a7=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"+"),Q("mn",null,"0")])],-1),t7={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},T7={style:{"vertical-align":"-2.036ex"},xmlns:"http://www.w3.org/2000/svg",width:"37.243ex",height:"5.204ex",role:"img",focusable:"false",viewBox:"0 -1400 16461.4 2300","aria-hidden":"true"},m7=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,650)"><g data-mml-node="mtd"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(1722.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g><g data-mml-node="mtd" transform="translate(2222.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(1833.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(8778.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-650)"><g data-mml-node="mtd" transform="translate(2222.4,0)"></g><g data-mml-node="mtd" transform="translate(2222.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2055.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(3056,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(3556,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(8778.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g></g></g></g>',1),n7=[m7],l7=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mn",null,"0"),Q("mo",null,"+"),Q("mn",null,"0")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])])])])],-1),e7={class:"MathJax",jax:"SVG",style:{position:"relative"}},s7={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},o7=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),r7=[o7],d7=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),h7={class:"MathJax",jax:"SVG",style:{position:"relative"}},i7={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"17.9ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 7912 748","aria-hidden":"true"},g7=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3656,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4533.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5589.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6411.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(7412,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),H7=[g7],L7=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"+"),Q("mn",null,"0")])],-1),c7={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},p7={style:{"vertical-align":"-3.507ex"},xmlns:"http://www.w3.org/2000/svg",width:"47.524ex",height:"8.145ex",role:"img",focusable:"false",viewBox:"0 -2050 21005.4 3600","aria-hidden":"true"},f7=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3116.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3505.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4105.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3716.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(4105.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13322.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(4494.4,0)"></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3938.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(4939,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(5439,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5828,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(15916.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(877.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1933.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2755.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(3756,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(4494.4,0)"></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3716.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4327.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(5328,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(5828,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13322.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),M7=[f7],u7=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"+"),Q("mn",null,"0")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])])])])],-1),x7={class:"MathJax",jax:"SVG",style:{position:"relative"}},Z7={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"17.9ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 7912 748","aria-hidden":"true"},V7=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3656,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4533.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5589.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6411.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(7412,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),w7=[V7],_7=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"+"),Q("mn",null,"0")])],-1),v7={class:"MathJax",jax:"SVG",style:{position:"relative"}},y7={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},D7=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),b7=[D7],j7=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),B7={class:"MathJax",jax:"SVG",style:{position:"relative"}},k7={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"39.105ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 17284.4 1000","aria-hidden":"true"},C7=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7989,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9089.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10089.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10689.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(11356.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(12412,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(13806,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(14195,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(15073,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(15684.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(16684.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),z7=[C7],S7=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),J7={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},G7={style:{"vertical-align":"-3.507ex"},xmlns:"http://www.w3.org/2000/svg",width:"47.524ex",height:"8.145ex",role:"img",focusable:"false",viewBox:"0 -2050 21005.4 3600","aria-hidden":"true"},A7=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3116.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3505.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4105.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3716.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(4105.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13322.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(4494.4,0)"></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(3116.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(3838.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4839,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5439,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5828,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13322.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(4494.4,0)"></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(3116.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(3616.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4227.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5228,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mstyle" transform="translate(5828,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13322.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),E7=[A7],F7=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])])])])],-1),O7={class:"MathJax",jax:"SVG",style:{position:"relative"}},R7={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.986ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 878 453","aria-hidden":"true"},P7=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45A",d:"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"})])])],-1),X7=[P7],N7=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m")])],-1),K7={class:"MathJax",jax:"SVG",style:{position:"relative"}},I7={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"39.105ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 17284.4 1000","aria-hidden":"true"},q7=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7989,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9089.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10089.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10689.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(11356.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(12412,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(13806,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(14195,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(15073,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(15684.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(16684.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),U7=[q7],W7=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),Y7={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},$7={style:{"vertical-align":"-4.977ex"},xmlns:"http://www.w3.org/2000/svg",width:"68.629ex",height:"11.086ex",role:"img",focusable:"false",viewBox:"0 -2700 30333.9 4900","aria-hidden":"true"},Q0=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1950)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(5666.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6055.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6655.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4216.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5217,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6611,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7000,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7989,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(8378,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(22650.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,650)"><g data-mml-node="mtd" transform="translate(7044.4,0)"></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4510.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4899.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5999.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7000,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7989,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(8378,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18422.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7989,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9089.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10089.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10689.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-650)"><g data-mml-node="mtd" transform="translate(7044.4,0)"></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4510.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4899.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5777.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6388.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7389,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7989,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(8378,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18422.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2883.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7989,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(8867,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(9478.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10478.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1950)"><g data-mml-node="mtd" transform="translate(7044.4,0)"></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4510.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4899.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5777.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6166.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6777.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7778,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mstyle" transform="translate(8378,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(22650.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),a0=[Q0],t0=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])])])])],-1),T0={class:"MathJax",jax:"SVG",style:{position:"relative"}},m0={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"39.105ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 17284.4 1000","aria-hidden":"true"},n0=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7989,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9089.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10089.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10689.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(11356.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(12412,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(13806,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(14195,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(15073,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(15684.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(16684.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),l0=[n0],e0=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),s0={class:"MathJax",jax:"SVG",style:{position:"relative"}},o0={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.35ex",height:"1.439ex",role:"img",focusable:"false",viewBox:"0 -442 1922.7 636","aria-hidden":"true"},r0=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),d0=[r0],h0=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"m")])],-1),i0=Q("strong",null,"加法运算规则 Ⅱ",-1),g0={class:"MathJax",jax:"SVG",style:{position:"relative"}},H0={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.236ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 6734.4 665","aria-hidden":"true"},L0=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),c0=[L0],p0=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),f0={class:"MathJax",jax:"SVG",style:{position:"relative"}},M0={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"14.784ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 6534.4 748","aria-hidden":"true"},u0=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2878.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3934,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5034.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(6034.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),x0=[u0],Z0=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"+"),Q("mn",null,"0")])],-1),V0={class:"MathJax",jax:"SVG",style:{position:"relative"}},w0={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},_0=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),v0=[_0],y0=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),D0={class:"MathJax",jax:"SVG",style:{position:"relative"}},b0={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.236ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 6734.4 665","aria-hidden":"true"},j0=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),B0=[j0],k0=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),C0={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},z0={style:{"vertical-align":"-3.507ex"},xmlns:"http://www.w3.org/2000/svg",width:"49.234ex",height:"8.145ex",role:"img",focusable:"false",viewBox:"0 -2050 21761.4 3600","aria-hidden":"true"},S0=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2383,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(2994.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3994.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3938.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4939,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5817,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(6206,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14078.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(4872.4,0)"></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4216.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5217,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5817,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(6206,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14194,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(4872.4,0)"></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2433.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3434,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4828,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5217,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5817,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(6206,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14078.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),J0=[S0],G0=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"m")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])])])])],-1),A0={class:"MathJax",jax:"SVG",style:{position:"relative"}},E0={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.236ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 6734.4 665","aria-hidden":"true"},F0=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),O0=[F0],R0=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),P0={class:"MathJax",jax:"SVG",style:{position:"relative"}},X0={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.35ex",height:"1.439ex",role:"img",focusable:"false",viewBox:"0 -442 1922.7 636","aria-hidden":"true"},N0=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),K0=[N0],I0=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"m")])],-1),q0=Q("h4",{id:"加法结合律",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#加法结合律"},[Q("span",null,"加法结合律")])],-1),U0={class:"MathJax",jax:"SVG",style:{position:"relative"}},W0={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.159ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 2280.3 888","aria-hidden":"true"},Y0=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),$0=[Y0],Q8=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b"),Q("mo",null,","),Q("mi",null,"c")])],-1),a8={class:"MathJax",jax:"SVG",style:{position:"relative"}},t8={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"23.894ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10561.3 1000","aria-hidden":"true"},T8=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5947.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6698.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(7698.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8739.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9739.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(10172.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),m8=[T8],n8=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),l8={class:"MathJax",jax:"SVG",style:{position:"relative"}},e8={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.128ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2266.6 748","aria-hidden":"true"},s8=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),o8=[s8],r8=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])],-1),d8={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},h8={style:{"vertical-align":"-4.977ex"},xmlns:"http://www.w3.org/2000/svg",width:"48.216ex",height:"11.086ex",role:"img",focusable:"false",viewBox:"0 -2700 21311.3 4900","aria-hidden":"true"},i8=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1950)"><g data-mml-node="mtd"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g><g data-mml-node="mtd" transform="translate(4613.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(1333.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2473.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3474,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(3903,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4514.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(5514.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(6014.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18211.8,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,650)"><g data-mml-node="mtd" transform="translate(4613.9,0)"></g><g data-mml-node="mtd" transform="translate(4613.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3085,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(3514,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13628.3,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-650)"><g data-mml-node="mtd" transform="translate(4613.9,0)"></g><g data-mml-node="mtd" transform="translate(4613.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(3085,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3474,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4125.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(5125.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(5625.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(6014.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13628.3,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1950)"><g data-mml-node="mtd" transform="translate(4613.9,0)"></g><g data-mml-node="mtd" transform="translate(4613.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(3085,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3474,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4125.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5125.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5558.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5947.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18211.8,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g></g></g></g>',1),g8=[i8],H8=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"c")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])])])])])],-1),L8={class:"MathJax",jax:"SVG",style:{position:"relative"}},c8={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.98ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 433 453","aria-hidden":"true"},p8=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D450",d:"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"})])])],-1),f8=[p8],M8=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c")])],-1),u8={class:"MathJax",jax:"SVG",style:{position:"relative"}},x8={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"23.894ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10561.3 1000","aria-hidden":"true"},Z8=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5947.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6698.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(7698.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8739.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9739.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(10172.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),V8=[Z8],w8=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),_8={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},v8={style:{"vertical-align":"-4.977ex"},xmlns:"http://www.w3.org/2000/svg",width:"66.289ex",height:"11.086ex",role:"img",focusable:"false",viewBox:"0 -2700 29299.7 4900","aria-hidden":"true"},y8=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1950)"><g data-mml-node="mtd"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(5574.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5963.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6396.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(6785.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mo" transform="translate(3116.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3505.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4256.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5257,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(5686,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6297.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7297.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(7730.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(8119.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(21616.7,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,650)"><g data-mml-node="mtd" transform="translate(6785.9,0)"></g><g data-mml-node="mtd" transform="translate(6785.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(3867.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(4868,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5257,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(5908.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6908.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(7341.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7730.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(8119.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(17905.3,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5947.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6698.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(7698.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8739.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9739.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(10172.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-650)"><g data-mml-node="mtd" transform="translate(6785.9,0)"></g><g data-mml-node="mtd" transform="translate(6785.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3085,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4479,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4868,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(5519.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6519.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6952.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(7341.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(21616.7,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1950)"><g data-mml-node="mtd" transform="translate(6785.9,0)"></g><g data-mml-node="mtd" transform="translate(6785.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(3085,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3474,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4125.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5125.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6519.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6908.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(7341.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7730.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(8119.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(21616.7,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),D8=[y8],b8=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])])])])],-1),j8={class:"MathJax",jax:"SVG",style:{position:"relative"}},B8={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"23.894ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10561.3 1000","aria-hidden":"true"},k8=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5947.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6698.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(7698.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8739.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9739.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(10172.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),C8=[k8],z8=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),S8={class:"MathJax",jax:"SVG",style:{position:"relative"}},J8={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.159ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 2280.3 888","aria-hidden":"true"},G8=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),A8=[G8],E8=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b"),Q("mo",null,","),Q("mi",null,"c")])],-1),F8=Q("h4",{id:"加法消去律",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#加法消去律"},[Q("span",null,"加法消去律")])],-1),O8={class:"MathJax",jax:"SVG",style:{position:"relative"}},R8={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.159ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 2280.3 888","aria-hidden":"true"},P8=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),X8=[P8],N8=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b"),Q("mo",null,","),Q("mi",null,"c")])],-1),K8={class:"MathJax",jax:"SVG",style:{position:"relative"}},I8={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.379ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 9449.6 776","aria-hidden":"true"},q8=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5880.2,0)"><path data-c="21D4" d="M308 524Q318 526 323 526Q340 526 340 514Q340 507 336 499Q326 476 314 454T292 417T274 391T260 374L255 368Q255 367 500 367Q744 367 744 368L739 374Q734 379 726 390T707 416T685 453T663 499Q658 511 658 515Q658 525 680 525Q687 524 690 523T695 519T701 507Q766 359 902 287Q921 276 939 269T961 259T966 250Q966 246 965 244T960 240T949 236T930 228T902 213Q763 137 701 -7Q697 -16 695 -19T690 -23T680 -25Q658 -25 658 -15Q658 -11 663 1Q673 24 685 46T707 83T725 109T739 126L744 132Q744 133 500 133Q255 133 255 132L260 126Q265 121 273 110T292 84T314 47T336 1Q341 -11 341 -15Q341 -25 319 -25Q312 -24 309 -23T304 -19T298 -7Q233 141 97 213Q83 221 70 227T51 235T41 239T35 243T34 250T35 256T40 261T51 265T70 273T97 287Q235 363 299 509Q305 522 308 524ZM792 319L783 327H216Q183 294 120 256L110 250L120 244Q173 212 207 181L216 173H783L792 181Q826 212 879 244L889 250L879 256Q826 288 792 319Z"></path></g><g data-mml-node="mi" transform="translate(7158,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7964.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9020.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),U8=[q8],W8=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},"⇔"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),Y8={class:"MathJax",jax:"SVG",style:{position:"relative"}},$8={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.379ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 9449.6 776","aria-hidden":"true"},Q9=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(3847.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4598.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5598.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6309.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(7365.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8016.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9016.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),a9=[Q9],t9=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c")])],-1),T9={class:"MathJax",jax:"SVG",style:{position:"relative"}},m9={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.128ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2266.6 748","aria-hidden":"true"},n9=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),l9=[n9],e9=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])],-1),s9={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},o9={style:{"vertical-align":"-6.448ex"},xmlns:"http://www.w3.org/2000/svg",width:"37.223ex",height:"14.027ex",role:"img",focusable:"false",viewBox:"0 -3350 16452.4 6200","aria-hidden":"true"},r9=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,2600)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g><g data-mml-node="mtd" transform="translate(2184.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(3085,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(3585,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13352.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd" transform="translate(2184.4,0)"></g><g data-mml-node="mtd" transform="translate(2184.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mstyle" transform="translate(1862.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(8769.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(2184.4,0)"></g><g data-mml-node="mtd" transform="translate(2184.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(1762.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13327.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(2184.4,0)"></g><g data-mml-node="mtd" transform="translate(2184.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(2985,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(3485,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(8769.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-2600)"><g data-mml-node="mtd" transform="translate(2184.4,0)"></g><g data-mml-node="mtd" transform="translate(2184.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mstyle" transform="translate(3418,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13352.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g></g></g></g>',1),d9=[r9],h9=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])])])])])],-1),i9={class:"MathJax",jax:"SVG",style:{position:"relative"}},g9={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.98ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 433 453","aria-hidden":"true"},H9=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D450",d:"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"})])])],-1),L9=[H9],c9=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c")])],-1),p9={class:"MathJax",jax:"SVG",style:{position:"relative"}},f9={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.379ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 9449.6 776","aria-hidden":"true"},M9=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(3847.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4598.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5598.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6309.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(7365.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8016.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9016.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),u9=[M9],x9=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c")])],-1),Z9={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},V9={style:{"vertical-align":"-3.507ex"},xmlns:"http://www.w3.org/2000/svg",width:"52.781ex",height:"8.145ex",role:"img",focusable:"false",viewBox:"0 -2050 23329 3600","aria-hidden":"true"},w9=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(3867.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4868,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5301,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5690,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(15646,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(3767.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5590,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13046.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(3847.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4598.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5598.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6309.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(7365.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8016.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9016.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5590,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(15646,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),_9=[w9],v9=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])])])])],-1),y9={class:"MathJax",jax:"SVG",style:{position:"relative"}},D9={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"47.402ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 20951.6 1000","aria-hidden":"true"},b9=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(3847.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4598.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5598.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6309.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(7365.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8016.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9016.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9727.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(11005.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(11756.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(12756.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(14150.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(14539.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(14972.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(15639.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(16695.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(17346.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(18346.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(19740.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(20129.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(20562.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),j9=[b9],B9=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),k9={class:"MathJax",jax:"SVG",style:{position:"relative"}},C9={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.379ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 9449.6 776","aria-hidden":"true"},z9=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(3847.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4598.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5598.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6309.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(7365.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8016.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9016.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),S9=[z9],J9=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c")])],-1),G9={class:"MathJax",jax:"SVG",style:{position:"relative"}},A9={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.159ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 2280.3 888","aria-hidden":"true"},E9=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),F9=[E9],O9=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b"),Q("mo",null,","),Q("mi",null,"c")])],-1),R9={class:"MathJax",jax:"SVG",style:{position:"relative"}},P9={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.379ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 9449.6 776","aria-hidden":"true"},X9=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5880.2,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(7158,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7964.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9020.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),N9=[X9],K9=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),I9={class:"MathJax",jax:"SVG",style:{position:"relative"}},q9={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.128ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2266.6 748","aria-hidden":"true"},U9=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),W9=[U9],Y9=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])],-1),$9={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},QQ={style:{"vertical-align":"-6.448ex"},xmlns:"http://www.w3.org/2000/svg",width:"33.477ex",height:"14.027ex",role:"img",focusable:"false",viewBox:"0 -3350 14797 6200","aria-hidden":"true"},aQ=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,2600)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g></g><g data-mml-node="mtd" transform="translate(529,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(3085,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(3585,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(7114,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd" transform="translate(529,0)"></g><g data-mml-node="mtd" transform="translate(529,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3085,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mstyle" transform="translate(3518,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(11697.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(529,0)"></g><g data-mml-node="mtd" transform="translate(529,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mstyle" transform="translate(3418,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(8361.6,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(529,0)"></g><g data-mml-node="mtd" transform="translate(529,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(2985,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(3485,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(11697.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-2600)"><g data-mml-node="mtd" transform="translate(529,0)"></g><g data-mml-node="mtd" transform="translate(529,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(1762.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(7114,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g></g></g></g>',1),tQ=[aQ],TQ=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"a")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])])])])],-1),mQ={class:"MathJax",jax:"SVG",style:{position:"relative"}},nQ={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.98ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 433 453","aria-hidden":"true"},lQ=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D450",d:"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"})])])],-1),eQ=[lQ],sQ=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c")])],-1),oQ={class:"MathJax",jax:"SVG",style:{position:"relative"}},rQ={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.379ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 9449.6 776","aria-hidden":"true"},dQ=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5880.2,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(7158,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7964.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9020.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),hQ=[dQ],iQ=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),gQ={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},HQ={style:{"vertical-align":"-4.977ex"},xmlns:"http://www.w3.org/2000/svg",width:"52.554ex",height:"11.086ex",role:"img",focusable:"false",viewBox:"0 -2700 23229 4900","aria-hidden":"true"},LQ=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1950)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5590,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18396,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">已</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">知</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">条</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">件</text></g></g></g><g data-mml-node="mtr" transform="translate(0,650)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2534.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(3767.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5590,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(15546,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-650)"><g data-mml-node="mtd" transform="translate(2172,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mstyle" transform="translate(3418,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(16615,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><path data-c="50" d="M130 622Q123 629 119 631T103 634T60 637H27V683H214Q237 683 276 683T331 684Q419 684 471 671T567 616Q624 563 624 489Q624 421 573 372T451 307Q429 302 328 301H234V181Q234 62 237 58Q245 47 304 46H337V0H326Q305 3 182 3Q47 3 38 0H27V46H60Q102 47 111 49T130 61V622ZM507 488Q507 514 506 528T500 564T483 597T450 620T397 635Q385 637 307 637H286Q237 637 234 628Q231 624 231 483V342H302H339Q390 342 423 349T481 382Q507 411 507 488Z"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(681,0)"></path><path data-c="61" d="M137 305T115 305T78 320T63 359Q63 394 97 421T218 448Q291 448 336 416T396 340Q401 326 401 309T402 194V124Q402 76 407 58T428 40Q443 40 448 56T453 109V145H493V106Q492 66 490 59Q481 29 455 12T400 -6T353 12T329 54V58L327 55Q325 52 322 49T314 40T302 29T287 17T269 6T247 -2T221 -8T190 -11Q130 -11 82 20T34 107Q34 128 41 147T68 188T116 225T194 253T304 268H318V290Q318 324 312 340Q290 411 215 411Q197 411 181 410T156 406T148 403Q170 388 170 359Q170 334 154 320ZM126 106Q126 75 150 51T209 26Q247 26 276 49T315 109Q317 116 318 175Q318 233 317 233Q309 233 296 232T251 223T193 203T147 166T126 106Z" transform="translate(1125,0)"></path><path data-c="6E" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z" transform="translate(1625,0)"></path><path data-c="6F" d="M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z" transform="translate(2181,0)"></path><path data-c="20" d="" transform="translate(2681,0)"></path><text data-variant="normal" transform="translate(2931,0) scale(1,-1)" font-size="884px" font-family="serif">公</text><text data-variant="normal" transform="translate(3931,0) scale(1,-1)" font-size="884px" font-family="serif">理</text><path data-c="20" d="" transform="translate(4931,0)"></path><text data-variant="normal" transform="translate(5181,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅳ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1950)"><g data-mml-node="mtd" transform="translate(3827.4,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(1762.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(12946.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5880.2,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(7158,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7964.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9020.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></g></g></g></g>',1),cQ=[LQ],pQ=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"已知条件")])]),Q("mtr",null,[Q("mtd",null,[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd",null,[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"Peano 公理 Ⅳ")])]),Q("mtr",null,[Q("mtd",null,[Q("mi",null,"a")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])])])])])],-1),fQ={class:"MathJax",jax:"SVG",style:{position:"relative"}},MQ={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"47.402ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 20951.6 1000","aria-hidden":"true"},uQ=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(10224.2,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(11502,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(12253.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(13253.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(13964.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(15020,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(15671.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(16671.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(17382.2,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(18660,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(19466.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(20522.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),xQ=[uQ],ZQ=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),VQ={class:"MathJax",jax:"SVG",style:{position:"relative"}},wQ={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.379ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 9449.6 776","aria-hidden":"true"},_Q=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5880.2,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(7158,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7964.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9020.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),vQ=[_Q],yQ=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),DQ={class:"MathJax",jax:"SVG",style:{position:"relative"}},bQ={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.159ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 2280.3 888","aria-hidden":"true"},jQ=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),BQ=[jQ],kQ=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b"),Q("mo",null,","),Q("mi",null,"c")])],-1),CQ={class:"MathJax",jax:"SVG",style:{position:"relative"}},zQ={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.379ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 9449.6 776","aria-hidden":"true"},SQ=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5880.2,0)"><path data-c="21D4" d="M308 524Q318 526 323 526Q340 526 340 514Q340 507 336 499Q326 476 314 454T292 417T274 391T260 374L255 368Q255 367 500 367Q744 367 744 368L739 374Q734 379 726 390T707 416T685 453T663 499Q658 511 658 515Q658 525 680 525Q687 524 690 523T695 519T701 507Q766 359 902 287Q921 276 939 269T961 259T966 250Q966 246 965 244T960 240T949 236T930 228T902 213Q763 137 701 -7Q697 -16 695 -19T690 -23T680 -25Q658 -25 658 -15Q658 -11 663 1Q673 24 685 46T707 83T725 109T739 126L744 132Q744 133 500 133Q255 133 255 132L260 126Q265 121 273 110T292 84T314 47T336 1Q341 -11 341 -15Q341 -25 319 -25Q312 -24 309 -23T304 -19T298 -7Q233 141 97 213Q83 221 70 227T51 235T41 239T35 243T34 250T35 256T40 261T51 265T70 273T97 287Q235 363 299 509Q305 522 308 524ZM792 319L783 327H216Q183 294 120 256L110 250L120 244Q173 212 207 181L216 173H783L792 181Q826 212 879 244L889 250L879 256Q826 288 792 319Z"></path></g><g data-mml-node="mi" transform="translate(7158,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7964.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9020.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),JQ=[SQ],GQ=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},"⇔"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),AQ={class:"MathJax",jax:"SVG",style:{position:"relative"}},EQ={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.159ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 2280.3 888","aria-hidden":"true"},FQ=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),OQ=[FQ],RQ=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b"),Q("mo",null,","),Q("mi",null,"c")])],-1),PQ=Q("h2",{id:"自然数的序",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#自然数的序"},[Q("span",null,"自然数的序")])],-1),XQ=Q("p",null,"自然数的序为两个自然数的关系。",-1),NQ=Q("h3",{id:"序的定义",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#序的定义"},[Q("span",null,"序的定义")])],-1),KQ={class:"MathJax",jax:"SVG",style:{position:"relative"}},IQ={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.361ex",height:"1.751ex",role:"img",focusable:"false",viewBox:"0 -636 2811.6 774","aria-hidden":"true"},qQ=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(877.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1933.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),UQ=[qQ],WQ=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"≤"),Q("mi",null,"m")])],-1),YQ={class:"MathJax",jax:"SVG",style:{position:"relative"}},$Q={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.294ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 572 453","aria-hidden":"true"},Qa=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D465",d:"M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"})])])],-1),aa=[Qa],ta=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"x")])],-1),Ta={class:"MathJax",jax:"SVG",style:{position:"relative"}},ma={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.421ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 4606 665","aria-hidden":"true"},na=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(877.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1933.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3033.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></g></g></g>',1),la=[na],ea=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"x")])],-1),sa={class:"MathJax",jax:"SVG",style:{position:"relative"}},oa={style:{"vertical-align":"-0.09ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.361ex",height:"1.312ex",role:"img",focusable:"false",viewBox:"0 -540 2811.6 580","aria-hidden":"true"},ra=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(877.8,0)"><path data-c="3C" d="M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z"></path></g><g data-mml-node="mi" transform="translate(1933.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),da=[ra],ha=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"<"),Q("mi",null,"m")])],-1),ia={class:"MathJax",jax:"SVG",style:{position:"relative"}},ga={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.361ex",height:"1.751ex",role:"img",focusable:"false",viewBox:"0 -636 2811.6 774","aria-hidden":"true"},Ha=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(877.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1933.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),La=[Ha],ca=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"≤"),Q("mi",null,"m")])],-1),pa={class:"MathJax",jax:"SVG",style:{position:"relative"}},fa={style:{"vertical-align":"-0.486ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.361ex",height:"2.106ex",role:"img",focusable:"false",viewBox:"0 -716 2811.6 931","aria-hidden":"true"},Ma=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(877.8,0)"><path data-c="2260" d="M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z"></path></g><g data-mml-node="mi" transform="translate(1933.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),ua=[Ma],xa=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"≠"),Q("mi",null,"m")])],-1),Za=Q("p",null,"自然数的序是全序关系，它应该具有反对称性、传递性和完全性。",-1),Va=Q("h3",{id:"正自然数",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#正自然数"},[Q("span",null,"正自然数")])],-1),wa=Q("p",null,"在考察序的性质之前，我们预先准备以方便证明。",-1),_a={class:"MathJax",jax:"SVG",style:{position:"relative"}},va={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 500 688","aria-hidden":"true"},ya=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"30",d:"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"})])])],-1),Da=[ya],ba=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0")])],-1),ja=Q("h4",{id:"正自然数的性质",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#正自然数的性质"},[Q("span",null,"正自然数的性质")])],-1),Ba={class:"MathJax",jax:"SVG",style:{position:"relative"}},ka={style:{"vertical-align":"-0.023ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.197ex",height:"1.02ex",role:"img",focusable:"false",viewBox:"0 -441 529 451","aria-hidden":"true"},Ca=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D44E",d:"M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"})])])],-1),za=[Ca],Sa=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a")])],-1),Ja={class:"MathJax",jax:"SVG",style:{position:"relative"}},Ga={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.971ex",height:"1.595ex",role:"img",focusable:"false",viewBox:"0 -694 429 705","aria-hidden":"true"},Aa=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D44F",d:"M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"})])])],-1),Ea=[Aa],Fa=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b")])],-1),Oa={class:"MathJax",jax:"SVG",style:{position:"relative"}},Ra={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.933ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 2180.4 776","aria-hidden":"true"},Pa=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),Xa=[Pa],Na=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b")])],-1),Ka={class:"MathJax",jax:"SVG",style:{position:"relative"}},Ia={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.119ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 2262.6 776","aria-hidden":"true"},qa=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1762.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),Ua=[qa],Wa=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"="),Q("mn",null,"0")])],-1),Ya={class:"MathJax",jax:"SVG",style:{position:"relative"}},$a={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.308ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 4114 748","aria-hidden":"true"},Qt=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(1751.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2529.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3585,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g></g></g>',1),at=[Qt],tt=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mo",null,"="),Q("mi",null,"a")])],-1),Tt={class:"MathJax",jax:"SVG",style:{position:"relative"}},mt={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.971ex",height:"1.595ex",role:"img",focusable:"false",viewBox:"0 -694 429 705","aria-hidden":"true"},nt=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D44F",d:"M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"})])])],-1),lt=[nt],et=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b")])],-1),st={class:"MathJax",jax:"SVG",style:{position:"relative"}},ot={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.933ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 2180.4 776","aria-hidden":"true"},rt=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),dt=[rt],ht=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b")])],-1),it={class:"MathJax",jax:"SVG",style:{position:"relative"}},gt={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.711ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10038.4 1000","aria-hidden":"true"},Ht=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(3963.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4630.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5686,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7080,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7469,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(8220.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9220.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(9649.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Lt=[Ht],ct=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")")])],-1),pt={class:"MathJax",jax:"SVG",style:{position:"relative"}},ft={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.847ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4352.4 1000","aria-hidden":"true"},Mt=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2534.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(3963.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),ut=[Mt],xt=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")")])],-1),Zt={class:"MathJax",jax:"SVG",style:{position:"relative"}},Vt={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.847ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4352.4 1000","aria-hidden":"true"},wt=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(3963.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),_t=[wt],vt=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")")])],-1),yt=Q("p",null,"根据 Peano 公理 Ⅴ，正自然数与自然数相加为正自然数。",-1),Dt=Q("h3",{id:"序的反对称性",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#序的反对称性"},[Q("span",null,"序的反对称性")])],-1),bt={class:"MathJax",jax:"SVG",style:{position:"relative"}},jt={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 832","aria-hidden":"true"},Bt=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),kt=[Bt],Ct=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≤"),Q("mi",null,"b")])],-1),zt={class:"MathJax",jax:"SVG",style:{position:"relative"}},St={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 832","aria-hidden":"true"},Jt=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g></g></g>',1),Gt=[Jt],At=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"≤"),Q("mi",null,"a")])],-1),Et={class:"MathJax",jax:"SVG",style:{position:"relative"}},Ft={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 776","aria-hidden":"true"},Ot=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),Rt=[Ot],Pt=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),Xt={class:"MathJax",jax:"SVG",style:{position:"relative"}},Nt={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 832","aria-hidden":"true"},Kt=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),It=[Kt],qt=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≤"),Q("mi",null,"b")])],-1),Ut={class:"MathJax",jax:"SVG",style:{position:"relative"}},Wt={style:{"vertical-align":"-0.339ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.924ex",height:"1.91ex",role:"img",focusable:"false",viewBox:"0 -694 4828.6 844","aria-hidden":"true"},Yt=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(3514,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g></g></g>',1),$t=[Yt],QT=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"1")])])],-1),aT={class:"MathJax",jax:"SVG",style:{position:"relative"}},tT={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 832","aria-hidden":"true"},TT=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g></g></g>',1),mT=[TT],nT=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"≤"),Q("mi",null,"a")])],-1),lT={class:"MathJax",jax:"SVG",style:{position:"relative"}},eT={style:{"vertical-align":"-0.339ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.924ex",height:"1.91ex",role:"img",focusable:"false",viewBox:"0 -694 4828.6 844","aria-hidden":"true"},sT=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(3514,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g></g></g>',1),oT=[sT],rT=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"2")])])],-1),dT={class:"MathJax",jax:"SVG",style:{position:"relative"}},hT={style:{"vertical-align":"-0.339ex"},xmlns:"http://www.w3.org/2000/svg",width:"34.729ex",height:"1.91ex",role:"img",focusable:"false",viewBox:"0 -694 15350.1 844","aria-hidden":"true"},iT=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2529.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3585,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4391.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5447.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6098.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(7099,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g><g data-mml-node="mo" transform="translate(8691.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9747.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(10498.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(11498.6,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g><g data-mml-node="mo" transform="translate(13035.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(14035.6,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g></g></g>',1),gT=[iT],HT=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"2")]),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"1")]),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"2")])])],-1),LT={class:"MathJax",jax:"SVG",style:{position:"relative"}},cT={style:{"vertical-align":"-0.339ex"},xmlns:"http://www.w3.org/2000/svg",width:"12.862ex",height:"1.846ex",role:"img",focusable:"false",viewBox:"0 -666 5685.1 816","aria-hidden":"true"},pT=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g><g data-mml-node="mo" transform="translate(1536.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(2537,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g><g data-mml-node="mo" transform="translate(4129.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(5185.1,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),fT=[pT],MT=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"1")]),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"2")]),Q("mo",null,"="),Q("mn",null,"0")])],-1),uT={class:"MathJax",jax:"SVG",style:{position:"relative"}},xT={style:{"vertical-align":"-0.339ex"},xmlns:"http://www.w3.org/2000/svg",width:"13.114ex",height:"1.846ex",role:"img",focusable:"false",viewBox:"0 -666 5796.2 816","aria-hidden":"true"},ZT=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g><g data-mml-node="mo" transform="translate(1592.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="msub" transform="translate(2648.1,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g><g data-mml-node="mo" transform="translate(4240.4,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(5296.2,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),VT=[ZT],wT=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"1")]),Q("mo",null,"="),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"2")]),Q("mo",null,"="),Q("mn",null,"0")])],-1),_T={class:"MathJax",jax:"SVG",style:{position:"relative"}},vT={style:{"vertical-align":"-0.339ex"},xmlns:"http://www.w3.org/2000/svg",width:"23.249ex",height:"1.91ex",role:"img",focusable:"false",viewBox:"0 -694 10276.1 844","aria-hidden":"true"},yT=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2613.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(3614,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(4391.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5447.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6198.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(7199,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g><g data-mml-node="mo" transform="translate(8791.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9847.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),DT=[yT],bT=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"1")]),Q("mo",null,"="),Q("mi",null,"b")])],-1),jT=Q("h3",{id:"序的传递性",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#序的传递性"},[Q("span",null,"序的传递性")])],-1),BT={class:"MathJax",jax:"SVG",style:{position:"relative"}},kT={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 832","aria-hidden":"true"},CT=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),zT=[CT],ST=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≤"),Q("mi",null,"b")])],-1),JT={class:"MathJax",jax:"SVG",style:{position:"relative"}},GT={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.967ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2195.6 832","aria-hidden":"true"},AT=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),ET=[AT],FT=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"≤"),Q("mi",null,"c")])],-1),OT={class:"MathJax",jax:"SVG",style:{position:"relative"}},RT={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.194ex",height:"1.751ex",role:"img",focusable:"false",viewBox:"0 -636 2295.6 774","aria-hidden":"true"},PT=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),XT=[PT],NT=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≤"),Q("mi",null,"c")])],-1),KT={class:"MathJax",jax:"SVG",style:{position:"relative"}},IT={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 832","aria-hidden":"true"},qT=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),UT=[qT],WT=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≤"),Q("mi",null,"b")])],-1),YT={class:"MathJax",jax:"SVG",style:{position:"relative"}},$T={style:{"vertical-align":"-0.339ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.924ex",height:"1.91ex",role:"img",focusable:"false",viewBox:"0 -694 4828.6 844","aria-hidden":"true"},Qm=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(3514,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g></g></g>',1),am=[Qm],tm=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"1")])])],-1),Tm={class:"MathJax",jax:"SVG",style:{position:"relative"}},mm={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.967ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2195.6 832","aria-hidden":"true"},nm=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),lm=[nm],em=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"≤"),Q("mi",null,"c")])],-1),sm={class:"MathJax",jax:"SVG",style:{position:"relative"}},om={style:{"vertical-align":"-0.339ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.707ex",height:"1.91ex",role:"img",focusable:"false",viewBox:"0 -694 4732.6 844","aria-hidden":"true"},rm=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1766.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2417.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(3418,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g></g></g>',1),dm=[rm],hm=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"2")])])],-1),im={class:"MathJax",jax:"SVG",style:{position:"relative"}},gm={style:{"vertical-align":"-0.339ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.714ex",height:"1.658ex",role:"img",focusable:"false",viewBox:"0 -583 3851.6 733","aria-hidden":"true"},Hm=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g><g data-mml-node="mo" transform="translate(1536.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(2537,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g></g></g>',1),Lm=[Hm],cm=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"1")]),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"2")])])],-1),pm={class:"MathJax",jax:"SVG",style:{position:"relative"}},fm={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"45.615ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 20161.7 1000","aria-hidden":"true"},Mm=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1766.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2417.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(3418,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g><g data-mml-node="mo" transform="translate(5010.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(6066.1,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6455.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7206.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(8206.6,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g><g data-mml-node="mo" transform="translate(9521.1,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(10132.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(11132.6,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g><g data-mml-node="mo" transform="translate(12724.9,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(13780.7,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(14531.9,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(15532.1,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="msub" transform="translate(15921.1,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g><g data-mml-node="mo" transform="translate(17457.9,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(18458.1,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g><g data-mml-node="mo" transform="translate(19772.7,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),um=[Mm],xm=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"2")]),Q("mo",null,"="),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"1")]),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"2")]),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mo",{stretchy:"false"},"("),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"1")]),Q("mo",null,"+"),Q("msub",null,[Q("mi",null,"m"),Q("mn",null,"2")]),Q("mo",{stretchy:"false"},")")])],-1),Zm={class:"MathJax",jax:"SVG",style:{position:"relative"}},Vm={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.194ex",height:"1.751ex",role:"img",focusable:"false",viewBox:"0 -636 2295.6 774","aria-hidden":"true"},wm=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),_m=[wm],vm=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≤"),Q("mi",null,"c")])],-1),ym=Q("h3",{id:"序的完全性",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#序的完全性"},[Q("span",null,"序的完全性")])],-1),Dm={class:"MathJax",jax:"SVG",style:{position:"relative"}},bm={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"3.173ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 1402.7 888","aria-hidden":"true"},jm=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),Bm=[jm],km=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b")])],-1),Cm={class:"MathJax",jax:"SVG",style:{position:"relative"}},zm={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"3.173ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 1402.7 888","aria-hidden":"true"},Sm=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),Jm=[Sm],Gm=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b")])],-1),Am={class:"MathJax",jax:"SVG",style:{position:"relative"}},Em={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.119ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 2262.6 776","aria-hidden":"true"},Fm=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1762.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),Om=[Fm],Rm=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"="),Q("mn",null,"0")])],-1),Pm={class:"MathJax",jax:"SVG",style:{position:"relative"}},Xm={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"17.258ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 7628 776","aria-hidden":"true"},Nm=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1862.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2584.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3585,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4391.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5447.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6098.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7099,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g></g></g>',1),Km=[Nm],Im=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"a")])],-1),qm={class:"MathJax",jax:"SVG",style:{position:"relative"}},Um={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 832","aria-hidden":"true"},Wm=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),Ym=[Wm],$m=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≤"),Q("mi",null,"b")])],-1),Qn={class:"MathJax",jax:"SVG",style:{position:"relative"}},an={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.971ex",height:"1.595ex",role:"img",focusable:"false",viewBox:"0 -694 429 705","aria-hidden":"true"},tn=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D44F",d:"M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"})])])],-1),Tn=[tn],mn=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b")])],-1),nn={class:"MathJax",jax:"SVG",style:{position:"relative"}},ln={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 776","aria-hidden":"true"},en=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),sn=[en],on=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),rn={class:"MathJax",jax:"SVG",style:{position:"relative"}},dn={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"18.91ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 8358 1000","aria-hidden":"true"},hn=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2212,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(2878.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3934.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4685.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5686,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7080,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(7469,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(7969,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),gn=[hn],Hn=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")")])],-1),Ln={class:"MathJax",jax:"SVG",style:{position:"relative"}},cn={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.099ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4463.6 1000","aria-hidden":"true"},pn=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3C" d="M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3256.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3645.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4074.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),fn=[pn],Mn=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"<"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")")])],-1),un={class:"MathJax",jax:"SVG",style:{position:"relative"}},xn={style:{"vertical-align":"-0.09ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.661ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 734","aria-hidden":"true"},Zn=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3C" d="M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),Vn=[Zn],wn=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"<"),Q("mi",null,"b")])],-1),_n={class:"MathJax",jax:"SVG",style:{position:"relative"}},vn={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"36.234ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 16015.4 1000","aria-hidden":"true"},yn=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2212,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(2878.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3934.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4585.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5586,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6980,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(7369,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(7869,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(8535.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9591.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(10242.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(11243,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(12343.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(13343.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(14737.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(15126.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(15626.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Dn=[yn],bn=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")")])],-1),jn={class:"MathJax",jax:"SVG",style:{position:"relative"}},Bn={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.099ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4463.6 1000","aria-hidden":"true"},kn=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3C" d="M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3256.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3645.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4074.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Cn=[kn],zn=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"<"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")")])],-1),Sn={class:"MathJax",jax:"SVG",style:{position:"relative"}},Jn={style:{"vertical-align":"-0.09ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.661ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 734","aria-hidden":"true"},Gn=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3E" d="M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),An=[Gn],En=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,">"),Q("mi",null,"b")])],-1),Fn={class:"MathJax",jax:"SVG",style:{position:"relative"}},On={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.099ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4463.6 1000","aria-hidden":"true"},Rn=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2265" d="M83 616Q83 624 89 630T99 636Q107 636 253 568T543 431T687 361Q694 356 694 346T687 331Q685 329 395 192L107 56H101Q83 58 83 76Q83 77 83 79Q82 86 98 95Q117 105 248 167Q326 204 378 228L626 346L360 472Q291 505 200 548Q112 589 98 597T83 616ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3256.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3645.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4074.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Pn=[Rn],Xn=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≥"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")")])],-1),Nn={class:"MathJax",jax:"SVG",style:{position:"relative"}},Kn={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"3.173ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 1402.7 888","aria-hidden":"true"},In=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),qn=[In],Un=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b")])],-1),Wn=Q("h3",{id:"加法保序性",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#加法保序性"},[Q("span",null,"加法保序性")])],-1),Yn={class:"MathJax",jax:"SVG",style:{position:"relative"}},$n={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 832","aria-hidden":"true"},Ql=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),al=[Ql],tl=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≤"),Q("mi",null,"b")])],-1),Tl={class:"MathJax",jax:"SVG",style:{position:"relative"}},ml={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"12.675ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 5602.4 832","aria-hidden":"true"},nl=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),ll=[nl],el=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"≤"),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c")])],-1),sl={class:"MathJax",jax:"SVG",style:{position:"relative"}},ol={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 832","aria-hidden":"true"},rl=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),dl=[rl],hl=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≤"),Q("mi",null,"b")])],-1),il={class:"MathJax",jax:"SVG",style:{position:"relative"}},gl={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 4392 776","aria-hidden":"true"},Hl=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3514,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Ll=[Hl],cl=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"m")])],-1),pl={class:"MathJax",jax:"SVG",style:{position:"relative"}},fl={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"46.371ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 20495.8 1000","aria-hidden":"true"},Ml=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(651.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1651.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2362.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(3418,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3807,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4558.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5558.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6436.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7047.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(8047.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(8758.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9814.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(10565.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(11565.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(12666.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(13666.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(14377.1,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(15432.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(15821.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(16573.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(17573.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(18006.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(18617.6,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(19617.8,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),ul=[Ml],xl=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"="),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"m")])],-1),Zl={class:"MathJax",jax:"SVG",style:{position:"relative"}},Vl={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"12.675ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 5602.4 832","aria-hidden":"true"},wl=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),_l=[wl],vl=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"c"),Q("mo",null,"≤"),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"c")])],-1),yl=Q("h2",{id:"自然数的乘法运算",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#自然数的乘法运算"},[Q("span",null,"自然数的乘法运算")])],-1),Dl=Q("p",null,"自然数的乘法也十分重要。",-1),bl=Q("h3",{id:"乘法的定义",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#乘法的定义"},[Q("span",null,"乘法的定义")])],-1),jl=Q("p",null,"定义乘法的运算规则：",-1),Bl={class:"MathJax",jax:"SVG",style:{position:"relative"}},kl={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Cl=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),zl=[Cl],Sl=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),Jl={class:"MathJax",jax:"SVG",style:{position:"relative"}},Gl={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.254ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 2322.4 688","aria-hidden":"true"},Al=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),El=[Al],Fl=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),Ol={class:"MathJax",jax:"SVG",style:{position:"relative"}},Rl={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 500 688","aria-hidden":"true"},Pl=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"30",d:"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"})])])],-1),Xl=[Pl],Nl=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0")])],-1),Kl={class:"MathJax",jax:"SVG",style:{position:"relative"}},Il={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.403ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 4156 748","aria-hidden":"true"},ql=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(3656,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),Ul=[ql],Wl=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"="),Q("mn",null,"0")])],-1),Yl={class:"MathJax",jax:"SVG",style:{position:"relative"}},$l={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.35ex",height:"1.439ex",role:"img",focusable:"false",viewBox:"0 -442 1922.7 636","aria-hidden":"true"},Qe=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),ae=[Qe],te=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"m")])],-1),Te={class:"MathJax",jax:"SVG",style:{position:"relative"}},me={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"24.274ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10728.9 1000","aria-hidden":"true"},ne=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7306.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8306.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9128.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10128.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),le=[ne],ee=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),se=Q("p",null,"下面我们需要证明对于任意两个自然数，都可以进行乘法运算，也就是说，我们需要证明乘法结果的存在性和唯一性。",-1),oe=Q("h4",{id:"乘法结果的存在性",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#乘法结果的存在性"},[Q("span",null,"乘法结果的存在性")])],-1),re={class:"MathJax",jax:"SVG",style:{position:"relative"}},de={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},he=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),ie=[he],ge=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),He={class:"MathJax",jax:"SVG",style:{position:"relative"}},Le={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},ce=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),pe=[ce],fe=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),Me={class:"MathJax",jax:"SVG",style:{position:"relative"}},ue={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.136ex",role:"img",focusable:"false",viewBox:"0 -491 2700.4 502","aria-hidden":"true"},xe=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Ze=[xe],Ve=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),we={class:"MathJax",jax:"SVG",style:{position:"relative"}},_e={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.136ex",role:"img",focusable:"false",viewBox:"0 -491 2700.4 502","aria-hidden":"true"},ve=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),ye=[ve],De=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),be={class:"MathJax",jax:"SVG",style:{position:"relative"}},je={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Be=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),ke=[Be],Ce=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),ze={class:"MathJax",jax:"SVG",style:{position:"relative"}},Se={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.403ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 4156 748","aria-hidden":"true"},Je=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(3656,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),Ge=[Je],Ae=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"="),Q("mn",null,"0")])],-1),Ee={class:"MathJax",jax:"SVG",style:{position:"relative"}},Fe={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.254ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 2322.4 688","aria-hidden":"true"},Oe=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Re=[Oe],Pe=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),Xe={class:"MathJax",jax:"SVG",style:{position:"relative"}},Ne={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.177ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2288.3 1000","aria-hidden":"true"},Ke=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(1399.3,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(1899.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Ie=[Ke],qe=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")")])],-1),Ue={class:"MathJax",jax:"SVG",style:{position:"relative"}},We={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Ye=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),$e=[Ye],Qs=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),as={class:"MathJax",jax:"SVG",style:{position:"relative"}},ts={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.136ex",role:"img",focusable:"false",viewBox:"0 -491 2700.4 502","aria-hidden":"true"},Ts=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),ms=[Ts],ns=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),ls={class:"MathJax",jax:"SVG",style:{position:"relative"}},es={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.233ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 4522.9 665","aria-hidden":"true"},ss=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2922.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3922.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),os=[ss],rs=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),ds={class:"MathJax",jax:"SVG",style:{position:"relative"}},hs={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"24.274ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10728.9 1000","aria-hidden":"true"},is=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7306.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8306.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9128.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10128.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),gs=[is],Hs=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),Ls={class:"MathJax",jax:"SVG",style:{position:"relative"}},cs={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.024ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4872.4 1000","aria-hidden":"true"},ps=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),fs=[ps],Ms=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),us={class:"MathJax",jax:"SVG",style:{position:"relative"}},xs={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.136ex",role:"img",focusable:"false",viewBox:"0 -491 2700.4 502","aria-hidden":"true"},Zs=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Vs=[Zs],ws=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),_s={class:"MathJax",jax:"SVG",style:{position:"relative"}},vs={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.024ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4872.4 1000","aria-hidden":"true"},ys=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Ds=[ys],bs=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),js={class:"MathJax",jax:"SVG",style:{position:"relative"}},Bs={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},ks=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Cs=[ks],zs=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),Ss={class:"MathJax",jax:"SVG",style:{position:"relative"}},Js={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.946ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4838.3 1000","aria-hidden":"true"},Gs=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2793.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3182.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4060.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4449.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),As=[Gs],Es=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")")])],-1),Fs={class:"MathJax",jax:"SVG",style:{position:"relative"}},Os={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},Rs=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Ps=[Rs],Xs=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),Ns={class:"MathJax",jax:"SVG",style:{position:"relative"}},Ks={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.986ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 878 453","aria-hidden":"true"},Is=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45A",d:"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"})])])],-1),qs=[Is],Us=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m")])],-1),Ws={class:"MathJax",jax:"SVG",style:{position:"relative"}},Ys={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},$s=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Qo=[$s],ao=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),to={class:"MathJax",jax:"SVG",style:{position:"relative"}},To={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.136ex",role:"img",focusable:"false",viewBox:"0 -491 2700.4 502","aria-hidden":"true"},mo=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),no=[mo],lo=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),eo={class:"MathJax",jax:"SVG",style:{position:"relative"}},so={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},oo=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),ro=[oo],ho=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),io={class:"MathJax",jax:"SVG",style:{position:"relative"}},go={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.35ex",height:"1.439ex",role:"img",focusable:"false",viewBox:"0 -442 1922.7 636","aria-hidden":"true"},Ho=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Lo=[Ho],co=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"m")])],-1),po={class:"MathJax",jax:"SVG",style:{position:"relative"}},fo={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.136ex",role:"img",focusable:"false",viewBox:"0 -491 2700.4 502","aria-hidden":"true"},Mo=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),uo=[Mo],xo=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),Zo=Q("h4",{id:"乘法结果的唯一性",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#乘法结果的唯一性"},[Q("span",null,"乘法结果的唯一性")])],-1),Vo={class:"MathJax",jax:"SVG",style:{position:"relative"}},wo={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},_o=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),vo=[_o],yo=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),Do={class:"MathJax",jax:"SVG",style:{position:"relative"}},bo={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},jo=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Bo=[jo],ko=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),Co={class:"MathJax",jax:"SVG",style:{position:"relative"}},zo={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.136ex",role:"img",focusable:"false",viewBox:"0 -491 2700.4 502","aria-hidden":"true"},So=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Jo=[So],Go=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),Ao={class:"MathJax",jax:"SVG",style:{position:"relative"}},Eo={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.136ex",role:"img",focusable:"false",viewBox:"0 -491 2700.4 502","aria-hidden":"true"},Fo=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Oo=[Fo],Ro=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),Po={class:"MathJax",jax:"SVG",style:{position:"relative"}},Xo={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},No=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),Ko=[No],Io=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),qo={class:"MathJax",jax:"SVG",style:{position:"relative"}},Uo={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.403ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 4156 748","aria-hidden":"true"},Wo=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(3656,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),Yo=[Wo],$o=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"="),Q("mn",null,"0")])],-1),Qr={class:"MathJax",jax:"SVG",style:{position:"relative"}},ar={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.254ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 2322.4 688","aria-hidden":"true"},tr=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Tr=[tr],mr=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),nr={class:"MathJax",jax:"SVG",style:{position:"relative"}},lr={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 500 688","aria-hidden":"true"},er=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"30",d:"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"})])])],-1),sr=[er],or=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0")])],-1),rr={class:"MathJax",jax:"SVG",style:{position:"relative"}},dr={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.177ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2288.3 1000","aria-hidden":"true"},hr=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(1399.3,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(1899.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),ir=[hr],gr=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")")])],-1),Hr={class:"MathJax",jax:"SVG",style:{position:"relative"}},Lr={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.986ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 878 453","aria-hidden":"true"},cr=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45A",d:"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"})])])],-1),pr=[cr],fr=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m")])],-1),Mr={class:"MathJax",jax:"SVG",style:{position:"relative"}},ur={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.136ex",role:"img",focusable:"false",viewBox:"0 -491 2700.4 502","aria-hidden":"true"},xr=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Zr=[xr],Vr=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),wr={class:"MathJax",jax:"SVG",style:{position:"relative"}},_r={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.233ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 4522.9 665","aria-hidden":"true"},vr=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2922.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3922.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),yr=[vr],Dr=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),br={class:"MathJax",jax:"SVG",style:{position:"relative"}},jr={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"24.274ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10728.9 1000","aria-hidden":"true"},Br=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7306.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8306.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9128.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10128.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),kr=[Br],Cr=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"n")])],-1),zr={class:"MathJax",jax:"SVG",style:{position:"relative"}},Sr={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.024ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4872.4 1000","aria-hidden":"true"},Jr=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Gr=[Jr],Ar=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),Er={class:"MathJax",jax:"SVG",style:{position:"relative"}},Fr={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.136ex",role:"img",focusable:"false",viewBox:"0 -491 2700.4 502","aria-hidden":"true"},Or=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Rr=[Or],Pr=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),Xr={class:"MathJax",jax:"SVG",style:{position:"relative"}},Nr={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.024ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4872.4 1000","aria-hidden":"true"},Kr=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Ir=[Kr],qr=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),Ur={class:"MathJax",jax:"SVG",style:{position:"relative"}},Wr={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},Yr=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),$r=[Yr],Qd=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),ad={class:"MathJax",jax:"SVG",style:{position:"relative"}},td={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.946ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4838.3 1000","aria-hidden":"true"},Td=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2793.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3182.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4060.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4449.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),md=[Td],nd=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")")])],-1),ld={class:"MathJax",jax:"SVG",style:{position:"relative"}},ed={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},sd=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),od=[sd],rd=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),dd={class:"MathJax",jax:"SVG",style:{position:"relative"}},hd={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.986ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 878 453","aria-hidden":"true"},id=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45A",d:"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"})])])],-1),gd=[id],Hd=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m")])],-1),Ld={class:"MathJax",jax:"SVG",style:{position:"relative"}},cd={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.032ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2666.3 1000","aria-hidden":"true"},pd=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),fd=[pd],Md=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"p"),Q("mi",null,"n")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),ud={class:"MathJax",jax:"SVG",style:{position:"relative"}},xd={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.136ex",role:"img",focusable:"false",viewBox:"0 -491 2700.4 502","aria-hidden":"true"},Zd=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Vd=[Zd],wd=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),_d={class:"MathJax",jax:"SVG",style:{position:"relative"}},vd={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},yd=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),Dd=[yd],bd=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),jd={class:"MathJax",jax:"SVG",style:{position:"relative"}},Bd={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.35ex",height:"1.439ex",role:"img",focusable:"false",viewBox:"0 -442 1922.7 636","aria-hidden":"true"},kd=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Cd=[kd],zd=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"m")])],-1),Sd={class:"MathJax",jax:"SVG",style:{position:"relative"}},Jd={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.11ex",height:"1.136ex",role:"img",focusable:"false",viewBox:"0 -491 2700.4 502","aria-hidden":"true"},Gd=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Ad=[Gd],Ed=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),Fd=Q("h3",{id:"乘法的性质",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#乘法的性质"},[Q("span",null,"乘法的性质")])],-1),Od=Q("p",null,"在明确证明了自然数乘法运算的良好性质，即任意两个自然数都可以进行乘法运算，且乘法运算的结果存在且唯一之后，我们终于可以对自然数乘法的性质进行进一步的探索。",-1),Rd=Q("h4",{id:"乘法交换律",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#乘法交换律"},[Q("span",null,"乘法交换律")])],-1),Pd={class:"MathJax",jax:"SVG",style:{position:"relative"}},Xd={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.35ex",height:"1.439ex",role:"img",focusable:"false",viewBox:"0 -442 1922.7 636","aria-hidden":"true"},Nd=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Kd=[Nd],Id=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"m")])],-1),qd={class:"MathJax",jax:"SVG",style:{position:"relative"}},Ud={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.236ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 6734.4 665","aria-hidden":"true"},Wd=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Yd=[Wd],$d=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),Qh=Q("p",null,"直接证明比较困难，考虑从乘法运算的定义下手，即先证明乘法的两条运算规则符合交换律。",-1),ah={class:"MathJax",jax:"SVG",style:{position:"relative"}},th={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"17.674ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 7812 748","aria-hidden":"true"},Th=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(3656,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(4433.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5489.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6311.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(7312,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),mh=[Th],nh=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mn",null,"0")])],-1),lh={class:"MathJax",jax:"SVG",style:{position:"relative"}},eh={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"17.222ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 7612 748","aria-hidden":"true"},sh=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(1722.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2500.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(3556,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(4333.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(5389.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(6111.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(7112,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),oh=[sh],rh=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"×"),Q("mn",null,"0"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"×"),Q("mn",null,"0")])],-1),dh={class:"MathJax",jax:"SVG",style:{position:"relative"}},hh={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},ih=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),gh=[ih],Hh=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),Lh={class:"MathJax",jax:"SVG",style:{position:"relative"}},ch={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"17.674ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 7812 748","aria-hidden":"true"},ph=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(3656,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(4433.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5489.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6311.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(7312,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),fh=[ph],Mh=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mn",null,"0")])],-1),uh={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},xh={style:{"vertical-align":"-4.977ex"},xmlns:"http://www.w3.org/2000/svg",width:"47.524ex",height:"11.086ex",role:"img",focusable:"false",viewBox:"0 -2700 21005.4 4900","aria-hidden":"true"},Zh=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1950)"><g data-mml-node="mtd"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3116.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3505.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4105.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(1833.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13322.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,650)"><g data-mml-node="mtd" transform="translate(4494.4,0)"></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2155.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(3156,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(3656,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(16016.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(777.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1833.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2655.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(3656,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-650)"><g data-mml-node="mtd" transform="translate(4494.4,0)"></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2155.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(3156,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(3878.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(4878.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(5378.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13322.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1950)"><g data-mml-node="mtd" transform="translate(4494.4,0)"></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3716.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4327.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(5328,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(5828,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13322.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),Vh=[Zh],wh=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mn",null,"0"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mn",null,"0")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mn",null,"0"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])])])])],-1),_h={class:"MathJax",jax:"SVG",style:{position:"relative"}},vh={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"17.674ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 7812 748","aria-hidden":"true"},yh=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(3656,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(4433.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5489.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6311.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(7312,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),Dh=[yh],bh=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mn",null,"0")])],-1),jh={class:"MathJax",jax:"SVG",style:{position:"relative"}},Bh={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},kh=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),Ch=[kh],zh=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),Sh={class:"MathJax",jax:"SVG",style:{position:"relative"}},Jh={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"24.902ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 11006.9 1000","aria-hidden":"true"},Gh=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7306.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8306.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9128.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10128.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Ah=[Gh],Eh=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m")])],-1),Fh={class:"MathJax",jax:"SVG",style:{position:"relative"}},Oh={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.135ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2711.6 748","aria-hidden":"true"},Rh=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1155.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(2211.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),Ph=[Rh],Xh=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"="),Q("mn",null,"0")])],-1),Nh={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},Kh={style:{"vertical-align":"-6.448ex"},xmlns:"http://www.w3.org/2000/svg",width:"49.072ex",height:"14.027ex",role:"img",focusable:"false",viewBox:"0 -3350 21689.9 6200","aria-hidden":"true"},Ih=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,2600)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2055.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3056,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4450,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4839,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5439,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5828,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18145.3,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1155.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(2211.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd" transform="translate(4872.4,0)"></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(1833.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14006.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(4872.4,0)"></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2055.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3056,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mstyle" transform="translate(3656,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14006.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(4872.4,0)"></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2055.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3056,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3878.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(4878.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(5378.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14006.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-2600)"><g data-mml-node="mtd" transform="translate(4872.4,0)"></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2433.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3434,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4256.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5256.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mstyle" transform="translate(6134.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18145.3,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1155.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(2211.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g></g></g></g>',1),qh=[Ih],Uh=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"m"),Q("mo",null,"="),Q("mn",null,"0")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"m"),Q("mo",null,"="),Q("mn",null,"0")])])])])])],-1),Wh={class:"MathJax",jax:"SVG",style:{position:"relative"}},Yh={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.986ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 878 453","aria-hidden":"true"},$h=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45A",d:"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"})])])],-1),Qi=[$h],ai=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m")])],-1),ti={class:"MathJax",jax:"SVG",style:{position:"relative"}},Ti={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"24.902ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 11006.9 1000","aria-hidden":"true"},mi=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7306.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8306.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9128.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10128.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),ni=[mi],li=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m")])],-1),ei={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},si={style:{"vertical-align":"-6.448ex"},xmlns:"http://www.w3.org/2000/svg",width:"63.814ex",height:"14.027ex",role:"img",focusable:"false",viewBox:"0 -3350 28205.9 6200","aria-hidden":"true"},oi=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,2600)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(5666.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6055.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6655.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2433.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3434,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4828,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5217,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5817,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6428.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7428.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8822.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9211.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9811.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(10200.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(20522.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd" transform="translate(7044.4,0)"></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2433.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3434,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4256.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5256.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6356.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7356.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8750.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9139.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9739.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(10128.9,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(22572,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2922.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3922.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(7044.4,0)"></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2433.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3434,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4256.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5256.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6650.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7039.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7917.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(8528.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9528.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mstyle" transform="translate(10128.9,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(20522.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(7044.4,0)"></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2433.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3434,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4256.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5256.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6078.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7078.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8472.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8861.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9739.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(10128.9,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(22372.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">交</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">换</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">律</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-2600)"><g data-mml-node="mtd" transform="translate(7044.4,0)"></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3994.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4605.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5606,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6428.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7428.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8822.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9211.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10089.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(10478.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(20522.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),ri=[oi],di=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法交换律")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])])])])],-1),hi={class:"MathJax",jax:"SVG",style:{position:"relative"}},ii={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"24.902ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 11006.9 1000","aria-hidden":"true"},gi=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7306.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8306.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9128.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10128.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Hi=[gi],Li=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m")])],-1),ci={class:"MathJax",jax:"SVG",style:{position:"relative"}},pi={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.35ex",height:"1.439ex",role:"img",focusable:"false",viewBox:"0 -442 1922.7 636","aria-hidden":"true"},fi=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Mi=[fi],ui=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"m")])],-1),xi=Q("strong",null,"乘法运算规则 Ⅱ",-1),Zi={class:"MathJax",jax:"SVG",style:{position:"relative"}},Vi={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.236ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 6734.4 665","aria-hidden":"true"},wi=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),_i=[wi],vi=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),yi={class:"MathJax",jax:"SVG",style:{position:"relative"}},Di={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.506ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2433.6 748","aria-hidden":"true"},bi=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(877.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1933.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),ji=[bi],Bi=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"="),Q("mn",null,"0")])],-1),ki={class:"MathJax",jax:"SVG",style:{position:"relative"}},Ci={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"14.784ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 6534.4 748","aria-hidden":"true"},zi=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2878.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3934,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5034.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(6034.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),Si=[zi],Ji=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mn",null,"0")])],-1),Gi={class:"MathJax",jax:"SVG",style:{position:"relative"}},Ai={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Ei=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),Fi=[Ei],Oi=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),Ri={class:"MathJax",jax:"SVG",style:{position:"relative"}},Pi={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.236ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 6734.4 665","aria-hidden":"true"},Xi=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Ni=[Xi],Ki=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),Ii={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},qi={style:{"vertical-align":"-3.507ex"},xmlns:"http://www.w3.org/2000/svg",width:"49.234ex",height:"8.145ex",role:"img",focusable:"false",viewBox:"0 -2050 21761.4 3600","aria-hidden":"true"},Ui=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2383,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(2994.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3994.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2155.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3156,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4256.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5256.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mstyle" transform="translate(6134.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14078.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(4872.4,0)"></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2433.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3434,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4256.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5256.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mstyle" transform="translate(6134.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14194,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(4872.4,0)"></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2433.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3434,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4828,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5217,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5817,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(6206,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14078.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),Wi=[Ui],Yi=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"m")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"m"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])])])])],-1),$i={class:"MathJax",jax:"SVG",style:{position:"relative"}},Qg={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.236ex",height:"1.505ex",role:"img",focusable:"false",viewBox:"0 -583 6734.4 665","aria-hidden":"true"},ag=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),tg=[ag],Tg=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"n")])],-1),mg={class:"MathJax",jax:"SVG",style:{position:"relative"}},ng={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.35ex",height:"1.439ex",role:"img",focusable:"false",viewBox:"0 -442 1922.7 636","aria-hidden":"true"},lg=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),eg=[lg],sg=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"m")])],-1),og=Q("h4",{id:"乘法分配律",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#乘法分配律"},[Q("span",null,"乘法分配律")])],-1),rg={class:"MathJax",jax:"SVG",style:{position:"relative"}},dg={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.537ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 2447.3 888","aria-hidden":"true"},hg=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),ig=[hg],gg=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b"),Q("mo",null,","),Q("mi",null,"n")])],-1),Hg={class:"MathJax",jax:"SVG",style:{position:"relative"}},Lg={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.013ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 11939.8 1000","aria-hidden":"true"},cg=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(1822.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(2211.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2962.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3962.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4391.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5058.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6114.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6936.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7936.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(8688.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9688.3,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10510.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(11510.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),pg=[cg],fg=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"b")])],-1),Mg={class:"MathJax",jax:"SVG",style:{position:"relative"}},ug={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.506ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2433.6 748","aria-hidden":"true"},xg=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(877.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1933.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),Zg=[xg],Vg=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"="),Q("mn",null,"0")])],-1),wg={class:"MathJax",jax:"SVG",style:{position:"relative"}},_g={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"68.558ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 30302.7 1000","aria-hidden":"true"},vg=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(1822.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(2211.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2962.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3962.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4391.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5058.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(6114.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(6836.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(7836.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8225.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(8977.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9977.3,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(10406.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(11073.1,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(12128.9,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(12906.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(13962.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(14684.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(15684.9,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(16462.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(17518.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(18240.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(19240.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(19992.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(20992.3,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(21714.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(22714.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(23421.6,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(24477.3,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(25299.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(26299.8,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(27051,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(28051.2,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(28873.4,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(29873.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),yg=[vg],Dg=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mn",null,"0"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"b")])],-1),bg={class:"MathJax",jax:"SVG",style:{position:"relative"}},jg={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Bg=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"})])])],-1),kg=[Bg],Cg=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n")])],-1),zg={class:"MathJax",jax:"SVG",style:{position:"relative"}},Sg={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.013ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 11939.8 1000","aria-hidden":"true"},Jg=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(1822.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(2211.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2962.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3962.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4391.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5058.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6114.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6936.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7936.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(8688.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9688.3,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10510.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(11510.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),Gg=[Jg],Ag=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"b")])],-1),Eg={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},Fg={style:{"vertical-align":"-7.919ex"},xmlns:"http://www.w3.org/2000/svg",width:"78.831ex",height:"16.968ex",role:"img",focusable:"false",viewBox:"0 -4000 34843.4 7500","aria-hidden":"true"},Og=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,3250)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2383,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(2994.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(3994.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4383.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(5134.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6134.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6563.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(6952.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2155.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(3156,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3545,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4296.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5296.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(5725.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6336.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(7336.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7725.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(8477.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9477.3,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(9906.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(10295.3,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(27160.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,1950)"><g data-mml-node="mtd" transform="translate(6952.9,0)"></g><g data-mml-node="mtd" transform="translate(6952.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2155.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3156,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(3907.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4907.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5729.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(6729.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(7381.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(8381.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8770.3,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(9521.6,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10521.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(10950.8,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(11339.8,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(22070.7,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(1822.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(2211.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2962.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3962.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4391.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5058.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6114.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6936.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7936.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(8688.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9688.3,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10510.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(11510.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,650)"><g data-mml-node="mtd" transform="translate(6952.9,0)"></g><g data-mml-node="mtd" transform="translate(6952.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2155.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3156,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(3907.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4907.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5729.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(6729.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(7381.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(8381.3,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(9132.6,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10132.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(10561.8,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(29010.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">结</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">合</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">律</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-650)"><g data-mml-node="mtd" transform="translate(6952.9,0)"></g><g data-mml-node="mtd" transform="translate(6952.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2155.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3156,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(3907.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4907.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(5658.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6658.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7481.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8481.3,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(9132.6,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10132.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(10561.8,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(29010.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">交</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">换</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">律</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1950)"><g data-mml-node="mtd" transform="translate(6952.9,0)"></g><g data-mml-node="mtd" transform="translate(6952.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(1333.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2544.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3545,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4296.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5296.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(5825.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6436.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(7436.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7825.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(8648.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(9648.3,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(10299.6,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(11299.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(11728.8,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(12117.8,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(29010.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">结</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">合</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">律</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-3250)"><g data-mml-node="mtd" transform="translate(6952.9,0)"></g><g data-mml-node="mtd" transform="translate(6952.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3716.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4327.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5328,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6079.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7079.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8473.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8862.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9462.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(10073.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(11073.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(11502.9,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(27160.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),Rg=[Og],Pg=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",null,"+"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"n"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"b")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法结合律")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法交换律")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"a"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法结合律")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"n"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])])])])],-1),Xg={class:"MathJax",jax:"SVG",style:{position:"relative"}},Ng={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.013ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 11939.8 1000","aria-hidden":"true"},Kg=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(1822.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(2211.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2962.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3962.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4391.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5058.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6114.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6936.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7936.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(8688.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9688.3,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10510.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(11510.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),Ig=[Kg],qg=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"n"),Q("mo",null,"×"),Q("mi",null,"b")])],-1),Ug={class:"MathJax",jax:"SVG",style:{position:"relative"}},Wg={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.537ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 2447.3 888","aria-hidden":"true"},Yg=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1573.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(2018.3,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),$g=[Yg],QH=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"n"),Q("mo",null,","),Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b")])],-1),aH=Q("h4",{id:"乘法结合律",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#乘法结合律"},[Q("span",null,"乘法结合律")])],-1),tH={class:"MathJax",jax:"SVG",style:{position:"relative"}},TH={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.159ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 2280.3 888","aria-hidden":"true"},mH=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),nH=[mH],lH=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b"),Q("mo",null,","),Q("mi",null,"c")])],-1),eH={class:"MathJax",jax:"SVG",style:{position:"relative"}},sH={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"23.894ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10561.3 1000","aria-hidden":"true"},oH=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5947.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6698.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(7698.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8739.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(9739.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(10172.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),rH=[oH],dH=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),hH={class:"MathJax",jax:"SVG",style:{position:"relative"}},iH={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.128ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2266.6 748","aria-hidden":"true"},gH=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),HH=[gH],LH=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])],-1),cH={class:"MathJax",jax:"SVG",style:{position:"relative"}},pH={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"63.368ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 28008.8 1000","aria-hidden":"true"},fH=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(5947.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6336.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7087.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8516.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(9128.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(10128.3,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(10906.1,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(11961.9,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(12739.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(13795.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(14546.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(15546.9,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(16324.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(17380.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(18131.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(19131.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(19520.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(20172.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(21172.3,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(21672.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(22339.1,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(23394.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(24146.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(25146.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(25535.3,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(26186.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(27186.8,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(27619.8,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),MH=[fH],uH=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",null,"="),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mn",null,"0"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mn",null,"0"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"×"),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),xH={class:"MathJax",jax:"SVG",style:{position:"relative"}},ZH={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.98ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 433 453","aria-hidden":"true"},VH=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D450",d:"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"})])])],-1),wH=[VH],_H=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c")])],-1),vH={class:"MathJax",jax:"SVG",style:{position:"relative"}},yH={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"23.894ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10561.3 1000","aria-hidden":"true"},DH=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5947.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6698.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(7698.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8739.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(9739.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(10172.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),bH=[DH],jH=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),BH={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},kH={style:{"vertical-align":"-4.977ex"},xmlns:"http://www.w3.org/2000/svg",width:"69.074ex",height:"11.086ex",role:"img",focusable:"false",viewBox:"0 -2700 30530.6 4900","aria-hidden":"true"},CH=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1950)"><g data-mml-node="mtd"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(5574.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5963.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6396.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(6785.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(1333.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2473.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3474,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(3903,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4514.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5514.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6169.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7169.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7921.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8921.3,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(9350.3,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(22847.6,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,650)"><g data-mml-node="mtd" transform="translate(6785.9,0)"></g><g data-mml-node="mtd" transform="translate(6785.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(3085,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3474,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4125.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5125.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5558.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6169.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7169.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7921.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8921.3,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(9350.3,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(19136.2,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5947.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6698.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(7698.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8739.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(9739.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(10172.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-650)"><g data-mml-node="mtd" transform="translate(6785.9,0)"></g><g data-mml-node="mtd" transform="translate(6785.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(3085,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3474,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4125.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5125.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5780.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6780.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(7209.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(7598.9,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(24697.6,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">分</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">配</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">律</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1950)"><g data-mml-node="mtd" transform="translate(6785.9,0)"></g><g data-mml-node="mtd" transform="translate(6785.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(3085,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3474,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4125.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5125.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6519.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6908.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(7341.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7730.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(8119.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(22847.6,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),zH=[CH],SH=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",null,"+"),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法分配律")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])])])])],-1),JH={class:"MathJax",jax:"SVG",style:{position:"relative"}},GH={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"23.894ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10561.3 1000","aria-hidden":"true"},AH=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5947.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6698.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(7698.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8739.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(9739.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(10172.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),EH=[AH],FH=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"b"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),OH={class:"MathJax",jax:"SVG",style:{position:"relative"}},RH={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.159ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 2280.3 888","aria-hidden":"true"},PH=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),XH=[PH],NH=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b"),Q("mo",null,","),Q("mi",null,"c")])],-1),KH=Q("h4",{id:"乘法消去律",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#乘法消去律"},[Q("span",null,"乘法消去律")])],-1),IH={class:"MathJax",jax:"SVG",style:{position:"relative"}},qH={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"3.173ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 1402.7 888","aria-hidden":"true"},UH=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),WH=[UH],YH=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b")])],-1),$H={class:"MathJax",jax:"SVG",style:{position:"relative"}},QL={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.98ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 433 453","aria-hidden":"true"},aL=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D450",d:"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"})])])],-1),tL=[aL],TL=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c")])],-1),mL={class:"MathJax",jax:"SVG",style:{position:"relative"}},nL={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"31.207ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 13793.6 1000","aria-hidden":"true"},lL=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(10224.2,0)"><path data-c="21D4" d="M308 524Q318 526 323 526Q340 526 340 514Q340 507 336 499Q326 476 314 454T292 417T274 391T260 374L255 368Q255 367 500 367Q744 367 744 368L739 374Q734 379 726 390T707 416T685 453T663 499Q658 511 658 515Q658 525 680 525Q687 524 690 523T695 519T701 507Q766 359 902 287Q921 276 939 269T961 259T966 250Q966 246 965 244T960 240T949 236T930 228T902 213Q763 137 701 -7Q697 -16 695 -19T690 -23T680 -25Q658 -25 658 -15Q658 -11 663 1Q673 24 685 46T707 83T725 109T739 126L744 132Q744 133 500 133Q255 133 255 132L260 126Q265 121 273 110T292 84T314 47T336 1Q341 -11 341 -15Q341 -25 319 -25Q312 -24 309 -23T304 -19T298 -7Q233 141 97 213Q83 221 70 227T51 235T41 239T35 243T34 250T35 256T40 261T51 265T70 273T97 287Q235 363 299 509Q305 522 308 524ZM792 319L783 327H216Q183 294 120 256L110 250L120 244Q173 212 207 181L216 173H783L792 181Q826 212 879 244L889 250L879 256Q826 288 792 319Z"></path></g><g data-mml-node="mi" transform="translate(11502,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(12308.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(13364.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),eL=[lL],sL=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},"⇔"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),oL={class:"MathJax",jax:"SVG",style:{position:"relative"}},rL={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"31.207ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 13793.6 1000","aria-hidden":"true"},dL=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(3847.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4598.3,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5598.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6992.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7381.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(7814.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(8481.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9537.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(10188.3,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(11188.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(12582.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(12971.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(13404.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),hL=[dL],iL=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),gL={class:"MathJax",jax:"SVG",style:{position:"relative"}},HL={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.128ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2266.6 748","aria-hidden":"true"},LL=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),cL=[LL],pL=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])],-1),fL={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},ML={style:{"vertical-align":"-12.33ex"},xmlns:"http://www.w3.org/2000/svg",width:"47.051ex",height:"25.792ex",role:"img",focusable:"false",viewBox:"0 -5950 20796.4 11400","aria-hidden":"true"},uL=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,5200)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3085,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4479,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(4868,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(5368,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5757,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(17696.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,3900)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(3085,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(3807.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4807.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mstyle" transform="translate(5336.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13113.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,2600)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2055.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3056,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mstyle" transform="translate(3585,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13113.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mstyle" transform="translate(1862.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13113.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(1762.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(17671.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2055.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3056,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(3485,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13113.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-2600)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(2985,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(3707.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4707.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(5136.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13113.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-3900)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(4768,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(5268,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5657,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13113.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-5200)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5590,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(17696.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g></g></g></g>',1),xL=[uL],ZL=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"a"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"a"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mn",null,"0"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅰ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"c"),Q("mo",null,"="),Q("mn",null,"0")])])])])])],-1),VL={class:"MathJax",jax:"SVG",style:{position:"relative"}},wL={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.98ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 433 453","aria-hidden":"true"},_L=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D450",d:"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"})])])],-1),vL=[_L],yL=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c")])],-1),DL={class:"MathJax",jax:"SVG",style:{position:"relative"}},bL={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.503ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 9946.4 1000","aria-hidden":"true"},jL=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),BL=[jL],kL=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),CL={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},zL={style:{"vertical-align":"-3.507ex"},xmlns:"http://www.w3.org/2000/svg",width:"72.085ex",height:"8.145ex",role:"img",focusable:"false",viewBox:"0 -2050 31861.4 3600","aria-hidden":"true"},SL=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4928.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5317.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5750.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6139.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(6528.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3085,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4479,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4868,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5301,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5912.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6912.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mstyle" transform="translate(7441.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(24178.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(6528.4,0)"></g><g data-mml-node="mtd" transform="translate(6528.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5812.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6812.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(7241.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(17290.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mrow" transform="translate(833,0)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g><g data-mml-node="mtext" transform="translate(2291.6,0)"><path data-c="A0" d=""></path><text data-variant="normal" transform="translate(250,0) scale(1,-1)" font-size="884px" font-family="serif">且</text><path data-c="A0" d="" transform="translate(1250,0)"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(3791.6,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(6528.4,0)"></g><g data-mml-node="mtd" transform="translate(6528.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6162,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6551,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6984,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7373,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(7762,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(24178.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),JL=[SL],GL=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"a"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"b"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",null,[Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")]),Q("mtext",null," 且 "),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])])])]),Q("mtr",null,[Q("mtd"),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])])])])],-1),AL={class:"MathJax",jax:"SVG",style:{position:"relative"}},EL={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"67.058ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 29639.6 1000","aria-hidden":"true"},FL=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(3847.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4598.3,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5598.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6992.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7381.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(7814.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(8481.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9537.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(10188.3,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(11188.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(12582.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(12971.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(13404.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(14071.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(15349.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(16100.3,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(17100.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(18494.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(18883.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(20277.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(20666.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(21099.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(21488.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(22155.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(23211.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(23862.3,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(24862.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(26256.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(26645.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(28039.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(28428.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(28861.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(29250.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),OL=[FL],RL=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")")])],-1),PL={class:"MathJax",jax:"SVG",style:{position:"relative"}},XL={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"31.207ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 13793.6 1000","aria-hidden":"true"},NL=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(3847.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4598.3,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5598.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6992.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7381.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(7814.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(8481.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9537.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(10188.3,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(11188.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(12582.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(12971.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(13404.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),KL=[NL],IL=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),qL={class:"MathJax",jax:"SVG",style:{position:"relative"}},UL={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.159ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 2280.3 888","aria-hidden":"true"},WL=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),YL=[WL],$L=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b"),Q("mo",null,","),Q("mi",null,"c")])],-1),Qc={class:"MathJax",jax:"SVG",style:{position:"relative"}},ac={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"31.207ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 13793.6 1000","aria-hidden":"true"},tc=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(10224.2,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(11502,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(12308.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(13364.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),Tc=[tc],mc=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),nc={class:"MathJax",jax:"SVG",style:{position:"relative"}},lc={style:{"vertical-align":"-0.486ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"2.106ex",role:"img",focusable:"false",viewBox:"0 -716 2291.6 931","aria-hidden":"true"},ec=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2260" d="M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),sc=[ec],oc=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≠"),Q("mi",null,"b")])],-1),rc={class:"MathJax",jax:"SVG",style:{position:"relative"}},dc={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 4392 776","aria-hidden":"true"},hc=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3514,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),ic=[hc],gc=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"m")])],-1),Hc={class:"MathJax",jax:"SVG",style:{position:"relative"}},Lc={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 4392 776","aria-hidden":"true"},cc=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3514,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),pc=[cc],fc=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"m")])],-1),Mc={class:"MathJax",jax:"SVG",style:{position:"relative"}},uc={style:{"vertical-align":"-0.486ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.135ex",height:"2.106ex",role:"img",focusable:"false",viewBox:"0 -716 2711.6 931","aria-hidden":"true"},xc=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1155.8,0)"><path data-c="2260" d="M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z"></path></g><g data-mml-node="mn" transform="translate(2211.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),Zc=[xc],Vc=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"≠"),Q("mn",null,"0")])],-1),wc={class:"MathJax",jax:"SVG",style:{position:"relative"}},_c={style:{"vertical-align":"-0.486ex"},xmlns:"http://www.w3.org/2000/svg",width:"17.077ex",height:"2.106ex",role:"img",focusable:"false",viewBox:"0 -716 7548.2 931","aria-hidden":"true"},vc=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3514,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4392,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(4836.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5992.4,0)"><path data-c="2260" d="M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z"></path></g><g data-mml-node="mn" transform="translate(7048.2,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),yc=[vc],Dc=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,","),Q("mi",null,"m"),Q("mo",null,"≠"),Q("mn",null,"0")])],-1),bc={class:"MathJax",jax:"SVG",style:{position:"relative"}},jc={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.042ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4438.6 1000","aria-hidden":"true"},Bc=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2216,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(2882.8,0)"><path data-c="2260" d="M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z"></path></g><g data-mml-node="mn" transform="translate(3938.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),kc=[Bc],Cc=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"≠"),Q("mn",null,"0")])],-1),zc={class:"MathJax",jax:"SVG",style:{position:"relative"}},Sc={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"0.98ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 433 453","aria-hidden":"true"},Jc=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D450",d:"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"})])])],-1),Gc=[Jc],Ac=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"c")])],-1),Ec={class:"MathJax",jax:"SVG",style:{position:"relative"}},Fc={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.294ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 572 453","aria-hidden":"true"},Oc=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D465",d:"M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"})])])],-1),Rc=[Oc],Pc=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"x")])],-1),Xc={class:"MathJax",jax:"SVG",style:{position:"relative"}},Nc={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.205ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4510.6 1000","aria-hidden":"true"},Kc=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></g><g data-mml-node="mo" transform="translate(2355,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3021.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4077.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),Ic=[Kc],qc=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"x"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"c")])],-1),Uc={class:"MathJax",jax:"SVG",style:{position:"relative"}},Wc={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.2ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4508.6 1000","aria-hidden":"true"},Yc=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="70" d="M36 -148H50Q89 -148 97 -134V-126Q97 -119 97 -107T97 -77T98 -38T98 6T98 55T98 106Q98 140 98 177T98 243T98 296T97 335T97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 61 434T98 436Q115 437 135 438T165 441T176 442H179V416L180 390L188 397Q247 441 326 441Q407 441 464 377T522 216Q522 115 457 52T310 -11Q242 -11 190 33L182 40V-45V-101Q182 -128 184 -134T195 -145Q216 -148 244 -148H260V-194H252L228 -193Q205 -192 178 -192T140 -191Q37 -191 28 -194H20V-148H36ZM424 218Q424 292 390 347T305 402Q234 402 182 337V98Q222 26 294 26Q345 26 384 80T424 218Z"></path><path data-c="72" d="M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z" transform="translate(556,0)"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(948,0)"></path></g><g data-mml-node="mo" transform="translate(1392,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1781,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2214,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(2880.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3936.6,0)"><path data-c="1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></g></g></g>',1),$c=[Yc],Qp=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"pre"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"x")])],-1),ap={class:"MathJax",jax:"SVG",style:{position:"relative"}},tp={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.503ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 9946.4 1000","aria-hidden":"true"},Tp=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),mp=[Tp],np=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),lp={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},ep={style:{"vertical-align":"-9.389ex"},xmlns:"http://www.w3.org/2000/svg",width:"69.571ex",height:"19.91ex",role:"img",focusable:"false",viewBox:"0 -4650 30750.4 8800","aria-hidden":"true"},sp=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,3900)"><g data-mml-node="mtd" transform="translate(5827.9,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(10184.3,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5590,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(25917.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">已</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">知</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">条</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">件</text></g></g></g><g data-mml-node="mtr" transform="translate(0,2600)"><g data-mml-node="mtd" transform="translate(3049.4,0)"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1040.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2040.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2918.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3529.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4529.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(5923.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6312.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6745.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(10184.3,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5590,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(25525.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3514,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(651.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1651.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3045.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3434.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3867.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4478.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5478.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6579.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7579.3,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8973.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9362.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9795.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(10184.3,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5590,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18917.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">交</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">换</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">律</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">、</text><text data-variant="normal" transform="translate(6000,0) scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(7000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(8000,0) scale(1,-1)" font-size="884px" font-family="serif">分</text><text data-variant="normal" transform="translate(9000,0) scale(1,-1)" font-size="884px" font-family="serif">配</text><text data-variant="normal" transform="translate(10000,0) scale(1,-1)" font-size="884px" font-family="serif">律</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(5478.9,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4316.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(10184.3,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(1833.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(24917.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">消</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">去</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">律</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(5550.4,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2755.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3755.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mtd" transform="translate(10184.3,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(1833.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(23067.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-2600)"><g data-mml-node="mtd" transform="translate(1208.4,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2755.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3755.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(5149.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5538.9,0)"><path data-c="70" d="M36 -148H50Q89 -148 97 -134V-126Q97 -119 97 -107T97 -77T98 -38T98 6T98 55T98 106Q98 140 98 177T98 243T98 296T97 335T97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 61 434T98 436Q115 437 135 438T165 441T176 442H179V416L180 390L188 397Q247 441 326 441Q407 441 464 377T522 216Q522 115 457 52T310 -11Q242 -11 190 33L182 40V-45V-101Q182 -128 184 -134T195 -145Q216 -148 244 -148H260V-194H252L228 -193Q205 -192 178 -192T140 -191Q37 -191 28 -194H20V-148H36ZM424 218Q424 292 390 347T305 402Q234 402 182 337V98Q222 26 294 26Q345 26 384 80T424 218Z"></path><path data-c="72" d="M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z" transform="translate(556,0)"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(948,0)"></path></g><g data-mml-node="mo" transform="translate(6930.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7319.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(8197.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(8586.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(10184.3,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(1833.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18774.3,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mrow" transform="translate(833,0)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1155.8,0)"><path data-c="2260" d="M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z"></path></g><g data-mml-node="mn" transform="translate(2211.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g><g data-mml-node="mtext" transform="translate(2711.6,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">、</text></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(3711.6,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1155.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(2211.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3605.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3994.6,0)"><path data-c="70" d="M36 -148H50Q89 -148 97 -134V-126Q97 -119 97 -107T97 -77T98 -38T98 6T98 55T98 106Q98 140 98 177T98 243T98 296T97 335T97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 61 434T98 436Q115 437 135 438T165 441T176 442H179V416L180 390L188 397Q247 441 326 441Q407 441 464 377T522 216Q522 115 457 52T310 -11Q242 -11 190 33L182 40V-45V-101Q182 -128 184 -134T195 -145Q216 -148 244 -148H260V-194H252L228 -193Q205 -192 178 -192T140 -191Q37 -191 28 -194H20V-148H36ZM424 218Q424 292 390 347T305 402Q234 402 182 337V98Q222 26 294 26Q345 26 384 80T424 218Z"></path><path data-c="72" d="M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z" transform="translate(556,0)"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(948,0)"></path></g><g data-mml-node="mo" transform="translate(5386.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5775.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6653.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7042.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-3900)"><g data-mml-node="mtd" transform="translate(1208.4,0)"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2883.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4538.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5538.9,0)"><path data-c="70" d="M36 -148H50Q89 -148 97 -134V-126Q97 -119 97 -107T97 -77T98 -38T98 6T98 55T98 106Q98 140 98 177T98 243T98 296T97 335T97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 61 434T98 436Q115 437 135 438T165 441T176 442H179V416L180 390L188 397Q247 441 326 441Q407 441 464 377T522 216Q522 115 457 52T310 -11Q242 -11 190 33L182 40V-45V-101Q182 -128 184 -134T195 -145Q216 -148 244 -148H260V-194H252L228 -193Q205 -192 178 -192T140 -191Q37 -191 28 -194H20V-148H36ZM424 218Q424 292 390 347T305 402Q234 402 182 337V98Q222 26 294 26Q345 26 384 80T424 218Z"></path><path data-c="72" d="M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z" transform="translate(556,0)"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(948,0)"></path></g><g data-mml-node="mo" transform="translate(6930.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7319.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(8197.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(8586.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(10184.3,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(1833.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(23067.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g>',1),op=[sp],rp=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mtable",{displaystyle:"true",columnalign:"right left right",columnspacing:"0em 2em",rowspacing:"3pt"},[Q("mtr",null,[Q("mtd",null,[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"已知条件")])]),Q("mtr",null,[Q("mtd",null,[Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"m")])])]),Q("mtr",null,[Q("mtd",null,[Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法交换律、乘法分配律")])]),Q("mtr",null,[Q("mtd",null,[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法消去律")])]),Q("mtr",null,[Q("mtd",null,[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",null,"+"),Q("mi",null,"m")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"乘法运算规则 Ⅱ")])]),Q("mtr",null,[Q("mtd",null,[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",null,"+"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"pre"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mrow",null,[Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"m"),Q("mo",null,"≠"),Q("mn",null,"0")]),Q("mtext",null,"、"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"m"),Q("mo",null,"="),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"pre"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")")])])])]),Q("mtr",null,[Q("mtd",null,[Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",null,"+"),Q("mi",null,"pre"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},")")]),Q("mtd",null,[Q("mi"),Q("mo",null,"="),Q("mn",null,"0"),Q("mstyle",{scriptlevel:"0"},[Q("mspace",{width:"1em"})])]),Q("mtd",null,[Q("mi",{mathvariant:"normal"},"#"),Q("mtext",null,"加法运算规则 Ⅱ")])])])])],-1),dp={class:"MathJax",jax:"SVG",style:{position:"relative"}},hp={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 500 688","aria-hidden":"true"},ip=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"30",d:"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"})])])],-1),gp=[ip],Hp=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0")])],-1),Lp={class:"MathJax",jax:"SVG",style:{position:"relative"}},cp={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.393ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 6803.9 1000","aria-hidden":"true"},pp=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2755.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3755.9,0)"><path data-c="70" d="M36 -148H50Q89 -148 97 -134V-126Q97 -119 97 -107T97 -77T98 -38T98 6T98 55T98 106Q98 140 98 177T98 243T98 296T97 335T97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 61 434T98 436Q115 437 135 438T165 441T176 442H179V416L180 390L188 397Q247 441 326 441Q407 441 464 377T522 216Q522 115 457 52T310 -11Q242 -11 190 33L182 40V-45V-101Q182 -128 184 -134T195 -145Q216 -148 244 -148H260V-194H252L228 -193Q205 -192 178 -192T140 -191Q37 -191 28 -194H20V-148H36ZM424 218Q424 292 390 347T305 402Q234 402 182 337V98Q222 26 294 26Q345 26 384 80T424 218Z"></path><path data-c="72" d="M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z" transform="translate(556,0)"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(948,0)"></path></g><g data-mml-node="mo" transform="translate(5147.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5536.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6414.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),fp=[pp],Mp=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"c"),Q("mo",null,"+"),Q("mi",null,"pre"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")")])],-1),up={class:"MathJax",jax:"SVG",style:{position:"relative"}},xp={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"31.207ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 13793.6 1000","aria-hidden":"true"},Zp=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(10224.2,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(11502,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(12308.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(13364.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),Vp=[Zp],wp=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},"⇒"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),_p={class:"MathJax",jax:"SVG",style:{position:"relative"}},vp={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"31.207ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 13793.6 1000","aria-hidden":"true"},yp=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(10224.2,0)"><path data-c="21D4" d="M308 524Q318 526 323 526Q340 526 340 514Q340 507 336 499Q326 476 314 454T292 417T274 391T260 374L255 368Q255 367 500 367Q744 367 744 368L739 374Q734 379 726 390T707 416T685 453T663 499Q658 511 658 515Q658 525 680 525Q687 524 690 523T695 519T701 507Q766 359 902 287Q921 276 939 269T961 259T966 250Q966 246 965 244T960 240T949 236T930 228T902 213Q763 137 701 -7Q697 -16 695 -19T690 -23T680 -25Q658 -25 658 -15Q658 -11 663 1Q673 24 685 46T707 83T725 109T739 126L744 132Q744 133 500 133Q255 133 255 132L260 126Q265 121 273 110T292 84T314 47T336 1Q341 -11 341 -15Q341 -25 319 -25Q312 -24 309 -23T304 -19T298 -7Q233 141 97 213Q83 221 70 227T51 235T41 239T35 243T34 250T35 256T40 261T51 265T70 273T97 287Q235 363 299 509Q305 522 308 524ZM792 319L783 327H216Q183 294 120 256L110 250L120 244Q173 212 207 181L216 173H783L792 181Q826 212 879 244L889 250L879 256Q826 288 792 319Z"></path></g><g data-mml-node="mi" transform="translate(11502,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(12308.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(13364.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),Dp=[yp],bp=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",{stretchy:"false"},"⇔"),Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),jp={class:"MathJax",jax:"SVG",style:{position:"relative"}},Bp={style:{"vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.159ex",height:"2.009ex",role:"img",focusable:"false",viewBox:"0 -694 2280.3 888","aria-hidden":"true"},kp=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g>',1),Cp=[kp],zp=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,","),Q("mi",null,"b"),Q("mo",null,","),Q("mi",null,"c")])],-1),Sp=Q("h2",{id:"peano-公理的合理性",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#peano-公理的合理性"},[Q("span",null,"Peano 公理的合理性")])],-1),Jp=Q("p",null,"通过上述步骤，我们成功地由 Peano 公理构建出了一个自然数代数系统。但 Peano 公理自身任有待研究。从上述步骤中我们看出 Peano 公理每一条公理都被使用过，少了任何一条都不足以构建出上述的自然数系统，这究竟是为什么呢？",-1),Gp=Q("p",null,"下面我将阐述为什么每条公理都是必须的，通过举反例的方式。研究 Peano 公理自然不能从 Peano 公理系统内出发，我们将借助另一个公理系统——图论。",-1),Ap=Q("h3",{id:"乘法保序性",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#乘法保序性"},[Q("span",null,"乘法保序性")])],-1),Ep={class:"MathJax",jax:"SVG",style:{position:"relative"}},Fp={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 832","aria-hidden":"true"},Op=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),Rp=[Op],Pp=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≤"),Q("mi",null,"b")])],-1),Xp={class:"MathJax",jax:"SVG",style:{position:"relative"}},Np={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.503ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 9946.4 1000","aria-hidden":"true"},Kp=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Ip=[Kp],qp=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"≤"),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),Up={class:"MathJax",jax:"SVG",style:{position:"relative"}},Wp={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 832","aria-hidden":"true"},Yp=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),$p=[Yp],Qf=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≤"),Q("mi",null,"b")])],-1),af={class:"MathJax",jax:"SVG",style:{position:"relative"}},tf={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 4392 776","aria-hidden":"true"},Tf=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3514,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),mf=[Tf],nf=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"m")])],-1),lf={class:"MathJax",jax:"SVG",style:{position:"relative"}},ef={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"55.3ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 24442.8 1000","aria-hidden":"true"},sf=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(651.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1651.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3045.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3434.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3867.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4534.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(5590,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5979,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6730.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7730.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(8608.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(9219.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(10219.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(11613.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(12002.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(12435.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(13102.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(14158.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(14909.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(15909.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(17303.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(17692.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(18125.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(18737.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(19737.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(20837.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(21837.8,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(23231.8,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(23620.8,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(24053.8,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),of=[sf],rf=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mo",{stretchy:"false"},"("),Q("mi",null,"a"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),df={class:"MathJax",jax:"SVG",style:{position:"relative"}},hf={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.503ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 9946.4 1000","aria-hidden":"true"},gf=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Hf=[gf],Lf=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"≤"),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),cf=Q("h3",{id:"乘法消去保序性",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#乘法消去保序性"},[Q("span",null,"乘法消去保序性")])],-1),pf={class:"MathJax",jax:"SVG",style:{position:"relative"}},ff={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.503ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 9946.4 1000","aria-hidden":"true"},Mf=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),uf=[Mf],xf=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"≤"),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),Zf={class:"MathJax",jax:"SVG",style:{position:"relative"}},Vf={style:{"vertical-align":"-0.312ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.882ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 832","aria-hidden":"true"},wf=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),_f=[wf],vf=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"≤"),Q("mi",null,"b")])],-1),yf={class:"MathJax",jax:"SVG",style:{position:"relative"}},Df={style:{"vertical-align":"-0.09ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.661ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 734","aria-hidden":"true"},bf=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3E" d="M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),jf=[bf],Bf=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,">"),Q("mi",null,"b")])],-1),kf={class:"MathJax",jax:"SVG",style:{position:"relative"}},Cf={style:{"vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.986ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 878 453","aria-hidden":"true"},zf=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D45A",d:"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"})])])],-1),Sf=[zf],Jf=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"m")])],-1),Gf={class:"MathJax",jax:"SVG",style:{position:"relative"}},Af={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"9.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 4392 776","aria-hidden":"true"},Ef=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3514,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g>',1),Ff=[Ef],Of=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"m")])],-1),Rf={class:"MathJax",jax:"SVG",display:"true",style:{position:"relative"}},Pf={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"55.074ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 24342.8 1000","aria-hidden":"true"},Xf=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(5690,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6079,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6730.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7730.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(8608.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(9219.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(10219.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(11613.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(12002.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(12435.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(13102.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(14158.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(14809.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(15809.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(17203.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(17592.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(18025.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(18637.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(19637.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(20737.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(21737.8,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(23131.8,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(23520.8,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(23953.8,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Nf=[Xf],Kf=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mo",{stretchy:"false"},"("),Q("mi",null,"b"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"+"),Q("mi",null,"m"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),If={class:"MathJax",jax:"SVG",style:{position:"relative"}},qf={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.503ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 9946.4 1000","aria-hidden":"true"},Uf=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(651.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1651.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3045.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3434.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3867.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4534.2,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(5590,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),Wf=[Uf],Yf=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"≤"),Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),$f={class:"MathJax",jax:"SVG",style:{position:"relative"}},QM={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.503ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 9946.4 1000","aria-hidden":"true"},aM=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),tM=[aM],TM=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mi",null,"b"),Q("mo",null,"×"),Q("mi",null,"suc"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"c"),Q("mo",{stretchy:"false"},")")])],-1),mM={class:"MathJax",jax:"SVG",style:{position:"relative"}},nM={style:{"vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 776","aria-hidden":"true"},lM=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),eM=[lM],sM=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,"="),Q("mi",null,"b")])],-1),oM={class:"MathJax",jax:"SVG",style:{position:"relative"}},rM={style:{"vertical-align":"-0.09ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.185ex",height:"1.661ex",role:"img",focusable:"false",viewBox:"0 -694 2291.6 734","aria-hidden":"true"},dM=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3E" d="M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g>',1),hM=[dM],iM=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"a"),Q("mo",null,">"),Q("mi",null,"b")])],-1),gM=Q("h3",{id:"用图论阐述-peano-系统",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#用图论阐述-peano-系统"},[Q("span",null,"用图论阐述 Peano 系统")])],-1),HM={class:"MathJax",jax:"SVG",style:{position:"relative"}},LM={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"7.78ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3438.7 1000","aria-hidden":"true"},cM=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mi"><path data-c="47" d="M56 342Q56 428 89 500T174 615T283 681T391 705Q394 705 400 705T408 704Q499 704 569 636L582 624L612 663Q639 700 643 704Q644 704 647 704T653 705H657Q660 705 666 699V419L660 413H626Q620 419 619 430Q610 512 571 572T476 651Q457 658 426 658Q401 658 376 654T316 633T254 592T205 519T177 411Q173 369 173 335Q173 259 192 201T238 111T302 58T370 31T431 24Q478 24 513 45T559 100Q562 110 562 160V212Q561 213 557 216T551 220T542 223T526 225T502 226T463 227H437V273H449L609 270Q715 270 727 273H735V227H721Q674 227 668 215Q666 211 666 108V6Q660 0 657 0Q653 0 639 10Q617 25 600 42L587 54Q571 27 524 3T406 -22Q317 -22 238 22T108 151T56 342Z"></path></g></g><g data-mml-node="mo" transform="translate(785,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(1174,0)"><g data-mml-node="mi"><path data-c="56" d="M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z"></path></g></g><g data-mml-node="mo" transform="translate(1924,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(2368.7,0)"><g data-mml-node="mi"><path data-c="45" d="M128 619Q121 626 117 628T101 631T58 634H25V680H597V676Q599 670 611 560T625 444V440H585V444Q584 447 582 465Q578 500 570 526T553 571T528 601T498 619T457 629T411 633T353 634Q266 634 251 633T233 622Q233 622 233 621Q232 619 232 497V376H286Q359 378 377 385Q413 401 416 469Q416 471 416 473V493H456V213H416V233Q415 268 408 288T383 317T349 328T297 330Q290 330 286 330H232V196V114Q232 57 237 52Q243 47 289 47H340H391Q428 47 452 50T505 62T552 92T584 146Q594 172 599 200T607 247T612 270V273H652V270Q651 267 632 137T610 3V0H25V46H58Q100 47 109 49T128 61V619Z"></path></g></g><g data-mml-node="mo" transform="translate(3049.7,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),pM=[cM],fM=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",{mathvariant:"normal"},"G")]),Q("mo",{stretchy:"false"},"("),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",{mathvariant:"normal"},"V")]),Q("mo",null,","),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",{mathvariant:"normal"},"E")]),Q("mo",{stretchy:"false"},")")])],-1),MM={class:"MathJax",jax:"SVG",style:{position:"relative"}},uM={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 500 688","aria-hidden":"true"},xM=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"30",d:"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"})])])],-1),ZM=[xM],VM=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0")])],-1),wM={class:"MathJax",jax:"SVG",style:{position:"relative"}},_M={style:{"vertical-align":"-0.375ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.548ex",height:"1.92ex",role:"img",focusable:"false",viewBox:"0 -683 2894.1 848.6","aria-hidden":"true"},vM=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path></g><g data-mml-node="mn" transform="translate(518,-150) scale(0.707)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g><g data-mml-node="mo" transform="translate(1199.3,0)"><path data-c="2208" d="M84 250Q84 372 166 450T360 539Q361 539 377 539T419 540T469 540H568Q583 532 583 520Q583 511 570 501L466 500Q355 499 329 494Q280 482 242 458T183 409T147 354T129 306T124 272V270H568Q583 262 583 250T568 230H124V228Q124 207 134 177T167 112T231 48T328 7Q355 1 466 0H570Q583 -10 583 -20Q583 -32 568 -40H471Q464 -40 446 -40T417 -41Q262 -41 172 45Q84 127 84 250Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(2144.1,0)"><g data-mml-node="mi"><path data-c="56" d="M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z"></path></g></g></g></g>',1),yM=[vM],DM=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"v"),Q("mn",null,"0")]),Q("mo",null,"∈"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",{mathvariant:"normal"},"V")])])],-1),bM={class:"MathJax",jax:"SVG",style:{position:"relative"}},jM={style:{"vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.507ex",role:"img",focusable:"false",viewBox:"0 -666 500 666","aria-hidden":"true"},BM=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"31",d:"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"})])])],-1),kM=[BM],CM=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"1")])],-1),zM={class:"MathJax",jax:"SVG",style:{position:"relative"}},SM={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"14.139ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 6249.6 1000","aria-hidden":"true"},JM=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="6F" d="M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(500,0)"></path><path data-c="74" d="M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z" transform="translate(1056,0)"></path><path data-c="44" d="M130 622Q123 629 119 631T103 634T60 637H27V683H228Q399 682 419 682T461 676Q504 667 546 641T626 573T685 470T708 336Q708 210 634 116T442 3Q429 1 228 0H27V46H60Q102 47 111 49T130 61V622ZM593 338Q593 439 571 501T493 602Q439 637 355 637H322H294Q238 637 234 628Q231 624 231 344Q231 62 232 59Q233 49 248 48T339 46H350Q456 46 515 95Q561 133 577 191T593 338Z" transform="translate(1445,0)"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(2209,0)"></path><path data-c="67" d="M329 409Q373 453 429 453Q459 453 472 434T485 396Q485 382 476 371T449 360Q416 360 412 390Q410 404 415 411Q415 412 416 414V415Q388 412 363 393Q355 388 355 386Q355 385 359 381T368 369T379 351T388 325T392 292Q392 230 343 187T222 143Q172 143 123 171Q112 153 112 133Q112 98 138 81Q147 75 155 75T227 73Q311 72 335 67Q396 58 431 26Q470 -13 470 -72Q470 -139 392 -175Q332 -206 250 -206Q167 -206 107 -175Q29 -140 29 -75Q29 -39 50 -15T92 18L103 24Q67 55 67 108Q67 155 96 193Q52 237 52 292Q52 355 102 398T223 442Q274 442 318 416L329 409ZM299 343Q294 371 273 387T221 404Q192 404 171 388T145 343Q142 326 142 292Q142 248 149 227T179 192Q196 182 222 182Q244 182 260 189T283 207T294 227T299 242Q302 258 302 292T299 343ZM403 -75Q403 -50 389 -34T348 -11T299 -2T245 0H218Q151 0 138 -6Q118 -15 107 -34T95 -74Q95 -84 101 -97T122 -127T170 -155T250 -167Q319 -167 361 -139T403 -75Z" transform="translate(2653,0)"></path></g><g data-mml-node="mo" transform="translate(3153,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3542,0)"><path data-c="1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path></g><g data-mml-node="mo" transform="translate(4027,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4693.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(5749.6,0)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g></g>',1),GM=[JM],AM=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"outDeg"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"v"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mn",null,"1")])],-1),EM={class:"MathJax",jax:"SVG",style:{position:"relative"}},FM={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 500 688","aria-hidden":"true"},OM=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"30",d:"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"})])])],-1),RM=[OM],PM=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0")])],-1),XM={class:"MathJax",jax:"SVG",style:{position:"relative"}},NM={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 500 688","aria-hidden":"true"},KM=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"30",d:"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"})])])],-1),IM=[KM],qM=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0")])],-1),UM={class:"MathJax",jax:"SVG",style:{position:"relative"}},WM={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"13.745ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 6075.1 1000","aria-hidden":"true"},YM=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="69" d="M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z"></path><path data-c="6E" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z" transform="translate(278,0)"></path><path data-c="44" d="M130 622Q123 629 119 631T103 634T60 637H27V683H228Q399 682 419 682T461 676Q504 667 546 641T626 573T685 470T708 336Q708 210 634 116T442 3Q429 1 228 0H27V46H60Q102 47 111 49T130 61V622ZM593 338Q593 439 571 501T493 602Q439 637 355 637H322H294Q238 637 234 628Q231 624 231 344Q231 62 232 59Q233 49 248 48T339 46H350Q456 46 515 95Q561 133 577 191T593 338Z" transform="translate(834,0)"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(1598,0)"></path><path data-c="67" d="M329 409Q373 453 429 453Q459 453 472 434T485 396Q485 382 476 371T449 360Q416 360 412 390Q410 404 415 411Q415 412 416 414V415Q388 412 363 393Q355 388 355 386Q355 385 359 381T368 369T379 351T388 325T392 292Q392 230 343 187T222 143Q172 143 123 171Q112 153 112 133Q112 98 138 81Q147 75 155 75T227 73Q311 72 335 67Q396 58 431 26Q470 -13 470 -72Q470 -139 392 -175Q332 -206 250 -206Q167 -206 107 -175Q29 -140 29 -75Q29 -39 50 -15T92 18L103 24Q67 55 67 108Q67 155 96 193Q52 237 52 292Q52 355 102 398T223 442Q274 442 318 416L329 409ZM299 343Q294 371 273 387T221 404Q192 404 171 388T145 343Q142 326 142 292Q142 248 149 227T179 192Q196 182 222 182Q244 182 260 189T283 207T294 227T299 242Q302 258 302 292T299 343ZM403 -75Q403 -50 389 -34T348 -11T299 -2T245 0H218Q151 0 138 -6Q118 -15 107 -34T95 -74Q95 -84 101 -97T122 -127T170 -155T250 -167Q319 -167 361 -139T403 -75Z" transform="translate(2042,0)"></path></g><g data-mml-node="mo" transform="translate(2542,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="msub" transform="translate(2931,0)"><g data-mml-node="mi"><path data-c="1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path></g><g data-mml-node="mn" transform="translate(518,-150) scale(0.707)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g><g data-mml-node="mo" transform="translate(3852.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4519.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(5575.1,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g>',1),$M=[YM],Qu=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"inDeg"),Q("mo",{stretchy:"false"},"("),Q("msub",null,[Q("mi",null,"v"),Q("mn",null,"0")]),Q("mo",{stretchy:"false"},")"),Q("mo",null,"="),Q("mn",null,"0")])],-1),au={class:"MathJax",jax:"SVG",style:{position:"relative"}},tu={style:{"vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.507ex",role:"img",focusable:"false",viewBox:"0 -666 500 666","aria-hidden":"true"},Tu=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"31",d:"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"})])])],-1),mu=[Tu],nu=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"1")])],-1),lu={class:"MathJax",jax:"SVG",style:{position:"relative"}},eu={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"12.757ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 5638.6 1000","aria-hidden":"true"},su=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="69" d="M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z"></path><path data-c="6E" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z" transform="translate(278,0)"></path><path data-c="44" d="M130 622Q123 629 119 631T103 634T60 637H27V683H228Q399 682 419 682T461 676Q504 667 546 641T626 573T685 470T708 336Q708 210 634 116T442 3Q429 1 228 0H27V46H60Q102 47 111 49T130 61V622ZM593 338Q593 439 571 501T493 602Q439 637 355 637H322H294Q238 637 234 628Q231 624 231 344Q231 62 232 59Q233 49 248 48T339 46H350Q456 46 515 95Q561 133 577 191T593 338Z" transform="translate(834,0)"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(1598,0)"></path><path data-c="67" d="M329 409Q373 453 429 453Q459 453 472 434T485 396Q485 382 476 371T449 360Q416 360 412 390Q410 404 415 411Q415 412 416 414V415Q388 412 363 393Q355 388 355 386Q355 385 359 381T368 369T379 351T388 325T392 292Q392 230 343 187T222 143Q172 143 123 171Q112 153 112 133Q112 98 138 81Q147 75 155 75T227 73Q311 72 335 67Q396 58 431 26Q470 -13 470 -72Q470 -139 392 -175Q332 -206 250 -206Q167 -206 107 -175Q29 -140 29 -75Q29 -39 50 -15T92 18L103 24Q67 55 67 108Q67 155 96 193Q52 237 52 292Q52 355 102 398T223 442Q274 442 318 416L329 409ZM299 343Q294 371 273 387T221 404Q192 404 171 388T145 343Q142 326 142 292Q142 248 149 227T179 192Q196 182 222 182Q244 182 260 189T283 207T294 227T299 242Q302 258 302 292T299 343ZM403 -75Q403 -50 389 -34T348 -11T299 -2T245 0H218Q151 0 138 -6Q118 -15 107 -34T95 -74Q95 -84 101 -97T122 -127T170 -155T250 -167Q319 -167 361 -139T403 -75Z" transform="translate(2042,0)"></path></g><g data-mml-node="mo" transform="translate(2542,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(2931,0)"><path data-c="1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path></g><g data-mml-node="mo" transform="translate(3416,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4082.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mn" transform="translate(5138.6,0)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g></g>',1),ou=[su],ru=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"inDeg"),Q("mo",{stretchy:"false"},"("),Q("mi",null,"v"),Q("mo",{stretchy:"false"},")"),Q("mo",null,"≤"),Q("mn",null,"1")])],-1),du={class:"MathJax",jax:"SVG",style:{position:"relative"}},hu={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 500 688","aria-hidden":"true"},iu=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"30",d:"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"})])])],-1),gu=[iu],Hu=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0")])],-1),Lu={class:"MathJax",jax:"SVG",style:{position:"relative"}},cu={style:{"vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.157ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4931.3 1000","aria-hidden":"true"},pu=m('<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="2203" d="M56 661T56 674T70 694H487Q497 686 500 679V15Q497 10 487 1L279 0H70Q56 7 56 20T70 40H460V327H84Q70 334 70 347T84 367H460V654H70Q56 661 56 674Z"></path></g><g data-mml-node="mi" transform="translate(722.7,0)"><path data-c="70" d="M36 -148H50Q89 -148 97 -134V-126Q97 -119 97 -107T97 -77T98 -38T98 6T98 55T98 106Q98 140 98 177T98 243T98 296T97 335T97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 61 434T98 436Q115 437 135 438T165 441T176 442H179V416L180 390L188 397Q247 441 326 441Q407 441 464 377T522 216Q522 115 457 52T310 -11Q242 -11 190 33L182 40V-45V-101Q182 -128 184 -134T195 -145Q216 -148 244 -148H260V-194H252L228 -193Q205 -192 178 -192T140 -191Q37 -191 28 -194H20V-148H36ZM424 218Q424 292 390 347T305 402Q234 402 182 337V98Q222 26 294 26Q345 26 384 80T424 218Z"></path><path data-c="61" d="M137 305T115 305T78 320T63 359Q63 394 97 421T218 448Q291 448 336 416T396 340Q401 326 401 309T402 194V124Q402 76 407 58T428 40Q443 40 448 56T453 109V145H493V106Q492 66 490 59Q481 29 455 12T400 -6T353 12T329 54V58L327 55Q325 52 322 49T314 40T302 29T287 17T269 6T247 -2T221 -8T190 -11Q130 -11 82 20T34 107Q34 128 41 147T68 188T116 225T194 253T304 268H318V290Q318 324 312 340Q290 411 215 411Q197 411 181 410T156 406T148 403Q170 388 170 359Q170 334 154 320ZM126 106Q126 75 150 51T209 26Q247 26 276 49T315 109Q317 116 318 175Q318 233 317 233Q309 233 296 232T251 223T193 203T147 166T126 106Z" transform="translate(556,0)"></path><path data-c="74" d="M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z" transform="translate(1056,0)"></path><path data-c="68" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z" transform="translate(1445,0)"></path></g><g data-mml-node="mo" transform="translate(2723.7,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(3112.7,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(3612.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(4057.3,0)"><path data-c="1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path></g><g data-mml-node="mo" transform="translate(4542.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g>',1),fu=[pu],Mu=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",{mathvariant:"normal"},"∃"),Q("mi",null,"path"),Q("mo",{stretchy:"false"},"("),Q("mn",null,"0"),Q("mo",null,","),Q("mi",null,"v"),Q("mo",{stretchy:"false"},")")])],-1),uu=Q("p",null,[a("下面我们试着通过"),Q("strong",null,"删除公理"),a("的方法来寻找反例。")],-1),xu=Q("h4",{id:"peano-公理-i",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#peano-公理-i"},[Q("span",null,"Peano 公理 Ⅰ")])],-1),Zu={class:"MathJax",jax:"SVG",style:{position:"relative"}},Vu={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 500 688","aria-hidden":"true"},wu=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"30",d:"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"})])])],-1),_u=[wu],vu=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0")])],-1),yu=Q("h4",{id:"peano-公理-ii",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#peano-公理-ii"},[Q("span",null,"Peano 公理 Ⅱ")])],-1),Du=Q("p",null,"若去除，则对点的出度无规定，可以构造出菊花图自然数系统。",-1),bu=Q("h4",{id:"peano-公理-iii",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#peano-公理-iii"},[Q("span",null,"Peano 公理 Ⅲ")])],-1),ju={class:"MathJax",jax:"SVG",style:{position:"relative"}},Bu={style:{"vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.557ex",role:"img",focusable:"false",viewBox:"0 -666 500 688","aria-hidden":"true"},ku=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mn"},[Q("path",{"data-c":"30",d:"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"})])])],-1),Cu=[ku],zu=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mn",null,"0")])],-1),Su=Q("h4",{id:"peano-公理-iv",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#peano-公理-iv"},[Q("span",null,"Peano 公理 Ⅳ")])],-1),Ju={class:"MathJax",jax:"SVG",style:{position:"relative"}},Gu={style:{"vertical-align":"-0.489ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.17ex",height:"1.489ex",role:"img",focusable:"false",viewBox:"0 -442 517 658","aria-hidden":"true"},Au=Q("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[Q("g",{"data-mml-node":"math"},[Q("g",{"data-mml-node":"mi"},[Q("path",{"data-c":"1D70C",d:"M58 -216Q25 -216 23 -186Q23 -176 73 26T127 234Q143 289 182 341Q252 427 341 441Q343 441 349 441T359 442Q432 442 471 394T510 276Q510 219 486 165T425 74T345 13T266 -10H255H248Q197 -10 165 35L160 41L133 -71Q108 -168 104 -181T92 -202Q76 -216 58 -216ZM424 322Q424 359 407 382T357 405Q322 405 287 376T231 300Q217 269 193 170L176 102Q193 26 260 26Q298 26 334 62Q367 92 389 158T418 266T424 322Z"})])])],-1),Eu=[Au],Fu=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"ρ")])],-1),Ou=Q("h4",{id:"peano-公理-v",tabindex:"-1"},[Q("a",{class:"header-anchor",href:"#peano-公理-v"},[Q("span",null,"Peano 公理 Ⅴ")])],-1),Ru=Q("p",null,"若去除，则对连通性无要求，可以构造出分段状自然数系统。",-1);function Pu(Xu,Nu){return t(),T("div",null,[s,o,l(" more "),r,d,Q("ol",null,[Q("li",null,[Q("p",null,[Q("mjx-container",h,[(t(),T("svg",i,H)),L]),a(" 是自然数；")])]),Q("li",null,[Q("p",null,[a("任何自然数的后继存在且唯一，下文用 "),Q("mjx-container",c,[(t(),T("svg",p,M)),u]),a(" 表示 "),Q("mjx-container",x,[(t(),T("svg",Z,w)),_]),a(" 的后继；")])]),Q("li",null,[Q("p",null,[Q("mjx-container",v,[(t(),T("svg",y,b)),j]),a(" 不是任何自然数的后继；")])]),B,Q("li",null,[Q("p",null,[Q("mjx-container",k,[(t(),T("svg",C,S)),J]),a(" 是关于自然数 "),Q("mjx-container",G,[(t(),T("svg",A,F)),O]),a(" 的一个命题，且满足两个条件：")]),Q("ul",null,[Q("li",null,[Q("mjx-container",R,[(t(),T("svg",P,N)),K]),a(" 是真命题；")]),Q("li",null,[a("由 "),Q("mjx-container",I,[(t(),T("svg",q,W)),Y]),a(" 为真命题可以推理出 "),Q("mjx-container",$,[(t(),T("svg",Q1,t1)),T1]),a(" 为真命题。")])]),Q("p",null,[a("则有，对于任意自然数 "),Q("mjx-container",m1,[(t(),T("svg",n1,e1)),s1]),a("，"),Q("mjx-container",o1,[(t(),T("svg",r1,h1)),i1]),a(" 为真命题。")])])]),g1,H1,L1,c1,p1,Q("ol",null,[Q("li",null,[a("若 "),Q("mjx-container",f1,[(t(),T("svg",M1,x1)),Z1]),a(" 是自然数，则 "),Q("mjx-container",V1,[(t(),T("svg",w1,v1)),y1]),a(" 的运算结果为 "),Q("mjx-container",D1,[(t(),T("svg",b1,B1)),k1]),a("，即 "),Q("mjx-container",C1,[(t(),T("svg",z1,J1)),G1]),a("；")]),Q("li",null,[a("若 "),Q("mjx-container",A1,[(t(),T("svg",E1,O1)),R1]),a(" 都是自然数，则 "),Q("mjx-container",P1,[(t(),T("svg",X1,K1)),I1]),a("。")])]),q1,U1,Q("p",null,[Q("mjx-container",W1,[(t(),T("svg",Y1,Q3)),a3]),a(" 是任意自然数，记 "),Q("mjx-container",t3,[(t(),T("svg",T3,n3)),l3]),a(" 表示 "),Q("mjx-container",e3,[(t(),T("svg",s3,r3)),d3]),a(" 是否是自然数，即 "),Q("mjx-container",h3,[(t(),T("svg",i3,H3)),L3]),a(" 是否存在。")]),Q("p",null,[Q("mjx-container",c3,[(t(),T("svg",p3,M3)),u3]),a(" 是自然数，由加法运算规则 Ⅰ 有 "),Q("mjx-container",x3,[(t(),T("svg",Z3,w3)),_3]),a("，进而有 "),Q("mjx-container",v3,[(t(),T("svg",y3,b3)),j3]),a(" 是自然数； "),Q("strong",null,[a("即 "),Q("mjx-container",B3,[(t(),T("svg",k3,z3)),S3]),a(" 得证。")])]),Q("p",null,[Q("mjx-container",J3,[(t(),T("svg",G3,E3)),F3]),a(" 和 "),Q("mjx-container",O3,[(t(),T("svg",R3,X3)),N3]),a(" 是自然数，由 Peano 公理 Ⅱ 有 "),Q("mjx-container",K3,[(t(),T("svg",I3,U3)),W3]),a(" 和 "),Q("mjx-container",Y3,[(t(),T("svg",$3,a2)),t2]),a(" 是自然数； 根据加法运算规则 Ⅱ 有 "),Q("mjx-container",T2,[(t(),T("svg",m2,l2)),e2]),a("，进有 "),Q("mjx-container",s2,[(t(),T("svg",o2,d2)),h2]),a(" 是自然数； 综上所述，若 "),Q("mjx-container",i2,[(t(),T("svg",g2,L2)),c2]),a(" 是自然数，则 "),Q("mjx-container",p2,[(t(),T("svg",f2,u2)),x2]),a(" 也是自然数； "),Q("strong",null,[a("即由 "),Q("mjx-container",Z2,[(t(),T("svg",V2,_2)),v2]),a(" 为真命题可以推出 "),Q("mjx-container",y2,[(t(),T("svg",D2,j2)),B2]),a(" 为真命题。")])]),Q("p",null,[a("由 "),Q("mjx-container",k2,[(t(),T("svg",C2,S2)),J2]),a(" 的性质和 Peano 公理 Ⅴ 有，对于任意自然数 "),Q("mjx-container",G2,[(t(),T("svg",A2,F2)),O2]),a("，"),Q("mjx-container",R2,[(t(),T("svg",P2,N2)),K2]),a(" 成立，即 "),Q("mjx-container",I2,[(t(),T("svg",q2,W2)),Y2]),a(" 是自然数，再根据 "),Q("mjx-container",$2,[(t(),T("svg",Q4,t4)),T4]),a(" 的任意性，得出对于任意自然数 "),Q("mjx-container",m4,[(t(),T("svg",n4,e4)),s4]),a("，"),Q("mjx-container",o4,[(t(),T("svg",r4,h4)),i4]),a(" 都是自然数。")]),g4,Q("p",null,[Q("mjx-container",H4,[(t(),T("svg",L4,p4)),f4]),a(" 是任意自然数，记 "),Q("mjx-container",M4,[(t(),T("svg",u4,Z4)),V4]),a(" 表示 "),Q("mjx-container",w4,[(t(),T("svg",_4,y4)),D4]),a(" 是否唯一，即 "),Q("mjx-container",b4,[(t(),T("svg",j4,k4)),C4]),a(" 的结果是否唯一。")]),Q("p",null,[Q("mjx-container",z4,[(t(),T("svg",S4,G4)),A4]),a(" 是自然数，由加法运算规则 Ⅰ 有 "),Q("mjx-container",E4,[(t(),T("svg",F4,R4)),P4]),a("，进而 "),Q("mjx-container",X4,[(t(),T("svg",N4,I4)),q4]),a(" 是唯一的，就是 "),Q("mjx-container",U4,[(t(),T("svg",W4,$4)),Q5]),a("； "),Q("strong",null,[a("即 "),Q("mjx-container",a5,[(t(),T("svg",t5,m5)),n5]),a(" 得证。")])]),Q("p",null,[Q("mjx-container",l5,[(t(),T("svg",e5,o5)),r5]),a(" 是自然数，"),Q("mjx-container",d5,[(t(),T("svg",h5,g5)),H5]),a(" 是唯一的，由 Peano 公理 Ⅱ 有 "),Q("mjx-container",L5,[(t(),T("svg",c5,f5)),M5]),a(" 是自然数且 "),Q("mjx-container",u5,[(t(),T("svg",x5,V5)),w5]),a(" 唯一； 根据加法运算规则 Ⅱ 有 "),Q("mjx-container",_5,[(t(),T("svg",v5,D5)),b5]),a("，进有 "),Q("mjx-container",j5,[(t(),T("svg",B5,C5)),z5]),a(" 唯一； 综上所述，若 "),Q("mjx-container",S5,[(t(),T("svg",J5,A5)),E5]),a(" 唯一，则 "),Q("mjx-container",F5,[(t(),T("svg",O5,P5)),X5]),a(" 也唯一； "),Q("strong",null,[a("即由 "),Q("mjx-container",N5,[(t(),T("svg",K5,q5)),U5]),a(" 为真命题可以推出 "),Q("mjx-container",W5,[(t(),T("svg",Y5,Q6)),a6]),a(" 为真命题。")])]),Q("p",null,[a("由 "),Q("mjx-container",t6,[(t(),T("svg",T6,n6)),l6]),a(" 的性质和 Peano 公理 Ⅴ 有，对于任意自然数 "),Q("mjx-container",e6,[(t(),T("svg",s6,r6)),d6]),a("，"),Q("mjx-container",h6,[(t(),T("svg",i6,H6)),L6]),a(" 成立，即 "),Q("mjx-container",c6,[(t(),T("svg",p6,M6)),u6]),a(" 唯一，再根据 "),Q("mjx-container",x6,[(t(),T("svg",Z6,w6)),_6]),a(" 的任意性，得出对于任意自然数 "),Q("mjx-container",v6,[(t(),T("svg",y6,b6)),j6]),a("，"),Q("mjx-container",B6,[(t(),T("svg",k6,z6)),S6]),a(" 都是唯一的。")]),J6,G6,A6,Q("p",null,[a("下面证明加法交换律，即对于任意自然数 "),Q("mjx-container",E6,[(t(),T("svg",F6,R6)),P6]),a("，有 "),Q("mjx-container",X6,[(t(),T("svg",N6,I6)),q6]),a("。")]),U6,Q("p",null,[a("试证 "),Q("mjx-container",W6,[(t(),T("svg",Y6,Q7)),a7]),a("，首先有")]),Q("mjx-container",t7,[(t(),T("svg",T7,n7)),l7]),Q("p",null,[a("进而当 "),Q("mjx-container",e7,[(t(),T("svg",s7,r7)),d7]),a(" 是自然数且 "),Q("mjx-container",h7,[(t(),T("svg",i7,H7)),L7]),a(" 时有")]),Q("mjx-container",c7,[(t(),T("svg",p7,M7)),u7]),Q("p",null,[a("根据 Peano 公理 Ⅴ，得知 "),Q("mjx-container",x7,[(t(),T("svg",Z7,w7)),_7]),a(" 对任意自然数 "),Q("mjx-container",v7,[(t(),T("svg",y7,b7)),j7]),a(" 成立。")]),Q("p",null,[a("试证 "),Q("mjx-container",B7,[(t(),T("svg",k7,z7)),S7]),a("，首先有")]),Q("mjx-container",J7,[(t(),T("svg",G7,E7)),F7]),Q("p",null,[a("进而当 "),Q("mjx-container",O7,[(t(),T("svg",R7,X7)),N7]),a(" 是自然数且 "),Q("mjx-container",K7,[(t(),T("svg",I7,U7)),W7]),a(" 时有")]),Q("mjx-container",Y7,[(t(),T("svg",$7,a0)),t0]),Q("p",null,[a("根据 Peano 公理 Ⅴ，得知 "),Q("mjx-container",T0,[(t(),T("svg",m0,l0)),e0]),a(" 对任意自然数 "),Q("mjx-container",s0,[(t(),T("svg",o0,d0)),h0]),a(" 成立，将其称为新的"),i0,a("。")]),Q("p",null,[a("证明了加法运算规则的交换律之后，试证加法交换律 "),Q("mjx-container",g0,[(t(),T("svg",H0,c0)),p0]),a("，首先由加法运算规则 Ⅰ 有 "),Q("mjx-container",f0,[(t(),T("svg",M0,x0)),Z0]),a("，进而当 "),Q("mjx-container",V0,[(t(),T("svg",w0,v0)),y0]),a(" 是自然数且 "),Q("mjx-container",D0,[(t(),T("svg",b0,B0)),k0]),a(" 时，有")]),Q("mjx-container",C0,[(t(),T("svg",z0,J0)),G0]),Q("p",null,[a("根据 Peano 公理 Ⅴ，得知 "),Q("mjx-container",A0,[(t(),T("svg",E0,O0)),R0]),a(" 对任意自然数 "),Q("mjx-container",P0,[(t(),T("svg",X0,K0)),I0]),a(" 成立，即加法交换律成立。")]),q0,Q("p",null,[a("下面证明加法结合律，即对于任意自然数 "),Q("mjx-container",U0,[(t(),T("svg",W0,$0)),Q8]),a("，有 "),Q("mjx-container",a8,[(t(),T("svg",t8,m8)),n8]),a("。")]),Q("p",null,[a("首先当 "),Q("mjx-container",l8,[(t(),T("svg",e8,o8)),r8]),a(" 时，有")]),Q("mjx-container",d8,[(t(),T("svg",h8,g8)),H8]),Q("p",null,[a("进而当 "),Q("mjx-container",L8,[(t(),T("svg",c8,f8)),M8]),a(" 为自然数且 "),Q("mjx-container",u8,[(t(),T("svg",x8,V8)),w8]),a(" 时有")]),Q("mjx-container",_8,[(t(),T("svg",v8,D8)),b8]),Q("p",null,[a("根据 Peano 公理 Ⅴ，得知 "),Q("mjx-container",j8,[(t(),T("svg",B8,C8)),z8]),a(" 对任意自然数 "),Q("mjx-container",S8,[(t(),T("svg",J8,A8)),E8]),a(" 成立，即加法结合律成立。")]),F8,Q("p",null,[a("下面证明加法消去律，即对于任意自然数 "),Q("mjx-container",O8,[(t(),T("svg",R8,X8)),N8]),a("，有 "),Q("mjx-container",K8,[(t(),T("svg",I8,U8)),W8]),a("。")]),Q("p",null,[a("试证 "),Q("mjx-container",Y8,[(t(),T("svg",$8,a9)),t9]),a("。")]),Q("p",null,[a("首先当 "),Q("mjx-container",T9,[(t(),T("svg",m9,l9)),e9]),a(" 时有")]),Q("mjx-container",s9,[(t(),T("svg",o9,d9)),h9]),Q("p",null,[a("进而当 "),Q("mjx-container",i9,[(t(),T("svg",g9,L9)),c9]),a(" 为自然数且 "),Q("mjx-container",p9,[(t(),T("svg",f9,u9)),x9]),a(" 时有")]),Q("mjx-container",Z9,[(t(),T("svg",V9,_9)),v9]),Q("p",null,[a("即 "),Q("mjx-container",y9,[(t(),T("svg",D9,j9)),B9]),a("，根据 Peano 公理 Ⅴ，得知 "),Q("mjx-container",k9,[(t(),T("svg",C9,S9)),J9]),a(" 对任意自然数 "),Q("mjx-container",G9,[(t(),T("svg",A9,F9)),O9]),a(" 成立。")]),Q("p",null,[a("试证 "),Q("mjx-container",R9,[(t(),T("svg",P9,N9)),K9]),a("。")]),Q("p",null,[a("首先当 "),Q("mjx-container",I9,[(t(),T("svg",q9,W9)),Y9]),a(" 时有")]),Q("mjx-container",$9,[(t(),T("svg",QQ,tQ)),TQ]),Q("p",null,[a("进而当 "),Q("mjx-container",mQ,[(t(),T("svg",nQ,eQ)),sQ]),a(" 为自然数且 "),Q("mjx-container",oQ,[(t(),T("svg",rQ,hQ)),iQ]),a(" 时有")]),Q("mjx-container",gQ,[(t(),T("svg",HQ,cQ)),pQ]),Q("p",null,[a("即 "),Q("mjx-container",fQ,[(t(),T("svg",MQ,xQ)),ZQ]),a("，根据 Peano 公理 Ⅴ，得知 "),Q("mjx-container",VQ,[(t(),T("svg",wQ,vQ)),yQ]),a(" 对任意自然数 "),Q("mjx-container",DQ,[(t(),T("svg",bQ,BQ)),kQ]),a(" 成立。")]),Q("p",null,[a("综上所述，加法消去律 "),Q("mjx-container",CQ,[(t(),T("svg",zQ,JQ)),GQ]),a("，对任意自然数 "),Q("mjx-container",AQ,[(t(),T("svg",EQ,OQ)),RQ]),a(" 成立。")]),PQ,XQ,NQ,Q("p",null,[a("定义自然数的序即定义 "),Q("mjx-container",KQ,[(t(),T("svg",IQ,UQ)),WQ]),a(" 当且仅当存在自然数 "),Q("mjx-container",YQ,[(t(),T("svg",$Q,aa)),ta]),a(" 满足 "),Q("mjx-container",Ta,[(t(),T("svg",ma,la)),ea]),a("。定义 "),Q("mjx-container",sa,[(t(),T("svg",oa,da)),ha]),a(" 当且仅当 "),Q("mjx-container",ia,[(t(),T("svg",ga,La)),ca]),a(" 且 "),Q("mjx-container",pa,[(t(),T("svg",fa,ua)),xa]),a("。")]),Za,Va,wa,Q("p",null,[a("定义正自然数为非 "),Q("mjx-container",_a,[(t(),T("svg",va,Da)),ba]),a(" 自然数。")]),ja,Q("p",null,[a("正自然数与自然数相加为正自然数，即对于正自然数 "),Q("mjx-container",Ba,[(t(),T("svg",ka,za)),Sa]),a("，其与自然数 "),Q("mjx-container",Ja,[(t(),T("svg",Ga,Ea)),Fa]),a(" 的和 "),Q("mjx-container",Oa,[(t(),T("svg",Ra,Xa)),Na]),a(" 为正自然数。")]),Q("p",null,[a("首先，当 "),Q("mjx-container",Ka,[(t(),T("svg",Ia,Ua)),Wa]),a(" 时，"),Q("mjx-container",Ya,[(t(),T("svg",$a,at)),tt]),a(" 为正自然数。")]),Q("p",null,[a("进而当 "),Q("mjx-container",Tt,[(t(),T("svg",mt,lt)),et]),a(" 为自然数且 "),Q("mjx-container",st,[(t(),T("svg",ot,dt)),ht]),a(" 为正自然数时有 "),Q("mjx-container",it,[(t(),T("svg",gt,Lt)),ct]),a("，根据 Peano 公理 Ⅲ，"),Q("mjx-container",pt,[(t(),T("svg",ft,ut)),xt]),a(" 为正自然数，进而 "),Q("mjx-container",Zt,[(t(),T("svg",Vt,_t)),vt]),a(" 为正自然数。")]),yt,Dt,Q("p",null,[a("若 "),Q("mjx-container",bt,[(t(),T("svg",jt,kt)),Ct]),a(" 且 "),Q("mjx-container",zt,[(t(),T("svg",St,Gt)),At]),a("，则 "),Q("mjx-container",Et,[(t(),T("svg",Ft,Rt)),Pt]),a("。")]),Q("p",null,[a("由 "),Q("mjx-container",Xt,[(t(),T("svg",Nt,It)),qt]),a(" 有 "),Q("mjx-container",Ut,[(t(),T("svg",Wt,$t)),QT]),a("，由 "),Q("mjx-container",aT,[(t(),T("svg",tT,mT)),nT]),a(" 有 "),Q("mjx-container",lT,[(t(),T("svg",eT,oT)),rT]),a("。")]),Q("p",null,[a("因此 "),Q("mjx-container",dT,[(t(),T("svg",hT,gT)),HT]),a("，由加法消去律得到 "),Q("mjx-container",LT,[(t(),T("svg",cT,fT)),MT]),a("，根据正自然数的性质得出 "),Q("mjx-container",uT,[(t(),T("svg",xT,VT)),wT]),a("，因此 "),Q("mjx-container",_T,[(t(),T("svg",vT,DT)),bT]),a("。")]),jT,Q("p",null,[a("若 "),Q("mjx-container",BT,[(t(),T("svg",kT,zT)),ST]),a(" 且 "),Q("mjx-container",JT,[(t(),T("svg",GT,ET)),FT]),a("，则 "),Q("mjx-container",OT,[(t(),T("svg",RT,XT)),NT]),a("。")]),Q("p",null,[a("由 "),Q("mjx-container",KT,[(t(),T("svg",IT,UT)),WT]),a(" 有 "),Q("mjx-container",YT,[(t(),T("svg",$T,am)),tm]),a("，由 "),Q("mjx-container",Tm,[(t(),T("svg",mm,lm)),em]),a(" 有 "),Q("mjx-container",sm,[(t(),T("svg",om,dm)),hm]),a("。")]),Q("p",null,[a("根据加法结果的存在性得到 "),Q("mjx-container",im,[(t(),T("svg",gm,Lm)),cm]),a(" 是自然数，根据加法结合律得出 "),Q("mjx-container",pm,[(t(),T("svg",fm,um)),xm]),a("，进而 "),Q("mjx-container",Zm,[(t(),T("svg",Vm,_m)),vm]),a("。")]),ym,Q("p",null,[a("任意两个自然数 "),Q("mjx-container",Dm,[(t(),T("svg",bm,Bm)),km]),a(" 都有序关系。")]),Q("p",null,[a("对于 "),Q("mjx-container",Cm,[(t(),T("svg",zm,Jm)),Gm]),a(" 两个自然数，当 "),Q("mjx-container",Am,[(t(),T("svg",Em,Om)),Rm]),a(" 时有 "),Q("mjx-container",Pm,[(t(),T("svg",Xm,Km)),Im]),a(" 所以 "),Q("mjx-container",qm,[(t(),T("svg",Um,Ym)),$m]),a("。")]),Q("p",null,[a("当 "),Q("mjx-container",Qn,[(t(),T("svg",an,Tn)),mn]),a(" 为自然数时。若 "),Q("mjx-container",nn,[(t(),T("svg",ln,sn)),on]),a("，则 "),Q("mjx-container",rn,[(t(),T("svg",dn,gn)),Hn]),a("，因此 "),Q("mjx-container",Ln,[(t(),T("svg",cn,fn)),Mn]),a("；若 "),Q("mjx-container",un,[(t(),T("svg",xn,Vn)),wn]),a("，则 "),Q("mjx-container",_n,[(t(),T("svg",vn,Dn)),bn]),a("，因此 "),Q("mjx-container",jn,[(t(),T("svg",Bn,Cn)),zn]),a("；若 "),Q("mjx-container",Sn,[(t(),T("svg",Jn,An)),En]),a("，则 "),Q("mjx-container",Fn,[(t(),T("svg",On,Pn)),Xn]),a("。")]),Q("p",null,[a("由 Peano 公理 Ⅴ 有任意两个自然数 "),Q("mjx-container",Nn,[(t(),T("svg",Kn,qn)),Un]),a(" 都有序关系。")]),Wn,Q("p",null,[a("若 "),Q("mjx-container",Yn,[(t(),T("svg",$n,al)),tl]),a("，则 "),Q("mjx-container",Tl,[(t(),T("svg",ml,ll)),el]),a("。")]),Q("p",null,[a("由 "),Q("mjx-container",sl,[(t(),T("svg",ol,dl)),hl]),a(" 有 "),Q("mjx-container",il,[(t(),T("svg",gl,Ll)),cl]),a("，进而 "),Q("mjx-container",pl,[(t(),T("svg",fl,ul)),xl]),a(" 因此 "),Q("mjx-container",Zl,[(t(),T("svg",Vl,_l)),vl]),a("。")]),yl,Dl,bl,jl,Q("ol",null,[Q("li",null,[a("若 "),Q("mjx-container",Bl,[(t(),T("svg",kl,zl)),Sl]),a(" 是自然数，则 "),Q("mjx-container",Jl,[(t(),T("svg",Gl,El)),Fl]),a(" 的运算结果为 "),Q("mjx-container",Ol,[(t(),T("svg",Rl,Xl)),Nl]),a("，即 "),Q("mjx-container",Kl,[(t(),T("svg",Il,Ul)),Wl]),a("；")]),Q("li",null,[a("若 "),Q("mjx-container",Yl,[(t(),T("svg",$l,ae)),te]),a(" 都是自然数，则 "),Q("mjx-container",Te,[(t(),T("svg",me,le)),ee]),a("。")])]),se,oe,Q("p",null,[Q("mjx-container",re,[(t(),T("svg",de,ie)),ge]),a(" 是任意自然数，记 "),Q("mjx-container",He,[(t(),T("svg",Le,pe)),fe]),a(" 表示 "),Q("mjx-container",Me,[(t(),T("svg",ue,Ze)),Ve]),a(" 是否是自然数，即 "),Q("mjx-container",we,[(t(),T("svg",_e,ye)),De]),a(" 是否存在。")]),Q("p",null,[Q("mjx-container",be,[(t(),T("svg",je,ke)),Ce]),a(" 是自然数，由乘法运算规则 Ⅰ 有 "),Q("mjx-container",ze,[(t(),T("svg",Se,Ge)),Ae]),a("，进而有 "),Q("mjx-container",Ee,[(t(),T("svg",Fe,Re)),Pe]),a(" 是自然数； "),Q("strong",null,[a("即 "),Q("mjx-container",Xe,[(t(),T("svg",Ne,Ie)),qe]),a(" 得证。")])]),Q("p",null,[Q("mjx-container",Ue,[(t(),T("svg",We,$e)),Qs]),a(" 和 "),Q("mjx-container",as,[(t(),T("svg",ts,ms)),ns]),a(" 是自然数，由加法结果的存在性有 "),Q("mjx-container",ls,[(t(),T("svg",es,os)),rs]),a(" 存在； 根据乘法运算规则 Ⅱ 有 "),Q("mjx-container",ds,[(t(),T("svg",hs,gs)),Hs]),a("，进有 "),Q("mjx-container",Ls,[(t(),T("svg",cs,fs)),Ms]),a(" 是自然数； 综上所述，若 "),Q("mjx-container",us,[(t(),T("svg",xs,Vs)),ws]),a(" 是自然数，则 "),Q("mjx-container",_s,[(t(),T("svg",vs,Ds)),bs]),a(" 也是自然数； "),Q("strong",null,[a("即由 "),Q("mjx-container",js,[(t(),T("svg",Bs,Cs)),zs]),a(" 为真命题可以推出 "),Q("mjx-container",Ss,[(t(),T("svg",Js,As)),Es]),a(" 为真命题。")])]),Q("p",null,[a("由 "),Q("mjx-container",Fs,[(t(),T("svg",Os,Ps)),Xs]),a(" 的性质和 Peano 公理 Ⅴ 有，对于任意自然数 "),Q("mjx-container",Ns,[(t(),T("svg",Ks,qs)),Us]),a("，"),Q("mjx-container",Ws,[(t(),T("svg",Ys,Qo)),ao]),a(" 成立，即 "),Q("mjx-container",to,[(t(),T("svg",To,no)),lo]),a(" 是自然数，再根据 "),Q("mjx-container",eo,[(t(),T("svg",so,ro)),ho]),a(" 的任意性，得出对于任意自然数 "),Q("mjx-container",io,[(t(),T("svg",go,Lo)),co]),a("，"),Q("mjx-container",po,[(t(),T("svg",fo,uo)),xo]),a(" 都是自然数。")]),Zo,Q("p",null,[Q("mjx-container",Vo,[(t(),T("svg",wo,vo)),yo]),a(" 是任意自然数，记 "),Q("mjx-container",Do,[(t(),T("svg",bo,Bo)),ko]),a(" 表示 "),Q("mjx-container",Co,[(t(),T("svg",zo,Jo)),Go]),a(" 是否唯一，即 "),Q("mjx-container",Ao,[(t(),T("svg",Eo,Oo)),Ro]),a(" 的结果是否唯一。")]),Q("p",null,[Q("mjx-container",Po,[(t(),T("svg",Xo,Ko)),Io]),a(" 是自然数，由乘法运算规则 Ⅰ 有 "),Q("mjx-container",qo,[(t(),T("svg",Uo,Yo)),$o]),a("，进而 "),Q("mjx-container",Qr,[(t(),T("svg",ar,Tr)),mr]),a(" 是唯一的，就是 "),Q("mjx-container",nr,[(t(),T("svg",lr,sr)),or]),a("； "),Q("strong",null,[a("即 "),Q("mjx-container",rr,[(t(),T("svg",dr,ir)),gr]),a(" 得证。")])]),Q("p",null,[Q("mjx-container",Hr,[(t(),T("svg",Lr,pr)),fr]),a(" 是自然数，"),Q("mjx-container",Mr,[(t(),T("svg",ur,Zr)),Vr]),a(" 是唯一的，由加法结果的唯一性有 "),Q("mjx-container",wr,[(t(),T("svg",_r,yr)),Dr]),a(" 唯一； 根据乘法运算规则 Ⅱ 有 "),Q("mjx-container",br,[(t(),T("svg",jr,kr)),Cr]),a("，进有 "),Q("mjx-container",zr,[(t(),T("svg",Sr,Gr)),Ar]),a(" 唯一； 综上所述，若 "),Q("mjx-container",Er,[(t(),T("svg",Fr,Rr)),Pr]),a(" 唯一，则 "),Q("mjx-container",Xr,[(t(),T("svg",Nr,Ir)),qr]),a(" 也唯一； "),Q("strong",null,[a("即由 "),Q("mjx-container",Ur,[(t(),T("svg",Wr,$r)),Qd]),a(" 为真命题可以推出 "),Q("mjx-container",ad,[(t(),T("svg",td,md)),nd]),a(" 为真命题。")])]),Q("p",null,[a("由 "),Q("mjx-container",ld,[(t(),T("svg",ed,od)),rd]),a(" 的性质和 Peano 公理 Ⅴ 有，对于任意自然数 "),Q("mjx-container",dd,[(t(),T("svg",hd,gd)),Hd]),a("，"),Q("mjx-container",Ld,[(t(),T("svg",cd,fd)),Md]),a(" 成立，即 "),Q("mjx-container",ud,[(t(),T("svg",xd,Vd)),wd]),a(" 唯一，再根据 "),Q("mjx-container",_d,[(t(),T("svg",vd,Dd)),bd]),a(" 的任意性，得出对于任意自然数 "),Q("mjx-container",jd,[(t(),T("svg",Bd,Cd)),zd]),a("，"),Q("mjx-container",Sd,[(t(),T("svg",Jd,Ad)),Ed]),a(" 都是唯一的。")]),Fd,Od,Rd,Q("p",null,[a("下面证明乘法交换律，即对于任意自然数 "),Q("mjx-container",Pd,[(t(),T("svg",Xd,Kd)),Id]),a("，有 "),Q("mjx-container",qd,[(t(),T("svg",Ud,Yd)),$d]),a("。")]),Qh,Q("p",null,[a("试证 "),Q("mjx-container",ah,[(t(),T("svg",th,mh)),nh]),a("。")]),Q("p",null,[a("首先有 "),Q("mjx-container",lh,[(t(),T("svg",eh,oh)),rh]),a("。")]),Q("p",null,[a("进而当 "),Q("mjx-container",dh,[(t(),T("svg",hh,gh)),Hh]),a(" 是自然数且 "),Q("mjx-container",Lh,[(t(),T("svg",ch,fh)),Mh]),a(" 时有")]),Q("mjx-container",uh,[(t(),T("svg",xh,Vh)),wh]),Q("p",null,[a("根据 Peano 公理 Ⅴ，得知 "),Q("mjx-container",_h,[(t(),T("svg",vh,Dh)),bh]),a(" 对任意自然数 "),Q("mjx-container",jh,[(t(),T("svg",Bh,Ch)),zh]),a(" 成立。")]),Q("p",null,[a("试证 "),Q("mjx-container",Sh,[(t(),T("svg",Jh,Ah)),Eh]),a("。")]),Q("p",null,[a("首先 "),Q("mjx-container",Fh,[(t(),T("svg",Oh,Ph)),Xh]),a(" 时有")]),Q("mjx-container",Nh,[(t(),T("svg",Kh,qh)),Uh]),Q("p",null,[a("进而当 "),Q("mjx-container",Wh,[(t(),T("svg",Yh,Qi)),ai]),a(" 是自然数且 "),Q("mjx-container",ti,[(t(),T("svg",Ti,ni)),li]),a(" 时有")]),Q("mjx-container",ei,[(t(),T("svg",si,ri)),di]),Q("p",null,[a("根据 Peano 公理 Ⅴ，得知 "),Q("mjx-container",hi,[(t(),T("svg",ii,Hi)),Li]),a(" 对任意自然数 "),Q("mjx-container",ci,[(t(),T("svg",pi,Mi)),ui]),a(" 成立，将其称为新的"),xi,a("。")]),Q("p",null,[a("证明了乘法运算规则的交换律之后，试证乘法交换律 "),Q("mjx-container",Zi,[(t(),T("svg",Vi,_i)),vi]),a("，首先当 "),Q("mjx-container",yi,[(t(),T("svg",Di,ji)),Bi]),a(" 时由乘法运算规则 Ⅰ 有 "),Q("mjx-container",ki,[(t(),T("svg",Ci,Si)),Ji]),a("。")]),Q("p",null,[a("进而当 "),Q("mjx-container",Gi,[(t(),T("svg",Ai,Fi)),Oi]),a(" 是自然数且 "),Q("mjx-container",Ri,[(t(),T("svg",Pi,Ni)),Ki]),a(" 时，有")]),Q("mjx-container",Ii,[(t(),T("svg",qi,Wi)),Yi]),Q("p",null,[a("根据 Peano 公理 Ⅴ，得知 "),Q("mjx-container",$i,[(t(),T("svg",Qg,tg)),Tg]),a(" 对任意自然数 "),Q("mjx-container",mg,[(t(),T("svg",ng,eg)),sg]),a(" 成立，即乘法交换律成立。")]),og,Q("p",null,[a("下面证明乘法分配律，即对于任意自然数 "),Q("mjx-container",rg,[(t(),T("svg",dg,ig)),gg]),a("，有 "),Q("mjx-container",Hg,[(t(),T("svg",Lg,pg)),fg]),a("。")]),Q("p",null,[a("首先当 "),Q("mjx-container",Mg,[(t(),T("svg",ug,Zg)),Vg]),a(" 时，"),Q("mjx-container",wg,[(t(),T("svg",_g,yg)),Dg]),a("，进而当 "),Q("mjx-container",bg,[(t(),T("svg",jg,kg)),Cg]),a(" 为自然数且 "),Q("mjx-container",zg,[(t(),T("svg",Sg,Gg)),Ag]),a(" 时有")]),Q("mjx-container",Eg,[(t(),T("svg",Fg,Rg)),Pg]),Q("p",null,[a("根据 Peano 公理 Ⅴ，得知 "),Q("mjx-container",Xg,[(t(),T("svg",Ng,Ig)),qg]),a(" 对任意自然数 "),Q("mjx-container",Ug,[(t(),T("svg",Wg,$g)),QH]),a(" 成立，即乘法分配律成立。")]),aH,Q("p",null,[a("下面证明乘法结合律，即对于任意自然数 "),Q("mjx-container",tH,[(t(),T("svg",TH,nH)),lH]),a("，有 "),Q("mjx-container",eH,[(t(),T("svg",sH,rH)),dH]),a("。")]),Q("p",null,[a("首先当 "),Q("mjx-container",hH,[(t(),T("svg",iH,HH)),LH]),a(" 时，有 "),Q("mjx-container",cH,[(t(),T("svg",pH,MH)),uH]),a("。")]),Q("p",null,[a("进而当 "),Q("mjx-container",xH,[(t(),T("svg",ZH,wH)),_H]),a(" 为自然数且 "),Q("mjx-container",vH,[(t(),T("svg",yH,bH)),jH]),a(" 时有")]),Q("mjx-container",BH,[(t(),T("svg",kH,zH)),SH]),Q("p",null,[a("根据 Peano 公理 Ⅴ，得知 "),Q("mjx-container",JH,[(t(),T("svg",GH,EH)),FH]),a(" 对任意自然数 "),Q("mjx-container",OH,[(t(),T("svg",RH,XH)),NH]),a(" 成立，即乘法结合律成立。")]),KH,Q("p",null,[a("下面证明乘法消去律，即对于任意自然数 "),Q("mjx-container",IH,[(t(),T("svg",qH,WH)),YH]),a(" 和 "),Q("mjx-container",$H,[(t(),T("svg",QL,tL)),TL]),a("，有 "),Q("mjx-container",mL,[(t(),T("svg",nL,eL)),sL]),a("。")]),Q("p",null,[a("试证 "),Q("mjx-container",oL,[(t(),T("svg",rL,hL)),iL]),a("。")]),Q("p",null,[a("首先当 "),Q("mjx-container",gL,[(t(),T("svg",HL,cL)),pL]),a(" 时有")]),Q("mjx-container",fL,[(t(),T("svg",ML,xL)),ZL]),Q("p",null,[a("进而当 "),Q("mjx-container",VL,[(t(),T("svg",wL,vL)),yL]),a(" 为自然数且 "),Q("mjx-container",DL,[(t(),T("svg",bL,BL)),kL]),a(" 时有")]),Q("mjx-container",CL,[(t(),T("svg",zL,JL)),GL]),Q("p",null,[a("即 "),Q("mjx-container",AL,[(t(),T("svg",EL,OL)),RL]),a("，根据 Peano 公理 Ⅴ，得知 "),Q("mjx-container",PL,[(t(),T("svg",XL,KL)),IL]),a(" 对任意自然数 "),Q("mjx-container",qL,[(t(),T("svg",UL,YL)),$L]),a(" 成立。")]),Q("p",null,[a("试证 "),Q("mjx-container",Qc,[(t(),T("svg",ac,Tc)),mc]),a("，采用反证法，假设 "),Q("mjx-container",nc,[(t(),T("svg",lc,sc)),oc]),a("，则由加法运算规则 Ⅱ 可知 "),Q("mjx-container",rc,[(t(),T("svg",dc,ic)),gc]),a(" 或 "),Q("mjx-container",Hc,[(t(),T("svg",Lc,pc)),fc]),a("，其中 "),Q("mjx-container",Mc,[(t(),T("svg",uc,Zc)),Vc]),a("，不妨设 "),Q("mjx-container",wc,[(t(),T("svg",_c,yc)),Dc]),a("。")]),Q("p",null,[a("由 Peano 公理 Ⅲ 有 "),Q("mjx-container",bc,[(t(),T("svg",jc,kc)),Cc]),a("。")]),Q("p",null,[a("由 Peano 公理 Ⅲ、Ⅳ 有，任意非零自然数 "),Q("mjx-container",zc,[(t(),T("svg",Sc,Gc)),Ac]),a(" 都有唯一的数 "),Q("mjx-container",Ec,[(t(),T("svg",Fc,Rc)),Pc]),a(" 满足 "),Q("mjx-container",Xc,[(t(),T("svg",Nc,Ic)),qc]),a("，不妨记作 "),Q("mjx-container",Uc,[(t(),T("svg",Wc,$c)),Qp]),a("。")]),Q("p",null,[a("若有 "),Q("mjx-container",ap,[(t(),T("svg",tp,mp)),np]),a("，则有")]),Q("mjx-container",lp,[(t(),T("svg",ep,op)),rp]),Q("p",null,[a("上述等式表明 "),Q("mjx-container",dp,[(t(),T("svg",hp,gp)),Hp]),a(" 是 "),Q("mjx-container",Lp,[(t(),T("svg",cp,fp)),Mp]),a(" 的后继，这违背了 Peano 公理 Ⅲ，由此知道假设不成立，即 "),Q("mjx-container",up,[(t(),T("svg",xp,Vp)),wp]),a("。")]),Q("p",null,[a("综上所述，乘法消去律 "),Q("mjx-container",_p,[(t(),T("svg",vp,Dp)),bp]),a("，对任意自然数 "),Q("mjx-container",jp,[(t(),T("svg",Bp,Cp)),zp]),a(" 成立。")]),Sp,Jp,Gp,Ap,Q("p",null,[a("若 "),Q("mjx-container",Ep,[(t(),T("svg",Fp,Rp)),Pp]),a("，则 "),Q("mjx-container",Xp,[(t(),T("svg",Np,Ip)),qp]),a("。")]),Q("p",null,[a("由 "),Q("mjx-container",Up,[(t(),T("svg",Wp,$p)),Qf]),a(" 有 "),Q("mjx-container",af,[(t(),T("svg",tf,mf)),nf]),a("，进而 "),Q("mjx-container",lf,[(t(),T("svg",ef,of)),rf]),a(" 因此 "),Q("mjx-container",df,[(t(),T("svg",hf,Hf)),Lf]),a("。")]),cf,Q("p",null,[a("若 "),Q("mjx-container",pf,[(t(),T("svg",ff,uf)),xf]),a("，则 "),Q("mjx-container",Zf,[(t(),T("svg",Vf,_f)),vf]),a("。")]),Q("p",null,[a("采用反证法，假设 "),Q("mjx-container",yf,[(t(),T("svg",Df,jf)),Bf]),a("，则存在正自然数 "),Q("mjx-container",kf,[(t(),T("svg",Cf,Sf)),Jf]),a(" 满足 "),Q("mjx-container",Gf,[(t(),T("svg",Af,Ff)),Of]),a("，有")]),Q("mjx-container",Rf,[(t(),T("svg",Pf,Nf)),Kf]),Q("p",null,[a("由此有 "),Q("mjx-container",If,[(t(),T("svg",qf,Wf)),Yf]),a("，根据序的反对称性有 "),Q("mjx-container",$f,[(t(),T("svg",QM,tM)),TM]),a("，根据乘法消去律有 "),Q("mjx-container",mM,[(t(),T("svg",nM,eM)),sM]),a("，这与 "),Q("mjx-container",oM,[(t(),T("svg",rM,hM)),iM]),a(" 的假设矛盾，因此假设不成立，即证明了乘法消去的保序性。")]),gM,Q("p",null,[a("自然数与有向图 "),Q("mjx-container",HM,[(t(),T("svg",LM,pM)),fM]),a(" 同构，这个图满足如下性质：")]),Q("ol",null,[Q("li",null,[a("存在点 "),Q("mjx-container",MM,[(t(),T("svg",uM,ZM)),VM]),a("，即 "),Q("mjx-container",wM,[(t(),T("svg",_M,yM)),DM]),a("；")]),Q("li",null,[a("所有点的出度为 "),Q("mjx-container",bM,[(t(),T("svg",jM,kM)),CM]),a("，即 "),Q("mjx-container",zM,[(t(),T("svg",SM,GM)),AM]),a("；")]),Q("li",null,[a("点 "),Q("mjx-container",EM,[(t(),T("svg",FM,RM)),PM]),a(" 入度为 "),Q("mjx-container",XM,[(t(),T("svg",NM,IM)),qM]),a("，即 "),Q("mjx-container",UM,[(t(),T("svg",WM,$M)),Qu]),a("；")]),Q("li",null,[a("任意点的入度小于等于 "),Q("mjx-container",au,[(t(),T("svg",tu,mu)),nu]),a("，即 "),Q("mjx-container",lu,[(t(),T("svg",eu,ou)),ru]),a("；")]),Q("li",null,[a("存在从 "),Q("mjx-container",du,[(t(),T("svg",hu,gu)),Hu]),a(" 到任意点的路径，即 "),Q("mjx-container",Lu,[(t(),T("svg",cu,fu)),Mu]),a("。")])]),uu,xu,Q("p",null,[a("若去除，则允许不存在 "),Q("mjx-container",Zu,[(t(),T("svg",Vu,_u)),vu]),a("，可以构造出空集自然数系统。")]),yu,Du,bu,Q("p",null,[a("若去除，则对 "),Q("mjx-container",ju,[(t(),T("svg",Bu,Cu)),zu]),a(" 的入度无规定，可以构造出环状自然数系统。")]),Su,Q("p",null,[a("若去除，则对一个数可以是多个数的后继，可以构造出 "),Q("mjx-container",Ju,[(t(),T("svg",Gu,Eu)),Fu]),a(" 状自然数系统。")]),Ou,Ru])}const Iu=n(e,[["render",Pu],["__file","「算术公理系统 1」自然数.html.vue"]]),qu=JSON.parse('{"path":"/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html","title":"「算术公理系统 1」自然数","lang":"zh-CN","frontmatter":{"lang":"zh-CN","date":"2023-07-09T00:00:00.000Z","category":["数学"],"tag":["公理系统"],"description":"假设存在一个算数系统的模型满足 Peano 公理，即假定 Peano 公理相容，在此承认次假设的基础之上，我们即可建立如今最常用的算术公理系统。自然数的定义则是构建此算术公理系统的第一步。","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"「算术公理系统 1」自然数"}],["meta",{"property":"og:description","content":"假设存在一个算数系统的模型满足 Peano 公理，即假定 Peano 公理相容，在此承认次假设的基础之上，我们即可建立如今最常用的算术公理系统。自然数的定义则是构建此算术公理系统的第一步。"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:tag","content":"公理系统"}],["meta",{"property":"article:published_time","content":"2023-07-09T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"「算术公理系统 1」自然数\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2023-07-09T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"自然数的定义","slug":"自然数的定义","link":"#自然数的定义","children":[]},{"level":2,"title":"自然数的加法运算","slug":"自然数的加法运算","link":"#自然数的加法运算","children":[{"level":3,"title":"加法的定义","slug":"加法的定义","link":"#加法的定义","children":[]},{"level":3,"title":"加法的性质","slug":"加法的性质","link":"#加法的性质","children":[]}]},{"level":2,"title":"自然数的序","slug":"自然数的序","link":"#自然数的序","children":[{"level":3,"title":"序的定义","slug":"序的定义","link":"#序的定义","children":[]},{"level":3,"title":"正自然数","slug":"正自然数","link":"#正自然数","children":[]},{"level":3,"title":"序的反对称性","slug":"序的反对称性","link":"#序的反对称性","children":[]},{"level":3,"title":"序的传递性","slug":"序的传递性","link":"#序的传递性","children":[]},{"level":3,"title":"序的完全性","slug":"序的完全性","link":"#序的完全性","children":[]},{"level":3,"title":"加法保序性","slug":"加法保序性","link":"#加法保序性","children":[]}]},{"level":2,"title":"自然数的乘法运算","slug":"自然数的乘法运算","link":"#自然数的乘法运算","children":[{"level":3,"title":"乘法的定义","slug":"乘法的定义","link":"#乘法的定义","children":[]},{"level":3,"title":"乘法的性质","slug":"乘法的性质","link":"#乘法的性质","children":[]}]},{"level":2,"title":"Peano 公理的合理性","slug":"peano-公理的合理性","link":"#peano-公理的合理性","children":[{"level":3,"title":"乘法保序性","slug":"乘法保序性","link":"#乘法保序性","children":[]},{"level":3,"title":"乘法消去保序性","slug":"乘法消去保序性","link":"#乘法消去保序性","children":[]},{"level":3,"title":"用图论阐述 Peano 系统","slug":"用图论阐述-peano-系统","link":"#用图论阐述-peano-系统","children":[]}]}],"readingTime":{"minutes":18.04,"words":5412},"filePathRelative":"tech/「算术公理系统 1」自然数.md","localizedDate":"2023年7月9日","excerpt":"\\n<p>假设存在一个算数系统的模型满足 Peano 公理，即假定 Peano 公理相容，在此承认次假设的基础之上，我们即可建立如今最常用的<strong>算术公理系统</strong>。<strong>自然数的定义</strong>则是构建此算术公理系统的第一步。</p>\\n","autoDesc":true}');export{Iu as comp,qu as data};
diff --git "a/assets/\344\275\277\347\224\250capacitor\345\222\214ionic\345\260\206vue\351\241\271\347\233\256\350\277\201\347\247\273\345\210\260mobile\347\253\257.html-CjY4pFX9.js" "b/assets/\344\275\277\347\224\250capacitor\345\222\214ionic\345\260\206vue\351\241\271\347\233\256\350\277\201\347\247\273\345\210\260mobile\347\253\257.html-CKHKQibh.js"
similarity index 98%
rename from "assets/\344\275\277\347\224\250capacitor\345\222\214ionic\345\260\206vue\351\241\271\347\233\256\350\277\201\347\247\273\345\210\260mobile\347\253\257.html-CjY4pFX9.js"
rename to "assets/\344\275\277\347\224\250capacitor\345\222\214ionic\345\260\206vue\351\241\271\347\233\256\350\277\201\347\247\273\345\210\260mobile\347\253\257.html-CKHKQibh.js"
index 99bc0ed..eac63d7 100644
--- "a/assets/\344\275\277\347\224\250capacitor\345\222\214ionic\345\260\206vue\351\241\271\347\233\256\350\277\201\347\247\273\345\210\260mobile\347\253\257.html-CjY4pFX9.js"
+++ "b/assets/\344\275\277\347\224\250capacitor\345\222\214ionic\345\260\206vue\351\241\271\347\233\256\350\277\201\347\247\273\345\210\260mobile\347\253\257.html-CKHKQibh.js"
@@ -1,4 +1,4 @@
-import{_ as a,r as o,o as c,c as l,a as r,b as e,e as t,d as n,f as s}from"./app-B69Gl_S-.js";const p={},d=e("h1",{id:"前言",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#前言"},[e("span",null,"前言")])],-1),u=e("p",null,"当我们写完了vue项目后，想做一个一样的移动app，此时我们可以使用ionic无缝将其迁移到移动端。",-1),h=e("h2",{id:"安装",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#安装"},[e("span",null,"安装")])],-1),m={href:"https://capacitorjs.com/",target:"_blank",rel:"noopener noreferrer"},v={href:"https://ionic.nodejs.cn/",target:"_blank",rel:"noopener noreferrer"},b=e("h2",{id:"tips",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#tips"},[e("span",null,"tips")])],-1),_={href:"https://ionic.nodejs.cn/vue/your-first-app/deploying-mobile",target:"_blank",rel:"noopener noreferrer"},g=s(`<p>每次执行更新你的 Web 目录的构建（例如 ionic build）时（默认：build)，你需要将这些更改复制到你的原生项目中：</p><p>ionic cap copy</p><p>注意：更新代码的原生部分（例如添加新插件）后，使用 sync 命令：</p><div class="language-bash line-numbers-mode" data-ext="sh" data-title="sh"><pre class="language-bash"><code>ionic cap <span class="token function">sync</span>
+import{_ as a,r as o,o as c,c as l,a as r,b as e,e as t,d as n,f as s}from"./app-B4LGNJZ0.js";const p={},d=e("h1",{id:"前言",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#前言"},[e("span",null,"前言")])],-1),u=e("p",null,"当我们写完了vue项目后，想做一个一样的移动app，此时我们可以使用ionic无缝将其迁移到移动端。",-1),h=e("h2",{id:"安装",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#安装"},[e("span",null,"安装")])],-1),m={href:"https://capacitorjs.com/",target:"_blank",rel:"noopener noreferrer"},v={href:"https://ionic.nodejs.cn/",target:"_blank",rel:"noopener noreferrer"},b=e("h2",{id:"tips",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#tips"},[e("span",null,"tips")])],-1),_={href:"https://ionic.nodejs.cn/vue/your-first-app/deploying-mobile",target:"_blank",rel:"noopener noreferrer"},g=s(`<p>每次执行更新你的 Web 目录的构建（例如 ionic build）时（默认：build)，你需要将这些更改复制到你的原生项目中：</p><p>ionic cap copy</p><p>注意：更新代码的原生部分（例如添加新插件）后，使用 sync 命令：</p><div class="language-bash line-numbers-mode" data-ext="sh" data-title="sh"><pre class="language-bash"><code>ionic cap <span class="token function">sync</span>
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div></div></div><div class="hint-container info"><p class="hint-container-title">相关信息</p><p>vscode中可以使用&quot;ionic&quot;插件</p></div><ul><li>默认不支持HTTP</li></ul><div class="language-text line-numbers-mode" data-ext="text" data-title="text"><pre class="language-text"><code>const config: CapacitorConfig = {
   plugins:{
     CapacitorHttp:{
diff --git "a/assets/\345\215\217\347\250\213(asyncio)\345\210\260\345\272\225\351\234\200\344\270\215\351\234\200\350\246\201\345\212\240\351\224\201.html-CTO2grll.js" "b/assets/\345\215\217\347\250\213(asyncio)\345\210\260\345\272\225\351\234\200\344\270\215\351\234\200\350\246\201\345\212\240\351\224\201.html-gfcHinKw.js"
similarity index 99%
rename from "assets/\345\215\217\347\250\213(asyncio)\345\210\260\345\272\225\351\234\200\344\270\215\351\234\200\350\246\201\345\212\240\351\224\201.html-CTO2grll.js"
rename to "assets/\345\215\217\347\250\213(asyncio)\345\210\260\345\272\225\351\234\200\344\270\215\351\234\200\350\246\201\345\212\240\351\224\201.html-gfcHinKw.js"
index 5473e8c..d8623fa 100644
--- "a/assets/\345\215\217\347\250\213(asyncio)\345\210\260\345\272\225\351\234\200\344\270\215\351\234\200\350\246\201\345\212\240\351\224\201.html-CTO2grll.js"
+++ "b/assets/\345\215\217\347\250\213(asyncio)\345\210\260\345\272\225\351\234\200\344\270\215\351\234\200\350\246\201\345\212\240\351\224\201.html-gfcHinKw.js"
@@ -1,4 +1,4 @@
-import{_ as i,r as t,o as l,c,b as n,e as a,d as e,a as o,f as p}from"./app-B69Gl_S-.js";const d={},u={id:"并发异步编程之争-协程-asyncio-到底需不需要加锁-线程-协程安全-挂起-主动切换-python3",tabindex:"-1"},r={class:"header-anchor",href:"#并发异步编程之争-协程-asyncio-到底需不需要加锁-线程-协程安全-挂起-主动切换-python3"},v={href:"https://segmentfault.com/a/1190000041568839",target:"_blank",rel:"noopener noreferrer"},m={href:"https://link.segmentfault.com/?enc=8btt3pfGP%2FRxuxLguNqhrg%3D%3D.f%2BWWJlm9AsMAbAJjJZT%2BOQBqYNXwZgTYGW7Jx9l%2BpxQ%3D",target:"_blank",rel:"noopener noreferrer"},b=p(`<p>协程与线程向来焦孟不离，但事实上是，线程更被我们所熟知，在Python编程领域，单核同时间内只能有一个线程运行，这并不是什么缺陷，这实际上是符合客观逻辑的，单核处理器本来就没法同时处理两件事情，要同时进行多件事情本来就需要正在运行的让出处理器，然后才能去处理另一件事情，左手画方右手画圆在现实中本来就不成立，只不过这个让出的过程是线程调度器主动抢占的。</p><h2 id="线程安全" tabindex="-1"><a class="header-anchor" href="#线程安全"><span>线程安全</span></a></h2><p>系统的线程调度器是假设不同的线程是毫无关系的，所以它平均地分配时间片让处理器一视同仁，雨露均沾。但是Python受限于GIL全局解释器锁，任何Python线程执行前，必须先获得GIL锁，然后，每执行100条字节码，解释器就自动释放GIL锁，让别的线程有机会执行。这个GIL全局解释器锁实际上把所有线程的执行代码都给上了锁，所以，多线程在Python中只能交替执行，即使多个线程跑在8核处理上，也只能用到1个核。</p><p>但其实，这并不是事情的全貌，就算只能用单核处理任务，多个线程之前也并不是完全独立的，它们会操作同一个资源。于是，大家又发明了同步锁，使得一段时间内只有一个线程可以操作这个资源，其他线程只能等待：</p><div class="language-mipsasm line-numbers-mode" data-ext="mipsasm" data-title="mipsasm"><pre class="language-mipsasm"><code>import threading
+import{_ as i,r as t,o as l,c,b as n,e as a,d as e,a as o,f as p}from"./app-B4LGNJZ0.js";const d={},u={id:"并发异步编程之争-协程-asyncio-到底需不需要加锁-线程-协程安全-挂起-主动切换-python3",tabindex:"-1"},r={class:"header-anchor",href:"#并发异步编程之争-协程-asyncio-到底需不需要加锁-线程-协程安全-挂起-主动切换-python3"},v={href:"https://segmentfault.com/a/1190000041568839",target:"_blank",rel:"noopener noreferrer"},m={href:"https://link.segmentfault.com/?enc=8btt3pfGP%2FRxuxLguNqhrg%3D%3D.f%2BWWJlm9AsMAbAJjJZT%2BOQBqYNXwZgTYGW7Jx9l%2BpxQ%3D",target:"_blank",rel:"noopener noreferrer"},b=p(`<p>协程与线程向来焦孟不离，但事实上是，线程更被我们所熟知，在Python编程领域，单核同时间内只能有一个线程运行，这并不是什么缺陷，这实际上是符合客观逻辑的，单核处理器本来就没法同时处理两件事情，要同时进行多件事情本来就需要正在运行的让出处理器，然后才能去处理另一件事情，左手画方右手画圆在现实中本来就不成立，只不过这个让出的过程是线程调度器主动抢占的。</p><h2 id="线程安全" tabindex="-1"><a class="header-anchor" href="#线程安全"><span>线程安全</span></a></h2><p>系统的线程调度器是假设不同的线程是毫无关系的，所以它平均地分配时间片让处理器一视同仁，雨露均沾。但是Python受限于GIL全局解释器锁，任何Python线程执行前，必须先获得GIL锁，然后，每执行100条字节码，解释器就自动释放GIL锁，让别的线程有机会执行。这个GIL全局解释器锁实际上把所有线程的执行代码都给上了锁，所以，多线程在Python中只能交替执行，即使多个线程跑在8核处理上，也只能用到1个核。</p><p>但其实，这并不是事情的全貌，就算只能用单核处理任务，多个线程之前也并不是完全独立的，它们会操作同一个资源。于是，大家又发明了同步锁，使得一段时间内只有一个线程可以操作这个资源，其他线程只能等待：</p><div class="language-mipsasm line-numbers-mode" data-ext="mipsasm" data-title="mipsasm"><pre class="language-mipsasm"><code>import threading
 
 balance = 0
 
diff --git "a/assets/\345\215\217\347\250\213.html-LdIMvjSl.js" "b/assets/\345\215\217\347\250\213.html-BovqfV_l.js"
similarity index 93%
rename from "assets/\345\215\217\347\250\213.html-LdIMvjSl.js"
rename to "assets/\345\215\217\347\250\213.html-BovqfV_l.js"
index c5012b1..0efda82 100644
--- "a/assets/\345\215\217\347\250\213.html-LdIMvjSl.js"
+++ "b/assets/\345\215\217\347\250\213.html-BovqfV_l.js"
@@ -1 +1 @@
-import{_ as n,r,o as a,c as o,b as t,e as c,d as s}from"./app-B69Gl_S-.js";const i={},p=t("h1",{id:"协程",tabindex:"-1"},[t("a",{class:"header-anchor",href:"#协程"},[t("span",null,"协程")])],-1),l={href:"https://course.rs/advance/async/getting-started.html#:~:text=async%20%E7%AE%80%E4%BB%8B.",target:"_blank",rel:"noopener noreferrer"},h=t("div",{class:"hint-container important"},[t("p",{class:"hint-container-title"},"重要"),t("p",null,"TODO")],-1);function d(m,_){const e=r("ExternalLinkIcon");return a(),o("div",null,[p,t("p",null,[t("a",l,[c("文档"),s(e)])]),h])}const u=n(i,[["render",d],["__file","协程.html.vue"]]),y=JSON.parse('{"path":"/tech/%E5%8D%8F%E7%A8%8B.html","title":"协程","lang":"zh-CN","frontmatter":{"description":"协程 文档 重要 TODO","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/%E5%8D%8F%E7%A8%8B.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"协程"}],["meta",{"property":"og:description","content":"协程 文档 重要 TODO"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"协程\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.06,"words":18},"filePathRelative":"tech/协程.md","excerpt":"\\n<p><a href=\\"https://course.rs/advance/async/getting-started.html#:~:text=async%20%E7%AE%80%E4%BB%8B.\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">文档</a></p>\\n<div class=\\"hint-container important\\">\\n<p class=\\"hint-container-title\\">重要</p>\\n<p>TODO</p>\\n</div>\\n","autoDesc":true}');export{u as comp,y as data};
+import{_ as n,r,o as a,c as o,b as t,e as c,d as s}from"./app-B4LGNJZ0.js";const i={},p=t("h1",{id:"协程",tabindex:"-1"},[t("a",{class:"header-anchor",href:"#协程"},[t("span",null,"协程")])],-1),l={href:"https://course.rs/advance/async/getting-started.html#:~:text=async%20%E7%AE%80%E4%BB%8B.",target:"_blank",rel:"noopener noreferrer"},h=t("div",{class:"hint-container important"},[t("p",{class:"hint-container-title"},"重要"),t("p",null,"TODO")],-1);function d(m,_){const e=r("ExternalLinkIcon");return a(),o("div",null,[p,t("p",null,[t("a",l,[c("文档"),s(e)])]),h])}const u=n(i,[["render",d],["__file","协程.html.vue"]]),y=JSON.parse('{"path":"/tech/%E5%8D%8F%E7%A8%8B.html","title":"协程","lang":"zh-CN","frontmatter":{"description":"协程 文档 重要 TODO","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/%E5%8D%8F%E7%A8%8B.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"协程"}],["meta",{"property":"og:description","content":"协程 文档 重要 TODO"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"协程\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.06,"words":18},"filePathRelative":"tech/协程.md","excerpt":"\\n<p><a href=\\"https://course.rs/advance/async/getting-started.html#:~:text=async%20%E7%AE%80%E4%BB%8B.\\" target=\\"_blank\\" rel=\\"noopener noreferrer\\">文档</a></p>\\n<div class=\\"hint-container important\\">\\n<p class=\\"hint-container-title\\">重要</p>\\n<p>TODO</p>\\n</div>\\n","autoDesc":true}');export{u as comp,y as data};
diff --git "a/assets/\345\221\275\351\207\214\346\234\211\346\227\266\347\273\210\351\241\273\346\234\211.html-DOvT7-xg.js" "b/assets/\345\221\275\351\207\214\346\234\211\346\227\266\347\273\210\351\241\273\346\234\211.html-B46pNP68.js"
similarity index 97%
rename from "assets/\345\221\275\351\207\214\346\234\211\346\227\266\347\273\210\351\241\273\346\234\211.html-DOvT7-xg.js"
rename to "assets/\345\221\275\351\207\214\346\234\211\346\227\266\347\273\210\351\241\273\346\234\211.html-B46pNP68.js"
index b13829a..a9c03bd 100644
--- "a/assets/\345\221\275\351\207\214\346\234\211\346\227\266\347\273\210\351\241\273\346\234\211.html-DOvT7-xg.js"
+++ "b/assets/\345\221\275\351\207\214\346\234\211\346\227\266\347\273\210\351\241\273\346\234\211.html-B46pNP68.js"
@@ -1 +1 @@
-import{_ as e,o as a,c as o,b as t}from"./app-B69Gl_S-.js";const n="/assets/966519d02c8ca050dc064d479fb711e-Bmk4mUCm.jpg",i={},r=t("figure",null,[t("img",{src:n,alt:"alt text",tabindex:"0",loading:"lazy"}),t("figcaption",null,"alt text")],-1),c=t("p",null,"昨日在玩“三国杀：一将成名”时，我抽奖一发就中了大奖——“清河公主”传说皮。这让我不禁感慨：“命里有时终须有，命里无时莫强求。”这句话真是道出了人生的真谛，有些事情是强求不来的，顺其自然反而能得到意想不到的收获。",-1),s=[r,c];function l(p,m){return a(),o("div",null,s)}const _=e(i,[["render",l],["__file","命里有时终须有.html.vue"]]),g=JSON.parse('{"path":"/essays/%E5%91%BD%E9%87%8C%E6%9C%89%E6%97%B6%E7%BB%88%E9%A1%BB%E6%9C%89.html","title":"命里有时终须有","lang":"zh-CN","frontmatter":{"date":"2024-10-30T00:00:00.000Z","title":"命里有时终须有","description":"alt textalt text 昨日在玩“三国杀：一将成名”时，我抽奖一发就中了大奖——“清河公主”传说皮。这让我不禁感慨：“命里有时终须有，命里无时莫强求。”这句话真是道出了人生的真谛，有些事情是强求不来的，顺其自然反而能得到意想不到的收获。","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/essays/%E5%91%BD%E9%87%8C%E6%9C%89%E6%97%B6%E7%BB%88%E9%A1%BB%E6%9C%89.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"命里有时终须有"}],["meta",{"property":"og:description","content":"alt textalt text 昨日在玩“三国杀：一将成名”时，我抽奖一发就中了大奖——“清河公主”传说皮。这让我不禁感慨：“命里有时终须有，命里无时莫强求。”这句话真是道出了人生的真谛，有些事情是强求不来的，顺其自然反而能得到意想不到的收获。"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:published_time","content":"2024-10-30T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"命里有时终须有\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-10-30T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.35,"words":104},"filePathRelative":"essays/命里有时终须有.md","localizedDate":"2024年10月30日","excerpt":"<figure><figcaption>alt text</figcaption></figure>\\n<p>昨日在玩“三国杀：一将成名”时，我抽奖一发就中了大奖——“清河公主”传说皮。这让我不禁感慨：“命里有时终须有，命里无时莫强求。”这句话真是道出了人生的真谛，有些事情是强求不来的，顺其自然反而能得到意想不到的收获。</p>\\n","autoDesc":true}');export{_ as comp,g as data};
+import{_ as e,o as a,c as o,b as t}from"./app-B4LGNJZ0.js";const n="/assets/966519d02c8ca050dc064d479fb711e-Bmk4mUCm.jpg",i={},r=t("figure",null,[t("img",{src:n,alt:"alt text",tabindex:"0",loading:"lazy"}),t("figcaption",null,"alt text")],-1),c=t("p",null,"昨日在玩“三国杀：一将成名”时，我抽奖一发就中了大奖——“清河公主”传说皮。这让我不禁感慨：“命里有时终须有，命里无时莫强求。”这句话真是道出了人生的真谛，有些事情是强求不来的，顺其自然反而能得到意想不到的收获。",-1),s=[r,c];function l(p,m){return a(),o("div",null,s)}const _=e(i,[["render",l],["__file","命里有时终须有.html.vue"]]),g=JSON.parse('{"path":"/essays/%E5%91%BD%E9%87%8C%E6%9C%89%E6%97%B6%E7%BB%88%E9%A1%BB%E6%9C%89.html","title":"命里有时终须有","lang":"zh-CN","frontmatter":{"date":"2024-10-30T00:00:00.000Z","title":"命里有时终须有","description":"alt textalt text 昨日在玩“三国杀：一将成名”时，我抽奖一发就中了大奖——“清河公主”传说皮。这让我不禁感慨：“命里有时终须有，命里无时莫强求。”这句话真是道出了人生的真谛，有些事情是强求不来的，顺其自然反而能得到意想不到的收获。","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/essays/%E5%91%BD%E9%87%8C%E6%9C%89%E6%97%B6%E7%BB%88%E9%A1%BB%E6%9C%89.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"命里有时终须有"}],["meta",{"property":"og:description","content":"alt textalt text 昨日在玩“三国杀：一将成名”时，我抽奖一发就中了大奖——“清河公主”传说皮。这让我不禁感慨：“命里有时终须有，命里无时莫强求。”这句话真是道出了人生的真谛，有些事情是强求不来的，顺其自然反而能得到意想不到的收获。"}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["meta",{"property":"article:published_time","content":"2024-10-30T00:00:00.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"命里有时终须有\\",\\"image\\":[\\"\\"],\\"datePublished\\":\\"2024-10-30T00:00:00.000Z\\",\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[],"readingTime":{"minutes":0.35,"words":104},"filePathRelative":"essays/命里有时终须有.md","localizedDate":"2024年10月30日","excerpt":"<figure><figcaption>alt text</figcaption></figure>\\n<p>昨日在玩“三国杀：一将成名”时，我抽奖一发就中了大奖——“清河公主”传说皮。这让我不禁感慨：“命里有时终须有，命里无时莫强求。”这句话真是道出了人生的真谛，有些事情是强求不来的，顺其自然反而能得到意想不到的收获。</p>\\n","autoDesc":true}');export{_ as comp,g as data};
diff --git "a/assets/\347\250\213\345\272\217\345\221\230\347\232\204PPT.html-CmGk8DAJ.js" "b/assets/\347\250\213\345\272\217\345\221\230\347\232\204PPT.html-D4bbFarZ.js"
similarity index 98%
rename from "assets/\347\250\213\345\272\217\345\221\230\347\232\204PPT.html-CmGk8DAJ.js"
rename to "assets/\347\250\213\345\272\217\345\221\230\347\232\204PPT.html-D4bbFarZ.js"
index fd8118a..6cd816d 100644
--- "a/assets/\347\250\213\345\272\217\345\221\230\347\232\204PPT.html-CmGk8DAJ.js"
+++ "b/assets/\347\250\213\345\272\217\345\221\230\347\232\204PPT.html-D4bbFarZ.js"
@@ -1 +1 @@
-import{_ as t,o as e,c as p,f as a}from"./app-B69Gl_S-.js";const n={},s=a('<h1 id="slidev" tabindex="-1"><a class="header-anchor" href="#slidev"><span>Slidev</span></a></h1><p>复杂演示推荐</p><h2 id="缺点" tabindex="-1"><a class="header-anchor" href="#缺点"><span>缺点</span></a></h2><p>不支持导出pptx</p><p>https://cn.sli.dev/guide</p><hr><h1 id="marp" tabindex="-1"><a class="header-anchor" href="#marp"><span>Marp</span></a></h1><p>简单PPT,且需要导出为pptx推荐</p><h2 id="缺点-1" tabindex="-1"><a class="header-anchor" href="#缺点-1"><span>缺点</span></a></h2><p>不支持动画</p><hr><p>https://sspai.com/post/55718</p><p>https://segmentfault.com/a/1190000040806239</p><p>⚠️注意事项 如果你的 VS Code 安装了 Markdown 渲染插件 Markdown Preview Enhanced，需要先将这个插件「禁用」或是「卸载」，转而使用 VS Code 后来集成的 Markdown 预览功能，才能正常看到渲染后的 PPT 页面。</p>',14),o=[s];function r(h,i){return e(),p("div",null,o)}const d=t(n,[["render",r],["__file","程序员的PPT.html.vue"]]),l=JSON.parse('{"path":"/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html","title":"Slidev","lang":"zh-CN","frontmatter":{"description":"Slidev 复杂演示推荐 缺点 不支持导出pptx https://cn.sli.dev/guide Marp 简单PPT,且需要导出为pptx推荐 缺点 不支持动画 https://sspai.com/post/55718 https://segmentfault.com/a/1190000040806239 ⚠️注意事项 如果你的 VS Code...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"Slidev"}],["meta",{"property":"og:description","content":"Slidev 复杂演示推荐 缺点 不支持导出pptx https://cn.sli.dev/guide Marp 简单PPT,且需要导出为pptx推荐 缺点 不支持动画 https://sspai.com/post/55718 https://segmentfault.com/a/1190000040806239 ⚠️注意事项 如果你的 VS Code..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"Slidev\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"缺点","slug":"缺点","link":"#缺点","children":[]},{"level":2,"title":"缺点","slug":"缺点-1","link":"#缺点-1","children":[]}],"readingTime":{"minutes":0.35,"words":105},"filePathRelative":"tech/程序员的PPT.md","excerpt":"\\n<p>复杂演示推荐</p>\\n<h2>缺点</h2>\\n<p>不支持导出pptx</p>\\n<p>https://cn.sli.dev/guide</p>\\n<hr>\\n<h1>Marp</h1>\\n<p>简单PPT,且需要导出为pptx推荐</p>\\n<h2>缺点</h2>\\n<p>不支持动画</p>\\n<hr>\\n<p>https://sspai.com/post/55718</p>\\n<p>https://segmentfault.com/a/1190000040806239</p>\\n<p>⚠️注意事项\\n如果你的 VS Code 安装了 Markdown 渲染插件 Markdown Preview Enhanced，需要先将这个插件「禁用」或是「卸载」，转而使用 VS Code 后来集成的 Markdown 预览功能，才能正常看到渲染后的 PPT 页面。</p>","autoDesc":true}');export{d as comp,l as data};
+import{_ as t,o as e,c as p,f as a}from"./app-B4LGNJZ0.js";const n={},s=a('<h1 id="slidev" tabindex="-1"><a class="header-anchor" href="#slidev"><span>Slidev</span></a></h1><p>复杂演示推荐</p><h2 id="缺点" tabindex="-1"><a class="header-anchor" href="#缺点"><span>缺点</span></a></h2><p>不支持导出pptx</p><p>https://cn.sli.dev/guide</p><hr><h1 id="marp" tabindex="-1"><a class="header-anchor" href="#marp"><span>Marp</span></a></h1><p>简单PPT,且需要导出为pptx推荐</p><h2 id="缺点-1" tabindex="-1"><a class="header-anchor" href="#缺点-1"><span>缺点</span></a></h2><p>不支持动画</p><hr><p>https://sspai.com/post/55718</p><p>https://segmentfault.com/a/1190000040806239</p><p>⚠️注意事项 如果你的 VS Code 安装了 Markdown 渲染插件 Markdown Preview Enhanced，需要先将这个插件「禁用」或是「卸载」，转而使用 VS Code 后来集成的 Markdown 预览功能，才能正常看到渲染后的 PPT 页面。</p>',14),o=[s];function r(h,i){return e(),p("div",null,o)}const d=t(n,[["render",r],["__file","程序员的PPT.html.vue"]]),l=JSON.parse('{"path":"/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html","title":"Slidev","lang":"zh-CN","frontmatter":{"description":"Slidev 复杂演示推荐 缺点 不支持导出pptx https://cn.sli.dev/guide Marp 简单PPT,且需要导出为pptx推荐 缺点 不支持动画 https://sspai.com/post/55718 https://segmentfault.com/a/1190000040806239 ⚠️注意事项 如果你的 VS Code...","gitInclude":[],"head":[["meta",{"property":"og:url","content":"https://github.com/King-sj/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html"}],["meta",{"property":"og:site_name","content":"blog"}],["meta",{"property":"og:title","content":"Slidev"}],["meta",{"property":"og:description","content":"Slidev 复杂演示推荐 缺点 不支持导出pptx https://cn.sli.dev/guide Marp 简单PPT,且需要导出为pptx推荐 缺点 不支持动画 https://sspai.com/post/55718 https://segmentfault.com/a/1190000040806239 ⚠️注意事项 如果你的 VS Code..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"article:author","content":"KSJ"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"Slidev\\",\\"image\\":[\\"\\"],\\"dateModified\\":null,\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"KSJ\\",\\"url\\":\\"https://github.com/King-sj\\"}]}"]]},"headers":[{"level":2,"title":"缺点","slug":"缺点","link":"#缺点","children":[]},{"level":2,"title":"缺点","slug":"缺点-1","link":"#缺点-1","children":[]}],"readingTime":{"minutes":0.35,"words":105},"filePathRelative":"tech/程序员的PPT.md","excerpt":"\\n<p>复杂演示推荐</p>\\n<h2>缺点</h2>\\n<p>不支持导出pptx</p>\\n<p>https://cn.sli.dev/guide</p>\\n<hr>\\n<h1>Marp</h1>\\n<p>简单PPT,且需要导出为pptx推荐</p>\\n<h2>缺点</h2>\\n<p>不支持动画</p>\\n<hr>\\n<p>https://sspai.com/post/55718</p>\\n<p>https://segmentfault.com/a/1190000040806239</p>\\n<p>⚠️注意事项\\n如果你的 VS Code 安装了 Markdown 渲染插件 Markdown Preview Enhanced，需要先将这个插件「禁用」或是「卸载」，转而使用 VS Code 后来集成的 Markdown 预览功能，才能正常看到渲染后的 PPT 页面。</p>","autoDesc":true}');export{d as comp,l as data};
diff --git "a/assets/\351\227\255\345\214\205\345\256\236\347\216\260\347\261\273.html-DjTAmLiV.js" "b/assets/\351\227\255\345\214\205\345\256\236\347\216\260\347\261\273.html-CeWxsqOK.js"
similarity index 99%
rename from "assets/\351\227\255\345\214\205\345\256\236\347\216\260\347\261\273.html-DjTAmLiV.js"
rename to "assets/\351\227\255\345\214\205\345\256\236\347\216\260\347\261\273.html-CeWxsqOK.js"
index 0aa7a27..fb377d1 100644
--- "a/assets/\351\227\255\345\214\205\345\256\236\347\216\260\347\261\273.html-DjTAmLiV.js"
+++ "b/assets/\351\227\255\345\214\205\345\256\236\347\216\260\347\261\273.html-CeWxsqOK.js"
@@ -1,4 +1,4 @@
-import{_ as c,r as p,o as l,c as u,a as i,d as r,w as a,b as n,e as s}from"./app-B69Gl_S-.js";const k="/assets/Closures-Bb-D5Kse.png",d={},m=n("h1",{id:"闭包实现类",tabindex:"-1"},[n("a",{class:"header-anchor",href:"#闭包实现类"},[n("span",null,"闭包实现类")])],-1),b=n("p",null,"你是否曾经想过，不用类也能封装数据和方法？这篇文章将带你走进闭包的奇妙世界，展示如何用闭包来实现这一点。通过一个有趣的代码示例，你将看到闭包是如何捕获变量并提供类似类的功能的。准备好了吗？让我们开始这段有趣的旅程吧！",-1),v=n("div",{class:"language-cpp line-numbers-mode","data-ext":"cpp","data-title":"cpp"},[n("pre",{class:"language-cpp"},[n("code",null,[n("span",{class:"token macro property"},[n("span",{class:"token directive-hash"},"#"),n("span",{class:"token directive keyword"},"include"),s(),n("span",{class:"token string"},"<iostream>")]),s(`
+import{_ as c,r as p,o as l,c as u,a as i,d as r,w as a,b as n,e as s}from"./app-B4LGNJZ0.js";const k="/assets/Closures-Bb-D5Kse.png",d={},m=n("h1",{id:"闭包实现类",tabindex:"-1"},[n("a",{class:"header-anchor",href:"#闭包实现类"},[n("span",null,"闭包实现类")])],-1),b=n("p",null,"你是否曾经想过，不用类也能封装数据和方法？这篇文章将带你走进闭包的奇妙世界，展示如何用闭包来实现这一点。通过一个有趣的代码示例，你将看到闭包是如何捕获变量并提供类似类的功能的。准备好了吗？让我们开始这段有趣的旅程吧！",-1),v=n("div",{class:"language-cpp line-numbers-mode","data-ext":"cpp","data-title":"cpp"},[n("pre",{class:"language-cpp"},[n("code",null,[n("span",{class:"token macro property"},[n("span",{class:"token directive-hash"},"#"),n("span",{class:"token directive keyword"},"include"),s(),n("span",{class:"token string"},"<iostream>")]),s(`
 `),n("span",{class:"token macro property"},[n("span",{class:"token directive-hash"},"#"),n("span",{class:"token directive keyword"},"include"),s(),n("span",{class:"token string"},"<string>")]),s(`
 
 `),n("span",{class:"token keyword"},"using"),s(),n("span",{class:"token keyword"},"namespace"),s(" std"),n("span",{class:"token punctuation"},";"),s(`
diff --git a/category/build-tools/index.html b/category/build-tools/index.html
index df92c40..341e427 100644
--- a/category/build-tools/index.html
+++ b/category/build-tools/index.html
@@ -30,15 +30,15 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/category/build-tools/"><meta property="og:site_name" content="blog"><meta property="og:title" content="build-tools 分类"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"build-tools 分类"}</script><title>build-tools 分类 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-B7IKPS0E.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-BCqj2PVi.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="vp-category-list"><li class="vp-category vp-category8"><a class="route-link" href="/category/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="count">26</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86/">编译原理<span class="count">8</span></a></li><li class="vp-category vp-category6"><a class="route-link" href="/category/oi/">OI<span class="count">2</span></a></li><li class="vp-category vp-category2 active"><a class="route-link" href="/category/build-tools/">build-tools<span class="count">1</span></a></li><li class="vp-category vp-category5"><a class="route-link" href="/category/cicd/">CI/CD<span class="count">1</span></a></li><li class="vp-category vp-category4"><a class="route-link" href="/category/nginx/">nginx<span class="count">1</span></a></li><li class="vp-category vp-category1"><a class="route-link" href="/category/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/">奇技淫巧<span class="count">1</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/docker/">docker<span class="count">1</span></a></li><li class="vp-category vp-category7"><a class="route-link" href="/category/python/">python<span class="count">1</span></a></li><li class="vp-category vp-category1"><a class="route-link" href="/category/%E9%A3%8E%E6%A0%BC/">风格<span class="count">1</span></a></li><li class="vp-category vp-category3"><a class="route-link" href="/category/%E6%95%B0%E5%AD%A6/">数学<span class="count">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html"><header class="vp-article-title"><!----><!----><span property="headline">android studio换源</span></header></a><div class="vp-article-excerpt">
 <p><a href="https://mirrors.cloud.tencent.com/gradle/" target="_blank" rel="noopener noreferrer">国内镜像</a></p>
 <p>Android Studio下载gradle太慢可换源</p>
 <p><a href="https://blog.csdn.net/qq_43811536/article/details/139447518" target="_blank" rel="noopener noreferrer">android.plugin version 下载错误查看</a></p>
-<p><strong>修改 settings.gradle.kts</strong></p></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-08-02T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category2 clickable" role="navigation">build-tools</span><!--]--><meta property="articleSection" content="build-tools"></span><!----></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+<p><strong>修改 settings.gradle.kts</strong></p></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-08-02T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category2 clickable" role="navigation">build-tools</span><!--]--><meta property="articleSection" content="build-tools"></span><!----></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/category/cicd/index.html b/category/cicd/index.html
index 0ccdee5..5fbd2b5 100644
--- a/category/cicd/index.html
+++ b/category/cicd/index.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/category/cicd/"><meta property="og:site_name" content="blog"><meta property="og:title" content="CI/CD 分类"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"CI/CD 分类"}</script><title>CI/CD 分类 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-BK-iNYKv.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-CE6ffKsf.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="vp-category-list"><li class="vp-category vp-category8"><a class="route-link" href="/category/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="count">26</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86/">编译原理<span class="count">8</span></a></li><li class="vp-category vp-category6"><a class="route-link" href="/category/oi/">OI<span class="count">2</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/build-tools/">build-tools<span class="count">1</span></a></li><li class="vp-category vp-category5 active"><a class="route-link" href="/category/cicd/">CI/CD<span class="count">1</span></a></li><li class="vp-category vp-category4"><a class="route-link" href="/category/nginx/">nginx<span class="count">1</span></a></li><li class="vp-category vp-category1"><a class="route-link" href="/category/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/">奇技淫巧<span class="count">1</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/docker/">docker<span class="count">1</span></a></li><li class="vp-category vp-category7"><a class="route-link" href="/category/python/">python<span class="count">1</span></a></li><li class="vp-category vp-category1"><a class="route-link" href="/category/%E9%A3%8E%E6%A0%BC/">风格<span class="count">1</span></a></li><li class="vp-category vp-category3"><a class="route-link" href="/category/%E6%95%B0%E5%AD%A6/">数学<span class="count">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/cicd.html"><header class="vp-article-title"><!----><!----><span property="headline">CI/CD</span></header></a><div class="vp-article-excerpt">
@@ -40,7 +40,7 @@
 <!-- TODO -->
 <p>也可另外指定</p>
 <div class="language-bash" data-ext="sh" data-title="sh"><pre class="language-bash"><code>act --var-file <span class="token string">"./.act/.vars"</span> --secret-file <span class="token string">"./.act/.secrets"</span> --env-file <span class="token string">"./.act/.env"</span> <span class="token punctuation">{</span><span class="token punctuation">{</span>other<span class="token punctuation">}</span><span class="token punctuation">}</span>
-</code></pre></div></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-08-02T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category5 clickable" role="navigation">CI/CD</span><!--]--><meta property="articleSection" content="CI/CD"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag5 clickable" role="navigation">CI/CD</span><!--]--><meta property="keywords" content="CI/CD"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</code></pre></div></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-08-02T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category5 clickable" role="navigation">CI/CD</span><!--]--><meta property="articleSection" content="CI/CD"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag5 clickable" role="navigation">CI/CD</span><!--]--><meta property="keywords" content="CI/CD"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/category/docker/index.html b/category/docker/index.html
index 9f9c912..4f1dd60 100644
--- a/category/docker/index.html
+++ b/category/docker/index.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/category/docker/"><meta property="og:site_name" content="blog"><meta property="og:title" content="docker 分类"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"docker 分类"}</script><title>docker 分类 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-DRlrhC7d.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-BgifGsNR.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="vp-category-list"><li class="vp-category vp-category8"><a class="route-link" href="/category/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="count">26</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86/">编译原理<span class="count">8</span></a></li><li class="vp-category vp-category6"><a class="route-link" href="/category/oi/">OI<span class="count">2</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/build-tools/">build-tools<span class="count">1</span></a></li><li class="vp-category vp-category5"><a class="route-link" href="/category/cicd/">CI/CD<span class="count">1</span></a></li><li class="vp-category vp-category4"><a class="route-link" href="/category/nginx/">nginx<span class="count">1</span></a></li><li class="vp-category vp-category1"><a class="route-link" href="/category/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/">奇技淫巧<span class="count">1</span></a></li><li class="vp-category vp-category2 active"><a class="route-link" href="/category/docker/">docker<span class="count">1</span></a></li><li class="vp-category vp-category7"><a class="route-link" href="/category/python/">python<span class="count">1</span></a></li><li class="vp-category vp-category1"><a class="route-link" href="/category/%E9%A3%8E%E6%A0%BC/">风格<span class="count">1</span></a></li><li class="vp-category vp-category3"><a class="route-link" href="/category/%E6%95%B0%E5%AD%A6/">数学<span class="count">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/docker.html"><header class="vp-article-title"><!----><!----><span property="headline"></span></header></a><div class="vp-article-excerpt"><h2>GitHub Container Registry 加速</h2>
@@ -40,7 +40,7 @@ <h3>ghcr.io简介</h3>
 <li>ghcr.io 是 GitHub Container Registry 的域名。GitHub Container Registry 是 GitHub 提供的容器镜像注册表服务，允许开发者在 GitHub 上存储、管理和分享 Docker 镜像。它与 GitHub 代码仓库紧密集成，可以使用相同的权限管理、团队协作和版本控制工具来管理容器镜像。</li>
 <li>通过 GitHub Container Registry，开发者可以方便地将他们的容器镜像与代码仓库关联起来，这样就可以在同一个平台上管理代码和镜像。这种集成性使得持续集成/持续交付 (CI/CD) 流程更加简化和统一，开发团队可以更容易地构建、测试和部署应用程序。</li>
 <li>对于使用 GitHub 作为代码托管平台的开发者来说，GitHub Container Registry 提供一个便捷且强大的容器镜像管理解决方案。通过该服务，可以更轻松地构建和部署容器化的应用程序，从而加速开发和交付周期。</li>
-</ul></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-09-12T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category1 clickable" role="navigation">奇技淫巧</span><span class="page-category-item category2 clickable" role="navigation">docker</span><!--]--><meta property="articleSection" content="奇技淫巧,docker"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag2 clickable" role="navigation">docker</span><!--]--><meta property="keywords" content="docker"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</ul></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-09-12T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category1 clickable" role="navigation">奇技淫巧</span><span class="page-category-item category2 clickable" role="navigation">docker</span><!--]--><meta property="articleSection" content="奇技淫巧,docker"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag2 clickable" role="navigation">docker</span><!--]--><meta property="keywords" content="docker"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/category/index.html b/category/index.html
index 20264e3..55ee8a9 100644
--- a/category/index.html
+++ b/category/index.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/category/"><meta property="og:site_name" content="blog"><meta property="og:title" content="分类"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"分类"}</script><title>分类 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-CO8-8uSt.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-TRJ6qSMT.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
-    <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="vp-category-list"><li class="vp-category vp-category8"><a class="route-link" href="/category/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="count">26</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86/">编译原理<span class="count">8</span></a></li><li class="vp-category vp-category6"><a class="route-link" href="/category/oi/">OI<span class="count">2</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/build-tools/">build-tools<span class="count">1</span></a></li><li class="vp-category vp-category5"><a class="route-link" href="/category/cicd/">CI/CD<span class="count">1</span></a></li><li class="vp-category vp-category4"><a class="route-link" href="/category/nginx/">nginx<span class="count">1</span></a></li><li class="vp-category vp-category1"><a class="route-link" href="/category/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/">奇技淫巧<span class="count">1</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/docker/">docker<span class="count">1</span></a></li><li class="vp-category vp-category7"><a class="route-link" href="/category/python/">python<span class="count">1</span></a></li><li class="vp-category vp-category1"><a class="route-link" href="/category/%E9%A3%8E%E6%A0%BC/">风格<span class="count">1</span></a></li><li class="vp-category vp-category3"><a class="route-link" href="/category/%E6%95%B0%E5%AD%A6/">数学<span class="count">1</span></a></li></ul><!----></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="vp-category-list"><li class="vp-category vp-category8"><a class="route-link" href="/category/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="count">26</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86/">编译原理<span class="count">8</span></a></li><li class="vp-category vp-category6"><a class="route-link" href="/category/oi/">OI<span class="count">2</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/build-tools/">build-tools<span class="count">1</span></a></li><li class="vp-category vp-category5"><a class="route-link" href="/category/cicd/">CI/CD<span class="count">1</span></a></li><li class="vp-category vp-category4"><a class="route-link" href="/category/nginx/">nginx<span class="count">1</span></a></li><li class="vp-category vp-category1"><a class="route-link" href="/category/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/">奇技淫巧<span class="count">1</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/docker/">docker<span class="count">1</span></a></li><li class="vp-category vp-category7"><a class="route-link" href="/category/python/">python<span class="count">1</span></a></li><li class="vp-category vp-category1"><a class="route-link" href="/category/%E9%A3%8E%E6%A0%BC/">风格<span class="count">1</span></a></li><li class="vp-category vp-category3"><a class="route-link" href="/category/%E6%95%B0%E5%AD%A6/">数学<span class="count">1</span></a></li></ul><!----></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/category/nginx/index.html b/category/nginx/index.html
index fbdb29b..42b1727 100644
--- a/category/nginx/index.html
+++ b/category/nginx/index.html
@@ -30,13 +30,13 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/category/nginx/"><meta property="og:site_name" content="blog"><meta property="og:title" content="nginx 分类"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"nginx 分类"}</script><title>nginx 分类 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-DDeLtmuh.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-CVNN5Fwq.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="vp-category-list"><li class="vp-category vp-category8"><a class="route-link" href="/category/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="count">26</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86/">编译原理<span class="count">8</span></a></li><li class="vp-category vp-category6"><a class="route-link" href="/category/oi/">OI<span class="count">2</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/build-tools/">build-tools<span class="count">1</span></a></li><li class="vp-category vp-category5"><a class="route-link" href="/category/cicd/">CI/CD<span class="count">1</span></a></li><li class="vp-category vp-category4 active"><a class="route-link" href="/category/nginx/">nginx<span class="count">1</span></a></li><li class="vp-category vp-category1"><a class="route-link" href="/category/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/">奇技淫巧<span class="count">1</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/docker/">docker<span class="count">1</span></a></li><li class="vp-category vp-category7"><a class="route-link" href="/category/python/">python<span class="count">1</span></a></li><li class="vp-category vp-category1"><a class="route-link" href="/category/%E9%A3%8E%E6%A0%BC/">风格<span class="count">1</span></a></li><li class="vp-category vp-category3"><a class="route-link" href="/category/%E6%95%B0%E5%AD%A6/">数学<span class="count">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html"><header class="vp-article-title"><!----><!----><span property="headline">docker + nginx + acme.sh 部署 vue/flask 项目</span></header></a><div class="vp-article-excerpt">
 <p>本文将介绍如何使用 Docker、Nginx 和 acme.sh 部署一个 Vue 和 Flask 项目。我们将详细讲解环境配置、项目结构、Nginx 配置、Docker 配置以及如何升级到 HTTPS。</p>
-</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><span class="page-author-item">King-sj</span></span><span property="author" content="King-sj"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-09-16T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 3 分钟</span><meta property="timeRequired" content="PT3M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category4 clickable" role="navigation">nginx</span><!--]--><meta property="articleSection" content="nginx"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">部署</span><!--]--><meta property="keywords" content="部署"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><span class="page-author-item">King-sj</span></span><span property="author" content="King-sj"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-09-16T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 3 分钟</span><meta property="timeRequired" content="PT3M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category4 clickable" role="navigation">nginx</span><!--]--><meta property="articleSection" content="nginx"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">部署</span><!--]--><meta property="keywords" content="部署"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/category/oi/index.html b/category/oi/index.html
index ef314cb..293f62b 100644
--- a/category/oi/index.html
+++ b/category/oi/index.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/category/oi/"><meta property="og:site_name" content="blog"><meta property="og:title" content="OI 分类"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"OI 分类"}</script><title>OI 分类 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-BXtqeyHq.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-DOXbY5aY.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="vp-category-list"><li class="vp-category vp-category8"><a class="route-link" href="/category/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="count">26</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86/">编译原理<span class="count">8</span></a></li><li class="vp-category vp-category6 active"><a class="route-link" href="/category/oi/">OI<span class="count">2</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/build-tools/">build-tools<span class="count">1</span></a></li><li class="vp-category vp-category5"><a class="route-link" href="/category/cicd/">CI/CD<span class="count">1</span></a></li><li class="vp-category vp-category4"><a class="route-link" href="/category/nginx/">nginx<span class="count">1</span></a></li><li class="vp-category vp-category1"><a class="route-link" href="/category/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/">奇技淫巧<span class="count">1</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/docker/">docker<span class="count">1</span></a></li><li class="vp-category vp-category7"><a class="route-link" href="/category/python/">python<span class="count">1</span></a></li><li class="vp-category vp-category1"><a class="route-link" href="/category/%E9%A3%8E%E6%A0%BC/">风格<span class="count">1</span></a></li><li class="vp-category vp-category3"><a class="route-link" href="/category/%E6%95%B0%E5%AD%A6/">数学<span class="count">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/modint.html"><header class="vp-article-title"><!----><!----><span property="headline">「泛型与 OI」modint</span></header></a><div class="vp-article-excerpt">
@@ -40,7 +40,7 @@ <h2>背景介绍</h2>
 <p>这些题目要么是因为答案太大，不方便输出结果，例如许多计数 dp；要么是因为答案是浮点数，出题人不愿意写一个确定精度的 Special Judge，例如很多期望概率题；要么是因为这道题目直接考察了模的性质和运用，比如大量的 998244353 类的多项式题目。</p>
 </div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2023-08-02T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category6 clickable" role="navigation">OI</span><!--]--><meta property="articleSection" content="OI"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">MODInt</span><!--]--><meta property="keywords" content="MODInt"></span></div></article></div><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html"><header class="vp-article-title"><!----><!----><span property="headline">闭包实现类</span></header></a><div class="vp-article-excerpt">
 <p>你是否曾经想过，不用类也能封装数据和方法？这篇文章将带你走进闭包的奇妙世界，展示如何用闭包来实现这一点。通过一个有趣的代码示例，你将看到闭包是如何捕获变量并提供类似类的功能的。准备好了吗？让我们开始这段有趣的旅程吧！</p>
-</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2023-08-02T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category6 clickable" role="navigation">OI</span><!--]--><meta property="articleSection" content="OI"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">MODInt</span><!--]--><meta property="keywords" content="MODInt"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2023-08-02T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category6 clickable" role="navigation">OI</span><!--]--><meta property="articleSection" content="OI"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">MODInt</span><!--]--><meta property="keywords" content="MODInt"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/category/python/index.html b/category/python/index.html
index e5bf9a4..7966f76 100644
--- a/category/python/index.html
+++ b/category/python/index.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/category/python/"><meta property="og:site_name" content="blog"><meta property="og:title" content="python 分类"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"python 分类"}</script><title>python 分类 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-UrkKwESw.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-ZzlVKqB8.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="vp-category-list"><li class="vp-category vp-category8"><a class="route-link" href="/category/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="count">26</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86/">编译原理<span class="count">8</span></a></li><li class="vp-category vp-category6"><a class="route-link" href="/category/oi/">OI<span class="count">2</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/build-tools/">build-tools<span class="count">1</span></a></li><li class="vp-category vp-category5"><a class="route-link" href="/category/cicd/">CI/CD<span class="count">1</span></a></li><li class="vp-category vp-category4"><a class="route-link" href="/category/nginx/">nginx<span class="count">1</span></a></li><li class="vp-category vp-category1"><a class="route-link" href="/category/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/">奇技淫巧<span class="count">1</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/docker/">docker<span class="count">1</span></a></li><li class="vp-category vp-category7 active"><a class="route-link" href="/category/python/">python<span class="count">1</span></a></li><li class="vp-category vp-category1"><a class="route-link" href="/category/%E9%A3%8E%E6%A0%BC/">风格<span class="count">1</span></a></li><li class="vp-category vp-category3"><a class="route-link" href="/category/%E6%95%B0%E5%AD%A6/">数学<span class="count">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/python_requrements.html"><header class="vp-article-title"><!----><!----><span property="headline">python requirements.txt</span></header></a><div class="vp-article-excerpt"><p>Python 生成 <code>requirements</code>有两种方式</p>
@@ -39,7 +39,7 @@
 <li><code>pip list --format=freeze &gt; requirements.txt</code> (推荐做法)</li>
 <li><code>pip freeze &gt; requirements.txt</code> (不推荐，会带有本地路径)</li>
 </ul>
-</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-29T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category7 clickable" role="navigation">python</span><!--]--><meta property="articleSection" content="python"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag2 clickable" role="navigation">踩坑记录</span><!--]--><meta property="keywords" content="踩坑记录"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-29T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category7 clickable" role="navigation">python</span><!--]--><meta property="articleSection" content="python"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag2 clickable" role="navigation">踩坑记录</span><!--]--><meta property="keywords" content="踩坑记录"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/category/\345\245\207\346\212\200\346\267\253\345\267\247/index.html" "b/category/\345\245\207\346\212\200\346\267\253\345\267\247/index.html"
index d07e436..012b918 100644
--- "a/category/\345\245\207\346\212\200\346\267\253\345\267\247/index.html"
+++ "b/category/\345\245\207\346\212\200\346\267\253\345\267\247/index.html"
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/category/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/"><meta property="og:site_name" content="blog"><meta property="og:title" content="奇技淫巧 分类"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"奇技淫巧 分类"}</script><title>奇技淫巧 分类 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-BSJr7qwh.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-DhCS_0vf.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="vp-category-list"><li class="vp-category vp-category8"><a class="route-link" href="/category/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="count">26</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86/">编译原理<span class="count">8</span></a></li><li class="vp-category vp-category6"><a class="route-link" href="/category/oi/">OI<span class="count">2</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/build-tools/">build-tools<span class="count">1</span></a></li><li class="vp-category vp-category5"><a class="route-link" href="/category/cicd/">CI/CD<span class="count">1</span></a></li><li class="vp-category vp-category4"><a class="route-link" href="/category/nginx/">nginx<span class="count">1</span></a></li><li class="vp-category vp-category1 active"><a class="route-link" href="/category/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/">奇技淫巧<span class="count">1</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/docker/">docker<span class="count">1</span></a></li><li class="vp-category vp-category7"><a class="route-link" href="/category/python/">python<span class="count">1</span></a></li><li class="vp-category vp-category1"><a class="route-link" href="/category/%E9%A3%8E%E6%A0%BC/">风格<span class="count">1</span></a></li><li class="vp-category vp-category3"><a class="route-link" href="/category/%E6%95%B0%E5%AD%A6/">数学<span class="count">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/docker.html"><header class="vp-article-title"><!----><!----><span property="headline"></span></header></a><div class="vp-article-excerpt"><h2>GitHub Container Registry 加速</h2>
@@ -40,7 +40,7 @@ <h3>ghcr.io简介</h3>
 <li>ghcr.io 是 GitHub Container Registry 的域名。GitHub Container Registry 是 GitHub 提供的容器镜像注册表服务，允许开发者在 GitHub 上存储、管理和分享 Docker 镜像。它与 GitHub 代码仓库紧密集成，可以使用相同的权限管理、团队协作和版本控制工具来管理容器镜像。</li>
 <li>通过 GitHub Container Registry，开发者可以方便地将他们的容器镜像与代码仓库关联起来，这样就可以在同一个平台上管理代码和镜像。这种集成性使得持续集成/持续交付 (CI/CD) 流程更加简化和统一，开发团队可以更容易地构建、测试和部署应用程序。</li>
 <li>对于使用 GitHub 作为代码托管平台的开发者来说，GitHub Container Registry 提供一个便捷且强大的容器镜像管理解决方案。通过该服务，可以更轻松地构建和部署容器化的应用程序，从而加速开发和交付周期。</li>
-</ul></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-09-12T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category1 clickable" role="navigation">奇技淫巧</span><span class="page-category-item category2 clickable" role="navigation">docker</span><!--]--><meta property="articleSection" content="奇技淫巧,docker"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag2 clickable" role="navigation">docker</span><!--]--><meta property="keywords" content="docker"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</ul></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-09-12T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category1 clickable" role="navigation">奇技淫巧</span><span class="page-category-item category2 clickable" role="navigation">docker</span><!--]--><meta property="articleSection" content="奇技淫巧,docker"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag2 clickable" role="navigation">docker</span><!--]--><meta property="keywords" content="docker"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/category/\346\225\260\345\255\246/index.html" "b/category/\346\225\260\345\255\246/index.html"
index 38ef28b..3b50d7a 100644
--- "a/category/\346\225\260\345\255\246/index.html"
+++ "b/category/\346\225\260\345\255\246/index.html"
@@ -30,13 +30,13 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/category/%E6%95%B0%E5%AD%A6/"><meta property="og:site_name" content="blog"><meta property="og:title" content="数学 分类"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"数学 分类"}</script><title>数学 分类 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-CZDJXbd3.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-B1eL3fl0.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="vp-category-list"><li class="vp-category vp-category8"><a class="route-link" href="/category/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="count">26</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86/">编译原理<span class="count">8</span></a></li><li class="vp-category vp-category6"><a class="route-link" href="/category/oi/">OI<span class="count">2</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/build-tools/">build-tools<span class="count">1</span></a></li><li class="vp-category vp-category5"><a class="route-link" href="/category/cicd/">CI/CD<span class="count">1</span></a></li><li class="vp-category vp-category4"><a class="route-link" href="/category/nginx/">nginx<span class="count">1</span></a></li><li class="vp-category vp-category1"><a class="route-link" href="/category/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/">奇技淫巧<span class="count">1</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/docker/">docker<span class="count">1</span></a></li><li class="vp-category vp-category7"><a class="route-link" href="/category/python/">python<span class="count">1</span></a></li><li class="vp-category vp-category1"><a class="route-link" href="/category/%E9%A3%8E%E6%A0%BC/">风格<span class="count">1</span></a></li><li class="vp-category vp-category3 active"><a class="route-link" href="/category/%E6%95%B0%E5%AD%A6/">数学<span class="count">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html"><header class="vp-article-title"><!----><!----><span property="headline">「算术公理系统 1」自然数</span></header></a><div class="vp-article-excerpt">
 <p>假设存在一个算数系统的模型满足 Peano 公理，即假定 Peano 公理相容，在此承认次假设的基础之上，我们即可建立如今最常用的<strong>算术公理系统</strong>。<strong>自然数的定义</strong>则是构建此算术公理系统的第一步。</p>
-</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2023-07-09T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 18 分钟</span><meta property="timeRequired" content="PT18M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category3 clickable" role="navigation">数学</span><!--]--><meta property="articleSection" content="数学"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag3 clickable" role="navigation">公理系统</span><!--]--><meta property="keywords" content="公理系统"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2023-07-09T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 18 分钟</span><meta property="timeRequired" content="PT18M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category3 clickable" role="navigation">数学</span><!--]--><meta property="articleSection" content="数学"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag3 clickable" role="navigation">公理系统</span><!--]--><meta property="keywords" content="公理系统"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/category/\347\274\226\350\257\221\345\216\237\347\220\206/index.html" "b/category/\347\274\226\350\257\221\345\216\237\347\220\206/index.html"
index 963de3a..349dce1 100644
--- "a/category/\347\274\226\350\257\221\345\216\237\347\220\206/index.html"
+++ "b/category/\347\274\226\350\257\221\345\216\237\347\220\206/index.html"
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/category/%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86/"><meta property="og:site_name" content="blog"><meta property="og:title" content="编译原理 分类"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"编译原理 分类"}</script><title>编译原理 分类 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-ZxSgoRoh.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-CL479cux.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="vp-category-list"><li class="vp-category vp-category8"><a class="route-link" href="/category/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="count">26</span></a></li><li class="vp-category vp-category2 active"><a class="route-link" href="/category/%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86/">编译原理<span class="count">8</span></a></li><li class="vp-category vp-category6"><a class="route-link" href="/category/oi/">OI<span class="count">2</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/build-tools/">build-tools<span class="count">1</span></a></li><li class="vp-category vp-category5"><a class="route-link" href="/category/cicd/">CI/CD<span class="count">1</span></a></li><li class="vp-category vp-category4"><a class="route-link" href="/category/nginx/">nginx<span class="count">1</span></a></li><li class="vp-category vp-category1"><a class="route-link" href="/category/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/">奇技淫巧<span class="count">1</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/docker/">docker<span class="count">1</span></a></li><li class="vp-category vp-category7"><a class="route-link" href="/category/python/">python<span class="count">1</span></a></li><li class="vp-category vp-category1"><a class="route-link" href="/category/%E9%A3%8E%E6%A0%BC/">风格<span class="count">1</span></a></li><li class="vp-category vp-category3"><a class="route-link" href="/category/%E6%95%B0%E5%AD%A6/">数学<span class="count">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/designASimpileCCompiler/0.html"><header class="vp-article-title"><!----><!----><span property="headline">手把手教你构建 C 语言编译器（0）- 前言</span></header></a><div class="vp-article-excerpt">
@@ -139,7 +139,7 @@ <h1>手把手教你构建 C 语言编译器（9）- 总结</h1>
 <li><a href="about:blank#%E8%AF%AD%E6%B3%95%E5%88%86%E6%9E%90">3. 语法分析</a></li>
 <li><a href="about:blank#%E5%85%B3%E4%BA%8E%E7%BC%96%E4%BB%A3%E7%A0%81">4. 关于编代码</a></li>
 <li><a href="about:blank#%E7%BB%93%E8%AF%AD">5. 结语</a></li>
-</ol></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category2 clickable" role="navigation">编译原理</span><!--]--><meta property="articleSection" content="编译原理"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag4 clickable" role="navigation">c</span><span class="page-tag-item tag4 clickable" role="navigation">编译器</span><span class="page-tag-item tag4 clickable" role="navigation">解释器</span><!--]--><meta property="keywords" content="c,编译器,解释器"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</ol></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category2 clickable" role="navigation">编译原理</span><!--]--><meta property="articleSection" content="编译原理"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag4 clickable" role="navigation">c</span><span class="page-tag-item tag4 clickable" role="navigation">编译器</span><span class="page-tag-item tag4 clickable" role="navigation">解释器</span><!--]--><meta property="keywords" content="c,编译器,解释器"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/category/\350\256\276\350\256\241\346\250\241\345\274\217/index.html" "b/category/\350\256\276\350\256\241\346\250\241\345\274\217/index.html"
index 20c2c66..471e3e8 100644
--- "a/category/\350\256\276\350\256\241\346\250\241\345\274\217/index.html"
+++ "b/category/\350\256\276\350\256\241\346\250\241\345\274\217/index.html"
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/category/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/"><meta property="og:site_name" content="blog"><meta property="og:title" content="设计模式 分类"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"设计模式 分类"}</script><title>设计模式 分类 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-B71I-yvI.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-DOZrz5tX.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="vp-category-list"><li class="vp-category vp-category8 active"><a class="route-link" href="/category/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="count">26</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86/">编译原理<span class="count">8</span></a></li><li class="vp-category vp-category6"><a class="route-link" href="/category/oi/">OI<span class="count">2</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/build-tools/">build-tools<span class="count">1</span></a></li><li class="vp-category vp-category5"><a class="route-link" href="/category/cicd/">CI/CD<span class="count">1</span></a></li><li class="vp-category vp-category4"><a class="route-link" href="/category/nginx/">nginx<span class="count">1</span></a></li><li class="vp-category vp-category1"><a class="route-link" href="/category/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/">奇技淫巧<span class="count">1</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/docker/">docker<span class="count">1</span></a></li><li class="vp-category vp-category7"><a class="route-link" href="/category/python/">python<span class="count">1</span></a></li><li class="vp-category vp-category1"><a class="route-link" href="/category/%E9%A3%8E%E6%A0%BC/">风格<span class="count">1</span></a></li><li class="vp-category vp-category3"><a class="route-link" href="/category/%E6%95%B0%E5%AD%A6/">数学<span class="count">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/DesignPatterns/command.html"><header class="vp-article-title"><!----><!----><span property="headline">Command 模式</span></header></a><div class="vp-article-excerpt"><h2>为什么使用此模式</h2>
@@ -70,7 +70,7 @@ <h2>示例代码</h2>
 <p>观察者模式非常适合用于需要自动更新的场景。例如，在图形用户界面（GUI）应用程序中，当数据模型发生变化时，所有显示该数据的视图都需要自动更新。通过使用观察者模式，我们可以将这些视图注册为观察者，当数据模型发生变化时，它们会自动收到通知并更新显示。</p>
 <h2>示例代码</h2>
 <p>在这个示例中，我们展示了如何使用观察者模式来管理状态变化。观察者模式定义了一种一对多的依赖关系，当一个对象的状态发生改变时，所有依赖于它的对象都会得到通知并自动更新。以下是 TypeScript 实现的代码示例：</p>
-<img src="https://www.plantuml.com/plantuml/svg/jL912i8m4Bpd5JbMf1_eoOFWJS4VR9kn1fgaRBP54VzkDRQKua4GRyliC3CxoIOAiNIkKTOB-4GLzA6Cu1wiRqhhTTSQ4cGrF9WaSA7tdIl1kn5O5ReFrgYxKbH6OQf4Lmt5k2GcFJ9cDCZ2UoWcpr5i81eq47p7zK7iwJekOZPRrP2Kumdwr_I4SK7L3NVDqgVGMrjRcIgmhctWu2N-K4iItZ6rvty87ycRu9PbuoBmvlCZvAc7UH_VrxGK37a-dQ0sW-Vmcnu0" alt=""></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-26T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag1 clickable" role="navigation">管理状态</span><!--]--><meta property="keywords" content="设计模式,TypeScript,管理状态"></span></div></article></div><div class="vp-pagination"><nav class="vp-pagination-list"><div class="vp-pagination-number"><!----><!----><!--[--><div class="active" role="navigation">1</div><div class="" role="navigation">2</div><div class="" role="navigation">3</div><!--]--><!----><div class="next" role="navigation" unselectable="on">下一页</div></div><div class="vp-pagination-nav"><label for="navigation-text">跳转到: </label><input id="navigation-text" value><button class="vp-pagination-button" type="button" role="navigation" title="前往">前往</button></div></nav></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+<img src="https://www.plantuml.com/plantuml/svg/jL912i8m4Bpd5JbMf1_eoOFWJS4VR9kn1fgaRBP54VzkDRQKua4GRyliC3CxoIOAiNIkKTOB-4GLzA6Cu1wiRqhhTTSQ4cGrF9WaSA7tdIl1kn5O5ReFrgYxKbH6OQf4Lmt5k2GcFJ9cDCZ2UoWcpr5i81eq47p7zK7iwJekOZPRrP2Kumdwr_I4SK7L3NVDqgVGMrjRcIgmhctWu2N-K4iItZ6rvty87ycRu9PbuoBmvlCZvAc7UH_VrxGK37a-dQ0sW-Vmcnu0" alt=""></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-26T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag1 clickable" role="navigation">管理状态</span><!--]--><meta property="keywords" content="设计模式,TypeScript,管理状态"></span></div></article></div><div class="vp-pagination"><nav class="vp-pagination-list"><div class="vp-pagination-number"><!----><!----><!--[--><div class="active" role="navigation">1</div><div class="" role="navigation">2</div><div class="" role="navigation">3</div><!--]--><!----><div class="next" role="navigation" unselectable="on">下一页</div></div><div class="vp-pagination-nav"><label for="navigation-text">跳转到: </label><input id="navigation-text" value><button class="vp-pagination-button" type="button" role="navigation" title="前往">前往</button></div></nav></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/category/\351\243\216\346\240\274/index.html" "b/category/\351\243\216\346\240\274/index.html"
index fd85e02..f3a464a 100644
--- "a/category/\351\243\216\346\240\274/index.html"
+++ "b/category/\351\243\216\346\240\274/index.html"
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/category/%E9%A3%8E%E6%A0%BC/"><meta property="og:site_name" content="blog"><meta property="og:title" content="风格 分类"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"风格 分类"}</script><title>风格 分类 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-C8X5E5_U.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-BjeRhPA4.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="vp-category-list"><li class="vp-category vp-category8"><a class="route-link" href="/category/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="count">26</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86/">编译原理<span class="count">8</span></a></li><li class="vp-category vp-category6"><a class="route-link" href="/category/oi/">OI<span class="count">2</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/build-tools/">build-tools<span class="count">1</span></a></li><li class="vp-category vp-category5"><a class="route-link" href="/category/cicd/">CI/CD<span class="count">1</span></a></li><li class="vp-category vp-category4"><a class="route-link" href="/category/nginx/">nginx<span class="count">1</span></a></li><li class="vp-category vp-category1"><a class="route-link" href="/category/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/">奇技淫巧<span class="count">1</span></a></li><li class="vp-category vp-category2"><a class="route-link" href="/category/docker/">docker<span class="count">1</span></a></li><li class="vp-category vp-category7"><a class="route-link" href="/category/python/">python<span class="count">1</span></a></li><li class="vp-category vp-category1 active"><a class="route-link" href="/category/%E9%A3%8E%E6%A0%BC/">风格<span class="count">1</span></a></li><li class="vp-category vp-category3"><a class="route-link" href="/category/%E6%95%B0%E5%AD%A6/">数学<span class="count">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/style.html"><header class="vp-article-title"><!----><!----><span property="headline">风格统一</span></header></a><div class="vp-article-excerpt">
@@ -49,7 +49,7 @@
 charset = utf-8
 trim_trailing_whitespace = true
 insert_final_newline = true
-</code></pre></div></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-08-25T12:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category1 clickable" role="navigation">风格</span><!--]--><meta property="articleSection" content="风格"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag1 clickable" role="navigation">风格</span><!--]--><meta property="keywords" content="风格"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</code></pre></div></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-08-25T12:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category1 clickable" role="navigation">风格</span><!--]--><meta property="articleSection" content="风格"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag1 clickable" role="navigation">风格</span><!--]--><meta property="keywords" content="风格"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/essays/index.html b/essays/index.html
index c6adae7..266cedb 100644
--- a/essays/index.html
+++ b/essays/index.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/essays/"><meta property="og:site_name" content="blog"><meta property="og:title" content="随笔"><meta property="og:description" content="随笔 这里是所有个人感想、生活记录等非技术类文章。"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:published_time" content="2024-10-18T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"随笔","image":[""],"datePublished":"2024-10-18T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>随笔 | blog</title><meta name="description" content="随笔 这里是所有个人感想、生活记录等非技术类文章。">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-DzJoMr4P.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-CdwZ1P48.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
-    <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->随笔</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-18T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><!----></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="随笔" tabindex="-1"><a class="header-anchor" href="#随笔"><span>随笔</span></a></h1><p>这里是所有个人感想、生活记录等非技术类文章。</p><!----></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/essays/index.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><!----><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->随笔</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-18T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><!----></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="随笔" tabindex="-1"><a class="header-anchor" href="#随笔"><span>随笔</span></a></h1><p>这里是所有个人感想、生活记录等非技术类文章。</p><!----><div class="vp-catalog-wrapper"><h2 class="vp-catalog-main-title">目录</h2><ul class="vp-catalogs"><li class="vp-catalog"><div class="vp-catalog-child-title"><a class="route-link vp-catalog-title" href="/essays/%E5%91%BD%E9%87%8C%E6%9C%89%E6%97%B6%E7%BB%88%E9%A1%BB%E6%9C%89.html">命里有时终须有</a></div></li></ul></div></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/essays/index.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><!----><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/essays/\345\221\275\351\207\214\346\234\211\346\227\266\347\273\210\351\241\273\346\234\211.html" "b/essays/\345\221\275\351\207\214\346\234\211\346\227\266\347\273\210\351\241\273\346\234\211.html"
index 8b21318..3ad28d2 100644
--- "a/essays/\345\221\275\351\207\214\346\234\211\346\227\266\347\273\210\351\241\273\346\234\211.html"
+++ "b/essays/\345\221\275\351\207\214\346\234\211\346\227\266\347\273\210\351\241\273\346\234\211.html"
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/essays/%E5%91%BD%E9%87%8C%E6%9C%89%E6%97%B6%E7%BB%88%E9%A1%BB%E6%9C%89.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="命里有时终须有"><meta property="og:description" content="alt textalt text 昨日在玩“三国杀：一将成名”时，我抽奖一发就中了大奖——“清河公主”传说皮。这让我不禁感慨：“命里有时终须有，命里无时莫强求。”这句话真是道出了人生的真谛，有些事情是强求不来的，顺其自然反而能得到意想不到的收获。"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:published_time" content="2024-10-30T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"命里有时终须有","image":[""],"datePublished":"2024-10-30T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>命里有时终须有 | blog</title><meta name="description" content="alt textalt text 昨日在玩“三国杀：一将成名”时，我抽奖一发就中了大奖——“清河公主”传说皮。这让我不禁感慨：“命里有时终须有，命里无时莫强求。”这句话真是道出了人生的真谛，有些事情是强求不来的，顺其自然反而能得到意想不到的收获。">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/命里有时终须有.html-DOvT7-xg.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/命里有时终须有.html-B46pNP68.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->命里有时终须有</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-30T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><!----></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><figure><img src="/assets/966519d02c8ca050dc064d479fb711e-Bmk4mUCm.jpg" alt="alt text" tabindex="0" loading="lazy"><figcaption>alt text</figcaption></figure><p>昨日在玩“三国杀：一将成名”时，我抽奖一发就中了大奖——“清河公主”传说皮。这让我不禁感慨：“命里有时终须有，命里无时莫强求。”这句话真是道出了人生的真谛，有些事情是强求不来的，顺其自然反而能得到意想不到的收获。</p></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/essays/命里有时终须有.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><!----><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/index.html b/index.html
index 1ead6a5..b5f966c 100644
--- a/index.html
+++ b/index.html
@@ -30,11 +30,19 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/"><meta property="og:site_name" content="blog"><meta property="og:title" content="主页"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="King-sj"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"主页"}</script><title>主页 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-BjAw7f-F.js">
-    <link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-Bq7J9cN0.js">
+    <link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
-    <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="vp-blog-hero fullscreen"><!--[--><!----><!--]--><!--[--><!--[--><!--[--><!--]--><h1 class="vp-blog-hero-title">KSJ</h1><div class="hitokoto"><p class="hitokoto-text"><span></span></p><p class="hitokoto-author" style="opacity:0;">——「」</p></div><!--]--><!--]--><button type="button" class="slide-down-button"><svg xmlns="http://www.w3.org/2000/svg" class="icon slide-down-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="slide-down icon"><path d="M108.775 312.23c13.553 0 27.106 3.734 39.153 11.806l375.205 250.338 363.641-252.808c32.587-21.624 76.499-12.83 98.123 19.757 21.685 32.467 12.95 76.56-19.576 98.184l-402.854 278.89c-23.733 15.901-54.694 15.962-78.547.12L69.501 442.097c-32.647-21.685-41.441-65.777-19.817-98.304 13.734-20.54 36.201-31.563 59.09-31.563Z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon slide-down-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="slide-down icon"><path d="M108.775 312.23c13.553 0 27.106 3.734 39.153 11.806l375.205 250.338 363.641-252.808c32.587-21.624 76.499-12.83 98.123 19.757 21.685 32.467 12.95 76.56-19.576 98.184l-402.854 278.89c-23.733 15.901-54.694 15.962-78.547.12L69.501 442.097c-32.647-21.685-41.441-65.777-19.817-98.304 13.734-20.54 36.201-31.563 59.09-31.563Z"></path></svg></button></div><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><div class="vp-project-panel"><div class="vp-project-card project0"><svg xmlns="http://www.w3.org/2000/svg" class="icon project-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="project icon"><path d="M987.456 425.152H864V295.296a36.48 36.48 0 0 0-36.544-36.544h-360l-134.08-128.256A9.344 9.344 0 0 0 327.04 128H36.48A36.48 36.48 0 0 0 0 164.544v676.608a36.48 36.48 0 0 0 36.544 36.544h797.76a36.672 36.672 0 0 0 33.92-22.848L1021.44 475.52a36.48 36.48 0 0 0-33.92-50.304zM82.304 210.304h215.424l136.64 130.752h347.328v84.096H198.848A36.672 36.672 0 0 0 164.928 448L82.304 652.8V210.304zM808.32 795.456H108.544l118.08-292.608h699.904L808.32 795.52z"></path></svg><div class="vp-project-name">自动机</div><div class="vp-project-desc">自动机</div></div></div><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/figure_bed.html"><header class="vp-article-title"><!----><!----><span property="headline">github 图床</span></header></a><div class="vp-article-excerpt"><p>参考</p>
+    <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="vp-blog-hero fullscreen"><!--[--><!----><!--]--><!--[--><!--[--><!--[--><!--]--><h1 class="vp-blog-hero-title">KSJ</h1><div class="hitokoto"><p class="hitokoto-text"><span></span></p><p class="hitokoto-author" style="opacity:0;">——「」</p></div><!--]--><!--]--><button type="button" class="slide-down-button"><svg xmlns="http://www.w3.org/2000/svg" class="icon slide-down-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="slide-down icon"><path d="M108.775 312.23c13.553 0 27.106 3.734 39.153 11.806l375.205 250.338 363.641-252.808c32.587-21.624 76.499-12.83 98.123 19.757 21.685 32.467 12.95 76.56-19.576 98.184l-402.854 278.89c-23.733 15.901-54.694 15.962-78.547.12L69.501 442.097c-32.647-21.685-41.441-65.777-19.817-98.304 13.734-20.54 36.201-31.563 59.09-31.563Z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon slide-down-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="slide-down icon"><path d="M108.775 312.23c13.553 0 27.106 3.734 39.153 11.806l375.205 250.338 363.641-252.808c32.587-21.624 76.499-12.83 98.123 19.757 21.685 32.467 12.95 76.56-19.576 98.184l-402.854 278.89c-23.733 15.901-54.694 15.962-78.547.12L69.501 442.097c-32.647-21.685-41.441-65.777-19.817-98.304 13.734-20.54 36.201-31.563 59.09-31.563Z"></path></svg></button></div><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><div class="vp-project-panel"><div class="vp-project-card project0"><svg xmlns="http://www.w3.org/2000/svg" class="icon project-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="project icon"><path d="M987.456 425.152H864V295.296a36.48 36.48 0 0 0-36.544-36.544h-360l-134.08-128.256A9.344 9.344 0 0 0 327.04 128H36.48A36.48 36.48 0 0 0 0 164.544v676.608a36.48 36.48 0 0 0 36.544 36.544h797.76a36.672 36.672 0 0 0 33.92-22.848L1021.44 475.52a36.48 36.48 0 0 0-33.92-50.304zM82.304 210.304h215.424l136.64 130.752h347.328v84.096H198.848A36.672 36.672 0 0 0 164.928 448L82.304 652.8V210.304zM808.32 795.456H108.544l118.08-292.608h699.904L808.32 795.52z"></path></svg><div class="vp-project-name">自动机</div><div class="vp-project-desc">自动机</div></div><div class="vp-project-card project1"><svg xmlns="http://www.w3.org/2000/svg" class="icon project-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="project icon"><path d="M987.456 425.152H864V295.296a36.48 36.48 0 0 0-36.544-36.544h-360l-134.08-128.256A9.344 9.344 0 0 0 327.04 128H36.48A36.48 36.48 0 0 0 0 164.544v676.608a36.48 36.48 0 0 0 36.544 36.544h797.76a36.672 36.672 0 0 0 33.92-22.848L1021.44 475.52a36.48 36.48 0 0 0-33.92-50.304zM82.304 210.304h215.424l136.64 130.752h347.328v84.096H198.848A36.672 36.672 0 0 0 164.928 448L82.304 652.8V210.304zM808.32 795.456H108.544l118.08-292.608h699.904L808.32 795.52z"></path></svg><div class="vp-project-name">智能车循迹</div><div class="vp-project-desc">北京邮电大学创新创业智能车循迹python版</div></div></div><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/projects/carrobot.html"><header class="vp-article-title"><!----><!----><span property="headline">北京邮电大学创新创业智能车循迹python版</span></header></a><div class="vp-article-excerpt"><p><a href="https://github.com/king-sj/carrobot" target="_blank" rel="noopener noreferrer">项目源码</a></p>
+<p><s>因为想要创新学分，所以选了创新创业智能车课程</s>，项目要求完成智能车的循迹和避障。</p>
+<p>由于笔者不喜欢使用VPL的图形化（<s>报用qWq</s>）, 故而使用手写代码的方式实现。</p>
+</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-11-07T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 4 分钟</span><meta property="timeRequired" content="PT4M"></span><!----><!----></div></article></div><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/resources/compile/"><header class="vp-article-title"><!----><!----><span property="headline">编译原理相关</span></header></a><div class="vp-article-excerpt"><ul>
+<li>anltr.grammar</li>
+<li>bison/yacc</li>
+<li>flex</li>
+</ul>
+</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-11-06T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><!----></div></article></div><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/figure_bed.html"><header class="vp-article-title"><!----><!----><span property="headline">github 图床</span></header></a><div class="vp-article-excerpt"><p>参考</p>
 <ul>
 <li>https://zhuanlan.zhihu.com/p/347342082</li>
 </ul>
@@ -64,12 +72,7 @@ <h2>示例代码</h2>
 <li><strong>简化语法解析</strong>：通过定义文法规则，可以轻松解析和执行特定的语言或指令集。</li>
 <li><strong>可扩展性</strong>：可以轻松添加新的语法规则或指令，而无需修改现有代码。</li>
 <li><strong>代码复用</strong>：通过将不同的语法规则封装在不同的类中，可以提高代码的复用性和可维护性。</li>
-</ol></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-29T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 3 分钟</span><meta property="timeRequired" content="PT3M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag1 clickable" role="navigation">用类实现</span><!--]--><meta property="keywords" content="设计模式,TypeScript,用类实现"></span></div></article></div><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/DesignPatterns/proxy.html"><header class="vp-article-title"><!----><!----><span property="headline">Proxy 模式</span></header></a><div class="vp-article-excerpt"><h2>为什么使用代理模式</h2>
-<p>在面向对象编程中，“本人”和“代理人”都是对象。如果“本人”对象太忙了．有些工作无法自己亲自完成，就将其交给“代理人"对象负责。</p>
-</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-29T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag5 clickable" role="navigation">避免浪费</span><!--]--><meta property="keywords" content="设计模式,TypeScript,避免浪费"></span></div></article></div><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/DesignPatterns/flyweight.html"><header class="vp-article-title"><!----><!----><span property="headline">Flyweight 模式</span></header></a><div class="vp-article-excerpt"><h2>为什么使用 Flyweight 模式</h2>
-<p>Flyweight 模式是一种结构型设计模式，它通过共享尽可能多的相同对象来减少内存使用，从而提高性能。在需要生成大量细粒度对象的场景中，Flyweight 模式非常有用。通过共享对象，Flyweight 模式可以显著减少内存消耗，并提高应用程序的效率。</p>
-<h2>实例代码</h2>
-<img src="https://www.plantuml.com/plantuml/svg/RL7B2i8m4BpdA_ROKli3GKfH43nuyYWUrZJMG4rAinL4_7VJz5rxMsPsPcTtKqjOKVqic2ZGMjYfVF_02ZuC80RXIerFoS5IfNJkmRlHb27X18oWT1K58OUNKHdxihdT0GMPwjsvbiOK74vORbk3JT-MUDeb8YN0EgQGP3HVkBJ9Z7RYkW62q2VePBcaewDG2zd4-PD6JKU71ilzHi5iXRCdk_GtbJSoExHUhjvsciWLW-NwUHQ7YUDac3mEdA3z0giaIwNEt0z_" alt=""></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-28T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 8 分钟</span><meta property="timeRequired" content="PT8M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag5 clickable" role="navigation">避免浪费</span><!--]--><meta property="keywords" content="设计模式,TypeScript,避免浪费"></span></div></article></div><div class="vp-pagination"><nav class="vp-pagination-list"><div class="vp-pagination-number"><!----><!----><!--[--><div class="active" role="navigation">1</div><div class="" role="navigation">2</div><div class="" role="navigation">3</div><div class="" role="navigation">4</div><div class="" role="navigation">5</div><!--]--><!--[--><div class="ellipsis">...</div><div role="navigation">7</div><!--]--><div class="next" role="navigation" unselectable="on">下一页</div></div><div class="vp-pagination-nav"><label for="navigation-text">跳转到: </label><input id="navigation-text" value><button class="vp-pagination-button" type="button" role="navigation" title="前往">前往</button></div></nav></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div><div class="theme-hope-content"><!-- https://theme-hope.vuejs.press/zh/guide/ --></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MIT 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</ol></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-29T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 3 分钟</span><meta property="timeRequired" content="PT3M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag1 clickable" role="navigation">用类实现</span><!--]--><meta property="keywords" content="设计模式,TypeScript,用类实现"></span></div></article></div><div class="vp-pagination"><nav class="vp-pagination-list"><div class="vp-pagination-number"><!----><!----><!--[--><div class="active" role="navigation">1</div><div class="" role="navigation">2</div><div class="" role="navigation">3</div><div class="" role="navigation">4</div><div class="" role="navigation">5</div><!--]--><!--[--><div class="ellipsis">...</div><div role="navigation">7</div><!--]--><div class="next" role="navigation" unselectable="on">下一页</div></div><div class="vp-pagination-nav"><label for="navigation-text">跳转到: </label><input id="navigation-text" value><button class="vp-pagination-button" type="button" role="navigation" title="前往">前往</button></div></nav></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div><div class="theme-hope-content"><!-- https://theme-hope.vuejs.press/zh/guide/ --></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MIT 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/intro.html b/intro.html
index 62edb20..e92efd1 100644
--- a/intro.html
+++ b/intro.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/intro.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="介绍页"><meta property="og:description" content="介绍页 一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:published_time" content="2023-07-08T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"介绍页","description":"介绍页 一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。"}</script><title>介绍页 | blog</title><meta name="description" content="介绍页 一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/intro.html-CEHYbhC9.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/intro.html-DcelwrZW.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-project-home" aria-labelledby="main-title"><!----><header class="vp-hero-info-wrapper"><!--[--><!----><!----><!--]--><div class="vp-hero-info"><!--[--><!--]--><div class="vp-hero-infos"><h1 id="main-title">blog</h1><p id="main-description">KSJ-blog</p><!----></div></div></header><!----><!----><div class="theme-hope-content"><h1 id="介绍页" tabindex="-1"><a class="header-anchor" href="#介绍页"><span>介绍页</span></a></h1><p>一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</p><!-- # LOGO 设计理念 --><!-- 使用“KSJ”三个字母的抽象化设计。字母“K”和“J”可以设计成镜像对称，中间的“S”则像一条流畅的线条将两者连接起来，代表博客内容的连贯性和深度。整个LOGO采用深海蓝为主色调，象征智慧和深度，辅以银色或白色，增加科技感和现代感。 --></div><!--[--><!-- TODO: it's not work --><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/projects/carrobot.html b/projects/carrobot.html
new file mode 100644
index 0000000..1594544
--- /dev/null
+++ b/projects/carrobot.html
@@ -0,0 +1,40 @@
+<!doctype html>
+<html lang="zh-CN" data-theme="light">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width,initial-scale=1" />
+    <meta name="generator" content="VuePress 2.0.0-rc.9" />
+    <meta name="theme" content="VuePress Theme Hope 2.0.0-rc.38" />
+    <style>
+      html {
+        background: var(--bg-color, #fff);
+      }
+
+      html[data-theme="dark"] {
+        background: var(--bg-color, #1d1e1f);
+      }
+
+      body {
+        background: var(--bg-color);
+      }
+    </style>
+    <script>
+      const userMode = localStorage.getItem("vuepress-theme-hope-scheme");
+      const systemDarkMode =
+        window.matchMedia &&
+        window.matchMedia("(prefers-color-scheme: dark)").matches;
+
+      if (userMode === "dark" || (userMode !== "light" && systemDarkMode)) {
+        document.documentElement.setAttribute("data-theme", "dark");
+      }
+    </script>
+    <meta property="og:url" content="https://github.com/King-sj/projects/carrobot.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="北京邮电大学创新创业智能车循迹python版"><meta property="og:description" content="项目源码 ，项目要求完成智能车的循迹和避障。 由于笔者不喜欢使用VPL的图形化（）, 故而使用手写代码的方式实现。"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:published_time" content="2024-11-07T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"北京邮电大学创新创业智能车循迹python版","image":[""],"datePublished":"2024-11-07T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>北京邮电大学创新创业智能车循迹python版 | blog</title><meta name="description" content="项目源码 ，项目要求完成智能车的循迹和避障。 由于笔者不喜欢使用VPL的图形化（）, 故而使用手写代码的方式实现。">
+    <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/carrobot.html-B7set7IG.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+  </head>
+  <body>
+    <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->北京邮电大学创新创业智能车循迹python版</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-11-07T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 4 分钟</span><meta property="timeRequired" content="PT4M"></span><!----><!----></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#主要思路">主要思路</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#编程语言的选择">编程语言的选择</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#通信协议">通信协议</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#初步思路">初步思路</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#遇到的问题和改进方案">遇到的问题和改进方案</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#小车左右轮力矩不一致">小车左右轮力矩不一致</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#小车容易冲出轨道">小车容易冲出轨道</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#小车总是左右左摆头太蠢了">小车总是左右左摆头太蠢了</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#其它问题">其它问题</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#设计方案参考">设计方案参考</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#和机械臂联动">和机械臂联动</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#结语">结语</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><p><a href="https://github.com/king-sj/carrobot" target="_blank" rel="noopener noreferrer">项目源码<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></p><p><s>因为想要创新学分，所以选了创新创业智能车课程</s>，项目要求完成智能车的循迹和避障。</p><p>由于笔者不喜欢使用VPL的图形化（<s>报用qWq</s>）, 故而使用手写代码的方式实现。</p><!-- more --><h2 id="主要思路" tabindex="-1"><a class="header-anchor" href="#主要思路"><span>主要思路</span></a></h2><p>通过接发TCP包的方法与智能车进行交互， 创建两个<strong>并行</strong>任务，一个用于实时接收TCP报文来更新小车状态， 一个用于读取小车状态，作出决策并发送报文控制小车。</p><h2 id="编程语言的选择" tabindex="-1"><a class="header-anchor" href="#编程语言的选择"><span>编程语言的选择</span></a></h2><ul><li><code>python</code> 笔者的项目采用了该语言，主要原因是方便且能快速实现（<s>以及没考虑到GIL会影响介么大</s>），并采用asyncio作为“并行”库（实际上只能并发，笔者最初以为只有两个任务，用python也足够了，<s>虽然实际上也够，但是写起来没那么舒服了</s>，可能使用threads会好一点）</li><li><code>go</code> 后续又采用go重构了一遍（<s>虽然实际效果貌似变化不大，emmm...应该是硬件/小车的原因</s>）</li></ul><p>当然采用什么编程语言并不是重要（吗？，不许用rust 😠 ）</p><h2 id="通信协议" tabindex="-1"><a class="header-anchor" href="#通信协议"><span>通信协议</span></a></h2><figure><img src="/assets/image-Dc9IOqtq.png" alt="alt text" tabindex="0" loading="lazy"><figcaption>alt text</figcaption></figure><h2 id="初步思路" tabindex="-1"><a class="header-anchor" href="#初步思路"><span>初步思路</span></a></h2><p>由于硬件限制，只有一个红外传感器用于判断底部是否为黑色， 一个红外传感器+超声波传感器用于确定前方是否有障碍，信息量非常小（<s>当然超声波传感器有大概的距离，本项目不考虑介么多，取较小距离为有障碍</s>）， 为 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.651ex;" xmlns="http://www.w3.org/2000/svg" width="28.73ex" height="2.538ex" role="img" focusable="false" viewBox="0 -833.9 12698.8 1121.9" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D456" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(734,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(1334,0)"><path data-c="1D445" d="M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z"></path></g><g data-mml-node="mi" transform="translate(2093,0)"><path data-c="1D45C" d="M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z"></path></g><g data-mml-node="mi" transform="translate(2578,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mi" transform="translate(3107,0)"><path data-c="1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path></g><g data-mml-node="mo" transform="translate(3627,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(4071.7,0)"><path data-c="210E" d="M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z"></path></g><g data-mml-node="mi" transform="translate(4647.7,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mi" transform="translate(5176.7,0)"><path data-c="1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path></g><g data-mml-node="mi" transform="translate(5661.7,0)"><path data-c="1D452" d="M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z"></path></g><g data-mml-node="mi" transform="translate(6127.7,0)"><path data-c="1D442" d="M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z"></path></g><g data-mml-node="mi" transform="translate(6890.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mi" transform="translate(7319.7,0)"><path data-c="1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path></g><g data-mml-node="mi" transform="translate(7788.7,0)"><path data-c="1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path></g><g data-mml-node="mi" transform="translate(8149.7,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mi" transform="translate(8678.7,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mi" transform="translate(9111.7,0)"><path data-c="1D459" d="M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z"></path></g><g data-mml-node="mi" transform="translate(9409.7,0)"><path data-c="1D452" d="M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z"></path></g><g data-mml-node="mo" transform="translate(9875.7,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(10542.4,0)"><path data-c="2208" d="M84 250Q84 372 166 450T360 539Q361 539 377 539T419 540T469 540H568Q583 532 583 520Q583 511 570 501L466 500Q355 499 329 494Q280 482 242 458T183 409T147 354T129 306T124 272V270H568Q583 262 583 250T568 230H124V228Q124 207 134 177T167 112T231 48T328 7Q355 1 466 0H570Q583 -10 583 -20Q583 -32 568 -40H471Q464 -40 446 -40T417 -41Q262 -41 172 45Q84 127 84 250Z"></path></g><g data-mml-node="msubsup" transform="translate(11487.2,0)"><g data-mml-node="mi"><path data-c="1D44D" d="M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z"></path></g><g data-mml-node="mn" transform="translate(808,363) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g><g data-mml-node="mn" transform="translate(716,-287.9) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>R</mi><mi>o</mi><mi>a</mi><mi>d</mi><mo>,</mo><mi>h</mi><mi>a</mi><mi>v</mi><mi>e</mi><mi>O</mi><mi>b</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>c</mi><mi>l</mi><mi>e</mi><mo stretchy="false">)</mo><mo>∈</mo><msubsup><mi>Z</mi><mn>2</mn><mn>2</mn></msubsup></math></mjx-assistive-mml></mjx-container>。 故而首先考虑的基本策略是偏航时左右摆头寻找<strong>正确</strong>的角度前行。</p><h2 id="遇到的问题和改进方案" tabindex="-1"><a class="header-anchor" href="#遇到的问题和改进方案"><span>遇到的问题和改进方案</span></a></h2><h3 id="小车左右轮力矩不一致" tabindex="-1"><a class="header-anchor" href="#小车左右轮力矩不一致"><span>小车左右轮力矩不一致</span></a></h3><p>由于硬件限制，若设置两个轮的速度一致的话小车直行也会偏转， 而且小车并不能知道自己“偏航”了，故而采取手动测试的方式， 通过二分左右轮的速度来得到使得小车直行的左右轮速度。并且这个关系并非简单的倍速或差量的关系。</p><p>因此无奈之下只能选取一个固定的速度来测试（比如左轮设置为0.8, 然后不断二分得到直行时右轮的速度为 0.x ）, 整个系统都在该速度下运行。</p><div class="hint-container tip"><p class="hint-container-title">提示</p><p>各个小车有各个的体质， 因此挑选一辆&quot;正确&quot;的小车是很重要的事情。 以及测试完小车后保护小车也是很重要的，不要找不到了或者被人踢坏了， 否则得重新找车及测速。</p></div><h3 id="小车容易冲出轨道" tabindex="-1"><a class="header-anchor" href="#小车容易冲出轨道"><span>小车容易冲出轨道</span></a></h3><p>小车还未找到合适的“姿势”就前进，导致频繁冲出赛道，耗费时间。</p><p>基于此，采取速度渐进增长的形式，使得刚回到正确姿势时速度较慢，从而不会前进太多，便于更快的回到正确的姿势。</p><h3 id="小车总是左右左摆头太蠢了" tabindex="-1"><a class="header-anchor" href="#小车总是左右左摆头太蠢了"><span>小车总是左右左摆头太蠢了</span></a></h3><p>首先采取的改进方案是先左小幅度转弯，后右大幅度转弯，最后左大幅度转弯寻找正确姿势，但效果不理想，遂放弃。</p><p>考虑到小车路线是闭合的，且局部多为凸多边形， 故而每次转弯时优先考虑上一次转弯的方向， 这样子能减少摆头次数， 多数情况转弯的方向都是对的。（<s>有一些启发式的smell</s>）</p><h3 id="其它问题" tabindex="-1"><a class="header-anchor" href="#其它问题"><span>其它问题</span></a></h3><p><s>时间有点久搞忘了，记起来再补充</s></p><h2 id="设计方案参考" tabindex="-1"><a class="header-anchor" href="#设计方案参考"><span>设计方案参考</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/TP9DRiCW48Ntd09bbIwI0tXHHSgsNNQDHa08bGqM395o-mu_ZcsYBcnZtlERRmPV8aB0D8qC9Fh0Vw8ERAOjA-qC3latMCSXyiD4Y-F7OIT-UMEiCqMF6jCinhhJ6wyGYecUdU0T1ZyMKTQra12ET544opZyz5ae1Yv4XX3YF3yphdq0wYAnGac-1ZJmZcQrDmTRq4-lz6RcX76p9WMjcD9ltxrAKIj3lct3wNMlKvRJ4djF7iTQk9dszR9jpQgJATRTY3QnLM7BG1U2D2kI1HqpwZUCpXinW3NtZDjBe7vJn4ax5ChcdhUehVH_zBLBY4ydhJyRmBlk4iePNhHJz2F-0G00" alt=""><img src="https://www.plantuml.com/plantuml/svg/LP7FRiCW3CRlF0N7L6jUe9gcIjbVQQUgT-I0qp8vK1cp7RQz-w29ckM0i3y-sp-BVH9WoICfIv2Ixe3rjzBwpiOGq4gpgKc-E10qnIiuAGd5f0kYQmY7ETpfWIB8LhC_dTVQjSRvqY1OdBKg-M0uGd7rCL8Lpl299lR5Q0bd-LVDS8VOH-aO1hbX9c6eqoOgYbzchKZcO2hYlvINPt0VESc8GOppt9Ipqu-Uo-8-XgrscQ56jyrycghD2LFfLGWx88AUS5CnAzRzJzkkIPN2aCUbxvNy_UdvMAx3sylhiPQkTslRXyMlzXXS-Q8_" alt=""><h2 id="和机械臂联动" tabindex="-1"><a class="header-anchor" href="#和机械臂联动"><span>和机械臂联动</span></a></h2><p>emm... 本来想让机械臂识别“货物”并放在车上托运并最后卸货的，但是小车不好运货。遂放弃，转而实验机械臂放置障碍在赛道上。</p><h2 id="结语" tabindex="-1"><a class="header-anchor" href="#结语"><span>结语</span></a></h2><p>本次智能车实验不是很愉快， 特别是重调了3，4次速度（几次换车<s>其中一次车被踩烂了</s>）</p><p>如果没有熟悉的编程语言（例如c）且不了解 多线程/协程，网络I/O的话 还是采用VPL图形化吧 <s>不过我认为报用就是了</s>。</p><p>记得给我的仓库点Star欧~</p></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/projects/carrobot.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><!----><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
+  </body>
+</html>
diff --git a/projects/index.html b/projects/index.html
index c2ac005..2bc6c62 100644
--- a/projects/index.html
+++ b/projects/index.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/projects/"><meta property="og:site_name" content="blog"><meta property="og:title" content="项目"><meta property="og:description" content="项目 这里是你参与或开发的项目介绍和进展。"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:published_time" content="2024-10-18T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"项目","image":[""],"datePublished":"2024-10-18T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>项目 | blog</title><meta name="description" content="项目 这里是你参与或开发的项目介绍和进展。">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-BjDh3PHW.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-jwKIpsPi.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
-    <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->项目</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-18T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><!----></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="项目" tabindex="-1"><a class="header-anchor" href="#项目"><span>项目</span></a></h1><p>这里是你参与或开发的项目介绍和进展。</p><!----></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/projects/index.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><!----><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->项目</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-18T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><!----></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="项目" tabindex="-1"><a class="header-anchor" href="#项目"><span>项目</span></a></h1><p>这里是你参与或开发的项目介绍和进展。</p><!----><div class="vp-catalog-wrapper"><h2 class="vp-catalog-main-title">目录</h2><ul class="vp-catalogs"><li class="vp-catalog"><div class="vp-catalog-child-title"><a class="route-link vp-catalog-title" href="/projects/carrobot.html">北京邮电大学创新创业智能车循迹python版</a></div></li></ul></div></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/projects/index.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><!----><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/resources/compile/index.html b/resources/compile/index.html
new file mode 100644
index 0000000..73c2977
--- /dev/null
+++ b/resources/compile/index.html
@@ -0,0 +1,40 @@
+<!doctype html>
+<html lang="zh-CN" data-theme="light">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width,initial-scale=1" />
+    <meta name="generator" content="VuePress 2.0.0-rc.9" />
+    <meta name="theme" content="VuePress Theme Hope 2.0.0-rc.38" />
+    <style>
+      html {
+        background: var(--bg-color, #fff);
+      }
+
+      html[data-theme="dark"] {
+        background: var(--bg-color, #1d1e1f);
+      }
+
+      body {
+        background: var(--bg-color);
+      }
+    </style>
+    <script>
+      const userMode = localStorage.getItem("vuepress-theme-hope-scheme");
+      const systemDarkMode =
+        window.matchMedia &&
+        window.matchMedia("(prefers-color-scheme: dark)").matches;
+
+      if (userMode === "dark" || (userMode !== "light" && systemDarkMode)) {
+        document.documentElement.setAttribute("data-theme", "dark");
+      }
+    </script>
+    <meta property="og:url" content="https://github.com/King-sj/resources/compile/"><meta property="og:site_name" content="blog"><meta property="og:title" content="编译原理相关"><meta property="og:description" content="anltr.grammar bison/yacc flex"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:published_time" content="2024-11-06T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"编译原理相关","image":[""],"datePublished":"2024-11-06T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>编译原理相关 | blog</title><meta name="description" content="anltr.grammar bison/yacc flex">
+    <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-ybZqFA4D.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+  </head>
+  <body>
+    <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><span class="font-icon icon book" style=""></span><span class="vp-sidebar-title">资源</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Compile</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/resources/compile/" aria-label="编译原理相关"><!---->编译原理相关<!----></a></li></ul></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Html2md</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/resources/" aria-label="资源"><!---->资源<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->编译原理相关</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-11-06T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><!----></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><ul><li>anltr.grammar</li><li>bison/yacc</li><li>flex</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/resources/compile/index.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><!----><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
+  </body>
+</html>
diff --git a/resources/html2md/index.html b/resources/html2md/index.html
index 454ab7d..3e60bf0 100644
--- a/resources/html2md/index.html
+++ b/resources/html2md/index.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/resources/html2md/"><meta property="og:site_name" content="blog"><meta property="og:title" content="html 转 md 工具"><meta property="og:description" content="html 转 md 工具 https://github.com/mixmark-io/turndown https://github.com/aaronsw/html2text"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"html 转 md 工具","image":[""],"dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>html 转 md 工具 | blog</title><meta name="description" content="html 转 md 工具 https://github.com/mixmark-io/turndown https://github.com/aaronsw/html2text">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-CXhg3e64.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-BlsqD0oa.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
-    <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><span class="font-icon icon book" style=""></span><span class="vp-sidebar-title">资源</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Html2md</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/resources/html2md/" aria-label="html 转 md 工具"><!---->html 转 md 工具<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/resources/" aria-label="资源"><!---->资源<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->html 转 md 工具</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><!----></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="html-转-md-工具" tabindex="-1"><a class="header-anchor" href="#html-转-md-工具"><span>html 转 md 工具</span></a></h1><ul><li>https://github.com/mixmark-io/turndown</li><li>https://github.com/aaronsw/html2text</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/resources/html2md/index.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><!----><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><span class="font-icon icon book" style=""></span><span class="vp-sidebar-title">资源</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Compile</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Html2md</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/resources/html2md/" aria-label="html 转 md 工具"><!---->html 转 md 工具<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/resources/" aria-label="资源"><!---->资源<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->html 转 md 工具</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><!----></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="html-转-md-工具" tabindex="-1"><a class="header-anchor" href="#html-转-md-工具"><span>html 转 md 工具</span></a></h1><ul><li>https://github.com/mixmark-io/turndown</li><li>https://github.com/aaronsw/html2text</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/resources/html2md/index.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><!----><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/resources/index.html b/resources/index.html
index 8e1f318..4f217ba 100644
--- a/resources/index.html
+++ b/resources/index.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/resources/"><meta property="og:site_name" content="blog"><meta property="og:title" content="资源"><meta property="og:description" content="这里是推荐的书籍、网站、工具等资源。"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:published_time" content="2024-10-18T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"资源","image":[""],"datePublished":"2024-10-18T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>资源 | blog</title><meta name="description" content="这里是推荐的书籍、网站、工具等资源。">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-Dv6rE_pN.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-DtPJaw_H.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
-    <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><span class="font-icon icon book" style=""></span><span class="vp-sidebar-title">资源</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Html2md</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/resources/" aria-label="资源"><!---->资源<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->资源</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-18T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><!----></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="资源" tabindex="-1"><a class="header-anchor" href="#资源"><span>资源</span></a></h1><p>这里是推荐的书籍、网站、工具等资源。</p><!-- more --><ul><li><a href="https://github.com/" target="_blank" rel="noopener noreferrer">github - 世界上最大的代码托管平台<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="https://zh.z-lib.gs/" target="_blank" rel="noopener noreferrer">Z-Library – 世界上最大的电子图书馆。自由访问知识和文化。<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="https://v2.vuepress.vuejs.org/zh/" target="_blank" rel="noopener noreferrer">Vuepress - 我的博客构建库<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="https://plantuml.com/zh/" target="_blank" rel="noopener noreferrer">plantUML - 一个通用性很强的工具，可以快速、直接地创建各种图表<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="https://github.com/ikatyang/emoji-cheat-sheet" target="_blank" rel="noopener noreferrer">emoji-cheat-sheet - A markdown version emoji cheat sheet<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="https://www.sci-hub.st/" target="_blank" rel="noopener noreferrer">Sci-hub —— 当今科学界最具争议性的项目。Sci-hub的目标是 免费并且不受限制地 提供所有科学知识。<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="https://libgen.mx/" target="_blank" rel="noopener noreferrer">Lib.Genesis —— Part of Library Genesis. ex libgen.io, libgen.org<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li></ul><!----></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/resources/index.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><!----><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><span class="font-icon icon book" style=""></span><span class="vp-sidebar-title">资源</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Compile</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Html2md</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/resources/" aria-label="资源"><!---->资源<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->资源</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-18T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><!----></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="资源" tabindex="-1"><a class="header-anchor" href="#资源"><span>资源</span></a></h1><p>这里是推荐的书籍、网站、工具等资源。</p><!-- more --><ul><li><a href="https://github.com/" target="_blank" rel="noopener noreferrer">github - 世界上最大的代码托管平台<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="https://zh.z-lib.gs/" target="_blank" rel="noopener noreferrer">Z-Library – 世界上最大的电子图书馆。自由访问知识和文化。<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="https://v2.vuepress.vuejs.org/zh/" target="_blank" rel="noopener noreferrer">Vuepress - 我的博客构建库<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="https://plantuml.com/zh/" target="_blank" rel="noopener noreferrer">plantUML - 一个通用性很强的工具，可以快速、直接地创建各种图表<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="https://github.com/ikatyang/emoji-cheat-sheet" target="_blank" rel="noopener noreferrer">emoji-cheat-sheet - A markdown version emoji cheat sheet<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="https://www.sci-hub.st/" target="_blank" rel="noopener noreferrer">Sci-hub —— 当今科学界最具争议性的项目。Sci-hub的目标是 免费并且不受限制地 提供所有科学知识。<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="https://libgen.mx/" target="_blank" rel="noopener noreferrer">Lib.Genesis —— Part of Library Genesis. ex libgen.io, libgen.org<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li></ul><!----></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/resources/index.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><!----><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/search-pro.worker.js b/search-pro.worker.js
index d3e68d5..e79a1b4 100644
--- a/search-pro.worker.js
+++ b/search-pro.worker.js
@@ -1,2 +1,2 @@
-const V=Object.entries,et=Object.fromEntries,st="ENTRIES",L="KEYS",T="VALUES",_="";class D{set;_type;_path;constructor(t,s){const n=t._tree,o=Array.from(n.keys());this.set=t,this._type=s,this._path=o.length>0?[{node:n,keys:o}]:[]}next(){const t=this.dive();return this.backtrack(),t}dive(){if(this._path.length===0)return{done:!0,value:void 0};const{node:t,keys:s}=E(this._path);if(E(s)===_)return{done:!1,value:this.result()};const n=t.get(E(s));return this._path.push({node:n,keys:Array.from(n.keys())}),this.dive()}backtrack(){if(this._path.length===0)return;const t=E(this._path).keys;t.pop(),!(t.length>0)&&(this._path.pop(),this.backtrack())}key(){return this.set._prefix+this._path.map(({keys:t})=>E(t)).filter(t=>t!==_).join("")}value(){return E(this._path).node.get(_)}result(){switch(this._type){case T:return this.value();case L:return this.key();default:return[this.key(),this.value()]}}[Symbol.iterator](){return this}}const E=e=>e[e.length-1],nt=(e,t,s)=>{const n=new Map;if(t===void 0)return n;const o=t.length+1,u=o+s,i=new Uint8Array(u*o).fill(s+1);for(let r=0;r<o;++r)i[r]=r;for(let r=1;r<u;++r)i[r*o]=r;return R(e,t,s,n,i,1,o,""),n},R=(e,t,s,n,o,u,i,r)=>{const d=u*i;t:for(const c of e.keys())if(c===_){const a=o[d-1];a<=s&&n.set(r,[e.get(c),a])}else{let a=u;for(let h=0;h<c.length;++h,++a){const g=c[h],m=i*a,p=m-i;let l=o[m];const f=Math.max(0,a-s-1),y=Math.min(i-1,a+s);for(let F=f;F<y;++F){const v=g!==t[F],z=o[p+F]+ +v,A=o[p+F+1]+1,w=o[m+F]+1,j=o[m+F+1]=Math.min(z,A,w);j<l&&(l=j)}if(l>s)continue t}R(e.get(c),t,s,n,o,a,i,r+c)}};class C{_tree;_prefix;_size=void 0;constructor(t=new Map,s=""){this._tree=t,this._prefix=s}atPrefix(t){if(!t.startsWith(this._prefix))throw new Error("Mismatched prefix");const[s,n]=x(this._tree,t.slice(this._prefix.length));if(s===void 0){const[o,u]=O(n);for(const i of o.keys())if(i!==_&&i.startsWith(u)){const r=new Map;return r.set(i.slice(u.length),o.get(i)),new C(r,t)}}return new C(s,t)}clear(){this._size=void 0,this._tree.clear()}delete(t){return this._size=void 0,ot(this._tree,t)}entries(){return new D(this,st)}forEach(t){for(const[s,n]of this)t(s,n,this)}fuzzyGet(t,s){return nt(this._tree,t,s)}get(t){const s=k(this._tree,t);return s!==void 0?s.get(_):void 0}has(t){const s=k(this._tree,t);return s!==void 0&&s.has(_)}keys(){return new D(this,L)}set(t,s){if(typeof t!="string")throw new Error("key must be a string");return this._size=void 0,I(this._tree,t).set(_,s),this}get size(){if(this._size)return this._size;this._size=0;const t=this.entries();for(;!t.next().done;)this._size+=1;return this._size}update(t,s){if(typeof t!="string")throw new Error("key must be a string");this._size=void 0;const n=I(this._tree,t);return n.set(_,s(n.get(_))),this}fetch(t,s){if(typeof t!="string")throw new Error("key must be a string");this._size=void 0;const n=I(this._tree,t);let o=n.get(_);return o===void 0&&n.set(_,o=s()),o}values(){return new D(this,T)}[Symbol.iterator](){return this.entries()}static from(t){const s=new C;for(const[n,o]of t)s.set(n,o);return s}static fromObject(t){return C.from(Object.entries(t))}}const x=(e,t,s=[])=>{if(t.length===0||e==null)return[e,s];for(const n of e.keys())if(n!==_&&t.startsWith(n))return s.push([e,n]),x(e.get(n),t.slice(n.length),s);return s.push([e,t]),x(void 0,"",s)},k=(e,t)=>{if(t.length===0||e==null)return e;for(const s of e.keys())if(s!==_&&t.startsWith(s))return k(e.get(s),t.slice(s.length))},I=(e,t)=>{const s=t.length;t:for(let n=0;e&&n<s;){for(const u of e.keys())if(u!==_&&t[n]===u[0]){const i=Math.min(s-n,u.length);let r=1;for(;r<i&&t[n+r]===u[r];)++r;const d=e.get(u);if(r===u.length)e=d;else{const c=new Map;c.set(u.slice(r),d),e.set(t.slice(n,n+r),c),e.delete(u),e=c}n+=r;continue t}const o=new Map;return e.set(t.slice(n),o),o}return e},ot=(e,t)=>{const[s,n]=x(e,t);if(s!==void 0){if(s.delete(_),s.size===0)W(n);else if(s.size===1){const[o,u]=s.entries().next().value;q(n,o,u)}}},W=e=>{if(e.length===0)return;const[t,s]=O(e);if(t.delete(s),t.size===0)W(e.slice(0,-1));else if(t.size===1){const[n,o]=t.entries().next().value;n!==_&&q(e.slice(0,-1),n,o)}},q=(e,t,s)=>{if(e.length===0)return;const[n,o]=O(e);n.set(o+t,s),n.delete(o)},O=e=>e[e.length-1],ut=(e,t)=>{const s=e._idToShortId.get(t);if(s!=null)return e._storedFields.get(s)},it=/[\n\r -#%-*,-/:;?@[-\]_{}\u00A0\u00A1\u00A7\u00AB\u00B6\u00B7\u00BB\u00BF\u037E\u0387\u055A-\u055F\u0589\u058A\u05BE\u05C0\u05C3\u05C6\u05F3\u05F4\u0609\u060A\u060C\u060D\u061B\u061E\u061F\u066A-\u066D\u06D4\u0700-\u070D\u07F7-\u07F9\u0830-\u083E\u085E\u0964\u0965\u0970\u09FD\u0A76\u0AF0\u0C77\u0C84\u0DF4\u0E4F\u0E5A\u0E5B\u0F04-\u0F12\u0F14\u0F3A-\u0F3D\u0F85\u0FD0-\u0FD4\u0FD9\u0FDA\u104A-\u104F\u10FB\u1360-\u1368\u1400\u166E\u1680\u169B\u169C\u16EB-\u16ED\u1735\u1736\u17D4-\u17D6\u17D8-\u17DA\u1800-\u180A\u1944\u1945\u1A1E\u1A1F\u1AA0-\u1AA6\u1AA8-\u1AAD\u1B5A-\u1B60\u1BFC-\u1BFF\u1C3B-\u1C3F\u1C7E\u1C7F\u1CC0-\u1CC7\u1CD3\u2000-\u200A\u2010-\u2029\u202F-\u2043\u2045-\u2051\u2053-\u205F\u207D\u207E\u208D\u208E\u2308-\u230B\u2329\u232A\u2768-\u2775\u27C5\u27C6\u27E6-\u27EF\u2983-\u2998\u29D8-\u29DB\u29FC\u29FD\u2CF9-\u2CFC\u2CFE\u2CFF\u2D70\u2E00-\u2E2E\u2E30-\u2E4F\u3000-\u3003\u3008-\u3011\u3014-\u301F\u3030\u303D\u30A0\u30FB\uA4FE\uA4FF\uA60D-\uA60F\uA673\uA67E\uA6F2-\uA6F7\uA874-\uA877\uA8CE\uA8CF\uA8F8-\uA8FA\uA8FC\uA92E\uA92F\uA95F\uA9C1-\uA9CD\uA9DE\uA9DF\uAA5C-\uAA5F\uAADE\uAADF\uAAF0\uAAF1\uABEB\uFD3E\uFD3F\uFE10-\uFE19\uFE30-\uFE52\uFE54-\uFE61\uFE63\uFE68\uFE6A\uFE6B\uFF01-\uFF03\uFF05-\uFF0A\uFF0C-\uFF0F\uFF1A\uFF1B\uFF1F\uFF20\uFF3B-\uFF3D\uFF3F\uFF5B\uFF5D\uFF5F-\uFF65]+/u,M="or",$="and",rt="and_not",ct=(e,t)=>{e.includes(t)||e.push(t)},N=(e,t)=>{for(const s of t)e.includes(s)||e.push(s)},P=({score:e},{score:t})=>t-e,lt=()=>new Map,b=e=>{const t=new Map;for(const s of Object.keys(e))t.set(parseInt(s,10),e[s]);return t},G=(e,t)=>Object.prototype.hasOwnProperty.call(e,t)?e[t]:void 0,ht={[M]:(e,t)=>{for(const s of t.keys()){const n=e.get(s);if(n==null)e.set(s,t.get(s));else{const{score:o,terms:u,match:i}=t.get(s);n.score=n.score+o,n.match=Object.assign(n.match,i),N(n.terms,u)}}return e},[$]:(e,t)=>{const s=new Map;for(const n of t.keys()){const o=e.get(n);if(o==null)continue;const{score:u,terms:i,match:r}=t.get(n);N(o.terms,i),s.set(n,{score:o.score+u,terms:o.terms,match:Object.assign(o.match,r)})}return s},[rt]:(e,t)=>{for(const s of t.keys())e.delete(s);return e}},dt=(e,t,s,n,o,u)=>{const{k:i,b:r,d}=u;return Math.log(1+(s-t+.5)/(t+.5))*(d+e*(i+1)/(e+i*(1-r+r*n/o)))},at=e=>(t,s,n)=>{const o=typeof e.fuzzy=="function"?e.fuzzy(t,s,n):e.fuzzy||!1,u=typeof e.prefix=="function"?e.prefix(t,s,n):e.prefix===!0;return{term:t,fuzzy:o,prefix:u}},H=(e,t,s,n)=>{for(const o of Object.keys(e._fieldIds))if(e._fieldIds[o]===s){e._options.logger("warn",`SlimSearch: document with ID ${e._documentIds.get(t)} has changed before removal: term "${n}" was not present in field "${o}". Removing a document after it has changed can corrupt the index!`,"version_conflict");return}},ft=(e,t,s,n)=>{if(!e._index.has(n)){H(e,s,t,n);return}const o=e._index.fetch(n,lt),u=o.get(t);u==null||u.get(s)==null?H(e,s,t,n):u.get(s)<=1?u.size<=1?o.delete(t):u.delete(s):u.set(s,u.get(s)-1),e._index.get(n).size===0&&e._index.delete(n)},gt={k:1.2,b:.7,d:.5},mt={idField:"id",extractField:(e,t)=>e[t],tokenize:e=>e.split(it),processTerm:e=>e.toLowerCase(),fields:void 0,searchOptions:void 0,storeFields:[],logger:(e,t)=>{typeof console?.[e]=="function"&&console[e](t)},autoVacuum:!0},J={combineWith:M,prefix:!1,fuzzy:!1,maxFuzzy:6,boost:{},weights:{fuzzy:.45,prefix:.375},bm25:gt},pt={combineWith:$,prefix:(e,t,s)=>t===s.length-1},Ft={batchSize:1e3,batchWait:10},U={minDirtFactor:.1,minDirtCount:20},_t={...Ft,...U},K=Symbol("*"),yt=(e,t)=>{const s=new Map,n={...e._options.searchOptions,...t};for(const[o,u]of e._documentIds){const i=n.boostDocument?n.boostDocument(u,"",e._storedFields.get(o)):1;s.set(o,{score:i,terms:[],match:{}})}return s},X=(e,t=M)=>{if(e.length===0)return new Map;const s=t.toLowerCase(),n=ht[s];if(!n)throw new Error(`Invalid combination operator: ${t}`);return e.reduce(n)||new Map},S=(e,t,s,n,o,u,i,r,d=new Map)=>{if(o==null)return d;for(const c of Object.keys(u)){const a=u[c],h=e._fieldIds[c],g=o.get(h);if(g==null)continue;let m=g.size;const p=e._avgFieldLength[h];for(const l of g.keys()){if(!e._documentIds.has(l)){ft(e,h,l,s),m-=1;continue}const f=i?i(e._documentIds.get(l),s,e._storedFields.get(l)):1;if(!f)continue;const y=g.get(l),F=e._fieldLength.get(l)[h],v=dt(y,m,e._documentCount,F,p,r),z=n*a*f*v,A=d.get(l);if(A){A.score+=z,ct(A.terms,t);const w=G(A.match,s);w?w.push(c):A.match[s]=[c]}else d.set(l,{score:z,terms:[t],match:{[s]:[c]}})}}return d},At=(e,t,s)=>{const n={...e._options.searchOptions,...s},o=(n.fields||e._options.fields).reduce((l,f)=>({...l,[f]:G(n.boost,f)||1}),{}),{boostDocument:u,weights:i,maxFuzzy:r,bm25:d}=n,{fuzzy:c,prefix:a}={...J.weights,...i},h=e._index.get(t.term),g=S(e,t.term,t.term,1,h,o,u,d);let m,p;if(t.prefix&&(m=e._index.atPrefix(t.term)),t.fuzzy){const l=t.fuzzy===!0?.2:t.fuzzy,f=l<1?Math.min(r,Math.round(t.term.length*l)):l;f&&(p=e._index.fuzzyGet(t.term,f))}if(m)for(const[l,f]of m){const y=l.length-t.term.length;if(!y)continue;p?.delete(l);const F=a*l.length/(l.length+.3*y);S(e,t.term,l,F,f,o,u,d,g)}if(p)for(const l of p.keys()){const[f,y]=p.get(l);if(!y)continue;const F=c*l.length/(l.length+y);S(e,t.term,l,F,f,o,u,d,g)}return g},Y=(e,t,s={})=>{if(t===K)return yt(e,s);if(typeof t!="string"){const a={...s,...t,queries:void 0},h=t.queries.map(g=>Y(e,g,a));return X(h,a.combineWith)}const{tokenize:n,processTerm:o,searchOptions:u}=e._options,i={tokenize:n,processTerm:o,...u,...s},{tokenize:r,processTerm:d}=i,c=r(t).flatMap(a=>d(a)).filter(a=>!!a).map(at(i)).map(a=>At(e,a,i));return X(c,i.combineWith)},Q=(e,t,s={})=>{const n=Y(e,t,s),o=[];for(const[u,{score:i,terms:r,match:d}]of n){const c=r.length||1,a={id:e._documentIds.get(u),score:i*c,terms:Object.keys(d),queryTerms:r,match:d};Object.assign(a,e._storedFields.get(u)),(s.filter==null||s.filter(a))&&o.push(a)}return t===K&&s.boostDocument==null&&e._options.searchOptions.boostDocument==null||o.sort(P),o},Ct=(e,t,s={})=>{s={...e._options.autoSuggestOptions,...s};const n=new Map;for(const{score:u,terms:i}of Q(e,t,s)){const r=i.join(" "),d=n.get(r);d!=null?(d.score+=u,d.count+=1):n.set(r,{score:u,terms:i,count:1})}const o=[];for(const[u,{score:i,terms:r,count:d}]of n)o.push({suggestion:u,terms:r,score:i/d});return o.sort(P),o};class Et{_options;_index;_documentCount;_documentIds;_idToShortId;_fieldIds;_fieldLength;_avgFieldLength;_nextId;_storedFields;_dirtCount;_currentVacuum;_enqueuedVacuum;_enqueuedVacuumConditions;constructor(t){if(t?.fields==null)throw new Error('SlimSearch: option "fields" must be provided');const s=t.autoVacuum==null||t.autoVacuum===!0?_t:t.autoVacuum;this._options={...mt,...t,autoVacuum:s,searchOptions:{...J,...t.searchOptions||{}},autoSuggestOptions:{...pt,...t.autoSuggestOptions||{}}},this._index=new C,this._documentCount=0,this._documentIds=new Map,this._idToShortId=new Map,this._fieldIds={},this._fieldLength=new Map,this._avgFieldLength=[],this._nextId=0,this._storedFields=new Map,this._dirtCount=0,this._currentVacuum=null,this._enqueuedVacuum=null,this._enqueuedVacuumConditions=U,this.addFields(this._options.fields)}get isVacuuming(){return this._currentVacuum!=null}get dirtCount(){return this._dirtCount}get dirtFactor(){return this._dirtCount/(1+this._documentCount+this._dirtCount)}get documentCount(){return this._documentCount}get termCount(){return this._index.size}toJSON(){const t=[];for(const[s,n]of this._index){const o={};for(const[u,i]of n)o[u]=Object.fromEntries(i);t.push([s,o])}return{documentCount:this._documentCount,nextId:this._nextId,documentIds:Object.fromEntries(this._documentIds),fieldIds:this._fieldIds,fieldLength:Object.fromEntries(this._fieldLength),averageFieldLength:this._avgFieldLength,storedFields:Object.fromEntries(this._storedFields),dirtCount:this._dirtCount,index:t,serializationVersion:2}}addFields(t){for(let s=0;s<t.length;s++)this._fieldIds[t[s]]=s}}const zt=({index:e,documentCount:t,nextId:s,documentIds:n,fieldIds:o,fieldLength:u,averageFieldLength:i,storedFields:r,dirtCount:d,serializationVersion:c},a)=>{if(c!==1&&c!==2)throw new Error("SlimSearch: cannot deserialize an index created with an incompatible version");const h=new Et(a);h._documentCount=t,h._nextId=s,h._documentIds=b(n),h._idToShortId=new Map,h._fieldIds=o,h._fieldLength=b(u),h._avgFieldLength=i,h._storedFields=b(r),h._dirtCount=d||0,h._index=new C;for(const[g,m]of h._documentIds)h._idToShortId.set(m,g);for(const[g,m]of e){const p=new Map;for(const l of Object.keys(m)){let f=m[l];c===1&&(f=f.ds),p.set(parseInt(l,10),b(f))}h._index.set(g,p)}return h},B=(e,t)=>{const s=e.toLowerCase(),n=t.toLowerCase(),o=[];let u=0,i=0;const r=(c,a=!1)=>{let h="";i===0?h=c.length>20?`… ${c.slice(-20)}`:c:a?h=c.length+i>100?`${c.slice(0,100-i)}… `:c:h=c.length>20?`${c.slice(0,20)} … ${c.slice(-20)}`:c,h&&o.push(h),i+=h.length,a||(o.push(["mark",t]),i+=t.length,i>=100&&o.push(" …"))};let d=s.indexOf(n,u);if(d===-1)return null;for(;d>=0;){const c=d+n.length;if(r(e.slice(u,d)),u=c,i>100)break;d=s.indexOf(n,u)}return i<100&&r(e.slice(u),!0),o},wt=(e,t)=>t.contents.reduce((s,[,n])=>s+n,0)-e.contents.reduce((s,[,n])=>s+n,0),xt=(e,t)=>Math.max(...t.contents.map(([,s])=>s))-Math.max(...e.contents.map(([,s])=>s)),Z=(e,t,s={})=>{const n={};return Q(t,e,{boost:{h:2,t:1,c:4},prefix:!0,...s}).forEach(o=>{const{id:u,terms:i,score:r}=o,d=u.includes("@"),c=u.includes("#"),[a,h]=u.split(/[#@]/),g=Number(a),m=i.sort((l,f)=>l.length-f.length).filter((l,f)=>i.slice(f+1).every(y=>!y.includes(l))),{contents:p}=n[g]??={title:"",contents:[]};if(d)p.push([{type:"customField",id:g,index:h,display:m.map(l=>o.c.map(f=>B(f,l))).flat().filter(l=>l!==null)},r]);else{const l=m.map(f=>B(o.h,f)).filter(f=>f!==null);if(l.length&&p.push([{type:c?"heading":"title",id:g,...c&&{anchor:h},display:l},r]),"t"in o)for(const f of o.t){const y=m.map(F=>B(f,F)).filter(F=>F!==null);y.length&&p.push([{type:"text",id:g,...c&&{anchor:h},display:y},r])}}}),V(n).sort(([,o],[,u])=>"max"==="total"?wt(o,u):xt(o,u)).map(([o,{title:u,contents:i}])=>{if(!u){const r=ut(t,o);r&&(u=r.h)}return{title:u,contents:i.map(([r])=>r)}})},tt=(e,t,s={})=>{const n=Ct(t,e,{fuzzy:.2,maxFuzzy:3,...s}).map(({suggestion:o})=>o);return e.includes(" ")?n:n.filter(o=>!o.includes(" "))},bt=et(V(JSON.parse("{\"/\":{\"documentCount\":515,\"nextId\":515,\"documentIds\":{\"0\":\"0\",\"1\":\"1\",\"2\":\"2\",\"3\":\"3\",\"4\":\"4\",\"5\":\"5\",\"6\":\"6\",\"7\":\"6#some-solutions-to-questions-about-qt\",\"8\":\"6#the-qt-5-isn-t-in-qt-maintenance-tools\",\"9\":\"7\",\"10\":\"8\",\"11\":\"8@0\",\"12\":\"8@1\",\"13\":\"9\",\"14\":\"9#环境\",\"15\":\"9#项目结构\",\"16\":\"9#配置http服务\",\"17\":\"9#配置nginx\",\"18\":\"9#配置docker\",\"19\":\"9#启动项目\",\"20\":\"9#升级为https\",\"21\":\"9#申请证书\",\"22\":\"9#安装证书\",\"23\":\"9#修改配置\",\"24\":\"9#重启container\",\"25\":\"9#配置nginx反向代理-使flask支持-https\",\"26\":\"9#参考资料\",\"27\":\"9@0\",\"28\":\"9@1\",\"29\":\"10\",\"30\":\"10#github-container-registry-加速\",\"31\":\"10#ghcr-io简介\",\"32\":\"10#镜像地址\",\"33\":\"10#配置方法\",\"34\":\"10#docker-wsl2-容器目录\",\"35\":\"11\",\"36\":\"12\",\"37\":\"13\",\"38\":\"14\",\"39\":\"14#使用python-发送示例\",\"40\":\"15\",\"41\":\"15#背景介绍\",\"42\":\"15#过去的做法\",\"43\":\"15#第一种-直接取模\",\"44\":\"15#第二种-函数取模\",\"45\":\"15#泛型编程\",\"46\":\"15@0\",\"47\":\"15@1\",\"48\":\"16\",\"49\":\"16@0\",\"50\":\"16@1\",\"51\":\"17\",\"52\":\"18\",\"53\":\"19\",\"54\":\"20\",\"55\":\"21\",\"56\":\"21#自然数的定义\",\"57\":\"21#自然数的加法运算\",\"58\":\"21#加法的定义\",\"59\":\"21#加法结果的存在性\",\"60\":\"21#加法结果的唯一性\",\"61\":\"21#加法的性质\",\"62\":\"21#加法交换律\",\"63\":\"21#加法结合律\",\"64\":\"21#加法消去律\",\"65\":\"21#自然数的序\",\"66\":\"21#序的定义\",\"67\":\"21#正自然数\",\"68\":\"21#正自然数的性质\",\"69\":\"21#序的反对称性\",\"70\":\"21#序的传递性\",\"71\":\"21#序的完全性\",\"72\":\"21#加法保序性\",\"73\":\"21#自然数的乘法运算\",\"74\":\"21#乘法的定义\",\"75\":\"21#乘法结果的存在性\",\"76\":\"21#乘法结果的唯一性\",\"77\":\"21#乘法的性质\",\"78\":\"21#乘法交换律\",\"79\":\"21#乘法分配律\",\"80\":\"21#乘法结合律\",\"81\":\"21#乘法消去律\",\"82\":\"21#peano-公理的合理性\",\"83\":\"21#乘法保序性\",\"84\":\"21#乘法消去保序性\",\"85\":\"21#用图论阐述-peano-系统\",\"86\":\"21#peano-公理-i\",\"87\":\"21#peano-公理-ii\",\"88\":\"21#peano-公理-iii\",\"89\":\"21#peano-公理-iv\",\"90\":\"21#peano-公理-v\",\"91\":\"21@0\",\"92\":\"21@1\",\"93\":\"22\",\"94\":\"22#安装\",\"95\":\"22#tips\",\"96\":\"22#bug-记录\",\"97\":\"22@1\",\"98\":\"23\",\"99\":\"23#线程安全\",\"100\":\"23#协程\",\"101\":\"23#协程安全\",\"102\":\"23#协程是否需要加锁\",\"103\":\"24\",\"104\":\"25\",\"105\":\"25#缺点\",\"106\":\"25#缺点-1\",\"107\":\"26\",\"108\":\"26@0\",\"109\":\"26@1\",\"110\":\"27\",\"111\":\"28\",\"112\":\"29\",\"113\":\"30\",\"114\":\"30#关系\",\"115\":\"30#开闭原则\",\"116\":\"30#实现方法\",\"117\":\"30#里氏代换原则\",\"118\":\"30#里氏代换原则-1\",\"119\":\"30#实现方法-1\",\"120\":\"30#示例\",\"121\":\"30#迪米特原则\",\"122\":\"30#迪米特原则-1\",\"123\":\"30#实现方法-2\",\"124\":\"30#单一职责原则\",\"125\":\"30#实现方法-3\",\"126\":\"30#示例-1\",\"127\":\"30#接口隔离原则\",\"128\":\"30#依赖倒置原则\",\"129\":\"30#实现方法-4\",\"130\":\"30#示例-2\",\"131\":\"30#组合-聚合复用原则\",\"132\":\"30#实现方法-5\",\"133\":\"30#示例-3\",\"134\":\"30#总结\",\"135\":\"30@0\",\"136\":\"30@1\",\"137\":\"31\",\"138\":\"31#为什么要使用抽象工厂模式\",\"139\":\"31#示例代码\",\"140\":\"31#增加其它工厂\",\"141\":\"31#拓展思路的要点\",\"142\":\"31#易于增加具体工厂\",\"143\":\"31#难以增加新的零件\",\"144\":\"31#相关的设计模式\",\"145\":\"31@0\",\"146\":\"31@1\",\"147\":\"32\",\"148\":\"32#适配器模式\",\"149\":\"32#为什么要用适配器模式\",\"150\":\"32#类比\",\"151\":\"32#类比-1\",\"152\":\"32#示例程序\",\"153\":\"32#运行结果\",\"154\":\"32#相关的设计模式\",\"155\":\"32@0\",\"156\":\"32@1\",\"157\":\"33\",\"158\":\"33#使用此设计模式的理由\",\"159\":\"33#类的层次结构的两个作用\",\"160\":\"33#增加新功能时\",\"161\":\"33#增加新的实现时\",\"162\":\"33#类的层次结构的混杂和分离\",\"163\":\"33#示例代码\",\"164\":\"33#类的一览表\",\"165\":\"33#countdisplay-ts\",\"166\":\"33#display-ts\",\"167\":\"33#displayimpl-ts\",\"168\":\"33#main-ts\",\"169\":\"33#stringdisplayimpl-ts\",\"170\":\"33#运行结果\",\"171\":\"33#拓展思路的要点\",\"172\":\"33#分开后更容易扩展\",\"173\":\"33#继承是强关联-委托是弱关联\",\"174\":\"33#相关的设计模式\",\"175\":\"33@0\",\"176\":\"33@1\",\"177\":\"34\",\"178\":\"34#为什么要使用-builder-模式\",\"179\":\"34#代码示例\",\"180\":\"34#运行结果\",\"181\":\"34#相关设计模式\",\"182\":\"34#拓展思路的要点\",\"183\":\"34#谁知道什么\",\"184\":\"34#设计时能够决定的事情和不能决定的事情\",\"185\":\"34#代码的阅读方法和修改方法\",\"186\":\"34@0\",\"187\":\"34@1\",\"188\":\"35\",\"189\":\"35#为什么使用此类\",\"190\":\"35#示例代码\",\"191\":\"35#运行结果\",\"192\":\"35#相关的设计模式\",\"193\":\"35@0\",\"194\":\"35@1\",\"195\":\"36\",\"196\":\"36#为什么使用此模式\",\"197\":\"36#示例代码\",\"198\":\"36#运行结果\",\"199\":\"36#拓展思路的要点\",\"200\":\"36#命令中应该包含哪些信息\",\"201\":\"36#保存历史记录\",\"202\":\"36#相关的设计模式\",\"203\":\"36@0\",\"204\":\"36@1\",\"205\":\"37\",\"206\":\"37#使用此设计模式的理由\",\"207\":\"37#示例代码\",\"208\":\"37#目录类-directory-ts\",\"209\":\"37#抽象条目类-entry-ts\",\"210\":\"37#文件类-file-ts\",\"211\":\"37#主程序-main-ts\",\"212\":\"37#运行结果\",\"213\":\"37#相关的设计模式\",\"214\":\"37@0\",\"215\":\"37@1\",\"216\":\"38\",\"217\":\"38#为什么使用装饰器模式\",\"218\":\"38#代码示例\",\"219\":\"38#运行结果\",\"220\":\"38#拓展思路的要点\",\"221\":\"38#api-的透明性\",\"222\":\"38#在不改变被装饰物的前提下增加功能\",\"223\":\"38#可以动态地增加功能\",\"224\":\"38#只需要一些装饰物即可添加许多功能\",\"225\":\"38#导致增加许多很小的类\",\"226\":\"38#相关的设计模式\",\"227\":\"38#继承和委托中的一致性\",\"228\":\"38#父类和子类的一致性\",\"229\":\"38#自己和被委托对象的一致性\",\"230\":\"38@0\",\"231\":\"38@1\",\"232\":\"39\",\"233\":\"39@0\",\"234\":\"39@1\",\"235\":\"40\",\"236\":\"40#示例代码\",\"237\":\"40#代码实现\",\"238\":\"40#运行结果\",\"239\":\"40#相关设计模式\",\"240\":\"40@0\",\"241\":\"40@1\",\"242\":\"41\",\"243\":\"41#为什么要使用-factory-method\",\"244\":\"41#示例代码\",\"245\":\"41#运行结果\",\"246\":\"41@0\",\"247\":\"41@1\",\"248\":\"42\",\"249\":\"42#为什么使用-flyweight-模式\",\"250\":\"42#实例代码\",\"251\":\"42#运行结果\",\"252\":\"42#拓展思路的要点\",\"253\":\"42#对多个地方产生影响\",\"254\":\"42#intrinsic-与-extrinsic\",\"255\":\"42#不要让被共享的实例被垃圾回收器回收了\",\"256\":\"42#内存之外的其它资源\",\"257\":\"42#相关的设计模式\",\"258\":\"42@0\",\"259\":\"42@1\",\"260\":\"43\",\"261\":\"43@0\",\"262\":\"43@1\",\"263\":\"44\",\"264\":\"44#为什么使用此模式\",\"265\":\"44#示例代码\",\"266\":\"44#运行结果\",\"267\":\"44@0\",\"268\":\"44@1\",\"269\":\"45\",\"270\":\"45#为什么要使用迭代器模式\",\"271\":\"45#typescript-实现迭代器模式\",\"272\":\"45#代码示例\",\"273\":\"45#运行结果\",\"274\":\"45#多个迭代器\",\"275\":\"45#相关的设计模式\",\"276\":\"45@0\",\"277\":\"45@1\",\"278\":\"46\",\"279\":\"46#为什么使用此类\",\"280\":\"46#示例代码\",\"281\":\"46#运行结果\",\"282\":\"46#拓展思路的要点\",\"283\":\"46#当发生分散灾难时\",\"284\":\"46#通信线路的增加\",\"285\":\"46#哪些角色可以复用\",\"286\":\"46#相关的设计模式\",\"287\":\"46@0\",\"288\":\"46@1\",\"289\":\"47\",\"290\":\"47#为什么使用-memento-模式\",\"291\":\"47#示例代码\",\"292\":\"47#运行结果\",\"293\":\"47#拓展思路的要点\",\"294\":\"47#两种接口和可见性\",\"295\":\"47#需要多少个-memento\",\"296\":\"47#memento-的有效期限是多久\",\"297\":\"47#划分-caretaker-和-originator-角色的意义\",\"298\":\"47#相关的设计模式\",\"299\":\"47@0\",\"300\":\"47@1\",\"301\":\"48\",\"302\":\"48#为什么使用观察者模式\",\"303\":\"48#示例代码\",\"304\":\"48#运行结果\",\"305\":\"48#拓展思路的要点\",\"306\":\"48#这里也出现了可替换性\",\"307\":\"48#observer-的顺序\",\"308\":\"48#当-observer-的行为会对被观察对象产生影响时\",\"309\":\"48#传递更新信息的方式\",\"310\":\"48#从观察变为通知\",\"311\":\"48#mvc-model-view-controller\",\"312\":\"48#相关的设计模式\",\"313\":\"48@0\",\"314\":\"48@1\",\"315\":\"49\",\"316\":\"49#为什么要使用-prototype-模式\",\"317\":\"49#示例代码\",\"318\":\"49#运行结果\",\"319\":\"49#相关设计模式\",\"320\":\"49@0\",\"321\":\"49@1\",\"322\":\"50\",\"323\":\"50#为什么使用代理模式\",\"324\":\"50#实例代码\",\"325\":\"50#运行结果\",\"326\":\"50#拓展思路的要点\",\"327\":\"50#使用代理人来提升处理速度\",\"328\":\"50#有必要划分代理人和本人吗\",\"329\":\"50#代理与委托\",\"330\":\"50#透明性\",\"331\":\"50#http-代理\",\"332\":\"50#各种-proxy-模式\",\"333\":\"50#相关的设计模式\",\"334\":\"50@0\",\"335\":\"50@1\",\"336\":\"51\",\"337\":\"51#为什么要使用-singleton-模式\",\"338\":\"51#总结\",\"339\":\"51#示例代码\",\"340\":\"51#运行结果\",\"341\":\"51#相关设计模式\",\"342\":\"51#多线程下\",\"343\":\"51#双重检查锁定示例代码\",\"344\":\"51@0\",\"345\":\"51@1\",\"346\":\"52\",\"347\":\"52#为什么使用-state-模式\",\"348\":\"52#示例代码\",\"349\":\"52#运行结果\",\"350\":\"52#拓展思路的要点\",\"351\":\"52#分而治之\",\"352\":\"52#依赖于状态的处理\",\"353\":\"52#应当是谁来管理状态的迁移\",\"354\":\"52#不会自相矛盾\",\"355\":\"52#易于增加新的状态\",\"356\":\"52#实例的多面性\",\"357\":\"52#相关的设计模式\",\"358\":\"52@0\",\"359\":\"52@1\",\"360\":\"53\",\"361\":\"53#使用此设计模式的理由\",\"362\":\"53#示例程序\",\"363\":\"53#运行结果\",\"364\":\"53#拓展思路的要点\",\"365\":\"53#为什么要特意编写-strategy\",\"366\":\"53#程序运行中也可以切换策略\",\"367\":\"53#相关的设计模式\",\"368\":\"53@0\",\"369\":\"53@1\",\"370\":\"54\",\"371\":\"54#为什么要使用-template-method-模式\",\"372\":\"54#示例代码\",\"373\":\"54#运行结果\",\"374\":\"54#相关设计模式\",\"375\":\"54#延申-类的层次与抽象类\",\"376\":\"54@0\",\"377\":\"54@1\",\"378\":\"55\",\"379\":\"55#为什么使用-visitor-模式\",\"380\":\"55#示例代码\",\"381\":\"55#运行结果\",\"382\":\"55#拓展思路的要点\",\"383\":\"55#双重分发\",\"384\":\"55#为什么要这么复杂\",\"385\":\"55#开闭原则——对扩展开放-对修改关闭\",\"386\":\"55#易于增加-concretevisitor-角色\",\"387\":\"55#难以增加-concreteelement-角色\",\"388\":\"55#visitor-工作所需的条件\",\"389\":\"55#相关的设计模式\",\"390\":\"55@0\",\"391\":\"55@1\",\"392\":\"56\",\"393\":\"56#为什么要学编译原理\",\"394\":\"56#理论很复杂-实现也很复杂\",\"395\":\"56#项目的初衷\",\"396\":\"56#做好心理准备\",\"397\":\"56#参考资料\",\"398\":\"56@0\",\"399\":\"56@1\",\"400\":\"57\",\"401\":\"57#编译器的构建流程\",\"402\":\"57#编译器框架\",\"403\":\"58\",\"404\":\"58#计算机的内部工作原理\",\"405\":\"58#内存\",\"406\":\"58#寄存器\",\"407\":\"58#指令集\",\"408\":\"58#mov\",\"409\":\"58#push\",\"410\":\"58#jmp\",\"411\":\"58#jz-jnz\",\"412\":\"58#子函数调用\",\"413\":\"58#ent\",\"414\":\"58#adj\",\"415\":\"58#lev\",\"416\":\"58#lea\",\"417\":\"58#运算符指令\",\"418\":\"58#内置函数\",\"419\":\"58#测试\",\"420\":\"58#小结\",\"421\":\"59\",\"422\":\"59#什么是词法分析器\",\"423\":\"59#词法分析器与编译器\",\"424\":\"59#词法分析器的实现\",\"425\":\"59#支持的标记\",\"426\":\"59#词法分析器的框架\",\"427\":\"59#换行符\",\"428\":\"59#宏定义\",\"429\":\"59#标识符与符号表\",\"430\":\"59#数字\",\"431\":\"59#字符串\",\"432\":\"59#注释\",\"433\":\"59#其它\",\"434\":\"59#关键字与内置函数\",\"435\":\"59#代码\",\"436\":\"59#小结\",\"437\":\"59@0\",\"438\":\"59@1\",\"439\":\"60\",\"440\":\"60#什么是递归下降\",\"441\":\"60#终结符与非终结符\",\"442\":\"60#四则运算的递归下降\",\"443\":\"60#为什么选择递归下降\",\"444\":\"60#左递归\",\"445\":\"60#四则运算的实现\",\"446\":\"60#小结\",\"447\":\"60@0\",\"448\":\"60@1\",\"449\":\"61\",\"450\":\"61#ebnf-表示\",\"451\":\"61#解析变量的定义\",\"452\":\"61#program\",\"453\":\"61#global-declaration\",\"454\":\"61#enum-declaration\",\"455\":\"61#其它\",\"456\":\"61#代码\",\"457\":\"61#小结\",\"458\":\"61@0\",\"459\":\"61@1\",\"460\":\"62\",\"461\":\"62#ebnf-表示\",\"462\":\"62#解析函数的定义\",\"463\":\"62#函数参数与汇编代码\",\"464\":\"62#函数定义的解析\",\"465\":\"62#解析参数\",\"466\":\"62#函数体的解析\",\"467\":\"62#代码\",\"468\":\"62#小结\",\"469\":\"62@0\",\"470\":\"62@1\",\"471\":\"63\",\"472\":\"63#语句\",\"473\":\"63#if-语句\",\"474\":\"63#while-语句\",\"475\":\"63#return-语句\",\"476\":\"63#其它语句\",\"477\":\"63#代码\",\"478\":\"63#小结\",\"479\":\"63@0\",\"480\":\"63@1\",\"481\":\"64\",\"482\":\"64#运算符的优先级\",\"483\":\"64#一元运算符\",\"484\":\"64#常量\",\"485\":\"64#sizeof\",\"486\":\"64#变量与函数调用\",\"487\":\"64#强制转换\",\"488\":\"64#指针取值\",\"489\":\"64#取址操作\",\"490\":\"64#逻辑取反\",\"491\":\"64#按位取反\",\"492\":\"64#正负号\",\"493\":\"64#自增自减\",\"494\":\"64#二元运算符\",\"495\":\"64#赋值操作\",\"496\":\"64#三目运算符\",\"497\":\"64#逻辑运算符\",\"498\":\"64#数学运算符\",\"499\":\"64#自增自减-1\",\"500\":\"64#数组取值操作\",\"501\":\"64#代码\",\"502\":\"64#小结\",\"503\":\"64@0\",\"504\":\"64@1\",\"505\":\"65\",\"506\":\"65#虚拟机与目标代码\",\"507\":\"65#词法分析\",\"508\":\"65#语法分析\",\"509\":\"65#关于编代码\",\"510\":\"65#结语\",\"511\":\"65@0\",\"512\":\"65@1\",\"513\":\"66\",\"514\":\"67\"},\"fieldIds\":{\"h\":0,\"t\":1,\"c\":2},\"fieldLength\":{\"0\":[1],\"1\":[1,5],\"2\":[1,3],\"3\":[1,16],\"4\":[1,2],\"5\":[1,35],\"6\":[1],\"7\":[6],\"8\":[9,21],\"9\":[2,49],\"10\":[2,12],\"11\":[null,null,2],\"12\":[null,null,2],\"13\":[9,20],\"14\":[1,7],\"15\":[1,24],\"16\":[1,5],\"17\":[1,95],\"18\":[1,37],\"19\":[1,12],\"20\":[1],\"21\":[1,15],\"22\":[1,29],\"23\":[1,49],\"24\":[1,6],\"25\":[3,4],\"26\":[1,19],\"27\":[null,null,1],\"28\":[null,null,1],\"29\":[1],\"30\":[4],\"31\":[2,34],\"32\":[1,5],\"33\":[1,23],\"34\":[3,6],\"35\":[2,7],\"36\":[2,4],\"37\":[1,5],\"38\":[2,25],\"39\":[2,63],\"40\":[4,6],\"41\":[1,14],\"42\":[1,5],\"43\":[2,21],\"44\":[2,32],\"45\":[1,51],\"46\":[null,null,1],\"47\":[null,null,1],\"48\":[3,14],\"49\":[null,null,1],\"50\":[null,null,1],\"51\":[2,15],\"52\":[1,32],\"53\":[2,41],\"54\":[2,27],\"55\":[4,9],\"56\":[1,23],\"57\":[1,2],\"58\":[1,12],\"59\":[1,35],\"60\":[1,38],\"61\":[1,5],\"62\":[1,27],\"63\":[1,17],\"64\":[1,19],\"65\":[1,2],\"66\":[1,10],\"67\":[1,5],\"68\":[1,18],\"69\":[1,9],\"70\":[1,10],\"71\":[1,17],\"72\":[1,7],\"73\":[1,2],\"74\":[1,12],\"75\":[1,37],\"76\":[1,38],\"77\":[1,5],\"78\":[1,29],\"79\":[1,17],\"80\":[1,17],\"81\":[1,42],\"82\":[2,18],\"83\":[1,7],\"84\":[1,15],\"85\":[3,13],\"86\":[3,4],\"87\":[3,4],\"88\":[3,5],\"89\":[3,5],\"90\":[3,4],\"91\":[null,null,1],\"92\":[null,null,1],\"93\":[1,4],\"94\":[1,2],\"95\":[1,34],\"96\":[2,8],\"97\":[null,null,1],\"98\":[9,21],\"99\":[1,100],\"100\":[1,71],\"101\":[1,179],\"102\":[1,41],\"103\":[1,3],\"104\":[1,1],\"105\":[1,8],\"106\":[1,29],\"107\":[1,10],\"108\":[null,null,1],\"109\":[null,null,1],\"110\":[1,2],\"111\":[1,45],\"112\":[4,8],\"113\":[1,12],\"114\":[1,19],\"115\":[1,7],\"116\":[1,14],\"117\":[1],\"118\":[1,8],\"119\":[1,10],\"120\":[1],\"121\":[1],\"122\":[1,5],\"123\":[1,11],\"124\":[1,7],\"125\":[1,11],\"126\":[1,13],\"127\":[1,5],\"128\":[1,8],\"129\":[1,12],\"130\":[1,25],\"131\":[2,7],\"132\":[1,9],\"133\":[1,22],\"134\":[1,22],\"135\":[null,null,1],\"136\":[null,null,2],\"137\":[1],\"138\":[1,14],\"139\":[1,133],\"140\":[1,15],\"141\":[1],\"142\":[1,27],\"143\":[1,26],\"144\":[1,6],\"145\":[null,null,1],\"146\":[null,null,3],\"147\":[1],\"148\":[1,7],\"149\":[1,7],\"150\":[1],\"151\":[1,11],\"152\":[1,45],\"153\":[1,11],\"154\":[1,2],\"155\":[null,null,1],\"156\":[null,null,2],\"157\":[2,7],\"158\":[1,7],\"159\":[1],\"160\":[1,15],\"161\":[1,30],\"162\":[1,23],\"163\":[1],\"164\":[1,50],\"165\":[2,28],\"166\":[2,20],\"167\":[2,9],\"168\":[2,21],\"169\":[2,36],\"170\":[1,18],\"171\":[1],\"172\":[1,44],\"173\":[2,29],\"174\":[1,6],\"175\":[null,null,1],\"176\":[null,null,3],\"177\":[2],\"178\":[3,17],\"179\":[1,83],\"180\":[1,42],\"181\":[1,7],\"182\":[1],\"183\":[1,20],\"184\":[1,9],\"185\":[1,41],\"186\":[null,null,1],\"187\":[null,null,3],\"188\":[2,26],\"189\":[1,12],\"190\":[1,94],\"191\":[1,39],\"192\":[1,3],\"193\":[null,null,1],\"194\":[null,null,3],\"195\":[2],\"196\":[1,6],\"197\":[1,56],\"198\":[1,24],\"199\":[1],\"200\":[1,23],\"201\":[1,23],\"202\":[1,4],\"203\":[null,null,1],\"204\":[null,null,3],\"205\":[2],\"206\":[1,15],\"207\":[1],\"208\":[4,39],\"209\":[4,26],\"210\":[4,29],\"211\":[4,49],\"212\":[1,46],\"213\":[1,4],\"214\":[null,null,1],\"215\":[null,null,3],\"216\":[2,5],\"217\":[2,9],\"218\":[1,62],\"219\":[1,20],\"220\":[1],\"221\":[2,55],\"222\":[1,42],\"223\":[1,7],\"224\":[1,23],\"225\":[1,3],\"226\":[1,3],\"227\":[1],\"228\":[1,9],\"229\":[1,7],\"230\":[null,null,1],\"231\":[null,null,3],\"232\":[1,37],\"233\":[null,null,1],\"234\":[null,null,2],\"235\":[2,23],\"236\":[1,8],\"237\":[1,89],\"238\":[1,41],\"239\":[1,5],\"240\":[null,null,1],\"241\":[null,null,3],\"242\":[3,8],\"243\":[3,21],\"244\":[1,50],\"245\":[1,20],\"246\":[null,null,1],\"247\":[null,null,4],\"248\":[2],\"249\":[3,10],\"250\":[1,74],\"251\":[1,21],\"252\":[1],\"253\":[1,66],\"254\":[3,44],\"255\":[1,54],\"256\":[1,25],\"257\":[1,4],\"258\":[null,null,1],\"259\":[null,null,3],\"260\":[1,20],\"261\":[null,null,1],\"262\":[null,null,2],\"263\":[2],\"264\":[1,17],\"265\":[1,117],\"266\":[1,22],\"267\":[null,null,1],\"268\":[null,null,3],\"269\":[1],\"270\":[1,25],\"271\":[2,8],\"272\":[1,63],\"273\":[1,45],\"274\":[1,9],\"275\":[1,5],\"276\":[null,null,1],\"277\":[null,null,2],\"278\":[2],\"279\":[1,26],\"280\":[1,118],\"281\":[1,28],\"282\":[1],\"283\":[1,43],\"284\":[1,38],\"285\":[1,26],\"286\":[1,3],\"287\":[null,null,1],\"288\":[null,null,3],\"289\":[2],\"290\":[3,8],\"291\":[1,96],\"292\":[1,29],\"293\":[1],\"294\":[1,22],\"295\":[2,14],\"296\":[2,13],\"297\":[5,32],\"298\":[1,4],\"299\":[null,null,1],\"300\":[null,null,3],\"301\":[2],\"302\":[1,11],\"303\":[1,77],\"304\":[1,33],\"305\":[1],\"306\":[1,12],\"307\":[2,32],\"308\":[3,11],\"309\":[1,9],\"310\":[1,9],\"311\":[5,18],\"312\":[1,2],\"313\":[null,null,1],\"314\":[null,null,3],\"315\":[2],\"316\":[3,14],\"317\":[1,71],\"318\":[1,15],\"319\":[1,6],\"320\":[null,null,1],\"321\":[null,null,3],\"322\":[2],\"323\":[1,22],\"324\":[1,82],\"325\":[1,20],\"326\":[1],\"327\":[1,11],\"328\":[1,11],\"329\":[1,7],\"330\":[1,6],\"331\":[2,9],\"332\":[3,25],\"333\":[1,3],\"334\":[null,null,1],\"335\":[null,null,3],\"336\":[2],\"337\":[3,10],\"338\":[2,6],\"339\":[1,39],\"340\":[1,19],\"341\":[1,5],\"342\":[1,14],\"343\":[1,44],\"344\":[null,null,1],\"345\":[null,null,3],\"346\":[2],\"347\":[3,8],\"348\":[1,79],\"349\":[1,49],\"350\":[1],\"351\":[1,44],\"352\":[1,49],\"353\":[1,88],\"354\":[1,21],\"355\":[1,50],\"356\":[1,54],\"357\":[1,3],\"358\":[null,null,1],\"359\":[null,null,3],\"360\":[2],\"361\":[1,16],\"362\":[1,121],\"363\":[1,26],\"364\":[1],\"365\":[2,28],\"366\":[1,26],\"367\":[1,5],\"368\":[null,null,1],\"369\":[null,null,4],\"370\":[3,10],\"371\":[5,10],\"372\":[1,59],\"373\":[1,22],\"374\":[1,4],\"375\":[2,25],\"376\":[null,null,1],\"377\":[null,null,3],\"378\":[2,13],\"379\":[4,11],\"380\":[1,103],\"381\":[1,46],\"382\":[1],\"383\":[1,24],\"384\":[1,33],\"385\":[3,35],\"386\":[3,10],\"387\":[3,25],\"388\":[2,32],\"389\":[1,4],\"390\":[null,null,1],\"391\":[null,null,3],\"392\":[5,46],\"393\":[1,28],\"394\":[3,56],\"395\":[1,40],\"396\":[1,14],\"397\":[1,45],\"398\":[null,null,1],\"399\":[null,null,3],\"400\":[5,55],\"401\":[1,27],\"402\":[1,130],\"403\":[1,71],\"404\":[1,9],\"405\":[1,125],\"406\":[1,58],\"407\":[1,58],\"408\":[1,119],\"409\":[1,24],\"410\":[1,27],\"411\":[2,24],\"412\":[1,127],\"413\":[1,35],\"414\":[1,25],\"415\":[1,36],\"416\":[1,62],\"417\":[1,51],\"418\":[1,68],\"419\":[1,63],\"420\":[1,35],\"421\":[5,54],\"422\":[1,35],\"423\":[1,26],\"424\":[1,18],\"425\":[1,86],\"426\":[1,42],\"427\":[1,12],\"428\":[1,28],\"429\":[1,135],\"430\":[1,61],\"431\":[1,63],\"432\":[1,61],\"433\":[1,56],\"434\":[1,81],\"435\":[1,24],\"436\":[1,18],\"437\":[null,null,1],\"438\":[null,null,3],\"439\":[5,47],\"440\":[1,11],\"441\":[1,33],\"442\":[1,37],\"443\":[1,37],\"444\":[1,23],\"445\":[1,70],\"446\":[1,16],\"447\":[null,null,1],\"448\":[null,null,3],\"449\":[5,55],\"450\":[2,44],\"451\":[1,7],\"452\":[2,20],\"453\":[3,130],\"454\":[3,51],\"455\":[1,25],\"456\":[1,22],\"457\":[1,13],\"458\":[null,null,1],\"459\":[null,null,3],\"460\":[5,51],\"461\":[2,21],\"462\":[1,37],\"463\":[1,56],\"464\":[1,67],\"465\":[1,77],\"466\":[1,93],\"467\":[1,24],\"468\":[1,18],\"469\":[null,null,1],\"470\":[null,null,3],\"471\":[5,49],\"472\":[1,28],\"473\":[2,62],\"474\":[2,32],\"475\":[2,22],\"476\":[1,21],\"477\":[1,21],\"478\":[1,16],\"479\":[null,null,1],\"480\":[null,null,3],\"481\":[5,76],\"482\":[1,95],\"483\":[1,15],\"484\":[1,60],\"485\":[1,45],\"486\":[1,151],\"487\":[1,36],\"488\":[1,42],\"489\":[1,47],\"490\":[1,28],\"491\":[1,31],\"492\":[1,33],\"493\":[1,62],\"494\":[1,76],\"495\":[1,57],\"496\":[1,39],\"497\":[1,33],\"498\":[1,101],\"499\":[1,39],\"500\":[1,50],\"501\":[1,60],\"502\":[1,17],\"503\":[null,null,1],\"504\":[null,null,3],\"505\":[5,46],\"506\":[1,18],\"507\":[1,13],\"508\":[1,32],\"509\":[1,24],\"510\":[1,3],\"511\":[null,null,1],\"512\":[null,null,3],\"513\":[1,3],\"514\":[3]},\"averageFieldLength\":[1.5158770718205052,28.59027642469382,0.7670384630110558],\"storedFields\":{\"0\":{\"h\":\"主页\"},\"1\":{\"h\":\"介绍页\",\"t\":[\"一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。\"]},\"2\":{\"h\":\"随笔\",\"t\":[\"这里是所有个人感想、生活记录等非技术类文章。\"]},\"3\":{\"h\":\"命里有时终须有\",\"t\":[\"alt text\",\"昨日在玩“三国杀：一将成名”时，我抽奖一发就中了大奖——“清河公主”传说皮。这让我不禁感慨：“命里有时终须有，命里无时莫强求。”这句话真是道出了人生的真谛，有些事情是强求不来的，顺其自然反而能得到意想不到的收获。\"]},\"4\":{\"h\":\"项目\",\"t\":[\"这里是你参与或开发的项目介绍和进展。\"]},\"5\":{\"h\":\"资源\",\"t\":[\"这里是推荐的书籍、网站、工具等资源。\",\"github - 世界上最大的代码托管平台\",\"Z-Library – 世界上最大的电子图书馆。自由访问知识和文化。\",\"Vuepress - 我的博客构建库\",\"plantUML - 一个通用性很强的工具，可以快速、直接地创建各种图表\",\"emoji-cheat-sheet - A markdown version emoji cheat sheet\",\"Sci-hub —— 当今科学界最具争议性的项目。Sci-hub的目标是 免费并且不受限制地 提供所有科学知识。\",\"Lib.Genesis —— Part of Library Genesis. ex libgen.io, libgen.org\"]},\"6\":{\"h\":\"Qt\"},\"7\":{\"h\":\"Some Solutions to Questions about Qt\"},\"8\":{\"h\":\"The qt-5 isn't in Qt Maintenance tools\",\"t\":[\"Open the Qt Maintenance Tools.\",\"click the Archive in the Select-Component section.\",\"click the filter button and you can see the qt-5 in the list.\"]},\"9\":{\"h\":\"android studio换源\",\"t\":[\"国内镜像\",\"Android Studio下载gradle太慢可换源\",\"android.plugin version 下载错误查看\",\"修改 settings.gradle.kts\",\"pluginManagement { repositories { maven { url=uri (\\\"https://jitpack.io\\\") } maven { url=uri (\\\"https://maven.aliyun.com/repository/releases\\\") } // maven { url 'https://maven.aliyun.com/repository/jcenter' } maven { url=uri (\\\"https://maven.aliyun.com/repository/google\\\") } maven { url=uri (\\\"https://maven.aliyun.com/repository/central\\\") } maven { url=uri (\\\"https://maven.aliyun.com/repository/gradle-plugin\\\") } maven { url=uri (\\\"https://maven.aliyun.com/repository/public\\\") } google() mavenCentral() gradlePluginPortal() } } dependencyResolutionManagement { repositoriesMode.set(RepositoriesMode.FAIL_ON_PROJECT_REPOS) repositories { maven { url=uri (\\\"https://jitpack.io\\\") } maven { url=uri (\\\"https://maven.aliyun.com/repository/releases\\\") } // maven { url 'https://maven.aliyun.com/repository/jcenter' } maven { url=uri (\\\"https://maven.aliyun.com/repository/google\\\") } maven { url=uri (\\\"https://maven.aliyun.com/repository/central\\\") } maven { url=uri (\\\"https://maven.aliyun.com/repository/gradle-plugin\\\") } maven { url=uri (\\\"https://maven.aliyun.com/repository/public\\\") } google() mavenCentral() } } \",\"gradle-wrapper.properties 换成对应的版本\",\"distributionUrl=https\\\\://mirrors.cloud.tencent.com/gradle/gradle-8.7-all.zip \"]},\"10\":{\"h\":\"CI/CD\",\"t\":[\"本地调试工具 act\",\"需要创建配置文件\",\"也可另外指定\",\"act --var-file \\\"./.act/.vars\\\" --secret-file \\\"./.act/.secrets\\\" --env-file \\\"./.act/.env\\\" {{other}} \"]},\"11\":{\"c\":[\"CI/CD\"]},\"12\":{\"c\":[\"CI/CD\"]},\"13\":{\"h\":\"docker + nginx + acme.sh 部署 vue/flask 项目\",\"t\":[\"本文将介绍如何使用 Docker、Nginx 和 acme.sh 部署一个 Vue 和 Flask 项目。我们将详细讲解环境配置、项目结构、Nginx 配置、Docker 配置以及如何升级到 HTTPS。\",\"提示\",\"需要先申请一个域名，本文是 bupt.online\"]},\"14\":{\"h\":\"环境\",\"t\":[\"Ubuntu\",\"Docker\",\"Docker-Compose\",\"acme.sh\",\"(python)\",\"nginx\"]},\"15\":{\"h\":\"项目结构\",\"t\":[\"./nginx ├── acme # 存放SSL证书 ├── conf.d │ ├── Automaton.conf │ ├── blog.conf ├── docker-compose.yml ├── DockerFile ├── logs # 存放日志 │ ├── access.log │ ├── Automaton │ ├── blog │ └── error.log ├── nginx.conf ./project # 要部署的（前端）项目 ├── Automaton └── blog \"]},\"16\":{\"h\":\"配置http服务\",\"t\":[\"在准备好前端项目及安装相应环境后，进行如下操作(部分路径以实际为准，进行修改)\"]},\"17\":{\"h\":\"配置nginx\",\"t\":[\"nginx.conf\",\"user nginx; worker_processes 1; error_log /var/log/nginx/error.log warn; pid /var/run/nginx.pid; events { worker_connections 4096; } http { include /etc/nginx/mime.types; default_type application/octet-stream; log_format main '$remote_addr - $remote_user [$time_local] \\\"$request\\\" ' '$status $body_bytes_sent \\\"$http_referer\\\" ' '\\\"$http_user_agent\\\" \\\"$http_x_forwarded_for\\\"'; # access_log /var/log/nginx/access.log main; access_log off; error_log /var/log/nginx/error.log warn; sendfile on; #tcp_nopush on; keepalive_timeout 65; # 定义DNS解析器 resolver 8.8.8.8 114.114.114.114 valid=300s; resolver_timeout 10s; # 增加请求头和Cookie的大小限制 client_header_buffer_size 16k; large_client_header_buffers 4 32k; include /etc/nginx/conf.d/*.conf; } \",\"Automaton.conf\",\"server { listen 80; server_name Automaton.bupt.online; location / { root /usr/share/nginx/html/Automaton; try_files $uri $uri/ =404; } access_log /var/log/nginx/Automaton/access.log; error_log /var/log/nginx/Automaton/error.log warn; } \",\"blog.conf\",\"server { listen 80; server_name bupt.online www.bupt.online; location / { root /usr/share/nginx/html/blog; try_files $uri $uri/ =404; # access_log /var/log/nginx/blog/access.log; error_log /var/log/nginx/blog/error.log warn; } location /Automaton { # 使用 proxy_pass 或 rewrite 重定向到Automaton.bupt.online 失败 alias /usr/share/nginx/html/Automaton/; try_files $uri $uri/ =404; # access_log /var/log/nginx/Automaton/access.log; error_log /var/log/nginx/Automaton/error.log warn; } } \"]},\"18\":{\"h\":\"配置docker\",\"t\":[\"DockerFile\",\"FROM nginx:latest COPY nginx.conf /etc/nginx/nginx.conf COPY conf.d /etc/nginx/conf.d \",\"docker-compose.yml\",\"services: nginx: build: context: . dockerfile: DockerFile ports: - \\\"80:80\\\" - \\\"443:443\\\" volumes: - ../project/blog:/usr/share/nginx/html/blog - ../project/Automaton:/usr/share/nginx/html/Automaton - ./logs:/var/log/nginx - ./conf.d:/etc/nginx/conf.d - ./acme:/etc/letsencrypt/live networks: - webnet environment: - TZ=Asia/Shanghai networks: webnet: \"]},\"19\":{\"h\":\"启动项目\",\"t\":[\"docker-compose up -d --build \",\"然后就能正常访问 http://bupt.online 及 http://automaton.bupt.online ， http://bupt.online/Automaton\"]},\"20\":{\"h\":\"升级为https\"},\"21\":{\"h\":\"申请证书\",\"t\":[\"进入acme.sh的安装目录(/root/.acme.sh)\",\"sudo su root acme.sh --issue -d bupt.online --nginx # Nginx acme.sh --issue -d Automaton.bupt.online --nginx # Nginx \"]},\"22\":{\"h\":\"安装证书\",\"t\":[\"这里将目录修改为目标目录\",\"# sudo su root # cd .acme.sh # use like below acme.sh --install-cert -d bupt.online \\\\ --cert-file /home/ubuntu/nginx/acme/bupt.online/cert.cer \\\\ --key-file /home/ubuntu/nginx/acme/bupt.online/privkey.key \\\\ --fullchain-file /home/ubuntu/nginx/acme/bupt.online/fullchain.cer \\\\ --reloadcmd \\\"cd /home/ubuntu/nginx && docker-compose up -d --build\\\" \"]},\"23\":{\"h\":\"修改配置\",\"t\":[\"blog.conf\",\"server { listen 80; server_name bupt.online www.bupt.online; return 301 https://$host$request_uri; } server { listen 443 ssl; server_name bupt.online; ssl_certificate /etc/letsencrypt/live/bupt.online/fullchain.cer; ssl_certificate_key /etc/letsencrypt/live/bupt.online/privkey.key; location / { root /usr/share/nginx/html/blog; try_files $uri $uri/ =404; # access_log /var/log/nginx/blog/access.log; error_log /var/log/nginx/blog/error.log warn; } location /Automaton { # 使用 proxy_pass 或 rewrite 重定向到Automaton.bupt.online 失败 alias /usr/share/nginx/html/Automaton/; try_files $uri $uri/ =404; # access_log /var/log/nginx/Automaton/access.log; error_log /var/log/nginx/Automaton/error.log warn; } } server { listen 443 ssl; server_name www.bupt.online; ssl_certificate /etc/letsencrypt/live/www.bupt.online/fullchain.cer; ssl_certificate_key /etc/letsencrypt/live/www.bupt.online/privkey.key; location / { root /usr/share/nginx/html/blog; try_files $uri $uri/ =404; # access_log /var/log/nginx/blog/access.log; error_log /var/log/nginx/blog/error.log warn; } location /Automaton { # 使用 proxy_pass 或 rewrite 重定向到Automaton.bupt.online 失败 alias /usr/share/nginx/html/Automaton/; try_files $uri $uri/ =404; # access_log /var/log/nginx/Automaton/access.log; error_log /var/log/nginx/Automaton/error.log warn; } } \",\"Automaton.conf\",\"server { listen 80; server_name Automaton.bupt.online; location / { return 301 https://$host$request_uri; } } server { listen 443 ssl; server_name Automaton.bupt.online; ssl_certificate /etc/letsencrypt/live/Automaton.bupt.online/fullchain.cer; ssl_certificate_key /etc/letsencrypt/live/Automaton.bupt.online/privkey.key; location / { root /usr/share/nginx/html/Automaton; try_files $uri $uri/ =404; } access_log /var/log/nginx/Automaton/access.log; error_log /var/log/nginx/Automaton/error.log warn; } \"]},\"24\":{\"h\":\"重启container\",\"t\":[\"docker-compose up -d --build \"]},\"25\":{\"h\":\"配置nginx反向代理，使flask支持 https\",\"t\":[\"Flask 部署\",\"#TODO - 添加flask+nginx配置\"]},\"26\":{\"h\":\"参考资料\",\"t\":[\"Nginx Documentation\",\"Flask Documentation\",\"Reverse Proxy Guide\",\"SSL Certificates\",\"用acme.sh帮你免费且自动更新的HTTPS证书，省时又省力\",\"docker部署certbot与nginx来获取ssl证书添加https及自动更新\",\"使用docker acme申请、续订泛域名证书，并自动重载docker nginx\",\"Flask: 如何给Python Flask Web服务器添加HTTPS功能\"]},\"27\":{\"c\":[\"nginx\"]},\"28\":{\"c\":[\"部署\"]},\"29\":{\"h\":\"\"},\"30\":{\"h\":\"GitHub Container Registry 加速\"},\"31\":{\"h\":\"ghcr.io简介\",\"t\":[\"ghcr.io 是 GitHub Container Registry 的域名。GitHub Container Registry 是 GitHub 提供的容器镜像注册表服务，允许开发者在 GitHub 上存储、管理和分享 Docker 镜像。它与 GitHub 代码仓库紧密集成，可以使用相同的权限管理、团队协作和版本控制工具来管理容器镜像。\",\"通过 GitHub Container Registry，开发者可以方便地将他们的容器镜像与代码仓库关联起来，这样就可以在同一个平台上管理代码和镜像。这种集成性使得持续集成/持续交付 (CI/CD) 流程更加简化和统一，开发团队可以更容易地构建、测试和部署应用程序。\",\"对于使用 GitHub 作为代码托管平台的开发者来说，GitHub Container Registry 提供一个便捷且强大的容器镜像管理解决方案。通过该服务，可以更轻松地构建和部署容器化的应用程序，从而加速开发和交付周期。\"]},\"32\":{\"h\":\"镜像地址\",\"t\":[\"https://ghcr.nju.edu.cn\"]},\"33\":{\"h\":\"配置方法\",\"t\":[\"sudo vim /etc/docker/daemon.json \",\"{ \\\"registry-mirrors\\\": [\\\"https://ghcr.nju.edu.cn\\\"] } \",\":wq保存退出\",\"sudo systemctl daemon-reload sudo systemctl restart docker \",\"拉取镜像方法\",\"docker pull ghcr.nju.edu.cn/open-webui/open-webui:main \"]},\"34\":{\"h\":\"docker wsl2 容器目录\",\"t\":[\"\\\\\\\\wsl$\\\\docker-desktop-data\\\\data\\\\docker\\\\containers \"]},\"35\":{\"h\":\"github 图床\",\"t\":[\"参考\",\"https://zhuanlan.zhihu.com/p/347342082\"]},\"36\":{\"h\":\"github 工作流程\",\"t\":[\"十分钟学会正确的github工作流，和开源作者们使用同一套流程\",\"相关信息\",\"TODO\"]},\"37\":{\"h\":\"技术\",\"t\":[\"这里是所有与技术相关的文章，包括编程、工具使用、技术分享等内容。\"]},\"38\":{\"h\":\"自建mail server\",\"t\":[\"参见:\",\"https://docker-mailserver.github.io/docker-mailserver/latest/\",\"https://blog.csdn.net/qq_25866579/article/details/140717115\",\"https://zhuanlan.zhihu.com/p/609639797\",\"值得注意的是docker-mailserver 并不支持通过ui注册/修改等操作， 当可以自行实现（后端通过shell命令即可\"]},\"39\":{\"h\":\"使用python 发送示例\",\"t\":[\"import smtplib from email.mime.text import MIMEText from email.mime.multipart import MIMEMultipart from email.utils import formatdate # Email configuration smtp_server = 'mail.bupt.online' smtp_port = 587 username = 'test@bupt.online' password = '12345678' from_email = 'test@bupt.online' to_email = 'ksj@bupt.online' subject = 'Test Email' body = 'This is a test email sent from Python.' # Create the email msg = MIMEMultipart() msg['From'] = from_email msg['To'] = to_email msg['Subject'] = subject msg['Date'] = formatdate(localtime=True) msg.attach(MIMEText(body, 'plain')) # Send the email try: server = smtplib.SMTP(smtp_server, smtp_port) server.starttls() server.login(username, password) server.sendmail(from_email, to_email, msg.as_string()) server.quit() print(\\\"Email sent successfully\\\") except Exception as e: print(f\\\"Failed to send email: {e}\\\") \",\"alt text\"]},\"40\":{\"h\":\"「泛型与 OI」modint\",\"t\":[\"在 OI 中，有大量的题目要求对一些数字取模，这便是本文写作的背景。\"]},\"41\":{\"h\":\"背景介绍\",\"t\":[\"这些题目要么是因为答案太大，不方便输出结果，例如许多计数 dp；要么是因为答案是浮点数，出题人不愿意写一个确定精度的 Special Judge，例如很多期望概率题；要么是因为这道题目直接考察了模的性质和运用，比如大量的 998244353 类的多项式题目。\"]},\"42\":{\"h\":\"过去的做法\",\"t\":[\"在这种要求之下，取模运算就成为了编程中不可缺少的一部分。下面以式子 为例介绍几种写法。\"]},\"43\":{\"h\":\"第一种 直接取模\",\"t\":[\"这种方法是直接取模，简单直接，清晰明了。\",\"constexpr int p=998244353; int ans=1ll*(((x+y)%p+z)%p)*u%p; \",\"但是这种方法有着严重的缺陷，一是容易忘记大括号，二是容易中间运算时搞错运算顺序、忘记取模，三是式子太长、括号太多、不易检验。\",\"因此，不推荐运用这种方法。\"]},\"44\":{\"h\":\"第二种 函数取模\",\"t\":[\"这种方法有效地解决了直接取模的忘记取模的漏洞。\",\"constexpr int p=998244353; int add(int a,int b){ return a+b>=p?a+b-p:a+b; } int sub(int a,int b){ return a<b?a-b+p:a-b; } int mul(int a,int b){ return 1ll*a*b%p; } int ans=mul(add(add(x,y),z),u); \",\"但是，这种写法的式子依旧太长，不易检验，并且如果编译器没有任何优化（现在不存在这种情况了）的话，大量的函数调用将会耗费不少的时间。并且如果要对多个模数取模，则需要写多个函数，显得代码冗长。\"]},\"45\":{\"h\":\"泛型编程\",\"t\":[\"考虑到函数取模的优点，我们不妨通过类的运算符重载来进一步优化 add 等函数。\",\"同时为了解决多个模数的问题，我们考虑泛型编程，将模数直接包含在类型中。\",\"template<typename T,const T p> class modint{ private: T v; public: modint(){} modint(const T& x){assert(0<=x&&x<p);v=x;} modint operator+(const modint& a)const{ return v+a.v>=p?v+a.v-p:v+a.v; } modint operator-(const modint& a)const{ return v<a.v?v-a.v+p:v-a.v; } modint operator*(const modint& a)const{ return 1ll*v*a.v%p; } T operator()(void)const{ return v; } }; modint<int,998244353> x(),y(),z(),u(); modint<int,998244353> ans=(x+y+z)*u; \",\"这样使用的时候，一方面减少了心智负担，不用操心运算时忘记取模；另一方面采取了常数更小的加减法操作，运算更快。\",\"唯一的缺点就是类型名难写，但是模数个数少的时候可以缩写，即写成：\",\"typedef modint<int,998244353> modInt1; \",\"这样就解决了类型名长的缺点。\"]},\"46\":{\"c\":[\"OI\"]},\"47\":{\"c\":[\"MODInt\"]},\"48\":{\"h\":\"python requirements.txt\",\"t\":[\"Python 生成 requirements有两种方式\",\"pip list --format=freeze > requirements.txt (推荐做法)\",\"pip freeze > requirements.txt (不推荐，会带有本地路径)\"]},\"49\":{\"c\":[\"python\"]},\"50\":{\"c\":[\"踩坑记录\"]},\"51\":{\"h\":\"Game Plugin\",\"t\":[\"This is the content of the game plugin post.\",\"BepInEx\",\"AssetStudioAssetStudio\",\"dnSpy\",\"Harmony\",\"UnityExplorer\",\"相关信息\",\"TODO\"]},\"52\":{\"h\":\"风格统一\",\"t\":[\"如何实现风格统一？ 可以使用*.editorconfig*文件来实现风格统一。\",\"安装EditorConfig插件 (部分IDE默认直接支持)\",\"在项目根目录下创建.editorconfig文件，并添加以下内容：\",\"root = true [*] indent_style = space tab_width = 2 end_of_line = lf charset = utf-8 trim_trailing_whitespace = true insert_final_newline = true \"]},\"53\":{\"h\":\"tensorflow 踩坑记录\",\"t\":[\"Pytorch 用于快速原型验证（学术研究）， TensorFlow 用于工业生产部署\",\"近日使用 TensorFlow 完成图像去噪任务，然而速度太慢，于是寻求 GPU 资源进行加速。本以为 TensorFlow 2 能轻松使用 GPU（当然需要配置相关驱动），谁知 TensorFlow 高版本（>=2.10.0）不再支持 Windows，而 Pytorch 仍然支持。最终 选择了 Pytorch 进行实验 寻得了Linux GPU 环境（感谢lucky&agicy）。\",\"此外，Pytorch 的动态计算图机制使得调试和开发更加灵活，适合快速迭代和原型验证。而 TensorFlow 虽然在工业部署中表现出色，但其静态计算图机制在开发过程中略显繁琐。综合考虑，决定以后在学术研究和快速原型验证阶段使用 Pytorch，而在工业生产部署阶段方才使用 TensorFlow（当然得是Linux环境）。\"]},\"54\":{\"h\":\"vscode plugin\",\"t\":[\"// TODO https://code.visualstudio.com/api/get-started/your-first-extension\",\"若activate function执行时间过长，会导致Activating extension 'undefined_publisher.kcodetime' failed: AggregateError., 从而启动失败\",\"若deactivate function执行时间超过5s, 会被强行终止，导致插件无法正常退出。\",\"关闭vscode 不会触发onDidCloseTextDocument事件\"]},\"55\":{\"h\":\"「算术公理系统 1」自然数\",\"t\":[\"假设存在一个算数系统的模型满足 Peano 公理，即假定 Peano 公理相容，在此承认次假设的基础之上，我们即可建立如今最常用的算术公理系统。自然数的定义则是构建此算术公理系统的第一步。\"]},\"56\":{\"h\":\"自然数的定义\",\"t\":[\"先介绍 Peano 公理，共有五条：\",\" 是自然数；\",\"任何自然数的后继存在且唯一，下文用 表示 的后继；\",\" 不是任何自然数的后继；\",\"不同的自然数后继不同；\",\" 是关于自然数 的一个命题，且满足两个条件：\",\" 是真命题；\",\"由 为真命题可以推理出 为真命题。\",\"则有，对于任意自然数 ， 为真命题。\",\"这样就定义了自然数，自然数这个新的数学对象因我们的假设而确立。\"]},\"57\":{\"h\":\"自然数的加法运算\",\"t\":[\"自然数中最重要的运算当然是加法。\"]},\"58\":{\"h\":\"加法的定义\",\"t\":[\"定义加法的运算规则：\",\"若 是自然数，则 的运算结果为 ，即 ；\",\"若 都是自然数，则 。\",\"下面我们需要证明对于任意两个自然数，都可以进行加法运算，也就是说，我们需要证明加法结果的存在性和唯一性。\"]},\"59\":{\"h\":\"加法结果的存在性\",\"t\":[\" 是任意自然数，记 表示 是否是自然数，即 是否存在。\",\" 是自然数，由加法运算规则 Ⅰ 有 ，进而有 是自然数； 即 得证。\",\" 和 是自然数，由 Peano 公理 Ⅱ 有 和 是自然数； 根据加法运算规则 Ⅱ 有 ，进有 是自然数； 综上所述，若 是自然数，则 也是自然数； 即由 为真命题可以推出 为真命题。\",\"由 的性质和 Peano 公理 Ⅴ 有，对于任意自然数 ， 成立，即 是自然数，再根据 的任意性，得出对于任意自然数 ， 都是自然数。\"]},\"60\":{\"h\":\"加法结果的唯一性\",\"t\":[\" 是任意自然数，记 表示 是否唯一，即 的结果是否唯一。\",\" 是自然数，由加法运算规则 Ⅰ 有 ，进而 是唯一的，就是 ； 即 得证。\",\" 是自然数， 是唯一的，由 Peano 公理 Ⅱ 有 是自然数且 唯一； 根据加法运算规则 Ⅱ 有 ，进有 唯一； 综上所述，若 唯一，则 也唯一； 即由 为真命题可以推出 为真命题。\",\"由 的性质和 Peano 公理 Ⅴ 有，对于任意自然数 ， 成立，即 唯一，再根据 的任意性，得出对于任意自然数 ， 都是唯一的。\"]},\"61\":{\"h\":\"加法的性质\",\"t\":[\"在明确证明了自然数加法运算的良好性质，即任意两个自然数都可以进行加法运算，且加法运算的结果存在且唯一之后，我们终于可以对自然数加法的性质进行进一步的探索。\"]},\"62\":{\"h\":\"加法交换律\",\"t\":[\"下面证明加法交换律，即对于任意自然数 ，有 。\",\"直接证明比较困难，考虑从加法运算的定义下手，即先证明加法的两条运算规则符合交换律。\",\"试证 ，首先有\",\"进而当 是自然数且 时有\",\"根据 Peano 公理 Ⅴ，得知 对任意自然数 成立。\",\"试证 ，首先有\",\"进而当 是自然数且 时有\",\"根据 Peano 公理 Ⅴ，得知 对任意自然数 成立，将其称为新的加法运算规则 Ⅱ。\",\"证明了加法运算规则的交换律之后，试证加法交换律 ，首先由加法运算规则 Ⅰ 有 ，进而当 是自然数且 时，有\",\"根据 Peano 公理 Ⅴ，得知 对任意自然数 成立，即加法交换律成立。\"]},\"63\":{\"h\":\"加法结合律\",\"t\":[\"下面证明加法结合律，即对于任意自然数 ，有 。\",\"首先当 时，有\",\"进而当 为自然数且 时有\",\"根据 Peano 公理 Ⅴ，得知 对任意自然数 成立，即加法结合律成立。\"]},\"64\":{\"h\":\"加法消去律\",\"t\":[\"下面证明加法消去律，即对于任意自然数 ，有 。\",\"试证 。\",\"首先当 时有\",\"进而当 为自然数且 时有\",\"即 ，根据 Peano 公理 Ⅴ，得知 对任意自然数 成立。\",\"试证 。\",\"首先当 时有\",\"进而当 为自然数且 时有\",\"即 ，根据 Peano 公理 Ⅴ，得知 对任意自然数 成立。\",\"综上所述，加法消去律 ，对任意自然数 成立。\"]},\"65\":{\"h\":\"自然数的序\",\"t\":[\"自然数的序为两个自然数的关系。\"]},\"66\":{\"h\":\"序的定义\",\"t\":[\"定义自然数的序即定义 当且仅当存在自然数 满足 。定义 当且仅当 且 。\",\"自然数的序是全序关系，它应该具有反对称性、传递性和完全性。\"]},\"67\":{\"h\":\"正自然数\",\"t\":[\"在考察序的性质之前，我们预先准备以方便证明。\",\"定义正自然数为非 自然数。\"]},\"68\":{\"h\":\"正自然数的性质\",\"t\":[\"正自然数与自然数相加为正自然数，即对于正自然数 ，其与自然数 的和 为正自然数。\",\"首先，当 时， 为正自然数。\",\"进而当 为自然数且 为正自然数时有 ，根据 Peano 公理 Ⅲ， 为正自然数，进而 为正自然数。\",\"根据 Peano 公理 Ⅴ，正自然数与自然数相加为正自然数。\"]},\"69\":{\"h\":\"序的反对称性\",\"t\":[\"若 且 ，则 。\",\"由 有 ，由 有 。\",\"因此 ，由加法消去律得到 ，根据正自然数的性质得出 ，因此 。\"]},\"70\":{\"h\":\"序的传递性\",\"t\":[\"若 且 ，则 。\",\"由 有 ，由 有 。\",\"根据加法结果的存在性得到 是自然数，根据加法结合律得出 ，进而 。\"]},\"71\":{\"h\":\"序的完全性\",\"t\":[\"任意两个自然数 都有序关系。\",\"对于 两个自然数，当 时有 所以 。\",\"当 为自然数时。若 ，则 ，因此 ；若 ，则 ，因此 ；若 ，则 。\",\"由 Peano 公理 Ⅴ 有任意两个自然数 都有序关系。\"]},\"72\":{\"h\":\"加法保序性\",\"t\":[\"若 ，则 。\",\"由 有 ，进而 因此 。\"]},\"73\":{\"h\":\"自然数的乘法运算\",\"t\":[\"自然数的乘法也十分重要。\"]},\"74\":{\"h\":\"乘法的定义\",\"t\":[\"定义乘法的运算规则：\",\"若 是自然数，则 的运算结果为 ，即 ；\",\"若 都是自然数，则 。\",\"下面我们需要证明对于任意两个自然数，都可以进行乘法运算，也就是说，我们需要证明乘法结果的存在性和唯一性。\"]},\"75\":{\"h\":\"乘法结果的存在性\",\"t\":[\" 是任意自然数，记 表示 是否是自然数，即 是否存在。\",\" 是自然数，由乘法运算规则 Ⅰ 有 ，进而有 是自然数； 即 得证。\",\" 和 是自然数，由加法结果的存在性有 存在； 根据乘法运算规则 Ⅱ 有 ，进有 是自然数； 综上所述，若 是自然数，则 也是自然数； 即由 为真命题可以推出 为真命题。\",\"由 的性质和 Peano 公理 Ⅴ 有，对于任意自然数 ， 成立，即 是自然数，再根据 的任意性，得出对于任意自然数 ， 都是自然数。\"]},\"76\":{\"h\":\"乘法结果的唯一性\",\"t\":[\" 是任意自然数，记 表示 是否唯一，即 的结果是否唯一。\",\" 是自然数，由乘法运算规则 Ⅰ 有 ，进而 是唯一的，就是 ； 即 得证。\",\" 是自然数， 是唯一的，由加法结果的唯一性有 唯一； 根据乘法运算规则 Ⅱ 有 ，进有 唯一； 综上所述，若 唯一，则 也唯一； 即由 为真命题可以推出 为真命题。\",\"由 的性质和 Peano 公理 Ⅴ 有，对于任意自然数 ， 成立，即 唯一，再根据 的任意性，得出对于任意自然数 ， 都是唯一的。\"]},\"77\":{\"h\":\"乘法的性质\",\"t\":[\"在明确证明了自然数乘法运算的良好性质，即任意两个自然数都可以进行乘法运算，且乘法运算的结果存在且唯一之后，我们终于可以对自然数乘法的性质进行进一步的探索。\"]},\"78\":{\"h\":\"乘法交换律\",\"t\":[\"下面证明乘法交换律，即对于任意自然数 ，有 。\",\"直接证明比较困难，考虑从乘法运算的定义下手，即先证明乘法的两条运算规则符合交换律。\",\"试证 。\",\"首先有 。\",\"进而当 是自然数且 时有\",\"根据 Peano 公理 Ⅴ，得知 对任意自然数 成立。\",\"试证 。\",\"首先 时有\",\"进而当 是自然数且 时有\",\"根据 Peano 公理 Ⅴ，得知 对任意自然数 成立，将其称为新的乘法运算规则 Ⅱ。\",\"证明了乘法运算规则的交换律之后，试证乘法交换律 ，首先当 时由乘法运算规则 Ⅰ 有 。\",\"进而当 是自然数且 时，有\",\"根据 Peano 公理 Ⅴ，得知 对任意自然数 成立，即乘法交换律成立。\"]},\"79\":{\"h\":\"乘法分配律\",\"t\":[\"下面证明乘法分配律，即对于任意自然数 ，有 。\",\"首先当 时，，进而当 为自然数且 时有\",\"根据 Peano 公理 Ⅴ，得知 对任意自然数 成立，即乘法分配律成立。\"]},\"80\":{\"h\":\"乘法结合律\",\"t\":[\"下面证明乘法结合律，即对于任意自然数 ，有 。\",\"首先当 时，有 。\",\"进而当 为自然数且 时有\",\"根据 Peano 公理 Ⅴ，得知 对任意自然数 成立，即乘法结合律成立。\"]},\"81\":{\"h\":\"乘法消去律\",\"t\":[\"下面证明乘法消去律，即对于任意自然数 和 ，有 。\",\"试证 。\",\"首先当 时有\",\"进而当 为自然数且 时有\",\"即 ，根据 Peano 公理 Ⅴ，得知 对任意自然数 成立。\",\"试证 ，采用反证法，假设 ，则由加法运算规则 Ⅱ 可知 或 ，其中 ，不妨设 。\",\"由 Peano 公理 Ⅲ 有 。\",\"由 Peano 公理 Ⅲ、Ⅳ 有，任意非零自然数 都有唯一的数 满足 ，不妨记作 。\",\"若有 ，则有\",\"上述等式表明 是 的后继，这违背了 Peano 公理 Ⅲ，由此知道假设不成立，即 。\",\"综上所述，乘法消去律 ，对任意自然数 成立。\"]},\"82\":{\"h\":\"Peano 公理的合理性\",\"t\":[\"通过上述步骤，我们成功地由 Peano 公理构建出了一个自然数代数系统。但 Peano 公理自身任有待研究。从上述步骤中我们看出 Peano 公理每一条公理都被使用过，少了任何一条都不足以构建出上述的自然数系统，这究竟是为什么呢？\",\"下面我将阐述为什么每条公理都是必须的，通过举反例的方式。研究 Peano 公理自然不能从 Peano 公理系统内出发，我们将借助另一个公理系统——图论。\"]},\"83\":{\"h\":\"乘法保序性\",\"t\":[\"若 ，则 。\",\"由 有 ，进而 因此 。\"]},\"84\":{\"h\":\"乘法消去保序性\",\"t\":[\"若 ，则 。\",\"采用反证法，假设 ，则存在正自然数 满足 ，有\",\"由此有 ，根据序的反对称性有 ，根据乘法消去律有 ，这与 的假设矛盾，因此假设不成立，即证明了乘法消去的保序性。\"]},\"85\":{\"h\":\"用图论阐述 Peano 系统\",\"t\":[\"自然数与有向图 同构，这个图满足如下性质：\",\"存在点 ，即 ；\",\"所有点的出度为 ，即 ；\",\"点 入度为 ，即 ；\",\"任意点的入度小于等于 ，即 ；\",\"存在从 到任意点的路径，即 。\",\"下面我们试着通过删除公理的方法来寻找反例。\"]},\"86\":{\"h\":\"Peano 公理 Ⅰ\",\"t\":[\"若去除，则允许不存在 ，可以构造出空集自然数系统。\"]},\"87\":{\"h\":\"Peano 公理 Ⅱ\",\"t\":[\"若去除，则对点的出度无规定，可以构造出菊花图自然数系统。\"]},\"88\":{\"h\":\"Peano 公理 Ⅲ\",\"t\":[\"若去除，则对 的入度无规定，可以构造出环状自然数系统。\"]},\"89\":{\"h\":\"Peano 公理 Ⅳ\",\"t\":[\"若去除，则对一个数可以是多个数的后继，可以构造出 状自然数系统。\"]},\"90\":{\"h\":\"Peano 公理 Ⅴ\",\"t\":[\"若去除，则对连通性无要求，可以构造出分段状自然数系统。\"]},\"91\":{\"c\":[\"数学\"]},\"92\":{\"c\":[\"公理系统\"]},\"93\":{\"h\":\"使用capacitor和ionic将vue项目迁移到mobile端\",\"t\":[\"当我们写完了vue项目后，想做一个一样的移动app，此时我们可以使用ionic无缝将其迁移到移动端。\"]},\"94\":{\"h\":\"安装\",\"t\":[\"Capacitor\",\"ionic\"]},\"95\":{\"h\":\"tips\",\"t\":[\"deploy\",\"每次执行更新你的 Web 目录的构建（例如 ionic build）时（默认：build)，你需要将这些更改复制到你的原生项目中：\",\"ionic cap copy\",\"注意：更新代码的原生部分（例如添加新插件）后，使用 sync 命令：\",\"ionic cap sync \",\"相关信息\",\"vscode中可以使用\\\"ionic\\\"插件\",\"默认不支持HTTP\",\"const config: CapacitorConfig = { plugins:{ CapacitorHttp:{ enabled:true, } }, android:{ allowMixedContent: true, } }; \"]},\"96\":{\"h\":\"bug 记录\",\"t\":[\"使用 vscode ionic打包后的相对路径不正确， 手动修改后可正常运行\",\"重要\",\"用Android Studio时不能打开360手机助手，会和ADB冲突\"]},\"97\":{\"c\":[\"mobile\"]},\"98\":{\"h\":\"并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3\",\"t\":[\"原文转载自「刘悦的技术博客」https://v3u.cn/a_id_208\",\"协程与线程向来焦孟不离，但事实上是，线程更被我们所熟知，在Python编程领域，单核同时间内只能有一个线程运行，这并不是什么缺陷，这实际上是符合客观逻辑的，单核处理器本来就没法同时处理两件事情，要同时进行多件事情本来就需要正在运行的让出处理器，然后才能去处理另一件事情，左手画方右手画圆在现实中本来就不成立，只不过这个让出的过程是线程调度器主动抢占的。\"]},\"99\":{\"h\":\"线程安全\",\"t\":[\"系统的线程调度器是假设不同的线程是毫无关系的，所以它平均地分配时间片让处理器一视同仁，雨露均沾。但是Python受限于GIL全局解释器锁，任何Python线程执行前，必须先获得GIL锁，然后，每执行100条字节码，解释器就自动释放GIL锁，让别的线程有机会执行。这个GIL全局解释器锁实际上把所有线程的执行代码都给上了锁，所以，多线程在Python中只能交替执行，即使多个线程跑在8核处理上，也只能用到1个核。\",\"但其实，这并不是事情的全貌，就算只能用单核处理任务，多个线程之前也并不是完全独立的，它们会操作同一个资源。于是，大家又发明了同步锁，使得一段时间内只有一个线程可以操作这个资源，其他线程只能等待：\",\"import threading balance = 0 def change_it_without_lock(n): global balance # 不加锁的话 最后的值不是0 # 线程共享数据危险在于 多个线程同时改同一个变量 # 如果每个线程按顺序执行，那么值会是0， 但是线程时系统调度，又不确定性，交替进行 # 没锁的话，同时修改变量 # 所以加锁是为了同时只有一个线程再修改，别的线程表一定不能改 for i in range(1000000): balance = balance + n balance = balance - n def change_it_with_lock(n): global balance if lock.acquire(): try: for i in range(1000000): balance = balance + n balance = balance - n # 这里的finally 防止中途出错了，也能释放锁 finally: lock.release() threads = [ threading.Thread(target=change_it_with_lock, args=(8, )), threading.Thread(target=change_it_with_lock, args=(10, )) ] lock = threading.Lock() [t.start() for t in threads] [t.join() for t in threads] print(balance) \",\"这种异步编程方式被广大开发者所认可，线程并不安全，线程操作共享资源需要加锁。然而人们很快发现，这种处理方式是在画蛇添足，处理器本来同一时间就只能有一个线程在运行。是线程调度器抢占划分时间片给其他线程跑，而现在，多了把锁，其他线程又说我拿不到锁，我得拿到锁才能操作。\",\"就像以前的公共电话亭，本来就只能一个人打电话，现在电话亭上加了把锁，还是只能一个人打电话，而有没有锁，有什么区别呢？所以，问题到底出在哪儿？\",\"事实上，在所有线程相互独立且不会操作同一资源的模式下，抢占式的线程调度器是非常不错的选择，因为它可以保证所有的线程都可以被分到时间片不被垃圾代码所拖累。而如果操作同一资源，抢占式的线程就不那么让人愉快了。\"]},\"100\":{\"h\":\"协程\",\"t\":[\"过了一段时间，人们发现经常需要异步操作共享资源的情况下，主动让出时间片的协程模式比线程抢占式分配的效率要好，也更简单。\",\"从实际开发角度看，与线程相比，这种主动让出型的调度方式更为高效。一方面，它让调用者自己来决定什么时候让出，比操作系统的抢占式调度所需要的时间代价要小很多。后者为了能恢复现场会在切换线程时保存相当多的状态，并且会非常频繁地进行切换。另一方面，协程本身可以做成用户态，每个协程的体积比线程要小得多，因此一个进程可以容纳数量相当可观的协程任务。\",\"import asyncio balance = 0 async def change_it_without_lock(n): global balance balance = balance + n balance = balance - n loop = asyncio.get_event_loop() res = loop.run_until_complete( asyncio.gather(change_it_without_lock(10), change_it_without_lock(8), change_it_without_lock(2), change_it_without_lock(7))) print(balance) \",\"从代码结构上看，协程保证了编写过程中的思维连贯性，使得函数（闭包）体本身就无缝保持了程序状态。逻辑紧凑，可读性高，不易写出错的代码，可调试性强。\",\"但归根结底，单核处理器还是同时间只能做一件事，所以同一时间点还是只能有一个协程任务运行，它和线程的最主要差别就是，协程是主动让出使用权，而线程是抢占使用权，即所谓的，协程是用户态，线程是系统态。\",\"img\",\"同时，如图所示，协程本身就是单线程的，即不会触发系统的全局解释器锁(GIL)，同时也不需要系统的线程调度器参与抢占式的调度，避免了多线程的上下文切换，所以它的性能要比多线程好。\"]},\"101\":{\"h\":\"协程安全\",\"t\":[\"回到并发竞争带来的安全问题上，既然同一时间只能有一个协程任务运行，并且协程切换并不是系统态抢占式，那么协程一定是安全的：\",\"import asyncio balance = 0 async def change_it_without_lock(n): global balance balance = balance + n balance = balance - n print(balance) loop = asyncio.get_event_loop() res = loop.run_until_complete( asyncio.gather(change_it_without_lock(10), change_it_without_lock(8), change_it_without_lock(2), change_it_without_lock(7))) print(balance) \",\"运行结果：\",\"0 0 0 0 0 liuyue:as-master liuyue$ \",\"看起来是这样的，无论是执行过程中，还是最后执行结果，都保证了其状态的一致性。\",\"于是，协程操作共享变量不需要加锁的结论开始在坊间流传。\",\"毫无疑问，谁主张，谁举证，上面的代码也充分说明了这个结论的正确性，然而我们都忽略了一个客观事实，那就是代码中没有“主动让出使用权”的操作，所谓主动让出使用权，即用户主动触发协程切换，那到底怎么主动让出使用权？使用 await 关键字。\",\"await 是 Python 3.5版本开始引入了新的关键字，即Python3.4版本的yield from，它能做什么？它可以在协程内部用await调用另一个协程实现异步操作，或者说的更简单一点，它可以挂起当前协程任务，去手动异步执行另一个协程，这就是主动让出“使用权”：\",\"async def hello(): print(\\\"Hello world!\\\") r = await asyncio.sleep(1) print(\\\"Hello again!\\\") \",\"当我们执行第一句代码print(\\\"Hello world!\\\")之后，使用await关键字让出使用权，也可以理解为把程序“暂时”挂起，此时使用权让出以后，别的协程就可以进行执行，随后当我们让出使用权1秒之后，当别的协程任务执行完毕，又或者别的协程任务也“主动”让出了使用权，协程又可以切回来，继续执行我们当前的任务，也就是第二行代码print(\\\"Hello again!\\\")。\",\"了解了协程如何主动切换，让我们继续之前的逻辑：\",\"import asyncio balance = 0 async def change_it_without_lock(n): global balance balance = balance + n await asyncio.sleep(1) balance = balance - n print(balance) loop = asyncio.get_event_loop() res = loop.run_until_complete( asyncio.gather(change_it_without_lock(10), change_it_without_lock(8), change_it_without_lock(2), change_it_without_lock(7))) print(balance) \",\"逻辑有了些许修改，当我对全局变量balance进行加法运算后，主动释放使用权，让别的协程运行，随后立刻切换回来，再进行减法运算，如此往复，同时开启四个协程任务，让我们来看一下代码运行结果：\",\"17 9 7 0 0 liuyue:mytornado liuyue$ \",\"可以看到，协程运行过程中，并没有保证“状态一致”，也就是一旦通过await关键字切换协程，变量的状态并不会进行同步，从而导致执行过程中变量状态的“混乱状态”，但是所有协程执行完毕后，变量balance的最终结果是0，意味着协程操作变量的最终一致性是可以保证的。\",\"为了对比，我们再用多线程试一下同样的逻辑：\",\"import threading import time balance = 0 def change_it_without_lock(n): global balance for i in range(1000000): balance = balance + n balance = balance - n print(balance) threads = [ threading.Thread(target=change_it_without_lock, args=(8, )), threading.Thread(target=change_it_without_lock, args=(10, )), threading.Thread(target=change_it_without_lock, args=(10, )), threading.Thread(target=change_it_without_lock, args=(8, )) ] [t.start() for t in threads] [t.join() for t in threads] print(balance) \",\"多线程逻辑执行结果：\",\"liuyue:mytornado liuyue$ python3 \\\"/Users/liuyue/wodfan/work/mytornado/test.py\\\" 28 18 10 0 8 \",\"可以看到，多线程在未加锁的情况下，连最终一致性也无法保证，因为线程是系统态切换，虽然同时只能有一个线程执行，但切换过程是争抢的，也就会导致写操作被原子性覆盖，而协程虽然在手动切换过程中也无法保证状态一致，但是可以保证最终一致性呢？因为协程是用户态，切换过程是协作的，所以写操作不会被争抢覆盖，会被顺序执行，所以肯定可以保证最终一致性。\",\"协程在工作状态中，主动切换了使用权，而我们又想在执行过程中保证共享数据的强一致性，该怎么办？毫无疑问，还是只能加锁：\",\"import asyncio balance = 0 async def change_it_with_lock(n): async with lock: global balance balance = balance + n await asyncio.sleep(1) balance = balance - n print(balance) lock = asyncio.Lock() loop = asyncio.get_event_loop() res = loop.run_until_complete( asyncio.gather(change_it_with_lock(10), change_it_with_lock(8), change_it_with_lock(2), change_it_with_lock(7))) print(balance) \",\"协程加锁执行后结果：\",\"liuyue:mytornado liuyue$ python3 \\\"/Users/liuyue/wodfan/work/mytornado/test.py\\\" 0 0 0 0 0 \",\"是的，无论是结果，还是过程中，都保持了其一致性，但是我们也付出了相应的代价，那就是任务又回到了线性同步执行，再也没有异步的加持了。话说回来，世界上的事情本来就是这样，本来就没有两全其美的解决方案，又要共享状态，又想多协程，还想变量安全，这可能吗？\"]},\"102\":{\"h\":\"协程是否需要加锁\",\"t\":[\"结论当然就是看使用场景，如果协程在操作共享变量的过程中，没有主动放弃执行权(await)，也就是没有切换挂起状态，那就不需要加锁，执行过程本身就是安全的；可是如果在执行事务逻辑块中主动放弃执行权了，会分两种情况，如果在逻辑执行过程中我们需要判断变量状态，或者执行过程中要根据变量状态进行一些下游操作，则必须加锁，如果我们不关注执行过程中的状态，只关注最终结果一致性，则不需要加锁。是的，抛开剂量谈毒性，是不客观的，给一个健康的人注射吗啡是犯罪，但是给一个垂死的人注射吗啡，那就是最大的道德，所以说，道德不是空泛的，脱离对象孤立存在的，同理，抛开场景谈逻辑，也是不客观的，协程也不是虚空的，脱离具体场景孤立存在的，我们应该养成具体问题具体分析的辩证唯物思想，只有掌握了辩证的矛盾思维才能更全面更灵活的看待问题，才能透过现象，把握本质。\",\"原文转载自「刘悦的技术博客」 https://v3u.cn/a_id_208\"]},\"103\":{\"h\":\"协程\",\"t\":[\"文档\",\"重要\",\"TODO\"]},\"104\":{\"h\":\"Slidev\",\"t\":[\"复杂演示推荐\"]},\"105\":{\"h\":\"缺点\",\"t\":[\"不支持导出pptx\",\"https://cn.sli.dev/guide\",\"简单PPT,且需要导出为pptx推荐\"]},\"106\":{\"h\":\"缺点\",\"t\":[\"不支持动画\",\"https://sspai.com/post/55718\",\"https://segmentfault.com/a/1190000040806239\",\"⚠️注意事项\\n如果你的 VS Code 安装了 Markdown 渲染插件 Markdown Preview Enhanced，需要先将这个插件「禁用」或是「卸载」，转而使用 VS Code 后来集成的 Markdown 预览功能，才能正常看到渲染后的 PPT 页面。\"]},\"107\":{\"h\":\"闭包实现类\",\"t\":[\"你是否曾经想过，不用类也能封装数据和方法？这篇文章将带你走进闭包的奇妙世界，展示如何用闭包来实现这一点。通过一个有趣的代码示例，你将看到闭包是如何捕获变量并提供类似类的功能的。准备好了吗？让我们开始这段有趣的旅程吧！\",\"alt text\"]},\"108\":{\"c\":[\"OI\"]},\"109\":{\"c\":[\"MODInt\"]},\"110\":{\"h\":\"教程\",\"t\":[\"这里是所有详细的教程和指南。\"]},\"111\":{\"h\":\"Typora激活教程\",\"t\":[\"Typora 是一款简洁高效的 Markdown 编辑器，支持实时预览和多种导出格式，适用于编写笔记、文档和博客等。\",\"Typora 官网\",\"Typora 中文官网\",\"工具下载：百度网盘，密码：dcqe\",\"一路点击“下一步”进行安装。将下载的工具解压后得到的两个 exe 文件（license-gen.exe 和 node_inject.exe）复制到 Typora 安装目录下（默认为 C:\\\\Program Files\\\\Typora\\\\）。\",\"以管理员身份在 Typora 安装路径打开 PowerShell。\",\"输入 node_inject.exe 并回车，等待提示 \\\"done!\\\"。\",\"输入 license-gen.exe 并回车，等待显示序列号。\",\"启动 Typora，输入任意邮箱和刚才生成的序列号到激活窗口，并点击激活。\",\"通过上述步骤，您可以免费安装并使用 Typora，但如有条件还请支持正版。\"]},\"112\":{\"h\":\"html 转 md 工具\",\"t\":[\"https://github.com/mixmark-io/turndown\",\"https://github.com/aaronsw/html2text\"]},\"113\":{\"h\":\"设计模式七大原则\",\"t\":[\"类的设计原则有七个，包括：开闭原则、里氏代换原则、迪米特原则（最少知道原则）、单一职责原则、接口分隔原则、依赖倒置原则、组合/聚合复用原则。\"]},\"114\":{\"h\":\"关系\",\"t\":[\"七大原则之间并不是相互孤立的，而是相互关联的。一个原则可以是另一个原则的加强或基础。违反其中一个原则，可能同时违反其他原则。\",\"开闭原则是面向对象可复用设计的基石，其他设计原则是实现开闭原则的手段和工具。\",\"通常，可以将这七个原则分为以下两部分：\",\"设计目标：开闭原则、里氏代换原则、迪米特原则\",\"设计方法：单一职责原则、接口分隔原则、依赖倒置原则、组合/聚合复用原则\"]},\"115\":{\"h\":\"开闭原则\",\"t\":[\"对扩展开放\",\"对修改关闭\",\"根据开闭原则，在设计一个系统模块的时候，应该可以在不修改原模块的基础上，扩展其功能。\"]},\"116\":{\"h\":\"实现方法\",\"t\":[\"使用抽象类和接口：通过定义抽象类和接口，可以在不修改现有代码的情况下，增加新的实现。\",\"使用设计模式：例如策略模式、装饰者模式等，可以在不改变原有代码的情况下，动态地扩展对象的行为。\",\"遵循单一职责原则：确保每个类只有一个职责，这样在扩展功能时，不会影响其他功能。\"]},\"117\":{\"h\":\"里氏代换原则\"},\"118\":{\"h\":\"里氏代换原则\",\"t\":[\"里氏代换原则规定子类不得重写父类的普通方法，只能重写父类的抽象方法；即子类可以扩展父类的功能，但是不能改变父类原有的功能。\",\"派生类应当可以替换基类并出现在基类能够出现的任何地方，或者说如果我们把代码中使用基类的地方用它的派生类所代替，代码还能正常工作。\"]},\"119\":{\"h\":\"实现方法\",\"t\":[\"使用抽象类和接口：确保子类实现父类的抽象方法，而不是重写父类的具体方法。\",\"遵循契约：子类的方法签名应与父类一致，返回类型应与父类相同或是其子类型。\",\"遵循行为一致性：子类应保持父类的行为，不应引入违反父类预期的新行为。\"]},\"120\":{\"h\":\"示例\"},\"121\":{\"h\":\"迪米特原则\"},\"122\":{\"h\":\"迪米特原则\",\"t\":[\"一个实体应当尽量少地与其他实体之间发生相互作用，使得系统功能模块相对独立；降低类之间的耦合度，提高模块的相对独立性。\"]},\"123\":{\"h\":\"实现方法\",\"t\":[\"引入中介者模式：通过中介者对象来管理对象之间的交互，减少对象之间的直接依赖。\",\"使用门面模式：通过门面对象提供统一的接口，隐藏系统的复杂性，减少对象之间的直接交互。\",\"限制公开方法：尽量减少类的公开方法，避免不必要的外部依赖。\"]},\"124\":{\"h\":\"单一职责原则\",\"t\":[\"一个类只对应一个职责，其职责是引起该类变化的原因。\",\"如果一个类需要改变，改变它的理由永远只有一个。如果存在多个改变它的理由，就需要重新设计该类。\"]},\"125\":{\"h\":\"实现方法\",\"t\":[\"职责分离：将不同的职责分离到不同的类中，每个类只负责一个职责。\",\"模块化设计：通过模块化设计，将不同的功能模块分开，确保每个模块只负责一个功能。\",\"重构：在发现类有多个职责时，及时进行重构，将不同的职责分离到不同的类中。\"]},\"126\":{\"h\":\"示例\",\"t\":[\"// 不符合单一职责原则的类 class User { login() { // 登录逻辑 } register() { // 注册逻辑 } displayProfile() { // 显示用户信息逻辑 } } // 符合单一职责原则的类 class AuthService { login() { // 登录逻辑 } register() { // 注册逻辑 } } class UserProfile { displayProfile() { // 显示用户信息逻辑 } } \"]},\"127\":{\"h\":\"接口隔离原则\",\"t\":[\"不应强迫用户依赖他们不使用的接口。\",\"一个类对另一个类的依赖应该建立在最小的接口上。\",\"简单来说，使用多个专门的接口比使用单个通用接口要好得多。\"]},\"128\":{\"h\":\"依赖倒置原则\",\"t\":[\"高层模块不应该依赖低层模块，二者都应该依赖其抽象。抽象不应该依赖细节，细节应该依赖抽象。核心思想是：面向接口编程，而不是面向实现编程。\"]},\"129\":{\"h\":\"实现方法\",\"t\":[\"使用接口和抽象类：定义接口或抽象类，让高层模块依赖这些抽象，而不是具体实现。\",\"依赖注入：通过构造函数注入、属性注入或方法注入，将具体实现传递给高层模块。\",\"工厂模式：使用工厂模式创建对象，避免高层模块直接依赖具体类。\"]},\"130\":{\"h\":\"示例\",\"t\":[\"// 定义抽象接口 interface IWorker { work(): void; } // 具体实现 class Worker implements IWorker { work() { console.log(\\\"Working...\\\"); } } // 高层模块依赖抽象接口 class Manager { private worker: IWorker; constructor(worker: IWorker) { this.worker = worker; } manage() { this.worker.work(); } } // 使用依赖注入 const worker = new Worker(); const manager = new Manager(worker); manager.manage(); \"]},\"131\":{\"h\":\"组合/聚合复用原则\",\"t\":[\"尽量使用组合/聚合，不要使用类继承。\",\"如果使用继承，会导致父类的任何变换都可能影响到子类的行为，所以优先使用组合的方式代替继承的方式。\"]},\"132\":{\"h\":\"实现方法\",\"t\":[\"使用组合：通过在类中包含其他类的实例来实现功能，而不是通过继承。\",\"使用聚合：通过在类中引用其他类的实例来实现功能，而不是通过继承。\",\"接口和抽象类：通过接口和抽象类定义行为，然后在具体类中实现这些行为。\"]},\"133\":{\"h\":\"示例\",\"t\":[\"// 使用继承的方式 class Engine { start() { console.log(\\\"Engine started\\\"); } } class Car extends Engine { drive() { this.start(); console.log(\\\"Car is driving\\\"); } } // 使用组合的方式 class Engine { start() { console.log(\\\"Engine started\\\"); } } class Car { private engine: Engine; constructor(engine: Engine) { this.engine = engine; } drive() { this.engine.start(); console.log(\\\"Car is driving\\\"); } } const engine = new Engine(); const car = new Car(engine); car.drive(); \"]},\"134\":{\"h\":\"总结\",\"t\":[\"开闭原则：对扩展开放，对修改关闭。\",\"里氏代换原则：子类可以替换父类，且程序行为不变。\",\"迪米特原则：尽量减少类之间的耦合。\",\"单一职责原则：一个类只负责一个职责。\",\"接口隔离原则：使用多个专门的接口，而不是一个通用接口。\",\"依赖倒置原则：高层模块不依赖低层模块，二者都依赖抽象。\",\"组合/聚合复用原则：优先使用组合/聚合，而不是继承。\"]},\"135\":{\"c\":[\"设计模式\"]},\"136\":{\"c\":[\"设计模式\",\"typescript\"]},\"137\":{\"h\":\"抽象工厂模式\"},\"138\":{\"h\":\"为什么要使用抽象工厂模式\",\"t\":[\"抽象工厂模式提供一个接口，用于创建相关或依赖对象的家族，而无需明确指定具体类。它通过定义一个创建对象的接口来实现，这样子类可以决定实例化哪个类。抽象工厂模式使得一个类的实例化延迟到其子类。\",\"解耦：抽象工厂模式通过将对象的创建过程抽象化，减少了客户端代码与具体类之间的耦合。\",\"一致性：确保同一工厂创建的一系列对象具有一致的接口和行为。\",\"扩展性：可以方便地增加新的产品族而不影响现有代码。\"]},\"139\":{\"h\":\"示例代码\",\"t\":[\"// factory.ts // 抽象工厂 import { Link } from './link'; import { Tray } from './tray'; import { Page } from './page'; export abstract class Factory { abstract createLink(caption: string, url: string): Link; abstract createTray(caption: string): Tray; abstract createPage(title: string, author: string): Page; } // item.ts // 抽象零件 export abstract class Item { protected caption: string; constructor(caption: string) { this.caption = caption; } abstract makeHTML(): string; } // link.ts // 抽象超链接 import { Item } from './item'; export abstract class Link extends Item { protected url: string; constructor(caption: string, url: string) { super(caption); this.url = url; } } // listFactory.ts import { Factory } from './factory'; import { ListLink } from './listLink'; import { ListTray } from './listTray'; import { ListPage } from './listPage'; export class ListFactory extends Factory { createLink(caption: string, url: string) { return new ListLink(caption, url); } createTray(caption: string) { return new ListTray(caption); } createPage(title: string, author: string) { return new ListPage(title, author); } } // listLink.ts import { Link } from './link'; export class ListLink extends Link { constructor(caption: string, url: string) { super(caption, url); } makeHTML() { return `<li><a href=\\\"${this.url}\\\">${this.caption}</a></li>\\\\n`; } } // listPage.ts import { Page } from './page'; export class ListPage extends Page { makeHTML() { let buffer = []; buffer.push(`<html><head><title>${this.title}</title></head>`); buffer.push(`<body>`); buffer.push(`<h1>${this.title}</h1>`); buffer.push(`<ul>`); this.content.forEach(item => { buffer.push(item.makeHTML()); }); buffer.push(`</ul>`); buffer.push(`<hr><address>${this.author}</address>`); buffer.push(`</body></html>`); return buffer.join('\\\\n'); } } // listTray.ts import { Tray } from \\\"./tray\\\"; export class ListTray extends Tray { constructor(caption: string) { super(caption); } makeHTML() { let buffer = []; buffer.push(\\\"<li>\\\\n\\\"); buffer.push(this.caption + \\\"\\\\n\\\"); buffer.push(\\\"<ul>\\\\n\\\"); this.tray.forEach(item => { buffer.push(item.makeHTML()); }); buffer.push(\\\"</ul>\\\\n\\\"); buffer.push(\\\"</li>\\\\n\\\"); return buffer.join(\\\"\\\"); } } // main.ts import { Factory } from \\\"./factory\\\"; import { ListFactory } from \\\"./listFactory\\\"; function getProduct(factory: Factory) { let people = factory.createLink(\\\"people\\\", \\\"http://www.people.com\\\"); let gmw = factory.createLink(\\\"gmw\\\", \\\"http://www.gmw.com\\\"); let us_yahoo = factory.createLink(\\\"us_yahoo\\\", \\\"http://www.us.yahoo.com\\\"); let jp_yahoo = factory.createLink(\\\"jp_yahoo\\\", \\\"http://www.jp.yahoo.com\\\"); let excite = factory.createLink(\\\"excite\\\", \\\"http://www.excite.com\\\"); let google = factory.createLink(\\\"google\\\", \\\"http://www.google.com\\\"); let traynews = factory.createTray(\\\"news\\\"); traynews.add(people); traynews.add(gmw); let trayyahoo = factory.createTray(\\\"yahoo\\\"); trayyahoo.add(us_yahoo); trayyahoo.add(jp_yahoo); let traysearch = factory.createTray(\\\"search\\\"); traysearch.add(trayyahoo); traysearch.add(excite); let page = factory.createPage(\\\"LinkPage\\\", \\\"gmw\\\"); page.add(traynews); page.add(traysearch); page.output(); } let factory = new ListFactory(); getProduct(factory); // page.ts // 抽象html页面 import { Item } from './item'; export abstract class Page { title: string; author: string; content: Array<Item>; buffer: string; constructor(title: string, author: string) { this.title = title; this.author = author; this.content = []; } add(item: Item): void { this.content.push(item); } output(): void { try { this.buffer = this.makeHTML(); console.log(this.buffer); } catch (error) { console.log(error); } } abstract makeHTML(): string; } // tray.ts // 抽象容器 import { Item } from './item'; export abstract class Tray extends Item { protected tray: Item[] = []; constructor(caption: string) { super(caption); } public add(item: Item): void { this.tray.push(item); } } \",\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\abstractFactory\\\\main.ts\\\" <html><head><title>LinkPage</title></head> <body> <h1>LinkPage</h1> <ul> <li> news <ul> <li><a href=\\\"http://www.people.com\\\">people</a></li> <li><a href=\\\"http://www.gmw.com\\\">gmw</a></li> </ul> </li> <li> search <ul> <li> yahoo <ul> <li><a href=\\\"http://www.us.yahoo.com\\\">us_yahoo</a></li> <li><a href=\\\"http://www.jp.yahoo.com\\\">jp_yahoo</a></li> </ul> </li> <li><a href=\\\"http://www.excite.com\\\">excite</a></li> </ul> </li> </ul> <hr><address>gmw</address> </body></html> \"]},\"140\":{\"h\":\"增加其它工厂\",\"t\":[\"如果只是为了编写包含 HTML 超链接集合的文件，这样的设计可能显得有些过于复杂。当只有一个具体工厂时，划分“抽象类”和“具体类”是没有必要的。然而，使用抽象工厂模式，我们可以轻松地添加其他具体工厂，例如TableFactory。\"]},\"141\":{\"h\":\"拓展思路的要点\"},\"142\":{\"h\":\"易于增加具体工厂\",\"t\":[\"在 Abstract Factory 模式中增加具体的工厂是非常容易的。这里说的“容易”指的是需要编写哪些类和需要实现哪些方法都非常清楚。\",\"假设现在我们要在示例程序中增加新的具体工厂，那么需要做的就是编写 Factory、Link、Tray、Page 这 4 个类的子类，并实现它们定义的抽象方法。也就是说将 factory 包中的抽象部分全部具体化即可。\",\"这样一来，无论要增加多少个具体工厂（或是要修改具体工厂的 Bug），都无需修改抽象工厂和 Main 部分。\"]},\"143\":{\"h\":\"难以增加新的零件\",\"t\":[\"请试想一下要在 Abstract Factory 模式中增加新的零件时应当如何做。例如，我们要在 factory 包中增加一个表示图像的 Picture 零件。这时，我们必须要对所有的具体工厂进行相应的修改才行。例如，在 listfactory 包中，我们必须要做以下修改：\",\"在 ListFactory 中增加 createPicture 方法，\",\"新增 ListPicture 类。\",\"已经编写完成的具体工厂越多，修改的工作量就会越大。\"]},\"144\":{\"h\":\"相关的设计模式\",\"t\":[\"Builder 模式\",\"Factory Method 模式\",\"Composite 模式\",\"Singleton 模式\"]},\"145\":{\"c\":[\"设计模式\"]},\"146\":{\"c\":[\"设计模式\",\"typescript\",\"生成实例\"]},\"147\":{\"h\":\"适配器模式\"},\"148\":{\"h\":\"适配器模式\",\"t\":[\"适配器模式（Adapter Pattern）是一种结构型设计模式，它允许将一个类的接口转换成客户希望的另一个接口。适配器模式使得原本由于接口不兼容而不能一起工作的那些类可以一起工作。\"]},\"149\":{\"h\":\"为什么要用适配器模式\",\"t\":[\"在软件开发中，经常会遇到需要使用一些现有的类，但它们的接口并不符合当前系统的需求。适配器模式通过创建一个适配器类，将现有类的接口转换为所需的接口，从而使得现有类可以在新的环境中使用。\"]},\"150\":{\"h\":\"类比\"},\"151\":{\"h\":\"类比\",\"t\":[\"比喻\",\"示例程序\",\"实际需求\",\"交流100V\",\"Banner\",\"变换装置\",\"适配器\",\"PrintBanner\",\"需求\",\"直流12V\",\"Print\"]},\"152\":{\"h\":\"示例程序\",\"t\":[\"Adapter 有两种方式实现\",\"// banner.ts export class Banner { private string: string; constructor(string: string) { this.string = string; } showWithParen(): void { console.log(`(${this.string})`); } showWithAster(): void { console.log(`*${this.string}*`); } } // print_inheritance.ts export interface Print { printWeak(): void; printStrong(): void; } // printBanner_inheritance.ts import { Banner } from './banner'; import { Print } from './print_inheritance'; export class PrintBanner extends Banner implements Print { constructor(string: string) { super(string); } printWeak(): void { this.showWithParen(); } printStrong(): void { this.showWithAster(); } } // print_delegation.ts export abstract class Print { abstract printWeak(): void; abstract printStrong(): void; } // printBanner_delegation.ts import { Print } from \\\"./print_delegation\\\"; import { Banner } from \\\"./banner\\\"; export class PrintBanner extends Print { private banner: Banner; constructor(string: string) { super(); this.banner = new Banner(string); } printWeak(): void { this.banner.showWithParen(); } printStrong(): void { this.banner.showWithAster(); } } // main.ts import { PrintBanner as pbi } from './printBanner_inheritance'; import { PrintBanner as pbd } from './printBanner_delegation'; // 使用继承 const printBanner = new pbi('Hello'); printBanner.printWeak(); printBanner.printStrong(); // 使用委托 const printBanner2 = new pbd('Hello'); printBanner2.printWeak(); printBanner2.printStrong(); \"]},\"153\":{\"h\":\"运行结果\",\"t\":[\"ts-node \\\"d:\\\\code\\\\design_pattern\\\\src\\\\adapter\\\\main.ts\\\" (Hello) *Hello* (Hello) *Hello* \"]},\"154\":{\"h\":\"相关的设计模式\",\"t\":[\"Bridge\",\"Decorator\"]},\"155\":{\"c\":[\"设计模式\"]},\"156\":{\"c\":[\"设计模式\",\"typescript\"]},\"157\":{\"h\":\"Bridge 模式\",\"t\":[\"Bridge 模式在“类的功能层次结构”和“类的实现层次结构”之间搭建桥梁。\"]},\"158\":{\"h\":\"使用此设计模式的理由\",\"t\":[\"Bridge 模式的主要目的是将抽象部分与实现部分分离，使它们可以独立变化。这种模式通过组合而不是继承来实现功能的扩展，减少了类之间的耦合度，提高了系统的可扩展性和可维护性。\"]},\"159\":{\"h\":\"类的层次结构的两个作用\"},\"160\":{\"h\":\"增加新功能时\",\"t\":[\"假设现在有一个类 Something，当我们想在 Something 中增加新功能时（例如增加一个具体方法），会编写一个 Something 类的子类（派生类），即 SomethingGood 类。这样就构成了一个小小的类层次结构。这就是为了增加新功能而产生的层次结构。\",\"SomeThing\",\"----\\\\ SomeThingGood\"]},\"161\":{\"h\":\"增加新的实现时\",\"t\":[\"在 Template Method 模式（第 3 章）中，我们学习了抽象类的作用。抽象类声明了一些抽象方法，定义了接口 (API)，然后子类负责实现这些抽象方法。父类的任务是通过声明抽象方法的方式定义接口 (API)，而子类的任务是实现抽象方法。正是由于父类和子类的这种任务分担，我们才可以编写出具有高可替换性的类。\",\"这里其实也存在层次结构。例如，当子类实现了父类 AbstractClass 类的抽象方法时，它们之间就构成了一个小小的层次结构。\",\"AbstractClass\",\"----\\\\ ConcreteClass\",\"但是，这里的类的层次结构并非用于增加功能，也就是说，这种层次结构并非用于方便我们增加新的方法。它的真正作用是帮助我们实现任务分担。\"]},\"162\":{\"h\":\"类的层次结构的混杂和分离\",\"t\":[\"当我们想要编写子类时，就需要先确认自己的意图：“我是要增加功能呢？还是要增加实现呢？”\",\"当类的层次结构只有一层时，功能层次结构与实现层次结构是混杂在一个层次结构中的。这样很容易使类的层次结构变得复杂，也难以透彻地理解类的层次结构。因为自己难以确定究竟应该在类的哪一个层次结构中去增加子类。\",\"因此，我们需要将“类的功能层次结构\\\"与“类的实现层次结构\\\"分离为两个独立的类层次结构。当然，如果只是简单地将它们分开，两者之间必然会缺少联系。所以我们还需要在它们之间搭建一座桥梁。本章中要学习的 Bridge 模式的作用就是搭建这座桥梁。\"]},\"163\":{\"h\":\"示例代码\"},\"164\":{\"h\":\"类的一览表\",\"t\":[\"在桥的哪一侧\",\"名字\",\"说明\",\"类的功能层次结构\",\"Display\",\"负责“显示”的类\",\"类的功能层次结构\",\"CountDisplay\",\"增加了“只显示规定次数”这一功能的类\",\"类的实现层次结构\",\"DisplayImpl\",\"负责“显示”的类\",\"类的实现层次结构\",\"StringDisplayImpl\",\"“用字符串显示”的类\",\"主程序\",\"Main\",\"试程序行为的类\",\"Display 类（代码清单 9 · 1 ）的功能是抽象的，负责“显示一些东西\\\"。该类位于“类的功能层次结构\\\"的最上层。在 impl 字段中保存的是实现了 Display 类的具体功能的实例（ impl 是 implementation （实现）的缩写）。该实例通过 Display 类的构造函数被传递给 Display 类，然后保存在字段中，以供后面的处理使用（ impl 字段即是类的两个层次结构的“桥梁\\\"）。\",\"CountDisplay 类继承了 Display 类的 open、print、close 方法，并使用它们来增加这个新功能。这就是“类的功能层次结构\\\"。\"]},\"165\":{\"h\":\"countDisplay.ts\",\"t\":[\"import { Display } from './display'; import { DisplayImpl } from './displayImpl'; export class CountDisplay extends Display { constructor(impl: DisplayImpl) { super(impl); } multiDisplay(times: number) { this.open(); for (let i = 0; i < times; i++) { this.print(); } this.close(); } } \"]},\"166\":{\"h\":\"display.ts\",\"t\":[\"import { DisplayImpl } from './displayImpl'; export class Display { private impl: DisplayImpl; constructor(impl: DisplayImpl) { this.impl = impl; } open() { this.impl.rawOpen(); } print() { this.impl.rawPrint(); } close() { this.impl.rawClose(); } display() { this.open(); this.print(); this.close(); } } \"]},\"167\":{\"h\":\"displayImpl.ts\",\"t\":[\"export abstract class DisplayImpl { abstract rawOpen(): void; abstract rawPrint(): void; abstract rawClose(): void; } \"]},\"168\":{\"h\":\"main.ts\",\"t\":[\"import { Display } from './display'; import { CountDisplay } from './countDisplay'; import { StringDisplayImpl } from './stringDisplayImpl'; const d1 = new Display(new StringDisplayImpl('Hello, China.')); const d2 = new CountDisplay(new StringDisplayImpl('Hello, World.')); const d3 = new CountDisplay(new StringDisplayImpl('Hello, Universe.')); d1.display(); d2.display(); d3.multiDisplay(5); \"]},\"169\":{\"h\":\"stringDisplayImpl.ts\",\"t\":[\"import { DisplayImpl } from './displayImpl'; export class StringDisplayImpl extends DisplayImpl { private str: string; private width: number; constructor(str: string) { super(); this.str = str; this.width = str.length; } rawOpen() { this.printLine(); } rawPrint() { console.log(`|${this.str}|`); } rawClose() { this.printLine(); } private printLine() { let buffer = '+'; for (let i = 0; i < this.width; i++) { buffer += '-'; } buffer += '+'; console.log(buffer); } } \"]},\"170\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\bridge\\\\main.ts\\\" +-------------+ |Hello, China.| +-------------+ +-------------+ |Hello, World.| +-------------+ +----------------+ |Hello, Universe.| |Hello, Universe.| |Hello, Universe.| |Hello, Universe.| |Hello, Universe.| +----------------+ \"]},\"171\":{\"h\":\"拓展思路的要点\"},\"172\":{\"h\":\"分开后更容易扩展\",\"t\":[\"Bridge 模式的特征是将“类的功能层次结构\\\"与“类的实现层次结构\\\"分离开了。将类的这两个层次结构分离开有利于独立地对它们进行扩展。当想要增加功能时，只需要在“类的功能层次结构\\\"一侧增加类即可，不必对“类的实现层次结构\\\"做任何修改。而且，增加后的功能可以被“所有的实现”使用。\",\"例如，我们可以将“类的功能层次结构\\\"应用于软件所运行的操作系统上。如果我们将某个程序中依赖于操作系统的部分划分为 Windows 版、Macintosh 版、Unix 版，那么我们就可以用 Bridge 模式中的“类的实现层次结构\\\"来表现这些依赖于操作系统的部分。也就是说，我们需要编写一个定义这些操作系统的共同接口（API）的 Implementor 角色，然后编写 Windows 版、Macintosh 版、Unix 版的 3 个 ConcreteImplementor 角色。这样一来，无论在“类的功能层次结构\\\"中增加多少个功能，它们都可以工作于这 3 个操作系统上。\"]},\"173\":{\"h\":\"继承是强关联，委托是弱关联\",\"t\":[\"继承是强关联关系，但委托是弱关联关系。这是因为只有 Display 类的实例生成时，才与作为参数被传入的类构成关联。例如，在示例程序中，当 Main 类生成 Display 类和 CountDisplay 类的实例时，才将 StringDisplayImpl 的实例作为参数传递给 Display 类和 CountDisplay 类。如果我们不传递 StringDisplayImpl 类的实例，而是将其他 ConcreteImplementor 角色的实例传递给 Display 类和 CountDisplay 类，就能很容易地改变实现。这时，发生变化的代码只有 Main 类，Display 类和 DisplayImpl 类则不需要做任何修改。\"]},\"174\":{\"h\":\"相关的设计模式\",\"t\":[\"Template Method 模式\",\"Abstract Factory 模式\",\"Adapter 模式\"]},\"175\":{\"c\":[\"设计模式\"]},\"176\":{\"c\":[\"设计模式\",\"TypeScript\",\"分开考虑\"]},\"177\":{\"h\":\"builder 模式\"},\"178\":{\"h\":\"为什么要使用 Builder 模式\",\"t\":[\"Builder 模式通过将对象的构建过程与其表示分离，使得同样的构建过程可以创建不同的表示。它主要用于以下情况：\",\"复杂对象的创建：当一个对象的构建过程非常复杂时，Builder 模式可以将构建过程分解为多个步骤，使代码更易于维护和理解。\",\"不同的表示：当需要创建不同表示的对象时，Builder 模式允许使用相同的构建过程来生成不同的对象表示。\",\"代码复用：通过将构建过程封装在 Director 类中，可以在不同的上下文中重用相同的构建逻辑。\"]},\"179\":{\"h\":\"代码示例\",\"t\":[\"// builder.ts export abstract class Builder { public abstract makeTitle(title: string): void; public abstract makeString(str: string): void; public abstract makeItems(items: string[]): void; public abstract close(): void; } // director.ts import { Builder } from './builder'; export class Director { private builder: Builder; constructor(builder: Builder) { this.builder = builder; } public construct(): void { this.builder.makeTitle('问候'); this.builder.makeString('从早上到下午'); this.builder.makeItems(['早上好。', '下午好。']); this.builder.makeString('晚上'); this.builder.makeItems(['晚上好。', '晚安。', '再见。']); this.builder.close(); } } // htmlBuilder.ts import { Builder } from './builder'; export class HTMLBuilder extends Builder { private filename: string = ''; private buffer: string = ''; public makeTitle(title: string): void { this.filename = `${title}.html`; this.buffer += `<html><head><title>${title}</title></head><body>`; this.buffer += `<h1>${title}</h1>`; } public makeString(str: string): void { this.buffer += `<p>${str}</p>`; } public makeItems(items: string[]): void { this.buffer += '<ul>'; items.forEach((item) => { this.buffer += `<li>${item}</li>`; }); this.buffer += '</ul>'; } public close(): void { this.buffer += '</body></html>'; } public getResult(): string { return this.buffer; } } // textBuilder.ts import { Builder } from './builder'; export class TextBuilder extends Builder { private buffer: string = ''; public makeTitle(title: string): void { this.buffer += '==============================\\\\n'; this.buffer += `『${title}』\\\\n`; this.buffer += '\\\\n'; } public makeString(str: string): void { this.buffer += `■${str}\\\\n`; this.buffer += '\\\\n'; } public makeItems(items: string[]): void { items.forEach((item) => { this.buffer += ` ・${item}\\\\n`; }); this.buffer += '\\\\n'; } public close(): void { this.buffer += '==============================\\\\n'; } public getResult(): string { return this.buffer; } } // main.ts import { Builder } from './builder'; import { Director } from './director'; import { HTMLBuilder } from './htmlBuilder'; import { TextBuilder } from './textBuilder'; // TextBuilder console.log(\\\"Creating a text file...\\\"); const textBuilder = new TextBuilder(); const director = new Director(textBuilder); director.construct(); const result = textBuilder.getResult(); console.log(result); // HTMLBuilder console.log(\\\"Creating an HTML file...\\\"); const htmlBuilder = new HTMLBuilder(); const director2 = new Director(htmlBuilder); director2.construct(); const filename = htmlBuilder.getResult(); console.log(`${filename}が作成されました。`); \"]},\"180\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\builder\\\\main.ts\\\" Creating a text file... ============================== 『问候』 ■从早上到下午 ・早上好。 ・下午好。 ■晚上 ・晚上好。 ・晚安。 ・再见。 ============================== Creating an HTML file... <html><head><title>问候</title></head><body><h1>问候</h1><p>从早上到下午</p><ul><li>早上好。</li><li>下午好。</li></ul><p>晚上</p><ul><li>晚上好。</li><li>晚安。</li><li>再见。</li></ul></body></html>が作成されました。 \"]},\"181\":{\"h\":\"相关设计模式\",\"t\":[\"Template Method 模式\",\"Composite 模式\",\"Abstract Factory 模式\",\"Facade 模式\"]},\"182\":{\"h\":\"拓展思路的要点\"},\"183\":{\"h\":\"谁知道什么\",\"t\":[\"在面向对象编程中，“谁知道什么”是非常重要的。Builder 模式通过将对象的构建过程与其表示分离，明确了各个类的职责分工。Director 类知道如何构建复杂对象，但不知道对象的具体表示；Builder 类知道如何生成对象的具体表示，但不知道构建的具体步骤。这种职责分离使得代码更加清晰、易于维护和扩展。\",\"正是因为不知道才能够替换，正是因为可以替换，组件才具有高价。作为设计人员，我们必须时刻关汴这种“可替換性”\"]},\"184\":{\"h\":\"设计时能够决定的事情和不能决定的事情\",\"t\":[\"在设计软件时，有些事情是可以在设计阶段决定的，而有些事情则需要在运行时决定。Builder 模式通过将构建过程与表示分离，使得在设计时可以决定构建的步骤和逻辑，而具体的表示则可以在运行时灵活选择。这种设计方式提高了系统的灵活性和可扩展性。\"]},\"185\":{\"h\":\"代码的阅读方法和修改方法\",\"t\":[\"在编程时，虽然有时需要从零开始编写代码，但更多时候我们都是在现有代码的基础上进行增加和修改。\",\"这时，我们需要先阅读现有代码。不过，只是阅读抽象类的代码是无法获取很多信息的（虽然可以从方法名中获得线索）。\",\"让我们再回顾一下示例程序。即使理解了 Builder 抽象类，也无法理解程序整体。至少必须在阅读了 Director 的代码后才能理解 Builder 类的使用方法（Builder 类的方法的调用方法）。然后再去看看 TextBuilder 类和 HTMLBuilder 类的代码，就可以明白调用 Builder 类的方法后具体会进行什么样的处理。\",\"如果没有理解各个类的角色就动手增加和修改代码，在判断到底应该修改哪个类时，就会很容易出错。例如，如果修改 Builder 类，那么就会对类中调用 Builder 类方法的地方和 Builder 类的子类产生影响。或是如果不小心修改了 Director 类，在其内部调用了类的特有的方法，则会导致其失去作为可复用组件的独立性，而且当将子类替换为 HTMLBuilder 时，程序可能会无法正常工作。\"]},\"186\":{\"c\":[\"设计模式\"]},\"187\":{\"c\":[\"设计模式\",\"typescript\",\"生成实例\"]},\"188\":{\"h\":\"chainOfResponsibility 模式\",\"t\":[\"“推卸责任\\\"听起来有些贬义的意思，但是有时候也确实存在需要“推卸责任\\\"的情况。例如，当外部请求程序进行某个处理，但程序暂时无法直接决定由哪个对象负责处理时，就需要推卸责任。这种情况下，我们可以考虑将多个对象组成一条职责链，然后按照它们在职责链上的顺序一个一个地找出到底应该谁来负责处理。\",\"当一个人被要求做什么事情时，如果他可以做就自己做，如果不能做就将“要求\\\"转给另外一个人。下一个人如果可以自己处理，就自己做；如果也不能自己处理，就再转给另外一个人““这就是 Chain Of Responsibility 模式。\"]},\"189\":{\"h\":\"为什么使用此类\",\"t\":[\"使用 Chain of Responsibility 模式有以下几个优点：\",\"解耦请求发送者和接收者：发送者无需知道哪个对象会处理请求。\",\"动态组合职责链：可以在运行时动态地改变职责链的结构。\",\"增加灵活性：可以很容易地添加新的处理者而不影响现有代码。\"]},\"190\":{\"h\":\"示例代码\",\"t\":[\"在这个示例中，我们使用了 Chain of Responsibility 模式来处理一系列的请求。每个请求都会沿着职责链传递，直到有一个对象能够处理它。这样做的好处是请求的发送者和接收者解耦，发送者无需知道哪个对象会处理请求。\",\"// limitSupport.ts import { Support } from './support'; import { Trouble } from './trouble'; export class LimitSupport extends Support { private limit: number; constructor(name: string, limit: number) { super(name); this.limit = limit; } protected resolve(trouble: Trouble): boolean { if (trouble.getNumber() < this.limit) { return true; } return false; } } // main.ts import { NoSupport } from \\\"./NoSupport\\\"; import { LimitSupport } from \\\"./LimitSupport\\\"; import { OddSupport } from \\\"./OddSupport\\\"; import { SpecialSupport } from \\\"./specialSupport\\\"; import { Support } from \\\"./support\\\"; import { Trouble } from \\\"./trouble\\\"; let alice: Support = new NoSupport(\\\"Alice\\\"); let bob: Support = new LimitSupport(\\\"Bob\\\", 100); let charlie: Support = new SpecialSupport(\\\"Charlie\\\", 429); let diana: Support = new LimitSupport(\\\"Diana\\\", 200); let elmo: Support = new OddSupport(\\\"Elmo\\\"); let fred: Support = new LimitSupport(\\\"Fred\\\", 300); alice.setNext(bob).setNext(charlie).setNext(diana).setNext(elmo).setNext(fred); for (let i = 0; i < 500; i += 33) { alice.support(new Trouble(i)); } // NoSupport.ts import { Support } from './support'; import { Trouble } from './trouble'; export class NoSupport extends Support { constructor(name: string) { super(name); } resolve(trouble: Trouble): boolean { return false; } } // OddSupport.ts import { Support } from './support'; export class OddSupport extends Support { resolve(trouble) { if (trouble.getNumber() % 2 === 1) { return true; } else { return false; } } } // specialSupport.ts import { Support } from './support'; import { Trouble } from './trouble'; export class SpecialSupport extends Support { private number: number; constructor(name: string, number: number) { super(name); this.number = number; } protected resolve(trouble: Trouble): boolean { if (trouble.getNumber() === this.number) { return true; } return false; } } // support.ts import { Trouble } from './trouble'; export abstract class Support { private next: Support; constructor(private name: string) { this.name = name; } setNext(next: Support): Support { this.next = next; return next; } support(trouble: Trouble): void { if (this.resolve(trouble)) { this.done(trouble); } else if (this.next != undefined && this.next !== null) { this.next.support(trouble); } else { this.fail(trouble); } } toString(): string { return `[${this.name}]`; } protected abstract resolve(trouble: Trouble): boolean; protected done(trouble: Trouble): void { console.log(`${trouble} is resolved by ${this}.`); } protected fail(trouble: Trouble): void { console.log(`${trouble} cannot be resolved.`); } } // trouble.ts export class Trouble { private number: number; constructor(number: number) { this.number = number; } getNumber(): number { return this.number; } toString(): string { return `[Trouble ${this.number}]`; } } \"]},\"191\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\chainOfResponsibility\\\\main.ts\\\" [Trouble 0] is resolved by [Bob]. [Trouble 33] is resolved by [Bob]. [Trouble 66] is resolved by [Bob]. [Trouble 99] is resolved by [Bob]. [Trouble 132] is resolved by [Diana]. [Trouble 165] is resolved by [Diana]. [Trouble 198] is resolved by [Diana]. [Trouble 231] is resolved by [Elmo]. [Trouble 264] is resolved by [Fred]. [Trouble 297] is resolved by [Elmo]. [Trouble 330] cannot be resolved. [Trouble 363] is resolved by [Elmo]. [Trouble 396] cannot be resolved. [Trouble 429] is resolved by [Charlie]. [Trouble 462] cannot be resolved. [Trouble 495] is resolved by [Elmo]. \"]},\"192\":{\"h\":\"相关的设计模式\",\"t\":[\"Composite 模式\",\"Command 模式\"]},\"193\":{\"c\":[\"设计模式\"]},\"194\":{\"c\":[\"设计模式\",\"TypeScript\",\"推卸责任\"]},\"195\":{\"h\":\"Command 模式\"},\"196\":{\"h\":\"为什么使用此模式\",\"t\":[\"Command 模式将请求封装成对象，使得可以用不同的请求、队列或者日志来参数化其他对象。Command 模式也支持可撤销的操作。\"]},\"197\":{\"h\":\"示例代码\",\"t\":[\"// command.ts export interface Command { execute(): void; } // drawable.ts export interface Drawable { draw(x:number,y:number): void; } // drawCanvas.ts import { Drawable } from './drawable'; import { MacroCommand } from './macroCommand'; export class DrawCanvas implements Drawable { private history: MacroCommand; constructor(history: MacroCommand) { this.history = history; } paint(): void { this.history.execute(); } draw(x: number, y: number): void { console.log(`Drawing at (${x}, ${y})`); } } // drawCommand.ts import { Command } from './command'; import { DrawCanvas } from './drawCanvas'; export class DrawCommand implements Command { private x: number; private y: number; constructor(private canv: DrawCanvas,x: number, y: number) { this.x = x; this.y = y; } execute(): void { this.canv.draw(this.x, this.y) } } // macroCommand.ts import { Command } from './command'; export class MacroCommand implements Command { private commands: Command[] = []; push(command: Command): void { this.commands.push(command); } undo(): void { this.commands.pop(); } clear(): void { this.commands = []; } execute(): void { this.commands.forEach((command) => { command.execute(); }); } } // main.ts import { DrawCanvas } from './drawCanvas'; import { MacroCommand } from './macroCommand'; import { DrawCommand } from './drawCommand'; const history = new MacroCommand(); const canvas = new DrawCanvas(history); for (let i = 0; i < 10; i++) { const cmd = new DrawCommand(canvas, i, i); history.push(cmd); } canvas.paint(); \"]},\"198\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\command\\\\main.ts\\\" Drawing at (0, 0) Drawing at (1, 1) Drawing at (2, 2) Drawing at (3, 3) Drawing at (4, 4) Drawing at (5, 5) Drawing at (6, 6) Drawing at (7, 7) Drawing at (8, 8) Drawing at (9, 9) \"]},\"199\":{\"h\":\"拓展思路的要点\"},\"200\":{\"h\":\"命令中应该包含哪些信息\",\"t\":[\"在命令模式中，命令对象通常包含以下信息：\",\"接收者（Receiver）：执行命令的对象。接收者包含了执行具体操作的逻辑。\",\"动作（Action）：要执行的具体操作。命令对象将动作封装为一个方法调用。\",\"参数（Parameters）：执行操作所需的参数。命令对象可以包含执行操作所需的所有参数。\",\"状态（State）：命令执行前后的状态信息。命令对象可以保存执行前的状态，以便在需要时进行撤销操作。\",\"通过将这些信息封装在命令对象中，可以实现命令的参数化和可撤销性，从而提高系统的灵活性和可维护性。\"]},\"201\":{\"h\":\"保存历史记录\",\"t\":[\"命令模式的一个重要应用是保存历史记录，以支持撤销和重做操作。通过将每个执行的命令对象保存到一个历史记录列表中，可以在需要时回滚到之前的状态。以下是实现保存历史记录的一些常见方法：\",\"命令栈（Command Stack）：使用栈数据结构保存执行的命令对象。每次执行命令时，将命令对象压入栈中；每次撤销操作时，从栈中弹出命令对象并执行撤销操作。\",\"命令队列（Command Queue）：使用队列数据结构保存执行的命令对象。适用于需要按顺序执行和撤销命令的场景。\",\"快照（Snapshot）：在执行命令前保存对象的快照，以便在需要时恢复到之前的状态。适用于需要保存复杂对象状态的场景。\"]},\"202\":{\"h\":\"相关的设计模式\",\"t\":[\"Composite 模式\",\"Memento 模式\",\"Prototype 模式\"]},\"203\":{\"c\":[\"设计模式\"]},\"204\":{\"c\":[\"设计模式\",\"TypeScript\",\"用类实现\"]},\"205\":{\"h\":\"Composite 模式\"},\"206\":{\"h\":\"使用此设计模式的理由\",\"t\":[\"Composite 模式允许你将对象组合成递归结构来表示“部分-整体”的层次结构。使用 Composite 模式，用户可以统一地对待单个对象和组合对象。例如，在文件系统中，目录和文件都可以被视为条目（Entry），目录可以包含其他目录和文件，而文件则是叶子节点。\"]},\"207\":{\"h\":\"示例代码\"},\"208\":{\"h\":\"目录类 (directory.ts)\",\"t\":[\"import { Entry } from './entry'; export class Directory extends Entry { private directory: Entry[] = []; constructor(private name: string) { super(); } getName(): string { return this.name; } getSize(): number { return this.directory.reduce((acc, entry) => acc + entry.getSize(), 0); } add(entry: Entry): Entry { this.directory.push(entry); return this; } protected printListWithPrefix(prefix: string): void { console.log(`${prefix}/${this}`); this.directory.forEach(entry => (entry as Directory).printListWithPrefix(`${prefix}/${this.name}`)); } } \"]},\"209\":{\"h\":\"抽象条目类 (entry.ts)\",\"t\":[\"export abstract class Entry { abstract getName(): string; abstract getSize(): number; add(entry: Entry): Entry { throw new Error(\\\"FileTreatmentException\\\"); } printList(): void { this.printListWithPrefix(\\\"\\\"); } protected abstract printListWithPrefix(prefix: string): void; toString(): string { return `${this.getName()} (${this.getSize()})`; } } \"]},\"210\":{\"h\":\"文件类 (file.ts)\",\"t\":[\"import { Entry } from './entry'; export class File extends Entry { constructor(private name: string, private size: number) { super(); } getName(): string { return this.name; } getSize(): number { return this.size; } protected printListWithPrefix(prefix: string): void { console.log(`${prefix}/${this}`); } } \"]},\"211\":{\"h\":\"主程序 (main.ts)\",\"t\":[\"import { Entry } from './entry'; import { Directory } from './directory'; import { File } from './file'; console.log('Making root entries...'); let rootdir: Directory = new Directory('root'); let bindir: Directory = new Directory('bin'); let tmpdir: Directory = new Directory('tmp'); let usrdir: Directory = new Directory('usr'); rootdir.add(bindir); rootdir.add(tmpdir); rootdir.add(usrdir); bindir.add(new File('vi', 10000)); bindir.add(new File('latex', 20000)); rootdir.printList(); console.log(\\\"Making user entries...\\\"); let yuki: Directory = new Directory('yuki'); let hanako: Directory = new Directory('hanako'); let tomura: Directory = new Directory('tomura'); usrdir.add(yuki); usrdir.add(hanako); usrdir.add(tomura); yuki.add(new File('diary.html', 100)); yuki.add(new File('Composite.java', 200)); hanako.add(new File('memo.tex', 300)); tomura.add(new File('game.doc', 400)); tomura.add(new File('junk.mail', 500)); rootdir.printList(); \"]},\"212\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\composite\\\\main.ts\\\" Making root entries... /root (30000) /root/bin (30000) /root/bin/vi (10000) /root/bin/latex (20000) /root/tmp (0) /root/usr (0) Making user entries... /root (31500) /root/bin (30000) /root/bin/vi (10000) /root/bin/latex (20000) /root/tmp (0) /root/usr (1500) /root/usr/yuki (300) /root/usr/yuki/diary.html (100) /root/usr/yuki/Composite.java (200) /root/usr/hanako (300) /root/usr/hanako/memo.tex (300) /root/usr/tomura (900) /root/usr/tomura/game.doc (400) /root/usr/tomura/junk.mail (500) \"]},\"213\":{\"h\":\"相关的设计模式\",\"t\":[\"Command 模式\",\"Visitor 模式\",\"Decorator 模式\"]},\"214\":{\"c\":[\"设计模式\"]},\"215\":{\"c\":[\"设计模式\",\"TypeScript\",\"容器与内容的一致性\"]},\"216\":{\"h\":\"Decorator 模式\",\"t\":[\"在这个示例中，我们使用装饰器模式来动态地给对象添加职责。装饰器模式允许我们通过将对象放入包含行为的特殊封装对象中来扩展对象的功能，而无需修改原始类的代码。\"]},\"217\":{\"h\":\"为什么使用装饰器模式？\",\"t\":[\"职责扩展：装饰器模式允许我们在不修改现有代码的情况下扩展对象的功能。\",\"灵活性：可以根据需要动态地添加或删除职责。\",\"遵循开闭原则：通过使用装饰器模式，我们可以在不修改现有类的情况下添加新功能，从而遵循开闭原则。\"]},\"218\":{\"h\":\"代码示例\",\"t\":[\"// border.ts import { Display } from \\\"./display\\\"; export abstract class Border extends Display { protected display: Display; constructor(display: Display) { super(); this.display = display; } } // display.ts export abstract class Display { abstract getColumns(): number; abstract getRows(): number; abstract getRowText(row: number): string; show(): void { for (let i = 0; i < this.getRows(); i++) { console.log(this.getRowText(i)); } } } // fullBorder.ts import { Border } from \\\"./border\\\"; export class FullBorder extends Border { constructor(display) { super(display); } getColumns() { return 1 + this.display.getColumns() + 1; } getRows() { return 1 + this.display.getRows() + 1; } getRowText(row) { if (row === 0) { return \\\"+\\\" + this.makeLine(\\\"-\\\", this.display.getColumns()) + \\\"+\\\"; } else if (row === this.display.getRows() + 1) { return \\\"+\\\" + this.makeLine(\\\"-\\\", this.display.getColumns()) + \\\"+\\\"; } else { return \\\"|\\\" + this.display.getRowText(row - 1) + \\\"|\\\"; } } private makeLine(ch, count) { let buf = \\\"\\\"; for (let i = 0; i < count; i++) { buf += ch; } return buf; } } // main.ts import { Display } from \\\"./display\\\"; import { StringDisplay } from \\\"./stringDisplay\\\"; import { SideBorder } from \\\"./sideBorder\\\"; import { FullBorder } from \\\"./fullBorder\\\"; let b1: Display = new StringDisplay(\\\"Hello, world.\\\"); let b2: Display = new SideBorder(b1, \\\"#\\\"); let b3: Display = new FullBorder(b2); b1.show(); b2.show(); b3.show(); let b4: Display = new SideBorder( new FullBorder( new FullBorder( new SideBorder( new FullBorder( new StringDisplay(\\\"Hello\\\") ), \\\"*\\\" ) ) ), \\\"/\\\" ); b4.show(); // sideBorder.ts import { Border } from \\\"./border\\\"; import { Display } from \\\"./display\\\"; export class SideBorder extends Border { private borderChar: string; constructor(display: Display, ch: string) { super(display); this.borderChar = ch; } getColumns(): number { return 1 + this.display.getColumns() + 1; } getRows(): number { return this.display.getRows(); } getRowText(row: number): string { return this.borderChar + this.display.getRowText(row) + this.borderChar; } } // stringDisplay.ts import { Display } from './display'; export class StringDisplay extends Display { private string: string; constructor(string: string) { super(); this.string = string; } getColumns(): number { return this.string.length; } getRows(): number { return 1; } getRowText(row: number): string { if (row === 0) { return this.string; } else { return ''; } } } \"]},\"219\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\decorator\\\\main.ts\\\" Hello, world. #Hello, world.# +---------------+ |#Hello, world.#| +---------------+ /+-----------+/ /|+---------+|/ /||*+-----+*||/ /||*|Hello|*||/ /||*+-----+*||/ /|+---------+|/ /+-----------+/ \"]},\"220\":{\"h\":\"拓展思路的要点\"},\"221\":{\"h\":\"API 的透明性\",\"t\":[\"在 Decorator 模式中，装饰边框与被装饰物具有一致性。具体而言，在示例程序中，表示装饰边框的 Border 类是表示被装饰物的 Display 类的子类，这就体现了它们之间的一致性。也就是说， Border 类（以及它的子类）与表示被装饰物的 Display 类具有相同的接口（API）。这样，即使被装饰物被边框装饰起来了，接口（API）也不会被隐藏起来。其他类依然可以调用 getColumns、getRows、getRowText 以及 show 方法。这就是接口（API）的“透明性”。在示例程序中，实例 b4 被装饰了多次，但是接口（API）却没有发生任何变化。得益于接口（API）的透明性，模式中也形成了类似于 Composite 模式中的递归结构。也就是说，装饰边框里面的“被装饰物”实际上又是别的物体的“装饰边框”。就像是剥洋葱时以为洋葱心要出来了，结果却发现还是皮。不过， Decorator 模式虽然与 Composite 模式一样，都具有递归结构，但是它们的使用目的不同。Decorator 模式的主要目的是通过添加装饰物来增加对象的功能。\"]},\"222\":{\"h\":\"在不改变被装饰物的前提下增加功能\",\"t\":[\"在 Decorator 模式中，装饰边框与被装饰物具有相同的接口（API）。虽然接口是相同的，但是越装饰，功能则越多。例如，用 SideBorder 装饰 Display 后，就可以在字符串的左右两侧加上装饰字符。如果再用 FullBorder 装饰，那么就可以在字符串的四周加上边框。此时，我们完全不需要对被装饰的类做任何修改。这样，我们就实现了不修改被装饰的类即可增加功能。Decorator 模式使用了委托。对“装饰边框”提出的要求（调用装饰边框的方法）会被转交（委托）给“被装饰物”去处理。以示例程序来说，就是 SideBorder 类的 getColumns 方法调用了 display.getColumns。此外，getRows 方法也调用了 display.getRows。\"]},\"223\":{\"h\":\"可以动态地增加功能\",\"t\":[\"Decorator 模式中用到了委托，它使类之间形成了弱关联关系。因此，不用改变框架代码，就可以生成一个与其他对象具有不同关系的新对象。\"]},\"224\":{\"h\":\"只需要一些装饰物即可添加许多功能\",\"t\":[\"使用 Decorator 模式可以为程序添加许多功能。只要准备一些装饰边框（ConcreteDecorator 角色），即使这些装饰边框都只具有非常简单的功能，也可以将它们自由组合成为新的对象。这就像我们可以自由选择香草味冰激凌、巧克力冰激凌、草莓冰激凌、猕猴桃冰激凌等各种口味的冰激凌一样。如果冰激凌店要为顾客准备所有的冰激凌成品那真是太麻烦了。因此，冰激凌店只会准备各种香料，当顾客下单后只需要在冰激凌上加上各种香料就可以了。不管是香草味，还是咖啡朗姆和开心果的混合口味，亦或是香草味、草莓味和猕猴桃三重口味，顾客想吃什么口味都可以。Decorator 模式就是可以应对这种多功能对象的需求的一种模式。\"]},\"225\":{\"h\":\"导致增加许多很小的类\",\"t\":[\"Decorator 模式的一个缺点是会导致程序中增加许多功能类似的很小的类。\"]},\"226\":{\"h\":\"相关的设计模式\",\"t\":[\"Adapter 模式\",\"Strategy 模式\"]},\"227\":{\"h\":\"继承和委托中的一致性\"},\"228\":{\"h\":\"父类和子类的一致性\",\"t\":[\"在面向对象编程中，父类和子类之间的一致性是指子类应当继承父类的行为和属性，并且可以扩展或重写这些行为和属性。子类应当能够替代父类的实例而不影响程序的正确性，这就是所谓的里氏替换原则（Liskov Substitution Principle）。\"]},\"229\":{\"h\":\"自己和被委托对象的一致性\",\"t\":[\"在委托模式中，一致性是指委托对象应当具有与委托者相同的接口或行为。委托者将某些任务委托给委托对象来执行，而委托对象应当能够无缝地完成这些任务，就像委托者自己完成一样。这种一致性确保了委托模式的灵活性和可维护性。\"]},\"230\":{\"c\":[\"设计模式\"]},\"231\":{\"c\":[\"设计模式\",\"TypeScript\",\"容器与内容的一致性\"]},\"232\":{\"h\":\"结语\",\"t\":[\"教程源码示例\",\"使用设计模式的目的是重用代码，并在增加需求时尽量不修改已有的类。我们不应死记硬背这些设计模式，而应理解其背后的核心思想。设计模式的使用不是最终目的，而是为了更好地解决问题和优化代码结构。同时，我们也要避免过早地进行“工程化”，应根据实际需求灵活应用设计模式。\",\"设计模式提供了一种通用的解决方案，可以帮助我们应对软件开发中的常见问题。通过学习和应用设计模式，我们可以提高代码的可读性、可维护性和可扩展性。然而，设计模式并不是万能的，它们也有其局限性和适用范围。在实际开发中，我们需要根据具体情况选择合适的设计模式，而不是盲目地套用。\",\"此外，设计模式的学习和应用需要不断的实践和积累。只有在实际项目中多次使用，才能真正理解和掌握这些模式。我们还应关注设计模式的演变和新模式的出现，以保持我们的知识体系与时俱进。\",\"总之，设计模式是软件开发中的一把利器，但它需要我们在理解其核心思想的基础上，灵活应用于实际项目中。希望通过本章的学习，您能够掌握这些设计模式，并在实际项目中灵活运用它们，编写出更加健壮和优雅的代码。\"]},\"233\":{\"c\":[\"设计模式\"]},\"234\":{\"c\":[\"设计模式\",\"TypeScript\"]},\"235\":{\"h\":\"facade 模式\",\"t\":[\"当某个程序员得意地说出\\\"啊，在调用那个类之前需要先调用这个类。在调用那个方法之前需要先在这个类中注册一下\\\"的时候，就意味着我们需要引人Facade了。\",\"对于那些能够明确地用语言描述出来的知识，我们不应该将它们隐藏在自己脑袋中，而是应该用代码将它们表现出来。\",\"—————《图解设计模式》 ## 为什么使用外观模式？ \",\"简化接口：外观模式为复杂的子系统提供了一个简单的接口，使得客户端代码不需要了解子系统的内部细节。\",\"松散耦合：通过引入外观类，客户端代码与子系统之间的耦合度降低，增强了代码的可维护性和可扩展性。\",\"更好的分层：外观模式有助于分层设计，使得每一层只关注自己的职责，层与层之间通过外观类进行交互。\"]},\"236\":{\"h\":\"示例代码\",\"t\":[\"在这个示例中，我们使用了外观模式（Facade Pattern）来简化与复杂子系统的交互。外观模式通过提供一个统一的接口来隐藏子系统的复杂性，使得客户端代码可以更容易地使用子系统的功能。\"]},\"237\":{\"h\":\"代码实现\",\"t\":[\"// dataBase.ts export class DataBase { static mailData: { [key: string]: string } = { 'hyuki@hyuki.com': 'Hiroshi Yuki', 'hanako@hyuki.com': 'Hanako Sato', 'tomura@hyuki.com': 'Tomura', 'mamoru@hyuki.com': 'Mamoru Takahashi', }; private constructor() {} static getProperties(databaseName: string) { return DataBase.mailData; } } // htmlWriter.ts export class HtmlWriter { constructor(private writer: string = '') { } title(title: string): void { this.writer += `<html><head><title>${title}</title></head><body>\\\\n<h1>${title}</h1>\\\\n`; } paragraph(message: string): void { this.writer += `<p>${message}</p>\\\\n`; } link(href: string, caption: string): void { this.writer += `<a href=\\\"${href}\\\">${caption}</a>\\\\n`; } mailto(mailaddr: string, username: string): void { this.link(`mailto:${mailaddr}`, username); } close(): void { this.writer += '</body></html>\\\\n'; } getHtml(): string { return this.writer; } } // main.ts import { PageMaker } from \\\"./pageMaker\\\"; PageMaker.makeWelcomePage('hyuki@hyuki.com', \\\"welcome.html\\\"); // pageMaker.ts import { DataBase } from './dataBase'; import { HtmlWriter } from './htmlWriter'; export class PageMaker { private constructor() {} static makeWelcomePage(mailAddress: string, fileName: string): void { console.log(`Making ${fileName} for ${mailAddress}`); let mailprop = DataBase.getProperties('maildata'); let username = mailprop[mailAddress]; let writer = new HtmlWriter(fileName); writer.title('Welcome to ' + username + \\\"'s page!\\\"); writer.paragraph(username + 'のページへようこそ。'); writer.paragraph('メール待っていますね。'); writer.mailto(mailAddress, username); writer.close(); console.log(writer.getHtml()); } } \"]},\"238\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\facade\\\\main.ts\\\" Making welcome.html for hyuki@hyuki.com welcome.html<html><head><title>Welcome to Hiroshi Yuki's page!</title></head><body> <h1>Welcome to Hiroshi Yuki's page!</h1> <p>Hiroshi Yukiのページへようこそ。</p> <p>メール待っていますね。</p> <a href=\\\"mailto:hyuki@hyuki.com\\\">Hiroshi Yuki</a> </body></html> \"]},\"239\":{\"h\":\"相关设计模式\",\"t\":[\"Abstract Factory 模式\",\"Singleton 模式\",\"Mediator 模式\"]},\"240\":{\"c\":[\"设计模式\"]},\"241\":{\"c\":[\"设计模式\",\"TypeScript\",\"简单化\"]},\"242\":{\"h\":\"Factory Method 模式\",\"t\":[\"在 Factory Method 模式中，我们定义一个用于创建对象的接口，但由子类决定要实例化的类是哪一个。Factory Method 使一个类的实例化延迟到其子类。\"]},\"243\":{\"h\":\"为什么要使用 Factory Method\",\"t\":[\"使用 Factory Method 模式有以下几个好处：\",\"解耦创建和使用：客户端代码不需要知道具体的产品类，只需要依赖抽象产品接口，降低了耦合性。\",\"扩展性强：增加新的产品类时，只需添加新的子类工厂，不需要修改现有代码，符合开闭原则。\",\"灵活性高：可以通过子类来定制产品的创建过程，满足不同的需求。\",\"通过使用 Factory Method 模式，我们可以更灵活地管理对象的创建过程，提高代码的可维护性和可扩展性。\"]},\"244\":{\"h\":\"示例代码\",\"t\":[\"@enduml\",\"// product.ts export interface Product { use(): void; } // factory.ts import { Product } from './product'; export abstract class Factory { create(owner: string): Product { const p = this.createProduct(owner); this.registerProduct(p); return p; } protected abstract createProduct(owner: string): Product; protected abstract registerProduct(product: Product): void; } // idCard.ts import { Product } from './product'; export class IDCard implements Product { private owner: string; constructor(owner: string) { this.owner = owner; } use(): void { console.log(`${this.owner}使用了ID卡`); } getOwner(): string { return this.owner; } } // idCardFactory.ts import { IDCard } from \\\"./idCard\\\"; import { Factory } from \\\"./factory\\\"; export class IDCardFactory extends Factory { private owners: string[] = []; createProduct(owner: string): IDCard { return new IDCard(owner); } registerProduct(product: IDCard): void { this.owners.push(product.getOwner()); } getOwners(): string[] { return this.owners; } } // main.ts import { Factory } from \\\"./factory\\\"; import { IDCardFactory } from \\\"./idCardFactory\\\"; const factory: Factory = new IDCardFactory(); const card1 = factory.create(\\\"Alice\\\"); const card2 = factory.create(\\\"Bob\\\"); const card3 = factory.create(\\\"Charlie\\\"); card1.use(); card2.use(); card3.use(); \"]},\"245\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\factory_method\\\\main.ts\\\" Alice使用了ID卡 Bob使用了ID卡 Charlie使用了ID卡 \",\"Template Method\",\"Singleton\",\"Composite\",\"Iterator\"]},\"246\":{\"c\":[\"设计模式\"]},\"247\":{\"c\":[\"设计模式\",\"typescript\",\"工厂方法\",\"交给子类\"]},\"248\":{\"h\":\"Flyweight 模式\"},\"249\":{\"h\":\"为什么使用 Flyweight 模式\",\"t\":[\"Flyweight 模式是一种结构型设计模式，它通过共享尽可能多的相同对象来减少内存使用，从而提高性能。在需要生成大量细粒度对象的场景中，Flyweight 模式非常有用。通过共享对象，Flyweight 模式可以显著减少内存消耗，并提高应用程序的效率。\"]},\"250\":{\"h\":\"实例代码\",\"t\":[\"// bigChar.ts export class BigChar { charname: string; fontdata: string; static fontdatas: { [key: string]: string } = { \\\"0\\\": \\\".....######.....\\\\n\\\" + \\\"....##....##....\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\"....##....##....\\\\n\\\" + \\\".....######.....\\\\n\\\", \\\"1\\\": \\\".......##.......\\\\n\\\" + \\\".....####.......\\\\n\\\" + \\\".......##.......\\\\n\\\" + \\\".......##.......\\\\n\\\" + \\\".......##.......\\\\n\\\" + \\\".......##.......\\\\n\\\" + \\\".......##.......\\\\n\\\" + \\\".......##.......\\\\n\\\" + \\\".......##.......\\\\n\\\" + \\\".....######.....\\\\n\\\" + \\\"................\\\\n\\\", \\\"2\\\": \\\".....######.....\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"..........##....\\\\n\\\" + \\\".........##.....\\\\n\\\" + \\\".......##.......\\\\n\\\" + \\\"......##........\\\\n\\\" + \\\".....##.........\\\\n\\\" + \\\"...##...........\\\\n\\\" + \\\"....##########..\\\\n\\\" + \\\"................\\\\n\\\", \\\"3\\\": \\\".....######.....\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"..........##....\\\\n\\\" + \\\".........##.....\\\\n\\\" + \\\"......####......\\\\n\\\" + \\\".........##.....\\\\n\\\" + \\\"..........##....\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\".....######.....\\\\n\\\", \\\"4\\\": \\\"........###.....\\\\n\\\" + \\\".......####.....\\\\n\\\" + \\\"......##.##.....\\\\n\\\" + \\\".....##..##.....\\\\n\\\" + \\\"....##...##.....\\\\n\\\" + \\\"...##....##.....\\\\n\\\" + \\\"..##########....\\\\n.\\\" + \\\"........##......\\\\n\\\" + \\\"........##......\\\\n\\\" + \\\".......######...\\\\n\\\", \\\"5\\\": \\\"....########....\\\\n\\\" + \\\"....########....\\\\n\\\" + \\\"....##..........\\\\n\\\" + \\\"....##..........\\\\n\\\" + \\\"....##..........\\\\n\\\" + \\\"....##..........\\\\n\\\" + \\\"....##..........\\\\n\\\" + \\\"....##..........\\\\n\\\" + \\\"....######......\\\\n\\\" + \\\"....######......\\\\n\\\" + \\\"..........##....\\\\n\\\" + \\\"..........##....\\\\n\\\" + \\\"...........##...\\\\n\\\" + \\\"...........##...\\\\n\\\" + \\\"...........##...\\\\n\\\" + \\\"...........##...\\\\n\\\" + \\\"..##.......##...\\\\n\\\" + \\\"..##.......##...\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\".....######.....\\\\n\\\", \\\"6\\\": \\\".......####.....\\\\n\\\" + \\\"......##........\\\\n\\\" + \\\".....##.........\\\\n\\\" + \\\"....##..........\\\\n\\\" + \\\"...##...........\\\\n\\\" + \\\"..######........\\\\n\\\" + \\\"..##...##.......\\\\n\\\" + \\\"..##....##......\\\\n\\\" + \\\"..##.....##.....\\\\n\\\" + \\\"...##....##.....\\\\n\\\" + \\\"....####........\\\\n\\\", \\\"7\\\": \\\"..##########....\\\\n\\\" + \\\"..##......##....\\\\n\\\" + \\\"........##......\\\\n\\\" + \\\".......##.......\\\\n\\\" + \\\"......##........\\\\n\\\" + \\\"......##........\\\\n\\\" + \\\".....##.........\\\\n\\\" + \\\".....##.........\\\\n\\\" + \\\"....##..........\\\\n\\\" + \\\"....##..........\\\\n\\\" + \\\"....##..........\\\\n\\\", \\\"8\\\": \\\".....######.....\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\"....######......\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\".....######.....\\\\n\\\", \\\"9\\\": \\\".....######.....\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\"....#######.....\\\\n\\\" + \\\"..........##....\\\\n\\\" + \\\".........##.....\\\\n\\\" + \\\"........##......\\\\n\\\" + \\\"......###.......\\\\n\\\" + \\\".....##.........\\\\n\\\", }; constructor(charname: string) { this.charname = charname; this.fontdata = BigChar.fontdatas[charname]; this.fontdata = this.fontdata.replace(/#/g, charname); } print(): void { console.log(this.fontdata); } } // bigCharFactory.ts import { BigChar } from './bigChar'; export class BigCharFactory { private pool: Map<string, BigChar> = new Map(); private static singleton: BigCharFactory = new BigCharFactory(); private constructor() { } public static getInstance(): BigCharFactory { return BigCharFactory.singleton; } public getBigChar(charname: string): BigChar { let bc: BigChar = this.pool.get(charname); // ts 是单线程的，所以不需要考虑多线程问题， 若为多线程则需要加锁 if (bc == null) { bc = new BigChar(charname); this.pool.set(charname, bc); } return bc; } } // bigString.ts import { Factory } from '../abstractFactory/factory'; import { BigChar } from './bigChar'; import { BigCharFactory } from './bigCharFactory'; export class BigString { bigchars: BigChar[] = []; constructor(public str: string) { let factory = BigCharFactory.getInstance(); str.split('').forEach((char) => { this.bigchars.push(factory.getBigChar(char)); }); } print() { this.bigchars.forEach((bigchar) => { bigchar.print(); }); } } // main.ts import { BigString } from './bigString'; let bs: BigString = new BigString('123'); bs.print(); \"]},\"251\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\flyweight\\\\main.ts\\\" .......11....... .....1111....... .......11....... .......11....... .......11....... .......11....... .......11....... .......11....... .......11....... .....111111..... ................ .....222222..... ...22......22... ..22........22.. ..........22.... .........22..... .......22....... ......22........ .....22......... ...22........... ....2222222222.. ................ .....333333..... ...33......33... ..33........33.. ..........33.... .........33..... ......3333...... .........33..... ..........33.... ..33........33.. ...33......33... .....333333..... \"]},\"252\":{\"h\":\"拓展思路的要点\"},\"253\":{\"h\":\"对多个地方产生影响\",\"t\":[\"Flyweight 模式的主题是“共享”。那么，在共享实例时应当注意什么呢？首先要想到的是“如果要改变被共享的对象，就会对多个地方产生影响”。也就是说，一个实例的改变会同时反映到所有使用该实例的地方。例如，假设我们改变了示例程序中 BigChar 类的 '3' 所对应的字体数据，那么 BigString 类中使用的所有 '3' 字符的字体（形状）都会发生改变。在编程时，像这样改一个地方会对多个地方产生影响并非总是不好。有些情况下这是好事，有些情况下这是坏事。不管怎样，“修改一个地方会对多个地方产生影响”，这就是共享的特点。\",\"因此，在决定 Flyweight 角色中的字段时，需要精挑细选。只将那些真正应该在多个地方共享的字段定义在 Flyweight 角色中即可。关于这一点，让我们简单地举个例子。假设我们要在示例程序中增加一个功能，实现显示“带颜色的大型文字”。那么此时，颜色信息应当放在哪个类中呢？首先，假设我们将颜色信息放在 BigChar 类中。由于 BigChar 类的实例是被共享的，因此颜色信息也被共享了。也就是说，BigString 类中用到的所有 BigChar 类的实例都带有相同的颜色。如果我们不把颜色信息放在 BigChar 类中，而是将它放在 BigString 类中。那么 BigString 类会负责管理“第三个字符的颜色是红色的”这样的颜色信息。这样一来，我们就可以实现以不同的颜色显示同一个 BigChar 类的实例。\",\"那么两种解决方案到底哪个是正确的呢？关于这个问题，其实并没有绝对的答案。哪些信息应当共享，哪些信息不应当共享，这取决于类的使用目的。设计者在使用 Flyweight 模式共享信息时必须仔细思考应当共享哪些信息。\"]},\"254\":{\"h\":\"Intrinsic 与 Extrinsic\",\"t\":[\"前面讲到的“应当共享的信息和不应当共享的信息”是有专有名词的。应当共享的信息被称作 Intrinsic 信息。Intrinsic 的意思是“本质的”“固有的”。换言之，它指的是不论实例在哪里、不论在什么情况下都不会改变的信息，或是不依赖于实例状态的信息。\",\"在示例程序中，BigChar 的字体数据不论在 BigString 中的哪个地方都不会改变。因此，BigChar 的字体数据属于 Intrinsic 信息。另一方面，不应当共享的信息被称作 Extrinsic 信息。Extrinsic 的意思是“外在的”“非本质的”。也就是说，它是当实例的位置、状况发生改变时会变化的信息，或是依赖于实例状态的信息。在示例程序中，BigChar 的实例在 BigString 中是第几个字符这种信息会根据 BigChar 在 BigString 中的位置变化而发生变化，因此，不应当在 BigChar 中保存这个信息，它属于 Extrinsic 信息。因此，前面提到的是否共享“颜色”信息这个问题，我们也可以换种说法，即应当将“颜色”看作是 Intrinsic 信息还是 Extrinsic 信息。\"]},\"255\":{\"h\":\"不要让被共享的实例被垃圾回收器回收了\",\"t\":[\"在有垃圾回收的语言中要注意共享内存未被使用时被 GC 的问题。在使用 Flyweight 模式时，我们通常会将共享对象存储在某种集合（如 HashMap 或 List）中，以便重复使用这些对象。然而，如果这些集合中的对象没有被其他任何地方引用，垃圾回收器可能会认为这些对象是垃圾，从而将其回收掉。这会导致共享对象在需要时无法被找到，从而引发程序错误。\",\"为了避免这种情况，我们需要确保共享对象在整个程序生命周期内都被引用。以下是一些常见的解决方案：\",\"强引用：将共享对象存储在一个全局的集合中，并确保这个集合在程序的整个生命周期内都存在。这种方法简单直接，但可能会导致内存泄漏，因为共享对象永远不会被回收。\",\"弱引用：使用弱引用（WeakReference）来存储共享对象。弱引用允许垃圾回收器在没有其他强引用时回收对象，从而避免内存泄漏。Java 提供了 WeakHashMap 类，可以用来存储弱引用的键值对。\",\"引用计数：通过引用计数来管理共享对象的生命周期。每当一个对象被引用时，增加计数；每当一个引用被释放时，减少计数。当计数为零时，表示该对象不再被使用，可以安全地回收。\",\"定期清理：定期检查集合中的对象，移除那些不再被使用的对象。这种方法需要额外的逻辑来判断对象是否仍然被使用，但可以有效地管理内存。\"]},\"256\":{\"h\":\"内存之外的其它资源\",\"t\":[\"在示例程序中，我们了解到共享实例可以减少内存使用量。一般来说，共享实例可以减少所需资源的使用量。这里的资源指的是计算机中的资源，而内存是资源中的一种。时间也是一种资源。使用 new 关键字生成实例会花费时间。通过 Flyweight 模式共享实例可以减少使用 new 关键字生成实例的次数。这样，就可以提高程序运行速度。文件句柄（文件描述符）和窗口句柄等也都是一种资源。在操作系统中，可以同时使用的文件句柄和窗口句柄是有限制的。因此，如果不共享实例，应用程序在运行时很容易就会达到资源极限而导致崩溃。\"]},\"257\":{\"h\":\"相关的设计模式\",\"t\":[\"Proxy 模式\",\"Composite 模式\",\"Singleton 模式\"]},\"258\":{\"c\":[\"设计模式\"]},\"259\":{\"c\":[\"设计模式\",\"TypeScript\",\"避免浪费\"]},\"260\":{\"h\":\"设计模式\",\"t\":[\"面向对象三大特性：封装、继承、多态。 设计模式需遵循面向对象的设计原则，由于笔者不太喜欢java, 并嫌弃cpp中没有interface, 遂使用ts作为实现语言(我才不用rust呢 😃 )\",\"本专栏源码大部分参考自参考资料[1]\",\"教程源码示例\",\"[1] 结城浩. 图解设计模式. 杨文轩译. 北京: 人民邮电出版社, 2017.\"]},\"261\":{\"c\":[\"设计模式\"]},\"262\":{\"c\":[\"设计模式\",\"typescript\"]},\"263\":{\"h\":\"Interpreter 模式\"},\"264\":{\"h\":\"为什么使用此模式\",\"t\":[\"解释器模式（Interpreter Pattern）是一种行为设计模式，它定义了一种语言的文法表示，并定义一个解释器来解释该语言中的句子。使用解释器模式的原因包括：\",\"简化语法解析：通过定义文法规则，可以轻松解析和执行特定的语言或指令集。\",\"可扩展性：可以轻松添加新的语法规则或指令，而无需修改现有代码。\",\"代码复用：通过将不同的语法规则封装在不同的类中，可以提高代码的复用性和可维护性。\"]},\"265\":{\"h\":\"示例代码\",\"t\":[\"本实例是一个控制小车的脚本语言解释器demo,文法如下， 分析方法为递归下降\",\"<program> ::= program <command list> <command list> ::= <command>* end <command> ::= <repeat command> | <primitive command> <repeat command> ::= repeat <number> <command list> <primitive command> ::= go | right | left \",\"// commandListNode.ts import { Node } from \\\"./node\\\"; import { Context } from \\\"./context\\\"; import { CommandNode } from \\\"./commandNode\\\"; // <command list> ::= <command>* end export class CommandListNode extends Node { list: Node[] = []; parse(context: Context): void { while (true) { if (context.getCurrentToken() === null) { throw new Error(\\\"Missing 'end'\\\"); } else if (context.getCurrentToken() === \\\"end\\\") { context.skipToken(\\\"end\\\"); break; } else { const commandNode = new CommandNode(); commandNode.parse(context); this.list.push(commandNode); } } } toString(): string { return this.list.join(\\\"\\\"); } } // commandNode.ts import { Context } from \\\"./context\\\"; import { Node } from \\\"./node\\\"; import { RepeatCommandNode } from \\\"./repeatCommandNode\\\"; import { PrimitiveCommandNode } from \\\"./primitiveCommandNode\\\"; // <command> ::= <repeat command> | <primitive command> export class CommandNode extends Node { node: Node; parse(context: Context): void { if (context.getCurrentToken() === \\\"repeat\\\") { this.node = new RepeatCommandNode(); this.node.parse(context); } else { this.node = new PrimitiveCommandNode(); this.node.parse(context); } } toString(): string { return this.node.toString(); } } // context.ts import { StringTokenizer } from './stringTokenizer'; export class Context { private stringTokenizer: StringTokenizer; private currentToken: string; constructor(text: string) { this.stringTokenizer = new StringTokenizer(text); this.nextToken(); } nextToken(): string { if (this.stringTokenizer.hasMoreTokens()) { this.currentToken = this.stringTokenizer.nextToken(); } else { this.currentToken = null; } return this.currentToken; } getCurrentToken(): string { return this.currentToken; } skipToken(token: string): void { if (token != this.currentToken) { throw new Error(`Warning: ${token} is expected, but ${this.currentToken} is found.`); } this.nextToken(); } getCurrentNumber(): number { let number: number; try { number = Number(this.currentToken); } catch (e) { throw new Error(`Warning: ${e}`); } return number; } } // main.ts import { Context } from \\\"./context\\\"; import { ProgramNode } from \\\"./programNode\\\"; // <program> ::= program <command list> // <command list> ::= <command>* end // <command> ::= <repeat command> | <primitive command> // <repeat command> ::= repeat <number> <command list> // <primitive command> ::= go | right | left let programs = \\\"program end\\\\n\\\"+ \\\"program go end\\\\n\\\"+ \\\"program go right go right go right end\\\\n\\\"+ \\\"program repeat 4 go right end end\\\\n\\\"+ \\\"program repeat 4 repeat 3 go right go left end right end end\\\\n\\\"; programs.split(\\\"\\\\n\\\").forEach((text:string)=>{ if (text.length == 0) return; console.log(`current:\\\\n ${text}\\\\n`) let node = new ProgramNode() node.parse(new Context(text)) console.log(`node = ${node}`) }) // node.ts import {Context} from \\\"./context\\\"; export abstract class Node { abstract parse(ctx:Context): void; } // primitiveCommandNode.ts import { Node } from \\\"./node\\\"; import { Context } from \\\"./context\\\"; // <primitive command> ::= <go> | <right> | <left> export class PrimitiveCommandNode extends Node { private name: string; parse(context: Context): void { this.name = context.getCurrentToken(); context.skipToken(this.name); if (this.name !== \\\"go\\\" && this.name !== \\\"right\\\" && this.name !== \\\"left\\\") { throw new Error(`${this.name} is undefined`); } } toString(): string { return this.name+\\\" \\\"; } } // programNode.ts import { Node } from \\\"./node\\\"; import { CommandListNode } from \\\"./commandListNode\\\"; import {Context} from \\\"./context\\\"; // <program> ::= program <command list> export class ProgramNode extends Node { commandListNode: Node; parse(context:Context): void { context.skipToken(\\\"program\\\"); this.commandListNode = new CommandListNode(); this.commandListNode.parse(context); } toString(): string { return \\\"[program \\\" + this.commandListNode + \\\"]\\\"; } } // repeatCommandNode.ts import { Node } from \\\"./node\\\"; import { Context } from \\\"./context\\\"; import { CommandListNode } from \\\"./commandListNode\\\"; // <repeat command> ::= \\\"repeat\\\" <number> \\\"end\\\" export class RepeatCommandNode extends Node { number: number; commandListNode: CommandListNode; parse(context: Context): void { context.skipToken(\\\"repeat\\\"); this.number = context.getCurrentNumber(); context.nextToken(); this.commandListNode = new CommandListNode(); this.commandListNode.parse(context); } toString(): string { return `[repeat [${this.number} ${this.commandListNode.toString()}]]`; } } // StringTokenizer.ts export class StringTokenizer{ private text: string; private tokens: string[]; private index: number; constructor(text: string) { this.text = text; this.tokens = text.split(\\\" \\\"); this.index = 0; } nextToken(): string { return this.tokens[this.index++]; } hasMoreTokens(): boolean { return this.index < this.tokens.length; } } \"]},\"266\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\interperter\\\\main.ts\\\" current: program end node = [program ] current: program go end node = [program go ] current: program go right go right go right end node = [program go right go right go right ] current: program repeat 4 go right end end node = [program [repeat [4 go right ]]] current: program repeat 4 repeat 3 go right go left end right end end node = [program [repeat [4 [repeat [3 go right go left ]]right ]]] \"]},\"267\":{\"c\":[\"设计模式\"]},\"268\":{\"c\":[\"设计模式\",\"TypeScript\",\"用类实现\"]},\"269\":{\"h\":\"迭代器模式\"},\"270\":{\"h\":\"为什么要使用迭代器模式\",\"t\":[\"迭代器模式提供了一种方法来顺序访问集合中的元素，而无需暴露其底层表示。使用迭代器模式有以下几个优点：\",\"简化代码：迭代器模式将遍历逻辑封装在迭代器对象中，使得客户端代码更加简洁和易读。\",\"解耦集合和遍历：集合对象和遍历算法分离，增加了代码的灵活性和可维护性。可以在不修改集合对象的情况下，改变遍历算法。\",\"统一接口：通过实现统一的迭代器接口，不同类型的集合可以使用相同的遍历方式，增强了代码的可扩展性。\",\"支持多种遍历方式：可以根据需要实现不同的迭代器，以支持多种遍历方式，如正向遍历、反向遍历、过滤遍历等。\",\"通过使用迭代器模式，我们可以更好地管理和操作集合数据，提高代码的可读性和可维护性。\"]},\"271\":{\"h\":\"TypeScript 实现迭代器模式\",\"t\":[\"在本节中，我们将展示如何使用 TypeScript 实现迭代器模式。迭代器模式是一种行为设计模式，它允许顺序访问集合中的元素，而无需暴露其底层表示。\"]},\"272\":{\"h\":\"代码示例\",\"t\":[\"以下是实现迭代器模式的 TypeScript 代码示例：\",\"// aggregate.ts import { Iterator } from './iterator'; export interface Aggregate { iterator(): Iterator; } // book.ts export class Book { private name: string; constructor(name: string) { this.name = name; } getName(): string { return this.name; } } // bookShelf.ts import { Book } from './book'; import { Iterator } from './iterator'; import { BookShelfIterator } from './bookShelfIterator'; import { Aggregate } from './aggregate'; export class BookShelf implements Aggregate { private books: Book[]; private last: number = 0; constructor() { this.books = []; } getBookAt(index: number): Book { return this.books[index]; } appendBook(book: Book): void { this.books[this.last] = book; this.last++; } getLength(): number { return this.last; } iterator(): Iterator { return new BookShelfIterator(this); } } // bookShelfIterator.ts import { BookShelf } from './bookShelf'; import { Iterator } from './iterator'; export class BookShelfIterator implements Iterator { private bookShelf: BookShelf; private index: number; constructor(bookShelf: BookShelf) { this.bookShelf = bookShelf; this.index = 0; } hasNext(): boolean { return this.index < this.bookShelf.getLength(); } next(): any { const book = this.bookShelf.getBookAt(this.index); this.index++; return book; } } // iterator.ts export interface Iterator { hasNext(): boolean; next(): any; } // main.ts import { BookShelf } from \\\"../bookShelf\\\"; import { Book } from \\\"../book\\\"; const bookShelf = new BookShelf(); bookShelf.appendBook(new Book(\\\"Around the World in 80 Days\\\")); bookShelf.appendBook(new Book(\\\"Bible\\\")); bookShelf.appendBook(new Book(\\\"Cinderella\\\")); bookShelf.appendBook(new Book(\\\"Daddy-Long-Legs\\\")); const it = bookShelf.iterator(); while (it.hasNext()) { const book = it.next(); console.log(book.getName()); } \"]},\"273\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\iterator\\\\main.ts\\\" Around the World in 80 Days Bible Cinderella Daddy-Long-Legs \",\"在上面的代码中，我们定义了几个类和接口来实现迭代器模式：\",\"Iterator 接口定义了 hasNext 和 next 方法。\",\"Aggregate 接口定义了 iterator 方法。\",\"Book 类表示一个书籍对象。\",\"BookShelf 类表示一个书架，它实现了 Aggregate 接口。\",\"BookShelfIterator 类实现了 Iterator 接口，用于遍历 BookShelf 中的书籍。\",\"通过这些类和接口，我们可以轻松地遍历 BookShelf 中的书籍，而无需了解其内部实现细节。\"]},\"274\":{\"h\":\"多个迭代器\",\"t\":[\"在某些情况下，我们可能需要为同一个集合编写多个具体迭代器（ConcreteIterator）。例如，我们可以为 BookShelf 编写一个反向迭代器，以便从后向前遍历书籍。\"]},\"275\":{\"h\":\"相关的设计模式\",\"t\":[\"Visitor 模式\",\"Composite 模式\",\"Factory Method 模式\"]},\"276\":{\"c\":[\"设计模式\"]},\"277\":{\"c\":[\"设计模式\",\"typescript\"]},\"278\":{\"h\":\"Mediator 模式\"},\"279\":{\"h\":\"为什么使用此类\",\"t\":[\"请大家想象一下一个乱糟糟的开发小组的工作状态。小组中的 10 个成员虽然一起协同工作，但是意见难以统一，总是互相指挥，导致工作进度始终滞后。不仅如此，他们还十分在意编码细节，经常为此争执不下。\",\"这时，我们就需要一个中立的仲裁者站出来说：“各位，请大家将情况报告给我，我来负责仲裁。我会从团队整体出发进行考虑，然后下达指示，但我不会评价大家的工作细节。”这样，当出现争执时大家就会找仲裁者进行商量，仲裁者会负责统一大家的意见。\",\"最后，整个团队的交流过程就变为了组员向仲裁者报告，仲裁者向组员下达指示。组员之间不再相互询问和相互指示。\"]},\"280\":{\"h\":\"示例代码\",\"t\":[\"源地址\",\"/** * EN: Real World Example for the Mediator design pattern * * Need: To have a messaging application to notify groups of people. Users * should not know about each other. * * Solution: Create a mediator to manage subscriptions and messages */ /** * EN: Extending the Mediator interface to have a payload to include messages */ interface Mediator { notify(sender: object, event: string, payload?: string): void; } /** * EN: The user plays the role of the independent component. It has an * instance of the mediator. */ class User { constructor(public name: string, private mediator: Mediator) { this.mediator.notify(this, 'subscribe'); } receiveMessage(message: string) { console.log(`Message received by ${this.name}: ${message}`); } publishMessage(message: string) { this.mediator.notify(this, 'publish', message); } } /** * EN: The app is the concrete Mediator and implements all the events that * collaborators can notify: subscribe and publish */ class ChatAppMediator implements Mediator { private users: User[] = []; public notify(sender: object, event: string, payload?: string): void { if (event === 'subscribe') { const user = sender as User; console.log(`Subscribing ${user.name}`); this.users.push(user); } if (event === 'publish') { console.log(`Publishing message \\\"${payload}\\\" to the group`); const usersExcludingSender = this.users.filter(u => u !== sender); for (const user of usersExcludingSender) { user.receiveMessage(payload); } } } } /** * EN: The client code. Creating a user automatically subscribes them to the * group. */ const chatAppMediator = new ChatAppMediator(); const user1 = new User('Lightning', chatAppMediator); const user2 = new User('Doc', chatAppMediator); const user3 = new User('Mater', chatAppMediator); user1.publishMessage('Catchaw'); user2.publishMessage('Ey kid'); user3.publishMessage('Tomato'); \"]},\"281\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\mediator\\\\main.ts\\\" Subscribing Lightning Subscribing Doc Subscribing Mater Publishing message \\\"Catchaw\\\" to the group Message received by Doc: Catchaw Message received by Mater: Catchaw Publishing message \\\"Ey kid\\\" to the group Message received by Lightning: Ey kid Message received by Mater: Ey kid Publishing message \\\"Tomato\\\" to the group Message received by Lightning: Tomato Message received by Doc: Tomato \"]},\"282\":{\"h\":\"拓展思路的要点\"},\"283\":{\"h\":\"当发生分散灾难时\",\"t\":[\"示例程序中的 ChatAppMediator 类的 notify 方法稍微有些复杂。如果发生需求变更，该方法中很容易发生 Bug。不过这并不是什么问题。因为即使 notify 方法中发生了 Bug，由于其他地方并没有控制消息发布和订阅的逻辑处理，因此只要调试该方法就能很容易地找出 Bug 的原因。请试想一下，如果这段逻辑分散在 User 类中，那么无论是编写代码还是调试代码和修改代码，都会非常困难。通常情况下，面向对象编程可以帮助我们分散处理，避免处理过于集中，也就是说可以“分而治之”。但是在本章中的示例程序中，把处理分散在各个类中是不明智的。如果只是将应当分散的处理分散在各个类中，但是没有将应当集中的处理集中起来，那么这些分散的类最终只会导致灾难。\",\"在这个示例程序中，ChatAppMediator 类作为中介者（Mediator），负责管理和协调各个用户（User）的交互。notify 方法集中处理了所有消息的发布和订阅逻辑，这样可以确保逻辑的一致性和可维护性。如果将这些逻辑分散到各个用户类中，不仅会增加代码的复杂性，还会使得调试和维护变得更加困难。因此，将这些逻辑集中在中介者类中是更明智的选择。\"]},\"284\":{\"h\":\"通信线路的增加\",\"t\":[\"假设现在有 A 和 B 这 2 个实例，它们之间互相通信（相互调用方法），那么通信线路有两条，即 A-B 和 A-B。如果是有 A、B 和 C 这 3 个实例，那么就会有 6 条通信线路，即 A-B、A-C、B-C、B-A 和 C-A。如果有 4 个实例，会有 12 条通信线路；5 个实例就会有 20 条通信线路，而 6 个实例则会有 30 条通信线路。如果存在很多这样的互相通信的实例，那么程序结构会变得非常复杂。可能会有读者认为，如果实例很少就不需要 Mediator 模式了。但是需要考虑到的是，即使最初实例很少，很可能随着需求变更实例数量会慢慢变多，迟早会暴露出问题。\"]},\"285\":{\"h\":\"哪些角色可以复用\",\"t\":[\"ConcreteColleague 角色可以复用，但 ConcreteMediator 角色很难复用。例如，假设我们现在需要制作另外一个对话框。这时，我们可将扮演 ConcreteColleague 角色的 colleagueButton 类、 colleagueTextField 类和 colleagueCheckbox 类用于新的对话框中。这是因为在 ConcreteColleague 角色中并没有任何依赖于特定对话框的代码。在示例程序中，依赖于特定应用程序的部分都被封装在扮演 ConcreteMediator 角色的 LoginFrame 类中，依赖于特定应用程序就意味着难以复用。因此， LoginFrame 类很难在其他对话框中被复用。\"]},\"286\":{\"h\":\"相关的设计模式\",\"t\":[\"Facade 模式\",\"Observer 模式\"]},\"287\":{\"c\":[\"设计模式\"]},\"288\":{\"c\":[\"设计模式\",\"TypeScript\",\"简单化\"]},\"289\":{\"h\":\"Memento 模式\"},\"290\":{\"h\":\"为什么使用 Memento 模式\",\"t\":[\"Memento 模式的主要目的是在不破坏封装性的前提下，捕获和恢复对象的内部状态。它在以下情况下特别有用：\",\"需要保存和恢复对象的多个状态。\",\"需要在对象状态变化时进行撤销操作。\",\"需要在不暴露对象实现细节的情况下保存对象状态。\"]},\"291\":{\"h\":\"示例代码\",\"t\":[\"在这个示例中，我们使用了 Memento 模式来管理 Gamer 对象的状态。Memento 模式允许我们在不暴露对象实现细节的情况下保存和恢复对象的状态。以下是示例代码：\",\"// gamer.ts import { Memento } from './memento'; export class Gamer { private money: number; private fruits: string[]; private static fruitsName: string[] = ['apple', 'grape', 'banana', 'orange']; constructor(money: number) { this.money = money; this.fruits = []; } getMoney(): number { return this.money; } bet(): void { const dice = Math.floor(Math.random() * 6) + 1; if (dice === 1) { this.money += 100; console.log('Money increased'); } else if (dice === 2) { this.money /= 2; console.log('Money halved'); } else if (dice === 6) { const f = this.getFruit(); console.log(`Got fruit: ${f}`); this.fruits.push(f); } else { console.log('Nothing happened'); } } createMemento(): Memento { const m = new Memento(this.money); this.fruits.forEach(f => { if (f.startsWith('delicious')) { m.addFruit(f); } }); return m; } restoreMemento(memento: Memento): void { this.money = memento.money; this.fruits = memento.fruits; } toString(): string { return `[money = ${this.money}, fruits = ${this.fruits.join(', ')}]`; } private getFruit(): string { const prefix = Math.random() > 0.5 ? 'delicious ' : ''; return prefix + Gamer.fruitsName[Math.floor(Math.random() * Gamer.fruitsName.length)]; } } // main.ts import { Gamer } from './gamer'; let gamer = new Gamer(100); let memento = gamer.createMemento(); for (let i = 0; i < 100; i++) { console.log(`==== ${i}`); console.log(`Current: ${gamer.toString()}`); gamer.bet(); console.log(`Money now: ${gamer.getMoney()}`); if (gamer.getMoney() > memento.getMoney()) { console.log('Money increased, saving current state'); memento = gamer.createMemento(); } else if (gamer.getMoney() < memento.getMoney() / 2) { console.log('Money halved, restoring to previous state'); gamer.restoreMemento(memento); } console.log(''); } // memento.ts export class Memento { money: number; fruits: string[]; constructor(money: number) { this.money = money; this.fruits = []; } public getMoney(): number { return this.money; } public addFruit(fruit: string): void { this.fruits.push(fruit); } public getFruits(): string[] { return [...this.fruits]; } } \"]},\"292\":{\"h\":\"运行结果\",\"t\":[\"...(省略) ==== 97 Current: [money = 462.5, fruits = delicious grape, delicious apple, delicious apple, delicious orange, delicious banana, delicious apple, delicious apple, delicious grape, delicious grape, banana, grape, delicious banana] Money halved Money now: 231.25 Money halved, restoring to previous state ==== 98 Current: [money = 925, fruits = delicious grape, delicious apple, delicious apple, delicious orange, delicious banana, delicious apple, delicious apple, delicious grape, delicious grape, banana, grape, delicious banana] Nothing happened Money now: 925 ==== 99 Current: [money = 925, fruits = delicious grape, delicious apple, delicious apple, delicious orange, delicious banana, delicious apple, delicious apple, delicious grape, delicious grape, banana, grape, delicious banana] Nothing happened Money now: 925 \"]},\"293\":{\"h\":\"拓展思路的要点\"},\"294\":{\"h\":\"两种接口和可见性\",\"t\":[\"在 Memento 模式中，通常会有两种接口：宽接口（wide interface）和窄接口（narrow interface）。宽接口提供了对 Memento 对象的所有操作权限，而窄接口则只提供了有限的操作权限。Originator 类使用宽接口来创建和恢复 Memento，而 Caretaker 类则使用窄接口来保存和传递 Memento。通过这种方式，可以确保 Memento 的内部状态不会被外部直接修改，从而保持封装性。\"]},\"295\":{\"h\":\"需要多少个 Memento\",\"t\":[\"在实际应用中，需要根据具体需求来决定需要保存多少个 Memento。对于一些简单的应用，可能只需要保存一个 Memento 来支持一次撤销操作。而对于一些复杂的应用，可能需要保存多个 Memento 以支持多次撤销操作。需要注意的是，保存过多的 Memento 会占用大量的内存资源，因此需要在性能和功能之间找到一个平衡点。\"]},\"296\":{\"h\":\"Memento 的有效期限是多久\",\"t\":[\"Memento 的有效期限取决于具体的应用场景。在某些情况下，Memento 可能只需要在短时间内有效，例如在用户进行撤销操作之前。而在其他情况下，Memento 可能需要长期保存，例如在应用程序关闭后重新打开时恢复状态。需要根据具体需求来决定 Memento 的有效期限，并在适当的时候清理过期的 Memento 以释放资源。\"]},\"297\":{\"h\":\"划分 Caretaker 和 Originator 角色的意义\",\"t\":[\"在 Memento 模式中，Caretaker 和 Originator 角色的划分具有重要意义。Caretaker 负责保存和管理 Memento，而 Originator 负责创建和恢复 Memento。通过这种划分，可以将状态保存和恢复的逻辑与业务逻辑分离，从而提高系统的可维护性和可扩展性。\",\"变更为可以多次撤销 通过保存多个 Memento，可以实现多次撤销操作。Caretaker 可以维护一个 Memento 的栈，每次撤销操作时从栈中弹出一个 Memento 并恢复状态。这样可以支持用户进行多次撤销和重做操作。\",\"变更为不仅可以撤销，还可以将现在的状态保存在文件中 通过将 Memento 保存到文件中，可以实现持久化存储。这样即使应用程序关闭后重新打开，也可以恢复到之前的状态。Caretaker 可以负责将 Memento 序列化并保存到文件中，以及从文件中读取并反序列化 Memento。\"]},\"298\":{\"h\":\"相关的设计模式\",\"t\":[\"Command 模式\",\"Prototype 模式\",\"State 模式\"]},\"299\":{\"c\":[\"设计模式\"]},\"300\":{\"c\":[\"设计模式\",\"TypeScript\",\"管理状态\"]},\"301\":{\"h\":\"Observer 模式\"},\"302\":{\"h\":\"为什么使用观察者模式\",\"t\":[\"观察者模式非常适合用于需要自动更新的场景。例如，在图形用户界面（GUI）应用程序中，当数据模型发生变化时，所有显示该数据的视图都需要自动更新。通过使用观察者模式，我们可以将这些视图注册为观察者，当数据模型发生变化时，它们会自动收到通知并更新显示。\"]},\"303\":{\"h\":\"示例代码\",\"t\":[\"在这个示例中，我们展示了如何使用观察者模式来管理状态变化。观察者模式定义了一种一对多的依赖关系，当一个对象的状态发生改变时，所有依赖于它的对象都会得到通知并自动更新。以下是 TypeScript 实现的代码示例：\",\"// DigitObserver.ts import { NumberGenerator } from './numberGenerator'; import { Observer } from './observer'; export class DigitObserver implements Observer { update(number: NumberGenerator): void { console.log(`DigitObserver: ${number.getNumber()}`); } } // graphObserver.ts import { Observer } from './observer'; import { NumberGenerator } from './numberGenerator'; export class GraphObserver implements Observer { update(generator: NumberGenerator): void { const count = generator.getNumber(); let graph = ''; for (let i = 0; i < count; i++) { graph += '*'; } console.log(`GraphObserver: \\\\n${graph}\\\\n ${generator.getNumber()}\\\\n${graph} `); } } // main.ts import { NumberGenerator } from './numberGenerator'; import { Observer } from './observer'; import { RandomNumberGenerator } from './randomNumberGenerator'; import { DigitObserver } from './DigitObserver'; import { GraphObserver } from './graphObserver'; const generator: NumberGenerator = new RandomNumberGenerator(); const observer1 = new DigitObserver(); const observer2 = new GraphObserver(); generator.addObserver(observer1); generator.addObserver(observer2); generator.execute(); // numberGenerator.ts import { Observer } from './observer'; export abstract class NumberGenerator { private observers: Observer[] = []; public addObserver(observer: Observer): void { this.observers.push(observer); } public deleteObserver(observer: Observer): void { this.observers = this.observers.filter((o) => o !== observer); } public notifyObservers(): void { this.observers.forEach((o) => o.update(this)); } public abstract getNumber(): number; public abstract execute(): void; } // observer.ts import {NumberGenerator} from './numberGenerator'; export interface Observer { update(generator: NumberGenerator): void; } // randomNumberGenerator.ts import {NumberGenerator} from './numberGenerator'; export class RandomNumberGenerator extends NumberGenerator { private number: number; constructor() { super(); this.number = 0; } getNumber(): number { return this.number; } execute(): void { for (let i = 0; i < 20; i++) { this.number = Math.floor(Math.random() * 50); this.notifyObservers(); } } } \"]},\"304\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\observer\\\\main.ts\\\" DigitObserver: 13 GraphObserver: ************* 13 ************* DigitObserver: 43 GraphObserver: ******************************************* 43 ******************************************* DigitObserver: 46 GraphObserver: ********************************************** 46 ********************************************** DigitObserver: 18 GraphObserver: ****************** 18 ****************** DigitObserver: 20 GraphObserver: ******************** 20 ******************** DigitObserver: 49 GraphObserver: ************************************************* 49 ************************************************* DigitObserver: 25 GraphObserver: ************************* 25 ************************* DigitObserver: 26 GraphObserver: ************************** 26 ************************** DigitObserver: 37 GraphObserver: ************************************* 37 ************************************* DigitObserver: 2 GraphObserver: ** 2 ** DigitObserver: 10 GraphObserver: ********** 10 ********** DigitObserver: 0 GraphObserver: 0 DigitObserver: 11 GraphObserver: *********** 11 *********** DigitObserver: 13 GraphObserver: ************* 13 ************* DigitObserver: 16 GraphObserver: **************** 16 **************** DigitObserver: 28 GraphObserver: **************************** 28 **************************** DigitObserver: 22 GraphObserver: ********************** 22 ********************** DigitObserver: 30 GraphObserver: ****************************** 30 ****************************** DigitObserver: 44 GraphObserver: ******************************************** 44 ******************************************** DigitObserver: 3 GraphObserver: *** 3 *** \"]},\"305\":{\"h\":\"拓展思路的要点\"},\"306\":{\"h\":\"这里也出现了可替换性\",\"t\":[\"在设计模式中，可替换性是指一个对象可以被另一个具有相同接口的对象替换，而不影响系统的功能。在观察者模式中，观察者（Observer）和被观察者（Subject）之间的关系是松耦合的，这意味着我们可以轻松地替换观察者或被观察者，而不会影响系统的其他部分。\"]},\"307\":{\"h\":\"Observer 的顺序\",\"t\":[\"Subject 角色（被观察对象）中注册有多个 Observer 角色。在示例程序的 notifyObservers 方法中，先注册的 Observer 的 update 方法会先被调用。通常，在设计 ConcreteObserver 角色的类时，需要注意这些 Observer 的 update 方法的调用顺序，不能因为方法的调用顺序发生改变而产生问题。例如，在示例程序中，绝不能因为先调用 DigitObserver 的 update 方法后调用 GraphObserver 的 update 方法而导致应用程序不能正常工作。当然，通常，只要保持各个类的独立性，就不会发生上面这种类的依赖关系混乱的问题。不过，我们还需要注意下面将要提到的情况。\"]},\"308\":{\"h\":\"当 Observer 的行为会对被观察对象产生影响时\",\"t\":[\"当观察者的行为会对被观察对象产生影响时，我们需要特别小心，以避免循环依赖和无限递归。例如，一个观察者在接收到通知后修改了被观察对象的状态，这可能会导致被观察对象再次通知所有观察者，从而引发无限循环。为了解决这个问题，我们可以引入一个标志位来跟踪通知状态，或者使用更复杂的事件处理机制。\"]},\"309\":{\"h\":\"传递更新信息的方式\",\"t\":[\"在观察者模式中，传递更新信息的方式有多种选择。最简单的方法是直接调用观察者的更新方法，并将被观察对象自身作为参数传递。另一种方法是传递具体的更新信息，例如事件对象或数据包。这种方法可以减少观察者对被观察对象的依赖，从而提高系统的灵活性和可维护性。\"]},\"310\":{\"h\":\"从观察变为通知\",\"t\":[\"在某些情况下，我们可能需要从观察模式转变为通知模式。例如，当系统中有大量的观察者时，逐个通知每个观察者可能会导致性能问题。此时，我们可以考虑使用事件总线或消息队列来集中处理通知，从而提高系统的性能和可扩展性。\"]},\"311\":{\"h\":\"MVC (Model/View/Controller)\",\"t\":[\"观察者模式在 MVC 架构中得到了广泛应用。模型（Model）作为被观察对象，视图（View）作为观察者，当模型的状态发生变化时，视图会自动更新。控制器（Controller）负责协调模型和视图之间的交互。通过使用观察者模式，MVC 架构实现了视图和模型的松耦合，从而提高了系统的可维护性和可扩展性。\"]},\"312\":{\"h\":\"相关的设计模式\",\"t\":[\"Mediator 模式\"]},\"313\":{\"c\":[\"设计模式\"]},\"314\":{\"c\":[\"设计模式\",\"TypeScript\",\"管理状态\"]},\"315\":{\"h\":\"Prototype 模式\"},\"316\":{\"h\":\"为什么要使用 Prototype 模式\",\"t\":[\"Prototype 模式是一种创建型设计模式，它允许你复制现有对象而无需使代码依赖它们所属的类。使用 Prototype 模式可以：\",\"避免重复初始化对象的复杂过程。\",\"提高性能，特别是在创建对象代价较高时。\",\"简化代码，使得对象的创建更加灵活。\",\"对象种类繁多，无法将它们整合到一个类中\",\"难以根据类生成实例\",\"解耦框架与生成的实例\"]},\"317\":{\"h\":\"示例代码\",\"t\":[\"// main.ts import { Manager } from './manager'; import { UnderlinePen } from './underlinePen'; import { MessageBox } from './messageBox'; let manager = new Manager(); let upen = new UnderlinePen('~'); let mbox = new MessageBox('*'); let sbox = new MessageBox('/'); manager.register('strong message', upen); manager.register('warning box', mbox); manager.register('slash box', sbox); let p1 = manager.create('strong message'); p1.use('Hello, world.'); let p2 = manager.create('warning box'); p2.use('Hello, world.'); let p3 = manager.create('slash box'); p3.use('Hello, world.'); // manager.ts export class Manager { private showcase: { [key: string]: any } = {}; register(name: string, proto: any) { this.showcase[name] = proto; } create(name: string): any { const p = this.showcase[name]; return p.createClone(); } } // messageBox.ts import { Product } from \\\"./product\\\"; export class MessageBox implements Product { private decochar: string; constructor(decochar: string) { this.decochar = decochar; } use(s: string): void { const length = s.length; console.log(this.decochar.repeat(length + 4)); console.log(`${this.decochar} ${s} ${this.decochar}`); console.log(this.decochar.repeat(length + 4)); } createClone(): Product { let p: Product = null; try { p = <Product>Object.create(this); } catch (e) { console.error(e); } return p; } } // product.ts export interface Product { use(s:String): void; createClone(): Product; } // underlinePen.ts import { Product } from './product'; export class UnderlinePen implements Product { private ulchar: string; constructor(ulchar: string) { this.ulchar = ulchar; } use(s: string): void { const length = s.length; console.log(`\\\"${s}\\\"`); console.log(' '); console.log(` ${this.ulchar.repeat(length)}`); console.log(' '); } createClone(): Product { let p: Product = null; try { p = Object.create(this); } catch (e) { console.log(e); } return p; } } \"]},\"318\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\prototype\\\\main.ts\\\" \\\"Hello, world.\\\" ~~~~~~~~~~~~~ ***************** * Hello, world. * ***************** ///////////////// / Hello, world. / ///////////////// \"]},\"319\":{\"h\":\"相关设计模式\",\"t\":[\"Flyweight 模式\",\"Memento 模式\",\"Composite 模式\",\"Decorator 模式\",\"Command 模式\"]},\"320\":{\"c\":[\"设计模式\"]},\"321\":{\"c\":[\"设计模式\",\"typescript\",\"生成实例\"]},\"322\":{\"h\":\"Proxy 模式\"},\"323\":{\"h\":\"为什么使用代理模式\",\"t\":[\"在面向对象编程中，“本人”和“代理人”都是对象。如果“本人”对象太忙了．有些工作无法自己亲自完成，就将其交给“代理人\\\"对象负责。\",\"Proxy 模式用于为某对象提供一个代理，以控制对该对象的访问。主要有以下几个优点：\",\"延迟实例化：代理对象可以在需要时才创建实际对象，节省资源。\",\"控制访问：可以在代理中加入额外的逻辑来控制对实际对象的访问。\",\"远程代理：可以用于访问远程对象。\"]},\"324\":{\"h\":\"实例代码\",\"t\":[\"为了让 PrinterProxy 类与 Printer 类具有一致性，我们定义了 Printable 接口。示例程序的前提是\\\"生成 Printer 类的实例\\\"这一处理需要花费很多时间。为了在程序中体现这一点，我们在 Printer 类的构造了数中调用了 heavyJob 方法，让它干一些“重活”（虽说是重活，也不过是让程序睡眠 5 秒钟）。\",\"// main.ts import { Printable } from './printable'; import { PrinterProxy } from './printerProxy'; let p: Printable = new PrinterProxy('Alice'); console.log('名字现在是' + p.getPrinterName() + '。'); p.setPrinterName('Bob'); console.log('名字现在是' + p.getPrinterName() + '。'); p.print('你好，世界。'); // printable.ts export interface Printable { setPrinterName(name: string): void; getPrinterName(): string; print(str:string): void; } // printer.ts import { Printable } from \\\"./printable\\\"; export class Printer implements Printable { private name: string; constructor(name: string) { this.name = name; this.heavyJob(`正在生成Printer的实例(${this.name})`); } setPrinterName(name: string): void { this.name = name; } getPrinterName(): string { return this.name; } print(str:string): void { console.log(`=== ${this.name} ===`); console.log(str); } private heavyJob(msg: string): void { console.log(msg); for (let i = 0; i < 5; i++) { try { console.log(\\\".\\\"); setTimeout(() => { console.log(\\\".\\\"); }, 1000); } catch (e) { console.log(e); } } console.log(\\\"完了。\\\"); } } // printerProxy.ts import { Printable } from './printable'; import { Printer } from './printer'; export class PrinterProxy implements Printable { private name: string; private real: Printer; constructor(name: string) { this.name = name; } setPrinterName(name: string): void { if (this.real !== undefined) { this.real.setPrinterName(name); } this.name = name; } getPrinterName(): string { return this.name; } print(str: string): void { this.realize(); this.real.print(str); } private realize(): void { if (this.real === undefined) { this.real = new Printer(this.name); } } } \"]},\"325\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\proxy\\\\main.ts\\\" 名字现在是Alice。 名字现在是Bob。 正在生成Printer的实例(Bob) . . . . . 完了。 === Bob === 你好，世界。 . . . . . \"]},\"326\":{\"h\":\"拓展思路的要点\"},\"327\":{\"h\":\"使用代理人来提升处理速度\",\"t\":[\"在某些情况下，使用代理可以显著提升处理速度。例如，虚拟代理（Virtual Proxy）可以在实际对象创建之前进行一些轻量级的操作，从而减少系统的开销。通过代理对象来延迟实际对象的创建，可以提高系统的响应速度和资源利用率。\"]},\"328\":{\"h\":\"有必要划分代理人和本人吗\",\"t\":[\"在设计模式中，代理人和本人的划分是为了实现职责分离和提高系统的灵活性。代理模式通过引入代理对象来控制对实际对象的访问，可以在不修改实际对象的情况下添加额外的功能。例如，远程代理（Remote Proxy）可以在客户端和远程服务器之间进行通信，而不需要客户端了解远程服务器的具体实现。\"]},\"329\":{\"h\":\"代理与委托\",\"t\":[\"代理模式和委托模式虽然在某些方面有相似之处，但它们的目的和实现方式有所不同。代理模式主要用于控制对对象的访问，而委托模式则用于将任务分配给其他对象来执行。代理模式通过代理对象来控制对实际对象的访问，而委托模式通过委托对象来执行具体的任务。\"]},\"330\":{\"h\":\"透明性\",\"t\":[\"代理模式的一个重要特点是透明性。代理对象和实际对象实现相同的接口，客户端可以像使用实际对象一样使用代理对象，而不需要关心代理对象的内部实现。这种透明性使得代理模式在不改变客户端代码的情况下添加额外的功能成为可能。\"]},\"331\":{\"h\":\"HTTP 代理\",\"t\":[\"HTTP 代理是一种常见的代理模式应用。HTTP 代理服务器位于客户端和目标服务器之间，负责转发客户端的请求和目标服务器的响应。HTTP 代理可以用于缓存、负载均衡、安全控制等功能，从而提高网络通信的效率和安全性。\"]},\"332\":{\"h\":\"各种 Proxy 模式\",\"t\":[\"Virtual Proxy：虚拟代理用于控制对资源密集型对象的访问。它在实际对象创建之前进行一些轻量级的操作，从而延迟实际对象的创建。例如，图像加载时可以使用虚拟代理来显示占位符图像，直到实际图像加载完成。\",\"Remote Proxy：远程代理用于控制对远程对象的访问。它在客户端和远程服务器之间进行通信，使得客户端可以像使用本地对象一样使用远程对象。例如，RMI（远程方法调用）就是一种远程代理的实现。\",\"Access Proxy：访问代理用于控制对实际对象的访问权限。它可以在访问实际对象之前进行权限检查，从而确保只有授权的客户端才能访问实际对象。例如，防火墙代理可以用于控制对内部网络资源的访问。\",\"通过这些不同类型的代理模式，我们可以在不同的应用场景中灵活地控制对对象的访问，提高系统的安全性、性能和可维护性。\"]},\"333\":{\"h\":\"相关的设计模式\",\"t\":[\"Adapter 模式\",\"Decorator 模式\"]},\"334\":{\"c\":[\"设计模式\"]},\"335\":{\"c\":[\"设计模式\",\"TypeScript\",\"避免浪费\"]},\"336\":{\"h\":\"Singleton 模式\"},\"337\":{\"h\":\"为什么要使用 Singleton 模式\",\"t\":[\"Singleton 模式确保一个类只有一个实例，并提供一个全局访问点。它常用于需要控制资源访问的场景，例如数据库连接、日志记录器等。通过 Singleton 模式，可以避免创建多个实例带来的资源浪费和不一致性问题。\"]},\"338\":{\"h\":\"总结:\",\"t\":[\"想确保任何情况下都绝对只有 1 个实例\",\"想在程序上表现出“只存在一个实例”\"]},\"339\":{\"h\":\"示例代码\",\"t\":[\"// main.ts import { Singleton } from './singleton'; const singleton1 = Singleton.getInstance(); const singleton2 = Singleton.getInstance(); console.log(singleton1 === singleton2); // true // singleton.ts export class Singleton { private static instance: Singleton | null = null; private static generatedId: number = 0; private constructor() { Singleton.generatedId++; console.log(`Singleton instance created with id: ${Singleton.generatedId}`); } public static getInstance(): Singleton { if (this.instance === null) { this.instance = new Singleton(); } return this.instance; } } \"]},\"340\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\singleton\\\\main.ts\\\" Singleton instance created with id: 1 true \"]},\"341\":{\"h\":\"相关设计模式\",\"t\":[\"abstractFactory 模式\",\"Builder 模式\",\"Facade 模式\",\"Prototype 模式\"]},\"342\":{\"h\":\"多线程下\",\"t\":[\"在多线程环境中，Singleton 模式的实现需要特别注意线程安全问题。如果多个线程同时访问 getInstance 方法，可能会导致创建多个实例。为了解决这个问题，可以使用双重检查锁定（Double-Checked Locking）或其他线程同步机制。\"]},\"343\":{\"h\":\"双重检查锁定示例代码\",\"t\":[\"export class Singleton { private static instance: Singleton | null = null; private static generatedId: number = 0; private static lock: any = {}; private constructor() { Singleton.generatedId++; console.log(`Singleton instance created with id: ${Singleton.generatedId}`); } public static getInstance(): Singleton { if (this.instance === null) { synchronized(this.lock, () => { if (this.instance === null) { this.instance = new Singleton(); } }); } return this.instance; } } function synchronized(lock: any, fn: () => void) { // Simulate a lock mechanism fn(); } \",\"在上面的代码中，synchronized 函数模拟了一个锁机制，以确保在多线程环境下 getInstance 方法的线程安全性。\"]},\"344\":{\"c\":[\"设计模式\"]},\"345\":{\"c\":[\"设计模式\",\"typescript\",\"生成实例\"]},\"346\":{\"h\":\"State 模式\"},\"347\":{\"h\":\"为什么使用 State 模式\",\"t\":[\"State 模式允许对象在其内部状态改变时改变其行为。它将与状态相关的行为封装在独立的类中，使得状态转换变得清晰且易于管理。使用 State 模式可以避免大量的条件语句，使代码更加简洁和可维护。\"]},\"348\":{\"h\":\"示例代码\",\"t\":[\"// context.ts import { State } from './state'; export interface Context { setClock(hour: number): void; changeState(state: State): void; callSecurityCenter(msg: string): void; recordLog(msg: string): void; } // dayState.ts import { State } from './state'; import { Context } from './context'; import { NightState } from './nightState'; export class DayState implements State { private static singleton: DayState = new DayState(); private constructor() {} public static getInstance(): State { return this.singleton; } public doClock(context: Context, hour: number): void { if (hour < 9 || 17 <= hour) { context.changeState(NightState.getInstance()); } } public doUse(context: Context): void { context.recordLog('金库使用(白天)'); } public doAlarm(context: Context): void { context.callSecurityCenter('紧急铃(白天)'); } public doPhone(context: Context): void { context.callSecurityCenter('正常通话(白天)'); } public toString(): string { return '[白天]'; } } // main.ts import { SafeFrame } from './safeFrame'; const safeFrame: SafeFrame = new SafeFrame(); for (let hour: number = 0; hour < 24; hour++) { safeFrame.setClock(hour); safeFrame.doUse(); safeFrame.doAlarm(); safeFrame.doPhone(); } // nightState.ts import { State } from './state'; import { Context } from './context'; import { DayState } from './dayState'; export class NightState implements State { private static singleton: NightState = new NightState(); private constructor() {} public static getInstance(): State { return this.singleton; } public doClock(context: Context, hour: number): void { if (9 <= hour && hour < 17) { context.changeState(DayState.getInstance()); } } public doUse(context: Context): void { context.callSecurityCenter('紧急：夜间使用金库！'); } public doAlarm(context: Context): void { context.callSecurityCenter('紧急铃(夜间)'); } public doPhone(context: Context): void { context.recordLog('夜间通话录音'); } public toString(): string { return '[夜间]'; } } // safeFrame.ts import { Context } from './context'; import { State } from './state'; import { DayState } from './dayState'; export class SafeFrame implements Context { private state: State = DayState.getInstance(); public setClock(hour: number): void { let clockString: string = '現在時刻は'; if (hour < 10) { clockString += `0${hour}:00`; } else { clockString += `${hour}:00`; } console.log(clockString); this.state.doClock(this, hour); } public changeState(state: State): void { console.log(`${this.state.toString()}から${state.toString()}へ状態が変化しました。`); this.state = state; } public callSecurityCenter(msg: string): void { console.log(`call! ${msg}`); } public recordLog(msg: string): void { console.log(`record ... ${msg}`); } public doUse(): void { this.state.doUse(this); } public doAlarm(): void { this.state.doAlarm(this); } public doPhone(): void { this.state.doPhone(this); } } // state.ts import { Context } from './context'; export interface State { doClock(context: Context, hour: number): void; doUse(context: Context): void; doAlarm(context: Context): void; doPhone(context: Context): void; } \"]},\"349\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\state\\\\main.ts\\\" 現在時刻は00:00 [白天]から[夜间]へ状態が変化しました。 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は01:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は02:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は03:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は04:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は05:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は06:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は07:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は08:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は09:00 [夜间]から[白天]へ状態が変化しました。 record ... 金库使用(白天) call! 紧急铃(白天) call! 正常通话(白天) 現在時刻は10:00 record ... 金库使用(白天) call! 紧急铃(白天) call! 正常通话(白天) 現在時刻は11:00 record ... 金库使用(白天) call! 紧急铃(白天) call! 正常通话(白天) 現在時刻は12:00 record ... 金库使用(白天) call! 紧急铃(白天) call! 正常通话(白天) 現在時刻は13:00 record ... 金库使用(白天) call! 紧急铃(白天) call! 正常通话(白天) 現在時刻は14:00 record ... 金库使用(白天) call! 紧急铃(白天) call! 正常通话(白天) 現在時刻は15:00 record ... 金库使用(白天) call! 紧急铃(白天) call! 正常通话(白天) 現在時刻は16:00 record ... 金库使用(白天) call! 紧急铃(白天) call! 正常通话(白天) 現在時刻は17:00 [白天]から[夜间]へ状態が変化しました。 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は18:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は19:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は20:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は21:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は22:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は23:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 \"]},\"350\":{\"h\":\"拓展思路的要点\"},\"351\":{\"h\":\"分而治之\",\"t\":[\"在编程时，我们经常会使用分而治之的方针。它非常适用于大规模的复杂处理。当遇到庞大且复杂的问题、不能用一般的方法解决时，我们会先将该问题分解为多个小问题。如果还是不能解决这些小问题，我们会将它们继续划分为更小的问题，直至可以解决它们为止。\",\"分而治之，简单而言就是将一个复杂的大问题分解为多个小问题然后逐个解决。在 State 模式中，我们用类来表示状态，并为每一种具体的状态都定义一个相应的类。这样，问题就被分解了。开发人员可以在编写一个 ConcreteState 角色的代码的同时，在头脑中（一定程度上）考虑其他的类。\",\"在本章的警报系统的示例程序中，只有“白天”和“晚上”两个状态，可能大家对此感受不深，但是当状态非常多的时候，State 模式的优势就会非常明显了。在不使用 State 模式时，我们需要使用条件分支语句判断当前的状态，然后进行相应的处理。状态越多，条件分支就会越多，而且我们必须在所有的事件处理方法中都编写这些条件分支语句。State 模式用类表示系统的“状态”，并以此将复杂的程序分解开来。\"]},\"352\":{\"h\":\"依赖于状态的处理\",\"t\":[\"我们来思考一下 SafeFrame 类的 setClock 方法和 State 接口的 doClock 方法之间的关系。Main 类会调用 SafeFrame 类的 setClock 方法，告诉 setClock 方法“请设置时间”。在 setClock 方法中，会像下面这样将处理委托给 State 类：state.doClock(this, hour);。也就是说，我们将设置时间的处理看作是“依赖于状态的处理”。当然，不只是 doClock 方法。在 State 接口中声明的所有方法都是“依赖于状态的处理”，都是“状态不同处理也不同”。这虽然看似理所当然，不过却需要我们特别注意。在 State 模式中，我们应该如何编程，以实现“依赖于状态的处理”呢？总结起来有如下两点：\",\"定义接口，声明抽象方法\",\"定义多个类，实现具体方法\",\"这就是 State 模式中的“依赖于状态的处理”的实现方法。这里故意将上面两点说得很笼统，但是，如果大家在读完这两点之后会点头表示赞同，那就意味着大家完全理解了 State 模式以及接口与类之间的关系。\"]},\"353\":{\"h\":\"应当是谁来管理状态的迁移\",\"t\":[\"用类来表示状态，将依赖于状态的处理分散在每个 ConcreteState 角色中，这是一种非常好的解决办法。不过，在使用模式时需要注意应当是谁来管理状态迁移。在示例程序中，扮演 Context 角色的 SafeFrame 类实现了实际进行状态迁移的 changeState 方法。但是，实际调用该方法的却是扮演 ConcreteState 角色的 DayState 类和 NightState 类。\",\"也就是说，在示例程序中，我们将“状态迁移”看作是“依赖于状态的处理”。这种处理方式既有优点也有缺点。优点是这种处理方式将“什么时候从一个状态迁移到其他状态”的信息集中在了一个类中。也就是说，当我们想知道“什么时候会从 DayState 类变化为其他状态”时，只需要阅读 DayState 类的代码就可以了。缺点是“每个 ConcreteState 角色都需要知道其他 ConcreteState 角色”。\",\"例如，DayState 类的 doClock 方法就使用了 NightState 类。这样，如果以后发生需求变更，需要删除 NightState 类时，就必须要相应地修改 DayState 类的代码。将状态迁移交给 ConcreteState 角色后，每个 ConcreteState 角色都需要或多或少地知道其他角色。也就是说，将状态迁移交给 ConcreteState 角色后，各个类之间的依赖关系就会加强。我们也可以不使用示例程序中的做法，而是将所有的状态迁移交给扮演 Context 角色的 SafeFrame 类来负责。\",\"有时，使用这种解决方法可以提高 ConcreteState 角色的独立性，程序的整体结构也会更加清晰。不过这样做的话，Context 角色就必须要知道“所有的 ConcreteState 角色”。在这种情况下，我们可以使用 Mediator 模式（第 16 章）。当然，还可以不用 State 模式，而是用状态迁移表来设计程序。所谓状态迁移表是可以根据“输入和内部状态”得到“输出和下一个状态”的一览表（这超出了本书的范围，我们暂且不深入学习该方法）。当状态迁移遵循一定的规则时，使用状态迁移表非常有效。此外，当状态数过多时，可以用程序来生成代码而不是手写代码。\"]},\"354\":{\"h\":\"不会自相矛盾\",\"t\":[\"如果不使用 State 模式，我们需要使用多个变量的值的集合来表示系统的状态。这时，必须十分小心，注意不要让变量的值之间互相矛盾。而在 State 模式中，是用类来表示状态的。这样，我们就只需要一个表示系统状态的变量即可。在示例程序中，SafeFrame 类的 state 字段就是这个变量，它决定了系统的状态。因此，不会存在自相矛盾的状态。\"]},\"355\":{\"h\":\"易于增加新的状态\",\"t\":[\"在 State 模式中增加新的状态是非常简单的。以示例程序来说，编写一个 XXXState 类，让它实现 State 接口，然后实现一些所需的方法就可以了。当然，在修改状态迁移部分的代码时，还是需要仔细一点的。因为状态迁移的部分正是与其他 ConcreteState 角色相关联的部分。\",\"但是，在 State 模式中增加其他“依赖于状态的处理”是很困难的。这是因为我们需要在 State 接口中增加新的方法，并在所有的 ConcreteState 角色中都实现这个方法。虽说很困难，但是好在我们绝对不会忘记实现这个方法。假设我们现在在 State 接口中增加了一个 doYYY 方法，而忘记了在 DayState 类和 NightState 类中实现这个方法，那么编译器在编译代码时就会报错，告诉我们存在还没有实现的方法。\",\"如果不使用 State 模式，那么增加新的状态时会怎样呢？这里，如果不使用 State 模式，就必须用条件分支语句判断状态。这样就很难在编译代码时检测出“忘记实现方法”这种错误了（在运行时检测出问题并不难。我们只要事先在每个方法内部都加上一段“当检测到没有考虑到的状态时就报错”的代码即可）。\"]},\"356\":{\"h\":\"实例的多面性\",\"t\":[\"请注意 SafeFrame 类中的以下两条语句（代码清单 19.7）：\",\"SafeFrame 类的构造函数中的 buttonUse.addActionListener(this);\",\"actionPerformed 方法中的 state.doUse(this);\",\"这两条语句中都有 this。那么这个 this 到底是什么呢？当然，它们都是 SafeFrame 类的实例。由于在示例程序中只生成了一个 SafeFrame 的实例，因此这两个 this 其实是同一个对象。不过，在 addActionListener 方法中和 doUse 方法中，对 this 的使用方式是不一样的。\",\"向 addActionListener 方法传递 this 时，该实例会被当作“实现了 ActionListener 接口的类的实例”来使用。这是因为 addActionListener 方法的参数类型是 ActionListener 类型。\",\"在 addActionListener 方法中会用到的方法也都是在 ActionListener 接口中定义了的方法。至于这个参数是否是 SafeFrame 类的实例并不重要。向 doUse 方法传递 this 时，该实例会被当作“实现了 Context 接口的类的实例”来使用。这是因为 doUse 方法的参数类型是 Context 类型。在 doUse 方法中会用到的方法也都是在 Context 接口中定义了的方法（大家只要再回顾一下 DayState 类和 NightState 类的 doUse 方法就会明白了）。请大家一定要透彻理解此处的实例的多面性。\"]},\"357\":{\"h\":\"相关的设计模式\",\"t\":[\"Singleton 模式\",\"Flyweight 模式\"]},\"358\":{\"c\":[\"设计模式\"]},\"359\":{\"c\":[\"设计模式\",\"TypeScript\",\"管理状态\"]},\"360\":{\"h\":\"Strategy 模式\"},\"361\":{\"h\":\"使用此设计模式的理由\",\"t\":[\"在这个示例程序中，我们使用了策略模式（Strategy Pattern）来实现不同的猜拳策略。策略模式的主要优点包括：\",\"易于扩展：可以很容易地添加新的策略，而不需要修改现有的代码。\",\"提高代码的可读性和可维护性：将不同的算法封装在独立的类中，使得代码更加清晰。\",\"减少重复代码：通过使用策略模式，可以避免在多个地方重复相同的算法逻辑。\"]},\"362\":{\"h\":\"示例程序\",\"t\":[\"下面我们来看一段使用了 strategy 模式的示例程序。这段示例程序的功能是让电脑玩“猜拳\\\"游戏。\",\"我们考虑了两种猜拳的策略。第一种策略是“如果这局猜拳获胜，那么下一局也出一样的手势\\\" (WinningStrategy), 这是一种稍微有些笨的策略；另外一种策略是“根据上一局的手势从概率上计算出下一局的手势\\\"（ ProbStrategy ）。\",\"// hand.ts export enum HandValue { GUU = 0, CHO = 1, PAA = 2, } export class Hand { //NOTE - 使用了单例模式 private static readonly hand: Hand[] = [ new Hand(HandValue.GUU), new Hand(HandValue.CHO), new Hand(HandValue.PAA), ]; private static readonly names: string[] = ['石头', '剪刀', '布']; private handValue: HandValue; private constructor(handValue: HandValue) { this.handValue = handValue; } static getHand(handValue: HandValue): Hand { return this.hand[handValue]; } isStrongerThan(h: Hand): boolean { return this.fight(h) === 1; } isWeakerThan(h: Hand): boolean { return this.fight(h) === -1; } private fight(h: Hand): number { if (this === h) { return 0; } else if ((this.handValue + 1) % 3 === h.handValue) { return 1; } else { return -1; } } toString(): string { return Hand.names[this.handValue]; } } // main.ts import { Player } from \\\"./player\\\"; import { WinningStrategy } from \\\"./winningStrategy\\\"; import { ProbStrategy } from \\\"./probStrategy\\\"; const player1 = new Player(\\\"Taro\\\", new WinningStrategy()); const player2 = new Player(\\\"Hana\\\", new ProbStrategy()); for (let i = 0; i < 10000; i++) { const nextHand1 = player1.nextHand(); const nextHand2 = player2.nextHand(); if (nextHand1.isStrongerThan(nextHand2)) { console.log(`Winner: ${player1.toString()}`); player1.win(); player2.lose(); } else if (nextHand2.isStrongerThan(nextHand1)) { console.log(`Winner: ${player2.toString()}`); player1.lose(); player2.win(); } else { console.log(\\\"Even...\\\"); player1.even(); player2.even(); } } console.log(\\\"Total result:\\\"); console.log(player1.toString()); console.log(player2.toString()); // Output // player.ts import { Hand } from './hand'; import { Strategy } from './strategy'; export class Player { private name: string; private strategy: Strategy; private wincount = 0; private losecount = 0; private gamecount = 0; constructor(name: string, strategy: Strategy) { this.name = name; this.strategy = strategy; } nextHand(): Hand { return this.strategy.nextHand(); } win(): void { this.strategy.study(true); this.wincount++; this.gamecount++; } lose(): void { this.strategy.study(false); this.losecount++; this.gamecount++; } even(): void { this.gamecount++; } toString(): string { return `[${this.name}:${this.gamecount} games, ${this.wincount} win, ${this.losecount} lose]`; } } // probStrategy.ts import { Hand } from './hand'; import { Strategy } from './strategy'; export class ProbStrategy implements Strategy { private prevHandValue = 0; private currentHandValue = 0; private history: number[][] = [ [1, 1, 1], [1, 1, 1], [1, 1, 1], ]; constructor() {} nextHand(): Hand { const bet = Math.floor(Math.random() * this.getSum(this.currentHandValue)); let handvalue = 0; if (bet < this.history[this.currentHandValue][0]) { handvalue = 0; } else if (bet < this.history[this.currentHandValue][0] + this.history[this.currentHandValue][1]) { handvalue = 1; } else { handvalue = 2; } this.prevHandValue = this.currentHandValue; this.currentHandValue = handvalue; return Hand.getHand(handvalue); } private getSum(hv: number): number { let sum = 0; for (let i = 0; i < 3; i++) { sum += this.history[hv][i]; } return sum; } study(win: boolean): void { if (win) { this.history[this.prevHandValue][this.currentHandValue]++; } else { this.history[this.prevHandValue][(this.currentHandValue + 1) % 3]++; this.history[this.prevHandValue][(this.currentHandValue + 2) % 3]++; } } } // strategy.ts import { Hand } from './hand'; export interface Strategy { nextHand(): Hand; study(win: boolean): void; } // winningStrategy.ts import { Hand } from './hand'; import { Strategy } from './strategy'; export class WinningStrategy implements Strategy { private won = false; private prevHand: Hand; constructor() {} nextHand(): Hand { if (!this.won) { this.prevHand = Hand.getHand(Math.floor(Math.random() * 3)); } return this.prevHand; } study(win: boolean): void { this.won = win; } } \"]},\"363\":{\"h\":\"运行结果\",\"t\":[\"...(省略) Winner: [Hana:9991 games, 3567 win, 3049 lose] Winner: [Hana:9992 games, 3568 win, 3049 lose] Even... Winner: [Hana:9994 games, 3569 win, 3049 lose] Even... Even... Winner: [Hana:9997 games, 3570 win, 3049 lose] Winner: [Hana:9998 games, 3571 win, 3049 lose] Winner: [Hana:9999 games, 3572 win, 3049 lose] Total result: [Taro:10000 games, 3049 win, 3573 lose] [Hana:10000 games, 3573 win, 3049 lose] \"]},\"364\":{\"h\":\"拓展思路的要点\"},\"365\":{\"h\":\"为什么要特意编写 Strategy\",\"t\":[\"通常在编程时算法会被写在具体方法中。Strategy 模式却特意将算法与其他部分分离开来，只是定义了与算法相关的接口（API），然后在程序中以委托的方式来使用算法。\",\"这样看起来程序好像变复杂了，其实不然。例如，当我们想要通过改善算法来提高算法的处理速度时，如果使用了 Strategy 模式，就不必修改 Strategy 角色的接口（API）了，仅仅修改 ConcreteStrategy 角色即可。而且，使用委托这种弱关联关系可以很方便地整体替换算法。例如，如果想比较原来的算法与改进后的算法的处理速度有多大区别，简单地替换下算法即可进行测试。\",\"使用 Strategy 模式编写象棋程序时，可以方便地根据棋手的选择切换 AI 例程的水平。\"]},\"366\":{\"h\":\"程序运行中也可以切换策略\",\"t\":[\"如果使用 Strategy 模式，在程序运行中也可以切换角色。例如，在内存容量少的运行环境中可以使用 SlowButLessMemoryStrategy（速度慢但省内存的策略），而在内存容量多的运行环境中则可以使用 FastButMoreMemoryStrategy（速度快但耗内存的策略）。\",\"此外，还可以用某种算法去“验算”另外一种算法。例如，假设要在某个表格计算软件的开发版本中进行复杂的计算。这时，我们可以准备两种算法，即“高速但计算上可能有 Bug 的算法”和“低速但计算准确的算法”，然后让后者去验算前者的计算结果。\"]},\"367\":{\"h\":\"相关的设计模式\",\"t\":[\"Flyweight 模式\",\"Abstract Factory 模式\",\"State 模式\"]},\"368\":{\"c\":[\"设计模式\"]},\"369\":{\"c\":[\"设计模式\",\"TypeScript\",\"分开考虑\",\"整体的替换算法\"]},\"370\":{\"h\":\"Template Method 模式\",\"t\":[\"在父类中定义处理流程的框架，在子类中实现具体处理。Template Method 模式的主要目的是为了定义一个算法的骨架，而将一些步骤的具体实现延迟到子类中。通过这种方式，子类可以在不改变算法结构的情况下，重新定义算法中的某些步骤。\"]},\"371\":{\"h\":\"为什么要使用 Template Method 模式？\",\"t\":[\"代码复用：将通用的算法结构放在父类中，避免重复代码。\",\"灵活性：允许子类实现具体的步骤，增加了灵活性。\",\"控制反转：父类控制算法的执行流程，子类只需关注具体步骤的实现。\"]},\"372\":{\"h\":\"示例代码\",\"t\":[\"// abstractDisplay.ts export abstract class AbstractDisplay { protected abstract open(): void; protected abstract print(): void; protected abstract close(): void; display(): void { this.open(); for (let i = 0; i < 5; i++) { this.print(); } this.close(); } } // charDisplay.ts import { AbstractDisplay } from './abstractDisplay'; export class CharDisplay extends AbstractDisplay { private ch: string; constructor(ch: string) { super(); this.ch = ch; } open() { console.log('<<'); } print() { console.log(this.ch); } close() { console.log('>>'); } } // stringDisplay.ts import { AbstractDisplay } from './abstractDisplay'; export class StringDisplay extends AbstractDisplay { private str: string; private width: number; constructor(str: string) { super(); this.str = str; this.width = str.length; } open() { this.printLine(); } print() { console.log(`|${this.str}|`); } close() { this.printLine(); } private printLine() { let line = '+'; for (let i = 0; i < this.width; i++) { line += '-'; } line += '+'; console.log(line); } } // main.ts import { CharDisplay } from './charDisplay'; import { StringDisplay } from './stringDisplay'; const d1 = new CharDisplay('H'); const d2 = new StringDisplay('Hello, world.'); const d3 = new StringDisplay('你好，世界。'); d1.display(); d2.display(); d3.display(); \"]},\"373\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\template_method\\\\main.ts\\\" << H H H H H >> +-------------+ |Hello, world.| |Hello, world.| |Hello, world.| |Hello, world.| |Hello, world.| +-------------+ +------+ |你好，世界。| |你好，世界。| |你好，世界。| |你好，世界。| |你好，世界。| +------+ \"]},\"374\":{\"h\":\"相关设计模式\",\"t\":[\"Factory Method 模式\",\"Strategy 模式\"]},\"375\":{\"h\":\"延申: 类的层次与抽象类\",\"t\":[\"我们在理解类的层次时，通常是站在子类的角度进行思考的。也就是说，很容易着眼于以下几点。\",\"在子类中可以使用父类中定义的方法\",\"可以通过在子类中增加方法以实现新的功能\",\"在子类中重写父类的方法可以改变程序的行为\",\"现在，让我们稍微改变一下立场，站在父类的角度进行思考。在父类中，我们声明了抽象方法，而将该方法的实现交给了子类。换言之，就程序而言，声明抽象方法是希望达到以下目的。\",\"期待子类去实现抽象方法\",\"要求子类去实现抽象方法\",\"也就是说，子类具有实现在父类中所声明的抽象方法的责任。因此，这种责任被称为“子类责任\\\"（ subclass responsibility ）。\"]},\"376\":{\"c\":[\"设计模式\"]},\"377\":{\"c\":[\"设计模式\",\"typescript\",\"交给子类\"]},\"378\":{\"h\":\"Visitor 模式\",\"t\":[\"在 Visitor 模式中，数据结构与处理被分离开来。我们编写一个表示“访问者”的类来访问数据结构中的元素，并把对各元素的处理交给访问者类。这样，当需要增加新的处理时，我们只需要编写新的访问者，然后让数据结构可以接受访问者的访问即可。\"]},\"379\":{\"h\":\"为什么使用 Visitor 模式？\",\"t\":[\"分离关注点：将数据结构与操作分离，使得代码更清晰、更易维护。\",\"增加新操作更容易：只需添加新的访问者类，而不需要修改现有的数据结构。\",\"符合开闭原则：对扩展开放，对修改关闭。\"]},\"380\":{\"h\":\"示例代码\",\"t\":[\"// directory.ts import { Entry } from './entry'; import { Visitor } from './visitor'; export class Directory extends Entry { private dir: Entry[] = []; constructor(private name: string) { super(); } getName() { return this.name; } getSize() { let size = 0; this.dir.forEach((entry) => { size += entry.getSize(); }); return size; } add(entry: Entry) { this.dir.push(entry); return this; } iterator() { return this.dir; } accept(visitor:Visitor) { visitor.visit(this); } } // element.ts import { Visitor } from './visitor'; export interface Element { accept(visitor: Visitor): void; } // entry.ts import { Element } from \\\"./element\\\"; import { Visitor } from \\\"./visitor\\\"; export abstract class Entry implements Element { abstract getName(): string; abstract getSize(): number; add(entry: Entry): Entry { throw new Error(\\\"Entry.add not implemented\\\"); } iterator(): Entry[] { throw new Error(\\\"Entry.iterator not implemented\\\"); } toString(): string { return `${this.getName()} (${this.getSize()})`; } abstract accept(visitor: Visitor): void; } // file.ts import { Visitor } from './visitor'; import { Entry } from './entry'; export class File extends Entry { constructor(private name: string, private size: number) { super(); } getName(): string { return this.name; } getSize(): number { return this.size; } accept(visitor: Visitor): void { visitor.visit(this); } } // listVisitor.ts import { Visitor } from \\\"./visitor\\\"; import { File } from \\\"./file\\\"; import { Directory } from \\\"./directory\\\"; import { Entry } from \\\"./entry\\\"; export class ListVisitor extends Visitor { private currentdir = \\\"\\\"; visit(entry:Entry) { if (entry instanceof File) { console.log(`${this.currentdir}/${entry}`); } else if (entry instanceof Directory) { console.log(`${this.currentdir}/${entry}`); const savedir = this.currentdir; this.currentdir = `${this.currentdir}/${entry.getName()}`; const it: Entry[] = entry.iterator(); for (let i = 0; i < it.length; i++) { it[i].accept(this); } this.currentdir = savedir; } } } // main.ts import { Directory } from \\\"./directory\\\"; import { File } from \\\"./file\\\"; import { ListVisitor } from \\\"./listVisitor\\\"; console.log(\\\"Making root entries...\\\"); let rootdir = new Directory(\\\"root\\\"); let bindir = new Directory(\\\"bin\\\"); let tmpdir = new Directory(\\\"tmp\\\"); let usrdir = new Directory(\\\"usr\\\"); rootdir.add(bindir); rootdir.add(tmpdir); rootdir.add(usrdir); bindir.add(new File(\\\"vi\\\", 10000)); bindir.add(new File(\\\"latex\\\", 20000)); rootdir.accept(new ListVisitor()); console.log(\\\"Making user entries...\\\"); let yuki = new Directory(\\\"yuki\\\"); let hanako = new Directory(\\\"hanako\\\"); let tomura = new Directory(\\\"tomura\\\"); usrdir.add(yuki); usrdir.add(hanako); usrdir.add(tomura); yuki.add(new File(\\\"diary.html\\\", 100)); yuki.add(new File(\\\"Composite.java\\\", 200)); hanako.add(new File(\\\"memo.tex\\\", 300)); tomura.add(new File(\\\"game.doc\\\", 400)); tomura.add(new File(\\\"junk.mail\\\", 500)); rootdir.accept(new ListVisitor()); // visitor.ts import { Entry } from './entry'; export abstract class Visitor { abstract visit(file:Entry); } \"]},\"381\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\visitor\\\\main.ts\\\" Making root entries... /root (30000) /root/bin (30000) /root/bin/vi (10000) /root/bin/latex (20000) /root/tmp (0) /root/usr (0) Making user entries... /root (31500) /root/bin (30000) /root/bin/vi (10000) /root/bin/latex (20000) /root/tmp (0) /root/usr (1500) /root/usr/yuki (300) /root/usr/yuki/diary.html (100) /root/usr/yuki/Composite.java (200) /root/usr/hanako (300) /root/usr/hanako/memo.tex (300) /root/usr/tomura (900) /root/usr/tomura/game.doc (400) /root/usr/tomura/junk.mail (500) \"]},\"382\":{\"h\":\"拓展思路的要点\"},\"383\":{\"h\":\"双重分发\",\"t\":[\"我们来整理一下 Visitor 模式中的方法调用关系。accept（接收）方法的调用方式如下：element.accept(visitor)；而 visit（访问）方法的调用方式如下：visitor.visit(element)。对比这两个方法会发现，它们呈现出一种相反的关系。element 接收 visitor，而 visitor 又访问 element。在 Visitor 模式中，ConcreteElement 和 ConcreteVisitor 这两个角色共同决定了实际进行的处理。这种消息分发的方式一般被称为双重分发（double dispatch）。\"]},\"384\":{\"h\":\"为什么要这么复杂\",\"t\":[\"Visitor 模式的目的是将处理逻辑从数据结构中分离出来。数据结构很重要，它能够将元素集合及其关联关系组织在一起。但是，需要注意的是，保存数据结构与基于数据结构进行处理是两种不同的概念。在示例程序中，我们创建了 ListVisitor 类作为显示文件夹内容的 ConcreteVisitor 角色。此外，在练习题中，我们还要编写进行其他处理的 ConcreteVisitor 角色。通常，ConcreteVisitor 角色的开发可以独立于 File 类和 Directory 类。也就是说，Visitor 模式提高了 File 类和 Directory 类作为组件的独立性。如果将处理逻辑的方法定义在 File 类和 Directory 类中，那么每次要扩展功能，增加新的“处理”时，就不得不去修改这些类。\"]},\"385\":{\"h\":\"开闭原则——对扩展开放，对修改关闭\",\"t\":[\"在设计类时，若无特殊理由，必须要考虑到将来可能会扩展类。绝不能毫无理由地禁止扩展类。这就是“对扩展是开放的”的意思。但是，如果在每次扩展类时都需要修改现有的类就太麻烦了。所以我们需要在不修改现有类的前提下能够扩展类，这就是“对修改是关闭的”的意思。我们提倡扩展，但如果需要修改现有代码，那就不行了。在不修改现有代码的前提下进行扩展，这就是开闭原则。至此，大家已经学习了多种设计模式。那么在看到这条设计原则后，大家应该都会点头表示赞同吧。功能需求总是在不断变化，而且这些功能需求大都是“希望扩展某个功能”。因此，如果不能比较容易地扩展类，开发过程将会变得非常困难。另一方面，如果要修改已经编写和测试完成的类，又可能会导致软件产品的质量降低。对扩展开放、对修改关闭的类具有高可复用性，可作为组件复用。设计模式和面向对象的目的正是为我们提供一种结构，可以帮助我们设计出这样的类。\"]},\"386\":{\"h\":\"易于增加 ConcreteVisitor 角色\",\"t\":[\"使用 Visitor 模式可以很容易地增加 ConcreteVisitor 角色。因为具体的处理被交给 ConcreteVisitor 角色负责，因此完全不用修改 ConcreteElement 角色。\"]},\"387\":{\"h\":\"难以增加 ConcreteElement 角色\",\"t\":[\"尽管使用 Visitor 模式可以很容易地增加 ConcreteVisitor 角色，但它却难以应对 ConcreteElement 角色的增加。例如，假设现在我们要在示例程序中增加一个 Device 类，它是 File 类和 Directory 类的兄弟类。这时，我们不得不在 Visitor 类中声明一个 visit(Device) 方法，并在所有的 Visitor 类的子类中都实现这个方法。\"]},\"388\":{\"h\":\"Visitor 工作所需的条件\",\"t\":[\"在 Visitor 模式中，对数据结构中的元素进行处理的任务被分离出来，交给 Visitor 类负责。这样，就实现了数据结构与处理的分离。这个主题，我们在本章的学习过程中已经提到过很多次了。但是要达到这个目的是有条件的，那就是 Element 角色必须向 Visitor 角色公开足够多的信息。例如，在示例程序中，visit(Directory) 方法需要调用每个目录条目的 accept 方法。为此，Directory 类必须提供用于获取每个目录条目的 iterator 方法。只有当访问者从数据结构中获取了足够多的信息后才能工作。如果无法获取到这些信息，它就无法工作。这样做的缺点是，如果公开了不应当被公开的信息，将来对数据结构的改良就会变得非常困难。\"]},\"389\":{\"h\":\"相关的设计模式\",\"t\":[\"Iterator 模式\",\"Composite 模式\",\"Interpreter 模式\"]},\"390\":{\"c\":[\"设计模式\"]},\"391\":{\"c\":[\"设计模式\",\"TypeScript\",\"访问数据结构并处理数据\"]},\"392\":{\"h\":\"手把手教你构建 C 语言编译器（0）- 前言\",\"t\":[\"本文转载自 手把手教你构建 C 语言编译器（0）- 前言，原作者 三点水，原文链接：原文链接，如有侵权，请联系删除。\",\"转载工具:devtool、helloworld\",\"“手把手教你构建 C 语言编译器” 这一系列教程将带你从头编写一个 C 语言的编译器。希望通过这个系列，我们能对编译器的构建有一定的了解，同时，我们也将构建出一个能用的 C 语言编译器，尽管有许多语法并不支持。\",\"手把手教你构建 C 语言编译器系列共有10个部分：\",\"手把手教你构建 C 语言编译器（0）——前言\",\"手把手教你构建 C 语言编译器（1）——设计\",\"手把手教你构建 C 语言编译器（2）——虚拟机\",\"手把手教你构建 C 语言编译器（3）——词法分析器\",\"手把手教你构建 C 语言编译器（4）——递归下降\",\"手把手教你构建 C 语言编译器（5）——变量定义\",\"手把手教你构建 C 语言编译器（6）——函数定义\",\"手把手教你构建 C 语言编译器（7）——语句\",\"手把手教你构建 C 语言编译器（8）——表达式\",\"手把手教你构建 C 语言编译器（9）——总结\",\"在开始进入正题之前，本篇是一些闲聊，谈谈这个系列的初衷。如果你急切地想进入正篇，请跳过本章。\"]},\"393\":{\"h\":\"为什么要学编译原理\",\"t\":[\"如果要我说计算机专业最重要的三门课，我会说是《数据结构》、《算法》和《编译原理》。在我看来，能不能理解“递归”像是程序员的第一道门槛，而会不会写编译器则是第二道。\",\"（当然，并不是说是没写过编译器就不是好程序员，只能说它是一个相当大的挑战吧）\",\"以前人们会说，学习了编译原理，你就能写出更加高效的代码，但随着计算机性能的提升，代码是否高效显得就不那么重要了。那么为什么要学习编译原理呢？\",\"原因只有一个：装B。\",\"好吧，也许现在还想学习编译原理的人只可能是因为兴趣了。一方面想了解它的工作原理；另一方面希望挑战一下自己，看看自己能走多远。\"]},\"394\":{\"h\":\"理论很复杂，实现也很复杂？\",\"t\":[\"我对编译器一直心存敬佩。所以当学校开《编译原理》的课程后，我是抱着满腔热情去上课的，但是两节课后我就放弃了。原因是太复杂了，听不懂。\",\"一般编译原理的课程会说一些：\",\"如何表示语法（BNF什么的）\",\"词法分析，用什么有穷自动机和无穷自动机\",\"语法分析，递归下降法，什么 LL(k)，LALR 分析。\",\"中间代码的表示\",\"代码的生成\",\"代码优化\",\"我相信绝大多数（98％）的学生顶多学到语法分析就结束了。并且最重要的是，学了这么多也没用！依旧帮助不了我们学习编译器！这其中最主要的原因是《编译原理》试图教会我们的是如何构造“编译器生成器”，即构造一个工具，根据文法来生成编译器（如 lex/yacc）等等。\",\"这些理论试图教会我们如何用通用的方法来自动解决问题，它们有很强的实际意义，只是对于一般的学生或程序员来说，它们过于强大，内容过于复杂。如果你尝试阅读 lex/yacc （或 flex/bison）的代码，就会发现太可怕了。\",\"然而如果你能跟我一样，真正来实现一个简单的编译器，那么你会发现，比起可怕的《编译原理》，这点复杂度还是不算什么的（因为好多理论根本用不上）。\"]},\"395\":{\"h\":\"项目的初衷\",\"t\":[\"有一次在 Github 上看到了一个项目（当时很火的），名叫 c4，号称用 4 个函数来实现了一个小的 C 语言编译器。它最让我震惊的是能够自举，即能自己编译自己。并且它用很少的代码就完成了一个功能相当完善的 C 语言编译器。\",\"一般的编译器相关的教程要么就十分简单（如实现四则运算），要么就是借助了自动生成的工具（如 flex/bison）。而 c4 的代码完全是手工实现的，不用外部工具。可惜的是它的代码初衷是代码最小化，所以写得很乱，很难懂。所以本项目的主要目的：\",\"实现一个功能完善的 C 语言编译器\",\"通过教程来说明这个过程。\",\"c4 大致500+行。重写的代码历时一周，总共代码加注释1400行。项目地址: Write a C Interpreter。\",\"声明：本项目中的代码逻辑绝大多数取自 c4 ，但确为自己重写。\"]},\"396\":{\"h\":\"做好心理准备\",\"t\":[\"在写编译器的时候会遇到两个主要问题：\",\"繁琐，会有许多相似的代码，写起来很无聊。\",\"难以调试，一方面没有很好的测试用例，另一方面需要对照生成的代码来调试（遇到的时候就知道了）。\",\"所以我希望你有足够的耐心和时间来学习，相信当你真正完成的时候会像我一样，十分有成就感。\",\"PS. 第一篇完全没有正题相关的内容也是希望你能有所心理准备再开始学习。\"]},\"397\":{\"h\":\"参考资料\",\"t\":[\"最后想介绍几个资料：\",\"Let’s Build a Compiler 很好的初学者教程，英文的。\",\"Lemon Parser Generator，一个语法分析器生成器，对照《编译原理》观看效果更佳。\",\"由于本人水平一般，文章、代码难免会有错误，敬请批评指正！\",\"最后祝你学得愉快。\",\"这篇博客并没有使用诸如 flex、bison 等工具来编写 token 和文法的定义，因而灵活性较差。相反，它通过定义自己的指令集并支持该指令集的虚拟机来模拟编译的部分过程，具有一定的参考价值。不过，我仍然认为通过定义 token 和文法并编写解析算法（如 regex、LL(k) 等）可能会更具普适性。\",\"相关信息\",\"不过据说c、cpp、java这些成熟的语言都是手动实现的？还没仔细了解过。\\nTODO\"]},\"398\":{\"c\":[\"编译原理\"]},\"399\":{\"c\":[\"c\",\"编译器\",\"解释器\"]},\"400\":{\"h\":\"手把手教你构建 C 语言编译器（1）- 设计\",\"t\":[\"本文转自 https://lotabout.me/2015/write-a-C-interpreter-1/，如有侵权，请联系删除。\",\"Table of Contents\",\"1. 编译器的构建流程\",\"2. 编译器框架\",\"这是“手把手教你构建 C 语言编译器”系列的第二篇，我们要从整体上讲解如何设计我们的 C 语言编译器。\",\"手把手教你构建 C 语言编译器系列共有10个部分：\",\"手把手教你构建 C 语言编译器（0）——前言\",\"手把手教你构建 C 语言编译器（1）——设计\",\"手把手教你构建 C 语言编译器（2）——虚拟机\",\"手把手教你构建 C 语言编译器（3）——词法分析器\",\"手把手教你构建 C 语言编译器（4）——递归下降\",\"手把手教你构建 C 语言编译器（5）——变量定义\",\"手把手教你构建 C 语言编译器（6）——函数定义\",\"手把手教你构建 C 语言编译器（7）——语句\",\"手把手教你构建 C 语言编译器（8）——表达式\",\"手把手教你构建 C 语言编译器（9）——总结\",\"首先要说明的是，虽然标题是编译器，但实际上我们构建的是 C 语言的解释器，这意味着我们可以像运行脚本一样去运行 C 语言的源代码文件。这么做的理由有两点：\",\"解释器与编译器仅在代码生成阶段有区别，而其它方面如词法分析、语法分析是一样的。\",\"解释器需要我们实现自己的虚拟机与指令集，而这部分能帮助我们了解计算机的工作原理。\"]},\"401\":{\"h\":\"编译器的构建流程\",\"t\":[\"一般而言，编译器的编写分为 3 个步骤：\",\"词法分析器，用于将字符串转化成内部的表示结构。\",\"语法分析器，将词法分析得到的标记流（token）生成一棵语法树。\",\"目标代码的生成，将语法树转化成目标代码。\",\"已经有许多工具能帮助我们处理阶段1和2，如 flex 用于词法分析，bison 用于语法分析。只是它们的功能都过于强大，屏蔽了许多实现上的细节，对于学习构建编译器帮助不大。所以我们要完全手写这些功能。\",\"所以我们会依照以下步骤来构建我们的编译器：\",\"构建我们自己的虚拟机以及指令集。这后生成的目标代码便是我们的指令集。\",\"构建我们的词法分析器\",\"构建语法分析器\"]},\"402\":{\"h\":\"编译器框架\",\"t\":[\"我们的编译器主要包括 4 个函数：\",\"next() 用于词法分析，获取下一个标记，它将自动忽略空白字符。\",\"program() 语法分析的入口，分析整个 C 语言程序。\",\"expression(level) 用于解析一个表达式。\",\"eval() 虚拟机的入口，用于解释目标代码。\",\"这里有一个单独用于解析“表达式”的函数 expression 是因为表达式在语法分析中相对独立并且比较复杂，所以我们将它单独作为一个模块（函数）。下面是相应的源代码：\",\"#include <stdio.h>#include <stdlib.h>#include <memory.h>#include <string.h>int token; // current tokenchar *src, *old_src; // pointer to source code string;int poolsize; // default size of text/data/stackint line; // line numbervoid next() { token = *src++; return;}void expression(int level) { // do nothing}void program() { next(); // get next token while (token > 0) { printf(\\\"token is: %c\\\\n\\\", token); next(); }}int eval() { // do nothing yet return 0;}int main(int argc, char **argv){ int i, fd; argc--; argv++; poolsize = 256 * 1024; // arbitrary size line = 1; if ((fd = open(*argv, 0)) < 0) { printf(\\\"could not open(%s)\\\\n\\\", *argv); return -1; } if (!(src = old_src = malloc(poolsize))) { printf(\\\"could not malloc(%d) for source area\\\\n\\\", poolsize); return -1; } // read the source file if ((i = read(fd, src, poolsize-1)) <= 0) { printf(\\\"read() returned %d\\\\n\\\", i); return -1; } src[i] = 0; // add EOF character close(fd); program(); return eval();}\",\"上面的代码看上去挺复杂，但其实内容不多。它的流程为：读取一个文件（内容为 C 语言代码），逐个读取文件中的字符，并输出。这里需要的是注意每个函数的作用，后面的文章中，我们将逐个填充每个函数的功能，最终构建起我们的编译器。\",\"本节的代码可以在 Github 上下载，也可以直接 clone\",\"git clone -b step-0 https://github.com/lotabout/write-a-C-interpreter\",\"这样我们就有了一个最简单的编译器：什么都不干的编译器，下一章中，我们将实现其中的eval函数，即我们自己的虚拟机。\"]},\"403\":{\"h\":\"转载声明\",\"t\":[\"title: \\\"手把手教你构建 C 语言编译器（2）——虚拟机\\\" category:\",\"编译原理 tag:\",\"c\",\"编译器\",\"解释器\",\"本文转自 https://lotabout.me/2015/write-a-C-interpreter-2/，如有侵权，请联系删除。\",\"Table of Contents\",\"1. 计算机的内部工作原理\",\"1.1. 内存\",\"1.2. 寄存器\",\"2. 指令集\",\"2.1. MOV\",\"2.2. PUSH\",\"2.3. JMP\",\"2.4. JZ/JNZ\",\"2.5. 子函数调用\",\"2.6. ENT\",\"2.7. ADJ\",\"2.8. LEV\",\"2.9. LEA\",\"2.10. 运算符指令\",\"2.11. 内置函数\",\"3. 测试\",\"4. 小结\",\"这是“手把手教你构建 C 语言编译器”系列的第三篇，本章我们要构建一台虚拟的电脑，设计我们自己的指令集，运行我们的指令集，说得通俗一点就是自己实现一套汇编语言。它们将作为我们的编译器最终输出的目标代码。\",\"手把手教你构建 C 语言编译器系列共有10个部分：\",\"手把手教你构建 C 语言编译器（0）——前言\",\"手把手教你构建 C 语言编译器（1）——设计\",\"手把手教你构建 C 语言编译器（2）——虚拟机\",\"手把手教你构建 C 语言编译器（3）——词法分析器\",\"手把手教你构建 C 语言编译器（4）——递归下降\",\"手把手教你构建 C 语言编译器（5）——变量定义\",\"手把手教你构建 C 语言编译器（6）——函数定义\",\"手把手教你构建 C 语言编译器（7）——语句\",\"手把手教你构建 C 语言编译器（8）——表达式\",\"手把手教你构建 C 语言编译器（9）——总结\"]},\"404\":{\"h\":\"计算机的内部工作原理\",\"t\":[\"计算机中有三个基本部件需要我们关注：CPU、寄存器及内存。代码（汇编指令）以二进制的形式保存在内存中；CPU 从中一条条地加载指令执行；程序运行的状态保存在寄存器中。\"]},\"405\":{\"h\":\"内存\",\"t\":[\"内存用于存储数据，这里的数据可以是代码，也可以是其它的数据。现代操作系统在操作内存时，并不是直接处理”物理内存“，而是操作”虚拟内存“。虚拟内存可以理解为一种映射，它的作用是屏蔽了物理的细节。例如 32 位的机器中，我们可以使用的内存地址为 2^32 = 4G，而电脑上的实际内存可能只有 256 M。操作系统将我们使用的虚拟地址映射到了到实际的内存上。\",\"当然，我们这里并不需要了解太多，但需要了解的是：进程的内存会被分成几个段：\",\"代码段（text）用于存放代码（指令）。\",\"数据段（data）用于存放初始化了的数据，如int i = 10;，就需要存放到数据段中。\",\"未初始化数据段（bss）用于存放未初始化的数据，如 int i[1000];，因为不关心其中的真正数值，所以单独存放可以节省空间，减少程序的体积。\",\"栈（stack）用于处理函数调用相关的数据，如调用帧（calling frame）或是函数的局部变量等。\",\"堆（heap）用于为程序动态分配内存。\",\"它们在内存中的位置类似于下图：\",\"+------------------+| stack | | high address| ... v || || || || || ... ^ || heap | |+------------------+| bss segment |+------------------+| data segment |+------------------+| text segment | low address+------------------+\",\"我们的虚拟机并不打算模拟完整的计算机，因此简单起见，我们只关心三个内容：代码段、数据段以及栈。其中的数据段我们只用来存放字符串，因为我们的编译器并不支持初始化变量，因此我们也不需要未初始化数据段。\",\"当用户的程序需要分配内存时，理论上我们的虚拟机需要维护一个堆用于内存分配，但实际实现上较为复杂且与编译无关，故我们引入一个指令MSET，使我们能直接使用编译器（解释器）中的内存。\",\"综上，我们需要首先在全局添加如下代码：\",\"int *text, // text segment *old_text, // for dump text segment *stack; // stackchar *data; // data segment\",\"注意这里的类型，虽然是int型，但理解起来应该作为无符号的整型，因为我们会在代码段（text）中存放如指针/内存地址的数据，它们就是无符号的。其中数据段（data）由于只存放字符串，所以是 char * 型的。\",\"接着，在main函数中加入初始化代码，真正为其分配内存：\",\"int main() { close(fd); ... // allocate memory for virtual machine if (!(text = old_text = malloc(poolsize))) { printf(\\\"could not malloc(%d) for text area\\\\n\\\", poolsize); return -1; } if (!(data = malloc(poolsize))) { printf(\\\"could not malloc(%d) for data area\\\\n\\\", poolsize); return -1; } if (!(stack = malloc(poolsize))) { printf(\\\"could not malloc(%d) for stack area\\\\n\\\", poolsize); return -1; } memset(text, 0, poolsize); memset(data, 0, poolsize); memset(stack, 0, poolsize); ... program();}\"]},\"406\":{\"h\":\"寄存器\",\"t\":[\"计算机中的寄存器用于存放计算机的运行状态，真正的计算机中有许多不同种类的寄存器，但我们的虚拟机中只使用 4 个寄存器，分别如下：\",\"PC 程序计数器，它存放的是一个内存地址，该地址中存放着 下一条 要执行的计算机指令。\",\"SP 指针寄存器，永远指向当前的栈顶。注意的是由于栈是位于高地址并向低地址增长的，所以入栈时 SP 的值减小。\",\"BP 基址指针。也是用于指向栈的某些位置，在调用函数时会使用到它。\",\"AX 通用寄存器，我们的虚拟机中，它用于存放一条指令执行后的结果。\",\"要理解这些寄存器的作用，需要去理解程序运行中会有哪些状态。而这些寄存器只是用于保存这些状态的。\",\"在全局中加入如下定义：\",\"int *pc, *bp, *sp, ax, cycle; // virtual machine registers\",\"在 main 函数中加入初始化代码，注意的是PC在初始应指向目标代码中的main函数，但我们还没有写任何编译相关的代码，因此先不处理。代码如下：\",\"memset(stack, 0, poolsize);...bp = sp = (int *)((int)stack + poolsize);ax = 0;...program();\",\"与 CPU 相关的是指令集，我们将专门作为一个小节。\"]},\"407\":{\"h\":\"指令集\",\"t\":[\"指令集是 CPU 能识别的命令的集合，也可以说是 CPU 能理解的语言。这里我们要为我们的虚拟机构建自己的指令集。它们基于 x86 的指令集，但更为简单。\",\"首先在全局变量中加入一个枚举类型，这是我们要支持的全部指令：\",\"// instructionsenum { LEA ,IMM ,JMP ,CALL,JZ ,JNZ ,ENT ,ADJ ,LEV ,LI ,LC ,SI ,SC ,PUSH, OR ,XOR ,AND ,EQ ,NE ,LT ,GT ,LE ,GE ,SHL ,SHR ,ADD ,SUB ,MUL ,DIV ,MOD , OPEN,READ,CLOS,PRTF,MALC,MSET,MCMP,EXIT };\",\"这些指令的顺序安排是有意的，稍后你会看到，带有参数的指令在前，没有参数的指令在后。这种顺序的唯一作用就是在打印调试信息时更加方便。但我们讲解的顺序并不依据它。\"]},\"408\":{\"h\":\"MOV\",\"t\":[\"MOV 是所有指令中最基础的一个，它用于将数据放进寄存器或内存地址，有点类似于 C 语言中的赋值语句。x86 的 MOV 指令有两个参数，分别是源地址和目标地址：MOV dest, source （Intel 风格），表示将 source 的内容放在 dest 中，它们可以是一个数、寄存器或是一个内存地址。\",\"一方面，我们的虚拟机只有一个寄存器，另一方面，识别这些参数的类型（是数据还是地址）是比较困难的，因此我们将 MOV 指令拆分成 5 个指令，这些指令只接受一个参数，如下：\",\"IMM <num> 将 <num> 放入寄存器 ax 中。\",\"LC 将对应地址中的字符载入 ax 中，要求 ax 中存放地址。\",\"LI 将对应地址中的整数载入 ax 中，要求 ax 中存放地址。\",\"SC 将 ax 中的数据作为字符存放入地址中，要求栈顶存放地址。\",\"SI 将 ax 中的数据作为整数存放入地址中，要求栈顶存放地址。\",\"你可能会觉得将一个指令变成了许多指令，整个系统就变得复杂了，但实际情况并非如此。首先是 x86 的 MOV 指令其实有许多变种，根据类型的不同有 MOVB, MOVW 等指令，我们这里的 LC/SC 和 LI/SI 就是对应字符型和整型的存取操作。\",\"但最为重要的是，通过将 MOV 指令拆分成这些指令，只有 IMM 需要有参数，且不需要判断类型，所以大大简化了实现的难度。\",\"在 eval() 函数中加入下列代码：\",\"void eval() { int op, *tmp; while (1) { if (op == IMM) {ax = *pc++;} // load immediate value to ax else if (op == LC) {ax = *(char *)ax;} // load character to ax, address in ax else if (op == LI) {ax = *(int *)ax;} // load integer to ax, address in ax else if (op == SC) {ax = *(char *)*sp++ = ax;} // save character to address, value in ax, address on stack else if (op == SI) {*(int *)*sp++ = ax;} // save integer to address, value in ax, address on stack } ... return 0;}\",\"其中的 *sp++ 的作用是退栈，相当于 POP 操作。\",\"这里要解释的一点是，为什么 SI/SC 指令中，地址存放在栈中，而 LI/LC 中，地址存放在 ax 中？原因是默认计算的结果是存放在 ax 中的，而地址通常是需要通过计算获得，所以执行 LI/LC 时直接从 ax 取值会更高效。另一点是我们的 PUSH 指令只能将 ax 的值放到栈上，而不能以值作为参数，详细见下文。\"]},\"409\":{\"h\":\"PUSH\",\"t\":[\"在 x86 中，PUSH 的作用是将值或寄存器，而在我们的虚拟机中，它的作用是将 ax 的值放入栈中。这样做的主要原因是为了简化虚拟机的实现，并且我们也只有一个寄存器 ax 。代码如下：\",\"else if (op == PUSH) {*--sp = ax;} // push the value of ax onto the stack\"]},\"410\":{\"h\":\"JMP\",\"t\":[\"JMP <addr> 是跳转指令，无条件地将当前的 PC 寄存器设置为指定的 <addr>，实现如下：\",\"else if (op == JMP) {pc = (int *)*pc;} // jump to the address\",\"需要注意的是，pc 寄存器指向的是 下一条 指令。所以此时它存放的是 JMP 指令的参数，即 <addr> 的值。\"]},\"411\":{\"h\":\"JZ/JNZ\",\"t\":[\"为了实现 if 语句，我们需要条件判断相关的指令。这里我们只实现两个最简单的条件判断，即结果（ax）为零或不为零情况下的跳转。\",\"实现如下：\",\"else if (op == JZ) {pc = ax ? pc + 1 : (int *)*pc;} // jump if ax is zeroelse if (op == JNZ) {pc = ax ? (int *)*pc : pc + 1;} // jump if ax is not zero\"]},\"412\":{\"h\":\"子函数调用\",\"t\":[\"这是汇编中最难理解的部分，所以合在一起说，要引入的命令有 CALL, ENT, ADJ 及 LEV。\",\"首先我们介绍 CALL <addr> 与 RET 指令，CALL 的作用是跳转到地址为 <addr> 的子函数，RET 则用于从子函数中返回。\",\"为什么不能直接使用 JMP 指令呢？原因是当我们从子函数中返回时，程序需要回到跳转之前的地方继续运行，这就需要事先将这个位置信息存储起来。反过来，子函数要返回时，就需要获取并恢复这个信息。因此实际中我们将 PC 保存在栈中。如下：\",\"else if (op == CALL) {*--sp = (int)(pc+1); pc = (int *)*pc;} // call subroutine//else if (op == RET) {pc = (int *)*sp++;} // return from subroutine;\",\"这里我们把 RET 相关的内容注释了，是因为之后我们将用 LEV 指令来代替它。\",\"在实际调用函数时，不仅要考虑函数的地址，还要考虑如何传递参数和如何返回结果。这里我们约定，如果子函数有返回结果，那么就在返回时保存在 ax 中，它可以是一个值，也可以是一个地址。那么参数的传递呢？\",\"各种编程语言关于如何调用子函数有不同的约定，例如 C 语言的调用标准是：\",\"由调用者将参数入栈。\",\"调用结束时，由调用者将参数出栈。\",\"参数逆序入栈。\",\"事先声明一下，我们的编译器参数是顺序入栈的，下面的例子（C 语言调用标准）取自 维基百科：\",\"int callee(int, int, int);int caller(void){ int i, ret; ret = callee(1, 2, 3); ret += 5; return ret;}\",\"会生成如下的 x86 汇编代码：\",\"caller: ; make new call frame push ebp mov ebp, esp sub 1, esp ; save stack for variable: i ; push call arguments push 3 push 2 push 1 ; call subroutine 'callee' call callee ; remove arguments from frame add esp, 12 ; use subroutine result add eax, 5 ; restore old call frame mov esp, ebp pop ebp ; return ret\",\"上面这段代码在我们自己的虚拟机里会有几个问题：\",\"push ebp，但我们的 PUSH 指令并无法指定寄存器。\",\"mov ebp, esp，我们的 MOV 指令同样功能不足。\",\"add esp, 12，也是一样的问题（尽管我们还没定义）。\",\"也就是说由于我们的指令过于简单（如只能操作ax寄存器），所以用上面提到的指令，我们连函数调用都无法实现。而我们又不希望扩充现有指令的功能，因为这样实现起来就会变得复杂，因此我们采用的方法是增加指令集。毕竟我们不是真正的计算机，增加指令会消耗许多资源（钱）。\"]},\"413\":{\"h\":\"ENT\",\"t\":[\"ENT <size> 指的是 enter，用于实现 ‘make new call frame’ 的功能，即保存当前的栈指针，同时在栈上保留一定的空间，用以存放局部变量。对应的汇编代码为：\",\"; make new call framepush ebpmov ebp, esp sub 1, esp ; save stack for variable: i\",\"实现如下：\",\"else if (op == ENT) {*--sp = (int)bp; bp = sp; sp = sp - *pc++;} // make new stack frame\"]},\"414\":{\"h\":\"ADJ\",\"t\":[\"ADJ <size> 用于实现 ‘remove arguments from frame’。在将调用子函数时压入栈中的数据清除，本质上是因为我们的 ADD 指令功能有限。对应的汇编代码为：\",\"; remove arguments from frameadd esp, 12\",\"实现如下：\",\"else if (op == ADJ) {sp = sp + *pc++;} // add esp, <size>\"]},\"415\":{\"h\":\"LEV\",\"t\":[\"本质上这个指令并不是必需的，只是我们的指令集中并没有 POP 指令。并且三条指令写来比较麻烦且浪费空间，所以用一个指令代替。对应的汇编指令为：\",\"; restore old call frame mov esp, ebppop ebp; returnret\",\"具体的实现如下：\",\"else if (op == LEV) {sp = bp; bp = (int *)*sp++; pc = (int *)*sp++;} // restore call frame and PC\",\"注意的是，LEV 已经把 RET 的功能包含了，所以我们不再需要 RET 指令。\"]},\"416\":{\"h\":\"LEA\",\"t\":[\"上面的一些指令解决了调用帧的问题，但还有一个问题是如何在子函数中获得传入的参数。这里我们首先要了解的是当参数调用时，栈中的调用帧是什么样的。我们依旧用上面的例子（只是现在用“顺序”调用参数）：\",\"sub_function(arg1, arg2, arg3);| .... | high address+---------------+| arg: 1 | new_bp + 4+---------------+| arg: 2 | new_bp + 3+---------------+| arg: 3 | new_bp + 2+---------------+|return address | new_bp + 1+---------------+| old BP | <- new BP+---------------+| local var 1 | new_bp - 1+---------------+| local var 2 | new_bp - 2+---------------+| .... | low address\",\"所以为了获取第一个参数，我们需要得到 new_bp + 4，但就如上面的说，我们的 ADD 指令无法操作除 ax 外的寄存器，所以我们提供了一个新的指令：LEA <offset>\",\"实现如下：\",\"else if (op == LEA) {ax = (int)(bp + *pc++);} // load address for arguments.\",\"以上就是我们为了实现函数调用需要的指令了。\"]},\"417\":{\"h\":\"运算符指令\",\"t\":[\"我们为 C 语言中支持的运算符都提供对应汇编指令。每个运算符都是二元的，即有两个参数，第一个参数放在栈顶，第二个参数放在 ax 中。这个顺序要特别注意。因为像 -，/ 之类的运算符是与参数顺序有关的。计算后会将栈顶的参数退栈，结果存放在寄存器 ax 中。因此计算结束后，两个参数都无法取得了（汇编的意义上，存在内存地址上就另当别论）。\",\"实现如下：\",\"else if (op == OR) ax = *sp++ | ax;else if (op == XOR) ax = *sp++ ^ ax;else if (op == AND) ax = *sp++ & ax;else if (op == EQ) ax = *sp++ == ax;else if (op == NE) ax = *sp++ != ax;else if (op == LT) ax = *sp++ < ax;else if (op == LE) ax = *sp++ <= ax;else if (op == GT) ax = *sp++ > ax;else if (op == GE) ax = *sp++ >= ax;else if (op == SHL) ax = *sp++ << ax;else if (op == SHR) ax = *sp++ >> ax;else if (op == ADD) ax = *sp++ + ax;else if (op == SUB) ax = *sp++ - ax;else if (op == MUL) ax = *sp++ * ax;else if (op == DIV) ax = *sp++ / ax;else if (op == MOD) ax = *sp++ % ax;\"]},\"418\":{\"h\":\"内置函数\",\"t\":[\"写的程序要”有用“，除了核心的逻辑外还需要输入输出，例如 C 语言中我们经常使用的 printf 函数就是用于输出。但是 printf 函数的实现本身就十分复杂，如果我们的编译器要达到自举，就势必要实现 printf 之类的函数，但它又与编译器没有太大的联系，因此我们继续实现新的指令，从虚拟机的角度予以支持。\",\"编译器中我们需要用到的函数有：exit, open, close, read, printf, malloc, memset 及 memcmp。代码如下：\",\"else if (op == EXIT) { printf(\\\"exit(%d)\\\", *sp); return *sp;}else if (op == OPEN) { ax = open((char *)sp[1], sp[0]); }else if (op == CLOS) { ax = close(*sp);}else if (op == READ) { ax = read(sp[2], (char *)sp[1], *sp); }else if (op == PRTF) { tmp = sp + pc[1]; ax = printf((char *)tmp[-1], tmp[-2], tmp[-3], tmp[-4], tmp[-5], tmp[-6]); }else if (op == MALC) { ax = (int)malloc(*sp);}else if (op == MSET) { ax = (int)memset((char *)sp[2], sp[1], *sp);}else if (op == MCMP) { ax = memcmp((char *)sp[2], (char *)sp[1], *sp);}\",\"这里的原理是，我们的电脑上已经有了这些函数的实现，因此编译编译器时，这些函数的二进制代码就被编译进了我们的编译器，因此在我们的编译器/虚拟机上运行我们提供的这些指令时，这些函数就是可用的。换句话说就是不需要我们自己去实现了。\",\"最后再加上一个错误判断：\",\"else { printf(\\\"unknown instruction:%d\\\\n\\\", op); return -1;}\"]},\"419\":{\"h\":\"测试\",\"t\":[\"下面我们用我们的汇编写一小段程序，来计算 10+20，在 main 函数中加入下列代码：\",\"int main(int argc, char *argv[]){ ax = 0; ... i = 0; text[i++] = IMM; text[i++] = 10; text[i++] = PUSH; text[i++] = IMM; text[i++] = 20; text[i++] = ADD; text[i++] = PUSH; text[i++] = EXIT; pc = text; ... program();}\",\"编译程序 gcc xc-tutor.c，运行程序：./a.out hello.c。输出\",\"exit(30)\",\"另外，我们的代码里有一些指针的强制转换，默认是 32 位的，因此在 64 位机器下，会出现 segmentation fault，解决方法（二选一）：\",\"编译时加上 -m32 参数：gcc -m32 xc-tutor.c\",\"在代码的开头，增加 #define int long long，long long 是 64 位的，不会出现强制转换后的问题。\",\"注意我们的之前的程序需要指令一个源文件，只是现在还用不着，但从结果可以看出，我们的虚拟机还是工作良好的。\"]},\"420\":{\"h\":\"小结\",\"t\":[\"本章中我们回顾了计算机的内部运行原理，并仿照 x86 汇编指令设计并实现了我们自己的指令集。希望通过本章的学习，你能对计算机程序的原理有一定的了解，同时能对汇编语言有一定的概念，因为汇编语言就是 C 编译器的输出。\",\"本章的代码可以在 Github 上下载，也可以直接 clone\",\"git clone -b step-1 https://github.com/lotabout/write-a-C-interpreter\",\"实际计算机中，添加一个新的指令需要设计许多新的电路，会增加许多的成本，但我们的虚拟机中，新的指令几乎不消耗资源，因此我们可以利用这一点，用更多的指令来完成更多的功能，从而简化具体的实现。\"]},\"421\":{\"h\":\"手把手教你构建 C 语言编译器（3）——词法分析器\",\"t\":[\"本文转自 https://lotabout.me/2015/write-a-C-interpreter-3/，如有侵权，请联系删除。\",\"Table of Contents\",\"1. 什么是词法分析器\",\"2. 词法分析器与编译器\",\"3. 词法分析器的实现\",\"3.1. 支持的标记\",\"3.2. 词法分析器的框架\",\"3.3. 换行符\",\"3.4. 宏定义\",\"3.5. 标识符与符号表\",\"3.6. 数字\",\"3.7. 字符串\",\"3.8. 注释\",\"3.9. 其它\",\"3.10. 关键字与内置函数\",\"4. 代码\",\"5. 小结\",\"本章我们要讲解如何构建词法分析器。\",\"手把手教你构建 C 语言编译器系列共有10个部分：\",\"手把手教你构建 C 语言编译器（0）——前言\",\"手把手教你构建 C 语言编译器（1）——设计\",\"手把手教你构建 C 语言编译器（2）——虚拟机\",\"手把手教你构建 C 语言编译器（3）——词法分析器\",\"手把手教你构建 C 语言编译器（4）——递归下降\",\"手把手教你构建 C 语言编译器（5）——变量定义\",\"手把手教你构建 C 语言编译器（6）——函数定义\",\"手把手教你构建 C 语言编译器（7）——语句\",\"手把手教你构建 C 语言编译器（8）——表达式\",\"手把手教你构建 C 语言编译器（9）——总结\"]},\"422\":{\"h\":\"什么是词法分析器\",\"t\":[\"简而言之，词法分析器用于对源码字符串做预处理，以减少语法分析器的复杂程度。\",\"词法分析器以源码字符串为输入，输出为标记流（token stream），即一连串的标记，每个标记通常包括： (token, token value) 即标记本身和标记的值。例如，源码中若包含一个数字 '998' ，词法分析器将输出 (Number, 998)，即（数字，998）。再例如：\",\"2 + 3 * (4 - 5)=>(Number, 2) Add (Number, 3) Multiply Left-Bracket (Number, 4) Subtract (Number, 5) Right-Bracket\",\"通过词法分析器的预处理，语法分析器的复杂度会大大降低，这点在后面的语法分析器我们就能体会。\"]},\"423\":{\"h\":\"词法分析器与编译器\",\"t\":[\"要是深入词法分析器，你就会发现，它的本质上也是编译器。我们的编译器是以标记流为输入，输出汇编代码，而词法分析器则是以源码字符串为输入，输出标记流。\",\" +-------+ +--------+-- source code --> | lexer | --> token stream --> | parser | --> assembly +-------+ +--------+\",\"在这个前提下，我们可以这样认为：直接从源代码编译成汇编代码是很困难的，因为输入的字符串比较难处理。所以我们先编写一个较为简单的编译器（词法分析器）来将字符串转换成标记流，而标记流对于语法分析器而言就容易处理得多了。\"]},\"424\":{\"h\":\"词法分析器的实现\",\"t\":[\"由于词法分析的工作很常见，但又枯燥且容易出错，所以人们已经开发出了许多工具来生成词法分析器，如 lex, flex。这些工具允许我们通过正则表达式来识别标记。\",\"这里注意的是，我们并不会一次性地将所有源码全部转换成标记流，原因有二：\",\"字符串转换成标记流有时是有状态的，即与代码的上下文是有关系的。\",\"保存所有的标记流没有意义且浪费空间。\",\"所以实际的处理方法是提供一个函数（即前几篇中提到的 next()），每次调用该函数则返回下一个标记。\"]},\"425\":{\"h\":\"支持的标记\",\"t\":[\"在全局中添加如下定义：\",\"// tokens and classes (operators last and in precedence order)enum { Num = 128, Fun, Sys, Glo, Loc, Id, Char, Else, Enum, If, Int, Return, Sizeof, While, Assign, Cond, Lor, Lan, Or, Xor, And, Eq, Ne, Lt, Gt, Le, Ge, Shl, Shr, Add, Sub, Mul, Div, Mod, Inc, Dec, Brak};\",\"这些就是我们要支持的标记符。例如，我们会将 = 解析为 Assign；将 == 解析为 Eq；将 != 解析为 Ne 等等。\",\"所以这里我们会有这样的印象，一个标记（token）可能包含多个字符，且多数情况下如此。而词法分析器能减小语法分析复杂度的原因，正是因为它相当于通过一定的编码（更多的标记）来压缩了源码字符串。\",\"当然，上面这些标记是有顺序的，跟它们在 C 语言中的优先级有关，如 *(Mul) 的优先级就要高于 +(Add)。它们的具体使用在后面的语法分析中会提到。\",\"最后要注意的是还有一些字符，它们自己就构成了标记，如右方括号 ] 或波浪号 ~ 等。我们不另外处理它们的原因是：\",\"它们是单字符的，即并不是多个字符共同构成标记（如 == 需要两个字符）；\",\"它们不涉及优先级关系。\"]},\"426\":{\"h\":\"词法分析器的框架\",\"t\":[\"即 next() 函数的主体：\",\"void next() { char *last_pos; int hash; while (token = *src) { ++src; // parse token here } return;}\",\"这里的一个问题是，为什么要用 while 循环呢？这就涉及到编译器（记得我们说过词法分析器也是某种意义上的编译器）的一个问题：如何处理错误？\",\"对词法分析器而言，若碰到了一个我们不认识的字符该怎么处理？一般处理的方法有两种：\",\"指出错误发生的位置，并退出整个程序\",\"指出错误发生的位置，跳过当前错误并继续编译\",\"这个 while 循环的作用就是跳过这些我们不识别的字符，我们同时还用它来处理空白字符。我们知道，C 语言中空格是用来作为分隔用的，并不作为语法的一部分。因此在实现中我们将它作为“不识别”的字符，这个 while 循环可以用来跳过它。\"]},\"427\":{\"h\":\"换行符\",\"t\":[\"换行符和空格类似，但有一点不同，每次遇到换行符，我们需要将当前的行号加一：\",\"// parse token here...if (token == '\\\\n') { ++line;}...\"]},\"428\":{\"h\":\"宏定义\",\"t\":[\"C 语言的宏定义以字符 # 开头，如 # include <stdio.h>。我们的编译器并不支持宏定义，所以直接跳过它们。\",\"else if (token == '#') { // skip macro, because we will not support it while (*src != 0 && *src != '\\\\n') { src++; }}\"]},\"429\":{\"h\":\"标识符与符号表\",\"t\":[\"标识符（identifier）可以理解为变量名。对于语法分析而言，我们并不关心一个变量具体叫什么名字，而只关心这个变量名代表的唯一标识。例如 int a; 定义了变量 a，而之后的语句 a = 10，我们需要知道这两个 a 指向的是同一个变量。\",\"基于这个理由，词法分析器会把扫描到的标识符全都保存到一张表中，遇到新的标识符就去查这张表，如果标识符已经存在，就返回它的唯一标识。\",\"那么我们怎么表示标识符呢？如下：\",\"struct identifier { int token; int hash; char * name; int class; int type; int value; int Bclass; int Btype; int Bvalue;}\",\"这里解释一下具体的含义：\",\"token：该标识符返回的标记，理论上所有的变量返回的标记都应该是 Id，但实际上由于我们还将在符号表中加入关键字如 if, while 等，它们都有对应的标记。\",\"hash：顾名思义，就是这个标识符的哈希值，用于标识符的快速比较。\",\"name：存放标识符本身的字符串。\",\"class：该标识符的类别，如数字，全局变量或局部变量等。\",\"type：标识符的类型，即如果它是个变量，变量是 int 型、char 型还是指针型。\",\"value：存放这个标识符的值，如标识符是函数，刚存放函数的地址。\",\"BXXXX：C 语言中标识符可以是全局的也可以是局部的，当局部标识符的名字与全局标识符相同时，用作保存全局标识符的信息。\",\"由上可以看出，我们实现的词法分析器与传统意义上的词法分析器不太相同。传统意义上的符号表只需要知道标识符的唯一标识即可，而我们还存放了一些只有语法分析器才会得到的信息，如 type 。\",\"由于我们的目标是能自举，而我们定义的语法不支持 struct，故而使用下列方式。\",\"Symbol table:----+-----+----+----+----+-----+-----+-----+------+------+---- .. |token|hash|name|type|class|value|btype|bclass|bvalue| ..----+-----+----+----+----+-----+-----+-----+------+------+---- |<--- one single identifier --->|\",\"即用一个整型数组来保存相关的ID信息。每个ID占用数组中的9个空间，分析标识符的相关代码如下：\",\"int token_val; // value of current token (mainly for number)int *current_id, // current parsed ID *symbols; // symbol table// fields of identifierenum {Token, Hash, Name, Type, Class, Value, BType, BClass, BValue, IdSize};void next() { ... else if ((token >= 'a' && token <= 'z') || (token >= 'A' && token <= 'Z') || (token == '_')) { // parse identifier last_pos = src - 1; hash = token; while ((*src >= 'a' && *src <= 'z') || (*src >= 'A' && *src <= 'Z') || (*src >= '0' && *src <= '9') || (*src == '_')) { hash = hash * 147 + *src; src++; } // look for existing identifier, linear search current_id = symbols; while (current_id[Token]) { if (current_id[Hash] == hash && !memcmp((char *)current_id[Name], last_pos, src - last_pos)) { //found one, return token = current_id[Token]; return; } current_id = current_id + IdSize; } // store new ID current_id[Name] = (int)last_pos; current_id[Hash] = hash; token = current_id[Token] = Id; return; } ...}\",\"查找已有标识符的方法是线性查找 symbols 表。\"]},\"430\":{\"h\":\"数字\",\"t\":[\"数字中较为复杂的一点是需要支持十进制、十六进制及八进制。逻辑也较为直接，可能唯一不好理解的是获取十六进制的值相关的代码。\",\"token_val = token_val * 16 + (token & 15) + (token >= 'A' ? 9 : 0);\",\"这里要注意的是在ASCII码中，字符a对应的十六进制值是 61, A是41，故通过 (token & 15) 可以得到个位数的值。其它就不多说了，这里这样写的目的是装B（其实是抄 c4 的源代码的）。\",\"void next() { ... else if (token >= '0' && token <= '9') { // parse number, three kinds: dec(123) hex(0x123) oct(017) token_val = token - '0'; if (token_val > 0) { // dec, starts with [1-9] while (*src >= '0' && *src <= '9') { token_val = token_val*10 + *src++ - '0'; } } else { // starts with number 0 if (*src == 'x' || *src == 'X') { //hex token = *++src; while ((token >= '0' && token <= '9') || (token >= 'a' && token <= 'f') || (token >= 'A' && token <= 'F')) { token_val = token_val * 16 + (token & 15) + (token >= 'A' ? 9 : 0); token = *++src; } } else { // oct while (*src >= '0' && *src <= '7') { token_val = token_val*8 + *src++ - '0'; } } } token = Num; return; } ...}\"]},\"431\":{\"h\":\"字符串\",\"t\":[\"在分析时，如果分析到字符串，我们需要将它存放到前一篇文章中说的 data 段中。然后返回它在 data 段中的地址。另一个特殊的地方是我们需要支持转义符。例如用 \\\\n 表示换行符。由于本编译器的目的是达到自己编译自己，所以代码中并没有支持除 \\\\n 的转义符，如 \\\\t, \\\\r 等，但仍支持 \\\\a 表示字符 a 的语法，如 \\\\\\\" 表示 \\\"。\",\"在分析时，我们将同时分析单个字符如 'a' 和字符串如 \\\"a string\\\"。若得到的是单个字符，我们以 Num 的形式返回。相关代码如下：\",\"void next() { ... else if (token == '\\\"' || token == '\\\\'') { // parse string literal, currently, the only supported escape // character is '\\\\n', store the string literal into data. last_pos = data; while (*src != 0 && *src != token) { token_val = *src++; if (token_val == '\\\\\\\\') { // escape character token_val = *src++; if (token_val == 'n') { token_val = '\\\\n'; } } if (token == '\\\"') { *data++ = token_val; } } src++; // if it is a single character, return Num token if (token == '\\\"') { token_val = (int)last_pos; } else { token = Num; } return; }}\"]},\"432\":{\"h\":\"注释\",\"t\":[\"在我们的 C 语言中，只支持 // 类型的注释，不支持 /* comments */ 的注释。\",\"void next() { ... else if (token == '/') { if (*src == '/') { // skip comments while (*src != 0 && *src != '\\\\n') { ++src; } } else { // divide operator token = Div; return; } } ...}\",\"这里我们要额外介绍 lookahead 的概念，即提前看多个字符。上述代码中我们看到，除了跳过注释，我们还可能返回除号 /(Div) 标记。\",\"提前看字符的原理是：有一个或多个标记是以同样的字符开头的（如本小节中的注释与除号），因此只凭当前的字符我们并无法确定具体应该解释成哪一个标记，所以只能再向前查看字符，如本例需向前查看一个字符，若是 / 则说明是注释，反之则是除号。\",\"我们之前说过，词法分析器本质上也是编译器，其实提前看字符的概念也存在于编译器，只是这时就是提前看k个“标记”而不是“字符”了。平时听到的 LL(k) 中的 k 就是需要向前看的标记的个数了。\",\"另外，我们用词法分析器将源码转换成标记流，能减小语法分析复杂度，原因之一就是减少了语法分析器需要“向前看”的字符个数。\"]},\"433\":{\"h\":\"其它\",\"t\":[\"其它的标记的解析就相对容易一些了，我们直接贴上代码：\",\"void next() { ... else if (token == '=') { // parse '==' and '=' if (*src == '=') { src ++; token = Eq; } else { token = Assign; } return; } else if (token == '+') { // parse '+' and '++' if (*src == '+') { src ++; token = Inc; } else { token = Add; } return; } else if (token == '-') { // parse '-' and '--' if (*src == '-') { src ++; token = Dec; } else { token = Sub; } return; } else if (token == '!') { // parse '!=' if (*src == '=') { src++; token = Ne; } return; } else if (token == '<') { // parse '<=', '<<' or '<' if (*src == '=') { src ++; token = Le; } else if (*src == '<') { src ++; token = Shl; } else { token = Lt; } return; } else if (token == '>') { // parse '>=', '>>' or '>' if (*src == '=') { src ++; token = Ge; } else if (*src == '>') { src ++; token = Shr; } else { token = Gt; } return; } else if (token == '|') { // parse '|' or '||' if (*src == '|') { src ++; token = Lor; } else { token = Or; } return; } else if (token == '&') { // parse '&' and '&&' if (*src == '&') { src ++; token = Lan; } else { token = And; } return; } else if (token == '^') { token = Xor; return; } else if (token == '%') { token = Mod; return; } else if (token == '*') { token = Mul; return; } else if (token == '[') { token = Brak; return; } else if (token == '?') { token = Cond; return; } else if (token == '~' || token == ';' || token == '{' || token == '}' || token == '(' || token == ')' || token == ']' || token == ',' || token == ':') { // directly return the character as token; return; } ...}\",\"代码较多，但主要逻辑就是向前看一个字符来确定真正的标记。\"]},\"434\":{\"h\":\"关键字与内置函数\",\"t\":[\"虽然上面写完了词法分析器，但还有一个问题需要考虑，那就是“关键字”，例如 if, while, return 等。它们不能被作为普通的标识符，因为有特殊的含义。\",\"一般有两种处理方法：\",\"词法分析器中直接解析这些关键字。\",\"在语法分析前将关键字提前加入符号表。\",\"这里我们就采用第二种方法，将它们加入符号表，并提前为它们赋予必要的信息（还记得前面说的标识符 Token 字段吗？）。这样当源代码中出现关键字时，它们会被解析成标识符，但由于符号表中已经有了相关的信息，我们就能知道它们是特殊的关键字。\",\"内置函数的行为也和关键字类似，不同的只是赋值的信息，在main函数中进行初始化如下：\",\"// types of variable/functionenum { CHAR, INT, PTR };int *idmain; // the `main` functionvoid main() { ... src = \\\"char else enum if int return sizeof while \\\" \\\"open read close printf malloc memset memcmp exit void main\\\"; // add keywords to symbol table i = Char; while (i <= While) { next(); current_id[Token] = i++; } // add library to symbol table i = OPEN; while (i <= EXIT) { next(); current_id[Class] = Sys; current_id[Type] = INT; current_id[Value] = i++; } next(); current_id[Token] = Char; // handle void type next(); idmain = current_id; // keep track of main ... program();}\"]},\"435\":{\"h\":\"代码\",\"t\":[\"本章的代码可以在 Github 上下载，也可以直接 clone\",\"git clone -b step-2 https://github.com/lotabout/write-a-C-interpreter\",\"上面的代码运行后会出现 ‘Segmentation Falt’，这是正常的，因为它会尝试运行我们上一章创建的虚拟机，但其中并没有任何汇编代码。\"]},\"436\":{\"h\":\"小结\",\"t\":[\"本章我们为我们的编译器构建了词法分析器，通过本章的学习，我认为有几个要点需要强调：\",\"词法分析器的作用是对源码字符串进行预处理，作用是减小语法分析器的复杂程度。\",\"词法分析器本身可以认为是一个编译器，输入是源码，输出是标记流。\",\"lookahead(k) 的概念，即向前看 k 个字符或标记。\",\"词法分析中如何处理标识符与符号表。\",\"下一章中，我们将介绍递归下降的语法分析器。我们下一章见。\"]},\"437\":{\"c\":[\"编译原理\"]},\"438\":{\"c\":[\"c\",\"编译器\",\"解释器\"]},\"439\":{\"h\":\"手把手教你构建 C 语言编译器（4）——递归下降\",\"t\":[\"[]\",\"本文转自 https://lotabout.me/2016/write-a-C-interpreter-4/，如有侵权，请联系删除。\",\"Table of Contents\",\"1. 什么是递归下降\",\"2. 终结符与非终结符\",\"3. 四则运算的递归下降\",\"4. 为什么选择递归下降\",\"5. 左递归\",\"6. 四则运算的实现\",\"7. 小结\",\"本章我们将讲解递归下降的方法，并用它完成一个基本的四则运算的语法分析器。\",\"手把手教你构建 C 语言编译器系列共有10个部分：\",\"手把手教你构建 C 语言编译器（0）——前言\",\"手把手教你构建 C 语言编译器（1）——设计\",\"手把手教你构建 C 语言编译器（2）——虚拟机\",\"手把手教你构建 C 语言编译器（3）——词法分析器\",\"手把手教你构建 C 语言编译器（4）——递归下降\",\"手把手教你构建 C 语言编译器（5）——变量定义\",\"手把手教你构建 C 语言编译器（6）——函数定义\",\"手把手教你构建 C 语言编译器（7）——语句\",\"手把手教你构建 C 语言编译器（8）——表达式\",\"手把手教你构建 C 语言编译器（9）——总结\"]},\"440\":{\"h\":\"什么是递归下降\",\"t\":[\"传统上，编写语法分析器有两种方法，一种是自顶向下，一种是自底向上。自顶向下是从起始非终结符开始，不断地对非终结符进行分解，直到匹配输入的终结符；自底向上是不断地将终结符进行合并，直到合并成起始的非终结符。\",\"其中的自顶向下方法就是我们所说的递归下降。\"]},\"441\":{\"h\":\"终结符与非终结符\",\"t\":[\"没有学过编译原理的话可能并不知道什么是“终结符”，“非终结符”。这里我简单介绍一下。首先是 BNF 范式，就是一种用来描述语法的语言，例如，四则运算的规则可以表示如下：\",\"<expr> ::= <expr> + <term> | <expr> - <term> | <term><term> ::= <term> * <factor> | <term> / <factor> | <factor><factor> ::= ( <expr> ) | Num\",\"用尖括号 <> 括起来的就称作 非终结符 ，因为它们可以用 ::= 右侧的式子代替。| 表示选择，如 <expr> 可以是 <expr> + <term>、<expr> - <term>或 <term> 中的一种。而没有出现在::=左边的就称作 终结符 ，一般终结符对应于词法分析器输出的标记。\"]},\"442\":{\"h\":\"四则运算的递归下降\",\"t\":[\"例如，我们对 3 * (4 + 2) 进行语法分析。我们假设词法分析器已经正确地将其中的数字识别成了标记 Num。\",\"递归下降是从起始的非终结符开始（顶），本例中是 <expr>，实际中可以自己指定，不指定的话一般认为是第一个出现的非终结符。\",\"1. <expr> => <expr>2. => <term> * <factor>3. => <factor> |4. => Num (3) |5. => ( <expr> )6. => <expr> + <term>7. => <term> |8. => <factor> |9. => Num (4) |10. => <factor>11. => Num (2)\",\"可以看到，整个解析的过程是在不断对非终结符进行替换（向下），直到遇见了终结符（底）。而我们可以从解析的过程中看出，一些非终结符如<expr>被递归地使用了。\"]},\"443\":{\"h\":\"为什么选择递归下降\",\"t\":[\"从上小节对四则运算的递归下降解析可以看出，整个解析的过程和语法的 BNF 表示是十分接近的，更为重要的是，我们可以很容易地直接将 BNF 表示转换成实际的代码。方法是为每个产生式（即 非终结符 ::= ...）生成一个同名的函数。\",\"这里会有一个疑问，就是上例中，当一个终结符有多个选择时，如何确定具体选择哪一个？如为什么用 <expr> ::= <term> * <factor> 而不是 <expr> ::= <term> / <factor> ？这就用到了上一章中提到的“向前看 k 个标记”的概念了。我们向前看一个标记，发现是 *，而这个标记足够让我们确定用哪个表达式了。\",\"另外，递归下下降方法对 BNF 方法本身有一定的要求，否则会有一些问题，如经典的“左递归”问题。\"]},\"444\":{\"h\":\"左递归\",\"t\":[\"原则上我们是不讲这么深入，但我们上面的四则运算的文法就是左递归的，而左递归的语法是没法直接使用递归下降的方法实现的。因此我们要消除左递归，消除后的文法如下：\",\"<expr> ::= <term> <expr_tail><expr_tail> ::= + <term> <expr_tail> | - <term> <expr_tail> | <empty><term> ::= <factor> <term_tail><term_tail> ::= * <factor> <term_tail> | / <factor> <term_tail> | <empty><factor> ::= ( <expr> ) | Num\",\"消除左递归的相关方法，这里不再多说，请自行查阅相关的资料。\"]},\"445\":{\"h\":\"四则运算的实现\",\"t\":[\"本节中我们专注语法分析器部分的实现，具体实现很容易，我们直接贴上代码，就是上述的消除左递归后的文法直接转换而来的：\",\"int expr();int factor() { int value = 0; if (token == '(') { match('('); value = expr(); match(')'); } else { value = token_val; match(Num); } return value;}int term_tail(int lvalue) { if (token == '*') { match('*'); int value = lvalue * factor(); return term_tail(value); } else if (token == '/') { match('/'); int value = lvalue / factor(); return term_tail(value); } else { return lvalue; }}int term() { int lvalue = factor(); return term_tail(lvalue);}int expr_tail(int lvalue) { if (token == '+') { match('+'); int value = lvalue + term(); return expr_tail(value); } else if (token == '-') { match('-'); int value = lvalue - term(); return expr_tail(value); } else { return lvalue; }}int expr() { int lvalue = term(); return expr_tail(lvalue);}\",\"可以看到，有了BNF方法后，采用递归向下的方法来实现编译器是很直观的。\",\"我们把词法分析器的代码一并贴上：\",\"##include <stdio.h>##include <stdlib.h>enum {Num};int token;int token_val;char *line = NULL;char *src = NULL;void next() { // skip white space while (*src == ' ' || *src == '\\\\t') { src ++; } token = *src++; if (token >= '0' && token <= '9' ) { token_val = token - '0'; token = Num; while (*src >= '0' && *src <= '9') { token_val = token_val*10 + *src - '0'; src ++; } return; }}void match(int tk) { if (token != tk) { printf(\\\"expected token: %d(%c), got: %d(%c)\\\\n\\\", tk, tk, token, token); exit(-1); } next();}\",\"最后是main函数：\",\"int main(int argc, char *argv[]){ size_t linecap = 0; ssize_t linelen; while ((linelen = getline(&line, &linecap, stdin)) > 0) { src = line; next(); printf(\\\"%d\\\\n\\\", expr()); } return 0;}\"]},\"446\":{\"h\":\"小结\",\"t\":[\"本章中我们介绍了递归下降的方法，并用它来实现了四则运算的语法分析器。\",\"花这么大精力讲解递归下降方法，是因为几乎所有手工编写的语法分析器都或多或少地有它的影子。换句话说，掌握了递归下降的方法，就可以应付大多数的语法分析器编写。\",\"同时我们也用实例看到了理论（BNF 语法，左递归的消除）是如何帮助我们的工程实现的。尽管理论不是必需的，但如果能掌握它，对于提高我们的水平还是很有帮助的。\"]},\"447\":{\"c\":[\"编译原理\"]},\"448\":{\"c\":[\"c\",\"编译器\",\"解释器\"]},\"449\":{\"h\":\"手把手教你构建 C 语言编译器（5）——变量定义\",\"t\":[\"本文转自 https://lotabout.me/2016/write-a-C-interpreter-5/，如有侵权，请联系删除。\",\"Table of Contents\",\"1. EBNF 表示\",\"2. 解析变量的定义\",\"2.1. program()\",\"2.2. global_declaration()\",\"2.3. enum_declaration()\",\"2.4. 其它\",\"3. 代码\",\"4. 小结\",\"本章中我们用 EBNF 来大致描述我们实现的 C 语言的文法，并实现其中解析变量定义部分。\",\"由于语法分析本身比较复杂，所以我们将它拆分成 3 个部分进行讲解，分别是：变量定义、函数定义、表达式。\",\"手把手教你构建 C 语言编译器系列共有10个部分：\",\"手把手教你构建 C 语言编译器（0）——前言\",\"手把手教你构建 C 语言编译器（1）——设计\",\"手把手教你构建 C 语言编译器（2）——虚拟机\",\"手把手教你构建 C 语言编译器（3）——词法分析器\",\"手把手教你构建 C 语言编译器（4）——递归下降\",\"手把手教你构建 C 语言编译器（5）——变量定义\",\"手把手教你构建 C 语言编译器（6）——函数定义\",\"手把手教你构建 C 语言编译器（7）——语句\",\"手把手教你构建 C 语言编译器（8）——表达式\",\"手把手教你构建 C 语言编译器（9）——总结\"]},\"450\":{\"h\":\"EBNF 表示\",\"t\":[\"EBNF 是对前一章提到的 BNF 的扩展，它的语法更容易理解，实现起来也更直观。但真正看起来还是很烦，如果不想看可以跳过。\",\"program ::= {global_declaration}+global_declaration ::= enum_decl | variable_decl | function_declenum_decl ::= 'enum' [id] '{' id ['=' 'num'] {',' id ['=' 'num'] '}'variable_decl ::= type {'*'} id { ',' {'*'} id } ';'function_decl ::= type {'*'} id '(' parameter_decl ')' '{' body_decl '}'parameter_decl ::= type {'*'} id {',' type {'*'} id}body_decl ::= {variable_decl}, {statement}statement ::= non_empty_statement | empty_statementnon_empty_statement ::= if_statement | while_statement | '{' statement '}' | 'return' expression | expression ';'if_statement ::= 'if' '(' expression ')' statement ['else' non_empty_statement]while_statement ::= 'while' '(' expression ')' non_empty_statement\",\"其中 expression 相关的内容我们放到后面解释，主要原因是我们的语言不支持跨函数递归，而为了实现自举，实际上我们也不能使用递归（亏我们说了一章的递归下降）。\",\"P.S. 我是先写程序再总结上面的文法，所以实际上它们间的对应关系并不是特别明显。\"]},\"451\":{\"h\":\"解析变量的定义\",\"t\":[\"本章要讲解的就是上节文法中的 enum_decl 和 variable_decl 部分。\"]},\"452\":{\"h\":\"program()\",\"t\":[\"首先是之前定义过的 program 函数，将它改成：\",\"void program() { // get next token next(); while (token > 0) { global_declaration(); }}\",\"我知道 global_declaration 函数还没有出现过，但没有关系，采用自顶向下的编写方法就是要不断地实现我们需要的内容。下面是 global_declaration 函数的内容：\"]},\"453\":{\"h\":\"global_declaration()\",\"t\":[\"即全局的定义语句，包括变量定义，类型定义（只支持枚举）及函数定义。代码如下：\",\"int basetype; // the type of a declaration, make it global for convenienceint expr_type; // the type of an expressionvoid global_declaration() { // global_declaration ::= enum_decl | variable_decl | function_decl // // enum_decl ::= 'enum' [id] '{' id ['=' 'num'] {',' id ['=' 'num'} '}' // // variable_decl ::= type {'*'} id { ',' {'*'} id } ';' // // function_decl ::= type {'*'} id '(' parameter_decl ')' '{' body_decl '}' int type; // tmp, actual type for variable int i; // tmp basetype = INT; // parse enum, this should be treated alone. if (token == Enum) { // enum [id] { a = 10, b = 20, ... } match(Enum); if (token != '{') { match(Id); // skip the [id] part } if (token == '{') { // parse the assign part match('{'); enum_declaration(); match('}'); } match(';'); return; } // parse type information if (token == Int) { match(Int); } else if (token == Char) { match(Char); basetype = CHAR; } // parse the comma seperated variable declaration. while (token != ';' && token != '}') { type = basetype; // parse pointer type, note that there may exist `int ****x;` while (token == Mul) { match(Mul); type = type + PTR; } if (token != Id) { // invalid declaration printf(\\\"%d: bad global declaration\\\\n\\\", line); exit(-1); } if (current_id[Class]) { // identifier exists printf(\\\"%d: duplicate global declaration\\\\n\\\", line); exit(-1); } match(Id); current_id[Type] = type; if (token == '(') { current_id[Class] = Fun; current_id[Value] = (int)(text + 1); // the memory address of function function_declaration(); } else { // variable declaration current_id[Class] = Glo; // global variable current_id[Value] = (int)data; // assign memory address data = data + sizeof(int); } if (token == ',') { match(','); } } next();}\",\"看了上面的代码，能大概理解吗？这里我们讲解其中的一些细节。\",\"向前看标记 ：其中的 if (token == xxx) 语句就是用来向前查看标记以确定使用哪一个产生式，例如只要遇到 enum 我们就知道是需要解析枚举类型。而如果只解析到类型，如 int identifier 时我们并不能确定 identifier 是一个普通的变量还是一个函数，所以还需要继续查看后续的标记，如果遇到 ( 则可以断定是函数了，反之则是变量。\",\"变量类型的表示 ：我们的编译器支持指针类型，那意味着也支持指针的指针，如 int **data;。那么我们如何表示指针类型呢？前文中我们定义了支持的类型：\",\"// types of variable/functionenum { CHAR, INT, PTR };\",\"所以一个类型首先有基本类型，如 CHAR 或 INT，当它是一个指向基本类型的指针时，如 int *data，我们就将它的类型加上 PTR 即代码中的：type = type + PTR;。同理，如果是指针的指针，则再加上 PTR。\"]},\"454\":{\"h\":\"enum_declaration()\",\"t\":[\"用于解析枚举类型的定义。主要的逻辑用于解析用逗号（,）分隔的变量，值得注意的是在编译器中如何保存枚举变量的信息。\",\"即我们将该变量的类别设置成了 Num，这样它就成了全局的常量了，而注意到上节中，正常的全局变量的类别则是 Glo，类别信息在后面章节中解析 expression 会使用到。\",\"void enum_declaration() { // parse enum [id] { a = 1, b = 3, ...} int i; i = 0; while (token != '}') { if (token != Id) { printf(\\\"%d: bad enum identifier %d\\\\n\\\", line, token); exit(-1); } next(); if (token == Assign) { // like {a=10} next(); if (token != Num) { printf(\\\"%d: bad enum initializer\\\\n\\\", line); exit(-1); } i = token_val; next(); } current_id[Class] = Num; current_id[Type] = INT; current_id[Value] = i++; if (token == ',') { next(); } }}\"]},\"455\":{\"h\":\"其它\",\"t\":[\"其中的 function_declaration 函数我们将放到下一章中讲解。match 函数是一个辅助函数：\",\"void match(int tk) { if (token == tk) { next(); } else { printf(\\\"%d: expected token: %d\\\\n\\\", line, tk); exit(-1); }}\",\"它将 next 函数包装起来，如果不是预期的标记则报错并退出。\"]},\"456\":{\"h\":\"代码\",\"t\":[\"本章的代码可以在 Github 上下载，也可以直接 clone\",\"git clone -b step-3 https://github.com/lotabout/write-a-C-interpreter\",\"本章的代码还无法正常运行，因为还有许多功能没有实现，但如果有兴趣的话，可以自己先试着去实现它。\"]},\"457\":{\"h\":\"小结\",\"t\":[\"本章的内容应该不难，除了开头的 EBNF 表达式可能相对不好理解一些，但如果你查看了 EBNF 的具体表示方法后就不难理解了。\",\"剩下的内容就是按部就班地将 EBNF 的产生式转换成函数的过程，如果你理解了上一章中的内容，相信这部分也不难理解。\",\"下一章中我们将介绍如何解析函数的定义，敬请期待。\"]},\"458\":{\"c\":[\"编译原理\"]},\"459\":{\"c\":[\"c\",\"编译器\",\"解释器\"]},\"460\":{\"h\":\"手把手教你构建 C 语言编译器（6）——函数定义\",\"t\":[\"本文转自 https://lotabout.me/2016/write-a-C-interpreter-6/，如有侵权，请联系删除。\",\"Table of Contents\",\"1. EBNF 表示\",\"2. 解析函数的定义\",\"2.1. 函数参数与汇编代码\",\"2.2. 函数定义的解析\",\"2.3. 解析参数\",\"2.4. 函数体的解析\",\"3. 代码\",\"4. 小结\",\"由于语法分析本身比较复杂，所以我们将它拆分成 3 个部分进行讲解，分别是：变量定义、函数定义、表达式。本章讲解函数定义相关的内容。\",\"手把手教你构建 C 语言编译器系列共有10个部分：\",\"手把手教你构建 C 语言编译器（0）——前言\",\"手把手教你构建 C 语言编译器（1）——设计\",\"手把手教你构建 C 语言编译器（2）——虚拟机\",\"手把手教你构建 C 语言编译器（3）——词法分析器\",\"手把手教你构建 C 语言编译器（4）——递归下降\",\"手把手教你构建 C 语言编译器（5）——变量定义\",\"手把手教你构建 C 语言编译器（6）——函数定义\",\"手把手教你构建 C 语言编译器（7）——语句\",\"手把手教你构建 C 语言编译器（8）——表达式\",\"手把手教你构建 C 语言编译器（9）——总结\"]},\"461\":{\"h\":\"EBNF 表示\",\"t\":[\"这是上一章的 EBNF 方法中与函数定义相关的内容。\",\"variable_decl ::= type {'*'} id { ',' {'*'} id } ';'function_decl ::= type {'*'} id '(' parameter_decl ')' '{' body_decl '}'parameter_decl ::= type {'*'} id {',' type {'*'} id}body_decl ::= {variable_decl}, {statement}statement ::= non_empty_statement | empty_statementnon_empty_statement ::= if_statement | while_statement | '{' statement '}' | 'return' expression | expression ';'if_statement ::= 'if' '(' expression ')' statement ['else' non_empty_statement]while_statement ::= 'while' '(' expression ')' non_empty_statement\"]},\"462\":{\"h\":\"解析函数的定义\",\"t\":[\"上一章的代码中，我们已经知道了什么时候开始解析函数的定义，相关的代码如下：\",\"...if (token == '(') { current_id[Class] = Fun; current_id[Value] = (int)(text + 1); // the memory address of function function_declaration();} else {...\",\"即在这断代码之前，我们已经为当前的标识符（identifier）设置了正确的类型，上面这断代码为当前的标识符设置了正确的类别（Fun），以及该函数在代码段（text segment）中的位置。接下来开始解析函数定义相关的内容：parameter_decl 及 body_decl。\"]},\"463\":{\"h\":\"函数参数与汇编代码\",\"t\":[\"现在我们要回忆如何将“函数”转换成对应的汇编代码，因为这决定了在解析时我们需要哪些相关的信息。考虑下列函数：\",\"int demo(int param_a, int *param_b) { int local_1; char local_2; ...}\",\"那么它应该被转换成什么样的汇编代码呢？在思考这个问题之前，我们需要了解当 demo函数被调用时，计算机的栈的状态，如下（参照第三章讲解的虚拟机）：\",\"| .... | high address+---------------+| arg: param_a | new_bp + 3+---------------+| arg: param_b | new_bp + 2+---------------+|return address | new_bp + 1+---------------+| old BP | <- new BP+---------------+| local_1 | new_bp - 1+---------------+| local_2 | new_bp - 2+---------------+| .... | low address\",\"这里最为重要的一点是，无论是函数的参数（如 param_a）还是函数的局部变量（如 local_1）都是存放在计算机的 栈 上的。因此，与存放在 数据段 中的全局变量不同，在函数内访问它们是通过 new_bp 指针和对应的位移量进行的。因此，在解析的过程中，我们需要知道参数的个数，各个参数的位移量。\"]},\"464\":{\"h\":\"函数定义的解析\",\"t\":[\"这相当于是整个函数定义的语法解析的框架，代码如下：\",\"void function_declaration() { // type func_name (...) {...} // | this part match('('); function_parameter(); match(')'); match('{'); function_body(); //match('}'); // ① // ② // unwind local variable declarations for all local variables. current_id = symbols; while (current_id[Token]) { if (current_id[Class] == Loc) { current_id[Class] = current_id[BClass]; current_id[Type] = current_id[BType]; current_id[Value] = current_id[BValue]; } current_id = current_id + IdSize; }}\",\"其中①中我们没有消耗最后的}字符。这么做的原因是：variable_decl 与 function_decl 是放在一起解析的，而 variable_decl 是以字符 ; 结束的。而 function_decl 是以字符 } 结束的，若在此通过 match 消耗了 ‘;’ 字符，那么外层的 while 循环就没法准确地知道函数定义已经结束。所以我们将结束符的解析放在了外层的 while 循环中。\",\"而②中的代码是用于将符号表中的信息恢复成全局的信息。这是因为，局部变量是可以和全局变量同名的，一旦同名，在函数体内局部变量就会覆盖全局变量，出了函数体，全局变量就恢复了原先的作用。这段代码线性地遍历所有标识符，并将保存在 BXXX 中的信息还原。\"]},\"465\":{\"h\":\"解析参数\",\"t\":[\"parameter_decl ::= type {'*'} id {',' type {'*'} id}\",\"解析函数的参数就是解析以逗号分隔的一个个标识符，同时记录它们的位置与类型。\",\"int index_of_bp; // index of bp pointer on stackvoid function_parameter() { int type; int params; params = 0; while (token != ')') { // ① // int name, ... type = INT; if (token == Int) { match(Int); } else if (token == Char) { type = CHAR; match(Char); } // pointer type while (token == Mul) { match(Mul); type = type + PTR; } // parameter name if (token != Id) { printf(\\\"%d: bad parameter declaration\\\\n\\\", line); exit(-1); } if (current_id[Class] == Loc) { printf(\\\"%d: duplicate parameter declaration\\\\n\\\", line); exit(-1); } match(Id); //② // store the local variable current_id[BClass] = current_id[Class]; current_id[Class] = Loc; current_id[BType] = current_id[Type]; current_id[Type] = type; current_id[BValue] = current_id[Value]; current_id[Value] = params++; // index of current parameter if (token == ',') { match(','); } } // ③ index_of_bp = params+1;}\",\"其中①与全局变量定义的解析十分一样，用于解析该参数的类型。\",\"而②则与上节中提到的“局部变量覆盖全局变量”相关，先将全局变量的信息保存（无论是是否真的在全局中用到了这个变量）在 BXXX 中，再赋上局部变量相关的信息，如 Value 中存放的是参数的位置（是第几个参数）。\",\"③则与汇编代码的生成有关，index_of_bp 就是前文提到的 new_bp 的位置。\"]},\"466\":{\"h\":\"函数体的解析\",\"t\":[\"我们实现的 C 语言与现代的 C 语言不太一致，我们需要所有的变量定义出现在所有的语句之前。函数体的代码如下：\",\"void function_body() { // type func_name (...) {...} // -->| |<-- // ... { // 1. local declarations // 2. statements // } int pos_local; // position of local variables on the stack. int type; pos_local = index_of_bp; // ① while (token == Int || token == Char) { // local variable declaration, just like global ones. basetype = (token == Int) ? INT : CHAR; match(token); while (token != ';') { type = basetype; while (token == Mul) { match(Mul); type = type + PTR; } if (token != Id) { // invalid declaration printf(\\\"%d: bad local declaration\\\\n\\\", line); exit(-1); } if (current_id[Class] == Loc) { // identifier exists printf(\\\"%d: duplicate local declaration\\\\n\\\", line); exit(-1); } match(Id); // store the local variable current_id[BClass] = current_id[Class]; current_id[Class] = Loc; current_id[BType] = current_id[Type]; current_id[Type] = type; current_id[BValue] = current_id[Value]; current_id[Value] = ++pos_local; // index of current parameter if (token == ',') { match(','); } } match(';'); } // ② // save the stack size for local variables *++text = ENT; *++text = pos_local - index_of_bp; // statements while (token != '}') { statement(); } // emit code for leaving the sub function *++text = LEV;}\",\"其中①用于解析函数体内的局部变量的定义，代码与全局的变量定义几乎一样。\",\"而②则用于生成汇编代码，我们在第三章的虚拟机中提到过，我们需要在栈上为局部变量预留空间，这两行代码起的就是这个作用。\"]},\"467\":{\"h\":\"代码\",\"t\":[\"本章的代码可以在 Github 上下载，也可以直接 clone\",\"git clone -b step-4 https://github.com/lotabout/write-a-C-interpreter\",\"本章的代码依旧无法运行，还有两个重要函数没有完成：statement 及 expression，感兴趣的话可以尝试自己实现它们。\"]},\"468\":{\"h\":\"小结\",\"t\":[\"本章中我们用了不多的代码完成了函数定义的解析。大部分的代码依旧是用于解析变量：参数和局部变量，而它们的逻辑和全局变量的解析几乎一致，最大的区别就是保存的信息不同。\",\"当然，要理解函数定义的解析过程，最重要的是理解我们会为函数生成怎样的汇编代码，因为这决定了我们需要从解析中获取什么样的信息（例如参数的位置，个数等），而这些可能需要你重新回顾一下“虚拟机”这一章，或是重新学习学习汇编相关的知识。\",\"下一章中我们将讲解语句的解析，敬请期待。\"]},\"469\":{\"c\":[\"编译原理\"]},\"470\":{\"c\":[\"c\",\"编译器\",\"解释器\"]},\"471\":{\"h\":\"手把手教你构建 C 语言编译器（7）——语句\",\"t\":[\"本文转自 https://lotabout.me/2016/write-a-C-interpreter-7/，如有侵权，请联系删除。\",\"Table of Contents\",\"1. 语句\",\"1.1. IF 语句\",\"1.2. While 语句\",\"1.3. Return 语句\",\"1.4. 其它语句\",\"2. 代码\",\"3. 小结\",\"整个编译器还剩下最后两个部分：语句和表达式的解析。它们的内容比较多，主要涉及如何将语句和表达式编译成汇编代码。这章讲解语句的解析，相对于表达式来说它还是较为容易的。\",\"手把手教你构建 C 语言编译器系列共有10个部分：\",\"手把手教你构建 C 语言编译器（0）——前言\",\"手把手教你构建 C 语言编译器（1）——设计\",\"手把手教你构建 C 语言编译器（2）——虚拟机\",\"手把手教你构建 C 语言编译器（3）——词法分析器\",\"手把手教你构建 C 语言编译器（4）——递归下降\",\"手把手教你构建 C 语言编译器（5）——变量定义\",\"手把手教你构建 C 语言编译器（6）——函数定义\",\"手把手教你构建 C 语言编译器（7）——语句\",\"手把手教你构建 C 语言编译器（8）——表达式\",\"手把手教你构建 C 语言编译器（9）——总结\"]},\"472\":{\"h\":\"语句\",\"t\":[\"C 语言区分“语句”（statement）和“表达式”（expression）两个概念。简单地说，可以认为语句就是表达式加上末尾的分号。\",\"在我们的编译器中共识别 6 种语句：\",\"if (...) <statement> [else <statement>]\",\"while (...) <statement>\",\"{ <statement> }\",\"return xxx;\",\"<empty statement>;\",\"expression; (expression end with semicolon)\",\"它们的语法分析都相对容易，重要的是去理解如何将这些语句编译成汇编代码，下面我们逐一解释。\"]},\"473\":{\"h\":\"IF 语句\",\"t\":[\"IF 语句的作用是跳转，跟据条件表达式决定跳转的位置。我们看看下面的伪代码：\",\"if (...) <statement> [else <statement>] if (<cond>) <cond> JZ a <true_statement> ===> <true_statement> else: JMP ba: a: <false_statement> <false_statement>b: b:\",\"对应的汇编代码流程为：\",\"执行条件表达式 <cond>。\",\"如果条件失败，则跳转到 a 的位置，执行 else 语句。这里 else 语句是可以省略的，此时 a 和 b 都指向 IF 语句后方的代码。\",\"因为汇编代码是顺序排列的，所以如果执行了 true_statement，为了防止因为顺序排列而执行了 false_statement，所以需要无条件跳转 JMP b。\",\"对应的 C 代码如下：\",\"if (token == If) { match(If); match('('); expression(Assign); // parse condition match(')'); *++text = JZ; b = ++text; statement(); // parse statement if (token == Else) { // parse else match(Else); // emit code for JMP B *b = (int)(text + 3); *++text = JMP; b = ++text; statement(); } *b = (int)(text + 1);}\"]},\"474\":{\"h\":\"While 语句\",\"t\":[\"While 语句比 If 语句简单，它对应的汇编代码如下：\",\"a: a: while (<cond>) <cond> JZ b <statement> <statement> JMP ab: b:\",\"没有什么值得说明的内容，它的 C 代码如下：\",\"else if (token == While) { match(While); a = text + 1; match('('); expression(Assign); match(')'); *++text = JZ; b = ++text; statement(); *++text = JMP; *++text = (int)a; *b = (int)(text + 1);}\"]},\"475\":{\"h\":\"Return 语句\",\"t\":[\"Return 唯一特殊的地方是：一旦遇到了 Return 语句，则意味着函数要退出了，所以需要生成汇编代码 LEV 来表示退出。\",\"else if (token == Return) { // return [expression]; match(Return); if (token != ';') { expression(Assign); } match(';'); // emit code for return *++text = LEV;}\"]},\"476\":{\"h\":\"其它语句\",\"t\":[\"其它语句并不直接生成汇编代码，所以不多做说明，代码如下：\",\"else if (token == '{') { // { <statement> ... } match('{'); while (token != '}') { statement(); } match('}');}else if (token == ';') { // empty statement match(';');}else { // a = b; or function_call(); expression(Assign); match(';');}\"]},\"477\":{\"h\":\"代码\",\"t\":[\"本章的代码可以在 Github 上下载，也可以直接 clone\",\"git clone -b step-5 https://github.com/lotabout/write-a-C-interpreter\",\"本章的代码依旧无法运行，还剩最后一部分没有完成：expression。\"]},\"478\":{\"h\":\"小结\",\"t\":[\"本章讲解了如何将语句编译成汇编代码，内容相对容易一些，关键就是去理解汇编代码的执行原理。\",\"同时值得一提的是，编译器的语法分析部分其实是很简单的，而真正的难点是如何在语法分析时收集足够多的信息，最终把源代码转换成目标代码（汇编）。我认为这也是初学者实现编译器的一大难点，往往比词法分析/语法分析更困难。\",\"所以建议如果没有学过汇编，可以学习学习，它本身不难，但对理解计算机的原理有很大帮助。\"]},\"479\":{\"c\":[\"编译原理\"]},\"480\":{\"c\":[\"c\",\"编译器\",\"解释器\"]},\"481\":{\"h\":\"手把手教你构建 C 语言编译器（8）——表达式\",\"t\":[\"本文转自 https://blog.csdn.net/xzp740813/article/details/142961332?spm=1001.2014.3001.5501，如有侵权，请联系删除。\",\"Table of Contents\",\"1. 运算符的优先级\",\"2. 一元运算符\",\"2.1. 常量\",\"2.2. sizeof\",\"2.3. 变量与函数调用\",\"2.4. 强制转换\",\"2.5. 指针取值\",\"2.6. 取址操作\",\"2.7. 逻辑取反\",\"2.8. 按位取反\",\"2.9. 正负号\",\"2.10. 自增自减\",\"3. 二元运算符\",\"3.1. 赋值操作\",\"3.2. 三目运算符\",\"3.3. 逻辑运算符\",\"3.4. 数学运算符\",\"3.5. 自增自减\",\"3.6. 数组取值操作\",\"4. 代码\",\"5. 小结\",\"这是整个编译器的最后一部分，解析表达式。什么是表达式？表达式是将各种语言要素的一个组合，用来求值。例如：函数调用、变量赋值、运算符运算等等。\",\"表达式的解析难点有二：一是运算符的优先级问题，二是如何将表达式编译成目标代码。我们就来逐一说明。\",\"手把手教你构建 C 语言编译器系列共有10个部分：\",\"手把手教你构建 C 语言编译器（0）——前言\",\"手把手教你构建 C 语言编译器（1）——设计\",\"手把手教你构建 C 语言编译器（2）——虚拟机\",\"手把手教你构建 C 语言编译器（3）——词法分析器\",\"手把手教你构建 C 语言编译器（4）——递归下降\",\"手把手教你构建 C 语言编译器（5）——变量定义\",\"手把手教你构建 C 语言编译器（6）——函数定义\",\"手把手教你构建 C 语言编译器（7）——语句\",\"手把手教你构建 C 语言编译器（8）——表达式\",\"手把手教你构建 C 语言编译器（9）——总结\"]},\"482\":{\"h\":\"运算符的优先级\",\"t\":[\"运算符的优先级决定了表达式的运算顺序，如在普通的四则运算中，乘法 * 优先级高于加法 +，这就意味着表达式 2 + 3 * 4 的实际运行顺序是 2 + (3 * 4) 而不是 (2 + 3) * 4。\",\"C 语言定义了各种表达式的优先级，可以参考 C 语言运算符优先级。\",\"传统的编程书籍会用“逆波兰式”实现四则运算来讲解优先级问题。实际上，优先级关心的就是哪个运算符先计算，哪个运算符后计算（毕竟叫做“优先级”嘛）。而这就意味着我们需要决定先为哪个运算符生成目标代码（汇编），因为汇编代码是顺序排列的，我们必须先计算优先级高的运算符。\",\"那么如何确定运算符的优先级呢？答曰：栈（递归调用的实质也是栈的处理）。\",\"举一个例子：2 + 3 - 4 * 5，它的运算顺序是这样的：\",\"将 2 入栈\",\"遇到运算符 +，入栈，此时我们期待的是+的另一个参数\",\"遇到数字 3，原则上我们需要立即计算 2+3的值，但我们不确定数字 3 是否属于优先级更高的运算符，所以先将它入栈。\",\"遇到运算符 -，它的优先级和 + 相同，此时判断参数 3 属于这前的 +。将运算符 + 出栈，并将之前的 2 和 3 出栈，计算 2+3 的结果，得到 5 入栈。同时将运算符 - 入栈。\",\"遇到数字4，同样不能确定是否能立即计算，入栈\",\"遇到运算符 * 优先级大于 -，入栈\",\"遇到数字5，依旧不能确定是否立即计算，入栈\",\"表达式结束，运算符出栈，为 *，将参数出栈，计算 4*5 得到结果 20 入栈。\",\"运算符出栈，为 -，将参数出栈，计算 5-20，得到 -15 入栈。\",\"此时运算符栈为空，因此得到结果 -15。\",\"// after step 1, 2| |+------+| 3 | | |+------+ +------+| 2 | | + |+------+ +------+// after step 4| | | |+------+ +------+| 5 | | - |+------+ +------+// after step 7| |+------+| 5 |+------+ +------+| 4 | | * |+------+ +------+| 5 | | - |+------+ +------+\",\"综上，在计算一个运算符‘x’之前，必须先查看它的右方，找出并计算所有优先级大于‘x’的运算符，之后再计算运算符‘x’。\",\"最后注意的是优先通常只与多元运算符相关，单元运算符往往没有这个问题（因为只有一个参数）。也可以认为“优先级”的实质就是两个运算符在抢参数。\"]},\"483\":{\"h\":\"一元运算符\",\"t\":[\"上节中说到了运算符的优先级，也提到了优先级一般只与多元运算符有关，这也意味着一元运算符的优先级总是高于多元运算符。因为我们需要先对它们进行解析。\",\"当然，这部分也将同时解析参数本身（如变量、数字、字符串等等）。\",\"关于表达式的解析，与语法分析相关的部分就是上文所说的优先级问题了，而剩下的较难较烦的部分是与目标代码的生成有关的。因此对于需要讲解的运算符，我们主要从它的目标代码入手。\"]},\"484\":{\"h\":\"常量\",\"t\":[\"首先是数字，用 IMM 指令将它加载到 AX 中即可：\",\"if (token == Num) { match(Num); // emit code *++text = IMM; *++text = token_val; expr_type = INT;}\",\"接着是字符串常量。它比较特殊的一点是 C 语言的字符串常量支持如下风格：\",\"char *p;p = \\\"first line\\\" \\\"second line\\\";\",\"即跨行的字符串拼接，它相当于：\",\"char *p;p = \\\"first linesecond line\\\";\",\"所以解析的时候要注意这一点：\",\"else if (token == '\\\"') { // emit code *++text = IMM; *++text = token_val; match('\\\"'); // store the rest strings while (token == '\\\"') { match('\\\"'); } // append the end of string character '\\\\0', all the data are default // to 0, so just move data one position forward. data = (char *)(((int)data + sizeof(int)) & (-sizeof(int))); expr_type = PTR;}\"]},\"485\":{\"h\":\"sizeof\",\"t\":[\"sizeof 是一个一元运算符，我们需要知道后面参数的类型，类型的解析在前面的文章中我们已经很熟悉了。\",\"else if (token == Sizeof) { // sizeof is actually an unary operator // now only `sizeof(int)`, `sizeof(char)` and `sizeof(*...)` are // supported. match(Sizeof); match('('); expr_type = INT; if (token == Int) { match(Int); } else if (token == Char) { match(Char); expr_type = CHAR; } while (token == Mul) { match(Mul); expr_type = expr_type + PTR; } match(')'); // emit code *++text = IMM; *++text = (expr_type == CHAR) ? sizeof(char) : sizeof(int); expr_type = INT;}\",\"注意的是只支持 sizeof(int)，sizeof(char) 及 sizeof(pointer type...)。并且它的结果是 int 型。\"]},\"486\":{\"h\":\"变量与函数调用\",\"t\":[\"由于取变量的值与函数的调用都是以 Id 标记开头的，因此将它们放在一起处理。\",\"else if (token == Id) { // there are several type when occurs to Id // but this is unit, so it can only be // 1. function call // 2. Enum variable // 3. global/local variable match(Id); id = current_id; if (token == '(') { // function call match('('); // ① // pass in arguments tmp = 0; // number of arguments while (token != ')') { expression(Assign); *++text = PUSH; tmp ++; if (token == ',') { match(','); } } match(')'); // ② // emit code if (id[Class] == Sys) { // system functions *++text = id[Value]; } else if (id[Class] == Fun) { // function call *++text = CALL; *++text = id[Value]; } else { printf(\\\"%d: bad function call\\\\n\\\", line); exit(-1); } // ③ // clean the stack for arguments if (tmp > 0) { *++text = ADJ; *++text = tmp; } expr_type = id[Type]; } else if (id[Class] == Num) { // ④ // enum variable *++text = IMM; *++text = id[Value]; expr_type = INT; } else { // ⑤ // variable if (id[Class] == Loc) { *++text = LEA; *++text = index_of_bp - id[Value]; } else if (id[Class] == Glo) { *++text = IMM; *++text = id[Value]; } else { printf(\\\"%d: undefined variable\\\\n\\\", line); exit(-1); } //⑥ // emit code, default behaviour is to load the value of the // address which is stored in `ax` expr_type = id[Type]; *++text = (expr_type == Char) ? LC : LI; }}\",\"①中注意我们是顺序将参数入栈，这和第三章：虚拟机中讲解的指令是对应的。与之不同，标准 C 是逆序将参数入栈的。\",\"②中判断函数的类型，同样在第三章：“虚拟机”中我们介绍过内置函数的支持，如 printf, read, malloc 等等。内置函数有对应的汇编指令，而普通的函数则编译成 CALL <addr> 的形式。\",\"③用于清除入栈的参数。因为我们不在乎出栈的值，所以直接修改栈指针的大小即可。\",\"④：当该标识符是全局定义的枚举类型时，直接将对应的值用 IMM 指令存入 AX 即可。\",\"⑤则是用于加载变量的值，如果是局部变量则采用与 bp 指针相对位置的形式（参见第 7章函数定义）。而如果是全局变量则用 IMM 加载变量的地址。\",\"⑥：无论是全局还是局部变量，最终都根据它们的类型用 LC 或 LI 指令加载对应的值。\",\"关于变量，你可能有疑问，如果遇到标识符就用 LC/LI 载入相应的值，那诸如 a[10] 之类的表达式要如何实现呢？后面我们会看到，根据标识符后的运算符，我们可能会修改或删除现有的 LC/LI 指令。\"]},\"487\":{\"h\":\"强制转换\",\"t\":[\"虽然我们前面没有提到，但我们一直用 expr_type 来保存一个表达式的类型，强制转换的作用是获取转换的类型，并直接修改 expr_type 的值。\",\"else if (token == '(') { // cast or parenthesis match('('); if (token == Int || token == Char) { tmp = (token == Char) ? CHAR : INT; // cast type match(token); while (token == Mul) { match(Mul); tmp = tmp + PTR; } match(')'); expression(Inc); // cast has precedence as Inc(++) expr_type = tmp; } else { // normal parenthesis expression(Assign); match(')'); }}\"]},\"488\":{\"h\":\"指针取值\",\"t\":[\"诸如 *a 的指针取值，关键是判断 a 的类型，而就像上节中提到的，当一个表达式解析结束时，它的类型保存在变量 expr_type 中。\",\"else if (token == Mul) { // dereference *<addr> match(Mul); expression(Inc); // dereference has the same precedence as Inc(++) if (expr_type >= PTR) { expr_type = expr_type - PTR; } else { printf(\\\"%d: bad dereference\\\\n\\\", line); exit(-1); } *++text = (expr_type == CHAR) ? LC : LI;}\"]},\"489\":{\"h\":\"取址操作\",\"t\":[\"这里我们就能看到“变量与函数调用”一节中所说的修改或删除 LC/LI 指令了。前文中我们说到，对于变量，我们会先加载它的地址，并根据它们类型使用 LC/LI 指令加载实际内容，例如对变量 a：\",\"IMM <addr>LI\",\"那么对变量 a 取址，其实只要不执行 LC/LI 即可。因此我们删除相应的指令。\",\"else if (token == And) { // get the address of match(And); expression(Inc); // get the address of if (*text == LC || *text == LI) { text --; } else { printf(\\\"%d: bad address of\\\\n\\\", line); exit(-1); } expr_type = expr_type + PTR;}\"]},\"490\":{\"h\":\"逻辑取反\",\"t\":[\"我们没有直接的逻辑取反指令，因此我们判断它是否与数字 0 相等。而数字 0 代表了逻辑 “False”。\",\"else if (token == '!') { // not match('!'); expression(Inc); // emit code, use <expr> == 0 *++text = PUSH; *++text = IMM; *++text = 0; *++text = EQ; expr_type = INT;}\"]},\"491\":{\"h\":\"按位取反\",\"t\":[\"同样我们没有相应的指令，所以我们用异或来实现，即 ~a = a ^ 0xFFFF。\",\"else if (token == '~') { // bitwise not match('~'); expression(Inc); // emit code, use <expr> XOR -1 *++text = PUSH; *++text = IMM; *++text = -1; *++text = XOR; expr_type = INT;}\"]},\"492\":{\"h\":\"正负号\",\"t\":[\"注意这里并不是四则运算中的加减法，而是单个数字的取正取负操作。同样，我们没有取负的操作，用 0 - x 来实现 -x。\",\"else if (token == Add) { // +var, do nothing match(Add); expression(Inc); expr_type = INT;}else if (token == Sub) { // -var match(Sub); if (token == Num) { *++text = IMM; *++text = -token_val; match(Num); } else { *++text = IMM; *++text = -1; *++text = PUSH; expression(Inc); *++text = MUL; } expr_type = INT;}\"]},\"493\":{\"h\":\"自增自减\",\"t\":[\"注意的是自增自减操作的优先级是和它的位置有关的。如 ++p 的优先级高于 p++，这里我们解析的就是类似 ++p 的操作。\",\"else if (token == Inc || token == Dec) { tmp = token; match(token); expression(Inc); // ① if (*text == LC) { *text = PUSH; // to duplicate the address *++text = LC; } else if (*text == LI) { *text = PUSH; *++text = LI; } else { printf(\\\"%d: bad lvalue of pre-increment\\\\n\\\", line); exit(-1); } *++text = PUSH; *++text = IMM; // ② *++text = (expr_type > PTR) ? sizeof(int) : sizeof(char); *++text = (tmp == Inc) ? ADD : SUB; *++text = (expr_type == CHAR) ? SC : SI;}\",\"对应的汇编代码也比较直观，只是在实现 ++p时，我们要使用变量 p 的地址两次，所以我们需要先 PUSH （①）。\",\"②则是因为自增自减操作还需要处理是指针的情形。\"]},\"494\":{\"h\":\"二元运算符\",\"t\":[\"这里，我们需要处理多运算符的优先级问题，就如前文的“优先级”一节提到的，我们需要不断地向右扫描，直到遇到优先级 小于 当前优先级的运算符。\",\"回想起我们之前定义过的各个标记，它们是以优先级从低到高排列的，即 Assign 的优先级最低，而 Brak（[） 的优先级最高。\",\"enum { Num = 128, Fun, Sys, Glo, Loc, Id, Char, Else, Enum, If, Int, Return, Sizeof, While, Assign, Cond, Lor, Lan, Or, Xor, And, Eq, Ne, Lt, Gt, Le, Ge, Shl, Shr, Add, Sub, Mul, Div, Mod, Inc, Dec, Brak};\",\"所以，当我们调用 expression(level) 进行解析的时候，我们其实通过了参数 level 指定了当前的优先级。在前文的一元运算符处理中也用到了这一点。\",\"所以，此时的二元运算符的解析的框架为：\",\"while (token >= level) { // parse token for binary operator and postfix operator}\",\"解决了优先级的问题，让我们继续讲解如何把运算符编译成汇编代码吧。\"]},\"495\":{\"h\":\"赋值操作\",\"t\":[\"赋值操作是优先级最低的运算符。考虑诸如 a = (expession) 的表达式，在解析 = 之前，我们已经为变量 a 生成了如下的汇编代码：\",\"IMM <addr>LC/LI\",\"当解析完=右边的表达式后，相应的值会存放在 ax 中，此时，为了实际将这个值保存起来，我们需要类似下面的汇编代码：\",\"IMM <addr>PUSHSC/SI\",\"明白了这点，也就能理解下面的源代码了：\",\"tmp = expr_type;if (token == Assign) { // var = expr; match(Assign); if (*text == LC || *text == LI) { *text = PUSH; // save the lvalue's pointer } else { printf(\\\"%d: bad lvalue in assignment\\\\n\\\", line); exit(-1); } expression(Assign); expr_type = tmp; *++text = (expr_type == CHAR) ? SC : SI;}\"]},\"496\":{\"h\":\"三目运算符\",\"t\":[\"这是 C 语言中唯一的一个三元运算符： ? :，它相当于一个小型的 If 语句，所以生成的代码也类似于 If 语句，这里就不多作解释。\",\"else if (token == Cond) { // expr ? a : b; match(Cond); *++text = JZ; addr = ++text; expression(Assign); if (token == ':') { match(':'); } else { printf(\\\"%d: missing colon in conditional\\\\n\\\", line); exit(-1); } *addr = (int)(text + 3); *++text = JMP; addr = ++text; expression(Cond); *addr = (int)(text + 1);}\"]},\"497\":{\"h\":\"逻辑运算符\",\"t\":[\"这包括 || 和 &&。它们对应的汇编代码如下：\",\"<expr1> || <expr2> <expr1> && <expr2> ...<expr1>... ...<expr1>... JNZ b JZ b ...<expr2>... ...<expr2>...b: b:\",\"所以源码如下：\",\"else if (token == Lor) { // logic or match(Lor); *++text = JNZ; addr = ++text; expression(Lan); *addr = (int)(text + 1); expr_type = INT;}else if (token == Lan) { // logic and match(Lan); *++text = JZ; addr = ++text; expression(Or); *addr = (int)(text + 1); expr_type = INT;}\"]},\"498\":{\"h\":\"数学运算符\",\"t\":[\"它们包括 |, ^, &, ==, !=<=, >=, <, >, <<, >>, +, -, *, /, %。它们的实现都很类似，我们以异或 ^ 为例：\",\"<expr1> ^ <expr2>...<expr1>... <- now the result is on axPUSH...<expr2>... <- now the value of <expr2> is on axXOR\",\"所以它对应的代码为：\",\"else if (token == Xor) { // bitwise xor match(Xor); *++text = PUSH; expression(And); *++text = XOR; expr_type = INT;}\",\"其它的我们便不再详述。但这当中还有一个问题，就是指针的加减。在 C 语言中，指针加上数值等于将指针移位，且根据不同的类型移动的位移不同。如 a + 1，如果 a 是 char * 型，则移动一字节，而如果 a 是 int * 型，则移动 4 个字节（32位系统）。\",\"另外，在作指针减法时，如果是两个指针相减（相同类型），则结果是两个指针间隔的元素个数。因此要有特殊的处理。\",\"下面以加法为例，对应的汇编代码为：\",\"<expr1> + <expr2>normal pointer<expr1> <expr1>PUSH PUSH<expr2> <expr2> |ADD PUSH | <expr2> * <unit> IMM <unit> | MUL | ADD\",\"即当 <expr1> 是指针时，要根据它的类型放大 <expr2> 的值，因此对应的源码如下：\",\"else if (token == Add) { // add match(Add); *++text = PUSH; expression(Mul); expr_type = tmp; if (expr_type > PTR) { // pointer type, and not `char *` *++text = PUSH; *++text = IMM; *++text = sizeof(int); *++text = MUL; } *++text = ADD;}\",\"相应的减法的代码就不贴了，可以自己实现看看，也可以看文末给出的链接。\"]},\"499\":{\"h\":\"自增自减\",\"t\":[\"这次是后缀形式的，即 p++ 或 p--。与前缀形式不同的是，在执行自增自减后， ax上需要保留原来的值。所以我们首先执行类似前缀自增自减的操作，再将 ax 中的值执行减/增的操作。\",\"// 前缀形式 生成汇编代码*++text = PUSH;*++text = IMM;*++text = (expr_type > PTR) ? sizeof(int) : sizeof(char);*++text = (tmp == Inc) ? ADD : SUB;*++text = (expr_type == CHAR) ? SC : SI;// 后缀形式 生成汇编代码*++text = PUSH;*++text = IMM;*++text = (expr_type > PTR) ? sizeof(int) : sizeof(char);*++text = (token == Inc) ? ADD : SUB;*++text = (expr_type == CHAR) ? SC : SI;*++text = PUSH; //*++text = IMM; // 执行相反的增/减操作*++text = (expr_type > PTR) ? sizeof(int) : sizeof(char); //*++text = (token == Inc) ? SUB : ADD; //\"]},\"500\":{\"h\":\"数组取值操作\",\"t\":[\"在学习 C 语言的时候你可能已经知道了，诸如 a[10] 的操作等价于 *(a + 10)。因此我们要做的就是生成类似的汇编代码：\",\"else if (token == Brak) { // array access var[xx] match(Brak); *++text = PUSH; expression(Assign); match(']'); if (tmp > PTR) { // pointer, `not char *` *++text = PUSH; *++text = IMM; *++text = sizeof(int); *++text = MUL; } else if (tmp < PTR) { printf(\\\"%d: pointer type expected\\\\n\\\", line); exit(-1); } expr_type = tmp - PTR; *++text = ADD; *++text = (expr_type == CHAR) ? LC : LI;}\"]},\"501\":{\"h\":\"代码\",\"t\":[\"除了上述对表达式的解析外，我们还需要初始化虚拟机的栈，我们可以正确调用 main 函数，且当 main 函数结束时退出进程。\",\"int *tmp;// setup stacksp = (int *)((int)stack + poolsize);*--sp = EXIT; // call exit if main returns*--sp = PUSH; tmp = sp;*--sp = argc;*--sp = (int)argv;*--sp = (int)tmp;\",\"当然，最后要注意的一点是：所有的变量定义必须放在语句之前。\",\"本章的代码可以在 Github 上下载，也可以直接 clone\",\"git clone -b step-6 https://github.com/lotabout/write-a-C-interpreter\",\"通过 gcc -o xc-tutor xc-tutor.c 进行编译。并执行 ./xc-tutor hello.c 查看结果。\",\"正如我们保证的那样，我们的代码是自举的，能自己编译自己，所以你可以执行 ./xc-tutor xc-tutor.c hello.c。可以看到和之前有同样的输出。\"]},\"502\":{\"h\":\"小结\",\"t\":[\"本章我们进行了最后的解析，解析表达式。本章有两个难点：\",\"如何通过递归调用 expression 来实现运算符的优先级。\",\"如何为每个运算符生成对应的汇编代码。\",\"尽管代码看起来比较简单（虽然多），但其中用到的原理还是需要仔细推敲的。\",\"最后，恭喜你！通过一步步的学习，自己实现了一个C语言的编译器（好吧，是解释器）。\"]},\"503\":{\"c\":[\"编译原理\"]},\"504\":{\"c\":[\"c\",\"编译器\",\"解释器\"]},\"505\":{\"h\":\"手把手教你构建 C 语言编译器（9）——总结\",\"t\":[\"本文转自 https://lotabout.me/2016/write-a-C-interpreter-9/，如有侵权，请联系删除。\",\"Table of Contents\",\"1. 虚拟机与目标代码\",\"2. 词法分析\",\"3. 语法分析\",\"4. 关于编代码\",\"5. 结语\",\"恭喜你完成了自己的 C 语言编译器，本章中我们发一发牢骚，说一说编写编译器值得注意的一些问题；编写编译器时遇到的一些难题。\",\"手把手教你构建 C 语言编译器系列共有10个部分：\",\"手把手教你构建 C 语言编译器（0）——前言\",\"手把手教你构建 C 语言编译器（1）——设计\",\"手把手教你构建 C 语言编译器（2）——虚拟机\",\"手把手教你构建 C 语言编译器（3）——词法分析器\",\"手把手教你构建 C 语言编译器（4）——递归下降\",\"手把手教你构建 C 语言编译器（5）——变量定义\",\"手把手教你构建 C 语言编译器（6）——函数定义\",\"手把手教你构建 C 语言编译器（7）——语句\",\"手把手教你构建 C 语言编译器（8）——表达式\",\"手把手教你构建 C 语言编译器（9）——总结\"]},\"506\":{\"h\":\"虚拟机与目标代码\",\"t\":[\"整个系列的一开始，我们就着手虚拟机的实现。不知道你是否有同感，这部分对于整个编译器的编写其实是十分重要的。我认为至少占了重要程度的50%。\",\"这里要说明这样一个观点，学习编译原理时常常着眼于词法分析和语法分析，而忽略了同样重要的代码生成。对于学习或考试而言或许可以，但实际编译项目时，最为重要的是能“跑起来”，所以我们需要给予代码生成高度的重视。\",\"同时我们也看到，在后期解析语句和表达式时，难点已经不再是语法分析了，而是如何为运算符生成相应的汇编代码。\"]},\"507\":{\"h\":\"词法分析\",\"t\":[\"我们用了很暴力的手段编写了我们的词法分析器，我认为这并无不可。\",\"但你依旧可以学习相关的知识，了解自动生成词法分析器的原理，它涉及到了“正则表达式”，“状态机”等等知识。相信这部分的知识能够很大程度上提高你的编程水平。\",\"同时，如果今后你仍然想编写编译器，不妨试试这些自动生成工具。\"]},\"508\":{\"h\":\"语法分析\",\"t\":[\"长期以来，语法分析对我而言一直是迷一样的存在，直到真正用递归下降的方式实现了一个。\",\"我们用了专门的一章讲解了“递归下降”与 BNF 文法的关系。希望能减少你对理论的厌恶。至少，实现起来并不是太难。\",\"如果有兴趣，可以学习学习这些文法，因为已经有许多自动生成的工具支持它们。这样你就不需要重复造轮子。可以看看 yacc 等工具，更先进的版本是 bsion。同时其它语言也有许多类似的支持。\",\"题外话，最近知道了一个叫“PEG 文法”的表示方法，无论是读起来，还是实现起来，都比 BNF 要容易，你也可以学习看看。\"]},\"509\":{\"h\":\"关于编代码\",\"t\":[\"这也是我自己的感慨吧。无论多好的教程，想要完全理解它，最好的方式恐怕还是要自己实现它。\",\"只是在编写代码的过程中，我们会遇到许多的挫折，例如需要考虑许多细节，或是调试起来十分困难。但也只有真正静下心来去克服它，我们才能有所成长吧。\",\"例如在编写表达式的解析时，大量重复的代码特别让人崩溃。还有就是调试编译器，简直痛苦地无话可说。\",\"P.S. 如果你按这个系列自己编写代码，记得事先写一些用于输出汇编代码的函数，很有帮助的。\",\"还有就是写这个系列的文章，开始的冲动过了之后，每写一篇都特别心烦，希望文章本身没有受我的这种情绪影响吧。\"]},\"510\":{\"h\":\"结语\",\"t\":[\"编程有趣又无趣，只有身在其中的我们才能体会吧。\"]},\"511\":{\"c\":[\"编译原理\"]},\"512\":{\"c\":[\"c\",\"编译器\",\"解释器\"]},\"513\":{\"h\":\"\",\"t\":[\"404 Not Found\"]},\"514\":{\"h\":\"Design ASimpile CCompiler\"}},\"dirtCount\":0,\"index\":[[\"题外话\",{\"1\":{\"508\":1}}],[\"长期以来\",{\"1\":{\"508\":1}}],[\"难点已经不再是语法分析了\",{\"1\":{\"506\":1}}],[\"难以调试\",{\"1\":{\"396\":1}}],[\"难以增加\",{\"0\":{\"387\":1}}],[\"难以增加新的零件\",{\"0\":{\"143\":1}}],[\"难以根据类生成实例\",{\"1\":{\"316\":1}}],[\"跑起来\",{\"1\":{\"506\":1}}],[\"恭喜你完成了自己的\",{\"1\":{\"505\":1}}],[\"恭喜你\",{\"1\":{\"502\":1}}],[\"查看结果\",{\"1\":{\"501\":1}}],[\"查找已有标识符的方法是线性查找\",{\"1\":{\"429\":1}}],[\"减操作\",{\"1\":{\"499\":1}}],[\"减少程序的体积\",{\"1\":{\"405\":1}}],[\"减少重复代码\",{\"1\":{\"361\":1}}],[\"减少计数\",{\"1\":{\"255\":1}}],[\"减少了类之间的耦合度\",{\"1\":{\"158\":1}}],[\"减少了客户端代码与具体类之间的耦合\",{\"1\":{\"138\":1}}],[\"减少对象之间的直接交互\",{\"1\":{\"123\":1}}],[\"减少对象之间的直接依赖\",{\"1\":{\"123\":1}}],[\"明白了这点\",{\"1\":{\"495\":1}}],[\"明确了各个类的职责分工\",{\"1\":{\"183\":1}}],[\"回想起我们之前定义过的各个标记\",{\"1\":{\"494\":1}}],[\"回到并发竞争带来的安全问题上\",{\"1\":{\"101\":1}}],[\"诸如\",{\"1\":{\"488\":1,\"500\":1}}],[\"载入相应的值\",{\"1\":{\"486\":1}}],[\"⑥\",{\"1\":{\"486\":2}}],[\"⑤则是用于加载变量的值\",{\"1\":{\"486\":1}}],[\"⑤\",{\"1\":{\"486\":1}}],[\"④\",{\"1\":{\"486\":2}}],[\"找出并计算所有优先级大于\",{\"1\":{\"482\":1}}],[\"属于这前的\",{\"1\":{\"482\":1}}],[\"属性注入或方法注入\",{\"1\":{\"129\":1}}],[\"入栈\",{\"1\":{\"482\":9}}],[\"入度为\",{\"1\":{\"85\":1}}],[\"举一个例子\",{\"1\":{\"482\":1}}],[\"答曰\",{\"1\":{\"482\":1}}],[\"嘛\",{\"1\":{\"482\":1}}],[\"毕竟叫做\",{\"1\":{\"482\":1}}],[\"毕竟我们不是真正的计算机\",{\"1\":{\"412\":1}}],[\"哪个运算符后计算\",{\"1\":{\"482\":1}}],[\"哪些角色可以复用\",{\"0\":{\"285\":1}}],[\"哪些信息不应当共享\",{\"1\":{\"253\":1}}],[\"哪些信息应当共享\",{\"1\":{\"253\":1}}],[\"逆波兰式\",{\"1\":{\"482\":1}}],[\"赋值操作是优先级最低的运算符\",{\"1\":{\"495\":1}}],[\"赋值操作\",{\"0\":{\"495\":1},\"1\":{\"481\":1}}],[\"按位取反\",{\"0\":{\"491\":1},\"1\":{\"481\":1}}],[\"强制转换的作用是获取转换的类型\",{\"1\":{\"487\":1}}],[\"强制转换\",{\"0\":{\"487\":1},\"1\":{\"481\":1}}],[\"强引用\",{\"1\":{\"255\":1}}],[\"常量\",{\"0\":{\"484\":1},\"1\":{\"481\":1}}],[\"往往比词法分析\",{\"1\":{\"478\":1}}],[\"跟据条件表达式决定跳转的位置\",{\"1\":{\"473\":1}}],[\"跟它们在\",{\"1\":{\"425\":1}}],[\"种语句\",{\"1\":{\"472\":1}}],[\"感兴趣的话可以尝试自己实现它们\",{\"1\":{\"467\":1}}],[\"感谢lucky\",{\"1\":{\"53\":1}}],[\"局部变量覆盖全局变量\",{\"1\":{\"465\":1}}],[\"局部变量是可以和全局变量同名的\",{\"1\":{\"464\":1}}],[\"③用于清除入栈的参数\",{\"1\":{\"486\":1}}],[\"③则与汇编代码的生成有关\",{\"1\":{\"465\":1}}],[\"③\",{\"1\":{\"465\":1,\"486\":1}}],[\"全局变量就恢复了原先的作用\",{\"1\":{\"464\":1}}],[\"全局变量或局部变量等\",{\"1\":{\"429\":1}}],[\"出栈\",{\"1\":{\"482\":2}}],[\"出了函数体\",{\"1\":{\"464\":1}}],[\"出题人不愿意写一个确定精度的\",{\"1\":{\"41\":1}}],[\"消耗了\",{\"1\":{\"464\":1}}],[\"消除左递归的相关方法\",{\"1\":{\"444\":1}}],[\"消除后的文法如下\",{\"1\":{\"444\":1}}],[\"②则是因为自增自减操作还需要处理是指针的情形\",{\"1\":{\"493\":1}}],[\"②中判断函数的类型\",{\"1\":{\"486\":1}}],[\"②\",{\"1\":{\"464\":1,\"465\":1,\"466\":1,\"486\":1,\"493\":1}}],[\"①中注意我们是顺序将参数入栈\",{\"1\":{\"486\":1}}],[\"①\",{\"1\":{\"464\":1,\"465\":1,\"466\":1,\"486\":1,\"493\":2}}],[\"设置了正确的类型\",{\"1\":{\"462\":1}}],[\"设计我们自己的指令集\",{\"1\":{\"403\":1}}],[\"设计\",{\"0\":{\"400\":1},\"1\":{\"392\":1,\"400\":1,\"403\":1,\"421\":1,\"439\":1,\"449\":1,\"460\":1,\"471\":1,\"481\":1,\"505\":1}}],[\"设计者在使用\",{\"1\":{\"253\":1}}],[\"设计时能够决定的事情和不能决定的事情\",{\"0\":{\"184\":1}}],[\"设计模式和面向对象的目的正是为我们提供一种结构\",{\"1\":{\"385\":1}}],[\"设计模式需遵循面向对象的设计原则\",{\"1\":{\"260\":1}}],[\"设计模式是软件开发中的一把利器\",{\"1\":{\"232\":1}}],[\"设计模式的学习和应用需要不断的实践和积累\",{\"1\":{\"232\":1}}],[\"设计模式的使用不是最终目的\",{\"1\":{\"232\":1}}],[\"设计模式并不是万能的\",{\"1\":{\"232\":1}}],[\"设计模式提供了一种通用的解决方案\",{\"1\":{\"232\":1}}],[\"设计模式\",{\"0\":{\"260\":1},\"2\":{\"135\":1,\"136\":1,\"145\":1,\"146\":1,\"155\":1,\"156\":1,\"175\":1,\"176\":1,\"186\":1,\"187\":1,\"193\":1,\"194\":1,\"203\":1,\"204\":1,\"214\":1,\"215\":1,\"230\":1,\"231\":1,\"233\":1,\"234\":1,\"240\":1,\"241\":1,\"246\":1,\"247\":1,\"258\":1,\"259\":1,\"261\":1,\"262\":1,\"267\":1,\"268\":1,\"276\":1,\"277\":1,\"287\":1,\"288\":1,\"299\":1,\"300\":1,\"313\":1,\"314\":1,\"320\":1,\"321\":1,\"334\":1,\"335\":1,\"344\":1,\"345\":1,\"358\":1,\"359\":1,\"368\":1,\"369\":1,\"376\":1,\"377\":1,\"390\":1,\"391\":1}}],[\"设计模式七大原则\",{\"0\":{\"113\":1}}],[\"设计方法\",{\"1\":{\"114\":1}}],[\"设计目标\",{\"1\":{\"114\":1}}],[\"敬请期待\",{\"1\":{\"457\":1,\"468\":1}}],[\"敬请批评指正\",{\"1\":{\"397\":1}}],[\"剩下的内容就是按部就班地将\",{\"1\":{\"457\":1}}],[\"值得注意的是在编译器中如何保存枚举变量的信息\",{\"1\":{\"454\":1}}],[\"值得注意的是docker\",{\"1\":{\"38\":1}}],[\"亏我们说了一章的递归下降\",{\"1\":{\"450\":1}}],[\"掌握了递归下降的方法\",{\"1\":{\"446\":1}}],[\"花这么大精力讲解递归下降方法\",{\"1\":{\"446\":1}}],[\"采用自顶向下的编写方法就是要不断地实现我们需要的内容\",{\"1\":{\"452\":1}}],[\"采用递归向下的方法来实现编译器是很直观的\",{\"1\":{\"445\":1}}],[\"采用反证法\",{\"1\":{\"81\":1,\"84\":1}}],[\"否则会有一些问题\",{\"1\":{\"443\":1}}],[\"底\",{\"1\":{\"442\":1}}],[\"顶\",{\"1\":{\"442\":1}}],[\"右侧的式子代替\",{\"1\":{\"441\":1}}],[\"括起来的就称作\",{\"1\":{\"441\":1}}],[\"括号太多\",{\"1\":{\"43\":1}}],[\"范式\",{\"1\":{\"441\":1}}],[\"非终结符\",{\"1\":{\"441\":2,\"443\":1}}],[\"非本质的\",{\"1\":{\"254\":1}}],[\"终结符\",{\"1\":{\"441\":2}}],[\"终结符与非终结符\",{\"0\":{\"441\":1},\"1\":{\"439\":1}}],[\"四则运算的规则可以表示如下\",{\"1\":{\"441\":1}}],[\"四则运算的实现\",{\"0\":{\"445\":1},\"1\":{\"439\":1}}],[\"四则运算的递归下降\",{\"0\":{\"442\":1},\"1\":{\"439\":1}}],[\"左递归的消除\",{\"1\":{\"446\":1}}],[\"左递归\",{\"0\":{\"444\":1},\"1\":{\"439\":1,\"443\":1}}],[\"左手画方右手画圆在现实中本来就不成立\",{\"1\":{\"98\":1}}],[\"作用是减小语法分析器的复杂程度\",{\"1\":{\"436\":1}}],[\"作为观察者\",{\"1\":{\"311\":1}}],[\"作为被观察对象\",{\"1\":{\"311\":1}}],[\"作为设计人员\",{\"1\":{\"183\":1}}],[\"作为代码托管平台的开发者来说\",{\"1\":{\"31\":1}}],[\"平时听到的\",{\"1\":{\"432\":1}}],[\"标准\",{\"1\":{\"486\":1}}],[\"标记开头的\",{\"1\":{\"486\":1}}],[\"标记\",{\"1\":{\"432\":2}}],[\"标识符的类型\",{\"1\":{\"429\":1}}],[\"标识符\",{\"1\":{\"429\":1}}],[\"标识符与符号表\",{\"0\":{\"429\":1},\"1\":{\"421\":1}}],[\"除了上述对表达式的解析外\",{\"1\":{\"501\":1}}],[\"除了开头的\",{\"1\":{\"457\":1}}],[\"除了跳过注释\",{\"1\":{\"432\":1}}],[\"除了核心的逻辑外还需要输入输出\",{\"1\":{\"418\":1}}],[\"段中的地址\",{\"1\":{\"431\":1}}],[\"段中\",{\"1\":{\"431\":1}}],[\"十六进制及八进制\",{\"1\":{\"430\":1}}],[\"十分有成就感\",{\"1\":{\"396\":1}}],[\"十分钟学会正确的github工作流\",{\"1\":{\"36\":1}}],[\"故通过\",{\"1\":{\"430\":1}}],[\"故而使用下列方式\",{\"1\":{\"429\":1}}],[\"故我们引入一个指令mset\",{\"1\":{\"405\":1}}],[\"刚存放函数的地址\",{\"1\":{\"429\":1}}],[\"型还是指针型\",{\"1\":{\"429\":1}}],[\"型\",{\"1\":{\"429\":1,\"485\":1,\"498\":2}}],[\"型的\",{\"1\":{\"405\":1}}],[\"顾名思义\",{\"1\":{\"429\":1}}],[\"顾客想吃什么口味都可以\",{\"1\":{\"224\":1}}],[\"遇到数字5\",{\"1\":{\"482\":1}}],[\"遇到数字4\",{\"1\":{\"482\":1}}],[\"遇到数字\",{\"1\":{\"482\":1}}],[\"遇到运算符\",{\"1\":{\"482\":3}}],[\"遇到新的标识符就去查这张表\",{\"1\":{\"429\":1}}],[\"遇到的时候就知道了\",{\"1\":{\"396\":1}}],[\"基于这个理由\",{\"1\":{\"429\":1}}],[\"基址指针\",{\"1\":{\"406\":1}}],[\"循环中\",{\"1\":{\"464\":1}}],[\"循环就没法准确地知道函数定义已经结束\",{\"1\":{\"464\":1}}],[\"循环可以用来跳过它\",{\"1\":{\"426\":1}}],[\"循环的作用就是跳过这些我们不识别的字符\",{\"1\":{\"426\":1}}],[\"循环呢\",{\"1\":{\"426\":1}}],[\"跳过当前错误并继续编译\",{\"1\":{\"426\":1}}],[\"源码中若包含一个数字\",{\"1\":{\"422\":1}}],[\"源地址\",{\"1\":{\"280\":1}}],[\"宏定义\",{\"0\":{\"428\":1},\"1\":{\"421\":1}}],[\"新的指令几乎不消耗资源\",{\"1\":{\"420\":1}}],[\"新增\",{\"1\":{\"143\":1}}],[\"添加一个新的指令需要设计许多新的电路\",{\"1\":{\"420\":1}}],[\"添加flask+nginx配置\",{\"1\":{\"25\":1}}],[\"位机器下\",{\"1\":{\"419\":1}}],[\"位的\",{\"1\":{\"419\":2}}],[\"位的机器中\",{\"1\":{\"405\":1}}],[\"写的程序要\",{\"1\":{\"418\":1}}],[\"写起来很无聊\",{\"1\":{\"396\":1}}],[\"计算\",{\"1\":{\"482\":3}}],[\"计算后会将栈顶的参数退栈\",{\"1\":{\"417\":1}}],[\"计算机的栈的状态\",{\"1\":{\"463\":1}}],[\"计算机的内部工作原理\",{\"0\":{\"404\":1},\"1\":{\"403\":1}}],[\"计算机中的寄存器用于存放计算机的运行状态\",{\"1\":{\"406\":1}}],[\"计算机中有三个基本部件需要我们关注\",{\"1\":{\"404\":1}}],[\"顺序\",{\"1\":{\"416\":1}}],[\"顺其自然反而能得到意想不到的收获\",{\"1\":{\"3\":1}}],[\"钱\",{\"1\":{\"412\":1}}],[\"汇编\",{\"1\":{\"478\":1,\"482\":1}}],[\"汇编的意义上\",{\"1\":{\"417\":1}}],[\"汇编代码\",{\"1\":{\"412\":1}}],[\"汇编指令设计并实现了我们自己的指令集\",{\"1\":{\"420\":1}}],[\"汇编指令\",{\"1\":{\"404\":1}}],[\"维基百科\",{\"1\":{\"412\":1}}],[\"事先声明一下\",{\"1\":{\"412\":1}}],[\"事实上\",{\"1\":{\"99\":1}}],[\"调用参数\",{\"1\":{\"416\":1}}],[\"调用结束时\",{\"1\":{\"412\":1}}],[\"调用装饰边框的方法\",{\"1\":{\"222\":1}}],[\"反之则是变量\",{\"1\":{\"453\":1}}],[\"反之则是除号\",{\"1\":{\"432\":1}}],[\"反过来\",{\"1\":{\"412\":1}}],[\"反向遍历\",{\"1\":{\"270\":1}}],[\"详细见下文\",{\"1\":{\"408\":1}}],[\"取址\",{\"1\":{\"489\":1}}],[\"取址操作\",{\"0\":{\"489\":1},\"1\":{\"481\":1}}],[\"取自\",{\"1\":{\"412\":1}}],[\"取值会更高效\",{\"1\":{\"408\":1}}],[\"取模运算就成为了编程中不可缺少的一部分\",{\"1\":{\"42\":1}}],[\"地址存放在\",{\"1\":{\"408\":1}}],[\"地址存放在栈中\",{\"1\":{\"408\":1}}],[\"操作\",{\"1\":{\"408\":1}}],[\"操作系统将我们使用的虚拟地址映射到了到实际的内存上\",{\"1\":{\"405\":1}}],[\"放入寄存器\",{\"1\":{\"408\":1}}],[\"识别这些参数的类型\",{\"1\":{\"408\":1}}],[\"风格\",{\"1\":{\"408\":1}}],[\"风格统一\",{\"0\":{\"52\":1}}],[\"带有参数的指令在前\",{\"1\":{\"407\":1}}],[\"带颜色的大型文字\",{\"1\":{\"253\":1}}],[\"稍后你会看到\",{\"1\":{\"407\":1}}],[\"永远指向当前的栈顶\",{\"1\":{\"406\":1}}],[\"真正的计算机中有许多不同种类的寄存器\",{\"1\":{\"406\":1}}],[\"真正为其分配内存\",{\"1\":{\"405\":1}}],[\"真正来实现一个简单的编译器\",{\"1\":{\"394\":1}}],[\"理论上所有的变量返回的标记都应该是\",{\"1\":{\"429\":1}}],[\"理论上我们的虚拟机需要维护一个堆用于内存分配\",{\"1\":{\"405\":1}}],[\"理论很复杂\",{\"0\":{\"394\":1}}],[\"^\",{\"1\":{\"405\":1,\"417\":1,\"433\":1,\"491\":1,\"498\":3}}],[\"堆\",{\"1\":{\"405\":1}}],[\"栈中的调用帧是什么样的\",{\"1\":{\"416\":1}}],[\"栈\",{\"1\":{\"405\":1,\"463\":1,\"482\":1}}],[\"未初始化数据段\",{\"1\":{\"405\":1}}],[\"物理内存\",{\"1\":{\"405\":1}}],[\"现代操作系统在操作内存时\",{\"1\":{\"405\":1}}],[\"现在我们要回忆如何将\",{\"1\":{\"463\":1}}],[\"现在\",{\"1\":{\"375\":1}}],[\"现在电话亭上加了把锁\",{\"1\":{\"99\":1}}],[\"现在不存在这种情况了\",{\"1\":{\"44\":1}}],[\"说一说编写编译器值得注意的一些问题\",{\"1\":{\"505\":1}}],[\"说得通俗一点就是自己实现一套汇编语言\",{\"1\":{\"403\":1}}],[\"说明\",{\"1\":{\"164\":1}}],[\"小于\",{\"1\":{\"494\":1}}],[\"小结\",{\"0\":{\"420\":1,\"436\":1,\"446\":1,\"457\":1,\"468\":1,\"478\":1,\"502\":1},\"1\":{\"403\":1,\"421\":1,\"439\":1,\"449\":1,\"460\":1,\"471\":1,\"481\":1}}],[\"小组中的\",{\"1\":{\"279\":1}}],[\"测试\",{\"0\":{\"419\":1},\"1\":{\"403\":1}}],[\"测试和部署应用程序\",{\"1\":{\"31\":1}}],[\"子函数要返回时\",{\"1\":{\"412\":1}}],[\"子函数调用\",{\"0\":{\"412\":1},\"1\":{\"403\":1}}],[\"子类责任\",{\"1\":{\"375\":1}}],[\"子类具有实现在父类中所声明的抽象方法的责任\",{\"1\":{\"375\":1}}],[\"子类只需关注具体步骤的实现\",{\"1\":{\"371\":1}}],[\"子类可以在不改变算法结构的情况下\",{\"1\":{\"370\":1}}],[\"子类可以替换父类\",{\"1\":{\"134\":1}}],[\"子类应当能够替代父类的实例而不影响程序的正确性\",{\"1\":{\"228\":1}}],[\"子类应保持父类的行为\",{\"1\":{\"119\":1}}],[\"子类的方法签名应与父类一致\",{\"1\":{\"119\":1}}],[\"指定了当前的优先级\",{\"1\":{\"494\":1}}],[\"指针加上数值等于将指针移位\",{\"1\":{\"498\":1}}],[\"指针相对位置的形式\",{\"1\":{\"486\":1}}],[\"指针取值\",{\"0\":{\"488\":1},\"1\":{\"481\":1}}],[\"指针和对应的位移量进行的\",{\"1\":{\"463\":1}}],[\"指针寄存器\",{\"1\":{\"406\":1}}],[\"指向的是同一个变量\",{\"1\":{\"429\":1}}],[\"指出错误发生的位置\",{\"1\":{\"426\":2}}],[\"指的是\",{\"1\":{\"413\":1}}],[\"指的是需要编写哪些类和需要实现哪些方法都非常清楚\",{\"1\":{\"142\":1}}],[\"指令加载实际内容\",{\"1\":{\"489\":1}}],[\"指令加载对应的值\",{\"1\":{\"486\":1}}],[\"指令了\",{\"1\":{\"489\":1}}],[\"指令存入\",{\"1\":{\"486\":1}}],[\"指令将它加载到\",{\"1\":{\"484\":1}}],[\"指令无法操作除\",{\"1\":{\"416\":1}}],[\"指令功能有限\",{\"1\":{\"414\":1}}],[\"指令同样功能不足\",{\"1\":{\"412\":1}}],[\"指令并无法指定寄存器\",{\"1\":{\"412\":1}}],[\"指令来代替它\",{\"1\":{\"412\":1}}],[\"指令呢\",{\"1\":{\"412\":1}}],[\"指令的参数\",{\"1\":{\"410\":1}}],[\"指令只能将\",{\"1\":{\"408\":1}}],[\"指令中\",{\"1\":{\"408\":1}}],[\"指令其实有许多变种\",{\"1\":{\"408\":1}}],[\"指令拆分成这些指令\",{\"1\":{\"408\":1}}],[\"指令拆分成\",{\"1\":{\"408\":1}}],[\"指令有两个参数\",{\"1\":{\"408\":1}}],[\"指令\",{\"1\":{\"405\":1,\"410\":1,\"412\":1,\"415\":2,\"486\":1}}],[\"指令集是\",{\"1\":{\"407\":1}}],[\"指令集\",{\"0\":{\"407\":1},\"1\":{\"403\":1}}],[\"寄存器指向的是\",{\"1\":{\"410\":1}}],[\"寄存器设置为指定的\",{\"1\":{\"410\":1}}],[\"寄存器或是一个内存地址\",{\"1\":{\"408\":1}}],[\"寄存器及内存\",{\"1\":{\"404\":1}}],[\"寄存器\",{\"0\":{\"406\":1},\"1\":{\"403\":1}}],[\"逐个读取文件中的字符\",{\"1\":{\"402\":1}}],[\"逐个通知每个观察者可能会导致性能问题\",{\"1\":{\"310\":1}}],[\"读取一个文件\",{\"1\":{\"402\":1}}],[\"获取下一个标记\",{\"1\":{\"402\":1}}],[\"构建语法分析器\",{\"1\":{\"401\":1}}],[\"构建我们的词法分析器\",{\"1\":{\"401\":1}}],[\"构建我们自己的虚拟机以及指令集\",{\"1\":{\"401\":1}}],[\"屏蔽了许多实现上的细节\",{\"1\":{\"401\":1}}],[\"已经把\",{\"1\":{\"415\":1}}],[\"已经有许多工具能帮助我们处理阶段1和2\",{\"1\":{\"401\":1}}],[\"已经编写完成的具体工厂越多\",{\"1\":{\"143\":1}}],[\"目标代码的生成\",{\"1\":{\"401\":1}}],[\"目录类\",{\"0\":{\"208\":1}}],[\"目录可以包含其他目录和文件\",{\"1\":{\"206\":1}}],[\"目录和文件都可以被视为条目\",{\"1\":{\"206\":1}}],[\"目录的构建\",{\"1\":{\"95\":1}}],[\"系列的第三篇\",{\"1\":{\"403\":1}}],[\"系列的第二篇\",{\"1\":{\"400\":1}}],[\"系统的线程调度器是假设不同的线程是毫无关系的\",{\"1\":{\"99\":1}}],[\"系统\",{\"0\":{\"85\":1}}],[\"具有一定的参考价值\",{\"1\":{\"397\":1}}],[\"具体的实现如下\",{\"1\":{\"415\":1}}],[\"具体而言\",{\"1\":{\"221\":1}}],[\"具体类\",{\"1\":{\"140\":1}}],[\"具体实现很容易\",{\"1\":{\"445\":1}}],[\"具体实现\",{\"1\":{\"130\":1}}],[\"观看效果更佳\",{\"1\":{\"397\":1}}],[\"观察者\",{\"1\":{\"306\":1}}],[\"观察者模式在\",{\"1\":{\"311\":1}}],[\"观察者模式定义了一种一对多的依赖关系\",{\"1\":{\"303\":1}}],[\"观察者模式非常适合用于需要自动更新的场景\",{\"1\":{\"302\":1}}],[\"英文的\",{\"1\":{\"397\":1}}],[\"繁琐\",{\"1\":{\"396\":1}}],[\"做好心理准备\",{\"0\":{\"396\":1}}],[\"做任何修改\",{\"1\":{\"172\":1}}],[\"声明\",{\"1\":{\"395\":1}}],[\"声明抽象方法是希望达到以下目的\",{\"1\":{\"375\":1}}],[\"声明抽象方法\",{\"1\":{\"352\":1}}],[\"号称用\",{\"1\":{\"395\":1}}],[\"名叫\",{\"1\":{\"395\":1}}],[\"名字现在是bob\",{\"1\":{\"325\":1}}],[\"名字现在是alice\",{\"1\":{\"325\":1}}],[\"名字现在是\",{\"1\":{\"324\":2}}],[\"名字\",{\"1\":{\"164\":1}}],[\"内置函数有对应的汇编指令\",{\"1\":{\"486\":1}}],[\"内置函数的行为也和关键字类似\",{\"1\":{\"434\":1}}],[\"内置函数\",{\"0\":{\"418\":1},\"1\":{\"403\":1}}],[\"内存地址的数据\",{\"1\":{\"405\":1}}],[\"内存用于存储数据\",{\"1\":{\"405\":1}}],[\"内存\",{\"0\":{\"405\":1},\"1\":{\"403\":1}}],[\"内存之外的其它资源\",{\"0\":{\"256\":1}}],[\"内容相对容易一些\",{\"1\":{\"478\":1}}],[\"内容为\",{\"1\":{\"402\":1}}],[\"内容过于复杂\",{\"1\":{\"394\":1}}],[\"依旧不能确定是否立即计算\",{\"1\":{\"482\":1}}],[\"依旧帮助不了我们学习编译器\",{\"1\":{\"394\":1}}],[\"依赖于状态的处理\",{\"0\":{\"352\":1},\"1\":{\"352\":4,\"353\":1,\"355\":1}}],[\"依赖于特定应用程序就意味着难以复用\",{\"1\":{\"285\":1}}],[\"依赖于特定应用程序的部分都被封装在扮演\",{\"1\":{\"285\":1}}],[\"依赖注入\",{\"1\":{\"129\":1}}],[\"依赖倒置原则\",{\"0\":{\"128\":1},\"1\":{\"113\":1,\"114\":1,\"134\":1}}],[\"什么是表达式\",{\"1\":{\"481\":1}}],[\"什么是递归下降\",{\"0\":{\"440\":1},\"1\":{\"439\":1}}],[\"什么是词法分析器\",{\"0\":{\"422\":1},\"1\":{\"421\":1}}],[\"什么都不干的编译器\",{\"1\":{\"402\":1}}],[\"什么\",{\"1\":{\"394\":1}}],[\"什么时候会从\",{\"1\":{\"353\":1}}],[\"什么时候从一个状态迁移到其他状态\",{\"1\":{\"353\":1}}],[\"词法分析中如何处理标识符与符号表\",{\"1\":{\"436\":1}}],[\"词法分析\",{\"0\":{\"507\":1},\"1\":{\"394\":1,\"505\":1}}],[\"词法分析器本身可以认为是一个编译器\",{\"1\":{\"436\":1}}],[\"词法分析器本质上也是编译器\",{\"1\":{\"432\":1}}],[\"词法分析器中直接解析这些关键字\",{\"1\":{\"434\":1}}],[\"词法分析器会把扫描到的标识符全都保存到一张表中\",{\"1\":{\"429\":1}}],[\"词法分析器将输出\",{\"1\":{\"422\":1}}],[\"词法分析器以源码字符串为输入\",{\"1\":{\"422\":1}}],[\"词法分析器用于对源码字符串做预处理\",{\"1\":{\"422\":1}}],[\"词法分析器的作用是对源码字符串进行预处理\",{\"1\":{\"436\":1}}],[\"词法分析器的框架\",{\"0\":{\"426\":1},\"1\":{\"421\":1}}],[\"词法分析器的实现\",{\"0\":{\"424\":1},\"1\":{\"421\":1}}],[\"词法分析器与编译器\",{\"0\":{\"423\":1},\"1\":{\"421\":1}}],[\"词法分析器\",{\"0\":{\"421\":1},\"1\":{\"392\":1,\"400\":1,\"401\":1,\"403\":1,\"421\":1,\"423\":1,\"439\":1,\"449\":1,\"460\":1,\"471\":1,\"481\":1,\"505\":1}}],[\"听不懂\",{\"1\":{\"394\":1}}],[\"听起来有些贬义的意思\",{\"1\":{\"188\":1}}],[\"好吧\",{\"1\":{\"393\":1,\"502\":1}}],[\"装b\",{\"1\":{\"393\":1}}],[\"装饰\",{\"1\":{\"222\":2}}],[\"装饰边框与被装饰物具有相同的接口\",{\"1\":{\"222\":1}}],[\"装饰边框与被装饰物具有一致性\",{\"1\":{\"221\":1}}],[\"装饰边框\",{\"1\":{\"221\":1,\"222\":1}}],[\"装饰边框里面的\",{\"1\":{\"221\":1}}],[\"装饰器模式允许我们在不修改现有代码的情况下扩展对象的功能\",{\"1\":{\"217\":1}}],[\"装饰器模式允许我们通过将对象放入包含行为的特殊封装对象中来扩展对象的功能\",{\"1\":{\"216\":1}}],[\"装饰者模式等\",{\"1\":{\"116\":1}}],[\"学习编译原理时常常着眼于词法分析和语法分析\",{\"1\":{\"506\":1}}],[\"学习了编译原理\",{\"1\":{\"393\":1}}],[\"学了这么多也没用\",{\"1\":{\"394\":1}}],[\"学术研究\",{\"1\":{\"53\":1}}],[\"像是程序员的第一道门槛\",{\"1\":{\"393\":1}}],[\"像这样改一个地方会对多个地方产生影响并非总是不好\",{\"1\":{\"253\":1}}],[\"递归调用的实质也是栈的处理\",{\"1\":{\"482\":1}}],[\"递归下下降方法对\",{\"1\":{\"443\":1}}],[\"递归下降是从起始的非终结符开始\",{\"1\":{\"442\":1}}],[\"递归下降法\",{\"1\":{\"394\":1}}],[\"递归下降\",{\"0\":{\"439\":1},\"1\":{\"392\":1,\"400\":1,\"403\":1,\"421\":1,\"439\":1,\"449\":1,\"460\":1,\"471\":1,\"481\":1,\"505\":1,\"508\":1}}],[\"递归\",{\"1\":{\"393\":1}}],[\"能自己编译自己\",{\"1\":{\"501\":1}}],[\"能大概理解吗\",{\"1\":{\"453\":1}}],[\"能减小语法分析复杂度\",{\"1\":{\"432\":1}}],[\"能理解的语言\",{\"1\":{\"407\":1}}],[\"能识别的命令的集合\",{\"1\":{\"407\":1}}],[\"能不能理解\",{\"1\":{\"393\":1}}],[\"能轻松使用\",{\"1\":{\"53\":1}}],[\"算法\",{\"1\":{\"393\":1}}],[\"算术公理系统\",{\"0\":{\"55\":1}}],[\"谈谈这个系列的初衷\",{\"1\":{\"392\":1}}],[\"表\",{\"1\":{\"429\":1}}],[\"表达式结束\",{\"1\":{\"482\":1}}],[\"表达式的解析难点有二\",{\"1\":{\"481\":1}}],[\"表达式是将各种语言要素的一个组合\",{\"1\":{\"481\":1}}],[\"表达式可能相对不好理解一些\",{\"1\":{\"457\":1}}],[\"表达式\",{\"0\":{\"481\":1},\"1\":{\"392\":1,\"400\":1,\"402\":1,\"403\":1,\"421\":1,\"439\":1,\"449\":2,\"460\":2,\"471\":1,\"472\":1,\"481\":1,\"505\":1}}],[\"表示转换成实际的代码\",{\"1\":{\"443\":1}}],[\"表示是十分接近的\",{\"1\":{\"443\":1}}],[\"表示选择\",{\"1\":{\"441\":1}}],[\"表示字符\",{\"1\":{\"431\":1}}],[\"表示换行符\",{\"1\":{\"431\":1}}],[\"表示将\",{\"1\":{\"408\":1}}],[\"表示该对象不再被使用\",{\"1\":{\"255\":1}}],[\"表示装饰边框的\",{\"1\":{\"221\":1}}],[\"表示\",{\"0\":{\"450\":1,\"461\":1},\"1\":{\"56\":1,\"59\":1,\"60\":1,\"75\":1,\"76\":1,\"431\":1,\"449\":1,\"460\":1}}],[\"语法\",{\"1\":{\"446\":1}}],[\"语法分析对我而言一直是迷一样的存在\",{\"1\":{\"508\":1}}],[\"语法分析更困难\",{\"1\":{\"478\":1}}],[\"语法分析的入口\",{\"1\":{\"402\":1}}],[\"语法分析器的复杂度会大大降低\",{\"1\":{\"422\":1}}],[\"语法分析器\",{\"1\":{\"401\":1}}],[\"语法分析是一样的\",{\"1\":{\"400\":1}}],[\"语法分析\",{\"0\":{\"508\":1},\"1\":{\"394\":1,\"505\":1}}],[\"语句简单\",{\"1\":{\"474\":1}}],[\"语句比\",{\"1\":{\"474\":1}}],[\"语句后方的代码\",{\"1\":{\"473\":1}}],[\"语句是可以省略的\",{\"1\":{\"473\":1}}],[\"语句的作用是跳转\",{\"1\":{\"473\":1}}],[\"语句和表达式的解析\",{\"1\":{\"471\":1}}],[\"语句就是用来向前查看标记以确定使用哪一个产生式\",{\"1\":{\"453\":1}}],[\"语句\",{\"0\":{\"471\":1,\"472\":1,\"473\":1,\"474\":1,\"475\":1},\"1\":{\"392\":1,\"400\":1,\"403\":1,\"411\":1,\"421\":1,\"439\":1,\"449\":1,\"460\":1,\"471\":5,\"472\":1,\"473\":1,\"475\":1,\"481\":1,\"496\":2,\"505\":1}}],[\"语言运算符优先级\",{\"1\":{\"482\":1}}],[\"语言定义了各种表达式的优先级\",{\"1\":{\"482\":1}}],[\"语言区分\",{\"1\":{\"472\":1}}],[\"语言不太一致\",{\"1\":{\"466\":1}}],[\"语言与现代的\",{\"1\":{\"466\":1}}],[\"语言中唯一的一个三元运算符\",{\"1\":{\"496\":1}}],[\"语言中\",{\"1\":{\"432\":1,\"498\":1}}],[\"语言中标识符可以是全局的也可以是局部的\",{\"1\":{\"429\":1}}],[\"语言中空格是用来作为分隔用的\",{\"1\":{\"426\":1}}],[\"语言中的优先级有关\",{\"1\":{\"425\":1}}],[\"语言中的赋值语句\",{\"1\":{\"408\":1}}],[\"语言中我们经常使用的\",{\"1\":{\"418\":1}}],[\"语言中支持的运算符都提供对应汇编指令\",{\"1\":{\"417\":1}}],[\"语言调用标准\",{\"1\":{\"412\":1}}],[\"语言代码\",{\"1\":{\"402\":1}}],[\"语言程序\",{\"1\":{\"402\":1}}],[\"语言的时候你可能已经知道了\",{\"1\":{\"500\":1}}],[\"语言的字符串常量支持如下风格\",{\"1\":{\"484\":1}}],[\"语言的文法\",{\"1\":{\"449\":1}}],[\"语言的宏定义以字符\",{\"1\":{\"428\":1}}],[\"语言的调用标准是\",{\"1\":{\"412\":1}}],[\"语言的源代码文件\",{\"1\":{\"400\":1}}],[\"语言的解释器\",{\"1\":{\"400\":1}}],[\"语言的编译器\",{\"1\":{\"392\":1}}],[\"语言编译器系列共有10个部分\",{\"1\":{\"392\":1,\"400\":1,\"403\":1,\"421\":1,\"439\":1,\"449\":1,\"460\":1,\"471\":1,\"481\":1,\"505\":1}}],[\"语言编译器\",{\"0\":{\"392\":1,\"400\":1,\"421\":1,\"439\":1,\"449\":1,\"460\":1,\"471\":1,\"481\":1,\"505\":1},\"1\":{\"392\":13,\"395\":3,\"400\":12,\"403\":12,\"421\":10,\"439\":10,\"449\":10,\"460\":10,\"471\":10,\"481\":10,\"505\":11}}],[\"虚拟内存可以理解为一种映射\",{\"1\":{\"405\":1}}],[\"虚拟内存\",{\"1\":{\"405\":1}}],[\"虚拟机与目标代码\",{\"0\":{\"506\":1},\"1\":{\"505\":1}}],[\"虚拟机中讲解的指令是对应的\",{\"1\":{\"486\":1}}],[\"虚拟机上运行我们提供的这些指令时\",{\"1\":{\"418\":1}}],[\"虚拟机的入口\",{\"1\":{\"402\":1}}],[\"虚拟机\",{\"1\":{\"392\":1,\"400\":1,\"403\":2,\"421\":1,\"439\":1,\"449\":1,\"460\":1,\"468\":1,\"471\":1,\"481\":1,\"486\":1,\"505\":1}}],[\"虚拟代理用于控制对资源密集型对象的访问\",{\"1\":{\"332\":1}}],[\"虚拟代理\",{\"1\":{\"327\":1}}],[\"原则上我们需要立即计算\",{\"1\":{\"482\":1}}],[\"原则上我们是不讲这么深入\",{\"1\":{\"444\":1}}],[\"原因之一就是减少了语法分析器需要\",{\"1\":{\"432\":1}}],[\"原因有二\",{\"1\":{\"424\":1}}],[\"原因是当我们从子函数中返回时\",{\"1\":{\"412\":1}}],[\"原因是默认计算的结果是存放在\",{\"1\":{\"408\":1}}],[\"原因是太复杂了\",{\"1\":{\"394\":1}}],[\"原因只有一个\",{\"1\":{\"393\":1}}],[\"原文链接\",{\"1\":{\"392\":2}}],[\"原文转载自\",{\"1\":{\"98\":1,\"102\":1}}],[\"原作者\",{\"1\":{\"392\":1}}],[\"手把手教你构建\",{\"0\":{\"392\":1,\"400\":1,\"421\":1,\"439\":1,\"449\":1,\"460\":1,\"471\":1,\"481\":1,\"505\":1},\"1\":{\"392\":13,\"400\":12,\"403\":13,\"421\":11,\"439\":11,\"449\":11,\"460\":11,\"471\":11,\"481\":11,\"505\":11}}],[\"手动修改后可正常运行\",{\"1\":{\"96\":1}}],[\"尽管代码看起来比较简单\",{\"1\":{\"502\":1}}],[\"尽管理论不是必需的\",{\"1\":{\"446\":1}}],[\"尽管我们还没定义\",{\"1\":{\"412\":1}}],[\"尽管有许多语法并不支持\",{\"1\":{\"392\":1}}],[\"尽管使用\",{\"1\":{\"387\":1}}],[\"尽量减少类之间的耦合\",{\"1\":{\"134\":1}}],[\"尽量减少类的公开方法\",{\"1\":{\"123\":1}}],[\"尽量使用组合\",{\"1\":{\"131\":1}}],[\"希望文章本身没有受我的这种情绪影响吧\",{\"1\":{\"509\":1}}],[\"希望能减少你对理论的厌恶\",{\"1\":{\"508\":1}}],[\"希望通过这个系列\",{\"1\":{\"392\":1}}],[\"希望通过本章的学习\",{\"1\":{\"232\":1,\"420\":1}}],[\"希望扩展某个功能\",{\"1\":{\"385\":1}}],[\"绝不能毫无理由地禁止扩展类\",{\"1\":{\"385\":1}}],[\"绝不能因为先调用\",{\"1\":{\"307\":1}}],[\"处理\",{\"1\":{\"384\":1}}],[\"处理器本来同一时间就只能有一个线程在运行\",{\"1\":{\"99\":1}}],[\"双重分发\",{\"0\":{\"383\":1}}],[\"双重检查锁定示例代码\",{\"0\":{\"343\":1}}],[\"访问数据结构并处理数据\",{\"2\":{\"391\":1}}],[\"访问\",{\"1\":{\"383\":1}}],[\"访问者\",{\"1\":{\"378\":1}}],[\"访问代理用于控制对实际对象的访问权限\",{\"1\":{\"332\":1}}],[\"数组取值操作\",{\"0\":{\"500\":1},\"1\":{\"481\":1}}],[\"数字中较为复杂的一点是需要支持十进制\",{\"1\":{\"430\":1}}],[\"数字\",{\"0\":{\"430\":1},\"1\":{\"421\":1,\"422\":1,\"483\":1}}],[\"数据段以及栈\",{\"1\":{\"405\":1}}],[\"数据段\",{\"1\":{\"405\":1,\"463\":1}}],[\"数据结构\",{\"1\":{\"393\":1}}],[\"数据结构很重要\",{\"1\":{\"384\":1}}],[\"数据结构与处理被分离开来\",{\"1\":{\"378\":1}}],[\"数学运算符\",{\"0\":{\"498\":1},\"1\":{\"481\":1}}],[\"数学\",{\"2\":{\"91\":1}}],[\"期待子类去实现抽象方法\",{\"1\":{\"375\":1}}],[\"站在父类的角度进行思考\",{\"1\":{\"375\":1}}],[\"很有帮助的\",{\"1\":{\"509\":1}}],[\"很好的初学者教程\",{\"1\":{\"397\":1}}],[\"很难懂\",{\"1\":{\"395\":1}}],[\"很容易着眼于以下几点\",{\"1\":{\"375\":1}}],[\"很可能随着需求变更实例数量会慢慢变多\",{\"1\":{\"284\":1}}],[\"延申\",{\"0\":{\"375\":1}}],[\"延迟实例化\",{\"1\":{\"323\":1}}],[\"允许子类实现具体的步骤\",{\"1\":{\"371\":1}}],[\"允许开发者在\",{\"1\":{\"31\":1}}],[\"低速但计算准确的算法\",{\"1\":{\"366\":1}}],[\"验算\",{\"1\":{\"366\":1}}],[\"速度快但耗内存的策略\",{\"1\":{\"366\":1}}],[\"速度慢但省内存的策略\",{\"1\":{\"366\":1}}],[\"例程的水平\",{\"1\":{\"365\":1}}],[\"例如需要考虑许多细节\",{\"1\":{\"509\":1}}],[\"例如对变量\",{\"1\":{\"489\":1}}],[\"例如参数的位置\",{\"1\":{\"468\":1}}],[\"例如只要遇到\",{\"1\":{\"453\":1}}],[\"例如用\",{\"1\":{\"431\":1}}],[\"例如数据库连接\",{\"1\":{\"337\":1}}],[\"例如事件对象或数据包\",{\"1\":{\"309\":1}}],[\"例如在编写表达式的解析时\",{\"1\":{\"509\":1}}],[\"例如在应用程序关闭后重新打开时恢复状态\",{\"1\":{\"296\":1}}],[\"例如在用户进行撤销操作之前\",{\"1\":{\"296\":1}}],[\"例如增加一个具体方法\",{\"1\":{\"160\":1}}],[\"例如tablefactory\",{\"1\":{\"140\":1}}],[\"例如策略模式\",{\"1\":{\"116\":1}}],[\"例如添加新插件\",{\"1\":{\"95\":1}}],[\"例如\",{\"1\":{\"95\":1,\"143\":2,\"161\":1,\"172\":1,\"173\":1,\"185\":1,\"188\":1,\"206\":1,\"222\":1,\"253\":1,\"274\":1,\"285\":1,\"302\":1,\"307\":1,\"308\":1,\"310\":1,\"327\":1,\"328\":1,\"332\":3,\"353\":1,\"365\":2,\"366\":2,\"387\":1,\"388\":1,\"405\":1,\"412\":1,\"418\":1,\"422\":1,\"425\":1,\"429\":1,\"434\":1,\"441\":1,\"442\":1,\"481\":1}}],[\"例如很多期望概率题\",{\"1\":{\"41\":1}}],[\"例如许多计数\",{\"1\":{\"41\":1}}],[\"仅仅修改\",{\"1\":{\"365\":1}}],[\"了解自动生成词法分析器的原理\",{\"1\":{\"507\":1}}],[\"了解了协程如何主动切换\",{\"1\":{\"101\":1}}],[\"了\",{\"1\":{\"365\":1,\"432\":1}}],[\"布\",{\"1\":{\"362\":1}}],[\"剪刀\",{\"1\":{\"362\":1}}],[\"石头\",{\"1\":{\"362\":1}}],[\"另外\",{\"1\":{\"419\":1,\"432\":1,\"443\":1,\"498\":1}}],[\"另外一种算法\",{\"1\":{\"366\":1}}],[\"另外一种策略是\",{\"1\":{\"362\":1}}],[\"另一个特殊的地方是我们需要支持转义符\",{\"1\":{\"431\":1}}],[\"另一点是我们的\",{\"1\":{\"408\":1}}],[\"另一种方法是传递具体的更新信息\",{\"1\":{\"309\":1}}],[\"另一方面需要对照生成的代码来调试\",{\"1\":{\"396\":1}}],[\"另一方面希望挑战一下自己\",{\"1\":{\"393\":1}}],[\"另一方面\",{\"1\":{\"100\":1,\"254\":1,\"385\":1,\"408\":1}}],[\"另一方面采取了常数更小的加减法操作\",{\"1\":{\"45\":1}}],[\"游戏\",{\"1\":{\"362\":1}}],[\"猜拳\",{\"1\":{\"362\":1}}],[\"策略模式的主要优点包括\",{\"1\":{\"361\":1}}],[\"至少\",{\"1\":{\"508\":1}}],[\"至少必须在阅读了\",{\"1\":{\"185\":1}}],[\"至此\",{\"1\":{\"385\":1}}],[\"至于这个参数是否是\",{\"1\":{\"356\":1}}],[\"向下\",{\"1\":{\"442\":1}}],[\"向前看标记\",{\"1\":{\"453\":1}}],[\"向前看\",{\"1\":{\"432\":1,\"443\":1}}],[\"向\",{\"1\":{\"356\":2}}],[\"忘记实现方法\",{\"1\":{\"355\":1}}],[\"忘记取模\",{\"1\":{\"43\":1}}],[\"必须先查看它的右方\",{\"1\":{\"482\":1}}],[\"必须先获得gil锁\",{\"1\":{\"99\":1}}],[\"必须要考虑到将来可能会扩展类\",{\"1\":{\"385\":1}}],[\"必须十分小心\",{\"1\":{\"354\":1}}],[\"输出是标记流\",{\"1\":{\"436\":1}}],[\"输出标记流\",{\"1\":{\"423\":1}}],[\"输出汇编代码\",{\"1\":{\"423\":1}}],[\"输出为标记流\",{\"1\":{\"422\":1}}],[\"输出\",{\"1\":{\"419\":1}}],[\"输出和下一个状态\",{\"1\":{\"353\":1}}],[\"输入是源码\",{\"1\":{\"436\":1}}],[\"输入和内部状态\",{\"1\":{\"353\":1}}],[\"输入任意邮箱和刚才生成的序列号到激活窗口\",{\"1\":{\"111\":1}}],[\"输入\",{\"1\":{\"111\":2}}],[\"程序需要回到跳转之前的地方继续运行\",{\"1\":{\"412\":1}}],[\"程序计数器\",{\"1\":{\"406\":1}}],[\"程序运行的状态保存在寄存器中\",{\"1\":{\"404\":1}}],[\"程序运行中也可以切换策略\",{\"0\":{\"366\":1}}],[\"程序的整体结构也会更加清晰\",{\"1\":{\"353\":1}}],[\"程序可能会无法正常工作\",{\"1\":{\"185\":1}}],[\"扮演\",{\"1\":{\"353\":1}}],[\"呢\",{\"1\":{\"352\":1}}],[\"告诉我们存在还没有实现的方法\",{\"1\":{\"355\":1}}],[\"告诉\",{\"1\":{\"352\":1}}],[\"条件分支就会越多\",{\"1\":{\"351\":1}}],[\"条通信线路\",{\"1\":{\"284\":4}}],[\"から\",{\"1\":{\"349\":3}}],[\"から$\",{\"1\":{\"348\":1}}],[\"へ状態が変化しました\",{\"1\":{\"348\":1,\"349\":3}}],[\"現在時刻は23\",{\"1\":{\"349\":1}}],[\"現在時刻は22\",{\"1\":{\"349\":1}}],[\"現在時刻は21\",{\"1\":{\"349\":1}}],[\"現在時刻は20\",{\"1\":{\"349\":1}}],[\"現在時刻は19\",{\"1\":{\"349\":1}}],[\"現在時刻は18\",{\"1\":{\"349\":1}}],[\"現在時刻は17\",{\"1\":{\"349\":1}}],[\"現在時刻は16\",{\"1\":{\"349\":1}}],[\"現在時刻は15\",{\"1\":{\"349\":1}}],[\"現在時刻は14\",{\"1\":{\"349\":1}}],[\"現在時刻は13\",{\"1\":{\"349\":1}}],[\"現在時刻は12\",{\"1\":{\"349\":1}}],[\"現在時刻は11\",{\"1\":{\"349\":1}}],[\"現在時刻は10\",{\"1\":{\"349\":1}}],[\"現在時刻は09\",{\"1\":{\"349\":1}}],[\"現在時刻は08\",{\"1\":{\"349\":1}}],[\"現在時刻は07\",{\"1\":{\"349\":1}}],[\"現在時刻は06\",{\"1\":{\"349\":1}}],[\"現在時刻は05\",{\"1\":{\"349\":1}}],[\"現在時刻は04\",{\"1\":{\"349\":1}}],[\"現在時刻は03\",{\"1\":{\"349\":1}}],[\"現在時刻は02\",{\"1\":{\"349\":1}}],[\"現在時刻は01\",{\"1\":{\"349\":1}}],[\"現在時刻は00\",{\"1\":{\"349\":1}}],[\"現在時刻は\",{\"1\":{\"348\":1}}],[\"夜间通话录音\",{\"1\":{\"348\":1,\"349\":16}}],[\"夜间\",{\"1\":{\"348\":2,\"349\":19}}],[\"夜间使用金库\",{\"1\":{\"348\":1,\"349\":16}}],[\"紧急\",{\"1\":{\"348\":1,\"349\":16}}],[\"紧急铃\",{\"1\":{\"348\":2,\"349\":24}}],[\"白天\",{\"1\":{\"348\":4,\"349\":27,\"351\":1}}],[\"金库使用\",{\"1\":{\"348\":1,\"349\":8}}],[\"函数结束时退出进程\",{\"1\":{\"501\":1}}],[\"函数调用\",{\"1\":{\"481\":1}}],[\"函数体的代码如下\",{\"1\":{\"466\":1}}],[\"函数体的解析\",{\"0\":{\"466\":1},\"1\":{\"460\":1}}],[\"函数参数与汇编代码\",{\"0\":{\"463\":1},\"1\":{\"460\":1}}],[\"函数包装起来\",{\"1\":{\"455\":1}}],[\"函数是一个辅助函数\",{\"1\":{\"455\":1}}],[\"函数我们将放到下一章中讲解\",{\"1\":{\"455\":1}}],[\"函数还没有出现过\",{\"1\":{\"452\":1}}],[\"函数的内容\",{\"1\":{\"452\":1}}],[\"函数的主体\",{\"1\":{\"426\":1}}],[\"函数的实现本身就十分复杂\",{\"1\":{\"418\":1}}],[\"函数就是用于输出\",{\"1\":{\"418\":1}}],[\"函数中加入下列代码\",{\"1\":{\"408\":1,\"419\":1}}],[\"函数中加入初始化代码\",{\"1\":{\"406\":1}}],[\"函数\",{\"1\":{\"402\":1,\"452\":1,\"463\":1,\"501\":1}}],[\"函数定义的解析\",{\"0\":{\"464\":1},\"1\":{\"460\":1}}],[\"函数定义\",{\"0\":{\"460\":1},\"1\":{\"392\":1,\"400\":1,\"403\":1,\"421\":1,\"439\":1,\"449\":2,\"460\":2,\"471\":1,\"481\":1,\"505\":1}}],[\"函数模拟了一个锁机制\",{\"1\":{\"343\":1}}],[\"函数取模\",{\"0\":{\"44\":1}}],[\"想要完全理解它\",{\"1\":{\"509\":1}}],[\"想在程序上表现出\",{\"1\":{\"338\":1}}],[\"想确保任何情况下都绝对只有\",{\"1\":{\"338\":1}}],[\"想做一个一样的移动app\",{\"1\":{\"93\":1}}],[\"日志记录器等\",{\"1\":{\"337\":1}}],[\"性能和可维护性\",{\"1\":{\"332\":1}}],[\"防火墙代理可以用于控制对内部网络资源的访问\",{\"1\":{\"332\":1}}],[\"防止中途出错了\",{\"1\":{\"99\":1}}],[\"远程方法调用\",{\"1\":{\"332\":1}}],[\"远程代理用于控制对远程对象的访问\",{\"1\":{\"332\":1}}],[\"远程代理\",{\"1\":{\"323\":1,\"328\":1}}],[\"各个参数的位移量\",{\"1\":{\"463\":1}}],[\"各个类之间的依赖关系就会加强\",{\"1\":{\"353\":1}}],[\"各种编程语言关于如何调用子函数有不同的约定\",{\"1\":{\"412\":1}}],[\"各种\",{\"0\":{\"332\":1}}],[\"各位\",{\"1\":{\"279\":1}}],[\"安全控制等功能\",{\"1\":{\"331\":1}}],[\"安装路径打开\",{\"1\":{\"111\":1}}],[\"安装目录下\",{\"1\":{\"111\":1}}],[\"安装了\",{\"1\":{\"106\":1}}],[\"安装\",{\"0\":{\"94\":1}}],[\"安装editorconfig插件\",{\"1\":{\"52\":1}}],[\"安装证书\",{\"0\":{\"22\":1}}],[\"负载均衡\",{\"1\":{\"331\":1}}],[\"负责转发客户端的请求和目标服务器的响应\",{\"1\":{\"331\":1}}],[\"负责协调模型和视图之间的交互\",{\"1\":{\"311\":1}}],[\"负责创建和恢复\",{\"1\":{\"297\":1}}],[\"负责保存和管理\",{\"1\":{\"297\":1}}],[\"负责管理和协调各个用户\",{\"1\":{\"283\":1}}],[\"负责\",{\"1\":{\"164\":3}}],[\"客户端可以像使用实际对象一样使用代理对象\",{\"1\":{\"330\":1}}],[\"客户端代码不需要知道具体的产品类\",{\"1\":{\"243\":1}}],[\"客户端代码与子系统之间的耦合度降低\",{\"1\":{\"235\":1}}],[\"完了\",{\"1\":{\"324\":1,\"325\":1}}],[\"完成图像去噪任务\",{\"1\":{\"53\":1}}],[\"世界\",{\"1\":{\"324\":1,\"325\":1,\"372\":1,\"373\":5}}],[\"世界上的事情本来就是这样\",{\"1\":{\"101\":1}}],[\"世界上最大的电子图书馆\",{\"1\":{\"5\":1}}],[\"世界上最大的代码托管平台\",{\"1\":{\"5\":1}}],[\"秒钟\",{\"1\":{\"324\":1}}],[\"虽说很困难\",{\"1\":{\"355\":1}}],[\"虽说是重活\",{\"1\":{\"324\":1}}],[\"虽然多\",{\"1\":{\"502\":1}}],[\"虽然我们前面没有提到\",{\"1\":{\"487\":1}}],[\"虽然上面写完了词法分析器\",{\"1\":{\"434\":1}}],[\"虽然是int型\",{\"1\":{\"405\":1}}],[\"虽然标题是编译器\",{\"1\":{\"400\":1}}],[\"虽然接口是相同的\",{\"1\":{\"222\":1}}],[\"虽然可以从方法名中获得线索\",{\"1\":{\"185\":1}}],[\"虽然有时需要从零开始编写代码\",{\"1\":{\"185\":1}}],[\"虽然同时只能有一个线程执行\",{\"1\":{\"101\":1}}],[\"虽然在工业部署中表现出色\",{\"1\":{\"53\":1}}],[\"控制反转\",{\"1\":{\"371\":1}}],[\"控制访问\",{\"1\":{\"323\":1}}],[\"控制器\",{\"1\":{\"311\":1}}],[\"节省资源\",{\"1\":{\"323\":1}}],[\"代表了逻辑\",{\"1\":{\"490\":1}}],[\"代理可以用于缓存\",{\"1\":{\"331\":1}}],[\"代理服务器位于客户端和目标服务器之间\",{\"1\":{\"331\":1}}],[\"代理是一种常见的代理模式应用\",{\"1\":{\"331\":1}}],[\"代理\",{\"0\":{\"331\":1}}],[\"代理对象和实际对象实现相同的接口\",{\"1\":{\"330\":1}}],[\"代理对象可以在需要时才创建实际对象\",{\"1\":{\"323\":1}}],[\"代理模式的一个重要特点是透明性\",{\"1\":{\"330\":1}}],[\"代理模式通过代理对象来控制对实际对象的访问\",{\"1\":{\"329\":1}}],[\"代理模式通过引入代理对象来控制对实际对象的访问\",{\"1\":{\"328\":1}}],[\"代理模式主要用于控制对对象的访问\",{\"1\":{\"329\":1}}],[\"代理模式和委托模式虽然在某些方面有相似之处\",{\"1\":{\"329\":1}}],[\"代理与委托\",{\"0\":{\"329\":1}}],[\"代理人和本人的划分是为了实现职责分离和提高系统的灵活性\",{\"1\":{\"328\":1}}],[\"代理人\",{\"1\":{\"323\":2}}],[\"代码与全局的变量定义几乎一样\",{\"1\":{\"466\":1}}],[\"代码较多\",{\"1\":{\"433\":1}}],[\"代码如下\",{\"1\":{\"406\":1,\"409\":1,\"418\":1,\"453\":1,\"464\":1,\"473\":1,\"474\":1,\"476\":1}}],[\"代码段\",{\"1\":{\"405\":2}}],[\"代码\",{\"0\":{\"435\":1,\"456\":1,\"467\":1,\"477\":1,\"501\":1},\"1\":{\"404\":1,\"421\":1,\"449\":1,\"460\":1,\"471\":1,\"481\":1}}],[\"代码难免会有错误\",{\"1\":{\"397\":1}}],[\"代码优化\",{\"1\":{\"394\":1}}],[\"代码的生成\",{\"1\":{\"394\":1}}],[\"代码的阅读方法和修改方法\",{\"0\":{\"185\":1}}],[\"代码是否高效显得就不那么重要了\",{\"1\":{\"393\":1}}],[\"代码实现\",{\"0\":{\"237\":1}}],[\"代码示例\",{\"0\":{\"179\":1,\"218\":1,\"272\":1},\"1\":{\"272\":1}}],[\"代码复用\",{\"1\":{\"178\":1,\"264\":1,\"371\":1}}],[\"代码清单\",{\"1\":{\"164\":1,\"356\":1}}],[\"代码还能正常工作\",{\"1\":{\"118\":1}}],[\"代码仓库紧密集成\",{\"1\":{\"31\":1}}],[\"~a\",{\"1\":{\"491\":1}}],[\"~~~~~~~~~~~~~\",{\"1\":{\"318\":1}}],[\"~\",{\"1\":{\"317\":1,\"425\":1,\"433\":1,\"491\":2}}],[\"无条件地将当前的\",{\"1\":{\"410\":1}}],[\"无法将它们整合到一个类中\",{\"1\":{\"316\":1}}],[\"无论多好的教程\",{\"1\":{\"509\":1}}],[\"无论在\",{\"1\":{\"172\":1}}],[\"无论要增加多少个具体工厂\",{\"1\":{\"142\":1}}],[\"无论是读起来\",{\"1\":{\"508\":1}}],[\"无论是全局还是局部变量\",{\"1\":{\"486\":1}}],[\"无论是是否真的在全局中用到了这个变量\",{\"1\":{\"465\":1}}],[\"无论是函数的参数\",{\"1\":{\"463\":1}}],[\"无论是结果\",{\"1\":{\"101\":1}}],[\"无论是执行过程中\",{\"1\":{\"101\":1}}],[\"特别是在创建对象代价较高时\",{\"1\":{\"316\":1}}],[\"架构实现了视图和模型的松耦合\",{\"1\":{\"311\":1}}],[\"架构中得到了广泛应用\",{\"1\":{\"311\":1}}],[\"视图会自动更新\",{\"1\":{\"311\":1}}],[\"视图\",{\"1\":{\"311\":1}}],[\"先将全局变量的信息保存\",{\"1\":{\"465\":1}}],[\"先注册的\",{\"1\":{\"307\":1}}],[\"先介绍\",{\"1\":{\"56\":1}}],[\"被观察对象\",{\"1\":{\"307\":1}}],[\"被装饰物\",{\"1\":{\"221\":1,\"222\":1}}],[\"被装饰了多次\",{\"1\":{\"221\":1}}],[\"管理状态\",{\"2\":{\"300\":1,\"314\":1,\"359\":1}}],[\"管理和分享\",{\"1\":{\"31\":1}}],[\"序列化并保存到文件中\",{\"1\":{\"297\":1}}],[\"序的完全性\",{\"0\":{\"71\":1}}],[\"序的传递性\",{\"0\":{\"70\":1}}],[\"序的反对称性\",{\"0\":{\"69\":1}}],[\"序的定义\",{\"0\":{\"66\":1}}],[\"保存所有的标记流没有意义且浪费空间\",{\"1\":{\"424\":1}}],[\"保存在栈中\",{\"1\":{\"412\":1}}],[\"保存数据结构与基于数据结构进行处理是两种不同的概念\",{\"1\":{\"384\":1}}],[\"保存到文件中\",{\"1\":{\"297\":1}}],[\"保存过多的\",{\"1\":{\"295\":1}}],[\"保存历史记录\",{\"0\":{\"201\":1}}],[\"宽接口提供了对\",{\"1\":{\"294\":1}}],[\"宽接口\",{\"1\":{\"294\":1}}],[\"省略\",{\"1\":{\"292\":1,\"363\":1}}],[\"省时又省力\",{\"1\":{\"26\":1}}],[\"捕获和恢复对象的内部状态\",{\"1\":{\"290\":1}}],[\"迟早会暴露出问题\",{\"1\":{\"284\":1}}],[\"相应的减法的代码就不贴了\",{\"1\":{\"498\":1}}],[\"相应的值会存放在\",{\"1\":{\"495\":1}}],[\"相等\",{\"1\":{\"490\":1}}],[\"相同类型\",{\"1\":{\"498\":1}}],[\"相同\",{\"1\":{\"482\":1}}],[\"相对于表达式来说它还是较为容易的\",{\"1\":{\"471\":1}}],[\"相信这部分的知识能够很大程度上提高你的编程水平\",{\"1\":{\"507\":1}}],[\"相信这部分也不难理解\",{\"1\":{\"457\":1}}],[\"相信当你真正完成的时候会像我一样\",{\"1\":{\"396\":1}}],[\"相当于\",{\"1\":{\"408\":1}}],[\"相反\",{\"1\":{\"397\":1}}],[\"相互调用方法\",{\"1\":{\"284\":1}}],[\"相关\",{\"1\":{\"465\":1}}],[\"相关代码如下\",{\"1\":{\"431\":1}}],[\"相关的代码如下\",{\"1\":{\"462\":1}}],[\"相关的内容我们放到后面解释\",{\"1\":{\"450\":1}}],[\"相关的内容注释了\",{\"1\":{\"412\":1}}],[\"相关的是指令集\",{\"1\":{\"406\":1}}],[\"相关的设计模式\",{\"0\":{\"144\":1,\"154\":1,\"174\":1,\"192\":1,\"202\":1,\"213\":1,\"226\":1,\"257\":1,\"275\":1,\"286\":1,\"298\":1,\"312\":1,\"333\":1,\"357\":1,\"367\":1,\"389\":1}}],[\"相关设计模式\",{\"0\":{\"181\":1,\"239\":1,\"319\":1,\"341\":1,\"374\":1}}],[\"相关信息\",{\"1\":{\"36\":1,\"51\":1,\"95\":1,\"397\":1}}],[\"把处理分散在各个类中是不明智的\",{\"1\":{\"283\":1}}],[\"把握本质\",{\"1\":{\"102\":1}}],[\"仲裁者向组员下达指示\",{\"1\":{\"279\":1}}],[\"仲裁者会负责统一大家的意见\",{\"1\":{\"279\":1}}],[\"整个系列的一开始\",{\"1\":{\"506\":1}}],[\"整个系统就变得复杂了\",{\"1\":{\"408\":1}}],[\"整个编译器还剩下最后两个部分\",{\"1\":{\"471\":1}}],[\"整个解析的过程和语法的\",{\"1\":{\"443\":1}}],[\"整个解析的过程是在不断对非终结符进行替换\",{\"1\":{\"442\":1}}],[\"整个团队的交流过程就变为了组员向仲裁者报告\",{\"1\":{\"279\":1}}],[\"整体的替换算法\",{\"2\":{\"369\":1}}],[\"整体\",{\"1\":{\"206\":1}}],[\"经常为此争执不下\",{\"1\":{\"279\":1}}],[\"经常会遇到需要使用一些现有的类\",{\"1\":{\"149\":1}}],[\"他们还十分在意编码细节\",{\"1\":{\"279\":1}}],[\"请自行查阅相关的资料\",{\"1\":{\"444\":1}}],[\"请跳过本章\",{\"1\":{\"392\":1}}],[\"请联系删除\",{\"1\":{\"392\":1,\"400\":1,\"403\":1,\"421\":1,\"439\":1,\"449\":1,\"460\":1,\"471\":1,\"481\":1,\"505\":1}}],[\"请注意\",{\"1\":{\"356\":1}}],[\"请设置时间\",{\"1\":{\"352\":1}}],[\"请试想一下\",{\"1\":{\"283\":1}}],[\"请试想一下要在\",{\"1\":{\"143\":1}}],[\"请大家一定要透彻理解此处的实例的多面性\",{\"1\":{\"356\":1}}],[\"请大家将情况报告给我\",{\"1\":{\"279\":1}}],[\"请大家想象一下一个乱糟糟的开发小组的工作状态\",{\"1\":{\"279\":1}}],[\"支持的标记\",{\"0\":{\"425\":1},\"1\":{\"421\":1}}],[\"支持多种遍历方式\",{\"1\":{\"270\":1}}],[\"支持实时预览和多种导出格式\",{\"1\":{\"111\":1}}],[\"统一接口\",{\"1\":{\"270\":1}}],[\"改变遍历算法\",{\"1\":{\"270\":1}}],[\"改变它的理由永远只有一个\",{\"1\":{\"124\":1}}],[\"集合对象和遍历算法分离\",{\"1\":{\"270\":1}}],[\"迭代器模式是一种行为设计模式\",{\"1\":{\"271\":1}}],[\"迭代器模式将遍历逻辑封装在迭代器对象中\",{\"1\":{\"270\":1}}],[\"迭代器模式提供了一种方法来顺序访问集合中的元素\",{\"1\":{\"270\":1}}],[\"迭代器模式\",{\"0\":{\"269\":1}}],[\"人民邮电出版社\",{\"1\":{\"260\":1}}],[\"人们发现经常需要异步操作共享资源的情况下\",{\"1\":{\"100\":1}}],[\"北京\",{\"1\":{\"260\":1}}],[\"杨文轩译\",{\"1\":{\"260\":1}}],[\"😃\",{\"1\":{\"260\":1}}],[\"遂使用ts作为实现语言\",{\"1\":{\"260\":1}}],[\"封装\",{\"1\":{\"260\":1}}],[\"面向对象编程可以帮助我们分散处理\",{\"1\":{\"283\":1}}],[\"面向对象三大特性\",{\"1\":{\"260\":1}}],[\"面向接口编程\",{\"1\":{\"128\":1}}],[\"移除那些不再被使用的对象\",{\"1\":{\"255\":1}}],[\"定期检查集合中的对象\",{\"1\":{\"255\":1}}],[\"定期清理\",{\"1\":{\"255\":1}}],[\"定义了变量\",{\"1\":{\"429\":1}}],[\"定义了接口\",{\"1\":{\"161\":1}}],[\"定义多个类\",{\"1\":{\"352\":1}}],[\"定义接口\",{\"1\":{\"352\":1}}],[\"定义接口或抽象类\",{\"1\":{\"129\":1}}],[\"定义抽象接口\",{\"1\":{\"130\":1}}],[\"定义乘法的运算规则\",{\"1\":{\"74\":1}}],[\"定义正自然数为非\",{\"1\":{\"67\":1}}],[\"定义\",{\"1\":{\"66\":1}}],[\"定义自然数的序即定义\",{\"1\":{\"66\":1}}],[\"定义加法的运算规则\",{\"1\":{\"58\":1}}],[\"定义dns解析器\",{\"1\":{\"17\":1}}],[\"引用计数\",{\"1\":{\"255\":1}}],[\"引入中介者模式\",{\"1\":{\"123\":1}}],[\"弱引用允许垃圾回收器在没有其他强引用时回收对象\",{\"1\":{\"255\":1}}],[\"弱引用\",{\"1\":{\"255\":1}}],[\"垃圾回收器可能会认为这些对象是垃圾\",{\"1\":{\"255\":1}}],[\"看了上面的代码\",{\"1\":{\"453\":1}}],[\"看看自己能走多远\",{\"1\":{\"393\":1}}],[\"看作是\",{\"1\":{\"254\":1,\"353\":1}}],[\"看起来是这样的\",{\"1\":{\"101\":1}}],[\"颜色\",{\"1\":{\"254\":2}}],[\"颜色信息应当放在哪个类中呢\",{\"1\":{\"253\":1}}],[\"外的寄存器\",{\"1\":{\"416\":1}}],[\"外在的\",{\"1\":{\"254\":1}}],[\"外观模式通过提供一个统一的接口来隐藏子系统的复杂性\",{\"1\":{\"236\":1}}],[\"外观模式有助于分层设计\",{\"1\":{\"235\":1}}],[\"外观模式为复杂的子系统提供了一个简单的接口\",{\"1\":{\"235\":1}}],[\"换句话说\",{\"1\":{\"446\":1}}],[\"换句话说就是不需要我们自己去实现了\",{\"1\":{\"418\":1}}],[\"换行符和空格类似\",{\"1\":{\"427\":1}}],[\"换行符\",{\"0\":{\"427\":1},\"1\":{\"421\":1}}],[\"换言之\",{\"1\":{\"254\":1,\"375\":1}}],[\"换成对应的版本\",{\"1\":{\"9\":1}}],[\"固有的\",{\"1\":{\"254\":1}}],[\"信息还是\",{\"1\":{\"254\":1}}],[\"信息这个问题\",{\"1\":{\"254\":1}}],[\"信息\",{\"1\":{\"254\":5}}],[\"前缀形式\",{\"1\":{\"499\":1}}],[\"前文中我们说到\",{\"1\":{\"489\":1}}],[\"前文中我们定义了支持的类型\",{\"1\":{\"453\":1}}],[\"前言\",{\"0\":{\"392\":1},\"1\":{\"392\":2,\"400\":1,\"403\":1,\"421\":1,\"439\":1,\"449\":1,\"460\":1,\"471\":1,\"481\":1,\"505\":1}}],[\"前面提到的是否共享\",{\"1\":{\"254\":1}}],[\"前面讲到的\",{\"1\":{\"254\":1}}],[\"前端\",{\"1\":{\"15\":1}}],[\"形状\",{\"1\":{\"253\":1}}],[\"字符\",{\"1\":{\"432\":1,\"464\":2}}],[\"字符a对应的十六进制值是\",{\"1\":{\"430\":1}}],[\"字符串等等\",{\"1\":{\"483\":1}}],[\"字符串转换成标记流有时是有状态的\",{\"1\":{\"424\":1}}],[\"字符串\",{\"0\":{\"431\":1},\"1\":{\"421\":1}}],[\"字符的字体\",{\"1\":{\"253\":1}}],[\"字段吗\",{\"1\":{\"434\":1}}],[\"字段就是这个变量\",{\"1\":{\"354\":1}}],[\"字段即是类的两个层次结构的\",{\"1\":{\"164\":1}}],[\"字段中保存的是实现了\",{\"1\":{\"164\":1}}],[\"共享实例可以减少所需资源的使用量\",{\"1\":{\"256\":1}}],[\"共享\",{\"1\":{\"253\":1}}],[\"共有五条\",{\"1\":{\"56\":1}}],[\"符合开闭原则\",{\"1\":{\"243\":1,\"379\":1}}],[\"符合单一职责原则的类\",{\"1\":{\"126\":1}}],[\"降低了耦合性\",{\"1\":{\"243\":1}}],[\"降低类之间的耦合度\",{\"1\":{\"122\":1}}],[\"メール待っていますね\",{\"1\":{\"237\":1}}],[\"のページへようこそ\",{\"1\":{\"237\":1}}],[\"来实现运算符的优先级\",{\"1\":{\"502\":1}}],[\"来实现\",{\"1\":{\"492\":1}}],[\"来实现不同的猜拳策略\",{\"1\":{\"361\":1}}],[\"来保存一个表达式的类型\",{\"1\":{\"487\":1}}],[\"来表示退出\",{\"1\":{\"475\":1}}],[\"来表现这些依赖于操作系统的部分\",{\"1\":{\"172\":1}}],[\"来大致描述我们实现的\",{\"1\":{\"449\":1}}],[\"来压缩了源码字符串\",{\"1\":{\"425\":1}}],[\"来将字符串转换成标记流\",{\"1\":{\"423\":1}}],[\"来计算\",{\"1\":{\"419\":1}}],[\"来使用\",{\"1\":{\"356\":2}}],[\"来支持一次撤销操作\",{\"1\":{\"295\":1}}],[\"来存储共享对象\",{\"1\":{\"255\":1}}],[\"来简化与复杂子系统的交互\",{\"1\":{\"236\":1}}],[\"层与层之间通过外观类进行交互\",{\"1\":{\"235\":1}}],[\"更先进的版本是\",{\"1\":{\"508\":1}}],[\"更为重要的是\",{\"1\":{\"443\":1}}],[\"更多的标记\",{\"1\":{\"425\":1}}],[\"更易维护\",{\"1\":{\"379\":1}}],[\"更好的分层\",{\"1\":{\"235\":1}}],[\"更新代码的原生部分\",{\"1\":{\"95\":1}}],[\"增的操作\",{\"1\":{\"499\":1}}],[\"增强了代码的可扩展性\",{\"1\":{\"270\":1}}],[\"增强了代码的可维护性和可扩展性\",{\"1\":{\"235\":1}}],[\"增加\",{\"1\":{\"419\":1}}],[\"增加指令会消耗许多资源\",{\"1\":{\"412\":1}}],[\"增加计数\",{\"1\":{\"255\":1}}],[\"增加灵活性\",{\"1\":{\"189\":1}}],[\"增加后的功能可以被\",{\"1\":{\"172\":1}}],[\"增加了灵活性\",{\"1\":{\"371\":1}}],[\"增加了代码的灵活性和可维护性\",{\"1\":{\"270\":1}}],[\"增加了\",{\"1\":{\"164\":1}}],[\"增加新操作更容易\",{\"1\":{\"379\":1}}],[\"增加新的\",{\"1\":{\"384\":1}}],[\"增加新的产品类时\",{\"1\":{\"243\":1}}],[\"增加新的实现时\",{\"0\":{\"161\":1}}],[\"增加新的实现\",{\"1\":{\"116\":1}}],[\"增加新功能时\",{\"0\":{\"160\":1}}],[\"增加其它工厂\",{\"0\":{\"140\":1}}],[\"增加请求头和cookie的大小限制\",{\"1\":{\"17\":1}}],[\"松散耦合\",{\"1\":{\"235\":1}}],[\"简直痛苦地无话可说\",{\"1\":{\"509\":1}}],[\"简而言之\",{\"1\":{\"422\":1}}],[\"简化代码\",{\"1\":{\"270\":1,\"316\":1}}],[\"简化语法解析\",{\"1\":{\"264\":1}}],[\"简化接口\",{\"1\":{\"235\":1}}],[\"简单地说\",{\"1\":{\"472\":1}}],[\"简单地替换下算法即可进行测试\",{\"1\":{\"365\":1}}],[\"简单而言就是将一个复杂的大问题分解为多个小问题然后逐个解决\",{\"1\":{\"351\":1}}],[\"简单化\",{\"2\":{\"241\":1,\"288\":1}}],[\"简单来说\",{\"1\":{\"127\":1}}],[\"简单ppt\",{\"1\":{\"105\":1}}],[\"简单直接\",{\"1\":{\"43\":1}}],[\"啊\",{\"1\":{\"235\":1}}],[\"编程有趣又无趣\",{\"1\":{\"510\":1}}],[\"编译时加上\",{\"1\":{\"419\":1}}],[\"编译程序\",{\"1\":{\"419\":1}}],[\"编译器中我们需要用到的函数有\",{\"1\":{\"418\":1}}],[\"编译器的语法分析部分其实是很简单的\",{\"1\":{\"478\":1}}],[\"编译器的输出\",{\"1\":{\"420\":1}}],[\"编译器的编写分为\",{\"1\":{\"401\":1}}],[\"编译器的构建流程\",{\"0\":{\"401\":1},\"1\":{\"400\":1}}],[\"编译器框架\",{\"0\":{\"402\":1},\"1\":{\"400\":1}}],[\"编译器\",{\"1\":{\"403\":1},\"2\":{\"399\":1,\"438\":1,\"448\":1,\"459\":1,\"470\":1,\"480\":1,\"504\":1,\"512\":1}}],[\"编译器生成器\",{\"1\":{\"394\":1}}],[\"编译原理\",{\"1\":{\"393\":1,\"394\":3,\"397\":1,\"403\":1},\"2\":{\"398\":1,\"437\":1,\"447\":1,\"458\":1,\"469\":1,\"479\":1,\"503\":1,\"511\":1}}],[\"编写编译器时遇到的一些难题\",{\"1\":{\"505\":1}}],[\"编写语法分析器有两种方法\",{\"1\":{\"440\":1}}],[\"编写一个\",{\"1\":{\"355\":1}}],[\"编写一个反向迭代器\",{\"1\":{\"274\":1}}],[\"编写出更加健壮和优雅的代码\",{\"1\":{\"232\":1}}],[\"编辑器\",{\"1\":{\"111\":1}}],[\"您能够掌握这些设计模式\",{\"1\":{\"232\":1}}],[\"您可以免费安装并使用\",{\"1\":{\"111\":1}}],[\"灵活应用于实际项目中\",{\"1\":{\"232\":1}}],[\"灵活性高\",{\"1\":{\"243\":1}}],[\"灵活性\",{\"1\":{\"217\":1,\"371\":1}}],[\"总共代码加注释1400行\",{\"1\":{\"395\":1}}],[\"总是互相指挥\",{\"1\":{\"279\":1}}],[\"总之\",{\"1\":{\"232\":1}}],[\"总结起来有如下两点\",{\"1\":{\"352\":1}}],[\"总结\",{\"0\":{\"134\":1,\"338\":1,\"505\":1},\"1\":{\"392\":1,\"400\":1,\"403\":1,\"421\":1,\"439\":1,\"449\":1,\"460\":1,\"471\":1,\"481\":1,\"505\":1}}],[\"父类控制算法的执行流程\",{\"1\":{\"371\":1}}],[\"父类和子类之间的一致性是指子类应当继承父类的行为和属性\",{\"1\":{\"228\":1}}],[\"父类和子类的一致性\",{\"0\":{\"228\":1}}],[\"父类的任务是通过声明抽象方法的方式定义接口\",{\"1\":{\"161\":1}}],[\"导致工作进度始终滞后\",{\"1\":{\"279\":1}}],[\"导致增加许多很小的类\",{\"0\":{\"225\":1}}],[\"导致插件无法正常退出\",{\"1\":{\"54\":1}}],[\"草莓味和猕猴桃三重口味\",{\"1\":{\"224\":1}}],[\"草莓冰激凌\",{\"1\":{\"224\":1}}],[\"亦或是香草味\",{\"1\":{\"224\":1}}],[\"冰激凌店只会准备各种香料\",{\"1\":{\"224\":1}}],[\"猕猴桃冰激凌等各种口味的冰激凌一样\",{\"1\":{\"224\":1}}],[\"巧克力冰激凌\",{\"1\":{\"224\":1}}],[\"去处理\",{\"1\":{\"222\":1}}],[\"去手动异步执行另一个协程\",{\"1\":{\"101\":1}}],[\"给\",{\"1\":{\"222\":1}}],[\"给一个健康的人注射吗啡是犯罪\",{\"1\":{\"102\":1}}],[\"委托者将某些任务委托给委托对象来执行\",{\"1\":{\"229\":1}}],[\"委托\",{\"1\":{\"222\":1}}],[\"委托是弱关联\",{\"0\":{\"173\":1}}],[\"功能需求总是在不断变化\",{\"1\":{\"385\":1}}],[\"功能则越多\",{\"1\":{\"222\":1}}],[\"功能层次结构与实现层次结构是混杂在一个层次结构中的\",{\"1\":{\"162\":1}}],[\"结束的\",{\"1\":{\"464\":2}}],[\"结果存放在寄存器\",{\"1\":{\"417\":1}}],[\"结果却发现还是皮\",{\"1\":{\"221\":1}}],[\"结城浩\",{\"1\":{\"260\":1}}],[\"结语\",{\"0\":{\"232\":1,\"510\":1},\"1\":{\"505\":1}}],[\"结论当然就是看使用场景\",{\"1\":{\"102\":1}}],[\"却没有发生任何变化\",{\"1\":{\"221\":1}}],[\"透明性\",{\"0\":{\"330\":1},\"1\":{\"221\":1}}],[\"职责扩展\",{\"1\":{\"217\":1}}],[\"职责分离\",{\"1\":{\"125\":1}}],[\"快照\",{\"1\":{\"201\":1}}],[\"动作\",{\"1\":{\"200\":1}}],[\"动态组合职责链\",{\"1\":{\"189\":1}}],[\"动态地扩展对象的行为\",{\"1\":{\"116\":1}}],[\"执行相反的增\",{\"1\":{\"499\":1}}],[\"执行\",{\"1\":{\"473\":1}}],[\"执行条件表达式\",{\"1\":{\"473\":1}}],[\"执行操作所需的参数\",{\"1\":{\"200\":1}}],[\"执行命令的对象\",{\"1\":{\"200\":1}}],[\"执行过程本身就是安全的\",{\"1\":{\"102\":1}}],[\"接下来开始解析函数定义相关的内容\",{\"1\":{\"462\":1}}],[\"接着是字符串常量\",{\"1\":{\"484\":1}}],[\"接着\",{\"1\":{\"405\":1}}],[\"接收\",{\"1\":{\"383\":2}}],[\"接收者包含了执行具体操作的逻辑\",{\"1\":{\"200\":1}}],[\"接收者\",{\"1\":{\"200\":1}}],[\"接口中定义了的方法\",{\"1\":{\"356\":2}}],[\"接口中增加了一个\",{\"1\":{\"355\":1}}],[\"接口中增加新的方法\",{\"1\":{\"355\":1}}],[\"接口中声明的所有方法都是\",{\"1\":{\"352\":1}}],[\"接口的类的实例\",{\"1\":{\"356\":2}}],[\"接口的\",{\"1\":{\"352\":1}}],[\"接口定义了\",{\"1\":{\"273\":2}}],[\"接口\",{\"1\":{\"221\":1,\"273\":2,\"324\":1,\"355\":1}}],[\"接口和抽象类\",{\"1\":{\"132\":1}}],[\"接口隔离原则\",{\"0\":{\"127\":1},\"1\":{\"134\":1}}],[\"接口分隔原则\",{\"1\":{\"113\":1,\"114\":1}}],[\"队列或者日志来参数化其他对象\",{\"1\":{\"196\":1}}],[\"推卸责任\",{\"1\":{\"188\":2},\"2\":{\"194\":1}}],[\"推荐做法\",{\"1\":{\"48\":1}}],[\"组员之间不再相互询问和相互指示\",{\"1\":{\"279\":1}}],[\"组件才具有高价\",{\"1\":{\"183\":1}}],[\"组合\",{\"0\":{\"131\":1},\"1\":{\"113\":1,\"114\":1,\"134\":1}}],[\"易于扩展\",{\"1\":{\"361\":1}}],[\"易于增加\",{\"0\":{\"386\":1}}],[\"易于增加新的状态\",{\"0\":{\"355\":1}}],[\"易于增加具体工厂\",{\"0\":{\"142\":1}}],[\"易于维护和扩展\",{\"1\":{\"183\":1}}],[\"■晚上\",{\"1\":{\"180\":1}}],[\"■从早上到下午\",{\"1\":{\"180\":1}}],[\"が作成されました\",{\"1\":{\"179\":1}}],[\"晚安\",{\"1\":{\"179\":1,\"180\":1}}],[\"晚上好\",{\"1\":{\"179\":1,\"180\":1}}],[\"晚上\",{\"1\":{\"179\":1,\"351\":1}}],[\"早上好\",{\"1\":{\"179\":1,\"180\":1}}],[\"问题\",{\"1\":{\"443\":1}}],[\"问题就被分解了\",{\"1\":{\"351\":1}}],[\"问题到底出在哪儿\",{\"1\":{\"99\":1}}],[\"问候\",{\"1\":{\"179\":1,\"180\":1}}],[\"发现是\",{\"1\":{\"443\":1}}],[\"发送者无需知道哪个对象会处理请求\",{\"1\":{\"189\":1,\"190\":1}}],[\"发送示例\",{\"0\":{\"39\":1}}],[\"发生变化的代码只有\",{\"1\":{\"173\":1}}],[\"才将\",{\"1\":{\"173\":1}}],[\"才与作为参数被传入的类构成关联\",{\"1\":{\"173\":1}}],[\"才能真正理解和掌握这些模式\",{\"1\":{\"232\":1}}],[\"才能正常看到渲染后的\",{\"1\":{\"106\":1}}],[\"才能透过现象\",{\"1\":{\"102\":1}}],[\"继承\",{\"1\":{\"260\":1}}],[\"继承和委托中的一致性\",{\"0\":{\"227\":1}}],[\"继承是强关联关系\",{\"1\":{\"173\":1}}],[\"继承是强关联\",{\"0\":{\"173\":1}}],[\"继续执行我们当前的任务\",{\"1\":{\"101\":1}}],[\"个字节\",{\"1\":{\"498\":1}}],[\"个字符或标记\",{\"1\":{\"436\":1}}],[\"个数等\",{\"1\":{\"468\":1}}],[\"个部分进行讲解\",{\"1\":{\"449\":1,\"460\":1}}],[\"个标记\",{\"1\":{\"443\":1}}],[\"个指令\",{\"1\":{\"408\":1}}],[\"个寄存器\",{\"1\":{\"406\":1}}],[\"个函数\",{\"1\":{\"402\":1}}],[\"个函数来实现了一个小的\",{\"1\":{\"395\":1}}],[\"个步骤\",{\"1\":{\"401\":1}}],[\"个实例则会有\",{\"1\":{\"284\":1}}],[\"个实例就会有\",{\"1\":{\"284\":1}}],[\"个实例\",{\"1\":{\"284\":3,\"338\":1}}],[\"个成员虽然一起协同工作\",{\"1\":{\"279\":1}}],[\"个操作系统上\",{\"1\":{\"172\":1}}],[\"个\",{\"1\":{\"172\":1}}],[\"个类的子类\",{\"1\":{\"142\":1}}],[\"角色公开足够多的信息\",{\"1\":{\"388\":1}}],[\"角色必须向\",{\"1\":{\"388\":1}}],[\"角色负责\",{\"1\":{\"386\":1}}],[\"角色即可\",{\"1\":{\"365\":1}}],[\"角色相关联的部分\",{\"1\":{\"355\":1}}],[\"角色就必须要知道\",{\"1\":{\"353\":1}}],[\"角色都需要或多或少地知道其他角色\",{\"1\":{\"353\":1}}],[\"角色都需要知道其他\",{\"1\":{\"353\":1}}],[\"角色后\",{\"1\":{\"353\":2}}],[\"角色的增加\",{\"1\":{\"387\":1}}],[\"角色的开发可以独立于\",{\"1\":{\"384\":1}}],[\"角色的接口\",{\"1\":{\"365\":1}}],[\"角色的独立性\",{\"1\":{\"353\":1}}],[\"角色的代码的同时\",{\"1\":{\"351\":1}}],[\"角色的类时\",{\"1\":{\"307\":1}}],[\"角色的划分具有重要意义\",{\"1\":{\"297\":1}}],[\"角色的意义\",{\"0\":{\"297\":1}}],[\"角色的\",{\"1\":{\"285\":2,\"353\":3}}],[\"角色的实例传递给\",{\"1\":{\"173\":1}}],[\"角色很难复用\",{\"1\":{\"285\":1}}],[\"角色可以复用\",{\"1\":{\"285\":1}}],[\"角色中都实现这个方法\",{\"1\":{\"355\":1}}],[\"角色中\",{\"1\":{\"353\":1}}],[\"角色中并没有任何依赖于特定对话框的代码\",{\"1\":{\"285\":1}}],[\"角色中即可\",{\"1\":{\"253\":1}}],[\"角色中的字段时\",{\"1\":{\"253\":1}}],[\"角色\",{\"0\":{\"386\":1,\"387\":1},\"1\":{\"172\":2,\"224\":1,\"307\":2,\"353\":2,\"384\":2,\"386\":2,\"387\":1}}],[\"版的\",{\"1\":{\"172\":1}}],[\"版\",{\"1\":{\"172\":5}}],[\"应当是谁来管理状态的迁移\",{\"0\":{\"353\":1}}],[\"应当共享的信息被称作\",{\"1\":{\"254\":1}}],[\"应当共享的信息和不应当共享的信息\",{\"1\":{\"254\":1}}],[\"应用程序中\",{\"1\":{\"302\":1}}],[\"应用程序在运行时很容易就会达到资源极限而导致崩溃\",{\"1\":{\"256\":1}}],[\"应用于软件所运行的操作系统上\",{\"1\":{\"172\":1}}],[\"应根据实际需求灵活应用设计模式\",{\"1\":{\"232\":1}}],[\"应该可以在不修改原模块的基础上\",{\"1\":{\"115\":1}}],[\"分隔的变量\",{\"1\":{\"454\":1}}],[\"分别是\",{\"1\":{\"449\":1,\"460\":1}}],[\"分别是源地址和目标地址\",{\"1\":{\"408\":1}}],[\"分别如下\",{\"1\":{\"406\":1}}],[\"分析标识符的相关代码如下\",{\"1\":{\"429\":1}}],[\"分析整个\",{\"1\":{\"402\":1}}],[\"分析\",{\"1\":{\"394\":1}}],[\"分析方法为递归下降\",{\"1\":{\"265\":1}}],[\"分而治之\",{\"0\":{\"351\":1},\"1\":{\"283\":1,\"351\":1}}],[\"分开考虑\",{\"2\":{\"176\":1,\"369\":1}}],[\"分开后更容易扩展\",{\"0\":{\"172\":1}}],[\"分离关注点\",{\"1\":{\"379\":1}}],[\"分离开了\",{\"1\":{\"172\":1}}],[\"分离为两个独立的类层次结构\",{\"1\":{\"162\":1}}],[\"|add\",{\"1\":{\"498\":1}}],[\"|10\",{\"1\":{\"442\":1}}],[\"|9\",{\"1\":{\"442\":1}}],[\"|8\",{\"1\":{\"442\":1}}],[\"|5\",{\"1\":{\"442\":1}}],[\"|4\",{\"1\":{\"442\":1}}],[\"|<\",{\"1\":{\"429\":1,\"466\":1}}],[\"|token|hash|name|type|class|value|btype|bclass|bvalue|\",{\"1\":{\"429\":1}}],[\"|你好\",{\"1\":{\"373\":5}}],[\"||\",{\"1\":{\"219\":6,\"348\":1,\"405\":6,\"429\":5,\"430\":3,\"431\":1,\"433\":9,\"445\":1,\"466\":1,\"487\":1,\"489\":1,\"493\":1,\"495\":1,\"497\":2}}],[\"|+\",{\"1\":{\"219\":2,\"405\":3,\"482\":9}}],[\"|\",{\"1\":{\"170\":7,\"218\":2,\"219\":2,\"265\":9,\"339\":1,\"343\":1,\"373\":10,\"405\":4,\"416\":10,\"417\":1,\"423\":4,\"433\":3,\"441\":6,\"444\":5,\"450\":7,\"453\":2,\"461\":5,\"463\":9,\"464\":1,\"482\":12,\"498\":4}}],[\"|hello|\",{\"1\":{\"219\":1}}],[\"|hello\",{\"1\":{\"170\":7,\"373\":5}}],[\"|`\",{\"1\":{\"169\":1,\"372\":1}}],[\"桥梁\",{\"1\":{\"164\":1}}],[\"以减少语法分析器的复杂程度\",{\"1\":{\"422\":1}}],[\"以上就是我们为了实现函数调用需要的指令了\",{\"1\":{\"416\":1}}],[\"以二进制的形式保存在内存中\",{\"1\":{\"404\":1}}],[\"以前人们会说\",{\"1\":{\"393\":1}}],[\"以实现\",{\"1\":{\"352\":1}}],[\"以确保在多线程环境下\",{\"1\":{\"343\":1}}],[\"以控制对该对象的访问\",{\"1\":{\"323\":1}}],[\"以避免循环依赖和无限递归\",{\"1\":{\"308\":1}}],[\"以释放资源\",{\"1\":{\"296\":1}}],[\"以支持多次撤销操作\",{\"1\":{\"295\":1}}],[\"以支持多种遍历方式\",{\"1\":{\"270\":1}}],[\"以支持撤销和重做操作\",{\"1\":{\"201\":1}}],[\"以下是\",{\"1\":{\"303\":1}}],[\"以下是示例代码\",{\"1\":{\"291\":1}}],[\"以下是实现迭代器模式的\",{\"1\":{\"272\":1}}],[\"以下是实现保存历史记录的一些常见方法\",{\"1\":{\"201\":1}}],[\"以下是一些常见的解决方案\",{\"1\":{\"255\":1}}],[\"以便从后向前遍历书籍\",{\"1\":{\"274\":1}}],[\"以便重复使用这些对象\",{\"1\":{\"255\":1}}],[\"以便在需要时恢复到之前的状态\",{\"1\":{\"201\":1}}],[\"以便在需要时进行撤销操作\",{\"1\":{\"200\":1}}],[\"以保持我们的知识体系与时俱进\",{\"1\":{\"232\":1}}],[\"以示例程序来说\",{\"1\":{\"222\":1,\"355\":1}}],[\"以及该函数在代码段\",{\"1\":{\"462\":1}}],[\"以及从文件中读取并反序列化\",{\"1\":{\"297\":1}}],[\"以及\",{\"1\":{\"221\":1}}],[\"以及它的子类\",{\"1\":{\"221\":1}}],[\"以供后面的处理使用\",{\"1\":{\"164\":1}}],[\"以管理员身份在\",{\"1\":{\"111\":1}}],[\"该标识符的类别\",{\"1\":{\"429\":1}}],[\"该标识符返回的标记\",{\"1\":{\"429\":1}}],[\"该地址中存放着\",{\"1\":{\"406\":1}}],[\"该实例会被当作\",{\"1\":{\"356\":2}}],[\"该实例通过\",{\"1\":{\"164\":1}}],[\"该方法中很容易发生\",{\"1\":{\"283\":1}}],[\"该类位于\",{\"1\":{\"164\":1}}],[\"该怎么办\",{\"1\":{\"101\":1}}],[\"试图教会我们的是如何构造\",{\"1\":{\"394\":1}}],[\"试程序行为的类\",{\"1\":{\"164\":1}}],[\"试证乘法交换律\",{\"1\":{\"78\":1}}],[\"试证加法交换律\",{\"1\":{\"62\":1}}],[\"试证\",{\"1\":{\"62\":2,\"64\":2,\"78\":2,\"81\":2}}],[\"两个概念\",{\"1\":{\"472\":1}}],[\"两个参数都无法取得了\",{\"1\":{\"417\":1}}],[\"两个状态\",{\"1\":{\"351\":1}}],[\"两个自然数\",{\"1\":{\"71\":1}}],[\"两种接口和可见性\",{\"0\":{\"294\":1}}],[\"两者之间必然会缺少联系\",{\"1\":{\"162\":1}}],[\"与前缀形式不同的是\",{\"1\":{\"499\":1}}],[\"与之不同\",{\"1\":{\"486\":1}}],[\"与语法分析相关的部分就是上文所说的优先级问题了\",{\"1\":{\"483\":1}}],[\"与存放在\",{\"1\":{\"463\":1}}],[\"与表示被装饰物的\",{\"1\":{\"221\":1}}],[\"与\",{\"0\":{\"254\":1},\"1\":{\"162\":1,\"172\":1,\"406\":1,\"412\":1,\"464\":1,\"508\":1}}],[\"与线程相比\",{\"1\":{\"100\":1}}],[\"正则表达式\",{\"1\":{\"507\":1}}],[\"正如我们保证的那样\",{\"1\":{\"501\":1}}],[\"正负号\",{\"0\":{\"492\":1},\"1\":{\"481\":1}}],[\"正常的全局变量的类别则是\",{\"1\":{\"454\":1}}],[\"正常通话\",{\"1\":{\"348\":1,\"349\":8}}],[\"正在生成printer的实例\",{\"1\":{\"325\":1}}],[\"正是因为它相当于通过一定的编码\",{\"1\":{\"425\":1}}],[\"正是因为可以替换\",{\"1\":{\"183\":1}}],[\"正是因为不知道才能够替换\",{\"1\":{\"183\":1}}],[\"正是由于父类和子类的这种任务分担\",{\"1\":{\"161\":1}}],[\"正自然数与自然数相加为正自然数\",{\"1\":{\"68\":2}}],[\"正自然数的性质\",{\"0\":{\"68\":1}}],[\"正自然数\",{\"0\":{\"67\":1}}],[\"章\",{\"1\":{\"161\":1,\"353\":1}}],[\"派生类\",{\"1\":{\"160\":1}}],[\"派生类应当可以替换基类并出现在基类能够出现的任何地方\",{\"1\":{\"118\":1}}],[\"之前\",{\"1\":{\"482\":1,\"495\":1}}],[\"之类的表达式要如何实现呢\",{\"1\":{\"486\":1}}],[\"之类的函数\",{\"1\":{\"418\":1}}],[\"之类的运算符是与参数顺序有关的\",{\"1\":{\"417\":1}}],[\"之间的关系是松耦合的\",{\"1\":{\"306\":1}}],[\"之间搭建桥梁\",{\"1\":{\"157\":1}}],[\"之后再计算运算符\",{\"1\":{\"482\":1}}],[\"之后\",{\"1\":{\"101\":1}}],[\"`not\",{\"1\":{\"500\":1}}],[\"`node\",{\"1\":{\"265\":1}}],[\"`ax`\",{\"1\":{\"486\":1}}],[\"`int\",{\"1\":{\"453\":1}}],[\"`winner\",{\"1\":{\"362\":2}}],[\"`warning\",{\"1\":{\"265\":2}}],[\"`record\",{\"1\":{\"348\":1}}],[\"`char\",{\"1\":{\"498\":1}}],[\"`call\",{\"1\":{\"348\":1}}],[\"`current\",{\"1\":{\"265\":1,\"291\":1}}],[\"`0$\",{\"1\":{\"348\":1}}],[\"`sizeof\",{\"1\":{\"485\":3}}],[\"`singleton\",{\"1\":{\"339\":1,\"343\":1}}],[\"`subscribing\",{\"1\":{\"280\":1}}],[\"`===\",{\"1\":{\"324\":1}}],[\"`====\",{\"1\":{\"291\":1}}],[\"`正在生成printer的实例\",{\"1\":{\"324\":1}}],[\"`graphobserver\",{\"1\":{\"303\":1}}],[\"`got\",{\"1\":{\"291\":1}}],[\"`digitobserver\",{\"1\":{\"303\":1}}],[\"`drawing\",{\"1\":{\"197\":1}}],[\"`publishing\",{\"1\":{\"280\":1}}],[\"`money\",{\"1\":{\"291\":1}}],[\"`message\",{\"1\":{\"280\":1}}],[\"`main`\",{\"1\":{\"434\":1}}],[\"`mailto\",{\"1\":{\"237\":1}}],[\"`making\",{\"1\":{\"237\":1}}],[\"`■$\",{\"1\":{\"179\":1}}],[\"`$\",{\"1\":{\"179\":2,\"190\":2,\"208\":2,\"209\":1,\"210\":1,\"244\":1,\"265\":1,\"317\":1,\"348\":2,\"380\":4}}],[\"`|$\",{\"1\":{\"169\":1,\"372\":1}}],[\"`\",{\"1\":{\"152\":4,\"179\":3,\"190\":6,\"197\":1,\"208\":2,\"209\":1,\"210\":1,\"237\":2,\"265\":5,\"280\":2,\"291\":6,\"303\":2,\"317\":5,\"324\":1,\"339\":1,\"343\":1,\"348\":3,\"362\":4,\"380\":4,\"453\":1,\"485\":3,\"498\":1,\"500\":1}}],[\"`<a\",{\"1\":{\"237\":1}}],[\"`<li>$\",{\"1\":{\"179\":1}}],[\"`<li><a\",{\"1\":{\"139\":1}}],[\"`<p>$\",{\"1\":{\"179\":1,\"237\":1}}],[\"`<\",{\"1\":{\"139\":2}}],[\"`<ul>`\",{\"1\":{\"139\":1}}],[\"`<hr><address>$\",{\"1\":{\"139\":1}}],[\"`<h1>$\",{\"1\":{\"139\":1,\"179\":1}}],[\"`<html><head><title>$\",{\"1\":{\"139\":1,\"179\":1,\"237\":1}}],[\"`<body>`\",{\"1\":{\"139\":1}}],[\"直至可以解决它们为止\",{\"1\":{\"351\":1}}],[\"直到真正用递归下降的方式实现了一个\",{\"1\":{\"508\":1}}],[\"直到遇到优先级\",{\"1\":{\"494\":1}}],[\"直到遇见了终结符\",{\"1\":{\"442\":1}}],[\"直到合并成起始的非终结符\",{\"1\":{\"440\":1}}],[\"直到匹配输入的终结符\",{\"1\":{\"440\":1}}],[\"直到实际图像加载完成\",{\"1\":{\"332\":1}}],[\"直到有一个对象能够处理它\",{\"1\":{\"190\":1}}],[\"直流12v\",{\"1\":{\"151\":1}}],[\"直接将对应的值用\",{\"1\":{\"486\":1}}],[\"直接从源代码编译成汇编代码是很困难的\",{\"1\":{\"423\":1}}],[\"直接证明比较困难\",{\"1\":{\"62\":1,\"78\":1}}],[\"直接取模\",{\"0\":{\"43\":1}}],[\"直接地创建各种图表\",{\"1\":{\"5\":1}}],[\"需求\",{\"1\":{\"151\":1}}],[\"需要两个字符\",{\"1\":{\"425\":1}}],[\"需要有参数\",{\"1\":{\"408\":1}}],[\"需要去理解程序运行中会有哪些状态\",{\"1\":{\"406\":1}}],[\"需要删除\",{\"1\":{\"353\":1}}],[\"需要注意这些\",{\"1\":{\"307\":1}}],[\"需要注意的是\",{\"1\":{\"295\":1,\"384\":1,\"410\":1}}],[\"需要根据具体需求来决定\",{\"1\":{\"296\":1}}],[\"需要根据具体需求来决定需要保存多少个\",{\"1\":{\"295\":1}}],[\"需要多少个\",{\"0\":{\"295\":1}}],[\"需要在不暴露对象实现细节的情况下保存对象状态\",{\"1\":{\"290\":1}}],[\"需要在对象状态变化时进行撤销操作\",{\"1\":{\"290\":1}}],[\"需要保存和恢复对象的多个状态\",{\"1\":{\"290\":1}}],[\"需要精挑细选\",{\"1\":{\"253\":1}}],[\"需要先将这个插件\",{\"1\":{\"106\":1}}],[\"需要先申请一个域名\",{\"1\":{\"13\":1}}],[\"需要创建配置文件\",{\"1\":{\"10\":1}}],[\"变更为不仅可以撤销\",{\"1\":{\"297\":1}}],[\"变更为可以多次撤销\",{\"1\":{\"297\":1}}],[\"变换装置\",{\"1\":{\"151\":1}}],[\"变量赋值\",{\"1\":{\"481\":1}}],[\"变量与函数调用\",{\"0\":{\"486\":1},\"1\":{\"481\":1,\"489\":1}}],[\"变量类型的表示\",{\"1\":{\"453\":1}}],[\"变量是\",{\"1\":{\"429\":1}}],[\"变量定义\",{\"0\":{\"449\":1},\"1\":{\"392\":1,\"400\":1,\"403\":1,\"421\":1,\"439\":1,\"449\":2,\"460\":2,\"471\":1,\"481\":1,\"505\":1}}],[\"变量balance的最终结果是0\",{\"1\":{\"101\":1}}],[\"变量的状态并不会进行同步\",{\"1\":{\"101\":1}}],[\"交给\",{\"1\":{\"388\":1}}],[\"交给子类\",{\"2\":{\"247\":1,\"377\":1}}],[\"交流100v\",{\"1\":{\"151\":1}}],[\"交替进行\",{\"1\":{\"99\":1}}],[\"实际上\",{\"1\":{\"482\":1}}],[\"实际上我们也不能使用递归\",{\"1\":{\"450\":1}}],[\"实际上又是别的物体的\",{\"1\":{\"221\":1}}],[\"实际中可以自己指定\",{\"1\":{\"442\":1}}],[\"实际计算机中\",{\"1\":{\"420\":1}}],[\"实际调用该方法的却是扮演\",{\"1\":{\"353\":1}}],[\"实际需求\",{\"1\":{\"151\":1}}],[\"实例的多面性\",{\"0\":{\"356\":1}}],[\"实例代码\",{\"0\":{\"250\":1,\"324\":1}}],[\"实例\",{\"1\":{\"221\":1}}],[\"实现起来并不是太难\",{\"1\":{\"508\":1}}],[\"实现起来也更直观\",{\"1\":{\"450\":1}}],[\"实现四则运算来讲解优先级问题\",{\"1\":{\"482\":1}}],[\"实现如下\",{\"1\":{\"410\":1,\"411\":1,\"413\":1,\"414\":1,\"416\":1,\"417\":1}}],[\"实现一个功能完善的\",{\"1\":{\"395\":1}}],[\"实现也很复杂\",{\"0\":{\"394\":1}}],[\"实现了\",{\"1\":{\"356\":2}}],[\"实现具体方法\",{\"1\":{\"352\":1}}],[\"实现的代码示例\",{\"1\":{\"303\":1}}],[\"实现迭代器模式\",{\"0\":{\"271\":1},\"1\":{\"271\":1}}],[\"实现显示\",{\"1\":{\"253\":1}}],[\"实现\",{\"1\":{\"164\":1}}],[\"实现方法\",{\"0\":{\"116\":1,\"119\":1,\"123\":1,\"125\":1,\"129\":1,\"132\":1}}],[\"类别信息在后面章节中解析\",{\"1\":{\"454\":1}}],[\"类必须提供用于获取每个目录条目的\",{\"1\":{\"388\":1}}],[\"类负责\",{\"1\":{\"388\":1}}],[\"类作为组件的独立性\",{\"1\":{\"384\":1}}],[\"类作为显示文件夹内容的\",{\"1\":{\"384\":1}}],[\"类作为中介者\",{\"1\":{\"283\":1}}],[\"类型的解析在前面的文章中我们已经很熟悉了\",{\"1\":{\"485\":1}}],[\"类型的注释\",{\"1\":{\"432\":1}}],[\"类型定义\",{\"1\":{\"453\":1}}],[\"类型\",{\"1\":{\"356\":2}}],[\"类来负责\",{\"1\":{\"353\":1}}],[\"类时\",{\"1\":{\"353\":1}}],[\"类变化为其他状态\",{\"1\":{\"353\":1}}],[\"类会调用\",{\"1\":{\"352\":1}}],[\"类会负责管理\",{\"1\":{\"253\":1}}],[\"类具有一致性\",{\"1\":{\"324\":1}}],[\"类具有相同的接口\",{\"1\":{\"221\":1}}],[\"类与\",{\"1\":{\"324\":1}}],[\"类则使用窄接口来保存和传递\",{\"1\":{\"294\":1}}],[\"类则不需要做任何修改\",{\"1\":{\"173\":1}}],[\"类使用宽接口来创建和恢复\",{\"1\":{\"294\":1}}],[\"类很难在其他对话框中被复用\",{\"1\":{\"285\":1}}],[\"类用于新的对话框中\",{\"1\":{\"285\":1}}],[\"类实现了实际进行状态迁移的\",{\"1\":{\"353\":1}}],[\"类实现了\",{\"1\":{\"273\":1}}],[\"类表示一个书架\",{\"1\":{\"273\":1}}],[\"类表示一个书籍对象\",{\"1\":{\"273\":1}}],[\"类是表示被装饰物的\",{\"1\":{\"221\":1}}],[\"类方法的地方和\",{\"1\":{\"185\":1}}],[\"类知道如何生成对象的具体表示\",{\"1\":{\"183\":1}}],[\"类知道如何构建复杂对象\",{\"1\":{\"183\":1}}],[\"类中声明一个\",{\"1\":{\"387\":1}}],[\"类中的以下两条语句\",{\"1\":{\"356\":1}}],[\"类中实现这个方法\",{\"1\":{\"355\":1}}],[\"类中用到的所有\",{\"1\":{\"253\":1}}],[\"类中使用的所有\",{\"1\":{\"253\":1}}],[\"类中\",{\"1\":{\"178\":1,\"253\":3,\"283\":1,\"285\":1,\"384\":1}}],[\"类和\",{\"1\":{\"173\":4,\"185\":1,\"285\":1,\"353\":1,\"355\":1,\"356\":1,\"384\":3,\"387\":1}}],[\"类生成\",{\"1\":{\"173\":1}}],[\"类继承了\",{\"1\":{\"164\":1}}],[\"类比\",{\"0\":{\"150\":1,\"151\":1}}],[\"类\",{\"1\":{\"143\":1,\"160\":1,\"164\":2,\"173\":3,\"185\":2,\"221\":1,\"255\":1,\"285\":1,\"352\":1,\"353\":2,\"355\":1,\"384\":1,\"387\":1}}],[\"类的兄弟类\",{\"1\":{\"387\":1}}],[\"类的层次与抽象类\",{\"0\":{\"375\":1}}],[\"类的层次结构的混杂和分离\",{\"0\":{\"162\":1}}],[\"类的层次结构的两个作用\",{\"0\":{\"159\":1}}],[\"类的构造函数中的\",{\"1\":{\"356\":1}}],[\"类的构造函数被传递给\",{\"1\":{\"164\":1}}],[\"类的构造了数中调用了\",{\"1\":{\"324\":1}}],[\"类的方法后具体会进行什么样的处理\",{\"1\":{\"185\":1}}],[\"类的方法的调用方法\",{\"1\":{\"185\":1}}],[\"类的代码就可以了\",{\"1\":{\"353\":1}}],[\"类的代码\",{\"1\":{\"185\":1,\"353\":1}}],[\"类的使用方法\",{\"1\":{\"185\":1}}],[\"类的实例并不重要\",{\"1\":{\"356\":1}}],[\"类的实例都带有相同的颜色\",{\"1\":{\"253\":1}}],[\"类的实例是被共享的\",{\"1\":{\"253\":1}}],[\"类的实例\",{\"1\":{\"173\":1,\"253\":1,\"324\":1,\"356\":1}}],[\"类的实例时\",{\"1\":{\"173\":1}}],[\"类的实例生成时\",{\"1\":{\"173\":1}}],[\"类的实现层次结构\",{\"1\":{\"157\":1,\"162\":1,\"164\":2,\"172\":3}}],[\"类的\",{\"1\":{\"164\":1,\"222\":1,\"253\":1,\"283\":1,\"352\":2,\"353\":1,\"354\":1,\"356\":1}}],[\"类的具体功能的实例\",{\"1\":{\"164\":1}}],[\"类的一览表\",{\"0\":{\"164\":1}}],[\"类的抽象方法时\",{\"1\":{\"161\":1}}],[\"类的子类中都实现这个方法\",{\"1\":{\"387\":1}}],[\"类的子类产生影响\",{\"1\":{\"185\":1}}],[\"类的子类\",{\"1\":{\"160\":1,\"221\":1}}],[\"类的功能层次结构\",{\"1\":{\"157\":1,\"162\":1,\"164\":4,\"172\":4}}],[\"类的设计原则有七个\",{\"1\":{\"113\":1}}],[\"类的多项式题目\",{\"1\":{\"41\":1}}],[\"方法本身有一定的要求\",{\"1\":{\"443\":1}}],[\"方法是为每个产生式\",{\"1\":{\"443\":1}}],[\"方法需要调用每个目录条目的\",{\"1\":{\"388\":1}}],[\"方法就会明白了\",{\"1\":{\"356\":1}}],[\"方法就使用了\",{\"1\":{\"353\":1}}],[\"方法传递\",{\"1\":{\"356\":2}}],[\"方法之间的关系\",{\"1\":{\"352\":1}}],[\"方法和\",{\"1\":{\"352\":1}}],[\"方法的调用方式如下\",{\"1\":{\"383\":2}}],[\"方法的调用顺序\",{\"1\":{\"307\":1}}],[\"方法的参数类型是\",{\"1\":{\"356\":2}}],[\"方法的线程安全性\",{\"1\":{\"343\":1}}],[\"方法而导致应用程序不能正常工作\",{\"1\":{\"307\":1}}],[\"方法后调用\",{\"1\":{\"307\":1}}],[\"方法会先被调用\",{\"1\":{\"307\":1}}],[\"方法中与函数定义相关的内容\",{\"1\":{\"461\":1}}],[\"方法中会用到的方法也都是在\",{\"1\":{\"356\":2}}],[\"方法中和\",{\"1\":{\"356\":1}}],[\"方法中的\",{\"1\":{\"356\":1}}],[\"方法中\",{\"1\":{\"307\":1,\"352\":1,\"356\":1}}],[\"方法中发生了\",{\"1\":{\"283\":1}}],[\"方法集中处理了所有消息的发布和订阅逻辑\",{\"1\":{\"283\":1}}],[\"方法稍微有些复杂\",{\"1\":{\"283\":1}}],[\"方法也调用了\",{\"1\":{\"222\":1}}],[\"方法调用了\",{\"1\":{\"222\":1}}],[\"方法\",{\"1\":{\"143\":1,\"164\":1,\"221\":1,\"273\":2,\"324\":1,\"342\":1,\"352\":3,\"353\":1,\"355\":1,\"387\":1,\"388\":2}}],[\"零件\",{\"1\":{\"143\":1}}],[\"包中\",{\"1\":{\"143\":1}}],[\"包中增加一个表示图像的\",{\"1\":{\"143\":1}}],[\"包中的抽象部分全部具体化即可\",{\"1\":{\"142\":1}}],[\"包括变量定义\",{\"1\":{\"453\":1}}],[\"包括\",{\"1\":{\"113\":1}}],[\"包括编程\",{\"1\":{\"37\":1}}],[\"容器与内容的一致性\",{\"2\":{\"215\":1,\"231\":1}}],[\"容器目录\",{\"0\":{\"34\":1}}],[\"容易\",{\"1\":{\"142\":1}}],[\"模型\",{\"1\":{\"311\":1}}],[\"模式提高了\",{\"1\":{\"384\":1}}],[\"模式编写象棋程序时\",{\"1\":{\"365\":1}}],[\"模式却特意将算法与其他部分分离开来\",{\"1\":{\"365\":1}}],[\"模式以及接口与类之间的关系\",{\"1\":{\"352\":1}}],[\"模式用类表示系统的\",{\"1\":{\"351\":1}}],[\"模式用于为某对象提供一个代理\",{\"1\":{\"323\":1}}],[\"模式确保一个类只有一个实例\",{\"1\":{\"337\":1}}],[\"模式是一种创建型设计模式\",{\"1\":{\"316\":1}}],[\"模式是一种结构型设计模式\",{\"1\":{\"249\":1}}],[\"模式来管理\",{\"1\":{\"291\":1}}],[\"模式来处理一系列的请求\",{\"1\":{\"190\":1}}],[\"模式了\",{\"1\":{\"284\":1}}],[\"模式共享实例可以减少使用\",{\"1\":{\"256\":1}}],[\"模式共享信息时必须仔细思考应当共享哪些信息\",{\"1\":{\"253\":1}}],[\"模式时\",{\"1\":{\"255\":1,\"351\":1}}],[\"模式非常有用\",{\"1\":{\"249\":1}}],[\"模式有以下几个好处\",{\"1\":{\"243\":1}}],[\"模式有以下几个优点\",{\"1\":{\"189\":1}}],[\"模式就是可以应对这种多功能对象的需求的一种模式\",{\"1\":{\"224\":1}}],[\"模式可以很容易地增加\",{\"1\":{\"386\":1,\"387\":1}}],[\"模式可以避免大量的条件语句\",{\"1\":{\"347\":1}}],[\"模式可以\",{\"1\":{\"316\":1}}],[\"模式可以显著减少内存消耗\",{\"1\":{\"249\":1}}],[\"模式可以为程序添加许多功能\",{\"1\":{\"224\":1}}],[\"模式可以将构建过程分解为多个步骤\",{\"1\":{\"178\":1}}],[\"模式使用了委托\",{\"1\":{\"222\":1}}],[\"模式一样\",{\"1\":{\"221\":1}}],[\"模式虽然与\",{\"1\":{\"221\":1}}],[\"模式允许对象在其内部状态改变时改变其行为\",{\"1\":{\"347\":1}}],[\"模式允许我们在不暴露对象实现细节的情况下保存和恢复对象的状态\",{\"1\":{\"291\":1}}],[\"模式允许你将对象组合成递归结构来表示\",{\"1\":{\"206\":1}}],[\"模式允许使用相同的构建过程来生成不同的对象表示\",{\"1\":{\"178\":1}}],[\"模式也支持可撤销的操作\",{\"1\":{\"196\":1}}],[\"模式将请求封装成对象\",{\"1\":{\"196\":1}}],[\"模式通过将构建过程与表示分离\",{\"1\":{\"184\":1}}],[\"模式通过将对象的构建过程与其表示分离\",{\"1\":{\"178\":1,\"183\":1}}],[\"模式中用到了委托\",{\"1\":{\"223\":1}}],[\"模式中也形成了类似于\",{\"1\":{\"221\":1}}],[\"模式中\",{\"1\":{\"221\":1,\"222\":1,\"242\":1,\"294\":1,\"297\":1,\"351\":1,\"352\":1,\"354\":1,\"378\":1,\"383\":1,\"388\":1}}],[\"模式中的方法调用关系\",{\"1\":{\"383\":1}}],[\"模式中的递归结构\",{\"1\":{\"221\":1}}],[\"模式中的\",{\"1\":{\"172\":1,\"352\":1}}],[\"模式中增加其他\",{\"1\":{\"355\":1}}],[\"模式中增加新的状态是非常简单的\",{\"1\":{\"355\":1}}],[\"模式中增加新的零件时应当如何做\",{\"1\":{\"143\":1}}],[\"模式中增加具体的工厂是非常容易的\",{\"1\":{\"142\":1}}],[\"模式的目的是将处理逻辑从数据结构中分离出来\",{\"1\":{\"384\":1}}],[\"模式的示例程序\",{\"1\":{\"362\":1}}],[\"模式的优势就会非常明显了\",{\"1\":{\"351\":1}}],[\"模式的实现需要特别注意线程安全问题\",{\"1\":{\"342\":1}}],[\"模式的主题是\",{\"1\":{\"253\":1}}],[\"模式的主要目的是为了定义一个算法的骨架\",{\"1\":{\"370\":1}}],[\"模式的主要目的是在不破坏封装性的前提下\",{\"1\":{\"290\":1}}],[\"模式的主要目的是通过添加装饰物来增加对象的功能\",{\"1\":{\"221\":1}}],[\"模式的主要目的是将抽象部分与实现部分分离\",{\"1\":{\"158\":1}}],[\"模式的一个缺点是会导致程序中增加许多功能类似的很小的类\",{\"1\":{\"225\":1}}],[\"模式的特征是将\",{\"1\":{\"172\":1}}],[\"模式的作用就是搭建这座桥梁\",{\"1\":{\"162\":1}}],[\"模式在\",{\"1\":{\"157\":1}}],[\"模式\",{\"0\":{\"157\":1,\"177\":1,\"178\":1,\"188\":1,\"195\":1,\"205\":1,\"216\":1,\"235\":1,\"242\":1,\"248\":1,\"249\":1,\"263\":1,\"278\":1,\"289\":1,\"290\":1,\"301\":1,\"315\":1,\"316\":1,\"322\":1,\"332\":1,\"336\":1,\"337\":1,\"346\":1,\"347\":1,\"360\":1,\"370\":1,\"371\":1,\"378\":1,\"379\":1},\"1\":{\"144\":4,\"161\":1,\"174\":3,\"181\":4,\"188\":1,\"192\":2,\"202\":3,\"206\":1,\"213\":3,\"226\":2,\"239\":3,\"243\":1,\"257\":3,\"275\":3,\"286\":2,\"298\":3,\"312\":1,\"319\":5,\"333\":2,\"337\":1,\"341\":4,\"353\":2,\"354\":1,\"355\":2,\"357\":2,\"365\":1,\"366\":1,\"367\":3,\"374\":2,\"389\":3}}],[\"模块化设计\",{\"1\":{\"125\":1}}],[\"拓展思路的要点\",{\"0\":{\"141\":1,\"171\":1,\"182\":1,\"199\":1,\"220\":1,\"252\":1,\"282\":1,\"293\":1,\"305\":1,\"326\":1,\"350\":1,\"364\":1,\"382\":1}}],[\"划分\",{\"0\":{\"297\":1},\"1\":{\"140\":1}}],[\"超链接集合的文件\",{\"1\":{\"140\":1}}],[\"<unit>\",{\"1\":{\"498\":2}}],[\"<ul>\",{\"1\":{\"139\":5,\"179\":1}}],[\"<false\",{\"1\":{\"473\":2}}],[\"<factor>11\",{\"1\":{\"442\":1}}],[\"<factor>3\",{\"1\":{\"442\":1}}],[\"<factor><factor>\",{\"1\":{\"441\":1}}],[\"<factor>\",{\"1\":{\"441\":2,\"442\":2,\"443\":2,\"444\":3}}],[\"<true\",{\"1\":{\"473\":2}}],[\"<term\",{\"1\":{\"444\":3}}],[\"<term>7\",{\"1\":{\"442\":1}}],[\"<term>或\",{\"1\":{\"441\":1}}],[\"<term><term>\",{\"1\":{\"441\":1}}],[\"<term>\",{\"1\":{\"441\":6,\"442\":2,\"443\":2,\"444\":3}}],[\"<cond>\",{\"1\":{\"473\":3,\"474\":2}}],[\"<command>\",{\"1\":{\"265\":6}}],[\"<command\",{\"1\":{\"265\":8}}],[\"<empty\",{\"1\":{\"472\":1}}],[\"<empty><factor>\",{\"1\":{\"444\":1}}],[\"<empty><term>\",{\"1\":{\"444\":1}}],[\"<expr2>normal\",{\"1\":{\"498\":1}}],[\"<expr2>\",{\"1\":{\"497\":4,\"498\":6}}],[\"<expr1>push\",{\"1\":{\"498\":1}}],[\"<expr1>\",{\"1\":{\"497\":4,\"498\":4}}],[\"<expr\",{\"1\":{\"444\":3}}],[\"<expr>2\",{\"1\":{\"442\":1}}],[\"<expr>\",{\"1\":{\"441\":7,\"442\":4,\"443\":2,\"444\":2,\"490\":1,\"491\":1}}],[\"<>\",{\"1\":{\"441\":1}}],[\"<offset>\",{\"1\":{\"416\":1}}],[\"<size>\",{\"1\":{\"413\":1,\"414\":2}}],[\"<statement>\",{\"1\":{\"472\":4,\"473\":2,\"474\":2,\"476\":1}}],[\"<string\",{\"1\":{\"402\":1}}],[\"<stdlib\",{\"1\":{\"402\":1,\"445\":1}}],[\"<stdio\",{\"1\":{\"402\":1,\"428\":1,\"445\":1}}],[\"<num>\",{\"1\":{\"408\":2}}],[\"<number>\",{\"1\":{\"265\":3}}],[\"<memory\",{\"1\":{\"402\":1}}],[\"<<\",{\"1\":{\"372\":1,\"373\":1,\"417\":1,\"433\":1,\"498\":1}}],[\"<=\",{\"1\":{\"348\":2,\"402\":1,\"417\":1,\"429\":5,\"430\":6,\"433\":1,\"434\":2,\"445\":2}}],[\"<left>\",{\"1\":{\"265\":1}}],[\"<li><a\",{\"1\":{\"139\":5}}],[\"<li>\",{\"1\":{\"139\":4}}],[\"<right>\",{\"1\":{\"265\":1}}],[\"<repeat\",{\"1\":{\"265\":6}}],[\"<go>\",{\"1\":{\"265\":1}}],[\"<product>object\",{\"1\":{\"317\":1}}],[\"<program>\",{\"1\":{\"265\":3}}],[\"<primitive\",{\"1\":{\"265\":6}}],[\"<p>メール待っていますね\",{\"1\":{\"238\":1}}],[\"<p>hiroshi\",{\"1\":{\"238\":1}}],[\"<addr>pushsc\",{\"1\":{\"495\":1}}],[\"<addr>lc\",{\"1\":{\"495\":1}}],[\"<addr>li\",{\"1\":{\"489\":1}}],[\"<addr>\",{\"1\":{\"410\":3,\"412\":2,\"486\":1,\"488\":1}}],[\"<a\",{\"1\":{\"238\":1}}],[\"<h1>welcome\",{\"1\":{\"238\":1}}],[\"<h1>linkpage<\",{\"1\":{\"139\":1}}],[\"<html><head><title>问候<\",{\"1\":{\"180\":1}}],[\"<html><head><title>linkpage<\",{\"1\":{\"139\":1}}],[\"<hr><address>gmw<\",{\"1\":{\"139\":1}}],[\"<body>\",{\"1\":{\"139\":1}}],[\"<\",{\"1\":{\"139\":14,\"165\":1,\"169\":1,\"179\":6,\"180\":5,\"190\":2,\"197\":1,\"218\":2,\"237\":5,\"238\":5,\"265\":1,\"272\":1,\"291\":2,\"303\":2,\"324\":1,\"348\":4,\"362\":4,\"372\":2,\"380\":1,\"402\":1,\"416\":1,\"417\":1,\"433\":3,\"463\":1,\"498\":3,\"500\":1}}],[\"扩展性强\",{\"1\":{\"243\":1}}],[\"扩展性\",{\"1\":{\"138\":1}}],[\"扩展其功能\",{\"1\":{\"115\":1}}],[\"解决了优先级的问题\",{\"1\":{\"494\":1}}],[\"解决方法\",{\"1\":{\"419\":1}}],[\"解析表达式\",{\"1\":{\"481\":1,\"502\":1}}],[\"解析函数的参数就是解析以逗号分隔的一个个标识符\",{\"1\":{\"465\":1}}],[\"解析函数的定义\",{\"0\":{\"462\":1},\"1\":{\"460\":1}}],[\"解析参数\",{\"0\":{\"465\":1},\"1\":{\"460\":1}}],[\"解析变量的定义\",{\"0\":{\"451\":1},\"1\":{\"449\":1}}],[\"解析为\",{\"1\":{\"425\":3}}],[\"解释器需要我们实现自己的虚拟机与指令集\",{\"1\":{\"400\":1}}],[\"解释器与编译器仅在代码生成阶段有区别\",{\"1\":{\"400\":1}}],[\"解释器\",{\"1\":{\"403\":1,\"405\":1},\"2\":{\"399\":1,\"438\":1,\"448\":1,\"459\":1,\"470\":1,\"480\":1,\"504\":1,\"512\":1}}],[\"解释器模式\",{\"1\":{\"264\":1}}],[\"解释器就自动释放gil锁\",{\"1\":{\"99\":1}}],[\"解耦框架与生成的实例\",{\"1\":{\"316\":1}}],[\"解耦集合和遍历\",{\"1\":{\"270\":1}}],[\"解耦创建和使用\",{\"1\":{\"243\":1}}],[\"解耦请求发送者和接收者\",{\"1\":{\"189\":1}}],[\"解耦\",{\"1\":{\"138\":1}}],[\"抽象条目类\",{\"0\":{\"209\":1}}],[\"抽象类声明了一些抽象方法\",{\"1\":{\"161\":1}}],[\"抽象类\",{\"1\":{\"140\":1,\"185\":1}}],[\"抽象容器\",{\"1\":{\"139\":1}}],[\"抽象html页面\",{\"1\":{\"139\":1}}],[\"抽象超链接\",{\"1\":{\"139\":1}}],[\"抽象零件\",{\"1\":{\"139\":1}}],[\"抽象工厂\",{\"1\":{\"139\":1}}],[\"抽象工厂模式通过将对象的创建过程抽象化\",{\"1\":{\"138\":1}}],[\"抽象工厂模式使得一个类的实例化延迟到其子类\",{\"1\":{\"138\":1}}],[\"抽象工厂模式提供一个接口\",{\"1\":{\"138\":1}}],[\"抽象工厂模式\",{\"0\":{\"137\":1}}],[\"抽象不应该依赖细节\",{\"1\":{\"128\":1}}],[\"优先级大于\",{\"1\":{\"482\":1}}],[\"优先级\",{\"1\":{\"482\":2,\"494\":1}}],[\"优先级关心的就是哪个运算符先计算\",{\"1\":{\"482\":1}}],[\"优先级高于加法\",{\"1\":{\"482\":1}}],[\"优先使用组合\",{\"1\":{\"134\":1}}],[\"优点是这种处理方式将\",{\"1\":{\"353\":1}}],[\"优雅的解决方案\",{\"1\":{\"1\":1}}],[\"聚合\",{\"1\":{\"131\":1,\"134\":1}}],[\"聚合复用原则\",{\"0\":{\"131\":1},\"1\":{\"113\":1,\"114\":1,\"134\":1}}],[\"核心思想是\",{\"1\":{\"128\":1}}],[\"细节应该依赖抽象\",{\"1\":{\"128\":1}}],[\"二是如何将表达式编译成目标代码\",{\"1\":{\"481\":1}}],[\"二是容易中间运算时搞错运算顺序\",{\"1\":{\"43\":1}}],[\"二元运算符\",{\"0\":{\"494\":1},\"1\":{\"481\":1}}],[\"二选一\",{\"1\":{\"419\":1}}],[\"二者都依赖抽象\",{\"1\":{\"134\":1}}],[\"二者都应该依赖其抽象\",{\"1\":{\"128\":1}}],[\"高速但计算上可能有\",{\"1\":{\"366\":1}}],[\"高层模块不依赖低层模块\",{\"1\":{\"134\":1}}],[\"高层模块不应该依赖低层模块\",{\"1\":{\"128\":1}}],[\"高层模块依赖抽象接口\",{\"1\":{\"130\":1}}],[\"高版本\",{\"1\":{\"53\":1}}],[\"显示一些东西\",{\"1\":{\"164\":1}}],[\"显示\",{\"1\":{\"164\":2}}],[\"显示用户信息逻辑\",{\"1\":{\"126\":2}}],[\"显得代码冗长\",{\"1\":{\"44\":1}}],[\"注释\",{\"0\":{\"432\":1},\"1\":{\"421\":1}}],[\"注册逻辑\",{\"1\":{\"126\":2}}],[\"注意这里并不是四则运算中的加减法\",{\"1\":{\"492\":1}}],[\"注意这里的类型\",{\"1\":{\"405\":1}}],[\"注意我们的之前的程序需要指令一个源文件\",{\"1\":{\"419\":1}}],[\"注意的是自增自减操作的优先级是和它的位置有关的\",{\"1\":{\"493\":1}}],[\"注意的是只支持\",{\"1\":{\"485\":1}}],[\"注意的是\",{\"1\":{\"415\":1}}],[\"注意的是pc在初始应指向目标代码中的main函数\",{\"1\":{\"406\":1}}],[\"注意的是由于栈是位于高地址并向低地址增长的\",{\"1\":{\"406\":1}}],[\"注意不要让变量的值之间互相矛盾\",{\"1\":{\"354\":1}}],[\"注意\",{\"1\":{\"95\":1}}],[\"登录逻辑\",{\"1\":{\"126\":2}}],[\"避免重复代码\",{\"1\":{\"371\":1}}],[\"避免重复初始化对象的复杂过程\",{\"1\":{\"316\":1}}],[\"避免处理过于集中\",{\"1\":{\"283\":1}}],[\"避免浪费\",{\"2\":{\"259\":1,\"335\":1}}],[\"避免高层模块直接依赖具体类\",{\"1\":{\"129\":1}}],[\"避免不必要的外部依赖\",{\"1\":{\"123\":1}}],[\"避免了多线程的上下文切换\",{\"1\":{\"100\":1}}],[\"限制公开方法\",{\"1\":{\"123\":1}}],[\"隐藏系统的复杂性\",{\"1\":{\"123\":1}}],[\"示例程序的前提是\",{\"1\":{\"324\":1}}],[\"示例程序中的\",{\"1\":{\"283\":1}}],[\"示例程序\",{\"0\":{\"152\":1,\"362\":1},\"1\":{\"151\":1}}],[\"示例代码\",{\"0\":{\"139\":1,\"163\":1,\"190\":1,\"197\":1,\"207\":1,\"236\":1,\"244\":1,\"265\":1,\"280\":1,\"291\":1,\"303\":1,\"317\":1,\"339\":1,\"348\":1,\"372\":1,\"380\":1}}],[\"示例\",{\"0\":{\"120\":1,\"126\":1,\"130\":1,\"133\":1}}],[\"返回类型应与父类相同或是其子类型\",{\"1\":{\"119\":1}}],[\"遵循开闭原则\",{\"1\":{\"217\":1}}],[\"遵循行为一致性\",{\"1\":{\"119\":1}}],[\"遵循契约\",{\"1\":{\"119\":1}}],[\"遵循单一职责原则\",{\"1\":{\"116\":1}}],[\"确保同一工厂创建的一系列对象具有一致的接口和行为\",{\"1\":{\"138\":1}}],[\"确保每个模块只负责一个功能\",{\"1\":{\"125\":1}}],[\"确保每个类只有一个职责\",{\"1\":{\"116\":1}}],[\"确保子类实现父类的抽象方法\",{\"1\":{\"119\":1}}],[\"通用寄存器\",{\"1\":{\"406\":1}}],[\"通信线路的增加\",{\"0\":{\"284\":1}}],[\"通常是站在子类的角度进行思考的\",{\"1\":{\"375\":1}}],[\"通常在编程时算法会被写在具体方法中\",{\"1\":{\"365\":1}}],[\"通常会有两种接口\",{\"1\":{\"294\":1}}],[\"通常情况下\",{\"1\":{\"283\":1}}],[\"通常\",{\"1\":{\"114\":1,\"307\":2,\"384\":1}}],[\"通过一步步的学习\",{\"1\":{\"502\":1}}],[\"通过一个有趣的代码示例\",{\"1\":{\"107\":1}}],[\"通过本章的学习\",{\"1\":{\"436\":1}}],[\"通过词法分析器的预处理\",{\"1\":{\"422\":1}}],[\"通过教程来说明这个过程\",{\"1\":{\"395\":1}}],[\"通过代理对象来延迟实际对象的创建\",{\"1\":{\"327\":1}}],[\"通过保存多个\",{\"1\":{\"297\":1}}],[\"通过这些不同类型的代理模式\",{\"1\":{\"332\":1}}],[\"通过这些类和接口\",{\"1\":{\"273\":1}}],[\"通过这种划分\",{\"1\":{\"297\":1}}],[\"通过这种方式\",{\"1\":{\"294\":1,\"370\":1}}],[\"通过实现统一的迭代器接口\",{\"1\":{\"270\":1}}],[\"通过定义文法规则\",{\"1\":{\"264\":1}}],[\"通过定义抽象类和接口\",{\"1\":{\"116\":1}}],[\"通过引用计数来管理共享对象的生命周期\",{\"1\":{\"255\":1}}],[\"通过引入外观类\",{\"1\":{\"235\":1}}],[\"通过共享对象\",{\"1\":{\"249\":1}}],[\"通过使用策略模式\",{\"1\":{\"361\":1}}],[\"通过使用观察者模式\",{\"1\":{\"302\":1,\"311\":1}}],[\"通过使用迭代器模式\",{\"1\":{\"270\":1}}],[\"通过使用\",{\"1\":{\"243\":1}}],[\"通过使用装饰器模式\",{\"1\":{\"217\":1}}],[\"通过学习和应用设计模式\",{\"1\":{\"232\":1}}],[\"通过将\",{\"1\":{\"297\":1,\"408\":1}}],[\"通过将不同的语法规则封装在不同的类中\",{\"1\":{\"264\":1}}],[\"通过将每个执行的命令对象保存到一个历史记录列表中\",{\"1\":{\"201\":1}}],[\"通过将这些信息封装在命令对象中\",{\"1\":{\"200\":1}}],[\"通过将构建过程封装在\",{\"1\":{\"178\":1}}],[\"通过接口和抽象类定义行为\",{\"1\":{\"132\":1}}],[\"通过在类中引用其他类的实例来实现功能\",{\"1\":{\"132\":1}}],[\"通过在类中包含其他类的实例来实现功能\",{\"1\":{\"132\":1}}],[\"通过构造函数注入\",{\"1\":{\"129\":1}}],[\"通过模块化设计\",{\"1\":{\"125\":1}}],[\"通过门面对象提供统一的接口\",{\"1\":{\"123\":1}}],[\"通过中介者对象来管理对象之间的交互\",{\"1\":{\"123\":1}}],[\"通过举反例的方式\",{\"1\":{\"82\":1}}],[\"通过上述步骤\",{\"1\":{\"82\":1,\"111\":1}}],[\"通过该服务\",{\"1\":{\"31\":1}}],[\"通过\",{\"1\":{\"31\":1,\"256\":1,\"337\":1,\"501\":1}}],[\"违反其中一个原则\",{\"1\":{\"114\":1}}],[\"七大原则之间并不是相互孤立的\",{\"1\":{\"114\":1}}],[\"单元运算符往往没有这个问题\",{\"1\":{\"482\":1}}],[\"单一职责原则\",{\"0\":{\"124\":1},\"1\":{\"113\":1,\"114\":1,\"134\":1}}],[\"单核处理器还是同时间只能做一件事\",{\"1\":{\"100\":1}}],[\"单核处理器本来就没法同时处理两件事情\",{\"1\":{\"98\":1}}],[\"单核同时间内只能有一个线程运行\",{\"1\":{\"98\":1}}],[\"迪米特原则\",{\"0\":{\"121\":1,\"122\":1},\"1\":{\"113\":1,\"114\":1,\"134\":1}}],[\"里氏代换原则规定子类不得重写父类的普通方法\",{\"1\":{\"118\":1}}],[\"里氏代换原则\",{\"0\":{\"117\":1,\"118\":1},\"1\":{\"113\":1,\"114\":1,\"134\":1}}],[\"开始的冲动过了之后\",{\"1\":{\"509\":1}}],[\"开头\",{\"1\":{\"428\":1}}],[\"开闭原则是面向对象可复用设计的基石\",{\"1\":{\"114\":1}}],[\"开闭原则\",{\"0\":{\"115\":1,\"385\":1},\"1\":{\"113\":1,\"114\":1,\"134\":1}}],[\"开发过程将会变得非常困难\",{\"1\":{\"385\":1}}],[\"开发人员可以在编写一个\",{\"1\":{\"351\":1}}],[\"开发团队可以更容易地构建\",{\"1\":{\"31\":1}}],[\"开发者可以方便地将他们的容器镜像与代码仓库关联起来\",{\"1\":{\"31\":1}}],[\"转换成对应的汇编代码\",{\"1\":{\"463\":1}}],[\"转载声明\",{\"0\":{\"403\":1}}],[\"转载工具\",{\"1\":{\"392\":1}}],[\"转给另外一个人\",{\"1\":{\"188\":1}}],[\"转\",{\"0\":{\"112\":1}}],[\"转而使用\",{\"1\":{\"106\":1}}],[\"启动\",{\"1\":{\"111\":1}}],[\"启动项目\",{\"0\":{\"19\":1}}],[\"等工具\",{\"1\":{\"508\":1}}],[\"等工具来编写\",{\"1\":{\"397\":1}}],[\"等指令\",{\"1\":{\"408\":1}}],[\"等\",{\"1\":{\"397\":1,\"425\":1,\"429\":1,\"431\":1,\"434\":1}}],[\"等等知识\",{\"1\":{\"507\":1}}],[\"等等\",{\"1\":{\"394\":1,\"425\":1,\"486\":1}}],[\"等待显示序列号\",{\"1\":{\"111\":1}}],[\"等待提示\",{\"1\":{\"111\":1}}],[\"等函数\",{\"1\":{\"45\":1}}],[\"复杂对象的创建\",{\"1\":{\"178\":1}}],[\"复杂演示推荐\",{\"1\":{\"104\":1}}],[\"复制到\",{\"1\":{\"111\":1}}],[\"密码\",{\"1\":{\"111\":1}}],[\"百度网盘\",{\"1\":{\"111\":1}}],[\"官网\",{\"1\":{\"111\":1}}],[\"适用于需要保存复杂对象状态的场景\",{\"1\":{\"201\":1}}],[\"适用于需要按顺序执行和撤销命令的场景\",{\"1\":{\"201\":1}}],[\"适用于编写笔记\",{\"1\":{\"111\":1}}],[\"适配器\",{\"1\":{\"151\":1}}],[\"适配器模式通过创建一个适配器类\",{\"1\":{\"149\":1}}],[\"适配器模式使得原本由于接口不兼容而不能一起工作的那些类可以一起工作\",{\"1\":{\"148\":1}}],[\"适配器模式\",{\"0\":{\"147\":1,\"148\":1},\"1\":{\"148\":1}}],[\"适合快速迭代和原型验证\",{\"1\":{\"53\":1}}],[\"教程源码示例\",{\"1\":{\"232\":1,\"260\":1}}],[\"教程\",{\"0\":{\"110\":1}}],[\"准备好了吗\",{\"1\":{\"107\":1}}],[\"展示如何用闭包来实现这一点\",{\"1\":{\"107\":1}}],[\"你也可以学习看看\",{\"1\":{\"508\":1}}],[\"你可能有疑问\",{\"1\":{\"486\":1}}],[\"你可能会觉得将一个指令变成了许多指令\",{\"1\":{\"408\":1}}],[\"你就会发现\",{\"1\":{\"423\":1}}],[\"你就能写出更加高效的代码\",{\"1\":{\"393\":1}}],[\"你能对计算机程序的原理有一定的了解\",{\"1\":{\"420\":1}}],[\"你好\",{\"1\":{\"324\":1,\"325\":1,\"372\":1}}],[\"你将看到闭包是如何捕获变量并提供类似类的功能的\",{\"1\":{\"107\":1}}],[\"你是否曾经想过\",{\"1\":{\"107\":1}}],[\"你需要将这些更改复制到你的原生项目中\",{\"1\":{\"95\":1}}],[\"页面\",{\"1\":{\"106\":1}}],[\"预览功能\",{\"1\":{\"106\":1}}],[\"卸载\",{\"1\":{\"106\":1}}],[\"禁用\",{\"1\":{\"106\":1}}],[\"渲染插件\",{\"1\":{\"106\":1}}],[\"⚠️注意事项\",{\"1\":{\"106\":1}}],[\"缺点是\",{\"1\":{\"353\":1}}],[\"缺点\",{\"0\":{\"105\":1,\"106\":1}}],[\"文法\",{\"1\":{\"508\":1}}],[\"文法的关系\",{\"1\":{\"508\":1}}],[\"文法如下\",{\"1\":{\"265\":1}}],[\"文章\",{\"1\":{\"397\":1}}],[\"文件描述符\",{\"1\":{\"256\":1}}],[\"文件句柄\",{\"1\":{\"256\":1}}],[\"文件类\",{\"0\":{\"210\":1}}],[\"文件\",{\"1\":{\"111\":1}}],[\"文件来实现风格统一\",{\"1\":{\"52\":1}}],[\"文档和博客等\",{\"1\":{\"111\":1}}],[\"文档\",{\"1\":{\"103\":1}}],[\"脱离具体场景孤立存在的\",{\"1\":{\"102\":1}}],[\"脱离对象孤立存在的\",{\"1\":{\"102\":1}}],[\"抛开场景谈逻辑\",{\"1\":{\"102\":1}}],[\"抛开剂量谈毒性\",{\"1\":{\"102\":1}}],[\"道德不是空泛的\",{\"1\":{\"102\":1}}],[\"只支持枚举\",{\"1\":{\"453\":1}}],[\"只支持\",{\"1\":{\"432\":1}}],[\"只能说它是一个相当大的挑战吧\",{\"1\":{\"393\":1}}],[\"只能重写父类的抽象方法\",{\"1\":{\"118\":1}}],[\"只是在编写代码的过程中\",{\"1\":{\"509\":1}}],[\"只是在实现\",{\"1\":{\"493\":1}}],[\"只是这时就是提前看k个\",{\"1\":{\"432\":1}}],[\"只是现在还用不着\",{\"1\":{\"419\":1}}],[\"只是现在用\",{\"1\":{\"416\":1}}],[\"只是我们的指令集中并没有\",{\"1\":{\"415\":1}}],[\"只是它们的功能都过于强大\",{\"1\":{\"401\":1}}],[\"只是对于一般的学生或程序员来说\",{\"1\":{\"394\":1}}],[\"只是定义了与算法相关的接口\",{\"1\":{\"365\":1}}],[\"只是阅读抽象类的代码是无法获取很多信息的\",{\"1\":{\"185\":1}}],[\"只存在一个实例\",{\"1\":{\"338\":1}}],[\"只要保持各个类的独立性\",{\"1\":{\"307\":1}}],[\"只要准备一些装饰边框\",{\"1\":{\"224\":1}}],[\"只将那些真正应该在多个地方共享的字段定义在\",{\"1\":{\"253\":1}}],[\"只需添加新的访问者类\",{\"1\":{\"379\":1}}],[\"只需添加新的子类工厂\",{\"1\":{\"243\":1}}],[\"只需要阅读\",{\"1\":{\"353\":1}}],[\"只需要依赖抽象产品接口\",{\"1\":{\"243\":1}}],[\"只需要一些装饰物即可添加许多功能\",{\"0\":{\"224\":1}}],[\"只需要在\",{\"1\":{\"172\":1}}],[\"只有身在其中的我们才能体会吧\",{\"1\":{\"510\":1}}],[\"只有当访问者从数据结构中获取了足够多的信息后才能工作\",{\"1\":{\"388\":1}}],[\"只有\",{\"1\":{\"351\":1,\"408\":1}}],[\"只有在实际项目中多次使用\",{\"1\":{\"232\":1}}],[\"只有掌握了辩证的矛盾思维才能更全面更灵活的看待问题\",{\"1\":{\"102\":1}}],[\"只显示规定次数\",{\"1\":{\"164\":1}}],[\"只关注最终结果一致性\",{\"1\":{\"102\":1}}],[\"只不过这个让出的过程是线程调度器主动抢占的\",{\"1\":{\"98\":1}}],[\"没有什么值得说明的内容\",{\"1\":{\"474\":1}}],[\"没有学过编译原理的话可能并不知道什么是\",{\"1\":{\"441\":1}}],[\"没有参数的指令在后\",{\"1\":{\"407\":1}}],[\"没有主动放弃执行权\",{\"1\":{\"102\":1}}],[\"没锁的话\",{\"1\":{\"99\":1}}],[\"还有就是写这个系列的文章\",{\"1\":{\"509\":1}}],[\"还有就是调试编译器\",{\"1\":{\"509\":1}}],[\"还有两个重要函数没有完成\",{\"1\":{\"467\":1}}],[\"还剩最后一部分没有完成\",{\"1\":{\"477\":1}}],[\"还记得前面说的标识符\",{\"1\":{\"434\":1}}],[\"还要考虑如何传递参数和如何返回结果\",{\"1\":{\"412\":1}}],[\"还没仔细了解过\",{\"1\":{\"397\":1}}],[\"还可以用某种算法去\",{\"1\":{\"366\":1}}],[\"还可以不用\",{\"1\":{\"353\":1}}],[\"还可以将现在的状态保存在文件中\",{\"1\":{\"297\":1}}],[\"还会使得调试和维护变得更加困难\",{\"1\":{\"283\":1}}],[\"还想变量安全\",{\"1\":{\"101\":1}}],[\"还是实现起来\",{\"1\":{\"508\":1}}],[\"还是函数的局部变量\",{\"1\":{\"463\":1}}],[\"还是需要仔细一点的\",{\"1\":{\"355\":1}}],[\"还是咖啡朗姆和开心果的混合口味\",{\"1\":{\"224\":1}}],[\"还是要增加实现呢\",{\"1\":{\"162\":1}}],[\"还是过程中\",{\"1\":{\"101\":1}}],[\"还是只能加锁\",{\"1\":{\"101\":1}}],[\"还是只能一个人打电话\",{\"1\":{\"99\":1}}],[\"还是最后执行结果\",{\"1\":{\"101\":1}}],[\"话说回来\",{\"1\":{\"101\":1}}],[\"切换过程是协作的\",{\"1\":{\"101\":1}}],[\"连最终一致性也无法保证\",{\"1\":{\"101\":1}}],[\"意味着协程操作变量的最终一致性是可以保证的\",{\"1\":{\"101\":1}}],[\"混乱状态\",{\"1\":{\"101\":1}}],[\"状况发生改变时会变化的信息\",{\"1\":{\"254\":1}}],[\"状态机\",{\"1\":{\"507\":1}}],[\"状态迁移\",{\"1\":{\"353\":1}}],[\"状态不同处理也不同\",{\"1\":{\"352\":1}}],[\"状态越多\",{\"1\":{\"351\":1}}],[\"状态\",{\"1\":{\"200\":1,\"351\":1}}],[\"状态一致\",{\"1\":{\"101\":1}}],[\"状自然数系统\",{\"1\":{\"89\":1}}],[\"925\",{\"1\":{\"292\":4}}],[\"98\",{\"1\":{\"292\":1,\"394\":1}}],[\"97\",{\"1\":{\"292\":1}}],[\"900\",{\"1\":{\"212\":1,\"381\":1}}],[\"998\",{\"1\":{\"422\":3}}],[\"998244353>\",{\"1\":{\"45\":3}}],[\"998244353\",{\"1\":{\"41\":1}}],[\"9999\",{\"1\":{\"363\":1}}],[\"9998\",{\"1\":{\"363\":1}}],[\"9997\",{\"1\":{\"363\":1}}],[\"9994\",{\"1\":{\"363\":1}}],[\"9992\",{\"1\":{\"363\":1}}],[\"9991\",{\"1\":{\"363\":1}}],[\"99\",{\"1\":{\"191\":1,\"292\":1}}],[\"9\",{\"0\":{\"505\":1},\"1\":{\"101\":1,\"164\":1,\"198\":2,\"250\":1,\"348\":2,\"392\":1,\"400\":1,\"403\":2,\"421\":2,\"429\":1,\"430\":6,\"439\":1,\"445\":2,\"449\":1,\"460\":1,\"471\":1,\"481\":2,\"505\":2}}],[\"再将\",{\"1\":{\"499\":1}}],[\"再赋上局部变量相关的信息\",{\"1\":{\"465\":1}}],[\"再例如\",{\"1\":{\"422\":1}}],[\"再见\",{\"1\":{\"179\":1,\"180\":1}}],[\"再也没有异步的加持了\",{\"1\":{\"101\":1}}],[\"再进行减法运算\",{\"1\":{\"101\":1}}],[\"再根据\",{\"1\":{\"59\":1,\"60\":1,\"75\":1,\"76\":1}}],[\"逻辑运算符\",{\"0\":{\"497\":1},\"1\":{\"481\":1}}],[\"逻辑取反\",{\"0\":{\"490\":1},\"1\":{\"481\":1}}],[\"逻辑也较为直接\",{\"1\":{\"430\":1}}],[\"逻辑有了些许修改\",{\"1\":{\"101\":1}}],[\"逻辑紧凑\",{\"1\":{\"100\":1}}],[\"让它实现\",{\"1\":{\"355\":1}}],[\"让它干一些\",{\"1\":{\"324\":1}}],[\"让高层模块依赖这些抽象\",{\"1\":{\"129\":1}}],[\"让我们继续讲解如何把运算符编译成汇编代码吧\",{\"1\":{\"494\":1}}],[\"让我们继续之前的逻辑\",{\"1\":{\"101\":1}}],[\"让我们稍微改变一下立场\",{\"1\":{\"375\":1}}],[\"让我们简单地举个例子\",{\"1\":{\"253\":1}}],[\"让我们再回顾一下示例程序\",{\"1\":{\"185\":1}}],[\"让我们开始这段有趣的旅程吧\",{\"1\":{\"107\":1}}],[\"让我们来看一下代码运行结果\",{\"1\":{\"101\":1}}],[\"让别的协程运行\",{\"1\":{\"101\":1}}],[\"让别的线程有机会执行\",{\"1\":{\"99\":1}}],[\"让出了使用权\",{\"1\":{\"101\":1}}],[\"又可能会导致软件产品的质量降低\",{\"1\":{\"385\":1}}],[\"又访问\",{\"1\":{\"383\":1}}],[\"又想多协程\",{\"1\":{\"101\":1}}],[\"又要共享状态\",{\"1\":{\"101\":1}}],[\"又或者别的协程任务也\",{\"1\":{\"101\":1}}],[\"又不确定性\",{\"1\":{\"99\":1}}],[\"随后立刻切换回来\",{\"1\":{\"101\":1}}],[\"随后当我们让出使用权1秒之后\",{\"1\":{\"101\":1}}],[\"随笔\",{\"0\":{\"2\":1}}],[\"别的协程就可以进行执行\",{\"1\":{\"101\":1}}],[\"别的线程表一定不能改\",{\"1\":{\"99\":1}}],[\"暂时\",{\"1\":{\"101\":1}}],[\"关于编代码\",{\"0\":{\"509\":1},\"1\":{\"505\":1}}],[\"关于变量\",{\"1\":{\"486\":1}}],[\"关于表达式的解析\",{\"1\":{\"483\":1}}],[\"关于这个问题\",{\"1\":{\"253\":1}}],[\"关于这一点\",{\"1\":{\"253\":1}}],[\"关键是判断\",{\"1\":{\"488\":1}}],[\"关键就是去理解汇编代码的执行原理\",{\"1\":{\"478\":1}}],[\"关键字与内置函数\",{\"0\":{\"434\":1},\"1\":{\"421\":1}}],[\"关键字生成实例的次数\",{\"1\":{\"256\":1}}],[\"关键字生成实例会花费时间\",{\"1\":{\"256\":1}}],[\"关键字\",{\"1\":{\"101\":1,\"434\":1}}],[\"关系\",{\"0\":{\"114\":1}}],[\"关闭vscode\",{\"1\":{\"54\":1}}],[\"那诸如\",{\"1\":{\"486\":1}}],[\"那意味着也支持指针的指针\",{\"1\":{\"453\":1}}],[\"那就不行了\",{\"1\":{\"385\":1}}],[\"那就不需要加锁\",{\"1\":{\"102\":1}}],[\"那就意味着大家完全理解了\",{\"1\":{\"352\":1}}],[\"那就是\",{\"1\":{\"388\":1,\"434\":1}}],[\"那就是最大的道德\",{\"1\":{\"102\":1}}],[\"那就是任务又回到了线性同步执行\",{\"1\":{\"101\":1}}],[\"那就是代码中没有\",{\"1\":{\"101\":1}}],[\"那到底怎么主动让出使用权\",{\"1\":{\"101\":1}}],[\"那么对变量\",{\"1\":{\"489\":1}}],[\"那么如何确定运算符的优先级呢\",{\"1\":{\"482\":1}}],[\"那么外层的\",{\"1\":{\"464\":1}}],[\"那么它应该被转换成什么样的汇编代码呢\",{\"1\":{\"463\":1}}],[\"那么我们如何表示指针类型呢\",{\"1\":{\"453\":1}}],[\"那么我们怎么表示标识符呢\",{\"1\":{\"429\":1}}],[\"那么我们就可以用\",{\"1\":{\"172\":1}}],[\"那么参数的传递呢\",{\"1\":{\"412\":1}}],[\"那么你会发现\",{\"1\":{\"394\":1}}],[\"那么为什么要学习编译原理呢\",{\"1\":{\"393\":1}}],[\"那么在看到这条设计原则后\",{\"1\":{\"385\":1}}],[\"那么每次要扩展功能\",{\"1\":{\"384\":1}}],[\"那么下一局也出一样的手势\",{\"1\":{\"362\":1}}],[\"那么这个\",{\"1\":{\"356\":1}}],[\"那么这些分散的类最终只会导致灾难\",{\"1\":{\"283\":1}}],[\"那么增加新的状态时会怎样呢\",{\"1\":{\"355\":1}}],[\"那么编译器在编译代码时就会报错\",{\"1\":{\"355\":1}}],[\"那么程序结构会变得非常复杂\",{\"1\":{\"284\":1}}],[\"那么通信线路有两条\",{\"1\":{\"284\":1}}],[\"那么无论是编写代码还是调试代码和修改代码\",{\"1\":{\"283\":1}}],[\"那么两种解决方案到底哪个是正确的呢\",{\"1\":{\"253\":1}}],[\"那么此时\",{\"1\":{\"253\":1}}],[\"那么\",{\"1\":{\"253\":3}}],[\"那么就在返回时保存在\",{\"1\":{\"412\":1}}],[\"那么就会有\",{\"1\":{\"284\":1}}],[\"那么就会对类中调用\",{\"1\":{\"185\":1}}],[\"那么就可以在字符串的四周加上边框\",{\"1\":{\"222\":1}}],[\"那么需要做的就是编写\",{\"1\":{\"142\":1}}],[\"那么协程一定是安全的\",{\"1\":{\"101\":1}}],[\"那么值会是0\",{\"1\":{\"99\":1}}],[\"谁举证\",{\"1\":{\"101\":1}}],[\"谁主张\",{\"1\":{\"101\":1}}],[\"谁知道什么\",{\"0\":{\"183\":1},\"1\":{\"183\":1}}],[\"谁知\",{\"1\":{\"53\":1}}],[\"毫无疑问\",{\"1\":{\"101\":2}}],[\"运行程序\",{\"1\":{\"419\":1}}],[\"运行我们的指令集\",{\"1\":{\"403\":1}}],[\"运行结果\",{\"0\":{\"153\":1,\"170\":1,\"180\":1,\"191\":1,\"198\":1,\"212\":1,\"219\":1,\"238\":1,\"245\":1,\"251\":1,\"266\":1,\"273\":1,\"281\":1,\"292\":1,\"304\":1,\"318\":1,\"325\":1,\"340\":1,\"349\":1,\"363\":1,\"373\":1,\"381\":1},\"1\":{\"101\":1}}],[\"运算符出栈\",{\"1\":{\"482\":2}}],[\"运算符运算等等\",{\"1\":{\"481\":1}}],[\"运算符的优先级决定了表达式的运算顺序\",{\"1\":{\"482\":1}}],[\"运算符的优先级\",{\"0\":{\"482\":1},\"1\":{\"481\":1}}],[\"运算符指令\",{\"0\":{\"417\":1},\"1\":{\"403\":1}}],[\"运算更快\",{\"1\":{\"45\":1}}],[\"既然同一时间只能有一个协程任务运行\",{\"1\":{\"101\":1}}],[\"体本身就无缝保持了程序状态\",{\"1\":{\"100\":1}}],[\"闭包实现类\",{\"0\":{\"107\":1}}],[\"闭包\",{\"1\":{\"100\":1}}],[\"比起可怕的\",{\"1\":{\"394\":1}}],[\"比喻\",{\"1\":{\"151\":1}}],[\"比操作系统的抢占式调度所需要的时间代价要小很多\",{\"1\":{\"100\":1}}],[\"比如大量的\",{\"1\":{\"41\":1}}],[\"过滤遍历等\",{\"1\":{\"270\":1}}],[\"过了一段时间\",{\"1\":{\"100\":1}}],[\"过去的做法\",{\"0\":{\"42\":1}}],[\"抢占式的线程就不那么让人愉快了\",{\"1\":{\"99\":1}}],[\"抢占式的线程调度器是非常不错的选择\",{\"1\":{\"99\":1}}],[\"因而灵活性较差\",{\"1\":{\"397\":1}}],[\"因为已经有许多自动生成的工具支持它们\",{\"1\":{\"508\":1}}],[\"因为只有一个参数\",{\"1\":{\"482\":1}}],[\"因为汇编代码是顺序排列的\",{\"1\":{\"473\":1,\"482\":1}}],[\"因为汇编语言就是\",{\"1\":{\"420\":1}}],[\"因为这决定了我们需要从解析中获取什么样的信息\",{\"1\":{\"468\":1}}],[\"因为这决定了在解析时我们需要哪些相关的信息\",{\"1\":{\"463\":1}}],[\"因为这样实现起来就会变得复杂\",{\"1\":{\"412\":1}}],[\"因为还有许多功能没有实现\",{\"1\":{\"456\":1}}],[\"因为它们可以用\",{\"1\":{\"441\":1}}],[\"因为它会尝试运行我们上一章创建的虚拟机\",{\"1\":{\"435\":1}}],[\"因为它可以保证所有的线程都可以被分到时间片不被垃圾代码所拖累\",{\"1\":{\"99\":1}}],[\"因为有特殊的含义\",{\"1\":{\"434\":1}}],[\"因为输入的字符串比较难处理\",{\"1\":{\"423\":1}}],[\"因为像\",{\"1\":{\"417\":1}}],[\"因为我们不在乎出栈的值\",{\"1\":{\"486\":1}}],[\"因为我们需要先对它们进行解析\",{\"1\":{\"483\":1}}],[\"因为我们会在代码段\",{\"1\":{\"405\":1}}],[\"因为我们的编译器并不支持初始化变量\",{\"1\":{\"405\":1}}],[\"因为不关心其中的真正数值\",{\"1\":{\"405\":1}}],[\"因为好多理论根本用不上\",{\"1\":{\"394\":1}}],[\"因为具体的处理被交给\",{\"1\":{\"386\":1}}],[\"因为状态迁移的部分正是与其他\",{\"1\":{\"355\":1}}],[\"因为即使\",{\"1\":{\"283\":1}}],[\"因为共享对象永远不会被回收\",{\"1\":{\"255\":1}}],[\"因为自己难以确定究竟应该在类的哪一个层次结构中去增加子类\",{\"1\":{\"162\":1}}],[\"因为协程是用户态\",{\"1\":{\"101\":1}}],[\"因为线程是系统态切换\",{\"1\":{\"101\":1}}],[\"因此对应的源码如下\",{\"1\":{\"498\":1}}],[\"因此对于需要讲解的运算符\",{\"1\":{\"483\":1}}],[\"因此要有特殊的处理\",{\"1\":{\"498\":1}}],[\"因此将它们放在一起处理\",{\"1\":{\"486\":1}}],[\"因此得到结果\",{\"1\":{\"482\":1}}],[\"因此只凭当前的字符我们并无法确定具体应该解释成哪一个标记\",{\"1\":{\"432\":1}}],[\"因此只要调试该方法就能很容易地找出\",{\"1\":{\"283\":1}}],[\"因此在实现中我们将它作为\",{\"1\":{\"426\":1}}],[\"因此在\",{\"1\":{\"419\":1}}],[\"因此在我们的编译器\",{\"1\":{\"418\":1}}],[\"因此编译编译器时\",{\"1\":{\"418\":1}}],[\"因此计算结束后\",{\"1\":{\"417\":1}}],[\"因此实际中我们将\",{\"1\":{\"412\":1}}],[\"因此我们要做的就是生成类似的汇编代码\",{\"1\":{\"500\":1}}],[\"因此我们要消除左递归\",{\"1\":{\"444\":1}}],[\"因此我们判断它是否与数字\",{\"1\":{\"490\":1}}],[\"因此我们删除相应的指令\",{\"1\":{\"489\":1}}],[\"因此我们可以利用这一点\",{\"1\":{\"420\":1}}],[\"因此我们继续实现新的指令\",{\"1\":{\"418\":1}}],[\"因此我们采用的方法是增加指令集\",{\"1\":{\"412\":1}}],[\"因此我们将\",{\"1\":{\"408\":1}}],[\"因此我们也不需要未初始化数据段\",{\"1\":{\"405\":1}}],[\"因此先不处理\",{\"1\":{\"406\":1}}],[\"因此简单起见\",{\"1\":{\"405\":1}}],[\"因此完全不用修改\",{\"1\":{\"386\":1}}],[\"因此这两个\",{\"1\":{\"356\":1}}],[\"因此需要在性能和功能之间找到一个平衡点\",{\"1\":{\"295\":1}}],[\"因此颜色信息也被共享了\",{\"1\":{\"253\":1}}],[\"因此一个进程可以容纳数量相当可观的协程任务\",{\"1\":{\"100\":1}}],[\"因此假设不成立\",{\"1\":{\"84\":1}}],[\"因此\",{\"1\":{\"43\":1,\"69\":2,\"71\":2,\"72\":1,\"83\":1,\"162\":1,\"223\":1,\"224\":1,\"253\":1,\"254\":3,\"256\":1,\"283\":1,\"285\":1,\"354\":1,\"375\":1,\"385\":1,\"463\":2}}],[\"如变量\",{\"1\":{\"483\":1}}],[\"如在普通的四则运算中\",{\"1\":{\"482\":1}}],[\"如经典的\",{\"1\":{\"443\":1}}],[\"如为什么用\",{\"1\":{\"443\":1}}],[\"如本例需向前查看一个字符\",{\"1\":{\"432\":1}}],[\"如本小节中的注释与除号\",{\"1\":{\"432\":1}}],[\"如标识符是函数\",{\"1\":{\"429\":1}}],[\"如数字\",{\"1\":{\"429\":1}}],[\"如右方括号\",{\"1\":{\"425\":1}}],[\"如只能操作ax寄存器\",{\"1\":{\"412\":1}}],[\"如下\",{\"1\":{\"408\":1,\"412\":1,\"429\":1,\"463\":1}}],[\"如调用帧\",{\"1\":{\"405\":1}}],[\"如int\",{\"1\":{\"405\":1}}],[\"如实现四则运算\",{\"1\":{\"395\":1}}],[\"如有侵权\",{\"1\":{\"392\":1,\"400\":1,\"403\":1,\"421\":1,\"439\":1,\"449\":1,\"460\":1,\"471\":1,\"481\":1,\"505\":1}}],[\"如正向遍历\",{\"1\":{\"270\":1}}],[\"如\",{\"1\":{\"255\":1,\"394\":1,\"395\":1,\"397\":1,\"401\":1,\"405\":1,\"424\":1,\"425\":2,\"428\":1,\"429\":1,\"431\":2,\"441\":1,\"453\":4,\"463\":2,\"465\":1,\"486\":1,\"493\":1,\"498\":1}}],[\"如果今后你仍然想编写编译器\",{\"1\":{\"507\":1}}],[\"如果条件失败\",{\"1\":{\"473\":1}}],[\"如果是两个指针相减\",{\"1\":{\"498\":1}}],[\"如果是局部变量则采用与\",{\"1\":{\"486\":1}}],[\"如果是指针的指针\",{\"1\":{\"453\":1}}],[\"如果是有\",{\"1\":{\"284\":1}}],[\"如果遇到标识符就用\",{\"1\":{\"486\":1}}],[\"如果遇到\",{\"1\":{\"453\":1}}],[\"如果分析到字符串\",{\"1\":{\"431\":1}}],[\"如果标识符已经存在\",{\"1\":{\"429\":1}}],[\"如果子函数有返回结果\",{\"1\":{\"412\":1}}],[\"如果你按这个系列自己编写代码\",{\"1\":{\"509\":1}}],[\"如果你理解了上一章中的内容\",{\"1\":{\"457\":1}}],[\"如果你尝试阅读\",{\"1\":{\"394\":1}}],[\"如果你急切地想进入正篇\",{\"1\":{\"392\":1}}],[\"如果你的\",{\"1\":{\"106\":1}}],[\"如果公开了不应当被公开的信息\",{\"1\":{\"388\":1}}],[\"如果无法获取到这些信息\",{\"1\":{\"388\":1}}],[\"如果要我说计算机专业最重要的三门课\",{\"1\":{\"393\":1}}],[\"如果要修改已经编写和测试完成的类\",{\"1\":{\"385\":1}}],[\"如果要改变被共享的对象\",{\"1\":{\"253\":1}}],[\"如果在每次扩展类时都需要修改现有的类就太麻烦了\",{\"1\":{\"385\":1}}],[\"如果在逻辑执行过程中我们需要判断变量状态\",{\"1\":{\"102\":1}}],[\"如果将处理逻辑的方法定义在\",{\"1\":{\"384\":1}}],[\"如果将这些逻辑分散到各个用户类中\",{\"1\":{\"283\":1}}],[\"如果想比较原来的算法与改进后的算法的处理速度有多大区别\",{\"1\":{\"365\":1}}],[\"如果使用\",{\"1\":{\"366\":1}}],[\"如果使用了\",{\"1\":{\"365\":1}}],[\"如果使用继承\",{\"1\":{\"131\":1}}],[\"如果以后发生需求变更\",{\"1\":{\"353\":1}}],[\"如果大家在读完这两点之后会点头表示赞同\",{\"1\":{\"352\":1}}],[\"如果还是不能解决这些小问题\",{\"1\":{\"351\":1}}],[\"如果多个线程同时访问\",{\"1\":{\"342\":1}}],[\"如果\",{\"1\":{\"323\":1,\"498\":1}}],[\"如果实例很少就不需要\",{\"1\":{\"284\":1}}],[\"如果存在很多这样的互相通信的实例\",{\"1\":{\"284\":1}}],[\"如果存在多个改变它的理由\",{\"1\":{\"124\":1}}],[\"如果有兴趣\",{\"1\":{\"508\":1}}],[\"如果有\",{\"1\":{\"284\":1}}],[\"如果这局猜拳获胜\",{\"1\":{\"362\":1}}],[\"如果这段逻辑分散在\",{\"1\":{\"283\":1}}],[\"如果这些集合中的对象没有被其他任何地方引用\",{\"1\":{\"255\":1}}],[\"如果发生需求变更\",{\"1\":{\"283\":1}}],[\"如果不是预期的标记则报错并退出\",{\"1\":{\"455\":1}}],[\"如果不想看可以跳过\",{\"1\":{\"450\":1}}],[\"如果不能比较容易地扩展类\",{\"1\":{\"385\":1}}],[\"如果不能做就将\",{\"1\":{\"188\":1}}],[\"如果不使用\",{\"1\":{\"354\":1,\"355\":2}}],[\"如果不共享实例\",{\"1\":{\"256\":1}}],[\"如果冰激凌店要为顾客准备所有的冰激凌成品那真是太麻烦了\",{\"1\":{\"224\":1}}],[\"如果再用\",{\"1\":{\"222\":1}}],[\"如果也不能自己处理\",{\"1\":{\"188\":1}}],[\"如果他可以做就自己做\",{\"1\":{\"188\":1}}],[\"如果修改\",{\"1\":{\"185\":1}}],[\"如果没有理解各个类的角色就动手增加和修改代码\",{\"1\":{\"185\":1}}],[\"如果我们的编译器要达到自举\",{\"1\":{\"418\":1}}],[\"如果我们不把颜色信息放在\",{\"1\":{\"253\":1}}],[\"如果我们不传递\",{\"1\":{\"173\":1}}],[\"如果我们不关注执行过程中的状态\",{\"1\":{\"102\":1}}],[\"如果我们将某个程序中依赖于操作系统的部分划分为\",{\"1\":{\"172\":1}}],[\"如果只是将应当分散的处理分散在各个类中\",{\"1\":{\"283\":1}}],[\"如果只是简单地将它们分开\",{\"1\":{\"162\":1}}],[\"如果只是为了编写包含\",{\"1\":{\"140\":1}}],[\"如果一个类需要改变\",{\"1\":{\"124\":1}}],[\"如果协程在操作共享变量的过程中\",{\"1\":{\"102\":1}}],[\"如果每个线程按顺序执行\",{\"1\":{\"99\":1}}],[\"如此往复\",{\"1\":{\"101\":1}}],[\"如图所示\",{\"1\":{\"100\":1}}],[\"如何为每个运算符生成对应的汇编代码\",{\"1\":{\"502\":1}}],[\"如何通过递归调用\",{\"1\":{\"502\":1}}],[\"如何确定具体选择哪一个\",{\"1\":{\"443\":1}}],[\"如何处理错误\",{\"1\":{\"426\":1}}],[\"如何表示语法\",{\"1\":{\"394\":1}}],[\"如何实现风格统一\",{\"1\":{\"52\":1}}],[\"如何给python\",{\"1\":{\"26\":1}}],[\"最好的方式恐怕还是要自己实现它\",{\"1\":{\"509\":1}}],[\"最近知道了一个叫\",{\"1\":{\"508\":1}}],[\"最为重要的是能\",{\"1\":{\"506\":1}}],[\"最重要的是理解我们会为函数生成怎样的汇编代码\",{\"1\":{\"468\":1}}],[\"最大的区别就是保存的信息不同\",{\"1\":{\"468\":1}}],[\"最简单的方法是直接调用观察者的更新方法\",{\"1\":{\"309\":1}}],[\"最后要注意的一点是\",{\"1\":{\"501\":1}}],[\"最后要注意的是还有一些字符\",{\"1\":{\"425\":1}}],[\"最后注意的是优先通常只与多元运算符相关\",{\"1\":{\"482\":1}}],[\"最后是main函数\",{\"1\":{\"445\":1}}],[\"最后再加上一个错误判断\",{\"1\":{\"418\":1}}],[\"最后祝你学得愉快\",{\"1\":{\"397\":1}}],[\"最后想介绍几个资料\",{\"1\":{\"397\":1}}],[\"最后\",{\"1\":{\"279\":1,\"502\":1}}],[\"最后的值不是0\",{\"1\":{\"99\":1}}],[\"最少知道原则\",{\"1\":{\"113\":1}}],[\"最终都根据它们的类型用\",{\"1\":{\"486\":1}}],[\"最终把源代码转换成目标代码\",{\"1\":{\"478\":1}}],[\"最终构建起我们的编译器\",{\"1\":{\"402\":1}}],[\"最终\",{\"1\":{\"53\":1}}],[\"大量重复的代码特别让人崩溃\",{\"1\":{\"509\":1}}],[\"大量的函数调用将会耗费不少的时间\",{\"1\":{\"44\":1}}],[\"大部分的代码依旧是用于解析变量\",{\"1\":{\"468\":1}}],[\"大致500+行\",{\"1\":{\"395\":1}}],[\"大家应该都会点头表示赞同吧\",{\"1\":{\"385\":1}}],[\"大家已经学习了多种设计模式\",{\"1\":{\"385\":1}}],[\"大家只要再回顾一下\",{\"1\":{\"356\":1}}],[\"大家又发明了同步锁\",{\"1\":{\"99\":1}}],[\"于是\",{\"1\":{\"99\":1,\"101\":1}}],[\"于是寻求\",{\"1\":{\"53\":1}}],[\"多个迭代器\",{\"0\":{\"274\":1}}],[\"多个线程同时改同一个变量\",{\"1\":{\"99\":1}}],[\"多个线程之前也并不是完全独立的\",{\"1\":{\"99\":1}}],[\"多态\",{\"1\":{\"260\":1}}],[\"多线程下\",{\"0\":{\"342\":1}}],[\"多线程在未加锁的情况下\",{\"1\":{\"101\":1}}],[\"多线程在python中只能交替执行\",{\"1\":{\"99\":1}}],[\"多线程逻辑执行结果\",{\"1\":{\"101\":1}}],[\"多了把锁\",{\"1\":{\"99\":1}}],[\"就如前文的\",{\"1\":{\"494\":1}}],[\"就返回它的唯一标识\",{\"1\":{\"429\":1}}],[\"就势必要实现\",{\"1\":{\"418\":1}}],[\"就实现了数据结构与处理的分离\",{\"1\":{\"388\":1}}],[\"就程序而言\",{\"1\":{\"375\":1}}],[\"就不得不去修改这些类\",{\"1\":{\"384\":1}}],[\"就不必修改\",{\"1\":{\"365\":1}}],[\"就不会发生上面这种类的依赖关系混乱的问题\",{\"1\":{\"307\":1}}],[\"就必须用条件分支语句判断状态\",{\"1\":{\"355\":1}}],[\"就必须要相应地修改\",{\"1\":{\"353\":1}}],[\"就将其交给\",{\"1\":{\"323\":1}}],[\"就会发现太可怕了\",{\"1\":{\"394\":1}}],[\"就会对多个地方产生影响\",{\"1\":{\"253\":1}}],[\"就会很容易出错\",{\"1\":{\"185\":1}}],[\"就意味着我们需要引人facade了\",{\"1\":{\"235\":1}}],[\"就可以应付大多数的语法分析器编写\",{\"1\":{\"446\":1}}],[\"就可以提高程序运行速度\",{\"1\":{\"256\":1}}],[\"就可以生成一个与其他对象具有不同关系的新对象\",{\"1\":{\"223\":1}}],[\"就可以在字符串的左右两侧加上装饰字符\",{\"1\":{\"222\":1}}],[\"就可以明白调用\",{\"1\":{\"185\":1}}],[\"就像委托者自己完成一样\",{\"1\":{\"229\":1}}],[\"就像是剥洋葱时以为洋葱心要出来了\",{\"1\":{\"221\":1}}],[\"就像以前的公共电话亭\",{\"1\":{\"99\":1}}],[\"就再转给另外一个人\",{\"1\":{\"188\":1}}],[\"就自己做\",{\"1\":{\"188\":1}}],[\"就能很容易地改变实现\",{\"1\":{\"173\":1}}],[\"就需要获取并恢复这个信息\",{\"1\":{\"412\":1}}],[\"就需要存放到数据段中\",{\"1\":{\"405\":1}}],[\"就需要推卸责任\",{\"1\":{\"188\":1}}],[\"就需要先确认自己的意图\",{\"1\":{\"162\":1}}],[\"就需要重新设计该类\",{\"1\":{\"124\":1}}],[\"就算只能用单核处理任务\",{\"1\":{\"99\":1}}],[\"就是指针的加减\",{\"1\":{\"498\":1}}],[\"就是前文提到的\",{\"1\":{\"465\":1}}],[\"就是上述的消除左递归后的文法直接转换而来的\",{\"1\":{\"445\":1}}],[\"就是上例中\",{\"1\":{\"443\":1}}],[\"就是一种用来描述语法的语言\",{\"1\":{\"441\":1}}],[\"就是一种远程代理的实现\",{\"1\":{\"332\":1}}],[\"就是需要向前看的标记的个数了\",{\"1\":{\"432\":1}}],[\"就是这个标识符的哈希值\",{\"1\":{\"429\":1}}],[\"就是对应字符型和整型的存取操作\",{\"1\":{\"408\":1}}],[\"就是\",{\"1\":{\"60\":1,\"76\":1,\"222\":1}}],[\"每写一篇都特别心烦\",{\"1\":{\"509\":1}}],[\"每当一个引用被释放时\",{\"1\":{\"255\":1}}],[\"每当一个对象被引用时\",{\"1\":{\"255\":1}}],[\"每次遇到换行符\",{\"1\":{\"427\":1}}],[\"每次调用该函数则返回下一个标记\",{\"1\":{\"424\":1}}],[\"每次撤销操作时从栈中弹出一个\",{\"1\":{\"297\":1}}],[\"每次撤销操作时\",{\"1\":{\"201\":1}}],[\"每次执行命令时\",{\"1\":{\"201\":1}}],[\"每次执行更新你的\",{\"1\":{\"95\":1}}],[\"每个id占用数组中的9个空间\",{\"1\":{\"429\":1}}],[\"每个标记通常包括\",{\"1\":{\"422\":1}}],[\"每个运算符都是二元的\",{\"1\":{\"417\":1}}],[\"每个\",{\"1\":{\"353\":2}}],[\"每个请求都会沿着职责链传递\",{\"1\":{\"190\":1}}],[\"每个类只负责一个职责\",{\"1\":{\"125\":1}}],[\"每个协程的体积比线程要小得多\",{\"1\":{\"100\":1}}],[\"每执行100条字节码\",{\"1\":{\"99\":1}}],[\"雨露均沾\",{\"1\":{\"99\":1}}],[\"刘悦的技术博客\",{\"1\":{\"98\":1,\"102\":1}}],[\"主要涉及如何将语句和表达式编译成汇编代码\",{\"1\":{\"471\":1}}],[\"主要的逻辑用于解析用逗号\",{\"1\":{\"454\":1}}],[\"主要原因是我们的语言不支持跨函数递归\",{\"1\":{\"450\":1}}],[\"主要有以下几个优点\",{\"1\":{\"323\":1}}],[\"主程序\",{\"0\":{\"211\":1},\"1\":{\"164\":1}}],[\"主动释放使用权\",{\"1\":{\"101\":1}}],[\"主动\",{\"1\":{\"101\":1}}],[\"主动让出使用权\",{\"1\":{\"101\":1}}],[\"主动让出时间片的协程模式比线程抢占式分配的效率要好\",{\"1\":{\"100\":1}}],[\"主动切换了使用权\",{\"1\":{\"101\":1}}],[\"主动切换\",{\"0\":{\"98\":1}}],[\"主页\",{\"0\":{\"0\":1}}],[\"挂起\",{\"0\":{\"98\":1},\"1\":{\"101\":1}}],[\"线程是系统态\",{\"1\":{\"100\":1}}],[\"线程操作共享资源需要加锁\",{\"1\":{\"99\":1}}],[\"线程并不安全\",{\"1\":{\"99\":1}}],[\"线程共享数据危险在于\",{\"1\":{\"99\":1}}],[\"线程安全\",{\"0\":{\"99\":1}}],[\"线程更被我们所熟知\",{\"1\":{\"98\":1}}],[\"线程\",{\"0\":{\"98\":1}}],[\"到底是什么呢\",{\"1\":{\"356\":1}}],[\"到底需不需要加锁\",{\"0\":{\"98\":1}}],[\"到任意点的路径\",{\"1\":{\"85\":1}}],[\"协程也不是虚空的\",{\"1\":{\"102\":1}}],[\"协程加锁执行后结果\",{\"1\":{\"101\":1}}],[\"协程在工作状态中\",{\"1\":{\"101\":1}}],[\"协程运行过程中\",{\"1\":{\"101\":1}}],[\"协程又可以切回来\",{\"1\":{\"101\":1}}],[\"协程操作共享变量不需要加锁的结论开始在坊间流传\",{\"1\":{\"101\":1}}],[\"协程本身就是单线程的\",{\"1\":{\"100\":1}}],[\"协程本身可以做成用户态\",{\"1\":{\"100\":1}}],[\"协程是否需要加锁\",{\"0\":{\"102\":1}}],[\"协程是用户态\",{\"1\":{\"100\":1}}],[\"协程是主动让出使用权\",{\"1\":{\"100\":1}}],[\"协程保证了编写过程中的思维连贯性\",{\"1\":{\"100\":1}}],[\"协程与线程向来焦孟不离\",{\"1\":{\"98\":1}}],[\"协程安全\",{\"0\":{\"98\":1,\"101\":1}}],[\"协程\",{\"0\":{\"98\":1,\"100\":1,\"103\":1}}],[\"插件\",{\"1\":{\"95\":1}}],[\"命令队列\",{\"1\":{\"201\":1}}],[\"命令栈\",{\"1\":{\"201\":1}}],[\"命令模式的一个重要应用是保存历史记录\",{\"1\":{\"201\":1}}],[\"命令执行前后的状态信息\",{\"1\":{\"200\":1}}],[\"命令对象可以保存执行前的状态\",{\"1\":{\"200\":1}}],[\"命令对象可以包含执行操作所需的所有参数\",{\"1\":{\"200\":1}}],[\"命令对象将动作封装为一个方法调用\",{\"1\":{\"200\":1}}],[\"命令对象通常包含以下信息\",{\"1\":{\"200\":1}}],[\"命令中应该包含哪些信息\",{\"0\":{\"200\":1}}],[\"命令\",{\"1\":{\"95\":1}}],[\"命里无时莫强求\",{\"1\":{\"3\":1}}],[\"命里有时终须有\",{\"0\":{\"3\":1},\"1\":{\"3\":1}}],[\"后缀形式\",{\"1\":{\"499\":1}}],[\"后面我们会看到\",{\"1\":{\"486\":1}}],[\"后面的文章中\",{\"1\":{\"402\":1}}],[\"后来集成的\",{\"1\":{\"106\":1}}],[\"后者为了能恢复现场会在切换线程时保存相当多的状态\",{\"1\":{\"100\":1}}],[\"后\",{\"1\":{\"95\":1,\"222\":1}}],[\"后端通过shell命令即可\",{\"1\":{\"38\":1}}],[\"默认是\",{\"1\":{\"419\":1}}],[\"默认为\",{\"1\":{\"111\":1}}],[\"默认不支持http\",{\"1\":{\"95\":1}}],[\"默认\",{\"1\":{\"95\":1}}],[\"此时的二元运算符的解析的框架为\",{\"1\":{\"494\":1}}],[\"此时运算符栈为空\",{\"1\":{\"482\":1}}],[\"此时判断参数\",{\"1\":{\"482\":1}}],[\"此时我们期待的是+的另一个参数\",{\"1\":{\"482\":1}}],[\"此时我们可以使用ionic无缝将其迁移到移动端\",{\"1\":{\"93\":1}}],[\"此时\",{\"1\":{\"222\":1,\"310\":1,\"473\":1,\"495\":1}}],[\"此时使用权让出以后\",{\"1\":{\"101\":1}}],[\"此外\",{\"1\":{\"53\":1,\"222\":1,\"232\":1,\"353\":1,\"366\":1,\"384\":1}}],[\"点\",{\"1\":{\"85\":1}}],[\"所谓状态迁移表是可以根据\",{\"1\":{\"353\":1}}],[\"所谓主动让出使用权\",{\"1\":{\"101\":1}}],[\"所对应的字体数据\",{\"1\":{\"253\":1}}],[\"所有的变量定义必须放在语句之前\",{\"1\":{\"501\":1}}],[\"所有的\",{\"1\":{\"353\":1}}],[\"所有的实现\",{\"1\":{\"172\":1}}],[\"所有依赖于它的对象都会得到通知并自动更新\",{\"1\":{\"303\":1}}],[\"所有显示该数据的视图都需要自动更新\",{\"1\":{\"302\":1}}],[\"所有点的出度为\",{\"1\":{\"85\":1}}],[\"所以你可以执行\",{\"1\":{\"501\":1}}],[\"所以源码如下\",{\"1\":{\"497\":1}}],[\"所以生成的代码也类似于\",{\"1\":{\"496\":1}}],[\"所以直接修改栈指针的大小即可\",{\"1\":{\"486\":1}}],[\"所以直接跳过它们\",{\"1\":{\"428\":1}}],[\"所以解析的时候要注意这一点\",{\"1\":{\"484\":1}}],[\"所以先将它入栈\",{\"1\":{\"482\":1}}],[\"所以建议如果没有学过汇编\",{\"1\":{\"478\":1}}],[\"所以不多做说明\",{\"1\":{\"476\":1}}],[\"所以不需要考虑多线程问题\",{\"1\":{\"250\":1}}],[\"所以需要生成汇编代码\",{\"1\":{\"475\":1}}],[\"所以需要无条件跳转\",{\"1\":{\"473\":1}}],[\"所以如果执行了\",{\"1\":{\"473\":1}}],[\"所以一个类型首先有基本类型\",{\"1\":{\"453\":1}}],[\"所以还需要继续查看后续的标记\",{\"1\":{\"453\":1}}],[\"所以实际上它们间的对应关系并不是特别明显\",{\"1\":{\"450\":1}}],[\"所以实际的处理方法是提供一个函数\",{\"1\":{\"424\":1}}],[\"所以只能再向前查看字符\",{\"1\":{\"432\":1}}],[\"所以代码中并没有支持除\",{\"1\":{\"431\":1}}],[\"所以这里我们会有这样的印象\",{\"1\":{\"425\":1}}],[\"所以人们已经开发出了许多工具来生成词法分析器\",{\"1\":{\"424\":1}}],[\"所以为了获取第一个参数\",{\"1\":{\"416\":1}}],[\"所以用一个指令代替\",{\"1\":{\"415\":1}}],[\"所以用上面提到的指令\",{\"1\":{\"412\":1}}],[\"所以合在一起说\",{\"1\":{\"412\":1}}],[\"所以此时它存放的是\",{\"1\":{\"410\":1}}],[\"所以执行\",{\"1\":{\"408\":1}}],[\"所以大大简化了实现的难度\",{\"1\":{\"408\":1}}],[\"所以入栈时\",{\"1\":{\"406\":1}}],[\"所以是\",{\"1\":{\"405\":1}}],[\"所以单独存放可以节省空间\",{\"1\":{\"405\":1}}],[\"所以我希望你有足够的耐心和时间来学习\",{\"1\":{\"396\":1}}],[\"所以我们首先执行类似前缀自增自减的操作\",{\"1\":{\"499\":1}}],[\"所以我们需要给予代码生成高度的重视\",{\"1\":{\"506\":1}}],[\"所以我们需要先\",{\"1\":{\"493\":1}}],[\"所以我们需要在不修改现有类的前提下能够扩展类\",{\"1\":{\"385\":1}}],[\"所以我们用异或来实现\",{\"1\":{\"491\":1}}],[\"所以我们将结束符的解析放在了外层的\",{\"1\":{\"464\":1}}],[\"所以我们将它拆分成\",{\"1\":{\"449\":1,\"460\":1}}],[\"所以我们将它单独作为一个模块\",{\"1\":{\"402\":1}}],[\"所以我们先编写一个较为简单的编译器\",{\"1\":{\"423\":1}}],[\"所以我们提供了一个新的指令\",{\"1\":{\"416\":1}}],[\"所以我们不再需要\",{\"1\":{\"415\":1}}],[\"所以我们会依照以下步骤来构建我们的编译器\",{\"1\":{\"401\":1}}],[\"所以我们要完全手写这些功能\",{\"1\":{\"401\":1}}],[\"所以我们还需要在它们之间搭建一座桥梁\",{\"1\":{\"162\":1}}],[\"所以本项目的主要目的\",{\"1\":{\"395\":1}}],[\"所以写得很乱\",{\"1\":{\"395\":1}}],[\"所以写操作不会被争抢覆盖\",{\"1\":{\"101\":1}}],[\"所以当学校开\",{\"1\":{\"394\":1}}],[\"所以优先使用组合的方式代替继承的方式\",{\"1\":{\"131\":1}}],[\"所以说\",{\"1\":{\"102\":1}}],[\"所以肯定可以保证最终一致性\",{\"1\":{\"101\":1}}],[\"所以它对应的代码为\",{\"1\":{\"498\":1}}],[\"所以它的性能要比多线程好\",{\"1\":{\"100\":1}}],[\"所以它平均地分配时间片让处理器一视同仁\",{\"1\":{\"99\":1}}],[\"所以同一时间点还是只能有一个协程任务运行\",{\"1\":{\"100\":1}}],[\"所以加锁是为了同时只有一个线程再修改\",{\"1\":{\"99\":1}}],[\"所以\",{\"1\":{\"71\":1,\"99\":2,\"494\":2}}],[\"同样\",{\"1\":{\"492\":1}}],[\"同样我们没有相应的指令\",{\"1\":{\"491\":1}}],[\"同样在第三章\",{\"1\":{\"486\":1}}],[\"同样不能确定是否能立即计算\",{\"1\":{\"482\":1}}],[\"同理\",{\"1\":{\"102\":1,\"453\":1}}],[\"同时其它语言也有许多类似的支持\",{\"1\":{\"508\":1}}],[\"同时我们也看到\",{\"1\":{\"506\":1}}],[\"同时我们也用实例看到了理论\",{\"1\":{\"446\":1}}],[\"同时将运算符\",{\"1\":{\"482\":1}}],[\"同时值得一提的是\",{\"1\":{\"478\":1}}],[\"同时记录它们的位置与类型\",{\"1\":{\"465\":1}}],[\"同时能对汇编语言有一定的概念\",{\"1\":{\"420\":1}}],[\"同时在栈上保留一定的空间\",{\"1\":{\"413\":1}}],[\"同时开启四个协程任务\",{\"1\":{\"101\":1}}],[\"同时也不需要系统的线程调度器参与抢占式的调度\",{\"1\":{\"100\":1}}],[\"同时\",{\"1\":{\"100\":1,\"232\":1,\"392\":1,\"507\":1}}],[\"同时修改变量\",{\"1\":{\"99\":1}}],[\"同时为了解决多个模数的问题\",{\"1\":{\"45\":1}}],[\"同构\",{\"1\":{\"85\":1}}],[\"图像加载时可以使用虚拟代理来显示占位符图像\",{\"1\":{\"332\":1}}],[\"图解设计模式\",{\"1\":{\"235\":1,\"260\":1}}],[\"图论\",{\"1\":{\"82\":1}}],[\"图床\",{\"0\":{\"35\":1}}],[\"研究\",{\"1\":{\"82\":1}}],[\"少了任何一条都不足以构建出上述的自然数系统\",{\"1\":{\"82\":1}}],[\"从上小节对四则运算的递归下降解析可以看出\",{\"1\":{\"443\":1}}],[\"从上述步骤中我们看出\",{\"1\":{\"82\":1}}],[\"从虚拟机的角度予以支持\",{\"1\":{\"418\":1}}],[\"从中一条条地加载指令执行\",{\"1\":{\"404\":1}}],[\"从观察变为通知\",{\"0\":{\"310\":1}}],[\"从栈中弹出命令对象并执行撤销操作\",{\"1\":{\"201\":1}}],[\"从早上到下午\",{\"1\":{\"179\":1}}],[\"从代码结构上看\",{\"1\":{\"100\":1}}],[\"从实际开发角度看\",{\"1\":{\"100\":1}}],[\"从而简化具体的实现\",{\"1\":{\"420\":1}}],[\"从而确保只有授权的客户端才能访问实际对象\",{\"1\":{\"332\":1}}],[\"从而延迟实际对象的创建\",{\"1\":{\"332\":1}}],[\"从而减少系统的开销\",{\"1\":{\"327\":1}}],[\"从而引发无限循环\",{\"1\":{\"308\":1}}],[\"从而引发程序错误\",{\"1\":{\"255\":1}}],[\"从而保持封装性\",{\"1\":{\"294\":1}}],[\"从而避免内存泄漏\",{\"1\":{\"255\":1}}],[\"从而将其回收掉\",{\"1\":{\"255\":1}}],[\"从而提高网络通信的效率和安全性\",{\"1\":{\"331\":1}}],[\"从而提高了系统的可维护性和可扩展性\",{\"1\":{\"311\":1}}],[\"从而提高系统的性能和可扩展性\",{\"1\":{\"310\":1}}],[\"从而提高系统的可维护性和可扩展性\",{\"1\":{\"297\":1}}],[\"从而提高系统的灵活性和可维护性\",{\"1\":{\"200\":1,\"309\":1}}],[\"从而提高性能\",{\"1\":{\"249\":1}}],[\"从而遵循开闭原则\",{\"1\":{\"217\":1}}],[\"从而使得现有类可以在新的环境中使用\",{\"1\":{\"149\":1}}],[\"从而导致执行过程中变量状态的\",{\"1\":{\"101\":1}}],[\"从而启动失败\",{\"1\":{\"54\":1}}],[\"从而加速开发和交付周期\",{\"1\":{\"31\":1}}],[\"上节中说到了运算符的优先级\",{\"1\":{\"483\":1}}],[\"上的\",{\"1\":{\"463\":1}}],[\"上一章的代码中\",{\"1\":{\"462\":1}}],[\"上述代码中我们看到\",{\"1\":{\"432\":1}}],[\"上述等式表明\",{\"1\":{\"81\":1}}],[\"上面这断代码为当前的标识符设置了正确的类别\",{\"1\":{\"462\":1}}],[\"上面这些标记是有顺序的\",{\"1\":{\"425\":1}}],[\"上面这段代码在我们自己的虚拟机里会有几个问题\",{\"1\":{\"412\":1}}],[\"上面的一些指令解决了调用帧的问题\",{\"1\":{\"416\":1}}],[\"上面的代码运行后会出现\",{\"1\":{\"435\":1}}],[\"上面的代码看上去挺复杂\",{\"1\":{\"402\":1}}],[\"上面的代码也充分说明了这个结论的正确性\",{\"1\":{\"101\":1}}],[\"上下载\",{\"1\":{\"402\":1,\"420\":1,\"435\":1,\"456\":1,\"467\":1,\"477\":1,\"501\":1}}],[\"上看到了一个项目\",{\"1\":{\"395\":1}}],[\"上存储\",{\"1\":{\"31\":1}}],[\"ⅳ\",{\"0\":{\"89\":1},\"1\":{\"81\":1}}],[\"其它的我们便不再详述\",{\"1\":{\"498\":1}}],[\"其它的标记的解析就相对容易一些了\",{\"1\":{\"433\":1}}],[\"其它语句并不直接生成汇编代码\",{\"1\":{\"476\":1}}],[\"其它语句\",{\"0\":{\"476\":1},\"1\":{\"471\":1}}],[\"其它就不多说了\",{\"1\":{\"430\":1}}],[\"其它\",{\"0\":{\"433\":1,\"455\":1},\"1\":{\"421\":1,\"449\":1}}],[\"其实只要不执行\",{\"1\":{\"489\":1}}],[\"其实提前看字符的概念也存在于编译器\",{\"1\":{\"432\":1}}],[\"其实是抄\",{\"1\":{\"430\":1}}],[\"其实是同一个对象\",{\"1\":{\"356\":1}}],[\"其实不然\",{\"1\":{\"365\":1}}],[\"其实并没有绝对的答案\",{\"1\":{\"253\":1}}],[\"其职责是引起该类变化的原因\",{\"1\":{\"124\":1}}],[\"其他类依然可以调用\",{\"1\":{\"221\":1}}],[\"其他设计原则是实现开闭原则的手段和工具\",{\"1\":{\"114\":1}}],[\"其他线程又说我拿不到锁\",{\"1\":{\"99\":1}}],[\"其他线程只能等待\",{\"1\":{\"99\":1}}],[\"其中①用于解析函数体内的局部变量的定义\",{\"1\":{\"466\":1}}],[\"其中①与全局变量定义的解析十分一样\",{\"1\":{\"465\":1}}],[\"其中①中我们没有消耗最后的\",{\"1\":{\"464\":1}}],[\"其中的自顶向下方法就是我们所说的递归下降\",{\"1\":{\"440\":1}}],[\"其中的\",{\"1\":{\"408\":1,\"453\":1,\"455\":1}}],[\"其中的数据段我们只用来存放字符串\",{\"1\":{\"405\":1}}],[\"其中数据段\",{\"1\":{\"405\":1}}],[\"其中\",{\"1\":{\"81\":1,\"450\":1}}],[\"其与自然数\",{\"1\":{\"68\":1}}],[\"可惜的是它的代码初衷是代码最小化\",{\"1\":{\"395\":1}}],[\"可作为组件复用\",{\"1\":{\"385\":1}}],[\"可替换性是指一个对象可以被另一个具有相同接口的对象替换\",{\"1\":{\"306\":1}}],[\"可替換性\",{\"1\":{\"183\":1}}],[\"可能唯一不好理解的是获取十六进制的值相关的代码\",{\"1\":{\"430\":1}}],[\"可能包含多个字符\",{\"1\":{\"425\":1}}],[\"可能大家对此感受不深\",{\"1\":{\"351\":1}}],[\"可能会更具普适性\",{\"1\":{\"397\":1}}],[\"可能会导致创建多个实例\",{\"1\":{\"342\":1}}],[\"可能会有读者认为\",{\"1\":{\"284\":1}}],[\"可能需要长期保存\",{\"1\":{\"296\":1}}],[\"可能需要保存多个\",{\"1\":{\"295\":1}}],[\"可能只需要在短时间内有效\",{\"1\":{\"296\":1}}],[\"可能只需要保存一个\",{\"1\":{\"295\":1}}],[\"可能同时违反其他原则\",{\"1\":{\"114\":1}}],[\"可扩展性\",{\"1\":{\"264\":1}}],[\"可维护性和可扩展性\",{\"1\":{\"232\":1}}],[\"可是如果在执行事务逻辑块中主动放弃执行权了\",{\"1\":{\"102\":1}}],[\"可调试性强\",{\"1\":{\"100\":1}}],[\"可读性高\",{\"1\":{\"100\":1}}],[\"可知\",{\"1\":{\"81\":1}}],[\"可以看看\",{\"1\":{\"508\":1}}],[\"可以看到和之前有同样的输出\",{\"1\":{\"501\":1}}],[\"可以看到\",{\"1\":{\"101\":2,\"442\":1,\"445\":1}}],[\"可以自己实现看看\",{\"1\":{\"498\":1}}],[\"可以自己先试着去实现它\",{\"1\":{\"456\":1}}],[\"可以参考\",{\"1\":{\"482\":1}}],[\"可以学习学习这些文法\",{\"1\":{\"508\":1}}],[\"可以学习学习\",{\"1\":{\"478\":1}}],[\"可以认为语句就是表达式加上末尾的分号\",{\"1\":{\"472\":1}}],[\"可以是\",{\"1\":{\"441\":1}}],[\"可以得到个位数的值\",{\"1\":{\"430\":1}}],[\"可以理解为变量名\",{\"1\":{\"429\":1}}],[\"可以帮助我们设计出这样的类\",{\"1\":{\"385\":1}}],[\"可以帮助我们应对软件开发中的常见问题\",{\"1\":{\"232\":1}}],[\"可以通过在子类中增加方法以实现新的功能\",{\"1\":{\"375\":1}}],[\"可以通过子类来定制产品的创建过程\",{\"1\":{\"243\":1}}],[\"可以方便地根据棋手的选择切换\",{\"1\":{\"365\":1}}],[\"可以方便地增加新的产品族而不影响现有代码\",{\"1\":{\"138\":1}}],[\"可以避免在多个地方重复相同的算法逻辑\",{\"1\":{\"361\":1}}],[\"可以避免创建多个实例带来的资源浪费和不一致性问题\",{\"1\":{\"337\":1}}],[\"可以很容易地添加新的策略\",{\"1\":{\"361\":1}}],[\"可以很容易地添加新的处理者而不影响现有代码\",{\"1\":{\"189\":1}}],[\"可以提高系统的响应速度和资源利用率\",{\"1\":{\"327\":1}}],[\"可以提高代码的复用性和可维护性\",{\"1\":{\"264\":1}}],[\"可以用程序来生成代码而不是手写代码\",{\"1\":{\"353\":1}}],[\"可以用于访问远程对象\",{\"1\":{\"323\":1}}],[\"可以用来存储弱引用的键值对\",{\"1\":{\"255\":1}}],[\"可以负责将\",{\"1\":{\"297\":1}}],[\"可以维护一个\",{\"1\":{\"297\":1}}],[\"可以实现持久化存储\",{\"1\":{\"297\":1}}],[\"可以实现多次撤销操作\",{\"1\":{\"297\":1}}],[\"可以实现命令的参数化和可撤销性\",{\"1\":{\"200\":1}}],[\"可以将状态保存和恢复的逻辑与业务逻辑分离\",{\"1\":{\"297\":1}}],[\"可以将这七个原则分为以下两部分\",{\"1\":{\"114\":1}}],[\"可以确保\",{\"1\":{\"294\":1}}],[\"可以根据需要实现不同的迭代器\",{\"1\":{\"270\":1}}],[\"可以根据需要动态地添加或删除职责\",{\"1\":{\"217\":1}}],[\"可以轻松添加新的语法规则或指令\",{\"1\":{\"264\":1}}],[\"可以轻松解析和执行特定的语言或指令集\",{\"1\":{\"264\":1}}],[\"可以同时使用的文件句柄和窗口句柄是有限制的\",{\"1\":{\"256\":1}}],[\"可以安全地回收\",{\"1\":{\"255\":1}}],[\"可以动态地增加功能\",{\"0\":{\"223\":1}}],[\"可以在客户端和远程服务器之间进行通信\",{\"1\":{\"328\":1}}],[\"可以在实际对象创建之前进行一些轻量级的操作\",{\"1\":{\"327\":1}}],[\"可以在代理中加入额外的逻辑来控制对实际对象的访问\",{\"1\":{\"323\":1}}],[\"可以在需要时回滚到之前的状态\",{\"1\":{\"201\":1}}],[\"可以在运行时动态地改变职责链的结构\",{\"1\":{\"189\":1}}],[\"可以在不修改实际对象的情况下添加额外的功能\",{\"1\":{\"328\":1}}],[\"可以在不修改集合对象的情况下\",{\"1\":{\"270\":1}}],[\"可以在不修改现有代码的情况下\",{\"1\":{\"116\":1}}],[\"可以在不同的上下文中重用相同的构建逻辑\",{\"1\":{\"178\":1}}],[\"可以在不改变原有代码的情况下\",{\"1\":{\"116\":1}}],[\"可以构造出分段状自然数系统\",{\"1\":{\"90\":1}}],[\"可以构造出\",{\"1\":{\"89\":1}}],[\"可以构造出环状自然数系统\",{\"1\":{\"88\":1}}],[\"可以构造出菊花图自然数系统\",{\"1\":{\"87\":1}}],[\"可以构造出空集自然数系统\",{\"1\":{\"86\":1}}],[\"可以使用双重检查锁定\",{\"1\":{\"342\":1}}],[\"可以使用\",{\"1\":{\"52\":1}}],[\"可以使用相同的权限管理\",{\"1\":{\"31\":1}}],[\"可以更轻松地构建和部署容器化的应用程序\",{\"1\":{\"31\":1}}],[\"可以快速\",{\"1\":{\"5\":1}}],[\"假设要在某个表格计算软件的开发版本中进行复杂的计算\",{\"1\":{\"366\":1}}],[\"假设我们现在在\",{\"1\":{\"355\":1}}],[\"假设我们现在需要制作另外一个对话框\",{\"1\":{\"285\":1}}],[\"假设我们将颜色信息放在\",{\"1\":{\"253\":1}}],[\"假设我们要在示例程序中增加一个功能\",{\"1\":{\"253\":1}}],[\"假设我们改变了示例程序中\",{\"1\":{\"253\":1}}],[\"假设现在我们要在示例程序中增加一个\",{\"1\":{\"387\":1}}],[\"假设现在我们要在示例程序中增加新的具体工厂\",{\"1\":{\"142\":1}}],[\"假设现在有\",{\"1\":{\"284\":1}}],[\"假设现在有一个类\",{\"1\":{\"160\":1}}],[\"假设\",{\"1\":{\"81\":1,\"84\":1}}],[\"假设存在一个算数系统的模型满足\",{\"1\":{\"55\":1}}],[\"证明了乘法运算规则的交换律之后\",{\"1\":{\"78\":1}}],[\"证明了加法运算规则的交换律之后\",{\"1\":{\"62\":1}}],[\"存在内存地址上就另当别论\",{\"1\":{\"417\":1}}],[\"存在从\",{\"1\":{\"85\":1}}],[\"存在点\",{\"1\":{\"85\":1}}],[\"存在\",{\"1\":{\"75\":1}}],[\"存放这个标识符的值\",{\"1\":{\"429\":1}}],[\"存放标识符本身的字符串\",{\"1\":{\"429\":1}}],[\"存放日志\",{\"1\":{\"15\":1}}],[\"存放ssl证书\",{\"1\":{\"15\":1}}],[\"乘法\",{\"1\":{\"482\":1}}],[\"乘法消去保序性\",{\"0\":{\"84\":1}}],[\"乘法消去律\",{\"0\":{\"81\":1},\"1\":{\"81\":1}}],[\"乘法保序性\",{\"0\":{\"83\":1}}],[\"乘法结合律\",{\"0\":{\"80\":1}}],[\"乘法结果的唯一性\",{\"0\":{\"76\":1}}],[\"乘法结果的存在性\",{\"0\":{\"75\":1}}],[\"乘法分配律\",{\"0\":{\"79\":1}}],[\"乘法交换律\",{\"0\":{\"78\":1}}],[\"乘法的性质\",{\"0\":{\"77\":1}}],[\"乘法的定义\",{\"0\":{\"74\":1}}],[\"任何python线程执行前\",{\"1\":{\"99\":1}}],[\"任何自然数的后继存在且唯一\",{\"1\":{\"56\":1}}],[\"任意点的入度小于等于\",{\"1\":{\"85\":1}}],[\"任意非零自然数\",{\"1\":{\"81\":1}}],[\"任意两个自然数\",{\"1\":{\"71\":1}}],[\"ⅲ\",{\"0\":{\"88\":1},\"1\":{\"68\":1,\"81\":3}}],[\"传统的编程书籍会用\",{\"1\":{\"482\":1}}],[\"传统上\",{\"1\":{\"440\":1}}],[\"传统意义上的符号表只需要知道标识符的唯一标识即可\",{\"1\":{\"429\":1}}],[\"传递更新信息的方式有多种选择\",{\"1\":{\"309\":1}}],[\"传递更新信息的方式\",{\"0\":{\"309\":1}}],[\"传递性和完全性\",{\"1\":{\"66\":1}}],[\"传说皮\",{\"1\":{\"3\":1}}],[\"它涉及到了\",{\"1\":{\"507\":1}}],[\"它相当于一个小型的\",{\"1\":{\"496\":1}}],[\"它相当于\",{\"1\":{\"484\":1}}],[\"它比较特殊的一点是\",{\"1\":{\"484\":1}}],[\"它本身不难\",{\"1\":{\"478\":1}}],[\"它对应的汇编代码如下\",{\"1\":{\"474\":1}}],[\"它用于将数据放进寄存器或内存地址\",{\"1\":{\"408\":1}}],[\"它用于存放一条指令执行后的结果\",{\"1\":{\"406\":1}}],[\"它存放的是一个内存地址\",{\"1\":{\"406\":1}}],[\"它的类型保存在变量\",{\"1\":{\"488\":1}}],[\"它的优先级和\",{\"1\":{\"482\":1}}],[\"它的运算顺序是这样的\",{\"1\":{\"482\":1}}],[\"它的\",{\"1\":{\"474\":1}}],[\"它的语法更容易理解\",{\"1\":{\"450\":1}}],[\"它的本质上也是编译器\",{\"1\":{\"423\":1}}],[\"它的作用是将\",{\"1\":{\"409\":1}}],[\"它的作用是屏蔽了物理的细节\",{\"1\":{\"405\":1}}],[\"它的流程为\",{\"1\":{\"402\":1}}],[\"它的真正作用是帮助我们实现任务分担\",{\"1\":{\"161\":1}}],[\"它将\",{\"1\":{\"455\":1}}],[\"它将自动忽略空白字符\",{\"1\":{\"402\":1}}],[\"它将与状态相关的行为封装在独立的类中\",{\"1\":{\"347\":1}}],[\"它最让我震惊的是能够自举\",{\"1\":{\"395\":1}}],[\"它就无法工作\",{\"1\":{\"388\":1}}],[\"它是\",{\"1\":{\"387\":1}}],[\"它是当实例的位置\",{\"1\":{\"254\":1}}],[\"它能够将元素集合及其关联关系组织在一起\",{\"1\":{\"384\":1}}],[\"它能做什么\",{\"1\":{\"101\":1}}],[\"它决定了系统的状态\",{\"1\":{\"354\":1}}],[\"它非常适用于大规模的复杂处理\",{\"1\":{\"351\":1}}],[\"它常用于需要控制资源访问的场景\",{\"1\":{\"337\":1}}],[\"它在客户端和远程服务器之间进行通信\",{\"1\":{\"332\":1}}],[\"它在实际对象创建之前进行一些轻量级的操作\",{\"1\":{\"332\":1}}],[\"它在以下情况下特别有用\",{\"1\":{\"290\":1}}],[\"它实现了\",{\"1\":{\"273\":1}}],[\"它允许你复制现有对象而无需使代码依赖它们所属的类\",{\"1\":{\"316\":1}}],[\"它允许顺序访问集合中的元素\",{\"1\":{\"271\":1}}],[\"它允许将一个类的接口转换成客户希望的另一个接口\",{\"1\":{\"148\":1}}],[\"它定义了一种语言的文法表示\",{\"1\":{\"264\":1}}],[\"它属于\",{\"1\":{\"254\":1}}],[\"它指的是不论实例在哪里\",{\"1\":{\"254\":1}}],[\"它通过定义自己的指令集并支持该指令集的虚拟机来模拟编译的部分过程\",{\"1\":{\"397\":1}}],[\"它通过定义一个创建对象的接口来实现\",{\"1\":{\"138\":1}}],[\"它通过共享尽可能多的相同对象来减少内存使用\",{\"1\":{\"249\":1}}],[\"它使类之间形成了弱关联关系\",{\"1\":{\"223\":1}}],[\"它主要用于以下情况\",{\"1\":{\"178\":1}}],[\"它们包括\",{\"1\":{\"498\":1}}],[\"它们对应的汇编代码如下\",{\"1\":{\"497\":1}}],[\"它们是以优先级从低到高排列的\",{\"1\":{\"494\":1}}],[\"它们是单字符的\",{\"1\":{\"425\":1}}],[\"它们的实现都很类似\",{\"1\":{\"498\":1}}],[\"它们的语法分析都相对容易\",{\"1\":{\"472\":1}}],[\"它们的内容比较多\",{\"1\":{\"471\":1}}],[\"它们的具体使用在后面的语法分析中会提到\",{\"1\":{\"425\":1}}],[\"它们不能被作为普通的标识符\",{\"1\":{\"434\":1}}],[\"它们不涉及优先级关系\",{\"1\":{\"425\":1}}],[\"它们自己就构成了标记\",{\"1\":{\"425\":1}}],[\"它们可以是一个数\",{\"1\":{\"408\":1}}],[\"它们基于\",{\"1\":{\"407\":1}}],[\"它们就是无符号的\",{\"1\":{\"405\":1}}],[\"它们在内存中的位置类似于下图\",{\"1\":{\"405\":1}}],[\"它们将作为我们的编译器最终输出的目标代码\",{\"1\":{\"403\":1}}],[\"它们过于强大\",{\"1\":{\"394\":1}}],[\"它们有很强的实际意义\",{\"1\":{\"394\":1}}],[\"它们呈现出一种相反的关系\",{\"1\":{\"383\":1}}],[\"它们都有对应的标记\",{\"1\":{\"429\":1}}],[\"它们都是\",{\"1\":{\"356\":1}}],[\"它们都可以工作于这\",{\"1\":{\"172\":1}}],[\"它们会被解析成标识符\",{\"1\":{\"434\":1}}],[\"它们会自动收到通知并更新显示\",{\"1\":{\"302\":1}}],[\"它们会操作同一个资源\",{\"1\":{\"99\":1}}],[\"它们之间互相通信\",{\"1\":{\"284\":1}}],[\"它们之间就构成了一个小小的层次结构\",{\"1\":{\"161\":1}}],[\"它们也有其局限性和适用范围\",{\"1\":{\"232\":1}}],[\"它可以是一个值\",{\"1\":{\"412\":1}}],[\"它可以在访问实际对象之前进行权限检查\",{\"1\":{\"332\":1}}],[\"它可以在协程内部用await调用另一个协程实现异步操作\",{\"1\":{\"101\":1}}],[\"它可以挂起当前协程任务\",{\"1\":{\"101\":1}}],[\"它和线程的最主要差别就是\",{\"1\":{\"100\":1}}],[\"它让调用者自己来决定什么时候让出\",{\"1\":{\"100\":1}}],[\"它应该具有反对称性\",{\"1\":{\"66\":1}}],[\"它与\",{\"1\":{\"31\":1}}],[\"满足不同的需求\",{\"1\":{\"243\":1}}],[\"满足\",{\"1\":{\"66\":1,\"81\":1,\"84\":1}}],[\"首先我们介绍\",{\"1\":{\"412\":1}}],[\"首先是数字\",{\"1\":{\"484\":1}}],[\"首先是之前定义过的\",{\"1\":{\"452\":1}}],[\"首先是\",{\"1\":{\"408\":1,\"441\":1}}],[\"首先在全局变量中加入一个枚举类型\",{\"1\":{\"407\":1}}],[\"首先要说明的是\",{\"1\":{\"400\":1}}],[\"首先要想到的是\",{\"1\":{\"253\":1}}],[\"首先\",{\"1\":{\"68\":1,\"78\":1,\"253\":1}}],[\"首先当\",{\"1\":{\"63\":1,\"64\":2,\"78\":1,\"79\":1,\"80\":1,\"81\":1}}],[\"首先由加法运算规则\",{\"1\":{\"62\":1}}],[\"首先有\",{\"1\":{\"62\":2,\"78\":1}}],[\"将参数出栈\",{\"1\":{\"482\":2}}],[\"将运算符\",{\"1\":{\"482\":1}}],[\"将它改成\",{\"1\":{\"452\":1}}],[\"将它们加入符号表\",{\"1\":{\"434\":1}}],[\"将对应地址中的整数载入\",{\"1\":{\"408\":1}}],[\"将对应地址中的字符载入\",{\"1\":{\"408\":1}}],[\"将\",{\"1\":{\"408\":3,\"425\":2,\"482\":1}}],[\"将语法树转化成目标代码\",{\"1\":{\"401\":1}}],[\"将词法分析得到的标记流\",{\"1\":{\"401\":1}}],[\"将来对数据结构的改良就会变得非常困难\",{\"1\":{\"388\":1}}],[\"将数据结构与操作分离\",{\"1\":{\"379\":1}}],[\"将通用的算法结构放在父类中\",{\"1\":{\"371\":1}}],[\"将状态迁移交给\",{\"1\":{\"353\":2}}],[\"将依赖于状态的处理分散在每个\",{\"1\":{\"353\":1}}],[\"将这些逻辑集中在中介者类中是更明智的选择\",{\"1\":{\"283\":1}}],[\"将共享对象存储在一个全局的集合中\",{\"1\":{\"255\":1}}],[\"将命令对象压入栈中\",{\"1\":{\"201\":1}}],[\"将类的这两个层次结构分离开有利于独立地对它们进行扩展\",{\"1\":{\"172\":1}}],[\"将现有类的接口转换为所需的接口\",{\"1\":{\"149\":1}}],[\"将具体实现传递给高层模块\",{\"1\":{\"129\":1}}],[\"将不同的算法封装在独立的类中\",{\"1\":{\"361\":1}}],[\"将不同的功能模块分开\",{\"1\":{\"125\":1}}],[\"将不同的职责分离到不同的类中\",{\"1\":{\"125\":2}}],[\"将下载的工具解压后得到的两个\",{\"1\":{\"111\":1}}],[\"将其称为新的乘法运算规则\",{\"1\":{\"78\":1}}],[\"将其称为新的加法运算规则\",{\"1\":{\"62\":1}}],[\"将模数直接包含在类型中\",{\"1\":{\"45\":1}}],[\"对应的\",{\"1\":{\"473\":1}}],[\"对应的汇编代码也比较直观\",{\"1\":{\"493\":1}}],[\"对应的汇编代码流程为\",{\"1\":{\"473\":1}}],[\"对应的汇编代码为\",{\"1\":{\"413\":1,\"414\":1,\"498\":1}}],[\"对应的汇编指令为\",{\"1\":{\"415\":1}}],[\"对词法分析器而言\",{\"1\":{\"426\":1}}],[\"对照\",{\"1\":{\"397\":1}}],[\"对数据结构中的元素进行处理的任务被分离出来\",{\"1\":{\"388\":1}}],[\"对修改是关闭的\",{\"1\":{\"385\":1}}],[\"对修改关闭的类具有高可复用性\",{\"1\":{\"385\":1}}],[\"对修改关闭\",{\"0\":{\"385\":1},\"1\":{\"115\":1,\"134\":1,\"379\":1}}],[\"对扩展是开放的\",{\"1\":{\"385\":1}}],[\"对扩展开放\",{\"0\":{\"385\":1},\"1\":{\"115\":1,\"134\":1,\"379\":1,\"385\":1}}],[\"对比这两个方法会发现\",{\"1\":{\"383\":1}}],[\"对象负责\",{\"1\":{\"323\":1}}],[\"对象太忙了\",{\"1\":{\"323\":1}}],[\"对象种类繁多\",{\"1\":{\"316\":1}}],[\"对象的所有操作权限\",{\"1\":{\"294\":1}}],[\"对象的状态\",{\"1\":{\"291\":1}}],[\"对多个地方产生影响\",{\"0\":{\"253\":1}}],[\"对\",{\"1\":{\"222\":1,\"356\":1}}],[\"对任意自然数\",{\"1\":{\"62\":3,\"63\":1,\"64\":3,\"78\":3,\"79\":1,\"80\":1,\"81\":2}}],[\"对于学习或考试而言或许可以\",{\"1\":{\"506\":1}}],[\"对于学习构建编译器帮助不大\",{\"1\":{\"401\":1}}],[\"对于变量\",{\"1\":{\"489\":1}}],[\"对于提高我们的水平还是很有帮助的\",{\"1\":{\"446\":1}}],[\"对于语法分析而言\",{\"1\":{\"429\":1}}],[\"对于一些简单的应用\",{\"1\":{\"295\":1}}],[\"对于那些能够明确地用语言描述出来的知识\",{\"1\":{\"235\":1}}],[\"对于\",{\"1\":{\"71\":1}}],[\"对于任意自然数\",{\"1\":{\"56\":1,\"59\":1,\"60\":1,\"75\":1,\"76\":1}}],[\"对于使用\",{\"1\":{\"31\":1}}],[\"根据标识符后的运算符\",{\"1\":{\"486\":1}}],[\"根据类型的不同有\",{\"1\":{\"408\":1}}],[\"根据文法来生成编译器\",{\"1\":{\"394\":1}}],[\"根据上一局的手势从概率上计算出下一局的手势\",{\"1\":{\"362\":1}}],[\"根据开闭原则\",{\"1\":{\"115\":1}}],[\"根据乘法消去律有\",{\"1\":{\"84\":1}}],[\"根据乘法运算规则\",{\"1\":{\"75\":1,\"76\":1}}],[\"根据序的反对称性有\",{\"1\":{\"84\":1}}],[\"根据加法结合律得出\",{\"1\":{\"70\":1}}],[\"根据加法结果的存在性得到\",{\"1\":{\"70\":1}}],[\"根据加法运算规则\",{\"1\":{\"59\":1,\"60\":1}}],[\"根据正自然数的性质得出\",{\"1\":{\"69\":1}}],[\"根据\",{\"1\":{\"62\":3,\"63\":1,\"64\":2,\"68\":2,\"78\":3,\"79\":1,\"80\":1,\"81\":1}}],[\"考虑诸如\",{\"1\":{\"495\":1}}],[\"考虑下列函数\",{\"1\":{\"463\":1}}],[\"考虑其他的类\",{\"1\":{\"351\":1}}],[\"考虑从乘法运算的定义下手\",{\"1\":{\"78\":1}}],[\"考虑从加法运算的定义下手\",{\"1\":{\"62\":1}}],[\"考虑到函数取模的优点\",{\"1\":{\"45\":1}}],[\"且当\",{\"1\":{\"501\":1}}],[\"且根据不同的类型移动的位移不同\",{\"1\":{\"498\":1}}],[\"且多数情况下如此\",{\"1\":{\"425\":1}}],[\"且不需要判断类型\",{\"1\":{\"408\":1}}],[\"且程序行为不变\",{\"1\":{\"134\":1}}],[\"且需要导出为pptx推荐\",{\"1\":{\"105\":1}}],[\"且乘法运算的结果存在且唯一之后\",{\"1\":{\"77\":1}}],[\"且\",{\"1\":{\"66\":1,\"69\":1,\"70\":1}}],[\"且加法运算的结果存在且唯一之后\",{\"1\":{\"61\":1}}],[\"且满足两个条件\",{\"1\":{\"56\":1}}],[\"唯一特殊的地方是\",{\"1\":{\"475\":1}}],[\"唯一\",{\"1\":{\"60\":4,\"76\":4}}],[\"唯一的缺点就是类型名难写\",{\"1\":{\"45\":1}}],[\"得到结果\",{\"1\":{\"482\":1}}],[\"得到\",{\"1\":{\"353\":1,\"482\":2}}],[\"得益于接口\",{\"1\":{\"221\":1}}],[\"得知\",{\"1\":{\"62\":3,\"63\":1,\"64\":2,\"78\":3,\"79\":1,\"80\":1,\"81\":1}}],[\"得出对于任意自然数\",{\"1\":{\"59\":1,\"60\":1,\"75\":1,\"76\":1}}],[\"得证\",{\"1\":{\"59\":1,\"60\":1,\"75\":1,\"76\":1}}],[\"成立\",{\"1\":{\"59\":1,\"60\":1,\"62\":3,\"63\":1,\"64\":3,\"75\":1,\"76\":1,\"78\":3,\"79\":1,\"80\":1,\"81\":2}}],[\"ⅴ\",{\"0\":{\"90\":1},\"1\":{\"59\":1,\"60\":1,\"62\":3,\"63\":1,\"64\":2,\"68\":1,\"71\":1,\"75\":1,\"76\":1,\"78\":3,\"79\":1,\"80\":1,\"81\":1}}],[\"综上\",{\"1\":{\"405\":1,\"482\":1}}],[\"综上所述\",{\"1\":{\"59\":1,\"60\":1,\"64\":1,\"75\":1,\"76\":1,\"81\":1}}],[\"综合考虑\",{\"1\":{\"53\":1}}],[\"ⅱ\",{\"0\":{\"87\":1},\"1\":{\"59\":2,\"60\":2,\"62\":1,\"75\":1,\"76\":1,\"78\":1,\"81\":1}}],[\"ⅰ\",{\"0\":{\"86\":1},\"1\":{\"59\":1,\"60\":1,\"62\":1,\"75\":1,\"76\":1,\"78\":1}}],[\"记得事先写一些用于输出汇编代码的函数\",{\"1\":{\"509\":1}}],[\"记得我们说过词法分析器也是某种意义上的编译器\",{\"1\":{\"426\":1}}],[\"记录\",{\"0\":{\"96\":1}}],[\"记\",{\"1\":{\"59\":1,\"60\":1,\"75\":1,\"76\":1}}],[\"也提到了优先级一般只与多元运算符有关\",{\"1\":{\"483\":1}}],[\"也许现在还想学习编译原理的人只可能是因为兴趣了\",{\"1\":{\"393\":1}}],[\"也不过是让程序睡眠\",{\"1\":{\"324\":1}}],[\"也不会被隐藏起来\",{\"1\":{\"221\":1}}],[\"也无法理解程序整体\",{\"1\":{\"185\":1}}],[\"也难以透彻地理解类的层次结构\",{\"1\":{\"162\":1}}],[\"也是一样的问题\",{\"1\":{\"412\":1}}],[\"也是用于指向栈的某些位置\",{\"1\":{\"406\":1}}],[\"也是不客观的\",{\"1\":{\"102\":1}}],[\"也是自然数\",{\"1\":{\"59\":1,\"75\":1}}],[\"也就能理解下面的源代码了\",{\"1\":{\"495\":1}}],[\"也就会导致写操作被原子性覆盖\",{\"1\":{\"101\":1}}],[\"也就是没有切换挂起状态\",{\"1\":{\"102\":1}}],[\"也就是一旦通过await关键字切换协程\",{\"1\":{\"101\":1}}],[\"也就是第二行代码print\",{\"1\":{\"101\":1}}],[\"也就是说由于我们的指令过于简单\",{\"1\":{\"412\":1}}],[\"也就是说可以\",{\"1\":{\"283\":1}}],[\"也就是说将\",{\"1\":{\"142\":1}}],[\"也就是说\",{\"1\":{\"58\":1,\"74\":1,\"161\":1,\"172\":1,\"221\":2,\"253\":2,\"254\":1,\"352\":1,\"353\":3,\"375\":2,\"384\":1}}],[\"也可以看文末给出的链接\",{\"1\":{\"498\":1}}],[\"也可以认为\",{\"1\":{\"482\":1}}],[\"也可以是一个地址\",{\"1\":{\"412\":1}}],[\"也可以是其它的数据\",{\"1\":{\"405\":1}}],[\"也可以说是\",{\"1\":{\"407\":1}}],[\"也可以直接\",{\"1\":{\"402\":1,\"420\":1,\"435\":1,\"456\":1,\"467\":1,\"477\":1,\"501\":1}}],[\"也可以恢复到之前的状态\",{\"1\":{\"297\":1}}],[\"也可以将它们自由组合成为新的对象\",{\"1\":{\"224\":1}}],[\"也可以理解为把程序\",{\"1\":{\"101\":1}}],[\"也可另外指定\",{\"1\":{\"10\":1}}],[\"也更简单\",{\"1\":{\"100\":1}}],[\"也能释放锁\",{\"1\":{\"99\":1}}],[\"也只能用到1个核\",{\"1\":{\"99\":1}}],[\"也唯一\",{\"1\":{\"60\":1,\"76\":1}}],[\"都比\",{\"1\":{\"508\":1}}],[\"都指向\",{\"1\":{\"473\":1}}],[\"都会非常困难\",{\"1\":{\"283\":1}}],[\"都会发生改变\",{\"1\":{\"253\":1}}],[\"都具有递归结构\",{\"1\":{\"221\":1}}],[\"都无需修改抽象工厂和\",{\"1\":{\"142\":1}}],[\"都保持了其一致性\",{\"1\":{\"101\":1}}],[\"都保证了其状态的一致性\",{\"1\":{\"101\":1}}],[\"都有唯一的数\",{\"1\":{\"81\":1}}],[\"都有序关系\",{\"1\":{\"71\":2}}],[\"都可以进行乘法运算\",{\"1\":{\"74\":1}}],[\"都可以进行加法运算\",{\"1\":{\"58\":1}}],[\"都是存放在计算机的\",{\"1\":{\"463\":1}}],[\"都是\",{\"1\":{\"352\":1}}],[\"都是对象\",{\"1\":{\"323\":1}}],[\"都是唯一的\",{\"1\":{\"60\":1,\"76\":1}}],[\"都是自然数\",{\"1\":{\"58\":1,\"59\":1,\"74\":1,\"75\":1}}],[\"加载变量的地址\",{\"1\":{\"486\":1}}],[\"加法保序性\",{\"0\":{\"72\":1}}],[\"加法消去律\",{\"0\":{\"64\":1},\"1\":{\"64\":1}}],[\"加法结合律\",{\"0\":{\"63\":1}}],[\"加法结果的唯一性\",{\"0\":{\"60\":1}}],[\"加法结果的存在性\",{\"0\":{\"59\":1}}],[\"加法交换律\",{\"0\":{\"62\":1}}],[\"加法的性质\",{\"0\":{\"61\":1}}],[\"加法的定义\",{\"0\":{\"58\":1}}],[\"加速\",{\"0\":{\"30\":1}}],[\"则结果是两个指针间隔的元素个数\",{\"1\":{\"498\":1}}],[\"则移动\",{\"1\":{\"498\":1}}],[\"则移动一字节\",{\"1\":{\"498\":1}}],[\"则意味着函数要退出了\",{\"1\":{\"475\":1}}],[\"则跳转到\",{\"1\":{\"473\":1}}],[\"则再加上\",{\"1\":{\"453\":1}}],[\"则可以断定是函数了\",{\"1\":{\"453\":1}}],[\"则说明是注释\",{\"1\":{\"432\":1}}],[\"则用于从子函数中返回\",{\"1\":{\"412\":1}}],[\"则会导致其失去作为可复用组件的独立性\",{\"1\":{\"185\":1}}],[\"则不需要加锁\",{\"1\":{\"102\":1}}],[\"则必须加锁\",{\"1\":{\"102\":1}}],[\"则对连通性无要求\",{\"1\":{\"90\":1}}],[\"则对一个数可以是多个数的后继\",{\"1\":{\"89\":1}}],[\"则对\",{\"1\":{\"88\":1}}],[\"则对点的出度无规定\",{\"1\":{\"87\":1}}],[\"则允许不存在\",{\"1\":{\"86\":1}}],[\"则存在正自然数\",{\"1\":{\"84\":1}}],[\"则由加法运算规则\",{\"1\":{\"81\":1}}],[\"则\",{\"1\":{\"58\":2,\"59\":1,\"60\":1,\"69\":1,\"70\":1,\"71\":3,\"72\":1,\"74\":2,\"75\":1,\"76\":1,\"83\":1,\"84\":1}}],[\"则有\",{\"1\":{\"56\":1,\"81\":1}}],[\"则需要写多个函数\",{\"1\":{\"44\":1}}],[\"为例\",{\"1\":{\"498\":1}}],[\"为例介绍几种写法\",{\"1\":{\"42\":1}}],[\"为\",{\"1\":{\"482\":2}}],[\"为零或不为零情况下的跳转\",{\"1\":{\"411\":1}}],[\"为此\",{\"1\":{\"388\":1}}],[\"为了实际将这个值保存起来\",{\"1\":{\"495\":1}}],[\"为了实现\",{\"1\":{\"411\":1}}],[\"为了防止因为顺序排列而执行了\",{\"1\":{\"473\":1}}],[\"为了在程序中体现这一点\",{\"1\":{\"324\":1}}],[\"为了让\",{\"1\":{\"324\":1}}],[\"为了解决这个问题\",{\"1\":{\"308\":1,\"342\":1}}],[\"为了避免这种情况\",{\"1\":{\"255\":1}}],[\"为了对比\",{\"1\":{\"101\":1}}],[\"为什么选择递归下降\",{\"0\":{\"443\":1},\"1\":{\"439\":1}}],[\"为什么不能直接使用\",{\"1\":{\"412\":1}}],[\"为什么\",{\"1\":{\"408\":1}}],[\"为什么使用代理模式\",{\"0\":{\"323\":1}}],[\"为什么使用观察者模式\",{\"0\":{\"302\":1}}],[\"为什么使用\",{\"0\":{\"249\":1,\"290\":1,\"347\":1,\"379\":1}}],[\"为什么使用外观模式\",{\"1\":{\"235\":1}}],[\"为什么使用装饰器模式\",{\"0\":{\"217\":1}}],[\"为什么使用此模式\",{\"0\":{\"196\":1,\"264\":1}}],[\"为什么使用此类\",{\"0\":{\"189\":1,\"279\":1}}],[\"为什么要用\",{\"1\":{\"426\":1}}],[\"为什么要用适配器模式\",{\"0\":{\"149\":1}}],[\"为什么要学编译原理\",{\"0\":{\"393\":1}}],[\"为什么要这么复杂\",{\"0\":{\"384\":1}}],[\"为什么要特意编写\",{\"0\":{\"365\":1}}],[\"为什么要使用迭代器模式\",{\"0\":{\"270\":1}}],[\"为什么要使用\",{\"0\":{\"178\":1,\"243\":1,\"316\":1,\"337\":1,\"371\":1}}],[\"为什么要使用抽象工厂模式\",{\"0\":{\"138\":1}}],[\"为自然数时\",{\"1\":{\"71\":1}}],[\"为自然数且\",{\"1\":{\"63\":1,\"64\":2,\"68\":1,\"79\":1,\"80\":1,\"81\":1}}],[\"为正自然数时有\",{\"1\":{\"68\":1}}],[\"为正自然数\",{\"1\":{\"68\":4}}],[\"为真命题可以推出\",{\"1\":{\"59\":1,\"60\":1,\"75\":1,\"76\":1}}],[\"为真命题可以推理出\",{\"1\":{\"56\":1}}],[\"为真命题\",{\"1\":{\"56\":2,\"59\":1,\"60\":1,\"75\":1,\"76\":1}}],[\"由上可以看出\",{\"1\":{\"429\":1}}],[\"由调用者将参数出栈\",{\"1\":{\"412\":1}}],[\"由调用者将参数入栈\",{\"1\":{\"412\":1}}],[\"由于取变量的值与函数的调用都是以\",{\"1\":{\"486\":1}}],[\"由于语法分析本身比较复杂\",{\"1\":{\"449\":1,\"460\":1}}],[\"由于本编译器的目的是达到自己编译自己\",{\"1\":{\"431\":1}}],[\"由于本人水平一般\",{\"1\":{\"397\":1}}],[\"由于我们的目标是能自举\",{\"1\":{\"429\":1}}],[\"由于词法分析的工作很常见\",{\"1\":{\"424\":1}}],[\"由于只存放字符串\",{\"1\":{\"405\":1}}],[\"由于在示例程序中只生成了一个\",{\"1\":{\"356\":1}}],[\"由于其他地方并没有控制消息发布和订阅的逻辑处理\",{\"1\":{\"283\":1}}],[\"由于笔者不太喜欢java\",{\"1\":{\"260\":1}}],[\"由于\",{\"1\":{\"253\":1}}],[\"由此有\",{\"1\":{\"84\":1}}],[\"由此知道假设不成立\",{\"1\":{\"81\":1}}],[\"由乘法运算规则\",{\"1\":{\"75\":1,\"76\":1}}],[\"由加法结果的唯一性有\",{\"1\":{\"76\":1}}],[\"由加法结果的存在性有\",{\"1\":{\"75\":1}}],[\"由加法消去律得到\",{\"1\":{\"69\":1}}],[\"由加法运算规则\",{\"1\":{\"59\":1,\"60\":1}}],[\"由\",{\"1\":{\"56\":1,\"59\":2,\"60\":2,\"69\":2,\"70\":2,\"71\":1,\"72\":1,\"75\":1,\"76\":1,\"81\":2,\"83\":1}}],[\"即当\",{\"1\":{\"498\":1}}],[\"即可\",{\"1\":{\"486\":1,\"489\":1}}],[\"即跨行的字符串拼接\",{\"1\":{\"484\":1}}],[\"即在这断代码之前\",{\"1\":{\"462\":1}}],[\"即我们将该变量的类别设置成了\",{\"1\":{\"454\":1}}],[\"即我们自己的虚拟机\",{\"1\":{\"402\":1}}],[\"即代码中的\",{\"1\":{\"453\":1}}],[\"即全局的定义语句\",{\"1\":{\"453\":1}}],[\"即向前看\",{\"1\":{\"436\":1}}],[\"即提前看多个字符\",{\"1\":{\"432\":1}}],[\"即用一个整型数组来保存相关的id信息\",{\"1\":{\"429\":1}}],[\"即用户主动触发协程切换\",{\"1\":{\"101\":1}}],[\"即如果它是个变量\",{\"1\":{\"429\":1}}],[\"即并不是多个字符共同构成标记\",{\"1\":{\"425\":1}}],[\"即前几篇中提到的\",{\"1\":{\"424\":1}}],[\"即与代码的上下文是有关系的\",{\"1\":{\"424\":1}}],[\"即标记本身和标记的值\",{\"1\":{\"422\":1}}],[\"即一连串的标记\",{\"1\":{\"422\":1}}],[\"即有两个参数\",{\"1\":{\"417\":1}}],[\"即保存当前的栈指针\",{\"1\":{\"413\":1}}],[\"即结果\",{\"1\":{\"411\":1}}],[\"即能自己编译自己\",{\"1\":{\"395\":1}}],[\"即构造一个工具\",{\"1\":{\"394\":1}}],[\"即应当将\",{\"1\":{\"254\":1}}],[\"即使最初实例很少\",{\"1\":{\"284\":1}}],[\"即使这些装饰边框都只具有非常简单的功能\",{\"1\":{\"224\":1}}],[\"即使被装饰物被边框装饰起来了\",{\"1\":{\"221\":1}}],[\"即使理解了\",{\"1\":{\"185\":1}}],[\"即使多个线程跑在8核处理上\",{\"1\":{\"99\":1}}],[\"即子类可以扩展父类的功能\",{\"1\":{\"118\":1}}],[\"即python3\",{\"1\":{\"101\":1}}],[\"即不会触发系统的全局解释器锁\",{\"1\":{\"100\":1}}],[\"即所谓的\",{\"1\":{\"100\":1}}],[\"即证明了乘法消去的保序性\",{\"1\":{\"84\":1}}],[\"即乘法结合律成立\",{\"1\":{\"80\":1}}],[\"即乘法分配律成立\",{\"1\":{\"79\":1}}],[\"即乘法交换律成立\",{\"1\":{\"78\":1}}],[\"即先证明乘法的两条运算规则符合交换律\",{\"1\":{\"78\":1}}],[\"即先证明加法的两条运算规则符合交换律\",{\"1\":{\"62\":1}}],[\"即任意两个自然数都可以进行乘法运算\",{\"1\":{\"77\":1}}],[\"即任意两个自然数都可以进行加法运算\",{\"1\":{\"61\":1}}],[\"即对于正自然数\",{\"1\":{\"68\":1}}],[\"即对于任意自然数\",{\"1\":{\"62\":1,\"63\":1,\"64\":1,\"78\":1,\"79\":1,\"80\":1,\"81\":1}}],[\"即加法结合律成立\",{\"1\":{\"63\":1}}],[\"即加法交换律成立\",{\"1\":{\"62\":1}}],[\"即由\",{\"1\":{\"59\":1,\"60\":1,\"75\":1,\"76\":1}}],[\"即\",{\"1\":{\"58\":1,\"59\":3,\"60\":3,\"64\":2,\"74\":1,\"75\":3,\"76\":3,\"81\":2,\"85\":5,\"160\":1,\"284\":2,\"366\":1,\"410\":1,\"422\":1,\"426\":1,\"443\":1,\"491\":1,\"494\":1,\"499\":1}}],[\"即假定\",{\"1\":{\"55\":1}}],[\"即写成\",{\"1\":{\"45\":1}}],[\"公理系统\",{\"2\":{\"92\":1}}],[\"公理系统内出发\",{\"1\":{\"82\":1}}],[\"公理自然不能从\",{\"1\":{\"82\":1}}],[\"公理自身任有待研究\",{\"1\":{\"82\":1}}],[\"公理每一条公理都被使用过\",{\"1\":{\"82\":1}}],[\"公理构建出了一个自然数代数系统\",{\"1\":{\"82\":1}}],[\"公理的合理性\",{\"0\":{\"82\":1}}],[\"公理相容\",{\"1\":{\"55\":1}}],[\"公理\",{\"0\":{\"86\":1,\"87\":1,\"88\":1,\"89\":1,\"90\":1},\"1\":{\"55\":1,\"56\":1,\"59\":2,\"60\":2,\"62\":3,\"63\":1,\"64\":2,\"68\":2,\"71\":1,\"75\":1,\"76\":1,\"78\":3,\"79\":1,\"80\":1,\"81\":4}}],[\"若在此通过\",{\"1\":{\"464\":1}}],[\"若是\",{\"1\":{\"432\":1}}],[\"若得到的是单个字符\",{\"1\":{\"431\":1}}],[\"若碰到了一个我们不认识的字符该怎么处理\",{\"1\":{\"426\":1}}],[\"若无特殊理由\",{\"1\":{\"385\":1}}],[\"若为多线程则需要加锁\",{\"1\":{\"250\":1}}],[\"若去除\",{\"1\":{\"86\":1,\"87\":1,\"88\":1,\"89\":1,\"90\":1}}],[\"若有\",{\"1\":{\"81\":1}}],[\"若\",{\"1\":{\"58\":2,\"59\":1,\"60\":1,\"69\":1,\"70\":1,\"71\":3,\"72\":1,\"74\":2,\"75\":1,\"76\":1,\"83\":1,\"84\":1}}],[\"若deactivate\",{\"1\":{\"54\":1}}],[\"若activate\",{\"1\":{\"54\":1}}],[\"会使用到\",{\"1\":{\"454\":1}}],[\"会增加许多的成本\",{\"1\":{\"420\":1}}],[\"会出现\",{\"1\":{\"419\":1}}],[\"会生成如下的\",{\"1\":{\"412\":1}}],[\"会像下面这样将处理委托给\",{\"1\":{\"352\":1}}],[\"会占用大量的内存资源\",{\"1\":{\"295\":1}}],[\"会有许多相似的代码\",{\"1\":{\"396\":1}}],[\"会有\",{\"1\":{\"284\":1}}],[\"会编写一个\",{\"1\":{\"160\":1}}],[\"会导致父类的任何变换都可能影响到子类的行为\",{\"1\":{\"131\":1}}],[\"会导致activating\",{\"1\":{\"54\":1}}],[\"会分两种情况\",{\"1\":{\"102\":1}}],[\"会被转交\",{\"1\":{\"222\":1}}],[\"会被顺序执行\",{\"1\":{\"101\":1}}],[\"会被强行终止\",{\"1\":{\"54\":1}}],[\"会和adb冲突\",{\"1\":{\"96\":1}}],[\"会带有本地路径\",{\"1\":{\"48\":1}}],[\"决定以后在学术研究和快速原型验证阶段使用\",{\"1\":{\"53\":1}}],[\"但也只有真正静下心来去克服它\",{\"1\":{\"509\":1}}],[\"但你依旧可以学习相关的知识\",{\"1\":{\"507\":1}}],[\"但这当中还有一个问题\",{\"1\":{\"498\":1}}],[\"但对理解计算机的原理有很大帮助\",{\"1\":{\"478\":1}}],[\"但没有关系\",{\"1\":{\"452\":1}}],[\"但真正看起来还是很烦\",{\"1\":{\"450\":1}}],[\"但由于符号表中已经有了相关的信息\",{\"1\":{\"434\":1}}],[\"但由子类决定要实例化的类是哪一个\",{\"1\":{\"242\":1}}],[\"但还有一个问题需要考虑\",{\"1\":{\"434\":1}}],[\"但还有一个问题是如何在子函数中获得传入的参数\",{\"1\":{\"416\":1}}],[\"但主要逻辑就是向前看一个字符来确定真正的标记\",{\"1\":{\"433\":1}}],[\"但仍支持\",{\"1\":{\"431\":1}}],[\"但有一点不同\",{\"1\":{\"427\":1}}],[\"但又枯燥且容易出错\",{\"1\":{\"424\":1}}],[\"但从结果可以看出\",{\"1\":{\"419\":1}}],[\"但就如上面的说\",{\"1\":{\"416\":1}}],[\"但最为重要的是\",{\"1\":{\"408\":1}}],[\"但更为简单\",{\"1\":{\"407\":1}}],[\"但更多时候我们都是在现有代码的基础上进行增加和修改\",{\"1\":{\"185\":1}}],[\"但我们一直用\",{\"1\":{\"487\":1}}],[\"但我们不确定数字\",{\"1\":{\"482\":1}}],[\"但我们上面的四则运算的文法就是左递归的\",{\"1\":{\"444\":1}}],[\"但我们的虚拟机中\",{\"1\":{\"420\":1}}],[\"但我们的虚拟机中只使用\",{\"1\":{\"406\":1}}],[\"但我们的\",{\"1\":{\"412\":1}}],[\"但我们讲解的顺序并不依据它\",{\"1\":{\"407\":1}}],[\"但我们还没有写任何编译相关的代码\",{\"1\":{\"406\":1}}],[\"但我不会评价大家的工作细节\",{\"1\":{\"279\":1}}],[\"但理解起来应该作为无符号的整型\",{\"1\":{\"405\":1}}],[\"但实际编译项目时\",{\"1\":{\"506\":1}}],[\"但实际上由于我们还将在符号表中加入关键字如\",{\"1\":{\"429\":1}}],[\"但实际上我们构建的是\",{\"1\":{\"400\":1}}],[\"但实际情况并非如此\",{\"1\":{\"408\":1}}],[\"但实际实现上较为复杂且与编译无关\",{\"1\":{\"405\":1}}],[\"但需要了解的是\",{\"1\":{\"405\":1}}],[\"但确为自己重写\",{\"1\":{\"395\":1}}],[\"但随着计算机性能的提升\",{\"1\":{\"393\":1}}],[\"但如果你查看了\",{\"1\":{\"457\":1}}],[\"但如果有兴趣的话\",{\"1\":{\"456\":1}}],[\"但如果能掌握它\",{\"1\":{\"446\":1}}],[\"但如果需要修改现有代码\",{\"1\":{\"385\":1}}],[\"但如有条件还请支持正版\",{\"1\":{\"111\":1}}],[\"但可以有效地管理内存\",{\"1\":{\"255\":1}}],[\"但可能会导致内存泄漏\",{\"1\":{\"255\":1}}],[\"但它又与编译器没有太大的联系\",{\"1\":{\"418\":1}}],[\"但它却难以应对\",{\"1\":{\"387\":1}}],[\"但它们的目的和实现方式有所不同\",{\"1\":{\"329\":1}}],[\"但它们的接口并不符合当前系统的需求\",{\"1\":{\"149\":1}}],[\"但它需要我们在理解其核心思想的基础上\",{\"1\":{\"232\":1}}],[\"但程序暂时无法直接决定由哪个对象负责处理时\",{\"1\":{\"188\":1}}],[\"但不知道构建的具体步骤\",{\"1\":{\"183\":1}}],[\"但不知道对象的具体表示\",{\"1\":{\"183\":1}}],[\"但委托是弱关联关系\",{\"1\":{\"173\":1}}],[\"但切换过程是争抢的\",{\"1\":{\"101\":1}}],[\"但归根结底\",{\"1\":{\"100\":1}}],[\"但其中用到的原理还是需要仔细推敲的\",{\"1\":{\"502\":1}}],[\"但其中并没有任何汇编代码\",{\"1\":{\"435\":1}}],[\"但其实内容不多\",{\"1\":{\"402\":1}}],[\"但其实\",{\"1\":{\"99\":1}}],[\"但其静态计算图机制在开发过程中略显繁琐\",{\"1\":{\"53\":1}}],[\"但事实上是\",{\"1\":{\"98\":1}}],[\"但\",{\"1\":{\"82\":1,\"285\":1}}],[\"但是两节课后我就放弃了\",{\"1\":{\"394\":1}}],[\"但是要达到这个目的是有条件的\",{\"1\":{\"388\":1}}],[\"但是好在我们绝对不会忘记实现这个方法\",{\"1\":{\"355\":1}}],[\"但是当状态非常多的时候\",{\"1\":{\"351\":1}}],[\"但是需要考虑到的是\",{\"1\":{\"284\":1}}],[\"但是没有将应当集中的处理集中起来\",{\"1\":{\"283\":1}}],[\"但是在本章中的示例程序中\",{\"1\":{\"283\":1}}],[\"但是意见难以统一\",{\"1\":{\"279\":1}}],[\"但是越装饰\",{\"1\":{\"222\":1}}],[\"但是它们的使用目的不同\",{\"1\":{\"221\":1}}],[\"但是接口\",{\"1\":{\"221\":1}}],[\"但是有时候也确实存在需要\",{\"1\":{\"188\":1}}],[\"但是不能改变父类原有的功能\",{\"1\":{\"118\":1}}],[\"但是给一个垂死的人注射吗啡\",{\"1\":{\"102\":1}}],[\"但是我们也付出了相应的代价\",{\"1\":{\"101\":1}}],[\"但是可以保证最终一致性呢\",{\"1\":{\"101\":1}}],[\"但是所有协程执行完毕后\",{\"1\":{\"101\":1}}],[\"但是线程时系统调度\",{\"1\":{\"99\":1}}],[\"但是python受限于gil全局解释器锁\",{\"1\":{\"99\":1}}],[\"但是模数个数少的时候可以缩写\",{\"1\":{\"45\":1}}],[\"但是\",{\"1\":{\"44\":1,\"161\":1,\"352\":1,\"353\":1,\"355\":1,\"384\":1,\"385\":1,\"418\":1}}],[\"但是这种方法有着严重的缺陷\",{\"1\":{\"43\":1}}],[\"寻得了linux\",{\"1\":{\"53\":1}}],[\"选择了\",{\"1\":{\"53\":1}}],[\"仍然支持\",{\"1\":{\"53\":1}}],[\"而忽略了同样重要的代码生成\",{\"1\":{\"506\":1}}],[\"而数字\",{\"1\":{\"490\":1}}],[\"而就像上节中提到的\",{\"1\":{\"488\":1}}],[\"而普通的函数则编译成\",{\"1\":{\"486\":1}}],[\"而剩下的较难较烦的部分是与目标代码的生成有关的\",{\"1\":{\"483\":1}}],[\"而真正的难点是如何在语法分析时收集足够多的信息\",{\"1\":{\"478\":1}}],[\"而它们的逻辑和全局变量的解析几乎一致\",{\"1\":{\"468\":1}}],[\"而②则用于生成汇编代码\",{\"1\":{\"466\":1}}],[\"而②则与上节中提到的\",{\"1\":{\"465\":1}}],[\"而②中的代码是用于将符号表中的信息恢复成全局的信息\",{\"1\":{\"464\":1}}],[\"而注意到上节中\",{\"1\":{\"454\":1}}],[\"而如果\",{\"1\":{\"498\":1}}],[\"而如果是全局变量则用\",{\"1\":{\"486\":1}}],[\"而如果只解析到类型\",{\"1\":{\"453\":1}}],[\"而如果操作同一资源\",{\"1\":{\"99\":1}}],[\"而为了实现自举\",{\"1\":{\"450\":1}}],[\"而左递归的语法是没法直接使用递归下降的方法实现的\",{\"1\":{\"444\":1}}],[\"而没有出现在\",{\"1\":{\"441\":1}}],[\"而我们可以从解析的过程中看出\",{\"1\":{\"442\":1}}],[\"而我们定义的语法不支持\",{\"1\":{\"429\":1}}],[\"而我们还存放了一些只有语法分析器才会得到的信息\",{\"1\":{\"429\":1}}],[\"而我们又不希望扩充现有指令的功能\",{\"1\":{\"412\":1}}],[\"而我们又想在执行过程中保证共享数据的强一致性\",{\"1\":{\"101\":1}}],[\"而之后的语句\",{\"1\":{\"429\":1}}],[\"而只关心这个变量名代表的唯一标识\",{\"1\":{\"429\":1}}],[\"而词法分析器能减小语法分析复杂度的原因\",{\"1\":{\"425\":1}}],[\"而词法分析器则是以源码字符串为输入\",{\"1\":{\"423\":1}}],[\"而标记流对于语法分析器而言就容易处理得多了\",{\"1\":{\"423\":1}}],[\"而地址通常是需要通过计算获得\",{\"1\":{\"408\":1}}],[\"而这就意味着我们需要决定先为哪个运算符生成目标代码\",{\"1\":{\"482\":1}}],[\"而这些可能需要你重新回顾一下\",{\"1\":{\"468\":1}}],[\"而这些寄存器只是用于保存这些状态的\",{\"1\":{\"406\":1}}],[\"而这个标记足够让我们确定用哪个表达式了\",{\"1\":{\"443\":1}}],[\"而这部分能帮助我们了解计算机的工作原理\",{\"1\":{\"400\":1}}],[\"而电脑上的实际内存可能只有\",{\"1\":{\"405\":1}}],[\"而其它方面如词法分析\",{\"1\":{\"400\":1}}],[\"而会不会写编译器则是第二道\",{\"1\":{\"393\":1}}],[\"而将该方法的实现交给了子类\",{\"1\":{\"375\":1}}],[\"而将一些步骤的具体实现延迟到子类中\",{\"1\":{\"370\":1}}],[\"而忘记了在\",{\"1\":{\"355\":1}}],[\"而委托模式通过委托对象来执行具体的任务\",{\"1\":{\"329\":1}}],[\"而委托模式则用于将任务分配给其他对象来执行\",{\"1\":{\"329\":1}}],[\"而委托对象应当能够无缝地完成这些任务\",{\"1\":{\"229\":1}}],[\"而不能以值作为参数\",{\"1\":{\"408\":1}}],[\"而不需要修改现有的数据结构\",{\"1\":{\"379\":1}}],[\"而不需要修改现有的代码\",{\"1\":{\"361\":1}}],[\"而不需要关心代理对象的内部实现\",{\"1\":{\"330\":1}}],[\"而不需要客户端了解远程服务器的具体实现\",{\"1\":{\"328\":1}}],[\"而不会影响系统的其他部分\",{\"1\":{\"306\":1}}],[\"而不影响系统的功能\",{\"1\":{\"306\":1}}],[\"而不是\",{\"1\":{\"432\":1,\"443\":1,\"482\":1}}],[\"而不是盲目地套用\",{\"1\":{\"232\":1}}],[\"而不是继承\",{\"1\":{\"134\":1}}],[\"而不是一个通用接口\",{\"1\":{\"134\":1}}],[\"而不是通过继承\",{\"1\":{\"132\":2}}],[\"而不是具体实现\",{\"1\":{\"129\":1}}],[\"而不是面向实现编程\",{\"1\":{\"128\":1}}],[\"而不是重写父类的具体方法\",{\"1\":{\"119\":1}}],[\"而在我们的虚拟机中\",{\"1\":{\"409\":1}}],[\"而在内存容量多的运行环境中则可以使用\",{\"1\":{\"366\":1}}],[\"而在\",{\"1\":{\"354\":1}}],[\"而在其他情况下\",{\"1\":{\"296\":1}}],[\"而在工业生产部署阶段方才使用\",{\"1\":{\"53\":1}}],[\"而对于一些复杂的应用\",{\"1\":{\"295\":1}}],[\"而窄接口则只提供了有限的操作权限\",{\"1\":{\"294\":1}}],[\"而内存是资源中的一种\",{\"1\":{\"256\":1}}],[\"而应理解其背后的核心思想\",{\"1\":{\"232\":1}}],[\"而无需了解其内部实现细节\",{\"1\":{\"273\":1}}],[\"而无需暴露其底层表示\",{\"1\":{\"270\":1,\"271\":1}}],[\"而无需修改现有代码\",{\"1\":{\"264\":1}}],[\"而无需修改原始类的代码\",{\"1\":{\"216\":1}}],[\"而无需明确指定具体类\",{\"1\":{\"138\":1}}],[\"而文件则是叶子节点\",{\"1\":{\"206\":1}}],[\"而具体的表示则可以在运行时灵活选择\",{\"1\":{\"184\":1}}],[\"而有些事情则需要在运行时决定\",{\"1\":{\"184\":1}}],[\"而有没有锁\",{\"1\":{\"99\":1}}],[\"而是如何为运算符生成相应的汇编代码\",{\"1\":{\"506\":1}}],[\"而是单个数字的取正取负操作\",{\"1\":{\"492\":1}}],[\"而是操作\",{\"1\":{\"405\":1}}],[\"而是用状态迁移表来设计程序\",{\"1\":{\"353\":1}}],[\"而是将所有的状态迁移交给扮演\",{\"1\":{\"353\":1}}],[\"而是将它放在\",{\"1\":{\"253\":1}}],[\"而是将其他\",{\"1\":{\"173\":1}}],[\"而是应该用代码将它们表现出来\",{\"1\":{\"235\":1}}],[\"而是为了更好地解决问题和优化代码结构\",{\"1\":{\"232\":1}}],[\"而是相互关联的\",{\"1\":{\"114\":1}}],[\"而且这些功能需求大都是\",{\"1\":{\"385\":1}}],[\"而且我们必须在所有的事件处理方法中都编写这些条件分支语句\",{\"1\":{\"351\":1}}],[\"而且当将子类替换为\",{\"1\":{\"185\":1}}],[\"而且\",{\"1\":{\"172\":1,\"365\":1}}],[\"而子类的任务是实现抽象方法\",{\"1\":{\"161\":1}}],[\"而协程虽然在手动切换过程中也无法保证状态一致\",{\"1\":{\"101\":1}}],[\"而线程是抢占使用权\",{\"1\":{\"100\":1}}],[\"而现在\",{\"1\":{\"99\":1}}],[\"而\",{\"1\":{\"53\":2,\"284\":1,\"294\":1,\"297\":1,\"383\":2,\"395\":1,\"408\":1,\"464\":2,\"494\":1}}],[\"0xffff\",{\"1\":{\"491\":1}}],[\"0x123\",{\"1\":{\"430\":1}}],[\"017\",{\"1\":{\"430\":1}}],[\"00\",{\"1\":{\"349\":24}}],[\"00`\",{\"1\":{\"348\":2}}],[\"0\",{\"0\":{\"392\":1},\"1\":{\"53\":1,\"99\":1,\"100\":1,\"101\":17,\"165\":1,\"169\":1,\"190\":1,\"191\":1,\"197\":1,\"198\":2,\"208\":1,\"212\":3,\"218\":4,\"250\":1,\"265\":2,\"272\":2,\"291\":2,\"303\":3,\"304\":2,\"324\":1,\"339\":1,\"343\":1,\"348\":1,\"362\":14,\"372\":2,\"380\":2,\"381\":3,\"392\":2,\"400\":1,\"402\":7,\"403\":1,\"405\":3,\"406\":2,\"408\":1,\"418\":1,\"419\":2,\"421\":1,\"428\":1,\"429\":1,\"430\":11,\"431\":1,\"432\":1,\"439\":1,\"445\":8,\"449\":1,\"452\":1,\"454\":1,\"460\":1,\"465\":1,\"471\":1,\"481\":1,\"484\":2,\"486\":2,\"490\":4,\"492\":1,\"505\":1}}],[\"0<=x\",{\"1\":{\"45\":1}}],[\"然而如果你能跟我一样\",{\"1\":{\"394\":1}}],[\"然而\",{\"1\":{\"140\":1,\"232\":1,\"255\":1}}],[\"然而我们都忽略了一个客观事实\",{\"1\":{\"101\":1}}],[\"然而人们很快发现\",{\"1\":{\"99\":1}}],[\"然而速度太慢\",{\"1\":{\"53\":1}}],[\"然后返回它在\",{\"1\":{\"431\":1}}],[\"然后让数据结构可以接受访问者的访问即可\",{\"1\":{\"378\":1}}],[\"然后让后者去验算前者的计算结果\",{\"1\":{\"366\":1}}],[\"然后在程序中以委托的方式来使用算法\",{\"1\":{\"365\":1}}],[\"然后在具体类中实现这些行为\",{\"1\":{\"132\":1}}],[\"然后实现一些所需的方法就可以了\",{\"1\":{\"355\":1}}],[\"然后进行相应的处理\",{\"1\":{\"351\":1}}],[\"然后下达指示\",{\"1\":{\"279\":1}}],[\"然后按照它们在职责链上的顺序一个一个地找出到底应该谁来负责处理\",{\"1\":{\"188\":1}}],[\"然后再去看看\",{\"1\":{\"185\":1}}],[\"然后编写\",{\"1\":{\"172\":1}}],[\"然后保存在字段中\",{\"1\":{\"164\":1}}],[\"然后子类负责实现这些抽象方法\",{\"1\":{\"161\":1}}],[\"然后\",{\"1\":{\"99\":1}}],[\"然后才能去处理另一件事情\",{\"1\":{\"98\":1}}],[\"然后就能正常访问\",{\"1\":{\"19\":1}}],[\"近日使用\",{\"1\":{\"53\":1}}],[\"用来求值\",{\"1\":{\"481\":1}}],[\"用尖括号\",{\"1\":{\"441\":1}}],[\"用作保存全局标识符的信息\",{\"1\":{\"429\":1}}],[\"用更多的指令来完成更多的功能\",{\"1\":{\"420\":1}}],[\"用以存放局部变量\",{\"1\":{\"413\":1}}],[\"用什么有穷自动机和无穷自动机\",{\"1\":{\"394\":1}}],[\"用类来表示状态\",{\"1\":{\"353\":1}}],[\"用类实现\",{\"2\":{\"204\":1,\"268\":1}}],[\"用\",{\"1\":{\"222\":1,\"484\":1,\"492\":1}}],[\"用户可以统一地对待单个对象和组合对象\",{\"1\":{\"206\":1}}],[\"用字符串显示\",{\"1\":{\"164\":1}}],[\"用android\",{\"1\":{\"96\":1}}],[\"用acme\",{\"1\":{\"26\":1}}],[\"用图论阐述\",{\"0\":{\"85\":1}}],[\"用于标识符的快速比较\",{\"1\":{\"429\":1}}],[\"用于实现\",{\"1\":{\"413\":1,\"414\":1}}],[\"用于为程序动态分配内存\",{\"1\":{\"405\":1}}],[\"用于处理函数调用相关的数据\",{\"1\":{\"405\":1}}],[\"用于存放未初始化的数据\",{\"1\":{\"405\":1}}],[\"用于存放初始化了的数据\",{\"1\":{\"405\":1}}],[\"用于存放代码\",{\"1\":{\"405\":1}}],[\"用于解析该参数的类型\",{\"1\":{\"465\":1}}],[\"用于解析枚举类型的定义\",{\"1\":{\"454\":1}}],[\"用于解析一个表达式\",{\"1\":{\"402\":1}}],[\"用于解释目标代码\",{\"1\":{\"402\":1}}],[\"用于语法分析\",{\"1\":{\"401\":1}}],[\"用于词法分析\",{\"1\":{\"401\":1,\"402\":1}}],[\"用于将字符串转化成内部的表示结构\",{\"1\":{\"401\":1}}],[\"用于遍历\",{\"1\":{\"273\":1}}],[\"用于创建相关或依赖对象的家族\",{\"1\":{\"138\":1}}],[\"用于工业生产部署\",{\"1\":{\"53\":1}}],[\"用于快速原型验证\",{\"1\":{\"53\":1}}],[\"2|\",{\"1\":{\"482\":1}}],[\"2+3\",{\"1\":{\"482\":1}}],[\"2+3的值\",{\"1\":{\"482\":1}}],[\"2+\",{\"1\":{\"416\":2,\"463\":2}}],[\"2^32\",{\"1\":{\"405\":1}}],[\"24\",{\"1\":{\"348\":1}}],[\"26\",{\"1\":{\"304\":2}}],[\"264\",{\"1\":{\"191\":1}}],[\"256\",{\"1\":{\"402\":1,\"405\":1}}],[\"25\",{\"1\":{\"292\":1,\"304\":2}}],[\"25866579\",{\"1\":{\"38\":1}}],[\"22\",{\"1\":{\"251\":10,\"304\":2}}],[\"2222222222\",{\"1\":{\"251\":1}}],[\"222222\",{\"1\":{\"251\":1}}],[\"297\",{\"1\":{\"191\":1}}],[\"231\",{\"1\":{\"191\":1,\"292\":1}}],[\"2014\",{\"1\":{\"481\":1}}],[\"2016\",{\"1\":{\"439\":1,\"449\":1,\"460\":1,\"471\":1,\"505\":1}}],[\"2015\",{\"1\":{\"400\":1,\"403\":1,\"421\":1}}],[\"2017\",{\"1\":{\"260\":1}}],[\"20\",{\"1\":{\"284\":1,\"303\":1,\"304\":2,\"419\":1,\"453\":1,\"482\":2}}],[\"20000\",{\"1\":{\"211\":1,\"212\":2,\"380\":1,\"381\":2}}],[\"200\",{\"1\":{\"190\":1,\"211\":1,\"212\":1,\"380\":1,\"381\":1}}],[\"208\",{\"1\":{\"98\":1,\"102\":1}}],[\"28\",{\"1\":{\"101\":1,\"304\":2}}],[\"2\",{\"1\":{\"52\":1,\"53\":1,\"100\":1,\"101\":3,\"190\":1,\"198\":2,\"250\":1,\"284\":1,\"291\":3,\"304\":2,\"362\":3,\"392\":1,\"400\":2,\"403\":17,\"412\":2,\"416\":2,\"418\":4,\"421\":3,\"422\":2,\"435\":1,\"439\":2,\"442\":2,\"449\":7,\"460\":7,\"463\":2,\"466\":1,\"471\":3,\"481\":14,\"482\":7,\"486\":1,\"505\":2}}],[\"踩坑记录\",{\"0\":{\"53\":1},\"2\":{\"50\":1}}],[\">|\",{\"1\":{\"429\":1,\"466\":1}}],[\">=\",{\"1\":{\"417\":1,\"429\":5,\"430\":8,\"433\":1,\"445\":2,\"488\":1,\"494\":1,\"498\":1}}],[\">=2\",{\"1\":{\"53\":1}}],[\">>\",{\"1\":{\"372\":1,\"373\":1,\"417\":1,\"433\":1,\"498\":1}}],[\">hiroshi\",{\"1\":{\"238\":1}}],[\">excite<\",{\"1\":{\"139\":1}}],[\">jp\",{\"1\":{\"139\":1}}],[\">us\",{\"1\":{\"139\":1}}],[\">gmw<\",{\"1\":{\"139\":1}}],[\">people<\",{\"1\":{\"139\":1}}],[\">$\",{\"1\":{\"139\":1,\"237\":1}}],[\">\",{\"1\":{\"48\":2,\"291\":2,\"402\":1,\"417\":1,\"423\":4,\"430\":1,\"433\":3,\"445\":1,\"452\":1,\"486\":1,\"493\":1,\"498\":2,\"499\":3,\"500\":1}}],[\"生成汇编代码\",{\"1\":{\"499\":2}}],[\"生成了如下的汇编代码\",{\"1\":{\"495\":1}}],[\"生成一个同名的函数\",{\"1\":{\"443\":1}}],[\"生成一棵语法树\",{\"1\":{\"401\":1}}],[\"生成实例\",{\"2\":{\"146\":1,\"187\":1,\"321\":1,\"345\":1}}],[\"生成\",{\"1\":{\"48\":1,\"324\":1}}],[\"生活记录等非技术类文章\",{\"1\":{\"2\":1}}],[\"泛型编程\",{\"0\":{\"45\":1}}],[\"泛型与\",{\"0\":{\"40\":1}}],[\"的表示方法\",{\"1\":{\"508\":1}}],[\"的表达式\",{\"1\":{\"495\":1}}],[\"的地址两次\",{\"1\":{\"493\":1}}],[\"的优先级最高\",{\"1\":{\"494\":1}}],[\"的优先级最低\",{\"1\":{\"494\":1}}],[\"的优先级高于\",{\"1\":{\"493\":1}}],[\"的优先级就要高于\",{\"1\":{\"425\":1}}],[\"的指针取值\",{\"1\":{\"488\":1}}],[\"的指令集\",{\"1\":{\"407\":1}}],[\"的形式\",{\"1\":{\"486\":1}}],[\"的形式返回\",{\"1\":{\"431\":1}}],[\"的运算符\",{\"1\":{\"482\":1}}],[\"的运算结果为\",{\"1\":{\"58\":1,\"74\":1}}],[\"的结果\",{\"1\":{\"482\":1}}],[\"的结果是否唯一\",{\"1\":{\"60\":1,\"76\":1}}],[\"的位置\",{\"1\":{\"465\":1,\"473\":1}}],[\"的产生式转换成函数的过程\",{\"1\":{\"457\":1}}],[\"的具体表示方法后就不难理解了\",{\"1\":{\"457\":1}}],[\"的扩展\",{\"1\":{\"450\":1}}],[\"的概念了\",{\"1\":{\"443\":1}}],[\"的概念\",{\"1\":{\"432\":1,\"436\":1}}],[\"的注释\",{\"1\":{\"432\":1}}],[\"的语法\",{\"1\":{\"431\":1}}],[\"的转义符\",{\"1\":{\"431\":1}}],[\"的源代码的\",{\"1\":{\"430\":1}}],[\"的字符个数\",{\"1\":{\"432\":1}}],[\"的字符\",{\"1\":{\"426\":1}}],[\"的字体数据属于\",{\"1\":{\"254\":1}}],[\"的字体数据不论在\",{\"1\":{\"254\":1}}],[\"的功能包含了\",{\"1\":{\"415\":1}}],[\"的功能\",{\"1\":{\"413\":1}}],[\"的功能是抽象的\",{\"1\":{\"164\":1}}],[\"的子函数\",{\"1\":{\"412\":1}}],[\"的作用是跳转到地址为\",{\"1\":{\"412\":1}}],[\"的作用是将值或寄存器\",{\"1\":{\"409\":1}}],[\"的作用是退栈\",{\"1\":{\"408\":1}}],[\"的值\",{\"1\":{\"410\":1,\"487\":1,\"498\":1}}],[\"的值放入栈中\",{\"1\":{\"409\":1}}],[\"的值放到栈上\",{\"1\":{\"408\":1}}],[\"的值减小\",{\"1\":{\"406\":1}}],[\"的内容放在\",{\"1\":{\"408\":1}}],[\"的内部状态不会被外部直接修改\",{\"1\":{\"294\":1}}],[\"的函数\",{\"1\":{\"402\":1}}],[\"的学生顶多学到语法分析就结束了\",{\"1\":{\"394\":1}}],[\"的课程后\",{\"1\":{\"394\":1}}],[\"的意思\",{\"1\":{\"385\":2}}],[\"的意思是\",{\"1\":{\"254\":2}}],[\"的算法\",{\"1\":{\"366\":1}}],[\"的使用方式是不一样的\",{\"1\":{\"356\":1}}],[\"的代码完全是手工实现的\",{\"1\":{\"395\":1}}],[\"的代码\",{\"1\":{\"394\":1}}],[\"的代码即可\",{\"1\":{\"355\":1}}],[\"的代码后才能理解\",{\"1\":{\"185\":1}}],[\"的一个问题\",{\"1\":{\"426\":1}}],[\"的一个命题\",{\"1\":{\"56\":1}}],[\"的一览表\",{\"1\":{\"353\":1}}],[\"的信息集中在了一个类中\",{\"1\":{\"353\":1}}],[\"的实质就是两个运算符在抢参数\",{\"1\":{\"482\":1}}],[\"的实际运行顺序是\",{\"1\":{\"482\":1}}],[\"的实现方法\",{\"1\":{\"352\":1}}],[\"的实例\",{\"1\":{\"356\":1}}],[\"的实例在\",{\"1\":{\"254\":1}}],[\"的实例作为参数传递给\",{\"1\":{\"173\":1}}],[\"的行为会对被观察对象产生影响时\",{\"0\":{\"308\":1}}],[\"的顺序\",{\"0\":{\"307\":1}}],[\"的栈\",{\"1\":{\"297\":1}}],[\"的有效期限\",{\"1\":{\"296\":1}}],[\"的有效期限取决于具体的应用场景\",{\"1\":{\"296\":1}}],[\"的有效期限是多久\",{\"0\":{\"296\":1}}],[\"的交互\",{\"1\":{\"283\":1}}],[\"的原因\",{\"1\":{\"283\":1}}],[\"的问题\",{\"1\":{\"255\":1}}],[\"的时候\",{\"1\":{\"235\":1}}],[\"的透明性\",{\"0\":{\"221\":1},\"1\":{\"221\":1}}],[\"的层次结构\",{\"1\":{\"206\":1}}],[\"的情况\",{\"1\":{\"188\":1}}],[\"的\",{\"1\":{\"172\":1,\"221\":1,\"307\":4,\"408\":2}}],[\"的缩写\",{\"1\":{\"164\":1}}],[\"的最上层\",{\"1\":{\"164\":1}}],[\"的类型\",{\"1\":{\"488\":1}}],[\"的类来访问数据结构中的元素\",{\"1\":{\"378\":1}}],[\"的类\",{\"1\":{\"164\":3}}],[\"的操作等价于\",{\"1\":{\"500\":1}}],[\"的操作\",{\"1\":{\"101\":1,\"493\":1}}],[\"的入度无规定\",{\"1\":{\"88\":1}}],[\"的假设矛盾\",{\"1\":{\"84\":1}}],[\"的和\",{\"1\":{\"68\":1}}],[\"的任意性\",{\"1\":{\"59\":1,\"60\":1,\"75\":1,\"76\":1}}],[\"的性质和\",{\"1\":{\"59\":1,\"60\":1,\"75\":1,\"76\":1}}],[\"的后继\",{\"1\":{\"56\":1,\"81\":1}}],[\"的动态计算图机制使得调试和开发更加灵活\",{\"1\":{\"53\":1}}],[\"的话\",{\"1\":{\"44\":1}}],[\"的域名\",{\"1\":{\"31\":1}}],[\"第二个参数放在\",{\"1\":{\"417\":1}}],[\"第二种\",{\"0\":{\"44\":1}}],[\"第一个参数放在栈顶\",{\"1\":{\"417\":1}}],[\"第一篇完全没有正题相关的内容也是希望你能有所心理准备再开始学习\",{\"1\":{\"396\":1}}],[\"第一种策略是\",{\"1\":{\"362\":1}}],[\"第一种\",{\"0\":{\"43\":1}}],[\"第三个字符的颜色是红色的\",{\"1\":{\"253\":1}}],[\"第\",{\"1\":{\"161\":1,\"353\":1}}],[\"不知道你是否有同感\",{\"1\":{\"506\":1}}],[\"不指定的话一般认为是第一个出现的非终结符\",{\"1\":{\"442\":1}}],[\"不断地对非终结符进行分解\",{\"1\":{\"440\":1}}],[\"不识别\",{\"1\":{\"426\":1}}],[\"不只是\",{\"1\":{\"352\":1}}],[\"不能用一般的方法解决时\",{\"1\":{\"351\":1}}],[\"不能因为方法的调用顺序发生改变而产生问题\",{\"1\":{\"307\":1}}],[\"不仅要考虑函数的地址\",{\"1\":{\"412\":1}}],[\"不仅会增加代码的复杂性\",{\"1\":{\"283\":1}}],[\"不仅如此\",{\"1\":{\"279\":1}}],[\"不同类型的集合可以使用相同的遍历方式\",{\"1\":{\"270\":1}}],[\"不同的只是赋值的信息\",{\"1\":{\"434\":1}}],[\"不同的表示\",{\"1\":{\"178\":1}}],[\"不同的自然数后继不同\",{\"1\":{\"56\":1}}],[\"不要让被共享的实例被垃圾回收器回收了\",{\"0\":{\"255\":1}}],[\"不要使用类继承\",{\"1\":{\"131\":1}}],[\"不论在什么情况下都不会改变的信息\",{\"1\":{\"254\":1}}],[\"不管怎样\",{\"1\":{\"253\":1}}],[\"不管是香草味\",{\"1\":{\"224\":1}}],[\"不需要修改现有代码\",{\"1\":{\"243\":1}}],[\"不过据说c\",{\"1\":{\"397\":1}}],[\"不过这样做的话\",{\"1\":{\"353\":1}}],[\"不过这并不是什么问题\",{\"1\":{\"283\":1}}],[\"不过却需要我们特别注意\",{\"1\":{\"352\":1}}],[\"不过\",{\"1\":{\"185\":1,\"221\":1,\"307\":1,\"353\":1,\"356\":1,\"397\":1}}],[\"不必对\",{\"1\":{\"172\":1}}],[\"不应当在\",{\"1\":{\"254\":1}}],[\"不应当共享的信息被称作\",{\"1\":{\"254\":1}}],[\"不应强迫用户依赖他们不使用的接口\",{\"1\":{\"127\":1}}],[\"不应引入违反父类预期的新行为\",{\"1\":{\"119\":1}}],[\"不符合单一职责原则的类\",{\"1\":{\"126\":1}}],[\"不会出现强制转换后的问题\",{\"1\":{\"419\":1}}],[\"不会存在自相矛盾的状态\",{\"1\":{\"354\":1}}],[\"不会自相矛盾\",{\"0\":{\"354\":1}}],[\"不会影响其他功能\",{\"1\":{\"116\":1}}],[\"不会触发ondidclosetextdocument事件\",{\"1\":{\"54\":1}}],[\"不用外部工具\",{\"1\":{\"395\":1}}],[\"不用改变框架代码\",{\"1\":{\"223\":1}}],[\"不用类也能封装数据和方法\",{\"1\":{\"107\":1}}],[\"不用操心运算时忘记取模\",{\"1\":{\"45\":1}}],[\"不支持\",{\"1\":{\"432\":1}}],[\"不支持动画\",{\"1\":{\"106\":1}}],[\"不支持导出pptx\",{\"1\":{\"105\":1}}],[\"不易写出错的代码\",{\"1\":{\"100\":1}}],[\"不易检验\",{\"1\":{\"43\":1,\"44\":1}}],[\"不加锁的话\",{\"1\":{\"99\":1}}],[\"不妨试试这些自动生成工具\",{\"1\":{\"507\":1}}],[\"不妨记作\",{\"1\":{\"81\":1}}],[\"不妨设\",{\"1\":{\"81\":1}}],[\"不是任何自然数的后继\",{\"1\":{\"56\":1}}],[\"不再支持\",{\"1\":{\"53\":1}}],[\"不推荐\",{\"1\":{\"48\":1}}],[\"不推荐运用这种方法\",{\"1\":{\"43\":1}}],[\"不方便输出结果\",{\"1\":{\"41\":1}}],[\"三目运算符\",{\"0\":{\"496\":1},\"1\":{\"481\":1}}],[\"三点水\",{\"1\":{\"392\":1}}],[\"三是式子太长\",{\"1\":{\"43\":1}}],[\"三国杀\",{\"1\":{\"3\":1}}],[\"清晰明了\",{\"1\":{\"43\":1}}],[\"清河公主\",{\"1\":{\"3\":1}}],[\"下一条\",{\"1\":{\"406\":1,\"410\":1}}],[\"下一章中我们将讲解语句的解析\",{\"1\":{\"468\":1}}],[\"下一章中我们将介绍如何解析函数的定义\",{\"1\":{\"457\":1}}],[\"下一章中\",{\"1\":{\"402\":1,\"436\":1}}],[\"下一个人如果可以自己处理\",{\"1\":{\"188\":1}}],[\"下一步\",{\"1\":{\"111\":1}}],[\"下午好\",{\"1\":{\"179\":1,\"180\":1}}],[\"下面以加法为例\",{\"1\":{\"498\":1}}],[\"下面以式子\",{\"1\":{\"42\":1}}],[\"下面是\",{\"1\":{\"452\":1}}],[\"下面是相应的源代码\",{\"1\":{\"402\":1}}],[\"下面的例子\",{\"1\":{\"412\":1}}],[\"下面我们逐一解释\",{\"1\":{\"472\":1}}],[\"下面我们用我们的汇编写一小段程序\",{\"1\":{\"419\":1}}],[\"下面我们来看一段使用了\",{\"1\":{\"362\":1}}],[\"下面我们试着通过删除公理的方法来寻找反例\",{\"1\":{\"85\":1}}],[\"下面我们需要证明对于任意两个自然数\",{\"1\":{\"58\":1,\"74\":1}}],[\"下面我将阐述为什么每条公理都是必须的\",{\"1\":{\"82\":1}}],[\"下面证明乘法消去律\",{\"1\":{\"81\":1}}],[\"下面证明乘法结合律\",{\"1\":{\"80\":1}}],[\"下面证明乘法分配律\",{\"1\":{\"79\":1}}],[\"下面证明乘法交换律\",{\"1\":{\"78\":1}}],[\"下面证明加法消去律\",{\"1\":{\"64\":1}}],[\"下面证明加法结合律\",{\"1\":{\"63\":1}}],[\"下面证明加法交换律\",{\"1\":{\"62\":1}}],[\"下文用\",{\"1\":{\"56\":1}}],[\"下载错误查看\",{\"1\":{\"9\":1}}],[\"要容易\",{\"1\":{\"508\":1}}],[\"要根据它的类型放大\",{\"1\":{\"498\":1}}],[\"要理解函数定义的解析过程\",{\"1\":{\"468\":1}}],[\"要理解这些寄存器的作用\",{\"1\":{\"406\":1}}],[\"要是深入词法分析器\",{\"1\":{\"423\":1}}],[\"要引入的命令有\",{\"1\":{\"412\":1}}],[\"要执行的计算机指令\",{\"1\":{\"406\":1}}],[\"要执行的具体操作\",{\"1\":{\"200\":1}}],[\"要么就是借助了自动生成的工具\",{\"1\":{\"395\":1}}],[\"要么是因为这道题目直接考察了模的性质和运用\",{\"1\":{\"41\":1}}],[\"要么是因为答案是浮点数\",{\"1\":{\"41\":1}}],[\"要求栈顶存放地址\",{\"1\":{\"408\":2}}],[\"要求子类去实现抽象方法\",{\"1\":{\"375\":1}}],[\"要求\",{\"1\":{\"188\":1,\"408\":2}}],[\"要同时进行多件事情本来就需要正在运行的让出处理器\",{\"1\":{\"98\":1}}],[\"要部署的\",{\"1\":{\"15\":1}}],[\"背景介绍\",{\"0\":{\"41\":1}}],[\"有了bnf方法后\",{\"1\":{\"445\":1}}],[\"有一个或多个标记是以同样的字符开头的\",{\"1\":{\"432\":1}}],[\"有一次在\",{\"1\":{\"395\":1}}],[\"有用\",{\"1\":{\"418\":1}}],[\"有点类似于\",{\"1\":{\"408\":1}}],[\"有时\",{\"1\":{\"353\":1}}],[\"有必要划分代理人和本人吗\",{\"0\":{\"328\":1}}],[\"有些工作无法自己亲自完成\",{\"1\":{\"323\":1}}],[\"有些情况下这是坏事\",{\"1\":{\"253\":1}}],[\"有些情况下这是好事\",{\"1\":{\"253\":1}}],[\"有些事情是可以在设计阶段决定的\",{\"1\":{\"184\":1}}],[\"有些事情是强求不来的\",{\"1\":{\"3\":1}}],[\"有两种方式实现\",{\"1\":{\"152\":1}}],[\"有什么区别呢\",{\"1\":{\"99\":1}}],[\"有任意两个自然数\",{\"1\":{\"71\":1}}],[\"有\",{\"1\":{\"59\":4,\"60\":4,\"62\":3,\"63\":2,\"64\":1,\"69\":2,\"70\":2,\"72\":1,\"75\":3,\"76\":3,\"78\":3,\"79\":1,\"80\":2,\"81\":3,\"83\":1,\"84\":1}}],[\"有大量的题目要求对一些数字取模\",{\"1\":{\"40\":1}}],[\"中我们介绍过内置函数的支持\",{\"1\":{\"486\":1}}],[\"中即可\",{\"1\":{\"484\":1}}],[\"中存放的是参数的位置\",{\"1\":{\"465\":1}}],[\"中存放地址\",{\"1\":{\"408\":2}}],[\"中存放如指针\",{\"1\":{\"405\":1}}],[\"中间代码的表示\",{\"1\":{\"394\":1}}],[\"中注册有多个\",{\"1\":{\"307\":1}}],[\"中保存这个信息\",{\"1\":{\"254\":1}}],[\"中的值执行减\",{\"1\":{\"499\":1}}],[\"中的信息还原\",{\"1\":{\"464\":1}}],[\"中的全局变量不同\",{\"1\":{\"463\":1}}],[\"中的位置\",{\"1\":{\"462\":1}}],[\"中的位置变化而发生变化\",{\"1\":{\"254\":1}}],[\"中的一种\",{\"1\":{\"441\":1}}],[\"中的\",{\"1\":{\"408\":1,\"432\":1}}],[\"中的数据作为整数存放入地址中\",{\"1\":{\"408\":1}}],[\"中的数据作为字符存放入地址中\",{\"1\":{\"408\":1}}],[\"中的内存\",{\"1\":{\"405\":1}}],[\"中的书籍\",{\"1\":{\"273\":2}}],[\"中的哪个地方都不会改变\",{\"1\":{\"254\":1}}],[\"中是第几个字符这种信息会根据\",{\"1\":{\"254\":1}}],[\"中增加多少个功能\",{\"1\":{\"172\":1}}],[\"中增加新功能时\",{\"1\":{\"160\":1}}],[\"中增加\",{\"1\":{\"143\":1}}],[\"中文官网\",{\"1\":{\"111\":1}}],[\"中\",{\"1\":{\"40\":1,\"161\":1,\"255\":1,\"408\":6,\"409\":1,\"412\":1,\"417\":2,\"465\":1,\"488\":1,\"495\":1}}],[\"在后期解析语句和表达式时\",{\"1\":{\"506\":1}}],[\"在学习\",{\"1\":{\"500\":1}}],[\"在执行自增自减后\",{\"1\":{\"499\":1}}],[\"在执行命令前保存对象的快照\",{\"1\":{\"201\":1}}],[\"在作指针减法时\",{\"1\":{\"498\":1}}],[\"在解析\",{\"1\":{\"495\":1}}],[\"在解析的过程中\",{\"1\":{\"463\":1}}],[\"在前文的一元运算符处理中也用到了这一点\",{\"1\":{\"494\":1}}],[\"在计算一个运算符\",{\"1\":{\"482\":1}}],[\"在函数体内局部变量就会覆盖全局变量\",{\"1\":{\"464\":1}}],[\"在函数内访问它们是通过\",{\"1\":{\"463\":1}}],[\"在思考这个问题之前\",{\"1\":{\"463\":1}}],[\"在main函数中进行初始化如下\",{\"1\":{\"434\":1}}],[\"在main函数中加入初始化代码\",{\"1\":{\"405\":1}}],[\"在语法分析前将关键字提前加入符号表\",{\"1\":{\"434\":1}}],[\"在我们的编译器中共识别\",{\"1\":{\"472\":1}}],[\"在我们的\",{\"1\":{\"432\":1}}],[\"在我看来\",{\"1\":{\"393\":1}}],[\"在分析时\",{\"1\":{\"431\":2}}],[\"在全局中添加如下定义\",{\"1\":{\"425\":1}}],[\"在全局中加入如下定义\",{\"1\":{\"406\":1}}],[\"在代码的开头\",{\"1\":{\"419\":1}}],[\"在将调用子函数时压入栈中的数据清除\",{\"1\":{\"414\":1}}],[\"在调用函数时会使用到它\",{\"1\":{\"406\":1}}],[\"在调用那个方法之前需要先在这个类中注册一下\",{\"1\":{\"235\":1}}],[\"在调用那个类之前需要先调用这个类\",{\"1\":{\"235\":1}}],[\"在写编译器的时候会遇到两个主要问题\",{\"1\":{\"396\":1}}],[\"在开始进入正题之前\",{\"1\":{\"392\":1}}],[\"在练习题中\",{\"1\":{\"384\":1}}],[\"在父类中\",{\"1\":{\"375\":1}}],[\"在父类中定义处理流程的框架\",{\"1\":{\"370\":1}}],[\"在子类中重写父类的方法可以改变程序的行为\",{\"1\":{\"375\":1}}],[\"在子类中可以使用父类中定义的方法\",{\"1\":{\"375\":1}}],[\"在子类中实现具体处理\",{\"1\":{\"370\":1}}],[\"在内存容量少的运行环境中可以使用\",{\"1\":{\"366\":1}}],[\"在程序运行中也可以切换角色\",{\"1\":{\"366\":1}}],[\"在运行时检测出问题并不难\",{\"1\":{\"355\":1}}],[\"在修改状态迁移部分的代码时\",{\"1\":{\"355\":1}}],[\"在不修改现有代码的前提下进行扩展\",{\"1\":{\"385\":1}}],[\"在不使用\",{\"1\":{\"351\":1}}],[\"在不改变被装饰物的前提下增加功能\",{\"0\":{\"222\":1}}],[\"在本章的警报系统的示例程序中\",{\"1\":{\"351\":1}}],[\"在本节中\",{\"1\":{\"271\":1}}],[\"在头脑中\",{\"1\":{\"351\":1}}],[\"在多线程环境中\",{\"1\":{\"342\":1}}],[\"在示例程序的\",{\"1\":{\"307\":1}}],[\"在示例程序中\",{\"1\":{\"173\":1,\"221\":2,\"254\":2,\"256\":1,\"285\":1,\"307\":1,\"353\":2,\"354\":1,\"384\":1,\"388\":1}}],[\"在观察者模式中\",{\"1\":{\"306\":1,\"309\":1}}],[\"在图形用户界面\",{\"1\":{\"302\":1}}],[\"在实际调用函数时\",{\"1\":{\"412\":1}}],[\"在实际应用中\",{\"1\":{\"295\":1}}],[\"在实际开发中\",{\"1\":{\"232\":1}}],[\"在某些情况下\",{\"1\":{\"274\":1,\"296\":1,\"310\":1,\"327\":1}}],[\"在上面的代码中\",{\"1\":{\"273\":1,\"343\":1}}],[\"在操作系统中\",{\"1\":{\"256\":1}}],[\"在使用模式时需要注意应当是谁来管理状态迁移\",{\"1\":{\"353\":1}}],[\"在使用\",{\"1\":{\"255\":1}}],[\"在有垃圾回收的语言中要注意共享内存未被使用时被\",{\"1\":{\"255\":1}}],[\"在决定\",{\"1\":{\"253\":1}}],[\"在共享实例时应当注意什么呢\",{\"1\":{\"253\":1}}],[\"在需要生成大量细粒度对象的场景中\",{\"1\":{\"249\":1}}],[\"在委托模式中\",{\"1\":{\"229\":1}}],[\"在文件系统中\",{\"1\":{\"206\":1}}],[\"在命令模式中\",{\"1\":{\"200\":1}}],[\"在这个前提下\",{\"1\":{\"423\":1}}],[\"在这个示例程序中\",{\"1\":{\"283\":1,\"361\":1}}],[\"在这个示例中\",{\"1\":{\"190\":1,\"216\":1,\"236\":1,\"291\":1,\"303\":1}}],[\"在这种情况下\",{\"1\":{\"353\":1}}],[\"在这种要求之下\",{\"1\":{\"42\":1}}],[\"在其内部调用了类的特有的方法\",{\"1\":{\"185\":1}}],[\"在判断到底应该修改哪个类时\",{\"1\":{\"185\":1}}],[\"在编程时\",{\"1\":{\"185\":1,\"253\":1,\"351\":1}}],[\"在设计类时\",{\"1\":{\"385\":1}}],[\"在设计\",{\"1\":{\"307\":1}}],[\"在设计模式中\",{\"1\":{\"306\":1,\"328\":1}}],[\"在设计软件时\",{\"1\":{\"184\":1}}],[\"在设计一个系统模块的时候\",{\"1\":{\"115\":1}}],[\"在面向对象编程中\",{\"1\":{\"183\":1,\"228\":1,\"323\":1}}],[\"在桥的哪一侧\",{\"1\":{\"164\":1}}],[\"在软件开发中\",{\"1\":{\"149\":1}}],[\"在发现类有多个职责时\",{\"1\":{\"125\":1}}],[\"在所有线程相互独立且不会操作同一资源的模式下\",{\"1\":{\"99\":1}}],[\"在python编程领域\",{\"1\":{\"98\":1}}],[\"在明确证明了自然数乘法运算的良好性质\",{\"1\":{\"77\":1}}],[\"在明确证明了自然数加法运算的良好性质\",{\"1\":{\"61\":1}}],[\"在考察序的性质之前\",{\"1\":{\"67\":1}}],[\"在此承认次假设的基础之上\",{\"1\":{\"55\":1}}],[\"在项目根目录下创建\",{\"1\":{\"52\":1}}],[\"在\",{\"1\":{\"40\":1,\"142\":1,\"143\":2,\"161\":1,\"164\":1,\"221\":1,\"222\":1,\"242\":1,\"254\":1,\"294\":1,\"297\":1,\"351\":1,\"352\":3,\"355\":2,\"356\":3,\"378\":1,\"383\":1,\"388\":1,\"406\":1,\"408\":1,\"409\":1,\"419\":1,\"465\":1,\"498\":1}}],[\"在准备好前端项目及安装相应环境后\",{\"1\":{\"16\":1}}],[\"=<=\",{\"1\":{\"498\":1}}],[\"=左边的就称作\",{\"1\":{\"441\":1}}],[\"==\",{\"1\":{\"190\":1,\"250\":1,\"265\":4,\"280\":1,\"303\":1,\"324\":1,\"408\":5,\"409\":1,\"410\":1,\"411\":2,\"412\":2,\"413\":1,\"414\":1,\"415\":1,\"416\":1,\"417\":17,\"418\":8,\"425\":2,\"427\":1,\"428\":1,\"429\":3,\"430\":2,\"431\":6,\"432\":2,\"433\":33,\"445\":7,\"453\":8,\"454\":2,\"455\":1,\"462\":1,\"464\":1,\"465\":5,\"466\":6,\"473\":2,\"474\":1,\"475\":1,\"476\":2,\"484\":3,\"485\":5,\"486\":9,\"487\":5,\"488\":2,\"489\":3,\"490\":2,\"491\":1,\"492\":3,\"493\":6,\"495\":4,\"496\":2,\"497\":2,\"498\":3,\"499\":5,\"500\":2}}],[\"===>\",{\"1\":{\"473\":1}}],[\"===`\",{\"1\":{\"324\":1}}],[\"====\",{\"1\":{\"292\":3}}],[\"==============================\",{\"1\":{\"179\":2,\"180\":2}}],[\"===\",{\"1\":{\"190\":2,\"218\":3,\"265\":3,\"280\":2,\"291\":3,\"324\":1,\"325\":2,\"339\":2,\"343\":2,\"362\":4}}],[\"=>\",{\"1\":{\"139\":2,\"179\":2,\"197\":1,\"208\":2,\"250\":2,\"265\":1,\"280\":1,\"291\":1,\"303\":2,\"324\":1,\"343\":2,\"380\":1,\"422\":1,\"442\":11}}],[\"=\",{\"1\":{\"39\":14,\"52\":7,\"95\":1,\"99\":7,\"100\":5,\"101\":21,\"130\":3,\"133\":3,\"139\":20,\"152\":4,\"165\":1,\"166\":1,\"168\":3,\"169\":4,\"179\":11,\"190\":13,\"197\":9,\"208\":1,\"211\":7,\"218\":10,\"237\":5,\"244\":7,\"250\":11,\"265\":34,\"266\":5,\"272\":10,\"280\":7,\"291\":18,\"292\":6,\"303\":11,\"317\":18,\"324\":7,\"339\":5,\"343\":4,\"348\":7,\"362\":31,\"372\":9,\"380\":15,\"402\":8,\"405\":6,\"406\":3,\"408\":6,\"409\":1,\"410\":1,\"411\":2,\"412\":4,\"413\":3,\"414\":1,\"415\":3,\"416\":1,\"417\":17,\"418\":8,\"419\":11,\"425\":3,\"426\":1,\"428\":2,\"429\":11,\"430\":8,\"431\":9,\"432\":3,\"433\":29,\"434\":9,\"441\":4,\"443\":3,\"444\":5,\"445\":19,\"450\":13,\"453\":23,\"454\":10,\"461\":8,\"462\":2,\"464\":5,\"465\":14,\"466\":16,\"473\":6,\"474\":6,\"475\":2,\"476\":2,\"484\":9,\"485\":6,\"486\":19,\"487\":3,\"488\":2,\"489\":1,\"490\":5,\"491\":6,\"492\":8,\"493\":10,\"494\":1,\"495\":7,\"496\":6,\"497\":8,\"498\":10,\"499\":14,\"500\":8,\"501\":7}}],[\"=404\",{\"1\":{\"17\":3,\"23\":5}}],[\"当解析完=右边的表达式后\",{\"1\":{\"495\":1}}],[\"当前优先级的运算符\",{\"1\":{\"494\":1}}],[\"当该标识符是全局定义的枚举类型时\",{\"1\":{\"486\":1}}],[\"当它是一个指向基本类型的指针时\",{\"1\":{\"453\":1}}],[\"当局部标识符的名字与全局标识符相同时\",{\"1\":{\"429\":1}}],[\"当用户的程序需要分配内存时\",{\"1\":{\"405\":1}}],[\"当时很火的\",{\"1\":{\"395\":1}}],[\"当需要增加新的处理时\",{\"1\":{\"378\":1}}],[\"当需要创建不同表示的对象时\",{\"1\":{\"178\":1}}],[\"当检测到没有考虑到的状态时就报错\",{\"1\":{\"355\":1}}],[\"当状态数过多时\",{\"1\":{\"353\":1}}],[\"当状态迁移遵循一定的规则时\",{\"1\":{\"353\":1}}],[\"当遇到庞大且复杂的问题\",{\"1\":{\"351\":1}}],[\"当模型的状态发生变化时\",{\"1\":{\"311\":1}}],[\"当系统中有大量的观察者时\",{\"1\":{\"310\":1}}],[\"当观察者的行为会对被观察对象产生影响时\",{\"1\":{\"308\":1}}],[\"当数据模型发生变化时\",{\"1\":{\"302\":2}}],[\"当发生分散灾难时\",{\"0\":{\"283\":1}}],[\"当出现争执时大家就会找仲裁者进行商量\",{\"1\":{\"279\":1}}],[\"当计数为零时\",{\"1\":{\"255\":1}}],[\"当某个程序员得意地说出\",{\"1\":{\"235\":1}}],[\"当顾客下单后只需要在冰激凌上加上各种香料就可以了\",{\"1\":{\"224\":1}}],[\"当一个表达式解析结束时\",{\"1\":{\"488\":1}}],[\"当一个终结符有多个选择时\",{\"1\":{\"443\":1}}],[\"当一个对象的状态发生改变时\",{\"1\":{\"303\":1}}],[\"当一个对象的构建过程非常复杂时\",{\"1\":{\"178\":1}}],[\"当一个人被要求做什么事情时\",{\"1\":{\"188\":1}}],[\"当外部请求程序进行某个处理\",{\"1\":{\"188\":1}}],[\"当想要增加功能时\",{\"1\":{\"172\":1}}],[\"当类的层次结构只有一层时\",{\"1\":{\"162\":1}}],[\"当子类实现了父类\",{\"1\":{\"161\":1}}],[\"当只有一个具体工厂时\",{\"1\":{\"140\":1}}],[\"当我对全局变量balance进行加法运算后\",{\"1\":{\"101\":1}}],[\"当我们调用\",{\"1\":{\"494\":1}}],[\"当我们想要通过改善算法来提高算法的处理速度时\",{\"1\":{\"365\":1}}],[\"当我们想要编写子类时\",{\"1\":{\"162\":1}}],[\"当我们想知道\",{\"1\":{\"353\":1}}],[\"当我们想在\",{\"1\":{\"160\":1}}],[\"当我们执行第一句代码print\",{\"1\":{\"101\":1}}],[\"当我们写完了vue项目后\",{\"1\":{\"93\":1}}],[\"当别的协程任务执行完毕\",{\"1\":{\"101\":1}}],[\"当\",{\"0\":{\"308\":1},\"1\":{\"68\":1,\"71\":2,\"173\":1}}],[\"当且仅当\",{\"1\":{\"66\":1}}],[\"当且仅当存在自然数\",{\"1\":{\"66\":1}}],[\"当然\",{\"1\":{\"162\":1,\"307\":1,\"352\":1,\"353\":1,\"355\":1,\"356\":1,\"393\":1,\"405\":1,\"425\":1,\"468\":1,\"483\":1,\"501\":1}}],[\"当然得是linux环境\",{\"1\":{\"53\":1}}],[\"当然需要配置相关驱动\",{\"1\":{\"53\":1}}],[\"当可以自行实现\",{\"1\":{\"38\":1}}],[\"当今科学界最具争议性的项目\",{\"1\":{\"5\":1}}],[\"并执行\",{\"1\":{\"501\":1}}],[\"并根据它们类型使用\",{\"1\":{\"489\":1}}],[\"并直接修改\",{\"1\":{\"487\":1}}],[\"并将之前的\",{\"1\":{\"482\":1}}],[\"并将保存在\",{\"1\":{\"464\":1}}],[\"并将被观察对象自身作为参数传递\",{\"1\":{\"309\":1}}],[\"并实现其中解析变量定义部分\",{\"1\":{\"449\":1}}],[\"并实现它们定义的抽象方法\",{\"1\":{\"142\":1}}],[\"并用它来实现了四则运算的语法分析器\",{\"1\":{\"446\":1}}],[\"并用它完成一个基本的四则运算的语法分析器\",{\"1\":{\"439\":1}}],[\"并退出整个程序\",{\"1\":{\"426\":1}}],[\"并仿照\",{\"1\":{\"420\":1}}],[\"并输出\",{\"1\":{\"402\":1}}],[\"并不作为语法的一部分\",{\"1\":{\"426\":1}}],[\"并不是直接处理\",{\"1\":{\"405\":1}}],[\"并不是说是没写过编译器就不是好程序员\",{\"1\":{\"393\":1}}],[\"并不支持通过ui注册\",{\"1\":{\"38\":1}}],[\"并把对各元素的处理交给访问者类\",{\"1\":{\"378\":1}}],[\"并以此将复杂的程序分解开来\",{\"1\":{\"351\":1}}],[\"并为每一种具体的状态都定义一个相应的类\",{\"1\":{\"351\":1}}],[\"并提前为它们赋予必要的信息\",{\"1\":{\"434\":1}}],[\"并提供一个全局访问点\",{\"1\":{\"337\":1}}],[\"并提高应用程序的效率\",{\"1\":{\"249\":1}}],[\"并恢复状态\",{\"1\":{\"297\":1}}],[\"并定义一个解释器来解释该语言中的句子\",{\"1\":{\"264\":1}}],[\"并嫌弃cpp中没有interface\",{\"1\":{\"260\":1}}],[\"并确保这个集合在程序的整个生命周期内都存在\",{\"1\":{\"255\":1}}],[\"并在所有的\",{\"1\":{\"355\":1,\"387\":1}}],[\"并在适当的时候清理过期的\",{\"1\":{\"296\":1}}],[\"并在实际项目中灵活运用它们\",{\"1\":{\"232\":1}}],[\"并在增加需求时尽量不修改已有的类\",{\"1\":{\"232\":1}}],[\"并使用它们来增加这个新功能\",{\"1\":{\"164\":1}}],[\"并点击激活\",{\"1\":{\"111\":1}}],[\"并回车\",{\"1\":{\"111\":2}}],[\"并没有保证\",{\"1\":{\"101\":1}}],[\"并且它的结果是\",{\"1\":{\"485\":1}}],[\"并且它用很少的代码就完成了一个功能相当完善的\",{\"1\":{\"395\":1}}],[\"并且三条指令写来比较麻烦且浪费空间\",{\"1\":{\"415\":1}}],[\"并且我们也只有一个寄存器\",{\"1\":{\"409\":1}}],[\"并且最重要的是\",{\"1\":{\"394\":1}}],[\"并且可以扩展或重写这些行为和属性\",{\"1\":{\"228\":1}}],[\"并且协程切换并不是系统态抢占式\",{\"1\":{\"101\":1}}],[\"并且会非常频繁地进行切换\",{\"1\":{\"100\":1}}],[\"并且如果要对多个模数取模\",{\"1\":{\"44\":1}}],[\"并且如果编译器没有任何优化\",{\"1\":{\"44\":1}}],[\"并发异步编程之争\",{\"0\":{\"98\":1}}],[\"并添加以下内容\",{\"1\":{\"52\":1}}],[\"并自动重载docker\",{\"1\":{\"26\":1}}],[\"61\",{\"1\":{\"430\":1}}],[\"64\",{\"1\":{\"419\":2}}],[\"6\",{\"0\":{\"460\":1},\"1\":{\"198\":2,\"250\":1,\"284\":2,\"291\":2,\"392\":1,\"400\":1,\"403\":2,\"418\":1,\"421\":2,\"439\":2,\"442\":1,\"449\":1,\"460\":2,\"471\":1,\"472\":1,\"481\":3,\"501\":1,\"505\":1}}],[\"66\",{\"1\":{\"191\":1}}],[\"609639797\",{\"1\":{\"38\":1}}],[\"65\",{\"1\":{\"17\":1}}],[\"参照第三章讲解的虚拟机\",{\"1\":{\"463\":1}}],[\"参数和局部变量\",{\"1\":{\"468\":1}}],[\"参数逆序入栈\",{\"1\":{\"412\":1}}],[\"参数\",{\"1\":{\"200\":1,\"419\":1}}],[\"参见第\",{\"1\":{\"486\":1}}],[\"参见\",{\"1\":{\"38\":1}}],[\"参考\",{\"1\":{\"35\":1}}],[\"参考资料\",{\"0\":{\"26\":1,\"397\":1}}],[\"自己实现了一个c语言的编译器\",{\"1\":{\"502\":1}}],[\"自己和被委托对象的一致性\",{\"0\":{\"229\":1}}],[\"自增自减\",{\"0\":{\"493\":1,\"499\":1},\"1\":{\"481\":2}}],[\"自底向上是不断地将终结符进行合并\",{\"1\":{\"440\":1}}],[\"自顶向下是从起始非终结符开始\",{\"1\":{\"440\":1}}],[\"自然数与有向图\",{\"1\":{\"85\":1}}],[\"自然数中最重要的运算当然是加法\",{\"1\":{\"57\":1}}],[\"自然数的乘法也十分重要\",{\"1\":{\"73\":1}}],[\"自然数的乘法运算\",{\"0\":{\"73\":1}}],[\"自然数的序是全序关系\",{\"1\":{\"66\":1}}],[\"自然数的序为两个自然数的关系\",{\"1\":{\"65\":1}}],[\"自然数的序\",{\"0\":{\"65\":1}}],[\"自然数的加法运算\",{\"0\":{\"57\":1}}],[\"自然数的定义\",{\"0\":{\"56\":1}}],[\"自然数的定义则是构建此算术公理系统的第一步\",{\"1\":{\"55\":1}}],[\"自然数这个新的数学对象因我们的假设而确立\",{\"1\":{\"56\":1}}],[\"自然数\",{\"0\":{\"55\":1},\"1\":{\"67\":1}}],[\"自建mail\",{\"0\":{\"38\":1}}],[\"自由访问知识和文化\",{\"1\":{\"5\":1}}],[\"技术分享等内容\",{\"1\":{\"37\":1}}],[\"技术\",{\"0\":{\"37\":1}}],[\"工作所需的条件\",{\"0\":{\"388\":1}}],[\"工作流程\",{\"0\":{\"36\":1}}],[\"工厂方法\",{\"2\":{\"247\":1}}],[\"工厂模式\",{\"1\":{\"129\":1}}],[\"工程化\",{\"1\":{\"232\":1}}],[\"工具\",{\"0\":{\"112\":1}}],[\"工具下载\",{\"1\":{\"111\":1}}],[\"工具使用\",{\"1\":{\"37\":1}}],[\"工具等资源\",{\"1\":{\"5\":1}}],[\"拉取镜像方法\",{\"1\":{\"33\":1}}],[\"流程更加简化和统一\",{\"1\":{\"31\":1}}],[\"持续交付\",{\"1\":{\"31\":1}}],[\"团队协作和版本控制工具来管理容器镜像\",{\"1\":{\"31\":1}}],[\"镜像地址\",{\"0\":{\"32\":1}}],[\"镜像\",{\"1\":{\"31\":1}}],[\"是解释器\",{\"1\":{\"502\":1}}],[\"是指针时\",{\"1\":{\"498\":1}}],[\"是逆序将参数入栈的\",{\"1\":{\"486\":1}}],[\"是第几个参数\",{\"1\":{\"465\":1}}],[\"是以字符\",{\"1\":{\"464\":2}}],[\"是放在一起解析的\",{\"1\":{\"464\":1}}],[\"是对前一章提到的\",{\"1\":{\"450\":1}}],[\"是如何帮助我们的工程实现的\",{\"1\":{\"446\":1}}],[\"是因为几乎所有手工编写的语法分析器都或多或少地有它的影子\",{\"1\":{\"446\":1}}],[\"是因为之后我们将用\",{\"1\":{\"412\":1}}],[\"是因为表达式在语法分析中相对独立并且比较复杂\",{\"1\":{\"402\":1}}],[\"是跳转指令\",{\"1\":{\"410\":1}}],[\"是比较困难的\",{\"1\":{\"408\":1}}],[\"是数据还是地址\",{\"1\":{\"408\":1}}],[\"是所有指令中最基础的一个\",{\"1\":{\"408\":1}}],[\"是很困难的\",{\"1\":{\"355\":1}}],[\"是用类来表示状态的\",{\"1\":{\"354\":1}}],[\"是有专有名词的\",{\"1\":{\"254\":1}}],[\"是单线程的\",{\"1\":{\"250\":1}}],[\"是非常重要的\",{\"1\":{\"183\":1}}],[\"是一个一元运算符\",{\"1\":{\"485\":1}}],[\"是一个普通的变量还是一个函数\",{\"1\":{\"453\":1}}],[\"是一种行为设计模式\",{\"1\":{\"264\":1}}],[\"是一种结构型设计模式\",{\"1\":{\"148\":1}}],[\"是一款简洁高效的\",{\"1\":{\"111\":1}}],[\"是没有必要的\",{\"1\":{\"140\":1}}],[\"是不客观的\",{\"1\":{\"102\":1}}],[\"是的\",{\"1\":{\"101\":1,\"102\":1}}],[\"是线程调度器抢占划分时间片给其他线程跑\",{\"1\":{\"99\":1}}],[\"是唯一的\",{\"1\":{\"60\":2,\"76\":2}}],[\"是否属于优先级更高的运算符\",{\"1\":{\"482\":1}}],[\"是否唯一\",{\"1\":{\"60\":1,\"76\":1}}],[\"是否存在\",{\"1\":{\"59\":1,\"75\":1}}],[\"是否是自然数\",{\"1\":{\"59\":1,\"75\":1}}],[\"是任意自然数\",{\"1\":{\"59\":1,\"60\":1,\"75\":1,\"76\":1}}],[\"是真命题\",{\"1\":{\"56\":1}}],[\"是关于自然数\",{\"1\":{\"56\":1}}],[\"是自然数且\",{\"1\":{\"60\":1,\"62\":3,\"78\":3}}],[\"是自然数\",{\"1\":{\"56\":1,\"58\":1,\"59\":7,\"60\":2,\"70\":1,\"74\":1,\"75\":6,\"76\":2}}],[\"是\",{\"1\":{\"31\":2,\"81\":1,\"101\":1,\"164\":1,\"419\":1,\"498\":2}}],[\"续订泛域名证书\",{\"1\":{\"26\":1}}],[\"使我们能直接使用编译器\",{\"1\":{\"405\":1}}],[\"使代码更加简洁和可维护\",{\"1\":{\"347\":1}}],[\"使代码更易于维护和理解\",{\"1\":{\"178\":1}}],[\"使一个类的实例化延迟到其子类\",{\"1\":{\"242\":1}}],[\"使它们可以独立变化\",{\"1\":{\"158\":1}}],[\"使得代码更清晰\",{\"1\":{\"379\":1}}],[\"使得代码更加清晰\",{\"1\":{\"361\":1}}],[\"使得状态转换变得清晰且易于管理\",{\"1\":{\"347\":1}}],[\"使得客户端可以像使用本地对象一样使用远程对象\",{\"1\":{\"332\":1}}],[\"使得客户端代码更加简洁和易读\",{\"1\":{\"270\":1}}],[\"使得客户端代码可以更容易地使用子系统的功能\",{\"1\":{\"236\":1}}],[\"使得客户端代码不需要了解子系统的内部细节\",{\"1\":{\"235\":1}}],[\"使得对象的创建更加灵活\",{\"1\":{\"316\":1}}],[\"使得每一层只关注自己的职责\",{\"1\":{\"235\":1}}],[\"使得可以用不同的请求\",{\"1\":{\"196\":1}}],[\"使得在设计时可以决定构建的步骤和逻辑\",{\"1\":{\"184\":1}}],[\"使得同样的构建过程可以创建不同的表示\",{\"1\":{\"178\":1}}],[\"使得系统功能模块相对独立\",{\"1\":{\"122\":1}}],[\"使得函数\",{\"1\":{\"100\":1}}],[\"使得一段时间内只有一个线程可以操作这个资源\",{\"1\":{\"99\":1}}],[\"使flask支持\",{\"0\":{\"25\":1}}],[\"使用了单例模式\",{\"1\":{\"362\":1}}],[\"使用了id卡`\",{\"1\":{\"244\":1}}],[\"使用状态迁移表非常有效\",{\"1\":{\"353\":1}}],[\"使用这种解决方法可以提高\",{\"1\":{\"353\":1}}],[\"使用代理可以显著提升处理速度\",{\"1\":{\"327\":1}}],[\"使用代理人来提升处理速度\",{\"0\":{\"327\":1}}],[\"使用迭代器模式有以下几个优点\",{\"1\":{\"270\":1}}],[\"使用解释器模式的原因包括\",{\"1\":{\"264\":1}}],[\"使用弱引用\",{\"1\":{\"255\":1}}],[\"使用队列数据结构保存执行的命令对象\",{\"1\":{\"201\":1}}],[\"使用栈数据结构保存执行的命令对象\",{\"1\":{\"201\":1}}],[\"使用此设计模式的理由\",{\"0\":{\"158\":1,\"206\":1,\"361\":1}}],[\"使用委托这种弱关联关系可以很方便地整体替换算法\",{\"1\":{\"365\":1}}],[\"使用委托\",{\"1\":{\"152\":1}}],[\"使用继承\",{\"1\":{\"152\":1}}],[\"使用继承的方式\",{\"1\":{\"133\":1}}],[\"使用抽象工厂模式\",{\"1\":{\"140\":1}}],[\"使用抽象类和接口\",{\"1\":{\"116\":1,\"119\":1}}],[\"使用多个专门的接口\",{\"1\":{\"134\":1}}],[\"使用多个专门的接口比使用单个通用接口要好得多\",{\"1\":{\"127\":1}}],[\"使用聚合\",{\"1\":{\"132\":1}}],[\"使用组合的方式\",{\"1\":{\"133\":1}}],[\"使用组合\",{\"1\":{\"132\":1}}],[\"使用依赖注入\",{\"1\":{\"130\":1}}],[\"使用工厂模式创建对象\",{\"1\":{\"129\":1}}],[\"使用接口和抽象类\",{\"1\":{\"129\":1}}],[\"使用门面模式\",{\"1\":{\"123\":1}}],[\"使用设计模式的目的是重用代码\",{\"1\":{\"232\":1}}],[\"使用设计模式\",{\"1\":{\"116\":1}}],[\"使用await关键字让出使用权\",{\"1\":{\"101\":1}}],[\"使用权\",{\"1\":{\"101\":1}}],[\"使用capacitor和ionic将vue项目迁移到mobile端\",{\"0\":{\"93\":1}}],[\"使用python\",{\"0\":{\"39\":1}}],[\"使用docker\",{\"1\":{\"26\":1}}],[\"使用\",{\"1\":{\"17\":1,\"23\":2,\"95\":1,\"96\":1,\"101\":1,\"172\":1,\"189\":1,\"206\":1,\"224\":1,\"243\":1,\"256\":1,\"316\":1,\"347\":1,\"365\":1,\"386\":1}}],[\"重写的代码历时一周\",{\"1\":{\"395\":1}}],[\"重新定义算法中的某些步骤\",{\"1\":{\"370\":1}}],[\"重活\",{\"1\":{\"324\":1}}],[\"重构\",{\"1\":{\"125\":1}}],[\"重要的是去理解如何将这些语句编译成汇编代码\",{\"1\":{\"472\":1}}],[\"重要\",{\"1\":{\"96\":1,\"103\":1}}],[\"重启container\",{\"0\":{\"24\":1}}],[\"重定向到automaton\",{\"1\":{\"17\":1,\"23\":2}}],[\"3+\",{\"1\":{\"416\":1,\"463\":1}}],[\"32位系统\",{\"1\":{\"498\":1}}],[\"32\",{\"1\":{\"405\":1,\"419\":1}}],[\"32k\",{\"1\":{\"17\":1}}],[\"3573\",{\"1\":{\"363\":2}}],[\"3572\",{\"1\":{\"363\":1}}],[\"3571\",{\"1\":{\"363\":1}}],[\"3570\",{\"1\":{\"363\":1}}],[\"3569\",{\"1\":{\"363\":1}}],[\"3568\",{\"1\":{\"363\":1}}],[\"3567\",{\"1\":{\"363\":1}}],[\"37\",{\"1\":{\"304\":2}}],[\"31500\",{\"1\":{\"212\":1,\"381\":1}}],[\"396\",{\"1\":{\"191\":1}}],[\"363\",{\"1\":{\"191\":1}}],[\"3333\",{\"1\":{\"251\":1}}],[\"333333\",{\"1\":{\"251\":2}}],[\"330\",{\"1\":{\"191\":1}}],[\"33\",{\"1\":{\"190\":1,\"191\":1,\"251\":12}}],[\"3049\",{\"1\":{\"363\":8}}],[\"30\",{\"1\":{\"284\":1,\"304\":2,\"419\":1}}],[\"3001\",{\"1\":{\"481\":1}}],[\"30000\",{\"1\":{\"212\":3,\"381\":3}}],[\"300\",{\"1\":{\"190\":1,\"211\":1,\"212\":3,\"380\":1,\"381\":3}}],[\"301\",{\"1\":{\"23\":2}}],[\"3\",{\"0\":{\"421\":1},\"1\":{\"101\":1,\"161\":1,\"172\":2,\"198\":2,\"250\":1,\"253\":2,\"265\":1,\"266\":2,\"284\":1,\"304\":2,\"362\":5,\"392\":1,\"400\":1,\"401\":1,\"403\":3,\"412\":2,\"416\":1,\"418\":1,\"421\":14,\"422\":2,\"439\":2,\"442\":2,\"449\":4,\"454\":1,\"456\":1,\"460\":4,\"471\":3,\"473\":1,\"481\":10,\"482\":9,\"486\":1,\"496\":1,\"505\":2}}],[\"347342082\",{\"1\":{\"35\":1}}],[\"进程的内存会被分成几个段\",{\"1\":{\"405\":1}}],[\"进而当\",{\"1\":{\"62\":3,\"63\":1,\"64\":2,\"68\":1,\"78\":3,\"79\":1,\"80\":1,\"81\":1}}],[\"进而\",{\"1\":{\"60\":1,\"68\":1,\"70\":1,\"72\":1,\"76\":1,\"83\":1}}],[\"进而有\",{\"1\":{\"59\":1,\"75\":1}}],[\"进有\",{\"1\":{\"59\":1,\"60\":1,\"75\":1,\"76\":1}}],[\"进入acme\",{\"1\":{\"21\":1}}],[\"进行编译\",{\"1\":{\"501\":1}}],[\"进行解析的时候\",{\"1\":{\"494\":1}}],[\"进行语法分析\",{\"1\":{\"442\":1}}],[\"进行安装\",{\"1\":{\"111\":1}}],[\"进行实验\",{\"1\":{\"53\":1}}],[\"进行修改\",{\"1\":{\"16\":1}}],[\"进行如下操作\",{\"1\":{\"16\":1}}],[\"申请证书\",{\"0\":{\"21\":1}}],[\"升级为https\",{\"0\":{\"20\":1}}],[\"及函数定义\",{\"1\":{\"453\":1}}],[\"及时进行重构\",{\"1\":{\"125\":1}}],[\"及\",{\"1\":{\"19\":1,\"412\":1,\"418\":1,\"462\":1,\"467\":1,\"485\":1}}],[\"失败\",{\"1\":{\"17\":1,\"23\":2}}],[\"或波浪号\",{\"1\":{\"425\":1}}],[\"或其他线程同步机制\",{\"1\":{\"342\":1}}],[\"或是调试起来十分困难\",{\"1\":{\"509\":1}}],[\"或是重新学习学习汇编相关的知识\",{\"1\":{\"468\":1}}],[\"或是函数的局部变量等\",{\"1\":{\"405\":1}}],[\"或是依赖于实例状态的信息\",{\"1\":{\"254\":1}}],[\"或是不依赖于实例状态的信息\",{\"1\":{\"254\":1}}],[\"或是如果不小心修改了\",{\"1\":{\"185\":1}}],[\"或是要修改具体工厂的\",{\"1\":{\"142\":1}}],[\"或是\",{\"1\":{\"106\":1}}],[\"或者使用更复杂的事件处理机制\",{\"1\":{\"308\":1}}],[\"或者说如果我们把代码中使用基类的地方用它的派生类所代替\",{\"1\":{\"118\":1}}],[\"或者说的更简单一点\",{\"1\":{\"101\":1}}],[\"或者执行过程中要根据变量状态进行一些下游操作\",{\"1\":{\"102\":1}}],[\"或\",{\"1\":{\"17\":1,\"23\":2,\"81\":1,\"255\":1,\"394\":1,\"453\":1,\"486\":1,\"499\":1}}],[\"4|\",{\"1\":{\"482\":1}}],[\"4+\",{\"1\":{\"416\":1}}],[\"4g\",{\"1\":{\"405\":1}}],[\"44\",{\"1\":{\"304\":2}}],[\"443\",{\"1\":{\"18\":2,\"23\":3}}],[\"49\",{\"1\":{\"304\":2}}],[\"495\",{\"1\":{\"191\":1}}],[\"46\",{\"1\":{\"304\":2}}],[\"462\",{\"1\":{\"191\":1,\"292\":1}}],[\"43\",{\"1\":{\"304\":2}}],[\"404\",{\"1\":{\"513\":1}}],[\"400\",{\"1\":{\"211\":1,\"212\":1,\"380\":1,\"381\":1}}],[\"4096\",{\"1\":{\"17\":1}}],[\"429\",{\"1\":{\"190\":1,\"191\":1}}],[\"4版本的yield\",{\"1\":{\"101\":1}}],[\"4\",{\"0\":{\"439\":1},\"1\":{\"17\":1,\"142\":1,\"198\":2,\"250\":1,\"265\":2,\"266\":4,\"284\":1,\"317\":2,\"392\":1,\"395\":1,\"400\":1,\"402\":1,\"403\":3,\"406\":1,\"416\":1,\"418\":1,\"421\":3,\"422\":2,\"439\":3,\"442\":2,\"449\":3,\"460\":3,\"467\":1,\"471\":2,\"481\":4,\"482\":6,\"498\":1,\"505\":2}}],[\"kinds\",{\"1\":{\"430\":1}}],[\"kid\",{\"1\":{\"280\":1,\"281\":3}}],[\"k\",{\"1\":{\"394\":1,\"397\":1,\"432\":2,\"436\":2,\"443\":1}}],[\"know\",{\"1\":{\"280\":1}}],[\"kcodetime\",{\"1\":{\"54\":1}}],[\"ksj\",{\"1\":{\"39\":1}}],[\"keep\",{\"1\":{\"434\":1}}],[\"keepalive\",{\"1\":{\"17\":1}}],[\"keywords\",{\"1\":{\"434\":1}}],[\"key\",{\"1\":{\"22\":2,\"23\":6,\"237\":1,\"250\":1,\"317\":1}}],[\"kts\",{\"1\":{\"9\":1}}],[\"nightstate\",{\"1\":{\"348\":7,\"353\":3,\"355\":1,\"356\":1}}],[\"n$\",{\"1\":{\"303\":2}}],[\"narrow\",{\"1\":{\"294\":1}}],[\"names\",{\"1\":{\"362\":2}}],[\"name+\",{\"1\":{\"265\":1}}],[\"name\",{\"1\":{\"17\":2,\"23\":5,\"190\":10,\"208\":3,\"210\":2,\"265\":7,\"272\":5,\"280\":3,\"317\":4,\"324\":21,\"362\":5,\"380\":4,\"429\":5,\"464\":1,\"465\":2,\"466\":1}}],[\"n<h1>$\",{\"1\":{\"237\":1}}],[\"num\",{\"1\":{\"425\":1,\"430\":1,\"431\":3,\"441\":1,\"442\":4,\"444\":1,\"445\":3,\"450\":2,\"453\":2,\"454\":3,\"484\":2,\"486\":1,\"492\":2,\"494\":1}}],[\"numbervoid\",{\"1\":{\"402\":1}}],[\"numbergenerator\",{\"1\":{\"303\":17}}],[\"number\",{\"1\":{\"165\":1,\"169\":1,\"190\":18,\"197\":8,\"208\":1,\"209\":1,\"210\":2,\"218\":9,\"265\":11,\"272\":4,\"291\":6,\"303\":9,\"339\":1,\"343\":1,\"348\":6,\"362\":4,\"372\":1,\"380\":3,\"422\":5,\"429\":1,\"430\":2,\"486\":1}}],[\"null\",{\"1\":{\"190\":1,\"250\":1,\"265\":2,\"317\":2,\"339\":3,\"343\":4,\"445\":2}}],[\"n`\",{\"1\":{\"139\":1,\"179\":3,\"237\":3,\"265\":1}}],[\"normal\",{\"1\":{\"487\":1}}],[\"non\",{\"1\":{\"450\":3,\"461\":3}}],[\"now\",{\"1\":{\"291\":1,\"292\":3,\"485\":1,\"498\":2}}],[\"note\",{\"1\":{\"362\":1,\"453\":1}}],[\"nothing\",{\"1\":{\"291\":1,\"292\":2,\"402\":2,\"492\":1}}],[\"not\",{\"1\":{\"280\":1,\"380\":2,\"402\":2,\"405\":3,\"411\":1,\"428\":1,\"490\":1,\"491\":1,\"498\":1,\"513\":1}}],[\"notifyobservers\",{\"1\":{\"303\":2,\"307\":1}}],[\"notify\",{\"1\":{\"280\":6,\"283\":3}}],[\"nosupport\",{\"1\":{\"190\":5}}],[\"node\",{\"1\":{\"111\":2,\"139\":1,\"153\":1,\"170\":1,\"180\":1,\"191\":1,\"198\":1,\"212\":1,\"219\":1,\"238\":1,\"245\":1,\"251\":1,\"265\":29,\"266\":6,\"273\":1,\"281\":1,\"304\":1,\"318\":1,\"325\":1,\"340\":1,\"349\":1,\"373\":1,\"381\":1}}],[\"nopush\",{\"1\":{\"17\":1}}],[\"n\",{\"1\":{\"99\":6,\"100\":3,\"101\":12,\"139\":6,\"179\":5,\"237\":1,\"250\":119,\"265\":7,\"303\":1,\"402\":4,\"405\":3,\"418\":1,\"427\":1,\"428\":1,\"431\":5,\"432\":1,\"445\":2,\"453\":2,\"454\":2,\"455\":1,\"465\":2,\"466\":2,\"486\":2,\"488\":1,\"489\":1,\"493\":1,\"495\":1,\"496\":1,\"500\":1}}],[\"ne\",{\"1\":{\"407\":1,\"417\":1,\"425\":2,\"433\":1,\"494\":1}}],[\"need\",{\"1\":{\"280\":1}}],[\"nexthand2\",{\"1\":{\"362\":3}}],[\"nexthand\",{\"1\":{\"362\":7}}],[\"nexthand1\",{\"1\":{\"362\":3}}],[\"nexttoken\",{\"1\":{\"265\":6}}],[\"next\",{\"1\":{\"190\":8,\"272\":3,\"273\":1,\"402\":5,\"424\":1,\"426\":2,\"429\":1,\"430\":1,\"431\":1,\"432\":1,\"433\":1,\"434\":4,\"445\":3,\"452\":2,\"453\":1,\"454\":4,\"455\":2}}],[\"news\",{\"1\":{\"139\":2}}],[\"new\",{\"1\":{\"130\":2,\"133\":2,\"139\":4,\"152\":3,\"168\":6,\"179\":4,\"190\":7,\"197\":3,\"209\":1,\"211\":14,\"218\":9,\"237\":1,\"244\":2,\"250\":4,\"256\":2,\"265\":12,\"272\":6,\"280\":4,\"291\":2,\"303\":3,\"317\":4,\"324\":2,\"339\":1,\"343\":1,\"348\":3,\"362\":7,\"372\":3,\"380\":18,\"412\":1,\"413\":3,\"416\":8,\"429\":1,\"463\":7,\"465\":1}}],[\"newline\",{\"1\":{\"52\":1}}],[\"net\",{\"1\":{\"38\":1,\"481\":1}}],[\"networks\",{\"1\":{\"18\":2}}],[\"nju\",{\"1\":{\"32\":1,\"33\":2}}],[\"nginx\",{\"0\":{\"13\":1},\"1\":{\"13\":2,\"14\":1,\"15\":2,\"17\":17,\"18\":10,\"21\":4,\"22\":4,\"23\":15,\"26\":2},\"2\":{\"27\":1}}],[\"xx\",{\"1\":{\"500\":1}}],[\"xxx\",{\"1\":{\"453\":1,\"472\":1}}],[\"xxxstate\",{\"1\":{\"355\":1}}],[\"xzp740813\",{\"1\":{\"481\":1}}],[\"xc\",{\"1\":{\"419\":2,\"501\":5}}],[\"xor\",{\"1\":{\"407\":1,\"417\":1,\"425\":1,\"433\":1,\"491\":2,\"494\":1,\"498\":4}}],[\"x86\",{\"1\":{\"407\":1,\"408\":2,\"409\":1,\"412\":1,\"420\":1}}],[\"x<p\",{\"1\":{\"45\":1}}],[\"x+y+z\",{\"1\":{\"45\":1}}],[\"x+y\",{\"1\":{\"43\":1}}],[\"x\",{\"1\":{\"17\":1,\"44\":1,\"45\":2,\"197\":8,\"430\":2,\"453\":1,\"482\":3,\"492\":2}}],[\"$\",{\"1\":{\"139\":1,\"152\":2,\"179\":2,\"190\":3,\"197\":2,\"208\":2,\"209\":1,\"210\":1,\"237\":4,\"265\":7,\"280\":4,\"291\":6,\"303\":2,\"317\":4,\"324\":2,\"339\":1,\"343\":1,\"348\":2,\"362\":6,\"380\":4}}],[\"$host$request\",{\"1\":{\"23\":2}}],[\"$http\",{\"1\":{\"17\":3}}],[\"$uri\",{\"1\":{\"17\":6,\"23\":10}}],[\"$body\",{\"1\":{\"17\":1}}],[\"$status\",{\"1\":{\"17\":1}}],[\"$request\",{\"1\":{\"17\":1}}],[\"$remote\",{\"1\":{\"17\":2}}],[\"$time\",{\"1\":{\"17\":1}}],[\"rmi\",{\"1\":{\"332\":1}}],[\"right\",{\"1\":{\"265\":9,\"266\":12,\"422\":1}}],[\"role\",{\"1\":{\"280\":1}}],[\"row\",{\"1\":{\"218\":9}}],[\"rootdir\",{\"1\":{\"211\":6,\"380\":6}}],[\"root\",{\"1\":{\"17\":2,\"21\":2,\"22\":1,\"23\":3,\"52\":1,\"211\":2,\"212\":21,\"380\":2,\"381\":21}}],[\"randomnumbergenerator\",{\"1\":{\"303\":5}}],[\"random\",{\"1\":{\"291\":3,\"303\":1,\"362\":2}}],[\"range\",{\"1\":{\"99\":2,\"101\":1}}],[\"rawclose\",{\"1\":{\"166\":1,\"167\":1,\"169\":1}}],[\"rawprint\",{\"1\":{\"166\":1,\"167\":1,\"169\":1}}],[\"rawopen\",{\"1\":{\"166\":1,\"167\":1,\"169\":1}}],[\"r\",{\"1\":{\"101\":1,\"431\":1}}],[\"run\",{\"1\":{\"17\":1,\"100\":1,\"101\":3}}],[\"remove\",{\"1\":{\"412\":1,\"414\":2}}],[\"remote\",{\"1\":{\"328\":1,\"332\":1}}],[\"ret\",{\"1\":{\"412\":9,\"415\":2}}],[\"returns\",{\"1\":{\"501\":1}}],[\"returnret\",{\"1\":{\"415\":1}}],[\"returned\",{\"1\":{\"402\":1}}],[\"return\",{\"0\":{\"475\":1},\"1\":{\"23\":2,\"44\":3,\"45\":4,\"139\":6,\"179\":2,\"190\":11,\"208\":3,\"209\":1,\"210\":2,\"218\":13,\"237\":2,\"244\":4,\"250\":2,\"265\":11,\"272\":6,\"291\":6,\"303\":1,\"317\":3,\"324\":2,\"339\":1,\"343\":1,\"348\":4,\"362\":12,\"380\":7,\"402\":6,\"405\":3,\"408\":1,\"412\":3,\"418\":2,\"425\":1,\"426\":1,\"429\":3,\"430\":1,\"431\":2,\"432\":1,\"433\":15,\"434\":2,\"445\":11,\"450\":1,\"453\":1,\"461\":1,\"471\":1,\"472\":1,\"475\":6,\"494\":1}}],[\"regex\",{\"1\":{\"397\":1}}],[\"registers\",{\"1\":{\"406\":1}}],[\"registerproduct\",{\"1\":{\"244\":3}}],[\"register\",{\"1\":{\"126\":2,\"317\":4}}],[\"registry\",{\"0\":{\"30\":1},\"1\":{\"31\":4,\"33\":1}}],[\"read\",{\"1\":{\"402\":3,\"407\":1,\"418\":3,\"434\":1,\"486\":1}}],[\"readonly\",{\"1\":{\"362\":2}}],[\"realize\",{\"1\":{\"324\":2}}],[\"real\",{\"1\":{\"280\":1,\"324\":6}}],[\"record\",{\"1\":{\"349\":24}}],[\"recordlog\",{\"1\":{\"348\":4}}],[\"received\",{\"1\":{\"280\":1,\"281\":6}}],[\"receivemessage\",{\"1\":{\"280\":2}}],[\"receiver\",{\"1\":{\"200\":1}}],[\"repeatcommandnode\",{\"1\":{\"265\":5}}],[\"repeat\",{\"1\":{\"265\":9,\"266\":6,\"317\":3}}],[\"replace\",{\"1\":{\"250\":1}}],[\"repos\",{\"1\":{\"9\":1}}],[\"repository\",{\"1\":{\"9\":12}}],[\"repositoriesmode\",{\"1\":{\"9\":2}}],[\"repositories\",{\"1\":{\"9\":2}}],[\"reduce\",{\"1\":{\"208\":1}}],[\"requirements有两种方式\",{\"1\":{\"48\":1}}],[\"requirements\",{\"0\":{\"48\":1},\"1\":{\"48\":2}}],[\"rest\",{\"1\":{\"484\":1}}],[\"restore\",{\"1\":{\"412\":1,\"415\":2}}],[\"restorememento\",{\"1\":{\"291\":2}}],[\"restoring\",{\"1\":{\"291\":1,\"292\":1}}],[\"restart\",{\"1\":{\"33\":1}}],[\"resolved\",{\"1\":{\"190\":2,\"191\":16}}],[\"resolve\",{\"1\":{\"190\":6}}],[\"resolver\",{\"1\":{\"17\":2}}],[\"responsibility\",{\"1\":{\"188\":1,\"189\":1,\"190\":1,\"375\":1}}],[\"result\",{\"1\":{\"179\":2,\"362\":1,\"363\":1,\"412\":1,\"498\":1}}],[\"res\",{\"1\":{\"100\":1,\"101\":3}}],[\"reverse\",{\"1\":{\"26\":1}}],[\"release\",{\"1\":{\"99\":1}}],[\"releases\",{\"1\":{\"9\":2}}],[\"reload\",{\"1\":{\"33\":1}}],[\"reloadcmd\",{\"1\":{\"22\":1}}],[\"rewrite\",{\"1\":{\"17\":1,\"23\":2}}],[\"referer\",{\"1\":{\"17\":1}}],[\"15\",{\"1\":{\"430\":3,\"482\":2}}],[\"1500\",{\"1\":{\"212\":1,\"381\":1}}],[\"142961332\",{\"1\":{\"481\":1}}],[\"147\",{\"1\":{\"429\":1}}],[\"140717115\",{\"1\":{\"38\":1}}],[\"1+\",{\"1\":{\"416\":2,\"463\":2}}],[\"19\",{\"1\":{\"356\":1}}],[\"198\",{\"1\":{\"191\":1}}],[\"13\",{\"1\":{\"304\":4}}],[\"132\",{\"1\":{\"191\":1}}],[\"128\",{\"1\":{\"425\":1,\"494\":1}}],[\"12\",{\"1\":{\"284\":1,\"412\":2,\"414\":1}}],[\"123\",{\"1\":{\"250\":1,\"430\":1}}],[\"12345678\",{\"1\":{\"39\":1}}],[\"16\",{\"1\":{\"304\":2,\"353\":1,\"430\":2}}],[\"165\",{\"1\":{\"191\":1}}],[\"16k\",{\"1\":{\"17\":1}}],[\"111111\",{\"1\":{\"251\":1}}],[\"1111\",{\"1\":{\"251\":1}}],[\"11\",{\"1\":{\"251\":8,\"304\":2,\"403\":1}}],[\"1190000040806239\",{\"1\":{\"106\":1}}],[\"114\",{\"1\":{\"17\":4}}],[\"18\",{\"1\":{\"101\":1,\"304\":2}}],[\"17\",{\"1\":{\"101\":1,\"348\":2}}],[\"10+20\",{\"1\":{\"419\":1}}],[\"1024\",{\"1\":{\"402\":1}}],[\"1000\",{\"1\":{\"324\":1,\"405\":1}}],[\"10000\",{\"1\":{\"211\":1,\"212\":2,\"362\":1,\"363\":2,\"380\":1,\"381\":2}}],[\"1000000\",{\"1\":{\"99\":2,\"101\":1}}],[\"100\",{\"1\":{\"190\":1,\"211\":1,\"212\":1,\"291\":3,\"380\":1,\"381\":1}}],[\"10\",{\"1\":{\"53\":1,\"99\":1,\"100\":1,\"101\":6,\"197\":1,\"279\":1,\"304\":2,\"348\":1,\"403\":1,\"405\":1,\"419\":1,\"421\":1,\"429\":1,\"430\":1,\"445\":1,\"453\":1,\"481\":1,\"486\":1,\"500\":2}}],[\"10s\",{\"1\":{\"17\":1}}],[\"1ll\",{\"1\":{\"44\":1,\"45\":1}}],[\"1\",{\"0\":{\"55\":1,\"400\":1},\"1\":{\"17\":1,\"101\":3,\"164\":1,\"190\":1,\"198\":2,\"218\":9,\"250\":1,\"260\":2,\"291\":2,\"338\":1,\"340\":1,\"362\":18,\"392\":1,\"400\":3,\"402\":5,\"403\":6,\"405\":3,\"408\":1,\"411\":2,\"412\":3,\"413\":1,\"416\":2,\"418\":7,\"420\":1,\"421\":3,\"429\":1,\"430\":1,\"439\":2,\"442\":1,\"445\":1,\"449\":3,\"453\":3,\"454\":3,\"455\":1,\"460\":3,\"462\":1,\"463\":3,\"465\":2,\"466\":3,\"471\":7,\"473\":1,\"474\":2,\"481\":4,\"482\":1,\"486\":3,\"488\":1,\"489\":1,\"491\":2,\"492\":1,\"493\":1,\"495\":1,\"496\":2,\"497\":2,\"498\":1,\"500\":1,\"505\":2}}],[\"when\",{\"1\":{\"486\":1}}],[\"which\",{\"1\":{\"486\":1}}],[\"white\",{\"1\":{\"445\":1}}],[\"whitespace\",{\"1\":{\"52\":1}}],[\"while\",{\"0\":{\"474\":1},\"1\":{\"265\":1,\"272\":1,\"402\":1,\"408\":1,\"425\":1,\"426\":4,\"428\":1,\"429\":3,\"430\":3,\"431\":1,\"432\":1,\"434\":5,\"445\":3,\"450\":3,\"452\":1,\"453\":2,\"454\":1,\"461\":3,\"464\":3,\"465\":2,\"466\":4,\"471\":1,\"472\":1,\"474\":4,\"476\":1,\"484\":1,\"485\":1,\"486\":1,\"487\":1,\"494\":2}}],[\"we\",{\"1\":{\"428\":1}}],[\"weakhashmap\",{\"1\":{\"255\":1}}],[\"weakreference\",{\"1\":{\"255\":1}}],[\"welcome\",{\"1\":{\"237\":2,\"238\":2}}],[\"web\",{\"1\":{\"95\":1}}],[\"webui\",{\"1\":{\"33\":2}}],[\"web服务器添加https功能\",{\"1\":{\"26\":1}}],[\"webnet\",{\"1\":{\"18\":2}}],[\"write\",{\"1\":{\"395\":1,\"400\":1,\"402\":1,\"403\":1,\"420\":1,\"421\":1,\"435\":1,\"439\":1,\"449\":1,\"456\":1,\"460\":1,\"467\":1,\"471\":1,\"477\":1,\"501\":1,\"505\":1}}],[\"writer\",{\"1\":{\"237\":13}}],[\"wrapper\",{\"1\":{\"9\":1}}],[\"won\",{\"1\":{\"362\":3}}],[\"wodfan\",{\"1\":{\"101\":2}}],[\"working\",{\"1\":{\"130\":1}}],[\"work\",{\"1\":{\"101\":2,\"130\":3}}],[\"worker\",{\"1\":{\"17\":2,\"130\":9}}],[\"world\",{\"1\":{\"101\":2,\"168\":1,\"170\":1,\"218\":1,\"219\":3,\"272\":1,\"273\":1,\"280\":1,\"317\":3,\"318\":3,\"372\":1,\"373\":5}}],[\"will\",{\"1\":{\"428\":1}}],[\"winner\",{\"1\":{\"363\":6}}],[\"winningstrategy\",{\"1\":{\"362\":6}}],[\"wincount++\",{\"1\":{\"362\":1}}],[\"wincount\",{\"1\":{\"362\":2}}],[\"win\",{\"1\":{\"362\":9,\"363\":8}}],[\"windows\",{\"1\":{\"53\":1,\"172\":2}}],[\"wide\",{\"1\":{\"294\":1}}],[\"width\",{\"1\":{\"52\":1,\"169\":3,\"372\":3}}],[\"with\",{\"1\":{\"99\":3,\"101\":6,\"339\":1,\"340\":1,\"343\":1,\"430\":2,\"472\":1}}],[\"without\",{\"1\":{\"99\":1,\"100\":5,\"101\":15}}],[\"wsl$\",{\"1\":{\"34\":1}}],[\"wsl2\",{\"0\":{\"34\":1}}],[\"wq保存退出\",{\"1\":{\"33\":1}}],[\"www\",{\"1\":{\"17\":1,\"23\":4,\"139\":11}}],[\"warning\",{\"1\":{\"317\":2}}],[\"warn\",{\"1\":{\"17\":5,\"23\":5}}],[\"部分\",{\"1\":{\"142\":1,\"206\":1,\"451\":1}}],[\"部分ide默认直接支持\",{\"1\":{\"52\":1}}],[\"部分路径以实际为准\",{\"1\":{\"16\":1}}],[\"部署一个\",{\"1\":{\"13\":1}}],[\"部署\",{\"0\":{\"13\":1},\"1\":{\"25\":1},\"2\":{\"28\":1}}],[\"└──\",{\"1\":{\"15\":2}}],[\"lvalue\",{\"1\":{\"445\":12,\"493\":1,\"495\":2}}],[\"lt\",{\"1\":{\"407\":1,\"417\":1,\"425\":1,\"433\":1,\"494\":1}}],[\"lc\",{\"1\":{\"407\":1,\"408\":5,\"486\":4,\"488\":1,\"489\":4,\"493\":2,\"495\":1,\"500\":1}}],[\"ll\",{\"1\":{\"394\":1,\"397\":1,\"432\":1}}],[\"le\",{\"1\":{\"407\":1,\"417\":1,\"425\":1,\"433\":1,\"494\":1}}],[\"leaving\",{\"1\":{\"466\":1}}],[\"lea\",{\"0\":{\"416\":1},\"1\":{\"403\":1,\"407\":1,\"416\":2,\"486\":1}}],[\"lev\",{\"0\":{\"415\":1},\"1\":{\"403\":1,\"407\":1,\"412\":2,\"415\":2,\"466\":1,\"475\":2}}],[\"level\",{\"1\":{\"402\":2,\"494\":3}}],[\"lemon\",{\"1\":{\"397\":1}}],[\"lexer\",{\"1\":{\"423\":1}}],[\"lex\",{\"1\":{\"394\":2,\"424\":1}}],[\"legs\",{\"1\":{\"272\":1,\"273\":1}}],[\"left\",{\"1\":{\"265\":4,\"266\":2,\"422\":1}}],[\"length\",{\"1\":{\"169\":1,\"218\":1,\"265\":2,\"291\":1,\"317\":7,\"372\":1,\"380\":1}}],[\"let\",{\"1\":{\"139\":13,\"165\":1,\"169\":2,\"190\":7,\"197\":1,\"211\":7,\"218\":7,\"237\":3,\"250\":3,\"265\":3,\"291\":3,\"303\":3,\"317\":9,\"324\":2,\"348\":2,\"362\":4,\"372\":3,\"380\":9,\"397\":1}}],[\"letsencrypt\",{\"1\":{\"18\":1,\"23\":6}}],[\"lf\",{\"1\":{\"52\":1}}],[\"lan\",{\"1\":{\"425\":1,\"433\":1,\"494\":1,\"497\":3}}],[\"lalr\",{\"1\":{\"394\":1}}],[\"last++\",{\"1\":{\"272\":1}}],[\"last\",{\"1\":{\"272\":3,\"425\":1,\"426\":1,\"429\":4,\"431\":2}}],[\"latex\",{\"1\":{\"211\":1,\"212\":2,\"380\":1,\"381\":2}}],[\"latest\",{\"1\":{\"18\":1,\"38\":1}}],[\"large\",{\"1\":{\"17\":1}}],[\"lookahead\",{\"1\":{\"432\":1,\"436\":1}}],[\"look\",{\"1\":{\"429\":1}}],[\"loop\",{\"1\":{\"100\":3,\"101\":9}}],[\"lor\",{\"1\":{\"425\":1,\"433\":1,\"494\":1,\"497\":2}}],[\"load\",{\"1\":{\"408\":3,\"416\":1,\"486\":1}}],[\"low\",{\"1\":{\"405\":1,\"416\":1,\"463\":1}}],[\"lotabout\",{\"1\":{\"400\":1,\"402\":1,\"403\":1,\"420\":1,\"421\":1,\"435\":1,\"439\":1,\"449\":1,\"456\":1,\"460\":1,\"467\":1,\"471\":1,\"477\":1,\"501\":1,\"505\":1}}],[\"losecount++\",{\"1\":{\"362\":1}}],[\"losecount\",{\"1\":{\"362\":2}}],[\"lose\",{\"1\":{\"362\":4,\"363\":8}}],[\"long\",{\"1\":{\"272\":1,\"273\":1,\"419\":4}}],[\"loc\",{\"1\":{\"425\":1,\"464\":1,\"465\":2,\"466\":2,\"486\":1,\"494\":1}}],[\"locking\",{\"1\":{\"342\":1}}],[\"lock\",{\"1\":{\"99\":8,\"100\":5,\"101\":23,\"343\":4}}],[\"location\",{\"1\":{\"17\":3,\"23\":6}}],[\"localtime=true\",{\"1\":{\"39\":1}}],[\"local\",{\"1\":{\"17\":1,\"416\":2,\"463\":5,\"464\":2,\"465\":1,\"466\":11,\"486\":1}}],[\"logic\",{\"1\":{\"497\":2}}],[\"loginframe\",{\"1\":{\"285\":2}}],[\"login\",{\"1\":{\"39\":1,\"126\":2}}],[\"log\",{\"1\":{\"15\":2,\"17\":29,\"18\":1,\"23\":30,\"130\":1,\"133\":4,\"139\":2,\"152\":2,\"169\":2,\"179\":4,\"190\":2,\"197\":1,\"208\":1,\"210\":1,\"211\":2,\"218\":1,\"237\":2,\"244\":1,\"250\":1,\"265\":2,\"272\":1,\"280\":3,\"291\":10,\"303\":2,\"317\":8,\"324\":9,\"339\":2,\"343\":1,\"348\":4,\"362\":6,\"372\":5,\"380\":4}}],[\"logs\",{\"1\":{\"15\":1,\"18\":1}}],[\"literal\",{\"1\":{\"431\":2}}],[\"li\",{\"1\":{\"407\":1,\"408\":5,\"486\":4,\"488\":1,\"489\":4,\"493\":2,\"495\":2,\"500\":1}}],[\"lightning\",{\"1\":{\"280\":1,\"281\":3}}],[\"liskov\",{\"1\":{\"228\":1}}],[\"listvisitor\",{\"1\":{\"380\":6,\"384\":1}}],[\"list>\",{\"1\":{\"265\":8}}],[\"listpicture\",{\"1\":{\"143\":1}}],[\"listpage\",{\"1\":{\"139\":5}}],[\"listtray\",{\"1\":{\"139\":5}}],[\"listlink\",{\"1\":{\"139\":5}}],[\"listfactory\",{\"1\":{\"139\":5,\"143\":2}}],[\"listen\",{\"1\":{\"17\":2,\"23\":5}}],[\"list\",{\"1\":{\"8\":1,\"48\":1,\"255\":1,\"265\":3}}],[\"limit\",{\"1\":{\"190\":5}}],[\"limitsupport\",{\"1\":{\"190\":7}}],[\"li><li>再见\",{\"1\":{\"180\":1}}],[\"li><li>晚安\",{\"1\":{\"180\":1}}],[\"li><li>下午好\",{\"1\":{\"180\":1}}],[\"li><\",{\"1\":{\"180\":2}}],[\"li>`\",{\"1\":{\"179\":1}}],[\"li>\",{\"1\":{\"139\":10}}],[\"linkpage\",{\"1\":{\"139\":1}}],[\"link\",{\"1\":{\"139\":8,\"142\":1,\"237\":2}}],[\"linesecond\",{\"1\":{\"484\":1}}],[\"linelen\",{\"1\":{\"445\":2}}],[\"linecap\",{\"1\":{\"445\":2}}],[\"linear\",{\"1\":{\"429\":1}}],[\"line\",{\"1\":{\"52\":1,\"372\":4,\"402\":3,\"445\":3,\"453\":2,\"454\":2,\"455\":1,\"465\":2,\"466\":2,\"484\":3,\"486\":2,\"488\":1,\"489\":1,\"493\":1,\"495\":1,\"496\":1,\"500\":1}}],[\"license\",{\"1\":{\"111\":2}}],[\"liuyue$\",{\"1\":{\"101\":4}}],[\"liuyue\",{\"1\":{\"101\":6}}],[\"like\",{\"1\":{\"22\":1,\"454\":1,\"466\":1}}],[\"live\",{\"1\":{\"18\":1,\"23\":6}}],[\"libgen\",{\"1\":{\"5\":2}}],[\"lib\",{\"1\":{\"5\":1}}],[\"library\",{\"1\":{\"5\":2,\"434\":1}}],[\"yet\",{\"1\":{\"402\":1}}],[\"yacc\",{\"1\":{\"394\":2,\"508\":1}}],[\"yahoo<\",{\"1\":{\"139\":2}}],[\"yahoo\",{\"1\":{\"139\":12}}],[\"yuki<\",{\"1\":{\"238\":1}}],[\"yukiのページへようこそ\",{\"1\":{\"238\":1}}],[\"yuki\",{\"1\":{\"211\":5,\"212\":3,\"237\":1,\"238\":2,\"380\":5,\"381\":3}}],[\"y\",{\"1\":{\"44\":1,\"45\":1,\"197\":8}}],[\"yml\",{\"1\":{\"15\":1,\"18\":1}}],[\"your\",{\"1\":{\"54\":1}}],[\"you\",{\"1\":{\"8\":1}}],[\"bxxx\",{\"1\":{\"464\":1,\"465\":1}}],[\"bxxxx\",{\"1\":{\"429\":1}}],[\"bnf\",{\"1\":{\"441\":1,\"443\":3,\"446\":1,\"450\":1,\"508\":2}}],[\"bnf什么的\",{\"1\":{\"394\":1}}],[\"bvalue\",{\"1\":{\"429\":2,\"464\":1,\"465\":1,\"466\":1}}],[\"btype\",{\"1\":{\"429\":2,\"464\":1,\"465\":1,\"466\":1}}],[\"bp+\",{\"1\":{\"416\":1,\"463\":1}}],[\"bp\",{\"1\":{\"406\":3,\"413\":2,\"415\":2,\"416\":9,\"463\":7,\"465\":5,\"466\":2,\"486\":2}}],[\"brak\",{\"1\":{\"425\":1,\"433\":1,\"494\":2,\"500\":2}}],[\"bracket\",{\"1\":{\"422\":2}}],[\"break\",{\"1\":{\"265\":1}}],[\"bridge\",{\"0\":{\"157\":1},\"1\":{\"154\":1,\"157\":1,\"158\":1,\"162\":1,\"170\":1,\"172\":2}}],[\"bsion\",{\"1\":{\"508\":1}}],[\"bss\",{\"1\":{\"405\":2}}],[\"bs\",{\"1\":{\"250\":2}}],[\"bclass\",{\"1\":{\"429\":2,\"464\":1,\"465\":1,\"466\":1}}],[\"bc\",{\"1\":{\"250\":5}}],[\"bitwise\",{\"1\":{\"491\":1,\"498\":1}}],[\"bison\",{\"1\":{\"394\":1,\"395\":1,\"397\":1,\"401\":1}}],[\"bible\",{\"1\":{\"272\":1,\"273\":1}}],[\"bigstring\",{\"1\":{\"250\":6,\"253\":4,\"254\":3}}],[\"bigchars\",{\"1\":{\"250\":3}}],[\"bigchar>\",{\"1\":{\"250\":1}}],[\"bigcharfactory\",{\"1\":{\"250\":9}}],[\"bigchar\",{\"1\":{\"250\":13,\"253\":6,\"254\":5}}],[\"binary\",{\"1\":{\"494\":1}}],[\"bin\",{\"1\":{\"211\":1,\"212\":6,\"380\":1,\"381\":6}}],[\"bindir\",{\"1\":{\"211\":4,\"380\":4}}],[\"b4\",{\"1\":{\"218\":2,\"221\":1}}],[\"b3\",{\"1\":{\"218\":2}}],[\"b2\",{\"1\":{\"218\":3}}],[\"b1\",{\"1\":{\"218\":3}}],[\"by\",{\"1\":{\"190\":1,\"191\":13,\"280\":1,\"281\":6}}],[\"bytes\",{\"1\":{\"17\":1}}],[\"box\",{\"1\":{\"317\":4}}],[\"books\",{\"1\":{\"272\":4}}],[\"bookshelfiterator\",{\"1\":{\"272\":5,\"273\":1}}],[\"bookshelf\",{\"1\":{\"272\":21,\"273\":3,\"274\":1}}],[\"book\",{\"1\":{\"272\":19,\"273\":1}}],[\"boolean\",{\"1\":{\"190\":4,\"265\":1,\"272\":2,\"362\":5}}],[\"borderchar\",{\"1\":{\"218\":4}}],[\"border\",{\"1\":{\"218\":8,\"221\":2}}],[\"bob使用了id卡\",{\"1\":{\"245\":1}}],[\"bob\",{\"1\":{\"190\":3,\"191\":4,\"244\":1,\"324\":1,\"325\":2}}],[\"body><\",{\"1\":{\"139\":2,\"179\":1,\"180\":1,\"237\":1,\"238\":1}}],[\"body\",{\"1\":{\"39\":2,\"450\":2,\"453\":1,\"461\":2,\"462\":1,\"464\":1,\"466\":1}}],[\"ba\",{\"1\":{\"473\":1}}],[\"bad\",{\"1\":{\"453\":1,\"454\":2,\"465\":1,\"466\":1,\"486\":1,\"488\":1,\"489\":1,\"493\":1,\"495\":1}}],[\"basetype\",{\"1\":{\"453\":4,\"466\":2}}],[\"banana\",{\"1\":{\"291\":1,\"292\":9}}],[\"banner\",{\"1\":{\"151\":1,\"152\":13}}],[\"balance\",{\"1\":{\"99\":12,\"100\":7,\"101\":32}}],[\"behaviour\",{\"1\":{\"486\":1}}],[\"because\",{\"1\":{\"428\":1}}],[\"bet\",{\"1\":{\"291\":2,\"362\":3}}],[\"be\",{\"1\":{\"190\":1,\"191\":3,\"453\":1,\"486\":1}}],[\"bepinex\",{\"1\":{\"51\":1}}],[\"below\",{\"1\":{\"22\":1}}],[\"b+p\",{\"1\":{\"44\":1}}],[\"b\",{\"1\":{\"44\":5,\"284\":7,\"402\":1,\"420\":1,\"435\":1,\"453\":1,\"454\":1,\"456\":1,\"463\":2,\"467\":1,\"473\":8,\"474\":4,\"476\":1,\"477\":1,\"496\":1,\"497\":4,\"501\":1}}],[\"blog\",{\"1\":{\"15\":3,\"17\":4,\"18\":2,\"23\":7,\"38\":1,\"481\":1}}],[\"but\",{\"1\":{\"265\":1,\"486\":1}}],[\"buttonuse\",{\"1\":{\"356\":1}}],[\"button\",{\"1\":{\"8\":1}}],[\"buf\",{\"1\":{\"218\":3}}],[\"buffers\",{\"1\":{\"17\":1}}],[\"buffer\",{\"1\":{\"17\":1,\"139\":21,\"169\":4,\"179\":19}}],[\"bug\",{\"0\":{\"96\":1},\"1\":{\"142\":1,\"283\":3,\"366\":1}}],[\"builder\",{\"0\":{\"177\":1,\"178\":1},\"1\":{\"144\":1,\"178\":3,\"179\":24,\"180\":1,\"183\":2,\"184\":1,\"185\":7,\"341\":1}}],[\"build\",{\"1\":{\"18\":1,\"19\":1,\"22\":1,\"24\":1,\"95\":2,\"397\":1}}],[\"bupt\",{\"1\":{\"13\":1,\"17\":4,\"19\":3,\"21\":2,\"22\":4,\"23\":14,\"39\":4}}],[\"│\",{\"1\":{\"15\":6}}],[\"├──\",{\"1\":{\"15\":12}}],[\"ulchar\",{\"1\":{\"317\":5}}],[\"ul><\",{\"1\":{\"180\":1}}],[\"ul><p>晚上<\",{\"1\":{\"180\":1}}],[\"ul>\",{\"1\":{\"139\":5,\"179\":1}}],[\"ul>`\",{\"1\":{\"139\":1}}],[\"unary\",{\"1\":{\"485\":1}}],[\"unwind\",{\"1\":{\"464\":1}}],[\"unknown\",{\"1\":{\"418\":1}}],[\"underlinepen\",{\"1\":{\"317\":5}}],[\"undefined`\",{\"1\":{\"265\":1}}],[\"undefined\",{\"1\":{\"54\":1,\"190\":1,\"324\":2,\"486\":1}}],[\"undo\",{\"1\":{\"197\":1}}],[\"unit\",{\"1\":{\"486\":1}}],[\"unityexplorer\",{\"1\":{\"51\":1}}],[\"unix\",{\"1\":{\"172\":2}}],[\"universe\",{\"1\":{\"168\":1,\"170\":5}}],[\"until\",{\"1\":{\"100\":1,\"101\":3}}],[\"utf\",{\"1\":{\"52\":1}}],[\"utils\",{\"1\":{\"39\":1}}],[\"u\",{\"1\":{\"43\":1,\"44\":1,\"45\":2,\"280\":2}}],[\"uri\",{\"1\":{\"23\":2}}],[\"url\",{\"1\":{\"9\":2,\"139\":10}}],[\"url=uri\",{\"1\":{\"9\":12}}],[\"upen\",{\"1\":{\"317\":2}}],[\"update\",{\"1\":{\"303\":4,\"307\":4}}],[\"up\",{\"1\":{\"19\":1,\"22\":1,\"24\":1}}],[\"us\",{\"1\":{\"139\":5}}],[\"use\",{\"1\":{\"22\":1,\"244\":5,\"317\":6,\"412\":1,\"490\":1,\"491\":1}}],[\"user3\",{\"1\":{\"280\":2}}],[\"user2\",{\"1\":{\"280\":2}}],[\"user1\",{\"1\":{\"280\":2}}],[\"userprofile\",{\"1\":{\"126\":1}}],[\"usersexcludingsender\",{\"1\":{\"280\":2}}],[\"users\",{\"1\":{\"101\":2,\"280\":4}}],[\"username\",{\"1\":{\"39\":2,\"237\":6}}],[\"user\",{\"1\":{\"17\":3,\"126\":1,\"211\":1,\"212\":1,\"280\":13,\"283\":2,\"380\":1,\"381\":1}}],[\"usrdir\",{\"1\":{\"211\":5,\"380\":5}}],[\"usr\",{\"1\":{\"17\":3,\"18\":2,\"23\":5,\"211\":1,\"212\":10,\"380\":1,\"381\":10}}],[\"ubuntu\",{\"1\":{\"14\":1,\"22\":4}}],[\"环境\",{\"0\":{\"14\":1},\"1\":{\"53\":1}}],[\"提前看字符的原理是\",{\"1\":{\"432\":1}}],[\"提出的要求\",{\"1\":{\"222\":1}}],[\"提高系统的安全性\",{\"1\":{\"332\":1}}],[\"提高性能\",{\"1\":{\"316\":1}}],[\"提高代码的可读性和可维护性\",{\"1\":{\"270\":1,\"361\":1}}],[\"提高代码的可维护性和可扩展性\",{\"1\":{\"243\":1}}],[\"提高了系统的可扩展性和可维护性\",{\"1\":{\"158\":1}}],[\"提高模块的相对独立性\",{\"1\":{\"122\":1}}],[\"提供了\",{\"1\":{\"255\":1}}],[\"提供一个便捷且强大的容器镜像管理解决方案\",{\"1\":{\"31\":1}}],[\"提供的容器镜像注册表服务\",{\"1\":{\"31\":1}}],[\"提供所有科学知识\",{\"1\":{\"5\":1}}],[\"提示\",{\"1\":{\"13\":1}}],[\"配置方法\",{\"0\":{\"33\":1}}],[\"配置docker\",{\"0\":{\"18\":1}}],[\"配置nginx反向代理\",{\"0\":{\"25\":1}}],[\"配置nginx\",{\"0\":{\"17\":1}}],[\"配置http服务\",{\"0\":{\"16\":1}}],[\"配置以及如何升级到\",{\"1\":{\"13\":1}}],[\"配置\",{\"1\":{\"13\":1}}],[\"和字符串如\",{\"1\":{\"431\":1}}],[\"和文法并编写解析算法\",{\"1\":{\"397\":1}}],[\"和文法的定义\",{\"1\":{\"397\":1}}],[\"和被观察者\",{\"1\":{\"306\":1}}],[\"和窄接口\",{\"1\":{\"294\":1}}],[\"和窗口句柄等也都是一种资源\",{\"1\":{\"256\":1}}],[\"和开源作者们使用同一套流程\",{\"1\":{\"36\":1}}],[\"和\",{\"0\":{\"297\":1},\"1\":{\"13\":2,\"59\":2,\"75\":1,\"81\":1,\"111\":1,\"140\":1,\"157\":1,\"273\":1,\"284\":4,\"297\":1,\"323\":1,\"351\":1,\"366\":1,\"383\":1,\"393\":1,\"408\":1,\"451\":1,\"472\":1,\"473\":1,\"482\":1,\"497\":1}}],[\"本节中我们专注语法分析器部分的实现\",{\"1\":{\"445\":1}}],[\"本节的代码可以在\",{\"1\":{\"402\":1}}],[\"本例中是\",{\"1\":{\"442\":1}}],[\"本质上这个指令并不是必需的\",{\"1\":{\"415\":1}}],[\"本质上是因为我们的\",{\"1\":{\"414\":1}}],[\"本质的\",{\"1\":{\"254\":1}}],[\"本章有两个难点\",{\"1\":{\"502\":1}}],[\"本章讲解了如何将语句编译成汇编代码\",{\"1\":{\"478\":1}}],[\"本章讲解函数定义相关的内容\",{\"1\":{\"460\":1}}],[\"本章的内容应该不难\",{\"1\":{\"457\":1}}],[\"本章的代码依旧无法运行\",{\"1\":{\"467\":1,\"477\":1}}],[\"本章的代码还无法正常运行\",{\"1\":{\"456\":1}}],[\"本章的代码可以在\",{\"1\":{\"420\":1,\"435\":1,\"456\":1,\"467\":1,\"477\":1,\"501\":1}}],[\"本章要讲解的就是上节文法中的\",{\"1\":{\"451\":1}}],[\"本章我们进行了最后的解析\",{\"1\":{\"502\":1}}],[\"本章我们将讲解递归下降的方法\",{\"1\":{\"439\":1}}],[\"本章我们为我们的编译器构建了词法分析器\",{\"1\":{\"436\":1}}],[\"本章我们要讲解如何构建词法分析器\",{\"1\":{\"421\":1}}],[\"本章我们要构建一台虚拟的电脑\",{\"1\":{\"403\":1}}],[\"本章中我们发一发牢骚\",{\"1\":{\"505\":1}}],[\"本章中我们用了不多的代码完成了函数定义的解析\",{\"1\":{\"468\":1}}],[\"本章中我们用\",{\"1\":{\"449\":1}}],[\"本章中我们介绍了递归下降的方法\",{\"1\":{\"446\":1}}],[\"本章中我们回顾了计算机的内部运行原理\",{\"1\":{\"420\":1}}],[\"本章中要学习的\",{\"1\":{\"162\":1}}],[\"本项目中的代码逻辑绝大多数取自\",{\"1\":{\"395\":1}}],[\"本篇是一些闲聊\",{\"1\":{\"392\":1}}],[\"本人\",{\"1\":{\"323\":2}}],[\"本实例是一个控制小车的脚本语言解释器demo\",{\"1\":{\"265\":1}}],[\"本专栏源码大部分参考自参考资料\",{\"1\":{\"260\":1}}],[\"本来就没有两全其美的解决方案\",{\"1\":{\"101\":1}}],[\"本来就只能一个人打电话\",{\"1\":{\"99\":1}}],[\"本以为\",{\"1\":{\"53\":1}}],[\"本文转自\",{\"1\":{\"400\":1,\"403\":1,\"421\":1,\"439\":1,\"449\":1,\"460\":1,\"471\":1,\"481\":1,\"505\":1}}],[\"本文转载自\",{\"1\":{\"392\":1}}],[\"本文是\",{\"1\":{\"13\":1}}],[\"本文将介绍如何使用\",{\"1\":{\"13\":1}}],[\"本地调试工具\",{\"1\":{\"10\":1}}],[\"+var\",{\"1\":{\"492\":1}}],[\"+global\",{\"1\":{\"450\":1}}],[\"++p时\",{\"1\":{\"493\":1}}],[\"++p\",{\"1\":{\"493\":2}}],[\"++pos\",{\"1\":{\"466\":1}}],[\"++text\",{\"1\":{\"466\":3,\"473\":4,\"474\":4,\"475\":1,\"484\":4,\"485\":2,\"486\":13,\"488\":1,\"490\":4,\"491\":4,\"492\":6,\"493\":7,\"495\":1,\"496\":4,\"497\":4,\"498\":8,\"499\":14,\"500\":7}}],[\"++line\",{\"1\":{\"427\":1}}],[\"++src\",{\"1\":{\"426\":1,\"430\":2,\"432\":1}}],[\"++\",{\"1\":{\"362\":3,\"433\":10,\"445\":2,\"486\":1,\"487\":1,\"488\":1}}],[\"+|return\",{\"1\":{\"416\":1,\"463\":1}}],[\"+|\",{\"1\":{\"219\":2,\"405\":4,\"416\":7,\"463\":6,\"482\":6}}],[\"+=\",{\"1\":{\"169\":2,\"179\":15,\"190\":1,\"218\":1,\"237\":4,\"291\":1,\"303\":1,\"348\":2,\"362\":1,\"372\":2,\"380\":1,\"412\":1}}],[\"+\",{\"0\":{\"13\":2},\"1\":{\"99\":2,\"100\":1,\"101\":4,\"139\":1,\"169\":2,\"170\":12,\"208\":1,\"218\":19,\"219\":12,\"237\":3,\"250\":109,\"265\":6,\"291\":2,\"317\":2,\"324\":4,\"362\":4,\"372\":2,\"373\":8,\"405\":2,\"406\":1,\"411\":2,\"414\":1,\"416\":6,\"417\":1,\"418\":1,\"422\":1,\"423\":8,\"425\":1,\"429\":22,\"430\":6,\"433\":3,\"441\":2,\"442\":2,\"444\":1,\"445\":4,\"453\":4,\"462\":1,\"463\":3,\"464\":1,\"465\":1,\"466\":1,\"473\":2,\"474\":2,\"482\":27,\"484\":1,\"485\":1,\"487\":1,\"489\":1,\"496\":2,\"497\":2,\"498\":3,\"500\":1,\"501\":1}}],[\"7章函数定义\",{\"1\":{\"486\":1}}],[\"7|\",{\"1\":{\"482\":1}}],[\"7\",{\"0\":{\"471\":1},\"1\":{\"9\":1,\"100\":1,\"101\":4,\"198\":2,\"250\":1,\"356\":1,\"392\":1,\"400\":1,\"403\":2,\"421\":2,\"430\":1,\"439\":2,\"449\":1,\"460\":1,\"471\":2,\"481\":2,\"505\":1}}],[\"80\",{\"1\":{\"17\":2,\"18\":2,\"23\":2,\"272\":1,\"273\":1}}],[\"8\",{\"0\":{\"481\":1},\"1\":{\"9\":1,\"17\":4,\"52\":1,\"99\":1,\"100\":1,\"101\":6,\"198\":2,\"250\":1,\"392\":1,\"400\":1,\"403\":2,\"421\":2,\"430\":1,\"439\":1,\"449\":1,\"460\":1,\"471\":1,\"481\":2,\"505\":1}}],[\"m32\",{\"1\":{\"419\":2}}],[\"mcmp\",{\"1\":{\"407\":1,\"418\":1}}],[\"mset\",{\"1\":{\"407\":1,\"418\":1}}],[\"msg\",{\"1\":{\"39\":7,\"324\":2,\"348\":6}}],[\"mbox\",{\"1\":{\"317\":2}}],[\"mvc\",{\"0\":{\"311\":1},\"1\":{\"311\":2}}],[\"m\",{\"1\":{\"291\":3,\"405\":1}}],[\"me\",{\"1\":{\"400\":1,\"403\":1,\"421\":1,\"439\":1,\"449\":1,\"460\":1,\"471\":1,\"505\":1}}],[\"mechanism\",{\"1\":{\"343\":1}}],[\"messaging\",{\"1\":{\"280\":1}}],[\"messagebox\",{\"1\":{\"317\":6}}],[\"messages\",{\"1\":{\"280\":2}}],[\"message\",{\"1\":{\"237\":2,\"280\":5,\"281\":9,\"317\":2}}],[\"mediator\",{\"0\":{\"278\":1},\"1\":{\"239\":1,\"280\":11,\"281\":1,\"283\":1,\"284\":1,\"312\":1,\"353\":1}}],[\"memcmp\",{\"1\":{\"418\":2,\"429\":1,\"434\":1}}],[\"memset\",{\"1\":{\"405\":3,\"406\":1,\"418\":2,\"434\":1}}],[\"memory\",{\"1\":{\"405\":1,\"453\":2,\"462\":1}}],[\"memo\",{\"1\":{\"211\":1,\"212\":1,\"380\":1,\"381\":1}}],[\"memento\",{\"0\":{\"289\":1,\"290\":1,\"295\":1,\"296\":1},\"1\":{\"202\":1,\"290\":1,\"291\":17,\"294\":5,\"295\":4,\"296\":5,\"297\":9,\"319\":1}}],[\"method\",{\"0\":{\"242\":1,\"243\":1,\"370\":1,\"371\":1},\"1\":{\"144\":1,\"161\":1,\"174\":1,\"181\":1,\"242\":2,\"243\":2,\"245\":2,\"275\":1,\"370\":1,\"373\":1,\"374\":1}}],[\"md\",{\"0\":{\"112\":1}}],[\"mytornado\",{\"1\":{\"101\":5}}],[\"move\",{\"1\":{\"484\":1}}],[\"movw\",{\"1\":{\"408\":1}}],[\"movb\",{\"1\":{\"408\":1}}],[\"mov\",{\"0\":{\"408\":1},\"1\":{\"403\":1,\"408\":6,\"412\":4,\"415\":1}}],[\"mod\",{\"1\":{\"407\":1,\"417\":1,\"425\":1,\"433\":1,\"494\":1}}],[\"model\",{\"0\":{\"311\":1},\"1\":{\"311\":1}}],[\"modint1\",{\"1\":{\"45\":1}}],[\"modint<int\",{\"1\":{\"45\":3}}],[\"modint\",{\"0\":{\"40\":1},\"1\":{\"45\":9},\"2\":{\"47\":1,\"109\":1}}],[\"money\",{\"1\":{\"291\":21,\"292\":8}}],[\"mobile\",{\"2\":{\"97\":1}}],[\"multiply\",{\"1\":{\"422\":1}}],[\"multipart\",{\"1\":{\"39\":1}}],[\"multidisplay\",{\"1\":{\"165\":1,\"168\":1}}],[\"mul\",{\"1\":{\"44\":1,\"407\":1,\"417\":1,\"425\":2,\"433\":1,\"453\":2,\"465\":2,\"466\":2,\"485\":2,\"487\":2,\"488\":2,\"492\":1,\"494\":1,\"498\":3,\"500\":1}}],[\"missing\",{\"1\":{\"265\":1,\"496\":1}}],[\"mixmark\",{\"1\":{\"112\":1}}],[\"mimemultipart\",{\"1\":{\"39\":2}}],[\"mimetext\",{\"1\":{\"39\":2}}],[\"mime\",{\"1\":{\"17\":1,\"39\":2}}],[\"mirrors\",{\"1\":{\"9\":1,\"33\":1}}],[\"may\",{\"1\":{\"453\":1}}],[\"malc\",{\"1\":{\"407\":1,\"418\":1}}],[\"malloc\",{\"1\":{\"402\":2,\"405\":6,\"418\":2,\"434\":1,\"486\":1}}],[\"match\",{\"1\":{\"445\":8,\"453\":10,\"455\":2,\"464\":5,\"465\":5,\"466\":5,\"473\":4,\"474\":3,\"475\":2,\"476\":4,\"484\":3,\"485\":6,\"486\":4,\"487\":5,\"488\":1,\"489\":1,\"490\":1,\"491\":1,\"492\":3,\"493\":1,\"495\":1,\"496\":2,\"497\":2,\"498\":2,\"500\":2}}],[\"math\",{\"1\":{\"291\":5,\"303\":2,\"362\":4}}],[\"mater\",{\"1\":{\"280\":1,\"281\":3}}],[\"map\",{\"1\":{\"250\":1}}],[\"map<string\",{\"1\":{\"250\":1}}],[\"mamoru\",{\"1\":{\"237\":2}}],[\"making\",{\"1\":{\"211\":2,\"212\":2,\"238\":1,\"380\":2,\"381\":2}}],[\"make\",{\"1\":{\"412\":1,\"413\":3,\"453\":1}}],[\"makewelcomepage\",{\"1\":{\"237\":2}}],[\"makeline\",{\"1\":{\"218\":3}}],[\"makeitems\",{\"1\":{\"179\":5}}],[\"makestring\",{\"1\":{\"179\":5}}],[\"maketitle\",{\"1\":{\"179\":4}}],[\"makehtml\",{\"1\":{\"139\":8}}],[\"macro\",{\"1\":{\"428\":1}}],[\"macrocommand\",{\"1\":{\"197\":9}}],[\"machine\",{\"1\":{\"405\":1,\"406\":1}}],[\"macintosh\",{\"1\":{\"172\":2}}],[\"manage\",{\"1\":{\"130\":2,\"280\":1}}],[\"manager\",{\"1\":{\"130\":4,\"317\":12}}],[\"master\",{\"1\":{\"101\":1}}],[\"mailprop\",{\"1\":{\"237\":2}}],[\"mailaddress\",{\"1\":{\"237\":4}}],[\"mailaddr\",{\"1\":{\"237\":2}}],[\"mailto\",{\"1\":{\"237\":2,\"238\":1}}],[\"maildata\",{\"1\":{\"237\":3}}],[\"mail\",{\"1\":{\"39\":1,\"211\":1,\"212\":1,\"380\":1,\"381\":1}}],[\"mailserver\",{\"1\":{\"38\":3}}],[\"mainly\",{\"1\":{\"429\":1}}],[\"main\",{\"0\":{\"168\":1,\"211\":1},\"1\":{\"17\":2,\"33\":1,\"139\":2,\"142\":1,\"152\":1,\"153\":1,\"164\":1,\"170\":1,\"173\":2,\"179\":1,\"180\":1,\"190\":1,\"191\":1,\"197\":1,\"198\":1,\"212\":1,\"218\":1,\"219\":1,\"237\":1,\"238\":1,\"244\":1,\"245\":1,\"250\":1,\"251\":1,\"265\":1,\"266\":1,\"272\":1,\"273\":1,\"281\":1,\"291\":1,\"303\":1,\"304\":1,\"317\":1,\"318\":1,\"324\":1,\"325\":1,\"339\":1,\"340\":1,\"348\":1,\"349\":1,\"352\":1,\"362\":1,\"372\":1,\"373\":1,\"380\":1,\"381\":1,\"402\":1,\"405\":1,\"406\":1,\"419\":2,\"434\":3,\"445\":1,\"501\":3}}],[\"maintenance\",{\"0\":{\"8\":1},\"1\":{\"8\":1}}],[\"mavencentral\",{\"1\":{\"9\":2}}],[\"maven\",{\"1\":{\"9\":26}}],[\"markdown\",{\"1\":{\"5\":1,\"106\":3,\"111\":1}}],[\"duplicate\",{\"1\":{\"453\":1,\"465\":1,\"466\":1,\"493\":1}}],[\"dump\",{\"1\":{\"405\":1}}],[\"drawing\",{\"1\":{\"198\":10}}],[\"drawcommand\",{\"1\":{\"197\":5}}],[\"drawcanvas\",{\"1\":{\"197\":8}}],[\"draw\",{\"1\":{\"197\":3}}],[\"drawable\",{\"1\":{\"197\":5}}],[\"driving\",{\"1\":{\"133\":2}}],[\"drive\",{\"1\":{\"133\":3}}],[\"divide\",{\"1\":{\"432\":1}}],[\"div\",{\"1\":{\"407\":1,\"417\":1,\"425\":1,\"432\":2,\"494\":1}}],[\"directly\",{\"1\":{\"433\":1}}],[\"directory\",{\"0\":{\"208\":1},\"1\":{\"208\":6,\"211\":16,\"380\":14,\"384\":3,\"387\":1,\"388\":2}}],[\"director2\",{\"1\":{\"179\":2}}],[\"director\",{\"1\":{\"178\":1,\"179\":8,\"183\":1,\"185\":2}}],[\"dir\",{\"1\":{\"380\":4}}],[\"digitobserver\",{\"1\":{\"303\":5,\"304\":20,\"307\":1}}],[\"dice\",{\"1\":{\"291\":4}}],[\"diary\",{\"1\":{\"211\":1,\"212\":1,\"380\":1,\"381\":1}}],[\"diana\",{\"1\":{\"190\":3,\"191\":3}}],[\"dispatch\",{\"1\":{\"383\":1}}],[\"displayimpl\",{\"0\":{\"167\":1},\"1\":{\"164\":1,\"165\":3,\"166\":4,\"167\":1,\"169\":3,\"173\":1}}],[\"display\",{\"0\":{\"166\":1},\"1\":{\"164\":6,\"165\":3,\"166\":2,\"168\":5,\"173\":5,\"218\":36,\"221\":2,\"222\":3,\"372\":4}}],[\"displayprofile\",{\"1\":{\"126\":2}}],[\"distributionurl=https\",{\"1\":{\"9\":1}}],[\"d3\",{\"1\":{\"168\":2,\"372\":2}}],[\"d2\",{\"1\":{\"168\":2,\"372\":2}}],[\"d1\",{\"1\":{\"168\":2,\"372\":2}}],[\"do\",{\"1\":{\"402\":2,\"492\":1}}],[\"doyyy\",{\"1\":{\"355\":1}}],[\"dophone\",{\"1\":{\"348\":6}}],[\"doalarm\",{\"1\":{\"348\":6}}],[\"douse\",{\"1\":{\"348\":6,\"356\":6}}],[\"double\",{\"1\":{\"342\":1,\"383\":1}}],[\"done\",{\"1\":{\"111\":1,\"190\":2}}],[\"doclock\",{\"1\":{\"348\":4,\"352\":3,\"353\":1}}],[\"doc\",{\"1\":{\"211\":1,\"212\":1,\"280\":1,\"281\":3,\"380\":1,\"381\":1}}],[\"documentation\",{\"1\":{\"26\":2}}],[\"docker部署certbot与nginx来获取ssl证书添加https及自动更新\",{\"1\":{\"26\":1}}],[\"dockerfile\",{\"1\":{\"15\":1,\"18\":3}}],[\"docker\",{\"0\":{\"13\":1,\"34\":1},\"1\":{\"13\":2,\"14\":2,\"15\":1,\"18\":1,\"19\":1,\"22\":1,\"24\":1,\"31\":1,\"33\":3,\"34\":2,\"38\":2}}],[\"dcqe\",{\"1\":{\"111\":1}}],[\"dnspy\",{\"1\":{\"51\":1}}],[\"dp\",{\"1\":{\"41\":1}}],[\"daddy\",{\"1\":{\"272\":1,\"273\":1}}],[\"daystate\",{\"1\":{\"348\":10,\"353\":5,\"355\":1,\"356\":1}}],[\"days\",{\"1\":{\"272\":1,\"273\":1}}],[\"date\",{\"1\":{\"39\":1}}],[\"data++\",{\"1\":{\"431\":1}}],[\"databasename\",{\"1\":{\"237\":1}}],[\"database\",{\"1\":{\"237\":6}}],[\"data\",{\"1\":{\"34\":2,\"402\":1,\"405\":8,\"431\":4,\"453\":5,\"484\":4}}],[\"daemon\",{\"1\":{\"33\":2}}],[\"dereference\",{\"1\":{\"488\":3}}],[\"demo函数被调用时\",{\"1\":{\"463\":1}}],[\"demo\",{\"1\":{\"463\":1}}],[\"declenum\",{\"1\":{\"450\":1}}],[\"decl\",{\"1\":{\"450\":10,\"451\":2,\"453\":8,\"461\":7,\"462\":2,\"464\":4,\"465\":1}}],[\"declarations\",{\"1\":{\"464\":1,\"466\":1}}],[\"declaration\",{\"0\":{\"453\":1,\"454\":1},\"1\":{\"449\":2,\"450\":2,\"452\":3,\"453\":10,\"454\":1,\"455\":1,\"462\":1,\"464\":1,\"465\":2,\"466\":4}}],[\"dec\",{\"1\":{\"425\":1,\"430\":2,\"433\":1,\"493\":1,\"494\":1}}],[\"decochar\",{\"1\":{\"317\":8}}],[\"decorator\",{\"0\":{\"216\":1},\"1\":{\"154\":1,\"213\":1,\"219\":1,\"221\":3,\"222\":2,\"223\":1,\"224\":2,\"225\":1,\"319\":1,\"333\":1}}],[\"deleteobserver\",{\"1\":{\"303\":1}}],[\"delegation\",{\"1\":{\"152\":4}}],[\"delicious\",{\"1\":{\"291\":2,\"292\":30}}],[\"dest\",{\"1\":{\"408\":2}}],[\"design\",{\"0\":{\"514\":1},\"1\":{\"139\":2,\"153\":1,\"170\":2,\"180\":2,\"191\":2,\"198\":2,\"212\":2,\"219\":2,\"238\":2,\"245\":2,\"251\":2,\"266\":2,\"273\":2,\"280\":1,\"281\":2,\"304\":2,\"318\":2,\"325\":2,\"340\":2,\"349\":2,\"373\":2,\"381\":2}}],[\"desktop\",{\"1\":{\"34\":1}}],[\"devtool\",{\"1\":{\"392\":1}}],[\"device\",{\"1\":{\"387\":2}}],[\"dev\",{\"1\":{\"105\":1}}],[\"define\",{\"1\":{\"419\":1}}],[\"def\",{\"1\":{\"99\":2,\"100\":1,\"101\":5}}],[\"default\",{\"1\":{\"17\":1,\"402\":1,\"484\":1,\"486\":1}}],[\"deploy\",{\"1\":{\"95\":1}}],[\"dependencyresolutionmanagement\",{\"1\":{\"9\":1}}],[\"details\",{\"1\":{\"38\":1,\"481\":1}}],[\"d\",{\"1\":{\"15\":1,\"17\":1,\"18\":4,\"19\":1,\"21\":2,\"22\":2,\"24\":1,\"139\":1,\"153\":1,\"170\":1,\"180\":1,\"191\":1,\"198\":1,\"212\":1,\"219\":1,\"238\":1,\"245\":1,\"251\":1,\"266\":1,\"273\":1,\"281\":1,\"304\":1,\"318\":1,\"325\":1,\"340\":1,\"349\":1,\"373\":1,\"381\":1,\"402\":2,\"405\":3,\"418\":2,\"445\":3,\"453\":2,\"454\":3,\"455\":2,\"465\":2,\"466\":2,\"486\":2,\"488\":1,\"489\":1,\"493\":1,\"495\":1,\"496\":1,\"500\":1}}],[\"fd\",{\"1\":{\"402\":4,\"405\":1}}],[\"fn\",{\"1\":{\"343\":2}}],[\"found\",{\"1\":{\"265\":1,\"429\":1,\"513\":1}}],[\"fontdatas\",{\"1\":{\"250\":2}}],[\"fontdata\",{\"1\":{\"250\":5}}],[\"forward\",{\"1\":{\"484\":1}}],[\"forwarded\",{\"1\":{\"17\":1}}],[\"foreach\",{\"1\":{\"139\":2,\"179\":2,\"197\":1,\"208\":1,\"250\":2,\"265\":1,\"291\":1,\"303\":1,\"380\":1}}],[\"for\",{\"1\":{\"17\":1,\"99\":4,\"101\":3,\"165\":1,\"169\":1,\"190\":1,\"197\":1,\"218\":2,\"237\":1,\"238\":1,\"280\":2,\"291\":1,\"303\":2,\"324\":1,\"348\":1,\"362\":2,\"372\":2,\"380\":1,\"402\":1,\"405\":5,\"412\":1,\"413\":1,\"416\":1,\"429\":2,\"453\":2,\"464\":1,\"466\":2,\"473\":1,\"475\":1,\"486\":1,\"494\":1}}],[\"format=freeze\",{\"1\":{\"48\":1}}],[\"formatdate\",{\"1\":{\"39\":2}}],[\"format\",{\"1\":{\"17\":1}}],[\"flex\",{\"1\":{\"394\":1,\"395\":1,\"397\":1,\"401\":1,\"424\":1}}],[\"floor\",{\"1\":{\"291\":2,\"303\":1,\"362\":2}}],[\"flyweight\",{\"0\":{\"248\":1,\"249\":1},\"1\":{\"249\":3,\"251\":1,\"253\":4,\"255\":1,\"256\":1,\"319\":1,\"357\":1,\"367\":1}}],[\"flask\",{\"0\":{\"13\":1},\"1\":{\"13\":1,\"25\":1,\"26\":3}}],[\"falt\",{\"1\":{\"435\":1}}],[\"false\",{\"1\":{\"190\":4,\"362\":2,\"473\":1,\"490\":1}}],[\"fault\",{\"1\":{\"419\":1}}],[\"fastbutmorememorystrategy\",{\"1\":{\"366\":1}}],[\"factor\",{\"1\":{\"445\":4}}],[\"factory\",{\"0\":{\"242\":1,\"243\":1},\"1\":{\"139\":21,\"142\":3,\"143\":2,\"144\":1,\"174\":1,\"181\":1,\"239\":1,\"242\":2,\"243\":2,\"244\":12,\"245\":1,\"250\":4,\"275\":1,\"367\":1,\"374\":1}}],[\"facade\",{\"0\":{\"235\":1},\"1\":{\"181\":1,\"236\":1,\"238\":1,\"286\":1,\"341\":1}}],[\"failed\",{\"1\":{\"39\":1,\"54\":1}}],[\"fail\",{\"1\":{\"9\":1,\"190\":2}}],[\"func\",{\"1\":{\"464\":1,\"466\":1}}],[\"functions\",{\"1\":{\"486\":1}}],[\"functionvoid\",{\"1\":{\"434\":1}}],[\"functionenum\",{\"1\":{\"434\":1,\"453\":1}}],[\"function\",{\"1\":{\"139\":1,\"343\":1,\"416\":1,\"450\":2,\"453\":4,\"455\":1,\"461\":1,\"462\":2,\"464\":5,\"465\":1,\"466\":2,\"476\":1,\"486\":4}}],[\"function执行时间超过5s\",{\"1\":{\"54\":1}}],[\"function执行时间过长\",{\"1\":{\"54\":1}}],[\"fun\",{\"1\":{\"425\":1,\"453\":1,\"462\":2,\"486\":1,\"494\":1}}],[\"fullborder\",{\"1\":{\"218\":8,\"222\":1}}],[\"fullchain\",{\"1\":{\"22\":2,\"23\":3}}],[\"fields\",{\"1\":{\"429\":1}}],[\"fight\",{\"1\":{\"362\":3}}],[\"first\",{\"1\":{\"54\":1,\"484\":2}}],[\"finally\",{\"1\":{\"99\":1}}],[\"final\",{\"1\":{\"52\":1}}],[\"filetreatmentexception\",{\"1\":{\"209\":1}}],[\"filename\",{\"1\":{\"179\":4,\"237\":3}}],[\"files\",{\"1\":{\"17\":3,\"23\":5,\"111\":1}}],[\"file\",{\"0\":{\"210\":1},\"1\":{\"10\":3,\"22\":3,\"179\":2,\"180\":2,\"210\":1,\"211\":9,\"380\":15,\"384\":3,\"387\":1,\"402\":1}}],[\"filter\",{\"1\":{\"8\":1,\"280\":1,\"303\":1}}],[\"frameadd\",{\"1\":{\"414\":1}}],[\"framepush\",{\"1\":{\"413\":1}}],[\"frame\",{\"1\":{\"405\":1,\"412\":3,\"413\":2,\"414\":1,\"415\":2}}],[\"fruit\",{\"1\":{\"291\":3}}],[\"fruitsname\",{\"1\":{\"291\":3}}],[\"fruits\",{\"1\":{\"291\":12,\"292\":3}}],[\"fred\",{\"1\":{\"190\":3,\"191\":1}}],[\"freeze\",{\"1\":{\"48\":1}}],[\"from\",{\"1\":{\"18\":1,\"39\":8,\"101\":1,\"139\":15,\"152\":6,\"165\":2,\"166\":1,\"168\":3,\"169\":1,\"179\":7,\"190\":14,\"197\":8,\"208\":1,\"210\":1,\"211\":3,\"218\":9,\"237\":3,\"244\":6,\"250\":5,\"265\":19,\"272\":9,\"291\":2,\"303\":12,\"317\":5,\"324\":5,\"339\":1,\"348\":12,\"362\":10,\"372\":4,\"380\":15,\"412\":2,\"414\":2}}],[\"f\",{\"1\":{\"39\":1,\"291\":6,\"430\":2}}],[\"jnz\",{\"0\":{\"411\":1},\"1\":{\"403\":1,\"407\":1,\"411\":1,\"497\":2}}],[\"jz\",{\"0\":{\"411\":1},\"1\":{\"403\":1,\"407\":1,\"411\":1,\"473\":2,\"474\":2,\"496\":1,\"497\":2}}],[\"jmp\",{\"0\":{\"410\":1},\"1\":{\"403\":1,\"407\":1,\"410\":3,\"412\":1,\"473\":4,\"474\":2,\"496\":1}}],[\"just\",{\"1\":{\"466\":1,\"484\":1}}],[\"jump\",{\"1\":{\"410\":1,\"411\":2}}],[\"junk\",{\"1\":{\"211\":1,\"212\":1,\"380\":1,\"381\":1}}],[\"judge\",{\"1\":{\"41\":1}}],[\"java这些成熟的语言都是手动实现的\",{\"1\":{\"397\":1}}],[\"java\",{\"1\":{\"211\":1,\"212\":1,\"255\":1,\"380\":1,\"381\":1}}],[\"jp\",{\"1\":{\"139\":5}}],[\"join\",{\"1\":{\"99\":1,\"101\":1,\"139\":2,\"265\":1,\"291\":1}}],[\"json\",{\"1\":{\"33\":1}}],[\"jcenter\",{\"1\":{\"9\":2}}],[\"jitpack\",{\"1\":{\"9\":2}}],[\"h>enum\",{\"1\":{\"445\":1}}],[\"h>int\",{\"1\":{\"402\":1}}],[\"h>\",{\"1\":{\"402\":3,\"428\":1,\"445\":1}}],[\"hv\",{\"1\":{\"362\":2}}],[\"h\",{\"1\":{\"362\":7,\"372\":1,\"373\":5}}],[\"hour++\",{\"1\":{\"348\":1}}],[\"hour\",{\"1\":{\"348\":16,\"352\":1}}],[\"home\",{\"1\":{\"22\":4}}],[\"href\",{\"1\":{\"237\":2}}],[\"href=\",{\"1\":{\"139\":6,\"237\":1,\"238\":1}}],[\"high\",{\"1\":{\"405\":1,\"416\":1,\"463\":1}}],[\"hiroshi\",{\"1\":{\"237\":1,\"238\":2}}],[\"history\",{\"1\":{\"197\":8,\"362\":8}}],[\"hyuki\",{\"1\":{\"237\":7,\"238\":4}}],[\"hana\",{\"1\":{\"362\":1,\"363\":7}}],[\"hanako\",{\"1\":{\"211\":4,\"212\":2,\"237\":2,\"380\":4,\"381\":2}}],[\"handle\",{\"1\":{\"434\":1}}],[\"handvalue\",{\"1\":{\"362\":22}}],[\"hand\",{\"1\":{\"362\":28}}],[\"happened\",{\"1\":{\"291\":1,\"292\":2}}],[\"halved\",{\"1\":{\"291\":2,\"292\":2}}],[\"have\",{\"1\":{\"280\":2}}],[\"hash\",{\"1\":{\"426\":1,\"429\":10}}],[\"hashmap\",{\"1\":{\"255\":1}}],[\"has\",{\"1\":{\"280\":1,\"487\":1,\"488\":1}}],[\"hasnext\",{\"1\":{\"272\":3,\"273\":1}}],[\"hasmoretokens\",{\"1\":{\"265\":2}}],[\"harmony\",{\"1\":{\"51\":1}}],[\"h1><p>从早上到下午<\",{\"1\":{\"180\":1}}],[\"h1>\",{\"1\":{\"139\":1,\"237\":1,\"238\":1}}],[\"h1>`\",{\"1\":{\"139\":1,\"179\":1}}],[\"hex\",{\"1\":{\"430\":2}}],[\"here\",{\"1\":{\"426\":1,\"427\":1}}],[\"heap\",{\"1\":{\"405\":2}}],[\"heavyjob\",{\"1\":{\"324\":3}}],[\"head><body>\",{\"1\":{\"237\":1,\"238\":1}}],[\"head><body><h1>问候<\",{\"1\":{\"180\":1}}],[\"head><body>`\",{\"1\":{\"179\":1}}],[\"head>\",{\"1\":{\"139\":1}}],[\"head>`\",{\"1\":{\"139\":1}}],[\"header\",{\"1\":{\"17\":2}}],[\"helloworld\",{\"1\":{\"392\":1}}],[\"hello\",{\"1\":{\"101\":5,\"152\":2,\"153\":4,\"168\":3,\"218\":2,\"219\":3,\"317\":3,\"318\":3,\"372\":1,\"419\":1,\"501\":2}}],[\"html<html><head><title>welcome\",{\"1\":{\"238\":1}}],[\"htmlwriter\",{\"1\":{\"237\":5}}],[\"html`\",{\"1\":{\"179\":1}}],[\"htmlbuilder\",{\"1\":{\"179\":9,\"185\":2}}],[\"html>が作成されました\",{\"1\":{\"180\":1}}],[\"html>\",{\"1\":{\"139\":1,\"179\":1,\"237\":1,\"238\":1}}],[\"html>`\",{\"1\":{\"139\":1}}],[\"html2text\",{\"1\":{\"112\":1}}],[\"html\",{\"0\":{\"112\":1},\"1\":{\"17\":3,\"18\":2,\"23\":5,\"140\":1,\"179\":1,\"180\":1,\"211\":1,\"212\":1,\"237\":1,\"238\":1,\"380\":1,\"381\":1}}],[\"http\",{\"0\":{\"331\":1},\"1\":{\"17\":1,\"19\":3,\"139\":11,\"331\":3}}],[\"https\",{\"0\":{\"25\":1},\"1\":{\"9\":14,\"13\":1,\"23\":2,\"32\":1,\"33\":1,\"35\":1,\"38\":3,\"54\":1,\"98\":1,\"102\":1,\"105\":1,\"106\":2,\"112\":2,\"400\":1,\"402\":1,\"403\":1,\"420\":1,\"421\":1,\"435\":1,\"439\":1,\"449\":1,\"456\":1,\"460\":1,\"467\":1,\"471\":1,\"477\":1,\"481\":1,\"501\":1,\"505\":1}}],[\"hub的目标是\",{\"1\":{\"5\":1}}],[\"hub\",{\"1\":{\"5\":1}}],[\"修改一个地方会对多个地方产生影响\",{\"1\":{\"253\":1}}],[\"修改的工作量就会越大\",{\"1\":{\"143\":1}}],[\"修改等操作\",{\"1\":{\"38\":1}}],[\"修改配置\",{\"0\":{\"23\":1}}],[\"修改\",{\"1\":{\"9\":1}}],[\"国内镜像\",{\"1\":{\"9\":1}}],[\"ccompiler\",{\"0\":{\"514\":1}}],[\"cycle\",{\"1\":{\"406\":1}}],[\"cpu\",{\"1\":{\"404\":2,\"406\":1,\"407\":2}}],[\"cpp\",{\"1\":{\"397\":1}}],[\"c4\",{\"1\":{\"395\":4,\"430\":1}}],[\"currently\",{\"1\":{\"431\":1}}],[\"currentdir\",{\"1\":{\"380\":7}}],[\"currenthandvalue\",{\"1\":{\"362\":10}}],[\"current\",{\"1\":{\"266\":5,\"291\":1,\"292\":3,\"402\":1,\"429\":13,\"434\":6,\"453\":6,\"454\":3,\"462\":2,\"464\":11,\"465\":11,\"466\":11,\"486\":1}}],[\"currenttoken\",{\"1\":{\"265\":8}}],[\"ctx\",{\"1\":{\"265\":1}}],[\"cmd\",{\"1\":{\"197\":2}}],[\"creating\",{\"1\":{\"179\":2,\"180\":2,\"280\":1}}],[\"created\",{\"1\":{\"339\":1,\"340\":1,\"343\":1}}],[\"createclone\",{\"1\":{\"317\":4}}],[\"creatememento\",{\"1\":{\"291\":3}}],[\"createproduct\",{\"1\":{\"244\":3}}],[\"createpicture\",{\"1\":{\"143\":1}}],[\"createpage\",{\"1\":{\"139\":3}}],[\"createtray\",{\"1\":{\"139\":5}}],[\"createlink\",{\"1\":{\"139\":8}}],[\"create\",{\"1\":{\"39\":1,\"244\":4,\"280\":1,\"317\":6}}],[\"c\",{\"0\":{\"392\":1,\"400\":1,\"421\":1,\"439\":1,\"449\":1,\"460\":1,\"471\":1,\"481\":1,\"505\":1},\"1\":{\"111\":1,\"284\":4,\"392\":15,\"395\":4,\"400\":16,\"402\":4,\"403\":15,\"408\":1,\"412\":2,\"417\":1,\"418\":1,\"419\":3,\"420\":2,\"421\":12,\"425\":1,\"426\":1,\"428\":1,\"429\":1,\"432\":1,\"435\":1,\"439\":12,\"445\":2,\"449\":13,\"456\":1,\"460\":12,\"466\":2,\"467\":1,\"471\":12,\"472\":1,\"473\":1,\"474\":1,\"477\":1,\"481\":11,\"482\":2,\"484\":1,\"486\":1,\"496\":1,\"498\":1,\"500\":1,\"501\":5,\"505\":13},\"2\":{\"399\":1,\"438\":1,\"448\":1,\"459\":1,\"470\":1,\"480\":1,\"504\":1,\"512\":1}}],[\"cast\",{\"1\":{\"487\":3}}],[\"category\",{\"1\":{\"403\":1}}],[\"catchaw\",{\"1\":{\"280\":1,\"281\":3}}],[\"catch\",{\"1\":{\"139\":1,\"265\":1,\"317\":2,\"324\":1}}],[\"caller\",{\"1\":{\"412\":2}}],[\"callee\",{\"1\":{\"412\":4}}],[\"calling\",{\"1\":{\"405\":1}}],[\"call\",{\"1\":{\"349\":48,\"407\":1,\"412\":10,\"413\":2,\"415\":2,\"476\":1,\"486\":6,\"501\":1}}],[\"callsecuritycenter\",{\"1\":{\"348\":6}}],[\"caretaker\",{\"0\":{\"297\":1},\"1\":{\"294\":1,\"297\":4}}],[\"card3\",{\"1\":{\"244\":2}}],[\"card2\",{\"1\":{\"244\":2}}],[\"card1\",{\"1\":{\"244\":2}}],[\"car\",{\"1\":{\"133\":7}}],[\"caption\",{\"1\":{\"139\":20,\"237\":2}}],[\"cap\",{\"1\":{\"95\":2}}],[\"capacitorhttp\",{\"1\":{\"95\":1}}],[\"capacitorconfig\",{\"1\":{\"95\":1}}],[\"capacitor\",{\"1\":{\"94\":1}}],[\"canvas\",{\"1\":{\"197\":3}}],[\"canv\",{\"1\":{\"197\":2}}],[\"cannot\",{\"1\":{\"190\":1,\"191\":3}}],[\"can\",{\"1\":{\"8\":1,\"280\":1,\"486\":1}}],[\"cho\",{\"1\":{\"362\":2}}],[\"checked\",{\"1\":{\"342\":1}}],[\"cheat\",{\"1\":{\"5\":2}}],[\"ch\",{\"1\":{\"218\":4,\"372\":5}}],[\"china\",{\"1\":{\"168\":1,\"170\":1}}],[\"chatappmediator\",{\"1\":{\"280\":6,\"283\":2}}],[\"character\",{\"1\":{\"402\":1,\"408\":2,\"431\":3,\"433\":1,\"484\":1}}],[\"chardisplay\",{\"1\":{\"372\":5}}],[\"char\",{\"1\":{\"250\":2,\"402\":1,\"405\":1,\"408\":2,\"418\":6,\"419\":1,\"425\":1,\"426\":1,\"429\":3,\"434\":4,\"445\":3,\"453\":5,\"463\":1,\"465\":3,\"466\":2,\"484\":3,\"485\":7,\"486\":1,\"487\":3,\"488\":1,\"493\":2,\"494\":1,\"495\":1,\"498\":1,\"499\":5,\"500\":2}}],[\"charname\",{\"1\":{\"250\":10}}],[\"charlie使用了id卡\",{\"1\":{\"245\":1}}],[\"charlie\",{\"1\":{\"190\":3,\"191\":1,\"244\":1}}],[\"charset\",{\"1\":{\"52\":1}}],[\"chain\",{\"1\":{\"188\":1,\"189\":1,\"190\":1}}],[\"chainofresponsibility\",{\"0\":{\"188\":1},\"1\":{\"191\":1}}],[\"changestate\",{\"1\":{\"348\":4,\"353\":1}}],[\"change\",{\"1\":{\"99\":2,\"100\":5,\"101\":16}}],[\"csdn\",{\"1\":{\"38\":1,\"481\":1}}],[\"cn\",{\"1\":{\"32\":1,\"33\":2,\"98\":1,\"102\":1,\"105\":1}}],[\"cer\",{\"1\":{\"22\":2,\"23\":3}}],[\"certificates\",{\"1\":{\"26\":1}}],[\"certificate\",{\"1\":{\"23\":6}}],[\"cert\",{\"1\":{\"22\":3}}],[\"central\",{\"1\":{\"9\":2}}],[\"colon\",{\"1\":{\"496\":1}}],[\"colleaguecheckbox\",{\"1\":{\"285\":1}}],[\"colleaguetextfield\",{\"1\":{\"285\":1}}],[\"colleaguebutton\",{\"1\":{\"285\":1}}],[\"collaborators\",{\"1\":{\"280\":1}}],[\"could\",{\"1\":{\"402\":2,\"405\":3}}],[\"count\",{\"1\":{\"218\":2,\"303\":2}}],[\"countdisplay\",{\"0\":{\"165\":1},\"1\":{\"164\":2,\"165\":1,\"168\":4,\"173\":3}}],[\"code\",{\"1\":{\"54\":1,\"106\":2,\"139\":1,\"153\":1,\"170\":1,\"180\":1,\"191\":1,\"198\":1,\"212\":1,\"219\":1,\"238\":1,\"245\":1,\"251\":1,\"266\":1,\"273\":1,\"280\":1,\"281\":1,\"304\":1,\"318\":1,\"325\":1,\"340\":1,\"349\":1,\"373\":1,\"381\":1,\"402\":1,\"423\":1,\"466\":1,\"473\":1,\"475\":1,\"484\":2,\"485\":1,\"486\":2,\"490\":1,\"491\":1}}],[\"copy\",{\"1\":{\"18\":2,\"95\":1}}],[\"convenienceint\",{\"1\":{\"453\":1}}],[\"conditional\",{\"1\":{\"496\":1}}],[\"condition\",{\"1\":{\"473\":1}}],[\"cond\",{\"1\":{\"425\":1,\"433\":1,\"494\":1,\"496\":3}}],[\"concretevisitor\",{\"0\":{\"386\":1},\"1\":{\"383\":1,\"384\":3,\"386\":2,\"387\":1}}],[\"concreteelement\",{\"0\":{\"387\":1},\"1\":{\"383\":1,\"386\":1,\"387\":1}}],[\"concretestrategy\",{\"1\":{\"365\":1}}],[\"concretestate\",{\"1\":{\"351\":1,\"353\":9,\"355\":2}}],[\"concreteobserver\",{\"1\":{\"307\":1}}],[\"concretemediator\",{\"1\":{\"285\":2}}],[\"concretecolleague\",{\"1\":{\"285\":3}}],[\"concreteclass\",{\"1\":{\"161\":1}}],[\"concrete\",{\"1\":{\"280\":1}}],[\"concreteiterator\",{\"1\":{\"274\":1}}],[\"concreteimplementor\",{\"1\":{\"172\":1,\"173\":1}}],[\"concretedecorator\",{\"1\":{\"224\":1}}],[\"console\",{\"1\":{\"130\":1,\"133\":4,\"139\":2,\"152\":2,\"169\":2,\"179\":4,\"190\":2,\"197\":1,\"208\":1,\"210\":1,\"211\":2,\"218\":1,\"237\":2,\"244\":1,\"250\":1,\"265\":2,\"272\":1,\"280\":3,\"291\":10,\"303\":2,\"317\":9,\"324\":9,\"339\":2,\"343\":1,\"348\":4,\"362\":6,\"372\":5,\"380\":4}}],[\"construct\",{\"1\":{\"179\":3}}],[\"constructor\",{\"1\":{\"130\":1,\"133\":1,\"139\":6,\"152\":3,\"165\":1,\"166\":1,\"169\":1,\"179\":1,\"190\":5,\"197\":2,\"208\":1,\"210\":1,\"218\":4,\"237\":3,\"244\":1,\"250\":3,\"265\":2,\"272\":3,\"280\":1,\"291\":2,\"303\":1,\"317\":2,\"324\":2,\"339\":1,\"343\":1,\"348\":2,\"362\":4,\"372\":2,\"380\":2}}],[\"const\",{\"1\":{\"45\":9,\"95\":1,\"130\":2,\"133\":2,\"152\":2,\"168\":3,\"179\":6,\"197\":3,\"244\":5,\"265\":1,\"272\":4,\"280\":7,\"291\":4,\"303\":4,\"317\":3,\"339\":2,\"348\":1,\"362\":5,\"372\":3,\"380\":2}}],[\"constexpr\",{\"1\":{\"43\":1,\"44\":1}}],[\"controller\",{\"0\":{\"311\":1},\"1\":{\"311\":1}}],[\"contents\",{\"1\":{\"400\":1,\"403\":1,\"421\":1,\"439\":1,\"449\":1,\"460\":1,\"471\":1,\"481\":1,\"505\":1}}],[\"content\",{\"1\":{\"51\":1,\"139\":4}}],[\"context\",{\"1\":{\"18\":1,\"265\":43,\"348\":43,\"353\":3,\"356\":3}}],[\"containers\",{\"1\":{\"34\":1}}],[\"container\",{\"0\":{\"30\":1},\"1\":{\"31\":4}}],[\"connections\",{\"1\":{\"17\":1}}],[\"config\",{\"1\":{\"95\":1}}],[\"configuration\",{\"1\":{\"39\":1}}],[\"conf\",{\"1\":{\"15\":4,\"17\":5,\"18\":6,\"23\":2}}],[\"comma\",{\"1\":{\"453\":1}}],[\"commandnode\",{\"1\":{\"265\":8}}],[\"commandlistnode\",{\"1\":{\"265\":17}}],[\"command>\",{\"1\":{\"265\":12}}],[\"commands\",{\"1\":{\"197\":5}}],[\"command\",{\"0\":{\"195\":1},\"1\":{\"192\":1,\"196\":2,\"197\":14,\"198\":1,\"201\":2,\"213\":1,\"298\":1,\"319\":1}}],[\"comments\",{\"1\":{\"432\":2}}],[\"compiler\",{\"1\":{\"397\":1}}],[\"complete\",{\"1\":{\"100\":1,\"101\":3}}],[\"composite\",{\"0\":{\"205\":1},\"1\":{\"144\":1,\"181\":1,\"192\":1,\"202\":1,\"206\":2,\"211\":1,\"212\":2,\"221\":2,\"245\":1,\"257\":1,\"275\":1,\"319\":1,\"380\":1,\"381\":1,\"389\":1}}],[\"compose\",{\"1\":{\"14\":1,\"15\":1,\"18\":1,\"19\":1,\"22\":1,\"24\":1}}],[\"component\",{\"1\":{\"8\":1,\"280\":1}}],[\"com\",{\"1\":{\"9\":13,\"35\":1,\"38\":1,\"54\":1,\"106\":2,\"112\":2,\"139\":11,\"237\":5,\"238\":2,\"402\":1,\"420\":1,\"435\":1,\"456\":1,\"467\":1,\"477\":1,\"501\":1}}],[\"cd\",{\"0\":{\"10\":1},\"1\":{\"22\":2,\"31\":1},\"2\":{\"11\":1,\"12\":1}}],[\"cinderella\",{\"1\":{\"272\":1,\"273\":1}}],[\"ci\",{\"0\":{\"10\":1},\"1\":{\"31\":1},\"2\":{\"11\":1,\"12\":1}}],[\"clean\",{\"1\":{\"486\":1}}],[\"clear\",{\"1\":{\"197\":1}}],[\"clos\",{\"1\":{\"407\":1,\"418\":1}}],[\"close\",{\"1\":{\"164\":1,\"165\":1,\"166\":2,\"179\":4,\"237\":2,\"372\":4,\"402\":1,\"405\":1,\"418\":2,\"434\":1}}],[\"clone\",{\"1\":{\"402\":2,\"420\":2,\"435\":2,\"456\":2,\"467\":2,\"477\":2,\"501\":2}}],[\"clockstring\",{\"1\":{\"348\":4}}],[\"cloud\",{\"1\":{\"9\":1}}],[\"classes\",{\"1\":{\"425\":1}}],[\"class\",{\"1\":{\"45\":1,\"126\":3,\"130\":2,\"133\":4,\"139\":9,\"152\":4,\"165\":1,\"166\":1,\"167\":1,\"169\":1,\"179\":4,\"190\":6,\"197\":3,\"208\":1,\"209\":1,\"210\":1,\"218\":5,\"237\":3,\"244\":3,\"250\":3,\"265\":8,\"272\":3,\"280\":2,\"291\":2,\"303\":4,\"317\":3,\"324\":2,\"339\":1,\"343\":1,\"348\":3,\"362\":4,\"372\":3,\"380\":5,\"429\":3,\"434\":1,\"453\":3,\"454\":1,\"462\":1,\"464\":2,\"465\":3,\"466\":3,\"486\":5}}],[\"client\",{\"1\":{\"17\":2,\"280\":1}}],[\"click\",{\"1\":{\"8\":2}}],[\"i++\",{\"1\":{\"165\":1,\"169\":1,\"197\":1,\"218\":2,\"291\":1,\"303\":2,\"324\":1,\"362\":2,\"372\":2,\"380\":1,\"419\":8,\"434\":2,\"454\":1}}],[\"iworker\",{\"1\":{\"130\":4}}],[\"immediate\",{\"1\":{\"408\":1}}],[\"imm\",{\"1\":{\"407\":1,\"408\":3,\"419\":2,\"484\":3,\"485\":1,\"486\":4,\"489\":1,\"490\":1,\"491\":1,\"492\":2,\"493\":1,\"495\":2,\"498\":2,\"499\":3,\"500\":1}}],[\"implemented\",{\"1\":{\"380\":2}}],[\"implementor\",{\"1\":{\"172\":1}}],[\"implementation\",{\"1\":{\"164\":1}}],[\"implements\",{\"1\":{\"130\":1,\"152\":1,\"197\":3,\"244\":1,\"272\":2,\"280\":2,\"303\":2,\"317\":2,\"324\":2,\"348\":3,\"362\":2,\"380\":1}}],[\"impl\",{\"1\":{\"164\":3,\"165\":2,\"166\":7}}],[\"import\",{\"1\":{\"39\":4,\"99\":1,\"100\":1,\"101\":5,\"139\":15,\"152\":6,\"165\":2,\"166\":1,\"168\":3,\"169\":1,\"179\":7,\"190\":14,\"197\":8,\"208\":1,\"210\":1,\"211\":3,\"218\":9,\"237\":3,\"244\":6,\"250\":5,\"265\":19,\"272\":9,\"291\":2,\"303\":12,\"317\":5,\"324\":5,\"339\":1,\"348\":12,\"362\":10,\"372\":4,\"380\":15}}],[\"img\",{\"1\":{\"100\":1}}],[\"if\",{\"0\":{\"473\":1},\"1\":{\"99\":1,\"190\":5,\"218\":3,\"250\":1,\"265\":7,\"280\":2,\"291\":6,\"324\":2,\"339\":1,\"343\":2,\"348\":3,\"362\":8,\"380\":2,\"402\":3,\"405\":3,\"408\":5,\"409\":1,\"410\":1,\"411\":5,\"412\":2,\"413\":1,\"414\":1,\"415\":1,\"416\":1,\"417\":16,\"418\":8,\"425\":1,\"427\":1,\"428\":1,\"429\":3,\"430\":3,\"431\":6,\"432\":2,\"433\":24,\"434\":2,\"445\":7,\"450\":3,\"453\":10,\"454\":4,\"455\":1,\"461\":3,\"462\":1,\"464\":1,\"465\":5,\"466\":3,\"471\":1,\"472\":1,\"473\":8,\"474\":2,\"475\":2,\"476\":2,\"484\":2,\"485\":3,\"486\":9,\"487\":2,\"488\":2,\"489\":2,\"490\":1,\"491\":1,\"492\":3,\"493\":3,\"494\":1,\"495\":2,\"496\":4,\"497\":2,\"498\":3,\"500\":3,\"501\":1}}],[\"i\",{\"1\":{\"99\":2,\"101\":1,\"165\":2,\"169\":2,\"190\":4,\"197\":4,\"218\":5,\"291\":3,\"303\":4,\"324\":2,\"362\":5,\"372\":4,\"380\":3,\"402\":4,\"405\":2,\"412\":2,\"413\":1,\"419\":1,\"434\":4,\"453\":1,\"454\":3}}],[\"iterator\",{\"1\":{\"245\":1,\"272\":14,\"273\":4,\"380\":4,\"388\":1,\"389\":1}}],[\"items\",{\"1\":{\"179\":5}}],[\"item\",{\"1\":{\"139\":21,\"179\":4}}],[\"it\",{\"1\":{\"99\":4,\"100\":5,\"101\":20,\"272\":3,\"280\":1,\"380\":3,\"428\":1,\"431\":1,\"453\":1,\"486\":1}}],[\"idmain\",{\"1\":{\"434\":2}}],[\"idsize\",{\"1\":{\"429\":2,\"464\":1}}],[\"identifierenum\",{\"1\":{\"429\":1}}],[\"identifier\",{\"1\":{\"429\":5,\"453\":3,\"454\":1,\"462\":1,\"466\":1}}],[\"idcardfactory\",{\"1\":{\"244\":5}}],[\"idcard\",{\"1\":{\"244\":7}}],[\"id\",{\"1\":{\"98\":1,\"102\":1,\"339\":1,\"340\":1,\"343\":1,\"425\":1,\"429\":15,\"434\":6,\"450\":8,\"453\":17,\"454\":5,\"461\":5,\"462\":2,\"464\":11,\"465\":14,\"466\":12,\"486\":18,\"494\":1}}],[\"isweakerthan\",{\"1\":{\"362\":1}}],[\"isstrongerthan\",{\"1\":{\"362\":3}}],[\"issue\",{\"1\":{\"21\":2}}],[\"is\",{\"1\":{\"39\":1,\"51\":1,\"133\":2,\"190\":1,\"191\":13,\"265\":3,\"280\":1,\"402\":1,\"411\":2,\"431\":2,\"485\":1,\"486\":3,\"498\":2}}],[\"isn\",{\"0\":{\"8\":1}}],[\"initializer\",{\"1\":{\"454\":1}}],[\"invalid\",{\"1\":{\"453\":1,\"466\":1}}],[\"information\",{\"1\":{\"453\":1}}],[\"increment\",{\"1\":{\"493\":1}}],[\"increased\",{\"1\":{\"291\":2}}],[\"inc\",{\"1\":{\"425\":1,\"433\":1,\"487\":2,\"488\":2,\"489\":1,\"490\":1,\"491\":1,\"492\":2,\"493\":3,\"494\":1,\"499\":3}}],[\"include\",{\"1\":{\"17\":2,\"280\":1,\"402\":4,\"428\":1,\"445\":2}}],[\"independent\",{\"1\":{\"280\":1}}],[\"index++\",{\"1\":{\"265\":1,\"272\":1}}],[\"index\",{\"1\":{\"265\":3,\"272\":6,\"465\":5,\"466\":3,\"486\":1}}],[\"indent\",{\"1\":{\"52\":1}}],[\"inheritance\",{\"1\":{\"152\":4}}],[\"inject\",{\"1\":{\"111\":2}}],[\"instruction\",{\"1\":{\"418\":1}}],[\"instructionsenum\",{\"1\":{\"407\":1}}],[\"instanceof\",{\"1\":{\"380\":2}}],[\"instance\",{\"1\":{\"280\":1,\"339\":5,\"340\":1,\"343\":6}}],[\"install\",{\"1\":{\"22\":1}}],[\"insert\",{\"1\":{\"52\":1}}],[\"into\",{\"1\":{\"431\":1}}],[\"integer\",{\"1\":{\"408\":2}}],[\"intel\",{\"1\":{\"408\":1}}],[\"interperter\",{\"1\":{\"266\":1}}],[\"interpreter\",{\"0\":{\"263\":1},\"1\":{\"264\":1,\"389\":1,\"395\":1,\"400\":1,\"402\":1,\"403\":1,\"420\":1,\"421\":1,\"435\":1,\"439\":1,\"449\":1,\"456\":1,\"460\":1,\"467\":1,\"471\":1,\"477\":1,\"501\":1,\"505\":1}}],[\"interface\",{\"1\":{\"130\":1,\"152\":1,\"197\":2,\"244\":1,\"272\":2,\"280\":2,\"294\":2,\"303\":1,\"317\":1,\"324\":1,\"348\":2,\"362\":1,\"380\":1}}],[\"intrinsic\",{\"0\":{\"254\":1},\"1\":{\"254\":4}}],[\"int\",{\"1\":{\"43\":2,\"44\":11,\"402\":6,\"405\":3,\"406\":3,\"408\":3,\"410\":1,\"411\":2,\"412\":9,\"413\":1,\"415\":2,\"416\":1,\"418\":2,\"419\":3,\"425\":1,\"426\":1,\"429\":13,\"431\":1,\"434\":4,\"445\":20,\"453\":14,\"454\":2,\"455\":1,\"462\":1,\"463\":4,\"465\":7,\"466\":5,\"473\":2,\"474\":2,\"484\":4,\"485\":8,\"486\":1,\"487\":2,\"490\":1,\"491\":1,\"492\":2,\"493\":1,\"494\":1,\"496\":2,\"497\":4,\"498\":3,\"499\":3,\"500\":1,\"501\":5}}],[\"in\",{\"0\":{\"8\":1},\"1\":{\"8\":2,\"99\":4,\"101\":3,\"272\":1,\"273\":1,\"408\":4,\"425\":1,\"486\":2,\"495\":1,\"496\":1}}],[\"ionic打包后的相对路径不正确\",{\"1\":{\"96\":1}}],[\"ionic\",{\"1\":{\"94\":1,\"95\":4}}],[\"io简介\",{\"0\":{\"31\":1}}],[\"io\",{\"1\":{\"5\":1,\"9\":2,\"31\":1,\"38\":1,\"112\":1}}],[\"5501\",{\"1\":{\"481\":1}}],[\"55718\",{\"1\":{\"106\":1}}],[\"50\",{\"1\":{\"303\":1}}],[\"500\",{\"1\":{\"190\":1,\"211\":1,\"212\":1,\"380\":1,\"381\":1}}],[\"5版本开始引入了新的关键字\",{\"1\":{\"101\":1}}],[\"587\",{\"1\":{\"39\":1}}],[\"5\",{\"0\":{\"8\":1,\"449\":1},\"1\":{\"8\":1,\"168\":1,\"198\":2,\"250\":1,\"284\":1,\"291\":1,\"292\":1,\"324\":2,\"372\":1,\"392\":1,\"400\":1,\"403\":2,\"408\":1,\"412\":2,\"418\":1,\"421\":3,\"422\":2,\"439\":2,\"449\":2,\"460\":1,\"471\":1,\"477\":1,\"481\":4,\"482\":7,\"505\":2}}],[\"queue\",{\"1\":{\"201\":1}}],[\"questions\",{\"0\":{\"7\":1}}],[\"quit\",{\"1\":{\"39\":1}}],[\"qq\",{\"1\":{\"38\":1}}],[\"qt\",{\"0\":{\"6\":1,\"7\":1,\"8\":2},\"1\":{\"8\":2}}],[\"tk\",{\"1\":{\"445\":4,\"455\":3}}],[\"tutor\",{\"1\":{\"419\":2,\"501\":5}}],[\"turndown\",{\"1\":{\"112\":1}}],[\"tmp\",{\"1\":{\"211\":1,\"212\":2,\"380\":1,\"381\":2,\"408\":1,\"418\":7,\"453\":2,\"486\":4,\"487\":4,\"493\":2,\"495\":2,\"498\":1,\"499\":1,\"500\":3,\"501\":3}}],[\"tmpdir\",{\"1\":{\"211\":2,\"380\":2}}],[\"ts\",{\"0\":{\"165\":1,\"166\":1,\"167\":1,\"168\":1,\"169\":1,\"208\":1,\"209\":1,\"210\":1,\"211\":1},\"1\":{\"139\":12,\"152\":6,\"153\":2,\"170\":2,\"179\":5,\"180\":2,\"190\":7,\"191\":2,\"197\":6,\"198\":2,\"212\":2,\"218\":6,\"219\":2,\"237\":4,\"238\":2,\"244\":5,\"245\":2,\"250\":5,\"251\":2,\"265\":9,\"266\":2,\"272\":6,\"273\":2,\"281\":2,\"291\":3,\"303\":6,\"304\":2,\"317\":5,\"318\":2,\"324\":4,\"325\":2,\"339\":2,\"340\":2,\"348\":6,\"349\":2,\"362\":6,\"372\":4,\"373\":2,\"380\":7,\"381\":2}}],[\"typora\",{\"1\":{\"111\":8}}],[\"typora激活教程\",{\"0\":{\"111\":1}}],[\"typedef\",{\"1\":{\"45\":1}}],[\"type\",{\"1\":{\"17\":1,\"429\":4,\"434\":2,\"450\":4,\"453\":16,\"454\":1,\"461\":4,\"464\":2,\"465\":11,\"466\":8,\"484\":2,\"485\":7,\"486\":7,\"487\":4,\"488\":5,\"489\":2,\"490\":1,\"491\":1,\"492\":2,\"493\":2,\"495\":3,\"497\":2,\"498\":4,\"499\":5,\"500\":3}}],[\"typescript\",{\"0\":{\"271\":1},\"1\":{\"271\":1,\"272\":1,\"303\":1},\"2\":{\"136\":1,\"146\":1,\"156\":1,\"176\":1,\"187\":1,\"194\":1,\"204\":1,\"215\":1,\"231\":1,\"234\":1,\"241\":1,\"247\":1,\"259\":1,\"262\":1,\"268\":1,\"277\":1,\"288\":1,\"300\":1,\"314\":1,\"321\":1,\"335\":1,\"345\":1,\"359\":1,\"369\":1,\"377\":1,\"391\":1}}],[\"types\",{\"1\":{\"17\":1,\"434\":1,\"453\":1}}],[\"tail\",{\"1\":{\"445\":8}}],[\"tail><term\",{\"1\":{\"444\":1}}],[\"tail><expr\",{\"1\":{\"444\":1}}],[\"tail>\",{\"1\":{\"444\":6}}],[\"tag\",{\"1\":{\"403\":1}}],[\"taro\",{\"1\":{\"362\":1,\"363\":1}}],[\"target=change\",{\"1\":{\"99\":2,\"101\":4}}],[\"takahashi\",{\"1\":{\"237\":1}}],[\"table\",{\"1\":{\"400\":1,\"403\":1,\"421\":1,\"429\":2,\"434\":2,\"439\":1,\"449\":1,\"460\":1,\"471\":1,\"481\":1,\"505\":1}}],[\"tab\",{\"1\":{\"52\":1}}],[\"title><\",{\"1\":{\"139\":2,\"179\":1,\"180\":1,\"237\":1,\"238\":1}}],[\"title\",{\"1\":{\"139\":9,\"179\":7,\"237\":5,\"403\":1}}],[\"times\",{\"1\":{\"165\":2}}],[\"time\",{\"1\":{\"101\":1}}],[\"timeout\",{\"1\":{\"17\":2}}],[\"tips\",{\"0\":{\"95\":1}}],[\"treated\",{\"1\":{\"453\":1}}],[\"trouble\",{\"1\":{\"190\":38,\"191\":16}}],[\"track\",{\"1\":{\"434\":1}}],[\"traysearch\",{\"1\":{\"139\":4}}],[\"trayyahoo\",{\"1\":{\"139\":4}}],[\"traynews\",{\"1\":{\"139\":4}}],[\"tray\",{\"1\":{\"139\":11,\"142\":1}}],[\"trailing\",{\"1\":{\"52\":1}}],[\"trim\",{\"1\":{\"52\":1}}],[\"true\",{\"1\":{\"52\":3,\"95\":2,\"190\":3,\"265\":1,\"339\":1,\"340\":1,\"362\":1,\"473\":1}}],[\"try\",{\"1\":{\"17\":3,\"23\":5,\"39\":1,\"99\":1,\"139\":1,\"265\":1,\"317\":2,\"324\":1}}],[\"txt\",{\"0\":{\"48\":1},\"1\":{\"48\":2}}],[\"that\",{\"1\":{\"280\":1,\"453\":1}}],[\"three\",{\"1\":{\"430\":1}}],[\"thread\",{\"1\":{\"99\":2,\"101\":4}}],[\"threads\",{\"1\":{\"99\":3,\"101\":3}}],[\"threading\",{\"1\":{\"99\":4,\"101\":5}}],[\"throw\",{\"1\":{\"209\":1,\"265\":4,\"380\":2}}],[\"this\",{\"1\":{\"39\":1,\"51\":1,\"130\":2,\"133\":3,\"139\":18,\"152\":8,\"165\":3,\"166\":7,\"169\":6,\"179\":25,\"190\":17,\"197\":11,\"208\":7,\"209\":3,\"210\":3,\"218\":20,\"237\":6,\"244\":7,\"250\":9,\"265\":41,\"272\":16,\"280\":7,\"291\":18,\"303\":9,\"317\":11,\"324\":16,\"339\":3,\"343\":5,\"348\":12,\"352\":1,\"356\":8,\"362\":46,\"372\":11,\"380\":18,\"453\":1,\"464\":1,\"486\":1}}],[\"there\",{\"1\":{\"453\":1,\"486\":1}}],[\"them\",{\"1\":{\"280\":1}}],[\"the\",{\"0\":{\"8\":1},\"1\":{\"8\":6,\"39\":2,\"51\":2,\"272\":1,\"273\":1,\"280\":12,\"281\":3,\"402\":1,\"409\":2,\"410\":1,\"431\":2,\"433\":1,\"434\":1,\"453\":6,\"462\":1,\"465\":1,\"466\":4,\"484\":3,\"486\":3,\"488\":1,\"489\":2,\"493\":1,\"495\":1,\"498\":2}}],[\"tz=asia\",{\"1\":{\"18\":1}}],[\"tcp\",{\"1\":{\"17\":1}}],[\"term\",{\"1\":{\"445\":8}}],[\"tex\",{\"1\":{\"211\":1,\"212\":1,\"380\":1,\"381\":1}}],[\"textbuilder\",{\"1\":{\"179\":9,\"185\":1}}],[\"text\",{\"1\":{\"3\":1,\"39\":2,\"107\":1,\"179\":1,\"180\":1,\"265\":11,\"402\":1,\"405\":11,\"419\":9,\"453\":1,\"462\":2,\"473\":2,\"474\":2,\"489\":3,\"493\":4,\"495\":3,\"496\":2,\"497\":2}}],[\"template\",{\"0\":{\"370\":1,\"371\":1},\"1\":{\"161\":1,\"174\":1,\"181\":1,\"245\":1,\"370\":1,\"373\":1}}],[\"template<typename\",{\"1\":{\"45\":1}}],[\"tensorflow\",{\"0\":{\"53\":1},\"1\":{\"53\":6}}],[\"tencent\",{\"1\":{\"9\":1}}],[\"test\",{\"1\":{\"39\":4,\"101\":2}}],[\"t\",{\"0\":{\"8\":1},\"1\":{\"45\":5,\"99\":4,\"101\":4,\"431\":1,\"445\":3}}],[\"total\",{\"1\":{\"362\":1,\"363\":1}}],[\"tomato\",{\"1\":{\"280\":1,\"281\":3}}],[\"tomura\",{\"1\":{\"211\":5,\"212\":3,\"237\":2,\"380\":5,\"381\":3}}],[\"tokenchar\",{\"1\":{\"402\":1}}],[\"tokens\",{\"1\":{\"265\":4,\"425\":1}}],[\"token\",{\"1\":{\"265\":3,\"397\":2,\"401\":1,\"402\":6,\"422\":3,\"423\":1,\"425\":1,\"426\":2,\"427\":2,\"428\":1,\"429\":16,\"430\":27,\"431\":14,\"432\":2,\"433\":45,\"434\":3,\"445\":20,\"452\":2,\"453\":12,\"454\":7,\"455\":2,\"462\":1,\"464\":1,\"465\":6,\"466\":9,\"473\":2,\"474\":1,\"475\":2,\"476\":3,\"484\":5,\"485\":4,\"486\":4,\"487\":6,\"488\":1,\"489\":1,\"490\":1,\"491\":1,\"492\":4,\"493\":4,\"494\":2,\"495\":1,\"496\":2,\"497\":2,\"498\":2,\"499\":2,\"500\":1}}],[\"tostring\",{\"1\":{\"190\":2,\"209\":1,\"265\":7,\"291\":2,\"348\":4,\"362\":6,\"380\":1}}],[\"todo\",{\"1\":{\"25\":1,\"36\":1,\"51\":1,\"54\":1,\"103\":1,\"397\":1}}],[\"tools\",{\"0\":{\"8\":1},\"1\":{\"8\":1}}],[\"to\",{\"0\":{\"7\":1},\"1\":{\"39\":5,\"237\":1,\"238\":2,\"280\":7,\"281\":3,\"291\":1,\"292\":1,\"402\":1,\"408\":5,\"410\":1,\"434\":2,\"484\":1,\"486\":2,\"493\":1}}],[\"occurs\",{\"1\":{\"486\":1}}],[\"oct\",{\"1\":{\"430\":2}}],[\"octet\",{\"1\":{\"17\":1}}],[\"out\",{\"1\":{\"419\":1}}],[\"output\",{\"1\":{\"139\":2,\"362\":1}}],[\"op\",{\"1\":{\"408\":6,\"409\":1,\"410\":1,\"411\":2,\"412\":2,\"413\":1,\"414\":1,\"415\":1,\"416\":1,\"417\":16,\"418\":9}}],[\"operators\",{\"1\":{\"425\":1}}],[\"operator\",{\"1\":{\"45\":3,\"432\":1,\"485\":1,\"494\":2}}],[\"operator+\",{\"1\":{\"45\":1}}],[\"open\",{\"1\":{\"8\":1,\"33\":2,\"164\":1,\"165\":1,\"166\":2,\"372\":4,\"402\":2,\"407\":1,\"418\":3,\"434\":2}}],[\"old\",{\"1\":{\"402\":2,\"405\":2,\"412\":1,\"415\":1,\"416\":1,\"463\":1}}],[\"o\",{\"1\":{\"303\":4,\"501\":1}}],[\"order\",{\"1\":{\"425\":1}}],[\"or\",{\"1\":{\"407\":1,\"417\":1,\"425\":1,\"433\":4,\"476\":1,\"487\":1,\"494\":1,\"497\":2}}],[\"originator\",{\"0\":{\"297\":1},\"1\":{\"294\":1,\"297\":2}}],[\"orange\",{\"1\":{\"291\":1,\"292\":3}}],[\"org\",{\"1\":{\"5\":1}}],[\"observers\",{\"1\":{\"303\":5}}],[\"observer2\",{\"1\":{\"303\":2}}],[\"observer1\",{\"1\":{\"303\":2}}],[\"observer\",{\"0\":{\"301\":1,\"307\":1,\"308\":1},\"1\":{\"286\":1,\"303\":19,\"304\":1,\"306\":1,\"307\":3}}],[\"object\",{\"1\":{\"280\":2,\"317\":1}}],[\"owners\",{\"1\":{\"244\":3}}],[\"owner\",{\"1\":{\"244\":11}}],[\"oddsupport\",{\"1\":{\"190\":5}}],[\"oi\",{\"0\":{\"40\":1},\"1\":{\"40\":1},\"2\":{\"46\":1,\"108\":1}}],[\"other\",{\"1\":{\"10\":1,\"280\":1}}],[\"only\",{\"1\":{\"431\":1,\"485\":1,\"486\":1}}],[\"online\",{\"1\":{\"13\":1,\"17\":4,\"19\":3,\"21\":2,\"22\":4,\"23\":14,\"39\":4}}],[\"ones\",{\"1\":{\"466\":1}}],[\"one\",{\"1\":{\"429\":2,\"484\":1}}],[\"onto\",{\"1\":{\"409\":1}}],[\"on\",{\"1\":{\"9\":1,\"17\":2,\"408\":2,\"465\":1,\"466\":1,\"498\":2}}],[\"off\",{\"1\":{\"17\":1}}],[\"of\",{\"1\":{\"5\":1,\"51\":1,\"52\":1,\"188\":1,\"189\":1,\"190\":1,\"280\":4,\"400\":1,\"402\":1,\"403\":1,\"409\":1,\"421\":1,\"429\":2,\"434\":2,\"439\":1,\"449\":1,\"453\":4,\"460\":1,\"462\":1,\"465\":5,\"466\":4,\"471\":1,\"481\":1,\"484\":1,\"486\":3,\"489\":3,\"493\":1,\"498\":1,\"505\":1}}],[\"ebnf\",{\"0\":{\"450\":1,\"461\":1},\"1\":{\"449\":2,\"450\":1,\"457\":3,\"460\":1,\"461\":1}}],[\"ebppop\",{\"1\":{\"415\":1}}],[\"ebpmov\",{\"1\":{\"413\":1}}],[\"ebp\",{\"1\":{\"412\":6,\"413\":1,\"415\":1}}],[\"escape\",{\"1\":{\"431\":2}}],[\"esp\",{\"1\":{\"412\":6,\"413\":2,\"414\":2,\"415\":1}}],[\"eax\",{\"1\":{\"412\":1}}],[\"each\",{\"1\":{\"280\":1}}],[\"eq\",{\"1\":{\"407\":1,\"417\":1,\"425\":2,\"433\":1,\"490\":1,\"494\":1}}],[\"eof\",{\"1\":{\"402\":1}}],[\"eval\",{\"1\":{\"402\":3,\"408\":2}}],[\"even\",{\"1\":{\"362\":4,\"363\":3}}],[\"event\",{\"1\":{\"100\":1,\"101\":3,\"280\":4}}],[\"events\",{\"1\":{\"17\":1,\"280\":1}}],[\"ey\",{\"1\":{\"280\":1,\"281\":3}}],[\"element\",{\"1\":{\"380\":5,\"383\":4,\"388\":1}}],[\"else\",{\"1\":{\"190\":3,\"218\":3,\"265\":4,\"291\":4,\"348\":1,\"362\":7,\"380\":1,\"408\":4,\"409\":1,\"410\":1,\"411\":1,\"412\":2,\"413\":1,\"414\":1,\"415\":1,\"416\":1,\"417\":16,\"418\":9,\"425\":1,\"428\":1,\"429\":1,\"430\":3,\"431\":2,\"432\":2,\"433\":23,\"434\":1,\"445\":5,\"450\":1,\"453\":2,\"455\":1,\"461\":1,\"462\":1,\"465\":1,\"472\":1,\"473\":7,\"474\":1,\"475\":1,\"476\":3,\"484\":1,\"485\":2,\"486\":7,\"487\":2,\"488\":2,\"489\":2,\"490\":1,\"491\":1,\"492\":3,\"493\":3,\"494\":1,\"495\":1,\"496\":2,\"497\":2,\"498\":2,\"500\":2}}],[\"elmo\",{\"1\":{\"190\":3,\"191\":4}}],[\"enter\",{\"1\":{\"413\":1}}],[\"ent\",{\"0\":{\"413\":1},\"1\":{\"403\":1,\"407\":1,\"412\":1,\"413\":2,\"466\":1}}],[\"entries\",{\"1\":{\"211\":2,\"212\":2,\"380\":2,\"381\":2}}],[\"entry\",{\"0\":{\"209\":1},\"1\":{\"206\":1,\"208\":12,\"209\":4,\"210\":3,\"211\":2,\"380\":34}}],[\"enum\",{\"0\":{\"454\":1},\"1\":{\"362\":1,\"425\":2,\"434\":1,\"449\":1,\"450\":2,\"451\":1,\"453\":9,\"454\":4,\"486\":2,\"494\":2}}],[\"en\",{\"1\":{\"280\":5}}],[\"engine\",{\"1\":{\"133\":15}}],[\"enhanced\",{\"1\":{\"106\":1}}],[\"enabled\",{\"1\":{\"95\":1}}],[\"enduml\",{\"1\":{\"244\":1}}],[\"end\",{\"1\":{\"52\":1,\"265\":15,\"266\":8,\"472\":1,\"484\":1}}],[\"environment\",{\"1\":{\"18\":1}}],[\"env\",{\"1\":{\"10\":2}}],[\"editorconfig文件\",{\"1\":{\"52\":1}}],[\"editorconfig\",{\"1\":{\"52\":1}}],[\"edu\",{\"1\":{\"32\":1,\"33\":2}}],[\"e\",{\"1\":{\"39\":2,\"265\":2,\"317\":4,\"324\":2}}],[\"emit\",{\"1\":{\"466\":1,\"473\":1,\"475\":1,\"484\":2,\"485\":1,\"486\":2,\"490\":1,\"491\":1}}],[\"empty\",{\"1\":{\"450\":5,\"461\":5,\"476\":1}}],[\"email\",{\"1\":{\"39\":16}}],[\"emoji\",{\"1\":{\"5\":2}}],[\"etc\",{\"1\":{\"17\":2,\"18\":4,\"23\":6,\"33\":1}}],[\"error\",{\"1\":{\"15\":1,\"17\":10,\"23\":10,\"139\":2,\"209\":1,\"265\":4,\"317\":1,\"380\":2}}],[\"exists\",{\"1\":{\"453\":1,\"466\":1}}],[\"exist\",{\"1\":{\"453\":1}}],[\"existing\",{\"1\":{\"429\":1}}],[\"exit\",{\"1\":{\"407\":1,\"418\":3,\"419\":2,\"434\":2,\"445\":1,\"453\":2,\"454\":2,\"455\":1,\"465\":2,\"466\":2,\"486\":2,\"488\":1,\"489\":1,\"493\":1,\"495\":1,\"496\":1,\"500\":1,\"501\":2}}],[\"example\",{\"1\":{\"280\":1}}],[\"expession\",{\"1\":{\"495\":1}}],[\"expected\",{\"1\":{\"265\":1,\"445\":1,\"455\":1,\"500\":1}}],[\"expr\",{\"1\":{\"445\":8,\"453\":1,\"484\":2,\"485\":6,\"486\":4,\"487\":3,\"488\":5,\"489\":2,\"490\":1,\"491\":1,\"492\":2,\"493\":2,\"495\":4,\"496\":1,\"497\":2,\"498\":3,\"499\":5,\"500\":2}}],[\"expressionvoid\",{\"1\":{\"453\":1}}],[\"expression\",{\"1\":{\"402\":3,\"450\":5,\"454\":1,\"461\":4,\"467\":1,\"472\":3,\"473\":1,\"474\":1,\"475\":2,\"476\":1,\"477\":1,\"486\":1,\"487\":2,\"488\":1,\"489\":1,\"490\":1,\"491\":1,\"492\":2,\"493\":1,\"494\":1,\"495\":1,\"496\":2,\"497\":2,\"498\":2,\"500\":1,\"502\":1}}],[\"export\",{\"1\":{\"139\":9,\"152\":5,\"165\":1,\"166\":1,\"167\":1,\"169\":1,\"179\":4,\"190\":6,\"197\":5,\"208\":1,\"209\":1,\"210\":1,\"218\":5,\"237\":3,\"244\":4,\"250\":3,\"265\":8,\"272\":5,\"291\":2,\"303\":5,\"317\":4,\"324\":3,\"339\":1,\"343\":1,\"348\":5,\"362\":6,\"372\":3,\"380\":6}}],[\"extrinsic\",{\"0\":{\"254\":1},\"1\":{\"254\":4}}],[\"extending\",{\"1\":{\"280\":1}}],[\"extends\",{\"1\":{\"133\":1,\"139\":6,\"152\":2,\"165\":1,\"169\":1,\"179\":2,\"190\":4,\"208\":1,\"210\":1,\"218\":4,\"244\":1,\"265\":5,\"303\":1,\"372\":2,\"380\":3}}],[\"extension\",{\"1\":{\"54\":2}}],[\"excite\",{\"1\":{\"139\":5}}],[\"exception\",{\"1\":{\"39\":1}}],[\"except\",{\"1\":{\"39\":1}}],[\"execute\",{\"1\":{\"197\":5,\"303\":3}}],[\"exe\",{\"1\":{\"111\":5}}],[\"ex\",{\"1\":{\"5\":1}}],[\"p++\",{\"1\":{\"493\":1,\"499\":1}}],[\"p+z\",{\"1\":{\"43\":1}}],[\"ptr\",{\"1\":{\"434\":1,\"453\":5,\"465\":1,\"466\":1,\"484\":1,\"485\":1,\"487\":1,\"488\":2,\"489\":1,\"493\":1,\"498\":1,\"499\":3,\"500\":3}}],[\"pc+1\",{\"1\":{\"412\":1}}],[\"pc++\",{\"1\":{\"408\":1,\"413\":1,\"414\":1,\"416\":1}}],[\"pc\",{\"1\":{\"406\":2,\"410\":4,\"411\":6,\"412\":4,\"415\":2,\"418\":1,\"419\":1}}],[\"p3\",{\"1\":{\"317\":2}}],[\"p2\",{\"1\":{\"317\":2}}],[\"p1\",{\"1\":{\"317\":2}}],[\"pbd\",{\"1\":{\"152\":2}}],[\"pbi\",{\"1\":{\"152\":2}}],[\"ps\",{\"1\":{\"139\":1,\"170\":1,\"180\":1,\"191\":1,\"198\":1,\"212\":1,\"219\":1,\"238\":1,\"245\":1,\"251\":1,\"266\":1,\"273\":1,\"281\":1,\"304\":1,\"318\":1,\"325\":1,\"340\":1,\"349\":1,\"373\":1,\"381\":1,\"396\":1}}],[\"peg\",{\"1\":{\"508\":1}}],[\"people\",{\"1\":{\"139\":5,\"280\":1}}],[\"peano\",{\"0\":{\"82\":1,\"85\":1,\"86\":1,\"87\":1,\"88\":1,\"89\":1,\"90\":1},\"1\":{\"55\":2,\"56\":1,\"59\":2,\"60\":2,\"62\":3,\"63\":1,\"64\":2,\"68\":2,\"71\":1,\"75\":1,\"76\":1,\"78\":3,\"79\":1,\"80\":1,\"81\":4,\"82\":5}}],[\"ppt\",{\"1\":{\"106\":1}}],[\"py\",{\"1\":{\"101\":2}}],[\"pytorch\",{\"1\":{\"53\":5}}],[\"python3\",{\"0\":{\"98\":1},\"1\":{\"101\":2}}],[\"python\",{\"0\":{\"48\":1},\"1\":{\"14\":1,\"39\":1,\"48\":1,\"101\":1},\"2\":{\"49\":1}}],[\"position\",{\"1\":{\"466\":1,\"484\":1}}],[\"pos\",{\"1\":{\"426\":1,\"429\":4,\"431\":2,\"466\":3}}],[\"postfix\",{\"1\":{\"494\":1}}],[\"post\",{\"1\":{\"51\":1,\"106\":1}}],[\"pointer<expr1>\",{\"1\":{\"498\":1}}],[\"pointer\",{\"1\":{\"402\":1,\"453\":1,\"465\":2,\"485\":1,\"495\":1,\"498\":1,\"500\":2}}],[\"poolsize\",{\"1\":{\"402\":5,\"405\":9,\"406\":2,\"501\":1}}],[\"pool\",{\"1\":{\"250\":3}}],[\"pop\",{\"1\":{\"197\":1,\"408\":1,\"412\":1,\"415\":1}}],[\"powershell\",{\"1\":{\"111\":1}}],[\"port\",{\"1\":{\"39\":2}}],[\"ports\",{\"1\":{\"18\":1}}],[\"picture\",{\"1\":{\"143\":1}}],[\"pip\",{\"1\":{\"48\":2}}],[\"pid\",{\"1\":{\"17\":2}}],[\"p><ul><li>晚上好\",{\"1\":{\"180\":1}}],[\"p><ul><li>早上好\",{\"1\":{\"180\":1}}],[\"p>`\",{\"1\":{\"179\":1}}],[\"p>\",{\"1\":{\"45\":1,\"237\":1,\"238\":2}}],[\"p=998244353\",{\"1\":{\"43\":1,\"44\":1}}],[\"p\",{\"1\":{\"35\":1,\"38\":1,\"43\":2,\"44\":2,\"45\":2,\"244\":3,\"317\":8,\"324\":5,\"450\":1,\"484\":4,\"493\":1,\"499\":1,\"509\":1}}],[\"push<expr2>\",{\"1\":{\"498\":1}}],[\"push\",{\"0\":{\"409\":1},\"1\":{\"139\":16,\"197\":3,\"208\":1,\"244\":1,\"250\":1,\"265\":1,\"280\":1,\"291\":2,\"303\":1,\"380\":1,\"403\":1,\"407\":1,\"408\":1,\"409\":3,\"412\":7,\"419\":2,\"486\":1,\"490\":1,\"491\":1,\"492\":1,\"493\":4,\"495\":1,\"498\":4,\"499\":3,\"500\":2,\"501\":1}}],[\"publishing\",{\"1\":{\"281\":3}}],[\"publish\",{\"1\":{\"280\":3}}],[\"publishmessage\",{\"1\":{\"280\":4}}],[\"publisher\",{\"1\":{\"54\":1}}],[\"public\",{\"1\":{\"9\":2,\"45\":1,\"139\":1,\"179\":15,\"250\":3,\"280\":2,\"291\":3,\"303\":5,\"339\":1,\"343\":1,\"348\":19}}],[\"pull\",{\"1\":{\"33\":1}}],[\"prtf\",{\"1\":{\"407\":1,\"418\":1}}],[\"pre\",{\"1\":{\"493\":1}}],[\"precedence\",{\"1\":{\"425\":1,\"487\":1,\"488\":1}}],[\"prevhand\",{\"1\":{\"362\":3}}],[\"prevhandvalue\",{\"1\":{\"362\":5}}],[\"previous\",{\"1\":{\"291\":1,\"292\":1}}],[\"preview\",{\"1\":{\"106\":1}}],[\"prefix\",{\"1\":{\"208\":3,\"209\":1,\"210\":2,\"291\":2}}],[\"primitivecommandnode\",{\"1\":{\"265\":5}}],[\"principle\",{\"1\":{\"228\":1}}],[\"printf\",{\"1\":{\"402\":4,\"405\":3,\"418\":7,\"434\":1,\"445\":2,\"453\":2,\"454\":2,\"455\":1,\"465\":2,\"466\":2,\"486\":3,\"488\":1,\"489\":1,\"493\":1,\"495\":1,\"496\":1,\"500\":1}}],[\"printable\",{\"1\":{\"324\":12}}],[\"printer\",{\"1\":{\"324\":9}}],[\"printerproxy\",{\"1\":{\"324\":6}}],[\"printlist\",{\"1\":{\"209\":1,\"211\":2}}],[\"printlistwithprefix\",{\"1\":{\"208\":2,\"209\":2,\"210\":1}}],[\"printline\",{\"1\":{\"169\":3,\"372\":3}}],[\"printstrong\",{\"1\":{\"152\":6}}],[\"printweak\",{\"1\":{\"152\":6}}],[\"printbanner2\",{\"1\":{\"152\":3}}],[\"printbanner\",{\"1\":{\"151\":1,\"152\":11}}],[\"print\",{\"1\":{\"39\":2,\"99\":1,\"100\":1,\"101\":10,\"151\":1,\"152\":10,\"164\":1,\"165\":1,\"166\":2,\"250\":4,\"324\":5,\"372\":4}}],[\"private\",{\"1\":{\"45\":1,\"130\":1,\"133\":1,\"152\":2,\"166\":1,\"169\":3,\"179\":4,\"190\":5,\"197\":5,\"208\":2,\"210\":2,\"218\":3,\"237\":3,\"244\":2,\"250\":3,\"265\":6,\"272\":5,\"280\":2,\"291\":4,\"303\":2,\"317\":3,\"324\":5,\"339\":3,\"343\":4,\"348\":5,\"362\":16,\"372\":4,\"380\":5}}],[\"privkey\",{\"1\":{\"22\":1,\"23\":3}}],[\"probstrategy\",{\"1\":{\"362\":6}}],[\"product\",{\"1\":{\"244\":13,\"317\":13}}],[\"proto\",{\"1\":{\"317\":2}}],[\"prototype\",{\"0\":{\"315\":1,\"316\":1},\"1\":{\"202\":1,\"298\":1,\"316\":2,\"318\":1,\"341\":1}}],[\"protected\",{\"1\":{\"139\":3,\"190\":5,\"208\":1,\"209\":1,\"210\":1,\"218\":1,\"244\":2,\"372\":3}}],[\"programs\",{\"1\":{\"265\":2}}],[\"programnode\",{\"1\":{\"265\":5}}],[\"program\",{\"0\":{\"452\":1},\"1\":{\"111\":1,\"265\":10,\"266\":10,\"402\":3,\"405\":1,\"406\":1,\"419\":1,\"434\":1,\"449\":1,\"450\":1,\"452\":2}}],[\"proxy\",{\"0\":{\"322\":1,\"332\":1},\"1\":{\"17\":1,\"23\":2,\"26\":1,\"257\":1,\"323\":1,\"325\":1,\"327\":1,\"328\":1,\"332\":3}}],[\"processes\",{\"1\":{\"17\":1}}],[\"properties\",{\"1\":{\"9\":1}}],[\"project\",{\"1\":{\"9\":1,\"15\":1,\"18\":2}}],[\"paa\",{\"1\":{\"362\":2}}],[\"payload\",{\"1\":{\"280\":5}}],[\"parenthesis\",{\"1\":{\"487\":2}}],[\"parsed\",{\"1\":{\"429\":1}}],[\"parser\",{\"1\":{\"397\":1,\"423\":1}}],[\"parse\",{\"1\":{\"265\":12,\"426\":1,\"427\":1,\"429\":1,\"430\":1,\"431\":1,\"433\":8,\"453\":5,\"454\":1,\"473\":3,\"494\":1}}],[\"params+1\",{\"1\":{\"465\":1}}],[\"params++\",{\"1\":{\"465\":1}}],[\"params\",{\"1\":{\"465\":2}}],[\"param\",{\"1\":{\"463\":5}}],[\"parameter\",{\"1\":{\"450\":2,\"453\":1,\"461\":2,\"462\":1,\"464\":1,\"465\":6,\"466\":1}}],[\"parameters\",{\"1\":{\"200\":1}}],[\"paragraph\",{\"1\":{\"237\":3}}],[\"part\",{\"1\":{\"5\":1,\"453\":2,\"464\":1}}],[\"paint\",{\"1\":{\"197\":2}}],[\"pattern\",{\"1\":{\"148\":1,\"153\":1,\"236\":1,\"264\":1,\"280\":1,\"361\":1}}],[\"patern\",{\"1\":{\"139\":1,\"170\":1,\"180\":1,\"191\":1,\"198\":1,\"212\":1,\"219\":1,\"238\":1,\"245\":1,\"251\":1,\"266\":1,\"273\":1,\"281\":1,\"304\":1,\"318\":1,\"325\":1,\"340\":1,\"349\":1,\"373\":1,\"381\":1}}],[\"patern>\",{\"1\":{\"139\":1,\"170\":1,\"180\":1,\"191\":1,\"198\":1,\"212\":1,\"219\":1,\"238\":1,\"245\":1,\"251\":1,\"266\":1,\"273\":1,\"281\":1,\"304\":1,\"318\":1,\"325\":1,\"340\":1,\"349\":1,\"373\":1,\"381\":1}}],[\"pagemaker\",{\"1\":{\"237\":5}}],[\"page\",{\"1\":{\"139\":12,\"142\":1,\"237\":1,\"238\":2}}],[\"password\",{\"1\":{\"39\":2}}],[\"pass\",{\"1\":{\"17\":1,\"23\":2,\"486\":1}}],[\"player2\",{\"1\":{\"362\":7}}],[\"player1\",{\"1\":{\"362\":7}}],[\"player\",{\"1\":{\"362\":6}}],[\"plays\",{\"1\":{\"280\":1}}],[\"plain\",{\"1\":{\"39\":1}}],[\"plantuml\",{\"1\":{\"5\":1}}],[\"plugins\",{\"1\":{\"95\":1}}],[\"pluginmanagement\",{\"1\":{\"9\":1}}],[\"plugin\",{\"0\":{\"51\":1,\"54\":1},\"1\":{\"9\":3,\"51\":1}}],[\"glo\",{\"1\":{\"425\":1,\"453\":1,\"454\":1,\"486\":1,\"494\":1}}],[\"global\",{\"0\":{\"453\":1},\"1\":{\"99\":2,\"100\":1,\"101\":4,\"449\":1,\"450\":1,\"452\":3,\"453\":6,\"466\":1,\"486\":1}}],[\"gt\",{\"1\":{\"407\":1,\"417\":1,\"425\":1,\"433\":1,\"494\":1}}],[\"guu\",{\"1\":{\"362\":2}}],[\"gui\",{\"1\":{\"302\":1}}],[\"guide\",{\"1\":{\"26\":1,\"105\":1}}],[\"graph\",{\"1\":{\"303\":4}}],[\"graphobserver\",{\"1\":{\"303\":5,\"304\":20,\"307\":1}}],[\"grape\",{\"1\":{\"291\":1,\"292\":12}}],[\"gradlepluginportal\",{\"1\":{\"9\":1}}],[\"gradle\",{\"1\":{\"9\":6}}],[\"group\",{\"1\":{\"280\":1,\"281\":3}}],[\"group`\",{\"1\":{\"280\":1}}],[\"groups\",{\"1\":{\"280\":1}}],[\"got\",{\"1\":{\"445\":1}}],[\"go\",{\"1\":{\"265\":10,\"266\":14}}],[\"google\",{\"1\":{\"9\":4,\"139\":3}}],[\"gcc\",{\"1\":{\"419\":2,\"501\":1}}],[\"gc\",{\"1\":{\"255\":1}}],[\"g\",{\"1\":{\"250\":1}}],[\"gmw\",{\"1\":{\"139\":6}}],[\"git\",{\"1\":{\"402\":1,\"420\":1,\"435\":1,\"456\":1,\"467\":1,\"477\":1,\"501\":1}}],[\"github\",{\"0\":{\"30\":1,\"35\":1,\"36\":1},\"1\":{\"5\":1,\"31\":8,\"38\":1,\"112\":2,\"395\":1,\"402\":2,\"420\":2,\"435\":2,\"456\":2,\"467\":2,\"477\":2,\"501\":2}}],[\"gil\",{\"1\":{\"100\":1}}],[\"gather\",{\"1\":{\"100\":1,\"101\":3}}],[\"games\",{\"1\":{\"362\":1,\"363\":8}}],[\"gamecount++\",{\"1\":{\"362\":3}}],[\"gamecount\",{\"1\":{\"362\":2}}],[\"gamer\",{\"1\":{\"291\":17}}],[\"game\",{\"0\":{\"51\":1},\"1\":{\"51\":1,\"211\":1,\"212\":1,\"380\":1,\"381\":1}}],[\"ge\",{\"1\":{\"407\":1,\"417\":1,\"425\":1,\"433\":1,\"494\":1}}],[\"generatedid++\",{\"1\":{\"339\":1,\"343\":1}}],[\"generatedid\",{\"1\":{\"339\":2,\"343\":2}}],[\"generator\",{\"1\":{\"303\":8,\"397\":1}}],[\"genesis\",{\"1\":{\"5\":2}}],[\"gen\",{\"1\":{\"111\":2}}],[\"getline\",{\"1\":{\"445\":1}}],[\"getlength\",{\"1\":{\"272\":2}}],[\"getsum\",{\"1\":{\"362\":2}}],[\"getsize\",{\"1\":{\"208\":2,\"209\":2,\"210\":1,\"380\":5}}],[\"gethand\",{\"1\":{\"362\":3}}],[\"gethtml\",{\"1\":{\"237\":2}}],[\"getprintername\",{\"1\":{\"324\":5}}],[\"getproperties\",{\"1\":{\"237\":2}}],[\"getproduct\",{\"1\":{\"139\":2}}],[\"getfruits\",{\"1\":{\"291\":1}}],[\"getfruit\",{\"1\":{\"291\":2}}],[\"getmoney\",{\"1\":{\"291\":7}}],[\"getbookat\",{\"1\":{\"272\":2}}],[\"getbigchar\",{\"1\":{\"250\":2}}],[\"getcurrentnumber\",{\"1\":{\"265\":2}}],[\"getcurrenttoken\",{\"1\":{\"265\":5}}],[\"getcolumns\",{\"1\":{\"218\":8,\"221\":1,\"222\":2}}],[\"getinstance\",{\"1\":{\"250\":2,\"339\":3,\"342\":1,\"343\":2,\"348\":5}}],[\"getowners\",{\"1\":{\"244\":1}}],[\"getowner\",{\"1\":{\"244\":2}}],[\"getrowtext\",{\"1\":{\"218\":7,\"221\":1}}],[\"getrows\",{\"1\":{\"218\":8,\"221\":1,\"222\":2}}],[\"getresult\",{\"1\":{\"179\":4}}],[\"getname\",{\"1\":{\"208\":1,\"209\":2,\"210\":1,\"272\":2,\"380\":5}}],[\"getnumber\",{\"1\":{\"190\":4,\"303\":5}}],[\"get\",{\"1\":{\"54\":1,\"100\":1,\"101\":3,\"250\":1,\"402\":1,\"452\":1,\"489\":2}}],[\"gpu\",{\"1\":{\"53\":3}}],[\"ghcr\",{\"0\":{\"31\":1},\"1\":{\"31\":1,\"32\":1,\"33\":2}}],[\"免费并且不受限制地\",{\"1\":{\"5\":1}}],[\"skip\",{\"1\":{\"428\":1,\"432\":1,\"445\":1,\"453\":1}}],[\"skiptoken\",{\"1\":{\"265\":5}}],[\"sc\",{\"1\":{\"407\":1,\"408\":4,\"493\":1,\"495\":1,\"499\":2}}],[\"sci\",{\"1\":{\"5\":2}}],[\"sbox\",{\"1\":{\"317\":2}}],[\"same\",{\"1\":{\"488\":1}}],[\"save\",{\"1\":{\"408\":2,\"412\":1,\"413\":1,\"466\":1,\"495\":1}}],[\"savedir\",{\"1\":{\"380\":2}}],[\"saving\",{\"1\":{\"291\":1}}],[\"safeframe\",{\"1\":{\"348\":11,\"352\":2,\"353\":2,\"354\":1,\"356\":5}}],[\"sato\",{\"1\":{\"237\":1}}],[\"s\",{\"1\":{\"237\":1,\"238\":2,\"317\":7,\"397\":1,\"402\":1,\"450\":1,\"495\":1,\"509\":1}}],[\"snapshot\",{\"1\":{\"201\":1}}],[\"single\",{\"1\":{\"429\":1,\"431\":1}}],[\"singleton2\",{\"1\":{\"339\":2}}],[\"singleton1\",{\"1\":{\"339\":2}}],[\"singleton\",{\"0\":{\"336\":1,\"337\":1},\"1\":{\"144\":1,\"239\":1,\"245\":1,\"250\":2,\"257\":1,\"337\":2,\"339\":11,\"340\":2,\"342\":1,\"343\":6,\"348\":4,\"357\":1}}],[\"si\",{\"1\":{\"407\":1,\"408\":4,\"493\":1,\"495\":2,\"499\":2}}],[\"simulate\",{\"1\":{\"343\":1}}],[\"sideborder\",{\"1\":{\"218\":7,\"222\":2}}],[\"sizeof\",{\"0\":{\"485\":1},\"1\":{\"425\":1,\"434\":1,\"453\":1,\"481\":1,\"484\":2,\"485\":9,\"493\":2,\"494\":1,\"498\":1,\"499\":6,\"500\":1}}],[\"size\",{\"1\":{\"17\":1,\"210\":2,\"380\":5,\"402\":2,\"445\":1,\"466\":1}}],[\"src++\",{\"1\":{\"402\":1,\"428\":1,\"429\":1,\"430\":2,\"431\":3,\"433\":1,\"445\":1}}],[\"src\",{\"1\":{\"139\":1,\"153\":1,\"170\":1,\"180\":1,\"191\":1,\"198\":1,\"212\":1,\"219\":1,\"238\":1,\"245\":1,\"251\":1,\"266\":1,\"273\":1,\"281\":1,\"304\":1,\"318\":1,\"325\":1,\"340\":1,\"349\":1,\"373\":1,\"381\":1,\"402\":6,\"426\":1,\"428\":2,\"429\":10,\"430\":6,\"431\":2,\"432\":3,\"433\":19,\"434\":1,\"445\":9}}],[\"ssize\",{\"1\":{\"445\":1}}],[\"sspai\",{\"1\":{\"106\":1}}],[\"ssl\",{\"1\":{\"23\":9,\"26\":1}}],[\"slowbutlessmemorystrategy\",{\"1\":{\"366\":1}}],[\"slash\",{\"1\":{\"317\":2}}],[\"sli\",{\"1\":{\"105\":1}}],[\"slidev\",{\"0\":{\"104\":1}}],[\"sleep\",{\"1\":{\"101\":3}}],[\"symbols\",{\"1\":{\"429\":3,\"464\":1}}],[\"symbol\",{\"1\":{\"429\":2,\"434\":2}}],[\"system\",{\"1\":{\"486\":1}}],[\"systemctl\",{\"1\":{\"33\":2}}],[\"sys\",{\"1\":{\"425\":1,\"434\":1,\"486\":1,\"494\":1}}],[\"synchronized\",{\"1\":{\"343\":3}}],[\"sync\",{\"1\":{\"95\":2}}],[\"spm=1001\",{\"1\":{\"481\":1}}],[\"sp++\",{\"1\":{\"408\":3,\"412\":1,\"415\":2,\"417\":16}}],[\"sp\",{\"1\":{\"406\":4,\"409\":1,\"412\":1,\"413\":4,\"414\":2,\"415\":1,\"418\":16,\"501\":6}}],[\"split\",{\"1\":{\"250\":1,\"265\":2}}],[\"space\",{\"1\":{\"52\":1,\"445\":1}}],[\"specialsupport\",{\"1\":{\"190\":5}}],[\"special\",{\"1\":{\"41\":1}}],[\"smtp\",{\"1\":{\"39\":5}}],[\"smtplib\",{\"1\":{\"39\":2}}],[\"sum\",{\"1\":{\"362\":3}}],[\"supported\",{\"1\":{\"431\":1,\"485\":1}}],[\"support\",{\"1\":{\"190\":28,\"428\":1}}],[\"super\",{\"1\":{\"139\":4,\"152\":2,\"165\":1,\"169\":1,\"190\":3,\"208\":1,\"210\":1,\"218\":4,\"303\":1,\"372\":2,\"380\":2}}],[\"subtract\",{\"1\":{\"422\":1}}],[\"subroutine\",{\"1\":{\"412\":4}}],[\"subclass\",{\"1\":{\"375\":1}}],[\"subscribing\",{\"1\":{\"281\":3}}],[\"subscribes\",{\"1\":{\"280\":1}}],[\"subscribe\",{\"1\":{\"280\":3}}],[\"subscriptions\",{\"1\":{\"280\":1}}],[\"substitution\",{\"1\":{\"228\":1}}],[\"sub\",{\"1\":{\"44\":1,\"407\":1,\"412\":1,\"413\":1,\"416\":1,\"417\":1,\"425\":1,\"433\":1,\"466\":1,\"492\":2,\"493\":1,\"494\":1,\"499\":3}}],[\"subject\",{\"1\":{\"39\":3,\"306\":1,\"307\":1}}],[\"successfully\",{\"1\":{\"39\":1}}],[\"su\",{\"1\":{\"21\":1,\"22\":1}}],[\"sudo\",{\"1\":{\"21\":1,\"22\":1,\"33\":3}}],[\"stdin\",{\"1\":{\"445\":1}}],[\"stored\",{\"1\":{\"486\":1}}],[\"store\",{\"1\":{\"429\":1,\"431\":1,\"465\":1,\"466\":1,\"484\":1}}],[\"step\",{\"1\":{\"402\":1,\"420\":1,\"435\":1,\"456\":1,\"467\":1,\"477\":1,\"482\":3,\"501\":1}}],[\"study\",{\"1\":{\"362\":5}}],[\"studio时不能打开360手机助手\",{\"1\":{\"96\":1}}],[\"studio下载gradle太慢可换源\",{\"1\":{\"9\":1}}],[\"studio换源\",{\"0\":{\"9\":1}}],[\"static\",{\"1\":{\"237\":3,\"250\":3,\"291\":1,\"339\":3,\"343\":4,\"348\":4,\"362\":3}}],[\"statement>b\",{\"1\":{\"473\":1}}],[\"statement>\",{\"1\":{\"472\":1,\"473\":3}}],[\"statements\",{\"1\":{\"466\":2}}],[\"statementnon\",{\"1\":{\"450\":1,\"461\":1}}],[\"statement\",{\"1\":{\"450\":12,\"461\":12,\"466\":1,\"467\":1,\"472\":1,\"473\":5,\"474\":1,\"476\":2}}],[\"state\",{\"0\":{\"346\":1,\"347\":1},\"1\":{\"200\":1,\"291\":2,\"292\":1,\"298\":1,\"347\":2,\"348\":28,\"349\":1,\"351\":4,\"352\":7,\"353\":1,\"354\":3,\"355\":7,\"356\":1,\"367\":1}}],[\"stacksp\",{\"1\":{\"501\":1}}],[\"stackvoid\",{\"1\":{\"465\":1}}],[\"stackchar\",{\"1\":{\"405\":1}}],[\"stackint\",{\"1\":{\"402\":1}}],[\"stack\",{\"1\":{\"201\":1,\"405\":6,\"406\":2,\"408\":2,\"409\":1,\"412\":1,\"413\":2,\"466\":2,\"486\":1,\"501\":1}}],[\"starts\",{\"1\":{\"430\":2}}],[\"startswith\",{\"1\":{\"291\":1}}],[\"start\",{\"1\":{\"99\":1,\"101\":1,\"133\":4}}],[\"started\",{\"1\":{\"54\":1,\"133\":2}}],[\"starttls\",{\"1\":{\"39\":1}}],[\"style\",{\"1\":{\"52\":1}}],[\"struct\",{\"1\":{\"429\":2}}],[\"strong\",{\"1\":{\"317\":2}}],[\"strategy\",{\"0\":{\"360\":1,\"365\":1},\"1\":{\"226\":1,\"361\":1,\"362\":20,\"365\":4,\"366\":1,\"374\":1}}],[\"str\",{\"1\":{\"169\":6,\"179\":5,\"250\":2,\"324\":5,\"372\":6}}],[\"strings\",{\"1\":{\"484\":1}}],[\"stringtokenizer\",{\"1\":{\"265\":10}}],[\"stringdisplay\",{\"1\":{\"218\":6,\"372\":6}}],[\"stringdisplayimpl\",{\"0\":{\"169\":1},\"1\":{\"164\":1,\"168\":5,\"169\":1,\"173\":2}}],[\"string\",{\"1\":{\"39\":1,\"139\":26,\"152\":14,\"169\":2,\"179\":14,\"190\":6,\"208\":3,\"209\":3,\"210\":3,\"218\":13,\"237\":13,\"244\":8,\"250\":7,\"265\":16,\"272\":3,\"280\":7,\"291\":7,\"317\":10,\"324\":14,\"348\":7,\"362\":5,\"372\":4,\"380\":5,\"402\":1,\"431\":3,\"484\":1}}],[\"stream\",{\"1\":{\"17\":1,\"422\":1,\"423\":1}}],[\"shr\",{\"1\":{\"407\":1,\"417\":1,\"425\":1,\"433\":1,\"494\":1}}],[\"shl\",{\"1\":{\"407\":1,\"417\":1,\"425\":1,\"433\":1,\"494\":1}}],[\"should\",{\"1\":{\"280\":1,\"453\":1}}],[\"showcase\",{\"1\":{\"317\":3}}],[\"show\",{\"1\":{\"218\":5,\"221\":1}}],[\"showwithaster\",{\"1\":{\"152\":3}}],[\"showwithparen\",{\"1\":{\"152\":3}}],[\"sh帮你免费且自动更新的https证书\",{\"1\":{\"26\":1}}],[\"sh的安装目录\",{\"1\":{\"21\":1}}],[\"shanghai\",{\"1\":{\"18\":1}}],[\"share\",{\"1\":{\"17\":3,\"18\":2,\"23\":5}}],[\"sh\",{\"0\":{\"13\":1},\"1\":{\"13\":1,\"14\":1,\"21\":3,\"22\":2}}],[\"sheet\",{\"1\":{\"5\":2}}],[\"several\",{\"1\":{\"486\":1}}],[\"semicolon\",{\"1\":{\"472\":1}}],[\"seperated\",{\"1\":{\"453\":1}}],[\"segmentation\",{\"1\":{\"419\":1,\"435\":1}}],[\"segment\",{\"1\":{\"405\":6,\"462\":1}}],[\"segmentfault\",{\"1\":{\"106\":1}}],[\"search\",{\"1\":{\"139\":2,\"429\":1}}],[\"services\",{\"1\":{\"18\":1}}],[\"server\",{\"0\":{\"38\":1},\"1\":{\"17\":4,\"23\":10,\"39\":7}}],[\"sender\",{\"1\":{\"280\":4}}],[\"sendmail\",{\"1\":{\"39\":1}}],[\"send\",{\"1\":{\"39\":2}}],[\"sendfile\",{\"1\":{\"17\":1}}],[\"sent\",{\"1\":{\"17\":1,\"39\":2}}],[\"second\",{\"1\":{\"484\":1}}],[\"secrets\",{\"1\":{\"10\":1}}],[\"secret\",{\"1\":{\"10\":1}}],[\"section\",{\"1\":{\"8\":1}}],[\"setup\",{\"1\":{\"501\":1}}],[\"setclock\",{\"1\":{\"348\":3,\"352\":4}}],[\"settimeout\",{\"1\":{\"324\":1}}],[\"settings\",{\"1\":{\"9\":1}}],[\"setprintername\",{\"1\":{\"324\":5}}],[\"setnext\",{\"1\":{\"190\":6}}],[\"set\",{\"1\":{\"9\":1,\"250\":1}}],[\"see\",{\"1\":{\"8\":1}}],[\"select\",{\"1\":{\"8\":1}}],[\"so\",{\"1\":{\"484\":1,\"486\":1}}],[\"source\",{\"1\":{\"402\":3,\"408\":2,\"423\":1}}],[\"solution\",{\"1\":{\"280\":1}}],[\"solutions\",{\"0\":{\"7\":1}}],[\"somethinggood\",{\"1\":{\"160\":2}}],[\"something\",{\"1\":{\"160\":4}}],[\"some\",{\"0\":{\"7\":1}}],[\"vs\",{\"1\":{\"106\":2}}],[\"vscode中可以使用\",{\"1\":{\"95\":1}}],[\"vscode\",{\"0\":{\"54\":1},\"1\":{\"96\":1}}],[\"v3u\",{\"1\":{\"98\":1,\"102\":1}}],[\"virtual\",{\"1\":{\"327\":1,\"332\":1,\"405\":1,\"406\":1}}],[\"view\",{\"0\":{\"311\":1},\"1\":{\"311\":1}}],[\"visit\",{\"1\":{\"380\":4,\"383\":2,\"387\":1,\"388\":1}}],[\"visitor\",{\"0\":{\"378\":1,\"379\":1,\"388\":1},\"1\":{\"213\":1,\"275\":1,\"378\":1,\"380\":23,\"381\":1,\"383\":6,\"384\":2,\"386\":1,\"387\":3,\"388\":3}}],[\"visualstudio\",{\"1\":{\"54\":1}}],[\"vi\",{\"1\":{\"211\":1,\"212\":2,\"380\":1,\"381\":2}}],[\"vim\",{\"1\":{\"33\":1}}],[\"void\",{\"1\":{\"45\":1,\"130\":1,\"139\":3,\"152\":10,\"167\":3,\"179\":13,\"190\":3,\"197\":9,\"208\":1,\"209\":2,\"210\":1,\"218\":1,\"237\":6,\"244\":4,\"250\":1,\"265\":7,\"272\":1,\"280\":2,\"291\":3,\"303\":8,\"317\":3,\"324\":8,\"343\":1,\"348\":23,\"362\":6,\"372\":4,\"380\":3,\"402\":2,\"408\":1,\"412\":1,\"426\":1,\"429\":1,\"430\":1,\"431\":1,\"432\":1,\"433\":1,\"434\":2,\"445\":2,\"452\":1,\"454\":1,\"455\":1,\"464\":1,\"466\":1}}],[\"volumes\",{\"1\":{\"18\":1}}],[\"v+p\",{\"1\":{\"45\":1}}],[\"v+a\",{\"1\":{\"45\":3}}],[\"v<a\",{\"1\":{\"45\":1}}],[\"v>=p\",{\"1\":{\"45\":1}}],[\"v=x\",{\"1\":{\"45\":1}}],[\"v\",{\"1\":{\"45\":10,\"405\":1}}],[\"val\",{\"1\":{\"429\":1,\"430\":10,\"431\":7,\"445\":5,\"454\":1,\"484\":2,\"492\":1}}],[\"value\",{\"1\":{\"408\":3,\"409\":1,\"422\":1,\"429\":4,\"434\":1,\"445\":12,\"453\":2,\"454\":1,\"462\":1,\"464\":1,\"465\":3,\"466\":2,\"486\":6,\"498\":1}}],[\"valid=300s\",{\"1\":{\"17\":1}}],[\"variables\",{\"1\":{\"464\":1,\"466\":2}}],[\"variable\",{\"1\":{\"412\":1,\"413\":1,\"434\":1,\"450\":3,\"451\":1,\"453\":7,\"461\":2,\"464\":3,\"465\":1,\"466\":2,\"486\":5}}],[\"vars\",{\"1\":{\"10\":1}}],[\"var\",{\"1\":{\"10\":1,\"17\":10,\"18\":1,\"23\":10,\"416\":2,\"492\":1,\"495\":1,\"500\":1}}],[\"vue\",{\"0\":{\"13\":1},\"1\":{\"13\":1}}],[\"vuepress\",{\"1\":{\"5\":1}}],[\"version\",{\"1\":{\"5\":1,\"9\":1}}],[\"after\",{\"1\":{\"482\":3}}],[\"a=10\",{\"1\":{\"454\":1}}],[\"a是41\",{\"1\":{\"430\":1}}],[\"ax上需要保留原来的值\",{\"1\":{\"499\":1}}],[\"axxor\",{\"1\":{\"498\":1}}],[\"axpush\",{\"1\":{\"498\":1}}],[\"ax\",{\"1\":{\"406\":3,\"408\":26,\"409\":4,\"411\":5,\"412\":1,\"416\":2,\"417\":34,\"418\":7,\"419\":1,\"484\":1,\"486\":1,\"495\":1,\"499\":1}}],[\"ai\",{\"1\":{\"365\":1}}],[\"a>\",{\"1\":{\"237\":1,\"238\":1}}],[\"a><\",{\"1\":{\"139\":6}}],[\"at\",{\"1\":{\"197\":1,\"198\":10}}],[\"attach\",{\"1\":{\"39\":1}}],[\"adj\",{\"0\":{\"414\":1},\"1\":{\"403\":1,\"407\":1,\"412\":1,\"414\":2,\"486\":1}}],[\"adapter\",{\"1\":{\"148\":1,\"152\":1,\"153\":1,\"174\":1,\"226\":1,\"333\":1}}],[\"addactionlistener\",{\"1\":{\"356\":5}}],[\"addobserver\",{\"1\":{\"303\":3}}],[\"addfruit\",{\"1\":{\"291\":2}}],[\"add\",{\"1\":{\"44\":3,\"45\":1,\"139\":10,\"208\":1,\"209\":1,\"211\":13,\"380\":16,\"402\":1,\"407\":1,\"412\":3,\"414\":2,\"416\":1,\"417\":1,\"419\":1,\"422\":1,\"425\":2,\"433\":1,\"434\":2,\"492\":2,\"493\":1,\"494\":1,\"498\":5,\"499\":3,\"500\":1}}],[\"address\",{\"1\":{\"408\":6,\"410\":1,\"416\":3,\"453\":2,\"462\":1,\"463\":2,\"486\":1,\"489\":3,\"493\":1}}],[\"address+\",{\"1\":{\"405\":1,\"416\":1,\"463\":1}}],[\"address|\",{\"1\":{\"405\":1}}],[\"address>\",{\"1\":{\"139\":1}}],[\"address>`\",{\"1\":{\"139\":1}}],[\"addr\",{\"1\":{\"17\":1,\"496\":4,\"497\":4}}],[\"ab\",{\"1\":{\"474\":1}}],[\"abstractdisplay\",{\"1\":{\"372\":8}}],[\"abstractclass\",{\"1\":{\"161\":2}}],[\"abstractfactory\",{\"1\":{\"139\":1,\"250\":1,\"341\":1}}],[\"abstract\",{\"1\":{\"139\":10,\"142\":1,\"143\":1,\"152\":3,\"167\":4,\"174\":1,\"179\":5,\"181\":1,\"190\":2,\"209\":4,\"218\":5,\"239\":1,\"244\":3,\"265\":2,\"303\":3,\"367\":1,\"372\":4,\"380\":6}}],[\"about\",{\"0\":{\"7\":1},\"1\":{\"280\":1}}],[\"automatically\",{\"1\":{\"280\":1}}],[\"automaton\",{\"1\":{\"15\":3,\"17\":9,\"18\":2,\"19\":2,\"21\":1,\"23\":16}}],[\"author\",{\"1\":{\"139\":8}}],[\"authservice\",{\"1\":{\"126\":1}}],[\"aaronsw\",{\"1\":{\"112\":1}}],[\"await\",{\"1\":{\"101\":5,\"102\":1}}],[\"append\",{\"1\":{\"484\":1}}],[\"appendbook\",{\"1\":{\"272\":5}}],[\"apple\",{\"1\":{\"291\":1,\"292\":12}}],[\"application\",{\"1\":{\"17\":1,\"280\":1}}],[\"app\",{\"1\":{\"280\":1}}],[\"api\",{\"0\":{\"221\":1},\"1\":{\"54\":1,\"161\":2,\"172\":1,\"221\":5,\"222\":1,\"365\":2}}],[\"aggregate\",{\"1\":{\"272\":5,\"273\":2}}],[\"aggregateerror\",{\"1\":{\"54\":1}}],[\"again\",{\"1\":{\"101\":2}}],[\"agicy\",{\"1\":{\"53\":1}}],[\"agent\",{\"1\":{\"17\":1}}],[\"a<b\",{\"1\":{\"44\":1}}],[\"a+b\",{\"1\":{\"44\":2}}],[\"a+b>=p\",{\"1\":{\"44\":1}}],[\"any\",{\"1\":{\"272\":2,\"317\":3,\"343\":2}}],[\"an\",{\"1\":{\"179\":1,\"180\":1,\"280\":1,\"453\":1,\"485\":1}}],[\"ans=\",{\"1\":{\"45\":1}}],[\"ans=mul\",{\"1\":{\"44\":1}}],[\"ans=1ll\",{\"1\":{\"43\":1}}],[\"android\",{\"0\":{\"9\":1},\"1\":{\"9\":2,\"95\":1}}],[\"and\",{\"1\":{\"8\":1,\"280\":3,\"407\":1,\"415\":1,\"417\":1,\"425\":3,\"433\":5,\"485\":1,\"489\":2,\"494\":2,\"497\":1,\"498\":2}}],[\"asimpile\",{\"0\":{\"514\":1}}],[\"assignment\",{\"1\":{\"495\":1}}],[\"assign\",{\"1\":{\"425\":2,\"433\":1,\"453\":2,\"454\":1,\"473\":1,\"474\":1,\"475\":1,\"476\":1,\"486\":1,\"487\":1,\"494\":2,\"495\":3,\"496\":1,\"500\":1}}],[\"assembly\",{\"1\":{\"423\":1}}],[\"assetstudioassetstudio\",{\"1\":{\"51\":1}}],[\"assert\",{\"1\":{\"45\":1}}],[\"async\",{\"1\":{\"100\":1,\"101\":5}}],[\"asyncio\",{\"0\":{\"98\":1},\"1\":{\"100\":3,\"101\":13}}],[\"as\",{\"1\":{\"39\":2,\"101\":1,\"152\":2,\"208\":1,\"280\":1,\"433\":1,\"487\":1,\"488\":1}}],[\"array\",{\"1\":{\"500\":1}}],[\"array<item>\",{\"1\":{\"139\":1}}],[\"are\",{\"1\":{\"484\":1,\"485\":1,\"486\":1}}],[\"area\",{\"1\":{\"402\":1,\"405\":3}}],[\"arbitrary\",{\"1\":{\"402\":1}}],[\"arg\",{\"1\":{\"416\":3,\"463\":2}}],[\"arg3\",{\"1\":{\"416\":1}}],[\"arg2\",{\"1\":{\"416\":1}}],[\"arg1\",{\"1\":{\"416\":1}}],[\"arguments\",{\"1\":{\"412\":2,\"414\":2,\"416\":1,\"486\":3}}],[\"argv++\",{\"1\":{\"402\":1}}],[\"argv\",{\"1\":{\"402\":3,\"419\":1,\"445\":1,\"501\":1}}],[\"argc\",{\"1\":{\"402\":2,\"419\":1,\"445\":1,\"501\":1}}],[\"args=\",{\"1\":{\"99\":2,\"101\":4}}],[\"around\",{\"1\":{\"272\":1,\"273\":1}}],[\"article\",{\"1\":{\"38\":1,\"481\":1}}],[\"archive\",{\"1\":{\"8\":1}}],[\"accept\",{\"1\":{\"380\":7,\"383\":2,\"388\":1}}],[\"access\",{\"1\":{\"15\":1,\"17\":9,\"23\":10,\"332\":1,\"500\":1}}],[\"acc\",{\"1\":{\"208\":2}}],[\"acquire\",{\"1\":{\"99\":1}}],[\"acme申请\",{\"1\":{\"26\":1}}],[\"acme\",{\"0\":{\"13\":1},\"1\":{\"13\":1,\"14\":1,\"15\":1,\"18\":1,\"21\":3,\"22\":5}}],[\"actually\",{\"1\":{\"485\":1}}],[\"actual\",{\"1\":{\"453\":1}}],[\"actionlistener\",{\"1\":{\"356\":3}}],[\"actionperformed\",{\"1\":{\"356\":1}}],[\"action\",{\"1\":{\"200\":1}}],[\"act\",{\"1\":{\"10\":5}}],[\"alone\",{\"1\":{\"453\":1}}],[\"alice使用了id卡\",{\"1\":{\"245\":1}}],[\"alice\",{\"1\":{\"190\":4,\"244\":1,\"324\":1}}],[\"alias\",{\"1\":{\"17\":1,\"23\":2}}],[\"aliyun\",{\"1\":{\"9\":12}}],[\"allocate\",{\"1\":{\"405\":1}}],[\"allowmixedcontent\",{\"1\":{\"95\":1}}],[\"all\",{\"1\":{\"9\":1,\"280\":1,\"464\":1,\"484\":1}}],[\"alt\",{\"1\":{\"3\":1,\"39\":1,\"107\":1}}],[\"a\",{\"1\":{\"5\":1,\"39\":1,\"44\":6,\"45\":6,\"98\":1,\"102\":1,\"106\":1,\"179\":1,\"180\":1,\"280\":4,\"284\":8,\"343\":1,\"395\":1,\"397\":1,\"400\":1,\"402\":1,\"403\":1,\"419\":1,\"420\":1,\"421\":1,\"429\":8,\"430\":4,\"431\":5,\"435\":1,\"439\":1,\"449\":1,\"453\":2,\"454\":1,\"456\":1,\"460\":1,\"463\":3,\"467\":1,\"471\":1,\"473\":4,\"474\":4,\"476\":1,\"477\":1,\"486\":1,\"488\":2,\"489\":2,\"491\":1,\"495\":2,\"496\":1,\"498\":3,\"500\":2,\"501\":1,\"505\":1}}],[\"我认为这并无不可\",{\"1\":{\"507\":1}}],[\"我认为这也是初学者实现编译器的一大难点\",{\"1\":{\"478\":1}}],[\"我认为至少占了重要程度的50\",{\"1\":{\"506\":1}}],[\"我认为有几个要点需要强调\",{\"1\":{\"436\":1}}],[\"我知道\",{\"1\":{\"452\":1}}],[\"我仍然认为通过定义\",{\"1\":{\"397\":1}}],[\"我相信绝大多数\",{\"1\":{\"394\":1}}],[\"我是先写程序再总结上面的文法\",{\"1\":{\"450\":1}}],[\"我是抱着满腔热情去上课的\",{\"1\":{\"394\":1}}],[\"我是要增加功能呢\",{\"1\":{\"162\":1}}],[\"我对编译器一直心存敬佩\",{\"1\":{\"394\":1}}],[\"我会说是\",{\"1\":{\"393\":1}}],[\"我会从团队整体出发进行考虑\",{\"1\":{\"279\":1}}],[\"我来负责仲裁\",{\"1\":{\"279\":1}}],[\"我才不用rust呢\",{\"1\":{\"260\":1}}],[\"我得拿到锁才能操作\",{\"1\":{\"99\":1}}],[\"我们才能有所成长吧\",{\"1\":{\"509\":1}}],[\"我们才可以编写出具有高可替换性的类\",{\"1\":{\"161\":1}}],[\"我们其实通过了参数\",{\"1\":{\"494\":1}}],[\"我们没有取负的操作\",{\"1\":{\"492\":1}}],[\"我们没有直接的逻辑取反指令\",{\"1\":{\"490\":1}}],[\"我们主要从它的目标代码入手\",{\"1\":{\"483\":1}}],[\"我们看看下面的伪代码\",{\"1\":{\"473\":1}}],[\"我们实现的\",{\"1\":{\"466\":1}}],[\"我们实现的词法分析器与传统意义上的词法分析器不太相同\",{\"1\":{\"429\":1}}],[\"我们已经为变量\",{\"1\":{\"495\":1}}],[\"我们已经为当前的标识符\",{\"1\":{\"462\":1}}],[\"我们已经知道了什么时候开始解析函数的定义\",{\"1\":{\"462\":1}}],[\"我们把词法分析器的代码一并贴上\",{\"1\":{\"445\":1}}],[\"我们向前看一个标记\",{\"1\":{\"443\":1}}],[\"我们假设词法分析器已经正确地将其中的数字识别成了标记\",{\"1\":{\"442\":1}}],[\"我们对\",{\"1\":{\"442\":1}}],[\"我们下一章见\",{\"1\":{\"436\":1}}],[\"我们直接贴上代码\",{\"1\":{\"433\":1,\"445\":1}}],[\"我们用了专门的一章讲解了\",{\"1\":{\"508\":1}}],[\"我们用了很暴力的手段编写了我们的词法分析器\",{\"1\":{\"507\":1}}],[\"我们用词法分析器将源码转换成标记流\",{\"1\":{\"432\":1}}],[\"我们用类来表示状态\",{\"1\":{\"351\":1}}],[\"我们之前说过\",{\"1\":{\"432\":1}}],[\"我们以异或\",{\"1\":{\"498\":1}}],[\"我们以\",{\"1\":{\"431\":1}}],[\"我们并不关心一个变量具体叫什么名字\",{\"1\":{\"429\":1}}],[\"我们并不会一次性地将所有源码全部转换成标记流\",{\"1\":{\"424\":1}}],[\"我们知道\",{\"1\":{\"426\":1}}],[\"我们同时还用它来处理空白字符\",{\"1\":{\"426\":1}}],[\"我们为\",{\"1\":{\"417\":1}}],[\"我们依旧用上面的例子\",{\"1\":{\"416\":1}}],[\"我们连函数调用都无法实现\",{\"1\":{\"412\":1}}],[\"我们这里的\",{\"1\":{\"408\":1}}],[\"我们这里并不需要了解太多\",{\"1\":{\"405\":1}}],[\"我们的代码是自举的\",{\"1\":{\"501\":1}}],[\"我们的代码里有一些指针的强制转换\",{\"1\":{\"419\":1}}],[\"我们的电脑上已经有了这些函数的实现\",{\"1\":{\"418\":1}}],[\"我们的\",{\"1\":{\"412\":1,\"416\":1}}],[\"我们的编译器支持指针类型\",{\"1\":{\"453\":1}}],[\"我们的编译器并不支持宏定义\",{\"1\":{\"428\":1}}],[\"我们的编译器是以标记流为输入\",{\"1\":{\"423\":1}}],[\"我们的编译器参数是顺序入栈的\",{\"1\":{\"412\":1}}],[\"我们的编译器主要包括\",{\"1\":{\"402\":1}}],[\"我们的虚拟机还是工作良好的\",{\"1\":{\"419\":1}}],[\"我们的虚拟机只有一个寄存器\",{\"1\":{\"408\":1}}],[\"我们的虚拟机中\",{\"1\":{\"406\":1}}],[\"我们的虚拟机并不打算模拟完整的计算机\",{\"1\":{\"405\":1}}],[\"我们要使用变量\",{\"1\":{\"493\":1}}],[\"我们要从整体上讲解如何设计我们的\",{\"1\":{\"400\":1}}],[\"我们要在\",{\"1\":{\"143\":1}}],[\"我们能对编译器的构建有一定的了解\",{\"1\":{\"392\":1}}],[\"我们提倡扩展\",{\"1\":{\"385\":1}}],[\"我们创建了\",{\"1\":{\"384\":1}}],[\"我们来整理一下\",{\"1\":{\"383\":1}}],[\"我们来思考一下\",{\"1\":{\"352\":1}}],[\"我们只关心三个内容\",{\"1\":{\"405\":1}}],[\"我们只需要编写新的访问者\",{\"1\":{\"378\":1}}],[\"我们只要事先在每个方法内部都加上一段\",{\"1\":{\"355\":1}}],[\"我们编写一个表示\",{\"1\":{\"378\":1}}],[\"我们声明了抽象方法\",{\"1\":{\"375\":1}}],[\"我们考虑了两种猜拳的策略\",{\"1\":{\"362\":1}}],[\"我们考虑泛型编程\",{\"1\":{\"45\":1}}],[\"我们暂且不深入学习该方法\",{\"1\":{\"353\":1}}],[\"我们应该如何编程\",{\"1\":{\"352\":1}}],[\"我们应该养成具体问题具体分析的辩证唯物思想\",{\"1\":{\"102\":1}}],[\"我们会遇到许多的挫折\",{\"1\":{\"509\":1}}],[\"我们会先加载它的地址\",{\"1\":{\"489\":1}}],[\"我们会先将该问题分解为多个小问题\",{\"1\":{\"351\":1}}],[\"我们会将\",{\"1\":{\"425\":1}}],[\"我们会将它们继续划分为更小的问题\",{\"1\":{\"351\":1}}],[\"我们经常会使用分而治之的方针\",{\"1\":{\"351\":1}}],[\"我们在第三章的虚拟机中提到过\",{\"1\":{\"466\":1}}],[\"我们在本章的学习过程中已经提到过很多次了\",{\"1\":{\"388\":1}}],[\"我们在理解类的层次时\",{\"1\":{\"375\":1}}],[\"我们在\",{\"1\":{\"324\":1}}],[\"我们还需要初始化虚拟机的栈\",{\"1\":{\"501\":1}}],[\"我们还需要注意下面将要提到的情况\",{\"1\":{\"307\":1}}],[\"我们还可能返回除号\",{\"1\":{\"432\":1}}],[\"我们还要编写进行其他处理的\",{\"1\":{\"384\":1}}],[\"我们还应关注设计模式的演变和新模式的出现\",{\"1\":{\"232\":1}}],[\"我们展示了如何使用观察者模式来管理状态变化\",{\"1\":{\"303\":1}}],[\"我们可能会修改或删除现有的\",{\"1\":{\"486\":1}}],[\"我们可能需要从观察模式转变为通知模式\",{\"1\":{\"310\":1}}],[\"我们可能需要为同一个集合编写多个具体迭代器\",{\"1\":{\"274\":1}}],[\"我们可将扮演\",{\"1\":{\"285\":1}}],[\"我们可以正确调用\",{\"1\":{\"501\":1}}],[\"我们可以很容易地直接将\",{\"1\":{\"443\":1}}],[\"我们可以这样认为\",{\"1\":{\"423\":1}}],[\"我们可以准备两种算法\",{\"1\":{\"366\":1}}],[\"我们可以使用的内存地址为\",{\"1\":{\"405\":1}}],[\"我们可以使用\",{\"1\":{\"353\":1}}],[\"我们可以在不同的应用场景中灵活地控制对对象的访问\",{\"1\":{\"332\":1}}],[\"我们可以在不修改现有类的情况下添加新功能\",{\"1\":{\"217\":1}}],[\"我们可以考虑使用事件总线或消息队列来集中处理通知\",{\"1\":{\"310\":1}}],[\"我们可以考虑将多个对象组成一条职责链\",{\"1\":{\"188\":1}}],[\"我们可以引入一个标志位来跟踪通知状态\",{\"1\":{\"308\":1}}],[\"我们可以为\",{\"1\":{\"274\":1}}],[\"我们可以轻松地遍历\",{\"1\":{\"273\":1}}],[\"我们可以轻松地添加其他具体工厂\",{\"1\":{\"140\":1}}],[\"我们可以更好地管理和操作集合数据\",{\"1\":{\"270\":1}}],[\"我们可以更灵活地管理对象的创建过程\",{\"1\":{\"243\":1}}],[\"我们可以提高代码的可读性\",{\"1\":{\"232\":1}}],[\"我们可以将这些视图注册为观察者\",{\"1\":{\"302\":1}}],[\"我们可以将\",{\"1\":{\"172\":1}}],[\"我们定义了\",{\"1\":{\"324\":1}}],[\"我们定义了几个类和接口来实现迭代器模式\",{\"1\":{\"273\":1}}],[\"我们定义一个用于创建对象的接口\",{\"1\":{\"242\":1}}],[\"我们了解到共享实例可以减少内存使用量\",{\"1\":{\"256\":1}}],[\"我们通常会将共享对象存储在某种集合\",{\"1\":{\"255\":1}}],[\"我们也将构建出一个能用的\",{\"1\":{\"392\":1}}],[\"我们也可以不使用示例程序中的做法\",{\"1\":{\"353\":1}}],[\"我们也可以换种说法\",{\"1\":{\"254\":1}}],[\"我们也要避免过早地进行\",{\"1\":{\"232\":1}}],[\"我们就着手虚拟机的实现\",{\"1\":{\"506\":1}}],[\"我们就来逐一说明\",{\"1\":{\"481\":1}}],[\"我们就将它的类型加上\",{\"1\":{\"453\":1}}],[\"我们就知道是需要解析枚举类型\",{\"1\":{\"453\":1}}],[\"我们就能知道它们是特殊的关键字\",{\"1\":{\"434\":1}}],[\"我们就只需要一个表示系统状态的变量即可\",{\"1\":{\"354\":1}}],[\"我们就需要一个中立的仲裁者站出来说\",{\"1\":{\"279\":1}}],[\"我们就可以实现以不同的颜色显示同一个\",{\"1\":{\"253\":1}}],[\"我们就实现了不修改被装饰的类即可增加功能\",{\"1\":{\"222\":1}}],[\"我们不另外处理它们的原因是\",{\"1\":{\"425\":1}}],[\"我们不得不在\",{\"1\":{\"387\":1}}],[\"我们不应该将它们隐藏在自己脑袋中\",{\"1\":{\"235\":1}}],[\"我们不应死记硬背这些设计模式\",{\"1\":{\"232\":1}}],[\"我们不妨通过类的运算符重载来进一步优化\",{\"1\":{\"45\":1}}],[\"我们完全不需要对被装饰的类做任何修改\",{\"1\":{\"222\":1}}],[\"我们使用装饰器模式来动态地给对象添加职责\",{\"1\":{\"216\":1}}],[\"我们使用了策略模式\",{\"1\":{\"361\":1}}],[\"我们使用了外观模式\",{\"1\":{\"236\":1}}],[\"我们使用了\",{\"1\":{\"190\":1,\"291\":1}}],[\"我们必须先计算优先级高的运算符\",{\"1\":{\"482\":1}}],[\"我们必须时刻关汴这种\",{\"1\":{\"183\":1}}],[\"我们必须要做以下修改\",{\"1\":{\"143\":1}}],[\"我们必须要对所有的具体工厂进行相应的修改才行\",{\"1\":{\"143\":1}}],[\"我们需要类似下面的汇编代码\",{\"1\":{\"495\":1}}],[\"我们需要不断地向右扫描\",{\"1\":{\"494\":1}}],[\"我们需要处理多运算符的优先级问题\",{\"1\":{\"494\":1}}],[\"我们需要在栈上为局部变量预留空间\",{\"1\":{\"466\":1}}],[\"我们需要所有的变量定义出现在所有的语句之前\",{\"1\":{\"466\":1}}],[\"我们需要知道后面参数的类型\",{\"1\":{\"485\":1}}],[\"我们需要知道参数的个数\",{\"1\":{\"463\":1}}],[\"我们需要知道这两个\",{\"1\":{\"429\":1}}],[\"我们需要了解当\",{\"1\":{\"463\":1}}],[\"我们需要得到\",{\"1\":{\"416\":1}}],[\"我们需要条件判断相关的指令\",{\"1\":{\"411\":1}}],[\"我们需要首先在全局添加如下代码\",{\"1\":{\"405\":1}}],[\"我们需要使用多个变量的值的集合来表示系统的状态\",{\"1\":{\"354\":1}}],[\"我们需要使用条件分支语句判断当前的状态\",{\"1\":{\"351\":1}}],[\"我们需要特别小心\",{\"1\":{\"308\":1}}],[\"我们需要确保共享对象在整个程序生命周期内都被引用\",{\"1\":{\"255\":1}}],[\"我们需要根据具体情况选择合适的设计模式\",{\"1\":{\"232\":1}}],[\"我们需要先阅读现有代码\",{\"1\":{\"185\":1}}],[\"我们需要编写一个定义这些操作系统的共同接口\",{\"1\":{\"172\":1}}],[\"我们需要将它存放到前一篇文章中说的\",{\"1\":{\"431\":1}}],[\"我们需要将当前的行号加一\",{\"1\":{\"427\":1}}],[\"我们需要将\",{\"1\":{\"162\":1}}],[\"我们需要证明乘法结果的存在性和唯一性\",{\"1\":{\"74\":1}}],[\"我们需要证明加法结果的存在性和唯一性\",{\"1\":{\"58\":1}}],[\"我们学习了抽象类的作用\",{\"1\":{\"161\":1}}],[\"我们再用多线程试一下同样的逻辑\",{\"1\":{\"101\":1}}],[\"我们将介绍递归下降的语法分析器\",{\"1\":{\"436\":1}}],[\"我们将同时分析单个字符如\",{\"1\":{\"431\":1}}],[\"我们将专门作为一个小节\",{\"1\":{\"406\":1}}],[\"我们将实现其中的eval函数\",{\"1\":{\"402\":1}}],[\"我们将逐个填充每个函数的功能\",{\"1\":{\"402\":1}}],[\"我们将\",{\"1\":{\"353\":1}}],[\"我们将设置时间的处理看作是\",{\"1\":{\"352\":1}}],[\"我们将展示如何使用\",{\"1\":{\"271\":1}}],[\"我们将借助另一个公理系统\",{\"1\":{\"82\":1}}],[\"我们将详细讲解环境配置\",{\"1\":{\"13\":1}}],[\"我们成功地由\",{\"1\":{\"82\":1}}],[\"我们终于可以对自然数乘法的性质进行进一步的探索\",{\"1\":{\"77\":1}}],[\"我们终于可以对自然数加法的性质进行进一步的探索\",{\"1\":{\"61\":1}}],[\"我们预先准备以方便证明\",{\"1\":{\"67\":1}}],[\"我们即可建立如今最常用的算术公理系统\",{\"1\":{\"55\":1}}],[\"我的博客构建库\",{\"1\":{\"5\":1}}],[\"我抽奖一发就中了大奖\",{\"1\":{\"3\":1}}],[\"zero\",{\"1\":{\"411\":1}}],[\"zeroelse\",{\"1\":{\"411\":1}}],[\"zhihu\",{\"1\":{\"35\":1,\"38\":1}}],[\"zhuanlan\",{\"1\":{\"35\":1,\"38\":1}}],[\"zip\",{\"1\":{\"9\":1}}],[\"z\",{\"1\":{\"5\":1,\"44\":1,\"45\":1,\"429\":4}}],[\"网站\",{\"1\":{\"5\":1}}],[\"资源进行加速\",{\"1\":{\"53\":1}}],[\"资源\",{\"0\":{\"5\":1}}],[\"项目地址\",{\"1\":{\"395\":1}}],[\"项目的初衷\",{\"0\":{\"395\":1}}],[\"项目结构\",{\"0\":{\"15\":1},\"1\":{\"13\":1}}],[\"项目\",{\"0\":{\"4\":1,\"13\":1},\"1\":{\"13\":1,\"15\":1}}],[\"这也是我自己的感慨吧\",{\"1\":{\"509\":1}}],[\"这也意味着一元运算符的优先级总是高于多元运算符\",{\"1\":{\"483\":1}}],[\"这部分对于整个编译器的编写其实是十分重要的\",{\"1\":{\"506\":1}}],[\"这部分也将同时解析参数本身\",{\"1\":{\"483\":1}}],[\"这次是后缀形式的\",{\"1\":{\"499\":1}}],[\"这包括\",{\"1\":{\"497\":1}}],[\"这和第三章\",{\"1\":{\"486\":1}}],[\"这章讲解语句的解析\",{\"1\":{\"471\":1}}],[\"这段代码线性地遍历所有标识符\",{\"1\":{\"464\":1}}],[\"这段示例程序的功能是让电脑玩\",{\"1\":{\"362\":1}}],[\"这么做的原因是\",{\"1\":{\"464\":1}}],[\"这么做的理由有两点\",{\"1\":{\"400\":1}}],[\"这相当于是整个函数定义的语法解析的框架\",{\"1\":{\"464\":1}}],[\"这点在后面的语法分析器我们就能体会\",{\"1\":{\"422\":1}}],[\"这点复杂度还是不算什么的\",{\"1\":{\"394\":1}}],[\"这后生成的目标代码便是我们的指令集\",{\"1\":{\"401\":1}}],[\"这意味着我们可以像运行脚本一样去运行\",{\"1\":{\"400\":1}}],[\"这意味着我们可以轻松地替换观察者或被观察者\",{\"1\":{\"306\":1}}],[\"这篇博客并没有使用诸如\",{\"1\":{\"397\":1}}],[\"这篇文章将带你走进闭包的奇妙世界\",{\"1\":{\"107\":1}}],[\"这些就是我们要支持的标记符\",{\"1\":{\"425\":1}}],[\"这些工具允许我们通过正则表达式来识别标记\",{\"1\":{\"424\":1}}],[\"这些函数就是可用的\",{\"1\":{\"418\":1}}],[\"这些函数的二进制代码就被编译进了我们的编译器\",{\"1\":{\"418\":1}}],[\"这些指令只接受一个参数\",{\"1\":{\"408\":1}}],[\"这些指令的顺序安排是有意的\",{\"1\":{\"407\":1}}],[\"这些理论试图教会我们如何用通用的方法来自动解决问题\",{\"1\":{\"394\":1}}],[\"这些题目要么是因为答案太大\",{\"1\":{\"41\":1}}],[\"这其中最主要的原因是\",{\"1\":{\"394\":1}}],[\"这两行代码起的就是这个作用\",{\"1\":{\"466\":1}}],[\"这两个角色共同决定了实际进行的处理\",{\"1\":{\"383\":1}}],[\"这两条语句中都有\",{\"1\":{\"356\":1}}],[\"这超出了本书的范围\",{\"1\":{\"353\":1}}],[\"这是整个编译器的最后一部分\",{\"1\":{\"481\":1}}],[\"这是上一章的\",{\"1\":{\"461\":1}}],[\"这是正常的\",{\"1\":{\"435\":1}}],[\"这是汇编中最难理解的部分\",{\"1\":{\"412\":1}}],[\"这是我们要支持的全部指令\",{\"1\":{\"407\":1}}],[\"这是\",{\"1\":{\"400\":1,\"403\":1,\"496\":1}}],[\"这是一种稍微有些笨的策略\",{\"1\":{\"362\":1}}],[\"这是一种非常好的解决办法\",{\"1\":{\"353\":1}}],[\"这是因为\",{\"1\":{\"356\":2,\"464\":1}}],[\"这是因为我们需要在\",{\"1\":{\"355\":1}}],[\"这是因为在\",{\"1\":{\"285\":1}}],[\"这是因为只有\",{\"1\":{\"173\":1}}],[\"这虽然看似理所当然\",{\"1\":{\"352\":1}}],[\"这一章\",{\"1\":{\"468\":1}}],[\"这一系列教程将带你从头编写一个\",{\"1\":{\"392\":1}}],[\"这一处理需要花费很多时间\",{\"1\":{\"324\":1}}],[\"这一功能的类\",{\"1\":{\"164\":1}}],[\"这可能会导致被观察对象再次通知所有观察者\",{\"1\":{\"308\":1}}],[\"这可能吗\",{\"1\":{\"101\":1}}],[\"这会导致共享对象在需要时无法被找到\",{\"1\":{\"255\":1}}],[\"这取决于类的使用目的\",{\"1\":{\"253\":1}}],[\"这就意味着表达式\",{\"1\":{\"482\":1}}],[\"这就用到了上一章中提到的\",{\"1\":{\"443\":1}}],[\"这就涉及到编译器\",{\"1\":{\"426\":1}}],[\"这就需要事先将这个位置信息存储起来\",{\"1\":{\"412\":1}}],[\"这就像我们可以自由选择香草味冰激凌\",{\"1\":{\"224\":1}}],[\"这就体现了它们之间的一致性\",{\"1\":{\"221\":1}}],[\"这就是开闭原则\",{\"1\":{\"385\":1}}],[\"这就是共享的特点\",{\"1\":{\"253\":1}}],[\"这就是所谓的里氏替换原则\",{\"1\":{\"228\":1}}],[\"这就是接口\",{\"1\":{\"221\":1}}],[\"这就是\",{\"1\":{\"164\":1,\"188\":1,\"352\":1,\"385\":2}}],[\"这就是为了增加新功能而产生的层次结构\",{\"1\":{\"160\":1}}],[\"这就是主动让出\",{\"1\":{\"101\":1}}],[\"这时\",{\"1\":{\"143\":1,\"173\":1,\"185\":1,\"279\":1,\"285\":1,\"354\":1,\"366\":1,\"387\":1}}],[\"这\",{\"1\":{\"142\":1,\"284\":2}}],[\"这并不是事情的全貌\",{\"1\":{\"99\":1}}],[\"这并不是什么缺陷\",{\"1\":{\"98\":1}}],[\"这个\",{\"1\":{\"426\":2}}],[\"这个顺序要特别注意\",{\"1\":{\"417\":1}}],[\"这个主题\",{\"1\":{\"388\":1}}],[\"这个gil全局解释器锁实际上把所有线程的执行代码都给上了锁\",{\"1\":{\"99\":1}}],[\"这个图满足如下性质\",{\"1\":{\"85\":1}}],[\"这实际上是符合客观逻辑的\",{\"1\":{\"98\":1}}],[\"这与\",{\"1\":{\"84\":1}}],[\"这究竟是为什么呢\",{\"1\":{\"82\":1}}],[\"这违背了\",{\"1\":{\"81\":1}}],[\"这样你就不需要重复造轮子\",{\"1\":{\"508\":1}}],[\"这样它就成了全局的常量了\",{\"1\":{\"454\":1}}],[\"这样当源代码中出现关键字时\",{\"1\":{\"434\":1}}],[\"这样我们就有了一个最简单的编译器\",{\"1\":{\"402\":1}}],[\"这样做的主要原因是为了简化虚拟机的实现\",{\"1\":{\"409\":1}}],[\"这样做的缺点是\",{\"1\":{\"388\":1}}],[\"这样做的好处是请求的发送者和接收者解耦\",{\"1\":{\"190\":1}}],[\"这样看起来程序好像变复杂了\",{\"1\":{\"365\":1}}],[\"这样即使应用程序关闭后重新打开\",{\"1\":{\"297\":1}}],[\"这样可以支持用户进行多次撤销和重做操作\",{\"1\":{\"297\":1}}],[\"这样可以确保逻辑的一致性和可维护性\",{\"1\":{\"283\":1}}],[\"这样的颜色信息\",{\"1\":{\"253\":1}}],[\"这样的设计可能显得有些过于复杂\",{\"1\":{\"140\":1}}],[\"这样\",{\"1\":{\"221\":1,\"222\":1,\"256\":1,\"279\":1,\"351\":1,\"353\":1,\"354\":1,\"378\":1,\"388\":1}}],[\"这样很容易使类的层次结构变得复杂\",{\"1\":{\"162\":1}}],[\"这样一来\",{\"1\":{\"142\":1,\"172\":1,\"253\":1}}],[\"这样子类可以决定实例化哪个类\",{\"1\":{\"138\":1}}],[\"这样在扩展功能时\",{\"1\":{\"116\":1}}],[\"这样就很难在编译代码时检测出\",{\"1\":{\"355\":1}}],[\"这样就构成了一个小小的类层次结构\",{\"1\":{\"160\":1}}],[\"这样就定义了自然数\",{\"1\":{\"56\":1}}],[\"这样就解决了类型名长的缺点\",{\"1\":{\"45\":1}}],[\"这样就可以在同一个平台上管理代码和镜像\",{\"1\":{\"31\":1}}],[\"这样使用的时候\",{\"1\":{\"45\":1}}],[\"这种顺序的唯一作用就是在打印调试信息时更加方便\",{\"1\":{\"407\":1}}],[\"这种消息分发的方式一般被称为双重分发\",{\"1\":{\"383\":1}}],[\"这种责任被称为\",{\"1\":{\"375\":1}}],[\"这种错误了\",{\"1\":{\"355\":1}}],[\"这种处理方式既有优点也有缺点\",{\"1\":{\"353\":1}}],[\"这种处理方式是在画蛇添足\",{\"1\":{\"99\":1}}],[\"这种透明性使得代理模式在不改变客户端代码的情况下添加额外的功能成为可能\",{\"1\":{\"330\":1}}],[\"这种一致性确保了委托模式的灵活性和可维护性\",{\"1\":{\"229\":1}}],[\"这种情况下\",{\"1\":{\"188\":1}}],[\"这种设计方式提高了系统的灵活性和可扩展性\",{\"1\":{\"184\":1}}],[\"这种职责分离使得代码更加清晰\",{\"1\":{\"183\":1}}],[\"这种层次结构并非用于方便我们增加新的方法\",{\"1\":{\"161\":1}}],[\"这种模式通过组合而不是继承来实现功能的扩展\",{\"1\":{\"158\":1}}],[\"这种主动让出型的调度方式更为高效\",{\"1\":{\"100\":1}}],[\"这种异步编程方式被广大开发者所认可\",{\"1\":{\"99\":1}}],[\"这种写法的式子依旧太长\",{\"1\":{\"44\":1}}],[\"这种方法可以减少观察者对被观察对象的依赖\",{\"1\":{\"309\":1}}],[\"这种方法需要额外的逻辑来判断对象是否仍然被使用\",{\"1\":{\"255\":1}}],[\"这种方法简单直接\",{\"1\":{\"255\":1}}],[\"这种方法有效地解决了直接取模的忘记取模的漏洞\",{\"1\":{\"44\":1}}],[\"这种方法是直接取模\",{\"1\":{\"43\":1}}],[\"这种集成性使得持续集成\",{\"1\":{\"31\":1}}],[\"这便是本文写作的背景\",{\"1\":{\"40\":1}}],[\"这里就不多作解释\",{\"1\":{\"496\":1}}],[\"这里最为重要的一点是\",{\"1\":{\"463\":1}}],[\"这里不再多说\",{\"1\":{\"444\":1}}],[\"这里会有一个疑问\",{\"1\":{\"443\":1}}],[\"这里我简单介绍一下\",{\"1\":{\"441\":1}}],[\"这里我们解析的就是类似\",{\"1\":{\"493\":1}}],[\"这里我们就能看到\",{\"1\":{\"489\":1}}],[\"这里我们就采用第二种方法\",{\"1\":{\"434\":1}}],[\"这里我们讲解其中的一些细节\",{\"1\":{\"453\":1}}],[\"这里我们要额外介绍\",{\"1\":{\"432\":1}}],[\"这里我们要为我们的虚拟机构建自己的指令集\",{\"1\":{\"407\":1}}],[\"这里我们首先要了解的是当参数调用时\",{\"1\":{\"416\":1}}],[\"这里我们约定\",{\"1\":{\"412\":1}}],[\"这里我们把\",{\"1\":{\"412\":1}}],[\"这里我们只实现两个最简单的条件判断\",{\"1\":{\"411\":1}}],[\"这里这样写的目的是装b\",{\"1\":{\"430\":1}}],[\"这里要说明这样一个观点\",{\"1\":{\"506\":1}}],[\"这里要注意的是在ascii码中\",{\"1\":{\"430\":1}}],[\"这里要解释的一点是\",{\"1\":{\"408\":1}}],[\"这里解释一下具体的含义\",{\"1\":{\"429\":1}}],[\"这里注意的是\",{\"1\":{\"424\":1}}],[\"这里需要的是注意每个函数的作用\",{\"1\":{\"402\":1}}],[\"这里有一个单独用于解析\",{\"1\":{\"402\":1}}],[\"这里\",{\"1\":{\"355\":1,\"473\":1,\"494\":1}}],[\"这里故意将上面两点说得很笼统\",{\"1\":{\"352\":1}}],[\"这里也出现了可替换性\",{\"0\":{\"306\":1}}],[\"这里的一个问题是\",{\"1\":{\"426\":1}}],[\"这里的原理是\",{\"1\":{\"418\":1}}],[\"这里的数据可以是代码\",{\"1\":{\"405\":1}}],[\"这里的资源指的是计算机中的资源\",{\"1\":{\"256\":1}}],[\"这里的类的层次结构并非用于增加功能\",{\"1\":{\"161\":1}}],[\"这里的finally\",{\"1\":{\"99\":1}}],[\"这里其实也存在层次结构\",{\"1\":{\"161\":1}}],[\"这里说的\",{\"1\":{\"142\":1}}],[\"这里将目录修改为目标目录\",{\"1\":{\"22\":1}}],[\"这里是所有详细的教程和指南\",{\"1\":{\"110\":1}}],[\"这里是所有与技术相关的文章\",{\"1\":{\"37\":1}}],[\"这里是所有个人感想\",{\"1\":{\"2\":1}}],[\"这里是推荐的书籍\",{\"1\":{\"5\":1}}],[\"这里是你参与或开发的项目介绍和进展\",{\"1\":{\"4\":1}}],[\"这句话真是道出了人生的真谛\",{\"1\":{\"3\":1}}],[\"这让我不禁感慨\",{\"1\":{\"3\":1}}],[\"时我们并不能确定\",{\"1\":{\"453\":1}}],[\"时直接从\",{\"1\":{\"408\":1}}],[\"时间也是一种资源\",{\"1\":{\"256\":1}}],[\"时由乘法运算规则\",{\"1\":{\"78\":1}}],[\"时有\",{\"1\":{\"62\":2,\"63\":1,\"64\":4,\"71\":1,\"78\":3,\"79\":1,\"80\":1,\"81\":2}}],[\"时\",{\"1\":{\"3\":1,\"62\":1,\"63\":1,\"68\":1,\"78\":1,\"79\":1,\"80\":1,\"95\":1,\"185\":1,\"353\":1,\"356\":2,\"384\":1}}],[\"一节提到的\",{\"1\":{\"494\":1}}],[\"一节中所说的修改或删除\",{\"1\":{\"489\":1}}],[\"一是运算符的优先级问题\",{\"1\":{\"481\":1}}],[\"一是容易忘记大括号\",{\"1\":{\"43\":1}}],[\"一元运算符\",{\"0\":{\"483\":1},\"1\":{\"481\":1}}],[\"一旦遇到了\",{\"1\":{\"475\":1}}],[\"一旦同名\",{\"1\":{\"464\":1}}],[\"一些非终结符如<expr>被递归地使用了\",{\"1\":{\"442\":1}}],[\"一种是自底向上\",{\"1\":{\"440\":1}}],[\"一种是自顶向下\",{\"1\":{\"440\":1}}],[\"一般终结符对应于词法分析器输出的标记\",{\"1\":{\"441\":1}}],[\"一般有两种处理方法\",{\"1\":{\"434\":1}}],[\"一般处理的方法有两种\",{\"1\":{\"426\":1}}],[\"一般而言\",{\"1\":{\"401\":1}}],[\"一般的编译器相关的教程要么就十分简单\",{\"1\":{\"395\":1}}],[\"一般编译原理的课程会说一些\",{\"1\":{\"394\":1}}],[\"一般来说\",{\"1\":{\"256\":1}}],[\"一定程度上\",{\"1\":{\"351\":1}}],[\"一侧增加类即可\",{\"1\":{\"172\":1}}],[\"一致性是指委托对象应当具有与委托者相同的接口或行为\",{\"1\":{\"229\":1}}],[\"一致性\",{\"1\":{\"138\":1}}],[\"一个标记\",{\"1\":{\"425\":1}}],[\"一个语法分析器生成器\",{\"1\":{\"397\":1}}],[\"一个观察者在接收到通知后修改了被观察对象的状态\",{\"1\":{\"308\":1}}],[\"一个实例的改变会同时反映到所有使用该实例的地方\",{\"1\":{\"253\":1}}],[\"一个实体应当尽量少地与其他实体之间发生相互作用\",{\"1\":{\"122\":1}}],[\"一个类只负责一个职责\",{\"1\":{\"134\":1}}],[\"一个类只对应一个职责\",{\"1\":{\"124\":1}}],[\"一个类对另一个类的依赖应该建立在最小的接口上\",{\"1\":{\"127\":1}}],[\"一个原则可以是另一个原则的加强或基础\",{\"1\":{\"114\":1}}],[\"一个通用性很强的工具\",{\"1\":{\"5\":1}}],[\"一路点击\",{\"1\":{\"111\":1}}],[\"一方面没有很好的测试用例\",{\"1\":{\"396\":1}}],[\"一方面想了解它的工作原理\",{\"1\":{\"393\":1}}],[\"一方面\",{\"1\":{\"100\":1,\"408\":1}}],[\"一方面减少了心智负担\",{\"1\":{\"45\":1}}],[\"一将成名\",{\"1\":{\"3\":1}}],[\"一位热衷于探索全栈开发领域的技术爱好者\",{\"1\":{\"1\":1}}],[\"昨日在玩\",{\"1\":{\"3\":1}}],[\"致力于打造高效\",{\"1\":{\"1\":1}}],[\"擅长将前端与后端技术无缝结合\",{\"1\":{\"1\":1}}],[\"介绍页\",{\"0\":{\"1\":1}}]],\"serializationVersion\":2}}")).map(([e,t])=>[e,zt(t,{fields:["h","t","c"],storeFields:["h","t","c"]})]));self.onmessage=({data:{type:e="all",query:t,locale:s,options:n,id:o}})=>{const u=bt[s];e==="suggest"?self.postMessage([e,o,tt(t,u,n)]):e==="search"?self.postMessage([e,o,Z(t,u,n)]):self.postMessage({suggestions:[e,o,tt(t,u,n)],results:[e,o,Z(t,u,n)]})};
+const V=Object.entries,et=Object.fromEntries,st="ENTRIES",L="KEYS",T="VALUES",_="";class D{set;_type;_path;constructor(t,s){const n=t._tree,o=Array.from(n.keys());this.set=t,this._type=s,this._path=o.length>0?[{node:n,keys:o}]:[]}next(){const t=this.dive();return this.backtrack(),t}dive(){if(this._path.length===0)return{done:!0,value:void 0};const{node:t,keys:s}=E(this._path);if(E(s)===_)return{done:!1,value:this.result()};const n=t.get(E(s));return this._path.push({node:n,keys:Array.from(n.keys())}),this.dive()}backtrack(){if(this._path.length===0)return;const t=E(this._path).keys;t.pop(),!(t.length>0)&&(this._path.pop(),this.backtrack())}key(){return this.set._prefix+this._path.map(({keys:t})=>E(t)).filter(t=>t!==_).join("")}value(){return E(this._path).node.get(_)}result(){switch(this._type){case T:return this.value();case L:return this.key();default:return[this.key(),this.value()]}}[Symbol.iterator](){return this}}const E=e=>e[e.length-1],nt=(e,t,s)=>{const n=new Map;if(t===void 0)return n;const o=t.length+1,u=o+s,i=new Uint8Array(u*o).fill(s+1);for(let r=0;r<o;++r)i[r]=r;for(let r=1;r<u;++r)i[r*o]=r;return R(e,t,s,n,i,1,o,""),n},R=(e,t,s,n,o,u,i,r)=>{const d=u*i;t:for(const c of e.keys())if(c===_){const a=o[d-1];a<=s&&n.set(r,[e.get(c),a])}else{let a=u;for(let h=0;h<c.length;++h,++a){const g=c[h],m=i*a,p=m-i;let l=o[m];const f=Math.max(0,a-s-1),y=Math.min(i-1,a+s);for(let F=f;F<y;++F){const v=g!==t[F],z=o[p+F]+ +v,A=o[p+F+1]+1,w=o[m+F]+1,j=o[m+F+1]=Math.min(z,A,w);j<l&&(l=j)}if(l>s)continue t}R(e.get(c),t,s,n,o,a,i,r+c)}};class C{_tree;_prefix;_size=void 0;constructor(t=new Map,s=""){this._tree=t,this._prefix=s}atPrefix(t){if(!t.startsWith(this._prefix))throw new Error("Mismatched prefix");const[s,n]=x(this._tree,t.slice(this._prefix.length));if(s===void 0){const[o,u]=O(n);for(const i of o.keys())if(i!==_&&i.startsWith(u)){const r=new Map;return r.set(i.slice(u.length),o.get(i)),new C(r,t)}}return new C(s,t)}clear(){this._size=void 0,this._tree.clear()}delete(t){return this._size=void 0,ot(this._tree,t)}entries(){return new D(this,st)}forEach(t){for(const[s,n]of this)t(s,n,this)}fuzzyGet(t,s){return nt(this._tree,t,s)}get(t){const s=k(this._tree,t);return s!==void 0?s.get(_):void 0}has(t){const s=k(this._tree,t);return s!==void 0&&s.has(_)}keys(){return new D(this,L)}set(t,s){if(typeof t!="string")throw new Error("key must be a string");return this._size=void 0,I(this._tree,t).set(_,s),this}get size(){if(this._size)return this._size;this._size=0;const t=this.entries();for(;!t.next().done;)this._size+=1;return this._size}update(t,s){if(typeof t!="string")throw new Error("key must be a string");this._size=void 0;const n=I(this._tree,t);return n.set(_,s(n.get(_))),this}fetch(t,s){if(typeof t!="string")throw new Error("key must be a string");this._size=void 0;const n=I(this._tree,t);let o=n.get(_);return o===void 0&&n.set(_,o=s()),o}values(){return new D(this,T)}[Symbol.iterator](){return this.entries()}static from(t){const s=new C;for(const[n,o]of t)s.set(n,o);return s}static fromObject(t){return C.from(Object.entries(t))}}const x=(e,t,s=[])=>{if(t.length===0||e==null)return[e,s];for(const n of e.keys())if(n!==_&&t.startsWith(n))return s.push([e,n]),x(e.get(n),t.slice(n.length),s);return s.push([e,t]),x(void 0,"",s)},k=(e,t)=>{if(t.length===0||e==null)return e;for(const s of e.keys())if(s!==_&&t.startsWith(s))return k(e.get(s),t.slice(s.length))},I=(e,t)=>{const s=t.length;t:for(let n=0;e&&n<s;){for(const u of e.keys())if(u!==_&&t[n]===u[0]){const i=Math.min(s-n,u.length);let r=1;for(;r<i&&t[n+r]===u[r];)++r;const d=e.get(u);if(r===u.length)e=d;else{const c=new Map;c.set(u.slice(r),d),e.set(t.slice(n,n+r),c),e.delete(u),e=c}n+=r;continue t}const o=new Map;return e.set(t.slice(n),o),o}return e},ot=(e,t)=>{const[s,n]=x(e,t);if(s!==void 0){if(s.delete(_),s.size===0)W(n);else if(s.size===1){const[o,u]=s.entries().next().value;q(n,o,u)}}},W=e=>{if(e.length===0)return;const[t,s]=O(e);if(t.delete(s),t.size===0)W(e.slice(0,-1));else if(t.size===1){const[n,o]=t.entries().next().value;n!==_&&q(e.slice(0,-1),n,o)}},q=(e,t,s)=>{if(e.length===0)return;const[n,o]=O(e);n.set(o+t,s),n.delete(o)},O=e=>e[e.length-1],ut=(e,t)=>{const s=e._idToShortId.get(t);if(s!=null)return e._storedFields.get(s)},it=/[\n\r -#%-*,-/:;?@[-\]_{}\u00A0\u00A1\u00A7\u00AB\u00B6\u00B7\u00BB\u00BF\u037E\u0387\u055A-\u055F\u0589\u058A\u05BE\u05C0\u05C3\u05C6\u05F3\u05F4\u0609\u060A\u060C\u060D\u061B\u061E\u061F\u066A-\u066D\u06D4\u0700-\u070D\u07F7-\u07F9\u0830-\u083E\u085E\u0964\u0965\u0970\u09FD\u0A76\u0AF0\u0C77\u0C84\u0DF4\u0E4F\u0E5A\u0E5B\u0F04-\u0F12\u0F14\u0F3A-\u0F3D\u0F85\u0FD0-\u0FD4\u0FD9\u0FDA\u104A-\u104F\u10FB\u1360-\u1368\u1400\u166E\u1680\u169B\u169C\u16EB-\u16ED\u1735\u1736\u17D4-\u17D6\u17D8-\u17DA\u1800-\u180A\u1944\u1945\u1A1E\u1A1F\u1AA0-\u1AA6\u1AA8-\u1AAD\u1B5A-\u1B60\u1BFC-\u1BFF\u1C3B-\u1C3F\u1C7E\u1C7F\u1CC0-\u1CC7\u1CD3\u2000-\u200A\u2010-\u2029\u202F-\u2043\u2045-\u2051\u2053-\u205F\u207D\u207E\u208D\u208E\u2308-\u230B\u2329\u232A\u2768-\u2775\u27C5\u27C6\u27E6-\u27EF\u2983-\u2998\u29D8-\u29DB\u29FC\u29FD\u2CF9-\u2CFC\u2CFE\u2CFF\u2D70\u2E00-\u2E2E\u2E30-\u2E4F\u3000-\u3003\u3008-\u3011\u3014-\u301F\u3030\u303D\u30A0\u30FB\uA4FE\uA4FF\uA60D-\uA60F\uA673\uA67E\uA6F2-\uA6F7\uA874-\uA877\uA8CE\uA8CF\uA8F8-\uA8FA\uA8FC\uA92E\uA92F\uA95F\uA9C1-\uA9CD\uA9DE\uA9DF\uAA5C-\uAA5F\uAADE\uAADF\uAAF0\uAAF1\uABEB\uFD3E\uFD3F\uFE10-\uFE19\uFE30-\uFE52\uFE54-\uFE61\uFE63\uFE68\uFE6A\uFE6B\uFF01-\uFF03\uFF05-\uFF0A\uFF0C-\uFF0F\uFF1A\uFF1B\uFF1F\uFF20\uFF3B-\uFF3D\uFF3F\uFF5B\uFF5D\uFF5F-\uFF65]+/u,M="or",$="and",rt="and_not",ct=(e,t)=>{e.includes(t)||e.push(t)},N=(e,t)=>{for(const s of t)e.includes(s)||e.push(s)},P=({score:e},{score:t})=>t-e,lt=()=>new Map,b=e=>{const t=new Map;for(const s of Object.keys(e))t.set(parseInt(s,10),e[s]);return t},G=(e,t)=>Object.prototype.hasOwnProperty.call(e,t)?e[t]:void 0,ht={[M]:(e,t)=>{for(const s of t.keys()){const n=e.get(s);if(n==null)e.set(s,t.get(s));else{const{score:o,terms:u,match:i}=t.get(s);n.score=n.score+o,n.match=Object.assign(n.match,i),N(n.terms,u)}}return e},[$]:(e,t)=>{const s=new Map;for(const n of t.keys()){const o=e.get(n);if(o==null)continue;const{score:u,terms:i,match:r}=t.get(n);N(o.terms,i),s.set(n,{score:o.score+u,terms:o.terms,match:Object.assign(o.match,r)})}return s},[rt]:(e,t)=>{for(const s of t.keys())e.delete(s);return e}},dt=(e,t,s,n,o,u)=>{const{k:i,b:r,d}=u;return Math.log(1+(s-t+.5)/(t+.5))*(d+e*(i+1)/(e+i*(1-r+r*n/o)))},at=e=>(t,s,n)=>{const o=typeof e.fuzzy=="function"?e.fuzzy(t,s,n):e.fuzzy||!1,u=typeof e.prefix=="function"?e.prefix(t,s,n):e.prefix===!0;return{term:t,fuzzy:o,prefix:u}},H=(e,t,s,n)=>{for(const o of Object.keys(e._fieldIds))if(e._fieldIds[o]===s){e._options.logger("warn",`SlimSearch: document with ID ${e._documentIds.get(t)} has changed before removal: term "${n}" was not present in field "${o}". Removing a document after it has changed can corrupt the index!`,"version_conflict");return}},ft=(e,t,s,n)=>{if(!e._index.has(n)){H(e,s,t,n);return}const o=e._index.fetch(n,lt),u=o.get(t);u==null||u.get(s)==null?H(e,s,t,n):u.get(s)<=1?u.size<=1?o.delete(t):u.delete(s):u.set(s,u.get(s)-1),e._index.get(n).size===0&&e._index.delete(n)},gt={k:1.2,b:.7,d:.5},mt={idField:"id",extractField:(e,t)=>e[t],tokenize:e=>e.split(it),processTerm:e=>e.toLowerCase(),fields:void 0,searchOptions:void 0,storeFields:[],logger:(e,t)=>{typeof console?.[e]=="function"&&console[e](t)},autoVacuum:!0},J={combineWith:M,prefix:!1,fuzzy:!1,maxFuzzy:6,boost:{},weights:{fuzzy:.45,prefix:.375},bm25:gt},pt={combineWith:$,prefix:(e,t,s)=>t===s.length-1},Ft={batchSize:1e3,batchWait:10},U={minDirtFactor:.1,minDirtCount:20},_t={...Ft,...U},K=Symbol("*"),yt=(e,t)=>{const s=new Map,n={...e._options.searchOptions,...t};for(const[o,u]of e._documentIds){const i=n.boostDocument?n.boostDocument(u,"",e._storedFields.get(o)):1;s.set(o,{score:i,terms:[],match:{}})}return s},X=(e,t=M)=>{if(e.length===0)return new Map;const s=t.toLowerCase(),n=ht[s];if(!n)throw new Error(`Invalid combination operator: ${t}`);return e.reduce(n)||new Map},S=(e,t,s,n,o,u,i,r,d=new Map)=>{if(o==null)return d;for(const c of Object.keys(u)){const a=u[c],h=e._fieldIds[c],g=o.get(h);if(g==null)continue;let m=g.size;const p=e._avgFieldLength[h];for(const l of g.keys()){if(!e._documentIds.has(l)){ft(e,h,l,s),m-=1;continue}const f=i?i(e._documentIds.get(l),s,e._storedFields.get(l)):1;if(!f)continue;const y=g.get(l),F=e._fieldLength.get(l)[h],v=dt(y,m,e._documentCount,F,p,r),z=n*a*f*v,A=d.get(l);if(A){A.score+=z,ct(A.terms,t);const w=G(A.match,s);w?w.push(c):A.match[s]=[c]}else d.set(l,{score:z,terms:[t],match:{[s]:[c]}})}}return d},At=(e,t,s)=>{const n={...e._options.searchOptions,...s},o=(n.fields||e._options.fields).reduce((l,f)=>({...l,[f]:G(n.boost,f)||1}),{}),{boostDocument:u,weights:i,maxFuzzy:r,bm25:d}=n,{fuzzy:c,prefix:a}={...J.weights,...i},h=e._index.get(t.term),g=S(e,t.term,t.term,1,h,o,u,d);let m,p;if(t.prefix&&(m=e._index.atPrefix(t.term)),t.fuzzy){const l=t.fuzzy===!0?.2:t.fuzzy,f=l<1?Math.min(r,Math.round(t.term.length*l)):l;f&&(p=e._index.fuzzyGet(t.term,f))}if(m)for(const[l,f]of m){const y=l.length-t.term.length;if(!y)continue;p?.delete(l);const F=a*l.length/(l.length+.3*y);S(e,t.term,l,F,f,o,u,d,g)}if(p)for(const l of p.keys()){const[f,y]=p.get(l);if(!y)continue;const F=c*l.length/(l.length+y);S(e,t.term,l,F,f,o,u,d,g)}return g},Y=(e,t,s={})=>{if(t===K)return yt(e,s);if(typeof t!="string"){const a={...s,...t,queries:void 0},h=t.queries.map(g=>Y(e,g,a));return X(h,a.combineWith)}const{tokenize:n,processTerm:o,searchOptions:u}=e._options,i={tokenize:n,processTerm:o,...u,...s},{tokenize:r,processTerm:d}=i,c=r(t).flatMap(a=>d(a)).filter(a=>!!a).map(at(i)).map(a=>At(e,a,i));return X(c,i.combineWith)},Q=(e,t,s={})=>{const n=Y(e,t,s),o=[];for(const[u,{score:i,terms:r,match:d}]of n){const c=r.length||1,a={id:e._documentIds.get(u),score:i*c,terms:Object.keys(d),queryTerms:r,match:d};Object.assign(a,e._storedFields.get(u)),(s.filter==null||s.filter(a))&&o.push(a)}return t===K&&s.boostDocument==null&&e._options.searchOptions.boostDocument==null||o.sort(P),o},Ct=(e,t,s={})=>{s={...e._options.autoSuggestOptions,...s};const n=new Map;for(const{score:u,terms:i}of Q(e,t,s)){const r=i.join(" "),d=n.get(r);d!=null?(d.score+=u,d.count+=1):n.set(r,{score:u,terms:i,count:1})}const o=[];for(const[u,{score:i,terms:r,count:d}]of n)o.push({suggestion:u,terms:r,score:i/d});return o.sort(P),o};class Et{_options;_index;_documentCount;_documentIds;_idToShortId;_fieldIds;_fieldLength;_avgFieldLength;_nextId;_storedFields;_dirtCount;_currentVacuum;_enqueuedVacuum;_enqueuedVacuumConditions;constructor(t){if(t?.fields==null)throw new Error('SlimSearch: option "fields" must be provided');const s=t.autoVacuum==null||t.autoVacuum===!0?_t:t.autoVacuum;this._options={...mt,...t,autoVacuum:s,searchOptions:{...J,...t.searchOptions||{}},autoSuggestOptions:{...pt,...t.autoSuggestOptions||{}}},this._index=new C,this._documentCount=0,this._documentIds=new Map,this._idToShortId=new Map,this._fieldIds={},this._fieldLength=new Map,this._avgFieldLength=[],this._nextId=0,this._storedFields=new Map,this._dirtCount=0,this._currentVacuum=null,this._enqueuedVacuum=null,this._enqueuedVacuumConditions=U,this.addFields(this._options.fields)}get isVacuuming(){return this._currentVacuum!=null}get dirtCount(){return this._dirtCount}get dirtFactor(){return this._dirtCount/(1+this._documentCount+this._dirtCount)}get documentCount(){return this._documentCount}get termCount(){return this._index.size}toJSON(){const t=[];for(const[s,n]of this._index){const o={};for(const[u,i]of n)o[u]=Object.fromEntries(i);t.push([s,o])}return{documentCount:this._documentCount,nextId:this._nextId,documentIds:Object.fromEntries(this._documentIds),fieldIds:this._fieldIds,fieldLength:Object.fromEntries(this._fieldLength),averageFieldLength:this._avgFieldLength,storedFields:Object.fromEntries(this._storedFields),dirtCount:this._dirtCount,index:t,serializationVersion:2}}addFields(t){for(let s=0;s<t.length;s++)this._fieldIds[t[s]]=s}}const zt=({index:e,documentCount:t,nextId:s,documentIds:n,fieldIds:o,fieldLength:u,averageFieldLength:i,storedFields:r,dirtCount:d,serializationVersion:c},a)=>{if(c!==1&&c!==2)throw new Error("SlimSearch: cannot deserialize an index created with an incompatible version");const h=new Et(a);h._documentCount=t,h._nextId=s,h._documentIds=b(n),h._idToShortId=new Map,h._fieldIds=o,h._fieldLength=b(u),h._avgFieldLength=i,h._storedFields=b(r),h._dirtCount=d||0,h._index=new C;for(const[g,m]of h._documentIds)h._idToShortId.set(m,g);for(const[g,m]of e){const p=new Map;for(const l of Object.keys(m)){let f=m[l];c===1&&(f=f.ds),p.set(parseInt(l,10),b(f))}h._index.set(g,p)}return h},B=(e,t)=>{const s=e.toLowerCase(),n=t.toLowerCase(),o=[];let u=0,i=0;const r=(c,a=!1)=>{let h="";i===0?h=c.length>20?`… ${c.slice(-20)}`:c:a?h=c.length+i>100?`${c.slice(0,100-i)}… `:c:h=c.length>20?`${c.slice(0,20)} … ${c.slice(-20)}`:c,h&&o.push(h),i+=h.length,a||(o.push(["mark",t]),i+=t.length,i>=100&&o.push(" …"))};let d=s.indexOf(n,u);if(d===-1)return null;for(;d>=0;){const c=d+n.length;if(r(e.slice(u,d)),u=c,i>100)break;d=s.indexOf(n,u)}return i<100&&r(e.slice(u),!0),o},wt=(e,t)=>t.contents.reduce((s,[,n])=>s+n,0)-e.contents.reduce((s,[,n])=>s+n,0),xt=(e,t)=>Math.max(...t.contents.map(([,s])=>s))-Math.max(...e.contents.map(([,s])=>s)),Z=(e,t,s={})=>{const n={};return Q(t,e,{boost:{h:2,t:1,c:4},prefix:!0,...s}).forEach(o=>{const{id:u,terms:i,score:r}=o,d=u.includes("@"),c=u.includes("#"),[a,h]=u.split(/[#@]/),g=Number(a),m=i.sort((l,f)=>l.length-f.length).filter((l,f)=>i.slice(f+1).every(y=>!y.includes(l))),{contents:p}=n[g]??={title:"",contents:[]};if(d)p.push([{type:"customField",id:g,index:h,display:m.map(l=>o.c.map(f=>B(f,l))).flat().filter(l=>l!==null)},r]);else{const l=m.map(f=>B(o.h,f)).filter(f=>f!==null);if(l.length&&p.push([{type:c?"heading":"title",id:g,...c&&{anchor:h},display:l},r]),"t"in o)for(const f of o.t){const y=m.map(F=>B(f,F)).filter(F=>F!==null);y.length&&p.push([{type:"text",id:g,...c&&{anchor:h},display:y},r])}}}),V(n).sort(([,o],[,u])=>"max"==="total"?wt(o,u):xt(o,u)).map(([o,{title:u,contents:i}])=>{if(!u){const r=ut(t,o);r&&(u=r.h)}return{title:u,contents:i.map(([r])=>r)}})},tt=(e,t,s={})=>{const n=Ct(t,e,{fuzzy:.2,maxFuzzy:3,...s}).map(({suggestion:o})=>o);return e.includes(" ")?n:n.filter(o=>!o.includes(" "))},bt=et(V(JSON.parse("{\"/\":{\"documentCount\":529,\"nextId\":529,\"documentIds\":{\"0\":\"0\",\"1\":\"1\",\"2\":\"2\",\"3\":\"3\",\"4\":\"4\",\"5\":\"4#主要思路\",\"6\":\"4#编程语言的选择\",\"7\":\"4#通信协议\",\"8\":\"4#初步思路\",\"9\":\"4#遇到的问题和改进方案\",\"10\":\"4#小车左右轮力矩不一致\",\"11\":\"4#小车容易冲出轨道\",\"12\":\"4#小车总是左右左摆头太蠢了\",\"13\":\"4#其它问题\",\"14\":\"4#设计方案参考\",\"15\":\"4#和机械臂联动\",\"16\":\"4#结语\",\"17\":\"5\",\"18\":\"6\",\"19\":\"7\",\"20\":\"7#some-solutions-to-questions-about-qt\",\"21\":\"7#the-qt-5-isn-t-in-qt-maintenance-tools\",\"22\":\"8\",\"23\":\"9\",\"24\":\"9@0\",\"25\":\"9@1\",\"26\":\"10\",\"27\":\"10#环境\",\"28\":\"10#项目结构\",\"29\":\"10#配置http服务\",\"30\":\"10#配置nginx\",\"31\":\"10#配置docker\",\"32\":\"10#启动项目\",\"33\":\"10#升级为https\",\"34\":\"10#申请证书\",\"35\":\"10#安装证书\",\"36\":\"10#修改配置\",\"37\":\"10#重启container\",\"38\":\"10#配置nginx反向代理-使flask支持-https\",\"39\":\"10#参考资料\",\"40\":\"10@0\",\"41\":\"10@1\",\"42\":\"11\",\"43\":\"11#github-container-registry-加速\",\"44\":\"11#ghcr-io简介\",\"45\":\"11#镜像地址\",\"46\":\"11#配置方法\",\"47\":\"11#docker-wsl2-容器目录\",\"48\":\"12\",\"49\":\"13\",\"50\":\"14\",\"51\":\"15\",\"52\":\"15#使用python-发送示例\",\"53\":\"16\",\"54\":\"16#背景介绍\",\"55\":\"16#过去的做法\",\"56\":\"16#第一种-直接取模\",\"57\":\"16#第二种-函数取模\",\"58\":\"16#泛型编程\",\"59\":\"16@0\",\"60\":\"16@1\",\"61\":\"17\",\"62\":\"17@0\",\"63\":\"17@1\",\"64\":\"18\",\"65\":\"19\",\"66\":\"20\",\"67\":\"21\",\"68\":\"22\",\"69\":\"22#自然数的定义\",\"70\":\"22#自然数的加法运算\",\"71\":\"22#加法的定义\",\"72\":\"22#加法结果的存在性\",\"73\":\"22#加法结果的唯一性\",\"74\":\"22#加法的性质\",\"75\":\"22#加法交换律\",\"76\":\"22#加法结合律\",\"77\":\"22#加法消去律\",\"78\":\"22#自然数的序\",\"79\":\"22#序的定义\",\"80\":\"22#正自然数\",\"81\":\"22#正自然数的性质\",\"82\":\"22#序的反对称性\",\"83\":\"22#序的传递性\",\"84\":\"22#序的完全性\",\"85\":\"22#加法保序性\",\"86\":\"22#自然数的乘法运算\",\"87\":\"22#乘法的定义\",\"88\":\"22#乘法结果的存在性\",\"89\":\"22#乘法结果的唯一性\",\"90\":\"22#乘法的性质\",\"91\":\"22#乘法交换律\",\"92\":\"22#乘法分配律\",\"93\":\"22#乘法结合律\",\"94\":\"22#乘法消去律\",\"95\":\"22#peano-公理的合理性\",\"96\":\"22#乘法保序性\",\"97\":\"22#乘法消去保序性\",\"98\":\"22#用图论阐述-peano-系统\",\"99\":\"22#peano-公理-i\",\"100\":\"22#peano-公理-ii\",\"101\":\"22#peano-公理-iii\",\"102\":\"22#peano-公理-iv\",\"103\":\"22#peano-公理-v\",\"104\":\"22@0\",\"105\":\"22@1\",\"106\":\"23\",\"107\":\"23#安装\",\"108\":\"23#tips\",\"109\":\"23#bug-记录\",\"110\":\"23@1\",\"111\":\"24\",\"112\":\"24#线程安全\",\"113\":\"24#协程\",\"114\":\"24#协程安全\",\"115\":\"24#协程是否需要加锁\",\"116\":\"25\",\"117\":\"26\",\"118\":\"26#缺点\",\"119\":\"26#缺点-1\",\"120\":\"27\",\"121\":\"27@0\",\"122\":\"27@1\",\"123\":\"28\",\"124\":\"29\",\"125\":\"30\",\"126\":\"31\",\"127\":\"32\",\"128\":\"32#关系\",\"129\":\"32#开闭原则\",\"130\":\"32#实现方法\",\"131\":\"32#里氏代换原则\",\"132\":\"32#里氏代换原则-1\",\"133\":\"32#实现方法-1\",\"134\":\"32#示例\",\"135\":\"32#迪米特原则\",\"136\":\"32#迪米特原则-1\",\"137\":\"32#实现方法-2\",\"138\":\"32#单一职责原则\",\"139\":\"32#实现方法-3\",\"140\":\"32#示例-1\",\"141\":\"32#接口隔离原则\",\"142\":\"32#依赖倒置原则\",\"143\":\"32#实现方法-4\",\"144\":\"32#示例-2\",\"145\":\"32#组合-聚合复用原则\",\"146\":\"32#实现方法-5\",\"147\":\"32#示例-3\",\"148\":\"32#总结\",\"149\":\"32@0\",\"150\":\"32@1\",\"151\":\"33\",\"152\":\"33#为什么要使用抽象工厂模式\",\"153\":\"33#示例代码\",\"154\":\"33#增加其它工厂\",\"155\":\"33#拓展思路的要点\",\"156\":\"33#易于增加具体工厂\",\"157\":\"33#难以增加新的零件\",\"158\":\"33#相关的设计模式\",\"159\":\"33@0\",\"160\":\"33@1\",\"161\":\"34\",\"162\":\"34#适配器模式\",\"163\":\"34#为什么要用适配器模式\",\"164\":\"34#类比\",\"165\":\"34#类比-1\",\"166\":\"34#示例程序\",\"167\":\"34#运行结果\",\"168\":\"34#相关的设计模式\",\"169\":\"34@0\",\"170\":\"34@1\",\"171\":\"35\",\"172\":\"35#使用此设计模式的理由\",\"173\":\"35#类的层次结构的两个作用\",\"174\":\"35#增加新功能时\",\"175\":\"35#增加新的实现时\",\"176\":\"35#类的层次结构的混杂和分离\",\"177\":\"35#示例代码\",\"178\":\"35#类的一览表\",\"179\":\"35#countdisplay-ts\",\"180\":\"35#display-ts\",\"181\":\"35#displayimpl-ts\",\"182\":\"35#main-ts\",\"183\":\"35#stringdisplayimpl-ts\",\"184\":\"35#运行结果\",\"185\":\"35#拓展思路的要点\",\"186\":\"35#分开后更容易扩展\",\"187\":\"35#继承是强关联-委托是弱关联\",\"188\":\"35#相关的设计模式\",\"189\":\"35@0\",\"190\":\"35@1\",\"191\":\"36\",\"192\":\"36#为什么要使用-builder-模式\",\"193\":\"36#代码示例\",\"194\":\"36#运行结果\",\"195\":\"36#相关设计模式\",\"196\":\"36#拓展思路的要点\",\"197\":\"36#谁知道什么\",\"198\":\"36#设计时能够决定的事情和不能决定的事情\",\"199\":\"36#代码的阅读方法和修改方法\",\"200\":\"36@0\",\"201\":\"36@1\",\"202\":\"37\",\"203\":\"37#为什么使用此类\",\"204\":\"37#示例代码\",\"205\":\"37#运行结果\",\"206\":\"37#相关的设计模式\",\"207\":\"37@0\",\"208\":\"37@1\",\"209\":\"38\",\"210\":\"38#为什么使用此模式\",\"211\":\"38#示例代码\",\"212\":\"38#运行结果\",\"213\":\"38#拓展思路的要点\",\"214\":\"38#命令中应该包含哪些信息\",\"215\":\"38#保存历史记录\",\"216\":\"38#相关的设计模式\",\"217\":\"38@0\",\"218\":\"38@1\",\"219\":\"39\",\"220\":\"39#使用此设计模式的理由\",\"221\":\"39#示例代码\",\"222\":\"39#目录类-directory-ts\",\"223\":\"39#抽象条目类-entry-ts\",\"224\":\"39#文件类-file-ts\",\"225\":\"39#主程序-main-ts\",\"226\":\"39#运行结果\",\"227\":\"39#相关的设计模式\",\"228\":\"39@0\",\"229\":\"39@1\",\"230\":\"40\",\"231\":\"40#为什么使用装饰器模式\",\"232\":\"40#代码示例\",\"233\":\"40#运行结果\",\"234\":\"40#拓展思路的要点\",\"235\":\"40#api-的透明性\",\"236\":\"40#在不改变被装饰物的前提下增加功能\",\"237\":\"40#可以动态地增加功能\",\"238\":\"40#只需要一些装饰物即可添加许多功能\",\"239\":\"40#导致增加许多很小的类\",\"240\":\"40#相关的设计模式\",\"241\":\"40#继承和委托中的一致性\",\"242\":\"40#父类和子类的一致性\",\"243\":\"40#自己和被委托对象的一致性\",\"244\":\"40@0\",\"245\":\"40@1\",\"246\":\"41\",\"247\":\"41@0\",\"248\":\"41@1\",\"249\":\"42\",\"250\":\"42#示例代码\",\"251\":\"42#代码实现\",\"252\":\"42#运行结果\",\"253\":\"42#相关设计模式\",\"254\":\"42@0\",\"255\":\"42@1\",\"256\":\"43\",\"257\":\"43#为什么要使用-factory-method\",\"258\":\"43#示例代码\",\"259\":\"43#运行结果\",\"260\":\"43@0\",\"261\":\"43@1\",\"262\":\"44\",\"263\":\"44#为什么使用-flyweight-模式\",\"264\":\"44#实例代码\",\"265\":\"44#运行结果\",\"266\":\"44#拓展思路的要点\",\"267\":\"44#对多个地方产生影响\",\"268\":\"44#intrinsic-与-extrinsic\",\"269\":\"44#不要让被共享的实例被垃圾回收器回收了\",\"270\":\"44#内存之外的其它资源\",\"271\":\"44#相关的设计模式\",\"272\":\"44@0\",\"273\":\"44@1\",\"274\":\"45\",\"275\":\"45@0\",\"276\":\"45@1\",\"277\":\"46\",\"278\":\"46#为什么使用此模式\",\"279\":\"46#示例代码\",\"280\":\"46#运行结果\",\"281\":\"46@0\",\"282\":\"46@1\",\"283\":\"47\",\"284\":\"47#为什么要使用迭代器模式\",\"285\":\"47#typescript-实现迭代器模式\",\"286\":\"47#代码示例\",\"287\":\"47#运行结果\",\"288\":\"47#多个迭代器\",\"289\":\"47#相关的设计模式\",\"290\":\"47@0\",\"291\":\"47@1\",\"292\":\"48\",\"293\":\"48#为什么使用此类\",\"294\":\"48#示例代码\",\"295\":\"48#运行结果\",\"296\":\"48#拓展思路的要点\",\"297\":\"48#当发生分散灾难时\",\"298\":\"48#通信线路的增加\",\"299\":\"48#哪些角色可以复用\",\"300\":\"48#相关的设计模式\",\"301\":\"48@0\",\"302\":\"48@1\",\"303\":\"49\",\"304\":\"49#为什么使用-memento-模式\",\"305\":\"49#示例代码\",\"306\":\"49#运行结果\",\"307\":\"49#拓展思路的要点\",\"308\":\"49#两种接口和可见性\",\"309\":\"49#需要多少个-memento\",\"310\":\"49#memento-的有效期限是多久\",\"311\":\"49#划分-caretaker-和-originator-角色的意义\",\"312\":\"49#相关的设计模式\",\"313\":\"49@0\",\"314\":\"49@1\",\"315\":\"50\",\"316\":\"50#为什么使用观察者模式\",\"317\":\"50#示例代码\",\"318\":\"50#运行结果\",\"319\":\"50#拓展思路的要点\",\"320\":\"50#这里也出现了可替换性\",\"321\":\"50#observer-的顺序\",\"322\":\"50#当-observer-的行为会对被观察对象产生影响时\",\"323\":\"50#传递更新信息的方式\",\"324\":\"50#从观察变为通知\",\"325\":\"50#mvc-model-view-controller\",\"326\":\"50#相关的设计模式\",\"327\":\"50@0\",\"328\":\"50@1\",\"329\":\"51\",\"330\":\"51#为什么要使用-prototype-模式\",\"331\":\"51#示例代码\",\"332\":\"51#运行结果\",\"333\":\"51#相关设计模式\",\"334\":\"51@0\",\"335\":\"51@1\",\"336\":\"52\",\"337\":\"52#为什么使用代理模式\",\"338\":\"52#实例代码\",\"339\":\"52#运行结果\",\"340\":\"52#拓展思路的要点\",\"341\":\"52#使用代理人来提升处理速度\",\"342\":\"52#有必要划分代理人和本人吗\",\"343\":\"52#代理与委托\",\"344\":\"52#透明性\",\"345\":\"52#http-代理\",\"346\":\"52#各种-proxy-模式\",\"347\":\"52#相关的设计模式\",\"348\":\"52@0\",\"349\":\"52@1\",\"350\":\"53\",\"351\":\"53#为什么要使用-singleton-模式\",\"352\":\"53#总结\",\"353\":\"53#示例代码\",\"354\":\"53#运行结果\",\"355\":\"53#相关设计模式\",\"356\":\"53#多线程下\",\"357\":\"53#双重检查锁定示例代码\",\"358\":\"53@0\",\"359\":\"53@1\",\"360\":\"54\",\"361\":\"54#为什么使用-state-模式\",\"362\":\"54#示例代码\",\"363\":\"54#运行结果\",\"364\":\"54#拓展思路的要点\",\"365\":\"54#分而治之\",\"366\":\"54#依赖于状态的处理\",\"367\":\"54#应当是谁来管理状态的迁移\",\"368\":\"54#不会自相矛盾\",\"369\":\"54#易于增加新的状态\",\"370\":\"54#实例的多面性\",\"371\":\"54#相关的设计模式\",\"372\":\"54@0\",\"373\":\"54@1\",\"374\":\"55\",\"375\":\"55#使用此设计模式的理由\",\"376\":\"55#示例程序\",\"377\":\"55#运行结果\",\"378\":\"55#拓展思路的要点\",\"379\":\"55#为什么要特意编写-strategy\",\"380\":\"55#程序运行中也可以切换策略\",\"381\":\"55#相关的设计模式\",\"382\":\"55@0\",\"383\":\"55@1\",\"384\":\"56\",\"385\":\"56#为什么要使用-template-method-模式\",\"386\":\"56#示例代码\",\"387\":\"56#运行结果\",\"388\":\"56#相关设计模式\",\"389\":\"56#延申-类的层次与抽象类\",\"390\":\"56@0\",\"391\":\"56@1\",\"392\":\"57\",\"393\":\"57#为什么使用-visitor-模式\",\"394\":\"57#示例代码\",\"395\":\"57#运行结果\",\"396\":\"57#拓展思路的要点\",\"397\":\"57#双重分发\",\"398\":\"57#为什么要这么复杂\",\"399\":\"57#开闭原则——对扩展开放-对修改关闭\",\"400\":\"57#易于增加-concretevisitor-角色\",\"401\":\"57#难以增加-concreteelement-角色\",\"402\":\"57#visitor-工作所需的条件\",\"403\":\"57#相关的设计模式\",\"404\":\"57@0\",\"405\":\"57@1\",\"406\":\"58\",\"407\":\"58#为什么要学编译原理\",\"408\":\"58#理论很复杂-实现也很复杂\",\"409\":\"58#项目的初衷\",\"410\":\"58#做好心理准备\",\"411\":\"58#参考资料\",\"412\":\"58@0\",\"413\":\"58@1\",\"414\":\"59\",\"415\":\"59#编译器的构建流程\",\"416\":\"59#编译器框架\",\"417\":\"60\",\"418\":\"60#计算机的内部工作原理\",\"419\":\"60#内存\",\"420\":\"60#寄存器\",\"421\":\"60#指令集\",\"422\":\"60#mov\",\"423\":\"60#push\",\"424\":\"60#jmp\",\"425\":\"60#jz-jnz\",\"426\":\"60#子函数调用\",\"427\":\"60#ent\",\"428\":\"60#adj\",\"429\":\"60#lev\",\"430\":\"60#lea\",\"431\":\"60#运算符指令\",\"432\":\"60#内置函数\",\"433\":\"60#测试\",\"434\":\"60#小结\",\"435\":\"61\",\"436\":\"61#什么是词法分析器\",\"437\":\"61#词法分析器与编译器\",\"438\":\"61#词法分析器的实现\",\"439\":\"61#支持的标记\",\"440\":\"61#词法分析器的框架\",\"441\":\"61#换行符\",\"442\":\"61#宏定义\",\"443\":\"61#标识符与符号表\",\"444\":\"61#数字\",\"445\":\"61#字符串\",\"446\":\"61#注释\",\"447\":\"61#其它\",\"448\":\"61#关键字与内置函数\",\"449\":\"61#代码\",\"450\":\"61#小结\",\"451\":\"61@0\",\"452\":\"61@1\",\"453\":\"62\",\"454\":\"62#什么是递归下降\",\"455\":\"62#终结符与非终结符\",\"456\":\"62#四则运算的递归下降\",\"457\":\"62#为什么选择递归下降\",\"458\":\"62#左递归\",\"459\":\"62#四则运算的实现\",\"460\":\"62#小结\",\"461\":\"62@0\",\"462\":\"62@1\",\"463\":\"63\",\"464\":\"63#ebnf-表示\",\"465\":\"63#解析变量的定义\",\"466\":\"63#program\",\"467\":\"63#global-declaration\",\"468\":\"63#enum-declaration\",\"469\":\"63#其它\",\"470\":\"63#代码\",\"471\":\"63#小结\",\"472\":\"63@0\",\"473\":\"63@1\",\"474\":\"64\",\"475\":\"64#ebnf-表示\",\"476\":\"64#解析函数的定义\",\"477\":\"64#函数参数与汇编代码\",\"478\":\"64#函数定义的解析\",\"479\":\"64#解析参数\",\"480\":\"64#函数体的解析\",\"481\":\"64#代码\",\"482\":\"64#小结\",\"483\":\"64@0\",\"484\":\"64@1\",\"485\":\"65\",\"486\":\"65#语句\",\"487\":\"65#if-语句\",\"488\":\"65#while-语句\",\"489\":\"65#return-语句\",\"490\":\"65#其它语句\",\"491\":\"65#代码\",\"492\":\"65#小结\",\"493\":\"65@0\",\"494\":\"65@1\",\"495\":\"66\",\"496\":\"66#运算符的优先级\",\"497\":\"66#一元运算符\",\"498\":\"66#常量\",\"499\":\"66#sizeof\",\"500\":\"66#变量与函数调用\",\"501\":\"66#强制转换\",\"502\":\"66#指针取值\",\"503\":\"66#取址操作\",\"504\":\"66#逻辑取反\",\"505\":\"66#按位取反\",\"506\":\"66#正负号\",\"507\":\"66#自增自减\",\"508\":\"66#二元运算符\",\"509\":\"66#赋值操作\",\"510\":\"66#三目运算符\",\"511\":\"66#逻辑运算符\",\"512\":\"66#数学运算符\",\"513\":\"66#自增自减-1\",\"514\":\"66#数组取值操作\",\"515\":\"66#代码\",\"516\":\"66#小结\",\"517\":\"66@0\",\"518\":\"66@1\",\"519\":\"67\",\"520\":\"67#虚拟机与目标代码\",\"521\":\"67#词法分析\",\"522\":\"67#语法分析\",\"523\":\"67#关于编代码\",\"524\":\"67#结语\",\"525\":\"67@0\",\"526\":\"67@1\",\"527\":\"68\",\"528\":\"69\"},\"fieldIds\":{\"h\":0,\"t\":1,\"c\":2},\"fieldLength\":{\"0\":[1],\"1\":[1,5],\"2\":[1,3],\"3\":[1,16],\"4\":[1,8],\"5\":[1,6],\"6\":[1,24],\"7\":[1,2],\"8\":[1,10],\"9\":[1],\"10\":[1,24],\"11\":[1,11],\"12\":[1,12],\"13\":[1,2],\"14\":[1],\"15\":[1,8],\"16\":[1,14],\"17\":[1,2],\"18\":[1,35],\"19\":[1],\"20\":[6],\"21\":[9,21],\"22\":[2,49],\"23\":[2,12],\"24\":[null,null,2],\"25\":[null,null,2],\"26\":[9,20],\"27\":[1,7],\"28\":[1,24],\"29\":[1,5],\"30\":[1,95],\"31\":[1,37],\"32\":[1,12],\"33\":[1],\"34\":[1,15],\"35\":[1,29],\"36\":[1,49],\"37\":[1,6],\"38\":[3,4],\"39\":[1,19],\"40\":[null,null,1],\"41\":[null,null,1],\"42\":[1],\"43\":[4],\"44\":[2,34],\"45\":[1,5],\"46\":[1,23],\"47\":[3,6],\"48\":[2,7],\"49\":[2,4],\"50\":[1,5],\"51\":[2,25],\"52\":[2,63],\"53\":[4,6],\"54\":[1,14],\"55\":[1,5],\"56\":[2,21],\"57\":[2,32],\"58\":[1,51],\"59\":[null,null,1],\"60\":[null,null,1],\"61\":[3,14],\"62\":[null,null,1],\"63\":[null,null,1],\"64\":[2,15],\"65\":[1,32],\"66\":[2,41],\"67\":[2,27],\"68\":[4,9],\"69\":[1,23],\"70\":[1,2],\"71\":[1,12],\"72\":[1,35],\"73\":[1,38],\"74\":[1,5],\"75\":[1,27],\"76\":[1,17],\"77\":[1,19],\"78\":[1,2],\"79\":[1,10],\"80\":[1,5],\"81\":[1,18],\"82\":[1,9],\"83\":[1,10],\"84\":[1,17],\"85\":[1,7],\"86\":[1,2],\"87\":[1,12],\"88\":[1,37],\"89\":[1,38],\"90\":[1,5],\"91\":[1,29],\"92\":[1,17],\"93\":[1,17],\"94\":[1,42],\"95\":[2,18],\"96\":[1,7],\"97\":[1,15],\"98\":[3,13],\"99\":[3,4],\"100\":[3,4],\"101\":[3,5],\"102\":[3,5],\"103\":[3,4],\"104\":[null,null,1],\"105\":[null,null,1],\"106\":[1,4],\"107\":[1,2],\"108\":[1,34],\"109\":[2,8],\"110\":[null,null,1],\"111\":[9,21],\"112\":[1,100],\"113\":[1,71],\"114\":[1,179],\"115\":[1,41],\"116\":[1,3],\"117\":[1,1],\"118\":[1,8],\"119\":[1,29],\"120\":[1,10],\"121\":[null,null,1],\"122\":[null,null,1],\"123\":[1,2],\"124\":[1,45],\"125\":[1,5],\"126\":[4,8],\"127\":[1,12],\"128\":[1,19],\"129\":[1,7],\"130\":[1,14],\"131\":[1],\"132\":[1,8],\"133\":[1,10],\"134\":[1],\"135\":[1],\"136\":[1,5],\"137\":[1,11],\"138\":[1,7],\"139\":[1,11],\"140\":[1,13],\"141\":[1,5],\"142\":[1,8],\"143\":[1,12],\"144\":[1,25],\"145\":[2,7],\"146\":[1,9],\"147\":[1,22],\"148\":[1,22],\"149\":[null,null,1],\"150\":[null,null,2],\"151\":[1],\"152\":[1,14],\"153\":[1,133],\"154\":[1,15],\"155\":[1],\"156\":[1,27],\"157\":[1,26],\"158\":[1,6],\"159\":[null,null,1],\"160\":[null,null,3],\"161\":[1],\"162\":[1,7],\"163\":[1,7],\"164\":[1],\"165\":[1,11],\"166\":[1,45],\"167\":[1,11],\"168\":[1,2],\"169\":[null,null,1],\"170\":[null,null,2],\"171\":[2,7],\"172\":[1,7],\"173\":[1],\"174\":[1,15],\"175\":[1,30],\"176\":[1,23],\"177\":[1],\"178\":[1,50],\"179\":[2,28],\"180\":[2,20],\"181\":[2,9],\"182\":[2,21],\"183\":[2,36],\"184\":[1,18],\"185\":[1],\"186\":[1,44],\"187\":[2,29],\"188\":[1,6],\"189\":[null,null,1],\"190\":[null,null,3],\"191\":[2],\"192\":[3,17],\"193\":[1,83],\"194\":[1,42],\"195\":[1,7],\"196\":[1],\"197\":[1,20],\"198\":[1,9],\"199\":[1,41],\"200\":[null,null,1],\"201\":[null,null,3],\"202\":[2,26],\"203\":[1,12],\"204\":[1,94],\"205\":[1,39],\"206\":[1,3],\"207\":[null,null,1],\"208\":[null,null,3],\"209\":[2],\"210\":[1,6],\"211\":[1,56],\"212\":[1,24],\"213\":[1],\"214\":[1,23],\"215\":[1,23],\"216\":[1,4],\"217\":[null,null,1],\"218\":[null,null,3],\"219\":[2],\"220\":[1,15],\"221\":[1],\"222\":[4,39],\"223\":[4,26],\"224\":[4,29],\"225\":[4,49],\"226\":[1,46],\"227\":[1,4],\"228\":[null,null,1],\"229\":[null,null,3],\"230\":[2,5],\"231\":[2,9],\"232\":[1,62],\"233\":[1,20],\"234\":[1],\"235\":[2,55],\"236\":[1,42],\"237\":[1,7],\"238\":[1,23],\"239\":[1,3],\"240\":[1,3],\"241\":[1],\"242\":[1,9],\"243\":[1,7],\"244\":[null,null,1],\"245\":[null,null,3],\"246\":[1,37],\"247\":[null,null,1],\"248\":[null,null,2],\"249\":[2,23],\"250\":[1,8],\"251\":[1,89],\"252\":[1,41],\"253\":[1,5],\"254\":[null,null,1],\"255\":[null,null,3],\"256\":[3,8],\"257\":[3,21],\"258\":[1,50],\"259\":[1,20],\"260\":[null,null,1],\"261\":[null,null,4],\"262\":[2],\"263\":[3,10],\"264\":[1,74],\"265\":[1,21],\"266\":[1],\"267\":[1,66],\"268\":[3,44],\"269\":[1,54],\"270\":[1,25],\"271\":[1,4],\"272\":[null,null,1],\"273\":[null,null,3],\"274\":[1,20],\"275\":[null,null,1],\"276\":[null,null,2],\"277\":[2],\"278\":[1,17],\"279\":[1,117],\"280\":[1,22],\"281\":[null,null,1],\"282\":[null,null,3],\"283\":[1],\"284\":[1,25],\"285\":[2,8],\"286\":[1,63],\"287\":[1,45],\"288\":[1,9],\"289\":[1,5],\"290\":[null,null,1],\"291\":[null,null,2],\"292\":[2],\"293\":[1,26],\"294\":[1,118],\"295\":[1,28],\"296\":[1],\"297\":[1,43],\"298\":[1,38],\"299\":[1,26],\"300\":[1,3],\"301\":[null,null,1],\"302\":[null,null,3],\"303\":[2],\"304\":[3,8],\"305\":[1,96],\"306\":[1,29],\"307\":[1],\"308\":[1,22],\"309\":[2,14],\"310\":[2,13],\"311\":[5,32],\"312\":[1,4],\"313\":[null,null,1],\"314\":[null,null,3],\"315\":[2],\"316\":[1,11],\"317\":[1,77],\"318\":[1,33],\"319\":[1],\"320\":[1,12],\"321\":[2,32],\"322\":[3,11],\"323\":[1,9],\"324\":[1,9],\"325\":[5,18],\"326\":[1,2],\"327\":[null,null,1],\"328\":[null,null,3],\"329\":[2],\"330\":[3,14],\"331\":[1,71],\"332\":[1,15],\"333\":[1,6],\"334\":[null,null,1],\"335\":[null,null,3],\"336\":[2],\"337\":[1,22],\"338\":[1,82],\"339\":[1,20],\"340\":[1],\"341\":[1,11],\"342\":[1,11],\"343\":[1,7],\"344\":[1,6],\"345\":[2,9],\"346\":[3,25],\"347\":[1,3],\"348\":[null,null,1],\"349\":[null,null,3],\"350\":[2],\"351\":[3,10],\"352\":[2,6],\"353\":[1,39],\"354\":[1,19],\"355\":[1,5],\"356\":[1,14],\"357\":[1,44],\"358\":[null,null,1],\"359\":[null,null,3],\"360\":[2],\"361\":[3,8],\"362\":[1,79],\"363\":[1,49],\"364\":[1],\"365\":[1,44],\"366\":[1,49],\"367\":[1,88],\"368\":[1,21],\"369\":[1,50],\"370\":[1,54],\"371\":[1,3],\"372\":[null,null,1],\"373\":[null,null,3],\"374\":[2],\"375\":[1,16],\"376\":[1,121],\"377\":[1,26],\"378\":[1],\"379\":[2,28],\"380\":[1,26],\"381\":[1,5],\"382\":[null,null,1],\"383\":[null,null,4],\"384\":[3,10],\"385\":[5,10],\"386\":[1,59],\"387\":[1,22],\"388\":[1,4],\"389\":[2,25],\"390\":[null,null,1],\"391\":[null,null,3],\"392\":[2,13],\"393\":[4,11],\"394\":[1,103],\"395\":[1,46],\"396\":[1],\"397\":[1,24],\"398\":[1,33],\"399\":[3,35],\"400\":[3,10],\"401\":[3,25],\"402\":[2,32],\"403\":[1,4],\"404\":[null,null,1],\"405\":[null,null,3],\"406\":[5,46],\"407\":[1,28],\"408\":[3,56],\"409\":[1,40],\"410\":[1,14],\"411\":[1,45],\"412\":[null,null,1],\"413\":[null,null,3],\"414\":[5,55],\"415\":[1,27],\"416\":[1,130],\"417\":[1,71],\"418\":[1,9],\"419\":[1,125],\"420\":[1,58],\"421\":[1,58],\"422\":[1,119],\"423\":[1,24],\"424\":[1,27],\"425\":[2,24],\"426\":[1,127],\"427\":[1,35],\"428\":[1,25],\"429\":[1,36],\"430\":[1,62],\"431\":[1,51],\"432\":[1,68],\"433\":[1,63],\"434\":[1,35],\"435\":[5,54],\"436\":[1,35],\"437\":[1,26],\"438\":[1,18],\"439\":[1,86],\"440\":[1,42],\"441\":[1,12],\"442\":[1,28],\"443\":[1,135],\"444\":[1,61],\"445\":[1,63],\"446\":[1,61],\"447\":[1,56],\"448\":[1,81],\"449\":[1,24],\"450\":[1,18],\"451\":[null,null,1],\"452\":[null,null,3],\"453\":[5,47],\"454\":[1,11],\"455\":[1,33],\"456\":[1,37],\"457\":[1,37],\"458\":[1,23],\"459\":[1,70],\"460\":[1,16],\"461\":[null,null,1],\"462\":[null,null,3],\"463\":[5,55],\"464\":[2,44],\"465\":[1,7],\"466\":[2,20],\"467\":[3,130],\"468\":[3,51],\"469\":[1,25],\"470\":[1,22],\"471\":[1,13],\"472\":[null,null,1],\"473\":[null,null,3],\"474\":[5,51],\"475\":[2,21],\"476\":[1,37],\"477\":[1,56],\"478\":[1,67],\"479\":[1,77],\"480\":[1,93],\"481\":[1,24],\"482\":[1,18],\"483\":[null,null,1],\"484\":[null,null,3],\"485\":[5,49],\"486\":[1,28],\"487\":[2,62],\"488\":[2,32],\"489\":[2,22],\"490\":[1,21],\"491\":[1,21],\"492\":[1,16],\"493\":[null,null,1],\"494\":[null,null,3],\"495\":[5,76],\"496\":[1,95],\"497\":[1,15],\"498\":[1,60],\"499\":[1,45],\"500\":[1,151],\"501\":[1,36],\"502\":[1,42],\"503\":[1,47],\"504\":[1,28],\"505\":[1,31],\"506\":[1,33],\"507\":[1,62],\"508\":[1,76],\"509\":[1,57],\"510\":[1,39],\"511\":[1,33],\"512\":[1,101],\"513\":[1,39],\"514\":[1,50],\"515\":[1,60],\"516\":[1,17],\"517\":[null,null,1],\"518\":[null,null,3],\"519\":[5,46],\"520\":[1,18],\"521\":[1,13],\"522\":[1,32],\"523\":[1,24],\"524\":[1,3],\"525\":[null,null,1],\"526\":[null,null,3],\"527\":[1,3],\"528\":[3]},\"averageFieldLength\":[1.4892428194579765,27.855683113721682,0.6264536848314234],\"storedFields\":{\"0\":{\"h\":\"主页\"},\"1\":{\"h\":\"介绍页\",\"t\":[\"一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。\"]},\"2\":{\"h\":\"随笔\",\"t\":[\"这里是所有个人感想、生活记录等非技术类文章。\"]},\"3\":{\"h\":\"命里有时终须有\",\"t\":[\"alt text\",\"昨日在玩“三国杀：一将成名”时，我抽奖一发就中了大奖——“清河公主”传说皮。这让我不禁感慨：“命里有时终须有，命里无时莫强求。”这句话真是道出了人生的真谛，有些事情是强求不来的，顺其自然反而能得到意想不到的收获。\"]},\"4\":{\"h\":\"北京邮电大学创新创业智能车循迹python版\",\"t\":[\"项目源码\",\"因为想要创新学分，所以选了创新创业智能车课程，项目要求完成智能车的循迹和避障。\",\"由于笔者不喜欢使用VPL的图形化（报用qWq）, 故而使用手写代码的方式实现。\"]},\"5\":{\"h\":\"主要思路\",\"t\":[\"通过接发TCP包的方法与智能车进行交互， 创建两个并行任务，一个用于实时接收TCP报文来更新小车状态， 一个用于读取小车状态，作出决策并发送报文控制小车。\"]},\"6\":{\"h\":\"编程语言的选择\",\"t\":[\"python 笔者的项目采用了该语言，主要原因是方便且能快速实现（以及没考虑到GIL会影响介么大），并采用asyncio作为“并行”库（实际上只能并发，笔者最初以为只有两个任务，用python也足够了，虽然实际上也够，但是写起来没那么舒服了，可能使用threads会好一点）\",\"go 后续又采用go重构了一遍（虽然实际效果貌似变化不大，emmm...应该是硬件/小车的原因）\",\"当然采用什么编程语言并不是重要（吗？，不许用rust 😠 ）\"]},\"7\":{\"h\":\"通信协议\",\"t\":[\"alt text\"]},\"8\":{\"h\":\"初步思路\",\"t\":[\"由于硬件限制，只有一个红外传感器用于判断底部是否为黑色， 一个红外传感器+超声波传感器用于确定前方是否有障碍，信息量非常小（当然超声波传感器有大概的距离，本项目不考虑介么多，取较小距离为有障碍）， 为 。 故而首先考虑的基本策略是偏航时左右摆头寻找正确的角度前行。\"]},\"9\":{\"h\":\"遇到的问题和改进方案\"},\"10\":{\"h\":\"小车左右轮力矩不一致\",\"t\":[\"由于硬件限制，若设置两个轮的速度一致的话小车直行也会偏转， 而且小车并不能知道自己“偏航”了，故而采取手动测试的方式， 通过二分左右轮的速度来得到使得小车直行的左右轮速度。并且这个关系并非简单的倍速或差量的关系。\",\"因此无奈之下只能选取一个固定的速度来测试（比如左轮设置为0.8, 然后不断二分得到直行时右轮的速度为 0.x ）, 整个系统都在该速度下运行。\",\"提示\",\"各个小车有各个的体质， 因此挑选一辆\\\"正确\\\"的小车是很重要的事情。 以及测试完小车后保护小车也是很重要的，不要找不到了或者被人踢坏了， 否则得重新找车及测速。\"]},\"11\":{\"h\":\"小车容易冲出轨道\",\"t\":[\"小车还未找到合适的“姿势”就前进，导致频繁冲出赛道，耗费时间。\",\"基于此，采取速度渐进增长的形式，使得刚回到正确姿势时速度较慢，从而不会前进太多，便于更快的回到正确的姿势。\"]},\"12\":{\"h\":\"小车总是左右左摆头太蠢了\",\"t\":[\"首先采取的改进方案是先左小幅度转弯，后右大幅度转弯，最后左大幅度转弯寻找正确姿势，但效果不理想，遂放弃。\",\"考虑到小车路线是闭合的，且局部多为凸多边形， 故而每次转弯时优先考虑上一次转弯的方向， 这样子能减少摆头次数， 多数情况转弯的方向都是对的。（有一些启发式的smell）\"]},\"13\":{\"h\":\"其它问题\",\"t\":[\"时间有点久搞忘了，记起来再补充\"]},\"14\":{\"h\":\"设计方案参考\"},\"15\":{\"h\":\"和机械臂联动\",\"t\":[\"emm... 本来想让机械臂识别“货物”并放在车上托运并最后卸货的，但是小车不好运货。遂放弃，转而实验机械臂放置障碍在赛道上。\"]},\"16\":{\"h\":\"结语\",\"t\":[\"本次智能车实验不是很愉快， 特别是重调了3，4次速度（几次换车其中一次车被踩烂了）\",\"如果没有熟悉的编程语言（例如c）且不了解 多线程/协程，网络I/O的话 还是采用VPL图形化吧 不过我认为报用就是了。\",\"记得给我的仓库点Star欧~\"]},\"17\":{\"h\":\"项目\",\"t\":[\"这里是你参与或开发的项目介绍和进展。\"]},\"18\":{\"h\":\"资源\",\"t\":[\"这里是推荐的书籍、网站、工具等资源。\",\"github - 世界上最大的代码托管平台\",\"Z-Library – 世界上最大的电子图书馆。自由访问知识和文化。\",\"Vuepress - 我的博客构建库\",\"plantUML - 一个通用性很强的工具，可以快速、直接地创建各种图表\",\"emoji-cheat-sheet - A markdown version emoji cheat sheet\",\"Sci-hub —— 当今科学界最具争议性的项目。Sci-hub的目标是 免费并且不受限制地 提供所有科学知识。\",\"Lib.Genesis —— Part of Library Genesis. ex libgen.io, libgen.org\"]},\"19\":{\"h\":\"Qt\"},\"20\":{\"h\":\"Some Solutions to Questions about Qt\"},\"21\":{\"h\":\"The qt-5 isn't in Qt Maintenance tools\",\"t\":[\"Open the Qt Maintenance Tools.\",\"click the Archive in the Select-Component section.\",\"click the filter button and you can see the qt-5 in the list.\"]},\"22\":{\"h\":\"android studio换源\",\"t\":[\"国内镜像\",\"Android Studio下载gradle太慢可换源\",\"android.plugin version 下载错误查看\",\"修改 settings.gradle.kts\",\"pluginManagement { repositories { maven { url=uri (\\\"https://jitpack.io\\\") } maven { url=uri (\\\"https://maven.aliyun.com/repository/releases\\\") } // maven { url 'https://maven.aliyun.com/repository/jcenter' } maven { url=uri (\\\"https://maven.aliyun.com/repository/google\\\") } maven { url=uri (\\\"https://maven.aliyun.com/repository/central\\\") } maven { url=uri (\\\"https://maven.aliyun.com/repository/gradle-plugin\\\") } maven { url=uri (\\\"https://maven.aliyun.com/repository/public\\\") } google() mavenCentral() gradlePluginPortal() } } dependencyResolutionManagement { repositoriesMode.set(RepositoriesMode.FAIL_ON_PROJECT_REPOS) repositories { maven { url=uri (\\\"https://jitpack.io\\\") } maven { url=uri (\\\"https://maven.aliyun.com/repository/releases\\\") } // maven { url 'https://maven.aliyun.com/repository/jcenter' } maven { url=uri (\\\"https://maven.aliyun.com/repository/google\\\") } maven { url=uri (\\\"https://maven.aliyun.com/repository/central\\\") } maven { url=uri (\\\"https://maven.aliyun.com/repository/gradle-plugin\\\") } maven { url=uri (\\\"https://maven.aliyun.com/repository/public\\\") } google() mavenCentral() } } \",\"gradle-wrapper.properties 换成对应的版本\",\"distributionUrl=https\\\\://mirrors.cloud.tencent.com/gradle/gradle-8.7-all.zip \"]},\"23\":{\"h\":\"CI/CD\",\"t\":[\"本地调试工具 act\",\"需要创建配置文件\",\"也可另外指定\",\"act --var-file \\\"./.act/.vars\\\" --secret-file \\\"./.act/.secrets\\\" --env-file \\\"./.act/.env\\\" {{other}} \"]},\"24\":{\"c\":[\"CI/CD\"]},\"25\":{\"c\":[\"CI/CD\"]},\"26\":{\"h\":\"docker + nginx + acme.sh 部署 vue/flask 项目\",\"t\":[\"本文将介绍如何使用 Docker、Nginx 和 acme.sh 部署一个 Vue 和 Flask 项目。我们将详细讲解环境配置、项目结构、Nginx 配置、Docker 配置以及如何升级到 HTTPS。\",\"提示\",\"需要先申请一个域名，本文是 bupt.online\"]},\"27\":{\"h\":\"环境\",\"t\":[\"Ubuntu\",\"Docker\",\"Docker-Compose\",\"acme.sh\",\"(python)\",\"nginx\"]},\"28\":{\"h\":\"项目结构\",\"t\":[\"./nginx ├── acme # 存放SSL证书 ├── conf.d │ ├── Automaton.conf │ ├── blog.conf ├── docker-compose.yml ├── DockerFile ├── logs # 存放日志 │ ├── access.log │ ├── Automaton │ ├── blog │ └── error.log ├── nginx.conf ./project # 要部署的（前端）项目 ├── Automaton └── blog \"]},\"29\":{\"h\":\"配置http服务\",\"t\":[\"在准备好前端项目及安装相应环境后，进行如下操作(部分路径以实际为准，进行修改)\"]},\"30\":{\"h\":\"配置nginx\",\"t\":[\"nginx.conf\",\"user nginx; worker_processes 1; error_log /var/log/nginx/error.log warn; pid /var/run/nginx.pid; events { worker_connections 4096; } http { include /etc/nginx/mime.types; default_type application/octet-stream; log_format main '$remote_addr - $remote_user [$time_local] \\\"$request\\\" ' '$status $body_bytes_sent \\\"$http_referer\\\" ' '\\\"$http_user_agent\\\" \\\"$http_x_forwarded_for\\\"'; # access_log /var/log/nginx/access.log main; access_log off; error_log /var/log/nginx/error.log warn; sendfile on; #tcp_nopush on; keepalive_timeout 65; # 定义DNS解析器 resolver 8.8.8.8 114.114.114.114 valid=300s; resolver_timeout 10s; # 增加请求头和Cookie的大小限制 client_header_buffer_size 16k; large_client_header_buffers 4 32k; include /etc/nginx/conf.d/*.conf; } \",\"Automaton.conf\",\"server { listen 80; server_name Automaton.bupt.online; location / { root /usr/share/nginx/html/Automaton; try_files $uri $uri/ =404; } access_log /var/log/nginx/Automaton/access.log; error_log /var/log/nginx/Automaton/error.log warn; } \",\"blog.conf\",\"server { listen 80; server_name bupt.online www.bupt.online; location / { root /usr/share/nginx/html/blog; try_files $uri $uri/ =404; # access_log /var/log/nginx/blog/access.log; error_log /var/log/nginx/blog/error.log warn; } location /Automaton { # 使用 proxy_pass 或 rewrite 重定向到Automaton.bupt.online 失败 alias /usr/share/nginx/html/Automaton/; try_files $uri $uri/ =404; # access_log /var/log/nginx/Automaton/access.log; error_log /var/log/nginx/Automaton/error.log warn; } } \"]},\"31\":{\"h\":\"配置docker\",\"t\":[\"DockerFile\",\"FROM nginx:latest COPY nginx.conf /etc/nginx/nginx.conf COPY conf.d /etc/nginx/conf.d \",\"docker-compose.yml\",\"services: nginx: build: context: . dockerfile: DockerFile ports: - \\\"80:80\\\" - \\\"443:443\\\" volumes: - ../project/blog:/usr/share/nginx/html/blog - ../project/Automaton:/usr/share/nginx/html/Automaton - ./logs:/var/log/nginx - ./conf.d:/etc/nginx/conf.d - ./acme:/etc/letsencrypt/live networks: - webnet environment: - TZ=Asia/Shanghai networks: webnet: \"]},\"32\":{\"h\":\"启动项目\",\"t\":[\"docker-compose up -d --build \",\"然后就能正常访问 http://bupt.online 及 http://automaton.bupt.online ， http://bupt.online/Automaton\"]},\"33\":{\"h\":\"升级为https\"},\"34\":{\"h\":\"申请证书\",\"t\":[\"进入acme.sh的安装目录(/root/.acme.sh)\",\"sudo su root acme.sh --issue -d bupt.online --nginx # Nginx acme.sh --issue -d Automaton.bupt.online --nginx # Nginx \"]},\"35\":{\"h\":\"安装证书\",\"t\":[\"这里将目录修改为目标目录\",\"# sudo su root # cd .acme.sh # use like below acme.sh --install-cert -d bupt.online \\\\ --cert-file /home/ubuntu/nginx/acme/bupt.online/cert.cer \\\\ --key-file /home/ubuntu/nginx/acme/bupt.online/privkey.key \\\\ --fullchain-file /home/ubuntu/nginx/acme/bupt.online/fullchain.cer \\\\ --reloadcmd \\\"cd /home/ubuntu/nginx && docker-compose up -d --build\\\" \"]},\"36\":{\"h\":\"修改配置\",\"t\":[\"blog.conf\",\"server { listen 80; server_name bupt.online www.bupt.online; return 301 https://$host$request_uri; } server { listen 443 ssl; server_name bupt.online; ssl_certificate /etc/letsencrypt/live/bupt.online/fullchain.cer; ssl_certificate_key /etc/letsencrypt/live/bupt.online/privkey.key; location / { root /usr/share/nginx/html/blog; try_files $uri $uri/ =404; # access_log /var/log/nginx/blog/access.log; error_log /var/log/nginx/blog/error.log warn; } location /Automaton { # 使用 proxy_pass 或 rewrite 重定向到Automaton.bupt.online 失败 alias /usr/share/nginx/html/Automaton/; try_files $uri $uri/ =404; # access_log /var/log/nginx/Automaton/access.log; error_log /var/log/nginx/Automaton/error.log warn; } } server { listen 443 ssl; server_name www.bupt.online; ssl_certificate /etc/letsencrypt/live/www.bupt.online/fullchain.cer; ssl_certificate_key /etc/letsencrypt/live/www.bupt.online/privkey.key; location / { root /usr/share/nginx/html/blog; try_files $uri $uri/ =404; # access_log /var/log/nginx/blog/access.log; error_log /var/log/nginx/blog/error.log warn; } location /Automaton { # 使用 proxy_pass 或 rewrite 重定向到Automaton.bupt.online 失败 alias /usr/share/nginx/html/Automaton/; try_files $uri $uri/ =404; # access_log /var/log/nginx/Automaton/access.log; error_log /var/log/nginx/Automaton/error.log warn; } } \",\"Automaton.conf\",\"server { listen 80; server_name Automaton.bupt.online; location / { return 301 https://$host$request_uri; } } server { listen 443 ssl; server_name Automaton.bupt.online; ssl_certificate /etc/letsencrypt/live/Automaton.bupt.online/fullchain.cer; ssl_certificate_key /etc/letsencrypt/live/Automaton.bupt.online/privkey.key; location / { root /usr/share/nginx/html/Automaton; try_files $uri $uri/ =404; } access_log /var/log/nginx/Automaton/access.log; error_log /var/log/nginx/Automaton/error.log warn; } \"]},\"37\":{\"h\":\"重启container\",\"t\":[\"docker-compose up -d --build \"]},\"38\":{\"h\":\"配置nginx反向代理，使flask支持 https\",\"t\":[\"Flask 部署\",\"#TODO - 添加flask+nginx配置\"]},\"39\":{\"h\":\"参考资料\",\"t\":[\"Nginx Documentation\",\"Flask Documentation\",\"Reverse Proxy Guide\",\"SSL Certificates\",\"用acme.sh帮你免费且自动更新的HTTPS证书，省时又省力\",\"docker部署certbot与nginx来获取ssl证书添加https及自动更新\",\"使用docker acme申请、续订泛域名证书，并自动重载docker nginx\",\"Flask: 如何给Python Flask Web服务器添加HTTPS功能\"]},\"40\":{\"c\":[\"nginx\"]},\"41\":{\"c\":[\"部署\"]},\"42\":{\"h\":\"\"},\"43\":{\"h\":\"GitHub Container Registry 加速\"},\"44\":{\"h\":\"ghcr.io简介\",\"t\":[\"ghcr.io 是 GitHub Container Registry 的域名。GitHub Container Registry 是 GitHub 提供的容器镜像注册表服务，允许开发者在 GitHub 上存储、管理和分享 Docker 镜像。它与 GitHub 代码仓库紧密集成，可以使用相同的权限管理、团队协作和版本控制工具来管理容器镜像。\",\"通过 GitHub Container Registry，开发者可以方便地将他们的容器镜像与代码仓库关联起来，这样就可以在同一个平台上管理代码和镜像。这种集成性使得持续集成/持续交付 (CI/CD) 流程更加简化和统一，开发团队可以更容易地构建、测试和部署应用程序。\",\"对于使用 GitHub 作为代码托管平台的开发者来说，GitHub Container Registry 提供一个便捷且强大的容器镜像管理解决方案。通过该服务，可以更轻松地构建和部署容器化的应用程序，从而加速开发和交付周期。\"]},\"45\":{\"h\":\"镜像地址\",\"t\":[\"https://ghcr.nju.edu.cn\"]},\"46\":{\"h\":\"配置方法\",\"t\":[\"sudo vim /etc/docker/daemon.json \",\"{ \\\"registry-mirrors\\\": [\\\"https://ghcr.nju.edu.cn\\\"] } \",\":wq保存退出\",\"sudo systemctl daemon-reload sudo systemctl restart docker \",\"拉取镜像方法\",\"docker pull ghcr.nju.edu.cn/open-webui/open-webui:main \"]},\"47\":{\"h\":\"docker wsl2 容器目录\",\"t\":[\"\\\\\\\\wsl$\\\\docker-desktop-data\\\\data\\\\docker\\\\containers \"]},\"48\":{\"h\":\"github 图床\",\"t\":[\"参考\",\"https://zhuanlan.zhihu.com/p/347342082\"]},\"49\":{\"h\":\"github 工作流程\",\"t\":[\"十分钟学会正确的github工作流，和开源作者们使用同一套流程\",\"相关信息\",\"TODO\"]},\"50\":{\"h\":\"技术\",\"t\":[\"这里是所有与技术相关的文章，包括编程、工具使用、技术分享等内容。\"]},\"51\":{\"h\":\"自建mail server\",\"t\":[\"参见:\",\"https://docker-mailserver.github.io/docker-mailserver/latest/\",\"https://blog.csdn.net/qq_25866579/article/details/140717115\",\"https://zhuanlan.zhihu.com/p/609639797\",\"值得注意的是docker-mailserver 并不支持通过ui注册/修改等操作， 当可以自行实现（后端通过shell命令即可\"]},\"52\":{\"h\":\"使用python 发送示例\",\"t\":[\"import smtplib from email.mime.text import MIMEText from email.mime.multipart import MIMEMultipart from email.utils import formatdate # Email configuration smtp_server = 'mail.bupt.online' smtp_port = 587 username = 'test@bupt.online' password = '12345678' from_email = 'test@bupt.online' to_email = 'ksj@bupt.online' subject = 'Test Email' body = 'This is a test email sent from Python.' # Create the email msg = MIMEMultipart() msg['From'] = from_email msg['To'] = to_email msg['Subject'] = subject msg['Date'] = formatdate(localtime=True) msg.attach(MIMEText(body, 'plain')) # Send the email try: server = smtplib.SMTP(smtp_server, smtp_port) server.starttls() server.login(username, password) server.sendmail(from_email, to_email, msg.as_string()) server.quit() print(\\\"Email sent successfully\\\") except Exception as e: print(f\\\"Failed to send email: {e}\\\") \",\"alt text\"]},\"53\":{\"h\":\"「泛型与 OI」modint\",\"t\":[\"在 OI 中，有大量的题目要求对一些数字取模，这便是本文写作的背景。\"]},\"54\":{\"h\":\"背景介绍\",\"t\":[\"这些题目要么是因为答案太大，不方便输出结果，例如许多计数 dp；要么是因为答案是浮点数，出题人不愿意写一个确定精度的 Special Judge，例如很多期望概率题；要么是因为这道题目直接考察了模的性质和运用，比如大量的 998244353 类的多项式题目。\"]},\"55\":{\"h\":\"过去的做法\",\"t\":[\"在这种要求之下，取模运算就成为了编程中不可缺少的一部分。下面以式子 为例介绍几种写法。\"]},\"56\":{\"h\":\"第一种 直接取模\",\"t\":[\"这种方法是直接取模，简单直接，清晰明了。\",\"constexpr int p=998244353; int ans=1ll*(((x+y)%p+z)%p)*u%p; \",\"但是这种方法有着严重的缺陷，一是容易忘记大括号，二是容易中间运算时搞错运算顺序、忘记取模，三是式子太长、括号太多、不易检验。\",\"因此，不推荐运用这种方法。\"]},\"57\":{\"h\":\"第二种 函数取模\",\"t\":[\"这种方法有效地解决了直接取模的忘记取模的漏洞。\",\"constexpr int p=998244353; int add(int a,int b){ return a+b>=p?a+b-p:a+b; } int sub(int a,int b){ return a<b?a-b+p:a-b; } int mul(int a,int b){ return 1ll*a*b%p; } int ans=mul(add(add(x,y),z),u); \",\"但是，这种写法的式子依旧太长，不易检验，并且如果编译器没有任何优化（现在不存在这种情况了）的话，大量的函数调用将会耗费不少的时间。并且如果要对多个模数取模，则需要写多个函数，显得代码冗长。\"]},\"58\":{\"h\":\"泛型编程\",\"t\":[\"考虑到函数取模的优点，我们不妨通过类的运算符重载来进一步优化 add 等函数。\",\"同时为了解决多个模数的问题，我们考虑泛型编程，将模数直接包含在类型中。\",\"template<typename T,const T p> class modint{ private: T v; public: modint(){} modint(const T& x){assert(0<=x&&x<p);v=x;} modint operator+(const modint& a)const{ return v+a.v>=p?v+a.v-p:v+a.v; } modint operator-(const modint& a)const{ return v<a.v?v-a.v+p:v-a.v; } modint operator*(const modint& a)const{ return 1ll*v*a.v%p; } T operator()(void)const{ return v; } }; modint<int,998244353> x(),y(),z(),u(); modint<int,998244353> ans=(x+y+z)*u; \",\"这样使用的时候，一方面减少了心智负担，不用操心运算时忘记取模；另一方面采取了常数更小的加减法操作，运算更快。\",\"唯一的缺点就是类型名难写，但是模数个数少的时候可以缩写，即写成：\",\"typedef modint<int,998244353> modInt1; \",\"这样就解决了类型名长的缺点。\"]},\"59\":{\"c\":[\"OI\"]},\"60\":{\"c\":[\"MODInt\"]},\"61\":{\"h\":\"python requirements.txt\",\"t\":[\"Python 生成 requirements有两种方式\",\"pip list --format=freeze > requirements.txt (推荐做法)\",\"pip freeze > requirements.txt (不推荐，会带有本地路径)\"]},\"62\":{\"c\":[\"python\"]},\"63\":{\"c\":[\"踩坑记录\"]},\"64\":{\"h\":\"Game Plugin\",\"t\":[\"This is the content of the game plugin post.\",\"BepInEx\",\"AssetStudioAssetStudio\",\"dnSpy\",\"Harmony\",\"UnityExplorer\",\"相关信息\",\"TODO\"]},\"65\":{\"h\":\"风格统一\",\"t\":[\"如何实现风格统一？ 可以使用*.editorconfig*文件来实现风格统一。\",\"安装EditorConfig插件 (部分IDE默认直接支持)\",\"在项目根目录下创建.editorconfig文件，并添加以下内容：\",\"root = true [*] indent_style = space tab_width = 2 end_of_line = lf charset = utf-8 trim_trailing_whitespace = true insert_final_newline = true \"]},\"66\":{\"h\":\"tensorflow 踩坑记录\",\"t\":[\"Pytorch 用于快速原型验证（学术研究）， TensorFlow 用于工业生产部署\",\"近日使用 TensorFlow 完成图像去噪任务，然而速度太慢，于是寻求 GPU 资源进行加速。本以为 TensorFlow 2 能轻松使用 GPU（当然需要配置相关驱动），谁知 TensorFlow 高版本（>=2.10.0）不再支持 Windows，而 Pytorch 仍然支持。最终 选择了 Pytorch 进行实验 寻得了Linux GPU 环境（感谢lucky&agicy）。\",\"此外，Pytorch 的动态计算图机制使得调试和开发更加灵活，适合快速迭代和原型验证。而 TensorFlow 虽然在工业部署中表现出色，但其静态计算图机制在开发过程中略显繁琐。综合考虑，决定以后在学术研究和快速原型验证阶段使用 Pytorch，而在工业生产部署阶段方才使用 TensorFlow（当然得是Linux环境）。\"]},\"67\":{\"h\":\"vscode plugin\",\"t\":[\"// TODO https://code.visualstudio.com/api/get-started/your-first-extension\",\"若activate function执行时间过长，会导致Activating extension 'undefined_publisher.kcodetime' failed: AggregateError., 从而启动失败\",\"若deactivate function执行时间超过5s, 会被强行终止，导致插件无法正常退出。\",\"关闭vscode 不会触发onDidCloseTextDocument事件\"]},\"68\":{\"h\":\"「算术公理系统 1」自然数\",\"t\":[\"假设存在一个算数系统的模型满足 Peano 公理，即假定 Peano 公理相容，在此承认次假设的基础之上，我们即可建立如今最常用的算术公理系统。自然数的定义则是构建此算术公理系统的第一步。\"]},\"69\":{\"h\":\"自然数的定义\",\"t\":[\"先介绍 Peano 公理，共有五条：\",\" 是自然数；\",\"任何自然数的后继存在且唯一，下文用 表示 的后继；\",\" 不是任何自然数的后继；\",\"不同的自然数后继不同；\",\" 是关于自然数 的一个命题，且满足两个条件：\",\" 是真命题；\",\"由 为真命题可以推理出 为真命题。\",\"则有，对于任意自然数 ， 为真命题。\",\"这样就定义了自然数，自然数这个新的数学对象因我们的假设而确立。\"]},\"70\":{\"h\":\"自然数的加法运算\",\"t\":[\"自然数中最重要的运算当然是加法。\"]},\"71\":{\"h\":\"加法的定义\",\"t\":[\"定义加法的运算规则：\",\"若 是自然数，则 的运算结果为 ，即 ；\",\"若 都是自然数，则 。\",\"下面我们需要证明对于任意两个自然数，都可以进行加法运算，也就是说，我们需要证明加法结果的存在性和唯一性。\"]},\"72\":{\"h\":\"加法结果的存在性\",\"t\":[\" 是任意自然数，记 表示 是否是自然数，即 是否存在。\",\" 是自然数，由加法运算规则 Ⅰ 有 ，进而有 是自然数； 即 得证。\",\" 和 是自然数，由 Peano 公理 Ⅱ 有 和 是自然数； 根据加法运算规则 Ⅱ 有 ，进有 是自然数； 综上所述，若 是自然数，则 也是自然数； 即由 为真命题可以推出 为真命题。\",\"由 的性质和 Peano 公理 Ⅴ 有，对于任意自然数 ， 成立，即 是自然数，再根据 的任意性，得出对于任意自然数 ， 都是自然数。\"]},\"73\":{\"h\":\"加法结果的唯一性\",\"t\":[\" 是任意自然数，记 表示 是否唯一，即 的结果是否唯一。\",\" 是自然数，由加法运算规则 Ⅰ 有 ，进而 是唯一的，就是 ； 即 得证。\",\" 是自然数， 是唯一的，由 Peano 公理 Ⅱ 有 是自然数且 唯一； 根据加法运算规则 Ⅱ 有 ，进有 唯一； 综上所述，若 唯一，则 也唯一； 即由 为真命题可以推出 为真命题。\",\"由 的性质和 Peano 公理 Ⅴ 有，对于任意自然数 ， 成立，即 唯一，再根据 的任意性，得出对于任意自然数 ， 都是唯一的。\"]},\"74\":{\"h\":\"加法的性质\",\"t\":[\"在明确证明了自然数加法运算的良好性质，即任意两个自然数都可以进行加法运算，且加法运算的结果存在且唯一之后，我们终于可以对自然数加法的性质进行进一步的探索。\"]},\"75\":{\"h\":\"加法交换律\",\"t\":[\"下面证明加法交换律，即对于任意自然数 ，有 。\",\"直接证明比较困难，考虑从加法运算的定义下手，即先证明加法的两条运算规则符合交换律。\",\"试证 ，首先有\",\"进而当 是自然数且 时有\",\"根据 Peano 公理 Ⅴ，得知 对任意自然数 成立。\",\"试证 ，首先有\",\"进而当 是自然数且 时有\",\"根据 Peano 公理 Ⅴ，得知 对任意自然数 成立，将其称为新的加法运算规则 Ⅱ。\",\"证明了加法运算规则的交换律之后，试证加法交换律 ，首先由加法运算规则 Ⅰ 有 ，进而当 是自然数且 时，有\",\"根据 Peano 公理 Ⅴ，得知 对任意自然数 成立，即加法交换律成立。\"]},\"76\":{\"h\":\"加法结合律\",\"t\":[\"下面证明加法结合律，即对于任意自然数 ，有 。\",\"首先当 时，有\",\"进而当 为自然数且 时有\",\"根据 Peano 公理 Ⅴ，得知 对任意自然数 成立，即加法结合律成立。\"]},\"77\":{\"h\":\"加法消去律\",\"t\":[\"下面证明加法消去律，即对于任意自然数 ，有 。\",\"试证 。\",\"首先当 时有\",\"进而当 为自然数且 时有\",\"即 ，根据 Peano 公理 Ⅴ，得知 对任意自然数 成立。\",\"试证 。\",\"首先当 时有\",\"进而当 为自然数且 时有\",\"即 ，根据 Peano 公理 Ⅴ，得知 对任意自然数 成立。\",\"综上所述，加法消去律 ，对任意自然数 成立。\"]},\"78\":{\"h\":\"自然数的序\",\"t\":[\"自然数的序为两个自然数的关系。\"]},\"79\":{\"h\":\"序的定义\",\"t\":[\"定义自然数的序即定义 当且仅当存在自然数 满足 。定义 当且仅当 且 。\",\"自然数的序是全序关系，它应该具有反对称性、传递性和完全性。\"]},\"80\":{\"h\":\"正自然数\",\"t\":[\"在考察序的性质之前，我们预先准备以方便证明。\",\"定义正自然数为非 自然数。\"]},\"81\":{\"h\":\"正自然数的性质\",\"t\":[\"正自然数与自然数相加为正自然数，即对于正自然数 ，其与自然数 的和 为正自然数。\",\"首先，当 时， 为正自然数。\",\"进而当 为自然数且 为正自然数时有 ，根据 Peano 公理 Ⅲ， 为正自然数，进而 为正自然数。\",\"根据 Peano 公理 Ⅴ，正自然数与自然数相加为正自然数。\"]},\"82\":{\"h\":\"序的反对称性\",\"t\":[\"若 且 ，则 。\",\"由 有 ，由 有 。\",\"因此 ，由加法消去律得到 ，根据正自然数的性质得出 ，因此 。\"]},\"83\":{\"h\":\"序的传递性\",\"t\":[\"若 且 ，则 。\",\"由 有 ，由 有 。\",\"根据加法结果的存在性得到 是自然数，根据加法结合律得出 ，进而 。\"]},\"84\":{\"h\":\"序的完全性\",\"t\":[\"任意两个自然数 都有序关系。\",\"对于 两个自然数，当 时有 所以 。\",\"当 为自然数时。若 ，则 ，因此 ；若 ，则 ，因此 ；若 ，则 。\",\"由 Peano 公理 Ⅴ 有任意两个自然数 都有序关系。\"]},\"85\":{\"h\":\"加法保序性\",\"t\":[\"若 ，则 。\",\"由 有 ，进而 因此 。\"]},\"86\":{\"h\":\"自然数的乘法运算\",\"t\":[\"自然数的乘法也十分重要。\"]},\"87\":{\"h\":\"乘法的定义\",\"t\":[\"定义乘法的运算规则：\",\"若 是自然数，则 的运算结果为 ，即 ；\",\"若 都是自然数，则 。\",\"下面我们需要证明对于任意两个自然数，都可以进行乘法运算，也就是说，我们需要证明乘法结果的存在性和唯一性。\"]},\"88\":{\"h\":\"乘法结果的存在性\",\"t\":[\" 是任意自然数，记 表示 是否是自然数，即 是否存在。\",\" 是自然数，由乘法运算规则 Ⅰ 有 ，进而有 是自然数； 即 得证。\",\" 和 是自然数，由加法结果的存在性有 存在； 根据乘法运算规则 Ⅱ 有 ，进有 是自然数； 综上所述，若 是自然数，则 也是自然数； 即由 为真命题可以推出 为真命题。\",\"由 的性质和 Peano 公理 Ⅴ 有，对于任意自然数 ， 成立，即 是自然数，再根据 的任意性，得出对于任意自然数 ， 都是自然数。\"]},\"89\":{\"h\":\"乘法结果的唯一性\",\"t\":[\" 是任意自然数，记 表示 是否唯一，即 的结果是否唯一。\",\" 是自然数，由乘法运算规则 Ⅰ 有 ，进而 是唯一的，就是 ； 即 得证。\",\" 是自然数， 是唯一的，由加法结果的唯一性有 唯一； 根据乘法运算规则 Ⅱ 有 ，进有 唯一； 综上所述，若 唯一，则 也唯一； 即由 为真命题可以推出 为真命题。\",\"由 的性质和 Peano 公理 Ⅴ 有，对于任意自然数 ， 成立，即 唯一，再根据 的任意性，得出对于任意自然数 ， 都是唯一的。\"]},\"90\":{\"h\":\"乘法的性质\",\"t\":[\"在明确证明了自然数乘法运算的良好性质，即任意两个自然数都可以进行乘法运算，且乘法运算的结果存在且唯一之后，我们终于可以对自然数乘法的性质进行进一步的探索。\"]},\"91\":{\"h\":\"乘法交换律\",\"t\":[\"下面证明乘法交换律，即对于任意自然数 ，有 。\",\"直接证明比较困难，考虑从乘法运算的定义下手，即先证明乘法的两条运算规则符合交换律。\",\"试证 。\",\"首先有 。\",\"进而当 是自然数且 时有\",\"根据 Peano 公理 Ⅴ，得知 对任意自然数 成立。\",\"试证 。\",\"首先 时有\",\"进而当 是自然数且 时有\",\"根据 Peano 公理 Ⅴ，得知 对任意自然数 成立，将其称为新的乘法运算规则 Ⅱ。\",\"证明了乘法运算规则的交换律之后，试证乘法交换律 ，首先当 时由乘法运算规则 Ⅰ 有 。\",\"进而当 是自然数且 时，有\",\"根据 Peano 公理 Ⅴ，得知 对任意自然数 成立，即乘法交换律成立。\"]},\"92\":{\"h\":\"乘法分配律\",\"t\":[\"下面证明乘法分配律，即对于任意自然数 ，有 。\",\"首先当 时，，进而当 为自然数且 时有\",\"根据 Peano 公理 Ⅴ，得知 对任意自然数 成立，即乘法分配律成立。\"]},\"93\":{\"h\":\"乘法结合律\",\"t\":[\"下面证明乘法结合律，即对于任意自然数 ，有 。\",\"首先当 时，有 。\",\"进而当 为自然数且 时有\",\"根据 Peano 公理 Ⅴ，得知 对任意自然数 成立，即乘法结合律成立。\"]},\"94\":{\"h\":\"乘法消去律\",\"t\":[\"下面证明乘法消去律，即对于任意自然数 和 ，有 。\",\"试证 。\",\"首先当 时有\",\"进而当 为自然数且 时有\",\"即 ，根据 Peano 公理 Ⅴ，得知 对任意自然数 成立。\",\"试证 ，采用反证法，假设 ，则由加法运算规则 Ⅱ 可知 或 ，其中 ，不妨设 。\",\"由 Peano 公理 Ⅲ 有 。\",\"由 Peano 公理 Ⅲ、Ⅳ 有，任意非零自然数 都有唯一的数 满足 ，不妨记作 。\",\"若有 ，则有\",\"上述等式表明 是 的后继，这违背了 Peano 公理 Ⅲ，由此知道假设不成立，即 。\",\"综上所述，乘法消去律 ，对任意自然数 成立。\"]},\"95\":{\"h\":\"Peano 公理的合理性\",\"t\":[\"通过上述步骤，我们成功地由 Peano 公理构建出了一个自然数代数系统。但 Peano 公理自身任有待研究。从上述步骤中我们看出 Peano 公理每一条公理都被使用过，少了任何一条都不足以构建出上述的自然数系统，这究竟是为什么呢？\",\"下面我将阐述为什么每条公理都是必须的，通过举反例的方式。研究 Peano 公理自然不能从 Peano 公理系统内出发，我们将借助另一个公理系统——图论。\"]},\"96\":{\"h\":\"乘法保序性\",\"t\":[\"若 ，则 。\",\"由 有 ，进而 因此 。\"]},\"97\":{\"h\":\"乘法消去保序性\",\"t\":[\"若 ，则 。\",\"采用反证法，假设 ，则存在正自然数 满足 ，有\",\"由此有 ，根据序的反对称性有 ，根据乘法消去律有 ，这与 的假设矛盾，因此假设不成立，即证明了乘法消去的保序性。\"]},\"98\":{\"h\":\"用图论阐述 Peano 系统\",\"t\":[\"自然数与有向图 同构，这个图满足如下性质：\",\"存在点 ，即 ；\",\"所有点的出度为 ，即 ；\",\"点 入度为 ，即 ；\",\"任意点的入度小于等于 ，即 ；\",\"存在从 到任意点的路径，即 。\",\"下面我们试着通过删除公理的方法来寻找反例。\"]},\"99\":{\"h\":\"Peano 公理 Ⅰ\",\"t\":[\"若去除，则允许不存在 ，可以构造出空集自然数系统。\"]},\"100\":{\"h\":\"Peano 公理 Ⅱ\",\"t\":[\"若去除，则对点的出度无规定，可以构造出菊花图自然数系统。\"]},\"101\":{\"h\":\"Peano 公理 Ⅲ\",\"t\":[\"若去除，则对 的入度无规定，可以构造出环状自然数系统。\"]},\"102\":{\"h\":\"Peano 公理 Ⅳ\",\"t\":[\"若去除，则对一个数可以是多个数的后继，可以构造出 状自然数系统。\"]},\"103\":{\"h\":\"Peano 公理 Ⅴ\",\"t\":[\"若去除，则对连通性无要求，可以构造出分段状自然数系统。\"]},\"104\":{\"c\":[\"数学\"]},\"105\":{\"c\":[\"公理系统\"]},\"106\":{\"h\":\"使用capacitor和ionic将vue项目迁移到mobile端\",\"t\":[\"当我们写完了vue项目后，想做一个一样的移动app，此时我们可以使用ionic无缝将其迁移到移动端。\"]},\"107\":{\"h\":\"安装\",\"t\":[\"Capacitor\",\"ionic\"]},\"108\":{\"h\":\"tips\",\"t\":[\"deploy\",\"每次执行更新你的 Web 目录的构建（例如 ionic build）时（默认：build)，你需要将这些更改复制到你的原生项目中：\",\"ionic cap copy\",\"注意：更新代码的原生部分（例如添加新插件）后，使用 sync 命令：\",\"ionic cap sync \",\"相关信息\",\"vscode中可以使用\\\"ionic\\\"插件\",\"默认不支持HTTP\",\"const config: CapacitorConfig = { plugins:{ CapacitorHttp:{ enabled:true, } }, android:{ allowMixedContent: true, } }; \"]},\"109\":{\"h\":\"bug 记录\",\"t\":[\"使用 vscode ionic打包后的相对路径不正确， 手动修改后可正常运行\",\"重要\",\"用Android Studio时不能打开360手机助手，会和ADB冲突\"]},\"110\":{\"c\":[\"mobile\"]},\"111\":{\"h\":\"并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3\",\"t\":[\"原文转载自「刘悦的技术博客」https://v3u.cn/a_id_208\",\"协程与线程向来焦孟不离，但事实上是，线程更被我们所熟知，在Python编程领域，单核同时间内只能有一个线程运行，这并不是什么缺陷，这实际上是符合客观逻辑的，单核处理器本来就没法同时处理两件事情，要同时进行多件事情本来就需要正在运行的让出处理器，然后才能去处理另一件事情，左手画方右手画圆在现实中本来就不成立，只不过这个让出的过程是线程调度器主动抢占的。\"]},\"112\":{\"h\":\"线程安全\",\"t\":[\"系统的线程调度器是假设不同的线程是毫无关系的，所以它平均地分配时间片让处理器一视同仁，雨露均沾。但是Python受限于GIL全局解释器锁，任何Python线程执行前，必须先获得GIL锁，然后，每执行100条字节码，解释器就自动释放GIL锁，让别的线程有机会执行。这个GIL全局解释器锁实际上把所有线程的执行代码都给上了锁，所以，多线程在Python中只能交替执行，即使多个线程跑在8核处理上，也只能用到1个核。\",\"但其实，这并不是事情的全貌，就算只能用单核处理任务，多个线程之前也并不是完全独立的，它们会操作同一个资源。于是，大家又发明了同步锁，使得一段时间内只有一个线程可以操作这个资源，其他线程只能等待：\",\"import threading balance = 0 def change_it_without_lock(n): global balance # 不加锁的话 最后的值不是0 # 线程共享数据危险在于 多个线程同时改同一个变量 # 如果每个线程按顺序执行，那么值会是0， 但是线程时系统调度，又不确定性，交替进行 # 没锁的话，同时修改变量 # 所以加锁是为了同时只有一个线程再修改，别的线程表一定不能改 for i in range(1000000): balance = balance + n balance = balance - n def change_it_with_lock(n): global balance if lock.acquire(): try: for i in range(1000000): balance = balance + n balance = balance - n # 这里的finally 防止中途出错了，也能释放锁 finally: lock.release() threads = [ threading.Thread(target=change_it_with_lock, args=(8, )), threading.Thread(target=change_it_with_lock, args=(10, )) ] lock = threading.Lock() [t.start() for t in threads] [t.join() for t in threads] print(balance) \",\"这种异步编程方式被广大开发者所认可，线程并不安全，线程操作共享资源需要加锁。然而人们很快发现，这种处理方式是在画蛇添足，处理器本来同一时间就只能有一个线程在运行。是线程调度器抢占划分时间片给其他线程跑，而现在，多了把锁，其他线程又说我拿不到锁，我得拿到锁才能操作。\",\"就像以前的公共电话亭，本来就只能一个人打电话，现在电话亭上加了把锁，还是只能一个人打电话，而有没有锁，有什么区别呢？所以，问题到底出在哪儿？\",\"事实上，在所有线程相互独立且不会操作同一资源的模式下，抢占式的线程调度器是非常不错的选择，因为它可以保证所有的线程都可以被分到时间片不被垃圾代码所拖累。而如果操作同一资源，抢占式的线程就不那么让人愉快了。\"]},\"113\":{\"h\":\"协程\",\"t\":[\"过了一段时间，人们发现经常需要异步操作共享资源的情况下，主动让出时间片的协程模式比线程抢占式分配的效率要好，也更简单。\",\"从实际开发角度看，与线程相比，这种主动让出型的调度方式更为高效。一方面，它让调用者自己来决定什么时候让出，比操作系统的抢占式调度所需要的时间代价要小很多。后者为了能恢复现场会在切换线程时保存相当多的状态，并且会非常频繁地进行切换。另一方面，协程本身可以做成用户态，每个协程的体积比线程要小得多，因此一个进程可以容纳数量相当可观的协程任务。\",\"import asyncio balance = 0 async def change_it_without_lock(n): global balance balance = balance + n balance = balance - n loop = asyncio.get_event_loop() res = loop.run_until_complete( asyncio.gather(change_it_without_lock(10), change_it_without_lock(8), change_it_without_lock(2), change_it_without_lock(7))) print(balance) \",\"从代码结构上看，协程保证了编写过程中的思维连贯性，使得函数（闭包）体本身就无缝保持了程序状态。逻辑紧凑，可读性高，不易写出错的代码，可调试性强。\",\"但归根结底，单核处理器还是同时间只能做一件事，所以同一时间点还是只能有一个协程任务运行，它和线程的最主要差别就是，协程是主动让出使用权，而线程是抢占使用权，即所谓的，协程是用户态，线程是系统态。\",\"img\",\"同时，如图所示，协程本身就是单线程的，即不会触发系统的全局解释器锁(GIL)，同时也不需要系统的线程调度器参与抢占式的调度，避免了多线程的上下文切换，所以它的性能要比多线程好。\"]},\"114\":{\"h\":\"协程安全\",\"t\":[\"回到并发竞争带来的安全问题上，既然同一时间只能有一个协程任务运行，并且协程切换并不是系统态抢占式，那么协程一定是安全的：\",\"import asyncio balance = 0 async def change_it_without_lock(n): global balance balance = balance + n balance = balance - n print(balance) loop = asyncio.get_event_loop() res = loop.run_until_complete( asyncio.gather(change_it_without_lock(10), change_it_without_lock(8), change_it_without_lock(2), change_it_without_lock(7))) print(balance) \",\"运行结果：\",\"0 0 0 0 0 liuyue:as-master liuyue$ \",\"看起来是这样的，无论是执行过程中，还是最后执行结果，都保证了其状态的一致性。\",\"于是，协程操作共享变量不需要加锁的结论开始在坊间流传。\",\"毫无疑问，谁主张，谁举证，上面的代码也充分说明了这个结论的正确性，然而我们都忽略了一个客观事实，那就是代码中没有“主动让出使用权”的操作，所谓主动让出使用权，即用户主动触发协程切换，那到底怎么主动让出使用权？使用 await 关键字。\",\"await 是 Python 3.5版本开始引入了新的关键字，即Python3.4版本的yield from，它能做什么？它可以在协程内部用await调用另一个协程实现异步操作，或者说的更简单一点，它可以挂起当前协程任务，去手动异步执行另一个协程，这就是主动让出“使用权”：\",\"async def hello(): print(\\\"Hello world!\\\") r = await asyncio.sleep(1) print(\\\"Hello again!\\\") \",\"当我们执行第一句代码print(\\\"Hello world!\\\")之后，使用await关键字让出使用权，也可以理解为把程序“暂时”挂起，此时使用权让出以后，别的协程就可以进行执行，随后当我们让出使用权1秒之后，当别的协程任务执行完毕，又或者别的协程任务也“主动”让出了使用权，协程又可以切回来，继续执行我们当前的任务，也就是第二行代码print(\\\"Hello again!\\\")。\",\"了解了协程如何主动切换，让我们继续之前的逻辑：\",\"import asyncio balance = 0 async def change_it_without_lock(n): global balance balance = balance + n await asyncio.sleep(1) balance = balance - n print(balance) loop = asyncio.get_event_loop() res = loop.run_until_complete( asyncio.gather(change_it_without_lock(10), change_it_without_lock(8), change_it_without_lock(2), change_it_without_lock(7))) print(balance) \",\"逻辑有了些许修改，当我对全局变量balance进行加法运算后，主动释放使用权，让别的协程运行，随后立刻切换回来，再进行减法运算，如此往复，同时开启四个协程任务，让我们来看一下代码运行结果：\",\"17 9 7 0 0 liuyue:mytornado liuyue$ \",\"可以看到，协程运行过程中，并没有保证“状态一致”，也就是一旦通过await关键字切换协程，变量的状态并不会进行同步，从而导致执行过程中变量状态的“混乱状态”，但是所有协程执行完毕后，变量balance的最终结果是0，意味着协程操作变量的最终一致性是可以保证的。\",\"为了对比，我们再用多线程试一下同样的逻辑：\",\"import threading import time balance = 0 def change_it_without_lock(n): global balance for i in range(1000000): balance = balance + n balance = balance - n print(balance) threads = [ threading.Thread(target=change_it_without_lock, args=(8, )), threading.Thread(target=change_it_without_lock, args=(10, )), threading.Thread(target=change_it_without_lock, args=(10, )), threading.Thread(target=change_it_without_lock, args=(8, )) ] [t.start() for t in threads] [t.join() for t in threads] print(balance) \",\"多线程逻辑执行结果：\",\"liuyue:mytornado liuyue$ python3 \\\"/Users/liuyue/wodfan/work/mytornado/test.py\\\" 28 18 10 0 8 \",\"可以看到，多线程在未加锁的情况下，连最终一致性也无法保证，因为线程是系统态切换，虽然同时只能有一个线程执行，但切换过程是争抢的，也就会导致写操作被原子性覆盖，而协程虽然在手动切换过程中也无法保证状态一致，但是可以保证最终一致性呢？因为协程是用户态，切换过程是协作的，所以写操作不会被争抢覆盖，会被顺序执行，所以肯定可以保证最终一致性。\",\"协程在工作状态中，主动切换了使用权，而我们又想在执行过程中保证共享数据的强一致性，该怎么办？毫无疑问，还是只能加锁：\",\"import asyncio balance = 0 async def change_it_with_lock(n): async with lock: global balance balance = balance + n await asyncio.sleep(1) balance = balance - n print(balance) lock = asyncio.Lock() loop = asyncio.get_event_loop() res = loop.run_until_complete( asyncio.gather(change_it_with_lock(10), change_it_with_lock(8), change_it_with_lock(2), change_it_with_lock(7))) print(balance) \",\"协程加锁执行后结果：\",\"liuyue:mytornado liuyue$ python3 \\\"/Users/liuyue/wodfan/work/mytornado/test.py\\\" 0 0 0 0 0 \",\"是的，无论是结果，还是过程中，都保持了其一致性，但是我们也付出了相应的代价，那就是任务又回到了线性同步执行，再也没有异步的加持了。话说回来，世界上的事情本来就是这样，本来就没有两全其美的解决方案，又要共享状态，又想多协程，还想变量安全，这可能吗？\"]},\"115\":{\"h\":\"协程是否需要加锁\",\"t\":[\"结论当然就是看使用场景，如果协程在操作共享变量的过程中，没有主动放弃执行权(await)，也就是没有切换挂起状态，那就不需要加锁，执行过程本身就是安全的；可是如果在执行事务逻辑块中主动放弃执行权了，会分两种情况，如果在逻辑执行过程中我们需要判断变量状态，或者执行过程中要根据变量状态进行一些下游操作，则必须加锁，如果我们不关注执行过程中的状态，只关注最终结果一致性，则不需要加锁。是的，抛开剂量谈毒性，是不客观的，给一个健康的人注射吗啡是犯罪，但是给一个垂死的人注射吗啡，那就是最大的道德，所以说，道德不是空泛的，脱离对象孤立存在的，同理，抛开场景谈逻辑，也是不客观的，协程也不是虚空的，脱离具体场景孤立存在的，我们应该养成具体问题具体分析的辩证唯物思想，只有掌握了辩证的矛盾思维才能更全面更灵活的看待问题，才能透过现象，把握本质。\",\"原文转载自「刘悦的技术博客」 https://v3u.cn/a_id_208\"]},\"116\":{\"h\":\"协程\",\"t\":[\"文档\",\"重要\",\"TODO\"]},\"117\":{\"h\":\"Slidev\",\"t\":[\"复杂演示推荐\"]},\"118\":{\"h\":\"缺点\",\"t\":[\"不支持导出pptx\",\"https://cn.sli.dev/guide\",\"简单PPT,且需要导出为pptx推荐\"]},\"119\":{\"h\":\"缺点\",\"t\":[\"不支持动画\",\"https://sspai.com/post/55718\",\"https://segmentfault.com/a/1190000040806239\",\"⚠️注意事项\\n如果你的 VS Code 安装了 Markdown 渲染插件 Markdown Preview Enhanced，需要先将这个插件「禁用」或是「卸载」，转而使用 VS Code 后来集成的 Markdown 预览功能，才能正常看到渲染后的 PPT 页面。\"]},\"120\":{\"h\":\"闭包实现类\",\"t\":[\"你是否曾经想过，不用类也能封装数据和方法？这篇文章将带你走进闭包的奇妙世界，展示如何用闭包来实现这一点。通过一个有趣的代码示例，你将看到闭包是如何捕获变量并提供类似类的功能的。准备好了吗？让我们开始这段有趣的旅程吧！\",\"alt text\"]},\"121\":{\"c\":[\"OI\"]},\"122\":{\"c\":[\"MODInt\"]},\"123\":{\"h\":\"教程\",\"t\":[\"这里是所有详细的教程和指南。\"]},\"124\":{\"h\":\"Typora激活教程\",\"t\":[\"Typora 是一款简洁高效的 Markdown 编辑器，支持实时预览和多种导出格式，适用于编写笔记、文档和博客等。\",\"Typora 官网\",\"Typora 中文官网\",\"工具下载：百度网盘，密码：dcqe\",\"一路点击“下一步”进行安装。将下载的工具解压后得到的两个 exe 文件（license-gen.exe 和 node_inject.exe）复制到 Typora 安装目录下（默认为 C:\\\\Program Files\\\\Typora\\\\）。\",\"以管理员身份在 Typora 安装路径打开 PowerShell。\",\"输入 node_inject.exe 并回车，等待提示 \\\"done!\\\"。\",\"输入 license-gen.exe 并回车，等待显示序列号。\",\"启动 Typora，输入任意邮箱和刚才生成的序列号到激活窗口，并点击激活。\",\"通过上述步骤，您可以免费安装并使用 Typora，但如有条件还请支持正版。\"]},\"125\":{\"h\":\"编译原理相关\",\"t\":[\"anltr.grammar\",\"bison/yacc\",\"flex\"]},\"126\":{\"h\":\"html 转 md 工具\",\"t\":[\"https://github.com/mixmark-io/turndown\",\"https://github.com/aaronsw/html2text\"]},\"127\":{\"h\":\"设计模式七大原则\",\"t\":[\"类的设计原则有七个，包括：开闭原则、里氏代换原则、迪米特原则（最少知道原则）、单一职责原则、接口分隔原则、依赖倒置原则、组合/聚合复用原则。\"]},\"128\":{\"h\":\"关系\",\"t\":[\"七大原则之间并不是相互孤立的，而是相互关联的。一个原则可以是另一个原则的加强或基础。违反其中一个原则，可能同时违反其他原则。\",\"开闭原则是面向对象可复用设计的基石，其他设计原则是实现开闭原则的手段和工具。\",\"通常，可以将这七个原则分为以下两部分：\",\"设计目标：开闭原则、里氏代换原则、迪米特原则\",\"设计方法：单一职责原则、接口分隔原则、依赖倒置原则、组合/聚合复用原则\"]},\"129\":{\"h\":\"开闭原则\",\"t\":[\"对扩展开放\",\"对修改关闭\",\"根据开闭原则，在设计一个系统模块的时候，应该可以在不修改原模块的基础上，扩展其功能。\"]},\"130\":{\"h\":\"实现方法\",\"t\":[\"使用抽象类和接口：通过定义抽象类和接口，可以在不修改现有代码的情况下，增加新的实现。\",\"使用设计模式：例如策略模式、装饰者模式等，可以在不改变原有代码的情况下，动态地扩展对象的行为。\",\"遵循单一职责原则：确保每个类只有一个职责，这样在扩展功能时，不会影响其他功能。\"]},\"131\":{\"h\":\"里氏代换原则\"},\"132\":{\"h\":\"里氏代换原则\",\"t\":[\"里氏代换原则规定子类不得重写父类的普通方法，只能重写父类的抽象方法；即子类可以扩展父类的功能，但是不能改变父类原有的功能。\",\"派生类应当可以替换基类并出现在基类能够出现的任何地方，或者说如果我们把代码中使用基类的地方用它的派生类所代替，代码还能正常工作。\"]},\"133\":{\"h\":\"实现方法\",\"t\":[\"使用抽象类和接口：确保子类实现父类的抽象方法，而不是重写父类的具体方法。\",\"遵循契约：子类的方法签名应与父类一致，返回类型应与父类相同或是其子类型。\",\"遵循行为一致性：子类应保持父类的行为，不应引入违反父类预期的新行为。\"]},\"134\":{\"h\":\"示例\"},\"135\":{\"h\":\"迪米特原则\"},\"136\":{\"h\":\"迪米特原则\",\"t\":[\"一个实体应当尽量少地与其他实体之间发生相互作用，使得系统功能模块相对独立；降低类之间的耦合度，提高模块的相对独立性。\"]},\"137\":{\"h\":\"实现方法\",\"t\":[\"引入中介者模式：通过中介者对象来管理对象之间的交互，减少对象之间的直接依赖。\",\"使用门面模式：通过门面对象提供统一的接口，隐藏系统的复杂性，减少对象之间的直接交互。\",\"限制公开方法：尽量减少类的公开方法，避免不必要的外部依赖。\"]},\"138\":{\"h\":\"单一职责原则\",\"t\":[\"一个类只对应一个职责，其职责是引起该类变化的原因。\",\"如果一个类需要改变，改变它的理由永远只有一个。如果存在多个改变它的理由，就需要重新设计该类。\"]},\"139\":{\"h\":\"实现方法\",\"t\":[\"职责分离：将不同的职责分离到不同的类中，每个类只负责一个职责。\",\"模块化设计：通过模块化设计，将不同的功能模块分开，确保每个模块只负责一个功能。\",\"重构：在发现类有多个职责时，及时进行重构，将不同的职责分离到不同的类中。\"]},\"140\":{\"h\":\"示例\",\"t\":[\"// 不符合单一职责原则的类 class User { login() { // 登录逻辑 } register() { // 注册逻辑 } displayProfile() { // 显示用户信息逻辑 } } // 符合单一职责原则的类 class AuthService { login() { // 登录逻辑 } register() { // 注册逻辑 } } class UserProfile { displayProfile() { // 显示用户信息逻辑 } } \"]},\"141\":{\"h\":\"接口隔离原则\",\"t\":[\"不应强迫用户依赖他们不使用的接口。\",\"一个类对另一个类的依赖应该建立在最小的接口上。\",\"简单来说，使用多个专门的接口比使用单个通用接口要好得多。\"]},\"142\":{\"h\":\"依赖倒置原则\",\"t\":[\"高层模块不应该依赖低层模块，二者都应该依赖其抽象。抽象不应该依赖细节，细节应该依赖抽象。核心思想是：面向接口编程，而不是面向实现编程。\"]},\"143\":{\"h\":\"实现方法\",\"t\":[\"使用接口和抽象类：定义接口或抽象类，让高层模块依赖这些抽象，而不是具体实现。\",\"依赖注入：通过构造函数注入、属性注入或方法注入，将具体实现传递给高层模块。\",\"工厂模式：使用工厂模式创建对象，避免高层模块直接依赖具体类。\"]},\"144\":{\"h\":\"示例\",\"t\":[\"// 定义抽象接口 interface IWorker { work(): void; } // 具体实现 class Worker implements IWorker { work() { console.log(\\\"Working...\\\"); } } // 高层模块依赖抽象接口 class Manager { private worker: IWorker; constructor(worker: IWorker) { this.worker = worker; } manage() { this.worker.work(); } } // 使用依赖注入 const worker = new Worker(); const manager = new Manager(worker); manager.manage(); \"]},\"145\":{\"h\":\"组合/聚合复用原则\",\"t\":[\"尽量使用组合/聚合，不要使用类继承。\",\"如果使用继承，会导致父类的任何变换都可能影响到子类的行为，所以优先使用组合的方式代替继承的方式。\"]},\"146\":{\"h\":\"实现方法\",\"t\":[\"使用组合：通过在类中包含其他类的实例来实现功能，而不是通过继承。\",\"使用聚合：通过在类中引用其他类的实例来实现功能，而不是通过继承。\",\"接口和抽象类：通过接口和抽象类定义行为，然后在具体类中实现这些行为。\"]},\"147\":{\"h\":\"示例\",\"t\":[\"// 使用继承的方式 class Engine { start() { console.log(\\\"Engine started\\\"); } } class Car extends Engine { drive() { this.start(); console.log(\\\"Car is driving\\\"); } } // 使用组合的方式 class Engine { start() { console.log(\\\"Engine started\\\"); } } class Car { private engine: Engine; constructor(engine: Engine) { this.engine = engine; } drive() { this.engine.start(); console.log(\\\"Car is driving\\\"); } } const engine = new Engine(); const car = new Car(engine); car.drive(); \"]},\"148\":{\"h\":\"总结\",\"t\":[\"开闭原则：对扩展开放，对修改关闭。\",\"里氏代换原则：子类可以替换父类，且程序行为不变。\",\"迪米特原则：尽量减少类之间的耦合。\",\"单一职责原则：一个类只负责一个职责。\",\"接口隔离原则：使用多个专门的接口，而不是一个通用接口。\",\"依赖倒置原则：高层模块不依赖低层模块，二者都依赖抽象。\",\"组合/聚合复用原则：优先使用组合/聚合，而不是继承。\"]},\"149\":{\"c\":[\"设计模式\"]},\"150\":{\"c\":[\"设计模式\",\"typescript\"]},\"151\":{\"h\":\"抽象工厂模式\"},\"152\":{\"h\":\"为什么要使用抽象工厂模式\",\"t\":[\"抽象工厂模式提供一个接口，用于创建相关或依赖对象的家族，而无需明确指定具体类。它通过定义一个创建对象的接口来实现，这样子类可以决定实例化哪个类。抽象工厂模式使得一个类的实例化延迟到其子类。\",\"解耦：抽象工厂模式通过将对象的创建过程抽象化，减少了客户端代码与具体类之间的耦合。\",\"一致性：确保同一工厂创建的一系列对象具有一致的接口和行为。\",\"扩展性：可以方便地增加新的产品族而不影响现有代码。\"]},\"153\":{\"h\":\"示例代码\",\"t\":[\"// factory.ts // 抽象工厂 import { Link } from './link'; import { Tray } from './tray'; import { Page } from './page'; export abstract class Factory { abstract createLink(caption: string, url: string): Link; abstract createTray(caption: string): Tray; abstract createPage(title: string, author: string): Page; } // item.ts // 抽象零件 export abstract class Item { protected caption: string; constructor(caption: string) { this.caption = caption; } abstract makeHTML(): string; } // link.ts // 抽象超链接 import { Item } from './item'; export abstract class Link extends Item { protected url: string; constructor(caption: string, url: string) { super(caption); this.url = url; } } // listFactory.ts import { Factory } from './factory'; import { ListLink } from './listLink'; import { ListTray } from './listTray'; import { ListPage } from './listPage'; export class ListFactory extends Factory { createLink(caption: string, url: string) { return new ListLink(caption, url); } createTray(caption: string) { return new ListTray(caption); } createPage(title: string, author: string) { return new ListPage(title, author); } } // listLink.ts import { Link } from './link'; export class ListLink extends Link { constructor(caption: string, url: string) { super(caption, url); } makeHTML() { return `<li><a href=\\\"${this.url}\\\">${this.caption}</a></li>\\\\n`; } } // listPage.ts import { Page } from './page'; export class ListPage extends Page { makeHTML() { let buffer = []; buffer.push(`<html><head><title>${this.title}</title></head>`); buffer.push(`<body>`); buffer.push(`<h1>${this.title}</h1>`); buffer.push(`<ul>`); this.content.forEach(item => { buffer.push(item.makeHTML()); }); buffer.push(`</ul>`); buffer.push(`<hr><address>${this.author}</address>`); buffer.push(`</body></html>`); return buffer.join('\\\\n'); } } // listTray.ts import { Tray } from \\\"./tray\\\"; export class ListTray extends Tray { constructor(caption: string) { super(caption); } makeHTML() { let buffer = []; buffer.push(\\\"<li>\\\\n\\\"); buffer.push(this.caption + \\\"\\\\n\\\"); buffer.push(\\\"<ul>\\\\n\\\"); this.tray.forEach(item => { buffer.push(item.makeHTML()); }); buffer.push(\\\"</ul>\\\\n\\\"); buffer.push(\\\"</li>\\\\n\\\"); return buffer.join(\\\"\\\"); } } // main.ts import { Factory } from \\\"./factory\\\"; import { ListFactory } from \\\"./listFactory\\\"; function getProduct(factory: Factory) { let people = factory.createLink(\\\"people\\\", \\\"http://www.people.com\\\"); let gmw = factory.createLink(\\\"gmw\\\", \\\"http://www.gmw.com\\\"); let us_yahoo = factory.createLink(\\\"us_yahoo\\\", \\\"http://www.us.yahoo.com\\\"); let jp_yahoo = factory.createLink(\\\"jp_yahoo\\\", \\\"http://www.jp.yahoo.com\\\"); let excite = factory.createLink(\\\"excite\\\", \\\"http://www.excite.com\\\"); let google = factory.createLink(\\\"google\\\", \\\"http://www.google.com\\\"); let traynews = factory.createTray(\\\"news\\\"); traynews.add(people); traynews.add(gmw); let trayyahoo = factory.createTray(\\\"yahoo\\\"); trayyahoo.add(us_yahoo); trayyahoo.add(jp_yahoo); let traysearch = factory.createTray(\\\"search\\\"); traysearch.add(trayyahoo); traysearch.add(excite); let page = factory.createPage(\\\"LinkPage\\\", \\\"gmw\\\"); page.add(traynews); page.add(traysearch); page.output(); } let factory = new ListFactory(); getProduct(factory); // page.ts // 抽象html页面 import { Item } from './item'; export abstract class Page { title: string; author: string; content: Array<Item>; buffer: string; constructor(title: string, author: string) { this.title = title; this.author = author; this.content = []; } add(item: Item): void { this.content.push(item); } output(): void { try { this.buffer = this.makeHTML(); console.log(this.buffer); } catch (error) { console.log(error); } } abstract makeHTML(): string; } // tray.ts // 抽象容器 import { Item } from './item'; export abstract class Tray extends Item { protected tray: Item[] = []; constructor(caption: string) { super(caption); } public add(item: Item): void { this.tray.push(item); } } \",\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\abstractFactory\\\\main.ts\\\" <html><head><title>LinkPage</title></head> <body> <h1>LinkPage</h1> <ul> <li> news <ul> <li><a href=\\\"http://www.people.com\\\">people</a></li> <li><a href=\\\"http://www.gmw.com\\\">gmw</a></li> </ul> </li> <li> search <ul> <li> yahoo <ul> <li><a href=\\\"http://www.us.yahoo.com\\\">us_yahoo</a></li> <li><a href=\\\"http://www.jp.yahoo.com\\\">jp_yahoo</a></li> </ul> </li> <li><a href=\\\"http://www.excite.com\\\">excite</a></li> </ul> </li> </ul> <hr><address>gmw</address> </body></html> \"]},\"154\":{\"h\":\"增加其它工厂\",\"t\":[\"如果只是为了编写包含 HTML 超链接集合的文件，这样的设计可能显得有些过于复杂。当只有一个具体工厂时，划分“抽象类”和“具体类”是没有必要的。然而，使用抽象工厂模式，我们可以轻松地添加其他具体工厂，例如TableFactory。\"]},\"155\":{\"h\":\"拓展思路的要点\"},\"156\":{\"h\":\"易于增加具体工厂\",\"t\":[\"在 Abstract Factory 模式中增加具体的工厂是非常容易的。这里说的“容易”指的是需要编写哪些类和需要实现哪些方法都非常清楚。\",\"假设现在我们要在示例程序中增加新的具体工厂，那么需要做的就是编写 Factory、Link、Tray、Page 这 4 个类的子类，并实现它们定义的抽象方法。也就是说将 factory 包中的抽象部分全部具体化即可。\",\"这样一来，无论要增加多少个具体工厂（或是要修改具体工厂的 Bug），都无需修改抽象工厂和 Main 部分。\"]},\"157\":{\"h\":\"难以增加新的零件\",\"t\":[\"请试想一下要在 Abstract Factory 模式中增加新的零件时应当如何做。例如，我们要在 factory 包中增加一个表示图像的 Picture 零件。这时，我们必须要对所有的具体工厂进行相应的修改才行。例如，在 listfactory 包中，我们必须要做以下修改：\",\"在 ListFactory 中增加 createPicture 方法，\",\"新增 ListPicture 类。\",\"已经编写完成的具体工厂越多，修改的工作量就会越大。\"]},\"158\":{\"h\":\"相关的设计模式\",\"t\":[\"Builder 模式\",\"Factory Method 模式\",\"Composite 模式\",\"Singleton 模式\"]},\"159\":{\"c\":[\"设计模式\"]},\"160\":{\"c\":[\"设计模式\",\"typescript\",\"生成实例\"]},\"161\":{\"h\":\"适配器模式\"},\"162\":{\"h\":\"适配器模式\",\"t\":[\"适配器模式（Adapter Pattern）是一种结构型设计模式，它允许将一个类的接口转换成客户希望的另一个接口。适配器模式使得原本由于接口不兼容而不能一起工作的那些类可以一起工作。\"]},\"163\":{\"h\":\"为什么要用适配器模式\",\"t\":[\"在软件开发中，经常会遇到需要使用一些现有的类，但它们的接口并不符合当前系统的需求。适配器模式通过创建一个适配器类，将现有类的接口转换为所需的接口，从而使得现有类可以在新的环境中使用。\"]},\"164\":{\"h\":\"类比\"},\"165\":{\"h\":\"类比\",\"t\":[\"比喻\",\"示例程序\",\"实际需求\",\"交流100V\",\"Banner\",\"变换装置\",\"适配器\",\"PrintBanner\",\"需求\",\"直流12V\",\"Print\"]},\"166\":{\"h\":\"示例程序\",\"t\":[\"Adapter 有两种方式实现\",\"// banner.ts export class Banner { private string: string; constructor(string: string) { this.string = string; } showWithParen(): void { console.log(`(${this.string})`); } showWithAster(): void { console.log(`*${this.string}*`); } } // print_inheritance.ts export interface Print { printWeak(): void; printStrong(): void; } // printBanner_inheritance.ts import { Banner } from './banner'; import { Print } from './print_inheritance'; export class PrintBanner extends Banner implements Print { constructor(string: string) { super(string); } printWeak(): void { this.showWithParen(); } printStrong(): void { this.showWithAster(); } } // print_delegation.ts export abstract class Print { abstract printWeak(): void; abstract printStrong(): void; } // printBanner_delegation.ts import { Print } from \\\"./print_delegation\\\"; import { Banner } from \\\"./banner\\\"; export class PrintBanner extends Print { private banner: Banner; constructor(string: string) { super(); this.banner = new Banner(string); } printWeak(): void { this.banner.showWithParen(); } printStrong(): void { this.banner.showWithAster(); } } // main.ts import { PrintBanner as pbi } from './printBanner_inheritance'; import { PrintBanner as pbd } from './printBanner_delegation'; // 使用继承 const printBanner = new pbi('Hello'); printBanner.printWeak(); printBanner.printStrong(); // 使用委托 const printBanner2 = new pbd('Hello'); printBanner2.printWeak(); printBanner2.printStrong(); \"]},\"167\":{\"h\":\"运行结果\",\"t\":[\"ts-node \\\"d:\\\\code\\\\design_pattern\\\\src\\\\adapter\\\\main.ts\\\" (Hello) *Hello* (Hello) *Hello* \"]},\"168\":{\"h\":\"相关的设计模式\",\"t\":[\"Bridge\",\"Decorator\"]},\"169\":{\"c\":[\"设计模式\"]},\"170\":{\"c\":[\"设计模式\",\"typescript\"]},\"171\":{\"h\":\"Bridge 模式\",\"t\":[\"Bridge 模式在“类的功能层次结构”和“类的实现层次结构”之间搭建桥梁。\"]},\"172\":{\"h\":\"使用此设计模式的理由\",\"t\":[\"Bridge 模式的主要目的是将抽象部分与实现部分分离，使它们可以独立变化。这种模式通过组合而不是继承来实现功能的扩展，减少了类之间的耦合度，提高了系统的可扩展性和可维护性。\"]},\"173\":{\"h\":\"类的层次结构的两个作用\"},\"174\":{\"h\":\"增加新功能时\",\"t\":[\"假设现在有一个类 Something，当我们想在 Something 中增加新功能时（例如增加一个具体方法），会编写一个 Something 类的子类（派生类），即 SomethingGood 类。这样就构成了一个小小的类层次结构。这就是为了增加新功能而产生的层次结构。\",\"SomeThing\",\"----\\\\ SomeThingGood\"]},\"175\":{\"h\":\"增加新的实现时\",\"t\":[\"在 Template Method 模式（第 3 章）中，我们学习了抽象类的作用。抽象类声明了一些抽象方法，定义了接口 (API)，然后子类负责实现这些抽象方法。父类的任务是通过声明抽象方法的方式定义接口 (API)，而子类的任务是实现抽象方法。正是由于父类和子类的这种任务分担，我们才可以编写出具有高可替换性的类。\",\"这里其实也存在层次结构。例如，当子类实现了父类 AbstractClass 类的抽象方法时，它们之间就构成了一个小小的层次结构。\",\"AbstractClass\",\"----\\\\ ConcreteClass\",\"但是，这里的类的层次结构并非用于增加功能，也就是说，这种层次结构并非用于方便我们增加新的方法。它的真正作用是帮助我们实现任务分担。\"]},\"176\":{\"h\":\"类的层次结构的混杂和分离\",\"t\":[\"当我们想要编写子类时，就需要先确认自己的意图：“我是要增加功能呢？还是要增加实现呢？”\",\"当类的层次结构只有一层时，功能层次结构与实现层次结构是混杂在一个层次结构中的。这样很容易使类的层次结构变得复杂，也难以透彻地理解类的层次结构。因为自己难以确定究竟应该在类的哪一个层次结构中去增加子类。\",\"因此，我们需要将“类的功能层次结构\\\"与“类的实现层次结构\\\"分离为两个独立的类层次结构。当然，如果只是简单地将它们分开，两者之间必然会缺少联系。所以我们还需要在它们之间搭建一座桥梁。本章中要学习的 Bridge 模式的作用就是搭建这座桥梁。\"]},\"177\":{\"h\":\"示例代码\"},\"178\":{\"h\":\"类的一览表\",\"t\":[\"在桥的哪一侧\",\"名字\",\"说明\",\"类的功能层次结构\",\"Display\",\"负责“显示”的类\",\"类的功能层次结构\",\"CountDisplay\",\"增加了“只显示规定次数”这一功能的类\",\"类的实现层次结构\",\"DisplayImpl\",\"负责“显示”的类\",\"类的实现层次结构\",\"StringDisplayImpl\",\"“用字符串显示”的类\",\"主程序\",\"Main\",\"试程序行为的类\",\"Display 类（代码清单 9 · 1 ）的功能是抽象的，负责“显示一些东西\\\"。该类位于“类的功能层次结构\\\"的最上层。在 impl 字段中保存的是实现了 Display 类的具体功能的实例（ impl 是 implementation （实现）的缩写）。该实例通过 Display 类的构造函数被传递给 Display 类，然后保存在字段中，以供后面的处理使用（ impl 字段即是类的两个层次结构的“桥梁\\\"）。\",\"CountDisplay 类继承了 Display 类的 open、print、close 方法，并使用它们来增加这个新功能。这就是“类的功能层次结构\\\"。\"]},\"179\":{\"h\":\"countDisplay.ts\",\"t\":[\"import { Display } from './display'; import { DisplayImpl } from './displayImpl'; export class CountDisplay extends Display { constructor(impl: DisplayImpl) { super(impl); } multiDisplay(times: number) { this.open(); for (let i = 0; i < times; i++) { this.print(); } this.close(); } } \"]},\"180\":{\"h\":\"display.ts\",\"t\":[\"import { DisplayImpl } from './displayImpl'; export class Display { private impl: DisplayImpl; constructor(impl: DisplayImpl) { this.impl = impl; } open() { this.impl.rawOpen(); } print() { this.impl.rawPrint(); } close() { this.impl.rawClose(); } display() { this.open(); this.print(); this.close(); } } \"]},\"181\":{\"h\":\"displayImpl.ts\",\"t\":[\"export abstract class DisplayImpl { abstract rawOpen(): void; abstract rawPrint(): void; abstract rawClose(): void; } \"]},\"182\":{\"h\":\"main.ts\",\"t\":[\"import { Display } from './display'; import { CountDisplay } from './countDisplay'; import { StringDisplayImpl } from './stringDisplayImpl'; const d1 = new Display(new StringDisplayImpl('Hello, China.')); const d2 = new CountDisplay(new StringDisplayImpl('Hello, World.')); const d3 = new CountDisplay(new StringDisplayImpl('Hello, Universe.')); d1.display(); d2.display(); d3.multiDisplay(5); \"]},\"183\":{\"h\":\"stringDisplayImpl.ts\",\"t\":[\"import { DisplayImpl } from './displayImpl'; export class StringDisplayImpl extends DisplayImpl { private str: string; private width: number; constructor(str: string) { super(); this.str = str; this.width = str.length; } rawOpen() { this.printLine(); } rawPrint() { console.log(`|${this.str}|`); } rawClose() { this.printLine(); } private printLine() { let buffer = '+'; for (let i = 0; i < this.width; i++) { buffer += '-'; } buffer += '+'; console.log(buffer); } } \"]},\"184\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\bridge\\\\main.ts\\\" +-------------+ |Hello, China.| +-------------+ +-------------+ |Hello, World.| +-------------+ +----------------+ |Hello, Universe.| |Hello, Universe.| |Hello, Universe.| |Hello, Universe.| |Hello, Universe.| +----------------+ \"]},\"185\":{\"h\":\"拓展思路的要点\"},\"186\":{\"h\":\"分开后更容易扩展\",\"t\":[\"Bridge 模式的特征是将“类的功能层次结构\\\"与“类的实现层次结构\\\"分离开了。将类的这两个层次结构分离开有利于独立地对它们进行扩展。当想要增加功能时，只需要在“类的功能层次结构\\\"一侧增加类即可，不必对“类的实现层次结构\\\"做任何修改。而且，增加后的功能可以被“所有的实现”使用。\",\"例如，我们可以将“类的功能层次结构\\\"应用于软件所运行的操作系统上。如果我们将某个程序中依赖于操作系统的部分划分为 Windows 版、Macintosh 版、Unix 版，那么我们就可以用 Bridge 模式中的“类的实现层次结构\\\"来表现这些依赖于操作系统的部分。也就是说，我们需要编写一个定义这些操作系统的共同接口（API）的 Implementor 角色，然后编写 Windows 版、Macintosh 版、Unix 版的 3 个 ConcreteImplementor 角色。这样一来，无论在“类的功能层次结构\\\"中增加多少个功能，它们都可以工作于这 3 个操作系统上。\"]},\"187\":{\"h\":\"继承是强关联，委托是弱关联\",\"t\":[\"继承是强关联关系，但委托是弱关联关系。这是因为只有 Display 类的实例生成时，才与作为参数被传入的类构成关联。例如，在示例程序中，当 Main 类生成 Display 类和 CountDisplay 类的实例时，才将 StringDisplayImpl 的实例作为参数传递给 Display 类和 CountDisplay 类。如果我们不传递 StringDisplayImpl 类的实例，而是将其他 ConcreteImplementor 角色的实例传递给 Display 类和 CountDisplay 类，就能很容易地改变实现。这时，发生变化的代码只有 Main 类，Display 类和 DisplayImpl 类则不需要做任何修改。\"]},\"188\":{\"h\":\"相关的设计模式\",\"t\":[\"Template Method 模式\",\"Abstract Factory 模式\",\"Adapter 模式\"]},\"189\":{\"c\":[\"设计模式\"]},\"190\":{\"c\":[\"设计模式\",\"TypeScript\",\"分开考虑\"]},\"191\":{\"h\":\"builder 模式\"},\"192\":{\"h\":\"为什么要使用 Builder 模式\",\"t\":[\"Builder 模式通过将对象的构建过程与其表示分离，使得同样的构建过程可以创建不同的表示。它主要用于以下情况：\",\"复杂对象的创建：当一个对象的构建过程非常复杂时，Builder 模式可以将构建过程分解为多个步骤，使代码更易于维护和理解。\",\"不同的表示：当需要创建不同表示的对象时，Builder 模式允许使用相同的构建过程来生成不同的对象表示。\",\"代码复用：通过将构建过程封装在 Director 类中，可以在不同的上下文中重用相同的构建逻辑。\"]},\"193\":{\"h\":\"代码示例\",\"t\":[\"// builder.ts export abstract class Builder { public abstract makeTitle(title: string): void; public abstract makeString(str: string): void; public abstract makeItems(items: string[]): void; public abstract close(): void; } // director.ts import { Builder } from './builder'; export class Director { private builder: Builder; constructor(builder: Builder) { this.builder = builder; } public construct(): void { this.builder.makeTitle('问候'); this.builder.makeString('从早上到下午'); this.builder.makeItems(['早上好。', '下午好。']); this.builder.makeString('晚上'); this.builder.makeItems(['晚上好。', '晚安。', '再见。']); this.builder.close(); } } // htmlBuilder.ts import { Builder } from './builder'; export class HTMLBuilder extends Builder { private filename: string = ''; private buffer: string = ''; public makeTitle(title: string): void { this.filename = `${title}.html`; this.buffer += `<html><head><title>${title}</title></head><body>`; this.buffer += `<h1>${title}</h1>`; } public makeString(str: string): void { this.buffer += `<p>${str}</p>`; } public makeItems(items: string[]): void { this.buffer += '<ul>'; items.forEach((item) => { this.buffer += `<li>${item}</li>`; }); this.buffer += '</ul>'; } public close(): void { this.buffer += '</body></html>'; } public getResult(): string { return this.buffer; } } // textBuilder.ts import { Builder } from './builder'; export class TextBuilder extends Builder { private buffer: string = ''; public makeTitle(title: string): void { this.buffer += '==============================\\\\n'; this.buffer += `『${title}』\\\\n`; this.buffer += '\\\\n'; } public makeString(str: string): void { this.buffer += `■${str}\\\\n`; this.buffer += '\\\\n'; } public makeItems(items: string[]): void { items.forEach((item) => { this.buffer += ` ・${item}\\\\n`; }); this.buffer += '\\\\n'; } public close(): void { this.buffer += '==============================\\\\n'; } public getResult(): string { return this.buffer; } } // main.ts import { Builder } from './builder'; import { Director } from './director'; import { HTMLBuilder } from './htmlBuilder'; import { TextBuilder } from './textBuilder'; // TextBuilder console.log(\\\"Creating a text file...\\\"); const textBuilder = new TextBuilder(); const director = new Director(textBuilder); director.construct(); const result = textBuilder.getResult(); console.log(result); // HTMLBuilder console.log(\\\"Creating an HTML file...\\\"); const htmlBuilder = new HTMLBuilder(); const director2 = new Director(htmlBuilder); director2.construct(); const filename = htmlBuilder.getResult(); console.log(`${filename}が作成されました。`); \"]},\"194\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\builder\\\\main.ts\\\" Creating a text file... ============================== 『问候』 ■从早上到下午 ・早上好。 ・下午好。 ■晚上 ・晚上好。 ・晚安。 ・再见。 ============================== Creating an HTML file... <html><head><title>问候</title></head><body><h1>问候</h1><p>从早上到下午</p><ul><li>早上好。</li><li>下午好。</li></ul><p>晚上</p><ul><li>晚上好。</li><li>晚安。</li><li>再见。</li></ul></body></html>が作成されました。 \"]},\"195\":{\"h\":\"相关设计模式\",\"t\":[\"Template Method 模式\",\"Composite 模式\",\"Abstract Factory 模式\",\"Facade 模式\"]},\"196\":{\"h\":\"拓展思路的要点\"},\"197\":{\"h\":\"谁知道什么\",\"t\":[\"在面向对象编程中，“谁知道什么”是非常重要的。Builder 模式通过将对象的构建过程与其表示分离，明确了各个类的职责分工。Director 类知道如何构建复杂对象，但不知道对象的具体表示；Builder 类知道如何生成对象的具体表示，但不知道构建的具体步骤。这种职责分离使得代码更加清晰、易于维护和扩展。\",\"正是因为不知道才能够替换，正是因为可以替换，组件才具有高价。作为设计人员，我们必须时刻关汴这种“可替換性”\"]},\"198\":{\"h\":\"设计时能够决定的事情和不能决定的事情\",\"t\":[\"在设计软件时，有些事情是可以在设计阶段决定的，而有些事情则需要在运行时决定。Builder 模式通过将构建过程与表示分离，使得在设计时可以决定构建的步骤和逻辑，而具体的表示则可以在运行时灵活选择。这种设计方式提高了系统的灵活性和可扩展性。\"]},\"199\":{\"h\":\"代码的阅读方法和修改方法\",\"t\":[\"在编程时，虽然有时需要从零开始编写代码，但更多时候我们都是在现有代码的基础上进行增加和修改。\",\"这时，我们需要先阅读现有代码。不过，只是阅读抽象类的代码是无法获取很多信息的（虽然可以从方法名中获得线索）。\",\"让我们再回顾一下示例程序。即使理解了 Builder 抽象类，也无法理解程序整体。至少必须在阅读了 Director 的代码后才能理解 Builder 类的使用方法（Builder 类的方法的调用方法）。然后再去看看 TextBuilder 类和 HTMLBuilder 类的代码，就可以明白调用 Builder 类的方法后具体会进行什么样的处理。\",\"如果没有理解各个类的角色就动手增加和修改代码，在判断到底应该修改哪个类时，就会很容易出错。例如，如果修改 Builder 类，那么就会对类中调用 Builder 类方法的地方和 Builder 类的子类产生影响。或是如果不小心修改了 Director 类，在其内部调用了类的特有的方法，则会导致其失去作为可复用组件的独立性，而且当将子类替换为 HTMLBuilder 时，程序可能会无法正常工作。\"]},\"200\":{\"c\":[\"设计模式\"]},\"201\":{\"c\":[\"设计模式\",\"typescript\",\"生成实例\"]},\"202\":{\"h\":\"chainOfResponsibility 模式\",\"t\":[\"“推卸责任\\\"听起来有些贬义的意思，但是有时候也确实存在需要“推卸责任\\\"的情况。例如，当外部请求程序进行某个处理，但程序暂时无法直接决定由哪个对象负责处理时，就需要推卸责任。这种情况下，我们可以考虑将多个对象组成一条职责链，然后按照它们在职责链上的顺序一个一个地找出到底应该谁来负责处理。\",\"当一个人被要求做什么事情时，如果他可以做就自己做，如果不能做就将“要求\\\"转给另外一个人。下一个人如果可以自己处理，就自己做；如果也不能自己处理，就再转给另外一个人““这就是 Chain Of Responsibility 模式。\"]},\"203\":{\"h\":\"为什么使用此类\",\"t\":[\"使用 Chain of Responsibility 模式有以下几个优点：\",\"解耦请求发送者和接收者：发送者无需知道哪个对象会处理请求。\",\"动态组合职责链：可以在运行时动态地改变职责链的结构。\",\"增加灵活性：可以很容易地添加新的处理者而不影响现有代码。\"]},\"204\":{\"h\":\"示例代码\",\"t\":[\"在这个示例中，我们使用了 Chain of Responsibility 模式来处理一系列的请求。每个请求都会沿着职责链传递，直到有一个对象能够处理它。这样做的好处是请求的发送者和接收者解耦，发送者无需知道哪个对象会处理请求。\",\"// limitSupport.ts import { Support } from './support'; import { Trouble } from './trouble'; export class LimitSupport extends Support { private limit: number; constructor(name: string, limit: number) { super(name); this.limit = limit; } protected resolve(trouble: Trouble): boolean { if (trouble.getNumber() < this.limit) { return true; } return false; } } // main.ts import { NoSupport } from \\\"./NoSupport\\\"; import { LimitSupport } from \\\"./LimitSupport\\\"; import { OddSupport } from \\\"./OddSupport\\\"; import { SpecialSupport } from \\\"./specialSupport\\\"; import { Support } from \\\"./support\\\"; import { Trouble } from \\\"./trouble\\\"; let alice: Support = new NoSupport(\\\"Alice\\\"); let bob: Support = new LimitSupport(\\\"Bob\\\", 100); let charlie: Support = new SpecialSupport(\\\"Charlie\\\", 429); let diana: Support = new LimitSupport(\\\"Diana\\\", 200); let elmo: Support = new OddSupport(\\\"Elmo\\\"); let fred: Support = new LimitSupport(\\\"Fred\\\", 300); alice.setNext(bob).setNext(charlie).setNext(diana).setNext(elmo).setNext(fred); for (let i = 0; i < 500; i += 33) { alice.support(new Trouble(i)); } // NoSupport.ts import { Support } from './support'; import { Trouble } from './trouble'; export class NoSupport extends Support { constructor(name: string) { super(name); } resolve(trouble: Trouble): boolean { return false; } } // OddSupport.ts import { Support } from './support'; export class OddSupport extends Support { resolve(trouble) { if (trouble.getNumber() % 2 === 1) { return true; } else { return false; } } } // specialSupport.ts import { Support } from './support'; import { Trouble } from './trouble'; export class SpecialSupport extends Support { private number: number; constructor(name: string, number: number) { super(name); this.number = number; } protected resolve(trouble: Trouble): boolean { if (trouble.getNumber() === this.number) { return true; } return false; } } // support.ts import { Trouble } from './trouble'; export abstract class Support { private next: Support; constructor(private name: string) { this.name = name; } setNext(next: Support): Support { this.next = next; return next; } support(trouble: Trouble): void { if (this.resolve(trouble)) { this.done(trouble); } else if (this.next != undefined && this.next !== null) { this.next.support(trouble); } else { this.fail(trouble); } } toString(): string { return `[${this.name}]`; } protected abstract resolve(trouble: Trouble): boolean; protected done(trouble: Trouble): void { console.log(`${trouble} is resolved by ${this}.`); } protected fail(trouble: Trouble): void { console.log(`${trouble} cannot be resolved.`); } } // trouble.ts export class Trouble { private number: number; constructor(number: number) { this.number = number; } getNumber(): number { return this.number; } toString(): string { return `[Trouble ${this.number}]`; } } \"]},\"205\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\chainOfResponsibility\\\\main.ts\\\" [Trouble 0] is resolved by [Bob]. [Trouble 33] is resolved by [Bob]. [Trouble 66] is resolved by [Bob]. [Trouble 99] is resolved by [Bob]. [Trouble 132] is resolved by [Diana]. [Trouble 165] is resolved by [Diana]. [Trouble 198] is resolved by [Diana]. [Trouble 231] is resolved by [Elmo]. [Trouble 264] is resolved by [Fred]. [Trouble 297] is resolved by [Elmo]. [Trouble 330] cannot be resolved. [Trouble 363] is resolved by [Elmo]. [Trouble 396] cannot be resolved. [Trouble 429] is resolved by [Charlie]. [Trouble 462] cannot be resolved. [Trouble 495] is resolved by [Elmo]. \"]},\"206\":{\"h\":\"相关的设计模式\",\"t\":[\"Composite 模式\",\"Command 模式\"]},\"207\":{\"c\":[\"设计模式\"]},\"208\":{\"c\":[\"设计模式\",\"TypeScript\",\"推卸责任\"]},\"209\":{\"h\":\"Command 模式\"},\"210\":{\"h\":\"为什么使用此模式\",\"t\":[\"Command 模式将请求封装成对象，使得可以用不同的请求、队列或者日志来参数化其他对象。Command 模式也支持可撤销的操作。\"]},\"211\":{\"h\":\"示例代码\",\"t\":[\"// command.ts export interface Command { execute(): void; } // drawable.ts export interface Drawable { draw(x:number,y:number): void; } // drawCanvas.ts import { Drawable } from './drawable'; import { MacroCommand } from './macroCommand'; export class DrawCanvas implements Drawable { private history: MacroCommand; constructor(history: MacroCommand) { this.history = history; } paint(): void { this.history.execute(); } draw(x: number, y: number): void { console.log(`Drawing at (${x}, ${y})`); } } // drawCommand.ts import { Command } from './command'; import { DrawCanvas } from './drawCanvas'; export class DrawCommand implements Command { private x: number; private y: number; constructor(private canv: DrawCanvas,x: number, y: number) { this.x = x; this.y = y; } execute(): void { this.canv.draw(this.x, this.y) } } // macroCommand.ts import { Command } from './command'; export class MacroCommand implements Command { private commands: Command[] = []; push(command: Command): void { this.commands.push(command); } undo(): void { this.commands.pop(); } clear(): void { this.commands = []; } execute(): void { this.commands.forEach((command) => { command.execute(); }); } } // main.ts import { DrawCanvas } from './drawCanvas'; import { MacroCommand } from './macroCommand'; import { DrawCommand } from './drawCommand'; const history = new MacroCommand(); const canvas = new DrawCanvas(history); for (let i = 0; i < 10; i++) { const cmd = new DrawCommand(canvas, i, i); history.push(cmd); } canvas.paint(); \"]},\"212\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\command\\\\main.ts\\\" Drawing at (0, 0) Drawing at (1, 1) Drawing at (2, 2) Drawing at (3, 3) Drawing at (4, 4) Drawing at (5, 5) Drawing at (6, 6) Drawing at (7, 7) Drawing at (8, 8) Drawing at (9, 9) \"]},\"213\":{\"h\":\"拓展思路的要点\"},\"214\":{\"h\":\"命令中应该包含哪些信息\",\"t\":[\"在命令模式中，命令对象通常包含以下信息：\",\"接收者（Receiver）：执行命令的对象。接收者包含了执行具体操作的逻辑。\",\"动作（Action）：要执行的具体操作。命令对象将动作封装为一个方法调用。\",\"参数（Parameters）：执行操作所需的参数。命令对象可以包含执行操作所需的所有参数。\",\"状态（State）：命令执行前后的状态信息。命令对象可以保存执行前的状态，以便在需要时进行撤销操作。\",\"通过将这些信息封装在命令对象中，可以实现命令的参数化和可撤销性，从而提高系统的灵活性和可维护性。\"]},\"215\":{\"h\":\"保存历史记录\",\"t\":[\"命令模式的一个重要应用是保存历史记录，以支持撤销和重做操作。通过将每个执行的命令对象保存到一个历史记录列表中，可以在需要时回滚到之前的状态。以下是实现保存历史记录的一些常见方法：\",\"命令栈（Command Stack）：使用栈数据结构保存执行的命令对象。每次执行命令时，将命令对象压入栈中；每次撤销操作时，从栈中弹出命令对象并执行撤销操作。\",\"命令队列（Command Queue）：使用队列数据结构保存执行的命令对象。适用于需要按顺序执行和撤销命令的场景。\",\"快照（Snapshot）：在执行命令前保存对象的快照，以便在需要时恢复到之前的状态。适用于需要保存复杂对象状态的场景。\"]},\"216\":{\"h\":\"相关的设计模式\",\"t\":[\"Composite 模式\",\"Memento 模式\",\"Prototype 模式\"]},\"217\":{\"c\":[\"设计模式\"]},\"218\":{\"c\":[\"设计模式\",\"TypeScript\",\"用类实现\"]},\"219\":{\"h\":\"Composite 模式\"},\"220\":{\"h\":\"使用此设计模式的理由\",\"t\":[\"Composite 模式允许你将对象组合成递归结构来表示“部分-整体”的层次结构。使用 Composite 模式，用户可以统一地对待单个对象和组合对象。例如，在文件系统中，目录和文件都可以被视为条目（Entry），目录可以包含其他目录和文件，而文件则是叶子节点。\"]},\"221\":{\"h\":\"示例代码\"},\"222\":{\"h\":\"目录类 (directory.ts)\",\"t\":[\"import { Entry } from './entry'; export class Directory extends Entry { private directory: Entry[] = []; constructor(private name: string) { super(); } getName(): string { return this.name; } getSize(): number { return this.directory.reduce((acc, entry) => acc + entry.getSize(), 0); } add(entry: Entry): Entry { this.directory.push(entry); return this; } protected printListWithPrefix(prefix: string): void { console.log(`${prefix}/${this}`); this.directory.forEach(entry => (entry as Directory).printListWithPrefix(`${prefix}/${this.name}`)); } } \"]},\"223\":{\"h\":\"抽象条目类 (entry.ts)\",\"t\":[\"export abstract class Entry { abstract getName(): string; abstract getSize(): number; add(entry: Entry): Entry { throw new Error(\\\"FileTreatmentException\\\"); } printList(): void { this.printListWithPrefix(\\\"\\\"); } protected abstract printListWithPrefix(prefix: string): void; toString(): string { return `${this.getName()} (${this.getSize()})`; } } \"]},\"224\":{\"h\":\"文件类 (file.ts)\",\"t\":[\"import { Entry } from './entry'; export class File extends Entry { constructor(private name: string, private size: number) { super(); } getName(): string { return this.name; } getSize(): number { return this.size; } protected printListWithPrefix(prefix: string): void { console.log(`${prefix}/${this}`); } } \"]},\"225\":{\"h\":\"主程序 (main.ts)\",\"t\":[\"import { Entry } from './entry'; import { Directory } from './directory'; import { File } from './file'; console.log('Making root entries...'); let rootdir: Directory = new Directory('root'); let bindir: Directory = new Directory('bin'); let tmpdir: Directory = new Directory('tmp'); let usrdir: Directory = new Directory('usr'); rootdir.add(bindir); rootdir.add(tmpdir); rootdir.add(usrdir); bindir.add(new File('vi', 10000)); bindir.add(new File('latex', 20000)); rootdir.printList(); console.log(\\\"Making user entries...\\\"); let yuki: Directory = new Directory('yuki'); let hanako: Directory = new Directory('hanako'); let tomura: Directory = new Directory('tomura'); usrdir.add(yuki); usrdir.add(hanako); usrdir.add(tomura); yuki.add(new File('diary.html', 100)); yuki.add(new File('Composite.java', 200)); hanako.add(new File('memo.tex', 300)); tomura.add(new File('game.doc', 400)); tomura.add(new File('junk.mail', 500)); rootdir.printList(); \"]},\"226\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\composite\\\\main.ts\\\" Making root entries... /root (30000) /root/bin (30000) /root/bin/vi (10000) /root/bin/latex (20000) /root/tmp (0) /root/usr (0) Making user entries... /root (31500) /root/bin (30000) /root/bin/vi (10000) /root/bin/latex (20000) /root/tmp (0) /root/usr (1500) /root/usr/yuki (300) /root/usr/yuki/diary.html (100) /root/usr/yuki/Composite.java (200) /root/usr/hanako (300) /root/usr/hanako/memo.tex (300) /root/usr/tomura (900) /root/usr/tomura/game.doc (400) /root/usr/tomura/junk.mail (500) \"]},\"227\":{\"h\":\"相关的设计模式\",\"t\":[\"Command 模式\",\"Visitor 模式\",\"Decorator 模式\"]},\"228\":{\"c\":[\"设计模式\"]},\"229\":{\"c\":[\"设计模式\",\"TypeScript\",\"容器与内容的一致性\"]},\"230\":{\"h\":\"Decorator 模式\",\"t\":[\"在这个示例中，我们使用装饰器模式来动态地给对象添加职责。装饰器模式允许我们通过将对象放入包含行为的特殊封装对象中来扩展对象的功能，而无需修改原始类的代码。\"]},\"231\":{\"h\":\"为什么使用装饰器模式？\",\"t\":[\"职责扩展：装饰器模式允许我们在不修改现有代码的情况下扩展对象的功能。\",\"灵活性：可以根据需要动态地添加或删除职责。\",\"遵循开闭原则：通过使用装饰器模式，我们可以在不修改现有类的情况下添加新功能，从而遵循开闭原则。\"]},\"232\":{\"h\":\"代码示例\",\"t\":[\"// border.ts import { Display } from \\\"./display\\\"; export abstract class Border extends Display { protected display: Display; constructor(display: Display) { super(); this.display = display; } } // display.ts export abstract class Display { abstract getColumns(): number; abstract getRows(): number; abstract getRowText(row: number): string; show(): void { for (let i = 0; i < this.getRows(); i++) { console.log(this.getRowText(i)); } } } // fullBorder.ts import { Border } from \\\"./border\\\"; export class FullBorder extends Border { constructor(display) { super(display); } getColumns() { return 1 + this.display.getColumns() + 1; } getRows() { return 1 + this.display.getRows() + 1; } getRowText(row) { if (row === 0) { return \\\"+\\\" + this.makeLine(\\\"-\\\", this.display.getColumns()) + \\\"+\\\"; } else if (row === this.display.getRows() + 1) { return \\\"+\\\" + this.makeLine(\\\"-\\\", this.display.getColumns()) + \\\"+\\\"; } else { return \\\"|\\\" + this.display.getRowText(row - 1) + \\\"|\\\"; } } private makeLine(ch, count) { let buf = \\\"\\\"; for (let i = 0; i < count; i++) { buf += ch; } return buf; } } // main.ts import { Display } from \\\"./display\\\"; import { StringDisplay } from \\\"./stringDisplay\\\"; import { SideBorder } from \\\"./sideBorder\\\"; import { FullBorder } from \\\"./fullBorder\\\"; let b1: Display = new StringDisplay(\\\"Hello, world.\\\"); let b2: Display = new SideBorder(b1, \\\"#\\\"); let b3: Display = new FullBorder(b2); b1.show(); b2.show(); b3.show(); let b4: Display = new SideBorder( new FullBorder( new FullBorder( new SideBorder( new FullBorder( new StringDisplay(\\\"Hello\\\") ), \\\"*\\\" ) ) ), \\\"/\\\" ); b4.show(); // sideBorder.ts import { Border } from \\\"./border\\\"; import { Display } from \\\"./display\\\"; export class SideBorder extends Border { private borderChar: string; constructor(display: Display, ch: string) { super(display); this.borderChar = ch; } getColumns(): number { return 1 + this.display.getColumns() + 1; } getRows(): number { return this.display.getRows(); } getRowText(row: number): string { return this.borderChar + this.display.getRowText(row) + this.borderChar; } } // stringDisplay.ts import { Display } from './display'; export class StringDisplay extends Display { private string: string; constructor(string: string) { super(); this.string = string; } getColumns(): number { return this.string.length; } getRows(): number { return 1; } getRowText(row: number): string { if (row === 0) { return this.string; } else { return ''; } } } \"]},\"233\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\decorator\\\\main.ts\\\" Hello, world. #Hello, world.# +---------------+ |#Hello, world.#| +---------------+ /+-----------+/ /|+---------+|/ /||*+-----+*||/ /||*|Hello|*||/ /||*+-----+*||/ /|+---------+|/ /+-----------+/ \"]},\"234\":{\"h\":\"拓展思路的要点\"},\"235\":{\"h\":\"API 的透明性\",\"t\":[\"在 Decorator 模式中，装饰边框与被装饰物具有一致性。具体而言，在示例程序中，表示装饰边框的 Border 类是表示被装饰物的 Display 类的子类，这就体现了它们之间的一致性。也就是说， Border 类（以及它的子类）与表示被装饰物的 Display 类具有相同的接口（API）。这样，即使被装饰物被边框装饰起来了，接口（API）也不会被隐藏起来。其他类依然可以调用 getColumns、getRows、getRowText 以及 show 方法。这就是接口（API）的“透明性”。在示例程序中，实例 b4 被装饰了多次，但是接口（API）却没有发生任何变化。得益于接口（API）的透明性，模式中也形成了类似于 Composite 模式中的递归结构。也就是说，装饰边框里面的“被装饰物”实际上又是别的物体的“装饰边框”。就像是剥洋葱时以为洋葱心要出来了，结果却发现还是皮。不过， Decorator 模式虽然与 Composite 模式一样，都具有递归结构，但是它们的使用目的不同。Decorator 模式的主要目的是通过添加装饰物来增加对象的功能。\"]},\"236\":{\"h\":\"在不改变被装饰物的前提下增加功能\",\"t\":[\"在 Decorator 模式中，装饰边框与被装饰物具有相同的接口（API）。虽然接口是相同的，但是越装饰，功能则越多。例如，用 SideBorder 装饰 Display 后，就可以在字符串的左右两侧加上装饰字符。如果再用 FullBorder 装饰，那么就可以在字符串的四周加上边框。此时，我们完全不需要对被装饰的类做任何修改。这样，我们就实现了不修改被装饰的类即可增加功能。Decorator 模式使用了委托。对“装饰边框”提出的要求（调用装饰边框的方法）会被转交（委托）给“被装饰物”去处理。以示例程序来说，就是 SideBorder 类的 getColumns 方法调用了 display.getColumns。此外，getRows 方法也调用了 display.getRows。\"]},\"237\":{\"h\":\"可以动态地增加功能\",\"t\":[\"Decorator 模式中用到了委托，它使类之间形成了弱关联关系。因此，不用改变框架代码，就可以生成一个与其他对象具有不同关系的新对象。\"]},\"238\":{\"h\":\"只需要一些装饰物即可添加许多功能\",\"t\":[\"使用 Decorator 模式可以为程序添加许多功能。只要准备一些装饰边框（ConcreteDecorator 角色），即使这些装饰边框都只具有非常简单的功能，也可以将它们自由组合成为新的对象。这就像我们可以自由选择香草味冰激凌、巧克力冰激凌、草莓冰激凌、猕猴桃冰激凌等各种口味的冰激凌一样。如果冰激凌店要为顾客准备所有的冰激凌成品那真是太麻烦了。因此，冰激凌店只会准备各种香料，当顾客下单后只需要在冰激凌上加上各种香料就可以了。不管是香草味，还是咖啡朗姆和开心果的混合口味，亦或是香草味、草莓味和猕猴桃三重口味，顾客想吃什么口味都可以。Decorator 模式就是可以应对这种多功能对象的需求的一种模式。\"]},\"239\":{\"h\":\"导致增加许多很小的类\",\"t\":[\"Decorator 模式的一个缺点是会导致程序中增加许多功能类似的很小的类。\"]},\"240\":{\"h\":\"相关的设计模式\",\"t\":[\"Adapter 模式\",\"Strategy 模式\"]},\"241\":{\"h\":\"继承和委托中的一致性\"},\"242\":{\"h\":\"父类和子类的一致性\",\"t\":[\"在面向对象编程中，父类和子类之间的一致性是指子类应当继承父类的行为和属性，并且可以扩展或重写这些行为和属性。子类应当能够替代父类的实例而不影响程序的正确性，这就是所谓的里氏替换原则（Liskov Substitution Principle）。\"]},\"243\":{\"h\":\"自己和被委托对象的一致性\",\"t\":[\"在委托模式中，一致性是指委托对象应当具有与委托者相同的接口或行为。委托者将某些任务委托给委托对象来执行，而委托对象应当能够无缝地完成这些任务，就像委托者自己完成一样。这种一致性确保了委托模式的灵活性和可维护性。\"]},\"244\":{\"c\":[\"设计模式\"]},\"245\":{\"c\":[\"设计模式\",\"TypeScript\",\"容器与内容的一致性\"]},\"246\":{\"h\":\"结语\",\"t\":[\"教程源码示例\",\"使用设计模式的目的是重用代码，并在增加需求时尽量不修改已有的类。我们不应死记硬背这些设计模式，而应理解其背后的核心思想。设计模式的使用不是最终目的，而是为了更好地解决问题和优化代码结构。同时，我们也要避免过早地进行“工程化”，应根据实际需求灵活应用设计模式。\",\"设计模式提供了一种通用的解决方案，可以帮助我们应对软件开发中的常见问题。通过学习和应用设计模式，我们可以提高代码的可读性、可维护性和可扩展性。然而，设计模式并不是万能的，它们也有其局限性和适用范围。在实际开发中，我们需要根据具体情况选择合适的设计模式，而不是盲目地套用。\",\"此外，设计模式的学习和应用需要不断的实践和积累。只有在实际项目中多次使用，才能真正理解和掌握这些模式。我们还应关注设计模式的演变和新模式的出现，以保持我们的知识体系与时俱进。\",\"总之，设计模式是软件开发中的一把利器，但它需要我们在理解其核心思想的基础上，灵活应用于实际项目中。希望通过本章的学习，您能够掌握这些设计模式，并在实际项目中灵活运用它们，编写出更加健壮和优雅的代码。\"]},\"247\":{\"c\":[\"设计模式\"]},\"248\":{\"c\":[\"设计模式\",\"TypeScript\"]},\"249\":{\"h\":\"facade 模式\",\"t\":[\"当某个程序员得意地说出\\\"啊，在调用那个类之前需要先调用这个类。在调用那个方法之前需要先在这个类中注册一下\\\"的时候，就意味着我们需要引人Facade了。\",\"对于那些能够明确地用语言描述出来的知识，我们不应该将它们隐藏在自己脑袋中，而是应该用代码将它们表现出来。\",\"—————《图解设计模式》 ## 为什么使用外观模式？ \",\"简化接口：外观模式为复杂的子系统提供了一个简单的接口，使得客户端代码不需要了解子系统的内部细节。\",\"松散耦合：通过引入外观类，客户端代码与子系统之间的耦合度降低，增强了代码的可维护性和可扩展性。\",\"更好的分层：外观模式有助于分层设计，使得每一层只关注自己的职责，层与层之间通过外观类进行交互。\"]},\"250\":{\"h\":\"示例代码\",\"t\":[\"在这个示例中，我们使用了外观模式（Facade Pattern）来简化与复杂子系统的交互。外观模式通过提供一个统一的接口来隐藏子系统的复杂性，使得客户端代码可以更容易地使用子系统的功能。\"]},\"251\":{\"h\":\"代码实现\",\"t\":[\"// dataBase.ts export class DataBase { static mailData: { [key: string]: string } = { 'hyuki@hyuki.com': 'Hiroshi Yuki', 'hanako@hyuki.com': 'Hanako Sato', 'tomura@hyuki.com': 'Tomura', 'mamoru@hyuki.com': 'Mamoru Takahashi', }; private constructor() {} static getProperties(databaseName: string) { return DataBase.mailData; } } // htmlWriter.ts export class HtmlWriter { constructor(private writer: string = '') { } title(title: string): void { this.writer += `<html><head><title>${title}</title></head><body>\\\\n<h1>${title}</h1>\\\\n`; } paragraph(message: string): void { this.writer += `<p>${message}</p>\\\\n`; } link(href: string, caption: string): void { this.writer += `<a href=\\\"${href}\\\">${caption}</a>\\\\n`; } mailto(mailaddr: string, username: string): void { this.link(`mailto:${mailaddr}`, username); } close(): void { this.writer += '</body></html>\\\\n'; } getHtml(): string { return this.writer; } } // main.ts import { PageMaker } from \\\"./pageMaker\\\"; PageMaker.makeWelcomePage('hyuki@hyuki.com', \\\"welcome.html\\\"); // pageMaker.ts import { DataBase } from './dataBase'; import { HtmlWriter } from './htmlWriter'; export class PageMaker { private constructor() {} static makeWelcomePage(mailAddress: string, fileName: string): void { console.log(`Making ${fileName} for ${mailAddress}`); let mailprop = DataBase.getProperties('maildata'); let username = mailprop[mailAddress]; let writer = new HtmlWriter(fileName); writer.title('Welcome to ' + username + \\\"'s page!\\\"); writer.paragraph(username + 'のページへようこそ。'); writer.paragraph('メール待っていますね。'); writer.mailto(mailAddress, username); writer.close(); console.log(writer.getHtml()); } } \"]},\"252\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\facade\\\\main.ts\\\" Making welcome.html for hyuki@hyuki.com welcome.html<html><head><title>Welcome to Hiroshi Yuki's page!</title></head><body> <h1>Welcome to Hiroshi Yuki's page!</h1> <p>Hiroshi Yukiのページへようこそ。</p> <p>メール待っていますね。</p> <a href=\\\"mailto:hyuki@hyuki.com\\\">Hiroshi Yuki</a> </body></html> \"]},\"253\":{\"h\":\"相关设计模式\",\"t\":[\"Abstract Factory 模式\",\"Singleton 模式\",\"Mediator 模式\"]},\"254\":{\"c\":[\"设计模式\"]},\"255\":{\"c\":[\"设计模式\",\"TypeScript\",\"简单化\"]},\"256\":{\"h\":\"Factory Method 模式\",\"t\":[\"在 Factory Method 模式中，我们定义一个用于创建对象的接口，但由子类决定要实例化的类是哪一个。Factory Method 使一个类的实例化延迟到其子类。\"]},\"257\":{\"h\":\"为什么要使用 Factory Method\",\"t\":[\"使用 Factory Method 模式有以下几个好处：\",\"解耦创建和使用：客户端代码不需要知道具体的产品类，只需要依赖抽象产品接口，降低了耦合性。\",\"扩展性强：增加新的产品类时，只需添加新的子类工厂，不需要修改现有代码，符合开闭原则。\",\"灵活性高：可以通过子类来定制产品的创建过程，满足不同的需求。\",\"通过使用 Factory Method 模式，我们可以更灵活地管理对象的创建过程，提高代码的可维护性和可扩展性。\"]},\"258\":{\"h\":\"示例代码\",\"t\":[\"@enduml\",\"// product.ts export interface Product { use(): void; } // factory.ts import { Product } from './product'; export abstract class Factory { create(owner: string): Product { const p = this.createProduct(owner); this.registerProduct(p); return p; } protected abstract createProduct(owner: string): Product; protected abstract registerProduct(product: Product): void; } // idCard.ts import { Product } from './product'; export class IDCard implements Product { private owner: string; constructor(owner: string) { this.owner = owner; } use(): void { console.log(`${this.owner}使用了ID卡`); } getOwner(): string { return this.owner; } } // idCardFactory.ts import { IDCard } from \\\"./idCard\\\"; import { Factory } from \\\"./factory\\\"; export class IDCardFactory extends Factory { private owners: string[] = []; createProduct(owner: string): IDCard { return new IDCard(owner); } registerProduct(product: IDCard): void { this.owners.push(product.getOwner()); } getOwners(): string[] { return this.owners; } } // main.ts import { Factory } from \\\"./factory\\\"; import { IDCardFactory } from \\\"./idCardFactory\\\"; const factory: Factory = new IDCardFactory(); const card1 = factory.create(\\\"Alice\\\"); const card2 = factory.create(\\\"Bob\\\"); const card3 = factory.create(\\\"Charlie\\\"); card1.use(); card2.use(); card3.use(); \"]},\"259\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\factory_method\\\\main.ts\\\" Alice使用了ID卡 Bob使用了ID卡 Charlie使用了ID卡 \",\"Template Method\",\"Singleton\",\"Composite\",\"Iterator\"]},\"260\":{\"c\":[\"设计模式\"]},\"261\":{\"c\":[\"设计模式\",\"typescript\",\"工厂方法\",\"交给子类\"]},\"262\":{\"h\":\"Flyweight 模式\"},\"263\":{\"h\":\"为什么使用 Flyweight 模式\",\"t\":[\"Flyweight 模式是一种结构型设计模式，它通过共享尽可能多的相同对象来减少内存使用，从而提高性能。在需要生成大量细粒度对象的场景中，Flyweight 模式非常有用。通过共享对象，Flyweight 模式可以显著减少内存消耗，并提高应用程序的效率。\"]},\"264\":{\"h\":\"实例代码\",\"t\":[\"// bigChar.ts export class BigChar { charname: string; fontdata: string; static fontdatas: { [key: string]: string } = { \\\"0\\\": \\\".....######.....\\\\n\\\" + \\\"....##....##....\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\"....##....##....\\\\n\\\" + \\\".....######.....\\\\n\\\", \\\"1\\\": \\\".......##.......\\\\n\\\" + \\\".....####.......\\\\n\\\" + \\\".......##.......\\\\n\\\" + \\\".......##.......\\\\n\\\" + \\\".......##.......\\\\n\\\" + \\\".......##.......\\\\n\\\" + \\\".......##.......\\\\n\\\" + \\\".......##.......\\\\n\\\" + \\\".......##.......\\\\n\\\" + \\\".....######.....\\\\n\\\" + \\\"................\\\\n\\\", \\\"2\\\": \\\".....######.....\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"..........##....\\\\n\\\" + \\\".........##.....\\\\n\\\" + \\\".......##.......\\\\n\\\" + \\\"......##........\\\\n\\\" + \\\".....##.........\\\\n\\\" + \\\"...##...........\\\\n\\\" + \\\"....##########..\\\\n\\\" + \\\"................\\\\n\\\", \\\"3\\\": \\\".....######.....\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"..........##....\\\\n\\\" + \\\".........##.....\\\\n\\\" + \\\"......####......\\\\n\\\" + \\\".........##.....\\\\n\\\" + \\\"..........##....\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\".....######.....\\\\n\\\", \\\"4\\\": \\\"........###.....\\\\n\\\" + \\\".......####.....\\\\n\\\" + \\\"......##.##.....\\\\n\\\" + \\\".....##..##.....\\\\n\\\" + \\\"....##...##.....\\\\n\\\" + \\\"...##....##.....\\\\n\\\" + \\\"..##########....\\\\n.\\\" + \\\"........##......\\\\n\\\" + \\\"........##......\\\\n\\\" + \\\".......######...\\\\n\\\", \\\"5\\\": \\\"....########....\\\\n\\\" + \\\"....########....\\\\n\\\" + \\\"....##..........\\\\n\\\" + \\\"....##..........\\\\n\\\" + \\\"....##..........\\\\n\\\" + \\\"....##..........\\\\n\\\" + \\\"....##..........\\\\n\\\" + \\\"....##..........\\\\n\\\" + \\\"....######......\\\\n\\\" + \\\"....######......\\\\n\\\" + \\\"..........##....\\\\n\\\" + \\\"..........##....\\\\n\\\" + \\\"...........##...\\\\n\\\" + \\\"...........##...\\\\n\\\" + \\\"...........##...\\\\n\\\" + \\\"...........##...\\\\n\\\" + \\\"..##.......##...\\\\n\\\" + \\\"..##.......##...\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\".....######.....\\\\n\\\", \\\"6\\\": \\\".......####.....\\\\n\\\" + \\\"......##........\\\\n\\\" + \\\".....##.........\\\\n\\\" + \\\"....##..........\\\\n\\\" + \\\"...##...........\\\\n\\\" + \\\"..######........\\\\n\\\" + \\\"..##...##.......\\\\n\\\" + \\\"..##....##......\\\\n\\\" + \\\"..##.....##.....\\\\n\\\" + \\\"...##....##.....\\\\n\\\" + \\\"....####........\\\\n\\\", \\\"7\\\": \\\"..##########....\\\\n\\\" + \\\"..##......##....\\\\n\\\" + \\\"........##......\\\\n\\\" + \\\".......##.......\\\\n\\\" + \\\"......##........\\\\n\\\" + \\\"......##........\\\\n\\\" + \\\".....##.........\\\\n\\\" + \\\".....##.........\\\\n\\\" + \\\"....##..........\\\\n\\\" + \\\"....##..........\\\\n\\\" + \\\"....##..........\\\\n\\\", \\\"8\\\": \\\".....######.....\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\"....######......\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\".....######.....\\\\n\\\", \\\"9\\\": \\\".....######.....\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"..##........##..\\\\n\\\" + \\\"...##......##...\\\\n\\\" + \\\"....#######.....\\\\n\\\" + \\\"..........##....\\\\n\\\" + \\\".........##.....\\\\n\\\" + \\\"........##......\\\\n\\\" + \\\"......###.......\\\\n\\\" + \\\".....##.........\\\\n\\\", }; constructor(charname: string) { this.charname = charname; this.fontdata = BigChar.fontdatas[charname]; this.fontdata = this.fontdata.replace(/#/g, charname); } print(): void { console.log(this.fontdata); } } // bigCharFactory.ts import { BigChar } from './bigChar'; export class BigCharFactory { private pool: Map<string, BigChar> = new Map(); private static singleton: BigCharFactory = new BigCharFactory(); private constructor() { } public static getInstance(): BigCharFactory { return BigCharFactory.singleton; } public getBigChar(charname: string): BigChar { let bc: BigChar = this.pool.get(charname); // ts 是单线程的，所以不需要考虑多线程问题， 若为多线程则需要加锁 if (bc == null) { bc = new BigChar(charname); this.pool.set(charname, bc); } return bc; } } // bigString.ts import { Factory } from '../abstractFactory/factory'; import { BigChar } from './bigChar'; import { BigCharFactory } from './bigCharFactory'; export class BigString { bigchars: BigChar[] = []; constructor(public str: string) { let factory = BigCharFactory.getInstance(); str.split('').forEach((char) => { this.bigchars.push(factory.getBigChar(char)); }); } print() { this.bigchars.forEach((bigchar) => { bigchar.print(); }); } } // main.ts import { BigString } from './bigString'; let bs: BigString = new BigString('123'); bs.print(); \"]},\"265\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\flyweight\\\\main.ts\\\" .......11....... .....1111....... .......11....... .......11....... .......11....... .......11....... .......11....... .......11....... .......11....... .....111111..... ................ .....222222..... ...22......22... ..22........22.. ..........22.... .........22..... .......22....... ......22........ .....22......... ...22........... ....2222222222.. ................ .....333333..... ...33......33... ..33........33.. ..........33.... .........33..... ......3333...... .........33..... ..........33.... ..33........33.. ...33......33... .....333333..... \"]},\"266\":{\"h\":\"拓展思路的要点\"},\"267\":{\"h\":\"对多个地方产生影响\",\"t\":[\"Flyweight 模式的主题是“共享”。那么，在共享实例时应当注意什么呢？首先要想到的是“如果要改变被共享的对象，就会对多个地方产生影响”。也就是说，一个实例的改变会同时反映到所有使用该实例的地方。例如，假设我们改变了示例程序中 BigChar 类的 '3' 所对应的字体数据，那么 BigString 类中使用的所有 '3' 字符的字体（形状）都会发生改变。在编程时，像这样改一个地方会对多个地方产生影响并非总是不好。有些情况下这是好事，有些情况下这是坏事。不管怎样，“修改一个地方会对多个地方产生影响”，这就是共享的特点。\",\"因此，在决定 Flyweight 角色中的字段时，需要精挑细选。只将那些真正应该在多个地方共享的字段定义在 Flyweight 角色中即可。关于这一点，让我们简单地举个例子。假设我们要在示例程序中增加一个功能，实现显示“带颜色的大型文字”。那么此时，颜色信息应当放在哪个类中呢？首先，假设我们将颜色信息放在 BigChar 类中。由于 BigChar 类的实例是被共享的，因此颜色信息也被共享了。也就是说，BigString 类中用到的所有 BigChar 类的实例都带有相同的颜色。如果我们不把颜色信息放在 BigChar 类中，而是将它放在 BigString 类中。那么 BigString 类会负责管理“第三个字符的颜色是红色的”这样的颜色信息。这样一来，我们就可以实现以不同的颜色显示同一个 BigChar 类的实例。\",\"那么两种解决方案到底哪个是正确的呢？关于这个问题，其实并没有绝对的答案。哪些信息应当共享，哪些信息不应当共享，这取决于类的使用目的。设计者在使用 Flyweight 模式共享信息时必须仔细思考应当共享哪些信息。\"]},\"268\":{\"h\":\"Intrinsic 与 Extrinsic\",\"t\":[\"前面讲到的“应当共享的信息和不应当共享的信息”是有专有名词的。应当共享的信息被称作 Intrinsic 信息。Intrinsic 的意思是“本质的”“固有的”。换言之，它指的是不论实例在哪里、不论在什么情况下都不会改变的信息，或是不依赖于实例状态的信息。\",\"在示例程序中，BigChar 的字体数据不论在 BigString 中的哪个地方都不会改变。因此，BigChar 的字体数据属于 Intrinsic 信息。另一方面，不应当共享的信息被称作 Extrinsic 信息。Extrinsic 的意思是“外在的”“非本质的”。也就是说，它是当实例的位置、状况发生改变时会变化的信息，或是依赖于实例状态的信息。在示例程序中，BigChar 的实例在 BigString 中是第几个字符这种信息会根据 BigChar 在 BigString 中的位置变化而发生变化，因此，不应当在 BigChar 中保存这个信息，它属于 Extrinsic 信息。因此，前面提到的是否共享“颜色”信息这个问题，我们也可以换种说法，即应当将“颜色”看作是 Intrinsic 信息还是 Extrinsic 信息。\"]},\"269\":{\"h\":\"不要让被共享的实例被垃圾回收器回收了\",\"t\":[\"在有垃圾回收的语言中要注意共享内存未被使用时被 GC 的问题。在使用 Flyweight 模式时，我们通常会将共享对象存储在某种集合（如 HashMap 或 List）中，以便重复使用这些对象。然而，如果这些集合中的对象没有被其他任何地方引用，垃圾回收器可能会认为这些对象是垃圾，从而将其回收掉。这会导致共享对象在需要时无法被找到，从而引发程序错误。\",\"为了避免这种情况，我们需要确保共享对象在整个程序生命周期内都被引用。以下是一些常见的解决方案：\",\"强引用：将共享对象存储在一个全局的集合中，并确保这个集合在程序的整个生命周期内都存在。这种方法简单直接，但可能会导致内存泄漏，因为共享对象永远不会被回收。\",\"弱引用：使用弱引用（WeakReference）来存储共享对象。弱引用允许垃圾回收器在没有其他强引用时回收对象，从而避免内存泄漏。Java 提供了 WeakHashMap 类，可以用来存储弱引用的键值对。\",\"引用计数：通过引用计数来管理共享对象的生命周期。每当一个对象被引用时，增加计数；每当一个引用被释放时，减少计数。当计数为零时，表示该对象不再被使用，可以安全地回收。\",\"定期清理：定期检查集合中的对象，移除那些不再被使用的对象。这种方法需要额外的逻辑来判断对象是否仍然被使用，但可以有效地管理内存。\"]},\"270\":{\"h\":\"内存之外的其它资源\",\"t\":[\"在示例程序中，我们了解到共享实例可以减少内存使用量。一般来说，共享实例可以减少所需资源的使用量。这里的资源指的是计算机中的资源，而内存是资源中的一种。时间也是一种资源。使用 new 关键字生成实例会花费时间。通过 Flyweight 模式共享实例可以减少使用 new 关键字生成实例的次数。这样，就可以提高程序运行速度。文件句柄（文件描述符）和窗口句柄等也都是一种资源。在操作系统中，可以同时使用的文件句柄和窗口句柄是有限制的。因此，如果不共享实例，应用程序在运行时很容易就会达到资源极限而导致崩溃。\"]},\"271\":{\"h\":\"相关的设计模式\",\"t\":[\"Proxy 模式\",\"Composite 模式\",\"Singleton 模式\"]},\"272\":{\"c\":[\"设计模式\"]},\"273\":{\"c\":[\"设计模式\",\"TypeScript\",\"避免浪费\"]},\"274\":{\"h\":\"设计模式\",\"t\":[\"面向对象三大特性：封装、继承、多态。 设计模式需遵循面向对象的设计原则，由于笔者不太喜欢java, 并嫌弃cpp中没有interface, 遂使用ts作为实现语言(我才不用rust呢 😃 )\",\"本专栏源码大部分参考自参考资料[1]\",\"教程源码示例\",\"[1] 结城浩. 图解设计模式. 杨文轩译. 北京: 人民邮电出版社, 2017.\"]},\"275\":{\"c\":[\"设计模式\"]},\"276\":{\"c\":[\"设计模式\",\"typescript\"]},\"277\":{\"h\":\"Interpreter 模式\"},\"278\":{\"h\":\"为什么使用此模式\",\"t\":[\"解释器模式（Interpreter Pattern）是一种行为设计模式，它定义了一种语言的文法表示，并定义一个解释器来解释该语言中的句子。使用解释器模式的原因包括：\",\"简化语法解析：通过定义文法规则，可以轻松解析和执行特定的语言或指令集。\",\"可扩展性：可以轻松添加新的语法规则或指令，而无需修改现有代码。\",\"代码复用：通过将不同的语法规则封装在不同的类中，可以提高代码的复用性和可维护性。\"]},\"279\":{\"h\":\"示例代码\",\"t\":[\"本实例是一个控制小车的脚本语言解释器demo,文法如下， 分析方法为递归下降\",\"<program> ::= program <command list> <command list> ::= <command>* end <command> ::= <repeat command> | <primitive command> <repeat command> ::= repeat <number> <command list> <primitive command> ::= go | right | left \",\"// commandListNode.ts import { Node } from \\\"./node\\\"; import { Context } from \\\"./context\\\"; import { CommandNode } from \\\"./commandNode\\\"; // <command list> ::= <command>* end export class CommandListNode extends Node { list: Node[] = []; parse(context: Context): void { while (true) { if (context.getCurrentToken() === null) { throw new Error(\\\"Missing 'end'\\\"); } else if (context.getCurrentToken() === \\\"end\\\") { context.skipToken(\\\"end\\\"); break; } else { const commandNode = new CommandNode(); commandNode.parse(context); this.list.push(commandNode); } } } toString(): string { return this.list.join(\\\"\\\"); } } // commandNode.ts import { Context } from \\\"./context\\\"; import { Node } from \\\"./node\\\"; import { RepeatCommandNode } from \\\"./repeatCommandNode\\\"; import { PrimitiveCommandNode } from \\\"./primitiveCommandNode\\\"; // <command> ::= <repeat command> | <primitive command> export class CommandNode extends Node { node: Node; parse(context: Context): void { if (context.getCurrentToken() === \\\"repeat\\\") { this.node = new RepeatCommandNode(); this.node.parse(context); } else { this.node = new PrimitiveCommandNode(); this.node.parse(context); } } toString(): string { return this.node.toString(); } } // context.ts import { StringTokenizer } from './stringTokenizer'; export class Context { private stringTokenizer: StringTokenizer; private currentToken: string; constructor(text: string) { this.stringTokenizer = new StringTokenizer(text); this.nextToken(); } nextToken(): string { if (this.stringTokenizer.hasMoreTokens()) { this.currentToken = this.stringTokenizer.nextToken(); } else { this.currentToken = null; } return this.currentToken; } getCurrentToken(): string { return this.currentToken; } skipToken(token: string): void { if (token != this.currentToken) { throw new Error(`Warning: ${token} is expected, but ${this.currentToken} is found.`); } this.nextToken(); } getCurrentNumber(): number { let number: number; try { number = Number(this.currentToken); } catch (e) { throw new Error(`Warning: ${e}`); } return number; } } // main.ts import { Context } from \\\"./context\\\"; import { ProgramNode } from \\\"./programNode\\\"; // <program> ::= program <command list> // <command list> ::= <command>* end // <command> ::= <repeat command> | <primitive command> // <repeat command> ::= repeat <number> <command list> // <primitive command> ::= go | right | left let programs = \\\"program end\\\\n\\\"+ \\\"program go end\\\\n\\\"+ \\\"program go right go right go right end\\\\n\\\"+ \\\"program repeat 4 go right end end\\\\n\\\"+ \\\"program repeat 4 repeat 3 go right go left end right end end\\\\n\\\"; programs.split(\\\"\\\\n\\\").forEach((text:string)=>{ if (text.length == 0) return; console.log(`current:\\\\n ${text}\\\\n`) let node = new ProgramNode() node.parse(new Context(text)) console.log(`node = ${node}`) }) // node.ts import {Context} from \\\"./context\\\"; export abstract class Node { abstract parse(ctx:Context): void; } // primitiveCommandNode.ts import { Node } from \\\"./node\\\"; import { Context } from \\\"./context\\\"; // <primitive command> ::= <go> | <right> | <left> export class PrimitiveCommandNode extends Node { private name: string; parse(context: Context): void { this.name = context.getCurrentToken(); context.skipToken(this.name); if (this.name !== \\\"go\\\" && this.name !== \\\"right\\\" && this.name !== \\\"left\\\") { throw new Error(`${this.name} is undefined`); } } toString(): string { return this.name+\\\" \\\"; } } // programNode.ts import { Node } from \\\"./node\\\"; import { CommandListNode } from \\\"./commandListNode\\\"; import {Context} from \\\"./context\\\"; // <program> ::= program <command list> export class ProgramNode extends Node { commandListNode: Node; parse(context:Context): void { context.skipToken(\\\"program\\\"); this.commandListNode = new CommandListNode(); this.commandListNode.parse(context); } toString(): string { return \\\"[program \\\" + this.commandListNode + \\\"]\\\"; } } // repeatCommandNode.ts import { Node } from \\\"./node\\\"; import { Context } from \\\"./context\\\"; import { CommandListNode } from \\\"./commandListNode\\\"; // <repeat command> ::= \\\"repeat\\\" <number> \\\"end\\\" export class RepeatCommandNode extends Node { number: number; commandListNode: CommandListNode; parse(context: Context): void { context.skipToken(\\\"repeat\\\"); this.number = context.getCurrentNumber(); context.nextToken(); this.commandListNode = new CommandListNode(); this.commandListNode.parse(context); } toString(): string { return `[repeat [${this.number} ${this.commandListNode.toString()}]]`; } } // StringTokenizer.ts export class StringTokenizer{ private text: string; private tokens: string[]; private index: number; constructor(text: string) { this.text = text; this.tokens = text.split(\\\" \\\"); this.index = 0; } nextToken(): string { return this.tokens[this.index++]; } hasMoreTokens(): boolean { return this.index < this.tokens.length; } } \"]},\"280\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\interperter\\\\main.ts\\\" current: program end node = [program ] current: program go end node = [program go ] current: program go right go right go right end node = [program go right go right go right ] current: program repeat 4 go right end end node = [program [repeat [4 go right ]]] current: program repeat 4 repeat 3 go right go left end right end end node = [program [repeat [4 [repeat [3 go right go left ]]right ]]] \"]},\"281\":{\"c\":[\"设计模式\"]},\"282\":{\"c\":[\"设计模式\",\"TypeScript\",\"用类实现\"]},\"283\":{\"h\":\"迭代器模式\"},\"284\":{\"h\":\"为什么要使用迭代器模式\",\"t\":[\"迭代器模式提供了一种方法来顺序访问集合中的元素，而无需暴露其底层表示。使用迭代器模式有以下几个优点：\",\"简化代码：迭代器模式将遍历逻辑封装在迭代器对象中，使得客户端代码更加简洁和易读。\",\"解耦集合和遍历：集合对象和遍历算法分离，增加了代码的灵活性和可维护性。可以在不修改集合对象的情况下，改变遍历算法。\",\"统一接口：通过实现统一的迭代器接口，不同类型的集合可以使用相同的遍历方式，增强了代码的可扩展性。\",\"支持多种遍历方式：可以根据需要实现不同的迭代器，以支持多种遍历方式，如正向遍历、反向遍历、过滤遍历等。\",\"通过使用迭代器模式，我们可以更好地管理和操作集合数据，提高代码的可读性和可维护性。\"]},\"285\":{\"h\":\"TypeScript 实现迭代器模式\",\"t\":[\"在本节中，我们将展示如何使用 TypeScript 实现迭代器模式。迭代器模式是一种行为设计模式，它允许顺序访问集合中的元素，而无需暴露其底层表示。\"]},\"286\":{\"h\":\"代码示例\",\"t\":[\"以下是实现迭代器模式的 TypeScript 代码示例：\",\"// aggregate.ts import { Iterator } from './iterator'; export interface Aggregate { iterator(): Iterator; } // book.ts export class Book { private name: string; constructor(name: string) { this.name = name; } getName(): string { return this.name; } } // bookShelf.ts import { Book } from './book'; import { Iterator } from './iterator'; import { BookShelfIterator } from './bookShelfIterator'; import { Aggregate } from './aggregate'; export class BookShelf implements Aggregate { private books: Book[]; private last: number = 0; constructor() { this.books = []; } getBookAt(index: number): Book { return this.books[index]; } appendBook(book: Book): void { this.books[this.last] = book; this.last++; } getLength(): number { return this.last; } iterator(): Iterator { return new BookShelfIterator(this); } } // bookShelfIterator.ts import { BookShelf } from './bookShelf'; import { Iterator } from './iterator'; export class BookShelfIterator implements Iterator { private bookShelf: BookShelf; private index: number; constructor(bookShelf: BookShelf) { this.bookShelf = bookShelf; this.index = 0; } hasNext(): boolean { return this.index < this.bookShelf.getLength(); } next(): any { const book = this.bookShelf.getBookAt(this.index); this.index++; return book; } } // iterator.ts export interface Iterator { hasNext(): boolean; next(): any; } // main.ts import { BookShelf } from \\\"../bookShelf\\\"; import { Book } from \\\"../book\\\"; const bookShelf = new BookShelf(); bookShelf.appendBook(new Book(\\\"Around the World in 80 Days\\\")); bookShelf.appendBook(new Book(\\\"Bible\\\")); bookShelf.appendBook(new Book(\\\"Cinderella\\\")); bookShelf.appendBook(new Book(\\\"Daddy-Long-Legs\\\")); const it = bookShelf.iterator(); while (it.hasNext()) { const book = it.next(); console.log(book.getName()); } \"]},\"287\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\iterator\\\\main.ts\\\" Around the World in 80 Days Bible Cinderella Daddy-Long-Legs \",\"在上面的代码中，我们定义了几个类和接口来实现迭代器模式：\",\"Iterator 接口定义了 hasNext 和 next 方法。\",\"Aggregate 接口定义了 iterator 方法。\",\"Book 类表示一个书籍对象。\",\"BookShelf 类表示一个书架，它实现了 Aggregate 接口。\",\"BookShelfIterator 类实现了 Iterator 接口，用于遍历 BookShelf 中的书籍。\",\"通过这些类和接口，我们可以轻松地遍历 BookShelf 中的书籍，而无需了解其内部实现细节。\"]},\"288\":{\"h\":\"多个迭代器\",\"t\":[\"在某些情况下，我们可能需要为同一个集合编写多个具体迭代器（ConcreteIterator）。例如，我们可以为 BookShelf 编写一个反向迭代器，以便从后向前遍历书籍。\"]},\"289\":{\"h\":\"相关的设计模式\",\"t\":[\"Visitor 模式\",\"Composite 模式\",\"Factory Method 模式\"]},\"290\":{\"c\":[\"设计模式\"]},\"291\":{\"c\":[\"设计模式\",\"typescript\"]},\"292\":{\"h\":\"Mediator 模式\"},\"293\":{\"h\":\"为什么使用此类\",\"t\":[\"请大家想象一下一个乱糟糟的开发小组的工作状态。小组中的 10 个成员虽然一起协同工作，但是意见难以统一，总是互相指挥，导致工作进度始终滞后。不仅如此，他们还十分在意编码细节，经常为此争执不下。\",\"这时，我们就需要一个中立的仲裁者站出来说：“各位，请大家将情况报告给我，我来负责仲裁。我会从团队整体出发进行考虑，然后下达指示，但我不会评价大家的工作细节。”这样，当出现争执时大家就会找仲裁者进行商量，仲裁者会负责统一大家的意见。\",\"最后，整个团队的交流过程就变为了组员向仲裁者报告，仲裁者向组员下达指示。组员之间不再相互询问和相互指示。\"]},\"294\":{\"h\":\"示例代码\",\"t\":[\"源地址\",\"/** * EN: Real World Example for the Mediator design pattern * * Need: To have a messaging application to notify groups of people. Users * should not know about each other. * * Solution: Create a mediator to manage subscriptions and messages */ /** * EN: Extending the Mediator interface to have a payload to include messages */ interface Mediator { notify(sender: object, event: string, payload?: string): void; } /** * EN: The user plays the role of the independent component. It has an * instance of the mediator. */ class User { constructor(public name: string, private mediator: Mediator) { this.mediator.notify(this, 'subscribe'); } receiveMessage(message: string) { console.log(`Message received by ${this.name}: ${message}`); } publishMessage(message: string) { this.mediator.notify(this, 'publish', message); } } /** * EN: The app is the concrete Mediator and implements all the events that * collaborators can notify: subscribe and publish */ class ChatAppMediator implements Mediator { private users: User[] = []; public notify(sender: object, event: string, payload?: string): void { if (event === 'subscribe') { const user = sender as User; console.log(`Subscribing ${user.name}`); this.users.push(user); } if (event === 'publish') { console.log(`Publishing message \\\"${payload}\\\" to the group`); const usersExcludingSender = this.users.filter(u => u !== sender); for (const user of usersExcludingSender) { user.receiveMessage(payload); } } } } /** * EN: The client code. Creating a user automatically subscribes them to the * group. */ const chatAppMediator = new ChatAppMediator(); const user1 = new User('Lightning', chatAppMediator); const user2 = new User('Doc', chatAppMediator); const user3 = new User('Mater', chatAppMediator); user1.publishMessage('Catchaw'); user2.publishMessage('Ey kid'); user3.publishMessage('Tomato'); \"]},\"295\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\mediator\\\\main.ts\\\" Subscribing Lightning Subscribing Doc Subscribing Mater Publishing message \\\"Catchaw\\\" to the group Message received by Doc: Catchaw Message received by Mater: Catchaw Publishing message \\\"Ey kid\\\" to the group Message received by Lightning: Ey kid Message received by Mater: Ey kid Publishing message \\\"Tomato\\\" to the group Message received by Lightning: Tomato Message received by Doc: Tomato \"]},\"296\":{\"h\":\"拓展思路的要点\"},\"297\":{\"h\":\"当发生分散灾难时\",\"t\":[\"示例程序中的 ChatAppMediator 类的 notify 方法稍微有些复杂。如果发生需求变更，该方法中很容易发生 Bug。不过这并不是什么问题。因为即使 notify 方法中发生了 Bug，由于其他地方并没有控制消息发布和订阅的逻辑处理，因此只要调试该方法就能很容易地找出 Bug 的原因。请试想一下，如果这段逻辑分散在 User 类中，那么无论是编写代码还是调试代码和修改代码，都会非常困难。通常情况下，面向对象编程可以帮助我们分散处理，避免处理过于集中，也就是说可以“分而治之”。但是在本章中的示例程序中，把处理分散在各个类中是不明智的。如果只是将应当分散的处理分散在各个类中，但是没有将应当集中的处理集中起来，那么这些分散的类最终只会导致灾难。\",\"在这个示例程序中，ChatAppMediator 类作为中介者（Mediator），负责管理和协调各个用户（User）的交互。notify 方法集中处理了所有消息的发布和订阅逻辑，这样可以确保逻辑的一致性和可维护性。如果将这些逻辑分散到各个用户类中，不仅会增加代码的复杂性，还会使得调试和维护变得更加困难。因此，将这些逻辑集中在中介者类中是更明智的选择。\"]},\"298\":{\"h\":\"通信线路的增加\",\"t\":[\"假设现在有 A 和 B 这 2 个实例，它们之间互相通信（相互调用方法），那么通信线路有两条，即 A-B 和 A-B。如果是有 A、B 和 C 这 3 个实例，那么就会有 6 条通信线路，即 A-B、A-C、B-C、B-A 和 C-A。如果有 4 个实例，会有 12 条通信线路；5 个实例就会有 20 条通信线路，而 6 个实例则会有 30 条通信线路。如果存在很多这样的互相通信的实例，那么程序结构会变得非常复杂。可能会有读者认为，如果实例很少就不需要 Mediator 模式了。但是需要考虑到的是，即使最初实例很少，很可能随着需求变更实例数量会慢慢变多，迟早会暴露出问题。\"]},\"299\":{\"h\":\"哪些角色可以复用\",\"t\":[\"ConcreteColleague 角色可以复用，但 ConcreteMediator 角色很难复用。例如，假设我们现在需要制作另外一个对话框。这时，我们可将扮演 ConcreteColleague 角色的 colleagueButton 类、 colleagueTextField 类和 colleagueCheckbox 类用于新的对话框中。这是因为在 ConcreteColleague 角色中并没有任何依赖于特定对话框的代码。在示例程序中，依赖于特定应用程序的部分都被封装在扮演 ConcreteMediator 角色的 LoginFrame 类中，依赖于特定应用程序就意味着难以复用。因此， LoginFrame 类很难在其他对话框中被复用。\"]},\"300\":{\"h\":\"相关的设计模式\",\"t\":[\"Facade 模式\",\"Observer 模式\"]},\"301\":{\"c\":[\"设计模式\"]},\"302\":{\"c\":[\"设计模式\",\"TypeScript\",\"简单化\"]},\"303\":{\"h\":\"Memento 模式\"},\"304\":{\"h\":\"为什么使用 Memento 模式\",\"t\":[\"Memento 模式的主要目的是在不破坏封装性的前提下，捕获和恢复对象的内部状态。它在以下情况下特别有用：\",\"需要保存和恢复对象的多个状态。\",\"需要在对象状态变化时进行撤销操作。\",\"需要在不暴露对象实现细节的情况下保存对象状态。\"]},\"305\":{\"h\":\"示例代码\",\"t\":[\"在这个示例中，我们使用了 Memento 模式来管理 Gamer 对象的状态。Memento 模式允许我们在不暴露对象实现细节的情况下保存和恢复对象的状态。以下是示例代码：\",\"// gamer.ts import { Memento } from './memento'; export class Gamer { private money: number; private fruits: string[]; private static fruitsName: string[] = ['apple', 'grape', 'banana', 'orange']; constructor(money: number) { this.money = money; this.fruits = []; } getMoney(): number { return this.money; } bet(): void { const dice = Math.floor(Math.random() * 6) + 1; if (dice === 1) { this.money += 100; console.log('Money increased'); } else if (dice === 2) { this.money /= 2; console.log('Money halved'); } else if (dice === 6) { const f = this.getFruit(); console.log(`Got fruit: ${f}`); this.fruits.push(f); } else { console.log('Nothing happened'); } } createMemento(): Memento { const m = new Memento(this.money); this.fruits.forEach(f => { if (f.startsWith('delicious')) { m.addFruit(f); } }); return m; } restoreMemento(memento: Memento): void { this.money = memento.money; this.fruits = memento.fruits; } toString(): string { return `[money = ${this.money}, fruits = ${this.fruits.join(', ')}]`; } private getFruit(): string { const prefix = Math.random() > 0.5 ? 'delicious ' : ''; return prefix + Gamer.fruitsName[Math.floor(Math.random() * Gamer.fruitsName.length)]; } } // main.ts import { Gamer } from './gamer'; let gamer = new Gamer(100); let memento = gamer.createMemento(); for (let i = 0; i < 100; i++) { console.log(`==== ${i}`); console.log(`Current: ${gamer.toString()}`); gamer.bet(); console.log(`Money now: ${gamer.getMoney()}`); if (gamer.getMoney() > memento.getMoney()) { console.log('Money increased, saving current state'); memento = gamer.createMemento(); } else if (gamer.getMoney() < memento.getMoney() / 2) { console.log('Money halved, restoring to previous state'); gamer.restoreMemento(memento); } console.log(''); } // memento.ts export class Memento { money: number; fruits: string[]; constructor(money: number) { this.money = money; this.fruits = []; } public getMoney(): number { return this.money; } public addFruit(fruit: string): void { this.fruits.push(fruit); } public getFruits(): string[] { return [...this.fruits]; } } \"]},\"306\":{\"h\":\"运行结果\",\"t\":[\"...(省略) ==== 97 Current: [money = 462.5, fruits = delicious grape, delicious apple, delicious apple, delicious orange, delicious banana, delicious apple, delicious apple, delicious grape, delicious grape, banana, grape, delicious banana] Money halved Money now: 231.25 Money halved, restoring to previous state ==== 98 Current: [money = 925, fruits = delicious grape, delicious apple, delicious apple, delicious orange, delicious banana, delicious apple, delicious apple, delicious grape, delicious grape, banana, grape, delicious banana] Nothing happened Money now: 925 ==== 99 Current: [money = 925, fruits = delicious grape, delicious apple, delicious apple, delicious orange, delicious banana, delicious apple, delicious apple, delicious grape, delicious grape, banana, grape, delicious banana] Nothing happened Money now: 925 \"]},\"307\":{\"h\":\"拓展思路的要点\"},\"308\":{\"h\":\"两种接口和可见性\",\"t\":[\"在 Memento 模式中，通常会有两种接口：宽接口（wide interface）和窄接口（narrow interface）。宽接口提供了对 Memento 对象的所有操作权限，而窄接口则只提供了有限的操作权限。Originator 类使用宽接口来创建和恢复 Memento，而 Caretaker 类则使用窄接口来保存和传递 Memento。通过这种方式，可以确保 Memento 的内部状态不会被外部直接修改，从而保持封装性。\"]},\"309\":{\"h\":\"需要多少个 Memento\",\"t\":[\"在实际应用中，需要根据具体需求来决定需要保存多少个 Memento。对于一些简单的应用，可能只需要保存一个 Memento 来支持一次撤销操作。而对于一些复杂的应用，可能需要保存多个 Memento 以支持多次撤销操作。需要注意的是，保存过多的 Memento 会占用大量的内存资源，因此需要在性能和功能之间找到一个平衡点。\"]},\"310\":{\"h\":\"Memento 的有效期限是多久\",\"t\":[\"Memento 的有效期限取决于具体的应用场景。在某些情况下，Memento 可能只需要在短时间内有效，例如在用户进行撤销操作之前。而在其他情况下，Memento 可能需要长期保存，例如在应用程序关闭后重新打开时恢复状态。需要根据具体需求来决定 Memento 的有效期限，并在适当的时候清理过期的 Memento 以释放资源。\"]},\"311\":{\"h\":\"划分 Caretaker 和 Originator 角色的意义\",\"t\":[\"在 Memento 模式中，Caretaker 和 Originator 角色的划分具有重要意义。Caretaker 负责保存和管理 Memento，而 Originator 负责创建和恢复 Memento。通过这种划分，可以将状态保存和恢复的逻辑与业务逻辑分离，从而提高系统的可维护性和可扩展性。\",\"变更为可以多次撤销 通过保存多个 Memento，可以实现多次撤销操作。Caretaker 可以维护一个 Memento 的栈，每次撤销操作时从栈中弹出一个 Memento 并恢复状态。这样可以支持用户进行多次撤销和重做操作。\",\"变更为不仅可以撤销，还可以将现在的状态保存在文件中 通过将 Memento 保存到文件中，可以实现持久化存储。这样即使应用程序关闭后重新打开，也可以恢复到之前的状态。Caretaker 可以负责将 Memento 序列化并保存到文件中，以及从文件中读取并反序列化 Memento。\"]},\"312\":{\"h\":\"相关的设计模式\",\"t\":[\"Command 模式\",\"Prototype 模式\",\"State 模式\"]},\"313\":{\"c\":[\"设计模式\"]},\"314\":{\"c\":[\"设计模式\",\"TypeScript\",\"管理状态\"]},\"315\":{\"h\":\"Observer 模式\"},\"316\":{\"h\":\"为什么使用观察者模式\",\"t\":[\"观察者模式非常适合用于需要自动更新的场景。例如，在图形用户界面（GUI）应用程序中，当数据模型发生变化时，所有显示该数据的视图都需要自动更新。通过使用观察者模式，我们可以将这些视图注册为观察者，当数据模型发生变化时，它们会自动收到通知并更新显示。\"]},\"317\":{\"h\":\"示例代码\",\"t\":[\"在这个示例中，我们展示了如何使用观察者模式来管理状态变化。观察者模式定义了一种一对多的依赖关系，当一个对象的状态发生改变时，所有依赖于它的对象都会得到通知并自动更新。以下是 TypeScript 实现的代码示例：\",\"// DigitObserver.ts import { NumberGenerator } from './numberGenerator'; import { Observer } from './observer'; export class DigitObserver implements Observer { update(number: NumberGenerator): void { console.log(`DigitObserver: ${number.getNumber()}`); } } // graphObserver.ts import { Observer } from './observer'; import { NumberGenerator } from './numberGenerator'; export class GraphObserver implements Observer { update(generator: NumberGenerator): void { const count = generator.getNumber(); let graph = ''; for (let i = 0; i < count; i++) { graph += '*'; } console.log(`GraphObserver: \\\\n${graph}\\\\n ${generator.getNumber()}\\\\n${graph} `); } } // main.ts import { NumberGenerator } from './numberGenerator'; import { Observer } from './observer'; import { RandomNumberGenerator } from './randomNumberGenerator'; import { DigitObserver } from './DigitObserver'; import { GraphObserver } from './graphObserver'; const generator: NumberGenerator = new RandomNumberGenerator(); const observer1 = new DigitObserver(); const observer2 = new GraphObserver(); generator.addObserver(observer1); generator.addObserver(observer2); generator.execute(); // numberGenerator.ts import { Observer } from './observer'; export abstract class NumberGenerator { private observers: Observer[] = []; public addObserver(observer: Observer): void { this.observers.push(observer); } public deleteObserver(observer: Observer): void { this.observers = this.observers.filter((o) => o !== observer); } public notifyObservers(): void { this.observers.forEach((o) => o.update(this)); } public abstract getNumber(): number; public abstract execute(): void; } // observer.ts import {NumberGenerator} from './numberGenerator'; export interface Observer { update(generator: NumberGenerator): void; } // randomNumberGenerator.ts import {NumberGenerator} from './numberGenerator'; export class RandomNumberGenerator extends NumberGenerator { private number: number; constructor() { super(); this.number = 0; } getNumber(): number { return this.number; } execute(): void { for (let i = 0; i < 20; i++) { this.number = Math.floor(Math.random() * 50); this.notifyObservers(); } } } \"]},\"318\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\observer\\\\main.ts\\\" DigitObserver: 13 GraphObserver: ************* 13 ************* DigitObserver: 43 GraphObserver: ******************************************* 43 ******************************************* DigitObserver: 46 GraphObserver: ********************************************** 46 ********************************************** DigitObserver: 18 GraphObserver: ****************** 18 ****************** DigitObserver: 20 GraphObserver: ******************** 20 ******************** DigitObserver: 49 GraphObserver: ************************************************* 49 ************************************************* DigitObserver: 25 GraphObserver: ************************* 25 ************************* DigitObserver: 26 GraphObserver: ************************** 26 ************************** DigitObserver: 37 GraphObserver: ************************************* 37 ************************************* DigitObserver: 2 GraphObserver: ** 2 ** DigitObserver: 10 GraphObserver: ********** 10 ********** DigitObserver: 0 GraphObserver: 0 DigitObserver: 11 GraphObserver: *********** 11 *********** DigitObserver: 13 GraphObserver: ************* 13 ************* DigitObserver: 16 GraphObserver: **************** 16 **************** DigitObserver: 28 GraphObserver: **************************** 28 **************************** DigitObserver: 22 GraphObserver: ********************** 22 ********************** DigitObserver: 30 GraphObserver: ****************************** 30 ****************************** DigitObserver: 44 GraphObserver: ******************************************** 44 ******************************************** DigitObserver: 3 GraphObserver: *** 3 *** \"]},\"319\":{\"h\":\"拓展思路的要点\"},\"320\":{\"h\":\"这里也出现了可替换性\",\"t\":[\"在设计模式中，可替换性是指一个对象可以被另一个具有相同接口的对象替换，而不影响系统的功能。在观察者模式中，观察者（Observer）和被观察者（Subject）之间的关系是松耦合的，这意味着我们可以轻松地替换观察者或被观察者，而不会影响系统的其他部分。\"]},\"321\":{\"h\":\"Observer 的顺序\",\"t\":[\"Subject 角色（被观察对象）中注册有多个 Observer 角色。在示例程序的 notifyObservers 方法中，先注册的 Observer 的 update 方法会先被调用。通常，在设计 ConcreteObserver 角色的类时，需要注意这些 Observer 的 update 方法的调用顺序，不能因为方法的调用顺序发生改变而产生问题。例如，在示例程序中，绝不能因为先调用 DigitObserver 的 update 方法后调用 GraphObserver 的 update 方法而导致应用程序不能正常工作。当然，通常，只要保持各个类的独立性，就不会发生上面这种类的依赖关系混乱的问题。不过，我们还需要注意下面将要提到的情况。\"]},\"322\":{\"h\":\"当 Observer 的行为会对被观察对象产生影响时\",\"t\":[\"当观察者的行为会对被观察对象产生影响时，我们需要特别小心，以避免循环依赖和无限递归。例如，一个观察者在接收到通知后修改了被观察对象的状态，这可能会导致被观察对象再次通知所有观察者，从而引发无限循环。为了解决这个问题，我们可以引入一个标志位来跟踪通知状态，或者使用更复杂的事件处理机制。\"]},\"323\":{\"h\":\"传递更新信息的方式\",\"t\":[\"在观察者模式中，传递更新信息的方式有多种选择。最简单的方法是直接调用观察者的更新方法，并将被观察对象自身作为参数传递。另一种方法是传递具体的更新信息，例如事件对象或数据包。这种方法可以减少观察者对被观察对象的依赖，从而提高系统的灵活性和可维护性。\"]},\"324\":{\"h\":\"从观察变为通知\",\"t\":[\"在某些情况下，我们可能需要从观察模式转变为通知模式。例如，当系统中有大量的观察者时，逐个通知每个观察者可能会导致性能问题。此时，我们可以考虑使用事件总线或消息队列来集中处理通知，从而提高系统的性能和可扩展性。\"]},\"325\":{\"h\":\"MVC (Model/View/Controller)\",\"t\":[\"观察者模式在 MVC 架构中得到了广泛应用。模型（Model）作为被观察对象，视图（View）作为观察者，当模型的状态发生变化时，视图会自动更新。控制器（Controller）负责协调模型和视图之间的交互。通过使用观察者模式，MVC 架构实现了视图和模型的松耦合，从而提高了系统的可维护性和可扩展性。\"]},\"326\":{\"h\":\"相关的设计模式\",\"t\":[\"Mediator 模式\"]},\"327\":{\"c\":[\"设计模式\"]},\"328\":{\"c\":[\"设计模式\",\"TypeScript\",\"管理状态\"]},\"329\":{\"h\":\"Prototype 模式\"},\"330\":{\"h\":\"为什么要使用 Prototype 模式\",\"t\":[\"Prototype 模式是一种创建型设计模式，它允许你复制现有对象而无需使代码依赖它们所属的类。使用 Prototype 模式可以：\",\"避免重复初始化对象的复杂过程。\",\"提高性能，特别是在创建对象代价较高时。\",\"简化代码，使得对象的创建更加灵活。\",\"对象种类繁多，无法将它们整合到一个类中\",\"难以根据类生成实例\",\"解耦框架与生成的实例\"]},\"331\":{\"h\":\"示例代码\",\"t\":[\"// main.ts import { Manager } from './manager'; import { UnderlinePen } from './underlinePen'; import { MessageBox } from './messageBox'; let manager = new Manager(); let upen = new UnderlinePen('~'); let mbox = new MessageBox('*'); let sbox = new MessageBox('/'); manager.register('strong message', upen); manager.register('warning box', mbox); manager.register('slash box', sbox); let p1 = manager.create('strong message'); p1.use('Hello, world.'); let p2 = manager.create('warning box'); p2.use('Hello, world.'); let p3 = manager.create('slash box'); p3.use('Hello, world.'); // manager.ts export class Manager { private showcase: { [key: string]: any } = {}; register(name: string, proto: any) { this.showcase[name] = proto; } create(name: string): any { const p = this.showcase[name]; return p.createClone(); } } // messageBox.ts import { Product } from \\\"./product\\\"; export class MessageBox implements Product { private decochar: string; constructor(decochar: string) { this.decochar = decochar; } use(s: string): void { const length = s.length; console.log(this.decochar.repeat(length + 4)); console.log(`${this.decochar} ${s} ${this.decochar}`); console.log(this.decochar.repeat(length + 4)); } createClone(): Product { let p: Product = null; try { p = <Product>Object.create(this); } catch (e) { console.error(e); } return p; } } // product.ts export interface Product { use(s:String): void; createClone(): Product; } // underlinePen.ts import { Product } from './product'; export class UnderlinePen implements Product { private ulchar: string; constructor(ulchar: string) { this.ulchar = ulchar; } use(s: string): void { const length = s.length; console.log(`\\\"${s}\\\"`); console.log(' '); console.log(` ${this.ulchar.repeat(length)}`); console.log(' '); } createClone(): Product { let p: Product = null; try { p = Object.create(this); } catch (e) { console.log(e); } return p; } } \"]},\"332\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\prototype\\\\main.ts\\\" \\\"Hello, world.\\\" ~~~~~~~~~~~~~ ***************** * Hello, world. * ***************** ///////////////// / Hello, world. / ///////////////// \"]},\"333\":{\"h\":\"相关设计模式\",\"t\":[\"Flyweight 模式\",\"Memento 模式\",\"Composite 模式\",\"Decorator 模式\",\"Command 模式\"]},\"334\":{\"c\":[\"设计模式\"]},\"335\":{\"c\":[\"设计模式\",\"typescript\",\"生成实例\"]},\"336\":{\"h\":\"Proxy 模式\"},\"337\":{\"h\":\"为什么使用代理模式\",\"t\":[\"在面向对象编程中，“本人”和“代理人”都是对象。如果“本人”对象太忙了．有些工作无法自己亲自完成，就将其交给“代理人\\\"对象负责。\",\"Proxy 模式用于为某对象提供一个代理，以控制对该对象的访问。主要有以下几个优点：\",\"延迟实例化：代理对象可以在需要时才创建实际对象，节省资源。\",\"控制访问：可以在代理中加入额外的逻辑来控制对实际对象的访问。\",\"远程代理：可以用于访问远程对象。\"]},\"338\":{\"h\":\"实例代码\",\"t\":[\"为了让 PrinterProxy 类与 Printer 类具有一致性，我们定义了 Printable 接口。示例程序的前提是\\\"生成 Printer 类的实例\\\"这一处理需要花费很多时间。为了在程序中体现这一点，我们在 Printer 类的构造了数中调用了 heavyJob 方法，让它干一些“重活”（虽说是重活，也不过是让程序睡眠 5 秒钟）。\",\"// main.ts import { Printable } from './printable'; import { PrinterProxy } from './printerProxy'; let p: Printable = new PrinterProxy('Alice'); console.log('名字现在是' + p.getPrinterName() + '。'); p.setPrinterName('Bob'); console.log('名字现在是' + p.getPrinterName() + '。'); p.print('你好，世界。'); // printable.ts export interface Printable { setPrinterName(name: string): void; getPrinterName(): string; print(str:string): void; } // printer.ts import { Printable } from \\\"./printable\\\"; export class Printer implements Printable { private name: string; constructor(name: string) { this.name = name; this.heavyJob(`正在生成Printer的实例(${this.name})`); } setPrinterName(name: string): void { this.name = name; } getPrinterName(): string { return this.name; } print(str:string): void { console.log(`=== ${this.name} ===`); console.log(str); } private heavyJob(msg: string): void { console.log(msg); for (let i = 0; i < 5; i++) { try { console.log(\\\".\\\"); setTimeout(() => { console.log(\\\".\\\"); }, 1000); } catch (e) { console.log(e); } } console.log(\\\"完了。\\\"); } } // printerProxy.ts import { Printable } from './printable'; import { Printer } from './printer'; export class PrinterProxy implements Printable { private name: string; private real: Printer; constructor(name: string) { this.name = name; } setPrinterName(name: string): void { if (this.real !== undefined) { this.real.setPrinterName(name); } this.name = name; } getPrinterName(): string { return this.name; } print(str: string): void { this.realize(); this.real.print(str); } private realize(): void { if (this.real === undefined) { this.real = new Printer(this.name); } } } \"]},\"339\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\proxy\\\\main.ts\\\" 名字现在是Alice。 名字现在是Bob。 正在生成Printer的实例(Bob) . . . . . 完了。 === Bob === 你好，世界。 . . . . . \"]},\"340\":{\"h\":\"拓展思路的要点\"},\"341\":{\"h\":\"使用代理人来提升处理速度\",\"t\":[\"在某些情况下，使用代理可以显著提升处理速度。例如，虚拟代理（Virtual Proxy）可以在实际对象创建之前进行一些轻量级的操作，从而减少系统的开销。通过代理对象来延迟实际对象的创建，可以提高系统的响应速度和资源利用率。\"]},\"342\":{\"h\":\"有必要划分代理人和本人吗\",\"t\":[\"在设计模式中，代理人和本人的划分是为了实现职责分离和提高系统的灵活性。代理模式通过引入代理对象来控制对实际对象的访问，可以在不修改实际对象的情况下添加额外的功能。例如，远程代理（Remote Proxy）可以在客户端和远程服务器之间进行通信，而不需要客户端了解远程服务器的具体实现。\"]},\"343\":{\"h\":\"代理与委托\",\"t\":[\"代理模式和委托模式虽然在某些方面有相似之处，但它们的目的和实现方式有所不同。代理模式主要用于控制对对象的访问，而委托模式则用于将任务分配给其他对象来执行。代理模式通过代理对象来控制对实际对象的访问，而委托模式通过委托对象来执行具体的任务。\"]},\"344\":{\"h\":\"透明性\",\"t\":[\"代理模式的一个重要特点是透明性。代理对象和实际对象实现相同的接口，客户端可以像使用实际对象一样使用代理对象，而不需要关心代理对象的内部实现。这种透明性使得代理模式在不改变客户端代码的情况下添加额外的功能成为可能。\"]},\"345\":{\"h\":\"HTTP 代理\",\"t\":[\"HTTP 代理是一种常见的代理模式应用。HTTP 代理服务器位于客户端和目标服务器之间，负责转发客户端的请求和目标服务器的响应。HTTP 代理可以用于缓存、负载均衡、安全控制等功能，从而提高网络通信的效率和安全性。\"]},\"346\":{\"h\":\"各种 Proxy 模式\",\"t\":[\"Virtual Proxy：虚拟代理用于控制对资源密集型对象的访问。它在实际对象创建之前进行一些轻量级的操作，从而延迟实际对象的创建。例如，图像加载时可以使用虚拟代理来显示占位符图像，直到实际图像加载完成。\",\"Remote Proxy：远程代理用于控制对远程对象的访问。它在客户端和远程服务器之间进行通信，使得客户端可以像使用本地对象一样使用远程对象。例如，RMI（远程方法调用）就是一种远程代理的实现。\",\"Access Proxy：访问代理用于控制对实际对象的访问权限。它可以在访问实际对象之前进行权限检查，从而确保只有授权的客户端才能访问实际对象。例如，防火墙代理可以用于控制对内部网络资源的访问。\",\"通过这些不同类型的代理模式，我们可以在不同的应用场景中灵活地控制对对象的访问，提高系统的安全性、性能和可维护性。\"]},\"347\":{\"h\":\"相关的设计模式\",\"t\":[\"Adapter 模式\",\"Decorator 模式\"]},\"348\":{\"c\":[\"设计模式\"]},\"349\":{\"c\":[\"设计模式\",\"TypeScript\",\"避免浪费\"]},\"350\":{\"h\":\"Singleton 模式\"},\"351\":{\"h\":\"为什么要使用 Singleton 模式\",\"t\":[\"Singleton 模式确保一个类只有一个实例，并提供一个全局访问点。它常用于需要控制资源访问的场景，例如数据库连接、日志记录器等。通过 Singleton 模式，可以避免创建多个实例带来的资源浪费和不一致性问题。\"]},\"352\":{\"h\":\"总结:\",\"t\":[\"想确保任何情况下都绝对只有 1 个实例\",\"想在程序上表现出“只存在一个实例”\"]},\"353\":{\"h\":\"示例代码\",\"t\":[\"// main.ts import { Singleton } from './singleton'; const singleton1 = Singleton.getInstance(); const singleton2 = Singleton.getInstance(); console.log(singleton1 === singleton2); // true // singleton.ts export class Singleton { private static instance: Singleton | null = null; private static generatedId: number = 0; private constructor() { Singleton.generatedId++; console.log(`Singleton instance created with id: ${Singleton.generatedId}`); } public static getInstance(): Singleton { if (this.instance === null) { this.instance = new Singleton(); } return this.instance; } } \"]},\"354\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\singleton\\\\main.ts\\\" Singleton instance created with id: 1 true \"]},\"355\":{\"h\":\"相关设计模式\",\"t\":[\"abstractFactory 模式\",\"Builder 模式\",\"Facade 模式\",\"Prototype 模式\"]},\"356\":{\"h\":\"多线程下\",\"t\":[\"在多线程环境中，Singleton 模式的实现需要特别注意线程安全问题。如果多个线程同时访问 getInstance 方法，可能会导致创建多个实例。为了解决这个问题，可以使用双重检查锁定（Double-Checked Locking）或其他线程同步机制。\"]},\"357\":{\"h\":\"双重检查锁定示例代码\",\"t\":[\"export class Singleton { private static instance: Singleton | null = null; private static generatedId: number = 0; private static lock: any = {}; private constructor() { Singleton.generatedId++; console.log(`Singleton instance created with id: ${Singleton.generatedId}`); } public static getInstance(): Singleton { if (this.instance === null) { synchronized(this.lock, () => { if (this.instance === null) { this.instance = new Singleton(); } }); } return this.instance; } } function synchronized(lock: any, fn: () => void) { // Simulate a lock mechanism fn(); } \",\"在上面的代码中，synchronized 函数模拟了一个锁机制，以确保在多线程环境下 getInstance 方法的线程安全性。\"]},\"358\":{\"c\":[\"设计模式\"]},\"359\":{\"c\":[\"设计模式\",\"typescript\",\"生成实例\"]},\"360\":{\"h\":\"State 模式\"},\"361\":{\"h\":\"为什么使用 State 模式\",\"t\":[\"State 模式允许对象在其内部状态改变时改变其行为。它将与状态相关的行为封装在独立的类中，使得状态转换变得清晰且易于管理。使用 State 模式可以避免大量的条件语句，使代码更加简洁和可维护。\"]},\"362\":{\"h\":\"示例代码\",\"t\":[\"// context.ts import { State } from './state'; export interface Context { setClock(hour: number): void; changeState(state: State): void; callSecurityCenter(msg: string): void; recordLog(msg: string): void; } // dayState.ts import { State } from './state'; import { Context } from './context'; import { NightState } from './nightState'; export class DayState implements State { private static singleton: DayState = new DayState(); private constructor() {} public static getInstance(): State { return this.singleton; } public doClock(context: Context, hour: number): void { if (hour < 9 || 17 <= hour) { context.changeState(NightState.getInstance()); } } public doUse(context: Context): void { context.recordLog('金库使用(白天)'); } public doAlarm(context: Context): void { context.callSecurityCenter('紧急铃(白天)'); } public doPhone(context: Context): void { context.callSecurityCenter('正常通话(白天)'); } public toString(): string { return '[白天]'; } } // main.ts import { SafeFrame } from './safeFrame'; const safeFrame: SafeFrame = new SafeFrame(); for (let hour: number = 0; hour < 24; hour++) { safeFrame.setClock(hour); safeFrame.doUse(); safeFrame.doAlarm(); safeFrame.doPhone(); } // nightState.ts import { State } from './state'; import { Context } from './context'; import { DayState } from './dayState'; export class NightState implements State { private static singleton: NightState = new NightState(); private constructor() {} public static getInstance(): State { return this.singleton; } public doClock(context: Context, hour: number): void { if (9 <= hour && hour < 17) { context.changeState(DayState.getInstance()); } } public doUse(context: Context): void { context.callSecurityCenter('紧急：夜间使用金库！'); } public doAlarm(context: Context): void { context.callSecurityCenter('紧急铃(夜间)'); } public doPhone(context: Context): void { context.recordLog('夜间通话录音'); } public toString(): string { return '[夜间]'; } } // safeFrame.ts import { Context } from './context'; import { State } from './state'; import { DayState } from './dayState'; export class SafeFrame implements Context { private state: State = DayState.getInstance(); public setClock(hour: number): void { let clockString: string = '現在時刻は'; if (hour < 10) { clockString += `0${hour}:00`; } else { clockString += `${hour}:00`; } console.log(clockString); this.state.doClock(this, hour); } public changeState(state: State): void { console.log(`${this.state.toString()}から${state.toString()}へ状態が変化しました。`); this.state = state; } public callSecurityCenter(msg: string): void { console.log(`call! ${msg}`); } public recordLog(msg: string): void { console.log(`record ... ${msg}`); } public doUse(): void { this.state.doUse(this); } public doAlarm(): void { this.state.doAlarm(this); } public doPhone(): void { this.state.doPhone(this); } } // state.ts import { Context } from './context'; export interface State { doClock(context: Context, hour: number): void; doUse(context: Context): void; doAlarm(context: Context): void; doPhone(context: Context): void; } \"]},\"363\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\state\\\\main.ts\\\" 現在時刻は00:00 [白天]から[夜间]へ状態が変化しました。 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は01:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は02:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は03:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は04:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は05:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は06:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は07:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は08:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は09:00 [夜间]から[白天]へ状態が変化しました。 record ... 金库使用(白天) call! 紧急铃(白天) call! 正常通话(白天) 現在時刻は10:00 record ... 金库使用(白天) call! 紧急铃(白天) call! 正常通话(白天) 現在時刻は11:00 record ... 金库使用(白天) call! 紧急铃(白天) call! 正常通话(白天) 現在時刻は12:00 record ... 金库使用(白天) call! 紧急铃(白天) call! 正常通话(白天) 現在時刻は13:00 record ... 金库使用(白天) call! 紧急铃(白天) call! 正常通话(白天) 現在時刻は14:00 record ... 金库使用(白天) call! 紧急铃(白天) call! 正常通话(白天) 現在時刻は15:00 record ... 金库使用(白天) call! 紧急铃(白天) call! 正常通话(白天) 現在時刻は16:00 record ... 金库使用(白天) call! 紧急铃(白天) call! 正常通话(白天) 現在時刻は17:00 [白天]から[夜间]へ状態が変化しました。 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は18:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は19:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は20:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は21:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は22:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 現在時刻は23:00 call! 紧急：夜间使用金库！ call! 紧急铃(夜间) record ... 夜间通话录音 \"]},\"364\":{\"h\":\"拓展思路的要点\"},\"365\":{\"h\":\"分而治之\",\"t\":[\"在编程时，我们经常会使用分而治之的方针。它非常适用于大规模的复杂处理。当遇到庞大且复杂的问题、不能用一般的方法解决时，我们会先将该问题分解为多个小问题。如果还是不能解决这些小问题，我们会将它们继续划分为更小的问题，直至可以解决它们为止。\",\"分而治之，简单而言就是将一个复杂的大问题分解为多个小问题然后逐个解决。在 State 模式中，我们用类来表示状态，并为每一种具体的状态都定义一个相应的类。这样，问题就被分解了。开发人员可以在编写一个 ConcreteState 角色的代码的同时，在头脑中（一定程度上）考虑其他的类。\",\"在本章的警报系统的示例程序中，只有“白天”和“晚上”两个状态，可能大家对此感受不深，但是当状态非常多的时候，State 模式的优势就会非常明显了。在不使用 State 模式时，我们需要使用条件分支语句判断当前的状态，然后进行相应的处理。状态越多，条件分支就会越多，而且我们必须在所有的事件处理方法中都编写这些条件分支语句。State 模式用类表示系统的“状态”，并以此将复杂的程序分解开来。\"]},\"366\":{\"h\":\"依赖于状态的处理\",\"t\":[\"我们来思考一下 SafeFrame 类的 setClock 方法和 State 接口的 doClock 方法之间的关系。Main 类会调用 SafeFrame 类的 setClock 方法，告诉 setClock 方法“请设置时间”。在 setClock 方法中，会像下面这样将处理委托给 State 类：state.doClock(this, hour);。也就是说，我们将设置时间的处理看作是“依赖于状态的处理”。当然，不只是 doClock 方法。在 State 接口中声明的所有方法都是“依赖于状态的处理”，都是“状态不同处理也不同”。这虽然看似理所当然，不过却需要我们特别注意。在 State 模式中，我们应该如何编程，以实现“依赖于状态的处理”呢？总结起来有如下两点：\",\"定义接口，声明抽象方法\",\"定义多个类，实现具体方法\",\"这就是 State 模式中的“依赖于状态的处理”的实现方法。这里故意将上面两点说得很笼统，但是，如果大家在读完这两点之后会点头表示赞同，那就意味着大家完全理解了 State 模式以及接口与类之间的关系。\"]},\"367\":{\"h\":\"应当是谁来管理状态的迁移\",\"t\":[\"用类来表示状态，将依赖于状态的处理分散在每个 ConcreteState 角色中，这是一种非常好的解决办法。不过，在使用模式时需要注意应当是谁来管理状态迁移。在示例程序中，扮演 Context 角色的 SafeFrame 类实现了实际进行状态迁移的 changeState 方法。但是，实际调用该方法的却是扮演 ConcreteState 角色的 DayState 类和 NightState 类。\",\"也就是说，在示例程序中，我们将“状态迁移”看作是“依赖于状态的处理”。这种处理方式既有优点也有缺点。优点是这种处理方式将“什么时候从一个状态迁移到其他状态”的信息集中在了一个类中。也就是说，当我们想知道“什么时候会从 DayState 类变化为其他状态”时，只需要阅读 DayState 类的代码就可以了。缺点是“每个 ConcreteState 角色都需要知道其他 ConcreteState 角色”。\",\"例如，DayState 类的 doClock 方法就使用了 NightState 类。这样，如果以后发生需求变更，需要删除 NightState 类时，就必须要相应地修改 DayState 类的代码。将状态迁移交给 ConcreteState 角色后，每个 ConcreteState 角色都需要或多或少地知道其他角色。也就是说，将状态迁移交给 ConcreteState 角色后，各个类之间的依赖关系就会加强。我们也可以不使用示例程序中的做法，而是将所有的状态迁移交给扮演 Context 角色的 SafeFrame 类来负责。\",\"有时，使用这种解决方法可以提高 ConcreteState 角色的独立性，程序的整体结构也会更加清晰。不过这样做的话，Context 角色就必须要知道“所有的 ConcreteState 角色”。在这种情况下，我们可以使用 Mediator 模式（第 16 章）。当然，还可以不用 State 模式，而是用状态迁移表来设计程序。所谓状态迁移表是可以根据“输入和内部状态”得到“输出和下一个状态”的一览表（这超出了本书的范围，我们暂且不深入学习该方法）。当状态迁移遵循一定的规则时，使用状态迁移表非常有效。此外，当状态数过多时，可以用程序来生成代码而不是手写代码。\"]},\"368\":{\"h\":\"不会自相矛盾\",\"t\":[\"如果不使用 State 模式，我们需要使用多个变量的值的集合来表示系统的状态。这时，必须十分小心，注意不要让变量的值之间互相矛盾。而在 State 模式中，是用类来表示状态的。这样，我们就只需要一个表示系统状态的变量即可。在示例程序中，SafeFrame 类的 state 字段就是这个变量，它决定了系统的状态。因此，不会存在自相矛盾的状态。\"]},\"369\":{\"h\":\"易于增加新的状态\",\"t\":[\"在 State 模式中增加新的状态是非常简单的。以示例程序来说，编写一个 XXXState 类，让它实现 State 接口，然后实现一些所需的方法就可以了。当然，在修改状态迁移部分的代码时，还是需要仔细一点的。因为状态迁移的部分正是与其他 ConcreteState 角色相关联的部分。\",\"但是，在 State 模式中增加其他“依赖于状态的处理”是很困难的。这是因为我们需要在 State 接口中增加新的方法，并在所有的 ConcreteState 角色中都实现这个方法。虽说很困难，但是好在我们绝对不会忘记实现这个方法。假设我们现在在 State 接口中增加了一个 doYYY 方法，而忘记了在 DayState 类和 NightState 类中实现这个方法，那么编译器在编译代码时就会报错，告诉我们存在还没有实现的方法。\",\"如果不使用 State 模式，那么增加新的状态时会怎样呢？这里，如果不使用 State 模式，就必须用条件分支语句判断状态。这样就很难在编译代码时检测出“忘记实现方法”这种错误了（在运行时检测出问题并不难。我们只要事先在每个方法内部都加上一段“当检测到没有考虑到的状态时就报错”的代码即可）。\"]},\"370\":{\"h\":\"实例的多面性\",\"t\":[\"请注意 SafeFrame 类中的以下两条语句（代码清单 19.7）：\",\"SafeFrame 类的构造函数中的 buttonUse.addActionListener(this);\",\"actionPerformed 方法中的 state.doUse(this);\",\"这两条语句中都有 this。那么这个 this 到底是什么呢？当然，它们都是 SafeFrame 类的实例。由于在示例程序中只生成了一个 SafeFrame 的实例，因此这两个 this 其实是同一个对象。不过，在 addActionListener 方法中和 doUse 方法中，对 this 的使用方式是不一样的。\",\"向 addActionListener 方法传递 this 时，该实例会被当作“实现了 ActionListener 接口的类的实例”来使用。这是因为 addActionListener 方法的参数类型是 ActionListener 类型。\",\"在 addActionListener 方法中会用到的方法也都是在 ActionListener 接口中定义了的方法。至于这个参数是否是 SafeFrame 类的实例并不重要。向 doUse 方法传递 this 时，该实例会被当作“实现了 Context 接口的类的实例”来使用。这是因为 doUse 方法的参数类型是 Context 类型。在 doUse 方法中会用到的方法也都是在 Context 接口中定义了的方法（大家只要再回顾一下 DayState 类和 NightState 类的 doUse 方法就会明白了）。请大家一定要透彻理解此处的实例的多面性。\"]},\"371\":{\"h\":\"相关的设计模式\",\"t\":[\"Singleton 模式\",\"Flyweight 模式\"]},\"372\":{\"c\":[\"设计模式\"]},\"373\":{\"c\":[\"设计模式\",\"TypeScript\",\"管理状态\"]},\"374\":{\"h\":\"Strategy 模式\"},\"375\":{\"h\":\"使用此设计模式的理由\",\"t\":[\"在这个示例程序中，我们使用了策略模式（Strategy Pattern）来实现不同的猜拳策略。策略模式的主要优点包括：\",\"易于扩展：可以很容易地添加新的策略，而不需要修改现有的代码。\",\"提高代码的可读性和可维护性：将不同的算法封装在独立的类中，使得代码更加清晰。\",\"减少重复代码：通过使用策略模式，可以避免在多个地方重复相同的算法逻辑。\"]},\"376\":{\"h\":\"示例程序\",\"t\":[\"下面我们来看一段使用了 strategy 模式的示例程序。这段示例程序的功能是让电脑玩“猜拳\\\"游戏。\",\"我们考虑了两种猜拳的策略。第一种策略是“如果这局猜拳获胜，那么下一局也出一样的手势\\\" (WinningStrategy), 这是一种稍微有些笨的策略；另外一种策略是“根据上一局的手势从概率上计算出下一局的手势\\\"（ ProbStrategy ）。\",\"// hand.ts export enum HandValue { GUU = 0, CHO = 1, PAA = 2, } export class Hand { //NOTE - 使用了单例模式 private static readonly hand: Hand[] = [ new Hand(HandValue.GUU), new Hand(HandValue.CHO), new Hand(HandValue.PAA), ]; private static readonly names: string[] = ['石头', '剪刀', '布']; private handValue: HandValue; private constructor(handValue: HandValue) { this.handValue = handValue; } static getHand(handValue: HandValue): Hand { return this.hand[handValue]; } isStrongerThan(h: Hand): boolean { return this.fight(h) === 1; } isWeakerThan(h: Hand): boolean { return this.fight(h) === -1; } private fight(h: Hand): number { if (this === h) { return 0; } else if ((this.handValue + 1) % 3 === h.handValue) { return 1; } else { return -1; } } toString(): string { return Hand.names[this.handValue]; } } // main.ts import { Player } from \\\"./player\\\"; import { WinningStrategy } from \\\"./winningStrategy\\\"; import { ProbStrategy } from \\\"./probStrategy\\\"; const player1 = new Player(\\\"Taro\\\", new WinningStrategy()); const player2 = new Player(\\\"Hana\\\", new ProbStrategy()); for (let i = 0; i < 10000; i++) { const nextHand1 = player1.nextHand(); const nextHand2 = player2.nextHand(); if (nextHand1.isStrongerThan(nextHand2)) { console.log(`Winner: ${player1.toString()}`); player1.win(); player2.lose(); } else if (nextHand2.isStrongerThan(nextHand1)) { console.log(`Winner: ${player2.toString()}`); player1.lose(); player2.win(); } else { console.log(\\\"Even...\\\"); player1.even(); player2.even(); } } console.log(\\\"Total result:\\\"); console.log(player1.toString()); console.log(player2.toString()); // Output // player.ts import { Hand } from './hand'; import { Strategy } from './strategy'; export class Player { private name: string; private strategy: Strategy; private wincount = 0; private losecount = 0; private gamecount = 0; constructor(name: string, strategy: Strategy) { this.name = name; this.strategy = strategy; } nextHand(): Hand { return this.strategy.nextHand(); } win(): void { this.strategy.study(true); this.wincount++; this.gamecount++; } lose(): void { this.strategy.study(false); this.losecount++; this.gamecount++; } even(): void { this.gamecount++; } toString(): string { return `[${this.name}:${this.gamecount} games, ${this.wincount} win, ${this.losecount} lose]`; } } // probStrategy.ts import { Hand } from './hand'; import { Strategy } from './strategy'; export class ProbStrategy implements Strategy { private prevHandValue = 0; private currentHandValue = 0; private history: number[][] = [ [1, 1, 1], [1, 1, 1], [1, 1, 1], ]; constructor() {} nextHand(): Hand { const bet = Math.floor(Math.random() * this.getSum(this.currentHandValue)); let handvalue = 0; if (bet < this.history[this.currentHandValue][0]) { handvalue = 0; } else if (bet < this.history[this.currentHandValue][0] + this.history[this.currentHandValue][1]) { handvalue = 1; } else { handvalue = 2; } this.prevHandValue = this.currentHandValue; this.currentHandValue = handvalue; return Hand.getHand(handvalue); } private getSum(hv: number): number { let sum = 0; for (let i = 0; i < 3; i++) { sum += this.history[hv][i]; } return sum; } study(win: boolean): void { if (win) { this.history[this.prevHandValue][this.currentHandValue]++; } else { this.history[this.prevHandValue][(this.currentHandValue + 1) % 3]++; this.history[this.prevHandValue][(this.currentHandValue + 2) % 3]++; } } } // strategy.ts import { Hand } from './hand'; export interface Strategy { nextHand(): Hand; study(win: boolean): void; } // winningStrategy.ts import { Hand } from './hand'; import { Strategy } from './strategy'; export class WinningStrategy implements Strategy { private won = false; private prevHand: Hand; constructor() {} nextHand(): Hand { if (!this.won) { this.prevHand = Hand.getHand(Math.floor(Math.random() * 3)); } return this.prevHand; } study(win: boolean): void { this.won = win; } } \"]},\"377\":{\"h\":\"运行结果\",\"t\":[\"...(省略) Winner: [Hana:9991 games, 3567 win, 3049 lose] Winner: [Hana:9992 games, 3568 win, 3049 lose] Even... Winner: [Hana:9994 games, 3569 win, 3049 lose] Even... Even... Winner: [Hana:9997 games, 3570 win, 3049 lose] Winner: [Hana:9998 games, 3571 win, 3049 lose] Winner: [Hana:9999 games, 3572 win, 3049 lose] Total result: [Taro:10000 games, 3049 win, 3573 lose] [Hana:10000 games, 3573 win, 3049 lose] \"]},\"378\":{\"h\":\"拓展思路的要点\"},\"379\":{\"h\":\"为什么要特意编写 Strategy\",\"t\":[\"通常在编程时算法会被写在具体方法中。Strategy 模式却特意将算法与其他部分分离开来，只是定义了与算法相关的接口（API），然后在程序中以委托的方式来使用算法。\",\"这样看起来程序好像变复杂了，其实不然。例如，当我们想要通过改善算法来提高算法的处理速度时，如果使用了 Strategy 模式，就不必修改 Strategy 角色的接口（API）了，仅仅修改 ConcreteStrategy 角色即可。而且，使用委托这种弱关联关系可以很方便地整体替换算法。例如，如果想比较原来的算法与改进后的算法的处理速度有多大区别，简单地替换下算法即可进行测试。\",\"使用 Strategy 模式编写象棋程序时，可以方便地根据棋手的选择切换 AI 例程的水平。\"]},\"380\":{\"h\":\"程序运行中也可以切换策略\",\"t\":[\"如果使用 Strategy 模式，在程序运行中也可以切换角色。例如，在内存容量少的运行环境中可以使用 SlowButLessMemoryStrategy（速度慢但省内存的策略），而在内存容量多的运行环境中则可以使用 FastButMoreMemoryStrategy（速度快但耗内存的策略）。\",\"此外，还可以用某种算法去“验算”另外一种算法。例如，假设要在某个表格计算软件的开发版本中进行复杂的计算。这时，我们可以准备两种算法，即“高速但计算上可能有 Bug 的算法”和“低速但计算准确的算法”，然后让后者去验算前者的计算结果。\"]},\"381\":{\"h\":\"相关的设计模式\",\"t\":[\"Flyweight 模式\",\"Abstract Factory 模式\",\"State 模式\"]},\"382\":{\"c\":[\"设计模式\"]},\"383\":{\"c\":[\"设计模式\",\"TypeScript\",\"分开考虑\",\"整体的替换算法\"]},\"384\":{\"h\":\"Template Method 模式\",\"t\":[\"在父类中定义处理流程的框架，在子类中实现具体处理。Template Method 模式的主要目的是为了定义一个算法的骨架，而将一些步骤的具体实现延迟到子类中。通过这种方式，子类可以在不改变算法结构的情况下，重新定义算法中的某些步骤。\"]},\"385\":{\"h\":\"为什么要使用 Template Method 模式？\",\"t\":[\"代码复用：将通用的算法结构放在父类中，避免重复代码。\",\"灵活性：允许子类实现具体的步骤，增加了灵活性。\",\"控制反转：父类控制算法的执行流程，子类只需关注具体步骤的实现。\"]},\"386\":{\"h\":\"示例代码\",\"t\":[\"// abstractDisplay.ts export abstract class AbstractDisplay { protected abstract open(): void; protected abstract print(): void; protected abstract close(): void; display(): void { this.open(); for (let i = 0; i < 5; i++) { this.print(); } this.close(); } } // charDisplay.ts import { AbstractDisplay } from './abstractDisplay'; export class CharDisplay extends AbstractDisplay { private ch: string; constructor(ch: string) { super(); this.ch = ch; } open() { console.log('<<'); } print() { console.log(this.ch); } close() { console.log('>>'); } } // stringDisplay.ts import { AbstractDisplay } from './abstractDisplay'; export class StringDisplay extends AbstractDisplay { private str: string; private width: number; constructor(str: string) { super(); this.str = str; this.width = str.length; } open() { this.printLine(); } print() { console.log(`|${this.str}|`); } close() { this.printLine(); } private printLine() { let line = '+'; for (let i = 0; i < this.width; i++) { line += '-'; } line += '+'; console.log(line); } } // main.ts import { CharDisplay } from './charDisplay'; import { StringDisplay } from './stringDisplay'; const d1 = new CharDisplay('H'); const d2 = new StringDisplay('Hello, world.'); const d3 = new StringDisplay('你好，世界。'); d1.display(); d2.display(); d3.display(); \"]},\"387\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\template_method\\\\main.ts\\\" << H H H H H >> +-------------+ |Hello, world.| |Hello, world.| |Hello, world.| |Hello, world.| |Hello, world.| +-------------+ +------+ |你好，世界。| |你好，世界。| |你好，世界。| |你好，世界。| |你好，世界。| +------+ \"]},\"388\":{\"h\":\"相关设计模式\",\"t\":[\"Factory Method 模式\",\"Strategy 模式\"]},\"389\":{\"h\":\"延申: 类的层次与抽象类\",\"t\":[\"我们在理解类的层次时，通常是站在子类的角度进行思考的。也就是说，很容易着眼于以下几点。\",\"在子类中可以使用父类中定义的方法\",\"可以通过在子类中增加方法以实现新的功能\",\"在子类中重写父类的方法可以改变程序的行为\",\"现在，让我们稍微改变一下立场，站在父类的角度进行思考。在父类中，我们声明了抽象方法，而将该方法的实现交给了子类。换言之，就程序而言，声明抽象方法是希望达到以下目的。\",\"期待子类去实现抽象方法\",\"要求子类去实现抽象方法\",\"也就是说，子类具有实现在父类中所声明的抽象方法的责任。因此，这种责任被称为“子类责任\\\"（ subclass responsibility ）。\"]},\"390\":{\"c\":[\"设计模式\"]},\"391\":{\"c\":[\"设计模式\",\"typescript\",\"交给子类\"]},\"392\":{\"h\":\"Visitor 模式\",\"t\":[\"在 Visitor 模式中，数据结构与处理被分离开来。我们编写一个表示“访问者”的类来访问数据结构中的元素，并把对各元素的处理交给访问者类。这样，当需要增加新的处理时，我们只需要编写新的访问者，然后让数据结构可以接受访问者的访问即可。\"]},\"393\":{\"h\":\"为什么使用 Visitor 模式？\",\"t\":[\"分离关注点：将数据结构与操作分离，使得代码更清晰、更易维护。\",\"增加新操作更容易：只需添加新的访问者类，而不需要修改现有的数据结构。\",\"符合开闭原则：对扩展开放，对修改关闭。\"]},\"394\":{\"h\":\"示例代码\",\"t\":[\"// directory.ts import { Entry } from './entry'; import { Visitor } from './visitor'; export class Directory extends Entry { private dir: Entry[] = []; constructor(private name: string) { super(); } getName() { return this.name; } getSize() { let size = 0; this.dir.forEach((entry) => { size += entry.getSize(); }); return size; } add(entry: Entry) { this.dir.push(entry); return this; } iterator() { return this.dir; } accept(visitor:Visitor) { visitor.visit(this); } } // element.ts import { Visitor } from './visitor'; export interface Element { accept(visitor: Visitor): void; } // entry.ts import { Element } from \\\"./element\\\"; import { Visitor } from \\\"./visitor\\\"; export abstract class Entry implements Element { abstract getName(): string; abstract getSize(): number; add(entry: Entry): Entry { throw new Error(\\\"Entry.add not implemented\\\"); } iterator(): Entry[] { throw new Error(\\\"Entry.iterator not implemented\\\"); } toString(): string { return `${this.getName()} (${this.getSize()})`; } abstract accept(visitor: Visitor): void; } // file.ts import { Visitor } from './visitor'; import { Entry } from './entry'; export class File extends Entry { constructor(private name: string, private size: number) { super(); } getName(): string { return this.name; } getSize(): number { return this.size; } accept(visitor: Visitor): void { visitor.visit(this); } } // listVisitor.ts import { Visitor } from \\\"./visitor\\\"; import { File } from \\\"./file\\\"; import { Directory } from \\\"./directory\\\"; import { Entry } from \\\"./entry\\\"; export class ListVisitor extends Visitor { private currentdir = \\\"\\\"; visit(entry:Entry) { if (entry instanceof File) { console.log(`${this.currentdir}/${entry}`); } else if (entry instanceof Directory) { console.log(`${this.currentdir}/${entry}`); const savedir = this.currentdir; this.currentdir = `${this.currentdir}/${entry.getName()}`; const it: Entry[] = entry.iterator(); for (let i = 0; i < it.length; i++) { it[i].accept(this); } this.currentdir = savedir; } } } // main.ts import { Directory } from \\\"./directory\\\"; import { File } from \\\"./file\\\"; import { ListVisitor } from \\\"./listVisitor\\\"; console.log(\\\"Making root entries...\\\"); let rootdir = new Directory(\\\"root\\\"); let bindir = new Directory(\\\"bin\\\"); let tmpdir = new Directory(\\\"tmp\\\"); let usrdir = new Directory(\\\"usr\\\"); rootdir.add(bindir); rootdir.add(tmpdir); rootdir.add(usrdir); bindir.add(new File(\\\"vi\\\", 10000)); bindir.add(new File(\\\"latex\\\", 20000)); rootdir.accept(new ListVisitor()); console.log(\\\"Making user entries...\\\"); let yuki = new Directory(\\\"yuki\\\"); let hanako = new Directory(\\\"hanako\\\"); let tomura = new Directory(\\\"tomura\\\"); usrdir.add(yuki); usrdir.add(hanako); usrdir.add(tomura); yuki.add(new File(\\\"diary.html\\\", 100)); yuki.add(new File(\\\"Composite.java\\\", 200)); hanako.add(new File(\\\"memo.tex\\\", 300)); tomura.add(new File(\\\"game.doc\\\", 400)); tomura.add(new File(\\\"junk.mail\\\", 500)); rootdir.accept(new ListVisitor()); // visitor.ts import { Entry } from './entry'; export abstract class Visitor { abstract visit(file:Entry); } \"]},\"395\":{\"h\":\"运行结果\",\"t\":[\"PS design_patern> ts-node \\\"d:\\\\code\\\\design_patern\\\\src\\\\visitor\\\\main.ts\\\" Making root entries... /root (30000) /root/bin (30000) /root/bin/vi (10000) /root/bin/latex (20000) /root/tmp (0) /root/usr (0) Making user entries... /root (31500) /root/bin (30000) /root/bin/vi (10000) /root/bin/latex (20000) /root/tmp (0) /root/usr (1500) /root/usr/yuki (300) /root/usr/yuki/diary.html (100) /root/usr/yuki/Composite.java (200) /root/usr/hanako (300) /root/usr/hanako/memo.tex (300) /root/usr/tomura (900) /root/usr/tomura/game.doc (400) /root/usr/tomura/junk.mail (500) \"]},\"396\":{\"h\":\"拓展思路的要点\"},\"397\":{\"h\":\"双重分发\",\"t\":[\"我们来整理一下 Visitor 模式中的方法调用关系。accept（接收）方法的调用方式如下：element.accept(visitor)；而 visit（访问）方法的调用方式如下：visitor.visit(element)。对比这两个方法会发现，它们呈现出一种相反的关系。element 接收 visitor，而 visitor 又访问 element。在 Visitor 模式中，ConcreteElement 和 ConcreteVisitor 这两个角色共同决定了实际进行的处理。这种消息分发的方式一般被称为双重分发（double dispatch）。\"]},\"398\":{\"h\":\"为什么要这么复杂\",\"t\":[\"Visitor 模式的目的是将处理逻辑从数据结构中分离出来。数据结构很重要，它能够将元素集合及其关联关系组织在一起。但是，需要注意的是，保存数据结构与基于数据结构进行处理是两种不同的概念。在示例程序中，我们创建了 ListVisitor 类作为显示文件夹内容的 ConcreteVisitor 角色。此外，在练习题中，我们还要编写进行其他处理的 ConcreteVisitor 角色。通常，ConcreteVisitor 角色的开发可以独立于 File 类和 Directory 类。也就是说，Visitor 模式提高了 File 类和 Directory 类作为组件的独立性。如果将处理逻辑的方法定义在 File 类和 Directory 类中，那么每次要扩展功能，增加新的“处理”时，就不得不去修改这些类。\"]},\"399\":{\"h\":\"开闭原则——对扩展开放，对修改关闭\",\"t\":[\"在设计类时，若无特殊理由，必须要考虑到将来可能会扩展类。绝不能毫无理由地禁止扩展类。这就是“对扩展是开放的”的意思。但是，如果在每次扩展类时都需要修改现有的类就太麻烦了。所以我们需要在不修改现有类的前提下能够扩展类，这就是“对修改是关闭的”的意思。我们提倡扩展，但如果需要修改现有代码，那就不行了。在不修改现有代码的前提下进行扩展，这就是开闭原则。至此，大家已经学习了多种设计模式。那么在看到这条设计原则后，大家应该都会点头表示赞同吧。功能需求总是在不断变化，而且这些功能需求大都是“希望扩展某个功能”。因此，如果不能比较容易地扩展类，开发过程将会变得非常困难。另一方面，如果要修改已经编写和测试完成的类，又可能会导致软件产品的质量降低。对扩展开放、对修改关闭的类具有高可复用性，可作为组件复用。设计模式和面向对象的目的正是为我们提供一种结构，可以帮助我们设计出这样的类。\"]},\"400\":{\"h\":\"易于增加 ConcreteVisitor 角色\",\"t\":[\"使用 Visitor 模式可以很容易地增加 ConcreteVisitor 角色。因为具体的处理被交给 ConcreteVisitor 角色负责，因此完全不用修改 ConcreteElement 角色。\"]},\"401\":{\"h\":\"难以增加 ConcreteElement 角色\",\"t\":[\"尽管使用 Visitor 模式可以很容易地增加 ConcreteVisitor 角色，但它却难以应对 ConcreteElement 角色的增加。例如，假设现在我们要在示例程序中增加一个 Device 类，它是 File 类和 Directory 类的兄弟类。这时，我们不得不在 Visitor 类中声明一个 visit(Device) 方法，并在所有的 Visitor 类的子类中都实现这个方法。\"]},\"402\":{\"h\":\"Visitor 工作所需的条件\",\"t\":[\"在 Visitor 模式中，对数据结构中的元素进行处理的任务被分离出来，交给 Visitor 类负责。这样，就实现了数据结构与处理的分离。这个主题，我们在本章的学习过程中已经提到过很多次了。但是要达到这个目的是有条件的，那就是 Element 角色必须向 Visitor 角色公开足够多的信息。例如，在示例程序中，visit(Directory) 方法需要调用每个目录条目的 accept 方法。为此，Directory 类必须提供用于获取每个目录条目的 iterator 方法。只有当访问者从数据结构中获取了足够多的信息后才能工作。如果无法获取到这些信息，它就无法工作。这样做的缺点是，如果公开了不应当被公开的信息，将来对数据结构的改良就会变得非常困难。\"]},\"403\":{\"h\":\"相关的设计模式\",\"t\":[\"Iterator 模式\",\"Composite 模式\",\"Interpreter 模式\"]},\"404\":{\"c\":[\"设计模式\"]},\"405\":{\"c\":[\"设计模式\",\"TypeScript\",\"访问数据结构并处理数据\"]},\"406\":{\"h\":\"手把手教你构建 C 语言编译器（0）- 前言\",\"t\":[\"本文转载自 手把手教你构建 C 语言编译器（0）- 前言，原作者 三点水，原文链接：原文链接，如有侵权，请联系删除。\",\"转载工具:devtool、helloworld\",\"“手把手教你构建 C 语言编译器” 这一系列教程将带你从头编写一个 C 语言的编译器。希望通过这个系列，我们能对编译器的构建有一定的了解，同时，我们也将构建出一个能用的 C 语言编译器，尽管有许多语法并不支持。\",\"手把手教你构建 C 语言编译器系列共有10个部分：\",\"手把手教你构建 C 语言编译器（0）——前言\",\"手把手教你构建 C 语言编译器（1）——设计\",\"手把手教你构建 C 语言编译器（2）——虚拟机\",\"手把手教你构建 C 语言编译器（3）——词法分析器\",\"手把手教你构建 C 语言编译器（4）——递归下降\",\"手把手教你构建 C 语言编译器（5）——变量定义\",\"手把手教你构建 C 语言编译器（6）——函数定义\",\"手把手教你构建 C 语言编译器（7）——语句\",\"手把手教你构建 C 语言编译器（8）——表达式\",\"手把手教你构建 C 语言编译器（9）——总结\",\"在开始进入正题之前，本篇是一些闲聊，谈谈这个系列的初衷。如果你急切地想进入正篇，请跳过本章。\"]},\"407\":{\"h\":\"为什么要学编译原理\",\"t\":[\"如果要我说计算机专业最重要的三门课，我会说是《数据结构》、《算法》和《编译原理》。在我看来，能不能理解“递归”像是程序员的第一道门槛，而会不会写编译器则是第二道。\",\"（当然，并不是说是没写过编译器就不是好程序员，只能说它是一个相当大的挑战吧）\",\"以前人们会说，学习了编译原理，你就能写出更加高效的代码，但随着计算机性能的提升，代码是否高效显得就不那么重要了。那么为什么要学习编译原理呢？\",\"原因只有一个：装B。\",\"好吧，也许现在还想学习编译原理的人只可能是因为兴趣了。一方面想了解它的工作原理；另一方面希望挑战一下自己，看看自己能走多远。\"]},\"408\":{\"h\":\"理论很复杂，实现也很复杂？\",\"t\":[\"我对编译器一直心存敬佩。所以当学校开《编译原理》的课程后，我是抱着满腔热情去上课的，但是两节课后我就放弃了。原因是太复杂了，听不懂。\",\"一般编译原理的课程会说一些：\",\"如何表示语法（BNF什么的）\",\"词法分析，用什么有穷自动机和无穷自动机\",\"语法分析，递归下降法，什么 LL(k)，LALR 分析。\",\"中间代码的表示\",\"代码的生成\",\"代码优化\",\"我相信绝大多数（98％）的学生顶多学到语法分析就结束了。并且最重要的是，学了这么多也没用！依旧帮助不了我们学习编译器！这其中最主要的原因是《编译原理》试图教会我们的是如何构造“编译器生成器”，即构造一个工具，根据文法来生成编译器（如 lex/yacc）等等。\",\"这些理论试图教会我们如何用通用的方法来自动解决问题，它们有很强的实际意义，只是对于一般的学生或程序员来说，它们过于强大，内容过于复杂。如果你尝试阅读 lex/yacc （或 flex/bison）的代码，就会发现太可怕了。\",\"然而如果你能跟我一样，真正来实现一个简单的编译器，那么你会发现，比起可怕的《编译原理》，这点复杂度还是不算什么的（因为好多理论根本用不上）。\"]},\"409\":{\"h\":\"项目的初衷\",\"t\":[\"有一次在 Github 上看到了一个项目（当时很火的），名叫 c4，号称用 4 个函数来实现了一个小的 C 语言编译器。它最让我震惊的是能够自举，即能自己编译自己。并且它用很少的代码就完成了一个功能相当完善的 C 语言编译器。\",\"一般的编译器相关的教程要么就十分简单（如实现四则运算），要么就是借助了自动生成的工具（如 flex/bison）。而 c4 的代码完全是手工实现的，不用外部工具。可惜的是它的代码初衷是代码最小化，所以写得很乱，很难懂。所以本项目的主要目的：\",\"实现一个功能完善的 C 语言编译器\",\"通过教程来说明这个过程。\",\"c4 大致500+行。重写的代码历时一周，总共代码加注释1400行。项目地址: Write a C Interpreter。\",\"声明：本项目中的代码逻辑绝大多数取自 c4 ，但确为自己重写。\"]},\"410\":{\"h\":\"做好心理准备\",\"t\":[\"在写编译器的时候会遇到两个主要问题：\",\"繁琐，会有许多相似的代码，写起来很无聊。\",\"难以调试，一方面没有很好的测试用例，另一方面需要对照生成的代码来调试（遇到的时候就知道了）。\",\"所以我希望你有足够的耐心和时间来学习，相信当你真正完成的时候会像我一样，十分有成就感。\",\"PS. 第一篇完全没有正题相关的内容也是希望你能有所心理准备再开始学习。\"]},\"411\":{\"h\":\"参考资料\",\"t\":[\"最后想介绍几个资料：\",\"Let’s Build a Compiler 很好的初学者教程，英文的。\",\"Lemon Parser Generator，一个语法分析器生成器，对照《编译原理》观看效果更佳。\",\"由于本人水平一般，文章、代码难免会有错误，敬请批评指正！\",\"最后祝你学得愉快。\",\"这篇博客并没有使用诸如 flex、bison 等工具来编写 token 和文法的定义，因而灵活性较差。相反，它通过定义自己的指令集并支持该指令集的虚拟机来模拟编译的部分过程，具有一定的参考价值。不过，我仍然认为通过定义 token 和文法并编写解析算法（如 regex、LL(k) 等）可能会更具普适性。\",\"相关信息\",\"不过据说c、cpp、java这些成熟的语言都是手动实现的？还没仔细了解过。\\nTODO\"]},\"412\":{\"c\":[\"编译原理\"]},\"413\":{\"c\":[\"c\",\"编译器\",\"解释器\"]},\"414\":{\"h\":\"手把手教你构建 C 语言编译器（1）- 设计\",\"t\":[\"本文转自 https://lotabout.me/2015/write-a-C-interpreter-1/，如有侵权，请联系删除。\",\"Table of Contents\",\"1. 编译器的构建流程\",\"2. 编译器框架\",\"这是“手把手教你构建 C 语言编译器”系列的第二篇，我们要从整体上讲解如何设计我们的 C 语言编译器。\",\"手把手教你构建 C 语言编译器系列共有10个部分：\",\"手把手教你构建 C 语言编译器（0）——前言\",\"手把手教你构建 C 语言编译器（1）——设计\",\"手把手教你构建 C 语言编译器（2）——虚拟机\",\"手把手教你构建 C 语言编译器（3）——词法分析器\",\"手把手教你构建 C 语言编译器（4）——递归下降\",\"手把手教你构建 C 语言编译器（5）——变量定义\",\"手把手教你构建 C 语言编译器（6）——函数定义\",\"手把手教你构建 C 语言编译器（7）——语句\",\"手把手教你构建 C 语言编译器（8）——表达式\",\"手把手教你构建 C 语言编译器（9）——总结\",\"首先要说明的是，虽然标题是编译器，但实际上我们构建的是 C 语言的解释器，这意味着我们可以像运行脚本一样去运行 C 语言的源代码文件。这么做的理由有两点：\",\"解释器与编译器仅在代码生成阶段有区别，而其它方面如词法分析、语法分析是一样的。\",\"解释器需要我们实现自己的虚拟机与指令集，而这部分能帮助我们了解计算机的工作原理。\"]},\"415\":{\"h\":\"编译器的构建流程\",\"t\":[\"一般而言，编译器的编写分为 3 个步骤：\",\"词法分析器，用于将字符串转化成内部的表示结构。\",\"语法分析器，将词法分析得到的标记流（token）生成一棵语法树。\",\"目标代码的生成，将语法树转化成目标代码。\",\"已经有许多工具能帮助我们处理阶段1和2，如 flex 用于词法分析，bison 用于语法分析。只是它们的功能都过于强大，屏蔽了许多实现上的细节，对于学习构建编译器帮助不大。所以我们要完全手写这些功能。\",\"所以我们会依照以下步骤来构建我们的编译器：\",\"构建我们自己的虚拟机以及指令集。这后生成的目标代码便是我们的指令集。\",\"构建我们的词法分析器\",\"构建语法分析器\"]},\"416\":{\"h\":\"编译器框架\",\"t\":[\"我们的编译器主要包括 4 个函数：\",\"next() 用于词法分析，获取下一个标记，它将自动忽略空白字符。\",\"program() 语法分析的入口，分析整个 C 语言程序。\",\"expression(level) 用于解析一个表达式。\",\"eval() 虚拟机的入口，用于解释目标代码。\",\"这里有一个单独用于解析“表达式”的函数 expression 是因为表达式在语法分析中相对独立并且比较复杂，所以我们将它单独作为一个模块（函数）。下面是相应的源代码：\",\"#include <stdio.h>#include <stdlib.h>#include <memory.h>#include <string.h>int token; // current tokenchar *src, *old_src; // pointer to source code string;int poolsize; // default size of text/data/stackint line; // line numbervoid next() { token = *src++; return;}void expression(int level) { // do nothing}void program() { next(); // get next token while (token > 0) { printf(\\\"token is: %c\\\\n\\\", token); next(); }}int eval() { // do nothing yet return 0;}int main(int argc, char **argv){ int i, fd; argc--; argv++; poolsize = 256 * 1024; // arbitrary size line = 1; if ((fd = open(*argv, 0)) < 0) { printf(\\\"could not open(%s)\\\\n\\\", *argv); return -1; } if (!(src = old_src = malloc(poolsize))) { printf(\\\"could not malloc(%d) for source area\\\\n\\\", poolsize); return -1; } // read the source file if ((i = read(fd, src, poolsize-1)) <= 0) { printf(\\\"read() returned %d\\\\n\\\", i); return -1; } src[i] = 0; // add EOF character close(fd); program(); return eval();}\",\"上面的代码看上去挺复杂，但其实内容不多。它的流程为：读取一个文件（内容为 C 语言代码），逐个读取文件中的字符，并输出。这里需要的是注意每个函数的作用，后面的文章中，我们将逐个填充每个函数的功能，最终构建起我们的编译器。\",\"本节的代码可以在 Github 上下载，也可以直接 clone\",\"git clone -b step-0 https://github.com/lotabout/write-a-C-interpreter\",\"这样我们就有了一个最简单的编译器：什么都不干的编译器，下一章中，我们将实现其中的eval函数，即我们自己的虚拟机。\"]},\"417\":{\"h\":\"转载声明\",\"t\":[\"title: \\\"手把手教你构建 C 语言编译器（2）——虚拟机\\\" category:\",\"编译原理 tag:\",\"c\",\"编译器\",\"解释器\",\"本文转自 https://lotabout.me/2015/write-a-C-interpreter-2/，如有侵权，请联系删除。\",\"Table of Contents\",\"1. 计算机的内部工作原理\",\"1.1. 内存\",\"1.2. 寄存器\",\"2. 指令集\",\"2.1. MOV\",\"2.2. PUSH\",\"2.3. JMP\",\"2.4. JZ/JNZ\",\"2.5. 子函数调用\",\"2.6. ENT\",\"2.7. ADJ\",\"2.8. LEV\",\"2.9. LEA\",\"2.10. 运算符指令\",\"2.11. 内置函数\",\"3. 测试\",\"4. 小结\",\"这是“手把手教你构建 C 语言编译器”系列的第三篇，本章我们要构建一台虚拟的电脑，设计我们自己的指令集，运行我们的指令集，说得通俗一点就是自己实现一套汇编语言。它们将作为我们的编译器最终输出的目标代码。\",\"手把手教你构建 C 语言编译器系列共有10个部分：\",\"手把手教你构建 C 语言编译器（0）——前言\",\"手把手教你构建 C 语言编译器（1）——设计\",\"手把手教你构建 C 语言编译器（2）——虚拟机\",\"手把手教你构建 C 语言编译器（3）——词法分析器\",\"手把手教你构建 C 语言编译器（4）——递归下降\",\"手把手教你构建 C 语言编译器（5）——变量定义\",\"手把手教你构建 C 语言编译器（6）——函数定义\",\"手把手教你构建 C 语言编译器（7）——语句\",\"手把手教你构建 C 语言编译器（8）——表达式\",\"手把手教你构建 C 语言编译器（9）——总结\"]},\"418\":{\"h\":\"计算机的内部工作原理\",\"t\":[\"计算机中有三个基本部件需要我们关注：CPU、寄存器及内存。代码（汇编指令）以二进制的形式保存在内存中；CPU 从中一条条地加载指令执行；程序运行的状态保存在寄存器中。\"]},\"419\":{\"h\":\"内存\",\"t\":[\"内存用于存储数据，这里的数据可以是代码，也可以是其它的数据。现代操作系统在操作内存时，并不是直接处理”物理内存“，而是操作”虚拟内存“。虚拟内存可以理解为一种映射，它的作用是屏蔽了物理的细节。例如 32 位的机器中，我们可以使用的内存地址为 2^32 = 4G，而电脑上的实际内存可能只有 256 M。操作系统将我们使用的虚拟地址映射到了到实际的内存上。\",\"当然，我们这里并不需要了解太多，但需要了解的是：进程的内存会被分成几个段：\",\"代码段（text）用于存放代码（指令）。\",\"数据段（data）用于存放初始化了的数据，如int i = 10;，就需要存放到数据段中。\",\"未初始化数据段（bss）用于存放未初始化的数据，如 int i[1000];，因为不关心其中的真正数值，所以单独存放可以节省空间，减少程序的体积。\",\"栈（stack）用于处理函数调用相关的数据，如调用帧（calling frame）或是函数的局部变量等。\",\"堆（heap）用于为程序动态分配内存。\",\"它们在内存中的位置类似于下图：\",\"+------------------+| stack | | high address| ... v || || || || || ... ^ || heap | |+------------------+| bss segment |+------------------+| data segment |+------------------+| text segment | low address+------------------+\",\"我们的虚拟机并不打算模拟完整的计算机，因此简单起见，我们只关心三个内容：代码段、数据段以及栈。其中的数据段我们只用来存放字符串，因为我们的编译器并不支持初始化变量，因此我们也不需要未初始化数据段。\",\"当用户的程序需要分配内存时，理论上我们的虚拟机需要维护一个堆用于内存分配，但实际实现上较为复杂且与编译无关，故我们引入一个指令MSET，使我们能直接使用编译器（解释器）中的内存。\",\"综上，我们需要首先在全局添加如下代码：\",\"int *text, // text segment *old_text, // for dump text segment *stack; // stackchar *data; // data segment\",\"注意这里的类型，虽然是int型，但理解起来应该作为无符号的整型，因为我们会在代码段（text）中存放如指针/内存地址的数据，它们就是无符号的。其中数据段（data）由于只存放字符串，所以是 char * 型的。\",\"接着，在main函数中加入初始化代码，真正为其分配内存：\",\"int main() { close(fd); ... // allocate memory for virtual machine if (!(text = old_text = malloc(poolsize))) { printf(\\\"could not malloc(%d) for text area\\\\n\\\", poolsize); return -1; } if (!(data = malloc(poolsize))) { printf(\\\"could not malloc(%d) for data area\\\\n\\\", poolsize); return -1; } if (!(stack = malloc(poolsize))) { printf(\\\"could not malloc(%d) for stack area\\\\n\\\", poolsize); return -1; } memset(text, 0, poolsize); memset(data, 0, poolsize); memset(stack, 0, poolsize); ... program();}\"]},\"420\":{\"h\":\"寄存器\",\"t\":[\"计算机中的寄存器用于存放计算机的运行状态，真正的计算机中有许多不同种类的寄存器，但我们的虚拟机中只使用 4 个寄存器，分别如下：\",\"PC 程序计数器，它存放的是一个内存地址，该地址中存放着 下一条 要执行的计算机指令。\",\"SP 指针寄存器，永远指向当前的栈顶。注意的是由于栈是位于高地址并向低地址增长的，所以入栈时 SP 的值减小。\",\"BP 基址指针。也是用于指向栈的某些位置，在调用函数时会使用到它。\",\"AX 通用寄存器，我们的虚拟机中，它用于存放一条指令执行后的结果。\",\"要理解这些寄存器的作用，需要去理解程序运行中会有哪些状态。而这些寄存器只是用于保存这些状态的。\",\"在全局中加入如下定义：\",\"int *pc, *bp, *sp, ax, cycle; // virtual machine registers\",\"在 main 函数中加入初始化代码，注意的是PC在初始应指向目标代码中的main函数，但我们还没有写任何编译相关的代码，因此先不处理。代码如下：\",\"memset(stack, 0, poolsize);...bp = sp = (int *)((int)stack + poolsize);ax = 0;...program();\",\"与 CPU 相关的是指令集，我们将专门作为一个小节。\"]},\"421\":{\"h\":\"指令集\",\"t\":[\"指令集是 CPU 能识别的命令的集合，也可以说是 CPU 能理解的语言。这里我们要为我们的虚拟机构建自己的指令集。它们基于 x86 的指令集，但更为简单。\",\"首先在全局变量中加入一个枚举类型，这是我们要支持的全部指令：\",\"// instructionsenum { LEA ,IMM ,JMP ,CALL,JZ ,JNZ ,ENT ,ADJ ,LEV ,LI ,LC ,SI ,SC ,PUSH, OR ,XOR ,AND ,EQ ,NE ,LT ,GT ,LE ,GE ,SHL ,SHR ,ADD ,SUB ,MUL ,DIV ,MOD , OPEN,READ,CLOS,PRTF,MALC,MSET,MCMP,EXIT };\",\"这些指令的顺序安排是有意的，稍后你会看到，带有参数的指令在前，没有参数的指令在后。这种顺序的唯一作用就是在打印调试信息时更加方便。但我们讲解的顺序并不依据它。\"]},\"422\":{\"h\":\"MOV\",\"t\":[\"MOV 是所有指令中最基础的一个，它用于将数据放进寄存器或内存地址，有点类似于 C 语言中的赋值语句。x86 的 MOV 指令有两个参数，分别是源地址和目标地址：MOV dest, source （Intel 风格），表示将 source 的内容放在 dest 中，它们可以是一个数、寄存器或是一个内存地址。\",\"一方面，我们的虚拟机只有一个寄存器，另一方面，识别这些参数的类型（是数据还是地址）是比较困难的，因此我们将 MOV 指令拆分成 5 个指令，这些指令只接受一个参数，如下：\",\"IMM <num> 将 <num> 放入寄存器 ax 中。\",\"LC 将对应地址中的字符载入 ax 中，要求 ax 中存放地址。\",\"LI 将对应地址中的整数载入 ax 中，要求 ax 中存放地址。\",\"SC 将 ax 中的数据作为字符存放入地址中，要求栈顶存放地址。\",\"SI 将 ax 中的数据作为整数存放入地址中，要求栈顶存放地址。\",\"你可能会觉得将一个指令变成了许多指令，整个系统就变得复杂了，但实际情况并非如此。首先是 x86 的 MOV 指令其实有许多变种，根据类型的不同有 MOVB, MOVW 等指令，我们这里的 LC/SC 和 LI/SI 就是对应字符型和整型的存取操作。\",\"但最为重要的是，通过将 MOV 指令拆分成这些指令，只有 IMM 需要有参数，且不需要判断类型，所以大大简化了实现的难度。\",\"在 eval() 函数中加入下列代码：\",\"void eval() { int op, *tmp; while (1) { if (op == IMM) {ax = *pc++;} // load immediate value to ax else if (op == LC) {ax = *(char *)ax;} // load character to ax, address in ax else if (op == LI) {ax = *(int *)ax;} // load integer to ax, address in ax else if (op == SC) {ax = *(char *)*sp++ = ax;} // save character to address, value in ax, address on stack else if (op == SI) {*(int *)*sp++ = ax;} // save integer to address, value in ax, address on stack } ... return 0;}\",\"其中的 *sp++ 的作用是退栈，相当于 POP 操作。\",\"这里要解释的一点是，为什么 SI/SC 指令中，地址存放在栈中，而 LI/LC 中，地址存放在 ax 中？原因是默认计算的结果是存放在 ax 中的，而地址通常是需要通过计算获得，所以执行 LI/LC 时直接从 ax 取值会更高效。另一点是我们的 PUSH 指令只能将 ax 的值放到栈上，而不能以值作为参数，详细见下文。\"]},\"423\":{\"h\":\"PUSH\",\"t\":[\"在 x86 中，PUSH 的作用是将值或寄存器，而在我们的虚拟机中，它的作用是将 ax 的值放入栈中。这样做的主要原因是为了简化虚拟机的实现，并且我们也只有一个寄存器 ax 。代码如下：\",\"else if (op == PUSH) {*--sp = ax;} // push the value of ax onto the stack\"]},\"424\":{\"h\":\"JMP\",\"t\":[\"JMP <addr> 是跳转指令，无条件地将当前的 PC 寄存器设置为指定的 <addr>，实现如下：\",\"else if (op == JMP) {pc = (int *)*pc;} // jump to the address\",\"需要注意的是，pc 寄存器指向的是 下一条 指令。所以此时它存放的是 JMP 指令的参数，即 <addr> 的值。\"]},\"425\":{\"h\":\"JZ/JNZ\",\"t\":[\"为了实现 if 语句，我们需要条件判断相关的指令。这里我们只实现两个最简单的条件判断，即结果（ax）为零或不为零情况下的跳转。\",\"实现如下：\",\"else if (op == JZ) {pc = ax ? pc + 1 : (int *)*pc;} // jump if ax is zeroelse if (op == JNZ) {pc = ax ? (int *)*pc : pc + 1;} // jump if ax is not zero\"]},\"426\":{\"h\":\"子函数调用\",\"t\":[\"这是汇编中最难理解的部分，所以合在一起说，要引入的命令有 CALL, ENT, ADJ 及 LEV。\",\"首先我们介绍 CALL <addr> 与 RET 指令，CALL 的作用是跳转到地址为 <addr> 的子函数，RET 则用于从子函数中返回。\",\"为什么不能直接使用 JMP 指令呢？原因是当我们从子函数中返回时，程序需要回到跳转之前的地方继续运行，这就需要事先将这个位置信息存储起来。反过来，子函数要返回时，就需要获取并恢复这个信息。因此实际中我们将 PC 保存在栈中。如下：\",\"else if (op == CALL) {*--sp = (int)(pc+1); pc = (int *)*pc;} // call subroutine//else if (op == RET) {pc = (int *)*sp++;} // return from subroutine;\",\"这里我们把 RET 相关的内容注释了，是因为之后我们将用 LEV 指令来代替它。\",\"在实际调用函数时，不仅要考虑函数的地址，还要考虑如何传递参数和如何返回结果。这里我们约定，如果子函数有返回结果，那么就在返回时保存在 ax 中，它可以是一个值，也可以是一个地址。那么参数的传递呢？\",\"各种编程语言关于如何调用子函数有不同的约定，例如 C 语言的调用标准是：\",\"由调用者将参数入栈。\",\"调用结束时，由调用者将参数出栈。\",\"参数逆序入栈。\",\"事先声明一下，我们的编译器参数是顺序入栈的，下面的例子（C 语言调用标准）取自 维基百科：\",\"int callee(int, int, int);int caller(void){ int i, ret; ret = callee(1, 2, 3); ret += 5; return ret;}\",\"会生成如下的 x86 汇编代码：\",\"caller: ; make new call frame push ebp mov ebp, esp sub 1, esp ; save stack for variable: i ; push call arguments push 3 push 2 push 1 ; call subroutine 'callee' call callee ; remove arguments from frame add esp, 12 ; use subroutine result add eax, 5 ; restore old call frame mov esp, ebp pop ebp ; return ret\",\"上面这段代码在我们自己的虚拟机里会有几个问题：\",\"push ebp，但我们的 PUSH 指令并无法指定寄存器。\",\"mov ebp, esp，我们的 MOV 指令同样功能不足。\",\"add esp, 12，也是一样的问题（尽管我们还没定义）。\",\"也就是说由于我们的指令过于简单（如只能操作ax寄存器），所以用上面提到的指令，我们连函数调用都无法实现。而我们又不希望扩充现有指令的功能，因为这样实现起来就会变得复杂，因此我们采用的方法是增加指令集。毕竟我们不是真正的计算机，增加指令会消耗许多资源（钱）。\"]},\"427\":{\"h\":\"ENT\",\"t\":[\"ENT <size> 指的是 enter，用于实现 ‘make new call frame’ 的功能，即保存当前的栈指针，同时在栈上保留一定的空间，用以存放局部变量。对应的汇编代码为：\",\"; make new call framepush ebpmov ebp, esp sub 1, esp ; save stack for variable: i\",\"实现如下：\",\"else if (op == ENT) {*--sp = (int)bp; bp = sp; sp = sp - *pc++;} // make new stack frame\"]},\"428\":{\"h\":\"ADJ\",\"t\":[\"ADJ <size> 用于实现 ‘remove arguments from frame’。在将调用子函数时压入栈中的数据清除，本质上是因为我们的 ADD 指令功能有限。对应的汇编代码为：\",\"; remove arguments from frameadd esp, 12\",\"实现如下：\",\"else if (op == ADJ) {sp = sp + *pc++;} // add esp, <size>\"]},\"429\":{\"h\":\"LEV\",\"t\":[\"本质上这个指令并不是必需的，只是我们的指令集中并没有 POP 指令。并且三条指令写来比较麻烦且浪费空间，所以用一个指令代替。对应的汇编指令为：\",\"; restore old call frame mov esp, ebppop ebp; returnret\",\"具体的实现如下：\",\"else if (op == LEV) {sp = bp; bp = (int *)*sp++; pc = (int *)*sp++;} // restore call frame and PC\",\"注意的是，LEV 已经把 RET 的功能包含了，所以我们不再需要 RET 指令。\"]},\"430\":{\"h\":\"LEA\",\"t\":[\"上面的一些指令解决了调用帧的问题，但还有一个问题是如何在子函数中获得传入的参数。这里我们首先要了解的是当参数调用时，栈中的调用帧是什么样的。我们依旧用上面的例子（只是现在用“顺序”调用参数）：\",\"sub_function(arg1, arg2, arg3);| .... | high address+---------------+| arg: 1 | new_bp + 4+---------------+| arg: 2 | new_bp + 3+---------------+| arg: 3 | new_bp + 2+---------------+|return address | new_bp + 1+---------------+| old BP | <- new BP+---------------+| local var 1 | new_bp - 1+---------------+| local var 2 | new_bp - 2+---------------+| .... | low address\",\"所以为了获取第一个参数，我们需要得到 new_bp + 4，但就如上面的说，我们的 ADD 指令无法操作除 ax 外的寄存器，所以我们提供了一个新的指令：LEA <offset>\",\"实现如下：\",\"else if (op == LEA) {ax = (int)(bp + *pc++);} // load address for arguments.\",\"以上就是我们为了实现函数调用需要的指令了。\"]},\"431\":{\"h\":\"运算符指令\",\"t\":[\"我们为 C 语言中支持的运算符都提供对应汇编指令。每个运算符都是二元的，即有两个参数，第一个参数放在栈顶，第二个参数放在 ax 中。这个顺序要特别注意。因为像 -，/ 之类的运算符是与参数顺序有关的。计算后会将栈顶的参数退栈，结果存放在寄存器 ax 中。因此计算结束后，两个参数都无法取得了（汇编的意义上，存在内存地址上就另当别论）。\",\"实现如下：\",\"else if (op == OR) ax = *sp++ | ax;else if (op == XOR) ax = *sp++ ^ ax;else if (op == AND) ax = *sp++ & ax;else if (op == EQ) ax = *sp++ == ax;else if (op == NE) ax = *sp++ != ax;else if (op == LT) ax = *sp++ < ax;else if (op == LE) ax = *sp++ <= ax;else if (op == GT) ax = *sp++ > ax;else if (op == GE) ax = *sp++ >= ax;else if (op == SHL) ax = *sp++ << ax;else if (op == SHR) ax = *sp++ >> ax;else if (op == ADD) ax = *sp++ + ax;else if (op == SUB) ax = *sp++ - ax;else if (op == MUL) ax = *sp++ * ax;else if (op == DIV) ax = *sp++ / ax;else if (op == MOD) ax = *sp++ % ax;\"]},\"432\":{\"h\":\"内置函数\",\"t\":[\"写的程序要”有用“，除了核心的逻辑外还需要输入输出，例如 C 语言中我们经常使用的 printf 函数就是用于输出。但是 printf 函数的实现本身就十分复杂，如果我们的编译器要达到自举，就势必要实现 printf 之类的函数，但它又与编译器没有太大的联系，因此我们继续实现新的指令，从虚拟机的角度予以支持。\",\"编译器中我们需要用到的函数有：exit, open, close, read, printf, malloc, memset 及 memcmp。代码如下：\",\"else if (op == EXIT) { printf(\\\"exit(%d)\\\", *sp); return *sp;}else if (op == OPEN) { ax = open((char *)sp[1], sp[0]); }else if (op == CLOS) { ax = close(*sp);}else if (op == READ) { ax = read(sp[2], (char *)sp[1], *sp); }else if (op == PRTF) { tmp = sp + pc[1]; ax = printf((char *)tmp[-1], tmp[-2], tmp[-3], tmp[-4], tmp[-5], tmp[-6]); }else if (op == MALC) { ax = (int)malloc(*sp);}else if (op == MSET) { ax = (int)memset((char *)sp[2], sp[1], *sp);}else if (op == MCMP) { ax = memcmp((char *)sp[2], (char *)sp[1], *sp);}\",\"这里的原理是，我们的电脑上已经有了这些函数的实现，因此编译编译器时，这些函数的二进制代码就被编译进了我们的编译器，因此在我们的编译器/虚拟机上运行我们提供的这些指令时，这些函数就是可用的。换句话说就是不需要我们自己去实现了。\",\"最后再加上一个错误判断：\",\"else { printf(\\\"unknown instruction:%d\\\\n\\\", op); return -1;}\"]},\"433\":{\"h\":\"测试\",\"t\":[\"下面我们用我们的汇编写一小段程序，来计算 10+20，在 main 函数中加入下列代码：\",\"int main(int argc, char *argv[]){ ax = 0; ... i = 0; text[i++] = IMM; text[i++] = 10; text[i++] = PUSH; text[i++] = IMM; text[i++] = 20; text[i++] = ADD; text[i++] = PUSH; text[i++] = EXIT; pc = text; ... program();}\",\"编译程序 gcc xc-tutor.c，运行程序：./a.out hello.c。输出\",\"exit(30)\",\"另外，我们的代码里有一些指针的强制转换，默认是 32 位的，因此在 64 位机器下，会出现 segmentation fault，解决方法（二选一）：\",\"编译时加上 -m32 参数：gcc -m32 xc-tutor.c\",\"在代码的开头，增加 #define int long long，long long 是 64 位的，不会出现强制转换后的问题。\",\"注意我们的之前的程序需要指令一个源文件，只是现在还用不着，但从结果可以看出，我们的虚拟机还是工作良好的。\"]},\"434\":{\"h\":\"小结\",\"t\":[\"本章中我们回顾了计算机的内部运行原理，并仿照 x86 汇编指令设计并实现了我们自己的指令集。希望通过本章的学习，你能对计算机程序的原理有一定的了解，同时能对汇编语言有一定的概念，因为汇编语言就是 C 编译器的输出。\",\"本章的代码可以在 Github 上下载，也可以直接 clone\",\"git clone -b step-1 https://github.com/lotabout/write-a-C-interpreter\",\"实际计算机中，添加一个新的指令需要设计许多新的电路，会增加许多的成本，但我们的虚拟机中，新的指令几乎不消耗资源，因此我们可以利用这一点，用更多的指令来完成更多的功能，从而简化具体的实现。\"]},\"435\":{\"h\":\"手把手教你构建 C 语言编译器（3）——词法分析器\",\"t\":[\"本文转自 https://lotabout.me/2015/write-a-C-interpreter-3/，如有侵权，请联系删除。\",\"Table of Contents\",\"1. 什么是词法分析器\",\"2. 词法分析器与编译器\",\"3. 词法分析器的实现\",\"3.1. 支持的标记\",\"3.2. 词法分析器的框架\",\"3.3. 换行符\",\"3.4. 宏定义\",\"3.5. 标识符与符号表\",\"3.6. 数字\",\"3.7. 字符串\",\"3.8. 注释\",\"3.9. 其它\",\"3.10. 关键字与内置函数\",\"4. 代码\",\"5. 小结\",\"本章我们要讲解如何构建词法分析器。\",\"手把手教你构建 C 语言编译器系列共有10个部分：\",\"手把手教你构建 C 语言编译器（0）——前言\",\"手把手教你构建 C 语言编译器（1）——设计\",\"手把手教你构建 C 语言编译器（2）——虚拟机\",\"手把手教你构建 C 语言编译器（3）——词法分析器\",\"手把手教你构建 C 语言编译器（4）——递归下降\",\"手把手教你构建 C 语言编译器（5）——变量定义\",\"手把手教你构建 C 语言编译器（6）——函数定义\",\"手把手教你构建 C 语言编译器（7）——语句\",\"手把手教你构建 C 语言编译器（8）——表达式\",\"手把手教你构建 C 语言编译器（9）——总结\"]},\"436\":{\"h\":\"什么是词法分析器\",\"t\":[\"简而言之，词法分析器用于对源码字符串做预处理，以减少语法分析器的复杂程度。\",\"词法分析器以源码字符串为输入，输出为标记流（token stream），即一连串的标记，每个标记通常包括： (token, token value) 即标记本身和标记的值。例如，源码中若包含一个数字 '998' ，词法分析器将输出 (Number, 998)，即（数字，998）。再例如：\",\"2 + 3 * (4 - 5)=>(Number, 2) Add (Number, 3) Multiply Left-Bracket (Number, 4) Subtract (Number, 5) Right-Bracket\",\"通过词法分析器的预处理，语法分析器的复杂度会大大降低，这点在后面的语法分析器我们就能体会。\"]},\"437\":{\"h\":\"词法分析器与编译器\",\"t\":[\"要是深入词法分析器，你就会发现，它的本质上也是编译器。我们的编译器是以标记流为输入，输出汇编代码，而词法分析器则是以源码字符串为输入，输出标记流。\",\" +-------+ +--------+-- source code --> | lexer | --> token stream --> | parser | --> assembly +-------+ +--------+\",\"在这个前提下，我们可以这样认为：直接从源代码编译成汇编代码是很困难的，因为输入的字符串比较难处理。所以我们先编写一个较为简单的编译器（词法分析器）来将字符串转换成标记流，而标记流对于语法分析器而言就容易处理得多了。\"]},\"438\":{\"h\":\"词法分析器的实现\",\"t\":[\"由于词法分析的工作很常见，但又枯燥且容易出错，所以人们已经开发出了许多工具来生成词法分析器，如 lex, flex。这些工具允许我们通过正则表达式来识别标记。\",\"这里注意的是，我们并不会一次性地将所有源码全部转换成标记流，原因有二：\",\"字符串转换成标记流有时是有状态的，即与代码的上下文是有关系的。\",\"保存所有的标记流没有意义且浪费空间。\",\"所以实际的处理方法是提供一个函数（即前几篇中提到的 next()），每次调用该函数则返回下一个标记。\"]},\"439\":{\"h\":\"支持的标记\",\"t\":[\"在全局中添加如下定义：\",\"// tokens and classes (operators last and in precedence order)enum { Num = 128, Fun, Sys, Glo, Loc, Id, Char, Else, Enum, If, Int, Return, Sizeof, While, Assign, Cond, Lor, Lan, Or, Xor, And, Eq, Ne, Lt, Gt, Le, Ge, Shl, Shr, Add, Sub, Mul, Div, Mod, Inc, Dec, Brak};\",\"这些就是我们要支持的标记符。例如，我们会将 = 解析为 Assign；将 == 解析为 Eq；将 != 解析为 Ne 等等。\",\"所以这里我们会有这样的印象，一个标记（token）可能包含多个字符，且多数情况下如此。而词法分析器能减小语法分析复杂度的原因，正是因为它相当于通过一定的编码（更多的标记）来压缩了源码字符串。\",\"当然，上面这些标记是有顺序的，跟它们在 C 语言中的优先级有关，如 *(Mul) 的优先级就要高于 +(Add)。它们的具体使用在后面的语法分析中会提到。\",\"最后要注意的是还有一些字符，它们自己就构成了标记，如右方括号 ] 或波浪号 ~ 等。我们不另外处理它们的原因是：\",\"它们是单字符的，即并不是多个字符共同构成标记（如 == 需要两个字符）；\",\"它们不涉及优先级关系。\"]},\"440\":{\"h\":\"词法分析器的框架\",\"t\":[\"即 next() 函数的主体：\",\"void next() { char *last_pos; int hash; while (token = *src) { ++src; // parse token here } return;}\",\"这里的一个问题是，为什么要用 while 循环呢？这就涉及到编译器（记得我们说过词法分析器也是某种意义上的编译器）的一个问题：如何处理错误？\",\"对词法分析器而言，若碰到了一个我们不认识的字符该怎么处理？一般处理的方法有两种：\",\"指出错误发生的位置，并退出整个程序\",\"指出错误发生的位置，跳过当前错误并继续编译\",\"这个 while 循环的作用就是跳过这些我们不识别的字符，我们同时还用它来处理空白字符。我们知道，C 语言中空格是用来作为分隔用的，并不作为语法的一部分。因此在实现中我们将它作为“不识别”的字符，这个 while 循环可以用来跳过它。\"]},\"441\":{\"h\":\"换行符\",\"t\":[\"换行符和空格类似，但有一点不同，每次遇到换行符，我们需要将当前的行号加一：\",\"// parse token here...if (token == '\\\\n') { ++line;}...\"]},\"442\":{\"h\":\"宏定义\",\"t\":[\"C 语言的宏定义以字符 # 开头，如 # include <stdio.h>。我们的编译器并不支持宏定义，所以直接跳过它们。\",\"else if (token == '#') { // skip macro, because we will not support it while (*src != 0 && *src != '\\\\n') { src++; }}\"]},\"443\":{\"h\":\"标识符与符号表\",\"t\":[\"标识符（identifier）可以理解为变量名。对于语法分析而言，我们并不关心一个变量具体叫什么名字，而只关心这个变量名代表的唯一标识。例如 int a; 定义了变量 a，而之后的语句 a = 10，我们需要知道这两个 a 指向的是同一个变量。\",\"基于这个理由，词法分析器会把扫描到的标识符全都保存到一张表中，遇到新的标识符就去查这张表，如果标识符已经存在，就返回它的唯一标识。\",\"那么我们怎么表示标识符呢？如下：\",\"struct identifier { int token; int hash; char * name; int class; int type; int value; int Bclass; int Btype; int Bvalue;}\",\"这里解释一下具体的含义：\",\"token：该标识符返回的标记，理论上所有的变量返回的标记都应该是 Id，但实际上由于我们还将在符号表中加入关键字如 if, while 等，它们都有对应的标记。\",\"hash：顾名思义，就是这个标识符的哈希值，用于标识符的快速比较。\",\"name：存放标识符本身的字符串。\",\"class：该标识符的类别，如数字，全局变量或局部变量等。\",\"type：标识符的类型，即如果它是个变量，变量是 int 型、char 型还是指针型。\",\"value：存放这个标识符的值，如标识符是函数，刚存放函数的地址。\",\"BXXXX：C 语言中标识符可以是全局的也可以是局部的，当局部标识符的名字与全局标识符相同时，用作保存全局标识符的信息。\",\"由上可以看出，我们实现的词法分析器与传统意义上的词法分析器不太相同。传统意义上的符号表只需要知道标识符的唯一标识即可，而我们还存放了一些只有语法分析器才会得到的信息，如 type 。\",\"由于我们的目标是能自举，而我们定义的语法不支持 struct，故而使用下列方式。\",\"Symbol table:----+-----+----+----+----+-----+-----+-----+------+------+---- .. |token|hash|name|type|class|value|btype|bclass|bvalue| ..----+-----+----+----+----+-----+-----+-----+------+------+---- |<--- one single identifier --->|\",\"即用一个整型数组来保存相关的ID信息。每个ID占用数组中的9个空间，分析标识符的相关代码如下：\",\"int token_val; // value of current token (mainly for number)int *current_id, // current parsed ID *symbols; // symbol table// fields of identifierenum {Token, Hash, Name, Type, Class, Value, BType, BClass, BValue, IdSize};void next() { ... else if ((token >= 'a' && token <= 'z') || (token >= 'A' && token <= 'Z') || (token == '_')) { // parse identifier last_pos = src - 1; hash = token; while ((*src >= 'a' && *src <= 'z') || (*src >= 'A' && *src <= 'Z') || (*src >= '0' && *src <= '9') || (*src == '_')) { hash = hash * 147 + *src; src++; } // look for existing identifier, linear search current_id = symbols; while (current_id[Token]) { if (current_id[Hash] == hash && !memcmp((char *)current_id[Name], last_pos, src - last_pos)) { //found one, return token = current_id[Token]; return; } current_id = current_id + IdSize; } // store new ID current_id[Name] = (int)last_pos; current_id[Hash] = hash; token = current_id[Token] = Id; return; } ...}\",\"查找已有标识符的方法是线性查找 symbols 表。\"]},\"444\":{\"h\":\"数字\",\"t\":[\"数字中较为复杂的一点是需要支持十进制、十六进制及八进制。逻辑也较为直接，可能唯一不好理解的是获取十六进制的值相关的代码。\",\"token_val = token_val * 16 + (token & 15) + (token >= 'A' ? 9 : 0);\",\"这里要注意的是在ASCII码中，字符a对应的十六进制值是 61, A是41，故通过 (token & 15) 可以得到个位数的值。其它就不多说了，这里这样写的目的是装B（其实是抄 c4 的源代码的）。\",\"void next() { ... else if (token >= '0' && token <= '9') { // parse number, three kinds: dec(123) hex(0x123) oct(017) token_val = token - '0'; if (token_val > 0) { // dec, starts with [1-9] while (*src >= '0' && *src <= '9') { token_val = token_val*10 + *src++ - '0'; } } else { // starts with number 0 if (*src == 'x' || *src == 'X') { //hex token = *++src; while ((token >= '0' && token <= '9') || (token >= 'a' && token <= 'f') || (token >= 'A' && token <= 'F')) { token_val = token_val * 16 + (token & 15) + (token >= 'A' ? 9 : 0); token = *++src; } } else { // oct while (*src >= '0' && *src <= '7') { token_val = token_val*8 + *src++ - '0'; } } } token = Num; return; } ...}\"]},\"445\":{\"h\":\"字符串\",\"t\":[\"在分析时，如果分析到字符串，我们需要将它存放到前一篇文章中说的 data 段中。然后返回它在 data 段中的地址。另一个特殊的地方是我们需要支持转义符。例如用 \\\\n 表示换行符。由于本编译器的目的是达到自己编译自己，所以代码中并没有支持除 \\\\n 的转义符，如 \\\\t, \\\\r 等，但仍支持 \\\\a 表示字符 a 的语法，如 \\\\\\\" 表示 \\\"。\",\"在分析时，我们将同时分析单个字符如 'a' 和字符串如 \\\"a string\\\"。若得到的是单个字符，我们以 Num 的形式返回。相关代码如下：\",\"void next() { ... else if (token == '\\\"' || token == '\\\\'') { // parse string literal, currently, the only supported escape // character is '\\\\n', store the string literal into data. last_pos = data; while (*src != 0 && *src != token) { token_val = *src++; if (token_val == '\\\\\\\\') { // escape character token_val = *src++; if (token_val == 'n') { token_val = '\\\\n'; } } if (token == '\\\"') { *data++ = token_val; } } src++; // if it is a single character, return Num token if (token == '\\\"') { token_val = (int)last_pos; } else { token = Num; } return; }}\"]},\"446\":{\"h\":\"注释\",\"t\":[\"在我们的 C 语言中，只支持 // 类型的注释，不支持 /* comments */ 的注释。\",\"void next() { ... else if (token == '/') { if (*src == '/') { // skip comments while (*src != 0 && *src != '\\\\n') { ++src; } } else { // divide operator token = Div; return; } } ...}\",\"这里我们要额外介绍 lookahead 的概念，即提前看多个字符。上述代码中我们看到，除了跳过注释，我们还可能返回除号 /(Div) 标记。\",\"提前看字符的原理是：有一个或多个标记是以同样的字符开头的（如本小节中的注释与除号），因此只凭当前的字符我们并无法确定具体应该解释成哪一个标记，所以只能再向前查看字符，如本例需向前查看一个字符，若是 / 则说明是注释，反之则是除号。\",\"我们之前说过，词法分析器本质上也是编译器，其实提前看字符的概念也存在于编译器，只是这时就是提前看k个“标记”而不是“字符”了。平时听到的 LL(k) 中的 k 就是需要向前看的标记的个数了。\",\"另外，我们用词法分析器将源码转换成标记流，能减小语法分析复杂度，原因之一就是减少了语法分析器需要“向前看”的字符个数。\"]},\"447\":{\"h\":\"其它\",\"t\":[\"其它的标记的解析就相对容易一些了，我们直接贴上代码：\",\"void next() { ... else if (token == '=') { // parse '==' and '=' if (*src == '=') { src ++; token = Eq; } else { token = Assign; } return; } else if (token == '+') { // parse '+' and '++' if (*src == '+') { src ++; token = Inc; } else { token = Add; } return; } else if (token == '-') { // parse '-' and '--' if (*src == '-') { src ++; token = Dec; } else { token = Sub; } return; } else if (token == '!') { // parse '!=' if (*src == '=') { src++; token = Ne; } return; } else if (token == '<') { // parse '<=', '<<' or '<' if (*src == '=') { src ++; token = Le; } else if (*src == '<') { src ++; token = Shl; } else { token = Lt; } return; } else if (token == '>') { // parse '>=', '>>' or '>' if (*src == '=') { src ++; token = Ge; } else if (*src == '>') { src ++; token = Shr; } else { token = Gt; } return; } else if (token == '|') { // parse '|' or '||' if (*src == '|') { src ++; token = Lor; } else { token = Or; } return; } else if (token == '&') { // parse '&' and '&&' if (*src == '&') { src ++; token = Lan; } else { token = And; } return; } else if (token == '^') { token = Xor; return; } else if (token == '%') { token = Mod; return; } else if (token == '*') { token = Mul; return; } else if (token == '[') { token = Brak; return; } else if (token == '?') { token = Cond; return; } else if (token == '~' || token == ';' || token == '{' || token == '}' || token == '(' || token == ')' || token == ']' || token == ',' || token == ':') { // directly return the character as token; return; } ...}\",\"代码较多，但主要逻辑就是向前看一个字符来确定真正的标记。\"]},\"448\":{\"h\":\"关键字与内置函数\",\"t\":[\"虽然上面写完了词法分析器，但还有一个问题需要考虑，那就是“关键字”，例如 if, while, return 等。它们不能被作为普通的标识符，因为有特殊的含义。\",\"一般有两种处理方法：\",\"词法分析器中直接解析这些关键字。\",\"在语法分析前将关键字提前加入符号表。\",\"这里我们就采用第二种方法，将它们加入符号表，并提前为它们赋予必要的信息（还记得前面说的标识符 Token 字段吗？）。这样当源代码中出现关键字时，它们会被解析成标识符，但由于符号表中已经有了相关的信息，我们就能知道它们是特殊的关键字。\",\"内置函数的行为也和关键字类似，不同的只是赋值的信息，在main函数中进行初始化如下：\",\"// types of variable/functionenum { CHAR, INT, PTR };int *idmain; // the `main` functionvoid main() { ... src = \\\"char else enum if int return sizeof while \\\" \\\"open read close printf malloc memset memcmp exit void main\\\"; // add keywords to symbol table i = Char; while (i <= While) { next(); current_id[Token] = i++; } // add library to symbol table i = OPEN; while (i <= EXIT) { next(); current_id[Class] = Sys; current_id[Type] = INT; current_id[Value] = i++; } next(); current_id[Token] = Char; // handle void type next(); idmain = current_id; // keep track of main ... program();}\"]},\"449\":{\"h\":\"代码\",\"t\":[\"本章的代码可以在 Github 上下载，也可以直接 clone\",\"git clone -b step-2 https://github.com/lotabout/write-a-C-interpreter\",\"上面的代码运行后会出现 ‘Segmentation Falt’，这是正常的，因为它会尝试运行我们上一章创建的虚拟机，但其中并没有任何汇编代码。\"]},\"450\":{\"h\":\"小结\",\"t\":[\"本章我们为我们的编译器构建了词法分析器，通过本章的学习，我认为有几个要点需要强调：\",\"词法分析器的作用是对源码字符串进行预处理，作用是减小语法分析器的复杂程度。\",\"词法分析器本身可以认为是一个编译器，输入是源码，输出是标记流。\",\"lookahead(k) 的概念，即向前看 k 个字符或标记。\",\"词法分析中如何处理标识符与符号表。\",\"下一章中，我们将介绍递归下降的语法分析器。我们下一章见。\"]},\"451\":{\"c\":[\"编译原理\"]},\"452\":{\"c\":[\"c\",\"编译器\",\"解释器\"]},\"453\":{\"h\":\"手把手教你构建 C 语言编译器（4）——递归下降\",\"t\":[\"[]\",\"本文转自 https://lotabout.me/2016/write-a-C-interpreter-4/，如有侵权，请联系删除。\",\"Table of Contents\",\"1. 什么是递归下降\",\"2. 终结符与非终结符\",\"3. 四则运算的递归下降\",\"4. 为什么选择递归下降\",\"5. 左递归\",\"6. 四则运算的实现\",\"7. 小结\",\"本章我们将讲解递归下降的方法，并用它完成一个基本的四则运算的语法分析器。\",\"手把手教你构建 C 语言编译器系列共有10个部分：\",\"手把手教你构建 C 语言编译器（0）——前言\",\"手把手教你构建 C 语言编译器（1）——设计\",\"手把手教你构建 C 语言编译器（2）——虚拟机\",\"手把手教你构建 C 语言编译器（3）——词法分析器\",\"手把手教你构建 C 语言编译器（4）——递归下降\",\"手把手教你构建 C 语言编译器（5）——变量定义\",\"手把手教你构建 C 语言编译器（6）——函数定义\",\"手把手教你构建 C 语言编译器（7）——语句\",\"手把手教你构建 C 语言编译器（8）——表达式\",\"手把手教你构建 C 语言编译器（9）——总结\"]},\"454\":{\"h\":\"什么是递归下降\",\"t\":[\"传统上，编写语法分析器有两种方法，一种是自顶向下，一种是自底向上。自顶向下是从起始非终结符开始，不断地对非终结符进行分解，直到匹配输入的终结符；自底向上是不断地将终结符进行合并，直到合并成起始的非终结符。\",\"其中的自顶向下方法就是我们所说的递归下降。\"]},\"455\":{\"h\":\"终结符与非终结符\",\"t\":[\"没有学过编译原理的话可能并不知道什么是“终结符”，“非终结符”。这里我简单介绍一下。首先是 BNF 范式，就是一种用来描述语法的语言，例如，四则运算的规则可以表示如下：\",\"<expr> ::= <expr> + <term> | <expr> - <term> | <term><term> ::= <term> * <factor> | <term> / <factor> | <factor><factor> ::= ( <expr> ) | Num\",\"用尖括号 <> 括起来的就称作 非终结符 ，因为它们可以用 ::= 右侧的式子代替。| 表示选择，如 <expr> 可以是 <expr> + <term>、<expr> - <term>或 <term> 中的一种。而没有出现在::=左边的就称作 终结符 ，一般终结符对应于词法分析器输出的标记。\"]},\"456\":{\"h\":\"四则运算的递归下降\",\"t\":[\"例如，我们对 3 * (4 + 2) 进行语法分析。我们假设词法分析器已经正确地将其中的数字识别成了标记 Num。\",\"递归下降是从起始的非终结符开始（顶），本例中是 <expr>，实际中可以自己指定，不指定的话一般认为是第一个出现的非终结符。\",\"1. <expr> => <expr>2. => <term> * <factor>3. => <factor> |4. => Num (3) |5. => ( <expr> )6. => <expr> + <term>7. => <term> |8. => <factor> |9. => Num (4) |10. => <factor>11. => Num (2)\",\"可以看到，整个解析的过程是在不断对非终结符进行替换（向下），直到遇见了终结符（底）。而我们可以从解析的过程中看出，一些非终结符如<expr>被递归地使用了。\"]},\"457\":{\"h\":\"为什么选择递归下降\",\"t\":[\"从上小节对四则运算的递归下降解析可以看出，整个解析的过程和语法的 BNF 表示是十分接近的，更为重要的是，我们可以很容易地直接将 BNF 表示转换成实际的代码。方法是为每个产生式（即 非终结符 ::= ...）生成一个同名的函数。\",\"这里会有一个疑问，就是上例中，当一个终结符有多个选择时，如何确定具体选择哪一个？如为什么用 <expr> ::= <term> * <factor> 而不是 <expr> ::= <term> / <factor> ？这就用到了上一章中提到的“向前看 k 个标记”的概念了。我们向前看一个标记，发现是 *，而这个标记足够让我们确定用哪个表达式了。\",\"另外，递归下下降方法对 BNF 方法本身有一定的要求，否则会有一些问题，如经典的“左递归”问题。\"]},\"458\":{\"h\":\"左递归\",\"t\":[\"原则上我们是不讲这么深入，但我们上面的四则运算的文法就是左递归的，而左递归的语法是没法直接使用递归下降的方法实现的。因此我们要消除左递归，消除后的文法如下：\",\"<expr> ::= <term> <expr_tail><expr_tail> ::= + <term> <expr_tail> | - <term> <expr_tail> | <empty><term> ::= <factor> <term_tail><term_tail> ::= * <factor> <term_tail> | / <factor> <term_tail> | <empty><factor> ::= ( <expr> ) | Num\",\"消除左递归的相关方法，这里不再多说，请自行查阅相关的资料。\"]},\"459\":{\"h\":\"四则运算的实现\",\"t\":[\"本节中我们专注语法分析器部分的实现，具体实现很容易，我们直接贴上代码，就是上述的消除左递归后的文法直接转换而来的：\",\"int expr();int factor() { int value = 0; if (token == '(') { match('('); value = expr(); match(')'); } else { value = token_val; match(Num); } return value;}int term_tail(int lvalue) { if (token == '*') { match('*'); int value = lvalue * factor(); return term_tail(value); } else if (token == '/') { match('/'); int value = lvalue / factor(); return term_tail(value); } else { return lvalue; }}int term() { int lvalue = factor(); return term_tail(lvalue);}int expr_tail(int lvalue) { if (token == '+') { match('+'); int value = lvalue + term(); return expr_tail(value); } else if (token == '-') { match('-'); int value = lvalue - term(); return expr_tail(value); } else { return lvalue; }}int expr() { int lvalue = term(); return expr_tail(lvalue);}\",\"可以看到，有了BNF方法后，采用递归向下的方法来实现编译器是很直观的。\",\"我们把词法分析器的代码一并贴上：\",\"##include <stdio.h>##include <stdlib.h>enum {Num};int token;int token_val;char *line = NULL;char *src = NULL;void next() { // skip white space while (*src == ' ' || *src == '\\\\t') { src ++; } token = *src++; if (token >= '0' && token <= '9' ) { token_val = token - '0'; token = Num; while (*src >= '0' && *src <= '9') { token_val = token_val*10 + *src - '0'; src ++; } return; }}void match(int tk) { if (token != tk) { printf(\\\"expected token: %d(%c), got: %d(%c)\\\\n\\\", tk, tk, token, token); exit(-1); } next();}\",\"最后是main函数：\",\"int main(int argc, char *argv[]){ size_t linecap = 0; ssize_t linelen; while ((linelen = getline(&line, &linecap, stdin)) > 0) { src = line; next(); printf(\\\"%d\\\\n\\\", expr()); } return 0;}\"]},\"460\":{\"h\":\"小结\",\"t\":[\"本章中我们介绍了递归下降的方法，并用它来实现了四则运算的语法分析器。\",\"花这么大精力讲解递归下降方法，是因为几乎所有手工编写的语法分析器都或多或少地有它的影子。换句话说，掌握了递归下降的方法，就可以应付大多数的语法分析器编写。\",\"同时我们也用实例看到了理论（BNF 语法，左递归的消除）是如何帮助我们的工程实现的。尽管理论不是必需的，但如果能掌握它，对于提高我们的水平还是很有帮助的。\"]},\"461\":{\"c\":[\"编译原理\"]},\"462\":{\"c\":[\"c\",\"编译器\",\"解释器\"]},\"463\":{\"h\":\"手把手教你构建 C 语言编译器（5）——变量定义\",\"t\":[\"本文转自 https://lotabout.me/2016/write-a-C-interpreter-5/，如有侵权，请联系删除。\",\"Table of Contents\",\"1. EBNF 表示\",\"2. 解析变量的定义\",\"2.1. program()\",\"2.2. global_declaration()\",\"2.3. enum_declaration()\",\"2.4. 其它\",\"3. 代码\",\"4. 小结\",\"本章中我们用 EBNF 来大致描述我们实现的 C 语言的文法，并实现其中解析变量定义部分。\",\"由于语法分析本身比较复杂，所以我们将它拆分成 3 个部分进行讲解，分别是：变量定义、函数定义、表达式。\",\"手把手教你构建 C 语言编译器系列共有10个部分：\",\"手把手教你构建 C 语言编译器（0）——前言\",\"手把手教你构建 C 语言编译器（1）——设计\",\"手把手教你构建 C 语言编译器（2）——虚拟机\",\"手把手教你构建 C 语言编译器（3）——词法分析器\",\"手把手教你构建 C 语言编译器（4）——递归下降\",\"手把手教你构建 C 语言编译器（5）——变量定义\",\"手把手教你构建 C 语言编译器（6）——函数定义\",\"手把手教你构建 C 语言编译器（7）——语句\",\"手把手教你构建 C 语言编译器（8）——表达式\",\"手把手教你构建 C 语言编译器（9）——总结\"]},\"464\":{\"h\":\"EBNF 表示\",\"t\":[\"EBNF 是对前一章提到的 BNF 的扩展，它的语法更容易理解，实现起来也更直观。但真正看起来还是很烦，如果不想看可以跳过。\",\"program ::= {global_declaration}+global_declaration ::= enum_decl | variable_decl | function_declenum_decl ::= 'enum' [id] '{' id ['=' 'num'] {',' id ['=' 'num'] '}'variable_decl ::= type {'*'} id { ',' {'*'} id } ';'function_decl ::= type {'*'} id '(' parameter_decl ')' '{' body_decl '}'parameter_decl ::= type {'*'} id {',' type {'*'} id}body_decl ::= {variable_decl}, {statement}statement ::= non_empty_statement | empty_statementnon_empty_statement ::= if_statement | while_statement | '{' statement '}' | 'return' expression | expression ';'if_statement ::= 'if' '(' expression ')' statement ['else' non_empty_statement]while_statement ::= 'while' '(' expression ')' non_empty_statement\",\"其中 expression 相关的内容我们放到后面解释，主要原因是我们的语言不支持跨函数递归，而为了实现自举，实际上我们也不能使用递归（亏我们说了一章的递归下降）。\",\"P.S. 我是先写程序再总结上面的文法，所以实际上它们间的对应关系并不是特别明显。\"]},\"465\":{\"h\":\"解析变量的定义\",\"t\":[\"本章要讲解的就是上节文法中的 enum_decl 和 variable_decl 部分。\"]},\"466\":{\"h\":\"program()\",\"t\":[\"首先是之前定义过的 program 函数，将它改成：\",\"void program() { // get next token next(); while (token > 0) { global_declaration(); }}\",\"我知道 global_declaration 函数还没有出现过，但没有关系，采用自顶向下的编写方法就是要不断地实现我们需要的内容。下面是 global_declaration 函数的内容：\"]},\"467\":{\"h\":\"global_declaration()\",\"t\":[\"即全局的定义语句，包括变量定义，类型定义（只支持枚举）及函数定义。代码如下：\",\"int basetype; // the type of a declaration, make it global for convenienceint expr_type; // the type of an expressionvoid global_declaration() { // global_declaration ::= enum_decl | variable_decl | function_decl // // enum_decl ::= 'enum' [id] '{' id ['=' 'num'] {',' id ['=' 'num'} '}' // // variable_decl ::= type {'*'} id { ',' {'*'} id } ';' // // function_decl ::= type {'*'} id '(' parameter_decl ')' '{' body_decl '}' int type; // tmp, actual type for variable int i; // tmp basetype = INT; // parse enum, this should be treated alone. if (token == Enum) { // enum [id] { a = 10, b = 20, ... } match(Enum); if (token != '{') { match(Id); // skip the [id] part } if (token == '{') { // parse the assign part match('{'); enum_declaration(); match('}'); } match(';'); return; } // parse type information if (token == Int) { match(Int); } else if (token == Char) { match(Char); basetype = CHAR; } // parse the comma seperated variable declaration. while (token != ';' && token != '}') { type = basetype; // parse pointer type, note that there may exist `int ****x;` while (token == Mul) { match(Mul); type = type + PTR; } if (token != Id) { // invalid declaration printf(\\\"%d: bad global declaration\\\\n\\\", line); exit(-1); } if (current_id[Class]) { // identifier exists printf(\\\"%d: duplicate global declaration\\\\n\\\", line); exit(-1); } match(Id); current_id[Type] = type; if (token == '(') { current_id[Class] = Fun; current_id[Value] = (int)(text + 1); // the memory address of function function_declaration(); } else { // variable declaration current_id[Class] = Glo; // global variable current_id[Value] = (int)data; // assign memory address data = data + sizeof(int); } if (token == ',') { match(','); } } next();}\",\"看了上面的代码，能大概理解吗？这里我们讲解其中的一些细节。\",\"向前看标记 ：其中的 if (token == xxx) 语句就是用来向前查看标记以确定使用哪一个产生式，例如只要遇到 enum 我们就知道是需要解析枚举类型。而如果只解析到类型，如 int identifier 时我们并不能确定 identifier 是一个普通的变量还是一个函数，所以还需要继续查看后续的标记，如果遇到 ( 则可以断定是函数了，反之则是变量。\",\"变量类型的表示 ：我们的编译器支持指针类型，那意味着也支持指针的指针，如 int **data;。那么我们如何表示指针类型呢？前文中我们定义了支持的类型：\",\"// types of variable/functionenum { CHAR, INT, PTR };\",\"所以一个类型首先有基本类型，如 CHAR 或 INT，当它是一个指向基本类型的指针时，如 int *data，我们就将它的类型加上 PTR 即代码中的：type = type + PTR;。同理，如果是指针的指针，则再加上 PTR。\"]},\"468\":{\"h\":\"enum_declaration()\",\"t\":[\"用于解析枚举类型的定义。主要的逻辑用于解析用逗号（,）分隔的变量，值得注意的是在编译器中如何保存枚举变量的信息。\",\"即我们将该变量的类别设置成了 Num，这样它就成了全局的常量了，而注意到上节中，正常的全局变量的类别则是 Glo，类别信息在后面章节中解析 expression 会使用到。\",\"void enum_declaration() { // parse enum [id] { a = 1, b = 3, ...} int i; i = 0; while (token != '}') { if (token != Id) { printf(\\\"%d: bad enum identifier %d\\\\n\\\", line, token); exit(-1); } next(); if (token == Assign) { // like {a=10} next(); if (token != Num) { printf(\\\"%d: bad enum initializer\\\\n\\\", line); exit(-1); } i = token_val; next(); } current_id[Class] = Num; current_id[Type] = INT; current_id[Value] = i++; if (token == ',') { next(); } }}\"]},\"469\":{\"h\":\"其它\",\"t\":[\"其中的 function_declaration 函数我们将放到下一章中讲解。match 函数是一个辅助函数：\",\"void match(int tk) { if (token == tk) { next(); } else { printf(\\\"%d: expected token: %d\\\\n\\\", line, tk); exit(-1); }}\",\"它将 next 函数包装起来，如果不是预期的标记则报错并退出。\"]},\"470\":{\"h\":\"代码\",\"t\":[\"本章的代码可以在 Github 上下载，也可以直接 clone\",\"git clone -b step-3 https://github.com/lotabout/write-a-C-interpreter\",\"本章的代码还无法正常运行，因为还有许多功能没有实现，但如果有兴趣的话，可以自己先试着去实现它。\"]},\"471\":{\"h\":\"小结\",\"t\":[\"本章的内容应该不难，除了开头的 EBNF 表达式可能相对不好理解一些，但如果你查看了 EBNF 的具体表示方法后就不难理解了。\",\"剩下的内容就是按部就班地将 EBNF 的产生式转换成函数的过程，如果你理解了上一章中的内容，相信这部分也不难理解。\",\"下一章中我们将介绍如何解析函数的定义，敬请期待。\"]},\"472\":{\"c\":[\"编译原理\"]},\"473\":{\"c\":[\"c\",\"编译器\",\"解释器\"]},\"474\":{\"h\":\"手把手教你构建 C 语言编译器（6）——函数定义\",\"t\":[\"本文转自 https://lotabout.me/2016/write-a-C-interpreter-6/，如有侵权，请联系删除。\",\"Table of Contents\",\"1. EBNF 表示\",\"2. 解析函数的定义\",\"2.1. 函数参数与汇编代码\",\"2.2. 函数定义的解析\",\"2.3. 解析参数\",\"2.4. 函数体的解析\",\"3. 代码\",\"4. 小结\",\"由于语法分析本身比较复杂，所以我们将它拆分成 3 个部分进行讲解，分别是：变量定义、函数定义、表达式。本章讲解函数定义相关的内容。\",\"手把手教你构建 C 语言编译器系列共有10个部分：\",\"手把手教你构建 C 语言编译器（0）——前言\",\"手把手教你构建 C 语言编译器（1）——设计\",\"手把手教你构建 C 语言编译器（2）——虚拟机\",\"手把手教你构建 C 语言编译器（3）——词法分析器\",\"手把手教你构建 C 语言编译器（4）——递归下降\",\"手把手教你构建 C 语言编译器（5）——变量定义\",\"手把手教你构建 C 语言编译器（6）——函数定义\",\"手把手教你构建 C 语言编译器（7）——语句\",\"手把手教你构建 C 语言编译器（8）——表达式\",\"手把手教你构建 C 语言编译器（9）——总结\"]},\"475\":{\"h\":\"EBNF 表示\",\"t\":[\"这是上一章的 EBNF 方法中与函数定义相关的内容。\",\"variable_decl ::= type {'*'} id { ',' {'*'} id } ';'function_decl ::= type {'*'} id '(' parameter_decl ')' '{' body_decl '}'parameter_decl ::= type {'*'} id {',' type {'*'} id}body_decl ::= {variable_decl}, {statement}statement ::= non_empty_statement | empty_statementnon_empty_statement ::= if_statement | while_statement | '{' statement '}' | 'return' expression | expression ';'if_statement ::= 'if' '(' expression ')' statement ['else' non_empty_statement]while_statement ::= 'while' '(' expression ')' non_empty_statement\"]},\"476\":{\"h\":\"解析函数的定义\",\"t\":[\"上一章的代码中，我们已经知道了什么时候开始解析函数的定义，相关的代码如下：\",\"...if (token == '(') { current_id[Class] = Fun; current_id[Value] = (int)(text + 1); // the memory address of function function_declaration();} else {...\",\"即在这断代码之前，我们已经为当前的标识符（identifier）设置了正确的类型，上面这断代码为当前的标识符设置了正确的类别（Fun），以及该函数在代码段（text segment）中的位置。接下来开始解析函数定义相关的内容：parameter_decl 及 body_decl。\"]},\"477\":{\"h\":\"函数参数与汇编代码\",\"t\":[\"现在我们要回忆如何将“函数”转换成对应的汇编代码，因为这决定了在解析时我们需要哪些相关的信息。考虑下列函数：\",\"int demo(int param_a, int *param_b) { int local_1; char local_2; ...}\",\"那么它应该被转换成什么样的汇编代码呢？在思考这个问题之前，我们需要了解当 demo函数被调用时，计算机的栈的状态，如下（参照第三章讲解的虚拟机）：\",\"| .... | high address+---------------+| arg: param_a | new_bp + 3+---------------+| arg: param_b | new_bp + 2+---------------+|return address | new_bp + 1+---------------+| old BP | <- new BP+---------------+| local_1 | new_bp - 1+---------------+| local_2 | new_bp - 2+---------------+| .... | low address\",\"这里最为重要的一点是，无论是函数的参数（如 param_a）还是函数的局部变量（如 local_1）都是存放在计算机的 栈 上的。因此，与存放在 数据段 中的全局变量不同，在函数内访问它们是通过 new_bp 指针和对应的位移量进行的。因此，在解析的过程中，我们需要知道参数的个数，各个参数的位移量。\"]},\"478\":{\"h\":\"函数定义的解析\",\"t\":[\"这相当于是整个函数定义的语法解析的框架，代码如下：\",\"void function_declaration() { // type func_name (...) {...} // | this part match('('); function_parameter(); match(')'); match('{'); function_body(); //match('}'); // ① // ② // unwind local variable declarations for all local variables. current_id = symbols; while (current_id[Token]) { if (current_id[Class] == Loc) { current_id[Class] = current_id[BClass]; current_id[Type] = current_id[BType]; current_id[Value] = current_id[BValue]; } current_id = current_id + IdSize; }}\",\"其中①中我们没有消耗最后的}字符。这么做的原因是：variable_decl 与 function_decl 是放在一起解析的，而 variable_decl 是以字符 ; 结束的。而 function_decl 是以字符 } 结束的，若在此通过 match 消耗了 ‘;’ 字符，那么外层的 while 循环就没法准确地知道函数定义已经结束。所以我们将结束符的解析放在了外层的 while 循环中。\",\"而②中的代码是用于将符号表中的信息恢复成全局的信息。这是因为，局部变量是可以和全局变量同名的，一旦同名，在函数体内局部变量就会覆盖全局变量，出了函数体，全局变量就恢复了原先的作用。这段代码线性地遍历所有标识符，并将保存在 BXXX 中的信息还原。\"]},\"479\":{\"h\":\"解析参数\",\"t\":[\"parameter_decl ::= type {'*'} id {',' type {'*'} id}\",\"解析函数的参数就是解析以逗号分隔的一个个标识符，同时记录它们的位置与类型。\",\"int index_of_bp; // index of bp pointer on stackvoid function_parameter() { int type; int params; params = 0; while (token != ')') { // ① // int name, ... type = INT; if (token == Int) { match(Int); } else if (token == Char) { type = CHAR; match(Char); } // pointer type while (token == Mul) { match(Mul); type = type + PTR; } // parameter name if (token != Id) { printf(\\\"%d: bad parameter declaration\\\\n\\\", line); exit(-1); } if (current_id[Class] == Loc) { printf(\\\"%d: duplicate parameter declaration\\\\n\\\", line); exit(-1); } match(Id); //② // store the local variable current_id[BClass] = current_id[Class]; current_id[Class] = Loc; current_id[BType] = current_id[Type]; current_id[Type] = type; current_id[BValue] = current_id[Value]; current_id[Value] = params++; // index of current parameter if (token == ',') { match(','); } } // ③ index_of_bp = params+1;}\",\"其中①与全局变量定义的解析十分一样，用于解析该参数的类型。\",\"而②则与上节中提到的“局部变量覆盖全局变量”相关，先将全局变量的信息保存（无论是是否真的在全局中用到了这个变量）在 BXXX 中，再赋上局部变量相关的信息，如 Value 中存放的是参数的位置（是第几个参数）。\",\"③则与汇编代码的生成有关，index_of_bp 就是前文提到的 new_bp 的位置。\"]},\"480\":{\"h\":\"函数体的解析\",\"t\":[\"我们实现的 C 语言与现代的 C 语言不太一致，我们需要所有的变量定义出现在所有的语句之前。函数体的代码如下：\",\"void function_body() { // type func_name (...) {...} // -->| |<-- // ... { // 1. local declarations // 2. statements // } int pos_local; // position of local variables on the stack. int type; pos_local = index_of_bp; // ① while (token == Int || token == Char) { // local variable declaration, just like global ones. basetype = (token == Int) ? INT : CHAR; match(token); while (token != ';') { type = basetype; while (token == Mul) { match(Mul); type = type + PTR; } if (token != Id) { // invalid declaration printf(\\\"%d: bad local declaration\\\\n\\\", line); exit(-1); } if (current_id[Class] == Loc) { // identifier exists printf(\\\"%d: duplicate local declaration\\\\n\\\", line); exit(-1); } match(Id); // store the local variable current_id[BClass] = current_id[Class]; current_id[Class] = Loc; current_id[BType] = current_id[Type]; current_id[Type] = type; current_id[BValue] = current_id[Value]; current_id[Value] = ++pos_local; // index of current parameter if (token == ',') { match(','); } } match(';'); } // ② // save the stack size for local variables *++text = ENT; *++text = pos_local - index_of_bp; // statements while (token != '}') { statement(); } // emit code for leaving the sub function *++text = LEV;}\",\"其中①用于解析函数体内的局部变量的定义，代码与全局的变量定义几乎一样。\",\"而②则用于生成汇编代码，我们在第三章的虚拟机中提到过，我们需要在栈上为局部变量预留空间，这两行代码起的就是这个作用。\"]},\"481\":{\"h\":\"代码\",\"t\":[\"本章的代码可以在 Github 上下载，也可以直接 clone\",\"git clone -b step-4 https://github.com/lotabout/write-a-C-interpreter\",\"本章的代码依旧无法运行，还有两个重要函数没有完成：statement 及 expression，感兴趣的话可以尝试自己实现它们。\"]},\"482\":{\"h\":\"小结\",\"t\":[\"本章中我们用了不多的代码完成了函数定义的解析。大部分的代码依旧是用于解析变量：参数和局部变量，而它们的逻辑和全局变量的解析几乎一致，最大的区别就是保存的信息不同。\",\"当然，要理解函数定义的解析过程，最重要的是理解我们会为函数生成怎样的汇编代码，因为这决定了我们需要从解析中获取什么样的信息（例如参数的位置，个数等），而这些可能需要你重新回顾一下“虚拟机”这一章，或是重新学习学习汇编相关的知识。\",\"下一章中我们将讲解语句的解析，敬请期待。\"]},\"483\":{\"c\":[\"编译原理\"]},\"484\":{\"c\":[\"c\",\"编译器\",\"解释器\"]},\"485\":{\"h\":\"手把手教你构建 C 语言编译器（7）——语句\",\"t\":[\"本文转自 https://lotabout.me/2016/write-a-C-interpreter-7/，如有侵权，请联系删除。\",\"Table of Contents\",\"1. 语句\",\"1.1. IF 语句\",\"1.2. While 语句\",\"1.3. Return 语句\",\"1.4. 其它语句\",\"2. 代码\",\"3. 小结\",\"整个编译器还剩下最后两个部分：语句和表达式的解析。它们的内容比较多，主要涉及如何将语句和表达式编译成汇编代码。这章讲解语句的解析，相对于表达式来说它还是较为容易的。\",\"手把手教你构建 C 语言编译器系列共有10个部分：\",\"手把手教你构建 C 语言编译器（0）——前言\",\"手把手教你构建 C 语言编译器（1）——设计\",\"手把手教你构建 C 语言编译器（2）——虚拟机\",\"手把手教你构建 C 语言编译器（3）——词法分析器\",\"手把手教你构建 C 语言编译器（4）——递归下降\",\"手把手教你构建 C 语言编译器（5）——变量定义\",\"手把手教你构建 C 语言编译器（6）——函数定义\",\"手把手教你构建 C 语言编译器（7）——语句\",\"手把手教你构建 C 语言编译器（8）——表达式\",\"手把手教你构建 C 语言编译器（9）——总结\"]},\"486\":{\"h\":\"语句\",\"t\":[\"C 语言区分“语句”（statement）和“表达式”（expression）两个概念。简单地说，可以认为语句就是表达式加上末尾的分号。\",\"在我们的编译器中共识别 6 种语句：\",\"if (...) <statement> [else <statement>]\",\"while (...) <statement>\",\"{ <statement> }\",\"return xxx;\",\"<empty statement>;\",\"expression; (expression end with semicolon)\",\"它们的语法分析都相对容易，重要的是去理解如何将这些语句编译成汇编代码，下面我们逐一解释。\"]},\"487\":{\"h\":\"IF 语句\",\"t\":[\"IF 语句的作用是跳转，跟据条件表达式决定跳转的位置。我们看看下面的伪代码：\",\"if (...) <statement> [else <statement>] if (<cond>) <cond> JZ a <true_statement> ===> <true_statement> else: JMP ba: a: <false_statement> <false_statement>b: b:\",\"对应的汇编代码流程为：\",\"执行条件表达式 <cond>。\",\"如果条件失败，则跳转到 a 的位置，执行 else 语句。这里 else 语句是可以省略的，此时 a 和 b 都指向 IF 语句后方的代码。\",\"因为汇编代码是顺序排列的，所以如果执行了 true_statement，为了防止因为顺序排列而执行了 false_statement，所以需要无条件跳转 JMP b。\",\"对应的 C 代码如下：\",\"if (token == If) { match(If); match('('); expression(Assign); // parse condition match(')'); *++text = JZ; b = ++text; statement(); // parse statement if (token == Else) { // parse else match(Else); // emit code for JMP B *b = (int)(text + 3); *++text = JMP; b = ++text; statement(); } *b = (int)(text + 1);}\"]},\"488\":{\"h\":\"While 语句\",\"t\":[\"While 语句比 If 语句简单，它对应的汇编代码如下：\",\"a: a: while (<cond>) <cond> JZ b <statement> <statement> JMP ab: b:\",\"没有什么值得说明的内容，它的 C 代码如下：\",\"else if (token == While) { match(While); a = text + 1; match('('); expression(Assign); match(')'); *++text = JZ; b = ++text; statement(); *++text = JMP; *++text = (int)a; *b = (int)(text + 1);}\"]},\"489\":{\"h\":\"Return 语句\",\"t\":[\"Return 唯一特殊的地方是：一旦遇到了 Return 语句，则意味着函数要退出了，所以需要生成汇编代码 LEV 来表示退出。\",\"else if (token == Return) { // return [expression]; match(Return); if (token != ';') { expression(Assign); } match(';'); // emit code for return *++text = LEV;}\"]},\"490\":{\"h\":\"其它语句\",\"t\":[\"其它语句并不直接生成汇编代码，所以不多做说明，代码如下：\",\"else if (token == '{') { // { <statement> ... } match('{'); while (token != '}') { statement(); } match('}');}else if (token == ';') { // empty statement match(';');}else { // a = b; or function_call(); expression(Assign); match(';');}\"]},\"491\":{\"h\":\"代码\",\"t\":[\"本章的代码可以在 Github 上下载，也可以直接 clone\",\"git clone -b step-5 https://github.com/lotabout/write-a-C-interpreter\",\"本章的代码依旧无法运行，还剩最后一部分没有完成：expression。\"]},\"492\":{\"h\":\"小结\",\"t\":[\"本章讲解了如何将语句编译成汇编代码，内容相对容易一些，关键就是去理解汇编代码的执行原理。\",\"同时值得一提的是，编译器的语法分析部分其实是很简单的，而真正的难点是如何在语法分析时收集足够多的信息，最终把源代码转换成目标代码（汇编）。我认为这也是初学者实现编译器的一大难点，往往比词法分析/语法分析更困难。\",\"所以建议如果没有学过汇编，可以学习学习，它本身不难，但对理解计算机的原理有很大帮助。\"]},\"493\":{\"c\":[\"编译原理\"]},\"494\":{\"c\":[\"c\",\"编译器\",\"解释器\"]},\"495\":{\"h\":\"手把手教你构建 C 语言编译器（8）——表达式\",\"t\":[\"本文转自 https://blog.csdn.net/xzp740813/article/details/142961332?spm=1001.2014.3001.5501，如有侵权，请联系删除。\",\"Table of Contents\",\"1. 运算符的优先级\",\"2. 一元运算符\",\"2.1. 常量\",\"2.2. sizeof\",\"2.3. 变量与函数调用\",\"2.4. 强制转换\",\"2.5. 指针取值\",\"2.6. 取址操作\",\"2.7. 逻辑取反\",\"2.8. 按位取反\",\"2.9. 正负号\",\"2.10. 自增自减\",\"3. 二元运算符\",\"3.1. 赋值操作\",\"3.2. 三目运算符\",\"3.3. 逻辑运算符\",\"3.4. 数学运算符\",\"3.5. 自增自减\",\"3.6. 数组取值操作\",\"4. 代码\",\"5. 小结\",\"这是整个编译器的最后一部分，解析表达式。什么是表达式？表达式是将各种语言要素的一个组合，用来求值。例如：函数调用、变量赋值、运算符运算等等。\",\"表达式的解析难点有二：一是运算符的优先级问题，二是如何将表达式编译成目标代码。我们就来逐一说明。\",\"手把手教你构建 C 语言编译器系列共有10个部分：\",\"手把手教你构建 C 语言编译器（0）——前言\",\"手把手教你构建 C 语言编译器（1）——设计\",\"手把手教你构建 C 语言编译器（2）——虚拟机\",\"手把手教你构建 C 语言编译器（3）——词法分析器\",\"手把手教你构建 C 语言编译器（4）——递归下降\",\"手把手教你构建 C 语言编译器（5）——变量定义\",\"手把手教你构建 C 语言编译器（6）——函数定义\",\"手把手教你构建 C 语言编译器（7）——语句\",\"手把手教你构建 C 语言编译器（8）——表达式\",\"手把手教你构建 C 语言编译器（9）——总结\"]},\"496\":{\"h\":\"运算符的优先级\",\"t\":[\"运算符的优先级决定了表达式的运算顺序，如在普通的四则运算中，乘法 * 优先级高于加法 +，这就意味着表达式 2 + 3 * 4 的实际运行顺序是 2 + (3 * 4) 而不是 (2 + 3) * 4。\",\"C 语言定义了各种表达式的优先级，可以参考 C 语言运算符优先级。\",\"传统的编程书籍会用“逆波兰式”实现四则运算来讲解优先级问题。实际上，优先级关心的就是哪个运算符先计算，哪个运算符后计算（毕竟叫做“优先级”嘛）。而这就意味着我们需要决定先为哪个运算符生成目标代码（汇编），因为汇编代码是顺序排列的，我们必须先计算优先级高的运算符。\",\"那么如何确定运算符的优先级呢？答曰：栈（递归调用的实质也是栈的处理）。\",\"举一个例子：2 + 3 - 4 * 5，它的运算顺序是这样的：\",\"将 2 入栈\",\"遇到运算符 +，入栈，此时我们期待的是+的另一个参数\",\"遇到数字 3，原则上我们需要立即计算 2+3的值，但我们不确定数字 3 是否属于优先级更高的运算符，所以先将它入栈。\",\"遇到运算符 -，它的优先级和 + 相同，此时判断参数 3 属于这前的 +。将运算符 + 出栈，并将之前的 2 和 3 出栈，计算 2+3 的结果，得到 5 入栈。同时将运算符 - 入栈。\",\"遇到数字4，同样不能确定是否能立即计算，入栈\",\"遇到运算符 * 优先级大于 -，入栈\",\"遇到数字5，依旧不能确定是否立即计算，入栈\",\"表达式结束，运算符出栈，为 *，将参数出栈，计算 4*5 得到结果 20 入栈。\",\"运算符出栈，为 -，将参数出栈，计算 5-20，得到 -15 入栈。\",\"此时运算符栈为空，因此得到结果 -15。\",\"// after step 1, 2| |+------+| 3 | | |+------+ +------+| 2 | | + |+------+ +------+// after step 4| | | |+------+ +------+| 5 | | - |+------+ +------+// after step 7| |+------+| 5 |+------+ +------+| 4 | | * |+------+ +------+| 5 | | - |+------+ +------+\",\"综上，在计算一个运算符‘x’之前，必须先查看它的右方，找出并计算所有优先级大于‘x’的运算符，之后再计算运算符‘x’。\",\"最后注意的是优先通常只与多元运算符相关，单元运算符往往没有这个问题（因为只有一个参数）。也可以认为“优先级”的实质就是两个运算符在抢参数。\"]},\"497\":{\"h\":\"一元运算符\",\"t\":[\"上节中说到了运算符的优先级，也提到了优先级一般只与多元运算符有关，这也意味着一元运算符的优先级总是高于多元运算符。因为我们需要先对它们进行解析。\",\"当然，这部分也将同时解析参数本身（如变量、数字、字符串等等）。\",\"关于表达式的解析，与语法分析相关的部分就是上文所说的优先级问题了，而剩下的较难较烦的部分是与目标代码的生成有关的。因此对于需要讲解的运算符，我们主要从它的目标代码入手。\"]},\"498\":{\"h\":\"常量\",\"t\":[\"首先是数字，用 IMM 指令将它加载到 AX 中即可：\",\"if (token == Num) { match(Num); // emit code *++text = IMM; *++text = token_val; expr_type = INT;}\",\"接着是字符串常量。它比较特殊的一点是 C 语言的字符串常量支持如下风格：\",\"char *p;p = \\\"first line\\\" \\\"second line\\\";\",\"即跨行的字符串拼接，它相当于：\",\"char *p;p = \\\"first linesecond line\\\";\",\"所以解析的时候要注意这一点：\",\"else if (token == '\\\"') { // emit code *++text = IMM; *++text = token_val; match('\\\"'); // store the rest strings while (token == '\\\"') { match('\\\"'); } // append the end of string character '\\\\0', all the data are default // to 0, so just move data one position forward. data = (char *)(((int)data + sizeof(int)) & (-sizeof(int))); expr_type = PTR;}\"]},\"499\":{\"h\":\"sizeof\",\"t\":[\"sizeof 是一个一元运算符，我们需要知道后面参数的类型，类型的解析在前面的文章中我们已经很熟悉了。\",\"else if (token == Sizeof) { // sizeof is actually an unary operator // now only `sizeof(int)`, `sizeof(char)` and `sizeof(*...)` are // supported. match(Sizeof); match('('); expr_type = INT; if (token == Int) { match(Int); } else if (token == Char) { match(Char); expr_type = CHAR; } while (token == Mul) { match(Mul); expr_type = expr_type + PTR; } match(')'); // emit code *++text = IMM; *++text = (expr_type == CHAR) ? sizeof(char) : sizeof(int); expr_type = INT;}\",\"注意的是只支持 sizeof(int)，sizeof(char) 及 sizeof(pointer type...)。并且它的结果是 int 型。\"]},\"500\":{\"h\":\"变量与函数调用\",\"t\":[\"由于取变量的值与函数的调用都是以 Id 标记开头的，因此将它们放在一起处理。\",\"else if (token == Id) { // there are several type when occurs to Id // but this is unit, so it can only be // 1. function call // 2. Enum variable // 3. global/local variable match(Id); id = current_id; if (token == '(') { // function call match('('); // ① // pass in arguments tmp = 0; // number of arguments while (token != ')') { expression(Assign); *++text = PUSH; tmp ++; if (token == ',') { match(','); } } match(')'); // ② // emit code if (id[Class] == Sys) { // system functions *++text = id[Value]; } else if (id[Class] == Fun) { // function call *++text = CALL; *++text = id[Value]; } else { printf(\\\"%d: bad function call\\\\n\\\", line); exit(-1); } // ③ // clean the stack for arguments if (tmp > 0) { *++text = ADJ; *++text = tmp; } expr_type = id[Type]; } else if (id[Class] == Num) { // ④ // enum variable *++text = IMM; *++text = id[Value]; expr_type = INT; } else { // ⑤ // variable if (id[Class] == Loc) { *++text = LEA; *++text = index_of_bp - id[Value]; } else if (id[Class] == Glo) { *++text = IMM; *++text = id[Value]; } else { printf(\\\"%d: undefined variable\\\\n\\\", line); exit(-1); } //⑥ // emit code, default behaviour is to load the value of the // address which is stored in `ax` expr_type = id[Type]; *++text = (expr_type == Char) ? LC : LI; }}\",\"①中注意我们是顺序将参数入栈，这和第三章：虚拟机中讲解的指令是对应的。与之不同，标准 C 是逆序将参数入栈的。\",\"②中判断函数的类型，同样在第三章：“虚拟机”中我们介绍过内置函数的支持，如 printf, read, malloc 等等。内置函数有对应的汇编指令，而普通的函数则编译成 CALL <addr> 的形式。\",\"③用于清除入栈的参数。因为我们不在乎出栈的值，所以直接修改栈指针的大小即可。\",\"④：当该标识符是全局定义的枚举类型时，直接将对应的值用 IMM 指令存入 AX 即可。\",\"⑤则是用于加载变量的值，如果是局部变量则采用与 bp 指针相对位置的形式（参见第 7章函数定义）。而如果是全局变量则用 IMM 加载变量的地址。\",\"⑥：无论是全局还是局部变量，最终都根据它们的类型用 LC 或 LI 指令加载对应的值。\",\"关于变量，你可能有疑问，如果遇到标识符就用 LC/LI 载入相应的值，那诸如 a[10] 之类的表达式要如何实现呢？后面我们会看到，根据标识符后的运算符，我们可能会修改或删除现有的 LC/LI 指令。\"]},\"501\":{\"h\":\"强制转换\",\"t\":[\"虽然我们前面没有提到，但我们一直用 expr_type 来保存一个表达式的类型，强制转换的作用是获取转换的类型，并直接修改 expr_type 的值。\",\"else if (token == '(') { // cast or parenthesis match('('); if (token == Int || token == Char) { tmp = (token == Char) ? CHAR : INT; // cast type match(token); while (token == Mul) { match(Mul); tmp = tmp + PTR; } match(')'); expression(Inc); // cast has precedence as Inc(++) expr_type = tmp; } else { // normal parenthesis expression(Assign); match(')'); }}\"]},\"502\":{\"h\":\"指针取值\",\"t\":[\"诸如 *a 的指针取值，关键是判断 a 的类型，而就像上节中提到的，当一个表达式解析结束时，它的类型保存在变量 expr_type 中。\",\"else if (token == Mul) { // dereference *<addr> match(Mul); expression(Inc); // dereference has the same precedence as Inc(++) if (expr_type >= PTR) { expr_type = expr_type - PTR; } else { printf(\\\"%d: bad dereference\\\\n\\\", line); exit(-1); } *++text = (expr_type == CHAR) ? LC : LI;}\"]},\"503\":{\"h\":\"取址操作\",\"t\":[\"这里我们就能看到“变量与函数调用”一节中所说的修改或删除 LC/LI 指令了。前文中我们说到，对于变量，我们会先加载它的地址，并根据它们类型使用 LC/LI 指令加载实际内容，例如对变量 a：\",\"IMM <addr>LI\",\"那么对变量 a 取址，其实只要不执行 LC/LI 即可。因此我们删除相应的指令。\",\"else if (token == And) { // get the address of match(And); expression(Inc); // get the address of if (*text == LC || *text == LI) { text --; } else { printf(\\\"%d: bad address of\\\\n\\\", line); exit(-1); } expr_type = expr_type + PTR;}\"]},\"504\":{\"h\":\"逻辑取反\",\"t\":[\"我们没有直接的逻辑取反指令，因此我们判断它是否与数字 0 相等。而数字 0 代表了逻辑 “False”。\",\"else if (token == '!') { // not match('!'); expression(Inc); // emit code, use <expr> == 0 *++text = PUSH; *++text = IMM; *++text = 0; *++text = EQ; expr_type = INT;}\"]},\"505\":{\"h\":\"按位取反\",\"t\":[\"同样我们没有相应的指令，所以我们用异或来实现，即 ~a = a ^ 0xFFFF。\",\"else if (token == '~') { // bitwise not match('~'); expression(Inc); // emit code, use <expr> XOR -1 *++text = PUSH; *++text = IMM; *++text = -1; *++text = XOR; expr_type = INT;}\"]},\"506\":{\"h\":\"正负号\",\"t\":[\"注意这里并不是四则运算中的加减法，而是单个数字的取正取负操作。同样，我们没有取负的操作，用 0 - x 来实现 -x。\",\"else if (token == Add) { // +var, do nothing match(Add); expression(Inc); expr_type = INT;}else if (token == Sub) { // -var match(Sub); if (token == Num) { *++text = IMM; *++text = -token_val; match(Num); } else { *++text = IMM; *++text = -1; *++text = PUSH; expression(Inc); *++text = MUL; } expr_type = INT;}\"]},\"507\":{\"h\":\"自增自减\",\"t\":[\"注意的是自增自减操作的优先级是和它的位置有关的。如 ++p 的优先级高于 p++，这里我们解析的就是类似 ++p 的操作。\",\"else if (token == Inc || token == Dec) { tmp = token; match(token); expression(Inc); // ① if (*text == LC) { *text = PUSH; // to duplicate the address *++text = LC; } else if (*text == LI) { *text = PUSH; *++text = LI; } else { printf(\\\"%d: bad lvalue of pre-increment\\\\n\\\", line); exit(-1); } *++text = PUSH; *++text = IMM; // ② *++text = (expr_type > PTR) ? sizeof(int) : sizeof(char); *++text = (tmp == Inc) ? ADD : SUB; *++text = (expr_type == CHAR) ? SC : SI;}\",\"对应的汇编代码也比较直观，只是在实现 ++p时，我们要使用变量 p 的地址两次，所以我们需要先 PUSH （①）。\",\"②则是因为自增自减操作还需要处理是指针的情形。\"]},\"508\":{\"h\":\"二元运算符\",\"t\":[\"这里，我们需要处理多运算符的优先级问题，就如前文的“优先级”一节提到的，我们需要不断地向右扫描，直到遇到优先级 小于 当前优先级的运算符。\",\"回想起我们之前定义过的各个标记，它们是以优先级从低到高排列的，即 Assign 的优先级最低，而 Brak（[） 的优先级最高。\",\"enum { Num = 128, Fun, Sys, Glo, Loc, Id, Char, Else, Enum, If, Int, Return, Sizeof, While, Assign, Cond, Lor, Lan, Or, Xor, And, Eq, Ne, Lt, Gt, Le, Ge, Shl, Shr, Add, Sub, Mul, Div, Mod, Inc, Dec, Brak};\",\"所以，当我们调用 expression(level) 进行解析的时候，我们其实通过了参数 level 指定了当前的优先级。在前文的一元运算符处理中也用到了这一点。\",\"所以，此时的二元运算符的解析的框架为：\",\"while (token >= level) { // parse token for binary operator and postfix operator}\",\"解决了优先级的问题，让我们继续讲解如何把运算符编译成汇编代码吧。\"]},\"509\":{\"h\":\"赋值操作\",\"t\":[\"赋值操作是优先级最低的运算符。考虑诸如 a = (expession) 的表达式，在解析 = 之前，我们已经为变量 a 生成了如下的汇编代码：\",\"IMM <addr>LC/LI\",\"当解析完=右边的表达式后，相应的值会存放在 ax 中，此时，为了实际将这个值保存起来，我们需要类似下面的汇编代码：\",\"IMM <addr>PUSHSC/SI\",\"明白了这点，也就能理解下面的源代码了：\",\"tmp = expr_type;if (token == Assign) { // var = expr; match(Assign); if (*text == LC || *text == LI) { *text = PUSH; // save the lvalue's pointer } else { printf(\\\"%d: bad lvalue in assignment\\\\n\\\", line); exit(-1); } expression(Assign); expr_type = tmp; *++text = (expr_type == CHAR) ? SC : SI;}\"]},\"510\":{\"h\":\"三目运算符\",\"t\":[\"这是 C 语言中唯一的一个三元运算符： ? :，它相当于一个小型的 If 语句，所以生成的代码也类似于 If 语句，这里就不多作解释。\",\"else if (token == Cond) { // expr ? a : b; match(Cond); *++text = JZ; addr = ++text; expression(Assign); if (token == ':') { match(':'); } else { printf(\\\"%d: missing colon in conditional\\\\n\\\", line); exit(-1); } *addr = (int)(text + 3); *++text = JMP; addr = ++text; expression(Cond); *addr = (int)(text + 1);}\"]},\"511\":{\"h\":\"逻辑运算符\",\"t\":[\"这包括 || 和 &&。它们对应的汇编代码如下：\",\"<expr1> || <expr2> <expr1> && <expr2> ...<expr1>... ...<expr1>... JNZ b JZ b ...<expr2>... ...<expr2>...b: b:\",\"所以源码如下：\",\"else if (token == Lor) { // logic or match(Lor); *++text = JNZ; addr = ++text; expression(Lan); *addr = (int)(text + 1); expr_type = INT;}else if (token == Lan) { // logic and match(Lan); *++text = JZ; addr = ++text; expression(Or); *addr = (int)(text + 1); expr_type = INT;}\"]},\"512\":{\"h\":\"数学运算符\",\"t\":[\"它们包括 |, ^, &, ==, !=<=, >=, <, >, <<, >>, +, -, *, /, %。它们的实现都很类似，我们以异或 ^ 为例：\",\"<expr1> ^ <expr2>...<expr1>... <- now the result is on axPUSH...<expr2>... <- now the value of <expr2> is on axXOR\",\"所以它对应的代码为：\",\"else if (token == Xor) { // bitwise xor match(Xor); *++text = PUSH; expression(And); *++text = XOR; expr_type = INT;}\",\"其它的我们便不再详述。但这当中还有一个问题，就是指针的加减。在 C 语言中，指针加上数值等于将指针移位，且根据不同的类型移动的位移不同。如 a + 1，如果 a 是 char * 型，则移动一字节，而如果 a 是 int * 型，则移动 4 个字节（32位系统）。\",\"另外，在作指针减法时，如果是两个指针相减（相同类型），则结果是两个指针间隔的元素个数。因此要有特殊的处理。\",\"下面以加法为例，对应的汇编代码为：\",\"<expr1> + <expr2>normal pointer<expr1> <expr1>PUSH PUSH<expr2> <expr2> |ADD PUSH | <expr2> * <unit> IMM <unit> | MUL | ADD\",\"即当 <expr1> 是指针时，要根据它的类型放大 <expr2> 的值，因此对应的源码如下：\",\"else if (token == Add) { // add match(Add); *++text = PUSH; expression(Mul); expr_type = tmp; if (expr_type > PTR) { // pointer type, and not `char *` *++text = PUSH; *++text = IMM; *++text = sizeof(int); *++text = MUL; } *++text = ADD;}\",\"相应的减法的代码就不贴了，可以自己实现看看，也可以看文末给出的链接。\"]},\"513\":{\"h\":\"自增自减\",\"t\":[\"这次是后缀形式的，即 p++ 或 p--。与前缀形式不同的是，在执行自增自减后， ax上需要保留原来的值。所以我们首先执行类似前缀自增自减的操作，再将 ax 中的值执行减/增的操作。\",\"// 前缀形式 生成汇编代码*++text = PUSH;*++text = IMM;*++text = (expr_type > PTR) ? sizeof(int) : sizeof(char);*++text = (tmp == Inc) ? ADD : SUB;*++text = (expr_type == CHAR) ? SC : SI;// 后缀形式 生成汇编代码*++text = PUSH;*++text = IMM;*++text = (expr_type > PTR) ? sizeof(int) : sizeof(char);*++text = (token == Inc) ? ADD : SUB;*++text = (expr_type == CHAR) ? SC : SI;*++text = PUSH; //*++text = IMM; // 执行相反的增/减操作*++text = (expr_type > PTR) ? sizeof(int) : sizeof(char); //*++text = (token == Inc) ? SUB : ADD; //\"]},\"514\":{\"h\":\"数组取值操作\",\"t\":[\"在学习 C 语言的时候你可能已经知道了，诸如 a[10] 的操作等价于 *(a + 10)。因此我们要做的就是生成类似的汇编代码：\",\"else if (token == Brak) { // array access var[xx] match(Brak); *++text = PUSH; expression(Assign); match(']'); if (tmp > PTR) { // pointer, `not char *` *++text = PUSH; *++text = IMM; *++text = sizeof(int); *++text = MUL; } else if (tmp < PTR) { printf(\\\"%d: pointer type expected\\\\n\\\", line); exit(-1); } expr_type = tmp - PTR; *++text = ADD; *++text = (expr_type == CHAR) ? LC : LI;}\"]},\"515\":{\"h\":\"代码\",\"t\":[\"除了上述对表达式的解析外，我们还需要初始化虚拟机的栈，我们可以正确调用 main 函数，且当 main 函数结束时退出进程。\",\"int *tmp;// setup stacksp = (int *)((int)stack + poolsize);*--sp = EXIT; // call exit if main returns*--sp = PUSH; tmp = sp;*--sp = argc;*--sp = (int)argv;*--sp = (int)tmp;\",\"当然，最后要注意的一点是：所有的变量定义必须放在语句之前。\",\"本章的代码可以在 Github 上下载，也可以直接 clone\",\"git clone -b step-6 https://github.com/lotabout/write-a-C-interpreter\",\"通过 gcc -o xc-tutor xc-tutor.c 进行编译。并执行 ./xc-tutor hello.c 查看结果。\",\"正如我们保证的那样，我们的代码是自举的，能自己编译自己，所以你可以执行 ./xc-tutor xc-tutor.c hello.c。可以看到和之前有同样的输出。\"]},\"516\":{\"h\":\"小结\",\"t\":[\"本章我们进行了最后的解析，解析表达式。本章有两个难点：\",\"如何通过递归调用 expression 来实现运算符的优先级。\",\"如何为每个运算符生成对应的汇编代码。\",\"尽管代码看起来比较简单（虽然多），但其中用到的原理还是需要仔细推敲的。\",\"最后，恭喜你！通过一步步的学习，自己实现了一个C语言的编译器（好吧，是解释器）。\"]},\"517\":{\"c\":[\"编译原理\"]},\"518\":{\"c\":[\"c\",\"编译器\",\"解释器\"]},\"519\":{\"h\":\"手把手教你构建 C 语言编译器（9）——总结\",\"t\":[\"本文转自 https://lotabout.me/2016/write-a-C-interpreter-9/，如有侵权，请联系删除。\",\"Table of Contents\",\"1. 虚拟机与目标代码\",\"2. 词法分析\",\"3. 语法分析\",\"4. 关于编代码\",\"5. 结语\",\"恭喜你完成了自己的 C 语言编译器，本章中我们发一发牢骚，说一说编写编译器值得注意的一些问题；编写编译器时遇到的一些难题。\",\"手把手教你构建 C 语言编译器系列共有10个部分：\",\"手把手教你构建 C 语言编译器（0）——前言\",\"手把手教你构建 C 语言编译器（1）——设计\",\"手把手教你构建 C 语言编译器（2）——虚拟机\",\"手把手教你构建 C 语言编译器（3）——词法分析器\",\"手把手教你构建 C 语言编译器（4）——递归下降\",\"手把手教你构建 C 语言编译器（5）——变量定义\",\"手把手教你构建 C 语言编译器（6）——函数定义\",\"手把手教你构建 C 语言编译器（7）——语句\",\"手把手教你构建 C 语言编译器（8）——表达式\",\"手把手教你构建 C 语言编译器（9）——总结\"]},\"520\":{\"h\":\"虚拟机与目标代码\",\"t\":[\"整个系列的一开始，我们就着手虚拟机的实现。不知道你是否有同感，这部分对于整个编译器的编写其实是十分重要的。我认为至少占了重要程度的50%。\",\"这里要说明这样一个观点，学习编译原理时常常着眼于词法分析和语法分析，而忽略了同样重要的代码生成。对于学习或考试而言或许可以，但实际编译项目时，最为重要的是能“跑起来”，所以我们需要给予代码生成高度的重视。\",\"同时我们也看到，在后期解析语句和表达式时，难点已经不再是语法分析了，而是如何为运算符生成相应的汇编代码。\"]},\"521\":{\"h\":\"词法分析\",\"t\":[\"我们用了很暴力的手段编写了我们的词法分析器，我认为这并无不可。\",\"但你依旧可以学习相关的知识，了解自动生成词法分析器的原理，它涉及到了“正则表达式”，“状态机”等等知识。相信这部分的知识能够很大程度上提高你的编程水平。\",\"同时，如果今后你仍然想编写编译器，不妨试试这些自动生成工具。\"]},\"522\":{\"h\":\"语法分析\",\"t\":[\"长期以来，语法分析对我而言一直是迷一样的存在，直到真正用递归下降的方式实现了一个。\",\"我们用了专门的一章讲解了“递归下降”与 BNF 文法的关系。希望能减少你对理论的厌恶。至少，实现起来并不是太难。\",\"如果有兴趣，可以学习学习这些文法，因为已经有许多自动生成的工具支持它们。这样你就不需要重复造轮子。可以看看 yacc 等工具，更先进的版本是 bsion。同时其它语言也有许多类似的支持。\",\"题外话，最近知道了一个叫“PEG 文法”的表示方法，无论是读起来，还是实现起来，都比 BNF 要容易，你也可以学习看看。\"]},\"523\":{\"h\":\"关于编代码\",\"t\":[\"这也是我自己的感慨吧。无论多好的教程，想要完全理解它，最好的方式恐怕还是要自己实现它。\",\"只是在编写代码的过程中，我们会遇到许多的挫折，例如需要考虑许多细节，或是调试起来十分困难。但也只有真正静下心来去克服它，我们才能有所成长吧。\",\"例如在编写表达式的解析时，大量重复的代码特别让人崩溃。还有就是调试编译器，简直痛苦地无话可说。\",\"P.S. 如果你按这个系列自己编写代码，记得事先写一些用于输出汇编代码的函数，很有帮助的。\",\"还有就是写这个系列的文章，开始的冲动过了之后，每写一篇都特别心烦，希望文章本身没有受我的这种情绪影响吧。\"]},\"524\":{\"h\":\"结语\",\"t\":[\"编程有趣又无趣，只有身在其中的我们才能体会吧。\"]},\"525\":{\"c\":[\"编译原理\"]},\"526\":{\"c\":[\"c\",\"编译器\",\"解释器\"]},\"527\":{\"h\":\"\",\"t\":[\"404 Not Found\"]},\"528\":{\"h\":\"Design ASimpile CCompiler\"}},\"dirtCount\":0,\"index\":[[\"题外话\",{\"1\":{\"522\":1}}],[\"长期以来\",{\"1\":{\"522\":1}}],[\"难点已经不再是语法分析了\",{\"1\":{\"520\":1}}],[\"难以调试\",{\"1\":{\"410\":1}}],[\"难以增加\",{\"0\":{\"401\":1}}],[\"难以增加新的零件\",{\"0\":{\"157\":1}}],[\"难以根据类生成实例\",{\"1\":{\"330\":1}}],[\"跑起来\",{\"1\":{\"520\":1}}],[\"恭喜你完成了自己的\",{\"1\":{\"519\":1}}],[\"恭喜你\",{\"1\":{\"516\":1}}],[\"查看结果\",{\"1\":{\"515\":1}}],[\"查找已有标识符的方法是线性查找\",{\"1\":{\"443\":1}}],[\"减操作\",{\"1\":{\"513\":1}}],[\"减少程序的体积\",{\"1\":{\"419\":1}}],[\"减少重复代码\",{\"1\":{\"375\":1}}],[\"减少计数\",{\"1\":{\"269\":1}}],[\"减少了类之间的耦合度\",{\"1\":{\"172\":1}}],[\"减少了客户端代码与具体类之间的耦合\",{\"1\":{\"152\":1}}],[\"减少对象之间的直接交互\",{\"1\":{\"137\":1}}],[\"减少对象之间的直接依赖\",{\"1\":{\"137\":1}}],[\"明白了这点\",{\"1\":{\"509\":1}}],[\"明确了各个类的职责分工\",{\"1\":{\"197\":1}}],[\"回想起我们之前定义过的各个标记\",{\"1\":{\"508\":1}}],[\"回到并发竞争带来的安全问题上\",{\"1\":{\"114\":1}}],[\"诸如\",{\"1\":{\"502\":1,\"514\":1}}],[\"载入相应的值\",{\"1\":{\"500\":1}}],[\"⑥\",{\"1\":{\"500\":2}}],[\"⑤则是用于加载变量的值\",{\"1\":{\"500\":1}}],[\"⑤\",{\"1\":{\"500\":1}}],[\"④\",{\"1\":{\"500\":2}}],[\"找出并计算所有优先级大于\",{\"1\":{\"496\":1}}],[\"属于这前的\",{\"1\":{\"496\":1}}],[\"属性注入或方法注入\",{\"1\":{\"143\":1}}],[\"入栈\",{\"1\":{\"496\":9}}],[\"入度为\",{\"1\":{\"98\":1}}],[\"举一个例子\",{\"1\":{\"496\":1}}],[\"答曰\",{\"1\":{\"496\":1}}],[\"嘛\",{\"1\":{\"496\":1}}],[\"毕竟叫做\",{\"1\":{\"496\":1}}],[\"毕竟我们不是真正的计算机\",{\"1\":{\"426\":1}}],[\"哪个运算符后计算\",{\"1\":{\"496\":1}}],[\"哪些角色可以复用\",{\"0\":{\"299\":1}}],[\"哪些信息不应当共享\",{\"1\":{\"267\":1}}],[\"哪些信息应当共享\",{\"1\":{\"267\":1}}],[\"逆波兰式\",{\"1\":{\"496\":1}}],[\"赋值操作是优先级最低的运算符\",{\"1\":{\"509\":1}}],[\"赋值操作\",{\"0\":{\"509\":1},\"1\":{\"495\":1}}],[\"按位取反\",{\"0\":{\"505\":1},\"1\":{\"495\":1}}],[\"强制转换的作用是获取转换的类型\",{\"1\":{\"501\":1}}],[\"强制转换\",{\"0\":{\"501\":1},\"1\":{\"495\":1}}],[\"强引用\",{\"1\":{\"269\":1}}],[\"常量\",{\"0\":{\"498\":1},\"1\":{\"495\":1}}],[\"往往比词法分析\",{\"1\":{\"492\":1}}],[\"跟据条件表达式决定跳转的位置\",{\"1\":{\"487\":1}}],[\"跟它们在\",{\"1\":{\"439\":1}}],[\"种语句\",{\"1\":{\"486\":1}}],[\"感兴趣的话可以尝试自己实现它们\",{\"1\":{\"481\":1}}],[\"感谢lucky\",{\"1\":{\"66\":1}}],[\"局部变量覆盖全局变量\",{\"1\":{\"479\":1}}],[\"局部变量是可以和全局变量同名的\",{\"1\":{\"478\":1}}],[\"③用于清除入栈的参数\",{\"1\":{\"500\":1}}],[\"③则与汇编代码的生成有关\",{\"1\":{\"479\":1}}],[\"③\",{\"1\":{\"479\":1,\"500\":1}}],[\"全局变量就恢复了原先的作用\",{\"1\":{\"478\":1}}],[\"全局变量或局部变量等\",{\"1\":{\"443\":1}}],[\"出栈\",{\"1\":{\"496\":2}}],[\"出了函数体\",{\"1\":{\"478\":1}}],[\"出题人不愿意写一个确定精度的\",{\"1\":{\"54\":1}}],[\"消耗了\",{\"1\":{\"478\":1}}],[\"消除左递归的相关方法\",{\"1\":{\"458\":1}}],[\"消除后的文法如下\",{\"1\":{\"458\":1}}],[\"②则是因为自增自减操作还需要处理是指针的情形\",{\"1\":{\"507\":1}}],[\"②中判断函数的类型\",{\"1\":{\"500\":1}}],[\"②\",{\"1\":{\"478\":1,\"479\":1,\"480\":1,\"500\":1,\"507\":1}}],[\"①中注意我们是顺序将参数入栈\",{\"1\":{\"500\":1}}],[\"①\",{\"1\":{\"478\":1,\"479\":1,\"480\":1,\"500\":1,\"507\":2}}],[\"设置了正确的类型\",{\"1\":{\"476\":1}}],[\"设计我们自己的指令集\",{\"1\":{\"417\":1}}],[\"设计\",{\"0\":{\"414\":1},\"1\":{\"406\":1,\"414\":1,\"417\":1,\"435\":1,\"453\":1,\"463\":1,\"474\":1,\"485\":1,\"495\":1,\"519\":1}}],[\"设计者在使用\",{\"1\":{\"267\":1}}],[\"设计时能够决定的事情和不能决定的事情\",{\"0\":{\"198\":1}}],[\"设计模式和面向对象的目的正是为我们提供一种结构\",{\"1\":{\"399\":1}}],[\"设计模式需遵循面向对象的设计原则\",{\"1\":{\"274\":1}}],[\"设计模式是软件开发中的一把利器\",{\"1\":{\"246\":1}}],[\"设计模式的学习和应用需要不断的实践和积累\",{\"1\":{\"246\":1}}],[\"设计模式的使用不是最终目的\",{\"1\":{\"246\":1}}],[\"设计模式并不是万能的\",{\"1\":{\"246\":1}}],[\"设计模式提供了一种通用的解决方案\",{\"1\":{\"246\":1}}],[\"设计模式\",{\"0\":{\"274\":1},\"2\":{\"149\":1,\"150\":1,\"159\":1,\"160\":1,\"169\":1,\"170\":1,\"189\":1,\"190\":1,\"200\":1,\"201\":1,\"207\":1,\"208\":1,\"217\":1,\"218\":1,\"228\":1,\"229\":1,\"244\":1,\"245\":1,\"247\":1,\"248\":1,\"254\":1,\"255\":1,\"260\":1,\"261\":1,\"272\":1,\"273\":1,\"275\":1,\"276\":1,\"281\":1,\"282\":1,\"290\":1,\"291\":1,\"301\":1,\"302\":1,\"313\":1,\"314\":1,\"327\":1,\"328\":1,\"334\":1,\"335\":1,\"348\":1,\"349\":1,\"358\":1,\"359\":1,\"372\":1,\"373\":1,\"382\":1,\"383\":1,\"390\":1,\"391\":1,\"404\":1,\"405\":1}}],[\"设计模式七大原则\",{\"0\":{\"127\":1}}],[\"设计方法\",{\"1\":{\"128\":1}}],[\"设计方案参考\",{\"0\":{\"14\":1}}],[\"设计目标\",{\"1\":{\"128\":1}}],[\"敬请期待\",{\"1\":{\"471\":1,\"482\":1}}],[\"敬请批评指正\",{\"1\":{\"411\":1}}],[\"剩下的内容就是按部就班地将\",{\"1\":{\"471\":1}}],[\"值得注意的是在编译器中如何保存枚举变量的信息\",{\"1\":{\"468\":1}}],[\"值得注意的是docker\",{\"1\":{\"51\":1}}],[\"亏我们说了一章的递归下降\",{\"1\":{\"464\":1}}],[\"掌握了递归下降的方法\",{\"1\":{\"460\":1}}],[\"花这么大精力讲解递归下降方法\",{\"1\":{\"460\":1}}],[\"否则会有一些问题\",{\"1\":{\"457\":1}}],[\"否则得重新找车及测速\",{\"1\":{\"10\":1}}],[\"底\",{\"1\":{\"456\":1}}],[\"顶\",{\"1\":{\"456\":1}}],[\"右侧的式子代替\",{\"1\":{\"455\":1}}],[\"括起来的就称作\",{\"1\":{\"455\":1}}],[\"括号太多\",{\"1\":{\"56\":1}}],[\"范式\",{\"1\":{\"455\":1}}],[\"非终结符\",{\"1\":{\"455\":2,\"457\":1}}],[\"非本质的\",{\"1\":{\"268\":1}}],[\"终结符\",{\"1\":{\"455\":2}}],[\"终结符与非终结符\",{\"0\":{\"455\":1},\"1\":{\"453\":1}}],[\"四则运算的规则可以表示如下\",{\"1\":{\"455\":1}}],[\"四则运算的实现\",{\"0\":{\"459\":1},\"1\":{\"453\":1}}],[\"四则运算的递归下降\",{\"0\":{\"456\":1},\"1\":{\"453\":1}}],[\"左递归的消除\",{\"1\":{\"460\":1}}],[\"左递归\",{\"0\":{\"458\":1},\"1\":{\"453\":1,\"457\":1}}],[\"左手画方右手画圆在现实中本来就不成立\",{\"1\":{\"111\":1}}],[\"平时听到的\",{\"1\":{\"446\":1}}],[\"标准\",{\"1\":{\"500\":1}}],[\"标记开头的\",{\"1\":{\"500\":1}}],[\"标记\",{\"1\":{\"446\":2}}],[\"标识符的类型\",{\"1\":{\"443\":1}}],[\"标识符\",{\"1\":{\"443\":1}}],[\"标识符与符号表\",{\"0\":{\"443\":1},\"1\":{\"435\":1}}],[\"除了上述对表达式的解析外\",{\"1\":{\"515\":1}}],[\"除了开头的\",{\"1\":{\"471\":1}}],[\"除了跳过注释\",{\"1\":{\"446\":1}}],[\"除了核心的逻辑外还需要输入输出\",{\"1\":{\"432\":1}}],[\"段中的地址\",{\"1\":{\"445\":1}}],[\"段中\",{\"1\":{\"445\":1}}],[\"十六进制及八进制\",{\"1\":{\"444\":1}}],[\"十分有成就感\",{\"1\":{\"410\":1}}],[\"十分钟学会正确的github工作流\",{\"1\":{\"49\":1}}],[\"刚存放函数的地址\",{\"1\":{\"443\":1}}],[\"型还是指针型\",{\"1\":{\"443\":1}}],[\"型\",{\"1\":{\"443\":1,\"499\":1,\"512\":2}}],[\"型的\",{\"1\":{\"419\":1}}],[\"顾名思义\",{\"1\":{\"443\":1}}],[\"顾客想吃什么口味都可以\",{\"1\":{\"238\":1}}],[\"遇到数字5\",{\"1\":{\"496\":1}}],[\"遇到数字4\",{\"1\":{\"496\":1}}],[\"遇到数字\",{\"1\":{\"496\":1}}],[\"遇到运算符\",{\"1\":{\"496\":3}}],[\"遇到新的标识符就去查这张表\",{\"1\":{\"443\":1}}],[\"遇到的时候就知道了\",{\"1\":{\"410\":1}}],[\"遇到的问题和改进方案\",{\"0\":{\"9\":1}}],[\"循环中\",{\"1\":{\"478\":1}}],[\"循环就没法准确地知道函数定义已经结束\",{\"1\":{\"478\":1}}],[\"循环可以用来跳过它\",{\"1\":{\"440\":1}}],[\"循环的作用就是跳过这些我们不识别的字符\",{\"1\":{\"440\":1}}],[\"循环呢\",{\"1\":{\"440\":1}}],[\"跳过当前错误并继续编译\",{\"1\":{\"440\":1}}],[\"源码中若包含一个数字\",{\"1\":{\"436\":1}}],[\"源地址\",{\"1\":{\"294\":1}}],[\"宏定义\",{\"0\":{\"442\":1},\"1\":{\"435\":1}}],[\"新的指令几乎不消耗资源\",{\"1\":{\"434\":1}}],[\"新增\",{\"1\":{\"157\":1}}],[\"添加一个新的指令需要设计许多新的电路\",{\"1\":{\"434\":1}}],[\"添加flask+nginx配置\",{\"1\":{\"38\":1}}],[\"位机器下\",{\"1\":{\"433\":1}}],[\"位的\",{\"1\":{\"433\":2}}],[\"位的机器中\",{\"1\":{\"419\":1}}],[\"写的程序要\",{\"1\":{\"432\":1}}],[\"写起来很无聊\",{\"1\":{\"410\":1}}],[\"计算\",{\"1\":{\"496\":3}}],[\"计算后会将栈顶的参数退栈\",{\"1\":{\"431\":1}}],[\"计算机的栈的状态\",{\"1\":{\"477\":1}}],[\"计算机的内部工作原理\",{\"0\":{\"418\":1},\"1\":{\"417\":1}}],[\"计算机中的寄存器用于存放计算机的运行状态\",{\"1\":{\"420\":1}}],[\"计算机中有三个基本部件需要我们关注\",{\"1\":{\"418\":1}}],[\"顺序\",{\"1\":{\"430\":1}}],[\"顺其自然反而能得到意想不到的收获\",{\"1\":{\"3\":1}}],[\"钱\",{\"1\":{\"426\":1}}],[\"汇编\",{\"1\":{\"492\":1,\"496\":1}}],[\"汇编的意义上\",{\"1\":{\"431\":1}}],[\"汇编代码\",{\"1\":{\"426\":1}}],[\"汇编指令设计并实现了我们自己的指令集\",{\"1\":{\"434\":1}}],[\"汇编指令\",{\"1\":{\"418\":1}}],[\"维基百科\",{\"1\":{\"426\":1}}],[\"事先声明一下\",{\"1\":{\"426\":1}}],[\"事实上\",{\"1\":{\"112\":1}}],[\"调用参数\",{\"1\":{\"430\":1}}],[\"调用结束时\",{\"1\":{\"426\":1}}],[\"调用装饰边框的方法\",{\"1\":{\"236\":1}}],[\"反之则是变量\",{\"1\":{\"467\":1}}],[\"反之则是除号\",{\"1\":{\"446\":1}}],[\"反过来\",{\"1\":{\"426\":1}}],[\"反向遍历\",{\"1\":{\"284\":1}}],[\"详细见下文\",{\"1\":{\"422\":1}}],[\"地址存放在\",{\"1\":{\"422\":1}}],[\"地址存放在栈中\",{\"1\":{\"422\":1}}],[\"操作\",{\"1\":{\"422\":1}}],[\"操作系统将我们使用的虚拟地址映射到了到实际的内存上\",{\"1\":{\"419\":1}}],[\"放入寄存器\",{\"1\":{\"422\":1}}],[\"识别这些参数的类型\",{\"1\":{\"422\":1}}],[\"风格\",{\"1\":{\"422\":1}}],[\"风格统一\",{\"0\":{\"65\":1}}],[\"带有参数的指令在前\",{\"1\":{\"421\":1}}],[\"带颜色的大型文字\",{\"1\":{\"267\":1}}],[\"稍后你会看到\",{\"1\":{\"421\":1}}],[\"基于这个理由\",{\"1\":{\"443\":1}}],[\"基于此\",{\"1\":{\"11\":1}}],[\"基址指针\",{\"1\":{\"420\":1}}],[\"永远指向当前的栈顶\",{\"1\":{\"420\":1}}],[\"真正的计算机中有许多不同种类的寄存器\",{\"1\":{\"420\":1}}],[\"真正为其分配内存\",{\"1\":{\"419\":1}}],[\"真正来实现一个简单的编译器\",{\"1\":{\"408\":1}}],[\"故通过\",{\"1\":{\"444\":1}}],[\"故我们引入一个指令mset\",{\"1\":{\"419\":1}}],[\"故而使用下列方式\",{\"1\":{\"443\":1}}],[\"故而使用手写代码的方式实现\",{\"1\":{\"4\":1}}],[\"故而每次转弯时优先考虑上一次转弯的方向\",{\"1\":{\"12\":1}}],[\"故而采取手动测试的方式\",{\"1\":{\"10\":1}}],[\"故而首先考虑的基本策略是偏航时左右摆头寻找正确的角度前行\",{\"1\":{\"8\":1}}],[\"理论上所有的变量返回的标记都应该是\",{\"1\":{\"443\":1}}],[\"理论上我们的虚拟机需要维护一个堆用于内存分配\",{\"1\":{\"419\":1}}],[\"理论很复杂\",{\"0\":{\"408\":1}}],[\"^\",{\"1\":{\"419\":1,\"431\":1,\"447\":1,\"505\":1,\"512\":3}}],[\"堆\",{\"1\":{\"419\":1}}],[\"栈中的调用帧是什么样的\",{\"1\":{\"430\":1}}],[\"栈\",{\"1\":{\"419\":1,\"477\":1,\"496\":1}}],[\"未初始化数据段\",{\"1\":{\"419\":1}}],[\"物理内存\",{\"1\":{\"419\":1}}],[\"现代操作系统在操作内存时\",{\"1\":{\"419\":1}}],[\"现在我们要回忆如何将\",{\"1\":{\"477\":1}}],[\"现在\",{\"1\":{\"389\":1}}],[\"现在电话亭上加了把锁\",{\"1\":{\"112\":1}}],[\"现在不存在这种情况了\",{\"1\":{\"57\":1}}],[\"说一说编写编译器值得注意的一些问题\",{\"1\":{\"519\":1}}],[\"说得通俗一点就是自己实现一套汇编语言\",{\"1\":{\"417\":1}}],[\"说明\",{\"1\":{\"178\":1}}],[\"测试\",{\"0\":{\"433\":1},\"1\":{\"417\":1}}],[\"测试和部署应用程序\",{\"1\":{\"44\":1}}],[\"子函数要返回时\",{\"1\":{\"426\":1}}],[\"子函数调用\",{\"0\":{\"426\":1},\"1\":{\"417\":1}}],[\"子类责任\",{\"1\":{\"389\":1}}],[\"子类具有实现在父类中所声明的抽象方法的责任\",{\"1\":{\"389\":1}}],[\"子类只需关注具体步骤的实现\",{\"1\":{\"385\":1}}],[\"子类可以在不改变算法结构的情况下\",{\"1\":{\"384\":1}}],[\"子类可以替换父类\",{\"1\":{\"148\":1}}],[\"子类应当能够替代父类的实例而不影响程序的正确性\",{\"1\":{\"242\":1}}],[\"子类应保持父类的行为\",{\"1\":{\"133\":1}}],[\"子类的方法签名应与父类一致\",{\"1\":{\"133\":1}}],[\"指定了当前的优先级\",{\"1\":{\"508\":1}}],[\"指针加上数值等于将指针移位\",{\"1\":{\"512\":1}}],[\"指针相对位置的形式\",{\"1\":{\"500\":1}}],[\"指针取值\",{\"0\":{\"502\":1},\"1\":{\"495\":1}}],[\"指针和对应的位移量进行的\",{\"1\":{\"477\":1}}],[\"指针寄存器\",{\"1\":{\"420\":1}}],[\"指向的是同一个变量\",{\"1\":{\"443\":1}}],[\"指出错误发生的位置\",{\"1\":{\"440\":2}}],[\"指的是\",{\"1\":{\"427\":1}}],[\"指的是需要编写哪些类和需要实现哪些方法都非常清楚\",{\"1\":{\"156\":1}}],[\"指令加载实际内容\",{\"1\":{\"503\":1}}],[\"指令加载对应的值\",{\"1\":{\"500\":1}}],[\"指令了\",{\"1\":{\"503\":1}}],[\"指令存入\",{\"1\":{\"500\":1}}],[\"指令将它加载到\",{\"1\":{\"498\":1}}],[\"指令无法操作除\",{\"1\":{\"430\":1}}],[\"指令功能有限\",{\"1\":{\"428\":1}}],[\"指令同样功能不足\",{\"1\":{\"426\":1}}],[\"指令并无法指定寄存器\",{\"1\":{\"426\":1}}],[\"指令来代替它\",{\"1\":{\"426\":1}}],[\"指令呢\",{\"1\":{\"426\":1}}],[\"指令的参数\",{\"1\":{\"424\":1}}],[\"指令只能将\",{\"1\":{\"422\":1}}],[\"指令中\",{\"1\":{\"422\":1}}],[\"指令其实有许多变种\",{\"1\":{\"422\":1}}],[\"指令拆分成这些指令\",{\"1\":{\"422\":1}}],[\"指令拆分成\",{\"1\":{\"422\":1}}],[\"指令有两个参数\",{\"1\":{\"422\":1}}],[\"指令\",{\"1\":{\"419\":1,\"424\":1,\"426\":1,\"429\":2,\"500\":1}}],[\"指令集是\",{\"1\":{\"421\":1}}],[\"指令集\",{\"0\":{\"421\":1},\"1\":{\"417\":1}}],[\"寄存器指向的是\",{\"1\":{\"424\":1}}],[\"寄存器设置为指定的\",{\"1\":{\"424\":1}}],[\"寄存器或是一个内存地址\",{\"1\":{\"422\":1}}],[\"寄存器及内存\",{\"1\":{\"418\":1}}],[\"寄存器\",{\"0\":{\"420\":1},\"1\":{\"417\":1}}],[\"逐个读取文件中的字符\",{\"1\":{\"416\":1}}],[\"逐个通知每个观察者可能会导致性能问题\",{\"1\":{\"324\":1}}],[\"读取一个文件\",{\"1\":{\"416\":1}}],[\"获取下一个标记\",{\"1\":{\"416\":1}}],[\"构建语法分析器\",{\"1\":{\"415\":1}}],[\"构建我们的词法分析器\",{\"1\":{\"415\":1}}],[\"构建我们自己的虚拟机以及指令集\",{\"1\":{\"415\":1}}],[\"屏蔽了许多实现上的细节\",{\"1\":{\"415\":1}}],[\"已经把\",{\"1\":{\"429\":1}}],[\"已经有许多工具能帮助我们处理阶段1和2\",{\"1\":{\"415\":1}}],[\"已经编写完成的具体工厂越多\",{\"1\":{\"157\":1}}],[\"目标代码的生成\",{\"1\":{\"415\":1}}],[\"目录类\",{\"0\":{\"222\":1}}],[\"目录可以包含其他目录和文件\",{\"1\":{\"220\":1}}],[\"目录和文件都可以被视为条目\",{\"1\":{\"220\":1}}],[\"目录的构建\",{\"1\":{\"108\":1}}],[\"系列的第三篇\",{\"1\":{\"417\":1}}],[\"系列的第二篇\",{\"1\":{\"414\":1}}],[\"系统的线程调度器是假设不同的线程是毫无关系的\",{\"1\":{\"112\":1}}],[\"系统\",{\"0\":{\"98\":1}}],[\"具有一定的参考价值\",{\"1\":{\"411\":1}}],[\"具体的实现如下\",{\"1\":{\"429\":1}}],[\"具体而言\",{\"1\":{\"235\":1}}],[\"具体类\",{\"1\":{\"154\":1}}],[\"具体实现很容易\",{\"1\":{\"459\":1}}],[\"具体实现\",{\"1\":{\"144\":1}}],[\"观看效果更佳\",{\"1\":{\"411\":1}}],[\"观察者\",{\"1\":{\"320\":1}}],[\"观察者模式在\",{\"1\":{\"325\":1}}],[\"观察者模式定义了一种一对多的依赖关系\",{\"1\":{\"317\":1}}],[\"观察者模式非常适合用于需要自动更新的场景\",{\"1\":{\"316\":1}}],[\"英文的\",{\"1\":{\"411\":1}}],[\"繁琐\",{\"1\":{\"410\":1}}],[\"做好心理准备\",{\"0\":{\"410\":1}}],[\"做任何修改\",{\"1\":{\"186\":1}}],[\"声明\",{\"1\":{\"409\":1}}],[\"声明抽象方法是希望达到以下目的\",{\"1\":{\"389\":1}}],[\"声明抽象方法\",{\"1\":{\"366\":1}}],[\"号称用\",{\"1\":{\"409\":1}}],[\"名叫\",{\"1\":{\"409\":1}}],[\"名字现在是bob\",{\"1\":{\"339\":1}}],[\"名字现在是alice\",{\"1\":{\"339\":1}}],[\"名字现在是\",{\"1\":{\"338\":2}}],[\"名字\",{\"1\":{\"178\":1}}],[\"内置函数有对应的汇编指令\",{\"1\":{\"500\":1}}],[\"内置函数的行为也和关键字类似\",{\"1\":{\"448\":1}}],[\"内置函数\",{\"0\":{\"432\":1},\"1\":{\"417\":1}}],[\"内存地址的数据\",{\"1\":{\"419\":1}}],[\"内存用于存储数据\",{\"1\":{\"419\":1}}],[\"内存\",{\"0\":{\"419\":1},\"1\":{\"417\":1}}],[\"内存之外的其它资源\",{\"0\":{\"270\":1}}],[\"内容相对容易一些\",{\"1\":{\"492\":1}}],[\"内容为\",{\"1\":{\"416\":1}}],[\"内容过于复杂\",{\"1\":{\"408\":1}}],[\"依旧不能确定是否立即计算\",{\"1\":{\"496\":1}}],[\"依旧帮助不了我们学习编译器\",{\"1\":{\"408\":1}}],[\"依赖于状态的处理\",{\"0\":{\"366\":1},\"1\":{\"366\":4,\"367\":1,\"369\":1}}],[\"依赖于特定应用程序就意味着难以复用\",{\"1\":{\"299\":1}}],[\"依赖于特定应用程序的部分都被封装在扮演\",{\"1\":{\"299\":1}}],[\"依赖注入\",{\"1\":{\"143\":1}}],[\"依赖倒置原则\",{\"0\":{\"142\":1},\"1\":{\"127\":1,\"128\":1,\"148\":1}}],[\"什么是表达式\",{\"1\":{\"495\":1}}],[\"什么是递归下降\",{\"0\":{\"454\":1},\"1\":{\"453\":1}}],[\"什么是词法分析器\",{\"0\":{\"436\":1},\"1\":{\"435\":1}}],[\"什么都不干的编译器\",{\"1\":{\"416\":1}}],[\"什么\",{\"1\":{\"408\":1}}],[\"什么时候会从\",{\"1\":{\"367\":1}}],[\"什么时候从一个状态迁移到其他状态\",{\"1\":{\"367\":1}}],[\"词法分析中如何处理标识符与符号表\",{\"1\":{\"450\":1}}],[\"词法分析\",{\"0\":{\"521\":1},\"1\":{\"408\":1,\"519\":1}}],[\"词法分析器本身可以认为是一个编译器\",{\"1\":{\"450\":1}}],[\"词法分析器本质上也是编译器\",{\"1\":{\"446\":1}}],[\"词法分析器中直接解析这些关键字\",{\"1\":{\"448\":1}}],[\"词法分析器会把扫描到的标识符全都保存到一张表中\",{\"1\":{\"443\":1}}],[\"词法分析器将输出\",{\"1\":{\"436\":1}}],[\"词法分析器以源码字符串为输入\",{\"1\":{\"436\":1}}],[\"词法分析器用于对源码字符串做预处理\",{\"1\":{\"436\":1}}],[\"词法分析器的作用是对源码字符串进行预处理\",{\"1\":{\"450\":1}}],[\"词法分析器的框架\",{\"0\":{\"440\":1},\"1\":{\"435\":1}}],[\"词法分析器的实现\",{\"0\":{\"438\":1},\"1\":{\"435\":1}}],[\"词法分析器与编译器\",{\"0\":{\"437\":1},\"1\":{\"435\":1}}],[\"词法分析器\",{\"0\":{\"435\":1},\"1\":{\"406\":1,\"414\":1,\"415\":1,\"417\":1,\"435\":1,\"437\":1,\"453\":1,\"463\":1,\"474\":1,\"485\":1,\"495\":1,\"519\":1}}],[\"听不懂\",{\"1\":{\"408\":1}}],[\"听起来有些贬义的意思\",{\"1\":{\"202\":1}}],[\"好吧\",{\"1\":{\"407\":1,\"516\":1}}],[\"装b\",{\"1\":{\"407\":1}}],[\"装饰\",{\"1\":{\"236\":2}}],[\"装饰边框与被装饰物具有相同的接口\",{\"1\":{\"236\":1}}],[\"装饰边框与被装饰物具有一致性\",{\"1\":{\"235\":1}}],[\"装饰边框\",{\"1\":{\"235\":1,\"236\":1}}],[\"装饰边框里面的\",{\"1\":{\"235\":1}}],[\"装饰器模式允许我们在不修改现有代码的情况下扩展对象的功能\",{\"1\":{\"231\":1}}],[\"装饰器模式允许我们通过将对象放入包含行为的特殊封装对象中来扩展对象的功能\",{\"1\":{\"230\":1}}],[\"装饰者模式等\",{\"1\":{\"130\":1}}],[\"学习编译原理时常常着眼于词法分析和语法分析\",{\"1\":{\"520\":1}}],[\"学习了编译原理\",{\"1\":{\"407\":1}}],[\"学了这么多也没用\",{\"1\":{\"408\":1}}],[\"学术研究\",{\"1\":{\"66\":1}}],[\"像是程序员的第一道门槛\",{\"1\":{\"407\":1}}],[\"像这样改一个地方会对多个地方产生影响并非总是不好\",{\"1\":{\"267\":1}}],[\"递归调用的实质也是栈的处理\",{\"1\":{\"496\":1}}],[\"递归下下降方法对\",{\"1\":{\"457\":1}}],[\"递归下降是从起始的非终结符开始\",{\"1\":{\"456\":1}}],[\"递归下降法\",{\"1\":{\"408\":1}}],[\"递归下降\",{\"0\":{\"453\":1},\"1\":{\"406\":1,\"414\":1,\"417\":1,\"435\":1,\"453\":1,\"463\":1,\"474\":1,\"485\":1,\"495\":1,\"519\":1,\"522\":1}}],[\"递归\",{\"1\":{\"407\":1}}],[\"能自己编译自己\",{\"1\":{\"515\":1}}],[\"能大概理解吗\",{\"1\":{\"467\":1}}],[\"能减小语法分析复杂度\",{\"1\":{\"446\":1}}],[\"能理解的语言\",{\"1\":{\"421\":1}}],[\"能识别的命令的集合\",{\"1\":{\"421\":1}}],[\"能不能理解\",{\"1\":{\"407\":1}}],[\"能轻松使用\",{\"1\":{\"66\":1}}],[\"算法\",{\"1\":{\"407\":1}}],[\"算术公理系统\",{\"0\":{\"68\":1}}],[\"谈谈这个系列的初衷\",{\"1\":{\"406\":1}}],[\"表\",{\"1\":{\"443\":1}}],[\"表达式结束\",{\"1\":{\"496\":1}}],[\"表达式的解析难点有二\",{\"1\":{\"495\":1}}],[\"表达式是将各种语言要素的一个组合\",{\"1\":{\"495\":1}}],[\"表达式可能相对不好理解一些\",{\"1\":{\"471\":1}}],[\"表达式\",{\"0\":{\"495\":1},\"1\":{\"406\":1,\"414\":1,\"416\":1,\"417\":1,\"435\":1,\"453\":1,\"463\":2,\"474\":2,\"485\":1,\"486\":1,\"495\":1,\"519\":1}}],[\"表示转换成实际的代码\",{\"1\":{\"457\":1}}],[\"表示是十分接近的\",{\"1\":{\"457\":1}}],[\"表示选择\",{\"1\":{\"455\":1}}],[\"表示字符\",{\"1\":{\"445\":1}}],[\"表示换行符\",{\"1\":{\"445\":1}}],[\"表示将\",{\"1\":{\"422\":1}}],[\"表示该对象不再被使用\",{\"1\":{\"269\":1}}],[\"表示装饰边框的\",{\"1\":{\"235\":1}}],[\"表示\",{\"0\":{\"464\":1,\"475\":1},\"1\":{\"69\":1,\"72\":1,\"73\":1,\"88\":1,\"89\":1,\"445\":1,\"463\":1,\"474\":1}}],[\"语法\",{\"1\":{\"460\":1}}],[\"语法分析对我而言一直是迷一样的存在\",{\"1\":{\"522\":1}}],[\"语法分析更困难\",{\"1\":{\"492\":1}}],[\"语法分析的入口\",{\"1\":{\"416\":1}}],[\"语法分析器的复杂度会大大降低\",{\"1\":{\"436\":1}}],[\"语法分析器\",{\"1\":{\"415\":1}}],[\"语法分析是一样的\",{\"1\":{\"414\":1}}],[\"语法分析\",{\"0\":{\"522\":1},\"1\":{\"408\":1,\"519\":1}}],[\"语句简单\",{\"1\":{\"488\":1}}],[\"语句比\",{\"1\":{\"488\":1}}],[\"语句后方的代码\",{\"1\":{\"487\":1}}],[\"语句是可以省略的\",{\"1\":{\"487\":1}}],[\"语句的作用是跳转\",{\"1\":{\"487\":1}}],[\"语句和表达式的解析\",{\"1\":{\"485\":1}}],[\"语句就是用来向前查看标记以确定使用哪一个产生式\",{\"1\":{\"467\":1}}],[\"语句\",{\"0\":{\"485\":1,\"486\":1,\"487\":1,\"488\":1,\"489\":1},\"1\":{\"406\":1,\"414\":1,\"417\":1,\"425\":1,\"435\":1,\"453\":1,\"463\":1,\"474\":1,\"485\":5,\"486\":1,\"487\":1,\"489\":1,\"495\":1,\"510\":2,\"519\":1}}],[\"语言运算符优先级\",{\"1\":{\"496\":1}}],[\"语言定义了各种表达式的优先级\",{\"1\":{\"496\":1}}],[\"语言区分\",{\"1\":{\"486\":1}}],[\"语言不太一致\",{\"1\":{\"480\":1}}],[\"语言与现代的\",{\"1\":{\"480\":1}}],[\"语言中唯一的一个三元运算符\",{\"1\":{\"510\":1}}],[\"语言中\",{\"1\":{\"446\":1,\"512\":1}}],[\"语言中标识符可以是全局的也可以是局部的\",{\"1\":{\"443\":1}}],[\"语言中空格是用来作为分隔用的\",{\"1\":{\"440\":1}}],[\"语言中的优先级有关\",{\"1\":{\"439\":1}}],[\"语言中的赋值语句\",{\"1\":{\"422\":1}}],[\"语言中我们经常使用的\",{\"1\":{\"432\":1}}],[\"语言中支持的运算符都提供对应汇编指令\",{\"1\":{\"431\":1}}],[\"语言调用标准\",{\"1\":{\"426\":1}}],[\"语言代码\",{\"1\":{\"416\":1}}],[\"语言程序\",{\"1\":{\"416\":1}}],[\"语言的时候你可能已经知道了\",{\"1\":{\"514\":1}}],[\"语言的字符串常量支持如下风格\",{\"1\":{\"498\":1}}],[\"语言的文法\",{\"1\":{\"463\":1}}],[\"语言的宏定义以字符\",{\"1\":{\"442\":1}}],[\"语言的调用标准是\",{\"1\":{\"426\":1}}],[\"语言的源代码文件\",{\"1\":{\"414\":1}}],[\"语言的解释器\",{\"1\":{\"414\":1}}],[\"语言的编译器\",{\"1\":{\"406\":1}}],[\"语言编译器系列共有10个部分\",{\"1\":{\"406\":1,\"414\":1,\"417\":1,\"435\":1,\"453\":1,\"463\":1,\"474\":1,\"485\":1,\"495\":1,\"519\":1}}],[\"语言编译器\",{\"0\":{\"406\":1,\"414\":1,\"435\":1,\"453\":1,\"463\":1,\"474\":1,\"485\":1,\"495\":1,\"519\":1},\"1\":{\"406\":13,\"409\":3,\"414\":12,\"417\":12,\"435\":10,\"453\":10,\"463\":10,\"474\":10,\"485\":10,\"495\":10,\"519\":11}}],[\"虚拟内存可以理解为一种映射\",{\"1\":{\"419\":1}}],[\"虚拟内存\",{\"1\":{\"419\":1}}],[\"虚拟机与目标代码\",{\"0\":{\"520\":1},\"1\":{\"519\":1}}],[\"虚拟机中讲解的指令是对应的\",{\"1\":{\"500\":1}}],[\"虚拟机上运行我们提供的这些指令时\",{\"1\":{\"432\":1}}],[\"虚拟机的入口\",{\"1\":{\"416\":1}}],[\"虚拟机\",{\"1\":{\"406\":1,\"414\":1,\"417\":2,\"435\":1,\"453\":1,\"463\":1,\"474\":1,\"482\":1,\"485\":1,\"495\":1,\"500\":1,\"519\":1}}],[\"虚拟代理用于控制对资源密集型对象的访问\",{\"1\":{\"346\":1}}],[\"虚拟代理\",{\"1\":{\"341\":1}}],[\"原则上我们需要立即计算\",{\"1\":{\"496\":1}}],[\"原则上我们是不讲这么深入\",{\"1\":{\"458\":1}}],[\"原因之一就是减少了语法分析器需要\",{\"1\":{\"446\":1}}],[\"原因有二\",{\"1\":{\"438\":1}}],[\"原因是当我们从子函数中返回时\",{\"1\":{\"426\":1}}],[\"原因是默认计算的结果是存放在\",{\"1\":{\"422\":1}}],[\"原因是太复杂了\",{\"1\":{\"408\":1}}],[\"原因只有一个\",{\"1\":{\"407\":1}}],[\"原文链接\",{\"1\":{\"406\":2}}],[\"原文转载自\",{\"1\":{\"111\":1,\"115\":1}}],[\"原作者\",{\"1\":{\"406\":1}}],[\"手把手教你构建\",{\"0\":{\"406\":1,\"414\":1,\"435\":1,\"453\":1,\"463\":1,\"474\":1,\"485\":1,\"495\":1,\"519\":1},\"1\":{\"406\":13,\"414\":12,\"417\":13,\"435\":11,\"453\":11,\"463\":11,\"474\":11,\"485\":11,\"495\":11,\"519\":11}}],[\"手动修改后可正常运行\",{\"1\":{\"109\":1}}],[\"尽管代码看起来比较简单\",{\"1\":{\"516\":1}}],[\"尽管理论不是必需的\",{\"1\":{\"460\":1}}],[\"尽管我们还没定义\",{\"1\":{\"426\":1}}],[\"尽管有许多语法并不支持\",{\"1\":{\"406\":1}}],[\"尽管使用\",{\"1\":{\"401\":1}}],[\"尽量减少类之间的耦合\",{\"1\":{\"148\":1}}],[\"尽量减少类的公开方法\",{\"1\":{\"137\":1}}],[\"尽量使用组合\",{\"1\":{\"145\":1}}],[\"希望文章本身没有受我的这种情绪影响吧\",{\"1\":{\"523\":1}}],[\"希望能减少你对理论的厌恶\",{\"1\":{\"522\":1}}],[\"希望通过这个系列\",{\"1\":{\"406\":1}}],[\"希望通过本章的学习\",{\"1\":{\"246\":1,\"434\":1}}],[\"希望扩展某个功能\",{\"1\":{\"399\":1}}],[\"绝不能毫无理由地禁止扩展类\",{\"1\":{\"399\":1}}],[\"绝不能因为先调用\",{\"1\":{\"321\":1}}],[\"处理\",{\"1\":{\"398\":1}}],[\"处理器本来同一时间就只能有一个线程在运行\",{\"1\":{\"112\":1}}],[\"双重分发\",{\"0\":{\"397\":1}}],[\"双重检查锁定示例代码\",{\"0\":{\"357\":1}}],[\"访问数据结构并处理数据\",{\"2\":{\"405\":1}}],[\"访问\",{\"1\":{\"397\":1}}],[\"访问者\",{\"1\":{\"392\":1}}],[\"访问代理用于控制对实际对象的访问权限\",{\"1\":{\"346\":1}}],[\"数组取值操作\",{\"0\":{\"514\":1},\"1\":{\"495\":1}}],[\"数字中较为复杂的一点是需要支持十进制\",{\"1\":{\"444\":1}}],[\"数字\",{\"0\":{\"444\":1},\"1\":{\"435\":1,\"436\":1,\"497\":1}}],[\"数据段以及栈\",{\"1\":{\"419\":1}}],[\"数据段\",{\"1\":{\"419\":1,\"477\":1}}],[\"数据结构\",{\"1\":{\"407\":1}}],[\"数据结构很重要\",{\"1\":{\"398\":1}}],[\"数据结构与处理被分离开来\",{\"1\":{\"392\":1}}],[\"数学运算符\",{\"0\":{\"512\":1},\"1\":{\"495\":1}}],[\"数学\",{\"2\":{\"104\":1}}],[\"期待子类去实现抽象方法\",{\"1\":{\"389\":1}}],[\"站在父类的角度进行思考\",{\"1\":{\"389\":1}}],[\"很有帮助的\",{\"1\":{\"523\":1}}],[\"很好的初学者教程\",{\"1\":{\"411\":1}}],[\"很难懂\",{\"1\":{\"409\":1}}],[\"很容易着眼于以下几点\",{\"1\":{\"389\":1}}],[\"很可能随着需求变更实例数量会慢慢变多\",{\"1\":{\"298\":1}}],[\"延申\",{\"0\":{\"389\":1}}],[\"延迟实例化\",{\"1\":{\"337\":1}}],[\"允许子类实现具体的步骤\",{\"1\":{\"385\":1}}],[\"允许开发者在\",{\"1\":{\"44\":1}}],[\"低速但计算准确的算法\",{\"1\":{\"380\":1}}],[\"验算\",{\"1\":{\"380\":1}}],[\"速度快但耗内存的策略\",{\"1\":{\"380\":1}}],[\"速度慢但省内存的策略\",{\"1\":{\"380\":1}}],[\"例程的水平\",{\"1\":{\"379\":1}}],[\"例如需要考虑许多细节\",{\"1\":{\"523\":1}}],[\"例如对变量\",{\"1\":{\"503\":1}}],[\"例如参数的位置\",{\"1\":{\"482\":1}}],[\"例如只要遇到\",{\"1\":{\"467\":1}}],[\"例如用\",{\"1\":{\"445\":1}}],[\"例如数据库连接\",{\"1\":{\"351\":1}}],[\"例如事件对象或数据包\",{\"1\":{\"323\":1}}],[\"例如在编写表达式的解析时\",{\"1\":{\"523\":1}}],[\"例如在应用程序关闭后重新打开时恢复状态\",{\"1\":{\"310\":1}}],[\"例如在用户进行撤销操作之前\",{\"1\":{\"310\":1}}],[\"例如增加一个具体方法\",{\"1\":{\"174\":1}}],[\"例如tablefactory\",{\"1\":{\"154\":1}}],[\"例如策略模式\",{\"1\":{\"130\":1}}],[\"例如添加新插件\",{\"1\":{\"108\":1}}],[\"例如\",{\"1\":{\"108\":1,\"157\":2,\"175\":1,\"186\":1,\"187\":1,\"199\":1,\"202\":1,\"220\":1,\"236\":1,\"267\":1,\"288\":1,\"299\":1,\"316\":1,\"321\":1,\"322\":1,\"324\":1,\"341\":1,\"342\":1,\"346\":3,\"367\":1,\"379\":2,\"380\":2,\"401\":1,\"402\":1,\"419\":1,\"426\":1,\"432\":1,\"436\":1,\"439\":1,\"443\":1,\"448\":1,\"455\":1,\"456\":1,\"495\":1}}],[\"例如很多期望概率题\",{\"1\":{\"54\":1}}],[\"例如许多计数\",{\"1\":{\"54\":1}}],[\"例如c\",{\"1\":{\"16\":1}}],[\"仅仅修改\",{\"1\":{\"379\":1}}],[\"布\",{\"1\":{\"376\":1}}],[\"剪刀\",{\"1\":{\"376\":1}}],[\"石头\",{\"1\":{\"376\":1}}],[\"另外\",{\"1\":{\"433\":1,\"446\":1,\"457\":1,\"512\":1}}],[\"另外一种算法\",{\"1\":{\"380\":1}}],[\"另外一种策略是\",{\"1\":{\"376\":1}}],[\"另一个特殊的地方是我们需要支持转义符\",{\"1\":{\"445\":1}}],[\"另一点是我们的\",{\"1\":{\"422\":1}}],[\"另一种方法是传递具体的更新信息\",{\"1\":{\"323\":1}}],[\"另一方面需要对照生成的代码来调试\",{\"1\":{\"410\":1}}],[\"另一方面希望挑战一下自己\",{\"1\":{\"407\":1}}],[\"另一方面\",{\"1\":{\"113\":1,\"268\":1,\"399\":1,\"422\":1}}],[\"另一方面采取了常数更小的加减法操作\",{\"1\":{\"58\":1}}],[\"游戏\",{\"1\":{\"376\":1}}],[\"猜拳\",{\"1\":{\"376\":1}}],[\"策略模式的主要优点包括\",{\"1\":{\"375\":1}}],[\"至少\",{\"1\":{\"522\":1}}],[\"至少必须在阅读了\",{\"1\":{\"199\":1}}],[\"至此\",{\"1\":{\"399\":1}}],[\"至于这个参数是否是\",{\"1\":{\"370\":1}}],[\"向下\",{\"1\":{\"456\":1}}],[\"向前看标记\",{\"1\":{\"467\":1}}],[\"向前看\",{\"1\":{\"446\":1,\"457\":1}}],[\"向\",{\"1\":{\"370\":2}}],[\"忘记实现方法\",{\"1\":{\"369\":1}}],[\"忘记取模\",{\"1\":{\"56\":1}}],[\"必须先查看它的右方\",{\"1\":{\"496\":1}}],[\"必须先获得gil锁\",{\"1\":{\"112\":1}}],[\"必须要考虑到将来可能会扩展类\",{\"1\":{\"399\":1}}],[\"必须十分小心\",{\"1\":{\"368\":1}}],[\"输出是标记流\",{\"1\":{\"450\":1}}],[\"输出标记流\",{\"1\":{\"437\":1}}],[\"输出汇编代码\",{\"1\":{\"437\":1}}],[\"输出为标记流\",{\"1\":{\"436\":1}}],[\"输出\",{\"1\":{\"433\":1}}],[\"输出和下一个状态\",{\"1\":{\"367\":1}}],[\"输入是源码\",{\"1\":{\"450\":1}}],[\"输入和内部状态\",{\"1\":{\"367\":1}}],[\"输入任意邮箱和刚才生成的序列号到激活窗口\",{\"1\":{\"124\":1}}],[\"输入\",{\"1\":{\"124\":2}}],[\"程序需要回到跳转之前的地方继续运行\",{\"1\":{\"426\":1}}],[\"程序计数器\",{\"1\":{\"420\":1}}],[\"程序运行的状态保存在寄存器中\",{\"1\":{\"418\":1}}],[\"程序运行中也可以切换策略\",{\"0\":{\"380\":1}}],[\"程序的整体结构也会更加清晰\",{\"1\":{\"367\":1}}],[\"程序可能会无法正常工作\",{\"1\":{\"199\":1}}],[\"扮演\",{\"1\":{\"367\":1}}],[\"呢\",{\"1\":{\"366\":1}}],[\"告诉我们存在还没有实现的方法\",{\"1\":{\"369\":1}}],[\"告诉\",{\"1\":{\"366\":1}}],[\"条件分支就会越多\",{\"1\":{\"365\":1}}],[\"条通信线路\",{\"1\":{\"298\":4}}],[\"から\",{\"1\":{\"363\":3}}],[\"から$\",{\"1\":{\"362\":1}}],[\"へ状態が変化しました\",{\"1\":{\"362\":1,\"363\":3}}],[\"現在時刻は23\",{\"1\":{\"363\":1}}],[\"現在時刻は22\",{\"1\":{\"363\":1}}],[\"現在時刻は21\",{\"1\":{\"363\":1}}],[\"現在時刻は20\",{\"1\":{\"363\":1}}],[\"現在時刻は19\",{\"1\":{\"363\":1}}],[\"現在時刻は18\",{\"1\":{\"363\":1}}],[\"現在時刻は17\",{\"1\":{\"363\":1}}],[\"現在時刻は16\",{\"1\":{\"363\":1}}],[\"現在時刻は15\",{\"1\":{\"363\":1}}],[\"現在時刻は14\",{\"1\":{\"363\":1}}],[\"現在時刻は13\",{\"1\":{\"363\":1}}],[\"現在時刻は12\",{\"1\":{\"363\":1}}],[\"現在時刻は11\",{\"1\":{\"363\":1}}],[\"現在時刻は10\",{\"1\":{\"363\":1}}],[\"現在時刻は09\",{\"1\":{\"363\":1}}],[\"現在時刻は08\",{\"1\":{\"363\":1}}],[\"現在時刻は07\",{\"1\":{\"363\":1}}],[\"現在時刻は06\",{\"1\":{\"363\":1}}],[\"現在時刻は05\",{\"1\":{\"363\":1}}],[\"現在時刻は04\",{\"1\":{\"363\":1}}],[\"現在時刻は03\",{\"1\":{\"363\":1}}],[\"現在時刻は02\",{\"1\":{\"363\":1}}],[\"現在時刻は01\",{\"1\":{\"363\":1}}],[\"現在時刻は00\",{\"1\":{\"363\":1}}],[\"現在時刻は\",{\"1\":{\"362\":1}}],[\"夜间通话录音\",{\"1\":{\"362\":1,\"363\":16}}],[\"夜间\",{\"1\":{\"362\":2,\"363\":19}}],[\"夜间使用金库\",{\"1\":{\"362\":1,\"363\":16}}],[\"紧急\",{\"1\":{\"362\":1,\"363\":16}}],[\"紧急铃\",{\"1\":{\"362\":2,\"363\":24}}],[\"白天\",{\"1\":{\"362\":4,\"363\":27,\"365\":1}}],[\"金库使用\",{\"1\":{\"362\":1,\"363\":8}}],[\"函数结束时退出进程\",{\"1\":{\"515\":1}}],[\"函数调用\",{\"1\":{\"495\":1}}],[\"函数体的代码如下\",{\"1\":{\"480\":1}}],[\"函数体的解析\",{\"0\":{\"480\":1},\"1\":{\"474\":1}}],[\"函数参数与汇编代码\",{\"0\":{\"477\":1},\"1\":{\"474\":1}}],[\"函数包装起来\",{\"1\":{\"469\":1}}],[\"函数是一个辅助函数\",{\"1\":{\"469\":1}}],[\"函数我们将放到下一章中讲解\",{\"1\":{\"469\":1}}],[\"函数还没有出现过\",{\"1\":{\"466\":1}}],[\"函数的内容\",{\"1\":{\"466\":1}}],[\"函数的主体\",{\"1\":{\"440\":1}}],[\"函数的实现本身就十分复杂\",{\"1\":{\"432\":1}}],[\"函数就是用于输出\",{\"1\":{\"432\":1}}],[\"函数中加入下列代码\",{\"1\":{\"422\":1,\"433\":1}}],[\"函数中加入初始化代码\",{\"1\":{\"420\":1}}],[\"函数\",{\"1\":{\"416\":1,\"466\":1,\"477\":1,\"515\":1}}],[\"函数定义的解析\",{\"0\":{\"478\":1},\"1\":{\"474\":1}}],[\"函数定义\",{\"0\":{\"474\":1},\"1\":{\"406\":1,\"414\":1,\"417\":1,\"435\":1,\"453\":1,\"463\":2,\"474\":2,\"485\":1,\"495\":1,\"519\":1}}],[\"函数模拟了一个锁机制\",{\"1\":{\"357\":1}}],[\"函数取模\",{\"0\":{\"57\":1}}],[\"想要完全理解它\",{\"1\":{\"523\":1}}],[\"想在程序上表现出\",{\"1\":{\"352\":1}}],[\"想确保任何情况下都绝对只有\",{\"1\":{\"352\":1}}],[\"想做一个一样的移动app\",{\"1\":{\"106\":1}}],[\"日志记录器等\",{\"1\":{\"351\":1}}],[\"性能和可维护性\",{\"1\":{\"346\":1}}],[\"防火墙代理可以用于控制对内部网络资源的访问\",{\"1\":{\"346\":1}}],[\"防止中途出错了\",{\"1\":{\"112\":1}}],[\"远程方法调用\",{\"1\":{\"346\":1}}],[\"远程代理用于控制对远程对象的访问\",{\"1\":{\"346\":1}}],[\"远程代理\",{\"1\":{\"337\":1,\"342\":1}}],[\"安全控制等功能\",{\"1\":{\"345\":1}}],[\"安装路径打开\",{\"1\":{\"124\":1}}],[\"安装目录下\",{\"1\":{\"124\":1}}],[\"安装了\",{\"1\":{\"119\":1}}],[\"安装\",{\"0\":{\"107\":1}}],[\"安装editorconfig插件\",{\"1\":{\"65\":1}}],[\"安装证书\",{\"0\":{\"35\":1}}],[\"负载均衡\",{\"1\":{\"345\":1}}],[\"负责转发客户端的请求和目标服务器的响应\",{\"1\":{\"345\":1}}],[\"负责协调模型和视图之间的交互\",{\"1\":{\"325\":1}}],[\"负责创建和恢复\",{\"1\":{\"311\":1}}],[\"负责保存和管理\",{\"1\":{\"311\":1}}],[\"负责管理和协调各个用户\",{\"1\":{\"297\":1}}],[\"负责\",{\"1\":{\"178\":3}}],[\"客户端可以像使用实际对象一样使用代理对象\",{\"1\":{\"344\":1}}],[\"客户端代码不需要知道具体的产品类\",{\"1\":{\"257\":1}}],[\"客户端代码与子系统之间的耦合度降低\",{\"1\":{\"249\":1}}],[\"完了\",{\"1\":{\"338\":1,\"339\":1}}],[\"完成图像去噪任务\",{\"1\":{\"66\":1}}],[\"世界\",{\"1\":{\"338\":1,\"339\":1,\"386\":1,\"387\":5}}],[\"世界上的事情本来就是这样\",{\"1\":{\"114\":1}}],[\"世界上最大的电子图书馆\",{\"1\":{\"18\":1}}],[\"世界上最大的代码托管平台\",{\"1\":{\"18\":1}}],[\"秒钟\",{\"1\":{\"338\":1}}],[\"虽说很困难\",{\"1\":{\"369\":1}}],[\"虽说是重活\",{\"1\":{\"338\":1}}],[\"虽然多\",{\"1\":{\"516\":1}}],[\"虽然我们前面没有提到\",{\"1\":{\"501\":1}}],[\"虽然上面写完了词法分析器\",{\"1\":{\"448\":1}}],[\"虽然是int型\",{\"1\":{\"419\":1}}],[\"虽然标题是编译器\",{\"1\":{\"414\":1}}],[\"虽然接口是相同的\",{\"1\":{\"236\":1}}],[\"虽然可以从方法名中获得线索\",{\"1\":{\"199\":1}}],[\"虽然有时需要从零开始编写代码\",{\"1\":{\"199\":1}}],[\"虽然同时只能有一个线程执行\",{\"1\":{\"114\":1}}],[\"虽然在工业部署中表现出色\",{\"1\":{\"66\":1}}],[\"虽然实际效果貌似变化不大\",{\"1\":{\"6\":1}}],[\"虽然实际上也够\",{\"1\":{\"6\":1}}],[\"控制反转\",{\"1\":{\"385\":1}}],[\"控制访问\",{\"1\":{\"337\":1}}],[\"控制器\",{\"1\":{\"325\":1}}],[\"节省资源\",{\"1\":{\"337\":1}}],[\"代表了逻辑\",{\"1\":{\"504\":1}}],[\"代理可以用于缓存\",{\"1\":{\"345\":1}}],[\"代理服务器位于客户端和目标服务器之间\",{\"1\":{\"345\":1}}],[\"代理是一种常见的代理模式应用\",{\"1\":{\"345\":1}}],[\"代理\",{\"0\":{\"345\":1}}],[\"代理对象和实际对象实现相同的接口\",{\"1\":{\"344\":1}}],[\"代理对象可以在需要时才创建实际对象\",{\"1\":{\"337\":1}}],[\"代理模式的一个重要特点是透明性\",{\"1\":{\"344\":1}}],[\"代理模式通过代理对象来控制对实际对象的访问\",{\"1\":{\"343\":1}}],[\"代理模式通过引入代理对象来控制对实际对象的访问\",{\"1\":{\"342\":1}}],[\"代理模式主要用于控制对对象的访问\",{\"1\":{\"343\":1}}],[\"代理模式和委托模式虽然在某些方面有相似之处\",{\"1\":{\"343\":1}}],[\"代理与委托\",{\"0\":{\"343\":1}}],[\"代理人和本人的划分是为了实现职责分离和提高系统的灵活性\",{\"1\":{\"342\":1}}],[\"代理人\",{\"1\":{\"337\":2}}],[\"代码与全局的变量定义几乎一样\",{\"1\":{\"480\":1}}],[\"代码较多\",{\"1\":{\"447\":1}}],[\"代码如下\",{\"1\":{\"420\":1,\"423\":1,\"432\":1,\"467\":1,\"478\":1,\"487\":1,\"488\":1,\"490\":1}}],[\"代码段\",{\"1\":{\"419\":2}}],[\"代码\",{\"0\":{\"449\":1,\"470\":1,\"481\":1,\"491\":1,\"515\":1},\"1\":{\"418\":1,\"435\":1,\"463\":1,\"474\":1,\"485\":1,\"495\":1}}],[\"代码难免会有错误\",{\"1\":{\"411\":1}}],[\"代码优化\",{\"1\":{\"408\":1}}],[\"代码的生成\",{\"1\":{\"408\":1}}],[\"代码的阅读方法和修改方法\",{\"0\":{\"199\":1}}],[\"代码是否高效显得就不那么重要了\",{\"1\":{\"407\":1}}],[\"代码实现\",{\"0\":{\"251\":1}}],[\"代码示例\",{\"0\":{\"193\":1,\"232\":1,\"286\":1},\"1\":{\"286\":1}}],[\"代码复用\",{\"1\":{\"192\":1,\"278\":1,\"385\":1}}],[\"代码清单\",{\"1\":{\"178\":1,\"370\":1}}],[\"代码还能正常工作\",{\"1\":{\"132\":1}}],[\"代码仓库紧密集成\",{\"1\":{\"44\":1}}],[\"~a\",{\"1\":{\"505\":1}}],[\"~~~~~~~~~~~~~\",{\"1\":{\"332\":1}}],[\"~\",{\"1\":{\"331\":1,\"439\":1,\"447\":1,\"505\":2}}],[\"无条件地将当前的\",{\"1\":{\"424\":1}}],[\"无法将它们整合到一个类中\",{\"1\":{\"330\":1}}],[\"无论多好的教程\",{\"1\":{\"523\":1}}],[\"无论在\",{\"1\":{\"186\":1}}],[\"无论要增加多少个具体工厂\",{\"1\":{\"156\":1}}],[\"无论是读起来\",{\"1\":{\"522\":1}}],[\"无论是全局还是局部变量\",{\"1\":{\"500\":1}}],[\"无论是是否真的在全局中用到了这个变量\",{\"1\":{\"479\":1}}],[\"无论是函数的参数\",{\"1\":{\"477\":1}}],[\"无论是结果\",{\"1\":{\"114\":1}}],[\"无论是执行过程中\",{\"1\":{\"114\":1}}],[\"特别是在创建对象代价较高时\",{\"1\":{\"330\":1}}],[\"特别是重调了3\",{\"1\":{\"16\":1}}],[\"架构实现了视图和模型的松耦合\",{\"1\":{\"325\":1}}],[\"架构中得到了广泛应用\",{\"1\":{\"325\":1}}],[\"视图会自动更新\",{\"1\":{\"325\":1}}],[\"视图\",{\"1\":{\"325\":1}}],[\"先将全局变量的信息保存\",{\"1\":{\"479\":1}}],[\"先注册的\",{\"1\":{\"321\":1}}],[\"先介绍\",{\"1\":{\"69\":1}}],[\"被观察对象\",{\"1\":{\"321\":1}}],[\"被装饰物\",{\"1\":{\"235\":1,\"236\":1}}],[\"被装饰了多次\",{\"1\":{\"235\":1}}],[\"管理状态\",{\"2\":{\"314\":1,\"328\":1,\"373\":1}}],[\"管理和分享\",{\"1\":{\"44\":1}}],[\"序列化并保存到文件中\",{\"1\":{\"311\":1}}],[\"序的完全性\",{\"0\":{\"84\":1}}],[\"序的传递性\",{\"0\":{\"83\":1}}],[\"序的反对称性\",{\"0\":{\"82\":1}}],[\"序的定义\",{\"0\":{\"79\":1}}],[\"保存所有的标记流没有意义且浪费空间\",{\"1\":{\"438\":1}}],[\"保存在栈中\",{\"1\":{\"426\":1}}],[\"保存数据结构与基于数据结构进行处理是两种不同的概念\",{\"1\":{\"398\":1}}],[\"保存到文件中\",{\"1\":{\"311\":1}}],[\"保存过多的\",{\"1\":{\"309\":1}}],[\"保存历史记录\",{\"0\":{\"215\":1}}],[\"宽接口提供了对\",{\"1\":{\"308\":1}}],[\"宽接口\",{\"1\":{\"308\":1}}],[\"省略\",{\"1\":{\"306\":1,\"377\":1}}],[\"省时又省力\",{\"1\":{\"39\":1}}],[\"捕获和恢复对象的内部状态\",{\"1\":{\"304\":1}}],[\"迟早会暴露出问题\",{\"1\":{\"298\":1}}],[\"相应的减法的代码就不贴了\",{\"1\":{\"512\":1}}],[\"相应的值会存放在\",{\"1\":{\"509\":1}}],[\"相等\",{\"1\":{\"504\":1}}],[\"相同类型\",{\"1\":{\"512\":1}}],[\"相同\",{\"1\":{\"496\":1}}],[\"相对于表达式来说它还是较为容易的\",{\"1\":{\"485\":1}}],[\"相信这部分的知识能够很大程度上提高你的编程水平\",{\"1\":{\"521\":1}}],[\"相信这部分也不难理解\",{\"1\":{\"471\":1}}],[\"相信当你真正完成的时候会像我一样\",{\"1\":{\"410\":1}}],[\"相当于\",{\"1\":{\"422\":1}}],[\"相反\",{\"1\":{\"411\":1}}],[\"相互调用方法\",{\"1\":{\"298\":1}}],[\"相关\",{\"1\":{\"479\":1}}],[\"相关代码如下\",{\"1\":{\"445\":1}}],[\"相关的代码如下\",{\"1\":{\"476\":1}}],[\"相关的内容我们放到后面解释\",{\"1\":{\"464\":1}}],[\"相关的内容注释了\",{\"1\":{\"426\":1}}],[\"相关的是指令集\",{\"1\":{\"420\":1}}],[\"相关的设计模式\",{\"0\":{\"158\":1,\"168\":1,\"188\":1,\"206\":1,\"216\":1,\"227\":1,\"240\":1,\"271\":1,\"289\":1,\"300\":1,\"312\":1,\"326\":1,\"347\":1,\"371\":1,\"381\":1,\"403\":1}}],[\"相关设计模式\",{\"0\":{\"195\":1,\"253\":1,\"333\":1,\"355\":1,\"388\":1}}],[\"相关信息\",{\"1\":{\"49\":1,\"64\":1,\"108\":1,\"411\":1}}],[\"把处理分散在各个类中是不明智的\",{\"1\":{\"297\":1}}],[\"把握本质\",{\"1\":{\"115\":1}}],[\"仲裁者向组员下达指示\",{\"1\":{\"293\":1}}],[\"仲裁者会负责统一大家的意见\",{\"1\":{\"293\":1}}],[\"各个参数的位移量\",{\"1\":{\"477\":1}}],[\"各个类之间的依赖关系就会加强\",{\"1\":{\"367\":1}}],[\"各个小车有各个的体质\",{\"1\":{\"10\":1}}],[\"各种编程语言关于如何调用子函数有不同的约定\",{\"1\":{\"426\":1}}],[\"各种\",{\"0\":{\"346\":1}}],[\"各位\",{\"1\":{\"293\":1}}],[\"经常为此争执不下\",{\"1\":{\"293\":1}}],[\"经常会遇到需要使用一些现有的类\",{\"1\":{\"163\":1}}],[\"他们还十分在意编码细节\",{\"1\":{\"293\":1}}],[\"小于\",{\"1\":{\"508\":1}}],[\"小结\",{\"0\":{\"434\":1,\"450\":1,\"460\":1,\"471\":1,\"482\":1,\"492\":1,\"516\":1},\"1\":{\"417\":1,\"435\":1,\"453\":1,\"463\":1,\"474\":1,\"485\":1,\"495\":1}}],[\"小组中的\",{\"1\":{\"293\":1}}],[\"小车总是左右左摆头太蠢了\",{\"0\":{\"12\":1}}],[\"小车还未找到合适的\",{\"1\":{\"11\":1}}],[\"小车容易冲出轨道\",{\"0\":{\"11\":1}}],[\"小车左右轮力矩不一致\",{\"0\":{\"10\":1}}],[\"小车的原因\",{\"1\":{\"6\":1}}],[\"请自行查阅相关的资料\",{\"1\":{\"458\":1}}],[\"请跳过本章\",{\"1\":{\"406\":1}}],[\"请联系删除\",{\"1\":{\"406\":1,\"414\":1,\"417\":1,\"435\":1,\"453\":1,\"463\":1,\"474\":1,\"485\":1,\"495\":1,\"519\":1}}],[\"请注意\",{\"1\":{\"370\":1}}],[\"请设置时间\",{\"1\":{\"366\":1}}],[\"请试想一下\",{\"1\":{\"297\":1}}],[\"请试想一下要在\",{\"1\":{\"157\":1}}],[\"请大家一定要透彻理解此处的实例的多面性\",{\"1\":{\"370\":1}}],[\"请大家将情况报告给我\",{\"1\":{\"293\":1}}],[\"请大家想象一下一个乱糟糟的开发小组的工作状态\",{\"1\":{\"293\":1}}],[\"支持的标记\",{\"0\":{\"439\":1},\"1\":{\"435\":1}}],[\"支持多种遍历方式\",{\"1\":{\"284\":1}}],[\"支持实时预览和多种导出格式\",{\"1\":{\"124\":1}}],[\"统一接口\",{\"1\":{\"284\":1}}],[\"改变遍历算法\",{\"1\":{\"284\":1}}],[\"改变它的理由永远只有一个\",{\"1\":{\"138\":1}}],[\"集合对象和遍历算法分离\",{\"1\":{\"284\":1}}],[\"迭代器模式是一种行为设计模式\",{\"1\":{\"285\":1}}],[\"迭代器模式将遍历逻辑封装在迭代器对象中\",{\"1\":{\"284\":1}}],[\"迭代器模式提供了一种方法来顺序访问集合中的元素\",{\"1\":{\"284\":1}}],[\"迭代器模式\",{\"0\":{\"283\":1}}],[\"人民邮电出版社\",{\"1\":{\"274\":1}}],[\"人们发现经常需要异步操作共享资源的情况下\",{\"1\":{\"113\":1}}],[\"北京\",{\"1\":{\"274\":1}}],[\"北京邮电大学创新创业智能车循迹python版\",{\"0\":{\"4\":1}}],[\"杨文轩译\",{\"1\":{\"274\":1}}],[\"😃\",{\"1\":{\"274\":1}}],[\"😠\",{\"1\":{\"6\":1}}],[\"遂使用ts作为实现语言\",{\"1\":{\"274\":1}}],[\"遂放弃\",{\"1\":{\"12\":1,\"15\":1}}],[\"封装\",{\"1\":{\"274\":1}}],[\"面向对象编程可以帮助我们分散处理\",{\"1\":{\"297\":1}}],[\"面向对象三大特性\",{\"1\":{\"274\":1}}],[\"面向接口编程\",{\"1\":{\"142\":1}}],[\"移除那些不再被使用的对象\",{\"1\":{\"269\":1}}],[\"定期检查集合中的对象\",{\"1\":{\"269\":1}}],[\"定期清理\",{\"1\":{\"269\":1}}],[\"定义了变量\",{\"1\":{\"443\":1}}],[\"定义了接口\",{\"1\":{\"175\":1}}],[\"定义多个类\",{\"1\":{\"366\":1}}],[\"定义接口\",{\"1\":{\"366\":1}}],[\"定义接口或抽象类\",{\"1\":{\"143\":1}}],[\"定义抽象接口\",{\"1\":{\"144\":1}}],[\"定义乘法的运算规则\",{\"1\":{\"87\":1}}],[\"定义正自然数为非\",{\"1\":{\"80\":1}}],[\"定义\",{\"1\":{\"79\":1}}],[\"定义自然数的序即定义\",{\"1\":{\"79\":1}}],[\"定义加法的运算规则\",{\"1\":{\"71\":1}}],[\"定义dns解析器\",{\"1\":{\"30\":1}}],[\"引用计数\",{\"1\":{\"269\":1}}],[\"引入中介者模式\",{\"1\":{\"137\":1}}],[\"弱引用允许垃圾回收器在没有其他强引用时回收对象\",{\"1\":{\"269\":1}}],[\"弱引用\",{\"1\":{\"269\":1}}],[\"垃圾回收器可能会认为这些对象是垃圾\",{\"1\":{\"269\":1}}],[\"看了上面的代码\",{\"1\":{\"467\":1}}],[\"看看自己能走多远\",{\"1\":{\"407\":1}}],[\"看作是\",{\"1\":{\"268\":1,\"367\":1}}],[\"看起来是这样的\",{\"1\":{\"114\":1}}],[\"颜色\",{\"1\":{\"268\":2}}],[\"颜色信息应当放在哪个类中呢\",{\"1\":{\"267\":1}}],[\"外的寄存器\",{\"1\":{\"430\":1}}],[\"外在的\",{\"1\":{\"268\":1}}],[\"外观模式通过提供一个统一的接口来隐藏子系统的复杂性\",{\"1\":{\"250\":1}}],[\"外观模式有助于分层设计\",{\"1\":{\"249\":1}}],[\"外观模式为复杂的子系统提供了一个简单的接口\",{\"1\":{\"249\":1}}],[\"换句话说\",{\"1\":{\"460\":1}}],[\"换句话说就是不需要我们自己去实现了\",{\"1\":{\"432\":1}}],[\"换行符和空格类似\",{\"1\":{\"441\":1}}],[\"换行符\",{\"0\":{\"441\":1},\"1\":{\"435\":1}}],[\"换言之\",{\"1\":{\"268\":1,\"389\":1}}],[\"换成对应的版本\",{\"1\":{\"22\":1}}],[\"固有的\",{\"1\":{\"268\":1}}],[\"信息还是\",{\"1\":{\"268\":1}}],[\"信息这个问题\",{\"1\":{\"268\":1}}],[\"信息\",{\"1\":{\"268\":5}}],[\"信息量非常小\",{\"1\":{\"8\":1}}],[\"前缀形式\",{\"1\":{\"513\":1}}],[\"前文中我们说到\",{\"1\":{\"503\":1}}],[\"前文中我们定义了支持的类型\",{\"1\":{\"467\":1}}],[\"前言\",{\"0\":{\"406\":1},\"1\":{\"406\":2,\"414\":1,\"417\":1,\"435\":1,\"453\":1,\"463\":1,\"474\":1,\"485\":1,\"495\":1,\"519\":1}}],[\"前面提到的是否共享\",{\"1\":{\"268\":1}}],[\"前面讲到的\",{\"1\":{\"268\":1}}],[\"前端\",{\"1\":{\"28\":1}}],[\"形状\",{\"1\":{\"267\":1}}],[\"字符\",{\"1\":{\"446\":1,\"478\":2}}],[\"字符a对应的十六进制值是\",{\"1\":{\"444\":1}}],[\"字符串等等\",{\"1\":{\"497\":1}}],[\"字符串转换成标记流有时是有状态的\",{\"1\":{\"438\":1}}],[\"字符串\",{\"0\":{\"445\":1},\"1\":{\"435\":1}}],[\"字符的字体\",{\"1\":{\"267\":1}}],[\"字段吗\",{\"1\":{\"448\":1}}],[\"字段就是这个变量\",{\"1\":{\"368\":1}}],[\"字段即是类的两个层次结构的\",{\"1\":{\"178\":1}}],[\"字段中保存的是实现了\",{\"1\":{\"178\":1}}],[\"共享实例可以减少所需资源的使用量\",{\"1\":{\"270\":1}}],[\"共享\",{\"1\":{\"267\":1}}],[\"共有五条\",{\"1\":{\"69\":1}}],[\"符合开闭原则\",{\"1\":{\"257\":1,\"393\":1}}],[\"符合单一职责原则的类\",{\"1\":{\"140\":1}}],[\"降低了耦合性\",{\"1\":{\"257\":1}}],[\"降低类之间的耦合度\",{\"1\":{\"136\":1}}],[\"メール待っていますね\",{\"1\":{\"251\":1}}],[\"のページへようこそ\",{\"1\":{\"251\":1}}],[\"来实现运算符的优先级\",{\"1\":{\"516\":1}}],[\"来实现\",{\"1\":{\"506\":1}}],[\"来实现不同的猜拳策略\",{\"1\":{\"375\":1}}],[\"来保存一个表达式的类型\",{\"1\":{\"501\":1}}],[\"来表示退出\",{\"1\":{\"489\":1}}],[\"来表现这些依赖于操作系统的部分\",{\"1\":{\"186\":1}}],[\"来大致描述我们实现的\",{\"1\":{\"463\":1}}],[\"来压缩了源码字符串\",{\"1\":{\"439\":1}}],[\"来将字符串转换成标记流\",{\"1\":{\"437\":1}}],[\"来计算\",{\"1\":{\"433\":1}}],[\"来使用\",{\"1\":{\"370\":2}}],[\"来支持一次撤销操作\",{\"1\":{\"309\":1}}],[\"来存储共享对象\",{\"1\":{\"269\":1}}],[\"来简化与复杂子系统的交互\",{\"1\":{\"250\":1}}],[\"层与层之间通过外观类进行交互\",{\"1\":{\"249\":1}}],[\"更先进的版本是\",{\"1\":{\"522\":1}}],[\"更为重要的是\",{\"1\":{\"457\":1}}],[\"更多的标记\",{\"1\":{\"439\":1}}],[\"更易维护\",{\"1\":{\"393\":1}}],[\"更好的分层\",{\"1\":{\"249\":1}}],[\"更新代码的原生部分\",{\"1\":{\"108\":1}}],[\"增的操作\",{\"1\":{\"513\":1}}],[\"增强了代码的可扩展性\",{\"1\":{\"284\":1}}],[\"增强了代码的可维护性和可扩展性\",{\"1\":{\"249\":1}}],[\"增加\",{\"1\":{\"433\":1}}],[\"增加指令会消耗许多资源\",{\"1\":{\"426\":1}}],[\"增加计数\",{\"1\":{\"269\":1}}],[\"增加灵活性\",{\"1\":{\"203\":1}}],[\"增加后的功能可以被\",{\"1\":{\"186\":1}}],[\"增加了灵活性\",{\"1\":{\"385\":1}}],[\"增加了代码的灵活性和可维护性\",{\"1\":{\"284\":1}}],[\"增加了\",{\"1\":{\"178\":1}}],[\"增加新操作更容易\",{\"1\":{\"393\":1}}],[\"增加新的\",{\"1\":{\"398\":1}}],[\"增加新的产品类时\",{\"1\":{\"257\":1}}],[\"增加新的实现时\",{\"0\":{\"175\":1}}],[\"增加新的实现\",{\"1\":{\"130\":1}}],[\"增加新功能时\",{\"0\":{\"174\":1}}],[\"增加其它工厂\",{\"0\":{\"154\":1}}],[\"增加请求头和cookie的大小限制\",{\"1\":{\"30\":1}}],[\"松散耦合\",{\"1\":{\"249\":1}}],[\"简直痛苦地无话可说\",{\"1\":{\"523\":1}}],[\"简而言之\",{\"1\":{\"436\":1}}],[\"简化代码\",{\"1\":{\"284\":1,\"330\":1}}],[\"简化语法解析\",{\"1\":{\"278\":1}}],[\"简化接口\",{\"1\":{\"249\":1}}],[\"简单地说\",{\"1\":{\"486\":1}}],[\"简单地替换下算法即可进行测试\",{\"1\":{\"379\":1}}],[\"简单而言就是将一个复杂的大问题分解为多个小问题然后逐个解决\",{\"1\":{\"365\":1}}],[\"简单化\",{\"2\":{\"255\":1,\"302\":1}}],[\"简单来说\",{\"1\":{\"141\":1}}],[\"简单ppt\",{\"1\":{\"118\":1}}],[\"简单直接\",{\"1\":{\"56\":1}}],[\"啊\",{\"1\":{\"249\":1}}],[\"您能够掌握这些设计模式\",{\"1\":{\"246\":1}}],[\"您可以免费安装并使用\",{\"1\":{\"124\":1}}],[\"灵活应用于实际项目中\",{\"1\":{\"246\":1}}],[\"灵活性高\",{\"1\":{\"257\":1}}],[\"灵活性\",{\"1\":{\"231\":1,\"385\":1}}],[\"总共代码加注释1400行\",{\"1\":{\"409\":1}}],[\"总是互相指挥\",{\"1\":{\"293\":1}}],[\"总之\",{\"1\":{\"246\":1}}],[\"总结起来有如下两点\",{\"1\":{\"366\":1}}],[\"总结\",{\"0\":{\"148\":1,\"352\":1,\"519\":1},\"1\":{\"406\":1,\"414\":1,\"417\":1,\"435\":1,\"453\":1,\"463\":1,\"474\":1,\"485\":1,\"495\":1,\"519\":1}}],[\"父类控制算法的执行流程\",{\"1\":{\"385\":1}}],[\"父类和子类之间的一致性是指子类应当继承父类的行为和属性\",{\"1\":{\"242\":1}}],[\"父类和子类的一致性\",{\"0\":{\"242\":1}}],[\"父类的任务是通过声明抽象方法的方式定义接口\",{\"1\":{\"175\":1}}],[\"草莓味和猕猴桃三重口味\",{\"1\":{\"238\":1}}],[\"草莓冰激凌\",{\"1\":{\"238\":1}}],[\"亦或是香草味\",{\"1\":{\"238\":1}}],[\"冰激凌店只会准备各种香料\",{\"1\":{\"238\":1}}],[\"猕猴桃冰激凌等各种口味的冰激凌一样\",{\"1\":{\"238\":1}}],[\"巧克力冰激凌\",{\"1\":{\"238\":1}}],[\"去处理\",{\"1\":{\"236\":1}}],[\"去手动异步执行另一个协程\",{\"1\":{\"114\":1}}],[\"给\",{\"1\":{\"236\":1}}],[\"给一个健康的人注射吗啡是犯罪\",{\"1\":{\"115\":1}}],[\"委托者将某些任务委托给委托对象来执行\",{\"1\":{\"243\":1}}],[\"委托\",{\"1\":{\"236\":1}}],[\"委托是弱关联\",{\"0\":{\"187\":1}}],[\"功能需求总是在不断变化\",{\"1\":{\"399\":1}}],[\"功能则越多\",{\"1\":{\"236\":1}}],[\"功能层次结构与实现层次结构是混杂在一个层次结构中的\",{\"1\":{\"176\":1}}],[\"却没有发生任何变化\",{\"1\":{\"235\":1}}],[\"透明性\",{\"0\":{\"344\":1},\"1\":{\"235\":1}}],[\"职责扩展\",{\"1\":{\"231\":1}}],[\"职责分离\",{\"1\":{\"139\":1}}],[\"整个系列的一开始\",{\"1\":{\"520\":1}}],[\"整个系统就变得复杂了\",{\"1\":{\"422\":1}}],[\"整个系统都在该速度下运行\",{\"1\":{\"10\":1}}],[\"整个编译器还剩下最后两个部分\",{\"1\":{\"485\":1}}],[\"整个解析的过程和语法的\",{\"1\":{\"457\":1}}],[\"整个解析的过程是在不断对非终结符进行替换\",{\"1\":{\"456\":1}}],[\"整个团队的交流过程就变为了组员向仲裁者报告\",{\"1\":{\"293\":1}}],[\"整体的替换算法\",{\"2\":{\"383\":1}}],[\"整体\",{\"1\":{\"220\":1}}],[\"快照\",{\"1\":{\"215\":1}}],[\"动作\",{\"1\":{\"214\":1}}],[\"动态组合职责链\",{\"1\":{\"203\":1}}],[\"动态地扩展对象的行为\",{\"1\":{\"130\":1}}],[\"执行相反的增\",{\"1\":{\"513\":1}}],[\"执行\",{\"1\":{\"487\":1}}],[\"执行条件表达式\",{\"1\":{\"487\":1}}],[\"执行操作所需的参数\",{\"1\":{\"214\":1}}],[\"执行命令的对象\",{\"1\":{\"214\":1}}],[\"执行过程本身就是安全的\",{\"1\":{\"115\":1}}],[\"接下来开始解析函数定义相关的内容\",{\"1\":{\"476\":1}}],[\"接着是字符串常量\",{\"1\":{\"498\":1}}],[\"接着\",{\"1\":{\"419\":1}}],[\"接收\",{\"1\":{\"397\":2}}],[\"接收者包含了执行具体操作的逻辑\",{\"1\":{\"214\":1}}],[\"接收者\",{\"1\":{\"214\":1}}],[\"接口中定义了的方法\",{\"1\":{\"370\":2}}],[\"接口中增加了一个\",{\"1\":{\"369\":1}}],[\"接口中增加新的方法\",{\"1\":{\"369\":1}}],[\"接口中声明的所有方法都是\",{\"1\":{\"366\":1}}],[\"接口的类的实例\",{\"1\":{\"370\":2}}],[\"接口的\",{\"1\":{\"366\":1}}],[\"接口定义了\",{\"1\":{\"287\":2}}],[\"接口\",{\"1\":{\"235\":1,\"287\":2,\"338\":1,\"369\":1}}],[\"接口和抽象类\",{\"1\":{\"146\":1}}],[\"接口隔离原则\",{\"0\":{\"141\":1},\"1\":{\"148\":1}}],[\"接口分隔原则\",{\"1\":{\"127\":1,\"128\":1}}],[\"队列或者日志来参数化其他对象\",{\"1\":{\"210\":1}}],[\"推卸责任\",{\"1\":{\"202\":2},\"2\":{\"208\":1}}],[\"推荐做法\",{\"1\":{\"61\":1}}],[\"组员之间不再相互询问和相互指示\",{\"1\":{\"293\":1}}],[\"组件才具有高价\",{\"1\":{\"197\":1}}],[\"组合\",{\"0\":{\"145\":1},\"1\":{\"127\":1,\"128\":1,\"148\":1}}],[\"易于扩展\",{\"1\":{\"375\":1}}],[\"易于增加\",{\"0\":{\"400\":1}}],[\"易于增加新的状态\",{\"0\":{\"369\":1}}],[\"易于增加具体工厂\",{\"0\":{\"156\":1}}],[\"易于维护和扩展\",{\"1\":{\"197\":1}}],[\"■晚上\",{\"1\":{\"194\":1}}],[\"■从早上到下午\",{\"1\":{\"194\":1}}],[\"が作成されました\",{\"1\":{\"193\":1}}],[\"晚安\",{\"1\":{\"193\":1,\"194\":1}}],[\"晚上好\",{\"1\":{\"193\":1,\"194\":1}}],[\"晚上\",{\"1\":{\"193\":1,\"365\":1}}],[\"早上好\",{\"1\":{\"193\":1,\"194\":1}}],[\"问题\",{\"1\":{\"457\":1}}],[\"问题就被分解了\",{\"1\":{\"365\":1}}],[\"问题到底出在哪儿\",{\"1\":{\"112\":1}}],[\"问候\",{\"1\":{\"193\":1,\"194\":1}}],[\"发现是\",{\"1\":{\"457\":1}}],[\"发送者无需知道哪个对象会处理请求\",{\"1\":{\"203\":1,\"204\":1}}],[\"发送示例\",{\"0\":{\"52\":1}}],[\"发生变化的代码只有\",{\"1\":{\"187\":1}}],[\"才将\",{\"1\":{\"187\":1}}],[\"才与作为参数被传入的类构成关联\",{\"1\":{\"187\":1}}],[\"才能真正理解和掌握这些模式\",{\"1\":{\"246\":1}}],[\"才能正常看到渲染后的\",{\"1\":{\"119\":1}}],[\"才能透过现象\",{\"1\":{\"115\":1}}],[\"继承\",{\"1\":{\"274\":1}}],[\"继承和委托中的一致性\",{\"0\":{\"241\":1}}],[\"继承是强关联关系\",{\"1\":{\"187\":1}}],[\"继承是强关联\",{\"0\":{\"187\":1}}],[\"继续执行我们当前的任务\",{\"1\":{\"114\":1}}],[\"个字节\",{\"1\":{\"512\":1}}],[\"个字符或标记\",{\"1\":{\"450\":1}}],[\"个数等\",{\"1\":{\"482\":1}}],[\"个部分进行讲解\",{\"1\":{\"463\":1,\"474\":1}}],[\"个标记\",{\"1\":{\"457\":1}}],[\"个指令\",{\"1\":{\"422\":1}}],[\"个寄存器\",{\"1\":{\"420\":1}}],[\"个函数\",{\"1\":{\"416\":1}}],[\"个函数来实现了一个小的\",{\"1\":{\"409\":1}}],[\"个步骤\",{\"1\":{\"415\":1}}],[\"个实例则会有\",{\"1\":{\"298\":1}}],[\"个实例就会有\",{\"1\":{\"298\":1}}],[\"个实例\",{\"1\":{\"298\":3,\"352\":1}}],[\"个成员虽然一起协同工作\",{\"1\":{\"293\":1}}],[\"个操作系统上\",{\"1\":{\"186\":1}}],[\"个\",{\"1\":{\"186\":1}}],[\"个类的子类\",{\"1\":{\"156\":1}}],[\"角色公开足够多的信息\",{\"1\":{\"402\":1}}],[\"角色必须向\",{\"1\":{\"402\":1}}],[\"角色负责\",{\"1\":{\"400\":1}}],[\"角色即可\",{\"1\":{\"379\":1}}],[\"角色相关联的部分\",{\"1\":{\"369\":1}}],[\"角色就必须要知道\",{\"1\":{\"367\":1}}],[\"角色都需要或多或少地知道其他角色\",{\"1\":{\"367\":1}}],[\"角色都需要知道其他\",{\"1\":{\"367\":1}}],[\"角色后\",{\"1\":{\"367\":2}}],[\"角色的增加\",{\"1\":{\"401\":1}}],[\"角色的开发可以独立于\",{\"1\":{\"398\":1}}],[\"角色的接口\",{\"1\":{\"379\":1}}],[\"角色的独立性\",{\"1\":{\"367\":1}}],[\"角色的代码的同时\",{\"1\":{\"365\":1}}],[\"角色的类时\",{\"1\":{\"321\":1}}],[\"角色的划分具有重要意义\",{\"1\":{\"311\":1}}],[\"角色的意义\",{\"0\":{\"311\":1}}],[\"角色的\",{\"1\":{\"299\":2,\"367\":3}}],[\"角色的实例传递给\",{\"1\":{\"187\":1}}],[\"角色很难复用\",{\"1\":{\"299\":1}}],[\"角色可以复用\",{\"1\":{\"299\":1}}],[\"角色中都实现这个方法\",{\"1\":{\"369\":1}}],[\"角色中\",{\"1\":{\"367\":1}}],[\"角色中并没有任何依赖于特定对话框的代码\",{\"1\":{\"299\":1}}],[\"角色中即可\",{\"1\":{\"267\":1}}],[\"角色中的字段时\",{\"1\":{\"267\":1}}],[\"角色\",{\"0\":{\"400\":1,\"401\":1},\"1\":{\"186\":2,\"238\":1,\"321\":2,\"367\":2,\"398\":2,\"400\":2,\"401\":1}}],[\"版的\",{\"1\":{\"186\":1}}],[\"版\",{\"1\":{\"186\":5}}],[\"应当是谁来管理状态的迁移\",{\"0\":{\"367\":1}}],[\"应当共享的信息被称作\",{\"1\":{\"268\":1}}],[\"应当共享的信息和不应当共享的信息\",{\"1\":{\"268\":1}}],[\"应用程序中\",{\"1\":{\"316\":1}}],[\"应用程序在运行时很容易就会达到资源极限而导致崩溃\",{\"1\":{\"270\":1}}],[\"应用于软件所运行的操作系统上\",{\"1\":{\"186\":1}}],[\"应根据实际需求灵活应用设计模式\",{\"1\":{\"246\":1}}],[\"应该可以在不修改原模块的基础上\",{\"1\":{\"129\":1}}],[\"应该是硬件\",{\"1\":{\"6\":1}}],[\"分隔的变量\",{\"1\":{\"468\":1}}],[\"分别是\",{\"1\":{\"463\":1,\"474\":1}}],[\"分别是源地址和目标地址\",{\"1\":{\"422\":1}}],[\"分别如下\",{\"1\":{\"420\":1}}],[\"分析标识符的相关代码如下\",{\"1\":{\"443\":1}}],[\"分析整个\",{\"1\":{\"416\":1}}],[\"分析\",{\"1\":{\"408\":1}}],[\"分析方法为递归下降\",{\"1\":{\"279\":1}}],[\"分而治之\",{\"0\":{\"365\":1},\"1\":{\"297\":1,\"365\":1}}],[\"分开考虑\",{\"2\":{\"190\":1,\"383\":1}}],[\"分开后更容易扩展\",{\"0\":{\"186\":1}}],[\"分离关注点\",{\"1\":{\"393\":1}}],[\"分离开了\",{\"1\":{\"186\":1}}],[\"分离为两个独立的类层次结构\",{\"1\":{\"176\":1}}],[\"|add\",{\"1\":{\"512\":1}}],[\"|10\",{\"1\":{\"456\":1}}],[\"|9\",{\"1\":{\"456\":1}}],[\"|8\",{\"1\":{\"456\":1}}],[\"|5\",{\"1\":{\"456\":1}}],[\"|4\",{\"1\":{\"456\":1}}],[\"|<\",{\"1\":{\"443\":1,\"480\":1}}],[\"|token|hash|name|type|class|value|btype|bclass|bvalue|\",{\"1\":{\"443\":1}}],[\"|你好\",{\"1\":{\"387\":5}}],[\"||\",{\"1\":{\"233\":6,\"362\":1,\"419\":6,\"443\":5,\"444\":3,\"445\":1,\"447\":9,\"459\":1,\"480\":1,\"501\":1,\"503\":1,\"507\":1,\"509\":1,\"511\":2}}],[\"|+\",{\"1\":{\"233\":2,\"419\":3,\"496\":9}}],[\"|\",{\"1\":{\"184\":7,\"232\":2,\"233\":2,\"279\":9,\"353\":1,\"357\":1,\"387\":10,\"419\":4,\"430\":10,\"431\":1,\"437\":4,\"447\":3,\"455\":6,\"458\":5,\"464\":7,\"467\":2,\"475\":5,\"477\":9,\"478\":1,\"496\":12,\"512\":4}}],[\"|hello|\",{\"1\":{\"233\":1}}],[\"|hello\",{\"1\":{\"184\":7,\"387\":5}}],[\"|`\",{\"1\":{\"183\":1,\"386\":1}}],[\"桥梁\",{\"1\":{\"178\":1}}],[\"该标识符的类别\",{\"1\":{\"443\":1}}],[\"该标识符返回的标记\",{\"1\":{\"443\":1}}],[\"该地址中存放着\",{\"1\":{\"420\":1}}],[\"该实例会被当作\",{\"1\":{\"370\":2}}],[\"该实例通过\",{\"1\":{\"178\":1}}],[\"该方法中很容易发生\",{\"1\":{\"297\":1}}],[\"该类位于\",{\"1\":{\"178\":1}}],[\"该怎么办\",{\"1\":{\"114\":1}}],[\"试图教会我们的是如何构造\",{\"1\":{\"408\":1}}],[\"试程序行为的类\",{\"1\":{\"178\":1}}],[\"试证乘法交换律\",{\"1\":{\"91\":1}}],[\"试证加法交换律\",{\"1\":{\"75\":1}}],[\"试证\",{\"1\":{\"75\":2,\"77\":2,\"91\":2,\"94\":2}}],[\"两个概念\",{\"1\":{\"486\":1}}],[\"两个参数都无法取得了\",{\"1\":{\"431\":1}}],[\"两个状态\",{\"1\":{\"365\":1}}],[\"两个自然数\",{\"1\":{\"84\":1}}],[\"两种接口和可见性\",{\"0\":{\"308\":1}}],[\"两者之间必然会缺少联系\",{\"1\":{\"176\":1}}],[\"与前缀形式不同的是\",{\"1\":{\"513\":1}}],[\"与之不同\",{\"1\":{\"500\":1}}],[\"与语法分析相关的部分就是上文所说的优先级问题了\",{\"1\":{\"497\":1}}],[\"与存放在\",{\"1\":{\"477\":1}}],[\"与表示被装饰物的\",{\"1\":{\"235\":1}}],[\"与\",{\"0\":{\"268\":1},\"1\":{\"176\":1,\"186\":1,\"420\":1,\"426\":1,\"478\":1,\"522\":1}}],[\"与线程相比\",{\"1\":{\"113\":1}}],[\"章\",{\"1\":{\"175\":1,\"367\":1}}],[\"派生类\",{\"1\":{\"174\":1}}],[\"派生类应当可以替换基类并出现在基类能够出现的任何地方\",{\"1\":{\"132\":1}}],[\"之前\",{\"1\":{\"496\":1,\"509\":1}}],[\"之类的表达式要如何实现呢\",{\"1\":{\"500\":1}}],[\"之类的函数\",{\"1\":{\"432\":1}}],[\"之类的运算符是与参数顺序有关的\",{\"1\":{\"431\":1}}],[\"之间的关系是松耦合的\",{\"1\":{\"320\":1}}],[\"之间搭建桥梁\",{\"1\":{\"171\":1}}],[\"之后再计算运算符\",{\"1\":{\"496\":1}}],[\"之后\",{\"1\":{\"114\":1}}],[\"`not\",{\"1\":{\"514\":1}}],[\"`node\",{\"1\":{\"279\":1}}],[\"`ax`\",{\"1\":{\"500\":1}}],[\"`int\",{\"1\":{\"467\":1}}],[\"`winner\",{\"1\":{\"376\":2}}],[\"`warning\",{\"1\":{\"279\":2}}],[\"`record\",{\"1\":{\"362\":1}}],[\"`char\",{\"1\":{\"512\":1}}],[\"`call\",{\"1\":{\"362\":1}}],[\"`current\",{\"1\":{\"279\":1,\"305\":1}}],[\"`0$\",{\"1\":{\"362\":1}}],[\"`sizeof\",{\"1\":{\"499\":3}}],[\"`singleton\",{\"1\":{\"353\":1,\"357\":1}}],[\"`subscribing\",{\"1\":{\"294\":1}}],[\"`===\",{\"1\":{\"338\":1}}],[\"`====\",{\"1\":{\"305\":1}}],[\"`正在生成printer的实例\",{\"1\":{\"338\":1}}],[\"`graphobserver\",{\"1\":{\"317\":1}}],[\"`got\",{\"1\":{\"305\":1}}],[\"`digitobserver\",{\"1\":{\"317\":1}}],[\"`drawing\",{\"1\":{\"211\":1}}],[\"`publishing\",{\"1\":{\"294\":1}}],[\"`money\",{\"1\":{\"305\":1}}],[\"`message\",{\"1\":{\"294\":1}}],[\"`main`\",{\"1\":{\"448\":1}}],[\"`mailto\",{\"1\":{\"251\":1}}],[\"`making\",{\"1\":{\"251\":1}}],[\"`■$\",{\"1\":{\"193\":1}}],[\"`$\",{\"1\":{\"193\":2,\"204\":2,\"222\":2,\"223\":1,\"224\":1,\"258\":1,\"279\":1,\"331\":1,\"362\":2,\"394\":4}}],[\"`|$\",{\"1\":{\"183\":1,\"386\":1}}],[\"`\",{\"1\":{\"166\":4,\"193\":3,\"204\":6,\"211\":1,\"222\":2,\"223\":1,\"224\":1,\"251\":2,\"279\":5,\"294\":2,\"305\":6,\"317\":2,\"331\":5,\"338\":1,\"353\":1,\"357\":1,\"362\":3,\"376\":4,\"394\":4,\"467\":1,\"499\":3,\"512\":1,\"514\":1}}],[\"`<a\",{\"1\":{\"251\":1}}],[\"`<li>$\",{\"1\":{\"193\":1}}],[\"`<li><a\",{\"1\":{\"153\":1}}],[\"`<p>$\",{\"1\":{\"193\":1,\"251\":1}}],[\"`<\",{\"1\":{\"153\":2}}],[\"`<ul>`\",{\"1\":{\"153\":1}}],[\"`<hr><address>$\",{\"1\":{\"153\":1}}],[\"`<h1>$\",{\"1\":{\"153\":1,\"193\":1}}],[\"`<html><head><title>$\",{\"1\":{\"153\":1,\"193\":1,\"251\":1}}],[\"`<body>`\",{\"1\":{\"153\":1}}],[\"直至可以解决它们为止\",{\"1\":{\"365\":1}}],[\"直到真正用递归下降的方式实现了一个\",{\"1\":{\"522\":1}}],[\"直到遇到优先级\",{\"1\":{\"508\":1}}],[\"直到遇见了终结符\",{\"1\":{\"456\":1}}],[\"直到合并成起始的非终结符\",{\"1\":{\"454\":1}}],[\"直到匹配输入的终结符\",{\"1\":{\"454\":1}}],[\"直到实际图像加载完成\",{\"1\":{\"346\":1}}],[\"直到有一个对象能够处理它\",{\"1\":{\"204\":1}}],[\"直流12v\",{\"1\":{\"165\":1}}],[\"直接将对应的值用\",{\"1\":{\"500\":1}}],[\"直接从源代码编译成汇编代码是很困难的\",{\"1\":{\"437\":1}}],[\"直接证明比较困难\",{\"1\":{\"75\":1,\"91\":1}}],[\"直接取模\",{\"0\":{\"56\":1}}],[\"直接地创建各种图表\",{\"1\":{\"18\":1}}],[\"需求\",{\"1\":{\"165\":1}}],[\"需要两个字符\",{\"1\":{\"439\":1}}],[\"需要有参数\",{\"1\":{\"422\":1}}],[\"需要去理解程序运行中会有哪些状态\",{\"1\":{\"420\":1}}],[\"需要删除\",{\"1\":{\"367\":1}}],[\"需要注意这些\",{\"1\":{\"321\":1}}],[\"需要注意的是\",{\"1\":{\"309\":1,\"398\":1,\"424\":1}}],[\"需要根据具体需求来决定\",{\"1\":{\"310\":1}}],[\"需要根据具体需求来决定需要保存多少个\",{\"1\":{\"309\":1}}],[\"需要多少个\",{\"0\":{\"309\":1}}],[\"需要在不暴露对象实现细节的情况下保存对象状态\",{\"1\":{\"304\":1}}],[\"需要在对象状态变化时进行撤销操作\",{\"1\":{\"304\":1}}],[\"需要保存和恢复对象的多个状态\",{\"1\":{\"304\":1}}],[\"需要精挑细选\",{\"1\":{\"267\":1}}],[\"需要先将这个插件\",{\"1\":{\"119\":1}}],[\"需要先申请一个域名\",{\"1\":{\"26\":1}}],[\"需要创建配置文件\",{\"1\":{\"23\":1}}],[\"变更为不仅可以撤销\",{\"1\":{\"311\":1}}],[\"变更为可以多次撤销\",{\"1\":{\"311\":1}}],[\"变换装置\",{\"1\":{\"165\":1}}],[\"变量赋值\",{\"1\":{\"495\":1}}],[\"变量与函数调用\",{\"0\":{\"500\":1},\"1\":{\"495\":1,\"503\":1}}],[\"变量类型的表示\",{\"1\":{\"467\":1}}],[\"变量是\",{\"1\":{\"443\":1}}],[\"变量定义\",{\"0\":{\"463\":1},\"1\":{\"406\":1,\"414\":1,\"417\":1,\"435\":1,\"453\":1,\"463\":2,\"474\":2,\"485\":1,\"495\":1,\"519\":1}}],[\"变量balance的最终结果是0\",{\"1\":{\"114\":1}}],[\"变量的状态并不会进行同步\",{\"1\":{\"114\":1}}],[\"交给\",{\"1\":{\"402\":1}}],[\"交给子类\",{\"2\":{\"261\":1,\"391\":1}}],[\"交流100v\",{\"1\":{\"165\":1}}],[\"交替进行\",{\"1\":{\"112\":1}}],[\"类别信息在后面章节中解析\",{\"1\":{\"468\":1}}],[\"类必须提供用于获取每个目录条目的\",{\"1\":{\"402\":1}}],[\"类负责\",{\"1\":{\"402\":1}}],[\"类作为组件的独立性\",{\"1\":{\"398\":1}}],[\"类作为显示文件夹内容的\",{\"1\":{\"398\":1}}],[\"类作为中介者\",{\"1\":{\"297\":1}}],[\"类型的解析在前面的文章中我们已经很熟悉了\",{\"1\":{\"499\":1}}],[\"类型的注释\",{\"1\":{\"446\":1}}],[\"类型定义\",{\"1\":{\"467\":1}}],[\"类型\",{\"1\":{\"370\":2}}],[\"类来负责\",{\"1\":{\"367\":1}}],[\"类时\",{\"1\":{\"367\":1}}],[\"类变化为其他状态\",{\"1\":{\"367\":1}}],[\"类会调用\",{\"1\":{\"366\":1}}],[\"类会负责管理\",{\"1\":{\"267\":1}}],[\"类具有一致性\",{\"1\":{\"338\":1}}],[\"类具有相同的接口\",{\"1\":{\"235\":1}}],[\"类与\",{\"1\":{\"338\":1}}],[\"类则使用窄接口来保存和传递\",{\"1\":{\"308\":1}}],[\"类则不需要做任何修改\",{\"1\":{\"187\":1}}],[\"类使用宽接口来创建和恢复\",{\"1\":{\"308\":1}}],[\"类很难在其他对话框中被复用\",{\"1\":{\"299\":1}}],[\"类用于新的对话框中\",{\"1\":{\"299\":1}}],[\"类实现了实际进行状态迁移的\",{\"1\":{\"367\":1}}],[\"类实现了\",{\"1\":{\"287\":1}}],[\"类表示一个书架\",{\"1\":{\"287\":1}}],[\"类表示一个书籍对象\",{\"1\":{\"287\":1}}],[\"类是表示被装饰物的\",{\"1\":{\"235\":1}}],[\"类方法的地方和\",{\"1\":{\"199\":1}}],[\"类知道如何生成对象的具体表示\",{\"1\":{\"197\":1}}],[\"类知道如何构建复杂对象\",{\"1\":{\"197\":1}}],[\"类中声明一个\",{\"1\":{\"401\":1}}],[\"类中的以下两条语句\",{\"1\":{\"370\":1}}],[\"类中实现这个方法\",{\"1\":{\"369\":1}}],[\"类中用到的所有\",{\"1\":{\"267\":1}}],[\"类中使用的所有\",{\"1\":{\"267\":1}}],[\"类中\",{\"1\":{\"192\":1,\"267\":3,\"297\":1,\"299\":1,\"398\":1}}],[\"类和\",{\"1\":{\"187\":4,\"199\":1,\"299\":1,\"367\":1,\"369\":1,\"370\":1,\"398\":3,\"401\":1}}],[\"类生成\",{\"1\":{\"187\":1}}],[\"类继承了\",{\"1\":{\"178\":1}}],[\"类比\",{\"0\":{\"164\":1,\"165\":1}}],[\"类\",{\"1\":{\"157\":1,\"174\":1,\"178\":2,\"187\":3,\"199\":2,\"235\":1,\"269\":1,\"299\":1,\"366\":1,\"367\":2,\"369\":1,\"398\":1,\"401\":1}}],[\"类的兄弟类\",{\"1\":{\"401\":1}}],[\"类的层次与抽象类\",{\"0\":{\"389\":1}}],[\"类的层次结构的混杂和分离\",{\"0\":{\"176\":1}}],[\"类的层次结构的两个作用\",{\"0\":{\"173\":1}}],[\"类的构造函数中的\",{\"1\":{\"370\":1}}],[\"类的构造函数被传递给\",{\"1\":{\"178\":1}}],[\"类的构造了数中调用了\",{\"1\":{\"338\":1}}],[\"类的方法后具体会进行什么样的处理\",{\"1\":{\"199\":1}}],[\"类的方法的调用方法\",{\"1\":{\"199\":1}}],[\"类的代码就可以了\",{\"1\":{\"367\":1}}],[\"类的代码\",{\"1\":{\"199\":1,\"367\":1}}],[\"类的使用方法\",{\"1\":{\"199\":1}}],[\"类的实例并不重要\",{\"1\":{\"370\":1}}],[\"类的实例都带有相同的颜色\",{\"1\":{\"267\":1}}],[\"类的实例是被共享的\",{\"1\":{\"267\":1}}],[\"类的实例\",{\"1\":{\"187\":1,\"267\":1,\"338\":1,\"370\":1}}],[\"类的实例时\",{\"1\":{\"187\":1}}],[\"类的实例生成时\",{\"1\":{\"187\":1}}],[\"类的实现层次结构\",{\"1\":{\"171\":1,\"176\":1,\"178\":2,\"186\":3}}],[\"类的\",{\"1\":{\"178\":1,\"236\":1,\"267\":1,\"297\":1,\"366\":2,\"367\":1,\"368\":1,\"370\":1}}],[\"类的具体功能的实例\",{\"1\":{\"178\":1}}],[\"类的一览表\",{\"0\":{\"178\":1}}],[\"类的抽象方法时\",{\"1\":{\"175\":1}}],[\"类的子类中都实现这个方法\",{\"1\":{\"401\":1}}],[\"类的子类产生影响\",{\"1\":{\"199\":1}}],[\"类的子类\",{\"1\":{\"174\":1,\"235\":1}}],[\"类的功能层次结构\",{\"1\":{\"171\":1,\"176\":1,\"178\":4,\"186\":4}}],[\"类的设计原则有七个\",{\"1\":{\"127\":1}}],[\"类的多项式题目\",{\"1\":{\"54\":1}}],[\"方法本身有一定的要求\",{\"1\":{\"457\":1}}],[\"方法是为每个产生式\",{\"1\":{\"457\":1}}],[\"方法需要调用每个目录条目的\",{\"1\":{\"402\":1}}],[\"方法就会明白了\",{\"1\":{\"370\":1}}],[\"方法就使用了\",{\"1\":{\"367\":1}}],[\"方法传递\",{\"1\":{\"370\":2}}],[\"方法之间的关系\",{\"1\":{\"366\":1}}],[\"方法和\",{\"1\":{\"366\":1}}],[\"方法的调用方式如下\",{\"1\":{\"397\":2}}],[\"方法的调用顺序\",{\"1\":{\"321\":1}}],[\"方法的参数类型是\",{\"1\":{\"370\":2}}],[\"方法的线程安全性\",{\"1\":{\"357\":1}}],[\"方法而导致应用程序不能正常工作\",{\"1\":{\"321\":1}}],[\"方法后调用\",{\"1\":{\"321\":1}}],[\"方法会先被调用\",{\"1\":{\"321\":1}}],[\"方法中与函数定义相关的内容\",{\"1\":{\"475\":1}}],[\"方法中会用到的方法也都是在\",{\"1\":{\"370\":2}}],[\"方法中和\",{\"1\":{\"370\":1}}],[\"方法中的\",{\"1\":{\"370\":1}}],[\"方法中\",{\"1\":{\"321\":1,\"366\":1,\"370\":1}}],[\"方法中发生了\",{\"1\":{\"297\":1}}],[\"方法集中处理了所有消息的发布和订阅逻辑\",{\"1\":{\"297\":1}}],[\"方法稍微有些复杂\",{\"1\":{\"297\":1}}],[\"方法也调用了\",{\"1\":{\"236\":1}}],[\"方法调用了\",{\"1\":{\"236\":1}}],[\"方法\",{\"1\":{\"157\":1,\"178\":1,\"235\":1,\"287\":2,\"338\":1,\"356\":1,\"366\":3,\"367\":1,\"369\":1,\"401\":1,\"402\":2}}],[\"零件\",{\"1\":{\"157\":1}}],[\"包中\",{\"1\":{\"157\":1}}],[\"包中增加一个表示图像的\",{\"1\":{\"157\":1}}],[\"包中的抽象部分全部具体化即可\",{\"1\":{\"156\":1}}],[\"包括变量定义\",{\"1\":{\"467\":1}}],[\"包括\",{\"1\":{\"127\":1}}],[\"包括编程\",{\"1\":{\"50\":1}}],[\"容器与内容的一致性\",{\"2\":{\"229\":1,\"245\":1}}],[\"容器目录\",{\"0\":{\"47\":1}}],[\"容易\",{\"1\":{\"156\":1}}],[\"模型\",{\"1\":{\"325\":1}}],[\"模式提高了\",{\"1\":{\"398\":1}}],[\"模式编写象棋程序时\",{\"1\":{\"379\":1}}],[\"模式却特意将算法与其他部分分离开来\",{\"1\":{\"379\":1}}],[\"模式以及接口与类之间的关系\",{\"1\":{\"366\":1}}],[\"模式用类表示系统的\",{\"1\":{\"365\":1}}],[\"模式用于为某对象提供一个代理\",{\"1\":{\"337\":1}}],[\"模式确保一个类只有一个实例\",{\"1\":{\"351\":1}}],[\"模式是一种创建型设计模式\",{\"1\":{\"330\":1}}],[\"模式是一种结构型设计模式\",{\"1\":{\"263\":1}}],[\"模式来管理\",{\"1\":{\"305\":1}}],[\"模式来处理一系列的请求\",{\"1\":{\"204\":1}}],[\"模式了\",{\"1\":{\"298\":1}}],[\"模式共享实例可以减少使用\",{\"1\":{\"270\":1}}],[\"模式共享信息时必须仔细思考应当共享哪些信息\",{\"1\":{\"267\":1}}],[\"模式时\",{\"1\":{\"269\":1,\"365\":1}}],[\"模式非常有用\",{\"1\":{\"263\":1}}],[\"模式有以下几个好处\",{\"1\":{\"257\":1}}],[\"模式有以下几个优点\",{\"1\":{\"203\":1}}],[\"模式就是可以应对这种多功能对象的需求的一种模式\",{\"1\":{\"238\":1}}],[\"模式可以很容易地增加\",{\"1\":{\"400\":1,\"401\":1}}],[\"模式可以避免大量的条件语句\",{\"1\":{\"361\":1}}],[\"模式可以\",{\"1\":{\"330\":1}}],[\"模式可以显著减少内存消耗\",{\"1\":{\"263\":1}}],[\"模式可以为程序添加许多功能\",{\"1\":{\"238\":1}}],[\"模式可以将构建过程分解为多个步骤\",{\"1\":{\"192\":1}}],[\"模式使用了委托\",{\"1\":{\"236\":1}}],[\"模式一样\",{\"1\":{\"235\":1}}],[\"模式虽然与\",{\"1\":{\"235\":1}}],[\"模式允许对象在其内部状态改变时改变其行为\",{\"1\":{\"361\":1}}],[\"模式允许我们在不暴露对象实现细节的情况下保存和恢复对象的状态\",{\"1\":{\"305\":1}}],[\"模式允许你将对象组合成递归结构来表示\",{\"1\":{\"220\":1}}],[\"模式允许使用相同的构建过程来生成不同的对象表示\",{\"1\":{\"192\":1}}],[\"模式也支持可撤销的操作\",{\"1\":{\"210\":1}}],[\"模式将请求封装成对象\",{\"1\":{\"210\":1}}],[\"模式通过将构建过程与表示分离\",{\"1\":{\"198\":1}}],[\"模式通过将对象的构建过程与其表示分离\",{\"1\":{\"192\":1,\"197\":1}}],[\"模式中用到了委托\",{\"1\":{\"237\":1}}],[\"模式中也形成了类似于\",{\"1\":{\"235\":1}}],[\"模式中\",{\"1\":{\"235\":1,\"236\":1,\"256\":1,\"308\":1,\"311\":1,\"365\":1,\"366\":1,\"368\":1,\"392\":1,\"397\":1,\"402\":1}}],[\"模式中的方法调用关系\",{\"1\":{\"397\":1}}],[\"模式中的递归结构\",{\"1\":{\"235\":1}}],[\"模式中的\",{\"1\":{\"186\":1,\"366\":1}}],[\"模式中增加其他\",{\"1\":{\"369\":1}}],[\"模式中增加新的状态是非常简单的\",{\"1\":{\"369\":1}}],[\"模式中增加新的零件时应当如何做\",{\"1\":{\"157\":1}}],[\"模式中增加具体的工厂是非常容易的\",{\"1\":{\"156\":1}}],[\"模式的目的是将处理逻辑从数据结构中分离出来\",{\"1\":{\"398\":1}}],[\"模式的示例程序\",{\"1\":{\"376\":1}}],[\"模式的优势就会非常明显了\",{\"1\":{\"365\":1}}],[\"模式的实现需要特别注意线程安全问题\",{\"1\":{\"356\":1}}],[\"模式的主题是\",{\"1\":{\"267\":1}}],[\"模式的主要目的是为了定义一个算法的骨架\",{\"1\":{\"384\":1}}],[\"模式的主要目的是在不破坏封装性的前提下\",{\"1\":{\"304\":1}}],[\"模式的主要目的是通过添加装饰物来增加对象的功能\",{\"1\":{\"235\":1}}],[\"模式的主要目的是将抽象部分与实现部分分离\",{\"1\":{\"172\":1}}],[\"模式的一个缺点是会导致程序中增加许多功能类似的很小的类\",{\"1\":{\"239\":1}}],[\"模式的特征是将\",{\"1\":{\"186\":1}}],[\"模式的作用就是搭建这座桥梁\",{\"1\":{\"176\":1}}],[\"模式在\",{\"1\":{\"171\":1}}],[\"模式\",{\"0\":{\"171\":1,\"191\":1,\"192\":1,\"202\":1,\"209\":1,\"219\":1,\"230\":1,\"249\":1,\"256\":1,\"262\":1,\"263\":1,\"277\":1,\"292\":1,\"303\":1,\"304\":1,\"315\":1,\"329\":1,\"330\":1,\"336\":1,\"346\":1,\"350\":1,\"351\":1,\"360\":1,\"361\":1,\"374\":1,\"384\":1,\"385\":1,\"392\":1,\"393\":1},\"1\":{\"158\":4,\"175\":1,\"188\":3,\"195\":4,\"202\":1,\"206\":2,\"216\":3,\"220\":1,\"227\":3,\"240\":2,\"253\":3,\"257\":1,\"271\":3,\"289\":3,\"300\":2,\"312\":3,\"326\":1,\"333\":5,\"347\":2,\"351\":1,\"355\":4,\"367\":2,\"368\":1,\"369\":2,\"371\":2,\"379\":1,\"380\":1,\"381\":3,\"388\":2,\"403\":3}}],[\"模块化设计\",{\"1\":{\"139\":1}}],[\"拓展思路的要点\",{\"0\":{\"155\":1,\"185\":1,\"196\":1,\"213\":1,\"234\":1,\"266\":1,\"296\":1,\"307\":1,\"319\":1,\"340\":1,\"364\":1,\"378\":1,\"396\":1}}],[\"划分\",{\"0\":{\"311\":1},\"1\":{\"154\":1}}],[\"超链接集合的文件\",{\"1\":{\"154\":1}}],[\"<unit>\",{\"1\":{\"512\":2}}],[\"<ul>\",{\"1\":{\"153\":5,\"193\":1}}],[\"<false\",{\"1\":{\"487\":2}}],[\"<factor>11\",{\"1\":{\"456\":1}}],[\"<factor>3\",{\"1\":{\"456\":1}}],[\"<factor><factor>\",{\"1\":{\"455\":1}}],[\"<factor>\",{\"1\":{\"455\":2,\"456\":2,\"457\":2,\"458\":3}}],[\"<true\",{\"1\":{\"487\":2}}],[\"<term\",{\"1\":{\"458\":3}}],[\"<term>7\",{\"1\":{\"456\":1}}],[\"<term>或\",{\"1\":{\"455\":1}}],[\"<term><term>\",{\"1\":{\"455\":1}}],[\"<term>\",{\"1\":{\"455\":6,\"456\":2,\"457\":2,\"458\":3}}],[\"<cond>\",{\"1\":{\"487\":3,\"488\":2}}],[\"<command>\",{\"1\":{\"279\":6}}],[\"<command\",{\"1\":{\"279\":8}}],[\"<empty\",{\"1\":{\"486\":1}}],[\"<empty><factor>\",{\"1\":{\"458\":1}}],[\"<empty><term>\",{\"1\":{\"458\":1}}],[\"<expr2>normal\",{\"1\":{\"512\":1}}],[\"<expr2>\",{\"1\":{\"511\":4,\"512\":6}}],[\"<expr1>push\",{\"1\":{\"512\":1}}],[\"<expr1>\",{\"1\":{\"511\":4,\"512\":4}}],[\"<expr\",{\"1\":{\"458\":3}}],[\"<expr>2\",{\"1\":{\"456\":1}}],[\"<expr>\",{\"1\":{\"455\":7,\"456\":4,\"457\":2,\"458\":2,\"504\":1,\"505\":1}}],[\"<>\",{\"1\":{\"455\":1}}],[\"<offset>\",{\"1\":{\"430\":1}}],[\"<size>\",{\"1\":{\"427\":1,\"428\":2}}],[\"<statement>\",{\"1\":{\"486\":4,\"487\":2,\"488\":2,\"490\":1}}],[\"<string\",{\"1\":{\"416\":1}}],[\"<stdlib\",{\"1\":{\"416\":1,\"459\":1}}],[\"<stdio\",{\"1\":{\"416\":1,\"442\":1,\"459\":1}}],[\"<num>\",{\"1\":{\"422\":2}}],[\"<number>\",{\"1\":{\"279\":3}}],[\"<memory\",{\"1\":{\"416\":1}}],[\"<<\",{\"1\":{\"386\":1,\"387\":1,\"431\":1,\"447\":1,\"512\":1}}],[\"<=\",{\"1\":{\"362\":2,\"416\":1,\"431\":1,\"443\":5,\"444\":6,\"447\":1,\"448\":2,\"459\":2}}],[\"<left>\",{\"1\":{\"279\":1}}],[\"<li><a\",{\"1\":{\"153\":5}}],[\"<li>\",{\"1\":{\"153\":4}}],[\"<right>\",{\"1\":{\"279\":1}}],[\"<repeat\",{\"1\":{\"279\":6}}],[\"<go>\",{\"1\":{\"279\":1}}],[\"<product>object\",{\"1\":{\"331\":1}}],[\"<program>\",{\"1\":{\"279\":3}}],[\"<primitive\",{\"1\":{\"279\":6}}],[\"<p>メール待っていますね\",{\"1\":{\"252\":1}}],[\"<p>hiroshi\",{\"1\":{\"252\":1}}],[\"<addr>pushsc\",{\"1\":{\"509\":1}}],[\"<addr>lc\",{\"1\":{\"509\":1}}],[\"<addr>li\",{\"1\":{\"503\":1}}],[\"<addr>\",{\"1\":{\"424\":3,\"426\":2,\"500\":1,\"502\":1}}],[\"<a\",{\"1\":{\"252\":1}}],[\"<h1>welcome\",{\"1\":{\"252\":1}}],[\"<h1>linkpage<\",{\"1\":{\"153\":1}}],[\"<html><head><title>问候<\",{\"1\":{\"194\":1}}],[\"<html><head><title>linkpage<\",{\"1\":{\"153\":1}}],[\"<hr><address>gmw<\",{\"1\":{\"153\":1}}],[\"<body>\",{\"1\":{\"153\":1}}],[\"<\",{\"1\":{\"153\":14,\"179\":1,\"183\":1,\"193\":6,\"194\":5,\"204\":2,\"211\":1,\"232\":2,\"251\":5,\"252\":5,\"279\":1,\"286\":1,\"305\":2,\"317\":2,\"338\":1,\"362\":4,\"376\":4,\"386\":2,\"394\":1,\"416\":1,\"430\":1,\"431\":1,\"447\":3,\"477\":1,\"512\":3,\"514\":1}}],[\"扩展性强\",{\"1\":{\"257\":1}}],[\"扩展性\",{\"1\":{\"152\":1}}],[\"扩展其功能\",{\"1\":{\"129\":1}}],[\"解决了优先级的问题\",{\"1\":{\"508\":1}}],[\"解决方法\",{\"1\":{\"433\":1}}],[\"解析表达式\",{\"1\":{\"495\":1,\"516\":1}}],[\"解析函数的参数就是解析以逗号分隔的一个个标识符\",{\"1\":{\"479\":1}}],[\"解析函数的定义\",{\"0\":{\"476\":1},\"1\":{\"474\":1}}],[\"解析参数\",{\"0\":{\"479\":1},\"1\":{\"474\":1}}],[\"解析变量的定义\",{\"0\":{\"465\":1},\"1\":{\"463\":1}}],[\"解析为\",{\"1\":{\"439\":3}}],[\"解释器需要我们实现自己的虚拟机与指令集\",{\"1\":{\"414\":1}}],[\"解释器与编译器仅在代码生成阶段有区别\",{\"1\":{\"414\":1}}],[\"解释器\",{\"1\":{\"417\":1,\"419\":1},\"2\":{\"413\":1,\"452\":1,\"462\":1,\"473\":1,\"484\":1,\"494\":1,\"518\":1,\"526\":1}}],[\"解释器模式\",{\"1\":{\"278\":1}}],[\"解释器就自动释放gil锁\",{\"1\":{\"112\":1}}],[\"解耦框架与生成的实例\",{\"1\":{\"330\":1}}],[\"解耦集合和遍历\",{\"1\":{\"284\":1}}],[\"解耦创建和使用\",{\"1\":{\"257\":1}}],[\"解耦请求发送者和接收者\",{\"1\":{\"203\":1}}],[\"解耦\",{\"1\":{\"152\":1}}],[\"抽象条目类\",{\"0\":{\"223\":1}}],[\"抽象类声明了一些抽象方法\",{\"1\":{\"175\":1}}],[\"抽象类\",{\"1\":{\"154\":1,\"199\":1}}],[\"抽象容器\",{\"1\":{\"153\":1}}],[\"抽象html页面\",{\"1\":{\"153\":1}}],[\"抽象超链接\",{\"1\":{\"153\":1}}],[\"抽象零件\",{\"1\":{\"153\":1}}],[\"抽象工厂\",{\"1\":{\"153\":1}}],[\"抽象工厂模式通过将对象的创建过程抽象化\",{\"1\":{\"152\":1}}],[\"抽象工厂模式使得一个类的实例化延迟到其子类\",{\"1\":{\"152\":1}}],[\"抽象工厂模式提供一个接口\",{\"1\":{\"152\":1}}],[\"抽象工厂模式\",{\"0\":{\"151\":1}}],[\"抽象不应该依赖细节\",{\"1\":{\"142\":1}}],[\"优先级大于\",{\"1\":{\"496\":1}}],[\"优先级\",{\"1\":{\"496\":2,\"508\":1}}],[\"优先级关心的就是哪个运算符先计算\",{\"1\":{\"496\":1}}],[\"优先级高于加法\",{\"1\":{\"496\":1}}],[\"优先使用组合\",{\"1\":{\"148\":1}}],[\"优点是这种处理方式将\",{\"1\":{\"367\":1}}],[\"优雅的解决方案\",{\"1\":{\"1\":1}}],[\"聚合\",{\"1\":{\"145\":1,\"148\":1}}],[\"聚合复用原则\",{\"0\":{\"145\":1},\"1\":{\"127\":1,\"128\":1,\"148\":1}}],[\"核心思想是\",{\"1\":{\"142\":1}}],[\"细节应该依赖抽象\",{\"1\":{\"142\":1}}],[\"二是如何将表达式编译成目标代码\",{\"1\":{\"495\":1}}],[\"二是容易中间运算时搞错运算顺序\",{\"1\":{\"56\":1}}],[\"二元运算符\",{\"0\":{\"508\":1},\"1\":{\"495\":1}}],[\"二选一\",{\"1\":{\"433\":1}}],[\"二者都依赖抽象\",{\"1\":{\"148\":1}}],[\"二者都应该依赖其抽象\",{\"1\":{\"142\":1}}],[\"高速但计算上可能有\",{\"1\":{\"380\":1}}],[\"高层模块不依赖低层模块\",{\"1\":{\"148\":1}}],[\"高层模块不应该依赖低层模块\",{\"1\":{\"142\":1}}],[\"高层模块依赖抽象接口\",{\"1\":{\"144\":1}}],[\"高版本\",{\"1\":{\"66\":1}}],[\"显示一些东西\",{\"1\":{\"178\":1}}],[\"显示\",{\"1\":{\"178\":2}}],[\"显示用户信息逻辑\",{\"1\":{\"140\":2}}],[\"显得代码冗长\",{\"1\":{\"57\":1}}],[\"注释\",{\"0\":{\"446\":1},\"1\":{\"435\":1}}],[\"注册逻辑\",{\"1\":{\"140\":2}}],[\"注意这里并不是四则运算中的加减法\",{\"1\":{\"506\":1}}],[\"注意这里的类型\",{\"1\":{\"419\":1}}],[\"注意我们的之前的程序需要指令一个源文件\",{\"1\":{\"433\":1}}],[\"注意的是自增自减操作的优先级是和它的位置有关的\",{\"1\":{\"507\":1}}],[\"注意的是只支持\",{\"1\":{\"499\":1}}],[\"注意的是\",{\"1\":{\"429\":1}}],[\"注意的是pc在初始应指向目标代码中的main函数\",{\"1\":{\"420\":1}}],[\"注意的是由于栈是位于高地址并向低地址增长的\",{\"1\":{\"420\":1}}],[\"注意不要让变量的值之间互相矛盾\",{\"1\":{\"368\":1}}],[\"注意\",{\"1\":{\"108\":1}}],[\"登录逻辑\",{\"1\":{\"140\":2}}],[\"避免重复代码\",{\"1\":{\"385\":1}}],[\"避免重复初始化对象的复杂过程\",{\"1\":{\"330\":1}}],[\"避免处理过于集中\",{\"1\":{\"297\":1}}],[\"避免浪费\",{\"2\":{\"273\":1,\"349\":1}}],[\"避免高层模块直接依赖具体类\",{\"1\":{\"143\":1}}],[\"避免不必要的外部依赖\",{\"1\":{\"137\":1}}],[\"避免了多线程的上下文切换\",{\"1\":{\"113\":1}}],[\"限制公开方法\",{\"1\":{\"137\":1}}],[\"隐藏系统的复杂性\",{\"1\":{\"137\":1}}],[\"示例程序的前提是\",{\"1\":{\"338\":1}}],[\"示例程序中的\",{\"1\":{\"297\":1}}],[\"示例程序\",{\"0\":{\"166\":1,\"376\":1},\"1\":{\"165\":1}}],[\"示例代码\",{\"0\":{\"153\":1,\"177\":1,\"204\":1,\"211\":1,\"221\":1,\"250\":1,\"258\":1,\"279\":1,\"294\":1,\"305\":1,\"317\":1,\"331\":1,\"353\":1,\"362\":1,\"386\":1,\"394\":1}}],[\"示例\",{\"0\":{\"134\":1,\"140\":1,\"144\":1,\"147\":1}}],[\"返回类型应与父类相同或是其子类型\",{\"1\":{\"133\":1}}],[\"遵循开闭原则\",{\"1\":{\"231\":1}}],[\"遵循行为一致性\",{\"1\":{\"133\":1}}],[\"遵循契约\",{\"1\":{\"133\":1}}],[\"遵循单一职责原则\",{\"1\":{\"130\":1}}],[\"确保同一工厂创建的一系列对象具有一致的接口和行为\",{\"1\":{\"152\":1}}],[\"确保每个模块只负责一个功能\",{\"1\":{\"139\":1}}],[\"确保每个类只有一个职责\",{\"1\":{\"130\":1}}],[\"确保子类实现父类的抽象方法\",{\"1\":{\"133\":1}}],[\"实例的多面性\",{\"0\":{\"370\":1}}],[\"实例代码\",{\"0\":{\"264\":1,\"338\":1}}],[\"实例\",{\"1\":{\"235\":1}}],[\"实现起来并不是太难\",{\"1\":{\"522\":1}}],[\"实现起来也更直观\",{\"1\":{\"464\":1}}],[\"实现四则运算来讲解优先级问题\",{\"1\":{\"496\":1}}],[\"实现如下\",{\"1\":{\"424\":1,\"425\":1,\"427\":1,\"428\":1,\"430\":1,\"431\":1}}],[\"实现一个功能完善的\",{\"1\":{\"409\":1}}],[\"实现也很复杂\",{\"0\":{\"408\":1}}],[\"实现了\",{\"1\":{\"370\":2}}],[\"实现具体方法\",{\"1\":{\"366\":1}}],[\"实现的代码示例\",{\"1\":{\"317\":1}}],[\"实现迭代器模式\",{\"0\":{\"285\":1},\"1\":{\"285\":1}}],[\"实现显示\",{\"1\":{\"267\":1}}],[\"实现\",{\"1\":{\"178\":1}}],[\"实现方法\",{\"0\":{\"130\":1,\"133\":1,\"137\":1,\"139\":1,\"143\":1,\"146\":1}}],[\"实际中可以自己指定\",{\"1\":{\"456\":1}}],[\"实际计算机中\",{\"1\":{\"434\":1}}],[\"实际调用该方法的却是扮演\",{\"1\":{\"367\":1}}],[\"实际上\",{\"1\":{\"496\":1}}],[\"实际上我们也不能使用递归\",{\"1\":{\"464\":1}}],[\"实际上又是别的物体的\",{\"1\":{\"235\":1}}],[\"实际上只能并发\",{\"1\":{\"6\":1}}],[\"实际需求\",{\"1\":{\"165\":1}}],[\"违反其中一个原则\",{\"1\":{\"128\":1}}],[\"七大原则之间并不是相互孤立的\",{\"1\":{\"128\":1}}],[\"单元运算符往往没有这个问题\",{\"1\":{\"496\":1}}],[\"单一职责原则\",{\"0\":{\"138\":1},\"1\":{\"127\":1,\"128\":1,\"148\":1}}],[\"单核处理器还是同时间只能做一件事\",{\"1\":{\"113\":1}}],[\"单核处理器本来就没法同时处理两件事情\",{\"1\":{\"111\":1}}],[\"单核同时间内只能有一个线程运行\",{\"1\":{\"111\":1}}],[\"迪米特原则\",{\"0\":{\"135\":1,\"136\":1},\"1\":{\"127\":1,\"128\":1,\"148\":1}}],[\"里氏代换原则规定子类不得重写父类的普通方法\",{\"1\":{\"132\":1}}],[\"里氏代换原则\",{\"0\":{\"131\":1,\"132\":1},\"1\":{\"127\":1,\"128\":1,\"148\":1}}],[\"开始的冲动过了之后\",{\"1\":{\"523\":1}}],[\"开头\",{\"1\":{\"442\":1}}],[\"开闭原则是面向对象可复用设计的基石\",{\"1\":{\"128\":1}}],[\"开闭原则\",{\"0\":{\"129\":1,\"399\":1},\"1\":{\"127\":1,\"128\":1,\"148\":1}}],[\"开发过程将会变得非常困难\",{\"1\":{\"399\":1}}],[\"开发人员可以在编写一个\",{\"1\":{\"365\":1}}],[\"开发团队可以更容易地构建\",{\"1\":{\"44\":1}}],[\"开发者可以方便地将他们的容器镜像与代码仓库关联起来\",{\"1\":{\"44\":1}}],[\"转换成对应的汇编代码\",{\"1\":{\"477\":1}}],[\"转载声明\",{\"0\":{\"417\":1}}],[\"转载工具\",{\"1\":{\"406\":1}}],[\"转给另外一个人\",{\"1\":{\"202\":1}}],[\"转\",{\"0\":{\"126\":1}}],[\"转而使用\",{\"1\":{\"119\":1}}],[\"转而实验机械臂放置障碍在赛道上\",{\"1\":{\"15\":1}}],[\"启动\",{\"1\":{\"124\":1}}],[\"启动项目\",{\"0\":{\"32\":1}}],[\"等工具\",{\"1\":{\"522\":1}}],[\"等工具来编写\",{\"1\":{\"411\":1}}],[\"等指令\",{\"1\":{\"422\":1}}],[\"等\",{\"1\":{\"411\":1,\"439\":1,\"443\":1,\"445\":1,\"448\":1}}],[\"等等知识\",{\"1\":{\"521\":1}}],[\"等等\",{\"1\":{\"408\":1,\"439\":1,\"500\":1}}],[\"等待显示序列号\",{\"1\":{\"124\":1}}],[\"等待提示\",{\"1\":{\"124\":1}}],[\"等函数\",{\"1\":{\"58\":1}}],[\"以减少语法分析器的复杂程度\",{\"1\":{\"436\":1}}],[\"以上就是我们为了实现函数调用需要的指令了\",{\"1\":{\"430\":1}}],[\"以二进制的形式保存在内存中\",{\"1\":{\"418\":1}}],[\"以前人们会说\",{\"1\":{\"407\":1}}],[\"以实现\",{\"1\":{\"366\":1}}],[\"以确保在多线程环境下\",{\"1\":{\"357\":1}}],[\"以控制对该对象的访问\",{\"1\":{\"337\":1}}],[\"以避免循环依赖和无限递归\",{\"1\":{\"322\":1}}],[\"以释放资源\",{\"1\":{\"310\":1}}],[\"以支持多次撤销操作\",{\"1\":{\"309\":1}}],[\"以支持多种遍历方式\",{\"1\":{\"284\":1}}],[\"以支持撤销和重做操作\",{\"1\":{\"215\":1}}],[\"以下是\",{\"1\":{\"317\":1}}],[\"以下是示例代码\",{\"1\":{\"305\":1}}],[\"以下是实现迭代器模式的\",{\"1\":{\"286\":1}}],[\"以下是实现保存历史记录的一些常见方法\",{\"1\":{\"215\":1}}],[\"以下是一些常见的解决方案\",{\"1\":{\"269\":1}}],[\"以便从后向前遍历书籍\",{\"1\":{\"288\":1}}],[\"以便重复使用这些对象\",{\"1\":{\"269\":1}}],[\"以便在需要时恢复到之前的状态\",{\"1\":{\"215\":1}}],[\"以便在需要时进行撤销操作\",{\"1\":{\"214\":1}}],[\"以保持我们的知识体系与时俱进\",{\"1\":{\"246\":1}}],[\"以示例程序来说\",{\"1\":{\"236\":1,\"369\":1}}],[\"以供后面的处理使用\",{\"1\":{\"178\":1}}],[\"以管理员身份在\",{\"1\":{\"124\":1}}],[\"以及该函数在代码段\",{\"1\":{\"476\":1}}],[\"以及从文件中读取并反序列化\",{\"1\":{\"311\":1}}],[\"以及\",{\"1\":{\"235\":1}}],[\"以及它的子类\",{\"1\":{\"235\":1}}],[\"以及测试完小车后保护小车也是很重要的\",{\"1\":{\"10\":1}}],[\"以及没考虑到gil会影响介么大\",{\"1\":{\"6\":1}}],[\"复杂对象的创建\",{\"1\":{\"192\":1}}],[\"复杂演示推荐\",{\"1\":{\"117\":1}}],[\"复制到\",{\"1\":{\"124\":1}}],[\"密码\",{\"1\":{\"124\":1}}],[\"百度网盘\",{\"1\":{\"124\":1}}],[\"官网\",{\"1\":{\"124\":1}}],[\"适用于需要保存复杂对象状态的场景\",{\"1\":{\"215\":1}}],[\"适用于需要按顺序执行和撤销命令的场景\",{\"1\":{\"215\":1}}],[\"适用于编写笔记\",{\"1\":{\"124\":1}}],[\"适配器\",{\"1\":{\"165\":1}}],[\"适配器模式通过创建一个适配器类\",{\"1\":{\"163\":1}}],[\"适配器模式使得原本由于接口不兼容而不能一起工作的那些类可以一起工作\",{\"1\":{\"162\":1}}],[\"适配器模式\",{\"0\":{\"161\":1,\"162\":1},\"1\":{\"162\":1}}],[\"适合快速迭代和原型验证\",{\"1\":{\"66\":1}}],[\"编程有趣又无趣\",{\"1\":{\"524\":1}}],[\"编程语言的选择\",{\"0\":{\"6\":1}}],[\"编译时加上\",{\"1\":{\"433\":1}}],[\"编译程序\",{\"1\":{\"433\":1}}],[\"编译器中我们需要用到的函数有\",{\"1\":{\"432\":1}}],[\"编译器的语法分析部分其实是很简单的\",{\"1\":{\"492\":1}}],[\"编译器的输出\",{\"1\":{\"434\":1}}],[\"编译器的编写分为\",{\"1\":{\"415\":1}}],[\"编译器的构建流程\",{\"0\":{\"415\":1},\"1\":{\"414\":1}}],[\"编译器框架\",{\"0\":{\"416\":1},\"1\":{\"414\":1}}],[\"编译器\",{\"1\":{\"417\":1},\"2\":{\"413\":1,\"452\":1,\"462\":1,\"473\":1,\"484\":1,\"494\":1,\"518\":1,\"526\":1}}],[\"编译器生成器\",{\"1\":{\"408\":1}}],[\"编译原理\",{\"1\":{\"407\":1,\"408\":3,\"411\":1,\"417\":1},\"2\":{\"412\":1,\"451\":1,\"461\":1,\"472\":1,\"483\":1,\"493\":1,\"517\":1,\"525\":1}}],[\"编译原理相关\",{\"0\":{\"125\":1}}],[\"编写编译器时遇到的一些难题\",{\"1\":{\"519\":1}}],[\"编写语法分析器有两种方法\",{\"1\":{\"454\":1}}],[\"编写一个\",{\"1\":{\"369\":1}}],[\"编写一个反向迭代器\",{\"1\":{\"288\":1}}],[\"编写出更加健壮和优雅的代码\",{\"1\":{\"246\":1}}],[\"编辑器\",{\"1\":{\"124\":1}}],[\"教程源码示例\",{\"1\":{\"246\":1,\"274\":1}}],[\"教程\",{\"0\":{\"123\":1}}],[\"准备好了吗\",{\"1\":{\"120\":1}}],[\"展示如何用闭包来实现这一点\",{\"1\":{\"120\":1}}],[\"你也可以学习看看\",{\"1\":{\"522\":1}}],[\"你可能有疑问\",{\"1\":{\"500\":1}}],[\"你可能会觉得将一个指令变成了许多指令\",{\"1\":{\"422\":1}}],[\"你就会发现\",{\"1\":{\"437\":1}}],[\"你就能写出更加高效的代码\",{\"1\":{\"407\":1}}],[\"你能对计算机程序的原理有一定的了解\",{\"1\":{\"434\":1}}],[\"你好\",{\"1\":{\"338\":1,\"339\":1,\"386\":1}}],[\"你将看到闭包是如何捕获变量并提供类似类的功能的\",{\"1\":{\"120\":1}}],[\"你是否曾经想过\",{\"1\":{\"120\":1}}],[\"你需要将这些更改复制到你的原生项目中\",{\"1\":{\"108\":1}}],[\"页面\",{\"1\":{\"119\":1}}],[\"预览功能\",{\"1\":{\"119\":1}}],[\"卸载\",{\"1\":{\"119\":1}}],[\"禁用\",{\"1\":{\"119\":1}}],[\"渲染插件\",{\"1\":{\"119\":1}}],[\"⚠️注意事项\",{\"1\":{\"119\":1}}],[\"缺点是\",{\"1\":{\"367\":1}}],[\"缺点\",{\"0\":{\"118\":1,\"119\":1}}],[\"文法\",{\"1\":{\"522\":1}}],[\"文法的关系\",{\"1\":{\"522\":1}}],[\"文法如下\",{\"1\":{\"279\":1}}],[\"文章\",{\"1\":{\"411\":1}}],[\"文件描述符\",{\"1\":{\"270\":1}}],[\"文件句柄\",{\"1\":{\"270\":1}}],[\"文件类\",{\"0\":{\"224\":1}}],[\"文件\",{\"1\":{\"124\":1}}],[\"文件来实现风格统一\",{\"1\":{\"65\":1}}],[\"文档和博客等\",{\"1\":{\"124\":1}}],[\"文档\",{\"1\":{\"116\":1}}],[\"脱离具体场景孤立存在的\",{\"1\":{\"115\":1}}],[\"脱离对象孤立存在的\",{\"1\":{\"115\":1}}],[\"抛开场景谈逻辑\",{\"1\":{\"115\":1}}],[\"抛开剂量谈毒性\",{\"1\":{\"115\":1}}],[\"道德不是空泛的\",{\"1\":{\"115\":1}}],[\"没有什么值得说明的内容\",{\"1\":{\"488\":1}}],[\"没有学过编译原理的话可能并不知道什么是\",{\"1\":{\"455\":1}}],[\"没有参数的指令在后\",{\"1\":{\"421\":1}}],[\"没有主动放弃执行权\",{\"1\":{\"115\":1}}],[\"没锁的话\",{\"1\":{\"112\":1}}],[\"结束的\",{\"1\":{\"478\":2}}],[\"结果存放在寄存器\",{\"1\":{\"431\":1}}],[\"结果却发现还是皮\",{\"1\":{\"235\":1}}],[\"结城浩\",{\"1\":{\"274\":1}}],[\"结论当然就是看使用场景\",{\"1\":{\"115\":1}}],[\"结语\",{\"0\":{\"16\":1,\"246\":1,\"524\":1},\"1\":{\"519\":1}}],[\"还有就是写这个系列的文章\",{\"1\":{\"523\":1}}],[\"还有就是调试编译器\",{\"1\":{\"523\":1}}],[\"还有两个重要函数没有完成\",{\"1\":{\"481\":1}}],[\"还剩最后一部分没有完成\",{\"1\":{\"491\":1}}],[\"还记得前面说的标识符\",{\"1\":{\"448\":1}}],[\"还要考虑如何传递参数和如何返回结果\",{\"1\":{\"426\":1}}],[\"还没仔细了解过\",{\"1\":{\"411\":1}}],[\"还可以用某种算法去\",{\"1\":{\"380\":1}}],[\"还可以不用\",{\"1\":{\"367\":1}}],[\"还可以将现在的状态保存在文件中\",{\"1\":{\"311\":1}}],[\"还会使得调试和维护变得更加困难\",{\"1\":{\"297\":1}}],[\"还想变量安全\",{\"1\":{\"114\":1}}],[\"还是实现起来\",{\"1\":{\"522\":1}}],[\"还是函数的局部变量\",{\"1\":{\"477\":1}}],[\"还是需要仔细一点的\",{\"1\":{\"369\":1}}],[\"还是咖啡朗姆和开心果的混合口味\",{\"1\":{\"238\":1}}],[\"还是要增加实现呢\",{\"1\":{\"176\":1}}],[\"还是过程中\",{\"1\":{\"114\":1}}],[\"还是只能加锁\",{\"1\":{\"114\":1}}],[\"还是只能一个人打电话\",{\"1\":{\"112\":1}}],[\"还是最后执行结果\",{\"1\":{\"114\":1}}],[\"还是采用vpl图形化吧\",{\"1\":{\"16\":1}}],[\"话说回来\",{\"1\":{\"114\":1}}],[\"切换过程是协作的\",{\"1\":{\"114\":1}}],[\"连最终一致性也无法保证\",{\"1\":{\"114\":1}}],[\"意味着协程操作变量的最终一致性是可以保证的\",{\"1\":{\"114\":1}}],[\"混乱状态\",{\"1\":{\"114\":1}}],[\"状况发生改变时会变化的信息\",{\"1\":{\"268\":1}}],[\"状态机\",{\"1\":{\"521\":1}}],[\"状态迁移\",{\"1\":{\"367\":1}}],[\"状态不同处理也不同\",{\"1\":{\"366\":1}}],[\"状态越多\",{\"1\":{\"365\":1}}],[\"状态\",{\"1\":{\"214\":1,\"365\":1}}],[\"状态一致\",{\"1\":{\"114\":1}}],[\"状自然数系统\",{\"1\":{\"102\":1}}],[\"925\",{\"1\":{\"306\":4}}],[\"98\",{\"1\":{\"306\":1,\"408\":1}}],[\"97\",{\"1\":{\"306\":1}}],[\"900\",{\"1\":{\"226\":1,\"395\":1}}],[\"998\",{\"1\":{\"436\":3}}],[\"998244353>\",{\"1\":{\"58\":3}}],[\"998244353\",{\"1\":{\"54\":1}}],[\"9999\",{\"1\":{\"377\":1}}],[\"9998\",{\"1\":{\"377\":1}}],[\"9997\",{\"1\":{\"377\":1}}],[\"9994\",{\"1\":{\"377\":1}}],[\"9992\",{\"1\":{\"377\":1}}],[\"9991\",{\"1\":{\"377\":1}}],[\"99\",{\"1\":{\"205\":1,\"306\":1}}],[\"9\",{\"0\":{\"519\":1},\"1\":{\"114\":1,\"178\":1,\"212\":2,\"264\":1,\"362\":2,\"406\":1,\"414\":1,\"417\":2,\"435\":2,\"443\":1,\"444\":6,\"453\":1,\"459\":2,\"463\":1,\"474\":1,\"485\":1,\"495\":2,\"519\":2}}],[\"再将\",{\"1\":{\"513\":1}}],[\"再赋上局部变量相关的信息\",{\"1\":{\"479\":1}}],[\"再例如\",{\"1\":{\"436\":1}}],[\"再见\",{\"1\":{\"193\":1,\"194\":1}}],[\"再也没有异步的加持了\",{\"1\":{\"114\":1}}],[\"再进行减法运算\",{\"1\":{\"114\":1}}],[\"再根据\",{\"1\":{\"72\":1,\"73\":1,\"88\":1,\"89\":1}}],[\"逻辑运算符\",{\"0\":{\"511\":1},\"1\":{\"495\":1}}],[\"逻辑取反\",{\"0\":{\"504\":1},\"1\":{\"495\":1}}],[\"逻辑也较为直接\",{\"1\":{\"444\":1}}],[\"逻辑有了些许修改\",{\"1\":{\"114\":1}}],[\"逻辑紧凑\",{\"1\":{\"113\":1}}],[\"让它实现\",{\"1\":{\"369\":1}}],[\"让它干一些\",{\"1\":{\"338\":1}}],[\"让高层模块依赖这些抽象\",{\"1\":{\"143\":1}}],[\"让我们继续讲解如何把运算符编译成汇编代码吧\",{\"1\":{\"508\":1}}],[\"让我们继续之前的逻辑\",{\"1\":{\"114\":1}}],[\"让我们稍微改变一下立场\",{\"1\":{\"389\":1}}],[\"让我们简单地举个例子\",{\"1\":{\"267\":1}}],[\"让我们再回顾一下示例程序\",{\"1\":{\"199\":1}}],[\"让我们开始这段有趣的旅程吧\",{\"1\":{\"120\":1}}],[\"让我们来看一下代码运行结果\",{\"1\":{\"114\":1}}],[\"让别的协程运行\",{\"1\":{\"114\":1}}],[\"让别的线程有机会执行\",{\"1\":{\"112\":1}}],[\"让出了使用权\",{\"1\":{\"114\":1}}],[\"又可能会导致软件产品的质量降低\",{\"1\":{\"399\":1}}],[\"又访问\",{\"1\":{\"397\":1}}],[\"又想多协程\",{\"1\":{\"114\":1}}],[\"又要共享状态\",{\"1\":{\"114\":1}}],[\"又或者别的协程任务也\",{\"1\":{\"114\":1}}],[\"又不确定性\",{\"1\":{\"112\":1}}],[\"随后立刻切换回来\",{\"1\":{\"114\":1}}],[\"随后当我们让出使用权1秒之后\",{\"1\":{\"114\":1}}],[\"随笔\",{\"0\":{\"2\":1}}],[\"别的协程就可以进行执行\",{\"1\":{\"114\":1}}],[\"别的线程表一定不能改\",{\"1\":{\"112\":1}}],[\"暂时\",{\"1\":{\"114\":1}}],[\"关于编代码\",{\"0\":{\"523\":1},\"1\":{\"519\":1}}],[\"关于变量\",{\"1\":{\"500\":1}}],[\"关于表达式的解析\",{\"1\":{\"497\":1}}],[\"关于这个问题\",{\"1\":{\"267\":1}}],[\"关于这一点\",{\"1\":{\"267\":1}}],[\"关键是判断\",{\"1\":{\"502\":1}}],[\"关键就是去理解汇编代码的执行原理\",{\"1\":{\"492\":1}}],[\"关键字与内置函数\",{\"0\":{\"448\":1},\"1\":{\"435\":1}}],[\"关键字生成实例的次数\",{\"1\":{\"270\":1}}],[\"关键字生成实例会花费时间\",{\"1\":{\"270\":1}}],[\"关键字\",{\"1\":{\"114\":1,\"448\":1}}],[\"关系\",{\"0\":{\"128\":1}}],[\"关闭vscode\",{\"1\":{\"67\":1}}],[\"那诸如\",{\"1\":{\"500\":1}}],[\"那意味着也支持指针的指针\",{\"1\":{\"467\":1}}],[\"那就不行了\",{\"1\":{\"399\":1}}],[\"那就不需要加锁\",{\"1\":{\"115\":1}}],[\"那就意味着大家完全理解了\",{\"1\":{\"366\":1}}],[\"那就是\",{\"1\":{\"402\":1,\"448\":1}}],[\"那就是最大的道德\",{\"1\":{\"115\":1}}],[\"那就是任务又回到了线性同步执行\",{\"1\":{\"114\":1}}],[\"那就是代码中没有\",{\"1\":{\"114\":1}}],[\"那到底怎么主动让出使用权\",{\"1\":{\"114\":1}}],[\"那么对变量\",{\"1\":{\"503\":1}}],[\"那么如何确定运算符的优先级呢\",{\"1\":{\"496\":1}}],[\"那么外层的\",{\"1\":{\"478\":1}}],[\"那么它应该被转换成什么样的汇编代码呢\",{\"1\":{\"477\":1}}],[\"那么我们如何表示指针类型呢\",{\"1\":{\"467\":1}}],[\"那么我们怎么表示标识符呢\",{\"1\":{\"443\":1}}],[\"那么我们就可以用\",{\"1\":{\"186\":1}}],[\"那么参数的传递呢\",{\"1\":{\"426\":1}}],[\"那么你会发现\",{\"1\":{\"408\":1}}],[\"那么为什么要学习编译原理呢\",{\"1\":{\"407\":1}}],[\"那么在看到这条设计原则后\",{\"1\":{\"399\":1}}],[\"那么每次要扩展功能\",{\"1\":{\"398\":1}}],[\"那么下一局也出一样的手势\",{\"1\":{\"376\":1}}],[\"那么这个\",{\"1\":{\"370\":1}}],[\"那么这些分散的类最终只会导致灾难\",{\"1\":{\"297\":1}}],[\"那么增加新的状态时会怎样呢\",{\"1\":{\"369\":1}}],[\"那么编译器在编译代码时就会报错\",{\"1\":{\"369\":1}}],[\"那么程序结构会变得非常复杂\",{\"1\":{\"298\":1}}],[\"那么通信线路有两条\",{\"1\":{\"298\":1}}],[\"那么无论是编写代码还是调试代码和修改代码\",{\"1\":{\"297\":1}}],[\"那么两种解决方案到底哪个是正确的呢\",{\"1\":{\"267\":1}}],[\"那么此时\",{\"1\":{\"267\":1}}],[\"那么\",{\"1\":{\"267\":3}}],[\"那么就在返回时保存在\",{\"1\":{\"426\":1}}],[\"那么就会有\",{\"1\":{\"298\":1}}],[\"那么就会对类中调用\",{\"1\":{\"199\":1}}],[\"那么就可以在字符串的四周加上边框\",{\"1\":{\"236\":1}}],[\"那么需要做的就是编写\",{\"1\":{\"156\":1}}],[\"那么协程一定是安全的\",{\"1\":{\"114\":1}}],[\"那么值会是0\",{\"1\":{\"112\":1}}],[\"谁举证\",{\"1\":{\"114\":1}}],[\"谁主张\",{\"1\":{\"114\":1}}],[\"谁知道什么\",{\"0\":{\"197\":1},\"1\":{\"197\":1}}],[\"谁知\",{\"1\":{\"66\":1}}],[\"毫无疑问\",{\"1\":{\"114\":2}}],[\"运行程序\",{\"1\":{\"433\":1}}],[\"运行我们的指令集\",{\"1\":{\"417\":1}}],[\"运行结果\",{\"0\":{\"167\":1,\"184\":1,\"194\":1,\"205\":1,\"212\":1,\"226\":1,\"233\":1,\"252\":1,\"259\":1,\"265\":1,\"280\":1,\"287\":1,\"295\":1,\"306\":1,\"318\":1,\"332\":1,\"339\":1,\"354\":1,\"363\":1,\"377\":1,\"387\":1,\"395\":1},\"1\":{\"114\":1}}],[\"运算符出栈\",{\"1\":{\"496\":2}}],[\"运算符运算等等\",{\"1\":{\"495\":1}}],[\"运算符的优先级决定了表达式的运算顺序\",{\"1\":{\"496\":1}}],[\"运算符的优先级\",{\"0\":{\"496\":1},\"1\":{\"495\":1}}],[\"运算符指令\",{\"0\":{\"431\":1},\"1\":{\"417\":1}}],[\"运算更快\",{\"1\":{\"58\":1}}],[\"既然同一时间只能有一个协程任务运行\",{\"1\":{\"114\":1}}],[\"体本身就无缝保持了程序状态\",{\"1\":{\"113\":1}}],[\"闭包实现类\",{\"0\":{\"120\":1}}],[\"闭包\",{\"1\":{\"113\":1}}],[\"比起可怕的\",{\"1\":{\"408\":1}}],[\"比喻\",{\"1\":{\"165\":1}}],[\"比操作系统的抢占式调度所需要的时间代价要小很多\",{\"1\":{\"113\":1}}],[\"比如大量的\",{\"1\":{\"54\":1}}],[\"比如左轮设置为0\",{\"1\":{\"10\":1}}],[\"过滤遍历等\",{\"1\":{\"284\":1}}],[\"过了一段时间\",{\"1\":{\"113\":1}}],[\"过去的做法\",{\"0\":{\"55\":1}}],[\"抢占式的线程就不那么让人愉快了\",{\"1\":{\"112\":1}}],[\"抢占式的线程调度器是非常不错的选择\",{\"1\":{\"112\":1}}],[\"大量重复的代码特别让人崩溃\",{\"1\":{\"523\":1}}],[\"大量的函数调用将会耗费不少的时间\",{\"1\":{\"57\":1}}],[\"大部分的代码依旧是用于解析变量\",{\"1\":{\"482\":1}}],[\"大致500+行\",{\"1\":{\"409\":1}}],[\"大家应该都会点头表示赞同吧\",{\"1\":{\"399\":1}}],[\"大家已经学习了多种设计模式\",{\"1\":{\"399\":1}}],[\"大家只要再回顾一下\",{\"1\":{\"370\":1}}],[\"大家又发明了同步锁\",{\"1\":{\"112\":1}}],[\"于是\",{\"1\":{\"112\":1,\"114\":1}}],[\"于是寻求\",{\"1\":{\"66\":1}}],[\"每写一篇都特别心烦\",{\"1\":{\"523\":1}}],[\"每当一个引用被释放时\",{\"1\":{\"269\":1}}],[\"每当一个对象被引用时\",{\"1\":{\"269\":1}}],[\"每次遇到换行符\",{\"1\":{\"441\":1}}],[\"每次调用该函数则返回下一个标记\",{\"1\":{\"438\":1}}],[\"每次撤销操作时从栈中弹出一个\",{\"1\":{\"311\":1}}],[\"每次撤销操作时\",{\"1\":{\"215\":1}}],[\"每次执行命令时\",{\"1\":{\"215\":1}}],[\"每次执行更新你的\",{\"1\":{\"108\":1}}],[\"每个id占用数组中的9个空间\",{\"1\":{\"443\":1}}],[\"每个标记通常包括\",{\"1\":{\"436\":1}}],[\"每个运算符都是二元的\",{\"1\":{\"431\":1}}],[\"每个\",{\"1\":{\"367\":2}}],[\"每个请求都会沿着职责链传递\",{\"1\":{\"204\":1}}],[\"每个类只负责一个职责\",{\"1\":{\"139\":1}}],[\"每个协程的体积比线程要小得多\",{\"1\":{\"113\":1}}],[\"每执行100条字节码\",{\"1\":{\"112\":1}}],[\"雨露均沾\",{\"1\":{\"112\":1}}],[\"只支持枚举\",{\"1\":{\"467\":1}}],[\"只支持\",{\"1\":{\"446\":1}}],[\"只能说它是一个相当大的挑战吧\",{\"1\":{\"407\":1}}],[\"只能重写父类的抽象方法\",{\"1\":{\"132\":1}}],[\"只是在编写代码的过程中\",{\"1\":{\"523\":1}}],[\"只是在实现\",{\"1\":{\"507\":1}}],[\"只是这时就是提前看k个\",{\"1\":{\"446\":1}}],[\"只是现在还用不着\",{\"1\":{\"433\":1}}],[\"只是现在用\",{\"1\":{\"430\":1}}],[\"只是我们的指令集中并没有\",{\"1\":{\"429\":1}}],[\"只是它们的功能都过于强大\",{\"1\":{\"415\":1}}],[\"只是对于一般的学生或程序员来说\",{\"1\":{\"408\":1}}],[\"只是定义了与算法相关的接口\",{\"1\":{\"379\":1}}],[\"只是阅读抽象类的代码是无法获取很多信息的\",{\"1\":{\"199\":1}}],[\"只存在一个实例\",{\"1\":{\"352\":1}}],[\"只要保持各个类的独立性\",{\"1\":{\"321\":1}}],[\"只要准备一些装饰边框\",{\"1\":{\"238\":1}}],[\"只将那些真正应该在多个地方共享的字段定义在\",{\"1\":{\"267\":1}}],[\"只需添加新的访问者类\",{\"1\":{\"393\":1}}],[\"只需添加新的子类工厂\",{\"1\":{\"257\":1}}],[\"只需要阅读\",{\"1\":{\"367\":1}}],[\"只需要依赖抽象产品接口\",{\"1\":{\"257\":1}}],[\"只需要一些装饰物即可添加许多功能\",{\"0\":{\"238\":1}}],[\"只需要在\",{\"1\":{\"186\":1}}],[\"只显示规定次数\",{\"1\":{\"178\":1}}],[\"只有身在其中的我们才能体会吧\",{\"1\":{\"524\":1}}],[\"只有当访问者从数据结构中获取了足够多的信息后才能工作\",{\"1\":{\"402\":1}}],[\"只有\",{\"1\":{\"365\":1,\"422\":1}}],[\"只有在实际项目中多次使用\",{\"1\":{\"246\":1}}],[\"只有掌握了辩证的矛盾思维才能更全面更灵活的看待问题\",{\"1\":{\"115\":1}}],[\"只有一个红外传感器用于判断底部是否为黑色\",{\"1\":{\"8\":1}}],[\"只关注最终结果一致性\",{\"1\":{\"115\":1}}],[\"只不过这个让出的过程是线程调度器主动抢占的\",{\"1\":{\"111\":1}}],[\"刘悦的技术博客\",{\"1\":{\"111\":1,\"115\":1}}],[\"挂起\",{\"0\":{\"111\":1},\"1\":{\"114\":1}}],[\"线程是系统态\",{\"1\":{\"113\":1}}],[\"线程操作共享资源需要加锁\",{\"1\":{\"112\":1}}],[\"线程并不安全\",{\"1\":{\"112\":1}}],[\"线程共享数据危险在于\",{\"1\":{\"112\":1}}],[\"线程安全\",{\"0\":{\"112\":1}}],[\"线程更被我们所熟知\",{\"1\":{\"111\":1}}],[\"线程\",{\"0\":{\"111\":1}}],[\"到底是什么呢\",{\"1\":{\"370\":1}}],[\"到底需不需要加锁\",{\"0\":{\"111\":1}}],[\"到任意点的路径\",{\"1\":{\"98\":1}}],[\"插件\",{\"1\":{\"108\":1}}],[\"命令队列\",{\"1\":{\"215\":1}}],[\"命令栈\",{\"1\":{\"215\":1}}],[\"命令模式的一个重要应用是保存历史记录\",{\"1\":{\"215\":1}}],[\"命令执行前后的状态信息\",{\"1\":{\"214\":1}}],[\"命令对象可以保存执行前的状态\",{\"1\":{\"214\":1}}],[\"命令对象可以包含执行操作所需的所有参数\",{\"1\":{\"214\":1}}],[\"命令对象将动作封装为一个方法调用\",{\"1\":{\"214\":1}}],[\"命令对象通常包含以下信息\",{\"1\":{\"214\":1}}],[\"命令中应该包含哪些信息\",{\"0\":{\"214\":1}}],[\"命令\",{\"1\":{\"108\":1}}],[\"命里无时莫强求\",{\"1\":{\"3\":1}}],[\"命里有时终须有\",{\"0\":{\"3\":1},\"1\":{\"3\":1}}],[\"默认是\",{\"1\":{\"433\":1}}],[\"默认为\",{\"1\":{\"124\":1}}],[\"默认不支持http\",{\"1\":{\"108\":1}}],[\"默认\",{\"1\":{\"108\":1}}],[\"此时的二元运算符的解析的框架为\",{\"1\":{\"508\":1}}],[\"此时运算符栈为空\",{\"1\":{\"496\":1}}],[\"此时判断参数\",{\"1\":{\"496\":1}}],[\"此时我们期待的是+的另一个参数\",{\"1\":{\"496\":1}}],[\"此时我们可以使用ionic无缝将其迁移到移动端\",{\"1\":{\"106\":1}}],[\"此时\",{\"1\":{\"236\":1,\"324\":1,\"487\":1,\"509\":1}}],[\"此时使用权让出以后\",{\"1\":{\"114\":1}}],[\"此外\",{\"1\":{\"66\":1,\"236\":1,\"246\":1,\"367\":1,\"380\":1,\"398\":1}}],[\"点\",{\"1\":{\"98\":1}}],[\"所谓状态迁移表是可以根据\",{\"1\":{\"367\":1}}],[\"所谓主动让出使用权\",{\"1\":{\"114\":1}}],[\"所对应的字体数据\",{\"1\":{\"267\":1}}],[\"所有的变量定义必须放在语句之前\",{\"1\":{\"515\":1}}],[\"所有的\",{\"1\":{\"367\":1}}],[\"所有的实现\",{\"1\":{\"186\":1}}],[\"所有依赖于它的对象都会得到通知并自动更新\",{\"1\":{\"317\":1}}],[\"所有显示该数据的视图都需要自动更新\",{\"1\":{\"316\":1}}],[\"所有点的出度为\",{\"1\":{\"98\":1}}],[\"所以你可以执行\",{\"1\":{\"515\":1}}],[\"所以源码如下\",{\"1\":{\"511\":1}}],[\"所以生成的代码也类似于\",{\"1\":{\"510\":1}}],[\"所以直接修改栈指针的大小即可\",{\"1\":{\"500\":1}}],[\"所以直接跳过它们\",{\"1\":{\"442\":1}}],[\"所以解析的时候要注意这一点\",{\"1\":{\"498\":1}}],[\"所以先将它入栈\",{\"1\":{\"496\":1}}],[\"所以建议如果没有学过汇编\",{\"1\":{\"492\":1}}],[\"所以不多做说明\",{\"1\":{\"490\":1}}],[\"所以不需要考虑多线程问题\",{\"1\":{\"264\":1}}],[\"所以需要生成汇编代码\",{\"1\":{\"489\":1}}],[\"所以需要无条件跳转\",{\"1\":{\"487\":1}}],[\"所以如果执行了\",{\"1\":{\"487\":1}}],[\"所以一个类型首先有基本类型\",{\"1\":{\"467\":1}}],[\"所以还需要继续查看后续的标记\",{\"1\":{\"467\":1}}],[\"所以实际上它们间的对应关系并不是特别明显\",{\"1\":{\"464\":1}}],[\"所以实际的处理方法是提供一个函数\",{\"1\":{\"438\":1}}],[\"所以只能再向前查看字符\",{\"1\":{\"446\":1}}],[\"所以代码中并没有支持除\",{\"1\":{\"445\":1}}],[\"所以这里我们会有这样的印象\",{\"1\":{\"439\":1}}],[\"所以人们已经开发出了许多工具来生成词法分析器\",{\"1\":{\"438\":1}}],[\"所以为了获取第一个参数\",{\"1\":{\"430\":1}}],[\"所以用一个指令代替\",{\"1\":{\"429\":1}}],[\"所以用上面提到的指令\",{\"1\":{\"426\":1}}],[\"所以合在一起说\",{\"1\":{\"426\":1}}],[\"所以此时它存放的是\",{\"1\":{\"424\":1}}],[\"所以执行\",{\"1\":{\"422\":1}}],[\"所以大大简化了实现的难度\",{\"1\":{\"422\":1}}],[\"所以入栈时\",{\"1\":{\"420\":1}}],[\"所以是\",{\"1\":{\"419\":1}}],[\"所以单独存放可以节省空间\",{\"1\":{\"419\":1}}],[\"所以我希望你有足够的耐心和时间来学习\",{\"1\":{\"410\":1}}],[\"所以我们首先执行类似前缀自增自减的操作\",{\"1\":{\"513\":1}}],[\"所以我们需要给予代码生成高度的重视\",{\"1\":{\"520\":1}}],[\"所以我们需要先\",{\"1\":{\"507\":1}}],[\"所以我们需要在不修改现有类的前提下能够扩展类\",{\"1\":{\"399\":1}}],[\"所以我们用异或来实现\",{\"1\":{\"505\":1}}],[\"所以我们将结束符的解析放在了外层的\",{\"1\":{\"478\":1}}],[\"所以我们将它拆分成\",{\"1\":{\"463\":1,\"474\":1}}],[\"所以我们将它单独作为一个模块\",{\"1\":{\"416\":1}}],[\"所以我们先编写一个较为简单的编译器\",{\"1\":{\"437\":1}}],[\"所以我们提供了一个新的指令\",{\"1\":{\"430\":1}}],[\"所以我们不再需要\",{\"1\":{\"429\":1}}],[\"所以我们会依照以下步骤来构建我们的编译器\",{\"1\":{\"415\":1}}],[\"所以我们要完全手写这些功能\",{\"1\":{\"415\":1}}],[\"所以我们还需要在它们之间搭建一座桥梁\",{\"1\":{\"176\":1}}],[\"所以本项目的主要目的\",{\"1\":{\"409\":1}}],[\"所以写得很乱\",{\"1\":{\"409\":1}}],[\"所以写操作不会被争抢覆盖\",{\"1\":{\"114\":1}}],[\"所以当学校开\",{\"1\":{\"408\":1}}],[\"所以优先使用组合的方式代替继承的方式\",{\"1\":{\"145\":1}}],[\"所以说\",{\"1\":{\"115\":1}}],[\"所以肯定可以保证最终一致性\",{\"1\":{\"114\":1}}],[\"所以它对应的代码为\",{\"1\":{\"512\":1}}],[\"所以它的性能要比多线程好\",{\"1\":{\"113\":1}}],[\"所以它平均地分配时间片让处理器一视同仁\",{\"1\":{\"112\":1}}],[\"所以同一时间点还是只能有一个协程任务运行\",{\"1\":{\"113\":1}}],[\"所以加锁是为了同时只有一个线程再修改\",{\"1\":{\"112\":1}}],[\"所以\",{\"1\":{\"84\":1,\"112\":2,\"508\":2}}],[\"所以选了创新创业智能车课程\",{\"1\":{\"4\":1}}],[\"同样\",{\"1\":{\"506\":1}}],[\"同样我们没有相应的指令\",{\"1\":{\"505\":1}}],[\"同样在第三章\",{\"1\":{\"500\":1}}],[\"同样不能确定是否能立即计算\",{\"1\":{\"496\":1}}],[\"同理\",{\"1\":{\"115\":1,\"467\":1}}],[\"同时其它语言也有许多类似的支持\",{\"1\":{\"522\":1}}],[\"同时我们也看到\",{\"1\":{\"520\":1}}],[\"同时我们也用实例看到了理论\",{\"1\":{\"460\":1}}],[\"同时将运算符\",{\"1\":{\"496\":1}}],[\"同时值得一提的是\",{\"1\":{\"492\":1}}],[\"同时记录它们的位置与类型\",{\"1\":{\"479\":1}}],[\"同时能对汇编语言有一定的概念\",{\"1\":{\"434\":1}}],[\"同时在栈上保留一定的空间\",{\"1\":{\"427\":1}}],[\"同时开启四个协程任务\",{\"1\":{\"114\":1}}],[\"同时也不需要系统的线程调度器参与抢占式的调度\",{\"1\":{\"113\":1}}],[\"同时\",{\"1\":{\"113\":1,\"246\":1,\"406\":1,\"521\":1}}],[\"同时修改变量\",{\"1\":{\"112\":1}}],[\"同时为了解决多个模数的问题\",{\"1\":{\"58\":1}}],[\"同构\",{\"1\":{\"98\":1}}],[\"图像加载时可以使用虚拟代理来显示占位符图像\",{\"1\":{\"346\":1}}],[\"图解设计模式\",{\"1\":{\"249\":1,\"274\":1}}],[\"图论\",{\"1\":{\"95\":1}}],[\"图床\",{\"0\":{\"48\":1}}],[\"研究\",{\"1\":{\"95\":1}}],[\"少了任何一条都不足以构建出上述的自然数系统\",{\"1\":{\"95\":1}}],[\"从上小节对四则运算的递归下降解析可以看出\",{\"1\":{\"457\":1}}],[\"从上述步骤中我们看出\",{\"1\":{\"95\":1}}],[\"从虚拟机的角度予以支持\",{\"1\":{\"432\":1}}],[\"从中一条条地加载指令执行\",{\"1\":{\"418\":1}}],[\"从观察变为通知\",{\"0\":{\"324\":1}}],[\"从栈中弹出命令对象并执行撤销操作\",{\"1\":{\"215\":1}}],[\"从早上到下午\",{\"1\":{\"193\":1}}],[\"从代码结构上看\",{\"1\":{\"113\":1}}],[\"从实际开发角度看\",{\"1\":{\"113\":1}}],[\"从而简化具体的实现\",{\"1\":{\"434\":1}}],[\"从而确保只有授权的客户端才能访问实际对象\",{\"1\":{\"346\":1}}],[\"从而延迟实际对象的创建\",{\"1\":{\"346\":1}}],[\"从而减少系统的开销\",{\"1\":{\"341\":1}}],[\"从而引发无限循环\",{\"1\":{\"322\":1}}],[\"从而引发程序错误\",{\"1\":{\"269\":1}}],[\"从而保持封装性\",{\"1\":{\"308\":1}}],[\"从而避免内存泄漏\",{\"1\":{\"269\":1}}],[\"从而将其回收掉\",{\"1\":{\"269\":1}}],[\"从而提高网络通信的效率和安全性\",{\"1\":{\"345\":1}}],[\"从而提高了系统的可维护性和可扩展性\",{\"1\":{\"325\":1}}],[\"从而提高系统的性能和可扩展性\",{\"1\":{\"324\":1}}],[\"从而提高系统的可维护性和可扩展性\",{\"1\":{\"311\":1}}],[\"从而提高系统的灵活性和可维护性\",{\"1\":{\"214\":1,\"323\":1}}],[\"从而提高性能\",{\"1\":{\"263\":1}}],[\"从而遵循开闭原则\",{\"1\":{\"231\":1}}],[\"从而使得现有类可以在新的环境中使用\",{\"1\":{\"163\":1}}],[\"从而导致执行过程中变量状态的\",{\"1\":{\"114\":1}}],[\"从而启动失败\",{\"1\":{\"67\":1}}],[\"从而加速开发和交付周期\",{\"1\":{\"44\":1}}],[\"从而不会前进太多\",{\"1\":{\"11\":1}}],[\"上节中说到了运算符的优先级\",{\"1\":{\"497\":1}}],[\"上的\",{\"1\":{\"477\":1}}],[\"上一章的代码中\",{\"1\":{\"476\":1}}],[\"上述代码中我们看到\",{\"1\":{\"446\":1}}],[\"上述等式表明\",{\"1\":{\"94\":1}}],[\"上面这断代码为当前的标识符设置了正确的类别\",{\"1\":{\"476\":1}}],[\"上面这些标记是有顺序的\",{\"1\":{\"439\":1}}],[\"上面这段代码在我们自己的虚拟机里会有几个问题\",{\"1\":{\"426\":1}}],[\"上面的一些指令解决了调用帧的问题\",{\"1\":{\"430\":1}}],[\"上面的代码运行后会出现\",{\"1\":{\"449\":1}}],[\"上面的代码看上去挺复杂\",{\"1\":{\"416\":1}}],[\"上面的代码也充分说明了这个结论的正确性\",{\"1\":{\"114\":1}}],[\"上下载\",{\"1\":{\"416\":1,\"434\":1,\"449\":1,\"470\":1,\"481\":1,\"491\":1,\"515\":1}}],[\"上看到了一个项目\",{\"1\":{\"409\":1}}],[\"上存储\",{\"1\":{\"44\":1}}],[\"ⅳ\",{\"0\":{\"102\":1},\"1\":{\"94\":1}}],[\"假设要在某个表格计算软件的开发版本中进行复杂的计算\",{\"1\":{\"380\":1}}],[\"假设我们现在在\",{\"1\":{\"369\":1}}],[\"假设我们现在需要制作另外一个对话框\",{\"1\":{\"299\":1}}],[\"假设我们将颜色信息放在\",{\"1\":{\"267\":1}}],[\"假设我们要在示例程序中增加一个功能\",{\"1\":{\"267\":1}}],[\"假设我们改变了示例程序中\",{\"1\":{\"267\":1}}],[\"假设现在我们要在示例程序中增加一个\",{\"1\":{\"401\":1}}],[\"假设现在我们要在示例程序中增加新的具体工厂\",{\"1\":{\"156\":1}}],[\"假设现在有\",{\"1\":{\"298\":1}}],[\"假设现在有一个类\",{\"1\":{\"174\":1}}],[\"假设\",{\"1\":{\"94\":1,\"97\":1}}],[\"假设存在一个算数系统的模型满足\",{\"1\":{\"68\":1}}],[\"采用自顶向下的编写方法就是要不断地实现我们需要的内容\",{\"1\":{\"466\":1}}],[\"采用递归向下的方法来实现编译器是很直观的\",{\"1\":{\"459\":1}}],[\"采用反证法\",{\"1\":{\"94\":1,\"97\":1}}],[\"采取速度渐进增长的形式\",{\"1\":{\"11\":1}}],[\"证明了乘法运算规则的交换律之后\",{\"1\":{\"91\":1}}],[\"证明了加法运算规则的交换律之后\",{\"1\":{\"75\":1}}],[\"存在内存地址上就另当别论\",{\"1\":{\"431\":1}}],[\"存在从\",{\"1\":{\"98\":1}}],[\"存在点\",{\"1\":{\"98\":1}}],[\"存在\",{\"1\":{\"88\":1}}],[\"存放这个标识符的值\",{\"1\":{\"443\":1}}],[\"存放标识符本身的字符串\",{\"1\":{\"443\":1}}],[\"存放日志\",{\"1\":{\"28\":1}}],[\"存放ssl证书\",{\"1\":{\"28\":1}}],[\"乘法\",{\"1\":{\"496\":1}}],[\"乘法消去保序性\",{\"0\":{\"97\":1}}],[\"乘法消去律\",{\"0\":{\"94\":1},\"1\":{\"94\":1}}],[\"乘法保序性\",{\"0\":{\"96\":1}}],[\"乘法结合律\",{\"0\":{\"93\":1}}],[\"乘法结果的唯一性\",{\"0\":{\"89\":1}}],[\"乘法结果的存在性\",{\"0\":{\"88\":1}}],[\"乘法分配律\",{\"0\":{\"92\":1}}],[\"乘法交换律\",{\"0\":{\"91\":1}}],[\"乘法的性质\",{\"0\":{\"90\":1}}],[\"乘法的定义\",{\"0\":{\"87\":1}}],[\"任何python线程执行前\",{\"1\":{\"112\":1}}],[\"任何自然数的后继存在且唯一\",{\"1\":{\"69\":1}}],[\"任意点的入度小于等于\",{\"1\":{\"98\":1}}],[\"任意非零自然数\",{\"1\":{\"94\":1}}],[\"任意两个自然数\",{\"1\":{\"84\":1}}],[\"ⅲ\",{\"0\":{\"101\":1},\"1\":{\"81\":1,\"94\":3}}],[\"其它的我们便不再详述\",{\"1\":{\"512\":1}}],[\"其它的标记的解析就相对容易一些了\",{\"1\":{\"447\":1}}],[\"其它语句并不直接生成汇编代码\",{\"1\":{\"490\":1}}],[\"其它语句\",{\"0\":{\"490\":1},\"1\":{\"485\":1}}],[\"其它就不多说了\",{\"1\":{\"444\":1}}],[\"其它\",{\"0\":{\"447\":1,\"469\":1},\"1\":{\"435\":1,\"463\":1}}],[\"其它问题\",{\"0\":{\"13\":1}}],[\"其实只要不执行\",{\"1\":{\"503\":1}}],[\"其实提前看字符的概念也存在于编译器\",{\"1\":{\"446\":1}}],[\"其实是抄\",{\"1\":{\"444\":1}}],[\"其实是同一个对象\",{\"1\":{\"370\":1}}],[\"其实不然\",{\"1\":{\"379\":1}}],[\"其实并没有绝对的答案\",{\"1\":{\"267\":1}}],[\"其职责是引起该类变化的原因\",{\"1\":{\"138\":1}}],[\"其他类依然可以调用\",{\"1\":{\"235\":1}}],[\"其他设计原则是实现开闭原则的手段和工具\",{\"1\":{\"128\":1}}],[\"其他线程又说我拿不到锁\",{\"1\":{\"112\":1}}],[\"其他线程只能等待\",{\"1\":{\"112\":1}}],[\"其中①用于解析函数体内的局部变量的定义\",{\"1\":{\"480\":1}}],[\"其中①与全局变量定义的解析十分一样\",{\"1\":{\"479\":1}}],[\"其中①中我们没有消耗最后的\",{\"1\":{\"478\":1}}],[\"其中的自顶向下方法就是我们所说的递归下降\",{\"1\":{\"454\":1}}],[\"其中的\",{\"1\":{\"422\":1,\"467\":1,\"469\":1}}],[\"其中的数据段我们只用来存放字符串\",{\"1\":{\"419\":1}}],[\"其中数据段\",{\"1\":{\"419\":1}}],[\"其中\",{\"1\":{\"94\":1,\"464\":1}}],[\"其与自然数\",{\"1\":{\"81\":1}}],[\"正则表达式\",{\"1\":{\"521\":1}}],[\"正如我们保证的那样\",{\"1\":{\"515\":1}}],[\"正负号\",{\"0\":{\"506\":1},\"1\":{\"495\":1}}],[\"正常的全局变量的类别则是\",{\"1\":{\"468\":1}}],[\"正常通话\",{\"1\":{\"362\":1,\"363\":8}}],[\"正在生成printer的实例\",{\"1\":{\"339\":1}}],[\"正是因为它相当于通过一定的编码\",{\"1\":{\"439\":1}}],[\"正是因为可以替换\",{\"1\":{\"197\":1}}],[\"正是因为不知道才能够替换\",{\"1\":{\"197\":1}}],[\"正是由于父类和子类的这种任务分担\",{\"1\":{\"175\":1}}],[\"正自然数与自然数相加为正自然数\",{\"1\":{\"81\":2}}],[\"正自然数的性质\",{\"0\":{\"81\":1}}],[\"正自然数\",{\"0\":{\"80\":1}}],[\"正确\",{\"1\":{\"10\":1}}],[\"传统的编程书籍会用\",{\"1\":{\"496\":1}}],[\"传统上\",{\"1\":{\"454\":1}}],[\"传统意义上的符号表只需要知道标识符的唯一标识即可\",{\"1\":{\"443\":1}}],[\"传递更新信息的方式有多种选择\",{\"1\":{\"323\":1}}],[\"传递更新信息的方式\",{\"0\":{\"323\":1}}],[\"传递性和完全性\",{\"1\":{\"79\":1}}],[\"传说皮\",{\"1\":{\"3\":1}}],[\"它涉及到了\",{\"1\":{\"521\":1}}],[\"它相当于一个小型的\",{\"1\":{\"510\":1}}],[\"它相当于\",{\"1\":{\"498\":1}}],[\"它比较特殊的一点是\",{\"1\":{\"498\":1}}],[\"它本身不难\",{\"1\":{\"492\":1}}],[\"它对应的汇编代码如下\",{\"1\":{\"488\":1}}],[\"它用于将数据放进寄存器或内存地址\",{\"1\":{\"422\":1}}],[\"它用于存放一条指令执行后的结果\",{\"1\":{\"420\":1}}],[\"它存放的是一个内存地址\",{\"1\":{\"420\":1}}],[\"它的类型保存在变量\",{\"1\":{\"502\":1}}],[\"它的优先级和\",{\"1\":{\"496\":1}}],[\"它的运算顺序是这样的\",{\"1\":{\"496\":1}}],[\"它的\",{\"1\":{\"488\":1}}],[\"它的语法更容易理解\",{\"1\":{\"464\":1}}],[\"它的本质上也是编译器\",{\"1\":{\"437\":1}}],[\"它的作用是将\",{\"1\":{\"423\":1}}],[\"它的作用是屏蔽了物理的细节\",{\"1\":{\"419\":1}}],[\"它的流程为\",{\"1\":{\"416\":1}}],[\"它的真正作用是帮助我们实现任务分担\",{\"1\":{\"175\":1}}],[\"它将\",{\"1\":{\"469\":1}}],[\"它将自动忽略空白字符\",{\"1\":{\"416\":1}}],[\"它将与状态相关的行为封装在独立的类中\",{\"1\":{\"361\":1}}],[\"它最让我震惊的是能够自举\",{\"1\":{\"409\":1}}],[\"它就无法工作\",{\"1\":{\"402\":1}}],[\"它是\",{\"1\":{\"401\":1}}],[\"它是当实例的位置\",{\"1\":{\"268\":1}}],[\"它能够将元素集合及其关联关系组织在一起\",{\"1\":{\"398\":1}}],[\"它能做什么\",{\"1\":{\"114\":1}}],[\"它决定了系统的状态\",{\"1\":{\"368\":1}}],[\"它非常适用于大规模的复杂处理\",{\"1\":{\"365\":1}}],[\"它常用于需要控制资源访问的场景\",{\"1\":{\"351\":1}}],[\"它在客户端和远程服务器之间进行通信\",{\"1\":{\"346\":1}}],[\"它在实际对象创建之前进行一些轻量级的操作\",{\"1\":{\"346\":1}}],[\"它在以下情况下特别有用\",{\"1\":{\"304\":1}}],[\"它实现了\",{\"1\":{\"287\":1}}],[\"它允许你复制现有对象而无需使代码依赖它们所属的类\",{\"1\":{\"330\":1}}],[\"它允许顺序访问集合中的元素\",{\"1\":{\"285\":1}}],[\"它允许将一个类的接口转换成客户希望的另一个接口\",{\"1\":{\"162\":1}}],[\"它定义了一种语言的文法表示\",{\"1\":{\"278\":1}}],[\"它属于\",{\"1\":{\"268\":1}}],[\"它指的是不论实例在哪里\",{\"1\":{\"268\":1}}],[\"它通过定义自己的指令集并支持该指令集的虚拟机来模拟编译的部分过程\",{\"1\":{\"411\":1}}],[\"它通过定义一个创建对象的接口来实现\",{\"1\":{\"152\":1}}],[\"它通过共享尽可能多的相同对象来减少内存使用\",{\"1\":{\"263\":1}}],[\"它使类之间形成了弱关联关系\",{\"1\":{\"237\":1}}],[\"它主要用于以下情况\",{\"1\":{\"192\":1}}],[\"它们包括\",{\"1\":{\"512\":1}}],[\"它们对应的汇编代码如下\",{\"1\":{\"511\":1}}],[\"它们是以优先级从低到高排列的\",{\"1\":{\"508\":1}}],[\"它们是单字符的\",{\"1\":{\"439\":1}}],[\"它们的实现都很类似\",{\"1\":{\"512\":1}}],[\"它们的语法分析都相对容易\",{\"1\":{\"486\":1}}],[\"它们的内容比较多\",{\"1\":{\"485\":1}}],[\"它们的具体使用在后面的语法分析中会提到\",{\"1\":{\"439\":1}}],[\"它们不能被作为普通的标识符\",{\"1\":{\"448\":1}}],[\"它们不涉及优先级关系\",{\"1\":{\"439\":1}}],[\"它们自己就构成了标记\",{\"1\":{\"439\":1}}],[\"它们可以是一个数\",{\"1\":{\"422\":1}}],[\"它们基于\",{\"1\":{\"421\":1}}],[\"它们就是无符号的\",{\"1\":{\"419\":1}}],[\"它们在内存中的位置类似于下图\",{\"1\":{\"419\":1}}],[\"它们将作为我们的编译器最终输出的目标代码\",{\"1\":{\"417\":1}}],[\"它们过于强大\",{\"1\":{\"408\":1}}],[\"它们有很强的实际意义\",{\"1\":{\"408\":1}}],[\"它们呈现出一种相反的关系\",{\"1\":{\"397\":1}}],[\"它们都有对应的标记\",{\"1\":{\"443\":1}}],[\"它们都是\",{\"1\":{\"370\":1}}],[\"它们都可以工作于这\",{\"1\":{\"186\":1}}],[\"它们会被解析成标识符\",{\"1\":{\"448\":1}}],[\"它们会自动收到通知并更新显示\",{\"1\":{\"316\":1}}],[\"它们会操作同一个资源\",{\"1\":{\"112\":1}}],[\"它们之间互相通信\",{\"1\":{\"298\":1}}],[\"它们之间就构成了一个小小的层次结构\",{\"1\":{\"175\":1}}],[\"它们也有其局限性和适用范围\",{\"1\":{\"246\":1}}],[\"它可以是一个值\",{\"1\":{\"426\":1}}],[\"它可以在访问实际对象之前进行权限检查\",{\"1\":{\"346\":1}}],[\"它可以在协程内部用await调用另一个协程实现异步操作\",{\"1\":{\"114\":1}}],[\"它可以挂起当前协程任务\",{\"1\":{\"114\":1}}],[\"它和线程的最主要差别就是\",{\"1\":{\"113\":1}}],[\"它让调用者自己来决定什么时候让出\",{\"1\":{\"113\":1}}],[\"它应该具有反对称性\",{\"1\":{\"79\":1}}],[\"它与\",{\"1\":{\"44\":1}}],[\"满足不同的需求\",{\"1\":{\"257\":1}}],[\"满足\",{\"1\":{\"79\":1,\"94\":1,\"97\":1}}],[\"将参数出栈\",{\"1\":{\"496\":2}}],[\"将运算符\",{\"1\":{\"496\":1}}],[\"将它改成\",{\"1\":{\"466\":1}}],[\"将它们加入符号表\",{\"1\":{\"448\":1}}],[\"将对应地址中的整数载入\",{\"1\":{\"422\":1}}],[\"将对应地址中的字符载入\",{\"1\":{\"422\":1}}],[\"将\",{\"1\":{\"422\":3,\"439\":2,\"496\":1}}],[\"将语法树转化成目标代码\",{\"1\":{\"415\":1}}],[\"将词法分析得到的标记流\",{\"1\":{\"415\":1}}],[\"将来对数据结构的改良就会变得非常困难\",{\"1\":{\"402\":1}}],[\"将数据结构与操作分离\",{\"1\":{\"393\":1}}],[\"将通用的算法结构放在父类中\",{\"1\":{\"385\":1}}],[\"将状态迁移交给\",{\"1\":{\"367\":2}}],[\"将依赖于状态的处理分散在每个\",{\"1\":{\"367\":1}}],[\"将这些逻辑集中在中介者类中是更明智的选择\",{\"1\":{\"297\":1}}],[\"将共享对象存储在一个全局的集合中\",{\"1\":{\"269\":1}}],[\"将命令对象压入栈中\",{\"1\":{\"215\":1}}],[\"将类的这两个层次结构分离开有利于独立地对它们进行扩展\",{\"1\":{\"186\":1}}],[\"将现有类的接口转换为所需的接口\",{\"1\":{\"163\":1}}],[\"将具体实现传递给高层模块\",{\"1\":{\"143\":1}}],[\"将不同的算法封装在独立的类中\",{\"1\":{\"375\":1}}],[\"将不同的功能模块分开\",{\"1\":{\"139\":1}}],[\"将不同的职责分离到不同的类中\",{\"1\":{\"139\":2}}],[\"将下载的工具解压后得到的两个\",{\"1\":{\"124\":1}}],[\"将其称为新的乘法运算规则\",{\"1\":{\"91\":1}}],[\"将其称为新的加法运算规则\",{\"1\":{\"75\":1}}],[\"将模数直接包含在类型中\",{\"1\":{\"58\":1}}],[\"对应的\",{\"1\":{\"487\":1}}],[\"对应的汇编代码也比较直观\",{\"1\":{\"507\":1}}],[\"对应的汇编代码流程为\",{\"1\":{\"487\":1}}],[\"对应的汇编代码为\",{\"1\":{\"427\":1,\"428\":1,\"512\":1}}],[\"对应的汇编指令为\",{\"1\":{\"429\":1}}],[\"对词法分析器而言\",{\"1\":{\"440\":1}}],[\"对照\",{\"1\":{\"411\":1}}],[\"对数据结构中的元素进行处理的任务被分离出来\",{\"1\":{\"402\":1}}],[\"对修改是关闭的\",{\"1\":{\"399\":1}}],[\"对修改关闭的类具有高可复用性\",{\"1\":{\"399\":1}}],[\"对修改关闭\",{\"0\":{\"399\":1},\"1\":{\"129\":1,\"148\":1,\"393\":1}}],[\"对扩展是开放的\",{\"1\":{\"399\":1}}],[\"对扩展开放\",{\"0\":{\"399\":1},\"1\":{\"129\":1,\"148\":1,\"393\":1,\"399\":1}}],[\"对比这两个方法会发现\",{\"1\":{\"397\":1}}],[\"对象负责\",{\"1\":{\"337\":1}}],[\"对象太忙了\",{\"1\":{\"337\":1}}],[\"对象种类繁多\",{\"1\":{\"330\":1}}],[\"对象的所有操作权限\",{\"1\":{\"308\":1}}],[\"对象的状态\",{\"1\":{\"305\":1}}],[\"对多个地方产生影响\",{\"0\":{\"267\":1}}],[\"对\",{\"1\":{\"236\":1,\"370\":1}}],[\"对任意自然数\",{\"1\":{\"75\":3,\"76\":1,\"77\":3,\"91\":3,\"92\":1,\"93\":1,\"94\":2}}],[\"对于学习或考试而言或许可以\",{\"1\":{\"520\":1}}],[\"对于学习构建编译器帮助不大\",{\"1\":{\"415\":1}}],[\"对于变量\",{\"1\":{\"503\":1}}],[\"对于提高我们的水平还是很有帮助的\",{\"1\":{\"460\":1}}],[\"对于语法分析而言\",{\"1\":{\"443\":1}}],[\"对于一些简单的应用\",{\"1\":{\"309\":1}}],[\"对于那些能够明确地用语言描述出来的知识\",{\"1\":{\"249\":1}}],[\"对于\",{\"1\":{\"84\":1}}],[\"对于任意自然数\",{\"1\":{\"69\":1,\"72\":1,\"73\":1,\"88\":1,\"89\":1}}],[\"对于使用\",{\"1\":{\"44\":1}}],[\"根据标识符后的运算符\",{\"1\":{\"500\":1}}],[\"根据类型的不同有\",{\"1\":{\"422\":1}}],[\"根据文法来生成编译器\",{\"1\":{\"408\":1}}],[\"根据上一局的手势从概率上计算出下一局的手势\",{\"1\":{\"376\":1}}],[\"根据开闭原则\",{\"1\":{\"129\":1}}],[\"根据乘法消去律有\",{\"1\":{\"97\":1}}],[\"根据乘法运算规则\",{\"1\":{\"88\":1,\"89\":1}}],[\"根据序的反对称性有\",{\"1\":{\"97\":1}}],[\"根据加法结合律得出\",{\"1\":{\"83\":1}}],[\"根据加法结果的存在性得到\",{\"1\":{\"83\":1}}],[\"根据加法运算规则\",{\"1\":{\"72\":1,\"73\":1}}],[\"根据正自然数的性质得出\",{\"1\":{\"82\":1}}],[\"根据\",{\"1\":{\"75\":3,\"76\":1,\"77\":2,\"81\":2,\"91\":3,\"92\":1,\"93\":1,\"94\":1}}],[\"首先我们介绍\",{\"1\":{\"426\":1}}],[\"首先是数字\",{\"1\":{\"498\":1}}],[\"首先是之前定义过的\",{\"1\":{\"466\":1}}],[\"首先是\",{\"1\":{\"422\":1,\"455\":1}}],[\"首先在全局变量中加入一个枚举类型\",{\"1\":{\"421\":1}}],[\"首先要说明的是\",{\"1\":{\"414\":1}}],[\"首先要想到的是\",{\"1\":{\"267\":1}}],[\"首先\",{\"1\":{\"81\":1,\"91\":1,\"267\":1}}],[\"首先当\",{\"1\":{\"76\":1,\"77\":2,\"91\":1,\"92\":1,\"93\":1,\"94\":1}}],[\"首先由加法运算规则\",{\"1\":{\"75\":1}}],[\"首先有\",{\"1\":{\"75\":2,\"91\":1}}],[\"首先采取的改进方案是先左小幅度转弯\",{\"1\":{\"12\":1}}],[\"考虑诸如\",{\"1\":{\"509\":1}}],[\"考虑下列函数\",{\"1\":{\"477\":1}}],[\"考虑其他的类\",{\"1\":{\"365\":1}}],[\"考虑从乘法运算的定义下手\",{\"1\":{\"91\":1}}],[\"考虑从加法运算的定义下手\",{\"1\":{\"75\":1}}],[\"考虑到函数取模的优点\",{\"1\":{\"58\":1}}],[\"考虑到小车路线是闭合的\",{\"1\":{\"12\":1}}],[\"唯一特殊的地方是\",{\"1\":{\"489\":1}}],[\"唯一\",{\"1\":{\"73\":4,\"89\":4}}],[\"唯一的缺点就是类型名难写\",{\"1\":{\"58\":1}}],[\"就如前文的\",{\"1\":{\"508\":1}}],[\"就返回它的唯一标识\",{\"1\":{\"443\":1}}],[\"就势必要实现\",{\"1\":{\"432\":1}}],[\"就实现了数据结构与处理的分离\",{\"1\":{\"402\":1}}],[\"就程序而言\",{\"1\":{\"389\":1}}],[\"就不得不去修改这些类\",{\"1\":{\"398\":1}}],[\"就不必修改\",{\"1\":{\"379\":1}}],[\"就不会发生上面这种类的依赖关系混乱的问题\",{\"1\":{\"321\":1}}],[\"就必须用条件分支语句判断状态\",{\"1\":{\"369\":1}}],[\"就必须要相应地修改\",{\"1\":{\"367\":1}}],[\"就将其交给\",{\"1\":{\"337\":1}}],[\"就会发现太可怕了\",{\"1\":{\"408\":1}}],[\"就会对多个地方产生影响\",{\"1\":{\"267\":1}}],[\"就会很容易出错\",{\"1\":{\"199\":1}}],[\"就意味着我们需要引人facade了\",{\"1\":{\"249\":1}}],[\"就可以应付大多数的语法分析器编写\",{\"1\":{\"460\":1}}],[\"就可以提高程序运行速度\",{\"1\":{\"270\":1}}],[\"就可以生成一个与其他对象具有不同关系的新对象\",{\"1\":{\"237\":1}}],[\"就可以在字符串的左右两侧加上装饰字符\",{\"1\":{\"236\":1}}],[\"就可以明白调用\",{\"1\":{\"199\":1}}],[\"就像委托者自己完成一样\",{\"1\":{\"243\":1}}],[\"就像是剥洋葱时以为洋葱心要出来了\",{\"1\":{\"235\":1}}],[\"就像以前的公共电话亭\",{\"1\":{\"112\":1}}],[\"就再转给另外一个人\",{\"1\":{\"202\":1}}],[\"就自己做\",{\"1\":{\"202\":1}}],[\"就能很容易地改变实现\",{\"1\":{\"187\":1}}],[\"就需要获取并恢复这个信息\",{\"1\":{\"426\":1}}],[\"就需要存放到数据段中\",{\"1\":{\"419\":1}}],[\"就需要推卸责任\",{\"1\":{\"202\":1}}],[\"就需要先确认自己的意图\",{\"1\":{\"176\":1}}],[\"就需要重新设计该类\",{\"1\":{\"138\":1}}],[\"就算只能用单核处理任务\",{\"1\":{\"112\":1}}],[\"就是指针的加减\",{\"1\":{\"512\":1}}],[\"就是前文提到的\",{\"1\":{\"479\":1}}],[\"就是上述的消除左递归后的文法直接转换而来的\",{\"1\":{\"459\":1}}],[\"就是上例中\",{\"1\":{\"457\":1}}],[\"就是一种用来描述语法的语言\",{\"1\":{\"455\":1}}],[\"就是一种远程代理的实现\",{\"1\":{\"346\":1}}],[\"就是需要向前看的标记的个数了\",{\"1\":{\"446\":1}}],[\"就是这个标识符的哈希值\",{\"1\":{\"443\":1}}],[\"就是对应字符型和整型的存取操作\",{\"1\":{\"422\":1}}],[\"就是\",{\"1\":{\"73\":1,\"89\":1,\"236\":1}}],[\"就前进\",{\"1\":{\"11\":1}}],[\"得到结果\",{\"1\":{\"496\":1}}],[\"得到\",{\"1\":{\"367\":1,\"496\":2}}],[\"得益于接口\",{\"1\":{\"235\":1}}],[\"得知\",{\"1\":{\"75\":3,\"76\":1,\"77\":2,\"91\":3,\"92\":1,\"93\":1,\"94\":1}}],[\"得出对于任意自然数\",{\"1\":{\"72\":1,\"73\":1,\"88\":1,\"89\":1}}],[\"得证\",{\"1\":{\"72\":1,\"73\":1,\"88\":1,\"89\":1}}],[\"成立\",{\"1\":{\"72\":1,\"73\":1,\"75\":3,\"76\":1,\"77\":3,\"88\":1,\"89\":1,\"91\":3,\"92\":1,\"93\":1,\"94\":2}}],[\"ⅴ\",{\"0\":{\"103\":1},\"1\":{\"72\":1,\"73\":1,\"75\":3,\"76\":1,\"77\":2,\"81\":1,\"84\":1,\"88\":1,\"89\":1,\"91\":3,\"92\":1,\"93\":1,\"94\":1}}],[\"综上\",{\"1\":{\"419\":1,\"496\":1}}],[\"综上所述\",{\"1\":{\"72\":1,\"73\":1,\"77\":1,\"88\":1,\"89\":1,\"94\":1}}],[\"综合考虑\",{\"1\":{\"66\":1}}],[\"ⅱ\",{\"0\":{\"100\":1},\"1\":{\"72\":2,\"73\":2,\"75\":1,\"88\":1,\"89\":1,\"91\":1,\"94\":1}}],[\"ⅰ\",{\"0\":{\"99\":1},\"1\":{\"72\":1,\"73\":1,\"75\":1,\"88\":1,\"89\":1,\"91\":1}}],[\"也提到了优先级一般只与多元运算符有关\",{\"1\":{\"497\":1}}],[\"也许现在还想学习编译原理的人只可能是因为兴趣了\",{\"1\":{\"407\":1}}],[\"也不过是让程序睡眠\",{\"1\":{\"338\":1}}],[\"也不会被隐藏起来\",{\"1\":{\"235\":1}}],[\"也无法理解程序整体\",{\"1\":{\"199\":1}}],[\"也难以透彻地理解类的层次结构\",{\"1\":{\"176\":1}}],[\"也是一样的问题\",{\"1\":{\"426\":1}}],[\"也是用于指向栈的某些位置\",{\"1\":{\"420\":1}}],[\"也是不客观的\",{\"1\":{\"115\":1}}],[\"也是自然数\",{\"1\":{\"72\":1,\"88\":1}}],[\"也就能理解下面的源代码了\",{\"1\":{\"509\":1}}],[\"也就会导致写操作被原子性覆盖\",{\"1\":{\"114\":1}}],[\"也就是没有切换挂起状态\",{\"1\":{\"115\":1}}],[\"也就是一旦通过await关键字切换协程\",{\"1\":{\"114\":1}}],[\"也就是第二行代码print\",{\"1\":{\"114\":1}}],[\"也就是说由于我们的指令过于简单\",{\"1\":{\"426\":1}}],[\"也就是说可以\",{\"1\":{\"297\":1}}],[\"也就是说将\",{\"1\":{\"156\":1}}],[\"也就是说\",{\"1\":{\"71\":1,\"87\":1,\"175\":1,\"186\":1,\"235\":2,\"267\":2,\"268\":1,\"366\":1,\"367\":3,\"389\":2,\"398\":1}}],[\"也可以看文末给出的链接\",{\"1\":{\"512\":1}}],[\"也可以认为\",{\"1\":{\"496\":1}}],[\"也可以是一个地址\",{\"1\":{\"426\":1}}],[\"也可以是其它的数据\",{\"1\":{\"419\":1}}],[\"也可以说是\",{\"1\":{\"421\":1}}],[\"也可以直接\",{\"1\":{\"416\":1,\"434\":1,\"449\":1,\"470\":1,\"481\":1,\"491\":1,\"515\":1}}],[\"也可以恢复到之前的状态\",{\"1\":{\"311\":1}}],[\"也可以将它们自由组合成为新的对象\",{\"1\":{\"238\":1}}],[\"也可以理解为把程序\",{\"1\":{\"114\":1}}],[\"也可另外指定\",{\"1\":{\"23\":1}}],[\"也更简单\",{\"1\":{\"113\":1}}],[\"也能释放锁\",{\"1\":{\"112\":1}}],[\"也只能用到1个核\",{\"1\":{\"112\":1}}],[\"也唯一\",{\"1\":{\"73\":1,\"89\":1}}],[\"都比\",{\"1\":{\"522\":1}}],[\"都指向\",{\"1\":{\"487\":1}}],[\"都会非常困难\",{\"1\":{\"297\":1}}],[\"都会发生改变\",{\"1\":{\"267\":1}}],[\"都具有递归结构\",{\"1\":{\"235\":1}}],[\"都无需修改抽象工厂和\",{\"1\":{\"156\":1}}],[\"都保持了其一致性\",{\"1\":{\"114\":1}}],[\"都保证了其状态的一致性\",{\"1\":{\"114\":1}}],[\"都有唯一的数\",{\"1\":{\"94\":1}}],[\"都有序关系\",{\"1\":{\"84\":2}}],[\"都可以进行乘法运算\",{\"1\":{\"87\":1}}],[\"都可以进行加法运算\",{\"1\":{\"71\":1}}],[\"都是存放在计算机的\",{\"1\":{\"477\":1}}],[\"都是\",{\"1\":{\"366\":1}}],[\"都是对象\",{\"1\":{\"337\":1}}],[\"都是唯一的\",{\"1\":{\"73\":1,\"89\":1}}],[\"都是自然数\",{\"1\":{\"71\":1,\"72\":1,\"87\":1,\"88\":1}}],[\"加载变量的地址\",{\"1\":{\"500\":1}}],[\"加法保序性\",{\"0\":{\"85\":1}}],[\"加法消去律\",{\"0\":{\"77\":1},\"1\":{\"77\":1}}],[\"加法结合律\",{\"0\":{\"76\":1}}],[\"加法结果的唯一性\",{\"0\":{\"73\":1}}],[\"加法结果的存在性\",{\"0\":{\"72\":1}}],[\"加法交换律\",{\"0\":{\"75\":1}}],[\"加法的性质\",{\"0\":{\"74\":1}}],[\"加法的定义\",{\"0\":{\"71\":1}}],[\"加速\",{\"0\":{\"43\":1}}],[\"则结果是两个指针间隔的元素个数\",{\"1\":{\"512\":1}}],[\"则移动\",{\"1\":{\"512\":1}}],[\"则移动一字节\",{\"1\":{\"512\":1}}],[\"则意味着函数要退出了\",{\"1\":{\"489\":1}}],[\"则跳转到\",{\"1\":{\"487\":1}}],[\"则再加上\",{\"1\":{\"467\":1}}],[\"则可以断定是函数了\",{\"1\":{\"467\":1}}],[\"则说明是注释\",{\"1\":{\"446\":1}}],[\"则用于从子函数中返回\",{\"1\":{\"426\":1}}],[\"则会导致其失去作为可复用组件的独立性\",{\"1\":{\"199\":1}}],[\"则不需要加锁\",{\"1\":{\"115\":1}}],[\"则必须加锁\",{\"1\":{\"115\":1}}],[\"则对连通性无要求\",{\"1\":{\"103\":1}}],[\"则对一个数可以是多个数的后继\",{\"1\":{\"102\":1}}],[\"则对\",{\"1\":{\"101\":1}}],[\"则对点的出度无规定\",{\"1\":{\"100\":1}}],[\"则允许不存在\",{\"1\":{\"99\":1}}],[\"则存在正自然数\",{\"1\":{\"97\":1}}],[\"则由加法运算规则\",{\"1\":{\"94\":1}}],[\"则\",{\"1\":{\"71\":2,\"72\":1,\"73\":1,\"82\":1,\"83\":1,\"84\":3,\"85\":1,\"87\":2,\"88\":1,\"89\":1,\"96\":1,\"97\":1}}],[\"则有\",{\"1\":{\"69\":1,\"94\":1}}],[\"则需要写多个函数\",{\"1\":{\"57\":1}}],[\"由上可以看出\",{\"1\":{\"443\":1}}],[\"由调用者将参数出栈\",{\"1\":{\"426\":1}}],[\"由调用者将参数入栈\",{\"1\":{\"426\":1}}],[\"由此有\",{\"1\":{\"97\":1}}],[\"由此知道假设不成立\",{\"1\":{\"94\":1}}],[\"由乘法运算规则\",{\"1\":{\"88\":1,\"89\":1}}],[\"由加法结果的唯一性有\",{\"1\":{\"89\":1}}],[\"由加法结果的存在性有\",{\"1\":{\"88\":1}}],[\"由加法消去律得到\",{\"1\":{\"82\":1}}],[\"由加法运算规则\",{\"1\":{\"72\":1,\"73\":1}}],[\"由\",{\"1\":{\"69\":1,\"72\":2,\"73\":2,\"82\":2,\"83\":2,\"84\":1,\"85\":1,\"88\":1,\"89\":1,\"94\":2,\"96\":1}}],[\"由于取变量的值与函数的调用都是以\",{\"1\":{\"500\":1}}],[\"由于语法分析本身比较复杂\",{\"1\":{\"463\":1,\"474\":1}}],[\"由于本编译器的目的是达到自己编译自己\",{\"1\":{\"445\":1}}],[\"由于本人水平一般\",{\"1\":{\"411\":1}}],[\"由于我们的目标是能自举\",{\"1\":{\"443\":1}}],[\"由于词法分析的工作很常见\",{\"1\":{\"438\":1}}],[\"由于只存放字符串\",{\"1\":{\"419\":1}}],[\"由于在示例程序中只生成了一个\",{\"1\":{\"370\":1}}],[\"由于其他地方并没有控制消息发布和订阅的逻辑处理\",{\"1\":{\"297\":1}}],[\"由于笔者不太喜欢java\",{\"1\":{\"274\":1}}],[\"由于笔者不喜欢使用vpl的图形化\",{\"1\":{\"4\":1}}],[\"由于\",{\"1\":{\"267\":1}}],[\"由于硬件限制\",{\"1\":{\"8\":1,\"10\":1}}],[\"即当\",{\"1\":{\"512\":1}}],[\"即可\",{\"1\":{\"500\":1,\"503\":1}}],[\"即跨行的字符串拼接\",{\"1\":{\"498\":1}}],[\"即在这断代码之前\",{\"1\":{\"476\":1}}],[\"即我们将该变量的类别设置成了\",{\"1\":{\"468\":1}}],[\"即我们自己的虚拟机\",{\"1\":{\"416\":1}}],[\"即代码中的\",{\"1\":{\"467\":1}}],[\"即全局的定义语句\",{\"1\":{\"467\":1}}],[\"即向前看\",{\"1\":{\"450\":1}}],[\"即提前看多个字符\",{\"1\":{\"446\":1}}],[\"即用一个整型数组来保存相关的id信息\",{\"1\":{\"443\":1}}],[\"即用户主动触发协程切换\",{\"1\":{\"114\":1}}],[\"即如果它是个变量\",{\"1\":{\"443\":1}}],[\"即并不是多个字符共同构成标记\",{\"1\":{\"439\":1}}],[\"即前几篇中提到的\",{\"1\":{\"438\":1}}],[\"即与代码的上下文是有关系的\",{\"1\":{\"438\":1}}],[\"即标记本身和标记的值\",{\"1\":{\"436\":1}}],[\"即一连串的标记\",{\"1\":{\"436\":1}}],[\"即有两个参数\",{\"1\":{\"431\":1}}],[\"即保存当前的栈指针\",{\"1\":{\"427\":1}}],[\"即结果\",{\"1\":{\"425\":1}}],[\"即能自己编译自己\",{\"1\":{\"409\":1}}],[\"即构造一个工具\",{\"1\":{\"408\":1}}],[\"即应当将\",{\"1\":{\"268\":1}}],[\"即使最初实例很少\",{\"1\":{\"298\":1}}],[\"即使这些装饰边框都只具有非常简单的功能\",{\"1\":{\"238\":1}}],[\"即使被装饰物被边框装饰起来了\",{\"1\":{\"235\":1}}],[\"即使理解了\",{\"1\":{\"199\":1}}],[\"即使多个线程跑在8核处理上\",{\"1\":{\"112\":1}}],[\"即子类可以扩展父类的功能\",{\"1\":{\"132\":1}}],[\"即python3\",{\"1\":{\"114\":1}}],[\"即不会触发系统的全局解释器锁\",{\"1\":{\"113\":1}}],[\"即所谓的\",{\"1\":{\"113\":1}}],[\"即证明了乘法消去的保序性\",{\"1\":{\"97\":1}}],[\"即乘法结合律成立\",{\"1\":{\"93\":1}}],[\"即乘法分配律成立\",{\"1\":{\"92\":1}}],[\"即乘法交换律成立\",{\"1\":{\"91\":1}}],[\"即先证明乘法的两条运算规则符合交换律\",{\"1\":{\"91\":1}}],[\"即先证明加法的两条运算规则符合交换律\",{\"1\":{\"75\":1}}],[\"即任意两个自然数都可以进行乘法运算\",{\"1\":{\"90\":1}}],[\"即任意两个自然数都可以进行加法运算\",{\"1\":{\"74\":1}}],[\"即对于正自然数\",{\"1\":{\"81\":1}}],[\"即对于任意自然数\",{\"1\":{\"75\":1,\"76\":1,\"77\":1,\"91\":1,\"92\":1,\"93\":1,\"94\":1}}],[\"即加法结合律成立\",{\"1\":{\"76\":1}}],[\"即加法交换律成立\",{\"1\":{\"75\":1}}],[\"即由\",{\"1\":{\"72\":1,\"73\":1,\"88\":1,\"89\":1}}],[\"即\",{\"1\":{\"71\":1,\"72\":3,\"73\":3,\"77\":2,\"87\":1,\"88\":3,\"89\":3,\"94\":2,\"98\":5,\"174\":1,\"298\":2,\"380\":1,\"424\":1,\"436\":1,\"440\":1,\"457\":1,\"505\":1,\"508\":1,\"513\":1}}],[\"即假定\",{\"1\":{\"68\":1}}],[\"即写成\",{\"1\":{\"58\":1}}],[\"公理系统\",{\"2\":{\"105\":1}}],[\"公理系统内出发\",{\"1\":{\"95\":1}}],[\"公理自然不能从\",{\"1\":{\"95\":1}}],[\"公理自身任有待研究\",{\"1\":{\"95\":1}}],[\"公理每一条公理都被使用过\",{\"1\":{\"95\":1}}],[\"公理构建出了一个自然数代数系统\",{\"1\":{\"95\":1}}],[\"公理的合理性\",{\"0\":{\"95\":1}}],[\"公理相容\",{\"1\":{\"68\":1}}],[\"公理\",{\"0\":{\"99\":1,\"100\":1,\"101\":1,\"102\":1,\"103\":1},\"1\":{\"68\":1,\"69\":1,\"72\":2,\"73\":2,\"75\":3,\"76\":1,\"77\":2,\"81\":2,\"84\":1,\"88\":1,\"89\":1,\"91\":3,\"92\":1,\"93\":1,\"94\":4}}],[\"导致工作进度始终滞后\",{\"1\":{\"293\":1}}],[\"导致增加许多很小的类\",{\"0\":{\"239\":1}}],[\"导致插件无法正常退出\",{\"1\":{\"67\":1}}],[\"导致频繁冲出赛道\",{\"1\":{\"11\":1}}],[\"会使用到\",{\"1\":{\"468\":1}}],[\"会增加许多的成本\",{\"1\":{\"434\":1}}],[\"会出现\",{\"1\":{\"433\":1}}],[\"会生成如下的\",{\"1\":{\"426\":1}}],[\"会像下面这样将处理委托给\",{\"1\":{\"366\":1}}],[\"会占用大量的内存资源\",{\"1\":{\"309\":1}}],[\"会有许多相似的代码\",{\"1\":{\"410\":1}}],[\"会有\",{\"1\":{\"298\":1}}],[\"会编写一个\",{\"1\":{\"174\":1}}],[\"会导致父类的任何变换都可能影响到子类的行为\",{\"1\":{\"145\":1}}],[\"会导致activating\",{\"1\":{\"67\":1}}],[\"会分两种情况\",{\"1\":{\"115\":1}}],[\"会被转交\",{\"1\":{\"236\":1}}],[\"会被顺序执行\",{\"1\":{\"114\":1}}],[\"会被强行终止\",{\"1\":{\"67\":1}}],[\"会和adb冲突\",{\"1\":{\"109\":1}}],[\"会带有本地路径\",{\"1\":{\"61\":1}}],[\"若在此通过\",{\"1\":{\"478\":1}}],[\"若是\",{\"1\":{\"446\":1}}],[\"若得到的是单个字符\",{\"1\":{\"445\":1}}],[\"若碰到了一个我们不认识的字符该怎么处理\",{\"1\":{\"440\":1}}],[\"若无特殊理由\",{\"1\":{\"399\":1}}],[\"若为多线程则需要加锁\",{\"1\":{\"264\":1}}],[\"若去除\",{\"1\":{\"99\":1,\"100\":1,\"101\":1,\"102\":1,\"103\":1}}],[\"若有\",{\"1\":{\"94\":1}}],[\"若\",{\"1\":{\"71\":2,\"72\":1,\"73\":1,\"82\":1,\"83\":1,\"84\":3,\"85\":1,\"87\":2,\"88\":1,\"89\":1,\"96\":1,\"97\":1}}],[\"若deactivate\",{\"1\":{\"67\":1}}],[\"若activate\",{\"1\":{\"67\":1}}],[\"若设置两个轮的速度一致的话小车直行也会偏转\",{\"1\":{\"10\":1}}],[\"决定以后在学术研究和快速原型验证阶段使用\",{\"1\":{\"66\":1}}],[\"寻得了linux\",{\"1\":{\"66\":1}}],[\"选择了\",{\"1\":{\"66\":1}}],[\"最好的方式恐怕还是要自己实现它\",{\"1\":{\"523\":1}}],[\"最近知道了一个叫\",{\"1\":{\"522\":1}}],[\"最为重要的是能\",{\"1\":{\"520\":1}}],[\"最重要的是理解我们会为函数生成怎样的汇编代码\",{\"1\":{\"482\":1}}],[\"最大的区别就是保存的信息不同\",{\"1\":{\"482\":1}}],[\"最简单的方法是直接调用观察者的更新方法\",{\"1\":{\"323\":1}}],[\"最少知道原则\",{\"1\":{\"127\":1}}],[\"最后要注意的一点是\",{\"1\":{\"515\":1}}],[\"最后要注意的是还有一些字符\",{\"1\":{\"439\":1}}],[\"最后注意的是优先通常只与多元运算符相关\",{\"1\":{\"496\":1}}],[\"最后是main函数\",{\"1\":{\"459\":1}}],[\"最后再加上一个错误判断\",{\"1\":{\"432\":1}}],[\"最后祝你学得愉快\",{\"1\":{\"411\":1}}],[\"最后想介绍几个资料\",{\"1\":{\"411\":1}}],[\"最后\",{\"1\":{\"293\":1,\"516\":1}}],[\"最后的值不是0\",{\"1\":{\"112\":1}}],[\"最后左大幅度转弯寻找正确姿势\",{\"1\":{\"12\":1}}],[\"最终都根据它们的类型用\",{\"1\":{\"500\":1}}],[\"最终把源代码转换成目标代码\",{\"1\":{\"492\":1}}],[\"最终构建起我们的编译器\",{\"1\":{\"416\":1}}],[\"最终\",{\"1\":{\"66\":1}}],[\"仍然支持\",{\"1\":{\"66\":1}}],[\"而忽略了同样重要的代码生成\",{\"1\":{\"520\":1}}],[\"而数字\",{\"1\":{\"504\":1}}],[\"而就像上节中提到的\",{\"1\":{\"502\":1}}],[\"而普通的函数则编译成\",{\"1\":{\"500\":1}}],[\"而剩下的较难较烦的部分是与目标代码的生成有关的\",{\"1\":{\"497\":1}}],[\"而真正的难点是如何在语法分析时收集足够多的信息\",{\"1\":{\"492\":1}}],[\"而它们的逻辑和全局变量的解析几乎一致\",{\"1\":{\"482\":1}}],[\"而②则用于生成汇编代码\",{\"1\":{\"480\":1}}],[\"而②则与上节中提到的\",{\"1\":{\"479\":1}}],[\"而②中的代码是用于将符号表中的信息恢复成全局的信息\",{\"1\":{\"478\":1}}],[\"而注意到上节中\",{\"1\":{\"468\":1}}],[\"而如果\",{\"1\":{\"512\":1}}],[\"而如果是全局变量则用\",{\"1\":{\"500\":1}}],[\"而如果只解析到类型\",{\"1\":{\"467\":1}}],[\"而如果操作同一资源\",{\"1\":{\"112\":1}}],[\"而为了实现自举\",{\"1\":{\"464\":1}}],[\"而左递归的语法是没法直接使用递归下降的方法实现的\",{\"1\":{\"458\":1}}],[\"而没有出现在\",{\"1\":{\"455\":1}}],[\"而我们可以从解析的过程中看出\",{\"1\":{\"456\":1}}],[\"而我们定义的语法不支持\",{\"1\":{\"443\":1}}],[\"而我们还存放了一些只有语法分析器才会得到的信息\",{\"1\":{\"443\":1}}],[\"而我们又不希望扩充现有指令的功能\",{\"1\":{\"426\":1}}],[\"而我们又想在执行过程中保证共享数据的强一致性\",{\"1\":{\"114\":1}}],[\"而之后的语句\",{\"1\":{\"443\":1}}],[\"而只关心这个变量名代表的唯一标识\",{\"1\":{\"443\":1}}],[\"而词法分析器能减小语法分析复杂度的原因\",{\"1\":{\"439\":1}}],[\"而词法分析器则是以源码字符串为输入\",{\"1\":{\"437\":1}}],[\"而标记流对于语法分析器而言就容易处理得多了\",{\"1\":{\"437\":1}}],[\"而地址通常是需要通过计算获得\",{\"1\":{\"422\":1}}],[\"而这就意味着我们需要决定先为哪个运算符生成目标代码\",{\"1\":{\"496\":1}}],[\"而这些可能需要你重新回顾一下\",{\"1\":{\"482\":1}}],[\"而这些寄存器只是用于保存这些状态的\",{\"1\":{\"420\":1}}],[\"而这个标记足够让我们确定用哪个表达式了\",{\"1\":{\"457\":1}}],[\"而这部分能帮助我们了解计算机的工作原理\",{\"1\":{\"414\":1}}],[\"而电脑上的实际内存可能只有\",{\"1\":{\"419\":1}}],[\"而其它方面如词法分析\",{\"1\":{\"414\":1}}],[\"而会不会写编译器则是第二道\",{\"1\":{\"407\":1}}],[\"而将该方法的实现交给了子类\",{\"1\":{\"389\":1}}],[\"而将一些步骤的具体实现延迟到子类中\",{\"1\":{\"384\":1}}],[\"而忘记了在\",{\"1\":{\"369\":1}}],[\"而委托模式通过委托对象来执行具体的任务\",{\"1\":{\"343\":1}}],[\"而委托模式则用于将任务分配给其他对象来执行\",{\"1\":{\"343\":1}}],[\"而委托对象应当能够无缝地完成这些任务\",{\"1\":{\"243\":1}}],[\"而不能以值作为参数\",{\"1\":{\"422\":1}}],[\"而不需要修改现有的数据结构\",{\"1\":{\"393\":1}}],[\"而不需要修改现有的代码\",{\"1\":{\"375\":1}}],[\"而不需要关心代理对象的内部实现\",{\"1\":{\"344\":1}}],[\"而不需要客户端了解远程服务器的具体实现\",{\"1\":{\"342\":1}}],[\"而不会影响系统的其他部分\",{\"1\":{\"320\":1}}],[\"而不影响系统的功能\",{\"1\":{\"320\":1}}],[\"而不是\",{\"1\":{\"446\":1,\"457\":1,\"496\":1}}],[\"而不是盲目地套用\",{\"1\":{\"246\":1}}],[\"而不是继承\",{\"1\":{\"148\":1}}],[\"而不是一个通用接口\",{\"1\":{\"148\":1}}],[\"而不是通过继承\",{\"1\":{\"146\":2}}],[\"而不是具体实现\",{\"1\":{\"143\":1}}],[\"而不是面向实现编程\",{\"1\":{\"142\":1}}],[\"而不是重写父类的具体方法\",{\"1\":{\"133\":1}}],[\"而在我们的虚拟机中\",{\"1\":{\"423\":1}}],[\"而在内存容量多的运行环境中则可以使用\",{\"1\":{\"380\":1}}],[\"而在\",{\"1\":{\"368\":1}}],[\"而在其他情况下\",{\"1\":{\"310\":1}}],[\"而在工业生产部署阶段方才使用\",{\"1\":{\"66\":1}}],[\"而对于一些复杂的应用\",{\"1\":{\"309\":1}}],[\"而窄接口则只提供了有限的操作权限\",{\"1\":{\"308\":1}}],[\"而内存是资源中的一种\",{\"1\":{\"270\":1}}],[\"而应理解其背后的核心思想\",{\"1\":{\"246\":1}}],[\"而无需了解其内部实现细节\",{\"1\":{\"287\":1}}],[\"而无需暴露其底层表示\",{\"1\":{\"284\":1,\"285\":1}}],[\"而无需修改现有代码\",{\"1\":{\"278\":1}}],[\"而无需修改原始类的代码\",{\"1\":{\"230\":1}}],[\"而无需明确指定具体类\",{\"1\":{\"152\":1}}],[\"而文件则是叶子节点\",{\"1\":{\"220\":1}}],[\"而具体的表示则可以在运行时灵活选择\",{\"1\":{\"198\":1}}],[\"而有些事情则需要在运行时决定\",{\"1\":{\"198\":1}}],[\"而有没有锁\",{\"1\":{\"112\":1}}],[\"而是如何为运算符生成相应的汇编代码\",{\"1\":{\"520\":1}}],[\"而是单个数字的取正取负操作\",{\"1\":{\"506\":1}}],[\"而是操作\",{\"1\":{\"419\":1}}],[\"而是用状态迁移表来设计程序\",{\"1\":{\"367\":1}}],[\"而是将所有的状态迁移交给扮演\",{\"1\":{\"367\":1}}],[\"而是将它放在\",{\"1\":{\"267\":1}}],[\"而是将其他\",{\"1\":{\"187\":1}}],[\"而是应该用代码将它们表现出来\",{\"1\":{\"249\":1}}],[\"而是为了更好地解决问题和优化代码结构\",{\"1\":{\"246\":1}}],[\"而是相互关联的\",{\"1\":{\"128\":1}}],[\"而且这些功能需求大都是\",{\"1\":{\"399\":1}}],[\"而且我们必须在所有的事件处理方法中都编写这些条件分支语句\",{\"1\":{\"365\":1}}],[\"而且当将子类替换为\",{\"1\":{\"199\":1}}],[\"而且\",{\"1\":{\"186\":1,\"379\":1}}],[\"而且小车并不能知道自己\",{\"1\":{\"10\":1}}],[\"而子类的任务是实现抽象方法\",{\"1\":{\"175\":1}}],[\"而协程虽然在手动切换过程中也无法保证状态一致\",{\"1\":{\"114\":1}}],[\"而线程是抢占使用权\",{\"1\":{\"113\":1}}],[\"而现在\",{\"1\":{\"112\":1}}],[\"而\",{\"1\":{\"66\":2,\"298\":1,\"308\":1,\"311\":1,\"397\":2,\"409\":1,\"422\":1,\"478\":2,\"508\":1}}],[\"然而如果你能跟我一样\",{\"1\":{\"408\":1}}],[\"然而\",{\"1\":{\"154\":1,\"246\":1,\"269\":1}}],[\"然而我们都忽略了一个客观事实\",{\"1\":{\"114\":1}}],[\"然而人们很快发现\",{\"1\":{\"112\":1}}],[\"然而速度太慢\",{\"1\":{\"66\":1}}],[\"然后返回它在\",{\"1\":{\"445\":1}}],[\"然后让数据结构可以接受访问者的访问即可\",{\"1\":{\"392\":1}}],[\"然后让后者去验算前者的计算结果\",{\"1\":{\"380\":1}}],[\"然后在程序中以委托的方式来使用算法\",{\"1\":{\"379\":1}}],[\"然后在具体类中实现这些行为\",{\"1\":{\"146\":1}}],[\"然后实现一些所需的方法就可以了\",{\"1\":{\"369\":1}}],[\"然后进行相应的处理\",{\"1\":{\"365\":1}}],[\"然后下达指示\",{\"1\":{\"293\":1}}],[\"然后按照它们在职责链上的顺序一个一个地找出到底应该谁来负责处理\",{\"1\":{\"202\":1}}],[\"然后再去看看\",{\"1\":{\"199\":1}}],[\"然后编写\",{\"1\":{\"186\":1}}],[\"然后保存在字段中\",{\"1\":{\"178\":1}}],[\"然后子类负责实现这些抽象方法\",{\"1\":{\"175\":1}}],[\"然后\",{\"1\":{\"112\":1}}],[\"然后才能去处理另一件事情\",{\"1\":{\"111\":1}}],[\"然后就能正常访问\",{\"1\":{\"32\":1}}],[\"然后不断二分得到直行时右轮的速度为\",{\"1\":{\"10\":1}}],[\"近日使用\",{\"1\":{\"66\":1}}],[\"2|\",{\"1\":{\"496\":1}}],[\"2+3\",{\"1\":{\"496\":1}}],[\"2+3的值\",{\"1\":{\"496\":1}}],[\"2+\",{\"1\":{\"430\":2,\"477\":2}}],[\"2^32\",{\"1\":{\"419\":1}}],[\"24\",{\"1\":{\"362\":1}}],[\"26\",{\"1\":{\"318\":2}}],[\"264\",{\"1\":{\"205\":1}}],[\"256\",{\"1\":{\"416\":1,\"419\":1}}],[\"25\",{\"1\":{\"306\":1,\"318\":2}}],[\"25866579\",{\"1\":{\"51\":1}}],[\"22\",{\"1\":{\"265\":10,\"318\":2}}],[\"2222222222\",{\"1\":{\"265\":1}}],[\"222222\",{\"1\":{\"265\":1}}],[\"297\",{\"1\":{\"205\":1}}],[\"231\",{\"1\":{\"205\":1,\"306\":1}}],[\"2014\",{\"1\":{\"495\":1}}],[\"2016\",{\"1\":{\"453\":1,\"463\":1,\"474\":1,\"485\":1,\"519\":1}}],[\"2015\",{\"1\":{\"414\":1,\"417\":1,\"435\":1}}],[\"2017\",{\"1\":{\"274\":1}}],[\"20\",{\"1\":{\"298\":1,\"317\":1,\"318\":2,\"433\":1,\"467\":1,\"496\":2}}],[\"20000\",{\"1\":{\"225\":1,\"226\":2,\"394\":1,\"395\":2}}],[\"200\",{\"1\":{\"204\":1,\"225\":1,\"226\":1,\"394\":1,\"395\":1}}],[\"208\",{\"1\":{\"111\":1,\"115\":1}}],[\"28\",{\"1\":{\"114\":1,\"318\":2}}],[\"2\",{\"1\":{\"65\":1,\"66\":1,\"113\":1,\"114\":3,\"204\":1,\"212\":2,\"264\":1,\"298\":1,\"305\":3,\"318\":2,\"376\":3,\"406\":1,\"414\":2,\"417\":17,\"426\":2,\"430\":2,\"432\":4,\"435\":3,\"436\":2,\"449\":1,\"453\":2,\"456\":2,\"463\":7,\"474\":7,\"477\":2,\"480\":1,\"485\":3,\"495\":14,\"496\":7,\"500\":1,\"519\":2}}],[\"踩坑记录\",{\"0\":{\"66\":1},\"2\":{\"63\":1}}],[\">|\",{\"1\":{\"443\":1,\"480\":1}}],[\">=\",{\"1\":{\"431\":1,\"443\":5,\"444\":8,\"447\":1,\"459\":2,\"502\":1,\"508\":1,\"512\":1}}],[\">=2\",{\"1\":{\"66\":1}}],[\">>\",{\"1\":{\"386\":1,\"387\":1,\"431\":1,\"447\":1,\"512\":1}}],[\">hiroshi\",{\"1\":{\"252\":1}}],[\">excite<\",{\"1\":{\"153\":1}}],[\">jp\",{\"1\":{\"153\":1}}],[\">us\",{\"1\":{\"153\":1}}],[\">gmw<\",{\"1\":{\"153\":1}}],[\">people<\",{\"1\":{\"153\":1}}],[\">$\",{\"1\":{\"153\":1,\"251\":1}}],[\">\",{\"1\":{\"61\":2,\"305\":2,\"416\":1,\"431\":1,\"437\":4,\"444\":1,\"447\":3,\"459\":1,\"466\":1,\"500\":1,\"507\":1,\"512\":2,\"513\":3,\"514\":1}}],[\"生成汇编代码\",{\"1\":{\"513\":2}}],[\"生成了如下的汇编代码\",{\"1\":{\"509\":1}}],[\"生成一个同名的函数\",{\"1\":{\"457\":1}}],[\"生成一棵语法树\",{\"1\":{\"415\":1}}],[\"生成实例\",{\"2\":{\"160\":1,\"201\":1,\"335\":1,\"359\":1}}],[\"生成\",{\"1\":{\"61\":1,\"338\":1}}],[\"生活记录等非技术类文章\",{\"1\":{\"2\":1}}],[\"泛型编程\",{\"0\":{\"58\":1}}],[\"泛型与\",{\"0\":{\"53\":1}}],[\"第二个参数放在\",{\"1\":{\"431\":1}}],[\"第二种\",{\"0\":{\"57\":1}}],[\"第一个参数放在栈顶\",{\"1\":{\"431\":1}}],[\"第一篇完全没有正题相关的内容也是希望你能有所心理准备再开始学习\",{\"1\":{\"410\":1}}],[\"第一种策略是\",{\"1\":{\"376\":1}}],[\"第一种\",{\"0\":{\"56\":1}}],[\"第三个字符的颜色是红色的\",{\"1\":{\"267\":1}}],[\"第\",{\"1\":{\"175\":1,\"367\":1}}],[\"三目运算符\",{\"0\":{\"510\":1},\"1\":{\"495\":1}}],[\"三点水\",{\"1\":{\"406\":1}}],[\"三是式子太长\",{\"1\":{\"56\":1}}],[\"三国杀\",{\"1\":{\"3\":1}}],[\"清晰明了\",{\"1\":{\"56\":1}}],[\"清河公主\",{\"1\":{\"3\":1}}],[\"下一条\",{\"1\":{\"420\":1,\"424\":1}}],[\"下一章中我们将讲解语句的解析\",{\"1\":{\"482\":1}}],[\"下一章中我们将介绍如何解析函数的定义\",{\"1\":{\"471\":1}}],[\"下一章中\",{\"1\":{\"416\":1,\"450\":1}}],[\"下一个人如果可以自己处理\",{\"1\":{\"202\":1}}],[\"下一步\",{\"1\":{\"124\":1}}],[\"下午好\",{\"1\":{\"193\":1,\"194\":1}}],[\"下面以加法为例\",{\"1\":{\"512\":1}}],[\"下面以式子\",{\"1\":{\"55\":1}}],[\"下面是\",{\"1\":{\"466\":1}}],[\"下面是相应的源代码\",{\"1\":{\"416\":1}}],[\"下面的例子\",{\"1\":{\"426\":1}}],[\"下面我们逐一解释\",{\"1\":{\"486\":1}}],[\"下面我们用我们的汇编写一小段程序\",{\"1\":{\"433\":1}}],[\"下面我们来看一段使用了\",{\"1\":{\"376\":1}}],[\"下面我们试着通过删除公理的方法来寻找反例\",{\"1\":{\"98\":1}}],[\"下面我们需要证明对于任意两个自然数\",{\"1\":{\"71\":1,\"87\":1}}],[\"下面我将阐述为什么每条公理都是必须的\",{\"1\":{\"95\":1}}],[\"下面证明乘法消去律\",{\"1\":{\"94\":1}}],[\"下面证明乘法结合律\",{\"1\":{\"93\":1}}],[\"下面证明乘法分配律\",{\"1\":{\"92\":1}}],[\"下面证明乘法交换律\",{\"1\":{\"91\":1}}],[\"下面证明加法消去律\",{\"1\":{\"77\":1}}],[\"下面证明加法结合律\",{\"1\":{\"76\":1}}],[\"下面证明加法交换律\",{\"1\":{\"75\":1}}],[\"下文用\",{\"1\":{\"69\":1}}],[\"下载错误查看\",{\"1\":{\"22\":1}}],[\"取址\",{\"1\":{\"503\":1}}],[\"取址操作\",{\"0\":{\"503\":1},\"1\":{\"495\":1}}],[\"取自\",{\"1\":{\"426\":1}}],[\"取值会更高效\",{\"1\":{\"422\":1}}],[\"取模运算就成为了编程中不可缺少的一部分\",{\"1\":{\"55\":1}}],[\"取较小距离为有障碍\",{\"1\":{\"8\":1}}],[\"要容易\",{\"1\":{\"522\":1}}],[\"要根据它的类型放大\",{\"1\":{\"512\":1}}],[\"要理解函数定义的解析过程\",{\"1\":{\"482\":1}}],[\"要理解这些寄存器的作用\",{\"1\":{\"420\":1}}],[\"要是深入词法分析器\",{\"1\":{\"437\":1}}],[\"要引入的命令有\",{\"1\":{\"426\":1}}],[\"要执行的计算机指令\",{\"1\":{\"420\":1}}],[\"要执行的具体操作\",{\"1\":{\"214\":1}}],[\"要么就是借助了自动生成的工具\",{\"1\":{\"409\":1}}],[\"要么是因为这道题目直接考察了模的性质和运用\",{\"1\":{\"54\":1}}],[\"要么是因为答案是浮点数\",{\"1\":{\"54\":1}}],[\"要求栈顶存放地址\",{\"1\":{\"422\":2}}],[\"要求子类去实现抽象方法\",{\"1\":{\"389\":1}}],[\"要求\",{\"1\":{\"202\":1,\"422\":2}}],[\"要同时进行多件事情本来就需要正在运行的让出处理器\",{\"1\":{\"111\":1}}],[\"要部署的\",{\"1\":{\"28\":1}}],[\"背景介绍\",{\"0\":{\"54\":1}}],[\"中我们介绍过内置函数的支持\",{\"1\":{\"500\":1}}],[\"中即可\",{\"1\":{\"498\":1}}],[\"中存放的是参数的位置\",{\"1\":{\"479\":1}}],[\"中存放地址\",{\"1\":{\"422\":2}}],[\"中存放如指针\",{\"1\":{\"419\":1}}],[\"中间代码的表示\",{\"1\":{\"408\":1}}],[\"中注册有多个\",{\"1\":{\"321\":1}}],[\"中保存这个信息\",{\"1\":{\"268\":1}}],[\"中的值执行减\",{\"1\":{\"513\":1}}],[\"中的信息还原\",{\"1\":{\"478\":1}}],[\"中的全局变量不同\",{\"1\":{\"477\":1}}],[\"中的位置\",{\"1\":{\"476\":1}}],[\"中的位置变化而发生变化\",{\"1\":{\"268\":1}}],[\"中的一种\",{\"1\":{\"455\":1}}],[\"中的\",{\"1\":{\"422\":1,\"446\":1}}],[\"中的数据作为整数存放入地址中\",{\"1\":{\"422\":1}}],[\"中的数据作为字符存放入地址中\",{\"1\":{\"422\":1}}],[\"中的内存\",{\"1\":{\"419\":1}}],[\"中的书籍\",{\"1\":{\"287\":2}}],[\"中的哪个地方都不会改变\",{\"1\":{\"268\":1}}],[\"中是第几个字符这种信息会根据\",{\"1\":{\"268\":1}}],[\"中增加多少个功能\",{\"1\":{\"186\":1}}],[\"中增加新功能时\",{\"1\":{\"174\":1}}],[\"中增加\",{\"1\":{\"157\":1}}],[\"中文官网\",{\"1\":{\"124\":1}}],[\"中\",{\"1\":{\"53\":1,\"175\":1,\"269\":1,\"422\":6,\"423\":1,\"426\":1,\"431\":2,\"479\":1,\"502\":1,\"509\":1}}],[\"在后期解析语句和表达式时\",{\"1\":{\"520\":1}}],[\"在学习\",{\"1\":{\"514\":1}}],[\"在执行自增自减后\",{\"1\":{\"513\":1}}],[\"在执行命令前保存对象的快照\",{\"1\":{\"215\":1}}],[\"在作指针减法时\",{\"1\":{\"512\":1}}],[\"在解析\",{\"1\":{\"509\":1}}],[\"在解析的过程中\",{\"1\":{\"477\":1}}],[\"在前文的一元运算符处理中也用到了这一点\",{\"1\":{\"508\":1}}],[\"在计算一个运算符\",{\"1\":{\"496\":1}}],[\"在函数体内局部变量就会覆盖全局变量\",{\"1\":{\"478\":1}}],[\"在函数内访问它们是通过\",{\"1\":{\"477\":1}}],[\"在思考这个问题之前\",{\"1\":{\"477\":1}}],[\"在main函数中进行初始化如下\",{\"1\":{\"448\":1}}],[\"在main函数中加入初始化代码\",{\"1\":{\"419\":1}}],[\"在语法分析前将关键字提前加入符号表\",{\"1\":{\"448\":1}}],[\"在我们的编译器中共识别\",{\"1\":{\"486\":1}}],[\"在我们的\",{\"1\":{\"446\":1}}],[\"在我看来\",{\"1\":{\"407\":1}}],[\"在分析时\",{\"1\":{\"445\":2}}],[\"在全局中添加如下定义\",{\"1\":{\"439\":1}}],[\"在全局中加入如下定义\",{\"1\":{\"420\":1}}],[\"在代码的开头\",{\"1\":{\"433\":1}}],[\"在将调用子函数时压入栈中的数据清除\",{\"1\":{\"428\":1}}],[\"在调用函数时会使用到它\",{\"1\":{\"420\":1}}],[\"在调用那个方法之前需要先在这个类中注册一下\",{\"1\":{\"249\":1}}],[\"在调用那个类之前需要先调用这个类\",{\"1\":{\"249\":1}}],[\"在写编译器的时候会遇到两个主要问题\",{\"1\":{\"410\":1}}],[\"在开始进入正题之前\",{\"1\":{\"406\":1}}],[\"在练习题中\",{\"1\":{\"398\":1}}],[\"在父类中\",{\"1\":{\"389\":1}}],[\"在父类中定义处理流程的框架\",{\"1\":{\"384\":1}}],[\"在子类中重写父类的方法可以改变程序的行为\",{\"1\":{\"389\":1}}],[\"在子类中可以使用父类中定义的方法\",{\"1\":{\"389\":1}}],[\"在子类中实现具体处理\",{\"1\":{\"384\":1}}],[\"在内存容量少的运行环境中可以使用\",{\"1\":{\"380\":1}}],[\"在程序运行中也可以切换角色\",{\"1\":{\"380\":1}}],[\"在运行时检测出问题并不难\",{\"1\":{\"369\":1}}],[\"在修改状态迁移部分的代码时\",{\"1\":{\"369\":1}}],[\"在不修改现有代码的前提下进行扩展\",{\"1\":{\"399\":1}}],[\"在不使用\",{\"1\":{\"365\":1}}],[\"在不改变被装饰物的前提下增加功能\",{\"0\":{\"236\":1}}],[\"在本章的警报系统的示例程序中\",{\"1\":{\"365\":1}}],[\"在本节中\",{\"1\":{\"285\":1}}],[\"在头脑中\",{\"1\":{\"365\":1}}],[\"在多线程环境中\",{\"1\":{\"356\":1}}],[\"在示例程序的\",{\"1\":{\"321\":1}}],[\"在示例程序中\",{\"1\":{\"187\":1,\"235\":2,\"268\":2,\"270\":1,\"299\":1,\"321\":1,\"367\":2,\"368\":1,\"398\":1,\"402\":1}}],[\"在观察者模式中\",{\"1\":{\"320\":1,\"323\":1}}],[\"在图形用户界面\",{\"1\":{\"316\":1}}],[\"在实际调用函数时\",{\"1\":{\"426\":1}}],[\"在实际应用中\",{\"1\":{\"309\":1}}],[\"在实际开发中\",{\"1\":{\"246\":1}}],[\"在某些情况下\",{\"1\":{\"288\":1,\"310\":1,\"324\":1,\"341\":1}}],[\"在上面的代码中\",{\"1\":{\"287\":1,\"357\":1}}],[\"在操作系统中\",{\"1\":{\"270\":1}}],[\"在使用模式时需要注意应当是谁来管理状态迁移\",{\"1\":{\"367\":1}}],[\"在使用\",{\"1\":{\"269\":1}}],[\"在有垃圾回收的语言中要注意共享内存未被使用时被\",{\"1\":{\"269\":1}}],[\"在决定\",{\"1\":{\"267\":1}}],[\"在共享实例时应当注意什么呢\",{\"1\":{\"267\":1}}],[\"在需要生成大量细粒度对象的场景中\",{\"1\":{\"263\":1}}],[\"在委托模式中\",{\"1\":{\"243\":1}}],[\"在文件系统中\",{\"1\":{\"220\":1}}],[\"在命令模式中\",{\"1\":{\"214\":1}}],[\"在这个前提下\",{\"1\":{\"437\":1}}],[\"在这个示例程序中\",{\"1\":{\"297\":1,\"375\":1}}],[\"在这个示例中\",{\"1\":{\"204\":1,\"230\":1,\"250\":1,\"305\":1,\"317\":1}}],[\"在这种情况下\",{\"1\":{\"367\":1}}],[\"在这种要求之下\",{\"1\":{\"55\":1}}],[\"在其内部调用了类的特有的方法\",{\"1\":{\"199\":1}}],[\"在判断到底应该修改哪个类时\",{\"1\":{\"199\":1}}],[\"在编程时\",{\"1\":{\"199\":1,\"267\":1,\"365\":1}}],[\"在设计类时\",{\"1\":{\"399\":1}}],[\"在设计\",{\"1\":{\"321\":1}}],[\"在设计模式中\",{\"1\":{\"320\":1,\"342\":1}}],[\"在设计软件时\",{\"1\":{\"198\":1}}],[\"在设计一个系统模块的时候\",{\"1\":{\"129\":1}}],[\"在面向对象编程中\",{\"1\":{\"197\":1,\"242\":1,\"337\":1}}],[\"在桥的哪一侧\",{\"1\":{\"178\":1}}],[\"在软件开发中\",{\"1\":{\"163\":1}}],[\"在发现类有多个职责时\",{\"1\":{\"139\":1}}],[\"在所有线程相互独立且不会操作同一资源的模式下\",{\"1\":{\"112\":1}}],[\"在python编程领域\",{\"1\":{\"111\":1}}],[\"在明确证明了自然数乘法运算的良好性质\",{\"1\":{\"90\":1}}],[\"在明确证明了自然数加法运算的良好性质\",{\"1\":{\"74\":1}}],[\"在考察序的性质之前\",{\"1\":{\"80\":1}}],[\"在此承认次假设的基础之上\",{\"1\":{\"68\":1}}],[\"在项目根目录下创建\",{\"1\":{\"65\":1}}],[\"在\",{\"1\":{\"53\":1,\"156\":1,\"157\":2,\"175\":1,\"178\":1,\"235\":1,\"236\":1,\"256\":1,\"268\":1,\"308\":1,\"311\":1,\"365\":1,\"366\":3,\"369\":2,\"370\":3,\"392\":1,\"397\":1,\"402\":1,\"420\":1,\"422\":1,\"423\":1,\"433\":1,\"479\":1,\"512\":1}}],[\"在准备好前端项目及安装相应环境后\",{\"1\":{\"29\":1}}],[\"=<=\",{\"1\":{\"512\":1}}],[\"=左边的就称作\",{\"1\":{\"455\":1}}],[\"==\",{\"1\":{\"204\":1,\"264\":1,\"279\":4,\"294\":1,\"317\":1,\"338\":1,\"422\":5,\"423\":1,\"424\":1,\"425\":2,\"426\":2,\"427\":1,\"428\":1,\"429\":1,\"430\":1,\"431\":17,\"432\":8,\"439\":2,\"441\":1,\"442\":1,\"443\":3,\"444\":2,\"445\":6,\"446\":2,\"447\":33,\"459\":7,\"467\":8,\"468\":2,\"469\":1,\"476\":1,\"478\":1,\"479\":5,\"480\":6,\"487\":2,\"488\":1,\"489\":1,\"490\":2,\"498\":3,\"499\":5,\"500\":9,\"501\":5,\"502\":2,\"503\":3,\"504\":2,\"505\":1,\"506\":3,\"507\":6,\"509\":4,\"510\":2,\"511\":2,\"512\":3,\"513\":5,\"514\":2}}],[\"===>\",{\"1\":{\"487\":1}}],[\"===`\",{\"1\":{\"338\":1}}],[\"====\",{\"1\":{\"306\":3}}],[\"==============================\",{\"1\":{\"193\":2,\"194\":2}}],[\"===\",{\"1\":{\"204\":2,\"232\":3,\"279\":3,\"294\":2,\"305\":3,\"338\":1,\"339\":2,\"353\":2,\"357\":2,\"376\":4}}],[\"=>\",{\"1\":{\"153\":2,\"193\":2,\"211\":1,\"222\":2,\"264\":2,\"279\":1,\"294\":1,\"305\":1,\"317\":2,\"338\":1,\"357\":2,\"394\":1,\"436\":1,\"456\":11}}],[\"=\",{\"1\":{\"52\":14,\"65\":7,\"108\":1,\"112\":7,\"113\":5,\"114\":21,\"144\":3,\"147\":3,\"153\":20,\"166\":4,\"179\":1,\"180\":1,\"182\":3,\"183\":4,\"193\":11,\"204\":13,\"211\":9,\"222\":1,\"225\":7,\"232\":10,\"251\":5,\"258\":7,\"264\":11,\"279\":34,\"280\":5,\"286\":10,\"294\":7,\"305\":18,\"306\":6,\"317\":11,\"331\":18,\"338\":7,\"353\":5,\"357\":4,\"362\":7,\"376\":31,\"386\":9,\"394\":15,\"416\":8,\"419\":6,\"420\":3,\"422\":6,\"423\":1,\"424\":1,\"425\":2,\"426\":4,\"427\":3,\"428\":1,\"429\":3,\"430\":1,\"431\":17,\"432\":8,\"433\":11,\"439\":3,\"440\":1,\"442\":2,\"443\":11,\"444\":8,\"445\":9,\"446\":3,\"447\":29,\"448\":9,\"455\":4,\"457\":3,\"458\":5,\"459\":19,\"464\":13,\"467\":23,\"468\":10,\"475\":8,\"476\":2,\"478\":5,\"479\":14,\"480\":16,\"487\":6,\"488\":6,\"489\":2,\"490\":2,\"498\":9,\"499\":6,\"500\":19,\"501\":3,\"502\":2,\"503\":1,\"504\":5,\"505\":6,\"506\":8,\"507\":10,\"508\":1,\"509\":7,\"510\":6,\"511\":8,\"512\":10,\"513\":14,\"514\":8,\"515\":7}}],[\"=404\",{\"1\":{\"30\":3,\"36\":5}}],[\"61\",{\"1\":{\"444\":1}}],[\"64\",{\"1\":{\"433\":2}}],[\"6\",{\"0\":{\"474\":1},\"1\":{\"212\":2,\"264\":1,\"298\":2,\"305\":2,\"406\":1,\"414\":1,\"417\":2,\"432\":1,\"435\":2,\"453\":2,\"456\":1,\"463\":1,\"474\":2,\"485\":1,\"486\":1,\"495\":3,\"515\":1,\"519\":1}}],[\"66\",{\"1\":{\"205\":1}}],[\"609639797\",{\"1\":{\"51\":1}}],[\"65\",{\"1\":{\"30\":1}}],[\"参照第三章讲解的虚拟机\",{\"1\":{\"477\":1}}],[\"参数和局部变量\",{\"1\":{\"482\":1}}],[\"参数逆序入栈\",{\"1\":{\"426\":1}}],[\"参数\",{\"1\":{\"214\":1,\"433\":1}}],[\"参见第\",{\"1\":{\"500\":1}}],[\"参见\",{\"1\":{\"51\":1}}],[\"参考\",{\"1\":{\"48\":1}}],[\"参考资料\",{\"0\":{\"39\":1,\"411\":1}}],[\"自己实现了一个c语言的编译器\",{\"1\":{\"516\":1}}],[\"自己和被委托对象的一致性\",{\"0\":{\"243\":1}}],[\"自增自减\",{\"0\":{\"507\":1,\"513\":1},\"1\":{\"495\":2}}],[\"自底向上是不断地将终结符进行合并\",{\"1\":{\"454\":1}}],[\"自顶向下是从起始非终结符开始\",{\"1\":{\"454\":1}}],[\"自然数与有向图\",{\"1\":{\"98\":1}}],[\"自然数中最重要的运算当然是加法\",{\"1\":{\"70\":1}}],[\"自然数的乘法也十分重要\",{\"1\":{\"86\":1}}],[\"自然数的乘法运算\",{\"0\":{\"86\":1}}],[\"自然数的序是全序关系\",{\"1\":{\"79\":1}}],[\"自然数的序为两个自然数的关系\",{\"1\":{\"78\":1}}],[\"自然数的序\",{\"0\":{\"78\":1}}],[\"自然数的加法运算\",{\"0\":{\"70\":1}}],[\"自然数的定义\",{\"0\":{\"69\":1}}],[\"自然数的定义则是构建此算术公理系统的第一步\",{\"1\":{\"68\":1}}],[\"自然数这个新的数学对象因我们的假设而确立\",{\"1\":{\"69\":1}}],[\"自然数\",{\"0\":{\"68\":1},\"1\":{\"80\":1}}],[\"自建mail\",{\"0\":{\"51\":1}}],[\"自由访问知识和文化\",{\"1\":{\"18\":1}}],[\"技术分享等内容\",{\"1\":{\"50\":1}}],[\"技术\",{\"0\":{\"50\":1}}],[\"工作所需的条件\",{\"0\":{\"402\":1}}],[\"工作流程\",{\"0\":{\"49\":1}}],[\"工厂方法\",{\"2\":{\"261\":1}}],[\"工厂模式\",{\"1\":{\"143\":1}}],[\"工程化\",{\"1\":{\"246\":1}}],[\"工具\",{\"0\":{\"126\":1}}],[\"工具下载\",{\"1\":{\"124\":1}}],[\"工具使用\",{\"1\":{\"50\":1}}],[\"工具等资源\",{\"1\":{\"18\":1}}],[\"拉取镜像方法\",{\"1\":{\"46\":1}}],[\"作用是减小语法分析器的复杂程度\",{\"1\":{\"450\":1}}],[\"作为观察者\",{\"1\":{\"325\":1}}],[\"作为被观察对象\",{\"1\":{\"325\":1}}],[\"作为设计人员\",{\"1\":{\"197\":1}}],[\"作为代码托管平台的开发者来说\",{\"1\":{\"44\":1}}],[\"作出决策并发送报文控制小车\",{\"1\":{\"5\":1}}],[\"流程更加简化和统一\",{\"1\":{\"44\":1}}],[\"持续交付\",{\"1\":{\"44\":1}}],[\"团队协作和版本控制工具来管理容器镜像\",{\"1\":{\"44\":1}}],[\"镜像地址\",{\"0\":{\"45\":1}}],[\"镜像\",{\"1\":{\"44\":1}}],[\"的表示方法\",{\"1\":{\"522\":1}}],[\"的表达式\",{\"1\":{\"509\":1}}],[\"的地址两次\",{\"1\":{\"507\":1}}],[\"的优先级最高\",{\"1\":{\"508\":1}}],[\"的优先级最低\",{\"1\":{\"508\":1}}],[\"的优先级高于\",{\"1\":{\"507\":1}}],[\"的优先级就要高于\",{\"1\":{\"439\":1}}],[\"的指针取值\",{\"1\":{\"502\":1}}],[\"的指令集\",{\"1\":{\"421\":1}}],[\"的形式\",{\"1\":{\"500\":1}}],[\"的形式返回\",{\"1\":{\"445\":1}}],[\"的运算符\",{\"1\":{\"496\":1}}],[\"的运算结果为\",{\"1\":{\"71\":1,\"87\":1}}],[\"的结果\",{\"1\":{\"496\":1}}],[\"的结果是否唯一\",{\"1\":{\"73\":1,\"89\":1}}],[\"的位置\",{\"1\":{\"479\":1,\"487\":1}}],[\"的产生式转换成函数的过程\",{\"1\":{\"471\":1}}],[\"的具体表示方法后就不难理解了\",{\"1\":{\"471\":1}}],[\"的扩展\",{\"1\":{\"464\":1}}],[\"的概念了\",{\"1\":{\"457\":1}}],[\"的概念\",{\"1\":{\"446\":1,\"450\":1}}],[\"的注释\",{\"1\":{\"446\":1}}],[\"的语法\",{\"1\":{\"445\":1}}],[\"的转义符\",{\"1\":{\"445\":1}}],[\"的源代码的\",{\"1\":{\"444\":1}}],[\"的字符个数\",{\"1\":{\"446\":1}}],[\"的字符\",{\"1\":{\"440\":1}}],[\"的字体数据属于\",{\"1\":{\"268\":1}}],[\"的字体数据不论在\",{\"1\":{\"268\":1}}],[\"的功能包含了\",{\"1\":{\"429\":1}}],[\"的功能\",{\"1\":{\"427\":1}}],[\"的功能是抽象的\",{\"1\":{\"178\":1}}],[\"的子函数\",{\"1\":{\"426\":1}}],[\"的作用是跳转到地址为\",{\"1\":{\"426\":1}}],[\"的作用是将值或寄存器\",{\"1\":{\"423\":1}}],[\"的作用是退栈\",{\"1\":{\"422\":1}}],[\"的值\",{\"1\":{\"424\":1,\"501\":1,\"512\":1}}],[\"的值放入栈中\",{\"1\":{\"423\":1}}],[\"的值放到栈上\",{\"1\":{\"422\":1}}],[\"的值减小\",{\"1\":{\"420\":1}}],[\"的内容放在\",{\"1\":{\"422\":1}}],[\"的内部状态不会被外部直接修改\",{\"1\":{\"308\":1}}],[\"的函数\",{\"1\":{\"416\":1}}],[\"的学生顶多学到语法分析就结束了\",{\"1\":{\"408\":1}}],[\"的课程后\",{\"1\":{\"408\":1}}],[\"的意思\",{\"1\":{\"399\":2}}],[\"的意思是\",{\"1\":{\"268\":2}}],[\"的算法\",{\"1\":{\"380\":1}}],[\"的使用方式是不一样的\",{\"1\":{\"370\":1}}],[\"的代码完全是手工实现的\",{\"1\":{\"409\":1}}],[\"的代码\",{\"1\":{\"408\":1}}],[\"的代码即可\",{\"1\":{\"369\":1}}],[\"的代码后才能理解\",{\"1\":{\"199\":1}}],[\"的一个问题\",{\"1\":{\"440\":1}}],[\"的一个命题\",{\"1\":{\"69\":1}}],[\"的一览表\",{\"1\":{\"367\":1}}],[\"的信息集中在了一个类中\",{\"1\":{\"367\":1}}],[\"的实质就是两个运算符在抢参数\",{\"1\":{\"496\":1}}],[\"的实际运行顺序是\",{\"1\":{\"496\":1}}],[\"的实现方法\",{\"1\":{\"366\":1}}],[\"的实例\",{\"1\":{\"370\":1}}],[\"的实例在\",{\"1\":{\"268\":1}}],[\"的实例作为参数传递给\",{\"1\":{\"187\":1}}],[\"的行为会对被观察对象产生影响时\",{\"0\":{\"322\":1}}],[\"的顺序\",{\"0\":{\"321\":1}}],[\"的栈\",{\"1\":{\"311\":1}}],[\"的有效期限\",{\"1\":{\"310\":1}}],[\"的有效期限取决于具体的应用场景\",{\"1\":{\"310\":1}}],[\"的有效期限是多久\",{\"0\":{\"310\":1}}],[\"的交互\",{\"1\":{\"297\":1}}],[\"的原因\",{\"1\":{\"297\":1}}],[\"的问题\",{\"1\":{\"269\":1}}],[\"的时候\",{\"1\":{\"249\":1}}],[\"的透明性\",{\"0\":{\"235\":1},\"1\":{\"235\":1}}],[\"的层次结构\",{\"1\":{\"220\":1}}],[\"的情况\",{\"1\":{\"202\":1}}],[\"的\",{\"1\":{\"186\":1,\"235\":1,\"321\":4,\"422\":2}}],[\"的缩写\",{\"1\":{\"178\":1}}],[\"的最上层\",{\"1\":{\"178\":1}}],[\"的类型\",{\"1\":{\"502\":1}}],[\"的类来访问数据结构中的元素\",{\"1\":{\"392\":1}}],[\"的类\",{\"1\":{\"178\":3}}],[\"的操作等价于\",{\"1\":{\"514\":1}}],[\"的操作\",{\"1\":{\"114\":1,\"507\":1}}],[\"的入度无规定\",{\"1\":{\"101\":1}}],[\"的假设矛盾\",{\"1\":{\"97\":1}}],[\"的和\",{\"1\":{\"81\":1}}],[\"的任意性\",{\"1\":{\"72\":1,\"73\":1,\"88\":1,\"89\":1}}],[\"的性质和\",{\"1\":{\"72\":1,\"73\":1,\"88\":1,\"89\":1}}],[\"的后继\",{\"1\":{\"69\":1,\"94\":1}}],[\"的动态计算图机制使得调试和开发更加灵活\",{\"1\":{\"66\":1}}],[\"的话\",{\"1\":{\"57\":1}}],[\"的域名\",{\"1\":{\"44\":1}}],[\"的小车是很重要的事情\",{\"1\":{\"10\":1}}],[\"是解释器\",{\"1\":{\"516\":1}}],[\"是指针时\",{\"1\":{\"512\":1}}],[\"是逆序将参数入栈的\",{\"1\":{\"500\":1}}],[\"是第几个参数\",{\"1\":{\"479\":1}}],[\"是以字符\",{\"1\":{\"478\":2}}],[\"是放在一起解析的\",{\"1\":{\"478\":1}}],[\"是对前一章提到的\",{\"1\":{\"464\":1}}],[\"是如何帮助我们的工程实现的\",{\"1\":{\"460\":1}}],[\"是因为几乎所有手工编写的语法分析器都或多或少地有它的影子\",{\"1\":{\"460\":1}}],[\"是因为之后我们将用\",{\"1\":{\"426\":1}}],[\"是因为表达式在语法分析中相对独立并且比较复杂\",{\"1\":{\"416\":1}}],[\"是跳转指令\",{\"1\":{\"424\":1}}],[\"是比较困难的\",{\"1\":{\"422\":1}}],[\"是数据还是地址\",{\"1\":{\"422\":1}}],[\"是所有指令中最基础的一个\",{\"1\":{\"422\":1}}],[\"是很困难的\",{\"1\":{\"369\":1}}],[\"是用类来表示状态的\",{\"1\":{\"368\":1}}],[\"是有专有名词的\",{\"1\":{\"268\":1}}],[\"是单线程的\",{\"1\":{\"264\":1}}],[\"是非常重要的\",{\"1\":{\"197\":1}}],[\"是一个一元运算符\",{\"1\":{\"499\":1}}],[\"是一个普通的变量还是一个函数\",{\"1\":{\"467\":1}}],[\"是一种行为设计模式\",{\"1\":{\"278\":1}}],[\"是一种结构型设计模式\",{\"1\":{\"162\":1}}],[\"是一款简洁高效的\",{\"1\":{\"124\":1}}],[\"是没有必要的\",{\"1\":{\"154\":1}}],[\"是不客观的\",{\"1\":{\"115\":1}}],[\"是的\",{\"1\":{\"114\":1,\"115\":1}}],[\"是线程调度器抢占划分时间片给其他线程跑\",{\"1\":{\"112\":1}}],[\"是唯一的\",{\"1\":{\"73\":2,\"89\":2}}],[\"是否属于优先级更高的运算符\",{\"1\":{\"496\":1}}],[\"是否唯一\",{\"1\":{\"73\":1,\"89\":1}}],[\"是否存在\",{\"1\":{\"72\":1,\"88\":1}}],[\"是否是自然数\",{\"1\":{\"72\":1,\"88\":1}}],[\"是任意自然数\",{\"1\":{\"72\":1,\"73\":1,\"88\":1,\"89\":1}}],[\"是真命题\",{\"1\":{\"69\":1}}],[\"是关于自然数\",{\"1\":{\"69\":1}}],[\"是自然数且\",{\"1\":{\"73\":1,\"75\":3,\"91\":3}}],[\"是自然数\",{\"1\":{\"69\":1,\"71\":1,\"72\":7,\"73\":2,\"83\":1,\"87\":1,\"88\":6,\"89\":2}}],[\"是\",{\"1\":{\"44\":2,\"94\":1,\"114\":1,\"178\":1,\"433\":1,\"512\":2}}],[\"如变量\",{\"1\":{\"497\":1}}],[\"如在普通的四则运算中\",{\"1\":{\"496\":1}}],[\"如经典的\",{\"1\":{\"457\":1}}],[\"如为什么用\",{\"1\":{\"457\":1}}],[\"如本例需向前查看一个字符\",{\"1\":{\"446\":1}}],[\"如本小节中的注释与除号\",{\"1\":{\"446\":1}}],[\"如标识符是函数\",{\"1\":{\"443\":1}}],[\"如数字\",{\"1\":{\"443\":1}}],[\"如右方括号\",{\"1\":{\"439\":1}}],[\"如只能操作ax寄存器\",{\"1\":{\"426\":1}}],[\"如下\",{\"1\":{\"422\":1,\"426\":1,\"443\":1,\"477\":1}}],[\"如调用帧\",{\"1\":{\"419\":1}}],[\"如int\",{\"1\":{\"419\":1}}],[\"如实现四则运算\",{\"1\":{\"409\":1}}],[\"如有侵权\",{\"1\":{\"406\":1,\"414\":1,\"417\":1,\"435\":1,\"453\":1,\"463\":1,\"474\":1,\"485\":1,\"495\":1,\"519\":1}}],[\"如正向遍历\",{\"1\":{\"284\":1}}],[\"如\",{\"1\":{\"269\":1,\"408\":1,\"409\":1,\"411\":1,\"415\":1,\"419\":1,\"438\":1,\"439\":2,\"442\":1,\"443\":1,\"445\":2,\"455\":1,\"467\":4,\"477\":2,\"479\":1,\"500\":1,\"507\":1,\"512\":1}}],[\"如此往复\",{\"1\":{\"114\":1}}],[\"如图所示\",{\"1\":{\"113\":1}}],[\"如果今后你仍然想编写编译器\",{\"1\":{\"521\":1}}],[\"如果条件失败\",{\"1\":{\"487\":1}}],[\"如果是两个指针相减\",{\"1\":{\"512\":1}}],[\"如果是局部变量则采用与\",{\"1\":{\"500\":1}}],[\"如果是指针的指针\",{\"1\":{\"467\":1}}],[\"如果是有\",{\"1\":{\"298\":1}}],[\"如果遇到标识符就用\",{\"1\":{\"500\":1}}],[\"如果遇到\",{\"1\":{\"467\":1}}],[\"如果分析到字符串\",{\"1\":{\"445\":1}}],[\"如果标识符已经存在\",{\"1\":{\"443\":1}}],[\"如果子函数有返回结果\",{\"1\":{\"426\":1}}],[\"如果你按这个系列自己编写代码\",{\"1\":{\"523\":1}}],[\"如果你理解了上一章中的内容\",{\"1\":{\"471\":1}}],[\"如果你尝试阅读\",{\"1\":{\"408\":1}}],[\"如果你急切地想进入正篇\",{\"1\":{\"406\":1}}],[\"如果你的\",{\"1\":{\"119\":1}}],[\"如果公开了不应当被公开的信息\",{\"1\":{\"402\":1}}],[\"如果无法获取到这些信息\",{\"1\":{\"402\":1}}],[\"如果要我说计算机专业最重要的三门课\",{\"1\":{\"407\":1}}],[\"如果要修改已经编写和测试完成的类\",{\"1\":{\"399\":1}}],[\"如果要改变被共享的对象\",{\"1\":{\"267\":1}}],[\"如果在每次扩展类时都需要修改现有的类就太麻烦了\",{\"1\":{\"399\":1}}],[\"如果在逻辑执行过程中我们需要判断变量状态\",{\"1\":{\"115\":1}}],[\"如果将处理逻辑的方法定义在\",{\"1\":{\"398\":1}}],[\"如果将这些逻辑分散到各个用户类中\",{\"1\":{\"297\":1}}],[\"如果想比较原来的算法与改进后的算法的处理速度有多大区别\",{\"1\":{\"379\":1}}],[\"如果使用\",{\"1\":{\"380\":1}}],[\"如果使用了\",{\"1\":{\"379\":1}}],[\"如果使用继承\",{\"1\":{\"145\":1}}],[\"如果以后发生需求变更\",{\"1\":{\"367\":1}}],[\"如果大家在读完这两点之后会点头表示赞同\",{\"1\":{\"366\":1}}],[\"如果还是不能解决这些小问题\",{\"1\":{\"365\":1}}],[\"如果多个线程同时访问\",{\"1\":{\"356\":1}}],[\"如果\",{\"1\":{\"337\":1,\"512\":1}}],[\"如果实例很少就不需要\",{\"1\":{\"298\":1}}],[\"如果存在很多这样的互相通信的实例\",{\"1\":{\"298\":1}}],[\"如果存在多个改变它的理由\",{\"1\":{\"138\":1}}],[\"如果有兴趣\",{\"1\":{\"522\":1}}],[\"如果有\",{\"1\":{\"298\":1}}],[\"如果这局猜拳获胜\",{\"1\":{\"376\":1}}],[\"如果这段逻辑分散在\",{\"1\":{\"297\":1}}],[\"如果这些集合中的对象没有被其他任何地方引用\",{\"1\":{\"269\":1}}],[\"如果发生需求变更\",{\"1\":{\"297\":1}}],[\"如果不是预期的标记则报错并退出\",{\"1\":{\"469\":1}}],[\"如果不想看可以跳过\",{\"1\":{\"464\":1}}],[\"如果不能比较容易地扩展类\",{\"1\":{\"399\":1}}],[\"如果不能做就将\",{\"1\":{\"202\":1}}],[\"如果不使用\",{\"1\":{\"368\":1,\"369\":2}}],[\"如果不共享实例\",{\"1\":{\"270\":1}}],[\"如果冰激凌店要为顾客准备所有的冰激凌成品那真是太麻烦了\",{\"1\":{\"238\":1}}],[\"如果再用\",{\"1\":{\"236\":1}}],[\"如果也不能自己处理\",{\"1\":{\"202\":1}}],[\"如果他可以做就自己做\",{\"1\":{\"202\":1}}],[\"如果修改\",{\"1\":{\"199\":1}}],[\"如果没有理解各个类的角色就动手增加和修改代码\",{\"1\":{\"199\":1}}],[\"如果没有熟悉的编程语言\",{\"1\":{\"16\":1}}],[\"如果我们的编译器要达到自举\",{\"1\":{\"432\":1}}],[\"如果我们不把颜色信息放在\",{\"1\":{\"267\":1}}],[\"如果我们不传递\",{\"1\":{\"187\":1}}],[\"如果我们不关注执行过程中的状态\",{\"1\":{\"115\":1}}],[\"如果我们将某个程序中依赖于操作系统的部分划分为\",{\"1\":{\"186\":1}}],[\"如果只是将应当分散的处理分散在各个类中\",{\"1\":{\"297\":1}}],[\"如果只是简单地将它们分开\",{\"1\":{\"176\":1}}],[\"如果只是为了编写包含\",{\"1\":{\"154\":1}}],[\"如果一个类需要改变\",{\"1\":{\"138\":1}}],[\"如果协程在操作共享变量的过程中\",{\"1\":{\"115\":1}}],[\"如果每个线程按顺序执行\",{\"1\":{\"112\":1}}],[\"如何为每个运算符生成对应的汇编代码\",{\"1\":{\"516\":1}}],[\"如何通过递归调用\",{\"1\":{\"516\":1}}],[\"如何确定具体选择哪一个\",{\"1\":{\"457\":1}}],[\"如何处理错误\",{\"1\":{\"440\":1}}],[\"如何表示语法\",{\"1\":{\"408\":1}}],[\"如何实现风格统一\",{\"1\":{\"65\":1}}],[\"如何给python\",{\"1\":{\"39\":1}}],[\"续订泛域名证书\",{\"1\":{\"39\":1}}],[\"用来求值\",{\"1\":{\"495\":1}}],[\"用尖括号\",{\"1\":{\"455\":1}}],[\"用作保存全局标识符的信息\",{\"1\":{\"443\":1}}],[\"用更多的指令来完成更多的功能\",{\"1\":{\"434\":1}}],[\"用以存放局部变量\",{\"1\":{\"427\":1}}],[\"用什么有穷自动机和无穷自动机\",{\"1\":{\"408\":1}}],[\"用类来表示状态\",{\"1\":{\"367\":1}}],[\"用类实现\",{\"2\":{\"218\":1,\"282\":1}}],[\"用\",{\"1\":{\"236\":1,\"498\":1,\"506\":1}}],[\"用户可以统一地对待单个对象和组合对象\",{\"1\":{\"220\":1}}],[\"用字符串显示\",{\"1\":{\"178\":1}}],[\"用android\",{\"1\":{\"109\":1}}],[\"用acme\",{\"1\":{\"39\":1}}],[\"用图论阐述\",{\"0\":{\"98\":1}}],[\"用于标识符的快速比较\",{\"1\":{\"443\":1}}],[\"用于实现\",{\"1\":{\"427\":1,\"428\":1}}],[\"用于为程序动态分配内存\",{\"1\":{\"419\":1}}],[\"用于处理函数调用相关的数据\",{\"1\":{\"419\":1}}],[\"用于存放未初始化的数据\",{\"1\":{\"419\":1}}],[\"用于存放初始化了的数据\",{\"1\":{\"419\":1}}],[\"用于存放代码\",{\"1\":{\"419\":1}}],[\"用于解析该参数的类型\",{\"1\":{\"479\":1}}],[\"用于解析枚举类型的定义\",{\"1\":{\"468\":1}}],[\"用于解析一个表达式\",{\"1\":{\"416\":1}}],[\"用于解释目标代码\",{\"1\":{\"416\":1}}],[\"用于语法分析\",{\"1\":{\"415\":1}}],[\"用于词法分析\",{\"1\":{\"415\":1,\"416\":1}}],[\"用于将字符串转化成内部的表示结构\",{\"1\":{\"415\":1}}],[\"用于遍历\",{\"1\":{\"287\":1}}],[\"用于创建相关或依赖对象的家族\",{\"1\":{\"152\":1}}],[\"用于工业生产部署\",{\"1\":{\"66\":1}}],[\"用于快速原型验证\",{\"1\":{\"66\":1}}],[\"用python也足够了\",{\"1\":{\"6\":1}}],[\"重写的代码历时一周\",{\"1\":{\"409\":1}}],[\"重新定义算法中的某些步骤\",{\"1\":{\"384\":1}}],[\"重活\",{\"1\":{\"338\":1}}],[\"重构\",{\"1\":{\"139\":1}}],[\"重要的是去理解如何将这些语句编译成汇编代码\",{\"1\":{\"486\":1}}],[\"重要\",{\"1\":{\"109\":1,\"116\":1}}],[\"重启container\",{\"0\":{\"37\":1}}],[\"重定向到automaton\",{\"1\":{\"30\":1,\"36\":2}}],[\"3+\",{\"1\":{\"430\":1,\"477\":1}}],[\"32位系统\",{\"1\":{\"512\":1}}],[\"32\",{\"1\":{\"419\":1,\"433\":1}}],[\"32k\",{\"1\":{\"30\":1}}],[\"3573\",{\"1\":{\"377\":2}}],[\"3572\",{\"1\":{\"377\":1}}],[\"3571\",{\"1\":{\"377\":1}}],[\"3570\",{\"1\":{\"377\":1}}],[\"3569\",{\"1\":{\"377\":1}}],[\"3568\",{\"1\":{\"377\":1}}],[\"3567\",{\"1\":{\"377\":1}}],[\"37\",{\"1\":{\"318\":2}}],[\"31500\",{\"1\":{\"226\":1,\"395\":1}}],[\"396\",{\"1\":{\"205\":1}}],[\"363\",{\"1\":{\"205\":1}}],[\"3333\",{\"1\":{\"265\":1}}],[\"333333\",{\"1\":{\"265\":2}}],[\"330\",{\"1\":{\"205\":1}}],[\"33\",{\"1\":{\"204\":1,\"205\":1,\"265\":12}}],[\"3049\",{\"1\":{\"377\":8}}],[\"30\",{\"1\":{\"298\":1,\"318\":2,\"433\":1}}],[\"3001\",{\"1\":{\"495\":1}}],[\"30000\",{\"1\":{\"226\":3,\"395\":3}}],[\"300\",{\"1\":{\"204\":1,\"225\":1,\"226\":3,\"394\":1,\"395\":3}}],[\"301\",{\"1\":{\"36\":2}}],[\"3\",{\"0\":{\"435\":1},\"1\":{\"114\":1,\"175\":1,\"186\":2,\"212\":2,\"264\":1,\"267\":2,\"279\":1,\"280\":2,\"298\":1,\"318\":2,\"376\":5,\"406\":1,\"414\":1,\"415\":1,\"417\":3,\"426\":2,\"430\":1,\"432\":1,\"435\":14,\"436\":2,\"453\":2,\"456\":2,\"463\":4,\"468\":1,\"470\":1,\"474\":4,\"485\":3,\"487\":1,\"495\":10,\"496\":9,\"500\":1,\"510\":1,\"519\":2}}],[\"347342082\",{\"1\":{\"48\":1}}],[\"进程的内存会被分成几个段\",{\"1\":{\"419\":1}}],[\"进而当\",{\"1\":{\"75\":3,\"76\":1,\"77\":2,\"81\":1,\"91\":3,\"92\":1,\"93\":1,\"94\":1}}],[\"进而\",{\"1\":{\"73\":1,\"81\":1,\"83\":1,\"85\":1,\"89\":1,\"96\":1}}],[\"进而有\",{\"1\":{\"72\":1,\"88\":1}}],[\"进有\",{\"1\":{\"72\":1,\"73\":1,\"88\":1,\"89\":1}}],[\"进入acme\",{\"1\":{\"34\":1}}],[\"进行编译\",{\"1\":{\"515\":1}}],[\"进行解析的时候\",{\"1\":{\"508\":1}}],[\"进行语法分析\",{\"1\":{\"456\":1}}],[\"进行安装\",{\"1\":{\"124\":1}}],[\"进行实验\",{\"1\":{\"66\":1}}],[\"进行修改\",{\"1\":{\"29\":1}}],[\"进行如下操作\",{\"1\":{\"29\":1}}],[\"申请证书\",{\"0\":{\"34\":1}}],[\"升级为https\",{\"0\":{\"33\":1}}],[\"及函数定义\",{\"1\":{\"467\":1}}],[\"及时进行重构\",{\"1\":{\"139\":1}}],[\"及\",{\"1\":{\"32\":1,\"426\":1,\"432\":1,\"476\":1,\"481\":1,\"499\":1}}],[\"失败\",{\"1\":{\"30\":1,\"36\":2}}],[\"或波浪号\",{\"1\":{\"439\":1}}],[\"或其他线程同步机制\",{\"1\":{\"356\":1}}],[\"或是调试起来十分困难\",{\"1\":{\"523\":1}}],[\"或是重新学习学习汇编相关的知识\",{\"1\":{\"482\":1}}],[\"或是函数的局部变量等\",{\"1\":{\"419\":1}}],[\"或是依赖于实例状态的信息\",{\"1\":{\"268\":1}}],[\"或是不依赖于实例状态的信息\",{\"1\":{\"268\":1}}],[\"或是如果不小心修改了\",{\"1\":{\"199\":1}}],[\"或是要修改具体工厂的\",{\"1\":{\"156\":1}}],[\"或是\",{\"1\":{\"119\":1}}],[\"或者使用更复杂的事件处理机制\",{\"1\":{\"322\":1}}],[\"或者说如果我们把代码中使用基类的地方用它的派生类所代替\",{\"1\":{\"132\":1}}],[\"或者说的更简单一点\",{\"1\":{\"114\":1}}],[\"或者执行过程中要根据变量状态进行一些下游操作\",{\"1\":{\"115\":1}}],[\"或\",{\"1\":{\"30\":1,\"36\":2,\"94\":1,\"269\":1,\"408\":1,\"467\":1,\"500\":1,\"513\":1}}],[\"使我们能直接使用编译器\",{\"1\":{\"419\":1}}],[\"使代码更加简洁和可维护\",{\"1\":{\"361\":1}}],[\"使代码更易于维护和理解\",{\"1\":{\"192\":1}}],[\"使一个类的实例化延迟到其子类\",{\"1\":{\"256\":1}}],[\"使它们可以独立变化\",{\"1\":{\"172\":1}}],[\"使得代码更清晰\",{\"1\":{\"393\":1}}],[\"使得代码更加清晰\",{\"1\":{\"375\":1}}],[\"使得状态转换变得清晰且易于管理\",{\"1\":{\"361\":1}}],[\"使得客户端可以像使用本地对象一样使用远程对象\",{\"1\":{\"346\":1}}],[\"使得客户端代码更加简洁和易读\",{\"1\":{\"284\":1}}],[\"使得客户端代码可以更容易地使用子系统的功能\",{\"1\":{\"250\":1}}],[\"使得客户端代码不需要了解子系统的内部细节\",{\"1\":{\"249\":1}}],[\"使得对象的创建更加灵活\",{\"1\":{\"330\":1}}],[\"使得每一层只关注自己的职责\",{\"1\":{\"249\":1}}],[\"使得可以用不同的请求\",{\"1\":{\"210\":1}}],[\"使得在设计时可以决定构建的步骤和逻辑\",{\"1\":{\"198\":1}}],[\"使得同样的构建过程可以创建不同的表示\",{\"1\":{\"192\":1}}],[\"使得系统功能模块相对独立\",{\"1\":{\"136\":1}}],[\"使得函数\",{\"1\":{\"113\":1}}],[\"使得一段时间内只有一个线程可以操作这个资源\",{\"1\":{\"112\":1}}],[\"使得刚回到正确姿势时速度较慢\",{\"1\":{\"11\":1}}],[\"使flask支持\",{\"0\":{\"38\":1}}],[\"使用了单例模式\",{\"1\":{\"376\":1}}],[\"使用了id卡`\",{\"1\":{\"258\":1}}],[\"使用状态迁移表非常有效\",{\"1\":{\"367\":1}}],[\"使用这种解决方法可以提高\",{\"1\":{\"367\":1}}],[\"使用代理可以显著提升处理速度\",{\"1\":{\"341\":1}}],[\"使用代理人来提升处理速度\",{\"0\":{\"341\":1}}],[\"使用迭代器模式有以下几个优点\",{\"1\":{\"284\":1}}],[\"使用解释器模式的原因包括\",{\"1\":{\"278\":1}}],[\"使用弱引用\",{\"1\":{\"269\":1}}],[\"使用队列数据结构保存执行的命令对象\",{\"1\":{\"215\":1}}],[\"使用栈数据结构保存执行的命令对象\",{\"1\":{\"215\":1}}],[\"使用此设计模式的理由\",{\"0\":{\"172\":1,\"220\":1,\"375\":1}}],[\"使用委托这种弱关联关系可以很方便地整体替换算法\",{\"1\":{\"379\":1}}],[\"使用委托\",{\"1\":{\"166\":1}}],[\"使用继承\",{\"1\":{\"166\":1}}],[\"使用继承的方式\",{\"1\":{\"147\":1}}],[\"使用抽象工厂模式\",{\"1\":{\"154\":1}}],[\"使用抽象类和接口\",{\"1\":{\"130\":1,\"133\":1}}],[\"使用多个专门的接口\",{\"1\":{\"148\":1}}],[\"使用多个专门的接口比使用单个通用接口要好得多\",{\"1\":{\"141\":1}}],[\"使用聚合\",{\"1\":{\"146\":1}}],[\"使用组合的方式\",{\"1\":{\"147\":1}}],[\"使用组合\",{\"1\":{\"146\":1}}],[\"使用依赖注入\",{\"1\":{\"144\":1}}],[\"使用工厂模式创建对象\",{\"1\":{\"143\":1}}],[\"使用接口和抽象类\",{\"1\":{\"143\":1}}],[\"使用门面模式\",{\"1\":{\"137\":1}}],[\"使用设计模式的目的是重用代码\",{\"1\":{\"246\":1}}],[\"使用设计模式\",{\"1\":{\"130\":1}}],[\"使用await关键字让出使用权\",{\"1\":{\"114\":1}}],[\"使用权\",{\"1\":{\"114\":1}}],[\"使用capacitor和ionic将vue项目迁移到mobile端\",{\"0\":{\"106\":1}}],[\"使用python\",{\"0\":{\"52\":1}}],[\"使用docker\",{\"1\":{\"39\":1}}],[\"使用\",{\"1\":{\"30\":1,\"36\":2,\"108\":1,\"109\":1,\"114\":1,\"186\":1,\"203\":1,\"220\":1,\"238\":1,\"257\":1,\"270\":1,\"330\":1,\"361\":1,\"379\":1,\"400\":1}}],[\"kinds\",{\"1\":{\"444\":1}}],[\"kid\",{\"1\":{\"294\":1,\"295\":3}}],[\"k\",{\"1\":{\"408\":1,\"411\":1,\"446\":2,\"450\":2,\"457\":1}}],[\"know\",{\"1\":{\"294\":1}}],[\"kcodetime\",{\"1\":{\"67\":1}}],[\"ksj\",{\"1\":{\"52\":1}}],[\"keep\",{\"1\":{\"448\":1}}],[\"keepalive\",{\"1\":{\"30\":1}}],[\"keywords\",{\"1\":{\"448\":1}}],[\"key\",{\"1\":{\"35\":2,\"36\":6,\"251\":1,\"264\":1,\"331\":1}}],[\"kts\",{\"1\":{\"22\":1}}],[\"nightstate\",{\"1\":{\"362\":7,\"367\":3,\"369\":1,\"370\":1}}],[\"n$\",{\"1\":{\"317\":2}}],[\"narrow\",{\"1\":{\"308\":1}}],[\"names\",{\"1\":{\"376\":2}}],[\"name+\",{\"1\":{\"279\":1}}],[\"name\",{\"1\":{\"30\":2,\"36\":5,\"204\":10,\"222\":3,\"224\":2,\"279\":7,\"286\":5,\"294\":3,\"331\":4,\"338\":21,\"376\":5,\"394\":4,\"443\":5,\"478\":1,\"479\":2,\"480\":1}}],[\"n<h1>$\",{\"1\":{\"251\":1}}],[\"num\",{\"1\":{\"439\":1,\"444\":1,\"445\":3,\"455\":1,\"456\":4,\"458\":1,\"459\":3,\"464\":2,\"467\":2,\"468\":3,\"498\":2,\"500\":1,\"506\":2,\"508\":1}}],[\"numbervoid\",{\"1\":{\"416\":1}}],[\"numbergenerator\",{\"1\":{\"317\":17}}],[\"number\",{\"1\":{\"179\":1,\"183\":1,\"204\":18,\"211\":8,\"222\":1,\"223\":1,\"224\":2,\"232\":9,\"279\":11,\"286\":4,\"305\":6,\"317\":9,\"353\":1,\"357\":1,\"362\":6,\"376\":4,\"386\":1,\"394\":3,\"436\":5,\"443\":1,\"444\":2,\"500\":1}}],[\"null\",{\"1\":{\"204\":1,\"264\":1,\"279\":2,\"331\":2,\"353\":3,\"357\":4,\"459\":2}}],[\"n`\",{\"1\":{\"153\":1,\"193\":3,\"251\":3,\"279\":1}}],[\"normal\",{\"1\":{\"501\":1}}],[\"non\",{\"1\":{\"464\":3,\"475\":3}}],[\"now\",{\"1\":{\"305\":1,\"306\":3,\"499\":1,\"512\":2}}],[\"note\",{\"1\":{\"376\":1,\"467\":1}}],[\"nothing\",{\"1\":{\"305\":1,\"306\":2,\"416\":2,\"506\":1}}],[\"not\",{\"1\":{\"294\":1,\"394\":2,\"416\":2,\"419\":3,\"425\":1,\"442\":1,\"504\":1,\"505\":1,\"512\":1,\"527\":1}}],[\"notifyobservers\",{\"1\":{\"317\":2,\"321\":1}}],[\"notify\",{\"1\":{\"294\":6,\"297\":3}}],[\"nosupport\",{\"1\":{\"204\":5}}],[\"node\",{\"1\":{\"124\":2,\"153\":1,\"167\":1,\"184\":1,\"194\":1,\"205\":1,\"212\":1,\"226\":1,\"233\":1,\"252\":1,\"259\":1,\"265\":1,\"279\":29,\"280\":6,\"287\":1,\"295\":1,\"318\":1,\"332\":1,\"339\":1,\"354\":1,\"363\":1,\"387\":1,\"395\":1}}],[\"nopush\",{\"1\":{\"30\":1}}],[\"n\",{\"1\":{\"112\":6,\"113\":3,\"114\":12,\"153\":6,\"193\":5,\"251\":1,\"264\":119,\"279\":7,\"317\":1,\"416\":4,\"419\":3,\"432\":1,\"441\":1,\"442\":1,\"445\":5,\"446\":1,\"459\":2,\"467\":2,\"468\":2,\"469\":1,\"479\":2,\"480\":2,\"500\":2,\"502\":1,\"503\":1,\"507\":1,\"509\":1,\"510\":1,\"514\":1}}],[\"ne\",{\"1\":{\"421\":1,\"431\":1,\"439\":2,\"447\":1,\"508\":1}}],[\"need\",{\"1\":{\"294\":1}}],[\"nexthand2\",{\"1\":{\"376\":3}}],[\"nexthand\",{\"1\":{\"376\":7}}],[\"nexthand1\",{\"1\":{\"376\":3}}],[\"nexttoken\",{\"1\":{\"279\":6}}],[\"next\",{\"1\":{\"204\":8,\"286\":3,\"287\":1,\"416\":5,\"438\":1,\"440\":2,\"443\":1,\"444\":1,\"445\":1,\"446\":1,\"447\":1,\"448\":4,\"459\":3,\"466\":2,\"467\":1,\"468\":4,\"469\":2}}],[\"news\",{\"1\":{\"153\":2}}],[\"new\",{\"1\":{\"144\":2,\"147\":2,\"153\":4,\"166\":3,\"182\":6,\"193\":4,\"204\":7,\"211\":3,\"223\":1,\"225\":14,\"232\":9,\"251\":1,\"258\":2,\"264\":4,\"270\":2,\"279\":12,\"286\":6,\"294\":4,\"305\":2,\"317\":3,\"331\":4,\"338\":2,\"353\":1,\"357\":1,\"362\":3,\"376\":7,\"386\":3,\"394\":18,\"426\":1,\"427\":3,\"430\":8,\"443\":1,\"477\":7,\"479\":1}}],[\"newline\",{\"1\":{\"65\":1}}],[\"net\",{\"1\":{\"51\":1,\"495\":1}}],[\"networks\",{\"1\":{\"31\":2}}],[\"nju\",{\"1\":{\"45\":1,\"46\":2}}],[\"nginx\",{\"0\":{\"26\":1},\"1\":{\"26\":2,\"27\":1,\"28\":2,\"30\":17,\"31\":10,\"34\":4,\"35\":4,\"36\":15,\"39\":2},\"2\":{\"40\":1}}],[\"$\",{\"1\":{\"153\":1,\"166\":2,\"193\":2,\"204\":3,\"211\":2,\"222\":2,\"223\":1,\"224\":1,\"251\":4,\"279\":7,\"294\":4,\"305\":6,\"317\":2,\"331\":4,\"338\":2,\"353\":1,\"357\":1,\"362\":2,\"376\":6,\"394\":4}}],[\"$host$request\",{\"1\":{\"36\":2}}],[\"$http\",{\"1\":{\"30\":3}}],[\"$uri\",{\"1\":{\"30\":6,\"36\":10}}],[\"$body\",{\"1\":{\"30\":1}}],[\"$status\",{\"1\":{\"30\":1}}],[\"$request\",{\"1\":{\"30\":1}}],[\"$remote\",{\"1\":{\"30\":2}}],[\"$time\",{\"1\":{\"30\":1}}],[\"4|\",{\"1\":{\"496\":1}}],[\"4+\",{\"1\":{\"430\":1}}],[\"4g\",{\"1\":{\"419\":1}}],[\"44\",{\"1\":{\"318\":2}}],[\"443\",{\"1\":{\"31\":2,\"36\":3}}],[\"49\",{\"1\":{\"318\":2}}],[\"495\",{\"1\":{\"205\":1}}],[\"46\",{\"1\":{\"318\":2}}],[\"462\",{\"1\":{\"205\":1,\"306\":1}}],[\"43\",{\"1\":{\"318\":2}}],[\"404\",{\"1\":{\"527\":1}}],[\"400\",{\"1\":{\"225\":1,\"226\":1,\"394\":1,\"395\":1}}],[\"4096\",{\"1\":{\"30\":1}}],[\"429\",{\"1\":{\"204\":1,\"205\":1}}],[\"4版本的yield\",{\"1\":{\"114\":1}}],[\"4\",{\"0\":{\"453\":1},\"1\":{\"30\":1,\"156\":1,\"212\":2,\"264\":1,\"279\":2,\"280\":4,\"298\":1,\"331\":2,\"406\":1,\"409\":1,\"414\":1,\"416\":1,\"417\":3,\"420\":1,\"430\":1,\"432\":1,\"435\":3,\"436\":2,\"453\":3,\"456\":2,\"463\":3,\"474\":3,\"481\":1,\"485\":2,\"495\":4,\"496\":6,\"512\":1,\"519\":2}}],[\"4次速度\",{\"1\":{\"16\":1}}],[\"rmi\",{\"1\":{\"346\":1}}],[\"right\",{\"1\":{\"279\":9,\"280\":12,\"436\":1}}],[\"role\",{\"1\":{\"294\":1}}],[\"row\",{\"1\":{\"232\":9}}],[\"rootdir\",{\"1\":{\"225\":6,\"394\":6}}],[\"root\",{\"1\":{\"30\":2,\"34\":2,\"35\":1,\"36\":3,\"65\":1,\"225\":2,\"226\":21,\"394\":2,\"395\":21}}],[\"randomnumbergenerator\",{\"1\":{\"317\":5}}],[\"random\",{\"1\":{\"305\":3,\"317\":1,\"376\":2}}],[\"range\",{\"1\":{\"112\":2,\"114\":1}}],[\"rawclose\",{\"1\":{\"180\":1,\"181\":1,\"183\":1}}],[\"rawprint\",{\"1\":{\"180\":1,\"181\":1,\"183\":1}}],[\"rawopen\",{\"1\":{\"180\":1,\"181\":1,\"183\":1}}],[\"r\",{\"1\":{\"114\":1,\"445\":1}}],[\"run\",{\"1\":{\"30\":1,\"113\":1,\"114\":3}}],[\"remove\",{\"1\":{\"426\":1,\"428\":2}}],[\"remote\",{\"1\":{\"342\":1,\"346\":1}}],[\"ret\",{\"1\":{\"426\":9,\"429\":2}}],[\"returns\",{\"1\":{\"515\":1}}],[\"returnret\",{\"1\":{\"429\":1}}],[\"returned\",{\"1\":{\"416\":1}}],[\"return\",{\"0\":{\"489\":1},\"1\":{\"36\":2,\"57\":3,\"58\":4,\"153\":6,\"193\":2,\"204\":11,\"222\":3,\"223\":1,\"224\":2,\"232\":13,\"251\":2,\"258\":4,\"264\":2,\"279\":11,\"286\":6,\"305\":6,\"317\":1,\"331\":3,\"338\":2,\"353\":1,\"357\":1,\"362\":4,\"376\":12,\"394\":7,\"416\":6,\"419\":3,\"422\":1,\"426\":3,\"432\":2,\"439\":1,\"440\":1,\"443\":3,\"444\":1,\"445\":2,\"446\":1,\"447\":15,\"448\":2,\"459\":11,\"464\":1,\"467\":1,\"475\":1,\"485\":1,\"486\":1,\"489\":6,\"508\":1}}],[\"regex\",{\"1\":{\"411\":1}}],[\"registers\",{\"1\":{\"420\":1}}],[\"registerproduct\",{\"1\":{\"258\":3}}],[\"register\",{\"1\":{\"140\":2,\"331\":4}}],[\"registry\",{\"0\":{\"43\":1},\"1\":{\"44\":4,\"46\":1}}],[\"read\",{\"1\":{\"416\":3,\"421\":1,\"432\":3,\"448\":1,\"500\":1}}],[\"readonly\",{\"1\":{\"376\":2}}],[\"realize\",{\"1\":{\"338\":2}}],[\"real\",{\"1\":{\"294\":1,\"338\":6}}],[\"record\",{\"1\":{\"363\":24}}],[\"recordlog\",{\"1\":{\"362\":4}}],[\"received\",{\"1\":{\"294\":1,\"295\":6}}],[\"receivemessage\",{\"1\":{\"294\":2}}],[\"receiver\",{\"1\":{\"214\":1}}],[\"repeatcommandnode\",{\"1\":{\"279\":5}}],[\"repeat\",{\"1\":{\"279\":9,\"280\":6,\"331\":3}}],[\"replace\",{\"1\":{\"264\":1}}],[\"repos\",{\"1\":{\"22\":1}}],[\"repository\",{\"1\":{\"22\":12}}],[\"repositoriesmode\",{\"1\":{\"22\":2}}],[\"repositories\",{\"1\":{\"22\":2}}],[\"reduce\",{\"1\":{\"222\":1}}],[\"requirements有两种方式\",{\"1\":{\"61\":1}}],[\"requirements\",{\"0\":{\"61\":1},\"1\":{\"61\":2}}],[\"rest\",{\"1\":{\"498\":1}}],[\"restore\",{\"1\":{\"426\":1,\"429\":2}}],[\"restorememento\",{\"1\":{\"305\":2}}],[\"restoring\",{\"1\":{\"305\":1,\"306\":1}}],[\"restart\",{\"1\":{\"46\":1}}],[\"resolved\",{\"1\":{\"204\":2,\"205\":16}}],[\"resolve\",{\"1\":{\"204\":6}}],[\"resolver\",{\"1\":{\"30\":2}}],[\"responsibility\",{\"1\":{\"202\":1,\"203\":1,\"204\":1,\"389\":1}}],[\"result\",{\"1\":{\"193\":2,\"376\":1,\"377\":1,\"426\":1,\"512\":1}}],[\"res\",{\"1\":{\"113\":1,\"114\":3}}],[\"reverse\",{\"1\":{\"39\":1}}],[\"release\",{\"1\":{\"112\":1}}],[\"releases\",{\"1\":{\"22\":2}}],[\"reload\",{\"1\":{\"46\":1}}],[\"reloadcmd\",{\"1\":{\"35\":1}}],[\"rewrite\",{\"1\":{\"30\":1,\"36\":2}}],[\"referer\",{\"1\":{\"30\":1}}],[\"15\",{\"1\":{\"444\":3,\"496\":2}}],[\"1500\",{\"1\":{\"226\":1,\"395\":1}}],[\"142961332\",{\"1\":{\"495\":1}}],[\"147\",{\"1\":{\"443\":1}}],[\"140717115\",{\"1\":{\"51\":1}}],[\"1+\",{\"1\":{\"430\":2,\"477\":2}}],[\"19\",{\"1\":{\"370\":1}}],[\"198\",{\"1\":{\"205\":1}}],[\"13\",{\"1\":{\"318\":4}}],[\"132\",{\"1\":{\"205\":1}}],[\"128\",{\"1\":{\"439\":1,\"508\":1}}],[\"12\",{\"1\":{\"298\":1,\"426\":2,\"428\":1}}],[\"123\",{\"1\":{\"264\":1,\"444\":1}}],[\"12345678\",{\"1\":{\"52\":1}}],[\"16\",{\"1\":{\"318\":2,\"367\":1,\"444\":2}}],[\"165\",{\"1\":{\"205\":1}}],[\"16k\",{\"1\":{\"30\":1}}],[\"111111\",{\"1\":{\"265\":1}}],[\"1111\",{\"1\":{\"265\":1}}],[\"11\",{\"1\":{\"265\":8,\"318\":2,\"417\":1}}],[\"1190000040806239\",{\"1\":{\"119\":1}}],[\"114\",{\"1\":{\"30\":4}}],[\"18\",{\"1\":{\"114\":1,\"318\":2}}],[\"17\",{\"1\":{\"114\":1,\"362\":2}}],[\"10+20\",{\"1\":{\"433\":1}}],[\"1024\",{\"1\":{\"416\":1}}],[\"1000\",{\"1\":{\"338\":1,\"419\":1}}],[\"10000\",{\"1\":{\"225\":1,\"226\":2,\"376\":1,\"377\":2,\"394\":1,\"395\":2}}],[\"1000000\",{\"1\":{\"112\":2,\"114\":1}}],[\"100\",{\"1\":{\"204\":1,\"225\":1,\"226\":1,\"305\":3,\"394\":1,\"395\":1}}],[\"10\",{\"1\":{\"66\":1,\"112\":1,\"113\":1,\"114\":6,\"211\":1,\"293\":1,\"318\":2,\"362\":1,\"417\":1,\"419\":1,\"433\":1,\"435\":1,\"443\":1,\"444\":1,\"459\":1,\"467\":1,\"495\":1,\"500\":1,\"514\":2}}],[\"10s\",{\"1\":{\"30\":1}}],[\"1ll\",{\"1\":{\"57\":1,\"58\":1}}],[\"1\",{\"0\":{\"68\":1,\"414\":1},\"1\":{\"30\":1,\"114\":3,\"178\":1,\"204\":1,\"212\":2,\"232\":9,\"264\":1,\"274\":2,\"305\":2,\"352\":1,\"354\":1,\"376\":18,\"406\":1,\"414\":3,\"416\":5,\"417\":6,\"419\":3,\"422\":1,\"425\":2,\"426\":3,\"427\":1,\"430\":2,\"432\":7,\"434\":1,\"435\":3,\"443\":1,\"444\":1,\"453\":2,\"456\":1,\"459\":1,\"463\":3,\"467\":3,\"468\":3,\"469\":1,\"474\":3,\"476\":1,\"477\":3,\"479\":2,\"480\":3,\"485\":7,\"487\":1,\"488\":2,\"495\":4,\"496\":1,\"500\":3,\"502\":1,\"503\":1,\"505\":2,\"506\":1,\"507\":1,\"509\":1,\"510\":2,\"511\":2,\"512\":1,\"514\":1,\"519\":2}}],[\"when\",{\"1\":{\"500\":1}}],[\"which\",{\"1\":{\"500\":1}}],[\"white\",{\"1\":{\"459\":1}}],[\"whitespace\",{\"1\":{\"65\":1}}],[\"while\",{\"0\":{\"488\":1},\"1\":{\"279\":1,\"286\":1,\"416\":1,\"422\":1,\"439\":1,\"440\":4,\"442\":1,\"443\":3,\"444\":3,\"445\":1,\"446\":1,\"448\":5,\"459\":3,\"464\":3,\"466\":1,\"467\":2,\"468\":1,\"475\":3,\"478\":3,\"479\":2,\"480\":4,\"485\":1,\"486\":1,\"488\":4,\"490\":1,\"498\":1,\"499\":1,\"500\":1,\"501\":1,\"508\":2}}],[\"we\",{\"1\":{\"442\":1}}],[\"weakhashmap\",{\"1\":{\"269\":1}}],[\"weakreference\",{\"1\":{\"269\":1}}],[\"welcome\",{\"1\":{\"251\":2,\"252\":2}}],[\"web\",{\"1\":{\"108\":1}}],[\"webui\",{\"1\":{\"46\":2}}],[\"web服务器添加https功能\",{\"1\":{\"39\":1}}],[\"webnet\",{\"1\":{\"31\":2}}],[\"write\",{\"1\":{\"409\":1,\"414\":1,\"416\":1,\"417\":1,\"434\":1,\"435\":1,\"449\":1,\"453\":1,\"463\":1,\"470\":1,\"474\":1,\"481\":1,\"485\":1,\"491\":1,\"515\":1,\"519\":1}}],[\"writer\",{\"1\":{\"251\":13}}],[\"wrapper\",{\"1\":{\"22\":1}}],[\"won\",{\"1\":{\"376\":3}}],[\"wodfan\",{\"1\":{\"114\":2}}],[\"working\",{\"1\":{\"144\":1}}],[\"work\",{\"1\":{\"114\":2,\"144\":3}}],[\"worker\",{\"1\":{\"30\":2,\"144\":9}}],[\"world\",{\"1\":{\"114\":2,\"182\":1,\"184\":1,\"232\":1,\"233\":3,\"286\":1,\"287\":1,\"294\":1,\"331\":3,\"332\":3,\"386\":1,\"387\":5}}],[\"will\",{\"1\":{\"442\":1}}],[\"winner\",{\"1\":{\"377\":6}}],[\"winningstrategy\",{\"1\":{\"376\":6}}],[\"wincount++\",{\"1\":{\"376\":1}}],[\"wincount\",{\"1\":{\"376\":2}}],[\"win\",{\"1\":{\"376\":9,\"377\":8}}],[\"windows\",{\"1\":{\"66\":1,\"186\":2}}],[\"wide\",{\"1\":{\"308\":1}}],[\"width\",{\"1\":{\"65\":1,\"183\":3,\"386\":3}}],[\"with\",{\"1\":{\"112\":3,\"114\":6,\"353\":1,\"354\":1,\"357\":1,\"444\":2,\"486\":1}}],[\"without\",{\"1\":{\"112\":1,\"113\":5,\"114\":15}}],[\"wsl$\",{\"1\":{\"47\":1}}],[\"wsl2\",{\"0\":{\"47\":1}}],[\"wq保存退出\",{\"1\":{\"46\":1}}],[\"www\",{\"1\":{\"30\":1,\"36\":4,\"153\":11}}],[\"warning\",{\"1\":{\"331\":2}}],[\"warn\",{\"1\":{\"30\":5,\"36\":5}}],[\"部分\",{\"1\":{\"156\":1,\"220\":1,\"465\":1}}],[\"部分ide默认直接支持\",{\"1\":{\"65\":1}}],[\"部分路径以实际为准\",{\"1\":{\"29\":1}}],[\"部署一个\",{\"1\":{\"26\":1}}],[\"部署\",{\"0\":{\"26\":1},\"1\":{\"38\":1},\"2\":{\"41\":1}}],[\"└──\",{\"1\":{\"28\":2}}],[\"lvalue\",{\"1\":{\"459\":12,\"507\":1,\"509\":2}}],[\"lt\",{\"1\":{\"421\":1,\"431\":1,\"439\":1,\"447\":1,\"508\":1}}],[\"lc\",{\"1\":{\"421\":1,\"422\":5,\"500\":4,\"502\":1,\"503\":4,\"507\":2,\"509\":1,\"514\":1}}],[\"ll\",{\"1\":{\"408\":1,\"411\":1,\"446\":1}}],[\"le\",{\"1\":{\"421\":1,\"431\":1,\"439\":1,\"447\":1,\"508\":1}}],[\"leaving\",{\"1\":{\"480\":1}}],[\"lea\",{\"0\":{\"430\":1},\"1\":{\"417\":1,\"421\":1,\"430\":2,\"500\":1}}],[\"lev\",{\"0\":{\"429\":1},\"1\":{\"417\":1,\"421\":1,\"426\":2,\"429\":2,\"480\":1,\"489\":2}}],[\"level\",{\"1\":{\"416\":2,\"508\":3}}],[\"lemon\",{\"1\":{\"411\":1}}],[\"lexer\",{\"1\":{\"437\":1}}],[\"lex\",{\"1\":{\"408\":2,\"438\":1}}],[\"legs\",{\"1\":{\"286\":1,\"287\":1}}],[\"left\",{\"1\":{\"279\":4,\"280\":2,\"436\":1}}],[\"length\",{\"1\":{\"183\":1,\"232\":1,\"279\":2,\"305\":1,\"331\":7,\"386\":1,\"394\":1}}],[\"let\",{\"1\":{\"153\":13,\"179\":1,\"183\":2,\"204\":7,\"211\":1,\"225\":7,\"232\":7,\"251\":3,\"264\":3,\"279\":3,\"305\":3,\"317\":3,\"331\":9,\"338\":2,\"362\":2,\"376\":4,\"386\":3,\"394\":9,\"411\":1}}],[\"letsencrypt\",{\"1\":{\"31\":1,\"36\":6}}],[\"lf\",{\"1\":{\"65\":1}}],[\"lan\",{\"1\":{\"439\":1,\"447\":1,\"508\":1,\"511\":3}}],[\"lalr\",{\"1\":{\"408\":1}}],[\"last++\",{\"1\":{\"286\":1}}],[\"last\",{\"1\":{\"286\":3,\"439\":1,\"440\":1,\"443\":4,\"445\":2}}],[\"latex\",{\"1\":{\"225\":1,\"226\":2,\"394\":1,\"395\":2}}],[\"latest\",{\"1\":{\"31\":1,\"51\":1}}],[\"large\",{\"1\":{\"30\":1}}],[\"lookahead\",{\"1\":{\"446\":1,\"450\":1}}],[\"look\",{\"1\":{\"443\":1}}],[\"loop\",{\"1\":{\"113\":3,\"114\":9}}],[\"lor\",{\"1\":{\"439\":1,\"447\":1,\"508\":1,\"511\":2}}],[\"load\",{\"1\":{\"422\":3,\"430\":1,\"500\":1}}],[\"low\",{\"1\":{\"419\":1,\"430\":1,\"477\":1}}],[\"lotabout\",{\"1\":{\"414\":1,\"416\":1,\"417\":1,\"434\":1,\"435\":1,\"449\":1,\"453\":1,\"463\":1,\"470\":1,\"474\":1,\"481\":1,\"485\":1,\"491\":1,\"515\":1,\"519\":1}}],[\"losecount++\",{\"1\":{\"376\":1}}],[\"losecount\",{\"1\":{\"376\":2}}],[\"lose\",{\"1\":{\"376\":4,\"377\":8}}],[\"long\",{\"1\":{\"286\":1,\"287\":1,\"433\":4}}],[\"loc\",{\"1\":{\"439\":1,\"478\":1,\"479\":2,\"480\":2,\"500\":1,\"508\":1}}],[\"locking\",{\"1\":{\"356\":1}}],[\"lock\",{\"1\":{\"112\":8,\"113\":5,\"114\":23,\"357\":4}}],[\"location\",{\"1\":{\"30\":3,\"36\":6}}],[\"localtime=true\",{\"1\":{\"52\":1}}],[\"local\",{\"1\":{\"30\":1,\"430\":2,\"477\":5,\"478\":2,\"479\":1,\"480\":11,\"500\":1}}],[\"logic\",{\"1\":{\"511\":2}}],[\"loginframe\",{\"1\":{\"299\":2}}],[\"login\",{\"1\":{\"52\":1,\"140\":2}}],[\"log\",{\"1\":{\"28\":2,\"30\":29,\"31\":1,\"36\":30,\"144\":1,\"147\":4,\"153\":2,\"166\":2,\"183\":2,\"193\":4,\"204\":2,\"211\":1,\"222\":1,\"224\":1,\"225\":2,\"232\":1,\"251\":2,\"258\":1,\"264\":1,\"279\":2,\"286\":1,\"294\":3,\"305\":10,\"317\":2,\"331\":8,\"338\":9,\"353\":2,\"357\":1,\"362\":4,\"376\":6,\"386\":5,\"394\":4}}],[\"logs\",{\"1\":{\"28\":1,\"31\":1}}],[\"literal\",{\"1\":{\"445\":2}}],[\"li\",{\"1\":{\"421\":1,\"422\":5,\"500\":4,\"502\":1,\"503\":4,\"507\":2,\"509\":2,\"514\":1}}],[\"lightning\",{\"1\":{\"294\":1,\"295\":3}}],[\"liskov\",{\"1\":{\"242\":1}}],[\"listvisitor\",{\"1\":{\"394\":6,\"398\":1}}],[\"list>\",{\"1\":{\"279\":8}}],[\"listpicture\",{\"1\":{\"157\":1}}],[\"listpage\",{\"1\":{\"153\":5}}],[\"listtray\",{\"1\":{\"153\":5}}],[\"listlink\",{\"1\":{\"153\":5}}],[\"listfactory\",{\"1\":{\"153\":5,\"157\":2}}],[\"listen\",{\"1\":{\"30\":2,\"36\":5}}],[\"list\",{\"1\":{\"21\":1,\"61\":1,\"269\":1,\"279\":3}}],[\"limit\",{\"1\":{\"204\":5}}],[\"limitsupport\",{\"1\":{\"204\":7}}],[\"li><li>再见\",{\"1\":{\"194\":1}}],[\"li><li>晚安\",{\"1\":{\"194\":1}}],[\"li><li>下午好\",{\"1\":{\"194\":1}}],[\"li><\",{\"1\":{\"194\":2}}],[\"li>`\",{\"1\":{\"193\":1}}],[\"li>\",{\"1\":{\"153\":10}}],[\"linkpage\",{\"1\":{\"153\":1}}],[\"link\",{\"1\":{\"153\":8,\"156\":1,\"251\":2}}],[\"linesecond\",{\"1\":{\"498\":1}}],[\"linelen\",{\"1\":{\"459\":2}}],[\"linecap\",{\"1\":{\"459\":2}}],[\"linear\",{\"1\":{\"443\":1}}],[\"line\",{\"1\":{\"65\":1,\"386\":4,\"416\":3,\"459\":3,\"467\":2,\"468\":2,\"469\":1,\"479\":2,\"480\":2,\"498\":3,\"500\":2,\"502\":1,\"503\":1,\"507\":1,\"509\":1,\"510\":1,\"514\":1}}],[\"license\",{\"1\":{\"124\":2}}],[\"liuyue$\",{\"1\":{\"114\":4}}],[\"liuyue\",{\"1\":{\"114\":6}}],[\"like\",{\"1\":{\"35\":1,\"468\":1,\"480\":1}}],[\"live\",{\"1\":{\"31\":1,\"36\":6}}],[\"libgen\",{\"1\":{\"18\":2}}],[\"lib\",{\"1\":{\"18\":1}}],[\"library\",{\"1\":{\"18\":2,\"448\":1}}],[\"yet\",{\"1\":{\"416\":1}}],[\"yuki<\",{\"1\":{\"252\":1}}],[\"yukiのページへようこそ\",{\"1\":{\"252\":1}}],[\"yuki\",{\"1\":{\"225\":5,\"226\":3,\"251\":1,\"252\":2,\"394\":5,\"395\":3}}],[\"yahoo<\",{\"1\":{\"153\":2}}],[\"yahoo\",{\"1\":{\"153\":12}}],[\"yacc\",{\"1\":{\"125\":1,\"408\":2,\"522\":1}}],[\"y\",{\"1\":{\"57\":1,\"58\":1,\"211\":8}}],[\"yml\",{\"1\":{\"28\":1,\"31\":1}}],[\"your\",{\"1\":{\"67\":1}}],[\"you\",{\"1\":{\"21\":1}}],[\"bxxx\",{\"1\":{\"478\":1,\"479\":1}}],[\"bxxxx\",{\"1\":{\"443\":1}}],[\"bnf\",{\"1\":{\"455\":1,\"457\":3,\"460\":1,\"464\":1,\"522\":2}}],[\"bnf什么的\",{\"1\":{\"408\":1}}],[\"bvalue\",{\"1\":{\"443\":2,\"478\":1,\"479\":1,\"480\":1}}],[\"btype\",{\"1\":{\"443\":2,\"478\":1,\"479\":1,\"480\":1}}],[\"bp+\",{\"1\":{\"430\":1,\"477\":1}}],[\"bp\",{\"1\":{\"420\":3,\"427\":2,\"429\":2,\"430\":9,\"477\":7,\"479\":5,\"480\":2,\"500\":2}}],[\"brak\",{\"1\":{\"439\":1,\"447\":1,\"508\":2,\"514\":2}}],[\"bracket\",{\"1\":{\"436\":2}}],[\"break\",{\"1\":{\"279\":1}}],[\"bridge\",{\"0\":{\"171\":1},\"1\":{\"168\":1,\"171\":1,\"172\":1,\"176\":1,\"184\":1,\"186\":2}}],[\"bsion\",{\"1\":{\"522\":1}}],[\"bss\",{\"1\":{\"419\":2}}],[\"bs\",{\"1\":{\"264\":2}}],[\"bclass\",{\"1\":{\"443\":2,\"478\":1,\"479\":1,\"480\":1}}],[\"bc\",{\"1\":{\"264\":5}}],[\"b4\",{\"1\":{\"232\":2,\"235\":1}}],[\"b3\",{\"1\":{\"232\":2}}],[\"b2\",{\"1\":{\"232\":3}}],[\"b1\",{\"1\":{\"232\":3}}],[\"bitwise\",{\"1\":{\"505\":1,\"512\":1}}],[\"bible\",{\"1\":{\"286\":1,\"287\":1}}],[\"bigstring\",{\"1\":{\"264\":6,\"267\":4,\"268\":3}}],[\"bigchars\",{\"1\":{\"264\":3}}],[\"bigchar>\",{\"1\":{\"264\":1}}],[\"bigcharfactory\",{\"1\":{\"264\":9}}],[\"bigchar\",{\"1\":{\"264\":13,\"267\":6,\"268\":5}}],[\"binary\",{\"1\":{\"508\":1}}],[\"bin\",{\"1\":{\"225\":1,\"226\":6,\"394\":1,\"395\":6}}],[\"bindir\",{\"1\":{\"225\":4,\"394\":4}}],[\"bison\",{\"1\":{\"125\":1,\"408\":1,\"409\":1,\"411\":1,\"415\":1}}],[\"by\",{\"1\":{\"204\":1,\"205\":13,\"294\":1,\"295\":6}}],[\"bytes\",{\"1\":{\"30\":1}}],[\"box\",{\"1\":{\"331\":4}}],[\"books\",{\"1\":{\"286\":4}}],[\"bookshelfiterator\",{\"1\":{\"286\":5,\"287\":1}}],[\"bookshelf\",{\"1\":{\"286\":21,\"287\":3,\"288\":1}}],[\"book\",{\"1\":{\"286\":19,\"287\":1}}],[\"boolean\",{\"1\":{\"204\":4,\"279\":1,\"286\":2,\"376\":5}}],[\"borderchar\",{\"1\":{\"232\":4}}],[\"border\",{\"1\":{\"232\":8,\"235\":2}}],[\"bob使用了id卡\",{\"1\":{\"259\":1}}],[\"bob\",{\"1\":{\"204\":3,\"205\":4,\"258\":1,\"338\":1,\"339\":2}}],[\"body><\",{\"1\":{\"153\":2,\"193\":1,\"194\":1,\"251\":1,\"252\":1}}],[\"body\",{\"1\":{\"52\":2,\"464\":2,\"467\":1,\"475\":2,\"476\":1,\"478\":1,\"480\":1}}],[\"ba\",{\"1\":{\"487\":1}}],[\"bad\",{\"1\":{\"467\":1,\"468\":2,\"479\":1,\"480\":1,\"500\":1,\"502\":1,\"503\":1,\"507\":1,\"509\":1}}],[\"basetype\",{\"1\":{\"467\":4,\"480\":2}}],[\"banana\",{\"1\":{\"305\":1,\"306\":9}}],[\"banner\",{\"1\":{\"165\":1,\"166\":13}}],[\"balance\",{\"1\":{\"112\":12,\"113\":7,\"114\":32}}],[\"behaviour\",{\"1\":{\"500\":1}}],[\"because\",{\"1\":{\"442\":1}}],[\"bet\",{\"1\":{\"305\":2,\"376\":3}}],[\"be\",{\"1\":{\"204\":1,\"205\":3,\"467\":1,\"500\":1}}],[\"bepinex\",{\"1\":{\"64\":1}}],[\"below\",{\"1\":{\"35\":1}}],[\"b+p\",{\"1\":{\"57\":1}}],[\"b\",{\"1\":{\"57\":5,\"298\":7,\"416\":1,\"434\":1,\"449\":1,\"467\":1,\"468\":1,\"470\":1,\"477\":2,\"481\":1,\"487\":8,\"488\":4,\"490\":1,\"491\":1,\"510\":1,\"511\":4,\"515\":1}}],[\"blog\",{\"1\":{\"28\":3,\"30\":4,\"31\":2,\"36\":7,\"51\":1,\"495\":1}}],[\"but\",{\"1\":{\"279\":1,\"500\":1}}],[\"buttonuse\",{\"1\":{\"370\":1}}],[\"button\",{\"1\":{\"21\":1}}],[\"buf\",{\"1\":{\"232\":3}}],[\"buffers\",{\"1\":{\"30\":1}}],[\"buffer\",{\"1\":{\"30\":1,\"153\":21,\"183\":4,\"193\":19}}],[\"bug\",{\"0\":{\"109\":1},\"1\":{\"156\":1,\"297\":3,\"380\":1}}],[\"builder\",{\"0\":{\"191\":1,\"192\":1},\"1\":{\"158\":1,\"192\":3,\"193\":24,\"194\":1,\"197\":2,\"198\":1,\"199\":7,\"355\":1}}],[\"build\",{\"1\":{\"31\":1,\"32\":1,\"35\":1,\"37\":1,\"108\":2,\"411\":1}}],[\"bupt\",{\"1\":{\"26\":1,\"30\":4,\"32\":3,\"34\":2,\"35\":4,\"36\":14,\"52\":4}}],[\"│\",{\"1\":{\"28\":6}}],[\"├──\",{\"1\":{\"28\":12}}],[\"ulchar\",{\"1\":{\"331\":5}}],[\"ul><\",{\"1\":{\"194\":1}}],[\"ul><p>晚上<\",{\"1\":{\"194\":1}}],[\"ul>\",{\"1\":{\"153\":5,\"193\":1}}],[\"ul>`\",{\"1\":{\"153\":1}}],[\"unary\",{\"1\":{\"499\":1}}],[\"unwind\",{\"1\":{\"478\":1}}],[\"unknown\",{\"1\":{\"432\":1}}],[\"underlinepen\",{\"1\":{\"331\":5}}],[\"undefined`\",{\"1\":{\"279\":1}}],[\"undefined\",{\"1\":{\"67\":1,\"204\":1,\"338\":2,\"500\":1}}],[\"undo\",{\"1\":{\"211\":1}}],[\"unit\",{\"1\":{\"500\":1}}],[\"unityexplorer\",{\"1\":{\"64\":1}}],[\"unix\",{\"1\":{\"186\":2}}],[\"universe\",{\"1\":{\"182\":1,\"184\":5}}],[\"until\",{\"1\":{\"113\":1,\"114\":3}}],[\"utf\",{\"1\":{\"65\":1}}],[\"utils\",{\"1\":{\"52\":1}}],[\"u\",{\"1\":{\"56\":1,\"57\":1,\"58\":2,\"294\":2}}],[\"uri\",{\"1\":{\"36\":2}}],[\"url\",{\"1\":{\"22\":2,\"153\":10}}],[\"url=uri\",{\"1\":{\"22\":12}}],[\"upen\",{\"1\":{\"331\":2}}],[\"update\",{\"1\":{\"317\":4,\"321\":4}}],[\"up\",{\"1\":{\"32\":1,\"35\":1,\"37\":1}}],[\"us\",{\"1\":{\"153\":5}}],[\"use\",{\"1\":{\"35\":1,\"258\":5,\"331\":6,\"426\":1,\"504\":1,\"505\":1}}],[\"user3\",{\"1\":{\"294\":2}}],[\"user2\",{\"1\":{\"294\":2}}],[\"user1\",{\"1\":{\"294\":2}}],[\"userprofile\",{\"1\":{\"140\":1}}],[\"usersexcludingsender\",{\"1\":{\"294\":2}}],[\"users\",{\"1\":{\"114\":2,\"294\":4}}],[\"username\",{\"1\":{\"52\":2,\"251\":6}}],[\"user\",{\"1\":{\"30\":3,\"140\":1,\"225\":1,\"226\":1,\"294\":13,\"297\":2,\"394\":1,\"395\":1}}],[\"usrdir\",{\"1\":{\"225\":5,\"394\":5}}],[\"usr\",{\"1\":{\"30\":3,\"31\":2,\"36\":5,\"225\":1,\"226\":10,\"394\":1,\"395\":10}}],[\"ubuntu\",{\"1\":{\"27\":1,\"35\":4}}],[\"环境\",{\"0\":{\"27\":1},\"1\":{\"66\":1}}],[\"配置方法\",{\"0\":{\"46\":1}}],[\"配置docker\",{\"0\":{\"31\":1}}],[\"配置nginx反向代理\",{\"0\":{\"38\":1}}],[\"配置nginx\",{\"0\":{\"30\":1}}],[\"配置http服务\",{\"0\":{\"29\":1}}],[\"配置以及如何升级到\",{\"1\":{\"26\":1}}],[\"配置\",{\"1\":{\"26\":1}}],[\"和字符串如\",{\"1\":{\"445\":1}}],[\"和文法并编写解析算法\",{\"1\":{\"411\":1}}],[\"和文法的定义\",{\"1\":{\"411\":1}}],[\"和被观察者\",{\"1\":{\"320\":1}}],[\"和窄接口\",{\"1\":{\"308\":1}}],[\"和窗口句柄等也都是一种资源\",{\"1\":{\"270\":1}}],[\"和开源作者们使用同一套流程\",{\"1\":{\"49\":1}}],[\"和\",{\"0\":{\"311\":1},\"1\":{\"26\":2,\"72\":2,\"88\":1,\"94\":1,\"124\":1,\"154\":1,\"171\":1,\"287\":1,\"298\":4,\"311\":1,\"337\":1,\"365\":1,\"380\":1,\"397\":1,\"407\":1,\"422\":1,\"465\":1,\"486\":1,\"487\":1,\"496\":1,\"511\":1}}],[\"和机械臂联动\",{\"0\":{\"15\":1}}],[\"+var\",{\"1\":{\"506\":1}}],[\"+global\",{\"1\":{\"464\":1}}],[\"++p时\",{\"1\":{\"507\":1}}],[\"++p\",{\"1\":{\"507\":2}}],[\"++pos\",{\"1\":{\"480\":1}}],[\"++text\",{\"1\":{\"480\":3,\"487\":4,\"488\":4,\"489\":1,\"498\":4,\"499\":2,\"500\":13,\"502\":1,\"504\":4,\"505\":4,\"506\":6,\"507\":7,\"509\":1,\"510\":4,\"511\":4,\"512\":8,\"513\":14,\"514\":7}}],[\"++line\",{\"1\":{\"441\":1}}],[\"++src\",{\"1\":{\"440\":1,\"444\":2,\"446\":1}}],[\"++\",{\"1\":{\"376\":3,\"447\":10,\"459\":2,\"500\":1,\"501\":1,\"502\":1}}],[\"+|return\",{\"1\":{\"430\":1,\"477\":1}}],[\"+|\",{\"1\":{\"233\":2,\"419\":4,\"430\":7,\"477\":6,\"496\":6}}],[\"+=\",{\"1\":{\"183\":2,\"193\":15,\"204\":1,\"232\":1,\"251\":4,\"305\":1,\"317\":1,\"362\":2,\"376\":1,\"386\":2,\"394\":1,\"426\":1}}],[\"+\",{\"0\":{\"26\":2},\"1\":{\"112\":2,\"113\":1,\"114\":4,\"153\":1,\"183\":2,\"184\":12,\"222\":1,\"232\":19,\"233\":12,\"251\":3,\"264\":109,\"279\":6,\"305\":2,\"331\":2,\"338\":4,\"376\":4,\"386\":2,\"387\":8,\"419\":2,\"420\":1,\"425\":2,\"428\":1,\"430\":6,\"431\":1,\"432\":1,\"436\":1,\"437\":8,\"439\":1,\"443\":22,\"444\":6,\"447\":3,\"455\":2,\"456\":2,\"458\":1,\"459\":4,\"467\":4,\"476\":1,\"477\":3,\"478\":1,\"479\":1,\"480\":1,\"487\":2,\"488\":2,\"496\":27,\"498\":1,\"499\":1,\"501\":1,\"503\":1,\"510\":2,\"511\":2,\"512\":3,\"514\":1,\"515\":1}}],[\"7章函数定义\",{\"1\":{\"500\":1}}],[\"7|\",{\"1\":{\"496\":1}}],[\"7\",{\"0\":{\"485\":1},\"1\":{\"22\":1,\"113\":1,\"114\":4,\"212\":2,\"264\":1,\"370\":1,\"406\":1,\"414\":1,\"417\":2,\"435\":2,\"444\":1,\"453\":2,\"463\":1,\"474\":1,\"485\":2,\"495\":2,\"519\":1}}],[\"m32\",{\"1\":{\"433\":2}}],[\"mcmp\",{\"1\":{\"421\":1,\"432\":1}}],[\"mset\",{\"1\":{\"421\":1,\"432\":1}}],[\"msg\",{\"1\":{\"52\":7,\"338\":2,\"362\":6}}],[\"mbox\",{\"1\":{\"331\":2}}],[\"mvc\",{\"0\":{\"325\":1},\"1\":{\"325\":2}}],[\"m\",{\"1\":{\"305\":3,\"419\":1}}],[\"me\",{\"1\":{\"414\":1,\"417\":1,\"435\":1,\"453\":1,\"463\":1,\"474\":1,\"485\":1,\"519\":1}}],[\"mechanism\",{\"1\":{\"357\":1}}],[\"messaging\",{\"1\":{\"294\":1}}],[\"messagebox\",{\"1\":{\"331\":6}}],[\"messages\",{\"1\":{\"294\":2}}],[\"message\",{\"1\":{\"251\":2,\"294\":5,\"295\":9,\"331\":2}}],[\"mediator\",{\"0\":{\"292\":1},\"1\":{\"253\":1,\"294\":11,\"295\":1,\"297\":1,\"298\":1,\"326\":1,\"367\":1}}],[\"memcmp\",{\"1\":{\"432\":2,\"443\":1,\"448\":1}}],[\"memset\",{\"1\":{\"419\":3,\"420\":1,\"432\":2,\"448\":1}}],[\"memory\",{\"1\":{\"419\":1,\"467\":2,\"476\":1}}],[\"memo\",{\"1\":{\"225\":1,\"226\":1,\"394\":1,\"395\":1}}],[\"memento\",{\"0\":{\"303\":1,\"304\":1,\"309\":1,\"310\":1},\"1\":{\"216\":1,\"304\":1,\"305\":17,\"308\":5,\"309\":4,\"310\":5,\"311\":9,\"333\":1}}],[\"method\",{\"0\":{\"256\":1,\"257\":1,\"384\":1,\"385\":1},\"1\":{\"158\":1,\"175\":1,\"188\":1,\"195\":1,\"256\":2,\"257\":2,\"259\":2,\"289\":1,\"384\":1,\"387\":1,\"388\":1}}],[\"md\",{\"0\":{\"126\":1}}],[\"mytornado\",{\"1\":{\"114\":5}}],[\"move\",{\"1\":{\"498\":1}}],[\"movw\",{\"1\":{\"422\":1}}],[\"movb\",{\"1\":{\"422\":1}}],[\"mov\",{\"0\":{\"422\":1},\"1\":{\"417\":1,\"422\":6,\"426\":4,\"429\":1}}],[\"mod\",{\"1\":{\"421\":1,\"431\":1,\"439\":1,\"447\":1,\"508\":1}}],[\"model\",{\"0\":{\"325\":1},\"1\":{\"325\":1}}],[\"modint1\",{\"1\":{\"58\":1}}],[\"modint<int\",{\"1\":{\"58\":3}}],[\"modint\",{\"0\":{\"53\":1},\"1\":{\"58\":9},\"2\":{\"60\":1,\"122\":1}}],[\"money\",{\"1\":{\"305\":21,\"306\":8}}],[\"mobile\",{\"2\":{\"110\":1}}],[\"multiply\",{\"1\":{\"436\":1}}],[\"multipart\",{\"1\":{\"52\":1}}],[\"multidisplay\",{\"1\":{\"179\":1,\"182\":1}}],[\"mul\",{\"1\":{\"57\":1,\"421\":1,\"431\":1,\"439\":2,\"447\":1,\"467\":2,\"479\":2,\"480\":2,\"499\":2,\"501\":2,\"502\":2,\"506\":1,\"508\":1,\"512\":3,\"514\":1}}],[\"missing\",{\"1\":{\"279\":1,\"510\":1}}],[\"mixmark\",{\"1\":{\"126\":1}}],[\"mimemultipart\",{\"1\":{\"52\":2}}],[\"mimetext\",{\"1\":{\"52\":2}}],[\"mime\",{\"1\":{\"30\":1,\"52\":2}}],[\"mirrors\",{\"1\":{\"22\":1,\"46\":1}}],[\"may\",{\"1\":{\"467\":1}}],[\"malc\",{\"1\":{\"421\":1,\"432\":1}}],[\"malloc\",{\"1\":{\"416\":2,\"419\":6,\"432\":2,\"448\":1,\"500\":1}}],[\"match\",{\"1\":{\"459\":8,\"467\":10,\"469\":2,\"478\":5,\"479\":5,\"480\":5,\"487\":4,\"488\":3,\"489\":2,\"490\":4,\"498\":3,\"499\":6,\"500\":4,\"501\":5,\"502\":1,\"503\":1,\"504\":1,\"505\":1,\"506\":3,\"507\":1,\"509\":1,\"510\":2,\"511\":2,\"512\":2,\"514\":2}}],[\"math\",{\"1\":{\"305\":5,\"317\":2,\"376\":4}}],[\"mater\",{\"1\":{\"294\":1,\"295\":3}}],[\"map\",{\"1\":{\"264\":1}}],[\"map<string\",{\"1\":{\"264\":1}}],[\"mamoru\",{\"1\":{\"251\":2}}],[\"making\",{\"1\":{\"225\":2,\"226\":2,\"252\":1,\"394\":2,\"395\":2}}],[\"make\",{\"1\":{\"426\":1,\"427\":3,\"467\":1}}],[\"makewelcomepage\",{\"1\":{\"251\":2}}],[\"makeline\",{\"1\":{\"232\":3}}],[\"makeitems\",{\"1\":{\"193\":5}}],[\"makestring\",{\"1\":{\"193\":5}}],[\"maketitle\",{\"1\":{\"193\":4}}],[\"makehtml\",{\"1\":{\"153\":8}}],[\"macro\",{\"1\":{\"442\":1}}],[\"macrocommand\",{\"1\":{\"211\":9}}],[\"machine\",{\"1\":{\"419\":1,\"420\":1}}],[\"macintosh\",{\"1\":{\"186\":2}}],[\"manage\",{\"1\":{\"144\":2,\"294\":1}}],[\"manager\",{\"1\":{\"144\":4,\"331\":12}}],[\"master\",{\"1\":{\"114\":1}}],[\"mailprop\",{\"1\":{\"251\":2}}],[\"mailaddress\",{\"1\":{\"251\":4}}],[\"mailaddr\",{\"1\":{\"251\":2}}],[\"mailto\",{\"1\":{\"251\":2,\"252\":1}}],[\"maildata\",{\"1\":{\"251\":3}}],[\"mail\",{\"1\":{\"52\":1,\"225\":1,\"226\":1,\"394\":1,\"395\":1}}],[\"mailserver\",{\"1\":{\"51\":3}}],[\"mainly\",{\"1\":{\"443\":1}}],[\"main\",{\"0\":{\"182\":1,\"225\":1},\"1\":{\"30\":2,\"46\":1,\"153\":2,\"156\":1,\"166\":1,\"167\":1,\"178\":1,\"184\":1,\"187\":2,\"193\":1,\"194\":1,\"204\":1,\"205\":1,\"211\":1,\"212\":1,\"226\":1,\"232\":1,\"233\":1,\"251\":1,\"252\":1,\"258\":1,\"259\":1,\"264\":1,\"265\":1,\"279\":1,\"280\":1,\"286\":1,\"287\":1,\"295\":1,\"305\":1,\"317\":1,\"318\":1,\"331\":1,\"332\":1,\"338\":1,\"339\":1,\"353\":1,\"354\":1,\"362\":1,\"363\":1,\"366\":1,\"376\":1,\"386\":1,\"387\":1,\"394\":1,\"395\":1,\"416\":1,\"419\":1,\"420\":1,\"433\":2,\"448\":3,\"459\":1,\"515\":3}}],[\"maintenance\",{\"0\":{\"21\":1},\"1\":{\"21\":1}}],[\"mavencentral\",{\"1\":{\"22\":2}}],[\"maven\",{\"1\":{\"22\":26}}],[\"markdown\",{\"1\":{\"18\":1,\"119\":3,\"124\":1}}],[\"duplicate\",{\"1\":{\"467\":1,\"479\":1,\"480\":1,\"507\":1}}],[\"dump\",{\"1\":{\"419\":1}}],[\"drawing\",{\"1\":{\"212\":10}}],[\"drawcommand\",{\"1\":{\"211\":5}}],[\"drawcanvas\",{\"1\":{\"211\":8}}],[\"draw\",{\"1\":{\"211\":3}}],[\"drawable\",{\"1\":{\"211\":5}}],[\"driving\",{\"1\":{\"147\":2}}],[\"drive\",{\"1\":{\"147\":3}}],[\"divide\",{\"1\":{\"446\":1}}],[\"div\",{\"1\":{\"421\":1,\"431\":1,\"439\":1,\"446\":2,\"508\":1}}],[\"directly\",{\"1\":{\"447\":1}}],[\"directory\",{\"0\":{\"222\":1},\"1\":{\"222\":6,\"225\":16,\"394\":14,\"398\":3,\"401\":1,\"402\":2}}],[\"director2\",{\"1\":{\"193\":2}}],[\"director\",{\"1\":{\"192\":1,\"193\":8,\"197\":1,\"199\":2}}],[\"dir\",{\"1\":{\"394\":4}}],[\"digitobserver\",{\"1\":{\"317\":5,\"318\":20,\"321\":1}}],[\"dice\",{\"1\":{\"305\":4}}],[\"diary\",{\"1\":{\"225\":1,\"226\":1,\"394\":1,\"395\":1}}],[\"diana\",{\"1\":{\"204\":3,\"205\":3}}],[\"dispatch\",{\"1\":{\"397\":1}}],[\"displayimpl\",{\"0\":{\"181\":1},\"1\":{\"178\":1,\"179\":3,\"180\":4,\"181\":1,\"183\":3,\"187\":1}}],[\"display\",{\"0\":{\"180\":1},\"1\":{\"178\":6,\"179\":3,\"180\":2,\"182\":5,\"187\":5,\"232\":36,\"235\":2,\"236\":3,\"386\":4}}],[\"displayprofile\",{\"1\":{\"140\":2}}],[\"distributionurl=https\",{\"1\":{\"22\":1}}],[\"d3\",{\"1\":{\"182\":2,\"386\":2}}],[\"d2\",{\"1\":{\"182\":2,\"386\":2}}],[\"d1\",{\"1\":{\"182\":2,\"386\":2}}],[\"do\",{\"1\":{\"416\":2,\"506\":1}}],[\"doyyy\",{\"1\":{\"369\":1}}],[\"dophone\",{\"1\":{\"362\":6}}],[\"doalarm\",{\"1\":{\"362\":6}}],[\"douse\",{\"1\":{\"362\":6,\"370\":6}}],[\"double\",{\"1\":{\"356\":1,\"397\":1}}],[\"done\",{\"1\":{\"124\":1,\"204\":2}}],[\"doclock\",{\"1\":{\"362\":4,\"366\":3,\"367\":1}}],[\"doc\",{\"1\":{\"225\":1,\"226\":1,\"294\":1,\"295\":3,\"394\":1,\"395\":1}}],[\"documentation\",{\"1\":{\"39\":2}}],[\"docker部署certbot与nginx来获取ssl证书添加https及自动更新\",{\"1\":{\"39\":1}}],[\"dockerfile\",{\"1\":{\"28\":1,\"31\":3}}],[\"docker\",{\"0\":{\"26\":1,\"47\":1},\"1\":{\"26\":2,\"27\":2,\"28\":1,\"31\":1,\"32\":1,\"35\":1,\"37\":1,\"44\":1,\"46\":3,\"47\":2,\"51\":2}}],[\"dcqe\",{\"1\":{\"124\":1}}],[\"dnspy\",{\"1\":{\"64\":1}}],[\"dp\",{\"1\":{\"54\":1}}],[\"daddy\",{\"1\":{\"286\":1,\"287\":1}}],[\"daystate\",{\"1\":{\"362\":10,\"367\":5,\"369\":1,\"370\":1}}],[\"days\",{\"1\":{\"286\":1,\"287\":1}}],[\"date\",{\"1\":{\"52\":1}}],[\"data++\",{\"1\":{\"445\":1}}],[\"databasename\",{\"1\":{\"251\":1}}],[\"database\",{\"1\":{\"251\":6}}],[\"data\",{\"1\":{\"47\":2,\"416\":1,\"419\":8,\"445\":4,\"467\":5,\"498\":4}}],[\"daemon\",{\"1\":{\"46\":2}}],[\"dereference\",{\"1\":{\"502\":3}}],[\"demo函数被调用时\",{\"1\":{\"477\":1}}],[\"demo\",{\"1\":{\"477\":1}}],[\"declenum\",{\"1\":{\"464\":1}}],[\"decl\",{\"1\":{\"464\":10,\"465\":2,\"467\":8,\"475\":7,\"476\":2,\"478\":4,\"479\":1}}],[\"declarations\",{\"1\":{\"478\":1,\"480\":1}}],[\"declaration\",{\"0\":{\"467\":1,\"468\":1},\"1\":{\"463\":2,\"464\":2,\"466\":3,\"467\":10,\"468\":1,\"469\":1,\"476\":1,\"478\":1,\"479\":2,\"480\":4}}],[\"dec\",{\"1\":{\"439\":1,\"444\":2,\"447\":1,\"507\":1,\"508\":1}}],[\"decochar\",{\"1\":{\"331\":8}}],[\"decorator\",{\"0\":{\"230\":1},\"1\":{\"168\":1,\"227\":1,\"233\":1,\"235\":3,\"236\":2,\"237\":1,\"238\":2,\"239\":1,\"333\":1,\"347\":1}}],[\"deleteobserver\",{\"1\":{\"317\":1}}],[\"delegation\",{\"1\":{\"166\":4}}],[\"delicious\",{\"1\":{\"305\":2,\"306\":30}}],[\"dest\",{\"1\":{\"422\":2}}],[\"design\",{\"0\":{\"528\":1},\"1\":{\"153\":2,\"167\":1,\"184\":2,\"194\":2,\"205\":2,\"212\":2,\"226\":2,\"233\":2,\"252\":2,\"259\":2,\"265\":2,\"280\":2,\"287\":2,\"294\":1,\"295\":2,\"318\":2,\"332\":2,\"339\":2,\"354\":2,\"363\":2,\"387\":2,\"395\":2}}],[\"desktop\",{\"1\":{\"47\":1}}],[\"devtool\",{\"1\":{\"406\":1}}],[\"device\",{\"1\":{\"401\":2}}],[\"dev\",{\"1\":{\"118\":1}}],[\"define\",{\"1\":{\"433\":1}}],[\"def\",{\"1\":{\"112\":2,\"113\":1,\"114\":5}}],[\"default\",{\"1\":{\"30\":1,\"416\":1,\"498\":1,\"500\":1}}],[\"deploy\",{\"1\":{\"108\":1}}],[\"dependencyresolutionmanagement\",{\"1\":{\"22\":1}}],[\"details\",{\"1\":{\"51\":1,\"495\":1}}],[\"d\",{\"1\":{\"28\":1,\"30\":1,\"31\":4,\"32\":1,\"34\":2,\"35\":2,\"37\":1,\"153\":1,\"167\":1,\"184\":1,\"194\":1,\"205\":1,\"212\":1,\"226\":1,\"233\":1,\"252\":1,\"259\":1,\"265\":1,\"280\":1,\"287\":1,\"295\":1,\"318\":1,\"332\":1,\"339\":1,\"354\":1,\"363\":1,\"387\":1,\"395\":1,\"416\":2,\"419\":3,\"432\":2,\"459\":3,\"467\":2,\"468\":3,\"469\":2,\"479\":2,\"480\":2,\"500\":2,\"502\":1,\"503\":1,\"507\":1,\"509\":1,\"510\":1,\"514\":1}}],[\"fd\",{\"1\":{\"416\":4,\"419\":1}}],[\"fn\",{\"1\":{\"357\":2}}],[\"found\",{\"1\":{\"279\":1,\"443\":1,\"527\":1}}],[\"fontdatas\",{\"1\":{\"264\":2}}],[\"fontdata\",{\"1\":{\"264\":5}}],[\"forward\",{\"1\":{\"498\":1}}],[\"forwarded\",{\"1\":{\"30\":1}}],[\"foreach\",{\"1\":{\"153\":2,\"193\":2,\"211\":1,\"222\":1,\"264\":2,\"279\":1,\"305\":1,\"317\":1,\"394\":1}}],[\"for\",{\"1\":{\"30\":1,\"112\":4,\"114\":3,\"179\":1,\"183\":1,\"204\":1,\"211\":1,\"232\":2,\"251\":1,\"252\":1,\"294\":2,\"305\":1,\"317\":2,\"338\":1,\"362\":1,\"376\":2,\"386\":2,\"394\":1,\"416\":1,\"419\":5,\"426\":1,\"427\":1,\"430\":1,\"443\":2,\"467\":2,\"478\":1,\"480\":2,\"487\":1,\"489\":1,\"500\":1,\"508\":1}}],[\"format=freeze\",{\"1\":{\"61\":1}}],[\"formatdate\",{\"1\":{\"52\":2}}],[\"format\",{\"1\":{\"30\":1}}],[\"falt\",{\"1\":{\"449\":1}}],[\"false\",{\"1\":{\"204\":4,\"376\":2,\"487\":1,\"504\":1}}],[\"fault\",{\"1\":{\"433\":1}}],[\"fastbutmorememorystrategy\",{\"1\":{\"380\":1}}],[\"factor\",{\"1\":{\"459\":4}}],[\"factory\",{\"0\":{\"256\":1,\"257\":1},\"1\":{\"153\":21,\"156\":3,\"157\":2,\"158\":1,\"188\":1,\"195\":1,\"253\":1,\"256\":2,\"257\":2,\"258\":12,\"259\":1,\"264\":4,\"289\":1,\"381\":1,\"388\":1}}],[\"facade\",{\"0\":{\"249\":1},\"1\":{\"195\":1,\"250\":1,\"252\":1,\"300\":1,\"355\":1}}],[\"failed\",{\"1\":{\"52\":1,\"67\":1}}],[\"fail\",{\"1\":{\"22\":1,\"204\":2}}],[\"floor\",{\"1\":{\"305\":2,\"317\":1,\"376\":2}}],[\"flyweight\",{\"0\":{\"262\":1,\"263\":1},\"1\":{\"263\":3,\"265\":1,\"267\":4,\"269\":1,\"270\":1,\"333\":1,\"371\":1,\"381\":1}}],[\"flex\",{\"1\":{\"125\":1,\"408\":1,\"409\":1,\"411\":1,\"415\":1,\"438\":1}}],[\"flask\",{\"0\":{\"26\":1},\"1\":{\"26\":1,\"38\":1,\"39\":3}}],[\"func\",{\"1\":{\"478\":1,\"480\":1}}],[\"functions\",{\"1\":{\"500\":1}}],[\"functionvoid\",{\"1\":{\"448\":1}}],[\"functionenum\",{\"1\":{\"448\":1,\"467\":1}}],[\"function\",{\"1\":{\"153\":1,\"357\":1,\"430\":1,\"464\":2,\"467\":4,\"469\":1,\"475\":1,\"476\":2,\"478\":5,\"479\":1,\"480\":2,\"490\":1,\"500\":4}}],[\"function执行时间超过5s\",{\"1\":{\"67\":1}}],[\"function执行时间过长\",{\"1\":{\"67\":1}}],[\"fun\",{\"1\":{\"439\":1,\"467\":1,\"476\":2,\"500\":1,\"508\":1}}],[\"fullborder\",{\"1\":{\"232\":8,\"236\":1}}],[\"fullchain\",{\"1\":{\"35\":2,\"36\":3}}],[\"fields\",{\"1\":{\"443\":1}}],[\"fight\",{\"1\":{\"376\":3}}],[\"first\",{\"1\":{\"67\":1,\"498\":2}}],[\"finally\",{\"1\":{\"112\":1}}],[\"final\",{\"1\":{\"65\":1}}],[\"filetreatmentexception\",{\"1\":{\"223\":1}}],[\"filename\",{\"1\":{\"193\":4,\"251\":3}}],[\"files\",{\"1\":{\"30\":3,\"36\":5,\"124\":1}}],[\"file\",{\"0\":{\"224\":1},\"1\":{\"23\":3,\"35\":3,\"193\":2,\"194\":2,\"224\":1,\"225\":9,\"394\":15,\"398\":3,\"401\":1,\"416\":1}}],[\"filter\",{\"1\":{\"21\":1,\"294\":1,\"317\":1}}],[\"frameadd\",{\"1\":{\"428\":1}}],[\"framepush\",{\"1\":{\"427\":1}}],[\"frame\",{\"1\":{\"419\":1,\"426\":3,\"427\":2,\"428\":1,\"429\":2}}],[\"fruit\",{\"1\":{\"305\":3}}],[\"fruitsname\",{\"1\":{\"305\":3}}],[\"fruits\",{\"1\":{\"305\":12,\"306\":3}}],[\"fred\",{\"1\":{\"204\":3,\"205\":1}}],[\"freeze\",{\"1\":{\"61\":1}}],[\"from\",{\"1\":{\"31\":1,\"52\":8,\"114\":1,\"153\":15,\"166\":6,\"179\":2,\"180\":1,\"182\":3,\"183\":1,\"193\":7,\"204\":14,\"211\":8,\"222\":1,\"224\":1,\"225\":3,\"232\":9,\"251\":3,\"258\":6,\"264\":5,\"279\":19,\"286\":9,\"305\":2,\"317\":12,\"331\":5,\"338\":5,\"353\":1,\"362\":12,\"376\":10,\"386\":4,\"394\":15,\"426\":2,\"428\":2}}],[\"f\",{\"1\":{\"52\":1,\"305\":6,\"444\":2}}],[\"jnz\",{\"0\":{\"425\":1},\"1\":{\"417\":1,\"421\":1,\"425\":1,\"511\":2}}],[\"jz\",{\"0\":{\"425\":1},\"1\":{\"417\":1,\"421\":1,\"425\":1,\"487\":2,\"488\":2,\"510\":1,\"511\":2}}],[\"jmp\",{\"0\":{\"424\":1},\"1\":{\"417\":1,\"421\":1,\"424\":3,\"426\":1,\"487\":4,\"488\":2,\"510\":1}}],[\"just\",{\"1\":{\"480\":1,\"498\":1}}],[\"jump\",{\"1\":{\"424\":1,\"425\":2}}],[\"junk\",{\"1\":{\"225\":1,\"226\":1,\"394\":1,\"395\":1}}],[\"judge\",{\"1\":{\"54\":1}}],[\"java这些成熟的语言都是手动实现的\",{\"1\":{\"411\":1}}],[\"java\",{\"1\":{\"225\":1,\"226\":1,\"269\":1,\"394\":1,\"395\":1}}],[\"jp\",{\"1\":{\"153\":5}}],[\"join\",{\"1\":{\"112\":1,\"114\":1,\"153\":2,\"279\":1,\"305\":1}}],[\"json\",{\"1\":{\"46\":1}}],[\"jcenter\",{\"1\":{\"22\":2}}],[\"jitpack\",{\"1\":{\"22\":2}}],[\"h>enum\",{\"1\":{\"459\":1}}],[\"h>int\",{\"1\":{\"416\":1}}],[\"h>\",{\"1\":{\"416\":3,\"442\":1,\"459\":1}}],[\"hv\",{\"1\":{\"376\":2}}],[\"h\",{\"1\":{\"376\":7,\"386\":1,\"387\":5}}],[\"hour++\",{\"1\":{\"362\":1}}],[\"hour\",{\"1\":{\"362\":16,\"366\":1}}],[\"home\",{\"1\":{\"35\":4}}],[\"href\",{\"1\":{\"251\":2}}],[\"href=\",{\"1\":{\"153\":6,\"251\":1,\"252\":1}}],[\"high\",{\"1\":{\"419\":1,\"430\":1,\"477\":1}}],[\"hiroshi\",{\"1\":{\"251\":1,\"252\":2}}],[\"history\",{\"1\":{\"211\":8,\"376\":8}}],[\"hyuki\",{\"1\":{\"251\":7,\"252\":4}}],[\"hana\",{\"1\":{\"376\":1,\"377\":7}}],[\"hanako\",{\"1\":{\"225\":4,\"226\":2,\"251\":2,\"394\":4,\"395\":2}}],[\"handle\",{\"1\":{\"448\":1}}],[\"handvalue\",{\"1\":{\"376\":22}}],[\"hand\",{\"1\":{\"376\":28}}],[\"happened\",{\"1\":{\"305\":1,\"306\":2}}],[\"halved\",{\"1\":{\"305\":2,\"306\":2}}],[\"have\",{\"1\":{\"294\":2}}],[\"hash\",{\"1\":{\"440\":1,\"443\":10}}],[\"hashmap\",{\"1\":{\"269\":1}}],[\"has\",{\"1\":{\"294\":1,\"501\":1,\"502\":1}}],[\"hasnext\",{\"1\":{\"286\":3,\"287\":1}}],[\"hasmoretokens\",{\"1\":{\"279\":2}}],[\"harmony\",{\"1\":{\"64\":1}}],[\"h1><p>从早上到下午<\",{\"1\":{\"194\":1}}],[\"h1>\",{\"1\":{\"153\":1,\"251\":1,\"252\":1}}],[\"h1>`\",{\"1\":{\"153\":1,\"193\":1}}],[\"hex\",{\"1\":{\"444\":2}}],[\"here\",{\"1\":{\"440\":1,\"441\":1}}],[\"heap\",{\"1\":{\"419\":2}}],[\"heavyjob\",{\"1\":{\"338\":3}}],[\"head><body>\",{\"1\":{\"251\":1,\"252\":1}}],[\"head><body><h1>问候<\",{\"1\":{\"194\":1}}],[\"head><body>`\",{\"1\":{\"193\":1}}],[\"head>\",{\"1\":{\"153\":1}}],[\"head>`\",{\"1\":{\"153\":1}}],[\"header\",{\"1\":{\"30\":2}}],[\"helloworld\",{\"1\":{\"406\":1}}],[\"hello\",{\"1\":{\"114\":5,\"166\":2,\"167\":4,\"182\":3,\"232\":2,\"233\":3,\"331\":3,\"332\":3,\"386\":1,\"433\":1,\"515\":2}}],[\"html<html><head><title>welcome\",{\"1\":{\"252\":1}}],[\"htmlwriter\",{\"1\":{\"251\":5}}],[\"html`\",{\"1\":{\"193\":1}}],[\"htmlbuilder\",{\"1\":{\"193\":9,\"199\":2}}],[\"html>が作成されました\",{\"1\":{\"194\":1}}],[\"html>\",{\"1\":{\"153\":1,\"193\":1,\"251\":1,\"252\":1}}],[\"html>`\",{\"1\":{\"153\":1}}],[\"html2text\",{\"1\":{\"126\":1}}],[\"html\",{\"0\":{\"126\":1},\"1\":{\"30\":3,\"31\":2,\"36\":5,\"154\":1,\"193\":1,\"194\":1,\"225\":1,\"226\":1,\"251\":1,\"252\":1,\"394\":1,\"395\":1}}],[\"http\",{\"0\":{\"345\":1},\"1\":{\"30\":1,\"32\":3,\"153\":11,\"345\":3}}],[\"https\",{\"0\":{\"38\":1},\"1\":{\"22\":14,\"26\":1,\"36\":2,\"45\":1,\"46\":1,\"48\":1,\"51\":3,\"67\":1,\"111\":1,\"115\":1,\"118\":1,\"119\":2,\"126\":2,\"414\":1,\"416\":1,\"417\":1,\"434\":1,\"435\":1,\"449\":1,\"453\":1,\"463\":1,\"470\":1,\"474\":1,\"481\":1,\"485\":1,\"491\":1,\"495\":1,\"515\":1,\"519\":1}}],[\"hub的目标是\",{\"1\":{\"18\":1}}],[\"hub\",{\"1\":{\"18\":1}}],[\"修改一个地方会对多个地方产生影响\",{\"1\":{\"267\":1}}],[\"修改的工作量就会越大\",{\"1\":{\"157\":1}}],[\"修改等操作\",{\"1\":{\"51\":1}}],[\"修改配置\",{\"0\":{\"36\":1}}],[\"修改\",{\"1\":{\"22\":1}}],[\"国内镜像\",{\"1\":{\"22\":1}}],[\"ccompiler\",{\"0\":{\"528\":1}}],[\"cycle\",{\"1\":{\"420\":1}}],[\"cpu\",{\"1\":{\"418\":2,\"420\":1,\"421\":2}}],[\"cpp\",{\"1\":{\"411\":1}}],[\"c4\",{\"1\":{\"409\":4,\"444\":1}}],[\"currently\",{\"1\":{\"445\":1}}],[\"currentdir\",{\"1\":{\"394\":7}}],[\"currenthandvalue\",{\"1\":{\"376\":10}}],[\"current\",{\"1\":{\"280\":5,\"305\":1,\"306\":3,\"416\":1,\"443\":13,\"448\":6,\"467\":6,\"468\":3,\"476\":2,\"478\":11,\"479\":11,\"480\":11,\"500\":1}}],[\"currenttoken\",{\"1\":{\"279\":8}}],[\"ctx\",{\"1\":{\"279\":1}}],[\"cmd\",{\"1\":{\"211\":2}}],[\"creating\",{\"1\":{\"193\":2,\"194\":2,\"294\":1}}],[\"created\",{\"1\":{\"353\":1,\"354\":1,\"357\":1}}],[\"createclone\",{\"1\":{\"331\":4}}],[\"creatememento\",{\"1\":{\"305\":3}}],[\"createproduct\",{\"1\":{\"258\":3}}],[\"createpicture\",{\"1\":{\"157\":1}}],[\"createpage\",{\"1\":{\"153\":3}}],[\"createtray\",{\"1\":{\"153\":5}}],[\"createlink\",{\"1\":{\"153\":8}}],[\"create\",{\"1\":{\"52\":1,\"258\":4,\"294\":1,\"331\":6}}],[\"c\",{\"0\":{\"406\":1,\"414\":1,\"435\":1,\"453\":1,\"463\":1,\"474\":1,\"485\":1,\"495\":1,\"519\":1},\"1\":{\"124\":1,\"298\":4,\"406\":15,\"409\":4,\"414\":16,\"416\":4,\"417\":15,\"422\":1,\"426\":2,\"431\":1,\"432\":1,\"433\":3,\"434\":2,\"435\":12,\"439\":1,\"440\":1,\"442\":1,\"443\":1,\"446\":1,\"449\":1,\"453\":12,\"459\":2,\"463\":13,\"470\":1,\"474\":12,\"480\":2,\"481\":1,\"485\":12,\"486\":1,\"487\":1,\"488\":1,\"491\":1,\"495\":11,\"496\":2,\"498\":1,\"500\":1,\"510\":1,\"512\":1,\"514\":1,\"515\":5,\"519\":13},\"2\":{\"413\":1,\"452\":1,\"462\":1,\"473\":1,\"484\":1,\"494\":1,\"518\":1,\"526\":1}}],[\"cast\",{\"1\":{\"501\":3}}],[\"category\",{\"1\":{\"417\":1}}],[\"catchaw\",{\"1\":{\"294\":1,\"295\":3}}],[\"catch\",{\"1\":{\"153\":1,\"279\":1,\"331\":2,\"338\":1}}],[\"caller\",{\"1\":{\"426\":2}}],[\"callee\",{\"1\":{\"426\":4}}],[\"calling\",{\"1\":{\"419\":1}}],[\"call\",{\"1\":{\"363\":48,\"421\":1,\"426\":10,\"427\":2,\"429\":2,\"490\":1,\"500\":6,\"515\":1}}],[\"callsecuritycenter\",{\"1\":{\"362\":6}}],[\"caretaker\",{\"0\":{\"311\":1},\"1\":{\"308\":1,\"311\":4}}],[\"card3\",{\"1\":{\"258\":2}}],[\"card2\",{\"1\":{\"258\":2}}],[\"card1\",{\"1\":{\"258\":2}}],[\"car\",{\"1\":{\"147\":7}}],[\"caption\",{\"1\":{\"153\":20,\"251\":2}}],[\"cap\",{\"1\":{\"108\":2}}],[\"capacitorhttp\",{\"1\":{\"108\":1}}],[\"capacitorconfig\",{\"1\":{\"108\":1}}],[\"capacitor\",{\"1\":{\"107\":1}}],[\"canvas\",{\"1\":{\"211\":3}}],[\"canv\",{\"1\":{\"211\":2}}],[\"cannot\",{\"1\":{\"204\":1,\"205\":3}}],[\"can\",{\"1\":{\"21\":1,\"294\":1,\"500\":1}}],[\"cho\",{\"1\":{\"376\":2}}],[\"checked\",{\"1\":{\"356\":1}}],[\"cheat\",{\"1\":{\"18\":2}}],[\"ch\",{\"1\":{\"232\":4,\"386\":5}}],[\"china\",{\"1\":{\"182\":1,\"184\":1}}],[\"chatappmediator\",{\"1\":{\"294\":6,\"297\":2}}],[\"character\",{\"1\":{\"416\":1,\"422\":2,\"445\":3,\"447\":1,\"498\":1}}],[\"chardisplay\",{\"1\":{\"386\":5}}],[\"char\",{\"1\":{\"264\":2,\"416\":1,\"419\":1,\"422\":2,\"432\":6,\"433\":1,\"439\":1,\"440\":1,\"443\":3,\"448\":4,\"459\":3,\"467\":5,\"477\":1,\"479\":3,\"480\":2,\"498\":3,\"499\":7,\"500\":1,\"501\":3,\"502\":1,\"507\":2,\"508\":1,\"509\":1,\"512\":1,\"513\":5,\"514\":2}}],[\"charname\",{\"1\":{\"264\":10}}],[\"charlie使用了id卡\",{\"1\":{\"259\":1}}],[\"charlie\",{\"1\":{\"204\":3,\"205\":1,\"258\":1}}],[\"charset\",{\"1\":{\"65\":1}}],[\"chain\",{\"1\":{\"202\":1,\"203\":1,\"204\":1}}],[\"chainofresponsibility\",{\"0\":{\"202\":1},\"1\":{\"205\":1}}],[\"changestate\",{\"1\":{\"362\":4,\"367\":1}}],[\"change\",{\"1\":{\"112\":2,\"113\":5,\"114\":16}}],[\"csdn\",{\"1\":{\"51\":1,\"495\":1}}],[\"cn\",{\"1\":{\"45\":1,\"46\":2,\"111\":1,\"115\":1,\"118\":1}}],[\"cer\",{\"1\":{\"35\":2,\"36\":3}}],[\"certificates\",{\"1\":{\"39\":1}}],[\"certificate\",{\"1\":{\"36\":6}}],[\"cert\",{\"1\":{\"35\":3}}],[\"central\",{\"1\":{\"22\":2}}],[\"colon\",{\"1\":{\"510\":1}}],[\"colleaguecheckbox\",{\"1\":{\"299\":1}}],[\"colleaguetextfield\",{\"1\":{\"299\":1}}],[\"colleaguebutton\",{\"1\":{\"299\":1}}],[\"collaborators\",{\"1\":{\"294\":1}}],[\"could\",{\"1\":{\"416\":2,\"419\":3}}],[\"count\",{\"1\":{\"232\":2,\"317\":2}}],[\"countdisplay\",{\"0\":{\"179\":1},\"1\":{\"178\":2,\"179\":1,\"182\":4,\"187\":3}}],[\"code\",{\"1\":{\"67\":1,\"119\":2,\"153\":1,\"167\":1,\"184\":1,\"194\":1,\"205\":1,\"212\":1,\"226\":1,\"233\":1,\"252\":1,\"259\":1,\"265\":1,\"280\":1,\"287\":1,\"294\":1,\"295\":1,\"318\":1,\"332\":1,\"339\":1,\"354\":1,\"363\":1,\"387\":1,\"395\":1,\"416\":1,\"437\":1,\"480\":1,\"487\":1,\"489\":1,\"498\":2,\"499\":1,\"500\":2,\"504\":1,\"505\":1}}],[\"copy\",{\"1\":{\"31\":2,\"108\":1}}],[\"convenienceint\",{\"1\":{\"467\":1}}],[\"conditional\",{\"1\":{\"510\":1}}],[\"condition\",{\"1\":{\"487\":1}}],[\"cond\",{\"1\":{\"439\":1,\"447\":1,\"508\":1,\"510\":3}}],[\"concretevisitor\",{\"0\":{\"400\":1},\"1\":{\"397\":1,\"398\":3,\"400\":2,\"401\":1}}],[\"concreteelement\",{\"0\":{\"401\":1},\"1\":{\"397\":1,\"400\":1,\"401\":1}}],[\"concretestrategy\",{\"1\":{\"379\":1}}],[\"concretestate\",{\"1\":{\"365\":1,\"367\":9,\"369\":2}}],[\"concreteobserver\",{\"1\":{\"321\":1}}],[\"concretemediator\",{\"1\":{\"299\":2}}],[\"concretecolleague\",{\"1\":{\"299\":3}}],[\"concreteclass\",{\"1\":{\"175\":1}}],[\"concrete\",{\"1\":{\"294\":1}}],[\"concreteiterator\",{\"1\":{\"288\":1}}],[\"concreteimplementor\",{\"1\":{\"186\":1,\"187\":1}}],[\"concretedecorator\",{\"1\":{\"238\":1}}],[\"console\",{\"1\":{\"144\":1,\"147\":4,\"153\":2,\"166\":2,\"183\":2,\"193\":4,\"204\":2,\"211\":1,\"222\":1,\"224\":1,\"225\":2,\"232\":1,\"251\":2,\"258\":1,\"264\":1,\"279\":2,\"286\":1,\"294\":3,\"305\":10,\"317\":2,\"331\":9,\"338\":9,\"353\":2,\"357\":1,\"362\":4,\"376\":6,\"386\":5,\"394\":4}}],[\"construct\",{\"1\":{\"193\":3}}],[\"constructor\",{\"1\":{\"144\":1,\"147\":1,\"153\":6,\"166\":3,\"179\":1,\"180\":1,\"183\":1,\"193\":1,\"204\":5,\"211\":2,\"222\":1,\"224\":1,\"232\":4,\"251\":3,\"258\":1,\"264\":3,\"279\":2,\"286\":3,\"294\":1,\"305\":2,\"317\":1,\"331\":2,\"338\":2,\"353\":1,\"357\":1,\"362\":2,\"376\":4,\"386\":2,\"394\":2}}],[\"const\",{\"1\":{\"58\":9,\"108\":1,\"144\":2,\"147\":2,\"166\":2,\"182\":3,\"193\":6,\"211\":3,\"258\":5,\"279\":1,\"286\":4,\"294\":7,\"305\":4,\"317\":4,\"331\":3,\"353\":2,\"362\":1,\"376\":5,\"386\":3,\"394\":2}}],[\"constexpr\",{\"1\":{\"56\":1,\"57\":1}}],[\"controller\",{\"0\":{\"325\":1},\"1\":{\"325\":1}}],[\"contents\",{\"1\":{\"414\":1,\"417\":1,\"435\":1,\"453\":1,\"463\":1,\"474\":1,\"485\":1,\"495\":1,\"519\":1}}],[\"content\",{\"1\":{\"64\":1,\"153\":4}}],[\"context\",{\"1\":{\"31\":1,\"279\":43,\"362\":43,\"367\":3,\"370\":3}}],[\"containers\",{\"1\":{\"47\":1}}],[\"container\",{\"0\":{\"43\":1},\"1\":{\"44\":4}}],[\"connections\",{\"1\":{\"30\":1}}],[\"config\",{\"1\":{\"108\":1}}],[\"configuration\",{\"1\":{\"52\":1}}],[\"conf\",{\"1\":{\"28\":4,\"30\":5,\"31\":6,\"36\":2}}],[\"comma\",{\"1\":{\"467\":1}}],[\"commandnode\",{\"1\":{\"279\":8}}],[\"commandlistnode\",{\"1\":{\"279\":17}}],[\"command>\",{\"1\":{\"279\":12}}],[\"commands\",{\"1\":{\"211\":5}}],[\"command\",{\"0\":{\"209\":1},\"1\":{\"206\":1,\"210\":2,\"211\":14,\"212\":1,\"215\":2,\"227\":1,\"312\":1,\"333\":1}}],[\"comments\",{\"1\":{\"446\":2}}],[\"compiler\",{\"1\":{\"411\":1}}],[\"complete\",{\"1\":{\"113\":1,\"114\":3}}],[\"composite\",{\"0\":{\"219\":1},\"1\":{\"158\":1,\"195\":1,\"206\":1,\"216\":1,\"220\":2,\"225\":1,\"226\":2,\"235\":2,\"259\":1,\"271\":1,\"289\":1,\"333\":1,\"394\":1,\"395\":1,\"403\":1}}],[\"compose\",{\"1\":{\"27\":1,\"28\":1,\"31\":1,\"32\":1,\"35\":1,\"37\":1}}],[\"component\",{\"1\":{\"21\":1,\"294\":1}}],[\"com\",{\"1\":{\"22\":13,\"48\":1,\"51\":1,\"67\":1,\"119\":2,\"126\":2,\"153\":11,\"251\":5,\"252\":2,\"416\":1,\"434\":1,\"449\":1,\"470\":1,\"481\":1,\"491\":1,\"515\":1}}],[\"cd\",{\"0\":{\"23\":1},\"1\":{\"35\":2,\"44\":1},\"2\":{\"24\":1,\"25\":1}}],[\"cinderella\",{\"1\":{\"286\":1,\"287\":1}}],[\"ci\",{\"0\":{\"23\":1},\"1\":{\"44\":1},\"2\":{\"24\":1,\"25\":1}}],[\"clean\",{\"1\":{\"500\":1}}],[\"clear\",{\"1\":{\"211\":1}}],[\"clos\",{\"1\":{\"421\":1,\"432\":1}}],[\"close\",{\"1\":{\"178\":1,\"179\":1,\"180\":2,\"193\":4,\"251\":2,\"386\":4,\"416\":1,\"419\":1,\"432\":2,\"448\":1}}],[\"clone\",{\"1\":{\"416\":2,\"434\":2,\"449\":2,\"470\":2,\"481\":2,\"491\":2,\"515\":2}}],[\"clockstring\",{\"1\":{\"362\":4}}],[\"cloud\",{\"1\":{\"22\":1}}],[\"classes\",{\"1\":{\"439\":1}}],[\"class\",{\"1\":{\"58\":1,\"140\":3,\"144\":2,\"147\":4,\"153\":9,\"166\":4,\"179\":1,\"180\":1,\"181\":1,\"183\":1,\"193\":4,\"204\":6,\"211\":3,\"222\":1,\"223\":1,\"224\":1,\"232\":5,\"251\":3,\"258\":3,\"264\":3,\"279\":8,\"286\":3,\"294\":2,\"305\":2,\"317\":4,\"331\":3,\"338\":2,\"353\":1,\"357\":1,\"362\":3,\"376\":4,\"386\":3,\"394\":5,\"443\":3,\"448\":1,\"467\":3,\"468\":1,\"476\":1,\"478\":2,\"479\":3,\"480\":3,\"500\":5}}],[\"client\",{\"1\":{\"30\":2,\"294\":1}}],[\"click\",{\"1\":{\"21\":2}}],[\"i++\",{\"1\":{\"179\":1,\"183\":1,\"211\":1,\"232\":2,\"305\":1,\"317\":2,\"338\":1,\"376\":2,\"386\":2,\"394\":1,\"433\":8,\"448\":2,\"468\":1}}],[\"iworker\",{\"1\":{\"144\":4}}],[\"immediate\",{\"1\":{\"422\":1}}],[\"imm\",{\"1\":{\"421\":1,\"422\":3,\"433\":2,\"498\":3,\"499\":1,\"500\":4,\"503\":1,\"504\":1,\"505\":1,\"506\":2,\"507\":1,\"509\":2,\"512\":2,\"513\":3,\"514\":1}}],[\"implemented\",{\"1\":{\"394\":2}}],[\"implementor\",{\"1\":{\"186\":1}}],[\"implementation\",{\"1\":{\"178\":1}}],[\"implements\",{\"1\":{\"144\":1,\"166\":1,\"211\":3,\"258\":1,\"286\":2,\"294\":2,\"317\":2,\"331\":2,\"338\":2,\"362\":3,\"376\":2,\"394\":1}}],[\"impl\",{\"1\":{\"178\":3,\"179\":2,\"180\":7}}],[\"import\",{\"1\":{\"52\":4,\"112\":1,\"113\":1,\"114\":5,\"153\":15,\"166\":6,\"179\":2,\"180\":1,\"182\":3,\"183\":1,\"193\":7,\"204\":14,\"211\":8,\"222\":1,\"224\":1,\"225\":3,\"232\":9,\"251\":3,\"258\":6,\"264\":5,\"279\":19,\"286\":9,\"305\":2,\"317\":12,\"331\":5,\"338\":5,\"353\":1,\"362\":12,\"376\":10,\"386\":4,\"394\":15}}],[\"img\",{\"1\":{\"113\":1}}],[\"if\",{\"0\":{\"487\":1},\"1\":{\"112\":1,\"204\":5,\"232\":3,\"264\":1,\"279\":7,\"294\":2,\"305\":6,\"338\":2,\"353\":1,\"357\":2,\"362\":3,\"376\":8,\"394\":2,\"416\":3,\"419\":3,\"422\":5,\"423\":1,\"424\":1,\"425\":5,\"426\":2,\"427\":1,\"428\":1,\"429\":1,\"430\":1,\"431\":16,\"432\":8,\"439\":1,\"441\":1,\"442\":1,\"443\":3,\"444\":3,\"445\":6,\"446\":2,\"447\":24,\"448\":2,\"459\":7,\"464\":3,\"467\":10,\"468\":4,\"469\":1,\"475\":3,\"476\":1,\"478\":1,\"479\":5,\"480\":3,\"485\":1,\"486\":1,\"487\":8,\"488\":2,\"489\":2,\"490\":2,\"498\":2,\"499\":3,\"500\":9,\"501\":2,\"502\":2,\"503\":2,\"504\":1,\"505\":1,\"506\":3,\"507\":3,\"508\":1,\"509\":2,\"510\":4,\"511\":2,\"512\":3,\"514\":3,\"515\":1}}],[\"i\",{\"1\":{\"112\":2,\"114\":1,\"179\":2,\"183\":2,\"204\":4,\"211\":4,\"232\":5,\"305\":3,\"317\":4,\"338\":2,\"376\":5,\"386\":4,\"394\":3,\"416\":4,\"419\":2,\"426\":2,\"427\":1,\"433\":1,\"448\":4,\"467\":1,\"468\":3}}],[\"iterator\",{\"1\":{\"259\":1,\"286\":14,\"287\":4,\"394\":4,\"402\":1,\"403\":1}}],[\"items\",{\"1\":{\"193\":5}}],[\"item\",{\"1\":{\"153\":21,\"193\":4}}],[\"it\",{\"1\":{\"112\":4,\"113\":5,\"114\":20,\"286\":3,\"294\":1,\"394\":3,\"442\":1,\"445\":1,\"467\":1,\"500\":1}}],[\"idmain\",{\"1\":{\"448\":2}}],[\"idsize\",{\"1\":{\"443\":2,\"478\":1}}],[\"identifierenum\",{\"1\":{\"443\":1}}],[\"identifier\",{\"1\":{\"443\":5,\"467\":3,\"468\":1,\"476\":1,\"480\":1}}],[\"idcardfactory\",{\"1\":{\"258\":5}}],[\"idcard\",{\"1\":{\"258\":7}}],[\"id\",{\"1\":{\"111\":1,\"115\":1,\"353\":1,\"354\":1,\"357\":1,\"439\":1,\"443\":15,\"448\":6,\"464\":8,\"467\":17,\"468\":5,\"475\":5,\"476\":2,\"478\":11,\"479\":14,\"480\":12,\"500\":18,\"508\":1}}],[\"isweakerthan\",{\"1\":{\"376\":1}}],[\"isstrongerthan\",{\"1\":{\"376\":3}}],[\"issue\",{\"1\":{\"34\":2}}],[\"is\",{\"1\":{\"52\":1,\"64\":1,\"147\":2,\"204\":1,\"205\":13,\"279\":3,\"294\":1,\"416\":1,\"425\":2,\"445\":2,\"499\":1,\"500\":3,\"512\":2}}],[\"isn\",{\"0\":{\"21\":1}}],[\"initializer\",{\"1\":{\"468\":1}}],[\"invalid\",{\"1\":{\"467\":1,\"480\":1}}],[\"information\",{\"1\":{\"467\":1}}],[\"increment\",{\"1\":{\"507\":1}}],[\"increased\",{\"1\":{\"305\":2}}],[\"inc\",{\"1\":{\"439\":1,\"447\":1,\"501\":2,\"502\":2,\"503\":1,\"504\":1,\"505\":1,\"506\":2,\"507\":3,\"508\":1,\"513\":3}}],[\"include\",{\"1\":{\"30\":2,\"294\":1,\"416\":4,\"442\":1,\"459\":2}}],[\"independent\",{\"1\":{\"294\":1}}],[\"index++\",{\"1\":{\"279\":1,\"286\":1}}],[\"index\",{\"1\":{\"279\":3,\"286\":6,\"479\":5,\"480\":3,\"500\":1}}],[\"indent\",{\"1\":{\"65\":1}}],[\"inheritance\",{\"1\":{\"166\":4}}],[\"inject\",{\"1\":{\"124\":2}}],[\"instruction\",{\"1\":{\"432\":1}}],[\"instructionsenum\",{\"1\":{\"421\":1}}],[\"instanceof\",{\"1\":{\"394\":2}}],[\"instance\",{\"1\":{\"294\":1,\"353\":5,\"354\":1,\"357\":6}}],[\"install\",{\"1\":{\"35\":1}}],[\"insert\",{\"1\":{\"65\":1}}],[\"into\",{\"1\":{\"445\":1}}],[\"integer\",{\"1\":{\"422\":2}}],[\"intel\",{\"1\":{\"422\":1}}],[\"interperter\",{\"1\":{\"280\":1}}],[\"interpreter\",{\"0\":{\"277\":1},\"1\":{\"278\":1,\"403\":1,\"409\":1,\"414\":1,\"416\":1,\"417\":1,\"434\":1,\"435\":1,\"449\":1,\"453\":1,\"463\":1,\"470\":1,\"474\":1,\"481\":1,\"485\":1,\"491\":1,\"515\":1,\"519\":1}}],[\"interface\",{\"1\":{\"144\":1,\"166\":1,\"211\":2,\"258\":1,\"286\":2,\"294\":2,\"308\":2,\"317\":1,\"331\":1,\"338\":1,\"362\":2,\"376\":1,\"394\":1}}],[\"intrinsic\",{\"0\":{\"268\":1},\"1\":{\"268\":4}}],[\"int\",{\"1\":{\"56\":2,\"57\":11,\"416\":6,\"419\":3,\"420\":3,\"422\":3,\"424\":1,\"425\":2,\"426\":9,\"427\":1,\"429\":2,\"430\":1,\"432\":2,\"433\":3,\"439\":1,\"440\":1,\"443\":13,\"445\":1,\"448\":4,\"459\":20,\"467\":14,\"468\":2,\"469\":1,\"476\":1,\"477\":4,\"479\":7,\"480\":5,\"487\":2,\"488\":2,\"498\":4,\"499\":8,\"500\":1,\"501\":2,\"504\":1,\"505\":1,\"506\":2,\"507\":1,\"508\":1,\"510\":2,\"511\":4,\"512\":3,\"513\":3,\"514\":1,\"515\":5}}],[\"in\",{\"0\":{\"21\":1},\"1\":{\"21\":2,\"112\":4,\"114\":3,\"286\":1,\"287\":1,\"422\":4,\"439\":1,\"500\":2,\"509\":1,\"510\":1}}],[\"ionic打包后的相对路径不正确\",{\"1\":{\"109\":1}}],[\"ionic\",{\"1\":{\"107\":1,\"108\":4}}],[\"io简介\",{\"0\":{\"44\":1}}],[\"io\",{\"1\":{\"18\":1,\"22\":2,\"44\":1,\"51\":1,\"126\":1}}],[\"5501\",{\"1\":{\"495\":1}}],[\"55718\",{\"1\":{\"119\":1}}],[\"50\",{\"1\":{\"317\":1}}],[\"500\",{\"1\":{\"204\":1,\"225\":1,\"226\":1,\"394\":1,\"395\":1}}],[\"5版本开始引入了新的关键字\",{\"1\":{\"114\":1}}],[\"587\",{\"1\":{\"52\":1}}],[\"5\",{\"0\":{\"21\":1,\"463\":1},\"1\":{\"21\":1,\"182\":1,\"212\":2,\"264\":1,\"298\":1,\"305\":1,\"306\":1,\"338\":2,\"386\":1,\"406\":1,\"414\":1,\"417\":2,\"422\":1,\"426\":2,\"432\":1,\"435\":3,\"436\":2,\"453\":2,\"463\":2,\"474\":1,\"485\":1,\"491\":1,\"495\":4,\"496\":7,\"519\":2}}],[\"queue\",{\"1\":{\"215\":1}}],[\"questions\",{\"0\":{\"20\":1}}],[\"quit\",{\"1\":{\"52\":1}}],[\"qq\",{\"1\":{\"51\":1}}],[\"qt\",{\"0\":{\"19\":1,\"20\":1,\"21\":2},\"1\":{\"21\":2}}],[\"tk\",{\"1\":{\"459\":4,\"469\":3}}],[\"tutor\",{\"1\":{\"433\":2,\"515\":5}}],[\"turndown\",{\"1\":{\"126\":1}}],[\"tmp\",{\"1\":{\"225\":1,\"226\":2,\"394\":1,\"395\":2,\"422\":1,\"432\":7,\"467\":2,\"500\":4,\"501\":4,\"507\":2,\"509\":2,\"512\":1,\"513\":1,\"514\":3,\"515\":3}}],[\"tmpdir\",{\"1\":{\"225\":2,\"394\":2}}],[\"ts\",{\"0\":{\"179\":1,\"180\":1,\"181\":1,\"182\":1,\"183\":1,\"222\":1,\"223\":1,\"224\":1,\"225\":1},\"1\":{\"153\":12,\"166\":6,\"167\":2,\"184\":2,\"193\":5,\"194\":2,\"204\":7,\"205\":2,\"211\":6,\"212\":2,\"226\":2,\"232\":6,\"233\":2,\"251\":4,\"252\":2,\"258\":5,\"259\":2,\"264\":5,\"265\":2,\"279\":9,\"280\":2,\"286\":6,\"287\":2,\"295\":2,\"305\":3,\"317\":6,\"318\":2,\"331\":5,\"332\":2,\"338\":4,\"339\":2,\"353\":2,\"354\":2,\"362\":6,\"363\":2,\"376\":6,\"386\":4,\"387\":2,\"394\":7,\"395\":2}}],[\"typora\",{\"1\":{\"124\":8}}],[\"typora激活教程\",{\"0\":{\"124\":1}}],[\"typedef\",{\"1\":{\"58\":1}}],[\"type\",{\"1\":{\"30\":1,\"443\":4,\"448\":2,\"464\":4,\"467\":16,\"468\":1,\"475\":4,\"478\":2,\"479\":11,\"480\":8,\"498\":2,\"499\":7,\"500\":7,\"501\":4,\"502\":5,\"503\":2,\"504\":1,\"505\":1,\"506\":2,\"507\":2,\"509\":3,\"511\":2,\"512\":4,\"513\":5,\"514\":3}}],[\"typescript\",{\"0\":{\"285\":1},\"1\":{\"285\":1,\"286\":1,\"317\":1},\"2\":{\"150\":1,\"160\":1,\"170\":1,\"190\":1,\"201\":1,\"208\":1,\"218\":1,\"229\":1,\"245\":1,\"248\":1,\"255\":1,\"261\":1,\"273\":1,\"276\":1,\"282\":1,\"291\":1,\"302\":1,\"314\":1,\"328\":1,\"335\":1,\"349\":1,\"359\":1,\"373\":1,\"383\":1,\"391\":1,\"405\":1}}],[\"types\",{\"1\":{\"30\":1,\"448\":1,\"467\":1}}],[\"tail\",{\"1\":{\"459\":8}}],[\"tail><term\",{\"1\":{\"458\":1}}],[\"tail><expr\",{\"1\":{\"458\":1}}],[\"tail>\",{\"1\":{\"458\":6}}],[\"tag\",{\"1\":{\"417\":1}}],[\"taro\",{\"1\":{\"376\":1,\"377\":1}}],[\"target=change\",{\"1\":{\"112\":2,\"114\":4}}],[\"takahashi\",{\"1\":{\"251\":1}}],[\"table\",{\"1\":{\"414\":1,\"417\":1,\"435\":1,\"443\":2,\"448\":2,\"453\":1,\"463\":1,\"474\":1,\"485\":1,\"495\":1,\"519\":1}}],[\"tab\",{\"1\":{\"65\":1}}],[\"title><\",{\"1\":{\"153\":2,\"193\":1,\"194\":1,\"251\":1,\"252\":1}}],[\"title\",{\"1\":{\"153\":9,\"193\":7,\"251\":5,\"417\":1}}],[\"times\",{\"1\":{\"179\":2}}],[\"time\",{\"1\":{\"114\":1}}],[\"timeout\",{\"1\":{\"30\":2}}],[\"tips\",{\"0\":{\"108\":1}}],[\"treated\",{\"1\":{\"467\":1}}],[\"trouble\",{\"1\":{\"204\":38,\"205\":16}}],[\"track\",{\"1\":{\"448\":1}}],[\"traysearch\",{\"1\":{\"153\":4}}],[\"trayyahoo\",{\"1\":{\"153\":4}}],[\"traynews\",{\"1\":{\"153\":4}}],[\"tray\",{\"1\":{\"153\":11,\"156\":1}}],[\"trailing\",{\"1\":{\"65\":1}}],[\"trim\",{\"1\":{\"65\":1}}],[\"true\",{\"1\":{\"65\":3,\"108\":2,\"204\":3,\"279\":1,\"353\":1,\"354\":1,\"376\":1,\"487\":1}}],[\"try\",{\"1\":{\"30\":3,\"36\":5,\"52\":1,\"112\":1,\"153\":1,\"279\":1,\"331\":2,\"338\":1}}],[\"txt\",{\"0\":{\"61\":1},\"1\":{\"61\":2}}],[\"that\",{\"1\":{\"294\":1,\"467\":1}}],[\"three\",{\"1\":{\"444\":1}}],[\"thread\",{\"1\":{\"112\":2,\"114\":4}}],[\"threads\",{\"1\":{\"112\":3,\"114\":3}}],[\"threading\",{\"1\":{\"112\":4,\"114\":5}}],[\"throw\",{\"1\":{\"223\":1,\"279\":4,\"394\":2}}],[\"this\",{\"1\":{\"52\":1,\"64\":1,\"144\":2,\"147\":3,\"153\":18,\"166\":8,\"179\":3,\"180\":7,\"183\":6,\"193\":25,\"204\":17,\"211\":11,\"222\":7,\"223\":3,\"224\":3,\"232\":20,\"251\":6,\"258\":7,\"264\":9,\"279\":41,\"286\":16,\"294\":7,\"305\":18,\"317\":9,\"331\":11,\"338\":16,\"353\":3,\"357\":5,\"362\":12,\"366\":1,\"370\":8,\"376\":46,\"386\":11,\"394\":18,\"467\":1,\"478\":1,\"500\":1}}],[\"there\",{\"1\":{\"467\":1,\"500\":1}}],[\"them\",{\"1\":{\"294\":1}}],[\"the\",{\"0\":{\"21\":1},\"1\":{\"21\":6,\"52\":2,\"64\":2,\"286\":1,\"287\":1,\"294\":12,\"295\":3,\"416\":1,\"423\":2,\"424\":1,\"445\":2,\"447\":1,\"448\":1,\"467\":6,\"476\":1,\"479\":1,\"480\":4,\"498\":3,\"500\":3,\"502\":1,\"503\":2,\"507\":1,\"509\":1,\"512\":2}}],[\"tz=asia\",{\"1\":{\"31\":1}}],[\"tcp\",{\"1\":{\"30\":1}}],[\"term\",{\"1\":{\"459\":8}}],[\"tex\",{\"1\":{\"225\":1,\"226\":1,\"394\":1,\"395\":1}}],[\"textbuilder\",{\"1\":{\"193\":9,\"199\":1}}],[\"text\",{\"1\":{\"3\":1,\"7\":1,\"52\":2,\"120\":1,\"193\":1,\"194\":1,\"279\":11,\"416\":1,\"419\":11,\"433\":9,\"467\":1,\"476\":2,\"487\":2,\"488\":2,\"503\":3,\"507\":4,\"509\":3,\"510\":2,\"511\":2}}],[\"template\",{\"0\":{\"384\":1,\"385\":1},\"1\":{\"175\":1,\"188\":1,\"195\":1,\"259\":1,\"384\":1,\"387\":1}}],[\"template<typename\",{\"1\":{\"58\":1}}],[\"tensorflow\",{\"0\":{\"66\":1},\"1\":{\"66\":6}}],[\"tencent\",{\"1\":{\"22\":1}}],[\"test\",{\"1\":{\"52\":4,\"114\":2}}],[\"t\",{\"0\":{\"21\":1},\"1\":{\"58\":5,\"112\":4,\"114\":4,\"445\":1,\"459\":3}}],[\"total\",{\"1\":{\"376\":1,\"377\":1}}],[\"tomato\",{\"1\":{\"294\":1,\"295\":3}}],[\"tomura\",{\"1\":{\"225\":5,\"226\":3,\"251\":2,\"394\":5,\"395\":3}}],[\"tokenchar\",{\"1\":{\"416\":1}}],[\"tokens\",{\"1\":{\"279\":4,\"439\":1}}],[\"token\",{\"1\":{\"279\":3,\"411\":2,\"415\":1,\"416\":6,\"436\":3,\"437\":1,\"439\":1,\"440\":2,\"441\":2,\"442\":1,\"443\":16,\"444\":27,\"445\":14,\"446\":2,\"447\":45,\"448\":3,\"459\":20,\"466\":2,\"467\":12,\"468\":7,\"469\":2,\"476\":1,\"478\":1,\"479\":6,\"480\":9,\"487\":2,\"488\":1,\"489\":2,\"490\":3,\"498\":5,\"499\":4,\"500\":4,\"501\":6,\"502\":1,\"503\":1,\"504\":1,\"505\":1,\"506\":4,\"507\":4,\"508\":2,\"509\":1,\"510\":2,\"511\":2,\"512\":2,\"513\":2,\"514\":1}}],[\"tostring\",{\"1\":{\"204\":2,\"223\":1,\"279\":7,\"305\":2,\"362\":4,\"376\":6,\"394\":1}}],[\"todo\",{\"1\":{\"38\":1,\"49\":1,\"64\":1,\"67\":1,\"116\":1,\"411\":1}}],[\"tools\",{\"0\":{\"21\":1},\"1\":{\"21\":1}}],[\"to\",{\"0\":{\"20\":1},\"1\":{\"52\":5,\"251\":1,\"252\":2,\"294\":7,\"295\":3,\"305\":1,\"306\":1,\"416\":1,\"422\":5,\"424\":1,\"448\":2,\"498\":1,\"500\":2,\"507\":1}}],[\"ebnf\",{\"0\":{\"464\":1,\"475\":1},\"1\":{\"463\":2,\"464\":1,\"471\":3,\"474\":1,\"475\":1}}],[\"ebppop\",{\"1\":{\"429\":1}}],[\"ebpmov\",{\"1\":{\"427\":1}}],[\"ebp\",{\"1\":{\"426\":6,\"427\":1,\"429\":1}}],[\"escape\",{\"1\":{\"445\":2}}],[\"esp\",{\"1\":{\"426\":6,\"427\":2,\"428\":2,\"429\":1}}],[\"eax\",{\"1\":{\"426\":1}}],[\"each\",{\"1\":{\"294\":1}}],[\"eq\",{\"1\":{\"421\":1,\"431\":1,\"439\":2,\"447\":1,\"504\":1,\"508\":1}}],[\"eof\",{\"1\":{\"416\":1}}],[\"eval\",{\"1\":{\"416\":3,\"422\":2}}],[\"even\",{\"1\":{\"376\":4,\"377\":3}}],[\"event\",{\"1\":{\"113\":1,\"114\":3,\"294\":4}}],[\"events\",{\"1\":{\"30\":1,\"294\":1}}],[\"ey\",{\"1\":{\"294\":1,\"295\":3}}],[\"element\",{\"1\":{\"394\":5,\"397\":4,\"402\":1}}],[\"else\",{\"1\":{\"204\":3,\"232\":3,\"279\":4,\"305\":4,\"362\":1,\"376\":7,\"394\":1,\"422\":4,\"423\":1,\"424\":1,\"425\":1,\"426\":2,\"427\":1,\"428\":1,\"429\":1,\"430\":1,\"431\":16,\"432\":9,\"439\":1,\"442\":1,\"443\":1,\"444\":3,\"445\":2,\"446\":2,\"447\":23,\"448\":1,\"459\":5,\"464\":1,\"467\":2,\"469\":1,\"475\":1,\"476\":1,\"479\":1,\"486\":1,\"487\":7,\"488\":1,\"489\":1,\"490\":3,\"498\":1,\"499\":2,\"500\":7,\"501\":2,\"502\":2,\"503\":2,\"504\":1,\"505\":1,\"506\":3,\"507\":3,\"508\":1,\"509\":1,\"510\":2,\"511\":2,\"512\":2,\"514\":2}}],[\"elmo\",{\"1\":{\"204\":3,\"205\":4}}],[\"enter\",{\"1\":{\"427\":1}}],[\"ent\",{\"0\":{\"427\":1},\"1\":{\"417\":1,\"421\":1,\"426\":1,\"427\":2,\"480\":1}}],[\"entries\",{\"1\":{\"225\":2,\"226\":2,\"394\":2,\"395\":2}}],[\"entry\",{\"0\":{\"223\":1},\"1\":{\"220\":1,\"222\":12,\"223\":4,\"224\":3,\"225\":2,\"394\":34}}],[\"enum\",{\"0\":{\"468\":1},\"1\":{\"376\":1,\"439\":2,\"448\":1,\"463\":1,\"464\":2,\"465\":1,\"467\":9,\"468\":4,\"500\":2,\"508\":2}}],[\"en\",{\"1\":{\"294\":5}}],[\"engine\",{\"1\":{\"147\":15}}],[\"enhanced\",{\"1\":{\"119\":1}}],[\"enabled\",{\"1\":{\"108\":1}}],[\"enduml\",{\"1\":{\"258\":1}}],[\"end\",{\"1\":{\"65\":1,\"279\":15,\"280\":8,\"486\":1,\"498\":1}}],[\"environment\",{\"1\":{\"31\":1}}],[\"env\",{\"1\":{\"23\":2}}],[\"editorconfig文件\",{\"1\":{\"65\":1}}],[\"editorconfig\",{\"1\":{\"65\":1}}],[\"edu\",{\"1\":{\"45\":1,\"46\":2}}],[\"e\",{\"1\":{\"52\":2,\"279\":2,\"331\":4,\"338\":2}}],[\"etc\",{\"1\":{\"30\":2,\"31\":4,\"36\":6,\"46\":1}}],[\"error\",{\"1\":{\"28\":1,\"30\":10,\"36\":10,\"153\":2,\"223\":1,\"279\":4,\"331\":1,\"394\":2}}],[\"exists\",{\"1\":{\"467\":1,\"480\":1}}],[\"exist\",{\"1\":{\"467\":1}}],[\"existing\",{\"1\":{\"443\":1}}],[\"exit\",{\"1\":{\"421\":1,\"432\":3,\"433\":2,\"448\":2,\"459\":1,\"467\":2,\"468\":2,\"469\":1,\"479\":2,\"480\":2,\"500\":2,\"502\":1,\"503\":1,\"507\":1,\"509\":1,\"510\":1,\"514\":1,\"515\":2}}],[\"example\",{\"1\":{\"294\":1}}],[\"expession\",{\"1\":{\"509\":1}}],[\"expected\",{\"1\":{\"279\":1,\"459\":1,\"469\":1,\"514\":1}}],[\"expr\",{\"1\":{\"459\":8,\"467\":1,\"498\":2,\"499\":6,\"500\":4,\"501\":3,\"502\":5,\"503\":2,\"504\":1,\"505\":1,\"506\":2,\"507\":2,\"509\":4,\"510\":1,\"511\":2,\"512\":3,\"513\":5,\"514\":2}}],[\"expressionvoid\",{\"1\":{\"467\":1}}],[\"expression\",{\"1\":{\"416\":3,\"464\":5,\"468\":1,\"475\":4,\"481\":1,\"486\":3,\"487\":1,\"488\":1,\"489\":2,\"490\":1,\"491\":1,\"500\":1,\"501\":2,\"502\":1,\"503\":1,\"504\":1,\"505\":1,\"506\":2,\"507\":1,\"508\":1,\"509\":1,\"510\":2,\"511\":2,\"512\":2,\"514\":1,\"516\":1}}],[\"export\",{\"1\":{\"153\":9,\"166\":5,\"179\":1,\"180\":1,\"181\":1,\"183\":1,\"193\":4,\"204\":6,\"211\":5,\"222\":1,\"223\":1,\"224\":1,\"232\":5,\"251\":3,\"258\":4,\"264\":3,\"279\":8,\"286\":5,\"305\":2,\"317\":5,\"331\":4,\"338\":3,\"353\":1,\"357\":1,\"362\":5,\"376\":6,\"386\":3,\"394\":6}}],[\"extrinsic\",{\"0\":{\"268\":1},\"1\":{\"268\":4}}],[\"extending\",{\"1\":{\"294\":1}}],[\"extends\",{\"1\":{\"147\":1,\"153\":6,\"166\":2,\"179\":1,\"183\":1,\"193\":2,\"204\":4,\"222\":1,\"224\":1,\"232\":4,\"258\":1,\"279\":5,\"317\":1,\"386\":2,\"394\":3}}],[\"extension\",{\"1\":{\"67\":2}}],[\"excite\",{\"1\":{\"153\":5}}],[\"exception\",{\"1\":{\"52\":1}}],[\"except\",{\"1\":{\"52\":1}}],[\"execute\",{\"1\":{\"211\":5,\"317\":3}}],[\"exe\",{\"1\":{\"124\":5}}],[\"ex\",{\"1\":{\"18\":1}}],[\"emit\",{\"1\":{\"480\":1,\"487\":1,\"489\":1,\"498\":2,\"499\":1,\"500\":2,\"504\":1,\"505\":1}}],[\"empty\",{\"1\":{\"464\":5,\"475\":5,\"490\":1}}],[\"email\",{\"1\":{\"52\":16}}],[\"emoji\",{\"1\":{\"18\":2}}],[\"emm\",{\"1\":{\"15\":1}}],[\"emmm\",{\"1\":{\"6\":1}}],[\"occurs\",{\"1\":{\"500\":1}}],[\"oct\",{\"1\":{\"444\":2}}],[\"octet\",{\"1\":{\"30\":1}}],[\"out\",{\"1\":{\"433\":1}}],[\"output\",{\"1\":{\"153\":2,\"376\":1}}],[\"op\",{\"1\":{\"422\":6,\"423\":1,\"424\":1,\"425\":2,\"426\":2,\"427\":1,\"428\":1,\"429\":1,\"430\":1,\"431\":16,\"432\":9}}],[\"operators\",{\"1\":{\"439\":1}}],[\"operator\",{\"1\":{\"58\":3,\"446\":1,\"499\":1,\"508\":2}}],[\"operator+\",{\"1\":{\"58\":1}}],[\"open\",{\"1\":{\"21\":1,\"46\":2,\"178\":1,\"179\":1,\"180\":2,\"386\":4,\"416\":2,\"421\":1,\"432\":3,\"448\":2}}],[\"old\",{\"1\":{\"416\":2,\"419\":2,\"426\":1,\"429\":1,\"430\":1,\"477\":1}}],[\"o\",{\"1\":{\"317\":4,\"515\":1}}],[\"order\",{\"1\":{\"439\":1}}],[\"or\",{\"1\":{\"421\":1,\"431\":1,\"439\":1,\"447\":4,\"490\":1,\"501\":1,\"508\":1,\"511\":2}}],[\"originator\",{\"0\":{\"311\":1},\"1\":{\"308\":1,\"311\":2}}],[\"orange\",{\"1\":{\"305\":1,\"306\":3}}],[\"org\",{\"1\":{\"18\":1}}],[\"observers\",{\"1\":{\"317\":5}}],[\"observer2\",{\"1\":{\"317\":2}}],[\"observer1\",{\"1\":{\"317\":2}}],[\"observer\",{\"0\":{\"315\":1,\"321\":1,\"322\":1},\"1\":{\"300\":1,\"317\":19,\"318\":1,\"320\":1,\"321\":3}}],[\"object\",{\"1\":{\"294\":2,\"331\":1}}],[\"owners\",{\"1\":{\"258\":3}}],[\"owner\",{\"1\":{\"258\":11}}],[\"oddsupport\",{\"1\":{\"204\":5}}],[\"oi\",{\"0\":{\"53\":1},\"1\":{\"53\":1},\"2\":{\"59\":1,\"121\":1}}],[\"other\",{\"1\":{\"23\":1,\"294\":1}}],[\"only\",{\"1\":{\"445\":1,\"499\":1,\"500\":1}}],[\"online\",{\"1\":{\"26\":1,\"30\":4,\"32\":3,\"34\":2,\"35\":4,\"36\":14,\"52\":4}}],[\"ones\",{\"1\":{\"480\":1}}],[\"one\",{\"1\":{\"443\":2,\"498\":1}}],[\"onto\",{\"1\":{\"423\":1}}],[\"on\",{\"1\":{\"22\":1,\"30\":2,\"422\":2,\"479\":1,\"480\":1,\"512\":2}}],[\"off\",{\"1\":{\"30\":1}}],[\"of\",{\"1\":{\"18\":1,\"64\":1,\"65\":1,\"202\":1,\"203\":1,\"204\":1,\"294\":4,\"414\":1,\"416\":1,\"417\":1,\"423\":1,\"435\":1,\"443\":2,\"448\":2,\"453\":1,\"463\":1,\"467\":4,\"474\":1,\"476\":1,\"479\":5,\"480\":4,\"485\":1,\"495\":1,\"498\":1,\"500\":3,\"503\":3,\"507\":1,\"512\":1,\"519\":1}}],[\"o的话\",{\"1\":{\"16\":1}}],[\"提前看字符的原理是\",{\"1\":{\"446\":1}}],[\"提出的要求\",{\"1\":{\"236\":1}}],[\"提高系统的安全性\",{\"1\":{\"346\":1}}],[\"提高性能\",{\"1\":{\"330\":1}}],[\"提高代码的可读性和可维护性\",{\"1\":{\"284\":1,\"375\":1}}],[\"提高代码的可维护性和可扩展性\",{\"1\":{\"257\":1}}],[\"提高了系统的可扩展性和可维护性\",{\"1\":{\"172\":1}}],[\"提高模块的相对独立性\",{\"1\":{\"136\":1}}],[\"提供了\",{\"1\":{\"269\":1}}],[\"提供一个便捷且强大的容器镜像管理解决方案\",{\"1\":{\"44\":1}}],[\"提供的容器镜像注册表服务\",{\"1\":{\"44\":1}}],[\"提供所有科学知识\",{\"1\":{\"18\":1}}],[\"提示\",{\"1\":{\"10\":1,\"26\":1}}],[\"免费并且不受限制地\",{\"1\":{\"18\":1}}],[\"当解析完=右边的表达式后\",{\"1\":{\"509\":1}}],[\"当前优先级的运算符\",{\"1\":{\"508\":1}}],[\"当该标识符是全局定义的枚举类型时\",{\"1\":{\"500\":1}}],[\"当它是一个指向基本类型的指针时\",{\"1\":{\"467\":1}}],[\"当局部标识符的名字与全局标识符相同时\",{\"1\":{\"443\":1}}],[\"当用户的程序需要分配内存时\",{\"1\":{\"419\":1}}],[\"当时很火的\",{\"1\":{\"409\":1}}],[\"当需要增加新的处理时\",{\"1\":{\"392\":1}}],[\"当需要创建不同表示的对象时\",{\"1\":{\"192\":1}}],[\"当检测到没有考虑到的状态时就报错\",{\"1\":{\"369\":1}}],[\"当状态数过多时\",{\"1\":{\"367\":1}}],[\"当状态迁移遵循一定的规则时\",{\"1\":{\"367\":1}}],[\"当遇到庞大且复杂的问题\",{\"1\":{\"365\":1}}],[\"当模型的状态发生变化时\",{\"1\":{\"325\":1}}],[\"当系统中有大量的观察者时\",{\"1\":{\"324\":1}}],[\"当观察者的行为会对被观察对象产生影响时\",{\"1\":{\"322\":1}}],[\"当数据模型发生变化时\",{\"1\":{\"316\":2}}],[\"当发生分散灾难时\",{\"0\":{\"297\":1}}],[\"当出现争执时大家就会找仲裁者进行商量\",{\"1\":{\"293\":1}}],[\"当计数为零时\",{\"1\":{\"269\":1}}],[\"当某个程序员得意地说出\",{\"1\":{\"249\":1}}],[\"当顾客下单后只需要在冰激凌上加上各种香料就可以了\",{\"1\":{\"238\":1}}],[\"当一个表达式解析结束时\",{\"1\":{\"502\":1}}],[\"当一个终结符有多个选择时\",{\"1\":{\"457\":1}}],[\"当一个对象的状态发生改变时\",{\"1\":{\"317\":1}}],[\"当一个对象的构建过程非常复杂时\",{\"1\":{\"192\":1}}],[\"当一个人被要求做什么事情时\",{\"1\":{\"202\":1}}],[\"当外部请求程序进行某个处理\",{\"1\":{\"202\":1}}],[\"当想要增加功能时\",{\"1\":{\"186\":1}}],[\"当类的层次结构只有一层时\",{\"1\":{\"176\":1}}],[\"当子类实现了父类\",{\"1\":{\"175\":1}}],[\"当只有一个具体工厂时\",{\"1\":{\"154\":1}}],[\"当我对全局变量balance进行加法运算后\",{\"1\":{\"114\":1}}],[\"当我们调用\",{\"1\":{\"508\":1}}],[\"当我们想要通过改善算法来提高算法的处理速度时\",{\"1\":{\"379\":1}}],[\"当我们想要编写子类时\",{\"1\":{\"176\":1}}],[\"当我们想知道\",{\"1\":{\"367\":1}}],[\"当我们想在\",{\"1\":{\"174\":1}}],[\"当我们执行第一句代码print\",{\"1\":{\"114\":1}}],[\"当我们写完了vue项目后\",{\"1\":{\"106\":1}}],[\"当别的协程任务执行完毕\",{\"1\":{\"114\":1}}],[\"当\",{\"0\":{\"322\":1},\"1\":{\"81\":1,\"84\":2,\"187\":1}}],[\"当且仅当\",{\"1\":{\"79\":1}}],[\"当且仅当存在自然数\",{\"1\":{\"79\":1}}],[\"当可以自行实现\",{\"1\":{\"51\":1}}],[\"当今科学界最具争议性的项目\",{\"1\":{\"18\":1}}],[\"当然\",{\"1\":{\"176\":1,\"321\":1,\"366\":1,\"367\":1,\"369\":1,\"370\":1,\"407\":1,\"419\":1,\"439\":1,\"482\":1,\"497\":1,\"515\":1}}],[\"当然得是linux环境\",{\"1\":{\"66\":1}}],[\"当然需要配置相关驱动\",{\"1\":{\"66\":1}}],[\"当然超声波传感器有大概的距离\",{\"1\":{\"8\":1}}],[\"当然采用什么编程语言并不是重要\",{\"1\":{\"6\":1}}],[\"skip\",{\"1\":{\"442\":1,\"446\":1,\"459\":1,\"467\":1}}],[\"skiptoken\",{\"1\":{\"279\":5}}],[\"sc\",{\"1\":{\"421\":1,\"422\":4,\"507\":1,\"509\":1,\"513\":2}}],[\"sci\",{\"1\":{\"18\":2}}],[\"sbox\",{\"1\":{\"331\":2}}],[\"same\",{\"1\":{\"502\":1}}],[\"save\",{\"1\":{\"422\":2,\"426\":1,\"427\":1,\"480\":1,\"509\":1}}],[\"savedir\",{\"1\":{\"394\":2}}],[\"saving\",{\"1\":{\"305\":1}}],[\"safeframe\",{\"1\":{\"362\":11,\"366\":2,\"367\":2,\"368\":1,\"370\":5}}],[\"sato\",{\"1\":{\"251\":1}}],[\"s\",{\"1\":{\"251\":1,\"252\":2,\"331\":7,\"411\":1,\"416\":1,\"464\":1,\"509\":1,\"523\":1}}],[\"snapshot\",{\"1\":{\"215\":1}}],[\"single\",{\"1\":{\"443\":1,\"445\":1}}],[\"singleton2\",{\"1\":{\"353\":2}}],[\"singleton1\",{\"1\":{\"353\":2}}],[\"singleton\",{\"0\":{\"350\":1,\"351\":1},\"1\":{\"158\":1,\"253\":1,\"259\":1,\"264\":2,\"271\":1,\"351\":2,\"353\":11,\"354\":2,\"356\":1,\"357\":6,\"362\":4,\"371\":1}}],[\"si\",{\"1\":{\"421\":1,\"422\":4,\"507\":1,\"509\":2,\"513\":2}}],[\"simulate\",{\"1\":{\"357\":1}}],[\"sideborder\",{\"1\":{\"232\":7,\"236\":2}}],[\"sizeof\",{\"0\":{\"499\":1},\"1\":{\"439\":1,\"448\":1,\"467\":1,\"495\":1,\"498\":2,\"499\":9,\"507\":2,\"508\":1,\"512\":1,\"513\":6,\"514\":1}}],[\"size\",{\"1\":{\"30\":1,\"224\":2,\"394\":5,\"416\":2,\"459\":1,\"480\":1}}],[\"src++\",{\"1\":{\"416\":1,\"442\":1,\"443\":1,\"444\":2,\"445\":3,\"447\":1,\"459\":1}}],[\"src\",{\"1\":{\"153\":1,\"167\":1,\"184\":1,\"194\":1,\"205\":1,\"212\":1,\"226\":1,\"233\":1,\"252\":1,\"259\":1,\"265\":1,\"280\":1,\"287\":1,\"295\":1,\"318\":1,\"332\":1,\"339\":1,\"354\":1,\"363\":1,\"387\":1,\"395\":1,\"416\":6,\"440\":1,\"442\":2,\"443\":10,\"444\":6,\"445\":2,\"446\":3,\"447\":19,\"448\":1,\"459\":9}}],[\"ssize\",{\"1\":{\"459\":1}}],[\"sspai\",{\"1\":{\"119\":1}}],[\"ssl\",{\"1\":{\"36\":9,\"39\":1}}],[\"slowbutlessmemorystrategy\",{\"1\":{\"380\":1}}],[\"slash\",{\"1\":{\"331\":2}}],[\"sli\",{\"1\":{\"118\":1}}],[\"slidev\",{\"0\":{\"117\":1}}],[\"sleep\",{\"1\":{\"114\":3}}],[\"symbols\",{\"1\":{\"443\":3,\"478\":1}}],[\"symbol\",{\"1\":{\"443\":2,\"448\":2}}],[\"system\",{\"1\":{\"500\":1}}],[\"systemctl\",{\"1\":{\"46\":2}}],[\"sys\",{\"1\":{\"439\":1,\"448\":1,\"500\":1,\"508\":1}}],[\"synchronized\",{\"1\":{\"357\":3}}],[\"sync\",{\"1\":{\"108\":2}}],[\"spm=1001\",{\"1\":{\"495\":1}}],[\"sp++\",{\"1\":{\"422\":3,\"426\":1,\"429\":2,\"431\":16}}],[\"sp\",{\"1\":{\"420\":4,\"423\":1,\"426\":1,\"427\":4,\"428\":2,\"429\":1,\"432\":16,\"515\":6}}],[\"split\",{\"1\":{\"264\":1,\"279\":2}}],[\"space\",{\"1\":{\"65\":1,\"459\":1}}],[\"specialsupport\",{\"1\":{\"204\":5}}],[\"special\",{\"1\":{\"54\":1}}],[\"smtp\",{\"1\":{\"52\":5}}],[\"smtplib\",{\"1\":{\"52\":2}}],[\"sum\",{\"1\":{\"376\":3}}],[\"supported\",{\"1\":{\"445\":1,\"499\":1}}],[\"support\",{\"1\":{\"204\":28,\"442\":1}}],[\"super\",{\"1\":{\"153\":4,\"166\":2,\"179\":1,\"183\":1,\"204\":3,\"222\":1,\"224\":1,\"232\":4,\"317\":1,\"386\":2,\"394\":2}}],[\"subtract\",{\"1\":{\"436\":1}}],[\"subroutine\",{\"1\":{\"426\":4}}],[\"subclass\",{\"1\":{\"389\":1}}],[\"subscribing\",{\"1\":{\"295\":3}}],[\"subscribes\",{\"1\":{\"294\":1}}],[\"subscribe\",{\"1\":{\"294\":3}}],[\"subscriptions\",{\"1\":{\"294\":1}}],[\"substitution\",{\"1\":{\"242\":1}}],[\"sub\",{\"1\":{\"57\":1,\"421\":1,\"426\":1,\"427\":1,\"430\":1,\"431\":1,\"439\":1,\"447\":1,\"480\":1,\"506\":2,\"507\":1,\"508\":1,\"513\":3}}],[\"subject\",{\"1\":{\"52\":3,\"320\":1,\"321\":1}}],[\"successfully\",{\"1\":{\"52\":1}}],[\"su\",{\"1\":{\"34\":1,\"35\":1}}],[\"sudo\",{\"1\":{\"34\":1,\"35\":1,\"46\":3}}],[\"stdin\",{\"1\":{\"459\":1}}],[\"stored\",{\"1\":{\"500\":1}}],[\"store\",{\"1\":{\"443\":1,\"445\":1,\"479\":1,\"480\":1,\"498\":1}}],[\"step\",{\"1\":{\"416\":1,\"434\":1,\"449\":1,\"470\":1,\"481\":1,\"491\":1,\"496\":3,\"515\":1}}],[\"study\",{\"1\":{\"376\":5}}],[\"studio时不能打开360手机助手\",{\"1\":{\"109\":1}}],[\"studio下载gradle太慢可换源\",{\"1\":{\"22\":1}}],[\"studio换源\",{\"0\":{\"22\":1}}],[\"static\",{\"1\":{\"251\":3,\"264\":3,\"305\":1,\"353\":3,\"357\":4,\"362\":4,\"376\":3}}],[\"statement>b\",{\"1\":{\"487\":1}}],[\"statement>\",{\"1\":{\"486\":1,\"487\":3}}],[\"statements\",{\"1\":{\"480\":2}}],[\"statementnon\",{\"1\":{\"464\":1,\"475\":1}}],[\"statement\",{\"1\":{\"464\":12,\"475\":12,\"480\":1,\"481\":1,\"486\":1,\"487\":5,\"488\":1,\"490\":2}}],[\"state\",{\"0\":{\"360\":1,\"361\":1},\"1\":{\"214\":1,\"305\":2,\"306\":1,\"312\":1,\"361\":2,\"362\":28,\"363\":1,\"365\":4,\"366\":7,\"367\":1,\"368\":3,\"369\":7,\"370\":1,\"381\":1}}],[\"stacksp\",{\"1\":{\"515\":1}}],[\"stackvoid\",{\"1\":{\"479\":1}}],[\"stackchar\",{\"1\":{\"419\":1}}],[\"stackint\",{\"1\":{\"416\":1}}],[\"stack\",{\"1\":{\"215\":1,\"419\":6,\"420\":2,\"422\":2,\"423\":1,\"426\":1,\"427\":2,\"480\":2,\"500\":1,\"515\":1}}],[\"starts\",{\"1\":{\"444\":2}}],[\"startswith\",{\"1\":{\"305\":1}}],[\"start\",{\"1\":{\"112\":1,\"114\":1,\"147\":4}}],[\"started\",{\"1\":{\"67\":1,\"147\":2}}],[\"starttls\",{\"1\":{\"52\":1}}],[\"style\",{\"1\":{\"65\":1}}],[\"struct\",{\"1\":{\"443\":2}}],[\"strong\",{\"1\":{\"331\":2}}],[\"strategy\",{\"0\":{\"374\":1,\"379\":1},\"1\":{\"240\":1,\"375\":1,\"376\":20,\"379\":4,\"380\":1,\"388\":1}}],[\"str\",{\"1\":{\"183\":6,\"193\":5,\"264\":2,\"338\":5,\"386\":6}}],[\"strings\",{\"1\":{\"498\":1}}],[\"stringtokenizer\",{\"1\":{\"279\":10}}],[\"stringdisplay\",{\"1\":{\"232\":6,\"386\":6}}],[\"stringdisplayimpl\",{\"0\":{\"183\":1},\"1\":{\"178\":1,\"182\":5,\"183\":1,\"187\":2}}],[\"string\",{\"1\":{\"52\":1,\"153\":26,\"166\":14,\"183\":2,\"193\":14,\"204\":6,\"222\":3,\"223\":3,\"224\":3,\"232\":13,\"251\":13,\"258\":8,\"264\":7,\"279\":16,\"286\":3,\"294\":7,\"305\":7,\"331\":10,\"338\":14,\"362\":7,\"376\":5,\"386\":4,\"394\":5,\"416\":1,\"445\":3,\"498\":1}}],[\"stream\",{\"1\":{\"30\":1,\"436\":1,\"437\":1}}],[\"shr\",{\"1\":{\"421\":1,\"431\":1,\"439\":1,\"447\":1,\"508\":1}}],[\"shl\",{\"1\":{\"421\":1,\"431\":1,\"439\":1,\"447\":1,\"508\":1}}],[\"should\",{\"1\":{\"294\":1,\"467\":1}}],[\"showcase\",{\"1\":{\"331\":3}}],[\"show\",{\"1\":{\"232\":5,\"235\":1}}],[\"showwithaster\",{\"1\":{\"166\":3}}],[\"showwithparen\",{\"1\":{\"166\":3}}],[\"sh帮你免费且自动更新的https证书\",{\"1\":{\"39\":1}}],[\"sh的安装目录\",{\"1\":{\"34\":1}}],[\"shanghai\",{\"1\":{\"31\":1}}],[\"share\",{\"1\":{\"30\":3,\"31\":2,\"36\":5}}],[\"sh\",{\"0\":{\"26\":1},\"1\":{\"26\":1,\"27\":1,\"34\":3,\"35\":2}}],[\"sheet\",{\"1\":{\"18\":2}}],[\"several\",{\"1\":{\"500\":1}}],[\"semicolon\",{\"1\":{\"486\":1}}],[\"seperated\",{\"1\":{\"467\":1}}],[\"segmentation\",{\"1\":{\"433\":1,\"449\":1}}],[\"segment\",{\"1\":{\"419\":6,\"476\":1}}],[\"segmentfault\",{\"1\":{\"119\":1}}],[\"search\",{\"1\":{\"153\":2,\"443\":1}}],[\"services\",{\"1\":{\"31\":1}}],[\"server\",{\"0\":{\"51\":1},\"1\":{\"30\":4,\"36\":10,\"52\":7}}],[\"sender\",{\"1\":{\"294\":4}}],[\"sendmail\",{\"1\":{\"52\":1}}],[\"send\",{\"1\":{\"52\":2}}],[\"sendfile\",{\"1\":{\"30\":1}}],[\"sent\",{\"1\":{\"30\":1,\"52\":2}}],[\"second\",{\"1\":{\"498\":1}}],[\"secrets\",{\"1\":{\"23\":1}}],[\"secret\",{\"1\":{\"23\":1}}],[\"section\",{\"1\":{\"21\":1}}],[\"setup\",{\"1\":{\"515\":1}}],[\"setclock\",{\"1\":{\"362\":3,\"366\":4}}],[\"settimeout\",{\"1\":{\"338\":1}}],[\"settings\",{\"1\":{\"22\":1}}],[\"setprintername\",{\"1\":{\"338\":5}}],[\"setnext\",{\"1\":{\"204\":6}}],[\"set\",{\"1\":{\"22\":1,\"264\":1}}],[\"see\",{\"1\":{\"21\":1}}],[\"select\",{\"1\":{\"21\":1}}],[\"so\",{\"1\":{\"498\":1,\"500\":1}}],[\"source\",{\"1\":{\"416\":3,\"422\":2,\"437\":1}}],[\"solution\",{\"1\":{\"294\":1}}],[\"solutions\",{\"0\":{\"20\":1}}],[\"somethinggood\",{\"1\":{\"174\":2}}],[\"something\",{\"1\":{\"174\":4}}],[\"some\",{\"0\":{\"20\":1}}],[\"vs\",{\"1\":{\"119\":2}}],[\"vscode中可以使用\",{\"1\":{\"108\":1}}],[\"vscode\",{\"0\":{\"67\":1},\"1\":{\"109\":1}}],[\"v3u\",{\"1\":{\"111\":1,\"115\":1}}],[\"virtual\",{\"1\":{\"341\":1,\"346\":1,\"419\":1,\"420\":1}}],[\"view\",{\"0\":{\"325\":1},\"1\":{\"325\":1}}],[\"visit\",{\"1\":{\"394\":4,\"397\":2,\"401\":1,\"402\":1}}],[\"visitor\",{\"0\":{\"392\":1,\"393\":1,\"402\":1},\"1\":{\"227\":1,\"289\":1,\"392\":1,\"394\":23,\"395\":1,\"397\":6,\"398\":2,\"400\":1,\"401\":3,\"402\":3}}],[\"visualstudio\",{\"1\":{\"67\":1}}],[\"vi\",{\"1\":{\"225\":1,\"226\":2,\"394\":1,\"395\":2}}],[\"vim\",{\"1\":{\"46\":1}}],[\"void\",{\"1\":{\"58\":1,\"144\":1,\"153\":3,\"166\":10,\"181\":3,\"193\":13,\"204\":3,\"211\":9,\"222\":1,\"223\":2,\"224\":1,\"232\":1,\"251\":6,\"258\":4,\"264\":1,\"279\":7,\"286\":1,\"294\":2,\"305\":3,\"317\":8,\"331\":3,\"338\":8,\"357\":1,\"362\":23,\"376\":6,\"386\":4,\"394\":3,\"416\":2,\"422\":1,\"426\":1,\"440\":1,\"443\":1,\"444\":1,\"445\":1,\"446\":1,\"447\":1,\"448\":2,\"459\":2,\"466\":1,\"468\":1,\"469\":1,\"478\":1,\"480\":1}}],[\"volumes\",{\"1\":{\"31\":1}}],[\"v+p\",{\"1\":{\"58\":1}}],[\"v+a\",{\"1\":{\"58\":3}}],[\"v<a\",{\"1\":{\"58\":1}}],[\"v>=p\",{\"1\":{\"58\":1}}],[\"v=x\",{\"1\":{\"58\":1}}],[\"v\",{\"1\":{\"58\":10,\"419\":1}}],[\"val\",{\"1\":{\"443\":1,\"444\":10,\"445\":7,\"459\":5,\"468\":1,\"498\":2,\"506\":1}}],[\"value\",{\"1\":{\"422\":3,\"423\":1,\"436\":1,\"443\":4,\"448\":1,\"459\":12,\"467\":2,\"468\":1,\"476\":1,\"478\":1,\"479\":3,\"480\":2,\"500\":6,\"512\":1}}],[\"valid=300s\",{\"1\":{\"30\":1}}],[\"variables\",{\"1\":{\"478\":1,\"480\":2}}],[\"variable\",{\"1\":{\"426\":1,\"427\":1,\"448\":1,\"464\":3,\"465\":1,\"467\":7,\"475\":2,\"478\":3,\"479\":1,\"480\":2,\"500\":5}}],[\"vars\",{\"1\":{\"23\":1}}],[\"var\",{\"1\":{\"23\":1,\"30\":10,\"31\":1,\"36\":10,\"430\":2,\"506\":1,\"509\":1,\"514\":1}}],[\"vue\",{\"0\":{\"26\":1},\"1\":{\"26\":1}}],[\"vuepress\",{\"1\":{\"18\":1}}],[\"version\",{\"1\":{\"18\":1,\"22\":1}}],[\"after\",{\"1\":{\"496\":3}}],[\"a=10\",{\"1\":{\"468\":1}}],[\"a是41\",{\"1\":{\"444\":1}}],[\"ax上需要保留原来的值\",{\"1\":{\"513\":1}}],[\"axxor\",{\"1\":{\"512\":1}}],[\"axpush\",{\"1\":{\"512\":1}}],[\"ax\",{\"1\":{\"420\":3,\"422\":26,\"423\":4,\"425\":5,\"426\":1,\"430\":2,\"431\":34,\"432\":7,\"433\":1,\"498\":1,\"500\":1,\"509\":1,\"513\":1}}],[\"ai\",{\"1\":{\"379\":1}}],[\"a>\",{\"1\":{\"251\":1,\"252\":1}}],[\"a><\",{\"1\":{\"153\":6}}],[\"at\",{\"1\":{\"211\":1,\"212\":10}}],[\"attach\",{\"1\":{\"52\":1}}],[\"adj\",{\"0\":{\"428\":1},\"1\":{\"417\":1,\"421\":1,\"426\":1,\"428\":2,\"500\":1}}],[\"adapter\",{\"1\":{\"162\":1,\"166\":1,\"167\":1,\"188\":1,\"240\":1,\"347\":1}}],[\"addactionlistener\",{\"1\":{\"370\":5}}],[\"addobserver\",{\"1\":{\"317\":3}}],[\"addfruit\",{\"1\":{\"305\":2}}],[\"add\",{\"1\":{\"57\":3,\"58\":1,\"153\":10,\"222\":1,\"223\":1,\"225\":13,\"394\":16,\"416\":1,\"421\":1,\"426\":3,\"428\":2,\"430\":1,\"431\":1,\"433\":1,\"436\":1,\"439\":2,\"447\":1,\"448\":2,\"506\":2,\"507\":1,\"508\":1,\"512\":5,\"513\":3,\"514\":1}}],[\"address\",{\"1\":{\"422\":6,\"424\":1,\"430\":3,\"467\":2,\"476\":1,\"477\":2,\"500\":1,\"503\":3,\"507\":1}}],[\"address+\",{\"1\":{\"419\":1,\"430\":1,\"477\":1}}],[\"address|\",{\"1\":{\"419\":1}}],[\"address>\",{\"1\":{\"153\":1}}],[\"address>`\",{\"1\":{\"153\":1}}],[\"addr\",{\"1\":{\"30\":1,\"510\":4,\"511\":4}}],[\"ab\",{\"1\":{\"488\":1}}],[\"abstractdisplay\",{\"1\":{\"386\":8}}],[\"abstractclass\",{\"1\":{\"175\":2}}],[\"abstractfactory\",{\"1\":{\"153\":1,\"264\":1,\"355\":1}}],[\"abstract\",{\"1\":{\"153\":10,\"156\":1,\"157\":1,\"166\":3,\"181\":4,\"188\":1,\"193\":5,\"195\":1,\"204\":2,\"223\":4,\"232\":5,\"253\":1,\"258\":3,\"279\":2,\"317\":3,\"381\":1,\"386\":4,\"394\":6}}],[\"about\",{\"0\":{\"20\":1},\"1\":{\"294\":1}}],[\"automatically\",{\"1\":{\"294\":1}}],[\"automaton\",{\"1\":{\"28\":3,\"30\":9,\"31\":2,\"32\":2,\"34\":1,\"36\":16}}],[\"author\",{\"1\":{\"153\":8}}],[\"authservice\",{\"1\":{\"140\":1}}],[\"aaronsw\",{\"1\":{\"126\":1}}],[\"await\",{\"1\":{\"114\":5,\"115\":1}}],[\"append\",{\"1\":{\"498\":1}}],[\"appendbook\",{\"1\":{\"286\":5}}],[\"apple\",{\"1\":{\"305\":1,\"306\":12}}],[\"application\",{\"1\":{\"30\":1,\"294\":1}}],[\"app\",{\"1\":{\"294\":1}}],[\"api\",{\"0\":{\"235\":1},\"1\":{\"67\":1,\"175\":2,\"186\":1,\"235\":5,\"236\":1,\"379\":2}}],[\"aggregate\",{\"1\":{\"286\":5,\"287\":2}}],[\"aggregateerror\",{\"1\":{\"67\":1}}],[\"again\",{\"1\":{\"114\":2}}],[\"agicy\",{\"1\":{\"66\":1}}],[\"agent\",{\"1\":{\"30\":1}}],[\"a<b\",{\"1\":{\"57\":1}}],[\"a+b\",{\"1\":{\"57\":2}}],[\"a+b>=p\",{\"1\":{\"57\":1}}],[\"any\",{\"1\":{\"286\":2,\"331\":3,\"357\":2}}],[\"an\",{\"1\":{\"193\":1,\"194\":1,\"294\":1,\"467\":1,\"499\":1}}],[\"anltr\",{\"1\":{\"125\":1}}],[\"ans=\",{\"1\":{\"58\":1}}],[\"ans=mul\",{\"1\":{\"57\":1}}],[\"ans=1ll\",{\"1\":{\"56\":1}}],[\"android\",{\"0\":{\"22\":1},\"1\":{\"22\":2,\"108\":1}}],[\"and\",{\"1\":{\"21\":1,\"294\":3,\"421\":1,\"429\":1,\"431\":1,\"439\":3,\"447\":5,\"499\":1,\"503\":2,\"508\":2,\"511\":1,\"512\":2}}],[\"asimpile\",{\"0\":{\"528\":1}}],[\"assignment\",{\"1\":{\"509\":1}}],[\"assign\",{\"1\":{\"439\":2,\"447\":1,\"467\":2,\"468\":1,\"487\":1,\"488\":1,\"489\":1,\"490\":1,\"500\":1,\"501\":1,\"508\":2,\"509\":3,\"510\":1,\"514\":1}}],[\"assembly\",{\"1\":{\"437\":1}}],[\"assetstudioassetstudio\",{\"1\":{\"64\":1}}],[\"assert\",{\"1\":{\"58\":1}}],[\"async\",{\"1\":{\"113\":1,\"114\":5}}],[\"asyncio\",{\"0\":{\"111\":1},\"1\":{\"113\":3,\"114\":13}}],[\"as\",{\"1\":{\"52\":2,\"114\":1,\"166\":2,\"222\":1,\"294\":1,\"447\":1,\"501\":1,\"502\":1}}],[\"array\",{\"1\":{\"514\":1}}],[\"array<item>\",{\"1\":{\"153\":1}}],[\"are\",{\"1\":{\"498\":1,\"499\":1,\"500\":1}}],[\"area\",{\"1\":{\"416\":1,\"419\":3}}],[\"arbitrary\",{\"1\":{\"416\":1}}],[\"arg\",{\"1\":{\"430\":3,\"477\":2}}],[\"arg3\",{\"1\":{\"430\":1}}],[\"arg2\",{\"1\":{\"430\":1}}],[\"arg1\",{\"1\":{\"430\":1}}],[\"arguments\",{\"1\":{\"426\":2,\"428\":2,\"430\":1,\"500\":3}}],[\"argv++\",{\"1\":{\"416\":1}}],[\"argv\",{\"1\":{\"416\":3,\"433\":1,\"459\":1,\"515\":1}}],[\"argc\",{\"1\":{\"416\":2,\"433\":1,\"459\":1,\"515\":1}}],[\"args=\",{\"1\":{\"112\":2,\"114\":4}}],[\"around\",{\"1\":{\"286\":1,\"287\":1}}],[\"article\",{\"1\":{\"51\":1,\"495\":1}}],[\"archive\",{\"1\":{\"21\":1}}],[\"accept\",{\"1\":{\"394\":7,\"397\":2,\"402\":1}}],[\"access\",{\"1\":{\"28\":1,\"30\":9,\"36\":10,\"346\":1,\"514\":1}}],[\"acc\",{\"1\":{\"222\":2}}],[\"acquire\",{\"1\":{\"112\":1}}],[\"acme申请\",{\"1\":{\"39\":1}}],[\"acme\",{\"0\":{\"26\":1},\"1\":{\"26\":1,\"27\":1,\"28\":1,\"31\":1,\"34\":3,\"35\":5}}],[\"actually\",{\"1\":{\"499\":1}}],[\"actual\",{\"1\":{\"467\":1}}],[\"actionlistener\",{\"1\":{\"370\":3}}],[\"actionperformed\",{\"1\":{\"370\":1}}],[\"action\",{\"1\":{\"214\":1}}],[\"act\",{\"1\":{\"23\":5}}],[\"alone\",{\"1\":{\"467\":1}}],[\"alice使用了id卡\",{\"1\":{\"259\":1}}],[\"alice\",{\"1\":{\"204\":4,\"258\":1,\"338\":1}}],[\"alias\",{\"1\":{\"30\":1,\"36\":2}}],[\"aliyun\",{\"1\":{\"22\":12}}],[\"allocate\",{\"1\":{\"419\":1}}],[\"allowmixedcontent\",{\"1\":{\"108\":1}}],[\"all\",{\"1\":{\"22\":1,\"294\":1,\"478\":1,\"498\":1}}],[\"alt\",{\"1\":{\"3\":1,\"7\":1,\"52\":1,\"120\":1}}],[\"a\",{\"1\":{\"18\":1,\"52\":1,\"57\":6,\"58\":6,\"111\":1,\"115\":1,\"119\":1,\"193\":1,\"194\":1,\"294\":4,\"298\":8,\"357\":1,\"409\":1,\"411\":1,\"414\":1,\"416\":1,\"417\":1,\"433\":1,\"434\":1,\"435\":1,\"443\":8,\"444\":4,\"445\":5,\"449\":1,\"453\":1,\"463\":1,\"467\":2,\"468\":1,\"470\":1,\"474\":1,\"477\":3,\"481\":1,\"485\":1,\"487\":4,\"488\":4,\"490\":1,\"491\":1,\"500\":1,\"502\":2,\"503\":2,\"505\":1,\"509\":2,\"510\":1,\"512\":3,\"514\":2,\"515\":1,\"519\":1}}],[\"可惜的是它的代码初衷是代码最小化\",{\"1\":{\"409\":1}}],[\"可作为组件复用\",{\"1\":{\"399\":1}}],[\"可替换性是指一个对象可以被另一个具有相同接口的对象替换\",{\"1\":{\"320\":1}}],[\"可替換性\",{\"1\":{\"197\":1}}],[\"可扩展性\",{\"1\":{\"278\":1}}],[\"可维护性和可扩展性\",{\"1\":{\"246\":1}}],[\"可能唯一不好理解的是获取十六进制的值相关的代码\",{\"1\":{\"444\":1}}],[\"可能包含多个字符\",{\"1\":{\"439\":1}}],[\"可能大家对此感受不深\",{\"1\":{\"365\":1}}],[\"可能会更具普适性\",{\"1\":{\"411\":1}}],[\"可能会导致创建多个实例\",{\"1\":{\"356\":1}}],[\"可能会有读者认为\",{\"1\":{\"298\":1}}],[\"可能需要长期保存\",{\"1\":{\"310\":1}}],[\"可能需要保存多个\",{\"1\":{\"309\":1}}],[\"可能只需要在短时间内有效\",{\"1\":{\"310\":1}}],[\"可能只需要保存一个\",{\"1\":{\"309\":1}}],[\"可能同时违反其他原则\",{\"1\":{\"128\":1}}],[\"可能使用threads会好一点\",{\"1\":{\"6\":1}}],[\"可是如果在执行事务逻辑块中主动放弃执行权了\",{\"1\":{\"115\":1}}],[\"可调试性强\",{\"1\":{\"113\":1}}],[\"可读性高\",{\"1\":{\"113\":1}}],[\"可知\",{\"1\":{\"94\":1}}],[\"可以看看\",{\"1\":{\"522\":1}}],[\"可以看到和之前有同样的输出\",{\"1\":{\"515\":1}}],[\"可以看到\",{\"1\":{\"114\":2,\"456\":1,\"459\":1}}],[\"可以自己实现看看\",{\"1\":{\"512\":1}}],[\"可以自己先试着去实现它\",{\"1\":{\"470\":1}}],[\"可以参考\",{\"1\":{\"496\":1}}],[\"可以学习学习这些文法\",{\"1\":{\"522\":1}}],[\"可以学习学习\",{\"1\":{\"492\":1}}],[\"可以认为语句就是表达式加上末尾的分号\",{\"1\":{\"486\":1}}],[\"可以是\",{\"1\":{\"455\":1}}],[\"可以得到个位数的值\",{\"1\":{\"444\":1}}],[\"可以理解为变量名\",{\"1\":{\"443\":1}}],[\"可以帮助我们设计出这样的类\",{\"1\":{\"399\":1}}],[\"可以帮助我们应对软件开发中的常见问题\",{\"1\":{\"246\":1}}],[\"可以通过在子类中增加方法以实现新的功能\",{\"1\":{\"389\":1}}],[\"可以通过子类来定制产品的创建过程\",{\"1\":{\"257\":1}}],[\"可以方便地根据棋手的选择切换\",{\"1\":{\"379\":1}}],[\"可以方便地增加新的产品族而不影响现有代码\",{\"1\":{\"152\":1}}],[\"可以避免在多个地方重复相同的算法逻辑\",{\"1\":{\"375\":1}}],[\"可以避免创建多个实例带来的资源浪费和不一致性问题\",{\"1\":{\"351\":1}}],[\"可以很容易地添加新的策略\",{\"1\":{\"375\":1}}],[\"可以很容易地添加新的处理者而不影响现有代码\",{\"1\":{\"203\":1}}],[\"可以提高系统的响应速度和资源利用率\",{\"1\":{\"341\":1}}],[\"可以提高代码的复用性和可维护性\",{\"1\":{\"278\":1}}],[\"可以用程序来生成代码而不是手写代码\",{\"1\":{\"367\":1}}],[\"可以用于访问远程对象\",{\"1\":{\"337\":1}}],[\"可以用来存储弱引用的键值对\",{\"1\":{\"269\":1}}],[\"可以负责将\",{\"1\":{\"311\":1}}],[\"可以维护一个\",{\"1\":{\"311\":1}}],[\"可以实现持久化存储\",{\"1\":{\"311\":1}}],[\"可以实现多次撤销操作\",{\"1\":{\"311\":1}}],[\"可以实现命令的参数化和可撤销性\",{\"1\":{\"214\":1}}],[\"可以将状态保存和恢复的逻辑与业务逻辑分离\",{\"1\":{\"311\":1}}],[\"可以将这七个原则分为以下两部分\",{\"1\":{\"128\":1}}],[\"可以确保\",{\"1\":{\"308\":1}}],[\"可以根据需要实现不同的迭代器\",{\"1\":{\"284\":1}}],[\"可以根据需要动态地添加或删除职责\",{\"1\":{\"231\":1}}],[\"可以轻松添加新的语法规则或指令\",{\"1\":{\"278\":1}}],[\"可以轻松解析和执行特定的语言或指令集\",{\"1\":{\"278\":1}}],[\"可以同时使用的文件句柄和窗口句柄是有限制的\",{\"1\":{\"270\":1}}],[\"可以安全地回收\",{\"1\":{\"269\":1}}],[\"可以动态地增加功能\",{\"0\":{\"237\":1}}],[\"可以在客户端和远程服务器之间进行通信\",{\"1\":{\"342\":1}}],[\"可以在实际对象创建之前进行一些轻量级的操作\",{\"1\":{\"341\":1}}],[\"可以在代理中加入额外的逻辑来控制对实际对象的访问\",{\"1\":{\"337\":1}}],[\"可以在需要时回滚到之前的状态\",{\"1\":{\"215\":1}}],[\"可以在运行时动态地改变职责链的结构\",{\"1\":{\"203\":1}}],[\"可以在不修改实际对象的情况下添加额外的功能\",{\"1\":{\"342\":1}}],[\"可以在不修改集合对象的情况下\",{\"1\":{\"284\":1}}],[\"可以在不修改现有代码的情况下\",{\"1\":{\"130\":1}}],[\"可以在不同的上下文中重用相同的构建逻辑\",{\"1\":{\"192\":1}}],[\"可以在不改变原有代码的情况下\",{\"1\":{\"130\":1}}],[\"可以构造出分段状自然数系统\",{\"1\":{\"103\":1}}],[\"可以构造出\",{\"1\":{\"102\":1}}],[\"可以构造出环状自然数系统\",{\"1\":{\"101\":1}}],[\"可以构造出菊花图自然数系统\",{\"1\":{\"100\":1}}],[\"可以构造出空集自然数系统\",{\"1\":{\"99\":1}}],[\"可以使用双重检查锁定\",{\"1\":{\"356\":1}}],[\"可以使用\",{\"1\":{\"65\":1}}],[\"可以使用相同的权限管理\",{\"1\":{\"44\":1}}],[\"可以更轻松地构建和部署容器化的应用程序\",{\"1\":{\"44\":1}}],[\"可以快速\",{\"1\":{\"18\":1}}],[\"p++\",{\"1\":{\"507\":1,\"513\":1}}],[\"p+z\",{\"1\":{\"56\":1}}],[\"ptr\",{\"1\":{\"448\":1,\"467\":5,\"479\":1,\"480\":1,\"498\":1,\"499\":1,\"501\":1,\"502\":2,\"503\":1,\"507\":1,\"512\":1,\"513\":3,\"514\":3}}],[\"pc+1\",{\"1\":{\"426\":1}}],[\"pc++\",{\"1\":{\"422\":1,\"427\":1,\"428\":1,\"430\":1}}],[\"pc\",{\"1\":{\"420\":2,\"424\":4,\"425\":6,\"426\":4,\"429\":2,\"432\":1,\"433\":1}}],[\"p3\",{\"1\":{\"331\":2}}],[\"p2\",{\"1\":{\"331\":2}}],[\"p1\",{\"1\":{\"331\":2}}],[\"pbd\",{\"1\":{\"166\":2}}],[\"pbi\",{\"1\":{\"166\":2}}],[\"ps\",{\"1\":{\"153\":1,\"184\":1,\"194\":1,\"205\":1,\"212\":1,\"226\":1,\"233\":1,\"252\":1,\"259\":1,\"265\":1,\"280\":1,\"287\":1,\"295\":1,\"318\":1,\"332\":1,\"339\":1,\"354\":1,\"363\":1,\"387\":1,\"395\":1,\"410\":1}}],[\"peg\",{\"1\":{\"522\":1}}],[\"people\",{\"1\":{\"153\":5,\"294\":1}}],[\"peano\",{\"0\":{\"95\":1,\"98\":1,\"99\":1,\"100\":1,\"101\":1,\"102\":1,\"103\":1},\"1\":{\"68\":2,\"69\":1,\"72\":2,\"73\":2,\"75\":3,\"76\":1,\"77\":2,\"81\":2,\"84\":1,\"88\":1,\"89\":1,\"91\":3,\"92\":1,\"93\":1,\"94\":4,\"95\":5}}],[\"ppt\",{\"1\":{\"119\":1}}],[\"py\",{\"1\":{\"114\":2}}],[\"pytorch\",{\"1\":{\"66\":5}}],[\"python3\",{\"0\":{\"111\":1},\"1\":{\"114\":2}}],[\"python\",{\"0\":{\"61\":1},\"1\":{\"6\":1,\"27\":1,\"52\":1,\"61\":1,\"114\":1},\"2\":{\"62\":1}}],[\"position\",{\"1\":{\"480\":1,\"498\":1}}],[\"pos\",{\"1\":{\"440\":1,\"443\":4,\"445\":2,\"480\":3}}],[\"postfix\",{\"1\":{\"508\":1}}],[\"post\",{\"1\":{\"64\":1,\"119\":1}}],[\"pointer<expr1>\",{\"1\":{\"512\":1}}],[\"pointer\",{\"1\":{\"416\":1,\"467\":1,\"479\":2,\"499\":1,\"509\":1,\"512\":1,\"514\":2}}],[\"poolsize\",{\"1\":{\"416\":5,\"419\":9,\"420\":2,\"515\":1}}],[\"pool\",{\"1\":{\"264\":3}}],[\"pop\",{\"1\":{\"211\":1,\"422\":1,\"426\":1,\"429\":1}}],[\"powershell\",{\"1\":{\"124\":1}}],[\"port\",{\"1\":{\"52\":2}}],[\"ports\",{\"1\":{\"31\":1}}],[\"picture\",{\"1\":{\"157\":1}}],[\"pip\",{\"1\":{\"61\":2}}],[\"pid\",{\"1\":{\"30\":2}}],[\"p><ul><li>晚上好\",{\"1\":{\"194\":1}}],[\"p><ul><li>早上好\",{\"1\":{\"194\":1}}],[\"p>`\",{\"1\":{\"193\":1}}],[\"p>\",{\"1\":{\"58\":1,\"251\":1,\"252\":2}}],[\"p=998244353\",{\"1\":{\"56\":1,\"57\":1}}],[\"p\",{\"1\":{\"48\":1,\"51\":1,\"56\":2,\"57\":2,\"58\":2,\"258\":3,\"331\":8,\"338\":5,\"464\":1,\"498\":4,\"507\":1,\"513\":1,\"523\":1}}],[\"push<expr2>\",{\"1\":{\"512\":1}}],[\"push\",{\"0\":{\"423\":1},\"1\":{\"153\":16,\"211\":3,\"222\":1,\"258\":1,\"264\":1,\"279\":1,\"294\":1,\"305\":2,\"317\":1,\"394\":1,\"417\":1,\"421\":1,\"422\":1,\"423\":3,\"426\":7,\"433\":2,\"500\":1,\"504\":1,\"505\":1,\"506\":1,\"507\":4,\"509\":1,\"512\":4,\"513\":3,\"514\":2,\"515\":1}}],[\"publishing\",{\"1\":{\"295\":3}}],[\"publish\",{\"1\":{\"294\":3}}],[\"publishmessage\",{\"1\":{\"294\":4}}],[\"publisher\",{\"1\":{\"67\":1}}],[\"public\",{\"1\":{\"22\":2,\"58\":1,\"153\":1,\"193\":15,\"264\":3,\"294\":2,\"305\":3,\"317\":5,\"353\":1,\"357\":1,\"362\":19}}],[\"pull\",{\"1\":{\"46\":1}}],[\"prtf\",{\"1\":{\"421\":1,\"432\":1}}],[\"pre\",{\"1\":{\"507\":1}}],[\"precedence\",{\"1\":{\"439\":1,\"501\":1,\"502\":1}}],[\"prevhand\",{\"1\":{\"376\":3}}],[\"prevhandvalue\",{\"1\":{\"376\":5}}],[\"previous\",{\"1\":{\"305\":1,\"306\":1}}],[\"preview\",{\"1\":{\"119\":1}}],[\"prefix\",{\"1\":{\"222\":3,\"223\":1,\"224\":2,\"305\":2}}],[\"primitivecommandnode\",{\"1\":{\"279\":5}}],[\"principle\",{\"1\":{\"242\":1}}],[\"printf\",{\"1\":{\"416\":4,\"419\":3,\"432\":7,\"448\":1,\"459\":2,\"467\":2,\"468\":2,\"469\":1,\"479\":2,\"480\":2,\"500\":3,\"502\":1,\"503\":1,\"507\":1,\"509\":1,\"510\":1,\"514\":1}}],[\"printable\",{\"1\":{\"338\":12}}],[\"printer\",{\"1\":{\"338\":9}}],[\"printerproxy\",{\"1\":{\"338\":6}}],[\"printlist\",{\"1\":{\"223\":1,\"225\":2}}],[\"printlistwithprefix\",{\"1\":{\"222\":2,\"223\":2,\"224\":1}}],[\"printline\",{\"1\":{\"183\":3,\"386\":3}}],[\"printstrong\",{\"1\":{\"166\":6}}],[\"printweak\",{\"1\":{\"166\":6}}],[\"printbanner2\",{\"1\":{\"166\":3}}],[\"printbanner\",{\"1\":{\"165\":1,\"166\":11}}],[\"print\",{\"1\":{\"52\":2,\"112\":1,\"113\":1,\"114\":10,\"165\":1,\"166\":10,\"178\":1,\"179\":1,\"180\":2,\"264\":4,\"338\":5,\"386\":4}}],[\"private\",{\"1\":{\"58\":1,\"144\":1,\"147\":1,\"166\":2,\"180\":1,\"183\":3,\"193\":4,\"204\":5,\"211\":5,\"222\":2,\"224\":2,\"232\":3,\"251\":3,\"258\":2,\"264\":3,\"279\":6,\"286\":5,\"294\":2,\"305\":4,\"317\":2,\"331\":3,\"338\":5,\"353\":3,\"357\":4,\"362\":5,\"376\":16,\"386\":4,\"394\":5}}],[\"privkey\",{\"1\":{\"35\":1,\"36\":3}}],[\"probstrategy\",{\"1\":{\"376\":6}}],[\"product\",{\"1\":{\"258\":13,\"331\":13}}],[\"proto\",{\"1\":{\"331\":2}}],[\"prototype\",{\"0\":{\"329\":1,\"330\":1},\"1\":{\"216\":1,\"312\":1,\"330\":2,\"332\":1,\"355\":1}}],[\"protected\",{\"1\":{\"153\":3,\"204\":5,\"222\":1,\"223\":1,\"224\":1,\"232\":1,\"258\":2,\"386\":3}}],[\"programs\",{\"1\":{\"279\":2}}],[\"programnode\",{\"1\":{\"279\":5}}],[\"program\",{\"0\":{\"466\":1},\"1\":{\"124\":1,\"279\":10,\"280\":10,\"416\":3,\"419\":1,\"420\":1,\"433\":1,\"448\":1,\"463\":1,\"464\":1,\"466\":2}}],[\"proxy\",{\"0\":{\"336\":1,\"346\":1},\"1\":{\"30\":1,\"36\":2,\"39\":1,\"271\":1,\"337\":1,\"339\":1,\"341\":1,\"342\":1,\"346\":3}}],[\"processes\",{\"1\":{\"30\":1}}],[\"properties\",{\"1\":{\"22\":1}}],[\"project\",{\"1\":{\"22\":1,\"28\":1,\"31\":2}}],[\"paa\",{\"1\":{\"376\":2}}],[\"payload\",{\"1\":{\"294\":5}}],[\"parenthesis\",{\"1\":{\"501\":2}}],[\"parsed\",{\"1\":{\"443\":1}}],[\"parser\",{\"1\":{\"411\":1,\"437\":1}}],[\"parse\",{\"1\":{\"279\":12,\"440\":1,\"441\":1,\"443\":1,\"444\":1,\"445\":1,\"447\":8,\"467\":5,\"468\":1,\"487\":3,\"508\":1}}],[\"params+1\",{\"1\":{\"479\":1}}],[\"params++\",{\"1\":{\"479\":1}}],[\"params\",{\"1\":{\"479\":2}}],[\"param\",{\"1\":{\"477\":5}}],[\"parameter\",{\"1\":{\"464\":2,\"467\":1,\"475\":2,\"476\":1,\"478\":1,\"479\":6,\"480\":1}}],[\"parameters\",{\"1\":{\"214\":1}}],[\"paragraph\",{\"1\":{\"251\":3}}],[\"part\",{\"1\":{\"18\":1,\"467\":2,\"478\":1}}],[\"paint\",{\"1\":{\"211\":2}}],[\"pattern\",{\"1\":{\"162\":1,\"167\":1,\"250\":1,\"278\":1,\"294\":1,\"375\":1}}],[\"patern\",{\"1\":{\"153\":1,\"184\":1,\"194\":1,\"205\":1,\"212\":1,\"226\":1,\"233\":1,\"252\":1,\"259\":1,\"265\":1,\"280\":1,\"287\":1,\"295\":1,\"318\":1,\"332\":1,\"339\":1,\"354\":1,\"363\":1,\"387\":1,\"395\":1}}],[\"patern>\",{\"1\":{\"153\":1,\"184\":1,\"194\":1,\"205\":1,\"212\":1,\"226\":1,\"233\":1,\"252\":1,\"259\":1,\"265\":1,\"280\":1,\"287\":1,\"295\":1,\"318\":1,\"332\":1,\"339\":1,\"354\":1,\"363\":1,\"387\":1,\"395\":1}}],[\"pagemaker\",{\"1\":{\"251\":5}}],[\"page\",{\"1\":{\"153\":12,\"156\":1,\"251\":1,\"252\":2}}],[\"password\",{\"1\":{\"52\":2}}],[\"pass\",{\"1\":{\"30\":1,\"36\":2,\"500\":1}}],[\"player2\",{\"1\":{\"376\":7}}],[\"player1\",{\"1\":{\"376\":7}}],[\"player\",{\"1\":{\"376\":6}}],[\"plays\",{\"1\":{\"294\":1}}],[\"plain\",{\"1\":{\"52\":1}}],[\"plantuml\",{\"1\":{\"18\":1}}],[\"plugins\",{\"1\":{\"108\":1}}],[\"pluginmanagement\",{\"1\":{\"22\":1}}],[\"plugin\",{\"0\":{\"64\":1,\"67\":1},\"1\":{\"22\":3,\"64\":1}}],[\"我认为这并无不可\",{\"1\":{\"521\":1}}],[\"我认为这也是初学者实现编译器的一大难点\",{\"1\":{\"492\":1}}],[\"我认为至少占了重要程度的50\",{\"1\":{\"520\":1}}],[\"我认为有几个要点需要强调\",{\"1\":{\"450\":1}}],[\"我知道\",{\"1\":{\"466\":1}}],[\"我仍然认为通过定义\",{\"1\":{\"411\":1}}],[\"我相信绝大多数\",{\"1\":{\"408\":1}}],[\"我是先写程序再总结上面的文法\",{\"1\":{\"464\":1}}],[\"我是抱着满腔热情去上课的\",{\"1\":{\"408\":1}}],[\"我是要增加功能呢\",{\"1\":{\"176\":1}}],[\"我对编译器一直心存敬佩\",{\"1\":{\"408\":1}}],[\"我会说是\",{\"1\":{\"407\":1}}],[\"我会从团队整体出发进行考虑\",{\"1\":{\"293\":1}}],[\"我来负责仲裁\",{\"1\":{\"293\":1}}],[\"我才不用rust呢\",{\"1\":{\"274\":1}}],[\"我得拿到锁才能操作\",{\"1\":{\"112\":1}}],[\"我们才能有所成长吧\",{\"1\":{\"523\":1}}],[\"我们才可以编写出具有高可替换性的类\",{\"1\":{\"175\":1}}],[\"我们其实通过了参数\",{\"1\":{\"508\":1}}],[\"我们没有取负的操作\",{\"1\":{\"506\":1}}],[\"我们没有直接的逻辑取反指令\",{\"1\":{\"504\":1}}],[\"我们主要从它的目标代码入手\",{\"1\":{\"497\":1}}],[\"我们看看下面的伪代码\",{\"1\":{\"487\":1}}],[\"我们实现的\",{\"1\":{\"480\":1}}],[\"我们实现的词法分析器与传统意义上的词法分析器不太相同\",{\"1\":{\"443\":1}}],[\"我们已经为变量\",{\"1\":{\"509\":1}}],[\"我们已经为当前的标识符\",{\"1\":{\"476\":1}}],[\"我们已经知道了什么时候开始解析函数的定义\",{\"1\":{\"476\":1}}],[\"我们把词法分析器的代码一并贴上\",{\"1\":{\"459\":1}}],[\"我们向前看一个标记\",{\"1\":{\"457\":1}}],[\"我们假设词法分析器已经正确地将其中的数字识别成了标记\",{\"1\":{\"456\":1}}],[\"我们对\",{\"1\":{\"456\":1}}],[\"我们下一章见\",{\"1\":{\"450\":1}}],[\"我们直接贴上代码\",{\"1\":{\"447\":1,\"459\":1}}],[\"我们用了专门的一章讲解了\",{\"1\":{\"522\":1}}],[\"我们用了很暴力的手段编写了我们的词法分析器\",{\"1\":{\"521\":1}}],[\"我们用词法分析器将源码转换成标记流\",{\"1\":{\"446\":1}}],[\"我们用类来表示状态\",{\"1\":{\"365\":1}}],[\"我们之前说过\",{\"1\":{\"446\":1}}],[\"我们以异或\",{\"1\":{\"512\":1}}],[\"我们以\",{\"1\":{\"445\":1}}],[\"我们并不关心一个变量具体叫什么名字\",{\"1\":{\"443\":1}}],[\"我们并不会一次性地将所有源码全部转换成标记流\",{\"1\":{\"438\":1}}],[\"我们知道\",{\"1\":{\"440\":1}}],[\"我们同时还用它来处理空白字符\",{\"1\":{\"440\":1}}],[\"我们为\",{\"1\":{\"431\":1}}],[\"我们依旧用上面的例子\",{\"1\":{\"430\":1}}],[\"我们连函数调用都无法实现\",{\"1\":{\"426\":1}}],[\"我们这里的\",{\"1\":{\"422\":1}}],[\"我们这里并不需要了解太多\",{\"1\":{\"419\":1}}],[\"我们的代码是自举的\",{\"1\":{\"515\":1}}],[\"我们的代码里有一些指针的强制转换\",{\"1\":{\"433\":1}}],[\"我们的电脑上已经有了这些函数的实现\",{\"1\":{\"432\":1}}],[\"我们的\",{\"1\":{\"426\":1,\"430\":1}}],[\"我们的编译器支持指针类型\",{\"1\":{\"467\":1}}],[\"我们的编译器并不支持宏定义\",{\"1\":{\"442\":1}}],[\"我们的编译器是以标记流为输入\",{\"1\":{\"437\":1}}],[\"我们的编译器参数是顺序入栈的\",{\"1\":{\"426\":1}}],[\"我们的编译器主要包括\",{\"1\":{\"416\":1}}],[\"我们的虚拟机还是工作良好的\",{\"1\":{\"433\":1}}],[\"我们的虚拟机只有一个寄存器\",{\"1\":{\"422\":1}}],[\"我们的虚拟机中\",{\"1\":{\"420\":1}}],[\"我们的虚拟机并不打算模拟完整的计算机\",{\"1\":{\"419\":1}}],[\"我们要使用变量\",{\"1\":{\"507\":1}}],[\"我们要从整体上讲解如何设计我们的\",{\"1\":{\"414\":1}}],[\"我们要在\",{\"1\":{\"157\":1}}],[\"我们能对编译器的构建有一定的了解\",{\"1\":{\"406\":1}}],[\"我们提倡扩展\",{\"1\":{\"399\":1}}],[\"我们创建了\",{\"1\":{\"398\":1}}],[\"我们来整理一下\",{\"1\":{\"397\":1}}],[\"我们来思考一下\",{\"1\":{\"366\":1}}],[\"我们只关心三个内容\",{\"1\":{\"419\":1}}],[\"我们只需要编写新的访问者\",{\"1\":{\"392\":1}}],[\"我们只要事先在每个方法内部都加上一段\",{\"1\":{\"369\":1}}],[\"我们编写一个表示\",{\"1\":{\"392\":1}}],[\"我们声明了抽象方法\",{\"1\":{\"389\":1}}],[\"我们考虑了两种猜拳的策略\",{\"1\":{\"376\":1}}],[\"我们考虑泛型编程\",{\"1\":{\"58\":1}}],[\"我们暂且不深入学习该方法\",{\"1\":{\"367\":1}}],[\"我们应该如何编程\",{\"1\":{\"366\":1}}],[\"我们应该养成具体问题具体分析的辩证唯物思想\",{\"1\":{\"115\":1}}],[\"我们会遇到许多的挫折\",{\"1\":{\"523\":1}}],[\"我们会先加载它的地址\",{\"1\":{\"503\":1}}],[\"我们会先将该问题分解为多个小问题\",{\"1\":{\"365\":1}}],[\"我们会将\",{\"1\":{\"439\":1}}],[\"我们会将它们继续划分为更小的问题\",{\"1\":{\"365\":1}}],[\"我们经常会使用分而治之的方针\",{\"1\":{\"365\":1}}],[\"我们在第三章的虚拟机中提到过\",{\"1\":{\"480\":1}}],[\"我们在本章的学习过程中已经提到过很多次了\",{\"1\":{\"402\":1}}],[\"我们在理解类的层次时\",{\"1\":{\"389\":1}}],[\"我们在\",{\"1\":{\"338\":1}}],[\"我们还需要初始化虚拟机的栈\",{\"1\":{\"515\":1}}],[\"我们还需要注意下面将要提到的情况\",{\"1\":{\"321\":1}}],[\"我们还可能返回除号\",{\"1\":{\"446\":1}}],[\"我们还要编写进行其他处理的\",{\"1\":{\"398\":1}}],[\"我们还应关注设计模式的演变和新模式的出现\",{\"1\":{\"246\":1}}],[\"我们展示了如何使用观察者模式来管理状态变化\",{\"1\":{\"317\":1}}],[\"我们可能会修改或删除现有的\",{\"1\":{\"500\":1}}],[\"我们可能需要从观察模式转变为通知模式\",{\"1\":{\"324\":1}}],[\"我们可能需要为同一个集合编写多个具体迭代器\",{\"1\":{\"288\":1}}],[\"我们可将扮演\",{\"1\":{\"299\":1}}],[\"我们可以正确调用\",{\"1\":{\"515\":1}}],[\"我们可以很容易地直接将\",{\"1\":{\"457\":1}}],[\"我们可以这样认为\",{\"1\":{\"437\":1}}],[\"我们可以准备两种算法\",{\"1\":{\"380\":1}}],[\"我们可以使用的内存地址为\",{\"1\":{\"419\":1}}],[\"我们可以使用\",{\"1\":{\"367\":1}}],[\"我们可以在不同的应用场景中灵活地控制对对象的访问\",{\"1\":{\"346\":1}}],[\"我们可以在不修改现有类的情况下添加新功能\",{\"1\":{\"231\":1}}],[\"我们可以考虑使用事件总线或消息队列来集中处理通知\",{\"1\":{\"324\":1}}],[\"我们可以考虑将多个对象组成一条职责链\",{\"1\":{\"202\":1}}],[\"我们可以引入一个标志位来跟踪通知状态\",{\"1\":{\"322\":1}}],[\"我们可以为\",{\"1\":{\"288\":1}}],[\"我们可以轻松地遍历\",{\"1\":{\"287\":1}}],[\"我们可以轻松地添加其他具体工厂\",{\"1\":{\"154\":1}}],[\"我们可以更好地管理和操作集合数据\",{\"1\":{\"284\":1}}],[\"我们可以更灵活地管理对象的创建过程\",{\"1\":{\"257\":1}}],[\"我们可以提高代码的可读性\",{\"1\":{\"246\":1}}],[\"我们可以将这些视图注册为观察者\",{\"1\":{\"316\":1}}],[\"我们可以将\",{\"1\":{\"186\":1}}],[\"我们定义了\",{\"1\":{\"338\":1}}],[\"我们定义了几个类和接口来实现迭代器模式\",{\"1\":{\"287\":1}}],[\"我们定义一个用于创建对象的接口\",{\"1\":{\"256\":1}}],[\"我们了解到共享实例可以减少内存使用量\",{\"1\":{\"270\":1}}],[\"我们通常会将共享对象存储在某种集合\",{\"1\":{\"269\":1}}],[\"我们也将构建出一个能用的\",{\"1\":{\"406\":1}}],[\"我们也可以不使用示例程序中的做法\",{\"1\":{\"367\":1}}],[\"我们也可以换种说法\",{\"1\":{\"268\":1}}],[\"我们也要避免过早地进行\",{\"1\":{\"246\":1}}],[\"我们就着手虚拟机的实现\",{\"1\":{\"520\":1}}],[\"我们就来逐一说明\",{\"1\":{\"495\":1}}],[\"我们就将它的类型加上\",{\"1\":{\"467\":1}}],[\"我们就知道是需要解析枚举类型\",{\"1\":{\"467\":1}}],[\"我们就能知道它们是特殊的关键字\",{\"1\":{\"448\":1}}],[\"我们就只需要一个表示系统状态的变量即可\",{\"1\":{\"368\":1}}],[\"我们就需要一个中立的仲裁者站出来说\",{\"1\":{\"293\":1}}],[\"我们就可以实现以不同的颜色显示同一个\",{\"1\":{\"267\":1}}],[\"我们就实现了不修改被装饰的类即可增加功能\",{\"1\":{\"236\":1}}],[\"我们不另外处理它们的原因是\",{\"1\":{\"439\":1}}],[\"我们不得不在\",{\"1\":{\"401\":1}}],[\"我们不应该将它们隐藏在自己脑袋中\",{\"1\":{\"249\":1}}],[\"我们不应死记硬背这些设计模式\",{\"1\":{\"246\":1}}],[\"我们不妨通过类的运算符重载来进一步优化\",{\"1\":{\"58\":1}}],[\"我们完全不需要对被装饰的类做任何修改\",{\"1\":{\"236\":1}}],[\"我们使用装饰器模式来动态地给对象添加职责\",{\"1\":{\"230\":1}}],[\"我们使用了策略模式\",{\"1\":{\"375\":1}}],[\"我们使用了外观模式\",{\"1\":{\"250\":1}}],[\"我们使用了\",{\"1\":{\"204\":1,\"305\":1}}],[\"我们必须先计算优先级高的运算符\",{\"1\":{\"496\":1}}],[\"我们必须时刻关汴这种\",{\"1\":{\"197\":1}}],[\"我们必须要做以下修改\",{\"1\":{\"157\":1}}],[\"我们必须要对所有的具体工厂进行相应的修改才行\",{\"1\":{\"157\":1}}],[\"我们需要类似下面的汇编代码\",{\"1\":{\"509\":1}}],[\"我们需要不断地向右扫描\",{\"1\":{\"508\":1}}],[\"我们需要处理多运算符的优先级问题\",{\"1\":{\"508\":1}}],[\"我们需要在栈上为局部变量预留空间\",{\"1\":{\"480\":1}}],[\"我们需要所有的变量定义出现在所有的语句之前\",{\"1\":{\"480\":1}}],[\"我们需要知道后面参数的类型\",{\"1\":{\"499\":1}}],[\"我们需要知道参数的个数\",{\"1\":{\"477\":1}}],[\"我们需要知道这两个\",{\"1\":{\"443\":1}}],[\"我们需要了解当\",{\"1\":{\"477\":1}}],[\"我们需要得到\",{\"1\":{\"430\":1}}],[\"我们需要条件判断相关的指令\",{\"1\":{\"425\":1}}],[\"我们需要首先在全局添加如下代码\",{\"1\":{\"419\":1}}],[\"我们需要使用多个变量的值的集合来表示系统的状态\",{\"1\":{\"368\":1}}],[\"我们需要使用条件分支语句判断当前的状态\",{\"1\":{\"365\":1}}],[\"我们需要特别小心\",{\"1\":{\"322\":1}}],[\"我们需要确保共享对象在整个程序生命周期内都被引用\",{\"1\":{\"269\":1}}],[\"我们需要根据具体情况选择合适的设计模式\",{\"1\":{\"246\":1}}],[\"我们需要先阅读现有代码\",{\"1\":{\"199\":1}}],[\"我们需要编写一个定义这些操作系统的共同接口\",{\"1\":{\"186\":1}}],[\"我们需要将它存放到前一篇文章中说的\",{\"1\":{\"445\":1}}],[\"我们需要将当前的行号加一\",{\"1\":{\"441\":1}}],[\"我们需要将\",{\"1\":{\"176\":1}}],[\"我们需要证明乘法结果的存在性和唯一性\",{\"1\":{\"87\":1}}],[\"我们需要证明加法结果的存在性和唯一性\",{\"1\":{\"71\":1}}],[\"我们学习了抽象类的作用\",{\"1\":{\"175\":1}}],[\"我们再用多线程试一下同样的逻辑\",{\"1\":{\"114\":1}}],[\"我们将介绍递归下降的语法分析器\",{\"1\":{\"450\":1}}],[\"我们将同时分析单个字符如\",{\"1\":{\"445\":1}}],[\"我们将专门作为一个小节\",{\"1\":{\"420\":1}}],[\"我们将实现其中的eval函数\",{\"1\":{\"416\":1}}],[\"我们将逐个填充每个函数的功能\",{\"1\":{\"416\":1}}],[\"我们将\",{\"1\":{\"367\":1}}],[\"我们将设置时间的处理看作是\",{\"1\":{\"366\":1}}],[\"我们将展示如何使用\",{\"1\":{\"285\":1}}],[\"我们将借助另一个公理系统\",{\"1\":{\"95\":1}}],[\"我们将详细讲解环境配置\",{\"1\":{\"26\":1}}],[\"我们成功地由\",{\"1\":{\"95\":1}}],[\"我们终于可以对自然数乘法的性质进行进一步的探索\",{\"1\":{\"90\":1}}],[\"我们终于可以对自然数加法的性质进行进一步的探索\",{\"1\":{\"74\":1}}],[\"我们预先准备以方便证明\",{\"1\":{\"80\":1}}],[\"我们即可建立如今最常用的算术公理系统\",{\"1\":{\"68\":1}}],[\"我的博客构建库\",{\"1\":{\"18\":1}}],[\"我抽奖一发就中了大奖\",{\"1\":{\"3\":1}}],[\"zero\",{\"1\":{\"425\":1}}],[\"zeroelse\",{\"1\":{\"425\":1}}],[\"zhihu\",{\"1\":{\"48\":1,\"51\":1}}],[\"zhuanlan\",{\"1\":{\"48\":1,\"51\":1}}],[\"zip\",{\"1\":{\"22\":1}}],[\"z\",{\"1\":{\"18\":1,\"57\":1,\"58\":1,\"443\":4}}],[\"glo\",{\"1\":{\"439\":1,\"467\":1,\"468\":1,\"500\":1,\"508\":1}}],[\"global\",{\"0\":{\"467\":1},\"1\":{\"112\":2,\"113\":1,\"114\":4,\"463\":1,\"464\":1,\"466\":3,\"467\":6,\"480\":1,\"500\":1}}],[\"gt\",{\"1\":{\"421\":1,\"431\":1,\"439\":1,\"447\":1,\"508\":1}}],[\"guu\",{\"1\":{\"376\":2}}],[\"gui\",{\"1\":{\"316\":1}}],[\"guide\",{\"1\":{\"39\":1,\"118\":1}}],[\"group\",{\"1\":{\"294\":1,\"295\":3}}],[\"group`\",{\"1\":{\"294\":1}}],[\"groups\",{\"1\":{\"294\":1}}],[\"graph\",{\"1\":{\"317\":4}}],[\"graphobserver\",{\"1\":{\"317\":5,\"318\":20,\"321\":1}}],[\"grape\",{\"1\":{\"305\":1,\"306\":12}}],[\"grammar\",{\"1\":{\"125\":1}}],[\"gradlepluginportal\",{\"1\":{\"22\":1}}],[\"gradle\",{\"1\":{\"22\":6}}],[\"gcc\",{\"1\":{\"433\":2,\"515\":1}}],[\"gc\",{\"1\":{\"269\":1}}],[\"g\",{\"1\":{\"264\":1}}],[\"gmw\",{\"1\":{\"153\":6}}],[\"git\",{\"1\":{\"416\":1,\"434\":1,\"449\":1,\"470\":1,\"481\":1,\"491\":1,\"515\":1}}],[\"github\",{\"0\":{\"43\":1,\"48\":1,\"49\":1},\"1\":{\"18\":1,\"44\":8,\"51\":1,\"126\":2,\"409\":1,\"416\":2,\"434\":2,\"449\":2,\"470\":2,\"481\":2,\"491\":2,\"515\":2}}],[\"gil\",{\"1\":{\"113\":1}}],[\"gather\",{\"1\":{\"113\":1,\"114\":3}}],[\"games\",{\"1\":{\"376\":1,\"377\":8}}],[\"gamecount++\",{\"1\":{\"376\":3}}],[\"gamecount\",{\"1\":{\"376\":2}}],[\"gamer\",{\"1\":{\"305\":17}}],[\"game\",{\"0\":{\"64\":1},\"1\":{\"64\":1,\"225\":1,\"226\":1,\"394\":1,\"395\":1}}],[\"ge\",{\"1\":{\"421\":1,\"431\":1,\"439\":1,\"447\":1,\"508\":1}}],[\"generatedid++\",{\"1\":{\"353\":1,\"357\":1}}],[\"generatedid\",{\"1\":{\"353\":2,\"357\":2}}],[\"generator\",{\"1\":{\"317\":8,\"411\":1}}],[\"genesis\",{\"1\":{\"18\":2}}],[\"gen\",{\"1\":{\"124\":2}}],[\"getline\",{\"1\":{\"459\":1}}],[\"getlength\",{\"1\":{\"286\":2}}],[\"getsum\",{\"1\":{\"376\":2}}],[\"getsize\",{\"1\":{\"222\":2,\"223\":2,\"224\":1,\"394\":5}}],[\"gethand\",{\"1\":{\"376\":3}}],[\"gethtml\",{\"1\":{\"251\":2}}],[\"getprintername\",{\"1\":{\"338\":5}}],[\"getproperties\",{\"1\":{\"251\":2}}],[\"getproduct\",{\"1\":{\"153\":2}}],[\"getfruits\",{\"1\":{\"305\":1}}],[\"getfruit\",{\"1\":{\"305\":2}}],[\"getmoney\",{\"1\":{\"305\":7}}],[\"getbookat\",{\"1\":{\"286\":2}}],[\"getbigchar\",{\"1\":{\"264\":2}}],[\"getcurrentnumber\",{\"1\":{\"279\":2}}],[\"getcurrenttoken\",{\"1\":{\"279\":5}}],[\"getcolumns\",{\"1\":{\"232\":8,\"235\":1,\"236\":2}}],[\"getinstance\",{\"1\":{\"264\":2,\"353\":3,\"356\":1,\"357\":2,\"362\":5}}],[\"getowners\",{\"1\":{\"258\":1}}],[\"getowner\",{\"1\":{\"258\":2}}],[\"getrowtext\",{\"1\":{\"232\":7,\"235\":1}}],[\"getrows\",{\"1\":{\"232\":8,\"235\":1,\"236\":2}}],[\"getresult\",{\"1\":{\"193\":4}}],[\"getname\",{\"1\":{\"222\":1,\"223\":2,\"224\":1,\"286\":2,\"394\":5}}],[\"getnumber\",{\"1\":{\"204\":4,\"317\":5}}],[\"get\",{\"1\":{\"67\":1,\"113\":1,\"114\":3,\"264\":1,\"416\":1,\"466\":1,\"503\":2}}],[\"gpu\",{\"1\":{\"66\":3}}],[\"ghcr\",{\"0\":{\"44\":1},\"1\":{\"44\":1,\"45\":1,\"46\":2}}],[\"got\",{\"1\":{\"459\":1}}],[\"google\",{\"1\":{\"22\":4,\"153\":3}}],[\"go\",{\"1\":{\"6\":1,\"279\":10,\"280\":14}}],[\"网站\",{\"1\":{\"18\":1}}],[\"网络i\",{\"1\":{\"16\":1}}],[\"资源进行加速\",{\"1\":{\"66\":1}}],[\"资源\",{\"0\":{\"18\":1}}],[\"记得事先写一些用于输出汇编代码的函数\",{\"1\":{\"523\":1}}],[\"记得我们说过词法分析器也是某种意义上的编译器\",{\"1\":{\"440\":1}}],[\"记得给我的仓库点star欧~\",{\"1\":{\"16\":1}}],[\"记录\",{\"0\":{\"109\":1}}],[\"记\",{\"1\":{\"72\":1,\"73\":1,\"88\":1,\"89\":1}}],[\"记起来再补充\",{\"1\":{\"13\":1}}],[\"协程也不是虚空的\",{\"1\":{\"115\":1}}],[\"协程加锁执行后结果\",{\"1\":{\"114\":1}}],[\"协程在工作状态中\",{\"1\":{\"114\":1}}],[\"协程运行过程中\",{\"1\":{\"114\":1}}],[\"协程又可以切回来\",{\"1\":{\"114\":1}}],[\"协程操作共享变量不需要加锁的结论开始在坊间流传\",{\"1\":{\"114\":1}}],[\"协程本身就是单线程的\",{\"1\":{\"113\":1}}],[\"协程本身可以做成用户态\",{\"1\":{\"113\":1}}],[\"协程是否需要加锁\",{\"0\":{\"115\":1}}],[\"协程是用户态\",{\"1\":{\"113\":1}}],[\"协程是主动让出使用权\",{\"1\":{\"113\":1}}],[\"协程保证了编写过程中的思维连贯性\",{\"1\":{\"113\":1}}],[\"协程与线程向来焦孟不离\",{\"1\":{\"111\":1}}],[\"协程安全\",{\"0\":{\"111\":1,\"114\":1}}],[\"协程\",{\"0\":{\"111\":1,\"113\":1,\"116\":1},\"1\":{\"16\":1}}],[\"多个迭代器\",{\"0\":{\"288\":1}}],[\"多个线程同时改同一个变量\",{\"1\":{\"112\":1}}],[\"多个线程之前也并不是完全独立的\",{\"1\":{\"112\":1}}],[\"多态\",{\"1\":{\"274\":1}}],[\"多了把锁\",{\"1\":{\"112\":1}}],[\"多线程下\",{\"0\":{\"356\":1}}],[\"多线程在未加锁的情况下\",{\"1\":{\"114\":1}}],[\"多线程在python中只能交替执行\",{\"1\":{\"112\":1}}],[\"多线程逻辑执行结果\",{\"1\":{\"114\":1}}],[\"多线程\",{\"1\":{\"16\":1}}],[\"多数情况转弯的方向都是对的\",{\"1\":{\"12\":1}}],[\"且当\",{\"1\":{\"515\":1}}],[\"且根据不同的类型移动的位移不同\",{\"1\":{\"512\":1}}],[\"且多数情况下如此\",{\"1\":{\"439\":1}}],[\"且不需要判断类型\",{\"1\":{\"422\":1}}],[\"且不了解\",{\"1\":{\"16\":1}}],[\"且程序行为不变\",{\"1\":{\"148\":1}}],[\"且需要导出为pptx推荐\",{\"1\":{\"118\":1}}],[\"且乘法运算的结果存在且唯一之后\",{\"1\":{\"90\":1}}],[\"且\",{\"1\":{\"79\":1,\"82\":1,\"83\":1}}],[\"且加法运算的结果存在且唯一之后\",{\"1\":{\"74\":1}}],[\"且满足两个条件\",{\"1\":{\"69\":1}}],[\"且局部多为凸多边形\",{\"1\":{\"12\":1}}],[\"几次换车其中一次车被踩烂了\",{\"1\":{\"16\":1}}],[\"货物\",{\"1\":{\"15\":1}}],[\"本节中我们专注语法分析器部分的实现\",{\"1\":{\"459\":1}}],[\"本节的代码可以在\",{\"1\":{\"416\":1}}],[\"本例中是\",{\"1\":{\"456\":1}}],[\"本质上这个指令并不是必需的\",{\"1\":{\"429\":1}}],[\"本质上是因为我们的\",{\"1\":{\"428\":1}}],[\"本质的\",{\"1\":{\"268\":1}}],[\"本章有两个难点\",{\"1\":{\"516\":1}}],[\"本章讲解了如何将语句编译成汇编代码\",{\"1\":{\"492\":1}}],[\"本章讲解函数定义相关的内容\",{\"1\":{\"474\":1}}],[\"本章的内容应该不难\",{\"1\":{\"471\":1}}],[\"本章的代码依旧无法运行\",{\"1\":{\"481\":1,\"491\":1}}],[\"本章的代码还无法正常运行\",{\"1\":{\"470\":1}}],[\"本章的代码可以在\",{\"1\":{\"434\":1,\"449\":1,\"470\":1,\"481\":1,\"491\":1,\"515\":1}}],[\"本章要讲解的就是上节文法中的\",{\"1\":{\"465\":1}}],[\"本章我们进行了最后的解析\",{\"1\":{\"516\":1}}],[\"本章我们将讲解递归下降的方法\",{\"1\":{\"453\":1}}],[\"本章我们为我们的编译器构建了词法分析器\",{\"1\":{\"450\":1}}],[\"本章我们要讲解如何构建词法分析器\",{\"1\":{\"435\":1}}],[\"本章我们要构建一台虚拟的电脑\",{\"1\":{\"417\":1}}],[\"本章中我们发一发牢骚\",{\"1\":{\"519\":1}}],[\"本章中我们用了不多的代码完成了函数定义的解析\",{\"1\":{\"482\":1}}],[\"本章中我们用\",{\"1\":{\"463\":1}}],[\"本章中我们介绍了递归下降的方法\",{\"1\":{\"460\":1}}],[\"本章中我们回顾了计算机的内部运行原理\",{\"1\":{\"434\":1}}],[\"本章中要学习的\",{\"1\":{\"176\":1}}],[\"本项目中的代码逻辑绝大多数取自\",{\"1\":{\"409\":1}}],[\"本项目不考虑介么多\",{\"1\":{\"8\":1}}],[\"本篇是一些闲聊\",{\"1\":{\"406\":1}}],[\"本人\",{\"1\":{\"337\":2}}],[\"本实例是一个控制小车的脚本语言解释器demo\",{\"1\":{\"279\":1}}],[\"本专栏源码大部分参考自参考资料\",{\"1\":{\"274\":1}}],[\"本来就没有两全其美的解决方案\",{\"1\":{\"114\":1}}],[\"本来就只能一个人打电话\",{\"1\":{\"112\":1}}],[\"本来想让机械臂识别\",{\"1\":{\"15\":1}}],[\"本以为\",{\"1\":{\"66\":1}}],[\"本文转自\",{\"1\":{\"414\":1,\"417\":1,\"435\":1,\"453\":1,\"463\":1,\"474\":1,\"485\":1,\"495\":1,\"519\":1}}],[\"本文转载自\",{\"1\":{\"406\":1}}],[\"本文是\",{\"1\":{\"26\":1}}],[\"本文将介绍如何使用\",{\"1\":{\"26\":1}}],[\"本地调试工具\",{\"1\":{\"23\":1}}],[\"本次智能车实验不是很愉快\",{\"1\":{\"16\":1}}],[\"有了bnf方法后\",{\"1\":{\"459\":1}}],[\"有用\",{\"1\":{\"432\":1}}],[\"有点类似于\",{\"1\":{\"422\":1}}],[\"有一个或多个标记是以同样的字符开头的\",{\"1\":{\"446\":1}}],[\"有一次在\",{\"1\":{\"409\":1}}],[\"有一些启发式的smell\",{\"1\":{\"12\":1}}],[\"有时\",{\"1\":{\"367\":1}}],[\"有必要划分代理人和本人吗\",{\"0\":{\"342\":1}}],[\"有些工作无法自己亲自完成\",{\"1\":{\"337\":1}}],[\"有些情况下这是坏事\",{\"1\":{\"267\":1}}],[\"有些情况下这是好事\",{\"1\":{\"267\":1}}],[\"有些事情是可以在设计阶段决定的\",{\"1\":{\"198\":1}}],[\"有些事情是强求不来的\",{\"1\":{\"3\":1}}],[\"有两种方式实现\",{\"1\":{\"166\":1}}],[\"有什么区别呢\",{\"1\":{\"112\":1}}],[\"有任意两个自然数\",{\"1\":{\"84\":1}}],[\"有\",{\"1\":{\"72\":4,\"73\":4,\"75\":3,\"76\":2,\"77\":1,\"82\":2,\"83\":2,\"85\":1,\"88\":3,\"89\":3,\"91\":3,\"92\":1,\"93\":2,\"94\":3,\"96\":1,\"97\":1}}],[\"有大量的题目要求对一些数字取模\",{\"1\":{\"53\":1}}],[\"但也只有真正静下心来去克服它\",{\"1\":{\"523\":1}}],[\"但你依旧可以学习相关的知识\",{\"1\":{\"521\":1}}],[\"但这当中还有一个问题\",{\"1\":{\"512\":1}}],[\"但对理解计算机的原理有很大帮助\",{\"1\":{\"492\":1}}],[\"但没有关系\",{\"1\":{\"466\":1}}],[\"但真正看起来还是很烦\",{\"1\":{\"464\":1}}],[\"但由于符号表中已经有了相关的信息\",{\"1\":{\"448\":1}}],[\"但由子类决定要实例化的类是哪一个\",{\"1\":{\"256\":1}}],[\"但还有一个问题需要考虑\",{\"1\":{\"448\":1}}],[\"但还有一个问题是如何在子函数中获得传入的参数\",{\"1\":{\"430\":1}}],[\"但主要逻辑就是向前看一个字符来确定真正的标记\",{\"1\":{\"447\":1}}],[\"但仍支持\",{\"1\":{\"445\":1}}],[\"但有一点不同\",{\"1\":{\"441\":1}}],[\"但又枯燥且容易出错\",{\"1\":{\"438\":1}}],[\"但从结果可以看出\",{\"1\":{\"433\":1}}],[\"但就如上面的说\",{\"1\":{\"430\":1}}],[\"但最为重要的是\",{\"1\":{\"422\":1}}],[\"但更为简单\",{\"1\":{\"421\":1}}],[\"但更多时候我们都是在现有代码的基础上进行增加和修改\",{\"1\":{\"199\":1}}],[\"但我们一直用\",{\"1\":{\"501\":1}}],[\"但我们不确定数字\",{\"1\":{\"496\":1}}],[\"但我们上面的四则运算的文法就是左递归的\",{\"1\":{\"458\":1}}],[\"但我们的虚拟机中\",{\"1\":{\"434\":1}}],[\"但我们的虚拟机中只使用\",{\"1\":{\"420\":1}}],[\"但我们的\",{\"1\":{\"426\":1}}],[\"但我们讲解的顺序并不依据它\",{\"1\":{\"421\":1}}],[\"但我们还没有写任何编译相关的代码\",{\"1\":{\"420\":1}}],[\"但我不会评价大家的工作细节\",{\"1\":{\"293\":1}}],[\"但理解起来应该作为无符号的整型\",{\"1\":{\"419\":1}}],[\"但实际编译项目时\",{\"1\":{\"520\":1}}],[\"但实际上由于我们还将在符号表中加入关键字如\",{\"1\":{\"443\":1}}],[\"但实际上我们构建的是\",{\"1\":{\"414\":1}}],[\"但实际情况并非如此\",{\"1\":{\"422\":1}}],[\"但实际实现上较为复杂且与编译无关\",{\"1\":{\"419\":1}}],[\"但需要了解的是\",{\"1\":{\"419\":1}}],[\"但确为自己重写\",{\"1\":{\"409\":1}}],[\"但随着计算机性能的提升\",{\"1\":{\"407\":1}}],[\"但如果你查看了\",{\"1\":{\"471\":1}}],[\"但如果有兴趣的话\",{\"1\":{\"470\":1}}],[\"但如果能掌握它\",{\"1\":{\"460\":1}}],[\"但如果需要修改现有代码\",{\"1\":{\"399\":1}}],[\"但如有条件还请支持正版\",{\"1\":{\"124\":1}}],[\"但可以有效地管理内存\",{\"1\":{\"269\":1}}],[\"但可能会导致内存泄漏\",{\"1\":{\"269\":1}}],[\"但它又与编译器没有太大的联系\",{\"1\":{\"432\":1}}],[\"但它却难以应对\",{\"1\":{\"401\":1}}],[\"但它们的目的和实现方式有所不同\",{\"1\":{\"343\":1}}],[\"但它们的接口并不符合当前系统的需求\",{\"1\":{\"163\":1}}],[\"但它需要我们在理解其核心思想的基础上\",{\"1\":{\"246\":1}}],[\"但程序暂时无法直接决定由哪个对象负责处理时\",{\"1\":{\"202\":1}}],[\"但不知道构建的具体步骤\",{\"1\":{\"197\":1}}],[\"但不知道对象的具体表示\",{\"1\":{\"197\":1}}],[\"但委托是弱关联关系\",{\"1\":{\"187\":1}}],[\"但切换过程是争抢的\",{\"1\":{\"114\":1}}],[\"但归根结底\",{\"1\":{\"113\":1}}],[\"但其中用到的原理还是需要仔细推敲的\",{\"1\":{\"516\":1}}],[\"但其中并没有任何汇编代码\",{\"1\":{\"449\":1}}],[\"但其实内容不多\",{\"1\":{\"416\":1}}],[\"但其实\",{\"1\":{\"112\":1}}],[\"但其静态计算图机制在开发过程中略显繁琐\",{\"1\":{\"66\":1}}],[\"但事实上是\",{\"1\":{\"111\":1}}],[\"但\",{\"1\":{\"95\":1,\"299\":1}}],[\"但是两节课后我就放弃了\",{\"1\":{\"408\":1}}],[\"但是要达到这个目的是有条件的\",{\"1\":{\"402\":1}}],[\"但是好在我们绝对不会忘记实现这个方法\",{\"1\":{\"369\":1}}],[\"但是当状态非常多的时候\",{\"1\":{\"365\":1}}],[\"但是需要考虑到的是\",{\"1\":{\"298\":1}}],[\"但是没有将应当集中的处理集中起来\",{\"1\":{\"297\":1}}],[\"但是在本章中的示例程序中\",{\"1\":{\"297\":1}}],[\"但是意见难以统一\",{\"1\":{\"293\":1}}],[\"但是越装饰\",{\"1\":{\"236\":1}}],[\"但是它们的使用目的不同\",{\"1\":{\"235\":1}}],[\"但是接口\",{\"1\":{\"235\":1}}],[\"但是有时候也确实存在需要\",{\"1\":{\"202\":1}}],[\"但是不能改变父类原有的功能\",{\"1\":{\"132\":1}}],[\"但是给一个垂死的人注射吗啡\",{\"1\":{\"115\":1}}],[\"但是我们也付出了相应的代价\",{\"1\":{\"114\":1}}],[\"但是可以保证最终一致性呢\",{\"1\":{\"114\":1}}],[\"但是所有协程执行完毕后\",{\"1\":{\"114\":1}}],[\"但是线程时系统调度\",{\"1\":{\"112\":1}}],[\"但是python受限于gil全局解释器锁\",{\"1\":{\"112\":1}}],[\"但是模数个数少的时候可以缩写\",{\"1\":{\"58\":1}}],[\"但是\",{\"1\":{\"57\":1,\"175\":1,\"366\":1,\"367\":1,\"369\":1,\"398\":1,\"399\":1,\"432\":1}}],[\"但是这种方法有着严重的缺陷\",{\"1\":{\"56\":1}}],[\"但是小车不好运货\",{\"1\":{\"15\":1}}],[\"但是写起来没那么舒服了\",{\"1\":{\"6\":1}}],[\"但效果不理想\",{\"1\":{\"12\":1}}],[\"后缀形式\",{\"1\":{\"513\":1}}],[\"后面我们会看到\",{\"1\":{\"500\":1}}],[\"后面的文章中\",{\"1\":{\"416\":1}}],[\"后来集成的\",{\"1\":{\"119\":1}}],[\"后者为了能恢复现场会在切换线程时保存相当多的状态\",{\"1\":{\"113\":1}}],[\"后\",{\"1\":{\"108\":1,\"236\":1}}],[\"后端通过shell命令即可\",{\"1\":{\"51\":1}}],[\"后右大幅度转弯\",{\"1\":{\"12\":1}}],[\"后续又采用go重构了一遍\",{\"1\":{\"6\":1}}],[\"便于更快的回到正确的姿势\",{\"1\":{\"11\":1}}],[\"耗费时间\",{\"1\":{\"11\":1}}],[\"姿势\",{\"1\":{\"11\":1}}],[\"不知道你是否有同感\",{\"1\":{\"520\":1}}],[\"不指定的话一般认为是第一个出现的非终结符\",{\"1\":{\"456\":1}}],[\"不断地对非终结符进行分解\",{\"1\":{\"454\":1}}],[\"不识别\",{\"1\":{\"440\":1}}],[\"不只是\",{\"1\":{\"366\":1}}],[\"不能用一般的方法解决时\",{\"1\":{\"365\":1}}],[\"不能因为方法的调用顺序发生改变而产生问题\",{\"1\":{\"321\":1}}],[\"不仅要考虑函数的地址\",{\"1\":{\"426\":1}}],[\"不仅会增加代码的复杂性\",{\"1\":{\"297\":1}}],[\"不仅如此\",{\"1\":{\"293\":1}}],[\"不同类型的集合可以使用相同的遍历方式\",{\"1\":{\"284\":1}}],[\"不同的只是赋值的信息\",{\"1\":{\"448\":1}}],[\"不同的表示\",{\"1\":{\"192\":1}}],[\"不同的自然数后继不同\",{\"1\":{\"69\":1}}],[\"不论在什么情况下都不会改变的信息\",{\"1\":{\"268\":1}}],[\"不管怎样\",{\"1\":{\"267\":1}}],[\"不管是香草味\",{\"1\":{\"238\":1}}],[\"不需要修改现有代码\",{\"1\":{\"257\":1}}],[\"不过据说c\",{\"1\":{\"411\":1}}],[\"不过这样做的话\",{\"1\":{\"367\":1}}],[\"不过这并不是什么问题\",{\"1\":{\"297\":1}}],[\"不过却需要我们特别注意\",{\"1\":{\"366\":1}}],[\"不过\",{\"1\":{\"199\":1,\"235\":1,\"321\":1,\"367\":1,\"370\":1,\"411\":1}}],[\"不过我认为报用就是了\",{\"1\":{\"16\":1}}],[\"不必对\",{\"1\":{\"186\":1}}],[\"不要让被共享的实例被垃圾回收器回收了\",{\"0\":{\"269\":1}}],[\"不要使用类继承\",{\"1\":{\"145\":1}}],[\"不要找不到了或者被人踢坏了\",{\"1\":{\"10\":1}}],[\"不应当在\",{\"1\":{\"268\":1}}],[\"不应当共享的信息被称作\",{\"1\":{\"268\":1}}],[\"不应强迫用户依赖他们不使用的接口\",{\"1\":{\"141\":1}}],[\"不应引入违反父类预期的新行为\",{\"1\":{\"133\":1}}],[\"不符合单一职责原则的类\",{\"1\":{\"140\":1}}],[\"不会出现强制转换后的问题\",{\"1\":{\"433\":1}}],[\"不会存在自相矛盾的状态\",{\"1\":{\"368\":1}}],[\"不会自相矛盾\",{\"0\":{\"368\":1}}],[\"不会影响其他功能\",{\"1\":{\"130\":1}}],[\"不会触发ondidclosetextdocument事件\",{\"1\":{\"67\":1}}],[\"不用外部工具\",{\"1\":{\"409\":1}}],[\"不用改变框架代码\",{\"1\":{\"237\":1}}],[\"不用类也能封装数据和方法\",{\"1\":{\"120\":1}}],[\"不用操心运算时忘记取模\",{\"1\":{\"58\":1}}],[\"不支持\",{\"1\":{\"446\":1}}],[\"不支持动画\",{\"1\":{\"119\":1}}],[\"不支持导出pptx\",{\"1\":{\"118\":1}}],[\"不易写出错的代码\",{\"1\":{\"113\":1}}],[\"不易检验\",{\"1\":{\"56\":1,\"57\":1}}],[\"不加锁的话\",{\"1\":{\"112\":1}}],[\"不妨试试这些自动生成工具\",{\"1\":{\"521\":1}}],[\"不妨记作\",{\"1\":{\"94\":1}}],[\"不妨设\",{\"1\":{\"94\":1}}],[\"不是任何自然数的后继\",{\"1\":{\"69\":1}}],[\"不再支持\",{\"1\":{\"66\":1}}],[\"不推荐\",{\"1\":{\"61\":1}}],[\"不推荐运用这种方法\",{\"1\":{\"56\":1}}],[\"不方便输出结果\",{\"1\":{\"54\":1}}],[\"不许用rust\",{\"1\":{\"6\":1}}],[\"xx\",{\"1\":{\"514\":1}}],[\"xxx\",{\"1\":{\"467\":1,\"486\":1}}],[\"xxxstate\",{\"1\":{\"369\":1}}],[\"xzp740813\",{\"1\":{\"495\":1}}],[\"xc\",{\"1\":{\"433\":2,\"515\":5}}],[\"xor\",{\"1\":{\"421\":1,\"431\":1,\"439\":1,\"447\":1,\"505\":2,\"508\":1,\"512\":4}}],[\"x86\",{\"1\":{\"421\":1,\"422\":2,\"423\":1,\"426\":1,\"434\":1}}],[\"x<p\",{\"1\":{\"58\":1}}],[\"x+y+z\",{\"1\":{\"58\":1}}],[\"x+y\",{\"1\":{\"56\":1}}],[\"x\",{\"1\":{\"10\":1,\"30\":1,\"57\":1,\"58\":2,\"211\":8,\"444\":2,\"467\":1,\"496\":3,\"506\":2}}],[\"0xffff\",{\"1\":{\"505\":1}}],[\"0x123\",{\"1\":{\"444\":1}}],[\"017\",{\"1\":{\"444\":1}}],[\"00\",{\"1\":{\"363\":24}}],[\"00`\",{\"1\":{\"362\":2}}],[\"0<=x\",{\"1\":{\"58\":1}}],[\"0\",{\"0\":{\"406\":1},\"1\":{\"10\":1,\"66\":1,\"112\":1,\"113\":1,\"114\":17,\"179\":1,\"183\":1,\"204\":1,\"205\":1,\"211\":1,\"212\":2,\"222\":1,\"226\":3,\"232\":4,\"264\":1,\"279\":2,\"286\":2,\"305\":2,\"317\":3,\"318\":2,\"338\":1,\"353\":1,\"357\":1,\"362\":1,\"376\":14,\"386\":2,\"394\":2,\"395\":3,\"406\":2,\"414\":1,\"416\":7,\"417\":1,\"419\":3,\"420\":2,\"422\":1,\"432\":1,\"433\":2,\"435\":1,\"442\":1,\"443\":1,\"444\":11,\"445\":1,\"446\":1,\"453\":1,\"459\":8,\"463\":1,\"466\":1,\"468\":1,\"474\":1,\"479\":1,\"485\":1,\"495\":1,\"498\":2,\"500\":2,\"504\":4,\"506\":1,\"519\":1}}],[\"80\",{\"1\":{\"30\":2,\"31\":2,\"36\":2,\"286\":1,\"287\":1}}],[\"8\",{\"0\":{\"495\":1},\"1\":{\"10\":1,\"22\":1,\"30\":4,\"65\":1,\"112\":1,\"113\":1,\"114\":6,\"212\":2,\"264\":1,\"406\":1,\"414\":1,\"417\":2,\"435\":2,\"444\":1,\"453\":1,\"463\":1,\"474\":1,\"485\":1,\"495\":2,\"519\":1}}],[\"因而灵活性较差\",{\"1\":{\"411\":1}}],[\"因为已经有许多自动生成的工具支持它们\",{\"1\":{\"522\":1}}],[\"因为只有一个参数\",{\"1\":{\"496\":1}}],[\"因为汇编代码是顺序排列的\",{\"1\":{\"487\":1,\"496\":1}}],[\"因为汇编语言就是\",{\"1\":{\"434\":1}}],[\"因为这决定了我们需要从解析中获取什么样的信息\",{\"1\":{\"482\":1}}],[\"因为这决定了在解析时我们需要哪些相关的信息\",{\"1\":{\"477\":1}}],[\"因为这样实现起来就会变得复杂\",{\"1\":{\"426\":1}}],[\"因为还有许多功能没有实现\",{\"1\":{\"470\":1}}],[\"因为它们可以用\",{\"1\":{\"455\":1}}],[\"因为它会尝试运行我们上一章创建的虚拟机\",{\"1\":{\"449\":1}}],[\"因为它可以保证所有的线程都可以被分到时间片不被垃圾代码所拖累\",{\"1\":{\"112\":1}}],[\"因为有特殊的含义\",{\"1\":{\"448\":1}}],[\"因为输入的字符串比较难处理\",{\"1\":{\"437\":1}}],[\"因为像\",{\"1\":{\"431\":1}}],[\"因为我们不在乎出栈的值\",{\"1\":{\"500\":1}}],[\"因为我们需要先对它们进行解析\",{\"1\":{\"497\":1}}],[\"因为我们会在代码段\",{\"1\":{\"419\":1}}],[\"因为我们的编译器并不支持初始化变量\",{\"1\":{\"419\":1}}],[\"因为不关心其中的真正数值\",{\"1\":{\"419\":1}}],[\"因为好多理论根本用不上\",{\"1\":{\"408\":1}}],[\"因为具体的处理被交给\",{\"1\":{\"400\":1}}],[\"因为状态迁移的部分正是与其他\",{\"1\":{\"369\":1}}],[\"因为即使\",{\"1\":{\"297\":1}}],[\"因为共享对象永远不会被回收\",{\"1\":{\"269\":1}}],[\"因为自己难以确定究竟应该在类的哪一个层次结构中去增加子类\",{\"1\":{\"176\":1}}],[\"因为协程是用户态\",{\"1\":{\"114\":1}}],[\"因为线程是系统态切换\",{\"1\":{\"114\":1}}],[\"因为想要创新学分\",{\"1\":{\"4\":1}}],[\"因此对应的源码如下\",{\"1\":{\"512\":1}}],[\"因此对于需要讲解的运算符\",{\"1\":{\"497\":1}}],[\"因此要有特殊的处理\",{\"1\":{\"512\":1}}],[\"因此将它们放在一起处理\",{\"1\":{\"500\":1}}],[\"因此得到结果\",{\"1\":{\"496\":1}}],[\"因此只凭当前的字符我们并无法确定具体应该解释成哪一个标记\",{\"1\":{\"446\":1}}],[\"因此只要调试该方法就能很容易地找出\",{\"1\":{\"297\":1}}],[\"因此在实现中我们将它作为\",{\"1\":{\"440\":1}}],[\"因此在\",{\"1\":{\"433\":1}}],[\"因此在我们的编译器\",{\"1\":{\"432\":1}}],[\"因此编译编译器时\",{\"1\":{\"432\":1}}],[\"因此计算结束后\",{\"1\":{\"431\":1}}],[\"因此实际中我们将\",{\"1\":{\"426\":1}}],[\"因此我们要做的就是生成类似的汇编代码\",{\"1\":{\"514\":1}}],[\"因此我们要消除左递归\",{\"1\":{\"458\":1}}],[\"因此我们判断它是否与数字\",{\"1\":{\"504\":1}}],[\"因此我们删除相应的指令\",{\"1\":{\"503\":1}}],[\"因此我们可以利用这一点\",{\"1\":{\"434\":1}}],[\"因此我们继续实现新的指令\",{\"1\":{\"432\":1}}],[\"因此我们采用的方法是增加指令集\",{\"1\":{\"426\":1}}],[\"因此我们将\",{\"1\":{\"422\":1}}],[\"因此我们也不需要未初始化数据段\",{\"1\":{\"419\":1}}],[\"因此先不处理\",{\"1\":{\"420\":1}}],[\"因此简单起见\",{\"1\":{\"419\":1}}],[\"因此完全不用修改\",{\"1\":{\"400\":1}}],[\"因此这两个\",{\"1\":{\"370\":1}}],[\"因此需要在性能和功能之间找到一个平衡点\",{\"1\":{\"309\":1}}],[\"因此颜色信息也被共享了\",{\"1\":{\"267\":1}}],[\"因此一个进程可以容纳数量相当可观的协程任务\",{\"1\":{\"113\":1}}],[\"因此假设不成立\",{\"1\":{\"97\":1}}],[\"因此\",{\"1\":{\"56\":1,\"82\":2,\"84\":2,\"85\":1,\"96\":1,\"176\":1,\"237\":1,\"238\":1,\"267\":1,\"268\":3,\"270\":1,\"297\":1,\"299\":1,\"368\":1,\"389\":1,\"399\":1,\"477\":2}}],[\"因此挑选一辆\",{\"1\":{\"10\":1}}],[\"因此无奈之下只能选取一个固定的速度来测试\",{\"1\":{\"10\":1}}],[\"了解自动生成词法分析器的原理\",{\"1\":{\"521\":1}}],[\"了解了协程如何主动切换\",{\"1\":{\"114\":1}}],[\"了\",{\"1\":{\"10\":1,\"379\":1,\"446\":1}}],[\"偏航\",{\"1\":{\"10\":1}}],[\"为例\",{\"1\":{\"512\":1}}],[\"为例介绍几种写法\",{\"1\":{\"55\":1}}],[\"为零或不为零情况下的跳转\",{\"1\":{\"425\":1}}],[\"为此\",{\"1\":{\"402\":1}}],[\"为了实际将这个值保存起来\",{\"1\":{\"509\":1}}],[\"为了实现\",{\"1\":{\"425\":1}}],[\"为了防止因为顺序排列而执行了\",{\"1\":{\"487\":1}}],[\"为了在程序中体现这一点\",{\"1\":{\"338\":1}}],[\"为了让\",{\"1\":{\"338\":1}}],[\"为了解决这个问题\",{\"1\":{\"322\":1,\"356\":1}}],[\"为了避免这种情况\",{\"1\":{\"269\":1}}],[\"为了对比\",{\"1\":{\"114\":1}}],[\"为什么选择递归下降\",{\"0\":{\"457\":1},\"1\":{\"453\":1}}],[\"为什么不能直接使用\",{\"1\":{\"426\":1}}],[\"为什么\",{\"1\":{\"422\":1}}],[\"为什么使用代理模式\",{\"0\":{\"337\":1}}],[\"为什么使用观察者模式\",{\"0\":{\"316\":1}}],[\"为什么使用\",{\"0\":{\"263\":1,\"304\":1,\"361\":1,\"393\":1}}],[\"为什么使用外观模式\",{\"1\":{\"249\":1}}],[\"为什么使用装饰器模式\",{\"0\":{\"231\":1}}],[\"为什么使用此模式\",{\"0\":{\"210\":1,\"278\":1}}],[\"为什么使用此类\",{\"0\":{\"203\":1,\"293\":1}}],[\"为什么要用\",{\"1\":{\"440\":1}}],[\"为什么要用适配器模式\",{\"0\":{\"163\":1}}],[\"为什么要学编译原理\",{\"0\":{\"407\":1}}],[\"为什么要这么复杂\",{\"0\":{\"398\":1}}],[\"为什么要特意编写\",{\"0\":{\"379\":1}}],[\"为什么要使用迭代器模式\",{\"0\":{\"284\":1}}],[\"为什么要使用\",{\"0\":{\"192\":1,\"257\":1,\"330\":1,\"351\":1,\"385\":1}}],[\"为什么要使用抽象工厂模式\",{\"0\":{\"152\":1}}],[\"为自然数时\",{\"1\":{\"84\":1}}],[\"为自然数且\",{\"1\":{\"76\":1,\"77\":2,\"81\":1,\"92\":1,\"93\":1,\"94\":1}}],[\"为正自然数时有\",{\"1\":{\"81\":1}}],[\"为正自然数\",{\"1\":{\"81\":4}}],[\"为真命题可以推出\",{\"1\":{\"72\":1,\"73\":1,\"88\":1,\"89\":1}}],[\"为真命题可以推理出\",{\"1\":{\"69\":1}}],[\"为真命题\",{\"1\":{\"69\":2,\"72\":1,\"73\":1,\"88\":1,\"89\":1}}],[\"为\",{\"1\":{\"8\":1,\"496\":2}}],[\"初步思路\",{\"0\":{\"8\":1}}],[\"通用寄存器\",{\"1\":{\"420\":1}}],[\"通信线路的增加\",{\"0\":{\"298\":1}}],[\"通信协议\",{\"0\":{\"7\":1}}],[\"通常是站在子类的角度进行思考的\",{\"1\":{\"389\":1}}],[\"通常在编程时算法会被写在具体方法中\",{\"1\":{\"379\":1}}],[\"通常会有两种接口\",{\"1\":{\"308\":1}}],[\"通常情况下\",{\"1\":{\"297\":1}}],[\"通常\",{\"1\":{\"128\":1,\"321\":2,\"398\":1}}],[\"通过一步步的学习\",{\"1\":{\"516\":1}}],[\"通过一个有趣的代码示例\",{\"1\":{\"120\":1}}],[\"通过本章的学习\",{\"1\":{\"450\":1}}],[\"通过词法分析器的预处理\",{\"1\":{\"436\":1}}],[\"通过教程来说明这个过程\",{\"1\":{\"409\":1}}],[\"通过代理对象来延迟实际对象的创建\",{\"1\":{\"341\":1}}],[\"通过保存多个\",{\"1\":{\"311\":1}}],[\"通过这些不同类型的代理模式\",{\"1\":{\"346\":1}}],[\"通过这些类和接口\",{\"1\":{\"287\":1}}],[\"通过这种划分\",{\"1\":{\"311\":1}}],[\"通过这种方式\",{\"1\":{\"308\":1,\"384\":1}}],[\"通过实现统一的迭代器接口\",{\"1\":{\"284\":1}}],[\"通过定义文法规则\",{\"1\":{\"278\":1}}],[\"通过定义抽象类和接口\",{\"1\":{\"130\":1}}],[\"通过引用计数来管理共享对象的生命周期\",{\"1\":{\"269\":1}}],[\"通过引入外观类\",{\"1\":{\"249\":1}}],[\"通过共享对象\",{\"1\":{\"263\":1}}],[\"通过使用策略模式\",{\"1\":{\"375\":1}}],[\"通过使用观察者模式\",{\"1\":{\"316\":1,\"325\":1}}],[\"通过使用迭代器模式\",{\"1\":{\"284\":1}}],[\"通过使用\",{\"1\":{\"257\":1}}],[\"通过使用装饰器模式\",{\"1\":{\"231\":1}}],[\"通过学习和应用设计模式\",{\"1\":{\"246\":1}}],[\"通过将\",{\"1\":{\"311\":1,\"422\":1}}],[\"通过将不同的语法规则封装在不同的类中\",{\"1\":{\"278\":1}}],[\"通过将每个执行的命令对象保存到一个历史记录列表中\",{\"1\":{\"215\":1}}],[\"通过将这些信息封装在命令对象中\",{\"1\":{\"214\":1}}],[\"通过将构建过程封装在\",{\"1\":{\"192\":1}}],[\"通过接口和抽象类定义行为\",{\"1\":{\"146\":1}}],[\"通过接发tcp包的方法与智能车进行交互\",{\"1\":{\"5\":1}}],[\"通过在类中引用其他类的实例来实现功能\",{\"1\":{\"146\":1}}],[\"通过在类中包含其他类的实例来实现功能\",{\"1\":{\"146\":1}}],[\"通过构造函数注入\",{\"1\":{\"143\":1}}],[\"通过模块化设计\",{\"1\":{\"139\":1}}],[\"通过门面对象提供统一的接口\",{\"1\":{\"137\":1}}],[\"通过中介者对象来管理对象之间的交互\",{\"1\":{\"137\":1}}],[\"通过举反例的方式\",{\"1\":{\"95\":1}}],[\"通过上述步骤\",{\"1\":{\"95\":1,\"124\":1}}],[\"通过该服务\",{\"1\":{\"44\":1}}],[\"通过\",{\"1\":{\"44\":1,\"270\":1,\"351\":1,\"515\":1}}],[\"通过二分左右轮的速度来得到使得小车直行的左右轮速度\",{\"1\":{\"10\":1}}],[\"吗\",{\"1\":{\"6\":1}}],[\"笔者最初以为只有两个任务\",{\"1\":{\"6\":1}}],[\"笔者的项目采用了该语言\",{\"1\":{\"6\":1}}],[\"库\",{\"1\":{\"6\":1}}],[\"并执行\",{\"1\":{\"515\":1}}],[\"并根据它们类型使用\",{\"1\":{\"503\":1}}],[\"并直接修改\",{\"1\":{\"501\":1}}],[\"并将之前的\",{\"1\":{\"496\":1}}],[\"并将保存在\",{\"1\":{\"478\":1}}],[\"并将被观察对象自身作为参数传递\",{\"1\":{\"323\":1}}],[\"并实现其中解析变量定义部分\",{\"1\":{\"463\":1}}],[\"并实现它们定义的抽象方法\",{\"1\":{\"156\":1}}],[\"并用它来实现了四则运算的语法分析器\",{\"1\":{\"460\":1}}],[\"并用它完成一个基本的四则运算的语法分析器\",{\"1\":{\"453\":1}}],[\"并退出整个程序\",{\"1\":{\"440\":1}}],[\"并仿照\",{\"1\":{\"434\":1}}],[\"并输出\",{\"1\":{\"416\":1}}],[\"并不作为语法的一部分\",{\"1\":{\"440\":1}}],[\"并不是直接处理\",{\"1\":{\"419\":1}}],[\"并不是说是没写过编译器就不是好程序员\",{\"1\":{\"407\":1}}],[\"并不支持通过ui注册\",{\"1\":{\"51\":1}}],[\"并把对各元素的处理交给访问者类\",{\"1\":{\"392\":1}}],[\"并以此将复杂的程序分解开来\",{\"1\":{\"365\":1}}],[\"并为每一种具体的状态都定义一个相应的类\",{\"1\":{\"365\":1}}],[\"并提前为它们赋予必要的信息\",{\"1\":{\"448\":1}}],[\"并提供一个全局访问点\",{\"1\":{\"351\":1}}],[\"并提高应用程序的效率\",{\"1\":{\"263\":1}}],[\"并恢复状态\",{\"1\":{\"311\":1}}],[\"并定义一个解释器来解释该语言中的句子\",{\"1\":{\"278\":1}}],[\"并嫌弃cpp中没有interface\",{\"1\":{\"274\":1}}],[\"并确保这个集合在程序的整个生命周期内都存在\",{\"1\":{\"269\":1}}],[\"并在所有的\",{\"1\":{\"369\":1,\"401\":1}}],[\"并在适当的时候清理过期的\",{\"1\":{\"310\":1}}],[\"并在实际项目中灵活运用它们\",{\"1\":{\"246\":1}}],[\"并在增加需求时尽量不修改已有的类\",{\"1\":{\"246\":1}}],[\"并使用它们来增加这个新功能\",{\"1\":{\"178\":1}}],[\"并点击激活\",{\"1\":{\"124\":1}}],[\"并回车\",{\"1\":{\"124\":2}}],[\"并没有保证\",{\"1\":{\"114\":1}}],[\"并发异步编程之争\",{\"0\":{\"111\":1}}],[\"并添加以下内容\",{\"1\":{\"65\":1}}],[\"并且它的结果是\",{\"1\":{\"499\":1}}],[\"并且它用很少的代码就完成了一个功能相当完善的\",{\"1\":{\"409\":1}}],[\"并且三条指令写来比较麻烦且浪费空间\",{\"1\":{\"429\":1}}],[\"并且我们也只有一个寄存器\",{\"1\":{\"423\":1}}],[\"并且最重要的是\",{\"1\":{\"408\":1}}],[\"并且可以扩展或重写这些行为和属性\",{\"1\":{\"242\":1}}],[\"并且协程切换并不是系统态抢占式\",{\"1\":{\"114\":1}}],[\"并且会非常频繁地进行切换\",{\"1\":{\"113\":1}}],[\"并且如果要对多个模数取模\",{\"1\":{\"57\":1}}],[\"并且如果编译器没有任何优化\",{\"1\":{\"57\":1}}],[\"并且这个关系并非简单的倍速或差量的关系\",{\"1\":{\"10\":1}}],[\"并自动重载docker\",{\"1\":{\"39\":1}}],[\"并放在车上托运并最后卸货的\",{\"1\":{\"15\":1}}],[\"并行\",{\"1\":{\"6\":1}}],[\"并采用asyncio作为\",{\"1\":{\"6\":1}}],[\"创建两个并行任务\",{\"1\":{\"5\":1}}],[\"主程序\",{\"0\":{\"225\":1},\"1\":{\"178\":1}}],[\"主动释放使用权\",{\"1\":{\"114\":1}}],[\"主动\",{\"1\":{\"114\":1}}],[\"主动让出使用权\",{\"1\":{\"114\":1}}],[\"主动让出时间片的协程模式比线程抢占式分配的效率要好\",{\"1\":{\"113\":1}}],[\"主动切换了使用权\",{\"1\":{\"114\":1}}],[\"主动切换\",{\"0\":{\"111\":1}}],[\"主要涉及如何将语句和表达式编译成汇编代码\",{\"1\":{\"485\":1}}],[\"主要的逻辑用于解析用逗号\",{\"1\":{\"468\":1}}],[\"主要原因是我们的语言不支持跨函数递归\",{\"1\":{\"464\":1}}],[\"主要原因是方便且能快速实现\",{\"1\":{\"6\":1}}],[\"主要有以下几个优点\",{\"1\":{\"337\":1}}],[\"主要思路\",{\"0\":{\"5\":1}}],[\"主页\",{\"0\":{\"0\":1}}],[\"报用qwq\",{\"1\":{\"4\":1}}],[\"项目地址\",{\"1\":{\"409\":1}}],[\"项目的初衷\",{\"0\":{\"409\":1}}],[\"项目结构\",{\"0\":{\"28\":1},\"1\":{\"26\":1}}],[\"项目\",{\"0\":{\"17\":1,\"26\":1},\"1\":{\"26\":1,\"28\":1}}],[\"项目要求完成智能车的循迹和避障\",{\"1\":{\"4\":1}}],[\"项目源码\",{\"1\":{\"4\":1}}],[\"这也是我自己的感慨吧\",{\"1\":{\"523\":1}}],[\"这也意味着一元运算符的优先级总是高于多元运算符\",{\"1\":{\"497\":1}}],[\"这部分对于整个编译器的编写其实是十分重要的\",{\"1\":{\"520\":1}}],[\"这部分也将同时解析参数本身\",{\"1\":{\"497\":1}}],[\"这次是后缀形式的\",{\"1\":{\"513\":1}}],[\"这包括\",{\"1\":{\"511\":1}}],[\"这和第三章\",{\"1\":{\"500\":1}}],[\"这章讲解语句的解析\",{\"1\":{\"485\":1}}],[\"这段代码线性地遍历所有标识符\",{\"1\":{\"478\":1}}],[\"这段示例程序的功能是让电脑玩\",{\"1\":{\"376\":1}}],[\"这么做的原因是\",{\"1\":{\"478\":1}}],[\"这么做的理由有两点\",{\"1\":{\"414\":1}}],[\"这相当于是整个函数定义的语法解析的框架\",{\"1\":{\"478\":1}}],[\"这点在后面的语法分析器我们就能体会\",{\"1\":{\"436\":1}}],[\"这点复杂度还是不算什么的\",{\"1\":{\"408\":1}}],[\"这后生成的目标代码便是我们的指令集\",{\"1\":{\"415\":1}}],[\"这意味着我们可以像运行脚本一样去运行\",{\"1\":{\"414\":1}}],[\"这意味着我们可以轻松地替换观察者或被观察者\",{\"1\":{\"320\":1}}],[\"这篇博客并没有使用诸如\",{\"1\":{\"411\":1}}],[\"这篇文章将带你走进闭包的奇妙世界\",{\"1\":{\"120\":1}}],[\"这些就是我们要支持的标记符\",{\"1\":{\"439\":1}}],[\"这些工具允许我们通过正则表达式来识别标记\",{\"1\":{\"438\":1}}],[\"这些函数就是可用的\",{\"1\":{\"432\":1}}],[\"这些函数的二进制代码就被编译进了我们的编译器\",{\"1\":{\"432\":1}}],[\"这些指令只接受一个参数\",{\"1\":{\"422\":1}}],[\"这些指令的顺序安排是有意的\",{\"1\":{\"421\":1}}],[\"这些理论试图教会我们如何用通用的方法来自动解决问题\",{\"1\":{\"408\":1}}],[\"这些题目要么是因为答案太大\",{\"1\":{\"54\":1}}],[\"这其中最主要的原因是\",{\"1\":{\"408\":1}}],[\"这两行代码起的就是这个作用\",{\"1\":{\"480\":1}}],[\"这两个角色共同决定了实际进行的处理\",{\"1\":{\"397\":1}}],[\"这两条语句中都有\",{\"1\":{\"370\":1}}],[\"这超出了本书的范围\",{\"1\":{\"367\":1}}],[\"这是整个编译器的最后一部分\",{\"1\":{\"495\":1}}],[\"这是上一章的\",{\"1\":{\"475\":1}}],[\"这是正常的\",{\"1\":{\"449\":1}}],[\"这是汇编中最难理解的部分\",{\"1\":{\"426\":1}}],[\"这是我们要支持的全部指令\",{\"1\":{\"421\":1}}],[\"这是\",{\"1\":{\"414\":1,\"417\":1,\"510\":1}}],[\"这是一种稍微有些笨的策略\",{\"1\":{\"376\":1}}],[\"这是一种非常好的解决办法\",{\"1\":{\"367\":1}}],[\"这是因为\",{\"1\":{\"370\":2,\"478\":1}}],[\"这是因为我们需要在\",{\"1\":{\"369\":1}}],[\"这是因为在\",{\"1\":{\"299\":1}}],[\"这是因为只有\",{\"1\":{\"187\":1}}],[\"这虽然看似理所当然\",{\"1\":{\"366\":1}}],[\"这一章\",{\"1\":{\"482\":1}}],[\"这一系列教程将带你从头编写一个\",{\"1\":{\"406\":1}}],[\"这一处理需要花费很多时间\",{\"1\":{\"338\":1}}],[\"这一功能的类\",{\"1\":{\"178\":1}}],[\"这可能会导致被观察对象再次通知所有观察者\",{\"1\":{\"322\":1}}],[\"这可能吗\",{\"1\":{\"114\":1}}],[\"这会导致共享对象在需要时无法被找到\",{\"1\":{\"269\":1}}],[\"这取决于类的使用目的\",{\"1\":{\"267\":1}}],[\"这就意味着表达式\",{\"1\":{\"496\":1}}],[\"这就用到了上一章中提到的\",{\"1\":{\"457\":1}}],[\"这就涉及到编译器\",{\"1\":{\"440\":1}}],[\"这就需要事先将这个位置信息存储起来\",{\"1\":{\"426\":1}}],[\"这就像我们可以自由选择香草味冰激凌\",{\"1\":{\"238\":1}}],[\"这就体现了它们之间的一致性\",{\"1\":{\"235\":1}}],[\"这就是开闭原则\",{\"1\":{\"399\":1}}],[\"这就是共享的特点\",{\"1\":{\"267\":1}}],[\"这就是所谓的里氏替换原则\",{\"1\":{\"242\":1}}],[\"这就是接口\",{\"1\":{\"235\":1}}],[\"这就是\",{\"1\":{\"178\":1,\"202\":1,\"366\":1,\"399\":2}}],[\"这就是为了增加新功能而产生的层次结构\",{\"1\":{\"174\":1}}],[\"这就是主动让出\",{\"1\":{\"114\":1}}],[\"这时\",{\"1\":{\"157\":1,\"187\":1,\"199\":1,\"293\":1,\"299\":1,\"368\":1,\"380\":1,\"401\":1}}],[\"这\",{\"1\":{\"156\":1,\"298\":2}}],[\"这并不是事情的全貌\",{\"1\":{\"112\":1}}],[\"这并不是什么缺陷\",{\"1\":{\"111\":1}}],[\"这个\",{\"1\":{\"440\":2}}],[\"这个顺序要特别注意\",{\"1\":{\"431\":1}}],[\"这个主题\",{\"1\":{\"402\":1}}],[\"这个gil全局解释器锁实际上把所有线程的执行代码都给上了锁\",{\"1\":{\"112\":1}}],[\"这个图满足如下性质\",{\"1\":{\"98\":1}}],[\"这实际上是符合客观逻辑的\",{\"1\":{\"111\":1}}],[\"这与\",{\"1\":{\"97\":1}}],[\"这究竟是为什么呢\",{\"1\":{\"95\":1}}],[\"这违背了\",{\"1\":{\"94\":1}}],[\"这种顺序的唯一作用就是在打印调试信息时更加方便\",{\"1\":{\"421\":1}}],[\"这种消息分发的方式一般被称为双重分发\",{\"1\":{\"397\":1}}],[\"这种责任被称为\",{\"1\":{\"389\":1}}],[\"这种错误了\",{\"1\":{\"369\":1}}],[\"这种处理方式既有优点也有缺点\",{\"1\":{\"367\":1}}],[\"这种处理方式是在画蛇添足\",{\"1\":{\"112\":1}}],[\"这种透明性使得代理模式在不改变客户端代码的情况下添加额外的功能成为可能\",{\"1\":{\"344\":1}}],[\"这种一致性确保了委托模式的灵活性和可维护性\",{\"1\":{\"243\":1}}],[\"这种情况下\",{\"1\":{\"202\":1}}],[\"这种设计方式提高了系统的灵活性和可扩展性\",{\"1\":{\"198\":1}}],[\"这种职责分离使得代码更加清晰\",{\"1\":{\"197\":1}}],[\"这种层次结构并非用于方便我们增加新的方法\",{\"1\":{\"175\":1}}],[\"这种模式通过组合而不是继承来实现功能的扩展\",{\"1\":{\"172\":1}}],[\"这种主动让出型的调度方式更为高效\",{\"1\":{\"113\":1}}],[\"这种异步编程方式被广大开发者所认可\",{\"1\":{\"112\":1}}],[\"这种写法的式子依旧太长\",{\"1\":{\"57\":1}}],[\"这种方法可以减少观察者对被观察对象的依赖\",{\"1\":{\"323\":1}}],[\"这种方法需要额外的逻辑来判断对象是否仍然被使用\",{\"1\":{\"269\":1}}],[\"这种方法简单直接\",{\"1\":{\"269\":1}}],[\"这种方法有效地解决了直接取模的忘记取模的漏洞\",{\"1\":{\"57\":1}}],[\"这种方法是直接取模\",{\"1\":{\"56\":1}}],[\"这种集成性使得持续集成\",{\"1\":{\"44\":1}}],[\"这便是本文写作的背景\",{\"1\":{\"53\":1}}],[\"这样你就不需要重复造轮子\",{\"1\":{\"522\":1}}],[\"这样它就成了全局的常量了\",{\"1\":{\"468\":1}}],[\"这样当源代码中出现关键字时\",{\"1\":{\"448\":1}}],[\"这样我们就有了一个最简单的编译器\",{\"1\":{\"416\":1}}],[\"这样做的主要原因是为了简化虚拟机的实现\",{\"1\":{\"423\":1}}],[\"这样做的缺点是\",{\"1\":{\"402\":1}}],[\"这样做的好处是请求的发送者和接收者解耦\",{\"1\":{\"204\":1}}],[\"这样看起来程序好像变复杂了\",{\"1\":{\"379\":1}}],[\"这样即使应用程序关闭后重新打开\",{\"1\":{\"311\":1}}],[\"这样可以支持用户进行多次撤销和重做操作\",{\"1\":{\"311\":1}}],[\"这样可以确保逻辑的一致性和可维护性\",{\"1\":{\"297\":1}}],[\"这样的颜色信息\",{\"1\":{\"267\":1}}],[\"这样的设计可能显得有些过于复杂\",{\"1\":{\"154\":1}}],[\"这样\",{\"1\":{\"235\":1,\"236\":1,\"270\":1,\"293\":1,\"365\":1,\"367\":1,\"368\":1,\"392\":1,\"402\":1}}],[\"这样很容易使类的层次结构变得复杂\",{\"1\":{\"176\":1}}],[\"这样一来\",{\"1\":{\"156\":1,\"186\":1,\"267\":1}}],[\"这样子类可以决定实例化哪个类\",{\"1\":{\"152\":1}}],[\"这样子能减少摆头次数\",{\"1\":{\"12\":1}}],[\"这样在扩展功能时\",{\"1\":{\"130\":1}}],[\"这样就很难在编译代码时检测出\",{\"1\":{\"369\":1}}],[\"这样就构成了一个小小的类层次结构\",{\"1\":{\"174\":1}}],[\"这样就定义了自然数\",{\"1\":{\"69\":1}}],[\"这样就解决了类型名长的缺点\",{\"1\":{\"58\":1}}],[\"这样就可以在同一个平台上管理代码和镜像\",{\"1\":{\"44\":1}}],[\"这样使用的时候\",{\"1\":{\"58\":1}}],[\"这里就不多作解释\",{\"1\":{\"510\":1}}],[\"这里最为重要的一点是\",{\"1\":{\"477\":1}}],[\"这里不再多说\",{\"1\":{\"458\":1}}],[\"这里会有一个疑问\",{\"1\":{\"457\":1}}],[\"这里我简单介绍一下\",{\"1\":{\"455\":1}}],[\"这里我们解析的就是类似\",{\"1\":{\"507\":1}}],[\"这里我们就能看到\",{\"1\":{\"503\":1}}],[\"这里我们就采用第二种方法\",{\"1\":{\"448\":1}}],[\"这里我们讲解其中的一些细节\",{\"1\":{\"467\":1}}],[\"这里我们要额外介绍\",{\"1\":{\"446\":1}}],[\"这里我们要为我们的虚拟机构建自己的指令集\",{\"1\":{\"421\":1}}],[\"这里我们首先要了解的是当参数调用时\",{\"1\":{\"430\":1}}],[\"这里我们约定\",{\"1\":{\"426\":1}}],[\"这里我们把\",{\"1\":{\"426\":1}}],[\"这里我们只实现两个最简单的条件判断\",{\"1\":{\"425\":1}}],[\"这里这样写的目的是装b\",{\"1\":{\"444\":1}}],[\"这里要说明这样一个观点\",{\"1\":{\"520\":1}}],[\"这里要注意的是在ascii码中\",{\"1\":{\"444\":1}}],[\"这里要解释的一点是\",{\"1\":{\"422\":1}}],[\"这里解释一下具体的含义\",{\"1\":{\"443\":1}}],[\"这里注意的是\",{\"1\":{\"438\":1}}],[\"这里需要的是注意每个函数的作用\",{\"1\":{\"416\":1}}],[\"这里有一个单独用于解析\",{\"1\":{\"416\":1}}],[\"这里\",{\"1\":{\"369\":1,\"487\":1,\"508\":1}}],[\"这里故意将上面两点说得很笼统\",{\"1\":{\"366\":1}}],[\"这里也出现了可替换性\",{\"0\":{\"320\":1}}],[\"这里的一个问题是\",{\"1\":{\"440\":1}}],[\"这里的原理是\",{\"1\":{\"432\":1}}],[\"这里的数据可以是代码\",{\"1\":{\"419\":1}}],[\"这里的资源指的是计算机中的资源\",{\"1\":{\"270\":1}}],[\"这里的类的层次结构并非用于增加功能\",{\"1\":{\"175\":1}}],[\"这里的finally\",{\"1\":{\"112\":1}}],[\"这里其实也存在层次结构\",{\"1\":{\"175\":1}}],[\"这里说的\",{\"1\":{\"156\":1}}],[\"这里将目录修改为目标目录\",{\"1\":{\"35\":1}}],[\"这里是所有详细的教程和指南\",{\"1\":{\"123\":1}}],[\"这里是所有与技术相关的文章\",{\"1\":{\"50\":1}}],[\"这里是所有个人感想\",{\"1\":{\"2\":1}}],[\"这里是推荐的书籍\",{\"1\":{\"18\":1}}],[\"这里是你参与或开发的项目介绍和进展\",{\"1\":{\"17\":1}}],[\"这句话真是道出了人生的真谛\",{\"1\":{\"3\":1}}],[\"这让我不禁感慨\",{\"1\":{\"3\":1}}],[\"时我们并不能确定\",{\"1\":{\"467\":1}}],[\"时直接从\",{\"1\":{\"422\":1}}],[\"时间也是一种资源\",{\"1\":{\"270\":1}}],[\"时间有点久搞忘了\",{\"1\":{\"13\":1}}],[\"时由乘法运算规则\",{\"1\":{\"91\":1}}],[\"时有\",{\"1\":{\"75\":2,\"76\":1,\"77\":4,\"84\":1,\"91\":3,\"92\":1,\"93\":1,\"94\":2}}],[\"时\",{\"1\":{\"3\":1,\"75\":1,\"76\":1,\"81\":1,\"91\":1,\"92\":1,\"93\":1,\"108\":1,\"199\":1,\"367\":1,\"370\":2,\"398\":1}}],[\"一节提到的\",{\"1\":{\"508\":1}}],[\"一节中所说的修改或删除\",{\"1\":{\"503\":1}}],[\"一是运算符的优先级问题\",{\"1\":{\"495\":1}}],[\"一是容易忘记大括号\",{\"1\":{\"56\":1}}],[\"一元运算符\",{\"0\":{\"497\":1},\"1\":{\"495\":1}}],[\"一旦遇到了\",{\"1\":{\"489\":1}}],[\"一旦同名\",{\"1\":{\"478\":1}}],[\"一些非终结符如<expr>被递归地使用了\",{\"1\":{\"456\":1}}],[\"一种是自底向上\",{\"1\":{\"454\":1}}],[\"一种是自顶向下\",{\"1\":{\"454\":1}}],[\"一般终结符对应于词法分析器输出的标记\",{\"1\":{\"455\":1}}],[\"一般有两种处理方法\",{\"1\":{\"448\":1}}],[\"一般处理的方法有两种\",{\"1\":{\"440\":1}}],[\"一般而言\",{\"1\":{\"415\":1}}],[\"一般的编译器相关的教程要么就十分简单\",{\"1\":{\"409\":1}}],[\"一般编译原理的课程会说一些\",{\"1\":{\"408\":1}}],[\"一般来说\",{\"1\":{\"270\":1}}],[\"一定程度上\",{\"1\":{\"365\":1}}],[\"一侧增加类即可\",{\"1\":{\"186\":1}}],[\"一致性是指委托对象应当具有与委托者相同的接口或行为\",{\"1\":{\"243\":1}}],[\"一致性\",{\"1\":{\"152\":1}}],[\"一路点击\",{\"1\":{\"124\":1}}],[\"一方面没有很好的测试用例\",{\"1\":{\"410\":1}}],[\"一方面想了解它的工作原理\",{\"1\":{\"407\":1}}],[\"一方面\",{\"1\":{\"113\":1,\"422\":1}}],[\"一方面减少了心智负担\",{\"1\":{\"58\":1}}],[\"一个标记\",{\"1\":{\"439\":1}}],[\"一个语法分析器生成器\",{\"1\":{\"411\":1}}],[\"一个观察者在接收到通知后修改了被观察对象的状态\",{\"1\":{\"322\":1}}],[\"一个实例的改变会同时反映到所有使用该实例的地方\",{\"1\":{\"267\":1}}],[\"一个实体应当尽量少地与其他实体之间发生相互作用\",{\"1\":{\"136\":1}}],[\"一个类只负责一个职责\",{\"1\":{\"148\":1}}],[\"一个类只对应一个职责\",{\"1\":{\"138\":1}}],[\"一个类对另一个类的依赖应该建立在最小的接口上\",{\"1\":{\"141\":1}}],[\"一个原则可以是另一个原则的加强或基础\",{\"1\":{\"128\":1}}],[\"一个通用性很强的工具\",{\"1\":{\"18\":1}}],[\"一个红外传感器+超声波传感器用于确定前方是否有障碍\",{\"1\":{\"8\":1}}],[\"一个用于读取小车状态\",{\"1\":{\"5\":1}}],[\"一个用于实时接收tcp报文来更新小车状态\",{\"1\":{\"5\":1}}],[\"一将成名\",{\"1\":{\"3\":1}}],[\"一位热衷于探索全栈开发领域的技术爱好者\",{\"1\":{\"1\":1}}],[\"昨日在玩\",{\"1\":{\"3\":1}}],[\"致力于打造高效\",{\"1\":{\"1\":1}}],[\"擅长将前端与后端技术无缝结合\",{\"1\":{\"1\":1}}],[\"介绍页\",{\"0\":{\"1\":1}}]],\"serializationVersion\":2}}")).map(([e,t])=>[e,zt(t,{fields:["h","t","c"],storeFields:["h","t","c"]})]));self.onmessage=({data:{type:e="all",query:t,locale:s,options:n,id:o}})=>{const u=bt[s];e==="suggest"?self.postMessage([e,o,tt(t,u,n)]):e==="search"?self.postMessage([e,o,Z(t,u,n)]):self.postMessage({suggestions:[e,o,tt(t,u,n)],results:[e,o,Z(t,u,n)]})};
 //# sourceMappingURL=index.js.map
diff --git a/sitemap.xml b/sitemap.xml
index 881caa3..06fdd1e 100644
--- a/sitemap.xml
+++ b/sitemap.xml
@@ -1,3 +1,3 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <?xml-stylesheet type="text/xsl" href="/sitemap.xsl"?>
-<urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9" xmlns:news="http://www.google.com/schemas/sitemap-news/0.9" xmlns:xhtml="http://www.w3.org/1999/xhtml" xmlns:image="http://www.google.com/schemas/sitemap-image/1.1" xmlns:video="http://www.google.com/schemas/sitemap-video/1.1"><url><loc>https://github.com/</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/intro.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/essays/</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/essays/%E5%91%BD%E9%87%8C%E6%9C%89%E6%97%B6%E7%BB%88%E9%A1%BB%E6%9C%89.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/projects/</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/resources/</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/android%20studio%E6%8D%A2%E6%BA%90.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/cicd.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/docker.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/figure_bed.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/mailserver.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/modint.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/python_requrements.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/style.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/tensorflow%E8%B8%A9%E5%9D%91.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/%E5%8D%8F%E7%A8%8B.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tutorials/</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tutorials/typora%E6%BF%80%E6%B4%BB.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/resources/html2md/</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/DesignPrinciples.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/abstractFactory.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/adapter.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/bridge.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/builder.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/chainOfResponsibility.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/command.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/composite.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/decorator.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/end.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/facade.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/factory_method.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/flyweight.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/interpreter.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/iterator.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/mediator.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/memento.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/observer.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/prototype.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/proxy.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/singleton.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/state.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/strategy.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/template_method.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/visitor.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/designASimpileCCompiler/0.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/designASimpileCCompiler/1.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/designASimpileCCompiler/2.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/designASimpileCCompiler/3.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/designASimpileCCompiler/4.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/designASimpileCCompiler/5.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/designASimpileCCompiler/6.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/designASimpileCCompiler/7.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/designASimpileCCompiler/8.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/designASimpileCCompiler/9.html</loc><changefreq>daily</changefreq></url></urlset>
\ No newline at end of file
+<urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9" xmlns:news="http://www.google.com/schemas/sitemap-news/0.9" xmlns:xhtml="http://www.w3.org/1999/xhtml" xmlns:image="http://www.google.com/schemas/sitemap-image/1.1" xmlns:video="http://www.google.com/schemas/sitemap-video/1.1"><url><loc>https://github.com/</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/intro.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/essays/</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/essays/%E5%91%BD%E9%87%8C%E6%9C%89%E6%97%B6%E7%BB%88%E9%A1%BB%E6%9C%89.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/projects/carrobot.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/projects/</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/resources/</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/android%20studio%E6%8D%A2%E6%BA%90.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/cicd.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/docker.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/figure_bed.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/mailserver.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/modint.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/python_requrements.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/style.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/tensorflow%E8%B8%A9%E5%9D%91.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/%E5%8D%8F%E7%A8%8B.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tutorials/</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tutorials/typora%E6%BF%80%E6%B4%BB.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/resources/compile/</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/resources/html2md/</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/DesignPrinciples.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/abstractFactory.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/adapter.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/bridge.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/builder.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/chainOfResponsibility.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/command.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/composite.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/decorator.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/end.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/facade.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/factory_method.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/flyweight.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/interpreter.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/iterator.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/mediator.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/memento.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/observer.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/prototype.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/proxy.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/singleton.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/state.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/strategy.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/template_method.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/DesignPatterns/visitor.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/designASimpileCCompiler/0.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/designASimpileCCompiler/1.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/designASimpileCCompiler/2.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/designASimpileCCompiler/3.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/designASimpileCCompiler/4.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/designASimpileCCompiler/5.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/designASimpileCCompiler/6.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/designASimpileCCompiler/7.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/designASimpileCCompiler/8.html</loc><changefreq>daily</changefreq></url><url><loc>https://github.com/tech/designASimpileCCompiler/9.html</loc><changefreq>daily</changefreq></url></urlset>
\ No newline at end of file
diff --git a/star/index.html b/star/index.html
index 6a665a0..0e98239 100644
--- a/star/index.html
+++ b/star/index.html
@@ -30,13 +30,13 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/star/"><meta property="og:site_name" content="blog"><meta property="og:title" content="星标"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"星标"}</script><title>星标 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-Dh_a7h_3.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-DottIbHL.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="vp-article-type-wrapper"><li class="vp-article-type"><a class="route-link" href="/article/">全部</a></li><li class="vp-article-type active"><a class="route-link" href="/star/">星标</a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html"><header class="vp-article-title"><!----><!----><span property="headline">docker + nginx + acme.sh 部署 vue/flask 项目</span></header></a><div class="vp-article-excerpt">
 <p>本文将介绍如何使用 Docker、Nginx 和 acme.sh 部署一个 Vue 和 Flask 项目。我们将详细讲解环境配置、项目结构、Nginx 配置、Docker 配置以及如何升级到 HTTPS。</p>
-</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><span class="page-author-item">King-sj</span></span><span property="author" content="King-sj"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-09-16T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 3 分钟</span><meta property="timeRequired" content="PT3M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category4 clickable" role="navigation">nginx</span><!--]--><meta property="articleSection" content="nginx"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">部署</span><!--]--><meta property="keywords" content="部署"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><span class="page-author-item">King-sj</span></span><span property="author" content="King-sj"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-09-16T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 3 分钟</span><meta property="timeRequired" content="PT3M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category4 clickable" role="navigation">nginx</span><!--]--><meta property="articleSection" content="nginx"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">部署</span><!--]--><meta property="keywords" content="部署"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tag/c/index.html b/tag/c/index.html
index f52ca9f..4e0692c 100644
--- a/tag/c/index.html
+++ b/tag/c/index.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/c/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: c"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: c"}</script><title>标签: c | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-BpjUVtkj.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-y8ELyp0v.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4 active"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/designASimpileCCompiler/0.html"><header class="vp-article-title"><!----><!----><span property="headline">手把手教你构建 C 语言编译器（0）- 前言</span></header></a><div class="vp-article-excerpt">
@@ -139,7 +139,7 @@ <h1>手把手教你构建 C 语言编译器（9）- 总结</h1>
 <li><a href="about:blank#%E8%AF%AD%E6%B3%95%E5%88%86%E6%9E%90">3. 语法分析</a></li>
 <li><a href="about:blank#%E5%85%B3%E4%BA%8E%E7%BC%96%E4%BB%A3%E7%A0%81">4. 关于编代码</a></li>
 <li><a href="about:blank#%E7%BB%93%E8%AF%AD">5. 结语</a></li>
-</ol></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category2 clickable" role="navigation">编译原理</span><!--]--><meta property="articleSection" content="编译原理"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag4 clickable" role="navigation">c</span><span class="page-tag-item tag4 clickable" role="navigation">编译器</span><span class="page-tag-item tag4 clickable" role="navigation">解释器</span><!--]--><meta property="keywords" content="c,编译器,解释器"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</ol></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category2 clickable" role="navigation">编译原理</span><!--]--><meta property="articleSection" content="编译原理"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag4 clickable" role="navigation">c</span><span class="page-tag-item tag4 clickable" role="navigation">编译器</span><span class="page-tag-item tag4 clickable" role="navigation">解释器</span><!--]--><meta property="keywords" content="c,编译器,解释器"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tag/cicd/index.html b/tag/cicd/index.html
index 7378cf1..db3d1e0 100644
--- a/tag/cicd/index.html
+++ b/tag/cicd/index.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/cicd/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: CI/CD"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: CI/CD"}</script><title>标签: CI/CD | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-DR-PJoSN.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-DW1c3ODz.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5 active"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/cicd.html"><header class="vp-article-title"><!----><!----><span property="headline">CI/CD</span></header></a><div class="vp-article-excerpt">
@@ -40,7 +40,7 @@
 <!-- TODO -->
 <p>也可另外指定</p>
 <div class="language-bash" data-ext="sh" data-title="sh"><pre class="language-bash"><code>act --var-file <span class="token string">"./.act/.vars"</span> --secret-file <span class="token string">"./.act/.secrets"</span> --env-file <span class="token string">"./.act/.env"</span> <span class="token punctuation">{</span><span class="token punctuation">{</span>other<span class="token punctuation">}</span><span class="token punctuation">}</span>
-</code></pre></div></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-08-02T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category5 clickable" role="navigation">CI/CD</span><!--]--><meta property="articleSection" content="CI/CD"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag5 clickable" role="navigation">CI/CD</span><!--]--><meta property="keywords" content="CI/CD"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</code></pre></div></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-08-02T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category5 clickable" role="navigation">CI/CD</span><!--]--><meta property="articleSection" content="CI/CD"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag5 clickable" role="navigation">CI/CD</span><!--]--><meta property="keywords" content="CI/CD"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tag/docker/index.html b/tag/docker/index.html
index 08df074..e78c4f9 100644
--- a/tag/docker/index.html
+++ b/tag/docker/index.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/docker/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: docker"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: docker"}</script><title>标签: docker | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-BvZSJ2r-.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-SMm58lXr.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2 active"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/docker.html"><header class="vp-article-title"><!----><!----><span property="headline"></span></header></a><div class="vp-article-excerpt"><h2>GitHub Container Registry 加速</h2>
@@ -40,7 +40,7 @@ <h3>ghcr.io简介</h3>
 <li>ghcr.io 是 GitHub Container Registry 的域名。GitHub Container Registry 是 GitHub 提供的容器镜像注册表服务，允许开发者在 GitHub 上存储、管理和分享 Docker 镜像。它与 GitHub 代码仓库紧密集成，可以使用相同的权限管理、团队协作和版本控制工具来管理容器镜像。</li>
 <li>通过 GitHub Container Registry，开发者可以方便地将他们的容器镜像与代码仓库关联起来，这样就可以在同一个平台上管理代码和镜像。这种集成性使得持续集成/持续交付 (CI/CD) 流程更加简化和统一，开发团队可以更容易地构建、测试和部署应用程序。</li>
 <li>对于使用 GitHub 作为代码托管平台的开发者来说，GitHub Container Registry 提供一个便捷且强大的容器镜像管理解决方案。通过该服务，可以更轻松地构建和部署容器化的应用程序，从而加速开发和交付周期。</li>
-</ul></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-09-12T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category1 clickable" role="navigation">奇技淫巧</span><span class="page-category-item category2 clickable" role="navigation">docker</span><!--]--><meta property="articleSection" content="奇技淫巧,docker"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag2 clickable" role="navigation">docker</span><!--]--><meta property="keywords" content="docker"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</ul></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-09-12T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category1 clickable" role="navigation">奇技淫巧</span><span class="page-category-item category2 clickable" role="navigation">docker</span><!--]--><meta property="articleSection" content="奇技淫巧,docker"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag2 clickable" role="navigation">docker</span><!--]--><meta property="keywords" content="docker"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tag/index.html b/tag/index.html
index 5d13d00..5c24175 100644
--- a/tag/index.html
+++ b/tag/index.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签"}</script><title>标签 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-bipylPNF.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-mplfcIL_.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
-    <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><!----></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><!----></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tag/mobile/index.html b/tag/mobile/index.html
index 1f5e357..3a7f1dc 100644
--- a/tag/mobile/index.html
+++ b/tag/mobile/index.html
@@ -30,13 +30,13 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/mobile/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: mobile"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: mobile"}</script><title>标签: mobile | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-D2pTqZFy.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-DeNCk-ye.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0 active"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html"><header class="vp-article-title"><!----><!----><span property="headline">使用capacitor和ionic将vue项目迁移到mobile端</span></header></a><div class="vp-article-excerpt">
 <p>当我们写完了vue项目后，想做一个一样的移动app，此时我们可以使用ionic无缝将其迁移到移动端。</p>
-</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag0 clickable" role="navigation">mobile</span><!--]--><meta property="keywords" content="mobile"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag0 clickable" role="navigation">mobile</span><!--]--><meta property="keywords" content="mobile"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tag/modint/index.html b/tag/modint/index.html
index 3058f5f..416b8e0 100644
--- a/tag/modint/index.html
+++ b/tag/modint/index.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/modint/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: MODInt"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: MODInt"}</script><title>标签: MODInt | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-BKjCcFT0.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-D8p9fsJ8.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8 active"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/modint.html"><header class="vp-article-title"><!----><!----><span property="headline">「泛型与 OI」modint</span></header></a><div class="vp-article-excerpt">
@@ -40,7 +40,7 @@ <h2>背景介绍</h2>
 <p>这些题目要么是因为答案太大，不方便输出结果，例如许多计数 dp；要么是因为答案是浮点数，出题人不愿意写一个确定精度的 Special Judge，例如很多期望概率题；要么是因为这道题目直接考察了模的性质和运用，比如大量的 998244353 类的多项式题目。</p>
 </div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2023-08-02T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category6 clickable" role="navigation">OI</span><!--]--><meta property="articleSection" content="OI"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">MODInt</span><!--]--><meta property="keywords" content="MODInt"></span></div></article></div><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html"><header class="vp-article-title"><!----><!----><span property="headline">闭包实现类</span></header></a><div class="vp-article-excerpt">
 <p>你是否曾经想过，不用类也能封装数据和方法？这篇文章将带你走进闭包的奇妙世界，展示如何用闭包来实现这一点。通过一个有趣的代码示例，你将看到闭包是如何捕获变量并提供类似类的功能的。准备好了吗？让我们开始这段有趣的旅程吧！</p>
-</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2023-08-02T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category6 clickable" role="navigation">OI</span><!--]--><meta property="articleSection" content="OI"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">MODInt</span><!--]--><meta property="keywords" content="MODInt"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2023-08-02T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category6 clickable" role="navigation">OI</span><!--]--><meta property="articleSection" content="OI"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">MODInt</span><!--]--><meta property="keywords" content="MODInt"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tag/typescript/index.html b/tag/typescript/index.html
index 90519bd..c51302d 100644
--- a/tag/typescript/index.html
+++ b/tag/typescript/index.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/typescript/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: TypeScript"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: TypeScript"}</script><title>标签: TypeScript | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-CRzs15I0.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-JQfnAIea.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5 active"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/DesignPatterns/command.html"><header class="vp-article-title"><!----><!----><span property="headline">Command 模式</span></header></a><div class="vp-article-excerpt"><h2>为什么使用此模式</h2>
@@ -70,7 +70,7 @@ <h2>示例代码</h2>
 <p>观察者模式非常适合用于需要自动更新的场景。例如，在图形用户界面（GUI）应用程序中，当数据模型发生变化时，所有显示该数据的视图都需要自动更新。通过使用观察者模式，我们可以将这些视图注册为观察者，当数据模型发生变化时，它们会自动收到通知并更新显示。</p>
 <h2>示例代码</h2>
 <p>在这个示例中，我们展示了如何使用观察者模式来管理状态变化。观察者模式定义了一种一对多的依赖关系，当一个对象的状态发生改变时，所有依赖于它的对象都会得到通知并自动更新。以下是 TypeScript 实现的代码示例：</p>
-<img src="https://www.plantuml.com/plantuml/svg/jL912i8m4Bpd5JbMf1_eoOFWJS4VR9kn1fgaRBP54VzkDRQKua4GRyliC3CxoIOAiNIkKTOB-4GLzA6Cu1wiRqhhTTSQ4cGrF9WaSA7tdIl1kn5O5ReFrgYxKbH6OQf4Lmt5k2GcFJ9cDCZ2UoWcpr5i81eq47p7zK7iwJekOZPRrP2Kumdwr_I4SK7L3NVDqgVGMrjRcIgmhctWu2N-K4iItZ6rvty87ycRu9PbuoBmvlCZvAc7UH_VrxGK37a-dQ0sW-Vmcnu0" alt=""></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-26T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag1 clickable" role="navigation">管理状态</span><!--]--><meta property="keywords" content="设计模式,TypeScript,管理状态"></span></div></article></div><div class="vp-pagination"><nav class="vp-pagination-list"><div class="vp-pagination-number"><!----><!----><!--[--><div class="active" role="navigation">1</div><div class="" role="navigation">2</div><!--]--><!----><div class="next" role="navigation" unselectable="on">下一页</div></div><div class="vp-pagination-nav"><label for="navigation-text">跳转到: </label><input id="navigation-text" value><button class="vp-pagination-button" type="button" role="navigation" title="前往">前往</button></div></nav></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+<img src="https://www.plantuml.com/plantuml/svg/jL912i8m4Bpd5JbMf1_eoOFWJS4VR9kn1fgaRBP54VzkDRQKua4GRyliC3CxoIOAiNIkKTOB-4GLzA6Cu1wiRqhhTTSQ4cGrF9WaSA7tdIl1kn5O5ReFrgYxKbH6OQf4Lmt5k2GcFJ9cDCZ2UoWcpr5i81eq47p7zK7iwJekOZPRrP2Kumdwr_I4SK7L3NVDqgVGMrjRcIgmhctWu2N-K4iItZ6rvty87ycRu9PbuoBmvlCZvAc7UH_VrxGK37a-dQ0sW-Vmcnu0" alt=""></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-26T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag1 clickable" role="navigation">管理状态</span><!--]--><meta property="keywords" content="设计模式,TypeScript,管理状态"></span></div></article></div><div class="vp-pagination"><nav class="vp-pagination-list"><div class="vp-pagination-number"><!----><!----><!--[--><div class="active" role="navigation">1</div><div class="" role="navigation">2</div><!--]--><!----><div class="next" role="navigation" unselectable="on">下一页</div></div><div class="vp-pagination-nav"><label for="navigation-text">跳转到: </label><input id="navigation-text" value><button class="vp-pagination-button" type="button" role="navigation" title="前往">前往</button></div></nav></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tag/\344\272\244\347\273\231\345\255\220\347\261\273/index.html" "b/tag/\344\272\244\347\273\231\345\255\220\347\261\273/index.html"
index c14ba5c..5a8b065 100644
--- "a/tag/\344\272\244\347\273\231\345\255\220\347\261\273/index.html"
+++ "b/tag/\344\272\244\347\273\231\345\255\220\347\261\273/index.html"
@@ -30,13 +30,13 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: 交给子类"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: 交给子类"}</script><title>标签: 交给子类 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-BlxatHgv.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-BJX9B5Ij.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1 active"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/DesignPatterns/factory_method.html"><header class="vp-article-title"><!----><!----><span property="headline">Factory Method 模式</span></header></a><div class="vp-article-excerpt"><p>在 Factory Method 模式中，我们定义一个用于创建对象的接口，但由子类决定要实例化的类是哪一个。Factory Method 使一个类的实例化延迟到其子类。</p>
 </div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-21T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag3 clickable" role="navigation">typescript</span><span class="page-tag-item tag0 clickable" role="navigation">工厂方法</span><span class="page-tag-item tag1 clickable" role="navigation">交给子类</span><!--]--><meta property="keywords" content="设计模式,typescript,工厂方法,交给子类"></span></div></article></div><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/DesignPatterns/template_method.html"><header class="vp-article-title"><!----><!----><span property="headline">Template Method 模式</span></header></a><div class="vp-article-excerpt"><p>在父类中定义处理流程的框架，在子类中实现具体处理。Template Method 模式的主要目的是为了定义一个算法的骨架，而将一些步骤的具体实现延迟到子类中。通过这种方式，子类可以在不改变算法结构的情况下，重新定义算法中的某些步骤。</p>
-</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-21T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag3 clickable" role="navigation">typescript</span><span class="page-tag-item tag1 clickable" role="navigation">交给子类</span><!--]--><meta property="keywords" content="设计模式,typescript,交给子类"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-21T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag3 clickable" role="navigation">typescript</span><span class="page-tag-item tag1 clickable" role="navigation">交给子类</span><!--]--><meta property="keywords" content="设计模式,typescript,交给子类"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tag/\345\205\254\347\220\206\347\263\273\347\273\237/index.html" "b/tag/\345\205\254\347\220\206\347\263\273\347\273\237/index.html"
index baec51f..5ab76c4 100644
--- "a/tag/\345\205\254\347\220\206\347\263\273\347\273\237/index.html"
+++ "b/tag/\345\205\254\347\220\206\347\263\273\347\273\237/index.html"
@@ -30,13 +30,13 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: 公理系统"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: 公理系统"}</script><title>标签: 公理系统 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-CLOegCHC.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-BwXv95cV.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3 active"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html"><header class="vp-article-title"><!----><!----><span property="headline">「算术公理系统 1」自然数</span></header></a><div class="vp-article-excerpt">
 <p>假设存在一个算数系统的模型满足 Peano 公理，即假定 Peano 公理相容，在此承认次假设的基础之上，我们即可建立如今最常用的<strong>算术公理系统</strong>。<strong>自然数的定义</strong>则是构建此算术公理系统的第一步。</p>
-</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2023-07-09T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 18 分钟</span><meta property="timeRequired" content="PT18M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category3 clickable" role="navigation">数学</span><!--]--><meta property="articleSection" content="数学"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag3 clickable" role="navigation">公理系统</span><!--]--><meta property="keywords" content="公理系统"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2023-07-09T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 18 分钟</span><meta property="timeRequired" content="PT18M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category3 clickable" role="navigation">数学</span><!--]--><meta property="articleSection" content="数学"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag3 clickable" role="navigation">公理系统</span><!--]--><meta property="keywords" content="公理系统"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tag/\345\210\206\345\274\200\350\200\203\350\231\221/index.html" "b/tag/\345\210\206\345\274\200\350\200\203\350\231\221/index.html"
index 1214d0c..895da1c 100644
--- "a/tag/\345\210\206\345\274\200\350\200\203\350\231\221/index.html"
+++ "b/tag/\345\210\206\345\274\200\350\200\203\350\231\221/index.html"
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: 分开考虑"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: 分开考虑"}</script><title>标签: 分开考虑 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-CGsa9ffM.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-Dpy8imS-.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6 active"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/DesignPatterns/bridge.html"><header class="vp-article-title"><!----><!----><span property="headline">Bridge 模式</span></header></a><div class="vp-article-excerpt"><p>Bridge 模式在“类的功能层次结构”和“类的实现层次结构”之间搭建桥梁。</p>
@@ -43,7 +43,7 @@
 <li><strong>减少重复代码</strong>：通过使用策略模式，可以避免在多个地方重复相同的算法逻辑。</li>
 </ol>
 <h2>示例程序</h2>
-<p>下面我们来看一段使用了 strategy 模式的示例程序。这段示例程序的功能是让电脑玩“猜拳"游戏。</p></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-25T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag6 clickable" role="navigation">分开考虑</span><span class="page-tag-item tag6 clickable" role="navigation">整体的替换算法</span><!--]--><meta property="keywords" content="设计模式,TypeScript,分开考虑,整体的替换算法"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+<p>下面我们来看一段使用了 strategy 模式的示例程序。这段示例程序的功能是让电脑玩“猜拳"游戏。</p></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-25T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag6 clickable" role="navigation">分开考虑</span><span class="page-tag-item tag6 clickable" role="navigation">整体的替换算法</span><!--]--><meta property="keywords" content="设计模式,TypeScript,分开考虑,整体的替换算法"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tag/\345\256\271\345\231\250\344\270\216\345\206\205\345\256\271\347\232\204\344\270\200\350\207\264\346\200\247/index.html" "b/tag/\345\256\271\345\231\250\344\270\216\345\206\205\345\256\271\347\232\204\344\270\200\350\207\264\346\200\247/index.html"
index b49d5e4..dc9e94e 100644
--- "a/tag/\345\256\271\345\231\250\344\270\216\345\206\205\345\256\271\347\232\204\344\270\200\350\207\264\346\200\247/index.html"
+++ "b/tag/\345\256\271\345\231\250\344\270\216\345\206\205\345\256\271\347\232\204\344\270\200\350\207\264\346\200\247/index.html"
@@ -30,15 +30,15 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: 容器与内容的一致性"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: 容器与内容的一致性"}</script><title>标签: 容器与内容的一致性 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-BHNGjpbb.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-DklcXGYl.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7 active"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/DesignPatterns/composite.html"><header class="vp-article-title"><!----><!----><span property="headline">Composite 模式</span></header></a><div class="vp-article-excerpt"><h2>使用此设计模式的理由</h2>
 <p>Composite 模式允许你将对象组合成递归结构来表示“部分-整体”的层次结构。使用 Composite 模式，用户可以统一地对待单个对象和组合对象。例如，在文件系统中，目录和文件都可以被视为条目（Entry），目录可以包含其他目录和文件，而文件则是叶子节点。</p>
 <h2>示例代码</h2>
 <img src="https://www.plantuml.com/plantuml/svg/hPAn3e8m48Ptdk8I5mZX1OW3WpePOyBWO1mAFR495D8U1ZM-kwM0A77GnEcI_-xQxsiQQMAAwY9tMA99iPGWpPdMi9IaBd1p07p8a3QiGDSBmSm8cGrfBAusbNMHeB8fuzp5TZViZl3wQfkLMQQrqDGkdKl1JJeRqvsWqrRXKJHkPSjmtpZj0vMnpLvexexJGI-4mfHA0uuDeUIzHciH01-QFT7-O6DfpAPU_x3znUifi18vVcAVG0QW3SiRoVVKlu6DJpeFWhAtYmoV-JCF" alt=""></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-25T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag7 clickable" role="navigation">容器与内容的一致性</span><!--]--><meta property="keywords" content="设计模式,TypeScript,容器与内容的一致性"></span></div></article></div><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/DesignPatterns/decorator.html"><header class="vp-article-title"><!----><!----><span property="headline">Decorator 模式</span></header></a><div class="vp-article-excerpt"><p>在这个示例中，我们使用装饰器模式来动态地给对象添加职责。装饰器模式允许我们通过将对象放入包含行为的特殊封装对象中来扩展对象的功能，而无需修改原始类的代码。</p>
-</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-25T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 6 分钟</span><meta property="timeRequired" content="PT6M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag7 clickable" role="navigation">容器与内容的一致性</span><!--]--><meta property="keywords" content="设计模式,TypeScript,容器与内容的一致性"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-25T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 6 分钟</span><meta property="timeRequired" content="PT6M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag7 clickable" role="navigation">容器与内容的一致性</span><!--]--><meta property="keywords" content="设计模式,TypeScript,容器与内容的一致性"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tag/\345\267\245\345\216\202\346\226\271\346\263\225/index.html" "b/tag/\345\267\245\345\216\202\346\226\271\346\263\225/index.html"
index b707f49..ef4033a 100644
--- "a/tag/\345\267\245\345\216\202\346\226\271\346\263\225/index.html"
+++ "b/tag/\345\267\245\345\216\202\346\226\271\346\263\225/index.html"
@@ -30,12 +30,12 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: 工厂方法"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: 工厂方法"}</script><title>标签: 工厂方法 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-kOhwCTdr.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-NUfXNLwU.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0 active"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/DesignPatterns/factory_method.html"><header class="vp-article-title"><!----><!----><span property="headline">Factory Method 模式</span></header></a><div class="vp-article-excerpt"><p>在 Factory Method 模式中，我们定义一个用于创建对象的接口，但由子类决定要实例化的类是哪一个。Factory Method 使一个类的实例化延迟到其子类。</p>
-</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-21T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag3 clickable" role="navigation">typescript</span><span class="page-tag-item tag0 clickable" role="navigation">工厂方法</span><span class="page-tag-item tag1 clickable" role="navigation">交给子类</span><!--]--><meta property="keywords" content="设计模式,typescript,工厂方法,交给子类"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-21T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag3 clickable" role="navigation">typescript</span><span class="page-tag-item tag0 clickable" role="navigation">工厂方法</span><span class="page-tag-item tag1 clickable" role="navigation">交给子类</span><!--]--><meta property="keywords" content="设计模式,typescript,工厂方法,交给子类"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tag/\346\216\250\345\215\270\350\264\243\344\273\273/index.html" "b/tag/\346\216\250\345\215\270\350\264\243\344\273\273/index.html"
index 8ae0840..168c9f3 100644
--- "a/tag/\346\216\250\345\215\270\350\264\243\344\273\273/index.html"
+++ "b/tag/\346\216\250\345\215\270\350\264\243\344\273\273/index.html"
@@ -30,12 +30,12 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: 推卸责任"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: 推卸责任"}</script><title>标签: 推卸责任 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-QNuKjuoZ.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-i5A_pLCb.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7 active"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/DesignPatterns/chainOfResponsibility.html"><header class="vp-article-title"><!----><!----><span property="headline">chainOfResponsibility 模式</span></header></a><div class="vp-article-excerpt"><p>“推卸责任"听起来有些贬义的意思，但是有时候也确实存在需要“推卸责任"的情况。例如，当外部请求程序进行某个处理，但程序暂时无法直接决定由哪个对象负责处理时，就需要推卸责任。这种情况下，我们可以考虑将多个对象组成一条职责链，然后按照它们在职责链上的顺序一个一个地找出到底应该谁来负责处理。</p>
-</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-25T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 3 分钟</span><meta property="timeRequired" content="PT3M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag7 clickable" role="navigation">推卸责任</span><!--]--><meta property="keywords" content="设计模式,TypeScript,推卸责任"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-25T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 3 分钟</span><meta property="timeRequired" content="PT3M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag7 clickable" role="navigation">推卸责任</span><!--]--><meta property="keywords" content="设计模式,TypeScript,推卸责任"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tag/\346\225\264\344\275\223\347\232\204\346\233\277\346\215\242\347\256\227\346\263\225/index.html" "b/tag/\346\225\264\344\275\223\347\232\204\346\233\277\346\215\242\347\256\227\346\263\225/index.html"
index bb3ddc8..b4d8cbc 100644
--- "a/tag/\346\225\264\344\275\223\347\232\204\346\233\277\346\215\242\347\256\227\346\263\225/index.html"
+++ "b/tag/\346\225\264\344\275\223\347\232\204\346\233\277\346\215\242\347\256\227\346\263\225/index.html"
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: 整体的替换算法"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: 整体的替换算法"}</script><title>标签: 整体的替换算法 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-CcgdDCiF.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-DYx5t_sy.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6 active"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/DesignPatterns/strategy.html"><header class="vp-article-title"><!----><!----><span property="headline">Strategy 模式</span></header></a><div class="vp-article-excerpt"><h2>使用此设计模式的理由</h2>
@@ -42,7 +42,7 @@
 <li><strong>减少重复代码</strong>：通过使用策略模式，可以避免在多个地方重复相同的算法逻辑。</li>
 </ol>
 <h2>示例程序</h2>
-<p>下面我们来看一段使用了 strategy 模式的示例程序。这段示例程序的功能是让电脑玩“猜拳"游戏。</p></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-25T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag6 clickable" role="navigation">分开考虑</span><span class="page-tag-item tag6 clickable" role="navigation">整体的替换算法</span><!--]--><meta property="keywords" content="设计模式,TypeScript,分开考虑,整体的替换算法"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+<p>下面我们来看一段使用了 strategy 模式的示例程序。这段示例程序的功能是让电脑玩“猜拳"游戏。</p></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-25T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag6 clickable" role="navigation">分开考虑</span><span class="page-tag-item tag6 clickable" role="navigation">整体的替换算法</span><!--]--><meta property="keywords" content="设计模式,TypeScript,分开考虑,整体的替换算法"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tag/\346\277\200\346\264\273/index.html" "b/tag/\346\277\200\346\264\273/index.html"
index 7d50ada..d3cf0e3 100644
--- "a/tag/\346\277\200\346\264\273/index.html"
+++ "b/tag/\346\277\200\346\264\273/index.html"
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/%E6%BF%80%E6%B4%BB/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: 激活"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: 激活"}</script><title>标签: 激活 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-DZYdDCPP.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-hPg6lxSo.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7 active"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tutorials/typora%E6%BF%80%E6%B4%BB.html"><header class="vp-article-title"><!----><!----><span property="headline">Typora激活教程</span></header></a><div class="vp-article-excerpt">
@@ -41,7 +41,7 @@ <h1>安装教程</h1>
 <li><a href="https://typora.io" target="_blank" rel="noopener noreferrer">Typora 官网</a></li>
 <li><a href="https://typoraio.cn" target="_blank" rel="noopener noreferrer">Typora 中文官网</a></li>
 </ul>
-<!-- TODO: 添加自己的静态服务 --></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-21T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag7 clickable" role="navigation">激活</span><!--]--><meta property="keywords" content="激活"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+<!-- TODO: 添加自己的静态服务 --></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-21T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag7 clickable" role="navigation">激活</span><!--]--><meta property="keywords" content="激活"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tag/\347\224\237\346\210\220\345\256\236\344\276\213/index.html" "b/tag/\347\224\237\346\210\220\345\256\236\344\276\213/index.html"
index 7e8aaa3..92650e1 100644
--- "a/tag/\347\224\237\346\210\220\345\256\236\344\276\213/index.html"
+++ "b/tag/\347\224\237\346\210\220\345\256\236\344\276\213/index.html"
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: 生成实例"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: 生成实例"}</script><title>标签: 生成实例 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-BZLD09T1.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-Cw9y1ZOg.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6 active"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/DesignPatterns/abstractFactory.html"><header class="vp-article-title"><!----><!----><span property="headline">抽象工厂模式</span></header></a><div class="vp-article-excerpt"><h2>为什么要使用抽象工厂模式</h2>
@@ -54,7 +54,7 @@
 </ul>
 </div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-22T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag3 clickable" role="navigation">typescript</span><span class="page-tag-item tag6 clickable" role="navigation">生成实例</span><!--]--><meta property="keywords" content="设计模式,typescript,生成实例"></span></div></article></div><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/DesignPatterns/singleton.html"><header class="vp-article-title"><!----><!----><span property="headline">Singleton 模式</span></header></a><div class="vp-article-excerpt"><h2>为什么要使用 Singleton 模式</h2>
 <p>Singleton 模式确保一个类只有一个实例，并提供一个全局访问点。它常用于需要控制资源访问的场景，例如数据库连接、日志记录器等。通过 Singleton 模式，可以避免创建多个实例带来的资源浪费和不一致性问题。</p>
-</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-21T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag3 clickable" role="navigation">typescript</span><span class="page-tag-item tag6 clickable" role="navigation">生成实例</span><!--]--><meta property="keywords" content="设计模式,typescript,生成实例"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-21T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag3 clickable" role="navigation">typescript</span><span class="page-tag-item tag6 clickable" role="navigation">生成实例</span><!--]--><meta property="keywords" content="设计模式,typescript,生成实例"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tag/\347\224\250\347\261\273\345\256\236\347\216\260/index.html" "b/tag/\347\224\250\347\261\273\345\256\236\347\216\260/index.html"
index 545280f..c6ce2c5 100644
--- "a/tag/\347\224\250\347\261\273\345\256\236\347\216\260/index.html"
+++ "b/tag/\347\224\250\347\261\273\345\256\236\347\216\260/index.html"
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: 用类实现"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: 用类实现"}</script><title>标签: 用类实现 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-9q-r5JHT.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-yUxPRBBH.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1 active"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/DesignPatterns/command.html"><header class="vp-article-title"><!----><!----><span property="headline">Command 模式</span></header></a><div class="vp-article-excerpt"><h2>为什么使用此模式</h2>
@@ -43,7 +43,7 @@ <h2>示例代码</h2>
 <li><strong>简化语法解析</strong>：通过定义文法规则，可以轻松解析和执行特定的语言或指令集。</li>
 <li><strong>可扩展性</strong>：可以轻松添加新的语法规则或指令，而无需修改现有代码。</li>
 <li><strong>代码复用</strong>：通过将不同的语法规则封装在不同的类中，可以提高代码的复用性和可维护性。</li>
-</ol></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-29T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 3 分钟</span><meta property="timeRequired" content="PT3M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag1 clickable" role="navigation">用类实现</span><!--]--><meta property="keywords" content="设计模式,TypeScript,用类实现"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</ol></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-29T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 3 分钟</span><meta property="timeRequired" content="PT3M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag1 clickable" role="navigation">用类实现</span><!--]--><meta property="keywords" content="设计模式,TypeScript,用类实现"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tag/\347\256\200\345\215\225\345\214\226/index.html" "b/tag/\347\256\200\345\215\225\345\214\226/index.html"
index 4d3c067..78bedbe 100644
--- "a/tag/\347\256\200\345\215\225\345\214\226/index.html"
+++ "b/tag/\347\256\200\345\215\225\345\214\226/index.html"
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/%E7%AE%80%E5%8D%95%E5%8C%96/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: 简单化"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: 简单化"}</script><title>标签: 简单化 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-0LHdE1Bw.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-BFj2MrdQ.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3 active"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/DesignPatterns/facade.html"><header class="vp-article-title"><!----><!----><span property="headline">facade 模式</span></header></a><div class="vp-article-excerpt"><p>当某个程序员得意地说出"啊，在调用那个类之前需要先调用这个类。在调用那个方法之前需要先在这个类中注册一下"的时候，就意味着我们需要引人Facade了。</p>
@@ -39,7 +39,7 @@
 <p style="text-align: right;">—————《图解设计模式》</p>
 </div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-26T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag3 clickable" role="navigation">简单化</span><!--]--><meta property="keywords" content="设计模式,TypeScript,简单化"></span></div></article></div><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/DesignPatterns/mediator.html"><header class="vp-article-title"><!----><!----><span property="headline">Mediator 模式</span></header></a><div class="vp-article-excerpt"><h2>为什么使用此类</h2>
 <p>请大家想象一下一个乱糟糟的开发小组的工作状态。小组中的 10 个成员虽然一起协同工作，但是意见难以统一，总是互相指挥，导致工作进度始终滞后。不仅如此，他们还十分在意编码细节，经常为此争执不下。</p>
-</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-26T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag3 clickable" role="navigation">简单化</span><!--]--><meta property="keywords" content="设计模式,TypeScript,简单化"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-26T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag3 clickable" role="navigation">简单化</span><!--]--><meta property="keywords" content="设计模式,TypeScript,简单化"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tag/\347\256\241\347\220\206\347\212\266\346\200\201/index.html" "b/tag/\347\256\241\347\220\206\347\212\266\346\200\201/index.html"
index c10f7e1..083c916 100644
--- "a/tag/\347\256\241\347\220\206\347\212\266\346\200\201/index.html"
+++ "b/tag/\347\256\241\347\220\206\347\212\266\346\200\201/index.html"
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: 管理状态"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: 管理状态"}</script><title>标签: 管理状态 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-B3D_5fpm.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-COyA9Sec.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1 active"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/DesignPatterns/memento.html"><header class="vp-article-title"><!----><!----><span property="headline">Memento 模式</span></header></a><div class="vp-article-excerpt"><h2>为什么使用 Memento 模式</h2>
@@ -49,7 +49,7 @@ <h2>示例代码</h2>
 <p>观察者模式非常适合用于需要自动更新的场景。例如，在图形用户界面（GUI）应用程序中，当数据模型发生变化时，所有显示该数据的视图都需要自动更新。通过使用观察者模式，我们可以将这些视图注册为观察者，当数据模型发生变化时，它们会自动收到通知并更新显示。</p>
 <h2>示例代码</h2>
 <p>在这个示例中，我们展示了如何使用观察者模式来管理状态变化。观察者模式定义了一种一对多的依赖关系，当一个对象的状态发生改变时，所有依赖于它的对象都会得到通知并自动更新。以下是 TypeScript 实现的代码示例：</p>
-<img src="https://www.plantuml.com/plantuml/svg/jL912i8m4Bpd5JbMf1_eoOFWJS4VR9kn1fgaRBP54VzkDRQKua4GRyliC3CxoIOAiNIkKTOB-4GLzA6Cu1wiRqhhTTSQ4cGrF9WaSA7tdIl1kn5O5ReFrgYxKbH6OQf4Lmt5k2GcFJ9cDCZ2UoWcpr5i81eq47p7zK7iwJekOZPRrP2Kumdwr_I4SK7L3NVDqgVGMrjRcIgmhctWu2N-K4iItZ6rvty87ycRu9PbuoBmvlCZvAc7UH_VrxGK37a-dQ0sW-Vmcnu0" alt=""></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-26T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag1 clickable" role="navigation">管理状态</span><!--]--><meta property="keywords" content="设计模式,TypeScript,管理状态"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+<img src="https://www.plantuml.com/plantuml/svg/jL912i8m4Bpd5JbMf1_eoOFWJS4VR9kn1fgaRBP54VzkDRQKua4GRyliC3CxoIOAiNIkKTOB-4GLzA6Cu1wiRqhhTTSQ4cGrF9WaSA7tdIl1kn5O5ReFrgYxKbH6OQf4Lmt5k2GcFJ9cDCZ2UoWcpr5i81eq47p7zK7iwJekOZPRrP2Kumdwr_I4SK7L3NVDqgVGMrjRcIgmhctWu2N-K4iItZ6rvty87ycRu9PbuoBmvlCZvAc7UH_VrxGK37a-dQ0sW-Vmcnu0" alt=""></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-26T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag1 clickable" role="navigation">管理状态</span><!--]--><meta property="keywords" content="设计模式,TypeScript,管理状态"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tag/\347\274\226\350\257\221\345\231\250/index.html" "b/tag/\347\274\226\350\257\221\345\231\250/index.html"
index 31b6e3f..c11b90e 100644
--- "a/tag/\347\274\226\350\257\221\345\231\250/index.html"
+++ "b/tag/\347\274\226\350\257\221\345\231\250/index.html"
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/%E7%BC%96%E8%AF%91%E5%99%A8/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: 编译器"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: 编译器"}</script><title>标签: 编译器 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-BNAyU6dK.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-auYNF0Cp.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4 active"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/designASimpileCCompiler/0.html"><header class="vp-article-title"><!----><!----><span property="headline">手把手教你构建 C 语言编译器（0）- 前言</span></header></a><div class="vp-article-excerpt">
@@ -139,7 +139,7 @@ <h1>手把手教你构建 C 语言编译器（9）- 总结</h1>
 <li><a href="about:blank#%E8%AF%AD%E6%B3%95%E5%88%86%E6%9E%90">3. 语法分析</a></li>
 <li><a href="about:blank#%E5%85%B3%E4%BA%8E%E7%BC%96%E4%BB%A3%E7%A0%81">4. 关于编代码</a></li>
 <li><a href="about:blank#%E7%BB%93%E8%AF%AD">5. 结语</a></li>
-</ol></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category2 clickable" role="navigation">编译原理</span><!--]--><meta property="articleSection" content="编译原理"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag4 clickable" role="navigation">c</span><span class="page-tag-item tag4 clickable" role="navigation">编译器</span><span class="page-tag-item tag4 clickable" role="navigation">解释器</span><!--]--><meta property="keywords" content="c,编译器,解释器"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</ol></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category2 clickable" role="navigation">编译原理</span><!--]--><meta property="articleSection" content="编译原理"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag4 clickable" role="navigation">c</span><span class="page-tag-item tag4 clickable" role="navigation">编译器</span><span class="page-tag-item tag4 clickable" role="navigation">解释器</span><!--]--><meta property="keywords" content="c,编译器,解释器"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tag/\350\247\243\351\207\212\345\231\250/index.html" "b/tag/\350\247\243\351\207\212\345\231\250/index.html"
index 8e527f1..75d460e 100644
--- "a/tag/\350\247\243\351\207\212\345\231\250/index.html"
+++ "b/tag/\350\247\243\351\207\212\345\231\250/index.html"
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: 解释器"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: 解释器"}</script><title>标签: 解释器 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-VMxXqaQ8.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-DCZKDe-x.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4 active"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/designASimpileCCompiler/0.html"><header class="vp-article-title"><!----><!----><span property="headline">手把手教你构建 C 语言编译器（0）- 前言</span></header></a><div class="vp-article-excerpt">
@@ -139,7 +139,7 @@ <h1>手把手教你构建 C 语言编译器（9）- 总结</h1>
 <li><a href="about:blank#%E8%AF%AD%E6%B3%95%E5%88%86%E6%9E%90">3. 语法分析</a></li>
 <li><a href="about:blank#%E5%85%B3%E4%BA%8E%E7%BC%96%E4%BB%A3%E7%A0%81">4. 关于编代码</a></li>
 <li><a href="about:blank#%E7%BB%93%E8%AF%AD">5. 结语</a></li>
-</ol></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category2 clickable" role="navigation">编译原理</span><!--]--><meta property="articleSection" content="编译原理"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag4 clickable" role="navigation">c</span><span class="page-tag-item tag4 clickable" role="navigation">编译器</span><span class="page-tag-item tag4 clickable" role="navigation">解释器</span><!--]--><meta property="keywords" content="c,编译器,解释器"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</ol></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category2 clickable" role="navigation">编译原理</span><!--]--><meta property="articleSection" content="编译原理"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag4 clickable" role="navigation">c</span><span class="page-tag-item tag4 clickable" role="navigation">编译器</span><span class="page-tag-item tag4 clickable" role="navigation">解释器</span><!--]--><meta property="keywords" content="c,编译器,解释器"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tag/\350\256\276\350\256\241\346\250\241\345\274\217/index.html" "b/tag/\350\256\276\350\256\241\346\250\241\345\274\217/index.html"
index df187e4..3efc103 100644
--- "a/tag/\350\256\276\350\256\241\346\250\241\345\274\217/index.html"
+++ "b/tag/\350\256\276\350\256\241\346\250\241\345\274\217/index.html"
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: 设计模式"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: 设计模式"}</script><title>标签: 设计模式 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-DzsdPiFk.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-CYOJa5u_.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8 active"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/DesignPatterns/command.html"><header class="vp-article-title"><!----><!----><span property="headline">Command 模式</span></header></a><div class="vp-article-excerpt"><h2>为什么使用此模式</h2>
@@ -70,7 +70,7 @@ <h2>示例代码</h2>
 <p>观察者模式非常适合用于需要自动更新的场景。例如，在图形用户界面（GUI）应用程序中，当数据模型发生变化时，所有显示该数据的视图都需要自动更新。通过使用观察者模式，我们可以将这些视图注册为观察者，当数据模型发生变化时，它们会自动收到通知并更新显示。</p>
 <h2>示例代码</h2>
 <p>在这个示例中，我们展示了如何使用观察者模式来管理状态变化。观察者模式定义了一种一对多的依赖关系，当一个对象的状态发生改变时，所有依赖于它的对象都会得到通知并自动更新。以下是 TypeScript 实现的代码示例：</p>
-<img src="https://www.plantuml.com/plantuml/svg/jL912i8m4Bpd5JbMf1_eoOFWJS4VR9kn1fgaRBP54VzkDRQKua4GRyliC3CxoIOAiNIkKTOB-4GLzA6Cu1wiRqhhTTSQ4cGrF9WaSA7tdIl1kn5O5ReFrgYxKbH6OQf4Lmt5k2GcFJ9cDCZ2UoWcpr5i81eq47p7zK7iwJekOZPRrP2Kumdwr_I4SK7L3NVDqgVGMrjRcIgmhctWu2N-K4iItZ6rvty87ycRu9PbuoBmvlCZvAc7UH_VrxGK37a-dQ0sW-Vmcnu0" alt=""></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-26T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag1 clickable" role="navigation">管理状态</span><!--]--><meta property="keywords" content="设计模式,TypeScript,管理状态"></span></div></article></div><div class="vp-pagination"><nav class="vp-pagination-list"><div class="vp-pagination-number"><!----><!----><!--[--><div class="active" role="navigation">1</div><div class="" role="navigation">2</div><div class="" role="navigation">3</div><!--]--><!----><div class="next" role="navigation" unselectable="on">下一页</div></div><div class="vp-pagination-nav"><label for="navigation-text">跳转到: </label><input id="navigation-text" value><button class="vp-pagination-button" type="button" role="navigation" title="前往">前往</button></div></nav></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+<img src="https://www.plantuml.com/plantuml/svg/jL912i8m4Bpd5JbMf1_eoOFWJS4VR9kn1fgaRBP54VzkDRQKua4GRyliC3CxoIOAiNIkKTOB-4GLzA6Cu1wiRqhhTTSQ4cGrF9WaSA7tdIl1kn5O5ReFrgYxKbH6OQf4Lmt5k2GcFJ9cDCZ2UoWcpr5i81eq47p7zK7iwJekOZPRrP2Kumdwr_I4SK7L3NVDqgVGMrjRcIgmhctWu2N-K4iItZ6rvty87ycRu9PbuoBmvlCZvAc7UH_VrxGK37a-dQ0sW-Vmcnu0" alt=""></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-26T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag1 clickable" role="navigation">管理状态</span><!--]--><meta property="keywords" content="设计模式,TypeScript,管理状态"></span></div></article></div><div class="vp-pagination"><nav class="vp-pagination-list"><div class="vp-pagination-number"><!----><!----><!--[--><div class="active" role="navigation">1</div><div class="" role="navigation">2</div><div class="" role="navigation">3</div><!--]--><!----><div class="next" role="navigation" unselectable="on">下一页</div></div><div class="vp-pagination-nav"><label for="navigation-text">跳转到: </label><input id="navigation-text" value><button class="vp-pagination-button" type="button" role="navigation" title="前往">前往</button></div></nav></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tag/\350\256\277\351\227\256\346\225\260\346\215\256\347\273\223\346\236\204\345\271\266\345\244\204\347\220\206\346\225\260\346\215\256/index.html" "b/tag/\350\256\277\351\227\256\346\225\260\346\215\256\347\273\223\346\236\204\345\271\266\345\244\204\347\220\206\346\225\260\346\215\256/index.html"
index 5e8a665..a6f7350 100644
--- "a/tag/\350\256\277\351\227\256\346\225\260\346\215\256\347\273\223\346\236\204\345\271\266\345\244\204\347\220\206\346\225\260\346\215\256/index.html"
+++ "b/tag/\350\256\277\351\227\256\346\225\260\346\215\256\347\273\223\346\236\204\345\271\266\345\244\204\347\220\206\346\225\260\346\215\256/index.html"
@@ -30,12 +30,12 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: 访问数据结构并处理数据"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: 访问数据结构并处理数据"}</script><title>标签: 访问数据结构并处理数据 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-B2T3kUK3.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-CryaZFG_.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8 active"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/DesignPatterns/visitor.html"><header class="vp-article-title"><!----><!----><span property="headline">Visitor 模式</span></header></a><div class="vp-article-excerpt"><p>在 Visitor 模式中，数据结构与处理被分离开来。我们编写一个表示“访问者”的类来访问数据结构中的元素，并把对各元素的处理交给访问者类。这样，当需要增加新的处理时，我们只需要编写新的访问者，然后让数据结构可以接受访问者的访问即可。</p>
-</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-25T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 6 分钟</span><meta property="timeRequired" content="PT6M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag8 clickable" role="navigation">访问数据结构并处理数据</span><!--]--><meta property="keywords" content="设计模式,TypeScript,访问数据结构并处理数据"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-25T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 6 分钟</span><meta property="timeRequired" content="PT6M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag8 clickable" role="navigation">访问数据结构并处理数据</span><!--]--><meta property="keywords" content="设计模式,TypeScript,访问数据结构并处理数据"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tag/\350\270\251\345\235\221\350\256\260\345\275\225/index.html" "b/tag/\350\270\251\345\235\221\350\256\260\345\275\225/index.html"
index 50bf2de..be4ae60 100644
--- "a/tag/\350\270\251\345\235\221\350\256\260\345\275\225/index.html"
+++ "b/tag/\350\270\251\345\235\221\350\256\260\345\275\225/index.html"
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: 踩坑记录"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: 踩坑记录"}</script><title>标签: 踩坑记录 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-CSRSsNOG.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-rivgPJ9m.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2 active"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/python_requrements.html"><header class="vp-article-title"><!----><!----><span property="headline">python requirements.txt</span></header></a><div class="vp-article-excerpt"><p>Python 生成 <code>requirements</code>有两种方式</p>
@@ -39,7 +39,7 @@
 <li><code>pip list --format=freeze &gt; requirements.txt</code> (推荐做法)</li>
 <li><code>pip freeze &gt; requirements.txt</code> (不推荐，会带有本地路径)</li>
 </ul>
-</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-29T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category7 clickable" role="navigation">python</span><!--]--><meta property="articleSection" content="python"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag2 clickable" role="navigation">踩坑记录</span><!--]--><meta property="keywords" content="踩坑记录"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-29T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category7 clickable" role="navigation">python</span><!--]--><meta property="articleSection" content="python"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag2 clickable" role="navigation">踩坑记录</span><!--]--><meta property="keywords" content="踩坑记录"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tag/\351\201\277\345\205\215\346\265\252\350\264\271/index.html" "b/tag/\351\201\277\345\205\215\346\265\252\350\264\271/index.html"
index e9206a9..d3eca3b 100644
--- "a/tag/\351\201\277\345\205\215\346\265\252\350\264\271/index.html"
+++ "b/tag/\351\201\277\345\205\215\346\265\252\350\264\271/index.html"
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: 避免浪费"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: 避免浪费"}</script><title>标签: 避免浪费 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-ayClYbZ3.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-F61LMFJS.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5 active"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/DesignPatterns/proxy.html"><header class="vp-article-title"><!----><!----><span property="headline">Proxy 模式</span></header></a><div class="vp-article-excerpt"><h2>为什么使用代理模式</h2>
@@ -39,7 +39,7 @@
 </div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-29T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag5 clickable" role="navigation">避免浪费</span><!--]--><meta property="keywords" content="设计模式,TypeScript,避免浪费"></span></div></article></div><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/DesignPatterns/flyweight.html"><header class="vp-article-title"><!----><!----><span property="headline">Flyweight 模式</span></header></a><div class="vp-article-excerpt"><h2>为什么使用 Flyweight 模式</h2>
 <p>Flyweight 模式是一种结构型设计模式，它通过共享尽可能多的相同对象来减少内存使用，从而提高性能。在需要生成大量细粒度对象的场景中，Flyweight 模式非常有用。通过共享对象，Flyweight 模式可以显著减少内存消耗，并提高应用程序的效率。</p>
 <h2>实例代码</h2>
-<img src="https://www.plantuml.com/plantuml/svg/RL7B2i8m4BpdA_ROKli3GKfH43nuyYWUrZJMG4rAinL4_7VJz5rxMsPsPcTtKqjOKVqic2ZGMjYfVF_02ZuC80RXIerFoS5IfNJkmRlHb27X18oWT1K58OUNKHdxihdT0GMPwjsvbiOK74vORbk3JT-MUDeb8YN0EgQGP3HVkBJ9Z7RYkW62q2VePBcaewDG2zd4-PD6JKU71ilzHi5iXRCdk_GtbJSoExHUhjvsciWLW-NwUHQ7YUDac3mEdA3z0giaIwNEt0z_" alt=""></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-28T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 8 分钟</span><meta property="timeRequired" content="PT8M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag5 clickable" role="navigation">避免浪费</span><!--]--><meta property="keywords" content="设计模式,TypeScript,避免浪费"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+<img src="https://www.plantuml.com/plantuml/svg/RL7B2i8m4BpdA_ROKli3GKfH43nuyYWUrZJMG4rAinL4_7VJz5rxMsPsPcTtKqjOKVqic2ZGMjYfVF_02ZuC80RXIerFoS5IfNJkmRlHb27X18oWT1K58OUNKHdxihdT0GMPwjsvbiOK74vORbk3JT-MUDeb8YN0EgQGP3HVkBJ9Z7RYkW62q2VePBcaewDG2zd4-PD6JKU71ilzHi5iXRCdk_GtbJSoExHUhjvsciWLW-NwUHQ7YUDac3mEdA3z0giaIwNEt0z_" alt=""></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-28T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 8 分钟</span><meta property="timeRequired" content="PT8M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag5 clickable" role="navigation">避免浪费</span><!--]--><meta property="keywords" content="设计模式,TypeScript,避免浪费"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tag/\351\203\250\347\275\262/index.html" "b/tag/\351\203\250\347\275\262/index.html"
index 78cfbfa..de46757 100644
--- "a/tag/\351\203\250\347\275\262/index.html"
+++ "b/tag/\351\203\250\347\275\262/index.html"
@@ -30,13 +30,13 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/%E9%83%A8%E7%BD%B2/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: 部署"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: 部署"}</script><title>标签: 部署 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-DDn6tClc.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-CzSwk-A5.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8 active"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html"><header class="vp-article-title"><!----><!----><span property="headline">docker + nginx + acme.sh 部署 vue/flask 项目</span></header></a><div class="vp-article-excerpt">
 <p>本文将介绍如何使用 Docker、Nginx 和 acme.sh 部署一个 Vue 和 Flask 项目。我们将详细讲解环境配置、项目结构、Nginx 配置、Docker 配置以及如何升级到 HTTPS。</p>
-</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><span class="page-author-item">King-sj</span></span><span property="author" content="King-sj"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-09-16T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 3 分钟</span><meta property="timeRequired" content="PT3M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category4 clickable" role="navigation">nginx</span><!--]--><meta property="articleSection" content="nginx"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">部署</span><!--]--><meta property="keywords" content="部署"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><span class="page-author-item">King-sj</span></span><span property="author" content="King-sj"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-09-16T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 3 分钟</span><meta property="timeRequired" content="PT3M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category4 clickable" role="navigation">nginx</span><!--]--><meta property="articleSection" content="nginx"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">部署</span><!--]--><meta property="keywords" content="部署"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tag/\351\243\216\346\240\274/index.html" "b/tag/\351\243\216\346\240\274/index.html"
index 7ef0ac7..60ce0ee 100644
--- "a/tag/\351\243\216\346\240\274/index.html"
+++ "b/tag/\351\243\216\346\240\274/index.html"
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tag/%E9%A3%8E%E6%A0%BC/"><meta property="og:site_name" content="blog"><meta property="og:title" content="标签: 风格"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"标签: 风格"}</script><title>标签: 风格 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-BLuB_Eoc.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-DwPUACaS.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><ul class="tag-list-wrapper"><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BE%E8%AE%A1%E6%A8%A1%E5%BC%8F/">设计模式<span class="tag-num">26</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/typescript/">TypeScript<span class="tag-num">16</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/typescript/">typescript<span class="tag-num">10</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/c/">c<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E7%BC%96%E8%AF%91%E5%99%A8/">编译器<span class="tag-num">8</span></a></li><li class="tag tag4"><a class="route-link" href="/tag/%E8%A7%A3%E9%87%8A%E5%99%A8/">解释器<span class="tag-num">8</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E7%94%9F%E6%88%90%E5%AE%9E%E4%BE%8B/">生成实例<span class="tag-num">4</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%AE%A1%E7%90%86%E7%8A%B6%E6%80%81/">管理状态<span class="tag-num">3</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/modint/">MODInt<span class="tag-num">2</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E5%88%86%E5%BC%80%E8%80%83%E8%99%91/">分开考虑<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E7%94%A8%E7%B1%BB%E5%AE%9E%E7%8E%B0/">用类实现<span class="tag-num">2</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E5%AE%B9%E5%99%A8%E4%B8%8E%E5%86%85%E5%AE%B9%E7%9A%84%E4%B8%80%E8%87%B4%E6%80%A7/">容器与内容的一致性<span class="tag-num">2</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E7%AE%80%E5%8D%95%E5%8C%96/">简单化<span class="tag-num">2</span></a></li><li class="tag tag1"><a class="route-link" href="/tag/%E4%BA%A4%E7%BB%99%E5%AD%90%E7%B1%BB/">交给子类<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/%E9%81%BF%E5%85%8D%E6%B5%AA%E8%B4%B9/">避免浪费<span class="tag-num">2</span></a></li><li class="tag tag5"><a class="route-link" href="/tag/cicd/">CI/CD<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E9%83%A8%E7%BD%B2/">部署<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/docker/">docker<span class="tag-num">1</span></a></li><li class="tag tag2"><a class="route-link" href="/tag/%E8%B8%A9%E5%9D%91%E8%AE%B0%E5%BD%95/">踩坑记录<span class="tag-num">1</span></a></li><li class="tag tag1 active"><a class="route-link" href="/tag/%E9%A3%8E%E6%A0%BC/">风格<span class="tag-num">1</span></a></li><li class="tag tag3"><a class="route-link" href="/tag/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F/">公理系统<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/mobile/">mobile<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%BF%80%E6%B4%BB/">激活<span class="tag-num">1</span></a></li><li class="tag tag7"><a class="route-link" href="/tag/%E6%8E%A8%E5%8D%B8%E8%B4%A3%E4%BB%BB/">推卸责任<span class="tag-num">1</span></a></li><li class="tag tag0"><a class="route-link" href="/tag/%E5%B7%A5%E5%8E%82%E6%96%B9%E6%B3%95/">工厂方法<span class="tag-num">1</span></a></li><li class="tag tag6"><a class="route-link" href="/tag/%E6%95%B4%E4%BD%93%E7%9A%84%E6%9B%BF%E6%8D%A2%E7%AE%97%E6%B3%95/">整体的替换算法<span class="tag-num">1</span></a></li><li class="tag tag8"><a class="route-link" href="/tag/%E8%AE%BF%E9%97%AE%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%B9%B6%E5%A4%84%E7%90%86%E6%95%B0%E6%8D%AE/">访问数据结构并处理数据<span class="tag-num">1</span></a></li></ul><div id="article-list" class="vp-article-list" role="feed"><div class="vp-article-wrapper"><article class="vp-article-item" vocab="https://schema.org/" typeof="Article"><!--[--><!--]--><!----><a class="route-link" href="/tech/style.html"><header class="vp-article-title"><!----><!----><span property="headline">风格统一</span></header></a><div class="vp-article-excerpt">
@@ -49,7 +49,7 @@
 charset = utf-8
 trim_trailing_whitespace = true
 insert_final_newline = true
-</code></pre></div></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-08-25T12:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category1 clickable" role="navigation">风格</span><!--]--><meta property="articleSection" content="风格"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag1 clickable" role="navigation">风格</span><!--]--><meta property="keywords" content="风格"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+</code></pre></div></div><hr class="vp-article-hr"><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-08-25T12:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category1 clickable" role="navigation">风格</span><!--]--><meta property="articleSection" content="风格"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag1 clickable" role="navigation">风格</span><!--]--><meta property="keywords" content="风格"></span></div></article></div><div class="vp-pagination"></div></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/DesignPrinciples.html b/tech/DesignPatterns/DesignPrinciples.html
index 4919753..027887f 100644
--- a/tech/DesignPatterns/DesignPrinciples.html
+++ b/tech/DesignPatterns/DesignPrinciples.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/DesignPrinciples.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="设计模式七大原则"><meta property="og:description" content="类的设计原则有七个，包括：开闭原则、里氏代换原则、迪米特原则（最少知道原则）、单一职责原则、接口分隔原则、依赖倒置原则、组合/聚合复用原则。"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="typescript"><meta property="article:published_time" content="2024-10-21T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"设计模式七大原则","image":[""],"datePublished":"2024-10-21T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>设计模式七大原则 | blog</title><meta name="description" content="类的设计原则有七个，包括：开闭原则、里氏代换原则、迪米特原则（最少知道原则）、单一职责原则、接口分隔原则、依赖倒置原则、组合/聚合复用原则。">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/DesignPrinciples.html-BLnXHGN8.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/DesignPrinciples.html-BAjp9viD.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->设计模式七大原则</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-21T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 6 分钟</span><meta property="timeRequired" content="PT6M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag3 clickable" role="navigation">typescript</span><!--]--><meta property="keywords" content="设计模式,typescript"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#关系">关系</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#开闭原则">开闭原则</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#实现方法">实现方法</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#里氏代换原则">里氏代换原则</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#里氏代换原则-1">里氏代换原则</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#实现方法-1">实现方法</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#示例">示例</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#迪米特原则">迪米特原则</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#迪米特原则-1">迪米特原则</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#实现方法-2">实现方法</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#单一职责原则">单一职责原则</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#实现方法-3">实现方法</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#示例-1">示例</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#接口隔离原则">接口隔离原则</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#依赖倒置原则">依赖倒置原则</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#实现方法-4">实现方法</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#示例-2">示例</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#组合-聚合复用原则">组合/聚合复用原则</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#实现方法-5">实现方法</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#示例-3">示例</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#总结">总结</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><p>类的设计原则有七个，包括：开闭原则、里氏代换原则、迪米特原则（最少知道原则）、单一职责原则、接口分隔原则、依赖倒置原则、组合/聚合复用原则。</p><!-- more --><h2 id="关系" tabindex="-1"><a class="header-anchor" href="#关系"><span>关系</span></a></h2><p>七大原则之间并不是相互孤立的，而是相互关联的。一个原则可以是另一个原则的加强或基础。违反其中一个原则，可能同时违反其他原则。</p><p>开闭原则是面向对象可复用设计的基石，其他设计原则是实现开闭原则的手段和工具。</p><p>通常，可以将这七个原则分为以下两部分：</p><ul><li>设计目标：开闭原则、里氏代换原则、迪米特原则</li><li>设计方法：单一职责原则、接口分隔原则、依赖倒置原则、组合/聚合复用原则</li></ul><h2 id="开闭原则" tabindex="-1"><a class="header-anchor" href="#开闭原则"><span>开闭原则</span></a></h2><ul><li>对扩展开放</li><li>对修改关闭</li></ul><p>根据开闭原则，在设计一个系统模块的时候，应该可以在不修改原模块的基础上，扩展其功能。</p><h3 id="实现方法" tabindex="-1"><a class="header-anchor" href="#实现方法"><span>实现方法</span></a></h3><ol><li>使用抽象类和接口：通过定义抽象类和接口，可以在不修改现有代码的情况下，增加新的实现。</li><li>使用设计模式：例如策略模式、装饰者模式等，可以在不改变原有代码的情况下，动态地扩展对象的行为。</li><li>遵循单一职责原则：确保每个类只有一个职责，这样在扩展功能时，不会影响其他功能。</li></ol><!-- some plantuml demo --><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuIh9BCb9LNY-PjdJ2HrFzpIydBxsQT_yfnqpkJBpIbABqXAJKnKSaug3KulAKeiKghaK5BGLYa4S3Kq5AuMWrEBId1AkMYwkv9p4uc85vvpCrBmIi39TXTnAg2uhX0bQO0DIyeFpSrD3CZBpqZKq4RgB8SepSmjoKdE1vXGJOpFKIbrTBOHgBeVKl1IWvm00" alt=""><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuIh9BCb9LNYoe_VvccLF9tGytTFmSlhQfttpdtRCv4hEIImkLd3EoKpDAr6evb9Gq5N8hGnEBIfBBLAmKe0mj832sWef-S7vkQaX6PbvwHgQNBLGdSKGfTLW9M2EXYPGOr1gSMbE2L0Lr6HTNIseKYw7rBmKeAi0" alt=""><h2 id="里氏代换原则" tabindex="-1"><a class="header-anchor" href="#里氏代换原则"><span>里氏代换原则</span></a></h2><h3 id="里氏代换原则-1" tabindex="-1"><a class="header-anchor" href="#里氏代换原则-1"><span>里氏代换原则</span></a></h3><ul><li>里氏代换原则规定子类不得重写父类的普通方法，只能重写父类的抽象方法；即子类可以扩展父类的功能，但是不能改变父类原有的功能。</li><li>派生类应当可以替换基类并出现在基类能够出现的任何地方，或者说如果我们把代码中使用基类的地方用它的派生类所代替，代码还能正常工作。</li></ul><h3 id="实现方法-1" tabindex="-1"><a class="header-anchor" href="#实现方法-1"><span>实现方法</span></a></h3><ol><li>使用抽象类和接口：确保子类实现父类的抽象方法，而不是重写父类的具体方法。</li><li>遵循契约：子类的方法签名应与父类一致，返回类型应与父类相同或是其子类型。</li><li>遵循行为一致性：子类应保持父类的行为，不应引入违反父类预期的新行为。</li></ol><h3 id="示例" tabindex="-1"><a class="header-anchor" href="#示例"><span>示例</span></a></h3><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuIh9BCb9LNY-PjdJ2HqlstkURUX_idlnizv5J_lcF-sOoPMOL5nIb9XSef2SarXShE2KMPIYKCsbeA2ja9PJgQ6fOALGbf-PmbNBnGLH45oGM5IKNwwGMb6IcfT2X0QGWl34akICr2Aekd8GJoC9fD4AB8si2LcvhguTM9xB0MWLq2y0" alt=""><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuIh9BCb9LNYoe_VvccLF9tIyREzvjg7_oUx5pteNFUsR_xHZ9bTYKd59KM9oYK9oJc9niO9JPb6AGZMNWeAsGbfEfOQcWfL2MNvc2bSj5nT4WJzGUMPoXa9gHKbgNWfE3GhL2YKPHVdb2dcfvGgXUSMb1GNvHIMfAVu5gKM99PdvUQuLoQa588Q6fhL2BS9ya7dXYIN96Qb5K6FBGJoD990zLc1fP4SXAzVLjGFBSpa0NGRqFG00" alt=""><h2 id="迪米特原则" tabindex="-1"><a class="header-anchor" href="#迪米特原则"><span>迪米特原则</span></a></h2><h3 id="迪米特原则-1" tabindex="-1"><a class="header-anchor" href="#迪米特原则-1"><span>迪米特原则</span></a></h3><p>一个实体应当尽量少地与其他实体之间发生相互作用，使得系统功能模块相对独立；降低类之间的耦合度，提高模块的相对独立性。</p><h3 id="实现方法-2" tabindex="-1"><a class="header-anchor" href="#实现方法-2"><span>实现方法</span></a></h3><ol><li><strong>引入中介者模式</strong>：通过中介者对象来管理对象之间的交互，减少对象之间的直接依赖。</li><li><strong>使用门面模式</strong>：通过门面对象提供统一的接口，隐藏系统的复杂性，减少对象之间的直接交互。</li><li><strong>限制公开方法</strong>：尽量减少类的公开方法，避免不必要的外部依赖。</li></ol><h2 id="单一职责原则" tabindex="-1"><a class="header-anchor" href="#单一职责原则"><span>单一职责原则</span></a></h2><ul><li>一个类只对应一个职责，其职责是引起该类变化的原因。</li><li>如果一个类需要改变，改变它的理由永远只有一个。如果存在多个改变它的理由，就需要重新设计该类。</li></ul><h3 id="实现方法-3" tabindex="-1"><a class="header-anchor" href="#实现方法-3"><span>实现方法</span></a></h3><ol><li><strong>职责分离</strong>：将不同的职责分离到不同的类中，每个类只负责一个职责。</li><li><strong>模块化设计</strong>：通过模块化设计，将不同的功能模块分开，确保每个模块只负责一个功能。</li><li><strong>重构</strong>：在发现类有多个职责时，及时进行重构，将不同的职责分离到不同的类中。</li></ol><h3 id="示例-1" tabindex="-1"><a class="header-anchor" href="#示例-1"><span>示例</span></a></h3><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// 不符合单一职责原则的类</span>
@@ -132,6 +132,6 @@
 <span class="token keyword">const</span> car <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">Car</span><span class="token punctuation">(</span>engine<span class="token punctuation">)</span><span class="token punctuation">;</span>
 car<span class="token punctuation">.</span><span class="token function">drive</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="总结" tabindex="-1"><a class="header-anchor" href="#总结"><span>总结</span></a></h2><ul><li><strong>开闭原则</strong>：对扩展开放，对修改关闭。</li><li><strong>里氏代换原则</strong>：子类可以替换父类，且程序行为不变。</li><li><strong>迪米特原则</strong>：尽量减少类之间的耦合。</li><li><strong>单一职责原则</strong>：一个类只负责一个职责。</li><li><strong>接口隔离原则</strong>：使用多个专门的接口，而不是一个通用接口。</li><li><strong>依赖倒置原则</strong>：高层模块不依赖低层模块，二者都依赖抽象。</li><li><strong>组合/聚合复用原则</strong>：优先使用组合/聚合，而不是继承。</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/DesignPrinciples.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link active prev" href="/tech/DesignPatterns/" aria-label="设计模式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->设计模式</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">迭代器模式<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/abstractFactory.html b/tech/DesignPatterns/abstractFactory.html
index 9628ead..7a64b40 100644
--- a/tech/DesignPatterns/abstractFactory.html
+++ b/tech/DesignPatterns/abstractFactory.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/abstractFactory.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="抽象工厂模式"><meta property="og:description" content="为什么要使用抽象工厂模式 抽象工厂模式提供一个接口，用于创建相关或依赖对象的家族，而无需明确指定具体类。它通过定义一个创建对象的接口来实现，这样子类可以决定实例化哪个类。抽象工厂模式使得一个类的实例化延迟到其子类。"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="typescript"><meta property="article:tag" content="生成实例"><meta property="article:published_time" content="2024-10-25T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"抽象工厂模式","image":[""],"datePublished":"2024-10-25T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>抽象工厂模式 | blog</title><meta name="description" content="为什么要使用抽象工厂模式 抽象工厂模式提供一个接口，用于创建相关或依赖对象的家族，而无需明确指定具体类。它通过定义一个创建对象的接口来实现，这样子类可以决定实例化哪个类。抽象工厂模式使得一个类的实例化延迟到其子类。">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/abstractFactory.html-DS3CgVqp.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/abstractFactory.html-D_oh5f2L.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->抽象工厂模式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-25T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 4 分钟</span><meta property="timeRequired" content="PT4M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag3 clickable" role="navigation">typescript</span><span class="page-tag-item tag6 clickable" role="navigation">生成实例</span><!--]--><meta property="keywords" content="设计模式,typescript,生成实例"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#为什么要使用抽象工厂模式">为什么要使用抽象工厂模式</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#示例代码">示例代码</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#增加其它工厂">增加其它工厂</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#拓展思路的要点">拓展思路的要点</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#易于增加具体工厂">易于增加具体工厂</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#难以增加新的零件">难以增加新的零件</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#相关的设计模式">相关的设计模式</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h2 id="为什么要使用抽象工厂模式" tabindex="-1"><a class="header-anchor" href="#为什么要使用抽象工厂模式"><span>为什么要使用抽象工厂模式</span></a></h2><p>抽象工厂模式提供一个接口，用于创建相关或依赖对象的家族，而无需明确指定具体类。它通过定义一个创建对象的接口来实现，这样子类可以决定实例化哪个类。抽象工厂模式使得一个类的实例化延迟到其子类。</p><!-- more --><ol><li><strong>解耦</strong>：抽象工厂模式通过将对象的创建过程抽象化，减少了客户端代码与具体类之间的耦合。</li><li><strong>一致性</strong>：确保同一工厂创建的一系列对象具有一致的接口和行为。</li><li><strong>扩展性</strong>：可以方便地增加新的产品族而不影响现有代码。</li></ol><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/dLJBJiCm4BptA_QO0k43Ske9WLGa3hqX3ajY5Qk94zaRH8JuTzPvsiQfIWyvT7TdTcSopSuGQcghSgEm4gR1N02-6zAOqmC_jUxWUmDp3V8IZG6t1N0BkHP8OY_LAScn8Lch31WWrV4EMbrEFxOPs1aFTD3OXI2UisLlxWMF8Y59fLYeiQMFMZieEyIedytVavz8LEEzAGJxnaKLdiJZuNcVR9r6ZCkA0F55GXK1iIDs1Mk5nR4yrMLzwVLjl0YB8f5S6CfyrcSjYnLYgttXSeqQQxvRanErubFemhssLxVKj9JunHNh-CubLxoANoK9DpoJdsPEssHDaCBxwoCNCbqQmH1tNIH35ZUYYtelKR63Pzth8LtOl8p5PFoBhG_M6fkJkZCfc5vUcjuCVvvijD3hz9T5E_sMkUF6PM0S3JmxuRF79lmjEzRB7yPV" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// factory.ts</span>
@@ -238,6 +238,6 @@
 <span class="token operator">&lt;</span>hr<span class="token operator">&gt;</span><span class="token operator">&lt;</span>address<span class="token operator">&gt;</span>gmw<span class="token operator">&lt;</span>/address<span class="token operator">&gt;</span>
 <span class="token operator">&lt;</span>/body<span class="token operator">&gt;</span><span class="token operator">&lt;</span>/html<span class="token operator">&gt;</span>
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="增加其它工厂" tabindex="-1"><a class="header-anchor" href="#增加其它工厂"><span>增加其它工厂</span></a></h2><p>如果只是为了编写包含 HTML 超链接集合的文件，这样的设计可能显得有些过于复杂。当只有一个具体工厂时，划分“抽象类”和“具体类”是没有必要的。然而，使用抽象工厂模式，我们可以轻松地添加其他具体工厂，例如TableFactory。</p><h2 id="拓展思路的要点" tabindex="-1"><a class="header-anchor" href="#拓展思路的要点"><span>拓展思路的要点</span></a></h2><h3 id="易于增加具体工厂" tabindex="-1"><a class="header-anchor" href="#易于增加具体工厂"><span>易于增加具体工厂</span></a></h3><p>在 Abstract Factory 模式中增加具体的工厂是非常容易的。这里说的“容易”指的是需要编写哪些类和需要实现哪些方法都非常清楚。</p><p>假设现在我们要在示例程序中增加新的具体工厂，那么需要做的就是编写 Factory、Link、Tray、Page 这 4 个类的子类，并实现它们定义的抽象方法。也就是说将 factory 包中的抽象部分全部具体化即可。</p><p>这样一来，无论要增加多少个具体工厂（或是要修改具体工厂的 Bug），都无需修改抽象工厂和 Main 部分。</p><h3 id="难以增加新的零件" tabindex="-1"><a class="header-anchor" href="#难以增加新的零件"><span>难以增加新的零件</span></a></h3><p>请试想一下要在 Abstract Factory 模式中增加新的零件时应当如何做。例如，我们要在 factory 包中增加一个表示图像的 Picture 零件。这时，我们必须要对所有的具体工厂进行相应的修改才行。例如，在 listfactory 包中，我们必须要做以下修改：</p><ul><li>在 ListFactory 中增加 createPicture 方法，</li><li>新增 ListPicture 类。</li></ul><p>已经编写完成的具体工厂越多，修改的工作量就会越大。</p><h2 id="相关的设计模式" tabindex="-1"><a class="header-anchor" href="#相关的设计模式"><span>相关的设计模式</span></a></h2><ul><li>Builder 模式</li><li>Factory Method 模式</li><li>Composite 模式</li><li>Singleton 模式</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/abstractFactory.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->builder 模式</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">Bridge 模式<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/adapter.html b/tech/DesignPatterns/adapter.html
index 43eb042..7b0e675 100644
--- a/tech/DesignPatterns/adapter.html
+++ b/tech/DesignPatterns/adapter.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/adapter.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="适配器模式"><meta property="og:description" content="适配器模式 适配器模式（Adapter Pattern）是一种结构型设计模式，它允许将一个类的接口转换成客户希望的另一个接口。适配器模式使得原本由于接口不兼容而不能一起工作的那些类可以一起工作。 为什么要用适配器模式 在软件开发中，经常会遇到需要使用一些现有的类，但它们的接口并不符合当前系统的需求。适配器模式通过创建一个适配器类，将现有类的接口转换为所..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="typescript"><meta property="article:published_time" content="2024-10-21T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"适配器模式","image":[""],"datePublished":"2024-10-21T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>适配器模式 | blog</title><meta name="description" content="适配器模式 适配器模式（Adapter Pattern）是一种结构型设计模式，它允许将一个类的接口转换成客户希望的另一个接口。适配器模式使得原本由于接口不兼容而不能一起工作的那些类可以一起工作。 为什么要用适配器模式 在软件开发中，经常会遇到需要使用一些现有的类，但它们的接口并不符合当前系统的需求。适配器模式通过创建一个适配器类，将现有类的接口转换为所...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/adapter.html-B2UlYWFL.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/adapter.html-x6kHt0VN.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->适配器模式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-21T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag3 clickable" role="navigation">typescript</span><!--]--><meta property="keywords" content="设计模式,typescript"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#适配器模式">适配器模式</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#为什么要用适配器模式">为什么要用适配器模式</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#类比">类比</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#类比-1">类比</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#示例程序">示例程序</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#运行结果">运行结果</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#相关的设计模式">相关的设计模式</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h2 id="适配器模式" tabindex="-1"><a class="header-anchor" href="#适配器模式"><span>适配器模式</span></a></h2><p>适配器模式（Adapter Pattern）是一种结构型设计模式，它允许将一个类的接口转换成客户希望的另一个接口。适配器模式使得原本由于接口不兼容而不能一起工作的那些类可以一起工作。</p><h3 id="为什么要用适配器模式" tabindex="-1"><a class="header-anchor" href="#为什么要用适配器模式"><span>为什么要用适配器模式</span></a></h3><p>在软件开发中，经常会遇到需要使用一些现有的类，但它们的接口并不符合当前系统的需求。适配器模式通过创建一个适配器类，将现有类的接口转换为所需的接口，从而使得现有类可以在新的环境中使用。</p><h3 id="类比" tabindex="-1"><a class="header-anchor" href="#类比"><span>类比</span></a></h3><h3 id="类比-1" tabindex="-1"><a class="header-anchor" href="#类比-1"><span>类比</span></a></h3><table><thead><tr><th></th><th>比喻</th><th>示例程序</th></tr></thead><tbody><tr><td>实际需求</td><td>交流100V</td><td>Banner</td></tr><tr><td>变换装置</td><td>适配器</td><td>PrintBanner</td></tr><tr><td>需求</td><td>直流12V</td><td>Print</td></tr></tbody></table><h3 id="示例程序" tabindex="-1"><a class="header-anchor" href="#示例程序"><span>示例程序</span></a></h3><p>Adapter 有两种方式实现</p><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuIh9BCb9jL9uldlviyxzN9bv9Qb5QOd9gGe1HK2sGZMNWe9s0OWPdfgOhQ49vmQN5ENdfGC5QhcuadCIYuiLd1BpybAB83gAC_BBmpDBCW8IYrBp8BfWGex5G1kGzO4jWcfEhIX9pKk1cvMPMv2JcfkQLr9CWdCSW2O0FGO0" alt=""><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuIh9BCb9jL9ukdpAiyuPN8b9nIL5YSab2iavYSN52W55cNab2jLS2WhQ1I1cU6fYjeOcd1jSKfIVbmuKgENYWcXmIipBIos2w2ZEo2yFpop924WiIis3w889EHQNf1OXwmDR1DMSMb6IcfS25GEPf9i4bh22caw4Qv2DqzNLWZaBxaq7e0L0pmC0" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// banner.ts</span>
@@ -111,6 +111,6 @@
 <span class="token punctuation">(</span>Hello<span class="token punctuation">)</span>
 *Hello*
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="相关的设计模式" tabindex="-1"><a class="header-anchor" href="#相关的设计模式"><span>相关的设计模式</span></a></h2><ul><li>Bridge</li><li>Decorator</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/adapter.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->迭代器模式</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">Template Method 模式<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/bridge.html b/tech/DesignPatterns/bridge.html
index c88673b..157e3cf 100644
--- a/tech/DesignPatterns/bridge.html
+++ b/tech/DesignPatterns/bridge.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/bridge.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="Bridge 模式"><meta property="og:description" content="Bridge 模式在“类的功能层次结构”和“类的实现层次结构”之间搭建桥梁。"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="TypeScript"><meta property="article:tag" content="分开考虑"><meta property="article:published_time" content="2024-10-25T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"Bridge 模式","image":[""],"datePublished":"2024-10-25T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>Bridge 模式 | blog</title><meta name="description" content="Bridge 模式在“类的功能层次结构”和“类的实现层次结构”之间搭建桥梁。">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/bridge.html-LTDknqB7.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/bridge.html-DzkNbynT.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->Bridge 模式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-25T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 6 分钟</span><meta property="timeRequired" content="PT6M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag6 clickable" role="navigation">分开考虑</span><!--]--><meta property="keywords" content="设计模式,TypeScript,分开考虑"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#使用此设计模式的理由">使用此设计模式的理由</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#类的层次结构的两个作用">类的层次结构的两个作用</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#增加新功能时">增加新功能时</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#增加新的实现时">增加新的实现时</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#类的层次结构的混杂和分离">类的层次结构的混杂和分离</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#示例代码">示例代码</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#类的一览表">类的一览表</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#countdisplay-ts">countDisplay.ts</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#运行结果">运行结果</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#拓展思路的要点">拓展思路的要点</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#分开后更容易扩展">分开后更容易扩展</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#继承是强关联-委托是弱关联">继承是强关联，委托是弱关联</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#相关的设计模式">相关的设计模式</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><p>Bridge 模式在“类的功能层次结构”和“类的实现层次结构”之间搭建桥梁。</p><!-- more --><h2 id="使用此设计模式的理由" tabindex="-1"><a class="header-anchor" href="#使用此设计模式的理由"><span>使用此设计模式的理由</span></a></h2><p>Bridge 模式的主要目的是将抽象部分与实现部分分离，使它们可以独立变化。这种模式通过组合而不是继承来实现功能的扩展，减少了类之间的耦合度，提高了系统的可扩展性和可维护性。</p><h2 id="类的层次结构的两个作用" tabindex="-1"><a class="header-anchor" href="#类的层次结构的两个作用"><span>类的层次结构的两个作用</span></a></h2><h3 id="增加新功能时" tabindex="-1"><a class="header-anchor" href="#增加新功能时"><span>增加新功能时</span></a></h3><p>假设现在有一个类 <code>Something</code>，当我们想在 <code>Something</code> 中增加新功能时（例如增加一个具体方法），会编写一个 <code>Something</code> 类的子类（派生类），即 <code>SomethingGood</code> 类。这样就构成了一个小小的类层次结构。这就是为了增加新功能而产生的层次结构。</p><p>SomeThing</p><p>----\ SomeThingGood</p><h3 id="增加新的实现时" tabindex="-1"><a class="header-anchor" href="#增加新的实现时"><span>增加新的实现时</span></a></h3><p>在 Template Method 模式（第 3 章）中，我们学习了抽象类的作用。抽象类声明了一些抽象方法，定义了接口 (API)，然后子类负责实现这些抽象方法。父类的任务是通过声明抽象方法的方式定义接口 (API)，而子类的任务是实现抽象方法。正是由于父类和子类的这种任务分担，我们才可以编写出具有高可替换性的类。</p><p>这里其实也存在层次结构。例如，当子类实现了父类 <code>AbstractClass</code> 类的抽象方法时，它们之间就构成了一个小小的层次结构。</p><p>AbstractClass</p><p>----\ ConcreteClass</p><p>但是，这里的类的层次结构并非用于增加功能，也就是说，这种层次结构并非用于方便我们增加新的方法。它的真正作用是帮助我们实现任务分担。</p><h3 id="类的层次结构的混杂和分离" tabindex="-1"><a class="header-anchor" href="#类的层次结构的混杂和分离"><span>类的层次结构的混杂和分离</span></a></h3><p>当我们想要编写子类时，就需要先确认自己的意图：“我是要增加功能呢？还是要增加实现呢？”</p><p>当类的层次结构只有一层时，功能层次结构与实现层次结构是混杂在一个层次结构中的。这样很容易使类的层次结构变得复杂，也难以透彻地理解类的层次结构。因为自己难以确定究竟应该在类的哪一个层次结构中去增加子类。</p><p>因此，我们需要将“类的功能层次结构&quot;与“类的实现层次结构&quot;分离为两个独立的类层次结构。当然，如果只是简单地将它们分开，两者之间必然会缺少联系。所以我们还需要在它们之间搭建一座桥梁。本章中要学习的 Bridge 模式的作用就是搭建这座桥梁。</p><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><h3 id="类的一览表" tabindex="-1"><a class="header-anchor" href="#类的一览表"><span>类的一览表</span></a></h3><table><thead><tr><th>在桥的哪一侧</th><th>名字</th><th>说明</th></tr></thead><tbody><tr><td>类的功能层次结构</td><td>Display</td><td>负责“显示”的类</td></tr><tr><td>类的功能层次结构</td><td>CountDisplay</td><td>增加了“只显示规定次数”这一功能的类</td></tr><tr><td>类的实现层次结构</td><td>DisplayImpl</td><td>负责“显示”的类</td></tr><tr><td>类的实现层次结构</td><td>StringDisplayImpl</td><td>“用字符串显示”的类</td></tr><tr><td>主程序</td><td>Main</td><td>试程序行为的类</td></tr></tbody></table><p>Display 类（代码清单 9 · 1 ）的功能是抽象的，负责“显示一些东西&quot;。该类位于“类的功能层次结构&quot;的最上层。在 impl 字段中保存的是实现了 Display 类的具体功能的实例（ impl 是 implementation （实现）的缩写）。该实例通过 Display 类的构造函数被传递给 Display 类，然后保存在字段中，以供后面的处理使用（ impl 字段即是类的两个层次结构的“桥梁&quot;）。</p><p>CountDisplay 类继承了 Display 类的 open、print、close 方法，并使用它们来增加这个新功能。这就是“类的功能层次结构&quot;。</p><img src="https://www.plantuml.com/plantuml/svg/fPBF2i8m3CRlUueSDsGlq9CmBuAWu1FKhMYXVqQREcNuxcRLokhmvAMGNzBa-zAkFNA7GQkYLTnxs4ZVAtw7iG2eGUfUiSIs511TfRXSPAkOjhqmPSNWQcKNGU-amOoqodgHaUxTCx57yHRKs60mgH8t5ARxg1pZrNd5BqqwA9If1gKMde49-YJSR20_UNIyHSXMCJM1roJ7X_stEMA7XJ-2JMRnO-U8L7oUj_xoDB7NyaaCcmwgZ_4WExmasN7CebavkrFzANaQ6Lzk9qrc93r6NTjiHmo25yMQpD1tUW80" alt=""><h3 id="countdisplay-ts" tabindex="-1"><a class="header-anchor" href="#countdisplay-ts"><span>countDisplay.ts</span></a></h3><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token keyword">import</span> <span class="token punctuation">{</span> Display <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&#39;./display&#39;</span><span class="token punctuation">;</span>
@@ -141,6 +141,6 @@
 <span class="token operator">|</span>Hello, Universe.<span class="token operator">|</span>
 +----------------+
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="拓展思路的要点" tabindex="-1"><a class="header-anchor" href="#拓展思路的要点"><span>拓展思路的要点</span></a></h2><h3 id="分开后更容易扩展" tabindex="-1"><a class="header-anchor" href="#分开后更容易扩展"><span>分开后更容易扩展</span></a></h3><p>Bridge 模式的特征是将“类的功能层次结构&quot;与“类的实现层次结构&quot;分离开了。将类的这两个层次结构分离开有利于独立地对它们进行扩展。当想要增加功能时，只需要在“类的功能层次结构&quot;一侧增加类即可，不必对“类的实现层次结构&quot;做任何修改。而且，增加后的功能可以被“所有的实现”使用。</p><p>例如，我们可以将“类的功能层次结构&quot;应用于软件所运行的操作系统上。如果我们将某个程序中依赖于操作系统的部分划分为 Windows 版、Macintosh 版、Unix 版，那么我们就可以用 Bridge 模式中的“类的实现层次结构&quot;来表现这些依赖于操作系统的部分。也就是说，我们需要编写一个定义这些操作系统的共同接口（API）的 Implementor 角色，然后编写 Windows 版、Macintosh 版、Unix 版的 3 个 ConcreteImplementor 角色。这样一来，无论在“类的功能层次结构&quot;中增加多少个功能，它们都可以工作于这 3 个操作系统上。</p><h3 id="继承是强关联-委托是弱关联" tabindex="-1"><a class="header-anchor" href="#继承是强关联-委托是弱关联"><span>继承是强关联，委托是弱关联</span></a></h3><p>继承是强关联关系，但委托是弱关联关系。这是因为只有 Display 类的实例生成时，才与作为参数被传入的类构成关联。例如，在示例程序中，当 Main 类生成 Display 类和 CountDisplay 类的实例时，才将 StringDisplayImpl 的实例作为参数传递给 Display 类和 CountDisplay 类。如果我们不传递 StringDisplayImpl 类的实例，而是将其他 ConcreteImplementor 角色的实例传递给 Display 类和 CountDisplay 类，就能很容易地改变实现。这时，发生变化的代码只有 Main 类，Display 类和 DisplayImpl 类则不需要做任何修改。</p><h2 id="相关的设计模式" tabindex="-1"><a class="header-anchor" href="#相关的设计模式"><span>相关的设计模式</span></a></h2><ul><li>Template Method 模式</li><li>Abstract Factory 模式</li><li>Adapter 模式</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/bridge.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->抽象工厂模式</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">Strategy 模式<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/builder.html b/tech/DesignPatterns/builder.html
index 65e383f..68c9b5a 100644
--- a/tech/DesignPatterns/builder.html
+++ b/tech/DesignPatterns/builder.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/builder.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="builder 模式"><meta property="og:description" content="为什么要使用 Builder 模式 Builder 模式通过将对象的构建过程与其表示分离，使得同样的构建过程可以创建不同的表示。它主要用于以下情况： 复杂对象的创建：当一个对象的构建过程非常复杂时，Builder 模式可以将构建过程分解为多个步骤，使代码更易于维护和理解。 不同的表示：当需要创建不同表示的对象时，Builder 模式允许使用相同的构建过..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="typescript"><meta property="article:tag" content="生成实例"><meta property="article:published_time" content="2024-10-22T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"builder 模式","image":[""],"datePublished":"2024-10-22T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>builder 模式 | blog</title><meta name="description" content="为什么要使用 Builder 模式 Builder 模式通过将对象的构建过程与其表示分离，使得同样的构建过程可以创建不同的表示。它主要用于以下情况： 复杂对象的创建：当一个对象的构建过程非常复杂时，Builder 模式可以将构建过程分解为多个步骤，使代码更易于维护和理解。 不同的表示：当需要创建不同表示的对象时，Builder 模式允许使用相同的构建过...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/builder.html-Ba33pTyP.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/builder.html-B7MALN7e.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->builder 模式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-22T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 4 分钟</span><meta property="timeRequired" content="PT4M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag3 clickable" role="navigation">typescript</span><span class="page-tag-item tag6 clickable" role="navigation">生成实例</span><!--]--><meta property="keywords" content="设计模式,typescript,生成实例"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#为什么要使用-builder-模式">为什么要使用 Builder 模式</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#代码示例">代码示例</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#运行结果">运行结果</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#相关设计模式">相关设计模式</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#拓展思路的要点">拓展思路的要点</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#谁知道什么">谁知道什么</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#设计时能够决定的事情和不能决定的事情">设计时能够决定的事情和不能决定的事情</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#代码的阅读方法和修改方法">代码的阅读方法和修改方法</a></li><!----><!--]--></ul></li><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h2 id="为什么要使用-builder-模式" tabindex="-1"><a class="header-anchor" href="#为什么要使用-builder-模式"><span>为什么要使用 Builder 模式</span></a></h2><p>Builder 模式通过将对象的构建过程与其表示分离，使得同样的构建过程可以创建不同的表示。它主要用于以下情况：</p><ol><li><strong>复杂对象的创建</strong>：当一个对象的构建过程非常复杂时，Builder 模式可以将构建过程分解为多个步骤，使代码更易于维护和理解。</li><li><strong>不同的表示</strong>：当需要创建不同表示的对象时，Builder 模式允许使用相同的构建过程来生成不同的对象表示。</li><li><strong>代码复用</strong>：通过将构建过程封装在 Director 类中，可以在不同的上下文中重用相同的构建逻辑。</li></ol><h2 id="代码示例" tabindex="-1"><a class="header-anchor" href="#代码示例"><span>代码示例</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/pPA_2i8m4CRtFaN65CaB594Y3WgwQ3TngEcr1DCMaei8whkR_ab85MTTRlZko-Nt9PTgp1MQMaPSvbgJfH6o04Nk4I6pEhz09b02nQucHACIJHKdvDgAmZaElKXjxujXWr1hAhhg7CTJuE6orK2Ty8n6b9LGmB4TMDXv04iSONVGEUXxC-x7jeszp73y7BtETjimAIk5X2QlVSJXnh845IY_UGyhL81xq4RsIKOSdoM36qwo_3stevq_60k_Oje8SaL-5HXR-0L8eIdiuhu0" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// builder.ts</span>
@@ -161,6 +161,6 @@
 Creating an HTML file<span class="token punctuation">..</span>.
 <span class="token operator">&lt;</span>html<span class="token operator">&gt;</span><span class="token operator">&lt;</span>head<span class="token operator">&gt;</span><span class="token operator">&lt;</span>title<span class="token operator">&gt;</span>问候<span class="token operator">&lt;</span>/title<span class="token operator">&gt;</span><span class="token operator">&lt;</span>/head<span class="token operator">&gt;</span><span class="token operator">&lt;</span>body<span class="token operator">&gt;</span><span class="token operator">&lt;</span>h<span class="token operator"><span class="token file-descriptor important">1</span>&gt;</span>问候<span class="token operator">&lt;</span>/h<span class="token operator"><span class="token file-descriptor important">1</span>&gt;</span><span class="token operator">&lt;</span>p<span class="token operator">&gt;</span>从早上到下午<span class="token operator">&lt;</span>/p<span class="token operator">&gt;</span><span class="token operator">&lt;</span>ul<span class="token operator">&gt;</span><span class="token operator">&lt;</span>li<span class="token operator">&gt;</span>早上好。<span class="token operator">&lt;</span>/li<span class="token operator">&gt;</span><span class="token operator">&lt;</span>li<span class="token operator">&gt;</span>下午好。<span class="token operator">&lt;</span>/li<span class="token operator">&gt;</span><span class="token operator">&lt;</span>/ul<span class="token operator">&gt;</span><span class="token operator">&lt;</span>p<span class="token operator">&gt;</span>晚上<span class="token operator">&lt;</span>/p<span class="token operator">&gt;</span><span class="token operator">&lt;</span>ul<span class="token operator">&gt;</span><span class="token operator">&lt;</span>li<span class="token operator">&gt;</span>晚上好。<span class="token operator">&lt;</span>/li<span class="token operator">&gt;</span><span class="token operator">&lt;</span>li<span class="token operator">&gt;</span>晚安。<span class="token operator">&lt;</span>/li<span class="token operator">&gt;</span><span class="token operator">&lt;</span>li<span class="token operator">&gt;</span>再见。<span class="token operator">&lt;</span>/li<span class="token operator">&gt;</span><span class="token operator">&lt;</span>/ul<span class="token operator">&gt;</span><span class="token operator">&lt;</span>/body<span class="token operator">&gt;</span><span class="token operator">&lt;</span>/html<span class="token operator">&gt;</span>が作成されました。
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="相关设计模式" tabindex="-1"><a class="header-anchor" href="#相关设计模式"><span>相关设计模式</span></a></h2><ul><li>Template Method 模式</li><li>Composite 模式</li><li>Abstract Factory 模式</li><li>Facade 模式</li></ul><h2 id="拓展思路的要点" tabindex="-1"><a class="header-anchor" href="#拓展思路的要点"><span>拓展思路的要点</span></a></h2><h3 id="谁知道什么" tabindex="-1"><a class="header-anchor" href="#谁知道什么"><span>谁知道什么</span></a></h3><p>在面向对象编程中，“谁知道什么”是非常重要的。Builder 模式通过将对象的构建过程与其表示分离，明确了各个类的职责分工。Director 类知道如何构建复杂对象，但不知道对象的具体表示；Builder 类知道如何生成对象的具体表示，但不知道构建的具体步骤。这种职责分离使得代码更加清晰、易于维护和扩展。</p><p>正是因为不知道才能够替换，正是因为可以替换，组件才具有高价。作为设计人员，我们必须时刻关汴这种“可替換性”</p><h3 id="设计时能够决定的事情和不能决定的事情" tabindex="-1"><a class="header-anchor" href="#设计时能够决定的事情和不能决定的事情"><span>设计时能够决定的事情和不能决定的事情</span></a></h3><p>在设计软件时，有些事情是可以在设计阶段决定的，而有些事情则需要在运行时决定。Builder 模式通过将构建过程与表示分离，使得在设计时可以决定构建的步骤和逻辑，而具体的表示则可以在运行时灵活选择。这种设计方式提高了系统的灵活性和可扩展性。</p><h3 id="代码的阅读方法和修改方法" tabindex="-1"><a class="header-anchor" href="#代码的阅读方法和修改方法"><span>代码的阅读方法和修改方法</span></a></h3><p>在编程时，虽然有时需要从零开始编写代码，但更多时候我们都是在现有代码的基础上进行增加和修改。</p><p>这时，我们需要先阅读现有代码。不过，只是阅读抽象类的代码是无法获取很多信息的（虽然可以从方法名中获得线索）。</p><p>让我们再回顾一下示例程序。即使理解了 Builder 抽象类，也无法理解程序整体。至少必须在阅读了 Director 的代码后才能理解 Builder 类的使用方法（Builder 类的方法的调用方法）。然后再去看看 TextBuilder 类和 HTMLBuilder 类的代码，就可以明白调用 Builder 类的方法后具体会进行什么样的处理。</p><p>如果没有理解各个类的角色就动手增加和修改代码，在判断到底应该修改哪个类时，就会很容易出错。例如，如果修改 Builder 类，那么就会对类中调用 Builder 类方法的地方和 Builder 类的子类产生影响。或是如果不小心修改了 Director 类，在其内部调用了类的特有的方法，则会导致其失去作为可复用组件的独立性，而且当将子类替换为 HTMLBuilder 时，程序可能会无法正常工作。</p></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/builder.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->Prototype 模式</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">抽象工厂模式<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/chainOfResponsibility.html b/tech/DesignPatterns/chainOfResponsibility.html
index 571c00c..f95401b 100644
--- a/tech/DesignPatterns/chainOfResponsibility.html
+++ b/tech/DesignPatterns/chainOfResponsibility.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/chainOfResponsibility.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="chainOfResponsibility 模式"><meta property="og:description" content="“推卸责任"听起来有些贬义的意思，但是有时候也确实存在需要“推卸责任"的情况。例如，当外部请求程序进行某个处理，但程序暂时无法直接决定由哪个对象负责处理时，就需要推卸责任。这种情况下，我们可以考虑将多个对象组成一条职责链，然后按照它们在职责链上的顺序一个一个地找出到底应该谁来负责处理。"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="TypeScript"><meta property="article:tag" content="推卸责任"><meta property="article:published_time" content="2024-10-25T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"chainOfResponsibility 模式","image":[""],"datePublished":"2024-10-25T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>chainOfResponsibility 模式 | blog</title><meta name="description" content="“推卸责任"听起来有些贬义的意思，但是有时候也确实存在需要“推卸责任"的情况。例如，当外部请求程序进行某个处理，但程序暂时无法直接决定由哪个对象负责处理时，就需要推卸责任。这种情况下，我们可以考虑将多个对象组成一条职责链，然后按照它们在职责链上的顺序一个一个地找出到底应该谁来负责处理。">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/chainOfResponsibility.html-DhJtx4gW.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/chainOfResponsibility.html-CpbeYqOk.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->chainOfResponsibility 模式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-25T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 3 分钟</span><meta property="timeRequired" content="PT3M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag7 clickable" role="navigation">推卸责任</span><!--]--><meta property="keywords" content="设计模式,TypeScript,推卸责任"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#为什么使用此类">为什么使用此类</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#示例代码">示例代码</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#运行结果">运行结果</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#相关的设计模式">相关的设计模式</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><p>“推卸责任&quot;听起来有些贬义的意思，但是有时候也确实存在需要“推卸责任&quot;的情况。例如，当外部请求程序进行某个处理，但程序暂时无法直接决定由哪个对象负责处理时，就需要推卸责任。这种情况下，我们可以考虑将多个对象组成一条职责链，然后按照它们在职责链上的顺序一个一个地找出到底应该谁来负责处理。</p><!-- more --><p>当一个人被要求做什么事情时，如果他可以做就自己做，如果不能做就将“要求&quot;转给另外一个人。下一个人如果可以自己处理，就自己做；如果也不能自己处理，就再转给另外一个人““这就是 Chain Of Responsibility 模式。</p><h3 id="为什么使用此类" tabindex="-1"><a class="header-anchor" href="#为什么使用此类"><span>为什么使用此类</span></a></h3><p>使用 Chain of Responsibility 模式有以下几个优点：</p><ol><li><strong>解耦请求发送者和接收者</strong>：发送者无需知道哪个对象会处理请求。</li><li><strong>动态组合职责链</strong>：可以在运行时动态地改变职责链的结构。</li><li><strong>增加灵活性</strong>：可以很容易地添加新的处理者而不影响现有代码。</li></ol><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><p>在这个示例中，我们使用了 Chain of Responsibility 模式来处理一系列的请求。每个请求都会沿着职责链传递，直到有一个对象能够处理它。这样做的好处是请求的发送者和接收者解耦，发送者无需知道哪个对象会处理请求。</p><img src="https://www.plantuml.com/plantuml/svg/hP912i8m44NtESM0cuhq0btr058NzG9fCqeWpPHaAeBqxewD2eeM5NV9dyVd3KmPMGSUEgTq4pdebg5rEaQeXxwdm71I03butM410bY_Jm4UkRX1agmW8bSIPW-JvHEJtXa76XedZTlq4En0rWYpW82Ht05VCGsHG-qdp937sPwTjkujC2gLrgpejgXeepVtnK-Jy0SozwgrxIpFjENWBaG1VkWQ35_tRupvcslTOskrcxLDcZ_hNaVmjcml1pFzikL3pbHFTtQ9hnStgbByv4hF" alt=""><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuKfCBialKd3EoKpDA-62K0gwTWf--S6b1GNvHILM2iKGXaP9KNvfKawg9XTS3gJG9pCtimItMcHfaFBWWjJapCGSt1fG5O2q-AUa4AtSHXT9EQhbG2bKnKZ-0CeXguM50r0OheRB8JKl1HXW0000" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// limitSupport.ts</span>
@@ -171,6 +171,6 @@
 <span class="token punctuation">[</span>Trouble <span class="token number">462</span><span class="token punctuation">]</span> cannot be resolved.
 <span class="token punctuation">[</span>Trouble <span class="token number">495</span><span class="token punctuation">]</span> is resolved by <span class="token punctuation">[</span>Elmo<span class="token punctuation">]</span>.
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="相关的设计模式" tabindex="-1"><a class="header-anchor" href="#相关的设计模式"><span>相关的设计模式</span></a></h2><ul><li>Composite 模式</li><li>Command 模式</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/chainOfResponsibility.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->Visitor 模式</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">facade 模式<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/command.html b/tech/DesignPatterns/command.html
index 31b0284..9c26120 100644
--- a/tech/DesignPatterns/command.html
+++ b/tech/DesignPatterns/command.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/command.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="Command 模式"><meta property="og:description" content="为什么使用此模式 Command 模式将请求封装成对象，使得可以用不同的请求、队列或者日志来参数化其他对象。Command 模式也支持可撤销的操作。 示例代码 运行结果 拓展思路的要点 命令中应该包含哪些信息 在命令模式中，命令对象通常包含以下信息： 接收者（Receiver）：执行命令的对象。接收者包含了执行具体操作的逻辑。 动作（Action）：要..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="TypeScript"><meta property="article:tag" content="用类实现"><meta property="article:published_time" content="2024-10-29T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"Command 模式","image":[""],"datePublished":"2024-10-29T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>Command 模式 | blog</title><meta name="description" content="为什么使用此模式 Command 模式将请求封装成对象，使得可以用不同的请求、队列或者日志来参数化其他对象。Command 模式也支持可撤销的操作。 示例代码 运行结果 拓展思路的要点 命令中应该包含哪些信息 在命令模式中，命令对象通常包含以下信息： 接收者（Receiver）：执行命令的对象。接收者包含了执行具体操作的逻辑。 动作（Action）：要...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/command.html-d4IhdjVF.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/command.html-Bzqk5uGA.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->Command 模式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-29T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 3 分钟</span><meta property="timeRequired" content="PT3M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag1 clickable" role="navigation">用类实现</span><!--]--><meta property="keywords" content="设计模式,TypeScript,用类实现"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#为什么使用此模式">为什么使用此模式</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#示例代码">示例代码</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#运行结果">运行结果</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#拓展思路的要点">拓展思路的要点</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#命令中应该包含哪些信息">命令中应该包含哪些信息</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#保存历史记录">保存历史记录</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#相关的设计模式">相关的设计模式</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h2 id="为什么使用此模式" tabindex="-1"><a class="header-anchor" href="#为什么使用此模式"><span>为什么使用此模式</span></a></h2><p>Command 模式将请求封装成对象，使得可以用不同的请求、队列或者日志来参数化其他对象。Command 模式也支持可撤销的操作。</p><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/bL992i8m5Dtt55bMj1VeGWfrwmd4nM_ofOKCag6sY7St7Va5kt2NzwStaC9vi3uecJJQetq0HrOQfK0BzauOEsA7F7XC3pbhJIEIJq8cBnPUK4cSHaL4QPSp7LI5ziJwvKbskGJdnhqIT0kEDUefKQ7sRdijgnldZOqthi2jcJKDD4-80bOz__FExWWnDPojXmRGKy2ZufnetubdegAgTxdu15o-b6_tqM5mTJhtrXOn7BGmD00k4Imj_5158i-oypPK6ilG91OBr2B-ZYy0" alt=""><img src="https://www.plantuml.com/plantuml/svg/RP512eGm34NtFKLmLS6vm2m6mTdE8K9RiA2nj75qRZ_51gpWBltvUVz3-yGOUPqdXOQN2CFa7R4AMVJ61oI6vXrn6v2-c1h01EOOhvOFchWCopmZsSCq-fHnlnjGPJ9bLggamkCby2UGs-3CrO9hAwT8nLhdwzeb4HLGJ2MeWxs3UsnOqwZblBrf6D0JvwpolfowtPcLNLwAT6boRaMggJPNrALJxyZcZ_a3" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// command.ts</span>
@@ -114,6 +114,6 @@
 Drawing at <span class="token punctuation">(</span><span class="token number">8</span>, <span class="token number">8</span><span class="token punctuation">)</span>
 Drawing at <span class="token punctuation">(</span><span class="token number">9</span>, <span class="token number">9</span><span class="token punctuation">)</span>
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="拓展思路的要点" tabindex="-1"><a class="header-anchor" href="#拓展思路的要点"><span>拓展思路的要点</span></a></h2><h3 id="命令中应该包含哪些信息" tabindex="-1"><a class="header-anchor" href="#命令中应该包含哪些信息"><span>命令中应该包含哪些信息</span></a></h3><p>在命令模式中，命令对象通常包含以下信息：</p><ul><li><strong>接收者（Receiver）</strong>：执行命令的对象。接收者包含了执行具体操作的逻辑。</li><li><strong>动作（Action）</strong>：要执行的具体操作。命令对象将动作封装为一个方法调用。</li><li><strong>参数（Parameters）</strong>：执行操作所需的参数。命令对象可以包含执行操作所需的所有参数。</li><li><strong>状态（State）</strong>：命令执行前后的状态信息。命令对象可以保存执行前的状态，以便在需要时进行撤销操作。</li></ul><p>通过将这些信息封装在命令对象中，可以实现命令的参数化和可撤销性，从而提高系统的灵活性和可维护性。</p><h3 id="保存历史记录" tabindex="-1"><a class="header-anchor" href="#保存历史记录"><span>保存历史记录</span></a></h3><p>命令模式的一个重要应用是保存历史记录，以支持撤销和重做操作。通过将每个执行的命令对象保存到一个历史记录列表中，可以在需要时回滚到之前的状态。以下是实现保存历史记录的一些常见方法：</p><ul><li><strong>命令栈（Command Stack）</strong>：使用栈数据结构保存执行的命令对象。每次执行命令时，将命令对象压入栈中；每次撤销操作时，从栈中弹出命令对象并执行撤销操作。</li><li><strong>命令队列（Command Queue）</strong>：使用队列数据结构保存执行的命令对象。适用于需要按顺序执行和撤销命令的场景。</li><li><strong>快照（Snapshot）</strong>：在执行命令前保存对象的快照，以便在需要时恢复到之前的状态。适用于需要保存复杂对象状态的场景。</li></ul><h2 id="相关的设计模式" tabindex="-1"><a class="header-anchor" href="#相关的设计模式"><span>相关的设计模式</span></a></h2><ul><li>Composite 模式</li><li>Memento 模式</li><li>Prototype 模式</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/command.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->Proxy 模式</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">Interpreter 模式<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/composite.html b/tech/DesignPatterns/composite.html
index 46738df..3494c71 100644
--- a/tech/DesignPatterns/composite.html
+++ b/tech/DesignPatterns/composite.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/composite.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="Composite 模式"><meta property="og:description" content="使用此设计模式的理由 Composite 模式允许你将对象组合成递归结构来表示“部分-整体”的层次结构。使用 Composite 模式，用户可以统一地对待单个对象和组合对象。例如，在文件系统中，目录和文件都可以被视为条目（Entry），目录可以包含其他目录和文件，而文件则是叶子节点。 示例代码 目录类 (directory.ts) 抽象条目类 (ent..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="TypeScript"><meta property="article:tag" content="容器与内容的一致性"><meta property="article:published_time" content="2024-10-25T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"Composite 模式","image":[""],"datePublished":"2024-10-25T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>Composite 模式 | blog</title><meta name="description" content="使用此设计模式的理由 Composite 模式允许你将对象组合成递归结构来表示“部分-整体”的层次结构。使用 Composite 模式，用户可以统一地对待单个对象和组合对象。例如，在文件系统中，目录和文件都可以被视为条目（Entry），目录可以包含其他目录和文件，而文件则是叶子节点。 示例代码 目录类 (directory.ts) 抽象条目类 (ent...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/composite.html-DOBxYen3.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/composite.html-D89dw1yo.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->Composite 模式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-25T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag7 clickable" role="navigation">容器与内容的一致性</span><!--]--><meta property="keywords" content="设计模式,TypeScript,容器与内容的一致性"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#使用此设计模式的理由">使用此设计模式的理由</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#示例代码">示例代码</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#目录类-directory-ts">目录类 (directory.ts)</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#抽象条目类-entry-ts">抽象条目类 (entry.ts)</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#文件类-file-ts">文件类 (file.ts)</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#主程序-main-ts">主程序 (main.ts)</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#运行结果">运行结果</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#相关的设计模式">相关的设计模式</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h2 id="使用此设计模式的理由" tabindex="-1"><a class="header-anchor" href="#使用此设计模式的理由"><span>使用此设计模式的理由</span></a></h2><p>Composite 模式允许你将对象组合成递归结构来表示“部分-整体”的层次结构。使用 Composite 模式，用户可以统一地对待单个对象和组合对象。例如，在文件系统中，目录和文件都可以被视为条目（Entry），目录可以包含其他目录和文件，而文件则是叶子节点。</p><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/hPAn3e8m48Ptdk8I5mZX1OW3WpePOyBWO1mAFR495D8U1ZM-kwM0A77GnEcI_-xQxsiQQMAAwY9tMA99iPGWpPdMi9IaBd1p07p8a3QiGDSBmSm8cGrfBAusbNMHeB8fuzp5TZViZl3wQfkLMQQrqDGkdKl1JJeRqvsWqrRXKJHkPSjmtpZj0vMnpLvexexJGI-4mfHA0uuDeUIzHciH01-QFT7-O6DfpAPU_x3znUifi18vVcAVG0QW3SiRoVVKlu6DJpeFWhAtYmoV-JCF" alt=""><h3 id="目录类-directory-ts" tabindex="-1"><a class="header-anchor" href="#目录类-directory-ts"><span>目录类 (directory.ts)</span></a></h3><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token keyword">import</span> <span class="token punctuation">{</span> Entry <span class="token punctuation">}</span> <span class="token keyword">from</span> <span class="token string">&#39;./entry&#39;</span><span class="token punctuation">;</span>
@@ -136,6 +136,6 @@
 /root/usr/tomura/game.doc <span class="token punctuation">(</span><span class="token number">400</span><span class="token punctuation">)</span>
 /root/usr/tomura/junk.mail <span class="token punctuation">(</span><span class="token number">500</span><span class="token punctuation">)</span>
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="相关的设计模式" tabindex="-1"><a class="header-anchor" href="#相关的设计模式"><span>相关的设计模式</span></a></h2><ul><li>Command 模式</li><li>Visitor 模式</li><li>Decorator 模式</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/composite.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->Strategy 模式</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">Decorator 模式<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/decorator.html b/tech/DesignPatterns/decorator.html
index 244453f..e856199 100644
--- a/tech/DesignPatterns/decorator.html
+++ b/tech/DesignPatterns/decorator.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/decorator.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="Decorator 模式"><meta property="og:description" content="在这个示例中，我们使用装饰器模式来动态地给对象添加职责。装饰器模式允许我们通过将对象放入包含行为的特殊封装对象中来扩展对象的功能，而无需修改原始类的代码。"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="TypeScript"><meta property="article:tag" content="容器与内容的一致性"><meta property="article:published_time" content="2024-10-25T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"Decorator 模式","image":[""],"datePublished":"2024-10-25T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>Decorator 模式 | blog</title><meta name="description" content="在这个示例中，我们使用装饰器模式来动态地给对象添加职责。装饰器模式允许我们通过将对象放入包含行为的特殊封装对象中来扩展对象的功能，而无需修改原始类的代码。">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/decorator.html-FfT8RlFX.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/decorator.html-0jwtowLH.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->Decorator 模式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-25T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 6 分钟</span><meta property="timeRequired" content="PT6M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag7 clickable" role="navigation">容器与内容的一致性</span><!--]--><meta property="keywords" content="设计模式,TypeScript,容器与内容的一致性"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#为什么使用装饰器模式">为什么使用装饰器模式？</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#代码示例">代码示例</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#运行结果">运行结果</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#拓展思路的要点">拓展思路的要点</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#api-的透明性">API 的透明性</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#在不改变被装饰物的前提下增加功能">在不改变被装饰物的前提下增加功能</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#可以动态地增加功能">可以动态地增加功能</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#只需要一些装饰物即可添加许多功能">只需要一些装饰物即可添加许多功能</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#导致增加许多很小的类">导致增加许多很小的类</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#相关的设计模式">相关的设计模式</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#继承和委托中的一致性">继承和委托中的一致性</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#父类和子类的一致性">父类和子类的一致性</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#自己和被委托对象的一致性">自己和被委托对象的一致性</a></li><!----><!--]--></ul></li><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><p>在这个示例中，我们使用装饰器模式来动态地给对象添加职责。装饰器模式允许我们通过将对象放入包含行为的特殊封装对象中来扩展对象的功能，而无需修改原始类的代码。</p><!-- more --><h2 id="为什么使用装饰器模式" tabindex="-1"><a class="header-anchor" href="#为什么使用装饰器模式"><span>为什么使用装饰器模式？</span></a></h2><ol><li><strong>职责扩展</strong>：装饰器模式允许我们在不修改现有代码的情况下扩展对象的功能。</li><li><strong>灵活性</strong>：可以根据需要动态地添加或删除职责。</li><li><strong>遵循开闭原则</strong>：通过使用装饰器模式，我们可以在不修改现有类的情况下添加新功能，从而遵循开闭原则。</li></ol><h2 id="代码示例" tabindex="-1"><a class="header-anchor" href="#代码示例"><span>代码示例</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/lLDB3i8W4DrpYbdIQ2zWN1Wrhbof5w25M285myTgZ7UN5b6fTQdBcJVpvirZc1bBj7MrGAGmLfFIGYc8CR3avYZ81Qu8O0HxPXTAk5eQd4r0khfWEW8RrGndT-niiLPDX7oD7y7blginbMhQjfFY5DrGV_vSQSeqU0ecQIed1ngYIKntXA43zx6i9G-Sssvwf1gc3WeJfKaRJWkoNzZp4imfwndn28FOeWiM5T6fu6VRXnjZAAl_Q5yv8Rvh7xtX0q_savlBeIO7jkQIuPS9tX3bf1rSvA4tprLw0oYUpBI5GXMQ-HNzFxe3" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// border.ts</span>
@@ -170,6 +170,6 @@
 /<span class="token operator">|</span>+---------+<span class="token operator">|</span>/
 /+-----------+/
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="拓展思路的要点" tabindex="-1"><a class="header-anchor" href="#拓展思路的要点"><span>拓展思路的要点</span></a></h2><h3 id="api-的透明性" tabindex="-1"><a class="header-anchor" href="#api-的透明性"><span>API 的透明性</span></a></h3><p>在 Decorator 模式中，装饰边框与被装饰物具有一致性。具体而言，在示例程序中，表示装饰边框的 <code>Border</code> 类是表示被装饰物的 <code>Display</code> 类的子类，这就体现了它们之间的一致性。也就是说， <code>Border</code> 类（以及它的子类）与表示被装饰物的 <code>Display</code> 类具有相同的接口（API）。这样，即使被装饰物被边框装饰起来了，接口（API）也不会被隐藏起来。其他类依然可以调用 <code>getColumns</code>、<code>getRows</code>、<code>getRowText</code> 以及 <code>show</code> 方法。这就是接口（API）的“透明性”。在示例程序中，实例 <code>b4</code> 被装饰了多次，但是接口（API）却没有发生任何变化。得益于接口（API）的透明性，模式中也形成了类似于 Composite 模式中的递归结构。也就是说，装饰边框里面的“被装饰物”实际上又是别的物体的“装饰边框”。就像是剥洋葱时以为洋葱心要出来了，结果却发现还是皮。不过， Decorator 模式虽然与 Composite 模式一样，都具有递归结构，但是它们的使用目的不同。Decorator 模式的主要目的是通过添加装饰物来增加对象的功能。</p><h3 id="在不改变被装饰物的前提下增加功能" tabindex="-1"><a class="header-anchor" href="#在不改变被装饰物的前提下增加功能"><span>在不改变被装饰物的前提下增加功能</span></a></h3><p>在 Decorator 模式中，装饰边框与被装饰物具有相同的接口（API）。虽然接口是相同的，但是越装饰，功能则越多。例如，用 <code>SideBorder</code> 装饰 <code>Display</code> 后，就可以在字符串的左右两侧加上装饰字符。如果再用 <code>FullBorder</code> 装饰，那么就可以在字符串的四周加上边框。此时，我们完全不需要对被装饰的类做任何修改。这样，我们就实现了不修改被装饰的类即可增加功能。Decorator 模式使用了委托。对“装饰边框”提出的要求（调用装饰边框的方法）会被转交（委托）给“被装饰物”去处理。以示例程序来说，就是 <code>SideBorder</code> 类的 <code>getColumns</code> 方法调用了 <code>display.getColumns</code>。此外，<code>getRows</code> 方法也调用了 <code>display.getRows</code>。</p><h3 id="可以动态地增加功能" tabindex="-1"><a class="header-anchor" href="#可以动态地增加功能"><span>可以动态地增加功能</span></a></h3><p>Decorator 模式中用到了委托，它使类之间形成了弱关联关系。因此，不用改变框架代码，就可以生成一个与其他对象具有不同关系的新对象。</p><h3 id="只需要一些装饰物即可添加许多功能" tabindex="-1"><a class="header-anchor" href="#只需要一些装饰物即可添加许多功能"><span>只需要一些装饰物即可添加许多功能</span></a></h3><p>使用 Decorator 模式可以为程序添加许多功能。只要准备一些装饰边框（ConcreteDecorator 角色），即使这些装饰边框都只具有非常简单的功能，也可以将它们自由组合成为新的对象。这就像我们可以自由选择香草味冰激凌、巧克力冰激凌、草莓冰激凌、猕猴桃冰激凌等各种口味的冰激凌一样。如果冰激凌店要为顾客准备所有的冰激凌成品那真是太麻烦了。因此，冰激凌店只会准备各种香料，当顾客下单后只需要在冰激凌上加上各种香料就可以了。不管是香草味，还是咖啡朗姆和开心果的混合口味，亦或是香草味、草莓味和猕猴桃三重口味，顾客想吃什么口味都可以。Decorator 模式就是可以应对这种多功能对象的需求的一种模式。</p><h3 id="导致增加许多很小的类" tabindex="-1"><a class="header-anchor" href="#导致增加许多很小的类"><span>导致增加许多很小的类</span></a></h3><p>Decorator 模式的一个缺点是会导致程序中增加许多功能类似的很小的类。</p><h2 id="相关的设计模式" tabindex="-1"><a class="header-anchor" href="#相关的设计模式"><span>相关的设计模式</span></a></h2><ul><li>Adapter 模式</li><li>Strategy 模式</li></ul><h2 id="继承和委托中的一致性" tabindex="-1"><a class="header-anchor" href="#继承和委托中的一致性"><span>继承和委托中的一致性</span></a></h2><h3 id="父类和子类的一致性" tabindex="-1"><a class="header-anchor" href="#父类和子类的一致性"><span>父类和子类的一致性</span></a></h3><p>在面向对象编程中，父类和子类之间的一致性是指子类应当继承父类的行为和属性，并且可以扩展或重写这些行为和属性。子类应当能够替代父类的实例而不影响程序的正确性，这就是所谓的里氏替换原则（Liskov Substitution Principle）。</p><h3 id="自己和被委托对象的一致性" tabindex="-1"><a class="header-anchor" href="#自己和被委托对象的一致性"><span>自己和被委托对象的一致性</span></a></h3><p>在委托模式中，一致性是指委托对象应当具有与委托者相同的接口或行为。委托者将某些任务委托给委托对象来执行，而委托对象应当能够无缝地完成这些任务，就像委托者自己完成一样。这种一致性确保了委托模式的灵活性和可维护性。</p></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/decorator.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->Composite 模式</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">Visitor 模式<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/end.html b/tech/DesignPatterns/end.html
index 71c3d49..e6d7c14 100644
--- a/tech/DesignPatterns/end.html
+++ b/tech/DesignPatterns/end.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/end.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="结语"><meta property="og:description" content="教程源码示例 使用设计模式的目的是重用代码，并在增加需求时尽量不修改已有的类。我们不应死记硬背这些设计模式，而应理解其背后的核心思想。设计模式的使用不是最终目的，而是为了更好地解决问题和优化代码结构。同时，我们也要避免过早地进行“工程化”，应根据实际需求灵活应用设计模式。 设计模式提供了一种通用的解决方案，可以帮助我们应对软件开发中的常见问题。通过学习..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="TypeScript"><meta property="article:published_time" content="2024-10-29T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"结语","image":[""],"datePublished":"2024-10-29T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>结语 | blog</title><meta name="description" content="教程源码示例 使用设计模式的目的是重用代码，并在增加需求时尽量不修改已有的类。我们不应死记硬背这些设计模式，而应理解其背后的核心思想。设计模式的使用不是最终目的，而是为了更好地解决问题和优化代码结构。同时，我们也要避免过早地进行“工程化”，应根据实际需求灵活应用设计模式。 设计模式提供了一种通用的解决方案，可以帮助我们应对软件开发中的常见问题。通过学习...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/end.html-De4ifiEs.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/end.html-CkqhlgwJ.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->结语</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-29T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><!--]--><meta property="keywords" content="设计模式,TypeScript"></span></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><p><a href="https://github.com/King-sj/DesignPatterns" target="_blank" rel="noopener noreferrer">教程源码示例<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></p><p>使用设计模式的目的是重用代码，并在增加需求时尽量不修改已有的类。我们不应死记硬背这些设计模式，而应理解其背后的核心思想。设计模式的使用不是最终目的，而是为了更好地解决问题和优化代码结构。同时，我们也要避免过早地进行“工程化”，应根据实际需求灵活应用设计模式。</p><p>设计模式提供了一种通用的解决方案，可以帮助我们应对软件开发中的常见问题。通过学习和应用设计模式，我们可以提高代码的可读性、可维护性和可扩展性。然而，设计模式并不是万能的，它们也有其局限性和适用范围。在实际开发中，我们需要根据具体情况选择合适的设计模式，而不是盲目地套用。</p><p>此外，设计模式的学习和应用需要不断的实践和积累。只有在实际项目中多次使用，才能真正理解和掌握这些模式。我们还应关注设计模式的演变和新模式的出现，以保持我们的知识体系与时俱进。</p><p>总之，设计模式是软件开发中的一把利器，但它需要我们在理解其核心思想的基础上，灵活应用于实际项目中。希望通过本章的学习，您能够掌握这些设计模式，并在实际项目中灵活运用它们，编写出更加健壮和优雅的代码。</p></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/end.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->Interpreter 模式</div></a><!----></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/facade.html b/tech/DesignPatterns/facade.html
index 7ebf390..b2192de 100644
--- a/tech/DesignPatterns/facade.html
+++ b/tech/DesignPatterns/facade.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/facade.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="facade 模式"><meta property="og:description" content="当某个程序员得意地说出"啊，在调用那个类之前需要先调用这个类。在调用那个方法之前需要先在这个类中注册一下"的时候，就意味着我们需要引人Facade了。 对于那些能够明确地用语言描述出来的知识，我们不应该将它们隐藏在自己脑袋中，而是应该用代码将它们表现出来。 —————《图解设计模式》"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="TypeScript"><meta property="article:tag" content="简单化"><meta property="article:published_time" content="2024-10-26T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"facade 模式","image":[""],"datePublished":"2024-10-26T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>facade 模式 | blog</title><meta name="description" content="当某个程序员得意地说出"啊，在调用那个类之前需要先调用这个类。在调用那个方法之前需要先在这个类中注册一下"的时候，就意味着我们需要引人Facade了。 对于那些能够明确地用语言描述出来的知识，我们不应该将它们隐藏在自己脑袋中，而是应该用代码将它们表现出来。 —————《图解设计模式》">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/facade.html-Cj3lyBcS.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/facade.html-BODpRH45.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->facade 模式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-26T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag3 clickable" role="navigation">简单化</span><!--]--><meta property="keywords" content="设计模式,TypeScript,简单化"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#示例代码">示例代码</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#代码实现">代码实现</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#运行结果">运行结果</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#相关设计模式">相关设计模式</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><p>当某个程序员得意地说出&quot;啊，在调用那个类之前需要先调用这个类。在调用那个方法之前需要先在这个类中注册一下&quot;的时候，就意味着我们需要引人Facade了。</p><p>对于那些能够明确地用语言描述出来的知识，我们不应该将它们隐藏在自己脑袋中，而是应该用代码将它们表现出来。</p><p style="text-align:right;">—————《图解设计模式》</p><!-- more --> ## 为什么使用外观模式？ <ol><li><strong>简化接口</strong>：外观模式为复杂的子系统提供了一个简单的接口，使得客户端代码不需要了解子系统的内部细节。</li><li><strong>松散耦合</strong>：通过引入外观类，客户端代码与子系统之间的耦合度降低，增强了代码的可维护性和可扩展性。</li><li><strong>更好的分层</strong>：外观模式有助于分层设计，使得每一层只关注自己的职责，层与层之间通过外观类进行交互。</li></ol><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><p>在这个示例中，我们使用了外观模式（Facade Pattern）来简化与复杂子系统的交互。外观模式通过提供一个统一的接口来隐藏子系统的复杂性，使得客户端代码可以更容易地使用子系统的功能。</p><img src="https://www.plantuml.com/plantuml/svg/VLBBJiCm4BpdAtnq1Vc175117BXGUki1SLZiRMh5ZsYz0K7LVyUEQf9MWOjVE-EPMNiT6OW7Pojb8KRn20mF454SAo5kKf6D4WwCpOL67CLhXr-DY4p6jszb8Ku9NQlWqtPG74YkPlGMUKkXHsA3KUfqqNjIs833mb_zT_EfEdjxOcTtP1XfT5T_Zkk2p89p1vVLqGyRjYZ7SQRy4OpErHu8MeB-81t62EqInXhVoGFXljHkXOAUJV0BuDms3Z9Fe3LDb24Y-SluXQDiY2Xd1wbvENS-EkVyxSSsUNo6hhJZh_Qx1DcXLS5XPen-xfEV57Aoj3Vs-aL61qbiagdhk-c3DEA5Ml3c6t9yeOB6A-ZilPR0Q_GwVRmV" alt=""><h2 id="代码实现" tabindex="-1"><a class="header-anchor" href="#代码实现"><span>代码实现</span></a></h2><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// dataBase.ts</span>
@@ -103,6 +103,6 @@
 <span class="token operator">&lt;</span>a <span class="token assign-left variable">href</span><span class="token operator">=</span><span class="token string">&quot;mailto:hyuki@hyuki.com&quot;</span><span class="token operator">&gt;</span>Hiroshi Yuki<span class="token operator">&lt;</span>/a<span class="token operator">&gt;</span>
 <span class="token operator">&lt;</span>/body<span class="token operator">&gt;</span><span class="token operator">&lt;</span>/html<span class="token operator">&gt;</span>
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="相关设计模式" tabindex="-1"><a class="header-anchor" href="#相关设计模式"><span>相关设计模式</span></a></h2><ul><li>Abstract Factory 模式</li><li>Singleton 模式</li><li>Mediator 模式</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/facade.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->chainOfResponsibility 模式</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">Mediator 模式<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/factory_method.html b/tech/DesignPatterns/factory_method.html
index 3b68169..e7a4450 100644
--- a/tech/DesignPatterns/factory_method.html
+++ b/tech/DesignPatterns/factory_method.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/factory_method.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="Factory Method 模式"><meta property="og:description" content="在 Factory Method 模式中，我们定义一个用于创建对象的接口，但由子类决定要实例化的类是哪一个。Factory Method 使一个类的实例化延迟到其子类。"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="typescript"><meta property="article:tag" content="工厂方法"><meta property="article:tag" content="交给子类"><meta property="article:published_time" content="2024-10-21T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"Factory Method 模式","image":[""],"datePublished":"2024-10-21T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>Factory Method 模式 | blog</title><meta name="description" content="在 Factory Method 模式中，我们定义一个用于创建对象的接口，但由子类决定要实例化的类是哪一个。Factory Method 使一个类的实例化延迟到其子类。">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/factory_method.html-B20phxz9.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/factory_method.html-NuMbQ7is.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->Factory Method 模式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-21T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag3 clickable" role="navigation">typescript</span><span class="page-tag-item tag0 clickable" role="navigation">工厂方法</span><span class="page-tag-item tag1 clickable" role="navigation">交给子类</span><!--]--><meta property="keywords" content="设计模式,typescript,工厂方法,交给子类"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#为什么要使用-factory-method">为什么要使用 Factory Method</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#示例代码">示例代码</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#运行结果">运行结果</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><p>在 Factory Method 模式中，我们定义一个用于创建对象的接口，但由子类决定要实例化的类是哪一个。Factory Method 使一个类的实例化延迟到其子类。</p><!-- more --><h2 id="为什么要使用-factory-method" tabindex="-1"><a class="header-anchor" href="#为什么要使用-factory-method"><span>为什么要使用 Factory Method</span></a></h2><p>使用 Factory Method 模式有以下几个好处：</p><ol><li><strong>解耦创建和使用</strong>：客户端代码不需要知道具体的产品类，只需要依赖抽象产品接口，降低了耦合性。</li><li><strong>扩展性强</strong>：增加新的产品类时，只需添加新的子类工厂，不需要修改现有代码，符合开闭原则。</li><li><strong>灵活性高</strong>：可以通过子类来定制产品的创建过程，满足不同的需求。</li></ol><p>通过使用 Factory Method 模式，我们可以更灵活地管理对象的创建过程，提高代码的可维护性和可扩展性。</p><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/XP9DJiGm38NtFOMN0wXpWAugWP1OmHwn2AcdYcYJoauP4EBkE6dw4-Y8JMkzFjlFdrgpL-J7lYlgfRAgHnwKHZYHb6T7R_1L01ZhaKv1VoBNZDf75U06HiR3LGNlpZIYV1VoKA_iIOb7TuePxgLqzBbqQ4BbyU3E5ga2iHhRoeGqE9hAP4hQFrx2rh3aczt3z5vistWISBrHEojxFCPeKzY7krj53PX-wB17wta5SSnFBo5BjOiZA2twns0CycADdBORPqZuuT4sswqvlhILvrdFBndLIy2c9SbwaTVase_FQ_wuCwBycx8ihtU8LIaU5pFoOtvsQFlrQTDK2nBvEty0" alt=""><p>@enduml</p><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// product.ts</span>
@@ -98,6 +98,6 @@
 Bob使用了ID卡
 Charlie使用了ID卡
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h1 id="相关的设计模式" tabindex="-1"><a class="header-anchor" href="#相关的设计模式"><span>相关的设计模式</span></a></h1><ul><li>Template Method</li><li>Singleton</li><li>Composite</li><li>Iterator</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/factory_method.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->Template Method 模式</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">Singleton 模式<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/flyweight.html b/tech/DesignPatterns/flyweight.html
index 938e429..da3b9a3 100644
--- a/tech/DesignPatterns/flyweight.html
+++ b/tech/DesignPatterns/flyweight.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/flyweight.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="Flyweight 模式"><meta property="og:description" content="为什么使用 Flyweight 模式 Flyweight 模式是一种结构型设计模式，它通过共享尽可能多的相同对象来减少内存使用，从而提高性能。在需要生成大量细粒度对象的场景中，Flyweight 模式非常有用。通过共享对象，Flyweight 模式可以显著减少内存消耗，并提高应用程序的效率。 实例代码 运行结果 拓展思路的要点 对多个地方产生影响 Fl..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="TypeScript"><meta property="article:tag" content="避免浪费"><meta property="article:published_time" content="2024-10-28T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"Flyweight 模式","image":[""],"datePublished":"2024-10-28T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>Flyweight 模式 | blog</title><meta name="description" content="为什么使用 Flyweight 模式 Flyweight 模式是一种结构型设计模式，它通过共享尽可能多的相同对象来减少内存使用，从而提高性能。在需要生成大量细粒度对象的场景中，Flyweight 模式非常有用。通过共享对象，Flyweight 模式可以显著减少内存消耗，并提高应用程序的效率。 实例代码 运行结果 拓展思路的要点 对多个地方产生影响 Fl...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/flyweight.html-CWx8TgTS.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/flyweight.html-DUTi0_Qx.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->Flyweight 模式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-28T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 8 分钟</span><meta property="timeRequired" content="PT8M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag5 clickable" role="navigation">避免浪费</span><!--]--><meta property="keywords" content="设计模式,TypeScript,避免浪费"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#为什么使用-flyweight-模式">为什么使用 Flyweight 模式</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#实例代码">实例代码</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#运行结果">运行结果</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#拓展思路的要点">拓展思路的要点</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#对多个地方产生影响">对多个地方产生影响</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#intrinsic-与-extrinsic">Intrinsic 与 Extrinsic</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#不要让被共享的实例被垃圾回收器回收了">不要让被共享的实例被垃圾回收器回收了</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#内存之外的其它资源">内存之外的其它资源</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#相关的设计模式">相关的设计模式</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h2 id="为什么使用-flyweight-模式" tabindex="-1"><a class="header-anchor" href="#为什么使用-flyweight-模式"><span>为什么使用 Flyweight 模式</span></a></h2><p>Flyweight 模式是一种结构型设计模式，它通过共享尽可能多的相同对象来减少内存使用，从而提高性能。在需要生成大量细粒度对象的场景中，Flyweight 模式非常有用。通过共享对象，Flyweight 模式可以显著减少内存消耗，并提高应用程序的效率。</p><h2 id="实例代码" tabindex="-1"><a class="header-anchor" href="#实例代码"><span>实例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/RL7B2i8m4BpdA_ROKli3GKfH43nuyYWUrZJMG4rAinL4_7VJz5rxMsPsPcTtKqjOKVqic2ZGMjYfVF_02ZuC80RXIerFoS5IfNJkmRlHb27X18oWT1K58OUNKHdxihdT0GMPwjsvbiOK74vORbk3JT-MUDeb8YN0EgQGP3HVkBJ9Z7RYkW62q2VePBcaewDG2zd4-PD6JKU71ilzHi5iXRCdk_GtbJSoExHUhjvsciWLW-NwUHQ7YUDac3mEdA3z0giaIwNEt0z_" alt=""><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuKfCBialKd3EoKpDA-62K0gwTWfEcUd19KMPUUbM2dcfvGYkXfAXaR6I9aXRPbbYIIf2XWlEWkftpaWiSWCRNscba9vQufa7j3GlELK3LJUICYvKBWvpe48QweRgc2QX6s6ZgmkJib8eIYqfBSfJG34W9PMG4GHSOKIfAuoeuGfZIbrXZDqLc498SGMBRg3R82a7sLXega0r02g8FQ4L0AaI3QBJ5am3E1hnAZ0Yf03Jyr1x7LBpKe2v1000" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// bigChar.ts</span>
@@ -256,6 +256,6 @@
 <span class="token punctuation">..</span>.33<span class="token punctuation">..</span><span class="token punctuation">..</span><span class="token punctuation">..</span><span class="token number">33</span><span class="token punctuation">..</span>.
 <span class="token punctuation">..</span><span class="token punctuation">..</span>.333333<span class="token punctuation">..</span><span class="token punctuation">..</span>.
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="拓展思路的要点" tabindex="-1"><a class="header-anchor" href="#拓展思路的要点"><span>拓展思路的要点</span></a></h2><h3 id="对多个地方产生影响" tabindex="-1"><a class="header-anchor" href="#对多个地方产生影响"><span>对多个地方产生影响</span></a></h3><p>Flyweight 模式的主题是“共享”。那么，在共享实例时应当注意什么呢？首先要想到的是“如果要改变被共享的对象，就会对多个地方产生影响”。也就是说，一个实例的改变会同时反映到所有使用该实例的地方。例如，假设我们改变了示例程序中 BigChar 类的 &#39;3&#39; 所对应的字体数据，那么 BigString 类中使用的所有 &#39;3&#39; 字符的字体（形状）都会发生改变。在编程时，像这样改一个地方会对多个地方产生影响并非总是不好。有些情况下这是好事，有些情况下这是坏事。不管怎样，“修改一个地方会对多个地方产生影响”，这就是共享的特点。</p><p>因此，在决定 Flyweight 角色中的字段时，需要精挑细选。只将那些真正应该在多个地方共享的字段定义在 Flyweight 角色中即可。关于这一点，让我们简单地举个例子。假设我们要在示例程序中增加一个功能，实现显示“带颜色的大型文字”。那么此时，颜色信息应当放在哪个类中呢？首先，假设我们将颜色信息放在 BigChar 类中。由于 BigChar 类的实例是被共享的，因此颜色信息也被共享了。也就是说，BigString 类中用到的所有 BigChar 类的实例都带有相同的颜色。如果我们不把颜色信息放在 BigChar 类中，而是将它放在 BigString 类中。那么 BigString 类会负责管理“第三个字符的颜色是红色的”这样的颜色信息。这样一来，我们就可以实现以不同的颜色显示同一个 BigChar 类的实例。</p><p>那么两种解决方案到底哪个是正确的呢？关于这个问题，其实并没有绝对的答案。哪些信息应当共享，哪些信息不应当共享，这取决于类的使用目的。设计者在使用 Flyweight 模式共享信息时必须仔细思考应当共享哪些信息。</p><h3 id="intrinsic-与-extrinsic" tabindex="-1"><a class="header-anchor" href="#intrinsic-与-extrinsic"><span>Intrinsic 与 Extrinsic</span></a></h3><p>前面讲到的“应当共享的信息和不应当共享的信息”是有专有名词的。应当共享的信息被称作 Intrinsic 信息。Intrinsic 的意思是“本质的”“固有的”。换言之，它指的是不论实例在哪里、不论在什么情况下都不会改变的信息，或是不依赖于实例状态的信息。</p><p>在示例程序中，BigChar 的字体数据不论在 BigString 中的哪个地方都不会改变。因此，BigChar 的字体数据属于 Intrinsic 信息。另一方面，不应当共享的信息被称作 Extrinsic 信息。Extrinsic 的意思是“外在的”“非本质的”。也就是说，它是当实例的位置、状况发生改变时会变化的信息，或是依赖于实例状态的信息。在示例程序中，BigChar 的实例在 BigString 中是第几个字符这种信息会根据 BigChar 在 BigString 中的位置变化而发生变化，因此，不应当在 BigChar 中保存这个信息，它属于 Extrinsic 信息。因此，前面提到的是否共享“颜色”信息这个问题，我们也可以换种说法，即应当将“颜色”看作是 Intrinsic 信息还是 Extrinsic 信息。</p><h3 id="不要让被共享的实例被垃圾回收器回收了" tabindex="-1"><a class="header-anchor" href="#不要让被共享的实例被垃圾回收器回收了"><span>不要让被共享的实例被垃圾回收器回收了</span></a></h3><p>在有垃圾回收的语言中要注意共享内存未被使用时被 GC 的问题。在使用 Flyweight 模式时，我们通常会将共享对象存储在某种集合（如 HashMap 或 List）中，以便重复使用这些对象。然而，如果这些集合中的对象没有被其他任何地方引用，垃圾回收器可能会认为这些对象是垃圾，从而将其回收掉。这会导致共享对象在需要时无法被找到，从而引发程序错误。</p><p>为了避免这种情况，我们需要确保共享对象在整个程序生命周期内都被引用。以下是一些常见的解决方案：</p><ol><li><p><strong>强引用</strong>：将共享对象存储在一个全局的集合中，并确保这个集合在程序的整个生命周期内都存在。这种方法简单直接，但可能会导致内存泄漏，因为共享对象永远不会被回收。</p></li><li><p><strong>弱引用</strong>：使用弱引用（WeakReference）来存储共享对象。弱引用允许垃圾回收器在没有其他强引用时回收对象，从而避免内存泄漏。Java 提供了 <code>WeakHashMap</code> 类，可以用来存储弱引用的键值对。</p></li><li><p><strong>引用计数</strong>：通过引用计数来管理共享对象的生命周期。每当一个对象被引用时，增加计数；每当一个引用被释放时，减少计数。当计数为零时，表示该对象不再被使用，可以安全地回收。</p></li><li><p><strong>定期清理</strong>：定期检查集合中的对象，移除那些不再被使用的对象。这种方法需要额外的逻辑来判断对象是否仍然被使用，但可以有效地管理内存。</p></li></ol><h3 id="内存之外的其它资源" tabindex="-1"><a class="header-anchor" href="#内存之外的其它资源"><span>内存之外的其它资源</span></a></h3><p>在示例程序中，我们了解到共享实例可以减少内存使用量。一般来说，共享实例可以减少所需资源的使用量。这里的资源指的是计算机中的资源，而内存是资源中的一种。时间也是一种资源。使用 new 关键字生成实例会花费时间。通过 Flyweight 模式共享实例可以减少使用 new 关键字生成实例的次数。这样，就可以提高程序运行速度。文件句柄（文件描述符）和窗口句柄等也都是一种资源。在操作系统中，可以同时使用的文件句柄和窗口句柄是有限制的。因此，如果不共享实例，应用程序在运行时很容易就会达到资源极限而导致崩溃。</p><h2 id="相关的设计模式" tabindex="-1"><a class="header-anchor" href="#相关的设计模式"><span>相关的设计模式</span></a></h2><ul><li>Proxy 模式</li><li>Composite 模式</li><li>Singleton 模式</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/flyweight.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->State 模式</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">Proxy 模式<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/index.html b/tech/DesignPatterns/index.html
index 26006d0..03ad553 100644
--- a/tech/DesignPatterns/index.html
+++ b/tech/DesignPatterns/index.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/"><meta property="og:site_name" content="blog"><meta property="og:title" content="设计模式"><meta property="og:description" content="面向对象三大特性：封装、继承、多态。 设计模式需遵循面向对象的设计原则，由于笔者不太喜欢java, 并嫌弃cpp中没有interface, 遂使用ts作为实现语言(我才不用rust呢 😃 )"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="typescript"><meta property="article:published_time" content="2024-10-21T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"设计模式","image":[""],"datePublished":"2024-10-21T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>设计模式 | blog</title><meta name="description" content="面向对象三大特性：封装、继承、多态。 设计模式需遵循面向对象的设计原则，由于笔者不太喜欢java, 并嫌弃cpp中没有interface, 遂使用ts作为实现语言(我才不用rust呢 😃 )">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-B5GIg4Ij.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-Dj_dWWjR.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->设计模式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-21T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag3 clickable" role="navigation">typescript</span><!--]--><meta property="keywords" content="设计模式,typescript"></span></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><p>面向对象三大特性：封装、继承、多态。 设计模式需遵循面向对象的设计原则，由于笔者不太喜欢java, 并嫌弃cpp中没有interface, 遂使用ts作为实现语言(我才不用rust呢 😃 )</p><!-- more --><p>本专栏源码大部分参考自参考资料[1]</p><p><a href="https://github.com/King-sj/DesignPatterns" target="_blank" rel="noopener noreferrer">教程源码示例<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></p><h1 id="参考资料" tabindex="-1"><a class="header-anchor" href="#参考资料"><span>参考资料</span></a></h1><p>[1] 结城浩. <em>图解设计模式</em>. 杨文轩译. 北京: 人民邮电出版社, 2017.</p></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/index.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/end.html" aria-label="结语"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->结语</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">设计模式七大原则<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/interpreter.html b/tech/DesignPatterns/interpreter.html
index 7a699f7..41dcd3f 100644
--- a/tech/DesignPatterns/interpreter.html
+++ b/tech/DesignPatterns/interpreter.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/interpreter.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="Interpreter 模式"><meta property="og:description" content="为什么使用此模式 解释器模式（Interpreter Pattern）是一种行为设计模式，它定义了一种语言的文法表示，并定义一个解释器来解释该语言中的句子。使用解释器模式的原因包括： 简化语法解析：通过定义文法规则，可以轻松解析和执行特定的语言或指令集。 可扩展性：可以轻松添加新的语法规则或指令，而无需修改现有代码。 代码复用：通过将不同的语法规则封装..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="TypeScript"><meta property="article:tag" content="用类实现"><meta property="article:published_time" content="2024-10-29T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"Interpreter 模式","image":[""],"datePublished":"2024-10-29T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>Interpreter 模式 | blog</title><meta name="description" content="为什么使用此模式 解释器模式（Interpreter Pattern）是一种行为设计模式，它定义了一种语言的文法表示，并定义一个解释器来解释该语言中的句子。使用解释器模式的原因包括： 简化语法解析：通过定义文法规则，可以轻松解析和执行特定的语言或指令集。 可扩展性：可以轻松添加新的语法规则或指令，而无需修改现有代码。 代码复用：通过将不同的语法规则封装...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/interpreter.html-CansycaD.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/interpreter.html-DfDQyPSV.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->Interpreter 模式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-29T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 3 分钟</span><meta property="timeRequired" content="PT3M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag1 clickable" role="navigation">用类实现</span><!--]--><meta property="keywords" content="设计模式,TypeScript,用类实现"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#为什么使用此模式">为什么使用此模式</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#示例代码">示例代码</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#运行结果">运行结果</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h2 id="为什么使用此模式" tabindex="-1"><a class="header-anchor" href="#为什么使用此模式"><span>为什么使用此模式</span></a></h2><p>解释器模式（Interpreter Pattern）是一种行为设计模式，它定义了一种语言的文法表示，并定义一个解释器来解释该语言中的句子。使用解释器模式的原因包括：</p><ol><li><strong>简化语法解析</strong>：通过定义文法规则，可以轻松解析和执行特定的语言或指令集。</li><li><strong>可扩展性</strong>：可以轻松添加新的语法规则或指令，而无需修改现有代码。</li><li><strong>代码复用</strong>：通过将不同的语法规则封装在不同的类中，可以提高代码的复用性和可维护性。</li></ol><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><p>本实例是一个控制小车的脚本语言解释器demo,文法如下， 分析方法为<a href="https://bupt.online/tech/designASimpileCCompiler/0.html" target="_blank" rel="noopener noreferrer">递归下降<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></p><div class="language-text line-numbers-mode" data-ext="text" data-title="text"><pre class="language-text"><code>&lt;program&gt; ::= program &lt;command list&gt;
@@ -241,6 +241,6 @@
 
 node = [program [repeat [4 [repeat [3 go right go left ]]right ]]]
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/interpreter.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->Command 模式</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/end.html" aria-label="结语"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">结语<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/iterator.html b/tech/DesignPatterns/iterator.html
index 53587cc..9958696 100644
--- a/tech/DesignPatterns/iterator.html
+++ b/tech/DesignPatterns/iterator.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/iterator.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="迭代器模式"><meta property="og:description" content="为什么要使用迭代器模式 迭代器模式提供了一种方法来顺序访问集合中的元素，而无需暴露其底层表示。使用迭代器模式有以下几个优点： 简化代码：迭代器模式将遍历逻辑封装在迭代器对象中，使得客户端代码更加简洁和易读。 解耦集合和遍历：集合对象和遍历算法分离，增加了代码的灵活性和可维护性。可以在不修改集合对象的情况下，改变遍历算法。 统一接口：通过实现统一的迭代器..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="typescript"><meta property="article:published_time" content="2024-10-21T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"迭代器模式","image":[""],"datePublished":"2024-10-21T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>迭代器模式 | blog</title><meta name="description" content="为什么要使用迭代器模式 迭代器模式提供了一种方法来顺序访问集合中的元素，而无需暴露其底层表示。使用迭代器模式有以下几个优点： 简化代码：迭代器模式将遍历逻辑封装在迭代器对象中，使得客户端代码更加简洁和易读。 解耦集合和遍历：集合对象和遍历算法分离，增加了代码的灵活性和可维护性。可以在不修改集合对象的情况下，改变遍历算法。 统一接口：通过实现统一的迭代器...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/iterator.html-USsHv5Pr.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/iterator.html-9EjNXcsT.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->迭代器模式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-21T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 3 分钟</span><meta property="timeRequired" content="PT3M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag3 clickable" role="navigation">typescript</span><!--]--><meta property="keywords" content="设计模式,typescript"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#为什么要使用迭代器模式">为什么要使用迭代器模式</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#typescript-实现迭代器模式">TypeScript 实现迭代器模式</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#代码示例">代码示例</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#运行结果">运行结果</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#多个迭代器">多个迭代器</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#相关的设计模式">相关的设计模式</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h2 id="为什么要使用迭代器模式" tabindex="-1"><a class="header-anchor" href="#为什么要使用迭代器模式"><span>为什么要使用迭代器模式</span></a></h2><p>迭代器模式提供了一种方法来顺序访问集合中的元素，而无需暴露其底层表示。使用迭代器模式有以下几个优点：</p><ol><li><strong>简化代码</strong>：迭代器模式将遍历逻辑封装在迭代器对象中，使得客户端代码更加简洁和易读。</li><li><strong>解耦集合和遍历</strong>：集合对象和遍历算法分离，增加了代码的灵活性和可维护性。可以在不修改集合对象的情况下，改变遍历算法。</li><li><strong>统一接口</strong>：通过实现统一的迭代器接口，不同类型的集合可以使用相同的遍历方式，增强了代码的可扩展性。</li><li><strong>支持多种遍历方式</strong>：可以根据需要实现不同的迭代器，以支持多种遍历方式，如正向遍历、反向遍历、过滤遍历等。</li></ol><p>通过使用迭代器模式，我们可以更好地管理和操作集合数据，提高代码的可读性和可维护性。</p><h2 id="typescript-实现迭代器模式" tabindex="-1"><a class="header-anchor" href="#typescript-实现迭代器模式"><span>TypeScript 实现迭代器模式</span></a></h2><p>在本节中，我们将展示如何使用 TypeScript 实现迭代器模式。迭代器模式是一种行为设计模式，它允许顺序访问集合中的元素，而无需暴露其底层表示。</p><h3 id="代码示例" tabindex="-1"><a class="header-anchor" href="#代码示例"><span>代码示例</span></a></h3><p>以下是实现迭代器模式的 TypeScript 代码示例：</p><img src="https://www.plantuml.com/plantuml/svg/ZL8nRiCm3Dpz2evE2tr0KzAjG96bOz51iHbPY4KP4bEaAFhtYh8Ts-ZGRjBnxdWKjKzi8bzzNpbYZ6VJ83pdW-4GuQi2UEnCEkADwvs6KmWz6XAK9iZGP_LThSG7QoDQmpYgtUGbtDbN14rlKeAd42w5fyXur90uEhAYiyZ738bi0ZUYrmxxCpW_zEYHE2rjYriEUacwCD_U1SX2ra1NVy8usKlnmBMZ5czpQJTgX6660QcLMorkOo7NFu9h9uSN9CkTH5oC_vwtHBy_yMg46RjFK9Xw4Gc-YVlVzImxKUfXMQ-69c96gz-nb0ghlcLDMsYV7oV_cXy0" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// aggregate.ts</span>
@@ -122,6 +122,6 @@
 Cinderella
 Daddy-Long-Legs
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><p>在上面的代码中，我们定义了几个类和接口来实现迭代器模式：</p><ul><li><code>Iterator</code> 接口定义了 <code>hasNext</code> 和 <code>next</code> 方法。</li><li><code>Aggregate</code> 接口定义了 <code>iterator</code> 方法。</li><li><code>Book</code> 类表示一个书籍对象。</li><li><code>BookShelf</code> 类表示一个书架，它实现了 <code>Aggregate</code> 接口。</li><li><code>BookShelfIterator</code> 类实现了 <code>Iterator</code> 接口，用于遍历 <code>BookShelf</code> 中的书籍。</li></ul><p>通过这些类和接口，我们可以轻松地遍历 <code>BookShelf</code> 中的书籍，而无需了解其内部实现细节。</p><h2 id="多个迭代器" tabindex="-1"><a class="header-anchor" href="#多个迭代器"><span>多个迭代器</span></a></h2><p>在某些情况下，我们可能需要为同一个集合编写多个具体迭代器（ConcreteIterator）。例如，我们可以为 <code>BookShelf</code> 编写一个反向迭代器，以便从后向前遍历书籍。</p><h2 id="相关的设计模式" tabindex="-1"><a class="header-anchor" href="#相关的设计模式"><span>相关的设计模式</span></a></h2><ul><li>Visitor 模式</li><li>Composite 模式</li><li>Factory Method 模式</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/iterator.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->设计模式七大原则</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">适配器模式<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/mediator.html b/tech/DesignPatterns/mediator.html
index 5774420..f264ed8 100644
--- a/tech/DesignPatterns/mediator.html
+++ b/tech/DesignPatterns/mediator.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/mediator.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="Mediator 模式"><meta property="og:description" content="为什么使用此类 请大家想象一下一个乱糟糟的开发小组的工作状态。小组中的 10 个成员虽然一起协同工作，但是意见难以统一，总是互相指挥，导致工作进度始终滞后。不仅如此，他们还十分在意编码细节，经常为此争执不下。"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="TypeScript"><meta property="article:tag" content="简单化"><meta property="article:published_time" content="2024-10-26T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"Mediator 模式","image":[""],"datePublished":"2024-10-26T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>Mediator 模式 | blog</title><meta name="description" content="为什么使用此类 请大家想象一下一个乱糟糟的开发小组的工作状态。小组中的 10 个成员虽然一起协同工作，但是意见难以统一，总是互相指挥，导致工作进度始终滞后。不仅如此，他们还十分在意编码细节，经常为此争执不下。">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/mediator.html-RBFBa63Z.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/mediator.html-C5vte2nl.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->Mediator 模式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-26T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag3 clickable" role="navigation">简单化</span><!--]--><meta property="keywords" content="设计模式,TypeScript,简单化"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#为什么使用此类">为什么使用此类</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#示例代码">示例代码</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#运行结果">运行结果</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#拓展思路的要点">拓展思路的要点</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#当发生分散灾难时">当发生分散灾难时</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#通信线路的增加">通信线路的增加</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#哪些角色可以复用">哪些角色可以复用</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#相关的设计模式">相关的设计模式</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h2 id="为什么使用此类" tabindex="-1"><a class="header-anchor" href="#为什么使用此类"><span>为什么使用此类</span></a></h2><p>请大家想象一下一个乱糟糟的开发小组的工作状态。小组中的 10 个成员虽然一起协同工作，但是意见难以统一，总是互相指挥，导致工作进度始终滞后。不仅如此，他们还十分在意编码细节，经常为此争执不下。</p><!-- more --><p>这时，我们就需要一个中立的仲裁者站出来说：“各位，请大家将情况报告给我，我来负责仲裁。我会从团队整体出发进行考虑，然后下达指示，但我不会评价大家的工作细节。”这样，当出现争执时大家就会找仲裁者进行商量，仲裁者会负责统一大家的意见。</p><p>最后，整个团队的交流过程就变为了组员向仲裁者报告，仲裁者向组员下达指示。组员之间不再相互询问和相互指示。</p><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><p><a href="https://github.com/RefactoringGuru/design-patterns-typescript/blob/main/src/Mediator/RealWorld/index.ts" target="_blank" rel="noopener noreferrer">源地址<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></p><img src="https://www.plantuml.com/plantuml/svg/hP6z3e8m4CVtFiMD6847wE17d1sTZCC9fzP0Ite7YL7VtQA2YeEBqwNNN_h_w8m5lTHbeOmLyZlC29QK6nJduQm0njQ9sPqY9fkJr-2sHyea1ch8YWOMR-m-XWfFXSDyscr66XfdSdLLAYkG6LPCtODOKeU5Sr8-vNGlt58j7xsZCNo3evRqb95fQ4dCkAUeVCoXaG1MzROmVFW1zeuN1vHvLNsqaTJ15kjxclNcB_NSYqcIoIlzK3XDBs-tFJ_4T5-GcWKtuKzl" alt=""><img src="https://www.plantuml.com/plantuml/svg/fPF1ReCm44Jl_egzaKhfeN3ZKALAUmkdfX-mc0sicXZBNXhnztK0jIIA40gtbJppFDwHDrxGINCwAjHIE_Zov5v6SpoQ4sM3bZLRD0BR2kNDsemAng1GghF2y-ljIGgc5ZwqgyWtkTUESugUr8teuki0ANmEAZObxBYin8IfnyTByV4r_htMFJXP2awkmHaApLg9RV8Z-ofQGxH5qHMU9yDdv3sM18uqyGyLaBUNHwGmc2VYtRDsCV_DCtOyollHmZSNarNUk_ElqXHwmcEP1--CzaQHz_Kfd2s9t1CUQMXmRiWKuRlz0W00" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token doc-comment comment">/**
@@ -118,6 +118,6 @@
 Message received by Lightning: Tomato
 Message received by Doc: Tomato
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="拓展思路的要点" tabindex="-1"><a class="header-anchor" href="#拓展思路的要点"><span>拓展思路的要点</span></a></h2><h3 id="当发生分散灾难时" tabindex="-1"><a class="header-anchor" href="#当发生分散灾难时"><span>当发生分散灾难时</span></a></h3><p>示例程序中的 <code>ChatAppMediator</code> 类的 <code>notify</code> 方法稍微有些复杂。如果发生需求变更，该方法中很容易发生 Bug。不过这并不是什么问题。因为即使 <code>notify</code> 方法中发生了 Bug，由于其他地方并没有控制消息发布和订阅的逻辑处理，因此只要调试该方法就能很容易地找出 Bug 的原因。请试想一下，如果这段逻辑分散在 <code>User</code> 类中，那么无论是编写代码还是调试代码和修改代码，都会非常困难。通常情况下，面向对象编程可以帮助我们分散处理，避免处理过于集中，也就是说可以“分而治之”。但是在本章中的示例程序中，把处理分散在各个类中是不明智的。如果只是将应当分散的处理分散在各个类中，但是没有将应当集中的处理集中起来，那么这些分散的类最终只会导致灾难。</p><p>在这个示例程序中，<code>ChatAppMediator</code> 类作为中介者（Mediator），负责管理和协调各个用户（User）的交互。<code>notify</code> 方法集中处理了所有消息的发布和订阅逻辑，这样可以确保逻辑的一致性和可维护性。如果将这些逻辑分散到各个用户类中，不仅会增加代码的复杂性，还会使得调试和维护变得更加困难。因此，将这些逻辑集中在中介者类中是更明智的选择。</p><h3 id="通信线路的增加" tabindex="-1"><a class="header-anchor" href="#通信线路的增加"><span>通信线路的增加</span></a></h3><p>假设现在有 A 和 B 这 2 个实例，它们之间互相通信（相互调用方法），那么通信线路有两条，即 A-B 和 A-B。如果是有 A、B 和 C 这 3 个实例，那么就会有 6 条通信线路，即 A-B、A-C、B-C、B-A 和 C-A。如果有 4 个实例，会有 12 条通信线路；5 个实例就会有 20 条通信线路，而 6 个实例则会有 30 条通信线路。如果存在很多这样的互相通信的实例，那么程序结构会变得非常复杂。可能会有读者认为，如果实例很少就不需要 Mediator 模式了。但是需要考虑到的是，即使最初实例很少，很可能随着需求变更实例数量会慢慢变多，迟早会暴露出问题。</p><h3 id="哪些角色可以复用" tabindex="-1"><a class="header-anchor" href="#哪些角色可以复用"><span>哪些角色可以复用</span></a></h3><p>ConcreteColleague 角色可以复用，但 ConcreteMediator 角色很难复用。例如，假设我们现在需要制作另外一个对话框。这时，我们可将扮演 ConcreteColleague 角色的 colleagueButton 类、 colleagueTextField 类和 colleagueCheckbox 类用于新的对话框中。这是因为在 ConcreteColleague 角色中并没有任何依赖于特定对话框的代码。在示例程序中，依赖于特定应用程序的部分都被封装在扮演 ConcreteMediator 角色的 LoginFrame 类中，依赖于特定应用程序就意味着难以复用。因此， LoginFrame 类很难在其他对话框中被复用。</p><h2 id="相关的设计模式" tabindex="-1"><a class="header-anchor" href="#相关的设计模式"><span>相关的设计模式</span></a></h2><ul><li>Facade 模式</li><li>Observer 模式</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/mediator.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->facade 模式</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">Observer 模式<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/memento.html b/tech/DesignPatterns/memento.html
index 94531a2..57b3e8e 100644
--- a/tech/DesignPatterns/memento.html
+++ b/tech/DesignPatterns/memento.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/memento.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="Memento 模式"><meta property="og:description" content="为什么使用 Memento 模式 Memento 模式的主要目的是在不破坏封装性的前提下，捕获和恢复对象的内部状态。它在以下情况下特别有用： 需要保存和恢复对象的多个状态。 需要在对象状态变化时进行撤销操作。 需要在不暴露对象实现细节的情况下保存对象状态。 示例代码 在这个示例中，我们使用了 Memento 模式来管理 Gamer 对象的状态。Meme..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="TypeScript"><meta property="article:tag" content="管理状态"><meta property="article:published_time" content="2024-10-28T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"Memento 模式","image":[""],"datePublished":"2024-10-28T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>Memento 模式 | blog</title><meta name="description" content="为什么使用 Memento 模式 Memento 模式的主要目的是在不破坏封装性的前提下，捕获和恢复对象的内部状态。它在以下情况下特别有用： 需要保存和恢复对象的多个状态。 需要在对象状态变化时进行撤销操作。 需要在不暴露对象实现细节的情况下保存对象状态。 示例代码 在这个示例中，我们使用了 Memento 模式来管理 Gamer 对象的状态。Meme...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/memento.html-CbbBldep.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/memento.html-Dw4vFzUb.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->Memento 模式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-28T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 4 分钟</span><meta property="timeRequired" content="PT4M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag1 clickable" role="navigation">管理状态</span><!--]--><meta property="keywords" content="设计模式,TypeScript,管理状态"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#为什么使用-memento-模式">为什么使用 Memento 模式</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#示例代码">示例代码</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#运行结果">运行结果</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#拓展思路的要点">拓展思路的要点</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#两种接口和可见性">两种接口和可见性</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#需要多少个-memento">需要多少个 Memento</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#memento-的有效期限是多久">Memento 的有效期限是多久</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#划分-caretaker-和-originator-角色的意义">划分 Caretaker 和 Originator 角色的意义</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#相关的设计模式">相关的设计模式</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h2 id="为什么使用-memento-模式" tabindex="-1"><a class="header-anchor" href="#为什么使用-memento-模式"><span>为什么使用 Memento 模式</span></a></h2><p>Memento 模式的主要目的是在不破坏封装性的前提下，捕获和恢复对象的内部状态。它在以下情况下特别有用：</p><ul><li>需要保存和恢复对象的多个状态。</li><li>需要在对象状态变化时进行撤销操作。</li><li>需要在不暴露对象实现细节的情况下保存对象状态。</li></ul><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><p>在这个示例中，我们使用了 Memento 模式来管理 <code>Gamer</code> 对象的状态。Memento 模式允许我们在不暴露对象实现细节的情况下保存和恢复对象的状态。以下是示例代码：</p><img src="https://www.plantuml.com/plantuml/svg/bP0z3i8m38Ntdi8ZAEe5650dc3en8eQqCLMb9f5i5maXxav-sXA9YId9i_FyFJSiccIsKzLFcXdEsYB1gmAemNg7pmEusNP8IRdJF0eVW8L6DrnlGLGmeBInSxSlUXLqA55v-D6aTq-e1LkqwCJ7od9DHK8MJrlLvdFhANt4NzBqQ94v4bgWE4MwGdvNIwZ59SLIFx7KNx6qCNbE-hJ-AG5N4lwY1Ci0atTRrySjUeFEXDr_0000" alt=""><img src="https://www.plantuml.com/plantuml/svg/VP1D2W8n38NtFKMMTU45kf01GLTpY3fzoi0qXJH5lBrrgbBmPvD7tal8HuQiNhJ4nVX9az1-cS5gcj1sHqSV8OvEKBinQzEvay0hHiGwdFhyQJbYNEbVxaCuI9dLdX-rcsW4ZWHQX5yBvfDCa2lu6o8s_NRh0XqJusP_X2j8hka03lKbTm00" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// gamer.ts</span>
@@ -137,6 +137,6 @@
 Nothing happened
 Money now<span class="token operator">:</span> <span class="token number">925</span>
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="拓展思路的要点" tabindex="-1"><a class="header-anchor" href="#拓展思路的要点"><span>拓展思路的要点</span></a></h2><h3 id="两种接口和可见性" tabindex="-1"><a class="header-anchor" href="#两种接口和可见性"><span>两种接口和可见性</span></a></h3><p>在 Memento 模式中，通常会有两种接口：宽接口（wide interface）和窄接口（narrow interface）。宽接口提供了对 Memento 对象的所有操作权限，而窄接口则只提供了有限的操作权限。Originator 类使用宽接口来创建和恢复 Memento，而 Caretaker 类则使用窄接口来保存和传递 Memento。通过这种方式，可以确保 Memento 的内部状态不会被外部直接修改，从而保持封装性。</p><h3 id="需要多少个-memento" tabindex="-1"><a class="header-anchor" href="#需要多少个-memento"><span>需要多少个 Memento</span></a></h3><p>在实际应用中，需要根据具体需求来决定需要保存多少个 Memento。对于一些简单的应用，可能只需要保存一个 Memento 来支持一次撤销操作。而对于一些复杂的应用，可能需要保存多个 Memento 以支持多次撤销操作。需要注意的是，保存过多的 Memento 会占用大量的内存资源，因此需要在性能和功能之间找到一个平衡点。</p><h3 id="memento-的有效期限是多久" tabindex="-1"><a class="header-anchor" href="#memento-的有效期限是多久"><span>Memento 的有效期限是多久</span></a></h3><p>Memento 的有效期限取决于具体的应用场景。在某些情况下，Memento 可能只需要在短时间内有效，例如在用户进行撤销操作之前。而在其他情况下，Memento 可能需要长期保存，例如在应用程序关闭后重新打开时恢复状态。需要根据具体需求来决定 Memento 的有效期限，并在适当的时候清理过期的 Memento 以释放资源。</p><h3 id="划分-caretaker-和-originator-角色的意义" tabindex="-1"><a class="header-anchor" href="#划分-caretaker-和-originator-角色的意义"><span>划分 Caretaker 和 Originator 角色的意义</span></a></h3><p>在 Memento 模式中，Caretaker 和 Originator 角色的划分具有重要意义。Caretaker 负责保存和管理 Memento，而 Originator 负责创建和恢复 Memento。通过这种划分，可以将状态保存和恢复的逻辑与业务逻辑分离，从而提高系统的可维护性和可扩展性。</p><ul><li><p>变更为可以多次撤销 通过保存多个 Memento，可以实现多次撤销操作。Caretaker 可以维护一个 Memento 的栈，每次撤销操作时从栈中弹出一个 Memento 并恢复状态。这样可以支持用户进行多次撤销和重做操作。</p></li><li><p>变更为不仅可以撤销，还可以将现在的状态保存在文件中 通过将 Memento 保存到文件中，可以实现持久化存储。这样即使应用程序关闭后重新打开，也可以恢复到之前的状态。Caretaker 可以负责将 Memento 序列化并保存到文件中，以及从文件中读取并反序列化 Memento。</p></li></ul><h2 id="相关的设计模式" tabindex="-1"><a class="header-anchor" href="#相关的设计模式"><span>相关的设计模式</span></a></h2><ul><li>Command 模式</li><li>Prototype 模式</li><li>State 模式</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/memento.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->Observer 模式</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">State 模式<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/observer.html b/tech/DesignPatterns/observer.html
index 870ec30..4c78961 100644
--- a/tech/DesignPatterns/observer.html
+++ b/tech/DesignPatterns/observer.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/observer.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="Observer 模式"><meta property="og:description" content="为什么使用观察者模式 观察者模式非常适合用于需要自动更新的场景。例如，在图形用户界面（GUI）应用程序中，当数据模型发生变化时，所有显示该数据的视图都需要自动更新。通过使用观察者模式，我们可以将这些视图注册为观察者，当数据模型发生变化时，它们会自动收到通知并更新显示。 示例代码 在这个示例中，我们展示了如何使用观察者模式来管理状态变化。观察者模式定义了..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="TypeScript"><meta property="article:tag" content="管理状态"><meta property="article:published_time" content="2024-10-26T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"Observer 模式","image":[""],"datePublished":"2024-10-26T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>Observer 模式 | blog</title><meta name="description" content="为什么使用观察者模式 观察者模式非常适合用于需要自动更新的场景。例如，在图形用户界面（GUI）应用程序中，当数据模型发生变化时，所有显示该数据的视图都需要自动更新。通过使用观察者模式，我们可以将这些视图注册为观察者，当数据模型发生变化时，它们会自动收到通知并更新显示。 示例代码 在这个示例中，我们展示了如何使用观察者模式来管理状态变化。观察者模式定义了...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/observer.html-BvrPoU9w.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/observer.html-DCoBW7Y-.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->Observer 模式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-26T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag1 clickable" role="navigation">管理状态</span><!--]--><meta property="keywords" content="设计模式,TypeScript,管理状态"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#为什么使用观察者模式">为什么使用观察者模式</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#示例代码">示例代码</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#运行结果">运行结果</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#拓展思路的要点">拓展思路的要点</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#这里也出现了可替换性">这里也出现了可替换性</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#observer-的顺序">Observer 的顺序</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#当-observer-的行为会对被观察对象产生影响时">当 Observer 的行为会对被观察对象产生影响时</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#传递更新信息的方式">传递更新信息的方式</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#从观察变为通知">从观察变为通知</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#mvc-model-view-controller">MVC (Model/View/Controller)</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#相关的设计模式">相关的设计模式</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h2 id="为什么使用观察者模式" tabindex="-1"><a class="header-anchor" href="#为什么使用观察者模式"><span>为什么使用观察者模式</span></a></h2><p>观察者模式非常适合用于需要自动更新的场景。例如，在图形用户界面（GUI）应用程序中，当数据模型发生变化时，所有显示该数据的视图都需要自动更新。通过使用观察者模式，我们可以将这些视图注册为观察者，当数据模型发生变化时，它们会自动收到通知并更新显示。</p><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><p>在这个示例中，我们展示了如何使用观察者模式来管理状态变化。观察者模式定义了一种一对多的依赖关系，当一个对象的状态发生改变时，所有依赖于它的对象都会得到通知并自动更新。以下是 TypeScript 实现的代码示例：</p><img src="https://www.plantuml.com/plantuml/svg/jL912i8m4Bpd5JbMf1_eoOFWJS4VR9kn1fgaRBP54VzkDRQKua4GRyliC3CxoIOAiNIkKTOB-4GLzA6Cu1wiRqhhTTSQ4cGrF9WaSA7tdIl1kn5O5ReFrgYxKbH6OQf4Lmt5k2GcFJ9cDCZ2UoWcpr5i81eq47p7zK7iwJekOZPRrP2Kumdwr_I4SK7L3NVDqgVGMrjRcIgmhctWu2N-K4iItZ6rvty87ycRu9PbuoBmvlCZvAc7UH_VrxGK37a-dQ0sW-Vmcnu0" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// DigitObserver.ts</span>
@@ -213,6 +213,6 @@
  <span class="token number">3</span>
 ***
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="拓展思路的要点" tabindex="-1"><a class="header-anchor" href="#拓展思路的要点"><span>拓展思路的要点</span></a></h2><h3 id="这里也出现了可替换性" tabindex="-1"><a class="header-anchor" href="#这里也出现了可替换性"><span>这里也出现了可替换性</span></a></h3><p>在设计模式中，可替换性是指一个对象可以被另一个具有相同接口的对象替换，而不影响系统的功能。在观察者模式中，观察者（Observer）和被观察者（Subject）之间的关系是松耦合的，这意味着我们可以轻松地替换观察者或被观察者，而不会影响系统的其他部分。</p><h3 id="observer-的顺序" tabindex="-1"><a class="header-anchor" href="#observer-的顺序"><span>Observer 的顺序</span></a></h3><p>Subject 角色（被观察对象）中注册有多个 Observer 角色。在示例程序的 <code>notifyObservers</code> 方法中，先注册的 Observer 的 <code>update</code> 方法会先被调用。通常，在设计 ConcreteObserver 角色的类时，需要注意这些 Observer 的 <code>update</code> 方法的调用顺序，不能因为方法的调用顺序发生改变而产生问题。例如，在示例程序中，绝不能因为先调用 <code>DigitObserver</code> 的 <code>update</code> 方法后调用 <code>GraphObserver</code> 的 <code>update</code> 方法而导致应用程序不能正常工作。当然，通常，只要保持各个类的独立性，就不会发生上面这种类的依赖关系混乱的问题。不过，我们还需要注意下面将要提到的情况。</p><h3 id="当-observer-的行为会对被观察对象产生影响时" tabindex="-1"><a class="header-anchor" href="#当-observer-的行为会对被观察对象产生影响时"><span>当 Observer 的行为会对被观察对象产生影响时</span></a></h3><p>当观察者的行为会对被观察对象产生影响时，我们需要特别小心，以避免循环依赖和无限递归。例如，一个观察者在接收到通知后修改了被观察对象的状态，这可能会导致被观察对象再次通知所有观察者，从而引发无限循环。为了解决这个问题，我们可以引入一个标志位来跟踪通知状态，或者使用更复杂的事件处理机制。</p><h3 id="传递更新信息的方式" tabindex="-1"><a class="header-anchor" href="#传递更新信息的方式"><span>传递更新信息的方式</span></a></h3><p>在观察者模式中，传递更新信息的方式有多种选择。最简单的方法是直接调用观察者的更新方法，并将被观察对象自身作为参数传递。另一种方法是传递具体的更新信息，例如事件对象或数据包。这种方法可以减少观察者对被观察对象的依赖，从而提高系统的灵活性和可维护性。</p><h3 id="从观察变为通知" tabindex="-1"><a class="header-anchor" href="#从观察变为通知"><span>从观察变为通知</span></a></h3><p>在某些情况下，我们可能需要从观察模式转变为通知模式。例如，当系统中有大量的观察者时，逐个通知每个观察者可能会导致性能问题。此时，我们可以考虑使用事件总线或消息队列来集中处理通知，从而提高系统的性能和可扩展性。</p><h3 id="mvc-model-view-controller" tabindex="-1"><a class="header-anchor" href="#mvc-model-view-controller"><span>MVC (Model/View/Controller)</span></a></h3><p>观察者模式在 MVC 架构中得到了广泛应用。模型（Model）作为被观察对象，视图（View）作为观察者，当模型的状态发生变化时，视图会自动更新。控制器（Controller）负责协调模型和视图之间的交互。通过使用观察者模式，MVC 架构实现了视图和模型的松耦合，从而提高了系统的可维护性和可扩展性。</p><h2 id="相关的设计模式" tabindex="-1"><a class="header-anchor" href="#相关的设计模式"><span>相关的设计模式</span></a></h2><ul><li>Mediator 模式</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/observer.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->Mediator 模式</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">Memento 模式<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/prototype.html b/tech/DesignPatterns/prototype.html
index 40ea442..18e173c 100644
--- a/tech/DesignPatterns/prototype.html
+++ b/tech/DesignPatterns/prototype.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/prototype.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="Prototype 模式"><meta property="og:description" content="为什么要使用 Prototype 模式 Prototype 模式是一种创建型设计模式，它允许你复制现有对象而无需使代码依赖它们所属的类。使用 Prototype 模式可以： 避免重复初始化对象的复杂过程。 提高性能，特别是在创建对象代价较高时。 简化代码，使得对象的创建更加灵活。 对象种类繁多，无法将它们整合到一个类中 难以根据类生成实例 解耦框架与生..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="typescript"><meta property="article:tag" content="生成实例"><meta property="article:published_time" content="2024-10-22T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"Prototype 模式","image":[""],"datePublished":"2024-10-22T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>Prototype 模式 | blog</title><meta name="description" content="为什么要使用 Prototype 模式 Prototype 模式是一种创建型设计模式，它允许你复制现有对象而无需使代码依赖它们所属的类。使用 Prototype 模式可以： 避免重复初始化对象的复杂过程。 提高性能，特别是在创建对象代价较高时。 简化代码，使得对象的创建更加灵活。 对象种类繁多，无法将它们整合到一个类中 难以根据类生成实例 解耦框架与生...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/prototype.html-Boe-0El2.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/prototype.html-Be3THUal.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->Prototype 模式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-22T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag3 clickable" role="navigation">typescript</span><span class="page-tag-item tag6 clickable" role="navigation">生成实例</span><!--]--><meta property="keywords" content="设计模式,typescript,生成实例"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#为什么要使用-prototype-模式">为什么要使用 Prototype 模式</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#示例代码">示例代码</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#运行结果">运行结果</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#相关设计模式">相关设计模式</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h2 id="为什么要使用-prototype-模式" tabindex="-1"><a class="header-anchor" href="#为什么要使用-prototype-模式"><span>为什么要使用 Prototype 模式</span></a></h2><p>Prototype 模式是一种创建型设计模式，它允许你复制现有对象而无需使代码依赖它们所属的类。使用 Prototype 模式可以：</p><ul><li>避免重复初始化对象的复杂过程。</li><li>提高性能，特别是在创建对象代价较高时。</li><li>简化代码，使得对象的创建更加灵活。</li><li>对象种类繁多，无法将它们整合到一个类中</li><li>难以根据类生成实例</li><li>解耦框架与生成的实例</li></ul><!-- more --><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/fP5FQm913CNlyoboN6dN3p2K8lKi2CMJU0WpwJeuPaeown-itxtZsYqhdiJhuvVtNfA9PfJSRgC9d4c-q17C9VdMPJWPW9TMgL8Bdra2DoCBknJyHNT2c6aQ4rDLvByPSpR6HLI56J8s99r9hUkqTwXauGJB3HqjQEUtie1yXFF5KAW9MYfKZ5lgWLVubfHJXzs5tv2ZZXdaasefy94ErmgUN79hb9uVxAQFxhPWJn83qvpuwjx6vxtxix_zZCU3-hVwCDhqDwxhz_-dMIZ9PaBiorD_0G00" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// main.ts</span>
@@ -128,6 +128,6 @@
 / Hello, world. /
 /////////////////
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="相关设计模式" tabindex="-1"><a class="header-anchor" href="#相关设计模式"><span>相关设计模式</span></a></h2><ul><li>Flyweight 模式</li><li>Memento 模式</li><li>Composite 模式</li><li>Decorator 模式</li><li>Command 模式</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/prototype.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->Singleton 模式</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">builder 模式<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/proxy.html b/tech/DesignPatterns/proxy.html
index 524aba8..53dadcd 100644
--- a/tech/DesignPatterns/proxy.html
+++ b/tech/DesignPatterns/proxy.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/proxy.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="Proxy 模式"><meta property="og:description" content="为什么使用代理模式 在面向对象编程中，“本人”和“代理人”都是对象。如果“本人”对象太忙了．有些工作无法自己亲自完成，就将其交给“代理人"对象负责。"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="TypeScript"><meta property="article:tag" content="避免浪费"><meta property="article:published_time" content="2024-10-29T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"Proxy 模式","image":[""],"datePublished":"2024-10-29T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>Proxy 模式 | blog</title><meta name="description" content="为什么使用代理模式 在面向对象编程中，“本人”和“代理人”都是对象。如果“本人”对象太忙了．有些工作无法自己亲自完成，就将其交给“代理人"对象负责。">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/proxy.html-CSHBH0Xk.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/proxy.html-DydmfTHY.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->Proxy 模式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-29T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag5 clickable" role="navigation">避免浪费</span><!--]--><meta property="keywords" content="设计模式,TypeScript,避免浪费"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#为什么使用代理模式">为什么使用代理模式</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#实例代码">实例代码</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#运行结果">运行结果</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#拓展思路的要点">拓展思路的要点</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#使用代理人来提升处理速度">使用代理人来提升处理速度</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#有必要划分代理人和本人吗">有必要划分代理人和本人吗</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#代理与委托">代理与委托</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#透明性">透明性</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#http-代理">HTTP 代理</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#各种-proxy-模式">各种 Proxy 模式</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#相关的设计模式">相关的设计模式</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h2 id="为什么使用代理模式" tabindex="-1"><a class="header-anchor" href="#为什么使用代理模式"><span>为什么使用代理模式</span></a></h2><p>在面向对象编程中，“本人”和“代理人”都是对象。如果“本人”对象太忙了．有些工作无法自己亲自完成，就将其交给“代理人&quot;对象负责。</p><!-- more --><p>Proxy 模式用于为某对象提供一个代理，以控制对该对象的访问。主要有以下几个优点：</p><ul><li>延迟实例化：代理对象可以在需要时才创建实际对象，节省资源。</li><li>控制访问：可以在代理中加入额外的逻辑来控制对实际对象的访问。</li><li>远程代理：可以用于访问远程对象。</li></ul><h2 id="实例代码" tabindex="-1"><a class="header-anchor" href="#实例代码"><span>实例代码</span></a></h2><p>为了让 PrinterProxy 类与 Printer 类具有一致性，我们定义了 Printable 接口。示例程序的前提是&quot;生成 Printer 类的实例&quot;这一处理需要花费很多时间。为了在程序中体现这一点，我们在 Printer 类的构造了数中调用了 heavyJob 方法，让它干一些“重活”（虽说是重活，也不过是让程序睡眠 5 秒钟）。</p><img src="https://www.plantuml.com/plantuml/svg/nP9D2eCm48NtESKibP8BP55STr6yGjIf3UH7Cb5gI-_U6BIecz95wIQ4cVTctaTIK90-z4OpPGFwYwmHIX_lij883mPm0CAGIkZFqc1cuo60GYorkO31gIR9sgqiNpIfsKsTB1RspYTZjPP4C7j1cKwZGHje5uJ3UdEQEdksaNwVUSfoHJcC9rTbXjfFJALtj_4BC0uUfHQBVOsQHls3TqgaxicoC6xe7EV7zniAw0bPWRQ9F-i5" alt=""><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuKfCBialKd3EoKpDA-62K0gwTWe1HPbv9Qb50KNv5PLM2iMf9L01lyJSL0qbf_ma9KsGrioon99K5CLSo1nCaufI4tCogr8rC7NZqcYba9TQ3kF0h4v99Lvx0OYXeVHaxuAdI_U-tzFpPCUqvrDx7ZSq0Ss1Aa9Hdv6QM5RfbP-aeVHixUAdSrOydpB_MSS4gFJpMIrFryrxigzR0-WGJQmcG7twT5tFarrjG6kGbK02s4h1rjPM0MW0Y8x9mtGPDlzX2a72so4rBmKOaG00" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// main.ts</span>
@@ -127,6 +127,6 @@
 <span class="token builtin class-name">.</span>
 <span class="token builtin class-name">.</span>
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="拓展思路的要点" tabindex="-1"><a class="header-anchor" href="#拓展思路的要点"><span>拓展思路的要点</span></a></h2><h3 id="使用代理人来提升处理速度" tabindex="-1"><a class="header-anchor" href="#使用代理人来提升处理速度"><span>使用代理人来提升处理速度</span></a></h3><p>在某些情况下，使用代理可以显著提升处理速度。例如，虚拟代理（Virtual Proxy）可以在实际对象创建之前进行一些轻量级的操作，从而减少系统的开销。通过代理对象来延迟实际对象的创建，可以提高系统的响应速度和资源利用率。</p><h3 id="有必要划分代理人和本人吗" tabindex="-1"><a class="header-anchor" href="#有必要划分代理人和本人吗"><span>有必要划分代理人和本人吗</span></a></h3><p>在设计模式中，代理人和本人的划分是为了实现职责分离和提高系统的灵活性。代理模式通过引入代理对象来控制对实际对象的访问，可以在不修改实际对象的情况下添加额外的功能。例如，远程代理（Remote Proxy）可以在客户端和远程服务器之间进行通信，而不需要客户端了解远程服务器的具体实现。</p><h3 id="代理与委托" tabindex="-1"><a class="header-anchor" href="#代理与委托"><span>代理与委托</span></a></h3><p>代理模式和委托模式虽然在某些方面有相似之处，但它们的目的和实现方式有所不同。代理模式主要用于控制对对象的访问，而委托模式则用于将任务分配给其他对象来执行。代理模式通过代理对象来控制对实际对象的访问，而委托模式通过委托对象来执行具体的任务。</p><h3 id="透明性" tabindex="-1"><a class="header-anchor" href="#透明性"><span>透明性</span></a></h3><p>代理模式的一个重要特点是透明性。代理对象和实际对象实现相同的接口，客户端可以像使用实际对象一样使用代理对象，而不需要关心代理对象的内部实现。这种透明性使得代理模式在不改变客户端代码的情况下添加额外的功能成为可能。</p><h3 id="http-代理" tabindex="-1"><a class="header-anchor" href="#http-代理"><span>HTTP 代理</span></a></h3><p>HTTP 代理是一种常见的代理模式应用。HTTP 代理服务器位于客户端和目标服务器之间，负责转发客户端的请求和目标服务器的响应。HTTP 代理可以用于缓存、负载均衡、安全控制等功能，从而提高网络通信的效率和安全性。</p><h3 id="各种-proxy-模式" tabindex="-1"><a class="header-anchor" href="#各种-proxy-模式"><span>各种 Proxy 模式</span></a></h3><ul><li><strong>Virtual Proxy</strong>：虚拟代理用于控制对资源密集型对象的访问。它在实际对象创建之前进行一些轻量级的操作，从而延迟实际对象的创建。例如，图像加载时可以使用虚拟代理来显示占位符图像，直到实际图像加载完成。</li><li><strong>Remote Proxy</strong>：远程代理用于控制对远程对象的访问。它在客户端和远程服务器之间进行通信，使得客户端可以像使用本地对象一样使用远程对象。例如，RMI（远程方法调用）就是一种远程代理的实现。</li><li><strong>Access Proxy</strong>：访问代理用于控制对实际对象的访问权限。它可以在访问实际对象之前进行权限检查，从而确保只有授权的客户端才能访问实际对象。例如，防火墙代理可以用于控制对内部网络资源的访问。</li></ul><p>通过这些不同类型的代理模式，我们可以在不同的应用场景中灵活地控制对对象的访问，提高系统的安全性、性能和可维护性。</p><h2 id="相关的设计模式" tabindex="-1"><a class="header-anchor" href="#相关的设计模式"><span>相关的设计模式</span></a></h2><ul><li>Adapter 模式</li><li>Decorator 模式</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/proxy.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->Flyweight 模式</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">Command 模式<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/singleton.html b/tech/DesignPatterns/singleton.html
index b6714f8..6c4403b 100644
--- a/tech/DesignPatterns/singleton.html
+++ b/tech/DesignPatterns/singleton.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/singleton.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="Singleton 模式"><meta property="og:description" content="为什么要使用 Singleton 模式 Singleton 模式确保一个类只有一个实例，并提供一个全局访问点。它常用于需要控制资源访问的场景，例如数据库连接、日志记录器等。通过 Singleton 模式，可以避免创建多个实例带来的资源浪费和不一致性问题。"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="typescript"><meta property="article:tag" content="生成实例"><meta property="article:published_time" content="2024-10-21T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"Singleton 模式","image":[""],"datePublished":"2024-10-21T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>Singleton 模式 | blog</title><meta name="description" content="为什么要使用 Singleton 模式 Singleton 模式确保一个类只有一个实例，并提供一个全局访问点。它常用于需要控制资源访问的场景，例如数据库连接、日志记录器等。通过 Singleton 模式，可以避免创建多个实例带来的资源浪费和不一致性问题。">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/singleton.html-Pzh1ZzrO.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/singleton.html-CJylCsqx.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->Singleton 模式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-21T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag3 clickable" role="navigation">typescript</span><span class="page-tag-item tag6 clickable" role="navigation">生成实例</span><!--]--><meta property="keywords" content="设计模式,typescript,生成实例"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#为什么要使用-singleton-模式">为什么要使用 Singleton 模式</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#总结">总结:</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#示例代码">示例代码</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#运行结果">运行结果</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#相关设计模式">相关设计模式</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#多线程下">多线程下</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#双重检查锁定示例代码">双重检查锁定示例代码</a></li><!----><!--]--></ul></li><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h2 id="为什么要使用-singleton-模式" tabindex="-1"><a class="header-anchor" href="#为什么要使用-singleton-模式"><span>为什么要使用 Singleton 模式</span></a></h2><p>Singleton 模式确保一个类只有一个实例，并提供一个全局访问点。它常用于需要控制资源访问的场景，例如数据库连接、日志记录器等。通过 Singleton 模式，可以避免创建多个实例带来的资源浪费和不一致性问题。</p><!-- more --><h3 id="总结" tabindex="-1"><a class="header-anchor" href="#总结"><span>总结:</span></a></h3><ul><li>想确保任何情况下都绝对只有 1 个实例</li><li>想在程序上表现出“只存在一个实例”</li></ul><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/JOun2iCm34LtdK9ZGl05F9IicNi2LnR1uCXWoLFetMjAmDw4tl-Vjwk5QktAG3ceuZl9cTcAu0s83ZksH9Ya7qBiHs369mlNO1oFw57QzU7wnrHwhpQoKfUrVxPHiEEPNDPvz0im59nxJK8UcxB2pXAxxmy0" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// main.ts</span>
@@ -87,6 +87,6 @@
   <span class="token function">fn</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
 <span class="token punctuation">}</span>
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><p>在上面的代码中，<code>synchronized</code> 函数模拟了一个锁机制，以确保在多线程环境下 <code>getInstance</code> 方法的线程安全性。</p></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/singleton.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->Factory Method 模式</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">Prototype 模式<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/state.html b/tech/DesignPatterns/state.html
index 4142731..be9a91b 100644
--- a/tech/DesignPatterns/state.html
+++ b/tech/DesignPatterns/state.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/state.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="State 模式"><meta property="og:description" content="为什么使用 State 模式 State 模式允许对象在其内部状态改变时改变其行为。它将与状态相关的行为封装在独立的类中，使得状态转换变得清晰且易于管理。使用 State 模式可以避免大量的条件语句，使代码更加简洁和可维护。 示例代码 运行结果 拓展思路的要点 分而治之 在编程时，我们经常会使用分而治之的方针。它非常适用于大规模的复杂处理。当遇到庞大且..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="TypeScript"><meta property="article:tag" content="管理状态"><meta property="article:published_time" content="2024-10-28T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"State 模式","image":[""],"datePublished":"2024-10-28T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>State 模式 | blog</title><meta name="description" content="为什么使用 State 模式 State 模式允许对象在其内部状态改变时改变其行为。它将与状态相关的行为封装在独立的类中，使得状态转换变得清晰且易于管理。使用 State 模式可以避免大量的条件语句，使代码更加简洁和可维护。 示例代码 运行结果 拓展思路的要点 分而治之 在编程时，我们经常会使用分而治之的方针。它非常适用于大规模的复杂处理。当遇到庞大且...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/state.html-DsXXtCU9.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/state.html-D0BJywlY.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->State 模式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-28T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 12 分钟</span><meta property="timeRequired" content="PT12M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag1 clickable" role="navigation">管理状态</span><!--]--><meta property="keywords" content="设计模式,TypeScript,管理状态"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#为什么使用-state-模式">为什么使用 State 模式</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#示例代码">示例代码</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#运行结果">运行结果</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#拓展思路的要点">拓展思路的要点</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#分而治之">分而治之</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#依赖于状态的处理">依赖于状态的处理</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#应当是谁来管理状态的迁移">应当是谁来管理状态的迁移</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#不会自相矛盾">不会自相矛盾</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#易于增加新的状态">易于增加新的状态</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#实例的多面性">实例的多面性</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#相关的设计模式">相关的设计模式</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h2 id="为什么使用-state-模式" tabindex="-1"><a class="header-anchor" href="#为什么使用-state-模式"><span>为什么使用 State 模式</span></a></h2><p>State 模式允许对象在其内部状态改变时改变其行为。它将与状态相关的行为封装在独立的类中，使得状态转换变得清晰且易于管理。使用 State 模式可以避免大量的条件语句，使代码更加简洁和可维护。</p><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/vPJ1JeGm48RlF4MFaCeBS5g3CJ4nneJi0zGoMnhRZca7inlZkzi2AnXnqRCN0fq_q--VydSNI7ZghScq8_078O7L65-FnDuonW9GRL0-vntslcAkjq_WYugzecvZMNR2AMX84EGXFIisV2mKmfW6PEyrdMf8U-Gsg8e5yjgfMUT1ec_lKQsLtxC5th310DVYo2P7uEfCViNMQLlS1_YcNjQlZV3sekAnG_TpZmWgZGY1tOZJoAdjYm4RZOSHF75p1NJduhoSXBoOHXRNozWs6kybeS-B9FohGxvbaMzxv5iceuIm6GueqOz7DLj_qAgZ_sg-4GUuzS9-yJwrIExBPKfIius0yUs4yTz6Z5_CsEVyLkQrCf_vZpzV5rYMawqTk3PUAHy0" alt=""><img src="https://www.plantuml.com/plantuml/svg/XP513e8m44NtFKMNcEW5M1YCngKn8HvWKaRQ21tI3edUNce50X7S_l_cpIIJUGR7RLq9K4nEtZmwqNIHKQO1opA7EvuTr3X9J_3A6NWQNaofESOYUEHkFuwdqYCVArAFH5FhDc9e0jRxKbbGX1HPnYTlPQHxOEPK6co9doOPry_aOx6e_t5kGLsOhAe2y1KjA0uLk7fT4f5rpLMJ_NDBH0PDXhRelle6" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// context.ts</span>
@@ -259,6 +259,6 @@
 call<span class="token operator">!</span> 紧急铃<span class="token punctuation">(</span>夜间<span class="token punctuation">)</span>
 record <span class="token punctuation">..</span>. 夜间通话录音
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="拓展思路的要点" tabindex="-1"><a class="header-anchor" href="#拓展思路的要点"><span>拓展思路的要点</span></a></h2><h3 id="分而治之" tabindex="-1"><a class="header-anchor" href="#分而治之"><span>分而治之</span></a></h3><p>在编程时，我们经常会使用分而治之的方针。它非常适用于大规模的复杂处理。当遇到庞大且复杂的问题、不能用一般的方法解决时，我们会先将该问题分解为多个小问题。如果还是不能解决这些小问题，我们会将它们继续划分为更小的问题，直至可以解决它们为止。</p><p>分而治之，简单而言就是将一个复杂的大问题分解为多个小问题然后逐个解决。在 State 模式中，我们用类来表示状态，并为每一种具体的状态都定义一个相应的类。这样，问题就被分解了。开发人员可以在编写一个 ConcreteState 角色的代码的同时，在头脑中（一定程度上）考虑其他的类。</p><p>在本章的警报系统的示例程序中，只有“白天”和“晚上”两个状态，可能大家对此感受不深，但是当状态非常多的时候，State 模式的优势就会非常明显了。在不使用 State 模式时，我们需要使用条件分支语句判断当前的状态，然后进行相应的处理。状态越多，条件分支就会越多，而且我们必须在所有的事件处理方法中都编写这些条件分支语句。State 模式用类表示系统的“状态”，并以此将复杂的程序分解开来。</p><h3 id="依赖于状态的处理" tabindex="-1"><a class="header-anchor" href="#依赖于状态的处理"><span>依赖于状态的处理</span></a></h3><p>我们来思考一下 SafeFrame 类的 setClock 方法和 State 接口的 doClock 方法之间的关系。Main 类会调用 SafeFrame 类的 setClock 方法，告诉 setClock 方法“请设置时间”。在 setClock 方法中，会像下面这样将处理委托给 State 类：<code>state.doClock(this, hour);</code>。也就是说，我们将设置时间的处理看作是“依赖于状态的处理”。当然，不只是 doClock 方法。在 State 接口中声明的所有方法都是“依赖于状态的处理”，都是“状态不同处理也不同”。这虽然看似理所当然，不过却需要我们特别注意。在 State 模式中，我们应该如何编程，以实现“依赖于状态的处理”呢？总结起来有如下两点：</p><ul><li>定义接口，声明抽象方法</li><li>定义多个类，实现具体方法</li></ul><p>这就是 State 模式中的“依赖于状态的处理”的实现方法。这里故意将上面两点说得很笼统，但是，如果大家在读完这两点之后会点头表示赞同，那就意味着大家完全理解了 State 模式以及接口与类之间的关系。</p><h3 id="应当是谁来管理状态的迁移" tabindex="-1"><a class="header-anchor" href="#应当是谁来管理状态的迁移"><span>应当是谁来管理状态的迁移</span></a></h3><p>用类来表示状态，将依赖于状态的处理分散在每个 ConcreteState 角色中，这是一种非常好的解决办法。不过，在使用模式时需要注意应当是谁来管理状态迁移。在示例程序中，扮演 Context 角色的 SafeFrame 类实现了实际进行状态迁移的 changeState 方法。但是，实际调用该方法的却是扮演 ConcreteState 角色的 DayState 类和 NightState 类。</p><p>也就是说，在示例程序中，我们将“状态迁移”看作是“依赖于状态的处理”。这种处理方式既有优点也有缺点。优点是这种处理方式将“什么时候从一个状态迁移到其他状态”的信息集中在了一个类中。也就是说，当我们想知道“什么时候会从 DayState 类变化为其他状态”时，只需要阅读 DayState 类的代码就可以了。缺点是“每个 ConcreteState 角色都需要知道其他 ConcreteState 角色”。</p><p>例如，DayState 类的 doClock 方法就使用了 NightState 类。这样，如果以后发生需求变更，需要删除 NightState 类时，就必须要相应地修改 DayState 类的代码。将状态迁移交给 ConcreteState 角色后，每个 ConcreteState 角色都需要或多或少地知道其他角色。也就是说，将状态迁移交给 ConcreteState 角色后，各个类之间的依赖关系就会加强。我们也可以不使用示例程序中的做法，而是将所有的状态迁移交给扮演 Context 角色的 SafeFrame 类来负责。</p><p>有时，使用这种解决方法可以提高 ConcreteState 角色的独立性，程序的整体结构也会更加清晰。不过这样做的话，Context 角色就必须要知道“所有的 ConcreteState 角色”。在这种情况下，我们可以使用 Mediator 模式（第 16 章）。当然，还可以不用 State 模式，而是用状态迁移表来设计程序。所谓状态迁移表是可以根据“输入和内部状态”得到“输出和下一个状态”的一览表（这超出了本书的范围，我们暂且不深入学习该方法）。当状态迁移遵循一定的规则时，使用状态迁移表非常有效。此外，当状态数过多时，可以用程序来生成代码而不是手写代码。</p><h3 id="不会自相矛盾" tabindex="-1"><a class="header-anchor" href="#不会自相矛盾"><span>不会自相矛盾</span></a></h3><p>如果不使用 State 模式，我们需要使用多个变量的值的集合来表示系统的状态。这时，必须十分小心，注意不要让变量的值之间互相矛盾。而在 State 模式中，是用类来表示状态的。这样，我们就只需要一个表示系统状态的变量即可。在示例程序中，SafeFrame 类的 state 字段就是这个变量，它决定了系统的状态。因此，不会存在自相矛盾的状态。</p><h3 id="易于增加新的状态" tabindex="-1"><a class="header-anchor" href="#易于增加新的状态"><span>易于增加新的状态</span></a></h3><p>在 State 模式中增加新的状态是非常简单的。以示例程序来说，编写一个 XXXState 类，让它实现 State 接口，然后实现一些所需的方法就可以了。当然，在修改状态迁移部分的代码时，还是需要仔细一点的。因为状态迁移的部分正是与其他 ConcreteState 角色相关联的部分。</p><p>但是，在 State 模式中增加其他“依赖于状态的处理”是很困难的。这是因为我们需要在 State 接口中增加新的方法，并在所有的 ConcreteState 角色中都实现这个方法。虽说很困难，但是好在我们绝对不会忘记实现这个方法。假设我们现在在 State 接口中增加了一个 doYYY 方法，而忘记了在 DayState 类和 NightState 类中实现这个方法，那么编译器在编译代码时就会报错，告诉我们存在还没有实现的方法。</p><p>如果不使用 State 模式，那么增加新的状态时会怎样呢？这里，如果不使用 State 模式，就必须用条件分支语句判断状态。这样就很难在编译代码时检测出“忘记实现方法”这种错误了（在运行时检测出问题并不难。我们只要事先在每个方法内部都加上一段“当检测到没有考虑到的状态时就报错”的代码即可）。</p><h3 id="实例的多面性" tabindex="-1"><a class="header-anchor" href="#实例的多面性"><span>实例的多面性</span></a></h3><p>请注意 SafeFrame 类中的以下两条语句（代码清单 19.7）：</p><ul><li>SafeFrame 类的构造函数中的 <code>buttonUse.addActionListener(this);</code></li><li>actionPerformed 方法中的 <code>state.doUse(this);</code></li></ul><p>这两条语句中都有 <code>this</code>。那么这个 <code>this</code> 到底是什么呢？当然，它们都是 SafeFrame 类的实例。由于在示例程序中只生成了一个 SafeFrame 的实例，因此这两个 <code>this</code> 其实是同一个对象。不过，在 addActionListener 方法中和 doUse 方法中，对 <code>this</code> 的使用方式是不一样的。</p><p>向 addActionListener 方法传递 <code>this</code> 时，该实例会被当作“实现了 ActionListener 接口的类的实例”来使用。这是因为 addActionListener 方法的参数类型是 ActionListener 类型。</p><p>在 addActionListener 方法中会用到的方法也都是在 ActionListener 接口中定义了的方法。至于这个参数是否是 SafeFrame 类的实例并不重要。向 doUse 方法传递 <code>this</code> 时，该实例会被当作“实现了 Context 接口的类的实例”来使用。这是因为 doUse 方法的参数类型是 Context 类型。在 doUse 方法中会用到的方法也都是在 Context 接口中定义了的方法（大家只要再回顾一下 DayState 类和 NightState 类的 doUse 方法就会明白了）。请大家一定要透彻理解此处的实例的多面性。</p><h2 id="相关的设计模式" tabindex="-1"><a class="header-anchor" href="#相关的设计模式"><span>相关的设计模式</span></a></h2><ul><li>Singleton 模式</li><li>Flyweight 模式</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/state.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->Memento 模式</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">Flyweight 模式<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/strategy.html b/tech/DesignPatterns/strategy.html
index 1bbacc0..f5848e3 100644
--- a/tech/DesignPatterns/strategy.html
+++ b/tech/DesignPatterns/strategy.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/strategy.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="Strategy 模式"><meta property="og:description" content="使用此设计模式的理由 在这个示例程序中，我们使用了策略模式（Strategy Pattern）来实现不同的猜拳策略。策略模式的主要优点包括： 易于扩展：可以很容易地添加新的策略，而不需要修改现有的代码。 提高代码的可读性和可维护性：将不同的算法封装在独立的类中，使得代码更加清晰。 减少重复代码：通过使用策略模式，可以避免在多个地方重复相同的算法逻辑。 ..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="TypeScript"><meta property="article:tag" content="分开考虑"><meta property="article:tag" content="整体的替换算法"><meta property="article:published_time" content="2024-10-25T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"Strategy 模式","image":[""],"datePublished":"2024-10-25T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>Strategy 模式 | blog</title><meta name="description" content="使用此设计模式的理由 在这个示例程序中，我们使用了策略模式（Strategy Pattern）来实现不同的猜拳策略。策略模式的主要优点包括： 易于扩展：可以很容易地添加新的策略，而不需要修改现有的代码。 提高代码的可读性和可维护性：将不同的算法封装在独立的类中，使得代码更加清晰。 减少重复代码：通过使用策略模式，可以避免在多个地方重复相同的算法逻辑。 ...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/strategy.html-Cprd53d9.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/strategy.html-BeQd57Ga.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->Strategy 模式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-25T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag6 clickable" role="navigation">分开考虑</span><span class="page-tag-item tag6 clickable" role="navigation">整体的替换算法</span><!--]--><meta property="keywords" content="设计模式,TypeScript,分开考虑,整体的替换算法"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#使用此设计模式的理由">使用此设计模式的理由</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#示例程序">示例程序</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#运行结果">运行结果</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#拓展思路的要点">拓展思路的要点</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#为什么要特意编写-strategy">为什么要特意编写 Strategy</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#程序运行中也可以切换策略">程序运行中也可以切换策略</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#相关的设计模式">相关的设计模式</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h2 id="使用此设计模式的理由" tabindex="-1"><a class="header-anchor" href="#使用此设计模式的理由"><span>使用此设计模式的理由</span></a></h2><p>在这个示例程序中，我们使用了策略模式（Strategy Pattern）来实现不同的猜拳策略。策略模式的主要优点包括：</p><ol><li><strong>易于扩展</strong>：可以很容易地添加新的策略，而不需要修改现有的代码。</li><li><strong>提高代码的可读性和可维护性</strong>：将不同的算法封装在独立的类中，使得代码更加清晰。</li><li><strong>减少重复代码</strong>：通过使用策略模式，可以避免在多个地方重复相同的算法逻辑。</li></ol><h2 id="示例程序" tabindex="-1"><a class="header-anchor" href="#示例程序"><span>示例程序</span></a></h2><p>下面我们来看一段使用了 strategy 模式的示例程序。这段示例程序的功能是让电脑玩“猜拳&quot;游戏。</p><p>我们考虑了两种猜拳的策略。第一种策略是“如果这局猜拳获胜，那么下一局也出一样的手势&quot; (WinningStrategy), 这是一种稍微有些笨的策略；另外一种策略是“根据上一局的手势从概率上计算出下一局的手势&quot;（ ProbStrategy ）。</p><img src="https://www.plantuml.com/plantuml/svg/fLFBRiCW4BpxApWwYlW1dnBrqDmQAKrpY78WziP6jQ7YuTIg-kzTm2PswpwaNX3C3iFiWvKsJ1dRr4bUCwt9Xec2l2M4K88HmtDI8P9v_7WQuu8re3CyAIxAFkIuJwos42xuBGQMmvqIZCFJETuYx3sTwvrHKfIW7f6QLY64ZBEKDJ3Hamx0dd-WK7BXPML6CM6RCoX_syYTTvukXXoIzoG1PDmi-KBSx_UutcqUSDskrux5XG5rOJaGr606oiupbqJ0QqXmd8msjkZIAnVH6qPRoGid5Qf-u4AWWwY6CY0A7UL3GwvIJDDxKT1kOdl-vM2hvFcNvuVN-iR5MbAIMwL0cFbWnRMHgXkmuydFognJwWPaPvkqQWVwj6b_IQHc7QX-XDsCnlQ6sGqPPJ6tK5akScc5cHYlfOQlQ8cIdz5loewgwU3FdPtW180MfepveRpDewGq_D2CM0r9R1YbSeptDN1ef8J82lkAd_q3" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// hand.ts</span>
@@ -214,6 +214,6 @@
 <span class="token punctuation">[</span>Taro:10000 games, <span class="token number">3049</span> win, <span class="token number">3573</span> lose<span class="token punctuation">]</span>
 <span class="token punctuation">[</span>Hana:10000 games, <span class="token number">3573</span> win, <span class="token number">3049</span> lose<span class="token punctuation">]</span>
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="拓展思路的要点" tabindex="-1"><a class="header-anchor" href="#拓展思路的要点"><span>拓展思路的要点</span></a></h2><h3 id="为什么要特意编写-strategy" tabindex="-1"><a class="header-anchor" href="#为什么要特意编写-strategy"><span>为什么要特意编写 Strategy</span></a></h3><p>通常在编程时算法会被写在具体方法中。Strategy 模式却特意将算法与其他部分分离开来，只是定义了与算法相关的接口（API），然后在程序中以委托的方式来使用算法。</p><p>这样看起来程序好像变复杂了，其实不然。例如，当我们想要通过改善算法来提高算法的处理速度时，如果使用了 Strategy 模式，就不必修改 Strategy 角色的接口（API）了，仅仅修改 ConcreteStrategy 角色即可。而且，使用委托这种弱关联关系可以很方便地整体替换算法。例如，如果想比较原来的算法与改进后的算法的处理速度有多大区别，简单地替换下算法即可进行测试。</p><p>使用 Strategy 模式编写象棋程序时，可以方便地根据棋手的选择切换 AI 例程的水平。</p><h3 id="程序运行中也可以切换策略" tabindex="-1"><a class="header-anchor" href="#程序运行中也可以切换策略"><span>程序运行中也可以切换策略</span></a></h3><p>如果使用 Strategy 模式，在程序运行中也可以切换角色。例如，在内存容量少的运行环境中可以使用 SlowButLessMemoryStrategy（速度慢但省内存的策略），而在内存容量多的运行环境中则可以使用 FastButMoreMemoryStrategy（速度快但耗内存的策略）。</p><p>此外，还可以用某种算法去“验算”另外一种算法。例如，假设要在某个表格计算软件的开发版本中进行复杂的计算。这时，我们可以准备两种算法，即“高速但计算上可能有 Bug 的算法”和“低速但计算准确的算法”，然后让后者去验算前者的计算结果。</p><h2 id="相关的设计模式" tabindex="-1"><a class="header-anchor" href="#相关的设计模式"><span>相关的设计模式</span></a></h2><ul><li>Flyweight 模式</li><li>Abstract Factory 模式</li><li>State 模式</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/strategy.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->Bridge 模式</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">Composite 模式<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/template_method.html b/tech/DesignPatterns/template_method.html
index 4311d08..1c6e943 100644
--- a/tech/DesignPatterns/template_method.html
+++ b/tech/DesignPatterns/template_method.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/template_method.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="Template Method 模式"><meta property="og:description" content="在父类中定义处理流程的框架，在子类中实现具体处理。Template Method 模式的主要目的是为了定义一个算法的骨架，而将一些步骤的具体实现延迟到子类中。通过这种方式，子类可以在不改变算法结构的情况下，重新定义算法中的某些步骤。"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="typescript"><meta property="article:tag" content="交给子类"><meta property="article:published_time" content="2024-10-21T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"Template Method 模式","image":[""],"datePublished":"2024-10-21T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>Template Method 模式 | blog</title><meta name="description" content="在父类中定义处理流程的框架，在子类中实现具体处理。Template Method 模式的主要目的是为了定义一个算法的骨架，而将一些步骤的具体实现延迟到子类中。通过这种方式，子类可以在不改变算法结构的情况下，重新定义算法中的某些步骤。">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/template_method.html-Do5aF6Sl.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/template_method.html-B7oRZ-kS.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->Template Method 模式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-21T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag3 clickable" role="navigation">typescript</span><span class="page-tag-item tag1 clickable" role="navigation">交给子类</span><!--]--><meta property="keywords" content="设计模式,typescript,交给子类"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#为什么要使用-template-method-模式">为什么要使用 Template Method 模式？</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#示例代码">示例代码</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#运行结果">运行结果</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#相关设计模式">相关设计模式</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#延申-类的层次与抽象类">延申: 类的层次与抽象类</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><p>在父类中定义处理流程的框架，在子类中实现具体处理。Template Method 模式的主要目的是为了定义一个算法的骨架，而将一些步骤的具体实现延迟到子类中。通过这种方式，子类可以在不改变算法结构的情况下，重新定义算法中的某些步骤。</p><!-- more --><h2 id="为什么要使用-template-method-模式" tabindex="-1"><a class="header-anchor" href="#为什么要使用-template-method-模式"><span>为什么要使用 Template Method 模式？</span></a></h2><ol><li><strong>代码复用</strong>：将通用的算法结构放在父类中，避免重复代码。</li><li><strong>灵活性</strong>：允许子类实现具体的步骤，增加了灵活性。</li><li><strong>控制反转</strong>：父类控制算法的执行流程，子类只需关注具体步骤的实现。</li></ol><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/dP513i8W44Ntd68IDpI42pGkQdJfpXDG89Q4GWEqngXt5wbHgBfnENy-__qCZG_CXR7NYBK-ECO3SCsyXyrpt2a_Q7Q62m8W8EO9LpLCLecehS0EqXJ2u9G9XSArzVAbt12Q6TkEkJoV0kzgY5nbZWcN6V1xLQNT0ai-iEGNzf1IId1CpiWKJag423HZtqgNmefNEFF_MUT1IPwzCaN9vUNNLqhpItmt5FLG8us8dte7" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// abstractDisplay.ts</span>
@@ -130,6 +130,6 @@
 <span class="token operator">|</span>你好，世界。<span class="token operator">|</span>
 +------+
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="相关设计模式" tabindex="-1"><a class="header-anchor" href="#相关设计模式"><span>相关设计模式</span></a></h2><ul><li>Factory Method 模式</li><li>Strategy 模式</li></ul><h2 id="延申-类的层次与抽象类" tabindex="-1"><a class="header-anchor" href="#延申-类的层次与抽象类"><span>延申: 类的层次与抽象类</span></a></h2><p>我们在理解类的层次时，通常是站在子类的角度进行思考的。也就是说，很容易着眼于以下几点。</p><ul><li>在子类中可以使用父类中定义的方法</li><li>可以通过在子类中增加方法以实现新的功能</li><li>在子类中重写父类的方法可以改变程序的行为</li></ul><p>现在，让我们稍微改变一下立场，站在父类的角度进行思考。在父类中，我们声明了抽象方法，而将该方法的实现交给了子类。换言之，就程序而言，声明抽象方法是希望达到以下目的。</p><ul><li>期待子类去实现抽象方法</li><li>要求子类去实现抽象方法</li></ul><p>也就是说，子类具有实现在父类中所声明的抽象方法的责任。因此，这种责任被称为“子类责任&quot;（ subclass responsibility ）。</p></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/template_method.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->适配器模式</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">Factory Method 模式<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/DesignPatterns/visitor.html b/tech/DesignPatterns/visitor.html
index fcdfafd..5f37a06 100644
--- a/tech/DesignPatterns/visitor.html
+++ b/tech/DesignPatterns/visitor.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/DesignPatterns/visitor.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="Visitor 模式"><meta property="og:description" content="在 Visitor 模式中，数据结构与处理被分离开来。我们编写一个表示“访问者”的类来访问数据结构中的元素，并把对各元素的处理交给访问者类。这样，当需要增加新的处理时，我们只需要编写新的访问者，然后让数据结构可以接受访问者的访问即可。"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="设计模式"><meta property="article:tag" content="TypeScript"><meta property="article:tag" content="访问数据结构并处理数据"><meta property="article:published_time" content="2024-10-25T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"Visitor 模式","image":[""],"datePublished":"2024-10-25T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>Visitor 模式 | blog</title><meta name="description" content="在 Visitor 模式中，数据结构与处理被分离开来。我们编写一个表示“访问者”的类来访问数据结构中的元素，并把对各元素的处理交给访问者类。这样，当需要增加新的处理时，我们只需要编写新的访问者，然后让数据结构可以接受访问者的访问即可。">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/visitor.html-C6V612X1.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/visitor.html-DaIekGHb.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/bridge.html" aria-label="Bridge 模式"><!---->Bridge 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/builder.html" aria-label="builder 模式"><!---->builder 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><!---->chainOfResponsibility 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/command.html" aria-label="Command 模式"><!---->Command 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/composite.html" aria-label="Composite 模式"><!---->Composite 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><!---->Decorator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/facade.html" aria-label="facade 模式"><!---->facade 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/factory_method.html" aria-label="Factory Method 模式"><!---->Factory Method 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/flyweight.html" aria-label="Flyweight 模式"><!---->Flyweight 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/interpreter.html" aria-label="Interpreter 模式"><!---->Interpreter 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/mediator.html" aria-label="Mediator 模式"><!---->Mediator 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/memento.html" aria-label="Memento 模式"><!---->Memento 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/observer.html" aria-label="Observer 模式"><!---->Observer 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/prototype.html" aria-label="Prototype 模式"><!---->Prototype 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/proxy.html" aria-label="Proxy 模式"><!---->Proxy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/singleton.html" aria-label="Singleton 模式"><!---->Singleton 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/state.html" aria-label="State 模式"><!---->State 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/strategy.html" aria-label="Strategy 模式"><!---->Strategy 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/template_method.html" aria-label="Template Method 模式"><!---->Template Method 模式<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/DesignPatterns/visitor.html" aria-label="Visitor 模式"><!---->Visitor 模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/abstractFactory.html" aria-label="抽象工厂模式"><!---->抽象工厂模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/end.html" aria-label="结语"><!---->结语<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/" aria-label="设计模式"><!---->设计模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/DesignPrinciples.html" aria-label="设计模式七大原则"><!---->设计模式七大原则<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/iterator.html" aria-label="迭代器模式"><!---->迭代器模式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/DesignPatterns/adapter.html" aria-label="适配器模式"><!---->适配器模式<!----></a></li></ul></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->Visitor 模式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-25T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 6 分钟</span><meta property="timeRequired" content="PT6M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category8 clickable" role="navigation">设计模式</span><!--]--><meta property="articleSection" content="设计模式"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">设计模式</span><span class="page-tag-item tag5 clickable" role="navigation">TypeScript</span><span class="page-tag-item tag8 clickable" role="navigation">访问数据结构并处理数据</span><!--]--><meta property="keywords" content="设计模式,TypeScript,访问数据结构并处理数据"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#为什么使用-visitor-模式">为什么使用 Visitor 模式？</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#示例代码">示例代码</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#运行结果">运行结果</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#拓展思路的要点">拓展思路的要点</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#双重分发">双重分发</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#为什么要这么复杂">为什么要这么复杂</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#开闭原则——对扩展开放-对修改关闭">开闭原则——对扩展开放，对修改关闭</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#易于增加-concretevisitor-角色">易于增加 ConcreteVisitor 角色</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#难以增加-concreteelement-角色">难以增加 ConcreteElement 角色</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#visitor-工作所需的条件">Visitor 工作所需的条件</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#相关的设计模式">相关的设计模式</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><p>在 Visitor 模式中，数据结构与处理被分离开来。我们编写一个表示“访问者”的类来访问数据结构中的元素，并把对各元素的处理交给访问者类。这样，当需要增加新的处理时，我们只需要编写新的访问者，然后让数据结构可以接受访问者的访问即可。</p><!-- more --><h3 id="为什么使用-visitor-模式" tabindex="-1"><a class="header-anchor" href="#为什么使用-visitor-模式"><span>为什么使用 Visitor 模式？</span></a></h3><ol><li><strong>分离关注点</strong>：将数据结构与操作分离，使得代码更清晰、更易维护。</li><li><strong>增加新操作更容易</strong>：只需添加新的访问者类，而不需要修改现有的数据结构。</li><li><strong>符合开闭原则</strong>：对扩展开放，对修改关闭。</li></ol><h2 id="示例代码" tabindex="-1"><a class="header-anchor" href="#示例代码"><span>示例代码</span></a></h2><img src="https://www.plantuml.com/plantuml/svg/fPCnRiCm34LtdOAZWq8Ny51aQ3eLNG9aAJeeCXiGiEH0eeCcGUzUIh9JkqEQe9E5J_7nVq9UHZQ1UzSgyepXmrY4LOiEFSDP0JmOQt7FrO4YSHTgs9J3eeP3HutwKifi8mTZ6MnhOeILvt04Slj2YNFS3ldLEAoaNxh8xmPnJQSi-jvjCUJ1JLDXOjK5kHY-gKPYrOYBQXJVtfFCtJepv_I_4nJZpzGYu2UZRyOKoRBsudV2qr6iJetU4Ub69qyKq4hXU8kTXi9i2V_Qy6NobItV_IA62-K1vBRVO-VnNoZos3CkOChGjWz123dvJyQhvB90hHylf1fA43KAgLYkILlIr596ow_n3G00" alt=""><img src="https://www.plantuml.com/plantuml/svg/SoWkIImgAStDuKfCBialKd3EoKpDA-62K0gwTWekcKMf89bA1Ik5n9GK3Q1mKQMLWYk8qiIbBZavjQ14eoopE1CeOgKG1c5eSY4K0NNuP1QNG6M0Ui2AqKn7Le5cHMP9Qb4YaAs1PgXRPaugFXUW6GbLZiroXzIy562u0000" alt=""><div class="language-typescript line-numbers-mode" data-ext="ts" data-title="ts"><pre class="language-typescript"><code><span class="token comment">// directory.ts</span>
@@ -185,6 +185,6 @@
 /root/usr/tomura/game.doc <span class="token punctuation">(</span><span class="token number">400</span><span class="token punctuation">)</span>
 /root/usr/tomura/junk.mail <span class="token punctuation">(</span><span class="token number">500</span><span class="token punctuation">)</span>
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="拓展思路的要点" tabindex="-1"><a class="header-anchor" href="#拓展思路的要点"><span>拓展思路的要点</span></a></h2><h3 id="双重分发" tabindex="-1"><a class="header-anchor" href="#双重分发"><span>双重分发</span></a></h3><p>我们来整理一下 Visitor 模式中的方法调用关系。<code>accept</code>（接收）方法的调用方式如下：<code>element.accept(visitor)</code>；而 <code>visit</code>（访问）方法的调用方式如下：<code>visitor.visit(element)</code>。对比这两个方法会发现，它们呈现出一种相反的关系。<code>element</code> 接收 <code>visitor</code>，而 <code>visitor</code> 又访问 <code>element</code>。在 Visitor 模式中，<code>ConcreteElement</code> 和 <code>ConcreteVisitor</code> 这两个角色共同决定了实际进行的处理。这种消息分发的方式一般被称为双重分发（double dispatch）。</p><h3 id="为什么要这么复杂" tabindex="-1"><a class="header-anchor" href="#为什么要这么复杂"><span>为什么要这么复杂</span></a></h3><p>Visitor 模式的目的是将处理逻辑从数据结构中分离出来。数据结构很重要，它能够将元素集合及其关联关系组织在一起。但是，需要注意的是，保存数据结构与基于数据结构进行处理是两种不同的概念。在示例程序中，我们创建了 <code>ListVisitor</code> 类作为显示文件夹内容的 <code>ConcreteVisitor</code> 角色。此外，在练习题中，我们还要编写进行其他处理的 <code>ConcreteVisitor</code> 角色。通常，<code>ConcreteVisitor</code> 角色的开发可以独立于 <code>File</code> 类和 <code>Directory</code> 类。也就是说，Visitor 模式提高了 <code>File</code> 类和 <code>Directory</code> 类作为组件的独立性。如果将处理逻辑的方法定义在 <code>File</code> 类和 <code>Directory</code> 类中，那么每次要扩展功能，增加新的“处理”时，就不得不去修改这些类。</p><h3 id="开闭原则——对扩展开放-对修改关闭" tabindex="-1"><a class="header-anchor" href="#开闭原则——对扩展开放-对修改关闭"><span>开闭原则——对扩展开放，对修改关闭</span></a></h3><p>在设计类时，若无特殊理由，必须要考虑到将来可能会扩展类。绝不能毫无理由地禁止扩展类。这就是“对扩展是开放的”的意思。但是，如果在每次扩展类时都需要修改现有的类就太麻烦了。所以我们需要在不修改现有类的前提下能够扩展类，这就是“对修改是关闭的”的意思。我们提倡扩展，但如果需要修改现有代码，那就不行了。在不修改现有代码的前提下进行扩展，这就是开闭原则。至此，大家已经学习了多种设计模式。那么在看到这条设计原则后，大家应该都会点头表示赞同吧。功能需求总是在不断变化，而且这些功能需求大都是“希望扩展某个功能”。因此，如果不能比较容易地扩展类，开发过程将会变得非常困难。另一方面，如果要修改已经编写和测试完成的类，又可能会导致软件产品的质量降低。对扩展开放、对修改关闭的类具有高可复用性，可作为组件复用。设计模式和面向对象的目的正是为我们提供一种结构，可以帮助我们设计出这样的类。</p><h3 id="易于增加-concretevisitor-角色" tabindex="-1"><a class="header-anchor" href="#易于增加-concretevisitor-角色"><span>易于增加 ConcreteVisitor 角色</span></a></h3><p>使用 Visitor 模式可以很容易地增加 <code>ConcreteVisitor</code> 角色。因为具体的处理被交给 <code>ConcreteVisitor</code> 角色负责，因此完全不用修改 <code>ConcreteElement</code> 角色。</p><h3 id="难以增加-concreteelement-角色" tabindex="-1"><a class="header-anchor" href="#难以增加-concreteelement-角色"><span>难以增加 ConcreteElement 角色</span></a></h3><p>尽管使用 Visitor 模式可以很容易地增加 <code>ConcreteVisitor</code> 角色，但它却难以应对 <code>ConcreteElement</code> 角色的增加。例如，假设现在我们要在示例程序中增加一个 <code>Device</code> 类，它是 <code>File</code> 类和 <code>Directory</code> 类的兄弟类。这时，我们不得不在 Visitor 类中声明一个 <code>visit(Device)</code> 方法，并在所有的 Visitor 类的子类中都实现这个方法。</p><h3 id="visitor-工作所需的条件" tabindex="-1"><a class="header-anchor" href="#visitor-工作所需的条件"><span>Visitor 工作所需的条件</span></a></h3><p>在 Visitor 模式中，对数据结构中的元素进行处理的任务被分离出来，交给 Visitor 类负责。这样，就实现了数据结构与处理的分离。这个主题，我们在本章的学习过程中已经提到过很多次了。但是要达到这个目的是有条件的，那就是 Element 角色必须向 Visitor 角色公开足够多的信息。例如，在示例程序中，<code>visit(Directory)</code> 方法需要调用每个目录条目的 <code>accept</code> 方法。为此，<code>Directory</code> 类必须提供用于获取每个目录条目的 <code>iterator</code> 方法。只有当访问者从数据结构中获取了足够多的信息后才能工作。如果无法获取到这些信息，它就无法工作。这样做的缺点是，如果公开了不应当被公开的信息，将来对数据结构的改良就会变得非常困难。</p><h2 id="相关的设计模式" tabindex="-1"><a class="header-anchor" href="#相关的设计模式"><span>相关的设计模式</span></a></h2><ul><li>Iterator 模式</li><li>Composite 模式</li><li>Interpreter 模式</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/DesignPatterns/visitor.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/DesignPatterns/decorator.html" aria-label="Decorator 模式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->Decorator 模式</div></a><a class="route-link nav-link next" href="/tech/DesignPatterns/chainOfResponsibility.html" aria-label="chainOfResponsibility 模式"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">chainOfResponsibility 模式<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tech/Qt6 Maintence tools\344\270\215\350\203\275\345\256\211\350\243\205Qt5.html" "b/tech/Qt6 Maintence tools\344\270\215\350\203\275\345\256\211\350\243\205Qt5.html"
index 818535d..b282c4f 100644
--- "a/tech/Qt6 Maintence tools\344\270\215\350\203\275\345\256\211\350\243\205Qt5.html"	
+++ "b/tech/Qt6 Maintence tools\344\270\215\350\203\275\345\256\211\350\243\205Qt5.html"	
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="Qt"><meta property="og:description" content="Qt Some Solutions to Questions about Qt The qt-5 isn't in Qt Maintenance tools Open the Qt Maintenance Tools. click the Archive in the Select-Component section. click the filter..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:published_time" content="2024-08-31T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"Qt","image":[""],"datePublished":"2024-08-31T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>Qt | blog</title><meta name="description" content="Qt Some Solutions to Questions about Qt The qt-5 isn't in Qt Maintenance tools Open the Qt Maintenance Tools. click the Archive in the Select-Component section. click the filter...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->Qt</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-08-31T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><!----></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#some-solutions-to-questions-about-qt">Some Solutions to Questions about Qt</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#the-qt-5-isn-t-in-qt-maintenance-tools">The qt-5 isn&#39;t in Qt Maintenance tools</a></li><!----><!--]--></ul></li><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="qt" tabindex="-1"><a class="header-anchor" href="#qt"><span>Qt</span></a></h1><h2 id="some-solutions-to-questions-about-qt" tabindex="-1"><a class="header-anchor" href="#some-solutions-to-questions-about-qt"><span>Some Solutions to Questions about Qt</span></a></h2><h3 id="the-qt-5-isn-t-in-qt-maintenance-tools" tabindex="-1"><a class="header-anchor" href="#the-qt-5-isn-t-in-qt-maintenance-tools"><span>The qt-5 isn&#39;t in Qt Maintenance tools</span></a></h3><ol><li>Open the Qt Maintenance Tools.</li><li>click the Archive in the Select-Component section.</li><li>click the filter button and you can see the qt-5 in the list.</li></ol></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/Qt6 Maintence tools不能安装Qt5.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/python_requrements.html" aria-label="python requirements.txt"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->python requirements.txt</div></a><a class="route-link nav-link next" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">Slidev<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tech/android studio\346\215\242\346\272\220.html" "b/tech/android studio\346\215\242\346\272\220.html"
index ad41fac..d191113 100644
--- "a/tech/android studio\346\215\242\346\272\220.html"	
+++ "b/tech/android studio\346\215\242\346\272\220.html"	
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/android%20studio%E6%8D%A2%E6%BA%90.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="android studio换源"><meta property="og:description" content="gradle 国内镜像 Android Studio下载gradle太慢可换源 android.plugin version 下载错误查看 修改 settings.gradle.kts gradle-wrapper.properties 换成对应的版本"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:published_time" content="2024-08-02T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"android studio换源","image":[""],"datePublished":"2024-08-02T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>android studio换源 | blog</title><meta name="description" content="gradle 国内镜像 Android Studio下载gradle太慢可换源 android.plugin version 下载错误查看 修改 settings.gradle.kts gradle-wrapper.properties 换成对应的版本">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/android studio换源.html-CxjDu5df.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/android studio换源.html-DkRIM6mj.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->android studio换源</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-08-02T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category2 clickable" role="navigation">build-tools</span><!--]--><meta property="articleSection" content="build-tools"></span><!----></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="gradle" tabindex="-1"><a class="header-anchor" href="#gradle"><span>gradle</span></a></h1><p><a href="https://mirrors.cloud.tencent.com/gradle/" target="_blank" rel="noopener noreferrer">国内镜像<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></p><p>Android Studio下载gradle太慢可换源</p><p><a href="https://blog.csdn.net/qq_43811536/article/details/139447518" target="_blank" rel="noopener noreferrer">android.plugin version 下载错误查看<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></p><p><strong>修改 settings.gradle.kts</strong></p><div class="language-text line-numbers-mode" data-ext="text" data-title="text"><pre class="language-text"><code>pluginManagement {
@@ -64,6 +64,6 @@
 }
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><p><strong>gradle-wrapper.properties 换成对应的版本</strong></p><div class="language-text line-numbers-mode" data-ext="text" data-title="text"><pre class="language-text"><code>distributionUrl=https\://mirrors.cloud.tencent.com/gradle/gradle-8.7-all.zip
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div></div></div></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/android studio换源.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->「算术公理系统 1」自然数</div></a><a class="route-link nav-link next" href="/tech/cicd.html" aria-label="CI/CD"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">CI/CD<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/cicd.html b/tech/cicd.html
index f3ffaba..30e3966 100644
--- a/tech/cicd.html
+++ b/tech/cicd.html
@@ -30,12 +30,12 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/cicd.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="CI/CD"><meta property="og:description" content="Github Actions 本地调试工具 act 需要创建配置文件 也可另外指定"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="CI/CD"><meta property="article:published_time" content="2024-08-02T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"CI/CD","image":[""],"datePublished":"2024-08-02T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>CI/CD | blog</title><meta name="description" content="Github Actions 本地调试工具 act 需要创建配置文件 也可另外指定">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/cicd.html-CedraPRV.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/cicd.html-BxLHD3yn.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->CI/CD</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-08-02T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category5 clickable" role="navigation">CI/CD</span><!--]--><meta property="articleSection" content="CI/CD"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag5 clickable" role="navigation">CI/CD</span><!--]--><meta property="keywords" content="CI/CD"></span></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="github-actions" tabindex="-1"><a class="header-anchor" href="#github-actions"><span>Github Actions</span></a></h1><p>本地调试工具 <a href="https://github.com/nektos/act" target="_blank" rel="noopener noreferrer">act<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></p><p>需要创建配置文件</p><!-- TODO --><p>也可另外指定</p><div class="language-bash line-numbers-mode" data-ext="sh" data-title="sh"><pre class="language-bash"><code>act --var-file <span class="token string">&quot;./.act/.vars&quot;</span> --secret-file <span class="token string">&quot;./.act/.secrets&quot;</span> --env-file <span class="token string">&quot;./.act/.env&quot;</span> <span class="token punctuation">{</span><span class="token punctuation">{</span>other<span class="token punctuation">}</span><span class="token punctuation">}</span>
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div></div></div></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/cicd.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->android studio换源</div></a><!----></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/designASimpileCCompiler/0.html b/tech/designASimpileCCompiler/0.html
index 768ffd6..84f1d94 100644
--- a/tech/designASimpileCCompiler/0.html
+++ b/tech/designASimpileCCompiler/0.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/designASimpileCCompiler/0.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="手把手教你构建 C 语言编译器（0）- 前言"><meta property="og:description" content="转载声明 本文转载自 手把手教你构建 C 语言编译器（0）- 前言，原作者 三点水，原文链接：原文链接，如有侵权，请联系删除。 转载工具:devtool、helloworld 原文内容 “手把手教你构建 C 语言编译器” 这一系列教程将带你从头编写一个 C 语言的编译器。希望通过这个系列，我们能对编译器的构建有一定的了解，同时，我们也将构建出一个能用的..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="c"><meta property="article:tag" content="编译器"><meta property="article:tag" content="解释器"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"手把手教你构建 C 语言编译器（0）- 前言","image":[""],"dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>手把手教你构建 C 语言编译器（0）- 前言 | blog</title><meta name="description" content="转载声明 本文转载自 手把手教你构建 C 语言编译器（0）- 前言，原作者 三点水，原文链接：原文链接，如有侵权，请联系删除。 转载工具:devtool、helloworld 原文内容 “手把手教你构建 C 语言编译器” 这一系列教程将带你从头编写一个 C 语言的编译器。希望通过这个系列，我们能对编译器的构建有一定的了解，同时，我们也将构建出一个能用的...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/0.html-BMihHxnS.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/0.html-CC8GZdvL.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/designASimpileCCompiler/0.html" aria-label="手把手教你构建 C 语言编译器（0）- 前言"><!---->手把手教你构建 C 语言编译器（0）- 前言<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/1.html" aria-label="手把手教你构建 C 语言编译器（1）- 设计"><!---->手把手教你构建 C 语言编译器（1）- 设计<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/3.html" aria-label="手把手教你构建 C 语言编译器（3）——词法分析器"><!---->手把手教你构建 C 语言编译器（3）——词法分析器<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/4.html" aria-label="手把手教你构建 C 语言编译器（4）——递归下降"><!---->手把手教你构建 C 语言编译器（4）——递归下降<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/5.html" aria-label="手把手教你构建 C 语言编译器（5）——变量定义"><!---->手把手教你构建 C 语言编译器（5）——变量定义<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/6.html" aria-label="手把手教你构建 C 语言编译器（6）——函数定义"><!---->手把手教你构建 C 语言编译器（6）——函数定义<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/7.html" aria-label="手把手教你构建 C 语言编译器（7）——语句"><!---->手把手教你构建 C 语言编译器（7）——语句<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/8.html" aria-label="手把手教你构建 C 语言编译器（8）——表达式"><!---->手把手教你构建 C 语言编译器（8）——表达式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/9.html" aria-label="手把手教你构建 C 语言编译器（9）——总结"><!---->手把手教你构建 C 语言编译器（9）——总结<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/2.html" aria-label="转载声明"><!---->转载声明<!----></a></li></ul></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->手把手教你构建 C 语言编译器（0）- 前言</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 6 分钟</span><meta property="timeRequired" content="PT6M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category2 clickable" role="navigation">编译原理</span><!--]--><meta property="articleSection" content="编译原理"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag4 clickable" role="navigation">c</span><span class="page-tag-item tag4 clickable" role="navigation">编译器</span><span class="page-tag-item tag4 clickable" role="navigation">解释器</span><!--]--><meta property="keywords" content="c,编译器,解释器"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#为什么要学编译原理">为什么要学编译原理</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#理论很复杂-实现也很复杂">理论很复杂，实现也很复杂？</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#项目的初衷">项目的初衷</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#做好心理准备">做好心理准备</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#参考资料">参考资料</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="转载声明" tabindex="-1"><a class="header-anchor" href="#转载声明"><span>转载声明</span></a></h1><p>本文转载自 <strong>手把手教你构建 C 语言编译器（0）- 前言</strong>，原作者 <strong>三点水</strong>，原文链接：<a href="https://lotabout.me/2015/write-a-C-interpreter-0/" target="_blank" rel="noopener noreferrer">原文链接<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a>，如有侵权，请联系删除。</p><p>转载工具:<a href="https://devtool.tech/html-md" target="_blank" rel="noopener noreferrer">devtool<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a>、<a href="https://www.helloworld.net/html2md" target="_blank" rel="noopener noreferrer">helloworld<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></p><h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><p>“手把手教你构建 C 语言编译器” 这一系列教程将带你从头编写一个 C 语言的编译器。希望通过这个系列，我们能对编译器的构建有一定的了解，同时，我们也将构建出一个能用的 C 语言编译器，尽管有许多语法并不支持。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p><ol><li><a href="http://lotabout.me/2015/write-a-C-interpreter-0/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（0）——前言<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-1/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（1）——设计<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-2/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（2）——虚拟机<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-3/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（3）——词法分析器<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-4/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（4）——递归下降<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-5/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（5）——变量定义<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-6/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（6）——函数定义<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-7/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（7）——语句<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-8/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（8）——表达式<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-9/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（9）——总结<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li></ol><p>在开始进入正题之前，本篇是一些闲聊，谈谈这个系列的初衷。如果你急切地想进入正篇，请跳过本章。</p><h2 id="为什么要学编译原理" tabindex="-1"><a class="header-anchor" href="#为什么要学编译原理"><span><a href="#%E4%B8%BA%E4%BB%80%E4%B9%88%E8%A6%81%E5%AD%A6%E7%BC%96%E8%AF%91%E5%8E%9F%E7%90%86"></a>为什么要学编译原理</span></a></h2><p>如果要我说计算机专业最重要的三门课，我会说是《数据结构》、《算法》和《编译原理》。在我看来，能不能理解“递归”像是程序员的第一道门槛，而会不会写编译器则是第二道。</p><p>（当然，并不是说是没写过编译器就不是好程序员，只能说它是一个相当大的挑战吧）</p><p>以前人们会说，学习了编译原理，你就能写出更加高效的代码，但随着计算机性能的提升，代码是否高效显得就不那么重要了。那么为什么要学习编译原理呢？</p><p>原因只有一个：装B。</p><p>好吧，也许现在还想学习编译原理的人只可能是因为兴趣了。一方面想了解它的工作原理；另一方面希望挑战一下自己，看看自己能走多远。</p><h2 id="理论很复杂-实现也很复杂" tabindex="-1"><a class="header-anchor" href="#理论很复杂-实现也很复杂"><span><a href="#%E7%90%86%E8%AE%BA%E5%BE%88%E5%A4%8D%E6%9D%82-%E5%AE%9E%E7%8E%B0%E4%B9%9F%E5%BE%88%E5%A4%8D%E6%9D%82%EF%BC%9F"></a>理论很复杂，实现也很复杂？</span></a></h2><p>我对编译器一直心存敬佩。所以当学校开《编译原理》的课程后，我是抱着满腔热情去上课的，但是两节课后我就放弃了。原因是太复杂了，听不懂。</p><p>一般编译原理的课程会说一些：</p><ol><li>如何表示语法（BNF什么的）</li><li>词法分析，用什么有穷自动机和无穷自动机</li><li>语法分析，递归下降法，什么 <code>LL(k)</code>，LALR 分析。</li><li>中间代码的表示</li><li>代码的生成</li><li>代码优化</li></ol><p>我相信绝大多数（98％）的学生顶多学到语法分析就结束了。并且最重要的是，学了这么多也没用！依旧帮助不了我们学习编译器！这其中最主要的原因是《编译原理》试图教会我们的是如何构造“编译器生成器”，即构造一个工具，根据文法来生成编译器（如 lex/yacc）等等。</p><p>这些理论试图教会我们如何用通用的方法来自动解决问题，它们有很强的实际意义，只是对于一般的学生或程序员来说，它们过于强大，内容过于复杂。如果你尝试阅读 lex/yacc （或 flex/bison）的代码，就会发现太可怕了。</p><p>然而如果你能跟我一样，真正来实现一个简单的编译器，那么你会发现，比起可怕的《编译原理》，这点复杂度还是不算什么的（因为好多理论根本用不上）。</p><h2 id="项目的初衷" tabindex="-1"><a class="header-anchor" href="#项目的初衷"><span><a href="#%E9%A1%B9%E7%9B%AE%E7%9A%84%E5%88%9D%E8%A1%B7"></a>项目的初衷</span></a></h2><p>有一次在 Github 上看到了一个项目（当时很火的），名叫 <a href="https://github.com/rswier/c4" target="_blank" rel="noopener noreferrer">c4<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a>，号称用 4 个函数来实现了一个小的 C 语言编译器。它最让我震惊的是能够自举，即能自己编译自己。并且它用很少的代码就完成了一个功能相当完善的 C 语言编译器。</p><p>一般的编译器相关的教程要么就十分简单（如实现四则运算），要么就是借助了自动生成的工具（如 flex/bison）。而 c4 的代码完全是手工实现的，不用外部工具。可惜的是它的代码初衷是代码最小化，所以写得很乱，很难懂。所以本项目的主要目的：</p><ol><li>实现一个功能完善的 C 语言编译器</li><li>通过教程来说明这个过程。</li></ol><p>c4 大致500+行。重写的代码历时一周，总共代码加注释1400行。项目地址: <a href="https://github.com/lotabout/write-a-C-interpreter" target="_blank" rel="noopener noreferrer">Write a C Interpreter<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a>。</p><p>声明：本项目中的代码逻辑绝大多数取自 c4 ，但确为自己重写。</p><h2 id="做好心理准备" tabindex="-1"><a class="header-anchor" href="#做好心理准备"><span><a href="#%E5%81%9A%E5%A5%BD%E5%BF%83%E7%90%86%E5%87%86%E5%A4%87"></a>做好心理准备</span></a></h2><p>在写编译器的时候会遇到两个主要问题：</p><ol><li>繁琐，会有许多相似的代码，写起来很无聊。</li><li>难以调试，一方面没有很好的测试用例，另一方面需要对照生成的代码来调试（遇到的时候就知道了）。</li></ol><p>所以我希望你有足够的耐心和时间来学习，相信当你真正完成的时候会像我一样，十分有成就感。</p><p>PS. 第一篇完全没有正题相关的内容也是希望你能有所心理准备再开始学习。</p><h2 id="参考资料" tabindex="-1"><a class="header-anchor" href="#参考资料"><span><a href="#%E5%8F%82%E8%80%83%E8%B5%84%E6%96%99"></a>参考资料</span></a></h2><p>最后想介绍几个资料：</p><ol><li><a href="http://compilers.iecc.com/crenshaw/" target="_blank" rel="noopener noreferrer">Let’s Build a Compiler<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a> 很好的初学者教程，英文的。</li><li><a href="http://www.hwaci.com/sw/lemon/" target="_blank" rel="noopener noreferrer">Lemon Parser Generator<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a>，一个语法分析器生成器，对照《编译原理》观看效果更佳。</li></ol><p>由于本人水平一般，文章、代码难免会有错误，敬请批评指正！</p><p>最后祝你学得愉快。</p><h1 id="转载者注" tabindex="-1"><a class="header-anchor" href="#转载者注"><span>转载者注</span></a></h1><p>这篇博客并没有使用诸如 flex、bison 等工具来编写 token 和文法的定义，因而灵活性较差。相反，它通过定义自己的指令集并支持该指令集的虚拟机来模拟编译的部分过程，具有一定的参考价值。不过，我仍然认为通过定义 token 和文法并编写解析算法（如 regex、LL(k) 等）可能会更具普适性。</p><div class="hint-container info"><p class="hint-container-title">相关信息</p><p>不过据说c、cpp、java这些成熟的语言都是手动实现的？还没仔细了解过。 TODO</p></div></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/designASimpileCCompiler/0.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><!----><a class="route-link nav-link next" href="/tech/designASimpileCCompiler/1.html" aria-label="手把手教你构建 C 语言编译器（1）- 设计"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">手把手教你构建 C 语言编译器（1）- 设计<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/designASimpileCCompiler/1.html b/tech/designASimpileCCompiler/1.html
index 1751e2b..28b9ed1 100644
--- a/tech/designASimpileCCompiler/1.html
+++ b/tech/designASimpileCCompiler/1.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/designASimpileCCompiler/1.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="手把手教你构建 C 语言编译器（1）- 设计"><meta property="og:description" content="转载声明 本文转自 https://lotabout.me/2015/write-a-C-interpreter-1/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（1）- 设计 Table of Contents 1. 编译器的构建流程 2. 编译器框架 这是“手把手教你构建 C 语言编译器”系列的第二篇，我们要从整体上讲解如何设..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"手把手教你构建 C 语言编译器（1）- 设计","image":[""],"dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>手把手教你构建 C 语言编译器（1）- 设计 | blog</title><meta name="description" content="转载声明 本文转自 https://lotabout.me/2015/write-a-C-interpreter-1/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（1）- 设计 Table of Contents 1. 编译器的构建流程 2. 编译器框架 这是“手把手教你构建 C 语言编译器”系列的第二篇，我们要从整体上讲解如何设...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/1.html-B2woGSgL.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/1.html-C8e1pvTo.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/0.html" aria-label="手把手教你构建 C 语言编译器（0）- 前言"><!---->手把手教你构建 C 语言编译器（0）- 前言<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/designASimpileCCompiler/1.html" aria-label="手把手教你构建 C 语言编译器（1）- 设计"><!---->手把手教你构建 C 语言编译器（1）- 设计<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/3.html" aria-label="手把手教你构建 C 语言编译器（3）——词法分析器"><!---->手把手教你构建 C 语言编译器（3）——词法分析器<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/4.html" aria-label="手把手教你构建 C 语言编译器（4）——递归下降"><!---->手把手教你构建 C 语言编译器（4）——递归下降<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/5.html" aria-label="手把手教你构建 C 语言编译器（5）——变量定义"><!---->手把手教你构建 C 语言编译器（5）——变量定义<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/6.html" aria-label="手把手教你构建 C 语言编译器（6）——函数定义"><!---->手把手教你构建 C 语言编译器（6）——函数定义<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/7.html" aria-label="手把手教你构建 C 语言编译器（7）——语句"><!---->手把手教你构建 C 语言编译器（7）——语句<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/8.html" aria-label="手把手教你构建 C 语言编译器（8）——表达式"><!---->手把手教你构建 C 语言编译器（8）——表达式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/9.html" aria-label="手把手教你构建 C 语言编译器（9）——总结"><!---->手把手教你构建 C 语言编译器（9）——总结<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/2.html" aria-label="转载声明"><!---->转载声明<!----></a></li></ul></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->手把手教你构建 C 语言编译器（1）- 设计</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 7 分钟</span><meta property="timeRequired" content="PT7M"></span><!----><!----></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#编译器的构建流程">编译器的构建流程</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#编译器框架">编译器框架</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="转载声明" tabindex="-1"><a class="header-anchor" href="#转载声明"><span>转载声明</span></a></h1><p>本文转自 <a href="https://lotabout.me/2015/write-a-C-interpreter-1/" target="_blank" rel="noopener noreferrer">https://lotabout.me/2015/write-a-C-interpreter-1/<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a>，如有侵权，请联系删除。</p><h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-1-设计" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-1-设计"><span>手把手教你构建 C 语言编译器（1）- 设计</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#%E7%BC%96%E8%AF%91%E5%99%A8%E7%9A%84%E6%9E%84%E5%BB%BA%E6%B5%81%E7%A8%8B">1. 编译器的构建流程</a></li><li><a href="about:blank#%E7%BC%96%E8%AF%91%E5%99%A8%E6%A1%86%E6%9E%B6">2. 编译器框架</a></li></ol><p>这是“手把手教你构建 C 语言编译器”系列的第二篇，我们要从整体上讲解如何设计我们的 C 语言编译器。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p><ol><li><a href="http://lotabout.me/2015/write-a-C-interpreter-0/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（0）——前言<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-1/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（1）——设计<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-2/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（2）——虚拟机<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-3/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（3）——词法分析器<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-4/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（4）——递归下降<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-5/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（5）——变量定义<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-6/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（6）——函数定义<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-7/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（7）——语句<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-8/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（8）——表达式<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-9/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（9）——总结<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li></ol><p>首先要说明的是，虽然标题是编译器，但实际上我们构建的是 C 语言的解释器，这意味着我们可以像运行脚本一样去运行 C 语言的源代码文件。这么做的理由有两点：</p><ol><li>解释器与编译器仅在代码生成阶段有区别，而其它方面如词法分析、语法分析是一样的。</li><li>解释器需要我们实现自己的虚拟机与指令集，而这部分能帮助我们了解计算机的工作原理。</li></ol><h2 id="编译器的构建流程" tabindex="-1"><a class="header-anchor" href="#编译器的构建流程"><span><a href="about:blank#%E7%BC%96%E8%AF%91%E5%99%A8%E7%9A%84%E6%9E%84%E5%BB%BA%E6%B5%81%E7%A8%8B"></a>编译器的构建流程</span></a></h2><p>一般而言，编译器的编写分为 3 个步骤：</p><ol><li>词法分析器，用于将字符串转化成内部的表示结构。</li><li>语法分析器，将词法分析得到的标记流（token）生成一棵语法树。</li><li>目标代码的生成，将语法树转化成目标代码。</li></ol><p>已经有许多工具能帮助我们处理阶段1和2，如 flex 用于词法分析，bison 用于语法分析。只是它们的功能都过于强大，屏蔽了许多实现上的细节，对于学习构建编译器帮助不大。所以我们要完全手写这些功能。</p><p>所以我们会依照以下步骤来构建我们的编译器：</p><ol><li>构建我们自己的虚拟机以及指令集。这后生成的目标代码便是我们的指令集。</li><li>构建我们的词法分析器</li><li>构建语法分析器</li></ol><h2 id="编译器框架" tabindex="-1"><a class="header-anchor" href="#编译器框架"><span><a href="about:blank#%E7%BC%96%E8%AF%91%E5%99%A8%E6%A1%86%E6%9E%B6"></a>编译器框架</span></a></h2><p>我们的编译器主要包括 4 个函数：</p><ol><li><code>next()</code> 用于词法分析，获取下一个标记，它将自动忽略空白字符。</li><li><code>program()</code> 语法分析的入口，分析整个 C 语言程序。</li><li><code>expression(level)</code> 用于解析一个表达式。</li><li><code>eval()</code> 虚拟机的入口，用于解释目标代码。</li></ol><p>这里有一个单独用于解析“表达式”的函数 <code>expression</code> 是因为表达式在语法分析中相对独立并且比较复杂，所以我们将它单独作为一个模块（函数）。下面是相应的源代码：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;stdio.h&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;stdlib.h&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;memory.h&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;string.h&gt;</span></span></span><br><span class="line"></span><br><span class="line"><span class="type">int</span> token;            <span class="comment">// current token</span></span><br><span class="line"><span class="type">char</span> *src, *old_src;  <span class="comment">// pointer to source code string;</span></span><br><span class="line"><span class="type">int</span> poolsize;         <span class="comment">// default size of text/data/stack</span></span><br><span class="line"><span class="type">int</span> line;             <span class="comment">// line number</span></span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">next</span><span class="params">()</span> {</span><br><span class="line">    token = *src++;</span><br><span class="line">    <span class="keyword">return</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">expression</span><span class="params">(<span class="type">int</span> level)</span> {</span><br><span class="line">    <span class="comment">// do nothing</span></span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">program</span><span class="params">()</span> {</span><br><span class="line">    next();                  <span class="comment">// get next token</span></span><br><span class="line">    <span class="keyword">while</span> (token &gt; <span class="number">0</span>) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;token is: %c\n&quot;</span>, token);</span><br><span class="line">        next();</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">eval</span><span class="params">()</span> { <span class="comment">// do nothing yet</span></span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">main</span><span class="params">(<span class="type">int</span> argc, <span class="type">char</span> **argv)</span></span><br><span class="line">{</span><br><span class="line">    <span class="type">int</span> i, fd;</span><br><span class="line"></span><br><span class="line">    argc--;</span><br><span class="line">    argv++;</span><br><span class="line"></span><br><span class="line">    poolsize = <span class="number">256</span> * <span class="number">1024</span>; <span class="comment">// arbitrary size</span></span><br><span class="line">    line = <span class="number">1</span>;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> ((fd = open(*argv, <span class="number">0</span>)) &lt; <span class="number">0</span>) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;could not open(%s)\n&quot;</span>, *argv);</span><br><span class="line">        <span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (!(src = old_src = <span class="built_in">malloc</span>(poolsize))) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;could not malloc(%d) for source area\n&quot;</span>, poolsize);</span><br><span class="line">        <span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="comment">// read the source file</span></span><br><span class="line">    <span class="keyword">if</span> ((i = read(fd, src, poolsize<span class="number">-1</span>)) &lt;= <span class="number">0</span>) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;read() returned %d\n&quot;</span>, i);</span><br><span class="line">        <span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">    }</span><br><span class="line">    src[i] = <span class="number">0</span>; <span class="comment">// add EOF character</span></span><br><span class="line">    close(fd);</span><br><span class="line"></span><br><span class="line">    program();</span><br><span class="line">    <span class="keyword">return</span> eval();</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>上面的代码看上去挺复杂，但其实内容不多。它的流程为：读取一个文件（内容为 C 语言代码），逐个读取文件中的字符，并输出。这里需要的是注意每个函数的作用，后面的文章中，我们将逐个填充每个函数的功能，最终构建起我们的编译器。</p><p>本节的代码可以在 <a href="https://github.com/lotabout/write-a-C-interpreter/tree/step-0" target="_blank" rel="noopener noreferrer">Github<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a> 上下载，也可以直接 clone</p><table><tbody><tr><td class="code"><pre><span class="line">git clone -b step-0 https://github.com/lotabout/write-a-C-interpreter</span><br></pre></td></tr></tbody></table><p>这样我们就有了一个最简单的编译器：什么都不干的编译器，下一章中，我们将实现其中的<code>eval</code>函数，即我们自己的虚拟机。</p></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/designASimpileCCompiler/1.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/designASimpileCCompiler/0.html" aria-label="手把手教你构建 C 语言编译器（0）- 前言"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->手把手教你构建 C 语言编译器（0）- 前言</div></a><a class="route-link nav-link next" href="/tech/designASimpileCCompiler/3.html" aria-label="手把手教你构建 C 语言编译器（3）——词法分析器"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">手把手教你构建 C 语言编译器（3）——词法分析器<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/designASimpileCCompiler/2.html b/tech/designASimpileCCompiler/2.html
index 28fadd3..43637f3 100644
--- a/tech/designASimpileCCompiler/2.html
+++ b/tech/designASimpileCCompiler/2.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/designASimpileCCompiler/2.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="转载声明"><meta property="og:description" content="title: "手把手教你构建 C 语言编译器（2）——虚拟机" category: 编译原理 tag: c 编译器 解释器 转载声明 本文转自 https://lotabout.me/2015/write-a-C-interpreter-2/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（2）- 虚拟机 Table of Cont..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"转载声明","image":[""],"dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>转载声明 | blog</title><meta name="description" content="title: "手把手教你构建 C 语言编译器（2）——虚拟机" category: 编译原理 tag: c 编译器 解释器 转载声明 本文转自 https://lotabout.me/2015/write-a-C-interpreter-2/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（2）- 虚拟机 Table of Cont...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/2.html-DuLx7xSk.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/2.html-CfN7D4gf.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/0.html" aria-label="手把手教你构建 C 语言编译器（0）- 前言"><!---->手把手教你构建 C 语言编译器（0）- 前言<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/1.html" aria-label="手把手教你构建 C 语言编译器（1）- 设计"><!---->手把手教你构建 C 语言编译器（1）- 设计<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/3.html" aria-label="手把手教你构建 C 语言编译器（3）——词法分析器"><!---->手把手教你构建 C 语言编译器（3）——词法分析器<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/4.html" aria-label="手把手教你构建 C 语言编译器（4）——递归下降"><!---->手把手教你构建 C 语言编译器（4）——递归下降<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/5.html" aria-label="手把手教你构建 C 语言编译器（5）——变量定义"><!---->手把手教你构建 C 语言编译器（5）——变量定义<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/6.html" aria-label="手把手教你构建 C 语言编译器（6）——函数定义"><!---->手把手教你构建 C 语言编译器（6）——函数定义<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/7.html" aria-label="手把手教你构建 C 语言编译器（7）——语句"><!---->手把手教你构建 C 语言编译器（7）——语句<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/8.html" aria-label="手把手教你构建 C 语言编译器（8）——表达式"><!---->手把手教你构建 C 语言编译器（8）——表达式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/9.html" aria-label="手把手教你构建 C 语言编译器（9）——总结"><!---->手把手教你构建 C 语言编译器（9）——总结<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/designASimpileCCompiler/2.html" aria-label="转载声明"><!---->转载声明<!----></a></li></ul></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->转载声明</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 25 分钟</span><meta property="timeRequired" content="PT25M"></span><!----><!----></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#计算机的内部工作原理">计算机的内部工作原理</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#内存">内存</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#寄存器">寄存器</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#指令集">指令集</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#mov">MOV</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#push">PUSH</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#jmp">JMP</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#jz-jnz">JZ/JNZ</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#子函数调用">子函数调用</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#ent">ENT</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#adj">ADJ</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#lev">LEV</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#lea">LEA</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#运算符指令">运算符指令</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#内置函数">内置函数</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#测试">测试</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#小结">小结</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><hr><p>title: &quot;手把手教你构建 C 语言编译器（2）——虚拟机&quot; category:</p><ul><li>编译原理 tag:</li><li>c</li><li>编译器</li><li>解释器</li></ul><hr><h1 id="转载声明" tabindex="-1"><a class="header-anchor" href="#转载声明"><span>转载声明</span></a></h1><p>本文转自 <a href="https://lotabout.me/2015/write-a-C-interpreter-2/" target="_blank" rel="noopener noreferrer">https://lotabout.me/2015/write-a-C-interpreter-2/<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a>，如有侵权，请联系删除。</p><h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-2-虚拟机" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-2-虚拟机"><span>手把手教你构建 C 语言编译器（2）- 虚拟机</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E5%86%85%E9%83%A8%E5%B7%A5%E4%BD%9C%E5%8E%9F%E7%90%86">1. 计算机的内部工作原理</a><ol><li><a href="about:blank#%E5%86%85%E5%AD%98">1.1. 内存</a></li><li><a href="about:blank#%E5%AF%84%E5%AD%98%E5%99%A8">1.2. 寄存器</a></li></ol></li><li><a href="about:blank#%E6%8C%87%E4%BB%A4%E9%9B%86">2. 指令集</a><ol><li><a href="about:blank#mov">2.1. MOV</a></li><li><a href="about:blank#push">2.2. PUSH</a></li><li><a href="about:blank#jmp">2.3. JMP</a></li><li><a href="about:blank#jz-jnz">2.4. JZ/JNZ</a></li><li><a href="about:blank#%E5%AD%90%E5%87%BD%E6%95%B0%E8%B0%83%E7%94%A8">2.5. 子函数调用</a></li><li><a href="about:blank#ent">2.6. ENT</a></li><li><a href="about:blank#adj">2.7. ADJ</a></li><li><a href="about:blank#lev">2.8. LEV</a></li><li><a href="about:blank#lea">2.9. LEA</a></li><li><a href="about:blank#%E8%BF%90%E7%AE%97%E7%AC%A6%E6%8C%87%E4%BB%A4">2.10. 运算符指令</a></li><li><a href="about:blank#%E5%86%85%E7%BD%AE%E5%87%BD%E6%95%B0">2.11. 内置函数</a></li></ol></li><li><a href="about:blank#%E6%B5%8B%E8%AF%95">3. 测试</a></li><li><a href="about:blank#%E5%B0%8F%E7%BB%93">4. 小结</a></li></ol><p>这是“手把手教你构建 C 语言编译器”系列的第三篇，本章我们要构建一台虚拟的电脑，设计我们自己的指令集，运行我们的指令集，说得通俗一点就是自己实现一套汇编语言。它们将作为我们的编译器最终输出的目标代码。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p><ol><li><a href="http://lotabout.me/2015/write-a-C-interpreter-0/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（0）——前言<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-1/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（1）——设计<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-2/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（2）——虚拟机<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-3/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（3）——词法分析器<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-4/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（4）——递归下降<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-5/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（5）——变量定义<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-6/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（6）——函数定义<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-7/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（7）——语句<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-8/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（8）——表达式<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-9/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（9）——总结<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li></ol><h2 id="计算机的内部工作原理" tabindex="-1"><a class="header-anchor" href="#计算机的内部工作原理"><span><a href="about:blank#%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E5%86%85%E9%83%A8%E5%B7%A5%E4%BD%9C%E5%8E%9F%E7%90%86"></a>计算机的内部工作原理</span></a></h2><p>计算机中有三个基本部件需要我们关注：CPU、寄存器及内存。代码（汇编指令）以二进制的形式保存在内存中；CPU 从中一条条地加载指令执行；程序运行的状态保存在寄存器中。</p><h3 id="内存" tabindex="-1"><a class="header-anchor" href="#内存"><span><a href="about:blank#%E5%86%85%E5%AD%98"></a>内存</span></a></h3><p>内存用于存储数据，这里的数据可以是代码，也可以是其它的数据。现代操作系统在操作内存时，并不是直接处理”物理内存“，而是操作”虚拟内存“。虚拟内存可以理解为一种映射，它的作用是屏蔽了物理的细节。例如 32 位的机器中，我们可以使用的内存地址为 <code>2^32 = 4G</code>，而电脑上的实际内存可能只有 <code>256 M</code>。操作系统将我们使用的虚拟地址映射到了到实际的内存上。</p><p>当然，我们这里并不需要了解太多，但需要了解的是：进程的内存会被分成几个段：</p><ol><li>代码段（text）用于存放代码（指令）。</li><li>数据段（data）用于存放初始化了的数据，如<code>int i = 10;</code>，就需要存放到数据段中。</li><li>未初始化数据段（bss）用于存放未初始化的数据，如 <code>int i[1000];</code>，因为不关心其中的真正数值，所以单独存放可以节省空间，减少程序的体积。</li><li>栈（stack）用于处理函数调用相关的数据，如调用帧（calling frame）或是函数的局部变量等。</li><li>堆（heap）用于为程序动态分配内存。</li></ol><p>它们在内存中的位置类似于下图：</p><table><tbody><tr><td class="code"><pre><span class="line">+------------------+</span><br><span class="line">|    stack   |     |      high address</span><br><span class="line">|    ...     v     |</span><br><span class="line">|                  |</span><br><span class="line">|                  |</span><br><span class="line">|                  |</span><br><span class="line">|                  |</span><br><span class="line">|    ...     ^     |</span><br><span class="line">|    heap    |     |</span><br><span class="line">+------------------+</span><br><span class="line">| bss  segment     |</span><br><span class="line">+------------------+</span><br><span class="line">| data segment     |</span><br><span class="line">+------------------+</span><br><span class="line">| text segment     |      low address</span><br><span class="line">+------------------+</span><br></pre></td></tr></tbody></table><p>我们的虚拟机并不打算模拟完整的计算机，因此简单起见，我们只关心三个内容：代码段、数据段以及栈。其中的数据段我们只用来存放字符串，因为我们的编译器并不支持初始化变量，因此我们也不需要未初始化数据段。</p><p>当用户的程序需要分配内存时，理论上我们的虚拟机需要维护一个堆用于内存分配，但实际实现上较为复杂且与编译无关，故我们引入一个指令<code>MSET</code>，使我们能直接使用编译器（解释器）中的内存。</p><p>综上，我们需要首先在全局添加如下代码：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> *text,            <span class="comment">// text segment</span></span><br><span class="line">    *old_text,        <span class="comment">// for dump text segment</span></span><br><span class="line">    *<span class="built_in">stack</span>;           <span class="comment">// stack</span></span><br><span class="line"><span class="type">char</span> *data;           <span class="comment">// data segment</span></span><br></pre></td></tr></tbody></table><p>注意这里的类型，虽然是<code>int</code>型，但理解起来应该作为无符号的整型，因为我们会在代码段（text）中存放如指针/内存地址的数据，它们就是无符号的。其中数据段（data）由于只存放字符串，所以是 <code>char *</code> 型的。</p><p>接着，在<code>main</code>函数中加入初始化代码，真正为其分配内存：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> <span class="title function_">main</span><span class="params">()</span> {</span><br><span class="line">    close(fd);</span><br><span class="line">    ...</span><br><span class="line"></span><br><span class="line">    <span class="comment">// allocate memory for virtual machine</span></span><br><span class="line">    <span class="keyword">if</span> (!(text = old_text = <span class="built_in">malloc</span>(poolsize))) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;could not malloc(%d) for text area\n&quot;</span>, poolsize);</span><br><span class="line">        <span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">if</span> (!(data = <span class="built_in">malloc</span>(poolsize))) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;could not malloc(%d) for data area\n&quot;</span>, poolsize);</span><br><span class="line">        <span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">if</span> (!(<span class="built_in">stack</span> = <span class="built_in">malloc</span>(poolsize))) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;could not malloc(%d) for stack area\n&quot;</span>, poolsize);</span><br><span class="line">        <span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="built_in">memset</span>(text, <span class="number">0</span>, poolsize);</span><br><span class="line">    <span class="built_in">memset</span>(data, <span class="number">0</span>, poolsize);</span><br><span class="line">    <span class="built_in">memset</span>(<span class="built_in">stack</span>, <span class="number">0</span>, poolsize);</span><br><span class="line"></span><br><span class="line">    ...</span><br><span class="line">    program();</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="寄存器" tabindex="-1"><a class="header-anchor" href="#寄存器"><span><a href="about:blank#%E5%AF%84%E5%AD%98%E5%99%A8"></a>寄存器</span></a></h3><p>计算机中的寄存器用于存放计算机的运行状态，真正的计算机中有许多不同种类的寄存器，但我们的虚拟机中只使用 4 个寄存器，分别如下：</p><ol><li><code>PC</code> 程序计数器，它存放的是一个内存地址，该地址中存放着 <strong>下一条</strong> 要执行的计算机指令。</li><li><code>SP</code> 指针寄存器，永远指向当前的栈顶。注意的是由于栈是位于高地址并向低地址增长的，所以入栈时 <code>SP</code> 的值减小。</li><li><code>BP</code> 基址指针。也是用于指向栈的某些位置，在调用函数时会使用到它。</li><li><code>AX</code> 通用寄存器，我们的虚拟机中，它用于存放一条指令执行后的结果。</li></ol><p>要理解这些寄存器的作用，需要去理解程序运行中会有哪些状态。而这些寄存器只是用于保存这些状态的。</p><p>在全局中加入如下定义：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> *pc, *bp, *sp, ax, cycle; <span class="comment">// virtual machine registers</span></span><br></pre></td></tr></tbody></table><p>在 <code>main</code> 函数中加入初始化代码，注意的是<code>PC</code>在初始应指向目标代码中的<code>main</code>函数，但我们还没有写任何编译相关的代码，因此先不处理。代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="built_in">memset</span>(<span class="built_in">stack</span>, <span class="number">0</span>, poolsize);</span><br><span class="line">...</span><br><span class="line"></span><br><span class="line">bp = sp = (<span class="type">int</span> *)((<span class="type">int</span>)<span class="built_in">stack</span> + poolsize);</span><br><span class="line">ax = <span class="number">0</span>;</span><br><span class="line"></span><br><span class="line">...</span><br><span class="line">program();</span><br></pre></td></tr></tbody></table><p>与 CPU 相关的是指令集，我们将专门作为一个小节。</p><h2 id="指令集" tabindex="-1"><a class="header-anchor" href="#指令集"><span><a href="about:blank#%E6%8C%87%E4%BB%A4%E9%9B%86"></a>指令集</span></a></h2><p>指令集是 CPU 能识别的命令的集合，也可以说是 CPU 能理解的语言。这里我们要为我们的虚拟机构建自己的指令集。它们基于 x86 的指令集，但更为简单。</p><p>首先在全局变量中加入一个枚举类型，这是我们要支持的全部指令：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="comment">// instructions</span></span><br><span class="line"><span class="class"><span class="keyword">enum</span> {</span> LEA ,IMM ,JMP ,CALL,JZ  ,JNZ ,ENT ,ADJ ,LEV ,LI  ,LC  ,SI  ,SC  ,PUSH,</span><br><span class="line">       OR  ,XOR ,AND ,EQ  ,NE  ,LT  ,GT  ,LE  ,GE  ,SHL ,SHR ,ADD ,SUB ,MUL ,DIV ,MOD ,</span><br><span class="line">       OPEN,READ,CLOS,PRTF,MALC,MSET,MCMP,EXIT };</span><br></pre></td></tr></tbody></table><p>这些指令的顺序安排是有意的，稍后你会看到，带有参数的指令在前，没有参数的指令在后。这种顺序的唯一作用就是在打印调试信息时更加方便。但我们讲解的顺序并不依据它。</p><h3 id="mov" tabindex="-1"><a class="header-anchor" href="#mov"><span><a href="about:blank#mov"></a>MOV</span></a></h3><p><code>MOV</code> 是所有指令中最基础的一个，它用于将数据放进寄存器或内存地址，有点类似于 C 语言中的赋值语句。x86 的 <code>MOV</code> 指令有两个参数，分别是源地址和目标地址：<code>MOV dest, source</code> （Intel 风格），表示将 <code>source</code> 的内容放在 <code>dest</code> 中，它们可以是一个数、寄存器或是一个内存地址。</p><p>一方面，我们的虚拟机只有一个寄存器，另一方面，识别这些参数的类型（是数据还是地址）是比较困难的，因此我们将 <code>MOV</code> 指令拆分成 5 个指令，这些指令只接受一个参数，如下：</p><ol><li><code>IMM &lt;num&gt;</code> 将 <code>&lt;num&gt;</code> 放入寄存器 <code>ax</code> 中。</li><li><code>LC</code> 将对应地址中的字符载入 <code>ax</code> 中，要求 <code>ax</code> 中存放地址。</li><li><code>LI</code> 将对应地址中的整数载入 <code>ax</code> 中，要求 <code>ax</code> 中存放地址。</li><li><code>SC</code> 将 <code>ax</code> 中的数据作为字符存放入地址中，要求栈顶存放地址。</li><li><code>SI</code> 将 <code>ax</code> 中的数据作为整数存放入地址中，要求栈顶存放地址。</li></ol><p>你可能会觉得将一个指令变成了许多指令，整个系统就变得复杂了，但实际情况并非如此。首先是 x86 的 <code>MOV</code> 指令其实有许多变种，根据类型的不同有 <code>MOVB</code>, <code>MOVW</code> 等指令，我们这里的 <code>LC/SC</code> 和 <code>LI/SI</code> 就是对应字符型和整型的存取操作。</p><p>但最为重要的是，通过将 <code>MOV</code> 指令拆分成这些指令，只有 <code>IMM</code> 需要有参数，且不需要判断类型，所以大大简化了实现的难度。</p><p>在 <code>eval()</code> 函数中加入下列代码：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">eval</span><span class="params">()</span> {</span><br><span class="line">    <span class="type">int</span> op, *tmp;</span><br><span class="line">    <span class="keyword">while</span> (<span class="number">1</span>) {</span><br><span class="line">        <span class="keyword">if</span> (op == IMM)       {ax = *pc++;}                                     <span class="comment">// load immediate value to ax</span></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (op == LC)   {ax = *(<span class="type">char</span> *)ax;}                               <span class="comment">// load character to ax, address in ax</span></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (op == LI)   {ax = *(<span class="type">int</span> *)ax;}                                <span class="comment">// load integer to ax, address in ax</span></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (op == SC)   {ax = *(<span class="type">char</span> *)*sp++ = ax;}                       <span class="comment">// save character to address, value in ax, address on stack</span></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (op == SI)   {*(<span class="type">int</span> *)*sp++ = ax;}                             <span class="comment">// save integer to address, value in ax, address on stack</span></span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    ...</span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>其中的 <code>*sp++</code> 的作用是退栈，相当于 <code>POP</code> 操作。</p><p>这里要解释的一点是，为什么 <code>SI/SC</code> 指令中，地址存放在栈中，而 <code>LI/LC</code> 中，地址存放在 <code>ax</code> 中？原因是默认计算的结果是存放在 <code>ax</code> 中的，而地址通常是需要通过计算获得，所以执行 <code>LI/LC</code> 时直接从 <code>ax</code> 取值会更高效。另一点是我们的 <code>PUSH</code> 指令只能将 <code>ax</code> 的值放到栈上，而不能以值作为参数，详细见下文。</p><h3 id="push" tabindex="-1"><a class="header-anchor" href="#push"><span><a href="about:blank#push"></a>PUSH</span></a></h3><p>在 x86 中，<code>PUSH</code> 的作用是将值或寄存器，而在我们的虚拟机中，它的作用是将 <code>ax</code> 的值放入栈中。这样做的主要原因是为了简化虚拟机的实现，并且我们也只有一个寄存器 <code>ax</code> 。代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == PUSH) {*--sp = ax;}                                     <span class="comment">// push the value of ax onto the stack</span></span><br></pre></td></tr></tbody></table><h3 id="jmp" tabindex="-1"><a class="header-anchor" href="#jmp"><span><a href="about:blank#jmp"></a>JMP</span></a></h3><p><code>JMP &lt;addr&gt;</code> 是跳转指令，无条件地将当前的 <code>PC</code> 寄存器设置为指定的 <code>&lt;addr&gt;</code>，实现如下：</p><table><tbody><tr><td class="code"><pre><span class="line">else if (op == JMP)  {pc = (int *)*pc;}                                // jump to the address</span><br></pre></td></tr></tbody></table><p>需要注意的是，<code>pc</code> 寄存器指向的是 <strong>下一条</strong> 指令。所以此时它存放的是 <code>JMP</code> 指令的参数，即 <code>&lt;addr&gt;</code> 的值。</p><h3 id="jz-jnz" tabindex="-1"><a class="header-anchor" href="#jz-jnz"><span><a href="about:blank#jz-jnz"></a>JZ/JNZ</span></a></h3><p>为了实现 <code>if</code> 语句，我们需要条件判断相关的指令。这里我们只实现两个最简单的条件判断，即结果（<code>ax</code>）为零或不为零情况下的跳转。</p><p>实现如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == JZ)   {pc = ax ? pc + <span class="number">1</span> : (<span class="type">int</span> *)*pc;}                   <span class="comment">// jump if ax is zero</span></span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == JNZ)  {pc = ax ? (<span class="type">int</span> *)*pc : pc + <span class="number">1</span>;}                   <span class="comment">// jump if ax is not zero</span></span><br></pre></td></tr></tbody></table><h3 id="子函数调用" tabindex="-1"><a class="header-anchor" href="#子函数调用"><span><a href="about:blank#%E5%AD%90%E5%87%BD%E6%95%B0%E8%B0%83%E7%94%A8"></a>子函数调用</span></a></h3><p>这是汇编中最难理解的部分，所以合在一起说，要引入的命令有 <code>CALL</code>, <code>ENT</code>, <code>ADJ</code> 及 <code>LEV</code>。</p><p>首先我们介绍 <code>CALL &lt;addr&gt;</code> 与 <code>RET</code> 指令，<code>CALL</code> 的作用是跳转到地址为 <code>&lt;addr&gt;</code> 的子函数，<code>RET</code> 则用于从子函数中返回。</p><p>为什么不能直接使用 <code>JMP</code> 指令呢？原因是当我们从子函数中返回时，程序需要回到跳转之前的地方继续运行，这就需要事先将这个位置信息存储起来。反过来，子函数要返回时，就需要获取并恢复这个信息。因此实际中我们将 <code>PC</code> 保存在栈中。如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == CALL) {*--sp = (<span class="type">int</span>)(pc+<span class="number">1</span>); pc = (<span class="type">int</span> *)*pc;}           <span class="comment">// call subroutine</span></span><br><span class="line"><span class="comment">//else if (op == RET)  {pc = (int *)*sp++;}                              // return from subroutine;</span></span><br></pre></td></tr></tbody></table><p>这里我们把 <code>RET</code> 相关的内容注释了，是因为之后我们将用 <code>LEV</code> 指令来代替它。</p><p>在实际调用函数时，不仅要考虑函数的地址，还要考虑如何传递参数和如何返回结果。这里我们约定，如果子函数有返回结果，那么就在返回时保存在 <code>ax</code> 中，它可以是一个值，也可以是一个地址。那么参数的传递呢？</p><p>各种编程语言关于如何调用子函数有不同的约定，例如 C 语言的调用标准是：</p><ol><li>由调用者将参数入栈。</li><li>调用结束时，由调用者将参数出栈。</li><li>参数逆序入栈。</li></ol><p>事先声明一下，我们的编译器参数是顺序入栈的，下面的例子（C 语言调用标准）取自 <a href="https://en.wikipedia.org/wiki/X86_calling_conventions" target="_blank" rel="noopener noreferrer">维基百科<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a>：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> <span class="title function_">callee</span><span class="params">(<span class="type">int</span>, <span class="type">int</span>, <span class="type">int</span>)</span>;</span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">caller</span><span class="params">(<span class="type">void</span>)</span></span><br><span class="line">{</span><br><span class="line">	<span class="type">int</span> i, ret;</span><br><span class="line"></span><br><span class="line">	ret = callee(<span class="number">1</span>, <span class="number">2</span>, <span class="number">3</span>);</span><br><span class="line">	ret += <span class="number">5</span>;</span><br><span class="line">	<span class="keyword">return</span> ret;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>会生成如下的 x86 汇编代码：</p><table><tbody><tr><td class="code"><pre><span class="line">caller:</span><br><span class="line">	; make new call frame</span><br><span class="line">	push    ebp</span><br><span class="line">	mov     ebp, esp</span><br><span class="line">        sub     1, esp       ; save stack for variable: i</span><br><span class="line">	; push call arguments</span><br><span class="line">	push    3</span><br><span class="line">	push    2</span><br><span class="line">	push    1</span><br><span class="line">	; call subroutine &#39;callee&#39;</span><br><span class="line">	call    callee</span><br><span class="line">	; remove arguments from frame</span><br><span class="line">	add     esp, 12</span><br><span class="line">	; use subroutine result</span><br><span class="line">	add     eax, 5</span><br><span class="line">	; restore old call frame</span><br><span class="line">        mov     esp, ebp</span><br><span class="line">	pop     ebp</span><br><span class="line">	; return</span><br><span class="line">	ret</span><br></pre></td></tr></tbody></table><p>上面这段代码在我们自己的虚拟机里会有几个问题：</p><ol><li><code>push ebp</code>，但我们的 <code>PUSH</code> 指令并无法指定寄存器。</li><li><code>mov ebp, esp</code>，我们的 <code>MOV</code> 指令同样功能不足。</li><li><code>add esp, 12</code>，也是一样的问题（尽管我们还没定义）。</li></ol><p>也就是说由于我们的指令过于简单（如只能操作<code>ax</code>寄存器），所以用上面提到的指令，我们连函数调用都无法实现。而我们又不希望扩充现有指令的功能，因为这样实现起来就会变得复杂，因此我们采用的方法是增加指令集。毕竟我们不是真正的计算机，增加指令会消耗许多资源（钱）。</p><h3 id="ent" tabindex="-1"><a class="header-anchor" href="#ent"><span><a href="about:blank#ent"></a>ENT</span></a></h3><p><code>ENT &lt;size&gt;</code> 指的是 <code>enter</code>，用于实现 ‘make new call frame’ 的功能，即保存当前的栈指针，同时在栈上保留一定的空间，用以存放局部变量。对应的汇编代码为：</p><table><tbody><tr><td class="code"><pre><span class="line">; make new call frame</span><br><span class="line">push    ebp</span><br><span class="line">mov     ebp, esp</span><br><span class="line">       sub     1, esp       ; save stack for variable: i</span><br></pre></td></tr></tbody></table><p>实现如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == ENT)  {*--sp = (<span class="type">int</span>)bp; bp = sp; sp = sp - *pc++;}      <span class="comment">// make new stack frame</span></span><br></pre></td></tr></tbody></table><h3 id="adj" tabindex="-1"><a class="header-anchor" href="#adj"><span><a href="about:blank#adj"></a>ADJ</span></a></h3><p><code>ADJ &lt;size&gt;</code> 用于实现 ‘remove arguments from frame’。在将调用子函数时压入栈中的数据清除，本质上是因为我们的 <code>ADD</code> 指令功能有限。对应的汇编代码为：</p><table><tbody><tr><td class="code"><pre><span class="line">; remove arguments from frame</span><br><span class="line">add     esp, 12</span><br></pre></td></tr></tbody></table><p>实现如下：</p><table><tbody><tr><td class="code"><pre><span class="line">else if (op == ADJ)  {sp = sp + *pc++;}                                // add esp, &lt;size&gt;</span><br></pre></td></tr></tbody></table><h3 id="lev" tabindex="-1"><a class="header-anchor" href="#lev"><span><a href="about:blank#lev"></a>LEV</span></a></h3><p>本质上这个指令并不是必需的，只是我们的指令集中并没有 <code>POP</code> 指令。并且三条指令写来比较麻烦且浪费空间，所以用一个指令代替。对应的汇编指令为：</p><table><tbody><tr><td class="code"><pre><span class="line">; restore old call frame</span><br><span class="line">       mov     esp, ebp</span><br><span class="line">pop     ebp</span><br><span class="line">; return</span><br><span class="line">ret</span><br></pre></td></tr></tbody></table><p>具体的实现如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == LEV)  {sp = bp; bp = (<span class="type">int</span> *)*sp++; pc = (<span class="type">int</span> *)*sp++;}  <span class="comment">// restore call frame and PC</span></span><br></pre></td></tr></tbody></table><p>注意的是，<code>LEV</code> 已经把 <code>RET</code> 的功能包含了，所以我们不再需要 <code>RET</code> 指令。</p><h3 id="lea" tabindex="-1"><a class="header-anchor" href="#lea"><span><a href="about:blank#lea"></a>LEA</span></a></h3><p>上面的一些指令解决了调用帧的问题，但还有一个问题是如何在子函数中获得传入的参数。这里我们首先要了解的是当参数调用时，栈中的调用帧是什么样的。我们依旧用上面的例子（只是现在用“顺序”调用参数）：</p><table><tbody><tr><td class="code"><pre><span class="line">sub_function(arg1, arg2, arg3);</span><br><span class="line"></span><br><span class="line">|    ....       | high address</span><br><span class="line">+---------------+</span><br><span class="line">| arg: 1        |    new_bp + 4</span><br><span class="line">+---------------+</span><br><span class="line">| arg: 2        |    new_bp + 3</span><br><span class="line">+---------------+</span><br><span class="line">| arg: 3        |    new_bp + 2</span><br><span class="line">+---------------+</span><br><span class="line">|return address |    new_bp + 1</span><br><span class="line">+---------------+</span><br><span class="line">| old BP        | &lt;- new BP</span><br><span class="line">+---------------+</span><br><span class="line">| local var 1   |    new_bp - 1</span><br><span class="line">+---------------+</span><br><span class="line">| local var 2   |    new_bp - 2</span><br><span class="line">+---------------+</span><br><span class="line">|    ....       |  low address</span><br></pre></td></tr></tbody></table><p>所以为了获取第一个参数，我们需要得到 <code>new_bp + 4</code>，但就如上面的说，我们的 <code>ADD</code> 指令无法操作除 <code>ax</code> 外的寄存器，所以我们提供了一个新的指令：<code>LEA &lt;offset&gt;</code></p><p>实现如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == LEA)  {ax = (<span class="type">int</span>)(bp + *pc++);}                         <span class="comment">// load address for arguments.</span></span><br></pre></td></tr></tbody></table><p>以上就是我们为了实现函数调用需要的指令了。</p><h3 id="运算符指令" tabindex="-1"><a class="header-anchor" href="#运算符指令"><span><a href="about:blank#%E8%BF%90%E7%AE%97%E7%AC%A6%E6%8C%87%E4%BB%A4"></a>运算符指令</span></a></h3><p>我们为 C 语言中支持的运算符都提供对应汇编指令。每个运算符都是二元的，即有两个参数，第一个参数放在栈顶，第二个参数放在 <code>ax</code> 中。这个顺序要特别注意。因为像 <code>-</code>，<code>/</code> 之类的运算符是与参数顺序有关的。计算后会将栈顶的参数退栈，结果存放在寄存器 <code>ax</code> 中。因此计算结束后，两个参数都无法取得了（汇编的意义上，存在内存地址上就另当别论）。</p><p>实现如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == OR)  ax = *sp++ | ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == XOR) ax = *sp++ ^ ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == AND) ax = *sp++ &amp; ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == EQ)  ax = *sp++ == ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == NE)  ax = *sp++ != ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == LT)  ax = *sp++ &lt; ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == LE)  ax = *sp++ &lt;= ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == GT)  ax = *sp++ &gt;  ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == GE)  ax = *sp++ &gt;= ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == SHL) ax = *sp++ &lt;&lt; ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == SHR) ax = *sp++ &gt;&gt; ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == ADD) ax = *sp++ + ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == SUB) ax = *sp++ - ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == MUL) ax = *sp++ * ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == DIV) ax = *sp++ / ax;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == MOD) ax = *sp++ % ax;</span><br></pre></td></tr></tbody></table><h3 id="内置函数" tabindex="-1"><a class="header-anchor" href="#内置函数"><span><a href="about:blank#%E5%86%85%E7%BD%AE%E5%87%BD%E6%95%B0"></a>内置函数</span></a></h3><p>写的程序要”有用“，除了核心的逻辑外还需要输入输出，例如 C 语言中我们经常使用的 <code>printf</code> 函数就是用于输出。但是 <code>printf</code> 函数的实现本身就十分复杂，如果我们的编译器要达到自举，就势必要实现 <code>printf</code> 之类的函数，但它又与编译器没有太大的联系，因此我们继续实现新的指令，从虚拟机的角度予以支持。</p><p>编译器中我们需要用到的函数有：<code>exit</code>, <code>open</code>, <code>close</code>, <code>read</code>, <code>printf</code>, <code>malloc</code>, <code>memset</code> 及 <code>memcmp</code>。代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == EXIT) { <span class="built_in">printf</span>(<span class="string">&quot;exit(%d)&quot;</span>, *sp); <span class="keyword">return</span> *sp;}</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == OPEN) { ax = open((<span class="type">char</span> *)sp[<span class="number">1</span>], sp[<span class="number">0</span>]); }</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == CLOS) { ax = close(*sp);}</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == READ) { ax = read(sp[<span class="number">2</span>], (<span class="type">char</span> *)sp[<span class="number">1</span>], *sp); }</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == PRTF) { tmp = sp + pc[<span class="number">1</span>]; ax = <span class="built_in">printf</span>((<span class="type">char</span> *)tmp[<span class="number">-1</span>], tmp[<span class="number">-2</span>], tmp[<span class="number">-3</span>], tmp[<span class="number">-4</span>], tmp[<span class="number">-5</span>], tmp[<span class="number">-6</span>]); }</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == MALC) { ax = (<span class="type">int</span>)<span class="built_in">malloc</span>(*sp);}</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == MSET) { ax = (<span class="type">int</span>)<span class="built_in">memset</span>((<span class="type">char</span> *)sp[<span class="number">2</span>], sp[<span class="number">1</span>], *sp);}</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (op == MCMP) { ax = <span class="built_in">memcmp</span>((<span class="type">char</span> *)sp[<span class="number">2</span>], (<span class="type">char</span> *)sp[<span class="number">1</span>], *sp);}</span><br></pre></td></tr></tbody></table><p>这里的原理是，我们的电脑上已经有了这些函数的实现，因此编译编译器时，这些函数的二进制代码就被编译进了我们的编译器，因此在我们的编译器/虚拟机上运行我们提供的这些指令时，这些函数就是可用的。换句话说就是不需要我们自己去实现了。</p><p>最后再加上一个错误判断：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> {</span><br><span class="line">    <span class="built_in">printf</span>(<span class="string">&quot;unknown instruction:%d\n&quot;</span>, op);</span><br><span class="line">    <span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h2 id="测试" tabindex="-1"><a class="header-anchor" href="#测试"><span><a href="about:blank#%E6%B5%8B%E8%AF%95"></a>测试</span></a></h2><p>下面我们用我们的汇编写一小段程序，来计算 <code>10+20</code>，在 <code>main</code> 函数中加入下列代码：</p><table><tbody><tr><td class="code"><pre><span class="line">int main(int argc, char *argv[])</span><br><span class="line">{</span><br><span class="line">    ax = 0;</span><br><span class="line">    ...</span><br><span class="line"></span><br><span class="line">    i = 0;</span><br><span class="line">    text[i++] = IMM;</span><br><span class="line">    text[i++] = 10;</span><br><span class="line">    text[i++] = PUSH;</span><br><span class="line">    text[i++] = IMM;</span><br><span class="line">    text[i++] = 20;</span><br><span class="line">    text[i++] = ADD;</span><br><span class="line">    text[i++] = PUSH;</span><br><span class="line">    text[i++] = EXIT;</span><br><span class="line">    pc = text;</span><br><span class="line"></span><br><span class="line">    ...</span><br><span class="line">    program();</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>编译程序 <code>gcc xc-tutor.c</code>，运行程序：<code>./a.out hello.c</code>。输出</p><table><tbody><tr><td class="code"><pre><span class="line">exit(30)</span><br></pre></td></tr></tbody></table><p>另外，我们的代码里有一些指针的强制转换，默认是 32 位的，因此在 64 位机器下，会出现 <code>segmentation fault</code>，解决方法（二选一）：</p><ol><li>编译时加上 <code>-m32</code> 参数：<code>gcc -m32 xc-tutor.c</code></li><li>在代码的开头，增加 <code>#define int long long</code>，<code>long long</code> 是 64 位的，不会出现强制转换后的问题。</li></ol><p>注意我们的之前的程序需要指令一个源文件，只是现在还用不着，但从结果可以看出，我们的虚拟机还是工作良好的。</p><h2 id="小结" tabindex="-1"><a class="header-anchor" href="#小结"><span><a href="about:blank#%E5%B0%8F%E7%BB%93"></a>小结</span></a></h2><p>本章中我们回顾了计算机的内部运行原理，并仿照 x86 汇编指令设计并实现了我们自己的指令集。希望通过本章的学习，你能对计算机程序的原理有一定的了解，同时能对汇编语言有一定的概念，因为汇编语言就是 C 编译器的输出。</p><p>本章的代码可以在 <a href="https://github.com/lotabout/write-a-C-interpreter/tree/step-1" target="_blank" rel="noopener noreferrer">Github<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a> 上下载，也可以直接 clone</p><table><tbody><tr><td class="code"><pre><span class="line">git clone -b step-1 https://github.com/lotabout/write-a-C-interpreter</span><br></pre></td></tr></tbody></table><p>实际计算机中，添加一个新的指令需要设计许多新的电路，会增加许多的成本，但我们的虚拟机中，新的指令几乎不消耗资源，因此我们可以利用这一点，用更多的指令来完成更多的功能，从而简化具体的实现。</p></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/designASimpileCCompiler/2.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/designASimpileCCompiler/9.html" aria-label="手把手教你构建 C 语言编译器（9）——总结"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->手把手教你构建 C 语言编译器（9）——总结</div></a><!----></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/designASimpileCCompiler/3.html b/tech/designASimpileCCompiler/3.html
index aed8e4c..319c239 100644
--- a/tech/designASimpileCCompiler/3.html
+++ b/tech/designASimpileCCompiler/3.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/designASimpileCCompiler/3.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="手把手教你构建 C 语言编译器（3）——词法分析器"><meta property="og:description" content="转载声明 本文转自 https://lotabout.me/2015/write-a-C-interpreter-3/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（3）- 词法分析器 Table of Contents 1. 什么是词法分析器 2. 词法分析器与编译器 3. 词法分析器的实现 3.1. 支持的标记 3.2. 词法分..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="c"><meta property="article:tag" content="编译器"><meta property="article:tag" content="解释器"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"手把手教你构建 C 语言编译器（3）——词法分析器","image":[""],"dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>手把手教你构建 C 语言编译器（3）——词法分析器 | blog</title><meta name="description" content="转载声明 本文转自 https://lotabout.me/2015/write-a-C-interpreter-3/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（3）- 词法分析器 Table of Contents 1. 什么是词法分析器 2. 词法分析器与编译器 3. 词法分析器的实现 3.1. 支持的标记 3.2. 词法分...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/3.html-CZB5joNY.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/3.html-D9pPtuiP.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/0.html" aria-label="手把手教你构建 C 语言编译器（0）- 前言"><!---->手把手教你构建 C 语言编译器（0）- 前言<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/1.html" aria-label="手把手教你构建 C 语言编译器（1）- 设计"><!---->手把手教你构建 C 语言编译器（1）- 设计<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/designASimpileCCompiler/3.html" aria-label="手把手教你构建 C 语言编译器（3）——词法分析器"><!---->手把手教你构建 C 语言编译器（3）——词法分析器<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/4.html" aria-label="手把手教你构建 C 语言编译器（4）——递归下降"><!---->手把手教你构建 C 语言编译器（4）——递归下降<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/5.html" aria-label="手把手教你构建 C 语言编译器（5）——变量定义"><!---->手把手教你构建 C 语言编译器（5）——变量定义<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/6.html" aria-label="手把手教你构建 C 语言编译器（6）——函数定义"><!---->手把手教你构建 C 语言编译器（6）——函数定义<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/7.html" aria-label="手把手教你构建 C 语言编译器（7）——语句"><!---->手把手教你构建 C 语言编译器（7）——语句<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/8.html" aria-label="手把手教你构建 C 语言编译器（8）——表达式"><!---->手把手教你构建 C 语言编译器（8）——表达式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/9.html" aria-label="手把手教你构建 C 语言编译器（9）——总结"><!---->手把手教你构建 C 语言编译器（9）——总结<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/2.html" aria-label="转载声明"><!---->转载声明<!----></a></li></ul></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->手把手教你构建 C 语言编译器（3）——词法分析器</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 25 分钟</span><meta property="timeRequired" content="PT25M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category2 clickable" role="navigation">编译原理</span><!--]--><meta property="articleSection" content="编译原理"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag4 clickable" role="navigation">c</span><span class="page-tag-item tag4 clickable" role="navigation">编译器</span><span class="page-tag-item tag4 clickable" role="navigation">解释器</span><!--]--><meta property="keywords" content="c,编译器,解释器"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#什么是词法分析器">什么是词法分析器</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#词法分析器与编译器">词法分析器与编译器</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#词法分析器的实现">词法分析器的实现</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#支持的标记">支持的标记</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#词法分析器的框架">词法分析器的框架</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#换行符">换行符</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#宏定义">宏定义</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#标识符与符号表">标识符与符号表</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#数字">数字</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#字符串">字符串</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#注释">注释</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#其它">其它</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#关键字与内置函数">关键字与内置函数</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#代码">代码</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#小结">小结</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="转载声明" tabindex="-1"><a class="header-anchor" href="#转载声明"><span>转载声明</span></a></h1><p>本文转自 <a href="https://lotabout.me/2015/write-a-C-interpreter-3/" target="_blank" rel="noopener noreferrer">https://lotabout.me/2015/write-a-C-interpreter-3/<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a>，如有侵权，请联系删除。</p><h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-3-词法分析器" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-3-词法分析器"><span>手把手教你构建 C 语言编译器（3）- 词法分析器</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#%E4%BB%80%E4%B9%88%E6%98%AF%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8">1. 什么是词法分析器</a></li><li><a href="about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8%E4%B8%8E%E7%BC%96%E8%AF%91%E5%99%A8">2. 词法分析器与编译器</a></li><li><a href="about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8%E7%9A%84%E5%AE%9E%E7%8E%B0">3. 词法分析器的实现</a><ol><li><a href="about:blank#%E6%94%AF%E6%8C%81%E7%9A%84%E6%A0%87%E8%AE%B0">3.1. 支持的标记</a></li><li><a href="about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8%E7%9A%84%E6%A1%86%E6%9E%B6">3.2. 词法分析器的框架</a></li><li><a href="about:blank#%E6%8D%A2%E8%A1%8C%E7%AC%A6">3.3. 换行符</a></li><li><a href="about:blank#%E5%AE%8F%E5%AE%9A%E4%B9%89">3.4. 宏定义</a></li><li><a href="about:blank#%E6%A0%87%E8%AF%86%E7%AC%A6%E4%B8%8E%E7%AC%A6%E5%8F%B7%E8%A1%A8">3.5. 标识符与符号表</a></li><li><a href="about:blank#%E6%95%B0%E5%AD%97">3.6. 数字</a></li><li><a href="about:blank#%E5%AD%97%E7%AC%A6%E4%B8%B2">3.7. 字符串</a></li><li><a href="about:blank#%E6%B3%A8%E9%87%8A">3.8. 注释</a></li><li><a href="about:blank#%E5%85%B6%E5%AE%83">3.9. 其它</a></li><li><a href="about:blank#%E5%85%B3%E9%94%AE%E5%AD%97%E4%B8%8E%E5%86%85%E7%BD%AE%E5%87%BD%E6%95%B0">3.10. 关键字与内置函数</a></li></ol></li><li><a href="about:blank#%E4%BB%A3%E7%A0%81">4. 代码</a></li><li><a href="about:blank#%E5%B0%8F%E7%BB%93">5. 小结</a></li></ol><p>本章我们要讲解如何构建词法分析器。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p><ol><li><a href="http://lotabout.me/2015/write-a-C-interpreter-0/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（0）——前言<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-1/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（1）——设计<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-2/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（2）——虚拟机<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-3/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（3）——词法分析器<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-4/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（4）——递归下降<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-5/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（5）——变量定义<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-6/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（6）——函数定义<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-7/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（7）——语句<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-8/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（8）——表达式<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-9/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（9）——总结<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li></ol><h2 id="什么是词法分析器" tabindex="-1"><a class="header-anchor" href="#什么是词法分析器"><span><a href="about:blank#%E4%BB%80%E4%B9%88%E6%98%AF%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8"></a>什么是词法分析器</span></a></h2><p>简而言之，词法分析器用于对源码字符串做预处理，以减少语法分析器的复杂程度。</p><p>词法分析器以源码字符串为输入，输出为标记流（token stream），即一连串的标记，每个标记通常包括： <code>(token, token value)</code> 即标记本身和标记的值。例如，源码中若包含一个数字 <code>&#39;998&#39;</code> ，词法分析器将输出 <code>(Number, 998)</code>，即（数字，998）。再例如：</p><table><tbody><tr><td class="code"><pre><span class="line">2 + 3 * (4 - 5)</span><br><span class="line">=&gt;</span><br><span class="line">(Number, 2) Add (Number, 3) Multiply Left-Bracket (Number, 4) Subtract (Number, 5) Right-Bracket</span><br></pre></td></tr></tbody></table><p>通过词法分析器的预处理，语法分析器的复杂度会大大降低，这点在后面的语法分析器我们就能体会。</p><h2 id="词法分析器与编译器" tabindex="-1"><a class="header-anchor" href="#词法分析器与编译器"><span><a href="about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8%E4%B8%8E%E7%BC%96%E8%AF%91%E5%99%A8"></a>词法分析器与编译器</span></a></h2><p>要是深入词法分析器，你就会发现，它的本质上也是编译器。我们的编译器是以标记流为输入，输出汇编代码，而词法分析器则是以源码字符串为输入，输出标记流。</p><table><tbody><tr><td class="code"><pre><span class="line">                   +-------+                      +--------+</span><br><span class="line">-- source code --&gt; | lexer | --&gt; token stream --&gt; | parser | --&gt; assembly</span><br><span class="line">                   +-------+                      +--------+</span><br></pre></td></tr></tbody></table><p>在这个前提下，我们可以这样认为：直接从源代码编译成汇编代码是很困难的，因为输入的字符串比较难处理。所以我们先编写一个较为简单的编译器（词法分析器）来将字符串转换成标记流，而标记流对于语法分析器而言就容易处理得多了。</p><h2 id="词法分析器的实现" tabindex="-1"><a class="header-anchor" href="#词法分析器的实现"><span><a href="about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8%E7%9A%84%E5%AE%9E%E7%8E%B0"></a>词法分析器的实现</span></a></h2><p>由于词法分析的工作很常见，但又枯燥且容易出错，所以人们已经开发出了许多工具来生成词法分析器，如 <code>lex, flex</code>。这些工具允许我们通过正则表达式来识别标记。</p><p>这里注意的是，我们并不会一次性地将所有源码全部转换成标记流，原因有二：</p><ol><li>字符串转换成标记流有时是有状态的，即与代码的上下文是有关系的。</li><li>保存所有的标记流没有意义且浪费空间。</li></ol><p>所以实际的处理方法是提供一个函数（即前几篇中提到的 <code>next()</code>），每次调用该函数则返回下一个标记。</p><h3 id="支持的标记" tabindex="-1"><a class="header-anchor" href="#支持的标记"><span><a href="about:blank#%E6%94%AF%E6%8C%81%E7%9A%84%E6%A0%87%E8%AE%B0"></a>支持的标记</span></a></h3><p>在全局中添加如下定义：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="comment">// tokens and classes (operators last and in precedence order)</span></span><br><span class="line"><span class="class"><span class="keyword">enum</span> {</span></span><br><span class="line">  Num = <span class="number">128</span>, Fun, Sys, Glo, Loc, Id,</span><br><span class="line">  Char, Else, Enum, If, Int, Return, Sizeof, While,</span><br><span class="line">  Assign, Cond, Lor, Lan, Or, Xor, And, Eq, Ne, Lt, Gt, Le, Ge, Shl, Shr, Add, Sub, Mul, Div, Mod, Inc, Dec, Brak</span><br><span class="line">};</span><br></pre></td></tr></tbody></table><p>这些就是我们要支持的标记符。例如，我们会将 <code>=</code> 解析为 <code>Assign</code>；将 <code>==</code> 解析为 <code>Eq</code>；将 <code>!=</code> 解析为 <code>Ne</code> 等等。</p><p>所以这里我们会有这样的印象，一个标记（token）可能包含多个字符，且多数情况下如此。而词法分析器能减小语法分析复杂度的原因，正是因为它相当于通过一定的编码（更多的标记）来压缩了源码字符串。</p><p>当然，上面这些标记是有顺序的，跟它们在 C 语言中的优先级有关，如 <code>*(Mul)</code> 的优先级就要高于 <code>+(Add)</code>。它们的具体使用在后面的语法分析中会提到。</p><p>最后要注意的是还有一些字符，它们自己就构成了标记，如右方括号 <code>]</code> 或波浪号 <code>~</code> 等。我们不另外处理它们的原因是：</p><ol><li>它们是单字符的，即并不是多个字符共同构成标记（如 <code>==</code> 需要两个字符）；</li><li>它们不涉及优先级关系。</li></ol><h3 id="词法分析器的框架" tabindex="-1"><a class="header-anchor" href="#词法分析器的框架"><span><a href="about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90%E5%99%A8%E7%9A%84%E6%A1%86%E6%9E%B6"></a>词法分析器的框架</span></a></h3><p>即 <code>next()</code> 函数的主体：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">next</span><span class="params">()</span> {</span><br><span class="line">    <span class="type">char</span> *last_pos;</span><br><span class="line">    <span class="type">int</span> hash;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">while</span> (token = *src) {</span><br><span class="line">        ++src;</span><br><span class="line">        <span class="comment">// parse token here</span></span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">return</span>;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>这里的一个问题是，为什么要用 <code>while</code> 循环呢？这就涉及到编译器（记得我们说过词法分析器也是某种意义上的编译器）的一个问题：如何处理错误？</p><p>对词法分析器而言，若碰到了一个我们不认识的字符该怎么处理？一般处理的方法有两种：</p><ol><li>指出错误发生的位置，并退出整个程序</li><li>指出错误发生的位置，跳过当前错误并继续编译</li></ol><p>这个 <code>while</code> 循环的作用就是跳过这些我们不识别的字符，我们同时还用它来处理空白字符。我们知道，C 语言中空格是用来作为分隔用的，并不作为语法的一部分。因此在实现中我们将它作为“不识别”的字符，这个 <code>while</code> 循环可以用来跳过它。</p><h3 id="换行符" tabindex="-1"><a class="header-anchor" href="#换行符"><span><a href="about:blank#%E6%8D%A2%E8%A1%8C%E7%AC%A6"></a>换行符</span></a></h3><p>换行符和空格类似，但有一点不同，每次遇到换行符，我们需要将当前的行号加一：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="comment">// parse token here</span></span><br><span class="line">...</span><br><span class="line"></span><br><span class="line"><span class="keyword">if</span> (token == <span class="string">&#39;\n&#39;</span>) {</span><br><span class="line">    ++line;</span><br><span class="line">}</span><br><span class="line">...</span><br></pre></td></tr></tbody></table><h3 id="宏定义" tabindex="-1"><a class="header-anchor" href="#宏定义"><span><a href="about:blank#%E5%AE%8F%E5%AE%9A%E4%B9%89"></a>宏定义</span></a></h3><p>C 语言的宏定义以字符 <code>#</code> 开头，如 <code># include &lt;stdio.h&gt;</code>。我们的编译器并不支持宏定义，所以直接跳过它们。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;#&#39;</span>) {</span><br><span class="line">    <span class="comment">// skip macro, because we will not support it</span></span><br><span class="line">    <span class="keyword">while</span> (*src != <span class="number">0</span> &amp;&amp; *src != <span class="string">&#39;\n&#39;</span>) {</span><br><span class="line">        src++;</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="标识符与符号表" tabindex="-1"><a class="header-anchor" href="#标识符与符号表"><span><a href="about:blank#%E6%A0%87%E8%AF%86%E7%AC%A6%E4%B8%8E%E7%AC%A6%E5%8F%B7%E8%A1%A8"></a>标识符与符号表</span></a></h3><p>标识符（identifier）可以理解为变量名。对于语法分析而言，我们并不关心一个变量具体叫什么名字，而只关心这个变量名代表的唯一标识。例如 <code>int a;</code> 定义了变量 <code>a</code>，而之后的语句 <code>a = 10</code>，我们需要知道这两个 <code>a</code> 指向的是同一个变量。</p><p>基于这个理由，词法分析器会把扫描到的标识符全都保存到一张表中，遇到新的标识符就去查这张表，如果标识符已经存在，就返回它的唯一标识。</p><p>那么我们怎么表示标识符呢？如下：</p><table><tbody><tr><td class="code"><pre><span class="line">struct identifier {</span><br><span class="line">    int token;</span><br><span class="line">    int hash;</span><br><span class="line">    char * name;</span><br><span class="line">    int class;</span><br><span class="line">    int type;</span><br><span class="line">    int value;</span><br><span class="line">    int Bclass;</span><br><span class="line">    int Btype;</span><br><span class="line">    int Bvalue;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>这里解释一下具体的含义：</p><ol><li><code>token</code>：该标识符返回的标记，理论上所有的变量返回的标记都应该是 <code>Id</code>，但实际上由于我们还将在符号表中加入关键字如 <code>if</code>, <code>while</code> 等，它们都有对应的标记。</li><li><code>hash</code>：顾名思义，就是这个标识符的哈希值，用于标识符的快速比较。</li><li><code>name</code>：存放标识符本身的字符串。</li><li><code>class</code>：该标识符的类别，如数字，全局变量或局部变量等。</li><li><code>type</code>：标识符的类型，即如果它是个变量，变量是 <code>int</code> 型、<code>char</code> 型还是指针型。</li><li><code>value</code>：存放这个标识符的值，如标识符是函数，刚存放函数的地址。</li><li><code>BXXXX</code>：C 语言中标识符可以是全局的也可以是局部的，当局部标识符的名字与全局标识符相同时，用作保存全局标识符的信息。</li></ol><p>由上可以看出，我们实现的词法分析器与传统意义上的词法分析器不太相同。传统意义上的符号表只需要知道标识符的唯一标识即可，而我们还存放了一些只有语法分析器才会得到的信息，如 <code>type</code> 。</p><p>由于我们的目标是能自举，而我们定义的语法不支持 <code>struct</code>，故而使用下列方式。</p><table><tbody><tr><td class="code"><pre><span class="line">Symbol table:</span><br><span class="line">----+-----+----+----+----+-----+-----+-----+------+------+----</span><br><span class="line"> .. |token|hash|name|type|class|value|btype|bclass|bvalue| ..</span><br><span class="line">----+-----+----+----+----+-----+-----+-----+------+------+----</span><br><span class="line">    |&lt;---       one single identifier                ---&gt;|</span><br></pre></td></tr></tbody></table><p>即用一个整型数组来保存相关的ID信息。每个ID占用数组中的9个空间，分析标识符的相关代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> token_val;                <span class="comment">// value of current token (mainly for number)</span></span><br><span class="line"><span class="type">int</span> *current_id,              <span class="comment">// current parsed ID</span></span><br><span class="line">    *symbols;                 <span class="comment">// symbol table</span></span><br><span class="line"></span><br><span class="line"><span class="comment">// fields of identifier</span></span><br><span class="line"><span class="class"><span class="keyword">enum</span> {</span>Token, Hash, Name, Type, Class, Value, BType, BClass, BValue, IdSize};</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">next</span><span class="params">()</span> {</span><br><span class="line">        ...</span><br><span class="line"></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> ((token &gt;= <span class="string">&#39;a&#39;</span> &amp;&amp; token &lt;= <span class="string">&#39;z&#39;</span>) || (token &gt;= <span class="string">&#39;A&#39;</span> &amp;&amp; token &lt;= <span class="string">&#39;Z&#39;</span>) || (token == <span class="string">&#39;_&#39;</span>)) {</span><br><span class="line"></span><br><span class="line">            <span class="comment">// parse identifier</span></span><br><span class="line">            last_pos = src - <span class="number">1</span>;</span><br><span class="line">            hash = token;</span><br><span class="line"></span><br><span class="line">            <span class="keyword">while</span> ((*src &gt;= <span class="string">&#39;a&#39;</span> &amp;&amp; *src &lt;= <span class="string">&#39;z&#39;</span>) || (*src &gt;= <span class="string">&#39;A&#39;</span> &amp;&amp; *src &lt;= <span class="string">&#39;Z&#39;</span>) || (*src &gt;= <span class="string">&#39;0&#39;</span> &amp;&amp; *src &lt;= <span class="string">&#39;9&#39;</span>) || (*src == <span class="string">&#39;_&#39;</span>)) {</span><br><span class="line">                hash = hash * <span class="number">147</span> + *src;</span><br><span class="line">                src++;</span><br><span class="line">            }</span><br><span class="line"></span><br><span class="line">            <span class="comment">// look for existing identifier, linear search</span></span><br><span class="line">            current_id = symbols;</span><br><span class="line">            <span class="keyword">while</span> (current_id[Token]) {</span><br><span class="line">                <span class="keyword">if</span> (current_id[Hash] == hash &amp;&amp; !<span class="built_in">memcmp</span>((<span class="type">char</span> *)current_id[Name], last_pos, src - last_pos)) {</span><br><span class="line">                    <span class="comment">//found one, return</span></span><br><span class="line">                    token = current_id[Token];</span><br><span class="line">                    <span class="keyword">return</span>;</span><br><span class="line">                }</span><br><span class="line">                current_id = current_id + IdSize;</span><br><span class="line">            }</span><br><span class="line"></span><br><span class="line"></span><br><span class="line">            <span class="comment">// store new ID</span></span><br><span class="line">            current_id[Name] = (<span class="type">int</span>)last_pos;</span><br><span class="line">            current_id[Hash] = hash;</span><br><span class="line">            token = current_id[Token] = Id;</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        ...</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>查找已有标识符的方法是线性查找 <code>symbols</code> 表。</p><h3 id="数字" tabindex="-1"><a class="header-anchor" href="#数字"><span><a href="about:blank#%E6%95%B0%E5%AD%97"></a>数字</span></a></h3><p>数字中较为复杂的一点是需要支持十进制、十六进制及八进制。逻辑也较为直接，可能唯一不好理解的是获取十六进制的值相关的代码。</p><table><tbody><tr><td class="code"><pre><span class="line">token_val = token_val * 16 + (token &amp; 15) + (token &gt;= &#39;A&#39; ? 9 : 0);</span><br></pre></td></tr></tbody></table><p>这里要注意的是在ASCII码中，字符<code>a</code>对应的十六进制值是 <code>61</code>, <code>A</code>是<code>41</code>，故通过 <code>(token &amp; 15)</code> 可以得到个位数的值。其它就不多说了，这里这样写的目的是装B（其实是抄 c4 的源代码的）。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">next</span><span class="params">()</span> {</span><br><span class="line">        ...</span><br><span class="line"></span><br><span class="line"></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token &gt;= <span class="string">&#39;0&#39;</span> &amp;&amp; token &lt;= <span class="string">&#39;9&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse number, three kinds: dec(123) hex(0x123) oct(017)</span></span><br><span class="line">            token_val = token - <span class="string">&#39;0&#39;</span>;</span><br><span class="line">            <span class="keyword">if</span> (token_val &gt; <span class="number">0</span>) {</span><br><span class="line">                <span class="comment">// dec, starts with [1-9]</span></span><br><span class="line">                <span class="keyword">while</span> (*src &gt;= <span class="string">&#39;0&#39;</span> &amp;&amp; *src &lt;= <span class="string">&#39;9&#39;</span>) {</span><br><span class="line">                    token_val = token_val*<span class="number">10</span> + *src++ - <span class="string">&#39;0&#39;</span>;</span><br><span class="line">                }</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                <span class="comment">// starts with number 0</span></span><br><span class="line">                <span class="keyword">if</span> (*src == <span class="string">&#39;x&#39;</span> || *src == <span class="string">&#39;X&#39;</span>) {</span><br><span class="line">                    <span class="comment">//hex</span></span><br><span class="line">                    token = *++src;</span><br><span class="line">                    <span class="keyword">while</span> ((token &gt;= <span class="string">&#39;0&#39;</span> &amp;&amp; token &lt;= <span class="string">&#39;9&#39;</span>) || (token &gt;= <span class="string">&#39;a&#39;</span> &amp;&amp; token &lt;= <span class="string">&#39;f&#39;</span>) || (token &gt;= <span class="string">&#39;A&#39;</span> &amp;&amp; token &lt;= <span class="string">&#39;F&#39;</span>)) {</span><br><span class="line">                        token_val = token_val * <span class="number">16</span> + (token &amp; <span class="number">15</span>) + (token &gt;= <span class="string">&#39;A&#39;</span> ? <span class="number">9</span> : <span class="number">0</span>);</span><br><span class="line">                        token = *++src;</span><br><span class="line">                    }</span><br><span class="line">                } <span class="keyword">else</span> {</span><br><span class="line">                    <span class="comment">// oct</span></span><br><span class="line">                    <span class="keyword">while</span> (*src &gt;= <span class="string">&#39;0&#39;</span> &amp;&amp; *src &lt;= <span class="string">&#39;7&#39;</span>) {</span><br><span class="line">                        token_val = token_val*<span class="number">8</span> + *src++ - <span class="string">&#39;0&#39;</span>;</span><br><span class="line">                    }</span><br><span class="line">                }</span><br><span class="line">            }</span><br><span class="line"></span><br><span class="line">            token = Num;</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        ...</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="字符串" tabindex="-1"><a class="header-anchor" href="#字符串"><span><a href="about:blank#%E5%AD%97%E7%AC%A6%E4%B8%B2"></a>字符串</span></a></h3><p>在分析时，如果分析到字符串，我们需要将它存放到前一篇文章中说的 <code>data</code> 段中。然后返回它在 <code>data</code> 段中的地址。另一个特殊的地方是我们需要支持转义符。例如用 <code>\n</code> 表示换行符。由于本编译器的目的是达到自己编译自己，所以代码中并没有支持除 <code>\n</code> 的转义符，如 <code>\t</code>, <code>\r</code> 等，但仍支持 <code>\a</code> 表示字符 <code>a</code> 的语法，如 <code>\&quot;</code> 表示 <code>&quot;</code>。</p><p>在分析时，我们将同时分析单个字符如 <code>&#39;a&#39;</code> 和字符串如 <code>&quot;a string&quot;</code>。若得到的是单个字符，我们以 <code>Num</code> 的形式返回。相关代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">next</span><span class="params">()</span> {</span><br><span class="line">        ...</span><br><span class="line"></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;&quot;&#39;</span> || token == <span class="string">&#39;\&#39;&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse string literal, currently, the only supported escape</span></span><br><span class="line">            <span class="comment">// character is &#39;\n&#39;, store the string literal into data.</span></span><br><span class="line">            last_pos = data;</span><br><span class="line">            <span class="keyword">while</span> (*src != <span class="number">0</span> &amp;&amp; *src != token) {</span><br><span class="line">                token_val = *src++;</span><br><span class="line">                <span class="keyword">if</span> (token_val == <span class="string">&#39;\\&#39;</span>) {</span><br><span class="line">                    <span class="comment">// escape character</span></span><br><span class="line">                    token_val = *src++;</span><br><span class="line">                    <span class="keyword">if</span> (token_val == <span class="string">&#39;n&#39;</span>) {</span><br><span class="line">                        token_val = <span class="string">&#39;\n&#39;</span>;</span><br><span class="line">                    }</span><br><span class="line">                }</span><br><span class="line"></span><br><span class="line">                <span class="keyword">if</span> (token == <span class="string">&#39;&quot;&#39;</span>) {</span><br><span class="line">                    *data++ = token_val;</span><br><span class="line">                }</span><br><span class="line">            }</span><br><span class="line"></span><br><span class="line">            src++;</span><br><span class="line">            <span class="comment">// if it is a single character, return Num token</span></span><br><span class="line">            <span class="keyword">if</span> (token == <span class="string">&#39;&quot;&#39;</span>) {</span><br><span class="line">                token_val = (<span class="type">int</span>)last_pos;</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                token = Num;</span><br><span class="line">            }</span><br><span class="line"></span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="注释" tabindex="-1"><a class="header-anchor" href="#注释"><span><a href="about:blank#%E6%B3%A8%E9%87%8A"></a>注释</span></a></h3><p>在我们的 C 语言中，只支持 <code>//</code> 类型的注释，不支持 <code>/* comments */</code> 的注释。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">next</span><span class="params">()</span> {</span><br><span class="line">        ...</span><br><span class="line"></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;/&#39;</span>) {</span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;/&#39;</span>) {</span><br><span class="line">                <span class="comment">// skip comments</span></span><br><span class="line">                <span class="keyword">while</span> (*src != <span class="number">0</span> &amp;&amp; *src != <span class="string">&#39;\n&#39;</span>) {</span><br><span class="line">                    ++src;</span><br><span class="line">                }</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                <span class="comment">// divide operator</span></span><br><span class="line">                token = Div;</span><br><span class="line">                <span class="keyword">return</span>;</span><br><span class="line">            }</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        ...</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>这里我们要额外介绍 <code>lookahead</code> 的概念，即提前看多个字符。上述代码中我们看到，除了跳过注释，我们还可能返回除号 <code>/(Div)</code> 标记。</p><p>提前看字符的原理是：有一个或多个标记是以同样的字符开头的（如本小节中的注释与除号），因此只凭当前的字符我们并无法确定具体应该解释成哪一个标记，所以只能再向前查看字符，如本例需向前查看一个字符，若是 <code>/</code> 则说明是注释，反之则是除号。</p><p>我们之前说过，词法分析器本质上也是编译器，其实提前看字符的概念也存在于编译器，只是这时就是提前看k个“标记”而不是“字符”了。平时听到的 <code>LL(k)</code> 中的 <code>k</code> 就是需要向前看的标记的个数了。</p><p>另外，我们用词法分析器将源码转换成标记流，能减小语法分析复杂度，原因之一就是减少了语法分析器需要“向前看”的字符个数。</p><h3 id="其它" tabindex="-1"><a class="header-anchor" href="#其它"><span><a href="about:blank#%E5%85%B6%E5%AE%83"></a>其它</span></a></h3><p>其它的标记的解析就相对容易一些了，我们直接贴上代码：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">next</span><span class="params">()</span> {</span><br><span class="line">        ...</span><br><span class="line"></span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;=&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse &#39;==&#39; and &#39;=&#39;</span></span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;=&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Eq;</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                token = Assign;</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;+&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse &#39;+&#39; and &#39;++&#39;</span></span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;+&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Inc;</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                token = Add;</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;-&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse &#39;-&#39; and &#39;--&#39;</span></span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;-&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Dec;</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                token = Sub;</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;!&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse &#39;!=&#39;</span></span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;=&#39;</span>) {</span><br><span class="line">                src++;</span><br><span class="line">                token = Ne;</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;&lt;&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse &#39;&lt;=&#39;, &#39;&lt;&lt;&#39; or &#39;&lt;&#39;</span></span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;=&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Le;</span><br><span class="line">            } <span class="keyword">else</span> <span class="keyword">if</span> (*src == <span class="string">&#39;&lt;&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Shl;</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                token = Lt;</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;&gt;&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse &#39;&gt;=&#39;, &#39;&gt;&gt;&#39; or &#39;&gt;&#39;</span></span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;=&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Ge;</span><br><span class="line">            } <span class="keyword">else</span> <span class="keyword">if</span> (*src == <span class="string">&#39;&gt;&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Shr;</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                token = Gt;</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;|&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse &#39;|&#39; or &#39;||&#39;</span></span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;|&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Lor;</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                token = Or;</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;&amp;&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse &#39;&amp;&#39; and &#39;&amp;&amp;&#39;</span></span><br><span class="line">            <span class="keyword">if</span> (*src == <span class="string">&#39;&amp;&#39;</span>) {</span><br><span class="line">                src ++;</span><br><span class="line">                token = Lan;</span><br><span class="line">            } <span class="keyword">else</span> {</span><br><span class="line">                token = And;</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;^&#39;</span>) {</span><br><span class="line">            token = Xor;</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;%&#39;</span>) {</span><br><span class="line">            token = Mod;</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;*&#39;</span>) {</span><br><span class="line">            token = Mul;</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;[&#39;</span>) {</span><br><span class="line">            token = Brak;</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;?&#39;</span>) {</span><br><span class="line">            token = Cond;</span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;~&#39;</span> || token == <span class="string">&#39;;&#39;</span> || token == <span class="string">&#39;{&#39;</span> || token == <span class="string">&#39;}&#39;</span> || token == <span class="string">&#39;(&#39;</span> || token == <span class="string">&#39;)&#39;</span> || token == <span class="string">&#39;]&#39;</span> || token == <span class="string">&#39;,&#39;</span> || token == <span class="string">&#39;:&#39;</span>) {</span><br><span class="line">            <span class="comment">// directly return the character as token;</span></span><br><span class="line">            <span class="keyword">return</span>;</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        ...</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>代码较多，但主要逻辑就是向前看一个字符来确定真正的标记。</p><h3 id="关键字与内置函数" tabindex="-1"><a class="header-anchor" href="#关键字与内置函数"><span><a href="about:blank#%E5%85%B3%E9%94%AE%E5%AD%97%E4%B8%8E%E5%86%85%E7%BD%AE%E5%87%BD%E6%95%B0"></a>关键字与内置函数</span></a></h3><p>虽然上面写完了词法分析器，但还有一个问题需要考虑，那就是“关键字”，例如 <code>if</code>, <code>while</code>, <code>return</code> 等。它们不能被作为普通的标识符，因为有特殊的含义。</p><p>一般有两种处理方法：</p><ol><li>词法分析器中直接解析这些关键字。</li><li>在语法分析前将关键字提前加入符号表。</li></ol><p>这里我们就采用第二种方法，将它们加入符号表，并提前为它们赋予必要的信息（还记得前面说的标识符 <code>Token</code> 字段吗？）。这样当源代码中出现关键字时，它们会被解析成标识符，但由于符号表中已经有了相关的信息，我们就能知道它们是特殊的关键字。</p><p>内置函数的行为也和关键字类似，不同的只是赋值的信息，在<code>main</code>函数中进行初始化如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="comment">// types of variable/function</span></span><br><span class="line"><span class="class"><span class="keyword">enum</span> {</span> CHAR, INT, PTR };</span><br><span class="line"><span class="type">int</span> *idmain;                  <span class="comment">// the `main` function</span></span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">main</span><span class="params">()</span> {</span><br><span class="line">    ...</span><br><span class="line"></span><br><span class="line">    src = <span class="string">&quot;char else enum if int return sizeof while &quot;</span></span><br><span class="line">          <span class="string">&quot;open read close printf malloc memset memcmp exit void main&quot;</span>;</span><br><span class="line"></span><br><span class="line">     <span class="comment">// add keywords to symbol table</span></span><br><span class="line">    i = Char;</span><br><span class="line">    <span class="keyword">while</span> (i &lt;= While) {</span><br><span class="line">        next();</span><br><span class="line">        current_id[Token] = i++;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="comment">// add library to symbol table</span></span><br><span class="line">    i = OPEN;</span><br><span class="line">    <span class="keyword">while</span> (i &lt;= EXIT) {</span><br><span class="line">        next();</span><br><span class="line">        current_id[Class] = Sys;</span><br><span class="line">        current_id[Type] = INT;</span><br><span class="line">        current_id[Value] = i++;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    next(); current_id[Token] = Char; <span class="comment">// handle void type</span></span><br><span class="line">    next(); idmain = current_id; <span class="comment">// keep track of main</span></span><br><span class="line"></span><br><span class="line">    ...</span><br><span class="line">    program();</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h2 id="代码" tabindex="-1"><a class="header-anchor" href="#代码"><span><a href="about:blank#%E4%BB%A3%E7%A0%81"></a>代码</span></a></h2><p>本章的代码可以在 <a href="https://github.com/lotabout/write-a-C-interpreter/tree/step-2" target="_blank" rel="noopener noreferrer">Github<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a> 上下载，也可以直接 clone</p><table><tbody><tr><td class="code"><pre><span class="line">git clone -b step-2 https://github.com/lotabout/write-a-C-interpreter</span><br></pre></td></tr></tbody></table><p>上面的代码运行后会出现 ‘Segmentation Falt’，这是正常的，因为它会尝试运行我们上一章创建的虚拟机，但其中并没有任何汇编代码。</p><h2 id="小结" tabindex="-1"><a class="header-anchor" href="#小结"><span><a href="about:blank#%E5%B0%8F%E7%BB%93"></a>小结</span></a></h2><p>本章我们为我们的编译器构建了词法分析器，通过本章的学习，我认为有几个要点需要强调：</p><ol><li>词法分析器的作用是对源码字符串进行预处理，作用是减小语法分析器的复杂程度。</li><li>词法分析器本身可以认为是一个编译器，输入是源码，输出是标记流。</li><li><code>lookahead(k)</code> 的概念，即向前看 <code>k</code> 个字符或标记。</li><li>词法分析中如何处理标识符与符号表。</li></ol><p>下一章中，我们将介绍递归下降的语法分析器。我们下一章见。</p></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/designASimpileCCompiler/3.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/designASimpileCCompiler/1.html" aria-label="手把手教你构建 C 语言编译器（1）- 设计"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->手把手教你构建 C 语言编译器（1）- 设计</div></a><a class="route-link nav-link next" href="/tech/designASimpileCCompiler/4.html" aria-label="手把手教你构建 C 语言编译器（4）——递归下降"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">手把手教你构建 C 语言编译器（4）——递归下降<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/designASimpileCCompiler/4.html b/tech/designASimpileCCompiler/4.html
index a8409b7..b363fc7 100644
--- a/tech/designASimpileCCompiler/4.html
+++ b/tech/designASimpileCCompiler/4.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/designASimpileCCompiler/4.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="手把手教你构建 C 语言编译器（4）——递归下降"><meta property="og:description" content="[] 转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-4/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（4）- 递归下降 Table of Contents 1. 什么是递归下降 2. 终结符与非终结符 3. 四则运算的递归下降 4. 为什么选择递归下降 5. 左递..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="c"><meta property="article:tag" content="编译器"><meta property="article:tag" content="解释器"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"手把手教你构建 C 语言编译器（4）——递归下降","image":[""],"dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>手把手教你构建 C 语言编译器（4）——递归下降 | blog</title><meta name="description" content="[] 转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-4/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（4）- 递归下降 Table of Contents 1. 什么是递归下降 2. 终结符与非终结符 3. 四则运算的递归下降 4. 为什么选择递归下降 5. 左递...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/4.html-C8TuLMaF.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/4.html-DavKkBaH.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/0.html" aria-label="手把手教你构建 C 语言编译器（0）- 前言"><!---->手把手教你构建 C 语言编译器（0）- 前言<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/1.html" aria-label="手把手教你构建 C 语言编译器（1）- 设计"><!---->手把手教你构建 C 语言编译器（1）- 设计<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/3.html" aria-label="手把手教你构建 C 语言编译器（3）——词法分析器"><!---->手把手教你构建 C 语言编译器（3）——词法分析器<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/designASimpileCCompiler/4.html" aria-label="手把手教你构建 C 语言编译器（4）——递归下降"><!---->手把手教你构建 C 语言编译器（4）——递归下降<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/5.html" aria-label="手把手教你构建 C 语言编译器（5）——变量定义"><!---->手把手教你构建 C 语言编译器（5）——变量定义<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/6.html" aria-label="手把手教你构建 C 语言编译器（6）——函数定义"><!---->手把手教你构建 C 语言编译器（6）——函数定义<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/7.html" aria-label="手把手教你构建 C 语言编译器（7）——语句"><!---->手把手教你构建 C 语言编译器（7）——语句<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/8.html" aria-label="手把手教你构建 C 语言编译器（8）——表达式"><!---->手把手教你构建 C 语言编译器（8）——表达式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/9.html" aria-label="手把手教你构建 C 语言编译器（9）——总结"><!---->手把手教你构建 C 语言编译器（9）——总结<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/2.html" aria-label="转载声明"><!---->转载声明<!----></a></li></ul></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->手把手教你构建 C 语言编译器（4）——递归下降</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 11 分钟</span><meta property="timeRequired" content="PT11M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category2 clickable" role="navigation">编译原理</span><!--]--><meta property="articleSection" content="编译原理"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag4 clickable" role="navigation">c</span><span class="page-tag-item tag4 clickable" role="navigation">编译器</span><span class="page-tag-item tag4 clickable" role="navigation">解释器</span><!--]--><meta property="keywords" content="c,编译器,解释器"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#什么是递归下降">什么是递归下降</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#终结符与非终结符">终结符与非终结符</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#四则运算的递归下降">四则运算的递归下降</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#为什么选择递归下降">为什么选择递归下降</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#左递归">左递归</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#四则运算的实现">四则运算的实现</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#小结">小结</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><p>[]</p><h1 id="转载声明" tabindex="-1"><a class="header-anchor" href="#转载声明"><span>转载声明</span></a></h1><p>本文转自 <a href="https://lotabout.me/2016/write-a-C-interpreter-4/" target="_blank" rel="noopener noreferrer">https://lotabout.me/2016/write-a-C-interpreter-4/<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a>，如有侵权，请联系删除。</p><h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-4-递归下降" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-4-递归下降"><span>手把手教你构建 C 语言编译器（4）- 递归下降</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#%E4%BB%80%E4%B9%88%E6%98%AF%E9%80%92%E5%BD%92%E4%B8%8B%E9%99%8D">1. 什么是递归下降</a></li><li><a href="about:blank#%E7%BB%88%E7%BB%93%E7%AC%A6%E4%B8%8E%E9%9D%9E%E7%BB%88%E7%BB%93%E7%AC%A6">2. 终结符与非终结符</a></li><li><a href="about:blank#%E5%9B%9B%E5%88%99%E8%BF%90%E7%AE%97%E7%9A%84%E9%80%92%E5%BD%92%E4%B8%8B%E9%99%8D">3. 四则运算的递归下降</a></li><li><a href="about:blank#%E4%B8%BA%E4%BB%80%E4%B9%88%E9%80%89%E6%8B%A9%E9%80%92%E5%BD%92%E4%B8%8B%E9%99%8D">4. 为什么选择递归下降</a></li><li><a href="about:blank#%E5%B7%A6%E9%80%92%E5%BD%92">5. 左递归</a></li><li><a href="about:blank#%E5%9B%9B%E5%88%99%E8%BF%90%E7%AE%97%E7%9A%84%E5%AE%9E%E7%8E%B0">6. 四则运算的实现</a></li><li><a href="about:blank#%E5%B0%8F%E7%BB%93">7. 小结</a></li></ol><p>本章我们将讲解递归下降的方法，并用它完成一个基本的四则运算的语法分析器。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p><ol><li><a href="http://lotabout.me/2015/write-a-C-interpreter-0/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（0）——前言<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-1/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（1）——设计<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-2/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（2）——虚拟机<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-3/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（3）——词法分析器<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-4/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（4）——递归下降<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-5/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（5）——变量定义<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-6/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（6）——函数定义<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-7/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（7）——语句<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-8/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（8）——表达式<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-9/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（9）——总结<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li></ol><h2 id="什么是递归下降" tabindex="-1"><a class="header-anchor" href="#什么是递归下降"><span><a href="about:blank#%E4%BB%80%E4%B9%88%E6%98%AF%E9%80%92%E5%BD%92%E4%B8%8B%E9%99%8D"></a>什么是递归下降</span></a></h2><p>传统上，编写语法分析器有两种方法，一种是自顶向下，一种是自底向上。自顶向下是从起始非终结符开始，不断地对非终结符进行分解，直到匹配输入的终结符；自底向上是不断地将终结符进行合并，直到合并成起始的非终结符。</p><p>其中的自顶向下方法就是我们所说的递归下降。</p><h2 id="终结符与非终结符" tabindex="-1"><a class="header-anchor" href="#终结符与非终结符"><span><a href="about:blank#%E7%BB%88%E7%BB%93%E7%AC%A6%E4%B8%8E%E9%9D%9E%E7%BB%88%E7%BB%93%E7%AC%A6"></a>终结符与非终结符</span></a></h2><p>没有学过编译原理的话可能并不知道什么是“终结符”，“非终结符”。这里我简单介绍一下。首先是 <a href="https://zh.wikipedia.org/wiki/%E5%B7%B4%E7%A7%91%E6%96%AF%E8%8C%83%E5%BC%8F" target="_blank" rel="noopener noreferrer">BNF<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a> 范式，就是一种用来描述语法的语言，例如，四则运算的规则可以表示如下：</p><table><tbody><tr><td class="code"><pre><span class="line">&lt;expr&gt; ::= &lt;expr&gt; + &lt;term&gt;</span><br><span class="line">         | &lt;expr&gt; - &lt;term&gt;</span><br><span class="line">         | &lt;term&gt;</span><br><span class="line"></span><br><span class="line">&lt;term&gt; ::= &lt;term&gt; * &lt;factor&gt;</span><br><span class="line">         | &lt;term&gt; / &lt;factor&gt;</span><br><span class="line">         | &lt;factor&gt;</span><br><span class="line"></span><br><span class="line">&lt;factor&gt; ::= ( &lt;expr&gt; )</span><br><span class="line">           | Num</span><br></pre></td></tr></tbody></table><p>用尖括号 <code>&lt;&gt;</code> 括起来的就称作 <strong>非终结符</strong> ，因为它们可以用 <code>::=</code> 右侧的式子代替。<code>|</code> 表示选择，如 <code>&lt;expr&gt;</code> 可以是 <code>&lt;expr&gt; + &lt;term&gt;</code>、<code>&lt;expr&gt; - &lt;term&gt;</code>或 <code>&lt;term&gt;</code> 中的一种。而没有出现在<code>::=</code>左边的就称作 <strong>终结符</strong> ，一般终结符对应于词法分析器输出的标记。</p><h2 id="四则运算的递归下降" tabindex="-1"><a class="header-anchor" href="#四则运算的递归下降"><span><a href="about:blank#%E5%9B%9B%E5%88%99%E8%BF%90%E7%AE%97%E7%9A%84%E9%80%92%E5%BD%92%E4%B8%8B%E9%99%8D"></a>四则运算的递归下降</span></a></h2><p>例如，我们对 <code>3 * (4 + 2)</code> 进行语法分析。我们假设词法分析器已经正确地将其中的数字识别成了标记 <code>Num</code>。</p><p>递归下降是从起始的非终结符开始（顶），本例中是 <code>&lt;expr&gt;</code>，实际中可以自己指定，不指定的话一般认为是第一个出现的非终结符。</p><table><tbody><tr><td class="code"><pre><span class="line">1. &lt;expr&gt; =&gt; &lt;expr&gt;</span><br><span class="line">2.           =&gt; &lt;term&gt;        * &lt;factor&gt;</span><br><span class="line">3.              =&gt; &lt;factor&gt;     |</span><br><span class="line">4.                 =&gt; Num (3)   |</span><br><span class="line">5.                              =&gt; ( &lt;expr&gt; )</span><br><span class="line">6.                                   =&gt; &lt;expr&gt;           + &lt;term&gt;</span><br><span class="line">7.                                      =&gt; &lt;term&gt;          |</span><br><span class="line">8.                                         =&gt; &lt;factor&gt;     |</span><br><span class="line">9.                                            =&gt; Num (4)   |</span><br><span class="line">10.                                                        =&gt; &lt;factor&gt;</span><br><span class="line">11.                                                           =&gt; Num (2)</span><br></pre></td></tr></tbody></table><p>可以看到，整个解析的过程是在不断对非终结符进行替换（向下），直到遇见了终结符（底）。而我们可以从解析的过程中看出，一些非终结符如<code>&lt;expr&gt;</code>被递归地使用了。</p><h2 id="为什么选择递归下降" tabindex="-1"><a class="header-anchor" href="#为什么选择递归下降"><span><a href="about:blank#%E4%B8%BA%E4%BB%80%E4%B9%88%E9%80%89%E6%8B%A9%E9%80%92%E5%BD%92%E4%B8%8B%E9%99%8D"></a>为什么选择递归下降</span></a></h2><p>从上小节对四则运算的递归下降解析可以看出，整个解析的过程和语法的 BNF 表示是十分接近的，更为重要的是，我们可以很容易地直接将 BNF 表示转换成实际的代码。方法是为每个产生式（即 <code>非终结符 ::= ...</code>）生成一个同名的函数。</p><p>这里会有一个疑问，就是上例中，当一个终结符有多个选择时，如何确定具体选择哪一个？如为什么用 <code>&lt;expr&gt; ::= &lt;term&gt; * &lt;factor&gt;</code> 而不是 <code>&lt;expr&gt; ::= &lt;term&gt; / &lt;factor&gt;</code> ？这就用到了上一章中提到的“向前看 k 个标记”的概念了。我们向前看一个标记，发现是 <code>*</code>，而这个标记足够让我们确定用哪个表达式了。</p><p>另外，递归下下降方法对 BNF 方法本身有一定的要求，否则会有一些问题，如经典的“左递归”问题。</p><h2 id="左递归" tabindex="-1"><a class="header-anchor" href="#左递归"><span><a href="about:blank#%E5%B7%A6%E9%80%92%E5%BD%92"></a>左递归</span></a></h2><p>原则上我们是不讲这么深入，但我们上面的四则运算的文法就是左递归的，而左递归的语法是没法直接使用递归下降的方法实现的。因此我们要消除左递归，消除后的文法如下：</p><table><tbody><tr><td class="code"><pre><span class="line">&lt;expr&gt; ::= &lt;term&gt; &lt;expr_tail&gt;</span><br><span class="line">&lt;expr_tail&gt; ::= + &lt;term&gt; &lt;expr_tail&gt;</span><br><span class="line">              | - &lt;term&gt; &lt;expr_tail&gt;</span><br><span class="line">              | &lt;empty&gt;</span><br><span class="line"></span><br><span class="line">&lt;term&gt; ::= &lt;factor&gt; &lt;term_tail&gt;</span><br><span class="line">&lt;term_tail&gt; ::= * &lt;factor&gt; &lt;term_tail&gt;</span><br><span class="line">              | / &lt;factor&gt; &lt;term_tail&gt;</span><br><span class="line">              | &lt;empty&gt;</span><br><span class="line"></span><br><span class="line">&lt;factor&gt; ::= ( &lt;expr&gt; )</span><br><span class="line">           | Num</span><br></pre></td></tr></tbody></table><p>消除左递归的相关方法，这里不再多说，请自行查阅相关的资料。</p><h2 id="四则运算的实现" tabindex="-1"><a class="header-anchor" href="#四则运算的实现"><span><a href="about:blank#%E5%9B%9B%E5%88%99%E8%BF%90%E7%AE%97%E7%9A%84%E5%AE%9E%E7%8E%B0"></a>四则运算的实现</span></a></h2><p>本节中我们专注语法分析器部分的实现，具体实现很容易，我们直接贴上代码，就是上述的消除左递归后的文法直接转换而来的：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> <span class="title function_">expr</span><span class="params">()</span>;</span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">factor</span><span class="params">()</span> {</span><br><span class="line">    <span class="type">int</span> value = <span class="number">0</span>;</span><br><span class="line">    <span class="keyword">if</span> (token == <span class="string">&#39;(&#39;</span>) {</span><br><span class="line">        match(<span class="string">&#39;(&#39;</span>);</span><br><span class="line">        value = expr();</span><br><span class="line">        match(<span class="string">&#39;)&#39;</span>);</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        value = token_val;</span><br><span class="line">        match(Num);</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">return</span> value;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">term_tail</span><span class="params">(<span class="type">int</span> lvalue)</span> {</span><br><span class="line">    <span class="keyword">if</span> (token == <span class="string">&#39;*&#39;</span>) {</span><br><span class="line">        match(<span class="string">&#39;*&#39;</span>);</span><br><span class="line">        <span class="type">int</span> value = lvalue * factor();</span><br><span class="line">        <span class="keyword">return</span> term_tail(value);</span><br><span class="line">    } <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;/&#39;</span>) {</span><br><span class="line">        match(<span class="string">&#39;/&#39;</span>);</span><br><span class="line">        <span class="type">int</span> value = lvalue / factor();</span><br><span class="line">        <span class="keyword">return</span> term_tail(value);</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="keyword">return</span> lvalue;</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">term</span><span class="params">()</span> {</span><br><span class="line">    <span class="type">int</span> lvalue = factor();</span><br><span class="line">    <span class="keyword">return</span> term_tail(lvalue);</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">expr_tail</span><span class="params">(<span class="type">int</span> lvalue)</span> {</span><br><span class="line">    <span class="keyword">if</span> (token == <span class="string">&#39;+&#39;</span>) {</span><br><span class="line">        match(<span class="string">&#39;+&#39;</span>);</span><br><span class="line">        <span class="type">int</span> value = lvalue + term();</span><br><span class="line">        <span class="keyword">return</span> expr_tail(value);</span><br><span class="line">    } <span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;-&#39;</span>) {</span><br><span class="line">        match(<span class="string">&#39;-&#39;</span>);</span><br><span class="line">        <span class="type">int</span> value = lvalue - term();</span><br><span class="line">        <span class="keyword">return</span> expr_tail(value);</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="keyword">return</span> lvalue;</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">expr</span><span class="params">()</span> {</span><br><span class="line">    <span class="type">int</span> lvalue = term();</span><br><span class="line">    <span class="keyword">return</span> expr_tail(lvalue);</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>可以看到，有了BNF方法后，采用递归向下的方法来实现编译器是很直观的。</p><p>我们把词法分析器的代码一并贴上：</p><table><tbody><tr><td class="code"><pre><span class="line">#<span class="meta">#<span class="keyword">include</span> <span class="string">&lt;stdio.h&gt;</span></span></span><br><span class="line">#<span class="meta">#<span class="keyword">include</span> <span class="string">&lt;stdlib.h&gt;</span></span></span><br><span class="line"></span><br><span class="line"><span class="class"><span class="keyword">enum</span> {</span>Num};</span><br><span class="line"><span class="type">int</span> token;</span><br><span class="line"><span class="type">int</span> token_val;</span><br><span class="line"><span class="type">char</span> *line = <span class="literal">NULL</span>;</span><br><span class="line"><span class="type">char</span> *src = <span class="literal">NULL</span>;</span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">next</span><span class="params">()</span> {</span><br><span class="line">    <span class="comment">// skip white space</span></span><br><span class="line">    <span class="keyword">while</span> (*src == <span class="string">&#39; &#39;</span> || *src == <span class="string">&#39;\t&#39;</span>) {</span><br><span class="line">        src ++;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    token = *src++;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (token &gt;= <span class="string">&#39;0&#39;</span> &amp;&amp; token &lt;= <span class="string">&#39;9&#39;</span> ) {</span><br><span class="line">        token_val = token - <span class="string">&#39;0&#39;</span>;</span><br><span class="line">        token = Num;</span><br><span class="line"></span><br><span class="line">        <span class="keyword">while</span> (*src &gt;= <span class="string">&#39;0&#39;</span> &amp;&amp; *src &lt;= <span class="string">&#39;9&#39;</span>) {</span><br><span class="line">            token_val = token_val*<span class="number">10</span> + *src - <span class="string">&#39;0&#39;</span>;</span><br><span class="line">            src ++;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">return</span>;</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">match</span><span class="params">(<span class="type">int</span> tk)</span> {</span><br><span class="line">    <span class="keyword">if</span> (token != tk) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;expected token: %d(%c), got: %d(%c)\n&quot;</span>, tk, tk, token, token);</span><br><span class="line">        <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line">    next();</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>最后是<code>main</code>函数：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> <span class="title function_">main</span><span class="params">(<span class="type">int</span> argc, <span class="type">char</span> *argv[])</span></span><br><span class="line">{</span><br><span class="line">    <span class="type">size_t</span> linecap = <span class="number">0</span>;</span><br><span class="line">    <span class="type">ssize_t</span> linelen;</span><br><span class="line">    <span class="keyword">while</span> ((linelen = getline(&amp;line, &amp;linecap, <span class="built_in">stdin</span>)) &gt; <span class="number">0</span>) {</span><br><span class="line">        src = line;</span><br><span class="line">        next();</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%d\n&quot;</span>, expr());</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h2 id="小结" tabindex="-1"><a class="header-anchor" href="#小结"><span><a href="about:blank#%E5%B0%8F%E7%BB%93"></a>小结</span></a></h2><p>本章中我们介绍了递归下降的方法，并用它来实现了四则运算的语法分析器。</p><p>花这么大精力讲解递归下降方法，是因为几乎所有手工编写的语法分析器都或多或少地有它的影子。换句话说，掌握了递归下降的方法，就可以应付大多数的语法分析器编写。</p><p>同时我们也用实例看到了理论（BNF 语法，左递归的消除）是如何帮助我们的工程实现的。尽管理论不是必需的，但如果能掌握它，对于提高我们的水平还是很有帮助的。</p></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/designASimpileCCompiler/4.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/designASimpileCCompiler/3.html" aria-label="手把手教你构建 C 语言编译器（3）——词法分析器"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->手把手教你构建 C 语言编译器（3）——词法分析器</div></a><a class="route-link nav-link next" href="/tech/designASimpileCCompiler/5.html" aria-label="手把手教你构建 C 语言编译器（5）——变量定义"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">手把手教你构建 C 语言编译器（5）——变量定义<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/designASimpileCCompiler/5.html b/tech/designASimpileCCompiler/5.html
index 509e89d..3e8374b 100644
--- a/tech/designASimpileCCompiler/5.html
+++ b/tech/designASimpileCCompiler/5.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/designASimpileCCompiler/5.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="手把手教你构建 C 语言编译器（5）——变量定义"><meta property="og:description" content="转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-5/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（5）- 变量定义 Table of Contents 1. EBNF 表示 2. 解析变量的定义 2.1. program() 2.2. global_declarat..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="c"><meta property="article:tag" content="编译器"><meta property="article:tag" content="解释器"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"手把手教你构建 C 语言编译器（5）——变量定义","image":[""],"dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>手把手教你构建 C 语言编译器（5）——变量定义 | blog</title><meta name="description" content="转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-5/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（5）- 变量定义 Table of Contents 1. EBNF 表示 2. 解析变量的定义 2.1. program() 2.2. global_declarat...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/5.html-qLlLbRlw.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/5.html-DpkUOZDe.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/0.html" aria-label="手把手教你构建 C 语言编译器（0）- 前言"><!---->手把手教你构建 C 语言编译器（0）- 前言<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/1.html" aria-label="手把手教你构建 C 语言编译器（1）- 设计"><!---->手把手教你构建 C 语言编译器（1）- 设计<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/3.html" aria-label="手把手教你构建 C 语言编译器（3）——词法分析器"><!---->手把手教你构建 C 语言编译器（3）——词法分析器<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/4.html" aria-label="手把手教你构建 C 语言编译器（4）——递归下降"><!---->手把手教你构建 C 语言编译器（4）——递归下降<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/designASimpileCCompiler/5.html" aria-label="手把手教你构建 C 语言编译器（5）——变量定义"><!---->手把手教你构建 C 语言编译器（5）——变量定义<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/6.html" aria-label="手把手教你构建 C 语言编译器（6）——函数定义"><!---->手把手教你构建 C 语言编译器（6）——函数定义<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/7.html" aria-label="手把手教你构建 C 语言编译器（7）——语句"><!---->手把手教你构建 C 语言编译器（7）——语句<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/8.html" aria-label="手把手教你构建 C 语言编译器（8）——表达式"><!---->手把手教你构建 C 语言编译器（8）——表达式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/9.html" aria-label="手把手教你构建 C 语言编译器（9）——总结"><!---->手把手教你构建 C 语言编译器（9）——总结<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/2.html" aria-label="转载声明"><!---->转载声明<!----></a></li></ul></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->手把手教你构建 C 语言编译器（5）——变量定义</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 11 分钟</span><meta property="timeRequired" content="PT11M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category2 clickable" role="navigation">编译原理</span><!--]--><meta property="articleSection" content="编译原理"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag4 clickable" role="navigation">c</span><span class="page-tag-item tag4 clickable" role="navigation">编译器</span><span class="page-tag-item tag4 clickable" role="navigation">解释器</span><!--]--><meta property="keywords" content="c,编译器,解释器"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#ebnf-表示">EBNF 表示</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#解析变量的定义">解析变量的定义</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#program">program()</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#global-declaration">global_declaration()</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#enum-declaration">enum_declaration()</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#其它">其它</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#代码">代码</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#小结">小结</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="转载声明" tabindex="-1"><a class="header-anchor" href="#转载声明"><span>转载声明</span></a></h1><p>本文转自 <a href="https://lotabout.me/2016/write-a-C-interpreter-5/" target="_blank" rel="noopener noreferrer">https://lotabout.me/2016/write-a-C-interpreter-5/<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a>，如有侵权，请联系删除。</p><h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-5-变量定义" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-5-变量定义"><span>手把手教你构建 C 语言编译器（5）- 变量定义</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#ebnf-%E8%A1%A8%E7%A4%BA">1. EBNF 表示</a></li><li><a href="about:blank#%E8%A7%A3%E6%9E%90%E5%8F%98%E9%87%8F%E7%9A%84%E5%AE%9A%E4%B9%89">2. 解析变量的定义</a><ol><li><a href="about:blank#program">2.1. program()</a></li><li><a href="about:blank#global-declaration">2.2. global_declaration()</a></li><li><a href="about:blank#enum-declaration">2.3. enum_declaration()</a></li><li><a href="about:blank#%E5%85%B6%E5%AE%83">2.4. 其它</a></li></ol></li><li><a href="about:blank#%E4%BB%A3%E7%A0%81">3. 代码</a></li><li><a href="about:blank#%E5%B0%8F%E7%BB%93">4. 小结</a></li></ol><p>本章中我们用 EBNF 来大致描述我们实现的 C 语言的文法，并实现其中解析变量定义部分。</p><p>由于语法分析本身比较复杂，所以我们将它拆分成 3 个部分进行讲解，分别是：变量定义、函数定义、表达式。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p><ol><li><a href="http://lotabout.me/2015/write-a-C-interpreter-0/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（0）——前言<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-1/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（1）——设计<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-2/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（2）——虚拟机<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-3/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（3）——词法分析器<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-4/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（4）——递归下降<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-5/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（5）——变量定义<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-6/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（6）——函数定义<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-7/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（7）——语句<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-8/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（8）——表达式<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-9/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（9）——总结<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li></ol><h2 id="ebnf-表示" tabindex="-1"><a class="header-anchor" href="#ebnf-表示"><span><a href="about:blank#ebnf-%E8%A1%A8%E7%A4%BA"></a>EBNF 表示</span></a></h2><p>EBNF 是对前一章提到的 BNF 的扩展，它的语法更容易理解，实现起来也更直观。但真正看起来还是很烦，如果不想看可以跳过。</p><table><tbody><tr><td class="code"><pre><span class="line">program ::= {global_declaration}+</span><br><span class="line"></span><br><span class="line">global_declaration ::= enum_decl | variable_decl | function_decl</span><br><span class="line"></span><br><span class="line">enum_decl ::= &#39;enum&#39; [id] &#39;{&#39; id [&#39;=&#39; &#39;num&#39;] {&#39;,&#39; id [&#39;=&#39; &#39;num&#39;] &#39;}&#39;</span><br><span class="line"></span><br><span class="line">variable_decl ::= type {&#39;*&#39;} id { &#39;,&#39; {&#39;*&#39;} id } &#39;;&#39;</span><br><span class="line"></span><br><span class="line">function_decl ::= type {&#39;*&#39;} id &#39;(&#39; parameter_decl &#39;)&#39; &#39;{&#39; body_decl &#39;}&#39;</span><br><span class="line"></span><br><span class="line">parameter_decl ::= type {&#39;*&#39;} id {&#39;,&#39; type {&#39;*&#39;} id}</span><br><span class="line"></span><br><span class="line">body_decl ::= {variable_decl}, {statement}</span><br><span class="line"></span><br><span class="line">statement ::= non_empty_statement | empty_statement</span><br><span class="line"></span><br><span class="line">non_empty_statement ::= if_statement | while_statement | &#39;{&#39; statement &#39;}&#39;</span><br><span class="line">                     | &#39;return&#39; expression | expression &#39;;&#39;</span><br><span class="line"></span><br><span class="line">if_statement ::= &#39;if&#39; &#39;(&#39; expression &#39;)&#39; statement [&#39;else&#39; non_empty_statement]</span><br><span class="line"></span><br><span class="line">while_statement ::= &#39;while&#39; &#39;(&#39; expression &#39;)&#39; non_empty_statement</span><br></pre></td></tr></tbody></table><p>其中 <code>expression</code> 相关的内容我们放到后面解释，主要原因是我们的语言不支持跨函数递归，而为了实现自举，实际上我们也不能使用递归（亏我们说了一章的递归下降）。</p><p>P.S. 我是先写程序再总结上面的文法，所以实际上它们间的对应关系并不是特别明显。</p><h2 id="解析变量的定义" tabindex="-1"><a class="header-anchor" href="#解析变量的定义"><span><a href="about:blank#%E8%A7%A3%E6%9E%90%E5%8F%98%E9%87%8F%E7%9A%84%E5%AE%9A%E4%B9%89"></a>解析变量的定义</span></a></h2><p>本章要讲解的就是上节文法中的 <code>enum_decl</code> 和 <code>variable_decl</code> 部分。</p><h3 id="program" tabindex="-1"><a class="header-anchor" href="#program"><span><a href="about:blank#program"></a>program()</span></a></h3><p>首先是之前定义过的 <code>program</code> 函数，将它改成：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">program</span><span class="params">()</span> {</span><br><span class="line">    <span class="comment">// get next token</span></span><br><span class="line">    next();</span><br><span class="line">    <span class="keyword">while</span> (token &gt; <span class="number">0</span>) {</span><br><span class="line">        global_declaration();</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>我知道 <code>global_declaration</code> 函数还没有出现过，但没有关系，采用自顶向下的编写方法就是要不断地实现我们需要的内容。下面是 <code>global_declaration</code> 函数的内容：</p><h3 id="global-declaration" tabindex="-1"><a class="header-anchor" href="#global-declaration"><span><a href="about:blank#global-declaration"></a>global_declaration()</span></a></h3><p>即全局的定义语句，包括变量定义，类型定义（只支持枚举）及函数定义。代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> basetype;    <span class="comment">// the type of a declaration, make it global for convenience</span></span><br><span class="line"><span class="type">int</span> expr_type;   <span class="comment">// the type of an expression</span></span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">global_declaration</span><span class="params">()</span> {</span><br><span class="line">    <span class="comment">// global_declaration ::= enum_decl | variable_decl | function_decl</span></span><br><span class="line">    <span class="comment">//</span></span><br><span class="line">    <span class="comment">// enum_decl ::= &#39;enum&#39; [id] &#39;{&#39; id [&#39;=&#39; &#39;num&#39;] {&#39;,&#39; id [&#39;=&#39; &#39;num&#39;} &#39;}&#39;</span></span><br><span class="line">    <span class="comment">//</span></span><br><span class="line">    <span class="comment">// variable_decl ::= type {&#39;*&#39;} id { &#39;,&#39; {&#39;*&#39;} id } &#39;;&#39;</span></span><br><span class="line">    <span class="comment">//</span></span><br><span class="line">    <span class="comment">// function_decl ::= type {&#39;*&#39;} id &#39;(&#39; parameter_decl &#39;)&#39; &#39;{&#39; body_decl &#39;}&#39;</span></span><br><span class="line"></span><br><span class="line"></span><br><span class="line">    <span class="type">int</span> type; <span class="comment">// tmp, actual type for variable</span></span><br><span class="line">    <span class="type">int</span> i; <span class="comment">// tmp</span></span><br><span class="line"></span><br><span class="line">    basetype = INT;</span><br><span class="line"></span><br><span class="line">    <span class="comment">// parse enum, this should be treated alone.</span></span><br><span class="line">    <span class="keyword">if</span> (token == Enum) {</span><br><span class="line">        <span class="comment">// enum [id] { a = 10, b = 20, ... }</span></span><br><span class="line">        match(Enum);</span><br><span class="line">        <span class="keyword">if</span> (token != <span class="string">&#39;{&#39;</span>) {</span><br><span class="line">            match(Id); <span class="comment">// skip the [id] part</span></span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">if</span> (token == <span class="string">&#39;{&#39;</span>) {</span><br><span class="line">            <span class="comment">// parse the assign part</span></span><br><span class="line">            match(<span class="string">&#39;{&#39;</span>);</span><br><span class="line">            enum_declaration();</span><br><span class="line">            match(<span class="string">&#39;}&#39;</span>);</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        match(<span class="string">&#39;;&#39;</span>);</span><br><span class="line">        <span class="keyword">return</span>;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="comment">// parse type information</span></span><br><span class="line">    <span class="keyword">if</span> (token == Int) {</span><br><span class="line">        match(Int);</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">else</span> <span class="keyword">if</span> (token == Char) {</span><br><span class="line">        match(Char);</span><br><span class="line">        basetype = CHAR;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="comment">// parse the comma seperated variable declaration.</span></span><br><span class="line">    <span class="keyword">while</span> (token != <span class="string">&#39;;&#39;</span> &amp;&amp; token != <span class="string">&#39;}&#39;</span>) {</span><br><span class="line">        type = basetype;</span><br><span class="line">        <span class="comment">// parse pointer type, note that there may exist `int ****x;`</span></span><br><span class="line">        <span class="keyword">while</span> (token == Mul) {</span><br><span class="line">            match(Mul);</span><br><span class="line">            type = type + PTR;</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        <span class="keyword">if</span> (token != Id) {</span><br><span class="line">            <span class="comment">// invalid declaration</span></span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot;%d: bad global declaration\n&quot;</span>, line);</span><br><span class="line">            <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">if</span> (current_id[Class]) {</span><br><span class="line">            <span class="comment">// identifier exists</span></span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot;%d: duplicate global declaration\n&quot;</span>, line);</span><br><span class="line">            <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">        }</span><br><span class="line">        match(Id);</span><br><span class="line">        current_id[Type] = type;</span><br><span class="line"></span><br><span class="line">        <span class="keyword">if</span> (token == <span class="string">&#39;(&#39;</span>) {</span><br><span class="line">            current_id[Class] = Fun;</span><br><span class="line">            current_id[Value] = (<span class="type">int</span>)(text + <span class="number">1</span>); <span class="comment">// the memory address of function</span></span><br><span class="line">            function_declaration();</span><br><span class="line">        } <span class="keyword">else</span> {</span><br><span class="line">            <span class="comment">// variable declaration</span></span><br><span class="line">            current_id[Class] = Glo; <span class="comment">// global variable</span></span><br><span class="line">            current_id[Value] = (<span class="type">int</span>)data; <span class="comment">// assign memory address</span></span><br><span class="line">            data = data + <span class="keyword">sizeof</span>(<span class="type">int</span>);</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        <span class="keyword">if</span> (token == <span class="string">&#39;,&#39;</span>) {</span><br><span class="line">            match(<span class="string">&#39;,&#39;</span>);</span><br><span class="line">        }</span><br><span class="line">    }</span><br><span class="line">    next();</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>看了上面的代码，能大概理解吗？这里我们讲解其中的一些细节。</p><p><strong>向前看标记</strong> ：其中的 <code>if (token == xxx)</code> 语句就是用来向前查看标记以确定使用哪一个产生式，例如只要遇到 <code>enum</code> 我们就知道是需要解析枚举类型。而如果只解析到类型，如 <code>int identifier</code> 时我们并不能确定 <code>identifier</code> 是一个普通的变量还是一个函数，所以还需要继续查看后续的标记，如果遇到 <code>(</code> 则可以断定是函数了，反之则是变量。</p><p><strong>变量类型的表示</strong> ：我们的编译器支持指针类型，那意味着也支持指针的指针，如 <code>int **data;</code>。那么我们如何表示指针类型呢？前文中我们定义了支持的类型：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="comment">// types of variable/function</span></span><br><span class="line"><span class="class"><span class="keyword">enum</span> {</span> CHAR, INT, PTR };</span><br></pre></td></tr></tbody></table><p>所以一个类型首先有基本类型，如 <code>CHAR</code> 或 <code>INT</code>，当它是一个指向基本类型的指针时，如 <code>int *data</code>，我们就将它的类型加上 <code>PTR</code> 即代码中的：<code>type = type + PTR;</code>。同理，如果是指针的指针，则再加上 <code>PTR</code>。</p><h3 id="enum-declaration" tabindex="-1"><a class="header-anchor" href="#enum-declaration"><span><a href="about:blank#enum-declaration"></a>enum_declaration()</span></a></h3><p>用于解析枚举类型的定义。主要的逻辑用于解析用逗号（<code>,</code>）分隔的变量，值得注意的是在编译器中如何保存枚举变量的信息。</p><p>即我们将该变量的类别设置成了 <code>Num</code>，这样它就成了全局的常量了，而注意到上节中，正常的全局变量的类别则是 <code>Glo</code>，类别信息在后面章节中解析 <code>expression</code> 会使用到。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">enum_declaration</span><span class="params">()</span> {</span><br><span class="line">    <span class="comment">// parse enum [id] { a = 1, b = 3, ...}</span></span><br><span class="line">    <span class="type">int</span> i;</span><br><span class="line">    i = <span class="number">0</span>;</span><br><span class="line">    <span class="keyword">while</span> (token != <span class="string">&#39;}&#39;</span>) {</span><br><span class="line">        <span class="keyword">if</span> (token != Id) {</span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot;%d: bad enum identifier %d\n&quot;</span>, line, token);</span><br><span class="line">            <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">        }</span><br><span class="line">        next();</span><br><span class="line">        <span class="keyword">if</span> (token == Assign) {</span><br><span class="line">            <span class="comment">// like {a=10}</span></span><br><span class="line">            next();</span><br><span class="line">            <span class="keyword">if</span> (token != Num) {</span><br><span class="line">                <span class="built_in">printf</span>(<span class="string">&quot;%d: bad enum initializer\n&quot;</span>, line);</span><br><span class="line">                <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">            }</span><br><span class="line">            i = token_val;</span><br><span class="line">            next();</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        current_id[Class] = Num;</span><br><span class="line">        current_id[Type] = INT;</span><br><span class="line">        current_id[Value] = i++;</span><br><span class="line"></span><br><span class="line">        <span class="keyword">if</span> (token == <span class="string">&#39;,&#39;</span>) {</span><br><span class="line">            next();</span><br><span class="line">        }</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="其它" tabindex="-1"><a class="header-anchor" href="#其它"><span><a href="about:blank#%E5%85%B6%E5%AE%83"></a>其它</span></a></h3><p>其中的 <code>function_declaration</code> 函数我们将放到下一章中讲解。<code>match</code> 函数是一个辅助函数：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">match</span><span class="params">(<span class="type">int</span> tk)</span> {</span><br><span class="line">    <span class="keyword">if</span> (token == tk) {</span><br><span class="line">        next();</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%d: expected token: %d\n&quot;</span>, line, tk);</span><br><span class="line">        <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>它将 <code>next</code> 函数包装起来，如果不是预期的标记则报错并退出。</p><h2 id="代码" tabindex="-1"><a class="header-anchor" href="#代码"><span><a href="about:blank#%E4%BB%A3%E7%A0%81"></a>代码</span></a></h2><p>本章的代码可以在 <a href="https://github.com/lotabout/write-a-C-interpreter/tree/step-3" target="_blank" rel="noopener noreferrer">Github<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a> 上下载，也可以直接 clone</p><table><tbody><tr><td class="code"><pre><span class="line">git clone -b step-3 https://github.com/lotabout/write-a-C-interpreter</span><br></pre></td></tr></tbody></table><p>本章的代码还无法正常运行，因为还有许多功能没有实现，但如果有兴趣的话，可以自己先试着去实现它。</p><h2 id="小结" tabindex="-1"><a class="header-anchor" href="#小结"><span><a href="about:blank#%E5%B0%8F%E7%BB%93"></a>小结</span></a></h2><p>本章的内容应该不难，除了开头的 EBNF 表达式可能相对不好理解一些，但如果你查看了 EBNF 的具体表示方法后就不难理解了。</p><p>剩下的内容就是按部就班地将 EBNF 的产生式转换成函数的过程，如果你理解了上一章中的内容，相信这部分也不难理解。</p><p>下一章中我们将介绍如何解析函数的定义，敬请期待。</p></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/designASimpileCCompiler/5.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/designASimpileCCompiler/4.html" aria-label="手把手教你构建 C 语言编译器（4）——递归下降"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->手把手教你构建 C 语言编译器（4）——递归下降</div></a><a class="route-link nav-link next" href="/tech/designASimpileCCompiler/6.html" aria-label="手把手教你构建 C 语言编译器（6）——函数定义"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">手把手教你构建 C 语言编译器（6）——函数定义<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/designASimpileCCompiler/6.html b/tech/designASimpileCCompiler/6.html
index 73a77d9..bcc22ab 100644
--- a/tech/designASimpileCCompiler/6.html
+++ b/tech/designASimpileCCompiler/6.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/designASimpileCCompiler/6.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="手把手教你构建 C 语言编译器（6）——函数定义"><meta property="og:description" content="转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-6/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（6）- 函数定义 Table of Contents 1. EBNF 表示 2. 解析函数的定义 2.1. 函数参数与汇编代码 2.2. 函数定义的解析 2.3. 解析..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="c"><meta property="article:tag" content="编译器"><meta property="article:tag" content="解释器"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"手把手教你构建 C 语言编译器（6）——函数定义","image":[""],"dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>手把手教你构建 C 语言编译器（6）——函数定义 | blog</title><meta name="description" content="转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-6/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（6）- 函数定义 Table of Contents 1. EBNF 表示 2. 解析函数的定义 2.1. 函数参数与汇编代码 2.2. 函数定义的解析 2.3. 解析...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/6.html-BPGbpgjm.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/6.html-4dTDTOb4.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/0.html" aria-label="手把手教你构建 C 语言编译器（0）- 前言"><!---->手把手教你构建 C 语言编译器（0）- 前言<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/1.html" aria-label="手把手教你构建 C 语言编译器（1）- 设计"><!---->手把手教你构建 C 语言编译器（1）- 设计<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/3.html" aria-label="手把手教你构建 C 语言编译器（3）——词法分析器"><!---->手把手教你构建 C 语言编译器（3）——词法分析器<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/4.html" aria-label="手把手教你构建 C 语言编译器（4）——递归下降"><!---->手把手教你构建 C 语言编译器（4）——递归下降<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/5.html" aria-label="手把手教你构建 C 语言编译器（5）——变量定义"><!---->手把手教你构建 C 语言编译器（5）——变量定义<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/designASimpileCCompiler/6.html" aria-label="手把手教你构建 C 语言编译器（6）——函数定义"><!---->手把手教你构建 C 语言编译器（6）——函数定义<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/7.html" aria-label="手把手教你构建 C 语言编译器（7）——语句"><!---->手把手教你构建 C 语言编译器（7）——语句<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/8.html" aria-label="手把手教你构建 C 语言编译器（8）——表达式"><!---->手把手教你构建 C 语言编译器（8）——表达式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/9.html" aria-label="手把手教你构建 C 语言编译器（9）——总结"><!---->手把手教你构建 C 语言编译器（9）——总结<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/2.html" aria-label="转载声明"><!---->转载声明<!----></a></li></ul></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->手把手教你构建 C 语言编译器（6）——函数定义</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 13 分钟</span><meta property="timeRequired" content="PT13M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category2 clickable" role="navigation">编译原理</span><!--]--><meta property="articleSection" content="编译原理"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag4 clickable" role="navigation">c</span><span class="page-tag-item tag4 clickable" role="navigation">编译器</span><span class="page-tag-item tag4 clickable" role="navigation">解释器</span><!--]--><meta property="keywords" content="c,编译器,解释器"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#ebnf-表示">EBNF 表示</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#解析函数的定义">解析函数的定义</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#函数参数与汇编代码">函数参数与汇编代码</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#函数定义的解析">函数定义的解析</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#解析参数">解析参数</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#函数体的解析">函数体的解析</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#代码">代码</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#小结">小结</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="转载声明" tabindex="-1"><a class="header-anchor" href="#转载声明"><span>转载声明</span></a></h1><p>本文转自 <a href="https://lotabout.me/2016/write-a-C-interpreter-6/" target="_blank" rel="noopener noreferrer">https://lotabout.me/2016/write-a-C-interpreter-6/<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a>，如有侵权，请联系删除。</p><h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-6-函数定义" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-6-函数定义"><span>手把手教你构建 C 语言编译器（6）- 函数定义</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#ebnf-%E8%A1%A8%E7%A4%BA">1. EBNF 表示</a></li><li><a href="about:blank#%E8%A7%A3%E6%9E%90%E5%87%BD%E6%95%B0%E7%9A%84%E5%AE%9A%E4%B9%89">2. 解析函数的定义</a><ol><li><a href="about:blank#%E5%87%BD%E6%95%B0%E5%8F%82%E6%95%B0%E4%B8%8E%E6%B1%87%E7%BC%96%E4%BB%A3%E7%A0%81">2.1. 函数参数与汇编代码</a></li><li><a href="about:blank#%E5%87%BD%E6%95%B0%E5%AE%9A%E4%B9%89%E7%9A%84%E8%A7%A3%E6%9E%90">2.2. 函数定义的解析</a></li><li><a href="about:blank#%E8%A7%A3%E6%9E%90%E5%8F%82%E6%95%B0">2.3. 解析参数</a></li><li><a href="about:blank#%E5%87%BD%E6%95%B0%E4%BD%93%E7%9A%84%E8%A7%A3%E6%9E%90">2.4. 函数体的解析</a></li></ol></li><li><a href="about:blank#%E4%BB%A3%E7%A0%81">3. 代码</a></li><li><a href="about:blank#%E5%B0%8F%E7%BB%93">4. 小结</a></li></ol><p>由于语法分析本身比较复杂，所以我们将它拆分成 3 个部分进行讲解，分别是：变量定义、函数定义、表达式。本章讲解函数定义相关的内容。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p><ol><li><a href="http://lotabout.me/2015/write-a-C-interpreter-0/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（0）——前言<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-1/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（1）——设计<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-2/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（2）——虚拟机<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-3/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（3）——词法分析器<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-4/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（4）——递归下降<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-5/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（5）——变量定义<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-6/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（6）——函数定义<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-7/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（7）——语句<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-8/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（8）——表达式<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-9/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（9）——总结<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li></ol><h2 id="ebnf-表示" tabindex="-1"><a class="header-anchor" href="#ebnf-表示"><span><a href="about:blank#ebnf-%E8%A1%A8%E7%A4%BA"></a>EBNF 表示</span></a></h2><p>这是上一章的 EBNF 方法中与函数定义相关的内容。</p><table><tbody><tr><td class="code"><pre><span class="line">variable_decl ::= type {&#39;*&#39;} id { &#39;,&#39; {&#39;*&#39;} id } &#39;;&#39;</span><br><span class="line"></span><br><span class="line">function_decl ::= type {&#39;*&#39;} id &#39;(&#39; parameter_decl &#39;)&#39; &#39;{&#39; body_decl &#39;}&#39;</span><br><span class="line"></span><br><span class="line">parameter_decl ::= type {&#39;*&#39;} id {&#39;,&#39; type {&#39;*&#39;} id}</span><br><span class="line"></span><br><span class="line">body_decl ::= {variable_decl}, {statement}</span><br><span class="line"></span><br><span class="line">statement ::= non_empty_statement | empty_statement</span><br><span class="line"></span><br><span class="line">non_empty_statement ::= if_statement | while_statement | &#39;{&#39; statement &#39;}&#39;</span><br><span class="line">                     | &#39;return&#39; expression | expression &#39;;&#39;</span><br><span class="line"></span><br><span class="line">if_statement ::= &#39;if&#39; &#39;(&#39; expression &#39;)&#39; statement [&#39;else&#39; non_empty_statement]</span><br><span class="line"></span><br><span class="line">while_statement ::= &#39;while&#39; &#39;(&#39; expression &#39;)&#39; non_empty_statement</span><br></pre></td></tr></tbody></table><h2 id="解析函数的定义" tabindex="-1"><a class="header-anchor" href="#解析函数的定义"><span><a href="about:blank#%E8%A7%A3%E6%9E%90%E5%87%BD%E6%95%B0%E7%9A%84%E5%AE%9A%E4%B9%89"></a>解析函数的定义</span></a></h2><p>上一章的代码中，我们已经知道了什么时候开始解析函数的定义，相关的代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line">...</span><br><span class="line"><span class="keyword">if</span> (token == <span class="string">&#39;(&#39;</span>) {</span><br><span class="line">    current_id[Class] = Fun;</span><br><span class="line">    current_id[Value] = (<span class="type">int</span>)(text + <span class="number">1</span>); <span class="comment">// the memory address of function</span></span><br><span class="line">    function_declaration();</span><br><span class="line">} <span class="keyword">else</span> {</span><br><span class="line">...</span><br></pre></td></tr></tbody></table><p>即在这断代码之前，我们已经为当前的标识符（identifier）设置了正确的类型，上面这断代码为当前的标识符设置了正确的类别（Fun），以及该函数在代码段（text segment）中的位置。接下来开始解析函数定义相关的内容：<code>parameter_decl</code> 及 <code>body_decl</code>。</p><h3 id="函数参数与汇编代码" tabindex="-1"><a class="header-anchor" href="#函数参数与汇编代码"><span><a href="about:blank#%E5%87%BD%E6%95%B0%E5%8F%82%E6%95%B0%E4%B8%8E%E6%B1%87%E7%BC%96%E4%BB%A3%E7%A0%81"></a>函数参数与汇编代码</span></a></h3><p>现在我们要回忆如何将“函数”转换成对应的汇编代码，因为这决定了在解析时我们需要哪些相关的信息。考虑下列函数：</p><table><tbody><tr><td class="code"><pre><span class="line">int demo(int param_a, int *param_b) {</span><br><span class="line">    int local_1;</span><br><span class="line">    char local_2;</span><br><span class="line"></span><br><span class="line">    ...</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>那么它应该被转换成什么样的汇编代码呢？在思考这个问题之前，我们需要了解当 <code>demo</code>函数被调用时，计算机的栈的状态，如下（参照第三章讲解的虚拟机）：</p><table><tbody><tr><td class="code"><pre><span class="line">|    ....       | high address</span><br><span class="line">+---------------+</span><br><span class="line">| arg: param_a  |    new_bp + 3</span><br><span class="line">+---------------+</span><br><span class="line">| arg: param_b  |    new_bp + 2</span><br><span class="line">+---------------+</span><br><span class="line">|return address |    new_bp + 1</span><br><span class="line">+---------------+</span><br><span class="line">| old BP        | &lt;- new BP</span><br><span class="line">+---------------+</span><br><span class="line">| local_1       |    new_bp - 1</span><br><span class="line">+---------------+</span><br><span class="line">| local_2       |    new_bp - 2</span><br><span class="line">+---------------+</span><br><span class="line">|    ....       |  low address</span><br></pre></td></tr></tbody></table><p>这里最为重要的一点是，无论是函数的参数（如 <code>param_a</code>）还是函数的局部变量（如 <code>local_1</code>）都是存放在计算机的 <strong>栈</strong> 上的。因此，与存放在 <strong>数据段</strong> 中的全局变量不同，在函数内访问它们是通过 <code>new_bp</code> 指针和对应的位移量进行的。因此，在解析的过程中，我们需要知道参数的个数，各个参数的位移量。</p><h3 id="函数定义的解析" tabindex="-1"><a class="header-anchor" href="#函数定义的解析"><span><a href="about:blank#%E5%87%BD%E6%95%B0%E5%AE%9A%E4%B9%89%E7%9A%84%E8%A7%A3%E6%9E%90"></a>函数定义的解析</span></a></h3><p>这相当于是整个函数定义的语法解析的框架，代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">function_declaration</span><span class="params">()</span> {</span><br><span class="line">    <span class="comment">// type func_name (...) {...}</span></span><br><span class="line">    <span class="comment">//               | this part</span></span><br><span class="line"></span><br><span class="line">    match(<span class="string">&#39;(&#39;</span>);</span><br><span class="line">    function_parameter();</span><br><span class="line">    match(<span class="string">&#39;)&#39;</span>);</span><br><span class="line">    match(<span class="string">&#39;{&#39;</span>);</span><br><span class="line">    function_body();</span><br><span class="line">    <span class="comment">//match(&#39;}&#39;);                 //  ①</span></span><br><span class="line"></span><br><span class="line">    <span class="comment">// ②</span></span><br><span class="line">    <span class="comment">// unwind local variable declarations for all local variables.</span></span><br><span class="line">    current_id = symbols;</span><br><span class="line">    <span class="keyword">while</span> (current_id[Token]) {</span><br><span class="line">        <span class="keyword">if</span> (current_id[Class] == Loc) {</span><br><span class="line">            current_id[Class] = current_id[BClass];</span><br><span class="line">            current_id[Type]  = current_id[BType];</span><br><span class="line">            current_id[Value] = current_id[BValue];</span><br><span class="line">        }</span><br><span class="line">        current_id = current_id + IdSize;</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>其中①中我们没有消耗最后的<code>}</code>字符。这么做的原因是：<code>variable_decl</code> 与 <code>function_decl</code> 是放在一起解析的，而 <code>variable_decl</code> 是以字符 <code>;</code> 结束的。而 <code>function_decl</code> 是以字符 <code>}</code> 结束的，若在此通过 <code>match</code> 消耗了 ‘;’ 字符，那么外层的 <code>while</code> 循环就没法准确地知道函数定义已经结束。所以我们将结束符的解析放在了外层的 <code>while</code> 循环中。</p><p>而②中的代码是用于将符号表中的信息恢复成全局的信息。这是因为，局部变量是可以和全局变量同名的，一旦同名，在函数体内局部变量就会覆盖全局变量，出了函数体，全局变量就恢复了原先的作用。这段代码线性地遍历所有标识符，并将保存在 <code>BXXX</code> 中的信息还原。</p><h3 id="解析参数" tabindex="-1"><a class="header-anchor" href="#解析参数"><span><a href="about:blank#%E8%A7%A3%E6%9E%90%E5%8F%82%E6%95%B0"></a>解析参数</span></a></h3><table><tbody><tr><td class="code"><pre><span class="line">parameter_decl ::= type {&#39;*&#39;} id {&#39;,&#39; type {&#39;*&#39;} id}</span><br></pre></td></tr></tbody></table><p>解析函数的参数就是解析以逗号分隔的一个个标识符，同时记录它们的位置与类型。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> index_of_bp; <span class="comment">// index of bp pointer on stack</span></span><br><span class="line"></span><br><span class="line"><span class="type">void</span> <span class="title function_">function_parameter</span><span class="params">()</span> {</span><br><span class="line">    <span class="type">int</span> type;</span><br><span class="line">    <span class="type">int</span> params;</span><br><span class="line">    params = <span class="number">0</span>;</span><br><span class="line">    <span class="keyword">while</span> (token != <span class="string">&#39;)&#39;</span>) {</span><br><span class="line">        <span class="comment">// ①</span></span><br><span class="line"></span><br><span class="line">        <span class="comment">// int name, ...</span></span><br><span class="line">        type = INT;</span><br><span class="line">        <span class="keyword">if</span> (token == Int) {</span><br><span class="line">            match(Int);</span><br><span class="line">        } <span class="keyword">else</span> <span class="keyword">if</span> (token == Char) {</span><br><span class="line">            type = CHAR;</span><br><span class="line">            match(Char);</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        <span class="comment">// pointer type</span></span><br><span class="line">        <span class="keyword">while</span> (token == Mul) {</span><br><span class="line">            match(Mul);</span><br><span class="line">            type = type + PTR;</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        <span class="comment">// parameter name</span></span><br><span class="line">        <span class="keyword">if</span> (token != Id) {</span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot;%d: bad parameter declaration\n&quot;</span>, line);</span><br><span class="line">            <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">if</span> (current_id[Class] == Loc) {</span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot;%d: duplicate parameter declaration\n&quot;</span>, line);</span><br><span class="line">            <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        match(Id);</span><br><span class="line"></span><br><span class="line">        <span class="comment">//②</span></span><br><span class="line">        <span class="comment">// store the local variable</span></span><br><span class="line">        current_id[BClass] = current_id[Class]; current_id[Class]  = Loc;</span><br><span class="line">        current_id[BType]  = current_id[Type];  current_id[Type]   = type;</span><br><span class="line">        current_id[BValue] = current_id[Value]; current_id[Value]  = params++;   <span class="comment">// index of current parameter</span></span><br><span class="line"></span><br><span class="line">        <span class="keyword">if</span> (token == <span class="string">&#39;,&#39;</span>) {</span><br><span class="line">            match(<span class="string">&#39;,&#39;</span>);</span><br><span class="line">        }</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="comment">// ③</span></span><br><span class="line">    index_of_bp = params+<span class="number">1</span>;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>其中①与全局变量定义的解析十分一样，用于解析该参数的类型。</p><p>而②则与上节中提到的“局部变量覆盖全局变量”相关，先将全局变量的信息保存（无论是是否真的在全局中用到了这个变量）在 <code>BXXX</code> 中，再赋上局部变量相关的信息，如 <code>Value</code> 中存放的是参数的位置（是第几个参数）。</p><p>③则与汇编代码的生成有关，<code>index_of_bp</code> 就是前文提到的 <code>new_bp</code> 的位置。</p><h3 id="函数体的解析" tabindex="-1"><a class="header-anchor" href="#函数体的解析"><span><a href="about:blank#%E5%87%BD%E6%95%B0%E4%BD%93%E7%9A%84%E8%A7%A3%E6%9E%90"></a>函数体的解析</span></a></h3><p>我们实现的 C 语言与现代的 C 语言不太一致，我们需要所有的变量定义出现在所有的语句之前。函数体的代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">void</span> <span class="title function_">function_body</span><span class="params">()</span> {</span><br><span class="line">    <span class="comment">// type func_name (...) {...}</span></span><br><span class="line">    <span class="comment">//                   --&gt;|   |&lt;--</span></span><br><span class="line"></span><br><span class="line">    <span class="comment">// ... {</span></span><br><span class="line">    <span class="comment">// 1. local declarations</span></span><br><span class="line">    <span class="comment">// 2. statements</span></span><br><span class="line">    <span class="comment">// }</span></span><br><span class="line"></span><br><span class="line">    <span class="type">int</span> pos_local; <span class="comment">// position of local variables on the stack.</span></span><br><span class="line">    <span class="type">int</span> type;</span><br><span class="line">    pos_local = index_of_bp;</span><br><span class="line"></span><br><span class="line">    <span class="comment">// ①</span></span><br><span class="line">    <span class="keyword">while</span> (token == Int || token == Char) {</span><br><span class="line">        <span class="comment">// local variable declaration, just like global ones.</span></span><br><span class="line">        basetype = (token == Int) ? INT : CHAR;</span><br><span class="line">        match(token);</span><br><span class="line"></span><br><span class="line">        <span class="keyword">while</span> (token != <span class="string">&#39;;&#39;</span>) {</span><br><span class="line">            type = basetype;</span><br><span class="line">            <span class="keyword">while</span> (token == Mul) {</span><br><span class="line">                match(Mul);</span><br><span class="line">                type = type + PTR;</span><br><span class="line">            }</span><br><span class="line"></span><br><span class="line">            <span class="keyword">if</span> (token != Id) {</span><br><span class="line">                <span class="comment">// invalid declaration</span></span><br><span class="line">                <span class="built_in">printf</span>(<span class="string">&quot;%d: bad local declaration\n&quot;</span>, line);</span><br><span class="line">                <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">            }</span><br><span class="line">            <span class="keyword">if</span> (current_id[Class] == Loc) {</span><br><span class="line">                <span class="comment">// identifier exists</span></span><br><span class="line">                <span class="built_in">printf</span>(<span class="string">&quot;%d: duplicate local declaration\n&quot;</span>, line);</span><br><span class="line">                <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">            }</span><br><span class="line">            match(Id);</span><br><span class="line"></span><br><span class="line">            <span class="comment">// store the local variable</span></span><br><span class="line">            current_id[BClass] = current_id[Class]; current_id[Class]  = Loc;</span><br><span class="line">            current_id[BType]  = current_id[Type];  current_id[Type]   = type;</span><br><span class="line">            current_id[BValue] = current_id[Value]; current_id[Value]  = ++pos_local;   <span class="comment">// index of current parameter</span></span><br><span class="line"></span><br><span class="line">            <span class="keyword">if</span> (token == <span class="string">&#39;,&#39;</span>) {</span><br><span class="line">                match(<span class="string">&#39;,&#39;</span>);</span><br><span class="line">            }</span><br><span class="line">        }</span><br><span class="line">        match(<span class="string">&#39;;&#39;</span>);</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="comment">// ②</span></span><br><span class="line">    <span class="comment">// save the stack size for local variables</span></span><br><span class="line">    *++text = ENT;</span><br><span class="line">    *++text = pos_local - index_of_bp;</span><br><span class="line"></span><br><span class="line">    <span class="comment">// statements</span></span><br><span class="line">    <span class="keyword">while</span> (token != <span class="string">&#39;}&#39;</span>) {</span><br><span class="line">        statement();</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="comment">// emit code for leaving the sub function</span></span><br><span class="line">    *++text = LEV;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>其中①用于解析函数体内的局部变量的定义，代码与全局的变量定义几乎一样。</p><p>而②则用于生成汇编代码，我们在第三章的虚拟机中提到过，我们需要在栈上为局部变量预留空间，这两行代码起的就是这个作用。</p><h2 id="代码" tabindex="-1"><a class="header-anchor" href="#代码"><span><a href="about:blank#%E4%BB%A3%E7%A0%81"></a>代码</span></a></h2><p>本章的代码可以在 <a href="https://github.com/lotabout/write-a-C-interpreter/tree/step-4" target="_blank" rel="noopener noreferrer">Github<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a> 上下载，也可以直接 clone</p><table><tbody><tr><td class="code"><pre><span class="line">git clone -b step-4 https://github.com/lotabout/write-a-C-interpreter</span><br></pre></td></tr></tbody></table><p>本章的代码依旧无法运行，还有两个重要函数没有完成：<code>statement</code> 及 <code>expression</code>，感兴趣的话可以尝试自己实现它们。</p><h2 id="小结" tabindex="-1"><a class="header-anchor" href="#小结"><span><a href="about:blank#%E5%B0%8F%E7%BB%93"></a>小结</span></a></h2><p>本章中我们用了不多的代码完成了函数定义的解析。大部分的代码依旧是用于解析变量：参数和局部变量，而它们的逻辑和全局变量的解析几乎一致，最大的区别就是保存的信息不同。</p><p>当然，要理解函数定义的解析过程，最重要的是理解我们会为函数生成怎样的汇编代码，因为这决定了我们需要从解析中获取什么样的信息（例如参数的位置，个数等），而这些可能需要你重新回顾一下“虚拟机”这一章，或是重新学习学习汇编相关的知识。</p><p>下一章中我们将讲解语句的解析，敬请期待。</p></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/designASimpileCCompiler/6.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/designASimpileCCompiler/5.html" aria-label="手把手教你构建 C 语言编译器（5）——变量定义"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->手把手教你构建 C 语言编译器（5）——变量定义</div></a><a class="route-link nav-link next" href="/tech/designASimpileCCompiler/7.html" aria-label="手把手教你构建 C 语言编译器（7）——语句"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">手把手教你构建 C 语言编译器（7）——语句<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/designASimpileCCompiler/7.html b/tech/designASimpileCCompiler/7.html
index e976df2..a7ad4bc 100644
--- a/tech/designASimpileCCompiler/7.html
+++ b/tech/designASimpileCCompiler/7.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/designASimpileCCompiler/7.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="手把手教你构建 C 语言编译器（7）——语句"><meta property="og:description" content="转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-7/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（7）- 语句 Table of Contents 1. 语句 1.1. IF 语句 1.2. While 语句 1.3. Return 语句 1.4. 其它语句 2. ..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="c"><meta property="article:tag" content="编译器"><meta property="article:tag" content="解释器"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"手把手教你构建 C 语言编译器（7）——语句","image":[""],"dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>手把手教你构建 C 语言编译器（7）——语句 | blog</title><meta name="description" content="转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-7/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（7）- 语句 Table of Contents 1. 语句 1.1. IF 语句 1.2. While 语句 1.3. Return 语句 1.4. 其它语句 2. ...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/7.html-DopH3hey.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/7.html-BzOHeKw-.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/0.html" aria-label="手把手教你构建 C 语言编译器（0）- 前言"><!---->手把手教你构建 C 语言编译器（0）- 前言<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/1.html" aria-label="手把手教你构建 C 语言编译器（1）- 设计"><!---->手把手教你构建 C 语言编译器（1）- 设计<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/3.html" aria-label="手把手教你构建 C 语言编译器（3）——词法分析器"><!---->手把手教你构建 C 语言编译器（3）——词法分析器<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/4.html" aria-label="手把手教你构建 C 语言编译器（4）——递归下降"><!---->手把手教你构建 C 语言编译器（4）——递归下降<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/5.html" aria-label="手把手教你构建 C 语言编译器（5）——变量定义"><!---->手把手教你构建 C 语言编译器（5）——变量定义<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/6.html" aria-label="手把手教你构建 C 语言编译器（6）——函数定义"><!---->手把手教你构建 C 语言编译器（6）——函数定义<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/designASimpileCCompiler/7.html" aria-label="手把手教你构建 C 语言编译器（7）——语句"><!---->手把手教你构建 C 语言编译器（7）——语句<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/8.html" aria-label="手把手教你构建 C 语言编译器（8）——表达式"><!---->手把手教你构建 C 语言编译器（8）——表达式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/9.html" aria-label="手把手教你构建 C 语言编译器（9）——总结"><!---->手把手教你构建 C 语言编译器（9）——总结<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/2.html" aria-label="转载声明"><!---->转载声明<!----></a></li></ul></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->手把手教你构建 C 语言编译器（7）——语句</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 7 分钟</span><meta property="timeRequired" content="PT7M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category2 clickable" role="navigation">编译原理</span><!--]--><meta property="articleSection" content="编译原理"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag4 clickable" role="navigation">c</span><span class="page-tag-item tag4 clickable" role="navigation">编译器</span><span class="page-tag-item tag4 clickable" role="navigation">解释器</span><!--]--><meta property="keywords" content="c,编译器,解释器"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#语句">语句</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#if-语句">IF 语句</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#while-语句">While 语句</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#return-语句">Return 语句</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#其它语句">其它语句</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#代码">代码</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#小结">小结</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="转载声明" tabindex="-1"><a class="header-anchor" href="#转载声明"><span>转载声明</span></a></h1><p>本文转自 <a href="https://lotabout.me/2016/write-a-C-interpreter-7/" target="_blank" rel="noopener noreferrer">https://lotabout.me/2016/write-a-C-interpreter-7/<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a>，如有侵权，请联系删除。</p><h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-7-语句" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-7-语句"><span>手把手教你构建 C 语言编译器（7）- 语句</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#%E8%AF%AD%E5%8F%A5">1. 语句</a><ol><li><a href="about:blank#if-%E8%AF%AD%E5%8F%A5">1.1. IF 语句</a></li><li><a href="about:blank#while-%E8%AF%AD%E5%8F%A5">1.2. While 语句</a></li><li><a href="about:blank#return-%E8%AF%AD%E5%8F%A5">1.3. Return 语句</a></li><li><a href="about:blank#%E5%85%B6%E5%AE%83%E8%AF%AD%E5%8F%A5">1.4. 其它语句</a></li></ol></li><li><a href="about:blank#%E4%BB%A3%E7%A0%81">2. 代码</a></li><li><a href="about:blank#%E5%B0%8F%E7%BB%93">3. 小结</a></li></ol><p>整个编译器还剩下最后两个部分：语句和表达式的解析。它们的内容比较多，主要涉及如何将语句和表达式编译成汇编代码。这章讲解语句的解析，相对于表达式来说它还是较为容易的。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p><ol><li><a href="http://lotabout.me/2015/write-a-C-interpreter-0/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（0）——前言<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-1/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（1）——设计<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-2/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（2）——虚拟机<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-3/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（3）——词法分析器<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-4/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（4）——递归下降<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-5/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（5）——变量定义<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-6/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（6）——函数定义<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-7/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（7）——语句<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-8/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（8）——表达式<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-9/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（9）——总结<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li></ol><h2 id="语句" tabindex="-1"><a class="header-anchor" href="#语句"><span><a href="about:blank#%E8%AF%AD%E5%8F%A5"></a>语句</span></a></h2><p>C 语言区分“语句”（statement）和“表达式”（expression）两个概念。简单地说，可以认为语句就是表达式加上末尾的分号。</p><p>在我们的编译器中共识别 6 种语句：</p><ol><li><code>if (...) &lt;statement&gt; [else &lt;statement&gt;]</code></li><li><code>while (...) &lt;statement&gt;</code></li><li><code>{ &lt;statement&gt; }</code></li><li><code>return xxx;</code></li><li><code>&lt;empty statement&gt;</code>;</li><li><code>expression;</code> (expression end with semicolon)</li></ol><p>它们的语法分析都相对容易，重要的是去理解如何将这些语句编译成汇编代码，下面我们逐一解释。</p><h3 id="if-语句" tabindex="-1"><a class="header-anchor" href="#if-语句"><span><a href="about:blank#if-%E8%AF%AD%E5%8F%A5"></a>IF 语句</span></a></h3><p>IF 语句的作用是跳转，跟据条件表达式决定跳转的位置。我们看看下面的伪代码：</p><table><tbody><tr><td class="code"><pre><span class="line">if (...) &lt;statement&gt; [else &lt;statement&gt;]</span><br><span class="line"></span><br><span class="line">  if (&lt;cond&gt;)                   &lt;cond&gt;</span><br><span class="line">                                JZ a</span><br><span class="line">    &lt;true_statement&gt;   ===&gt;     &lt;true_statement&gt;</span><br><span class="line">  else:                         JMP b</span><br><span class="line">a:                           a:</span><br><span class="line">    &lt;false_statement&gt;           &lt;false_statement&gt;</span><br><span class="line">b:                           b:</span><br></pre></td></tr></tbody></table><p>对应的汇编代码流程为：</p><ol><li>执行条件表达式 <code>&lt;cond&gt;</code>。</li><li>如果条件失败，则跳转到 <code>a</code> 的位置，执行 <code>else</code> 语句。这里 <code>else</code> 语句是可以省略的，此时 <code>a</code> 和 <code>b</code> 都指向 IF 语句后方的代码。</li><li>因为汇编代码是顺序排列的，所以如果执行了 <code>true_statement</code>，为了防止因为顺序排列而执行了 <code>false_statement</code>，所以需要无条件跳转 <code>JMP b</code>。</li></ol><p>对应的 C 代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">if</span> (token == If) {</span><br><span class="line">    match(If);</span><br><span class="line">    match(<span class="string">&#39;(&#39;</span>);</span><br><span class="line">    expression(Assign);  <span class="comment">// parse condition</span></span><br><span class="line">    match(<span class="string">&#39;)&#39;</span>);</span><br><span class="line"></span><br><span class="line">    *++text = JZ;</span><br><span class="line">    b = ++text;</span><br><span class="line"></span><br><span class="line">    statement();         <span class="comment">// parse statement</span></span><br><span class="line">    <span class="keyword">if</span> (token == Else) { <span class="comment">// parse else</span></span><br><span class="line">        match(Else);</span><br><span class="line"></span><br><span class="line">        <span class="comment">// emit code for JMP B</span></span><br><span class="line">        *b = (<span class="type">int</span>)(text + <span class="number">3</span>);</span><br><span class="line">        *++text = JMP;</span><br><span class="line">        b = ++text;</span><br><span class="line"></span><br><span class="line">        statement();</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    *b = (<span class="type">int</span>)(text + <span class="number">1</span>);</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="while-语句" tabindex="-1"><a class="header-anchor" href="#while-语句"><span><a href="about:blank#while-%E8%AF%AD%E5%8F%A5"></a>While 语句</span></a></h3><p>While 语句比 If 语句简单，它对应的汇编代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line">a:                     a:</span><br><span class="line">   while (&lt;cond&gt;)        &lt;cond&gt;</span><br><span class="line">                         JZ b</span><br><span class="line">    &lt;statement&gt;          &lt;statement&gt;</span><br><span class="line">                         JMP a</span><br><span class="line">b:                     b:</span><br></pre></td></tr></tbody></table><p>没有什么值得说明的内容，它的 C 代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == While) {</span><br><span class="line">    match(While);</span><br><span class="line"></span><br><span class="line">    a = text + <span class="number">1</span>;</span><br><span class="line"></span><br><span class="line">    match(<span class="string">&#39;(&#39;</span>);</span><br><span class="line">    expression(Assign);</span><br><span class="line">    match(<span class="string">&#39;)&#39;</span>);</span><br><span class="line"></span><br><span class="line">    *++text = JZ;</span><br><span class="line">    b = ++text;</span><br><span class="line"></span><br><span class="line">    statement();</span><br><span class="line"></span><br><span class="line">    *++text = JMP;</span><br><span class="line">    *++text = (<span class="type">int</span>)a;</span><br><span class="line">    *b = (<span class="type">int</span>)(text + <span class="number">1</span>);</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="return-语句" tabindex="-1"><a class="header-anchor" href="#return-语句"><span><a href="about:blank#return-%E8%AF%AD%E5%8F%A5"></a>Return 语句</span></a></h3><p>Return 唯一特殊的地方是：一旦遇到了 Return 语句，则意味着函数要退出了，所以需要生成汇编代码 <code>LEV</code> 来表示退出。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Return) {</span><br><span class="line">    <span class="comment">// return [expression];</span></span><br><span class="line">    match(Return);</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (token != <span class="string">&#39;;&#39;</span>) {</span><br><span class="line">        expression(Assign);</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    match(<span class="string">&#39;;&#39;</span>);</span><br><span class="line"></span><br><span class="line">    <span class="comment">// emit code for return</span></span><br><span class="line">    *++text = LEV;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="其它语句" tabindex="-1"><a class="header-anchor" href="#其它语句"><span><a href="about:blank#%E5%85%B6%E5%AE%83%E8%AF%AD%E5%8F%A5"></a>其它语句</span></a></h3><p>其它语句并不直接生成汇编代码，所以不多做说明，代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;{&#39;</span>) {</span><br><span class="line">    <span class="comment">// { &lt;statement&gt; ... }</span></span><br><span class="line">    match(<span class="string">&#39;{&#39;</span>);</span><br><span class="line"></span><br><span class="line">    <span class="keyword">while</span> (token != <span class="string">&#39;}&#39;</span>) {</span><br><span class="line">        statement();</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    match(<span class="string">&#39;}&#39;</span>);</span><br><span class="line">}</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;;&#39;</span>) {</span><br><span class="line">    <span class="comment">// empty statement</span></span><br><span class="line">    match(<span class="string">&#39;;&#39;</span>);</span><br><span class="line">}</span><br><span class="line"><span class="keyword">else</span> {</span><br><span class="line">    <span class="comment">// a = b; or function_call();</span></span><br><span class="line">    expression(Assign);</span><br><span class="line">    match(<span class="string">&#39;;&#39;</span>);</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h2 id="代码" tabindex="-1"><a class="header-anchor" href="#代码"><span><a href="about:blank#%E4%BB%A3%E7%A0%81"></a>代码</span></a></h2><p>本章的代码可以在 <a href="https://github.com/lotabout/write-a-C-interpreter/tree/step-5" target="_blank" rel="noopener noreferrer">Github<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a> 上下载，也可以直接 clone</p><table><tbody><tr><td class="code"><pre><span class="line">git clone -b step-5 https://github.com/lotabout/write-a-C-interpreter</span><br></pre></td></tr></tbody></table><p>本章的代码依旧无法运行，还剩最后一部分没有完成：<code>expression</code>。</p><h2 id="小结" tabindex="-1"><a class="header-anchor" href="#小结"><span><a href="about:blank#%E5%B0%8F%E7%BB%93"></a>小结</span></a></h2><p>本章讲解了如何将语句编译成汇编代码，内容相对容易一些，关键就是去理解汇编代码的执行原理。</p><p>同时值得一提的是，编译器的语法分析部分其实是很简单的，而真正的难点是如何在语法分析时收集足够多的信息，最终把源代码转换成目标代码（汇编）。我认为这也是初学者实现编译器的一大难点，往往比词法分析/语法分析更困难。</p><p>所以建议如果没有学过汇编，可以学习学习，它本身不难，但对理解计算机的原理有很大帮助。</p></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/designASimpileCCompiler/7.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/designASimpileCCompiler/6.html" aria-label="手把手教你构建 C 语言编译器（6）——函数定义"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->手把手教你构建 C 语言编译器（6）——函数定义</div></a><a class="route-link nav-link next" href="/tech/designASimpileCCompiler/8.html" aria-label="手把手教你构建 C 语言编译器（8）——表达式"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">手把手教你构建 C 语言编译器（8）——表达式<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/designASimpileCCompiler/8.html b/tech/designASimpileCCompiler/8.html
index ec0dd7f..ac8f6b5 100644
--- a/tech/designASimpileCCompiler/8.html
+++ b/tech/designASimpileCCompiler/8.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/designASimpileCCompiler/8.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="手把手教你构建 C 语言编译器（8）——表达式"><meta property="og:description" content="转载声明 本文转自 https://blog.csdn.net/xzp740813/article/details/142961332?spm=1001.2014.3001.5501，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（8）- 表达式 Table of Contents 1. 运算符的优先级 2. 一元运算符 2.1. 常..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="c"><meta property="article:tag" content="编译器"><meta property="article:tag" content="解释器"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"手把手教你构建 C 语言编译器（8）——表达式","image":[""],"dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>手把手教你构建 C 语言编译器（8）——表达式 | blog</title><meta name="description" content="转载声明 本文转自 https://blog.csdn.net/xzp740813/article/details/142961332?spm=1001.2014.3001.5501，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（8）- 表达式 Table of Contents 1. 运算符的优先级 2. 一元运算符 2.1. 常...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/8.html-D1TnfZgI.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/8.html-C-sA1tiy.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/0.html" aria-label="手把手教你构建 C 语言编译器（0）- 前言"><!---->手把手教你构建 C 语言编译器（0）- 前言<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/1.html" aria-label="手把手教你构建 C 语言编译器（1）- 设计"><!---->手把手教你构建 C 语言编译器（1）- 设计<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/3.html" aria-label="手把手教你构建 C 语言编译器（3）——词法分析器"><!---->手把手教你构建 C 语言编译器（3）——词法分析器<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/4.html" aria-label="手把手教你构建 C 语言编译器（4）——递归下降"><!---->手把手教你构建 C 语言编译器（4）——递归下降<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/5.html" aria-label="手把手教你构建 C 语言编译器（5）——变量定义"><!---->手把手教你构建 C 语言编译器（5）——变量定义<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/6.html" aria-label="手把手教你构建 C 语言编译器（6）——函数定义"><!---->手把手教你构建 C 语言编译器（6）——函数定义<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/7.html" aria-label="手把手教你构建 C 语言编译器（7）——语句"><!---->手把手教你构建 C 语言编译器（7）——语句<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/designASimpileCCompiler/8.html" aria-label="手把手教你构建 C 语言编译器（8）——表达式"><!---->手把手教你构建 C 语言编译器（8）——表达式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/9.html" aria-label="手把手教你构建 C 语言编译器（9）——总结"><!---->手把手教你构建 C 语言编译器（9）——总结<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/2.html" aria-label="转载声明"><!---->转载声明<!----></a></li></ul></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->手把手教你构建 C 语言编译器（8）——表达式</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 30 分钟</span><meta property="timeRequired" content="PT30M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category2 clickable" role="navigation">编译原理</span><!--]--><meta property="articleSection" content="编译原理"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag4 clickable" role="navigation">c</span><span class="page-tag-item tag4 clickable" role="navigation">编译器</span><span class="page-tag-item tag4 clickable" role="navigation">解释器</span><!--]--><meta property="keywords" content="c,编译器,解释器"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#运算符的优先级">运算符的优先级</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#一元运算符">一元运算符</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#常量">常量</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#sizeof">sizeof</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#变量与函数调用">变量与函数调用</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#强制转换">强制转换</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#指针取值">指针取值</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#取址操作">取址操作</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#逻辑取反">逻辑取反</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#按位取反">按位取反</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#正负号">正负号</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#自增自减">自增自减</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#二元运算符">二元运算符</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#赋值操作">赋值操作</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#三目运算符">三目运算符</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#逻辑运算符">逻辑运算符</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#数学运算符">数学运算符</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#自增自减-1">自增自减</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#数组取值操作">数组取值操作</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#代码">代码</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#小结">小结</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="转载声明" tabindex="-1"><a class="header-anchor" href="#转载声明"><span>转载声明</span></a></h1><p>本文转自 <a href="https://blog.csdn.net/xzp740813/article/details/142961332?spm=1001.2014.3001.5501" target="_blank" rel="noopener noreferrer">https://blog.csdn.net/xzp740813/article/details/142961332?spm=1001.2014.3001.5501<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a>，如有侵权，请联系删除。</p><h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-8-表达式" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-8-表达式"><span>手把手教你构建 C 语言编译器（8）- 表达式</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#%E8%BF%90%E7%AE%97%E7%AC%A6%E7%9A%84%E4%BC%98%E5%85%88%E7%BA%A7">1. 运算符的优先级</a></li><li><a href="about:blank#%E4%B8%80%E5%85%83%E8%BF%90%E7%AE%97%E7%AC%A6">2. 一元运算符</a><ol><li><a href="about:blank#%E5%B8%B8%E9%87%8F">2.1. 常量</a></li><li><a href="about:blank#sizeof">2.2. sizeof</a></li><li><a href="about:blank#%E5%8F%98%E9%87%8F%E4%B8%8E%E5%87%BD%E6%95%B0%E8%B0%83%E7%94%A8">2.3. 变量与函数调用</a></li><li><a href="about:blank#%E5%BC%BA%E5%88%B6%E8%BD%AC%E6%8D%A2">2.4. 强制转换</a></li><li><a href="about:blank#%E6%8C%87%E9%92%88%E5%8F%96%E5%80%BC">2.5. 指针取值</a></li><li><a href="about:blank#%E5%8F%96%E5%9D%80%E6%93%8D%E4%BD%9C">2.6. 取址操作</a></li><li><a href="about:blank#%E9%80%BB%E8%BE%91%E5%8F%96%E5%8F%8D">2.7. 逻辑取反</a></li><li><a href="about:blank#%E6%8C%89%E4%BD%8D%E5%8F%96%E5%8F%8D">2.8. 按位取反</a></li><li><a href="about:blank#%E6%AD%A3%E8%B4%9F%E5%8F%B7">2.9. 正负号</a></li><li><a href="about:blank#%E8%87%AA%E5%A2%9E%E8%87%AA%E5%87%8F">2.10. 自增自减</a></li></ol></li><li><a href="about:blank#%E4%BA%8C%E5%85%83%E8%BF%90%E7%AE%97%E7%AC%A6">3. 二元运算符</a><ol><li><a href="about:blank#%E8%B5%8B%E5%80%BC%E6%93%8D%E4%BD%9C">3.1. 赋值操作</a></li><li><a href="about:blank#%E4%B8%89%E7%9B%AE%E8%BF%90%E7%AE%97%E7%AC%A6">3.2. 三目运算符</a></li><li><a href="about:blank#%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6">3.3. 逻辑运算符</a></li><li><a href="about:blank#%E6%95%B0%E5%AD%A6%E8%BF%90%E7%AE%97%E7%AC%A6">3.4. 数学运算符</a></li><li><a href="about:blank#%E8%87%AA%E5%A2%9E%E8%87%AA%E5%87%8F-v2">3.5. 自增自减</a></li><li><a href="about:blank#%E6%95%B0%E7%BB%84%E5%8F%96%E5%80%BC%E6%93%8D%E4%BD%9C">3.6. 数组取值操作</a></li></ol></li><li><a href="about:blank#%E4%BB%A3%E7%A0%81">4. 代码</a></li><li><a href="about:blank#%E5%B0%8F%E7%BB%93">5. 小结</a></li></ol><p>这是整个编译器的最后一部分，解析表达式。什么是表达式？表达式是将各种语言要素的一个组合，用来求值。例如：函数调用、变量赋值、运算符运算等等。</p><p>表达式的解析难点有二：一是运算符的优先级问题，二是如何将表达式编译成目标代码。我们就来逐一说明。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p><ol><li><a href="http://lotabout.me/2015/write-a-C-interpreter-0/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（0）——前言<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-1/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（1）——设计<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-2/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（2）——虚拟机<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-3/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（3）——词法分析器<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-4/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（4）——递归下降<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-5/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（5）——变量定义<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-6/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（6）——函数定义<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-7/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（7）——语句<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-8/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（8）——表达式<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-9/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（9）——总结<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li></ol><h2 id="运算符的优先级" tabindex="-1"><a class="header-anchor" href="#运算符的优先级"><span><a href="about:blank#%E8%BF%90%E7%AE%97%E7%AC%A6%E7%9A%84%E4%BC%98%E5%85%88%E7%BA%A7"></a>运算符的优先级</span></a></h2><p>运算符的优先级决定了表达式的运算顺序，如在普通的四则运算中，乘法 <code>*</code> 优先级高于加法 <code>+</code>，这就意味着表达式 <code>2 + 3 * 4</code> 的实际运行顺序是 <code>2 + (3 * 4)</code> 而不是 <code>(2 + 3) * 4</code>。</p><p>C 语言定义了各种表达式的优先级，可以参考 <a href="http://en.cppreference.com/w/c/language/operator_precedence" target="_blank" rel="noopener noreferrer">C 语言运算符优先级<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a>。</p><p>传统的编程书籍会用“逆波兰式”实现四则运算来讲解优先级问题。实际上，优先级关心的就是哪个运算符先计算，哪个运算符后计算（毕竟叫做“优先级”嘛）。而这就意味着我们需要决定先为哪个运算符生成目标代码（汇编），因为汇编代码是顺序排列的，我们必须先计算优先级高的运算符。</p><p>那么如何确定运算符的优先级呢？答曰：栈（递归调用的实质也是栈的处理）。</p><p>举一个例子：<code>2 + 3 - 4 * 5</code>，它的运算顺序是这样的：</p><ol><li>将 <code>2</code> 入栈</li><li>遇到运算符 <code>+</code>，入栈，此时我们期待的是<code>+</code>的另一个参数</li><li>遇到数字 <code>3</code>，原则上我们需要立即计算 <code>2+3</code>的值，但我们不确定数字 <code>3</code> 是否属于优先级更高的运算符，所以先将它入栈。</li><li>遇到运算符 <code>-</code>，它的优先级和 <code>+</code> 相同，此时判断参数 <code>3</code> 属于这前的 <code>+</code>。将运算符 <code>+</code> 出栈，并将之前的 <code>2</code> 和 <code>3</code> 出栈，计算 <code>2+3</code> 的结果，得到 <code>5</code> 入栈。同时将运算符 <code>-</code> 入栈。</li><li>遇到数字<code>4</code>，同样不能确定是否能立即计算，入栈</li><li>遇到运算符 <code>*</code> 优先级大于 <code>-</code>，入栈</li><li>遇到数字<code>5</code>，依旧不能确定是否立即计算，入栈</li><li>表达式结束，运算符出栈，为 <code>*</code>，将参数出栈，计算 <code>4*5</code> 得到结果 <code>20</code> 入栈。</li><li>运算符出栈，为 <code>-</code>，将参数出栈，计算 <code>5-20</code>，得到 <code>-15</code> 入栈。</li><li>此时运算符栈为空，因此得到结果 <code>-15</code>。</li></ol><table><tbody><tr><td class="code"><pre><span class="line">// after step 1, 2</span><br><span class="line">|      |</span><br><span class="line">+------+</span><br><span class="line">| 3    |   |      |</span><br><span class="line">+------+   +------+</span><br><span class="line">| 2    |   | +    |</span><br><span class="line">+------+   +------+</span><br><span class="line"></span><br><span class="line">// after step 4</span><br><span class="line">|      |   |      |</span><br><span class="line">+------+   +------+</span><br><span class="line">| 5    |   | -    |</span><br><span class="line">+------+   +------+</span><br><span class="line"></span><br><span class="line">// after step 7</span><br><span class="line">|      |</span><br><span class="line">+------+</span><br><span class="line">| 5    |</span><br><span class="line">+------+   +------+</span><br><span class="line">| 4    |   | *    |</span><br><span class="line">+------+   +------+</span><br><span class="line">| 5    |   | -    |</span><br><span class="line">+------+   +------+</span><br></pre></td></tr></tbody></table><p>综上，在计算一个运算符‘x’之前，必须先查看它的右方，找出并计算所有优先级大于‘x’的运算符，之后再计算运算符‘x’。</p><p>最后注意的是优先通常只与多元运算符相关，单元运算符往往没有这个问题（因为只有一个参数）。也可以认为“优先级”的实质就是两个运算符在抢参数。</p><h2 id="一元运算符" tabindex="-1"><a class="header-anchor" href="#一元运算符"><span><a href="about:blank#%E4%B8%80%E5%85%83%E8%BF%90%E7%AE%97%E7%AC%A6"></a>一元运算符</span></a></h2><p>上节中说到了运算符的优先级，也提到了优先级一般只与多元运算符有关，这也意味着一元运算符的优先级总是高于多元运算符。因为我们需要先对它们进行解析。</p><p>当然，这部分也将同时解析参数本身（如变量、数字、字符串等等）。</p><p>关于表达式的解析，与语法分析相关的部分就是上文所说的优先级问题了，而剩下的较难较烦的部分是与目标代码的生成有关的。因此对于需要讲解的运算符，我们主要从它的目标代码入手。</p><h3 id="常量" tabindex="-1"><a class="header-anchor" href="#常量"><span><a href="about:blank#%E5%B8%B8%E9%87%8F"></a>常量</span></a></h3><p>首先是数字，用 <code>IMM</code> 指令将它加载到 <code>AX</code> 中即可：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">if</span> (token == Num) {</span><br><span class="line">    match(Num);</span><br><span class="line"></span><br><span class="line">    <span class="comment">// emit code</span></span><br><span class="line">    *++text = IMM;</span><br><span class="line">    *++text = token_val;</span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br><span class="line"></span><br></pre></td></tr></tbody></table><p>接着是字符串常量。它比较特殊的一点是 C 语言的字符串常量支持如下风格：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">char</span> *p;</span><br><span class="line">p = <span class="string">&quot;first line&quot;</span></span><br><span class="line">    <span class="string">&quot;second line&quot;</span>;</span><br></pre></td></tr></tbody></table><p>即跨行的字符串拼接，它相当于：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">char</span> *p;</span><br><span class="line">p = <span class="string">&quot;first linesecond line&quot;</span>;</span><br></pre></td></tr></tbody></table><p>所以解析的时候要注意这一点：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;&quot;&#39;</span>) {</span><br><span class="line">    <span class="comment">// emit code</span></span><br><span class="line">    *++text = IMM;</span><br><span class="line">    *++text = token_val;</span><br><span class="line"></span><br><span class="line">    match(<span class="string">&#39;&quot;&#39;</span>);</span><br><span class="line">    <span class="comment">// store the rest strings</span></span><br><span class="line">    <span class="keyword">while</span> (token == <span class="string">&#39;&quot;&#39;</span>) {</span><br><span class="line">        match(<span class="string">&#39;&quot;&#39;</span>);</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="comment">// append the end of string character &#39;\0&#39;, all the data are default</span></span><br><span class="line">    <span class="comment">// to 0, so just move data one position forward.</span></span><br><span class="line">    data = (<span class="type">char</span> *)(((<span class="type">int</span>)data + <span class="keyword">sizeof</span>(<span class="type">int</span>)) &amp; (-<span class="keyword">sizeof</span>(<span class="type">int</span>)));</span><br><span class="line">    expr_type = PTR;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="sizeof" tabindex="-1"><a class="header-anchor" href="#sizeof"><span><a href="about:blank#sizeof"></a>sizeof</span></a></h3><p><code>sizeof</code> 是一个一元运算符，我们需要知道后面参数的类型，类型的解析在前面的文章中我们已经很熟悉了。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Sizeof) {</span><br><span class="line">    <span class="comment">// sizeof is actually an unary operator</span></span><br><span class="line">    <span class="comment">// now only `sizeof(int)`, `sizeof(char)` and `sizeof(*...)` are</span></span><br><span class="line">    <span class="comment">// supported.</span></span><br><span class="line">    match(Sizeof);</span><br><span class="line">    match(<span class="string">&#39;(&#39;</span>);</span><br><span class="line">    expr_type = INT;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (token == Int) {</span><br><span class="line">        match(Int);</span><br><span class="line">    } <span class="keyword">else</span> <span class="keyword">if</span> (token == Char) {</span><br><span class="line">        match(Char);</span><br><span class="line">        expr_type = CHAR;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    <span class="keyword">while</span> (token == Mul) {</span><br><span class="line">        match(Mul);</span><br><span class="line">        expr_type = expr_type + PTR;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    match(<span class="string">&#39;)&#39;</span>);</span><br><span class="line"></span><br><span class="line">    <span class="comment">// emit code</span></span><br><span class="line">    *++text = IMM;</span><br><span class="line">    *++text = (expr_type == CHAR) ? <span class="keyword">sizeof</span>(<span class="type">char</span>) : <span class="keyword">sizeof</span>(<span class="type">int</span>);</span><br><span class="line"></span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>注意的是只支持 <code>sizeof(int)</code>，<code>sizeof(char)</code> 及 <code>sizeof(pointer type...)</code>。并且它的结果是 <code>int</code> 型。</p><h3 id="变量与函数调用" tabindex="-1"><a class="header-anchor" href="#变量与函数调用"><span><a href="about:blank#%E5%8F%98%E9%87%8F%E4%B8%8E%E5%87%BD%E6%95%B0%E8%B0%83%E7%94%A8"></a>变量与函数调用</span></a></h3><p>由于取变量的值与函数的调用都是以 <code>Id</code> 标记开头的，因此将它们放在一起处理。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Id) {</span><br><span class="line">    <span class="comment">// there are several type when occurs to Id</span></span><br><span class="line">    <span class="comment">// but this is unit, so it can only be</span></span><br><span class="line">    <span class="comment">// 1. function call</span></span><br><span class="line">    <span class="comment">// 2. Enum variable</span></span><br><span class="line">    <span class="comment">// 3. global/local variable</span></span><br><span class="line">    match(Id);</span><br><span class="line"></span><br><span class="line">    id = current_id;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (token == <span class="string">&#39;(&#39;</span>) {</span><br><span class="line">        <span class="comment">// function call</span></span><br><span class="line">        match(<span class="string">&#39;(&#39;</span>);</span><br><span class="line"></span><br><span class="line">        <span class="comment">// ①</span></span><br><span class="line">        <span class="comment">// pass in arguments</span></span><br><span class="line">        tmp = <span class="number">0</span>; <span class="comment">// number of arguments</span></span><br><span class="line">        <span class="keyword">while</span> (token != <span class="string">&#39;)&#39;</span>) {</span><br><span class="line">            expression(Assign);</span><br><span class="line">            *++text = PUSH;</span><br><span class="line">            tmp ++;</span><br><span class="line"></span><br><span class="line">            <span class="keyword">if</span> (token == <span class="string">&#39;,&#39;</span>) {</span><br><span class="line">                match(<span class="string">&#39;,&#39;</span>);</span><br><span class="line">            }</span><br><span class="line">        }</span><br><span class="line">        match(<span class="string">&#39;)&#39;</span>);</span><br><span class="line"></span><br><span class="line">        <span class="comment">// ②</span></span><br><span class="line">        <span class="comment">// emit code</span></span><br><span class="line">        <span class="keyword">if</span> (id[Class] == Sys) {</span><br><span class="line">            <span class="comment">// system functions</span></span><br><span class="line">            *++text = id[Value];</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (id[Class] == Fun) {</span><br><span class="line">            <span class="comment">// function call</span></span><br><span class="line">            *++text = CALL;</span><br><span class="line">            *++text = id[Value];</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> {</span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot;%d: bad function call\n&quot;</span>, line);</span><br><span class="line">            <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        <span class="comment">// ③</span></span><br><span class="line">        <span class="comment">// clean the stack for arguments</span></span><br><span class="line">        <span class="keyword">if</span> (tmp &gt; <span class="number">0</span>) {</span><br><span class="line">            *++text = ADJ;</span><br><span class="line">            *++text = tmp;</span><br><span class="line">        }</span><br><span class="line">        expr_type = id[Type];</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">else</span> <span class="keyword">if</span> (id[Class] == Num) {</span><br><span class="line">        <span class="comment">// ④</span></span><br><span class="line">        <span class="comment">// enum variable</span></span><br><span class="line">        *++text = IMM;</span><br><span class="line">        *++text = id[Value];</span><br><span class="line">        expr_type = INT;</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">else</span> {</span><br><span class="line">        <span class="comment">// ⑤</span></span><br><span class="line">        <span class="comment">// variable</span></span><br><span class="line">        <span class="keyword">if</span> (id[Class] == Loc) {</span><br><span class="line">            *++text = LEA;</span><br><span class="line">            *++text = index_of_bp - id[Value];</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (id[Class] == Glo) {</span><br><span class="line">            *++text = IMM;</span><br><span class="line">            *++text = id[Value];</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span> {</span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot;%d: undefined variable\n&quot;</span>, line);</span><br><span class="line">            <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        <span class="comment">//⑥</span></span><br><span class="line">        <span class="comment">// emit code, default behaviour is to load the value of the</span></span><br><span class="line">        <span class="comment">// address which is stored in `ax`</span></span><br><span class="line">        expr_type = id[Type];</span><br><span class="line">        *++text = (expr_type == Char) ? LC : LI;</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>①中注意我们是顺序将参数入栈，这和第三章：虚拟机中讲解的指令是对应的。与之不同，标准 C 是逆序将参数入栈的。</p><p>②中判断函数的类型，同样在第三章：“虚拟机”中我们介绍过内置函数的支持，如 <code>printf</code>, <code>read</code>, <code>malloc</code> 等等。内置函数有对应的汇编指令，而普通的函数则编译成 <code>CALL &lt;addr&gt;</code> 的形式。</p><p>③用于清除入栈的参数。因为我们不在乎出栈的值，所以直接修改栈指针的大小即可。</p><p>④：当该标识符是全局定义的枚举类型时，直接将对应的值用 <code>IMM</code> 指令存入 <code>AX</code> 即可。</p><p>⑤则是用于加载变量的值，如果是局部变量则采用与 <code>bp</code> 指针相对位置的形式（参见第 7章函数定义）。而如果是全局变量则用 <code>IMM</code> 加载变量的地址。</p><p>⑥：无论是全局还是局部变量，最终都根据它们的类型用 <code>LC</code> 或 <code>LI</code> 指令加载对应的值。</p><p>关于变量，你可能有疑问，如果遇到标识符就用 <code>LC/LI</code> 载入相应的值，那诸如 <code>a[10]</code> 之类的表达式要如何实现呢？后面我们会看到，根据标识符后的运算符，我们可能会修改或删除现有的 <code>LC/LI</code> 指令。</p><h3 id="强制转换" tabindex="-1"><a class="header-anchor" href="#强制转换"><span><a href="about:blank#%E5%BC%BA%E5%88%B6%E8%BD%AC%E6%8D%A2"></a>强制转换</span></a></h3><p>虽然我们前面没有提到，但我们一直用 <code>expr_type</code> 来保存一个表达式的类型，强制转换的作用是获取转换的类型，并直接修改 <code>expr_type</code> 的值。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;(&#39;</span>) {</span><br><span class="line">    <span class="comment">// cast or parenthesis</span></span><br><span class="line">    match(<span class="string">&#39;(&#39;</span>);</span><br><span class="line">    <span class="keyword">if</span> (token == Int || token == Char) {</span><br><span class="line">        tmp = (token == Char) ? CHAR : INT; <span class="comment">// cast type</span></span><br><span class="line">        match(token);</span><br><span class="line">        <span class="keyword">while</span> (token == Mul) {</span><br><span class="line">            match(Mul);</span><br><span class="line">            tmp = tmp + PTR;</span><br><span class="line">        }</span><br><span class="line"></span><br><span class="line">        match(<span class="string">&#39;)&#39;</span>);</span><br><span class="line"></span><br><span class="line">        expression(Inc); <span class="comment">// cast has precedence as Inc(++)</span></span><br><span class="line"></span><br><span class="line">        expr_type  = tmp;</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="comment">// normal parenthesis</span></span><br><span class="line">        expression(Assign);</span><br><span class="line">        match(<span class="string">&#39;)&#39;</span>);</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="指针取值" tabindex="-1"><a class="header-anchor" href="#指针取值"><span><a href="about:blank#%E6%8C%87%E9%92%88%E5%8F%96%E5%80%BC"></a>指针取值</span></a></h3><p>诸如 <code>*a</code> 的指针取值，关键是判断 <code>a</code> 的类型，而就像上节中提到的，当一个表达式解析结束时，它的类型保存在变量 <code>expr_type</code> 中。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Mul) {</span><br><span class="line">    <span class="comment">// dereference *&lt;addr&gt;</span></span><br><span class="line">    match(Mul);</span><br><span class="line">    expression(Inc); <span class="comment">// dereference has the same precedence as Inc(++)</span></span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (expr_type &gt;= PTR) {</span><br><span class="line">        expr_type = expr_type - PTR;</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%d: bad dereference\n&quot;</span>, line);</span><br><span class="line">        <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    *++text = (expr_type == CHAR) ? LC : LI;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="取址操作" tabindex="-1"><a class="header-anchor" href="#取址操作"><span><a href="about:blank#%E5%8F%96%E5%9D%80%E6%93%8D%E4%BD%9C"></a>取址操作</span></a></h3><p>这里我们就能看到“变量与函数调用”一节中所说的修改或删除 <code>LC/LI</code> 指令了。前文中我们说到，对于变量，我们会先加载它的地址，并根据它们类型使用 <code>LC/LI</code> 指令加载实际内容，例如对变量 <code>a</code>：</p><table><tbody><tr><td class="code"><pre><span class="line">IMM &lt;addr&gt;</span><br><span class="line">LI</span><br></pre></td></tr></tbody></table><p>那么对变量 <code>a</code> 取址，其实只要不执行 <code>LC/LI</code> 即可。因此我们删除相应的指令。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == And) {</span><br><span class="line">    <span class="comment">// get the address of</span></span><br><span class="line">    match(And);</span><br><span class="line">    expression(Inc); <span class="comment">// get the address of</span></span><br><span class="line">    <span class="keyword">if</span> (*text == LC || *text == LI) {</span><br><span class="line">        text --;</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%d: bad address of\n&quot;</span>, line);</span><br><span class="line">        <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    expr_type = expr_type + PTR;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="逻辑取反" tabindex="-1"><a class="header-anchor" href="#逻辑取反"><span><a href="about:blank#%E9%80%BB%E8%BE%91%E5%8F%96%E5%8F%8D"></a>逻辑取反</span></a></h3><p>我们没有直接的逻辑取反指令，因此我们判断它是否与数字 0 相等。而数字 0 代表了逻辑 “False”。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;!&#39;</span>) {</span><br><span class="line">    <span class="comment">// not</span></span><br><span class="line">    match(<span class="string">&#39;!&#39;</span>);</span><br><span class="line">    expression(Inc);</span><br><span class="line"></span><br><span class="line">    <span class="comment">// emit code, use &lt;expr&gt; == 0</span></span><br><span class="line">    *++text = PUSH;</span><br><span class="line">    *++text = IMM;</span><br><span class="line">    *++text = <span class="number">0</span>;</span><br><span class="line">    *++text = EQ;</span><br><span class="line"></span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="按位取反" tabindex="-1"><a class="header-anchor" href="#按位取反"><span><a href="about:blank#%E6%8C%89%E4%BD%8D%E5%8F%96%E5%8F%8D"></a>按位取反</span></a></h3><p>同样我们没有相应的指令，所以我们用异或来实现，即 <code>~a = a ^ 0xFFFF</code>。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == <span class="string">&#39;~&#39;</span>) {</span><br><span class="line">    <span class="comment">// bitwise not</span></span><br><span class="line">    match(<span class="string">&#39;~&#39;</span>);</span><br><span class="line">    expression(Inc);</span><br><span class="line"></span><br><span class="line">    <span class="comment">// emit code, use &lt;expr&gt; XOR -1</span></span><br><span class="line">    *++text = PUSH;</span><br><span class="line">    *++text = IMM;</span><br><span class="line">    *++text = <span class="number">-1</span>;</span><br><span class="line">    *++text = XOR;</span><br><span class="line"></span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="正负号" tabindex="-1"><a class="header-anchor" href="#正负号"><span><a href="about:blank#%E6%AD%A3%E8%B4%9F%E5%8F%B7"></a>正负号</span></a></h3><p>注意这里并不是四则运算中的加减法，而是单个数字的取正取负操作。同样，我们没有取负的操作，用 <code>0 - x</code> 来实现 <code>-x</code>。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Add) {</span><br><span class="line">    <span class="comment">// +var, do nothing</span></span><br><span class="line">    match(Add);</span><br><span class="line">    expression(Inc);</span><br><span class="line"></span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Sub) {</span><br><span class="line">    <span class="comment">// -var</span></span><br><span class="line">    match(Sub);</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (token == Num) {</span><br><span class="line">        *++text = IMM;</span><br><span class="line">        *++text = -token_val;</span><br><span class="line">        match(Num);</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line"></span><br><span class="line">        *++text = IMM;</span><br><span class="line">        *++text = <span class="number">-1</span>;</span><br><span class="line">        *++text = PUSH;</span><br><span class="line">        expression(Inc);</span><br><span class="line">        *++text = MUL;</span><br><span class="line">    }</span><br><span class="line"></span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="自增自减" tabindex="-1"><a class="header-anchor" href="#自增自减"><span><a href="about:blank#%E8%87%AA%E5%A2%9E%E8%87%AA%E5%87%8F"></a>自增自减</span></a></h3><p>注意的是自增自减操作的优先级是和它的位置有关的。如 <code>++p</code> 的优先级高于 <code>p++</code>，这里我们解析的就是类似 <code>++p</code> 的操作。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Inc || token == Dec) {</span><br><span class="line">    tmp = token;</span><br><span class="line">    match(token);</span><br><span class="line">    expression(Inc);</span><br><span class="line">    <span class="comment">// ①</span></span><br><span class="line">    <span class="keyword">if</span> (*text == LC) {</span><br><span class="line">        *text = PUSH;  <span class="comment">// to duplicate the address</span></span><br><span class="line">        *++text = LC;</span><br><span class="line">    } <span class="keyword">else</span> <span class="keyword">if</span> (*text == LI) {</span><br><span class="line">        *text = PUSH;</span><br><span class="line">        *++text = LI;</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%d: bad lvalue of pre-increment\n&quot;</span>, line);</span><br><span class="line">        <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line">    *++text = PUSH;</span><br><span class="line">    *++text = IMM;</span><br><span class="line">    <span class="comment">// ②</span></span><br><span class="line">    *++text = (expr_type &gt; PTR) ? <span class="keyword">sizeof</span>(<span class="type">int</span>) : <span class="keyword">sizeof</span>(<span class="type">char</span>);</span><br><span class="line">    *++text = (tmp == Inc) ? ADD : SUB;</span><br><span class="line">    *++text = (expr_type == CHAR) ? SC : SI;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>对应的汇编代码也比较直观，只是在实现 <code>++p</code>时，我们要使用变量 <code>p</code> 的地址两次，所以我们需要先 <code>PUSH</code> （①）。</p><p>②则是因为自增自减操作还需要处理是指针的情形。</p><h2 id="二元运算符" tabindex="-1"><a class="header-anchor" href="#二元运算符"><span><a href="about:blank#%E4%BA%8C%E5%85%83%E8%BF%90%E7%AE%97%E7%AC%A6"></a>二元运算符</span></a></h2><p>这里，我们需要处理多运算符的优先级问题，就如前文的“优先级”一节提到的，我们需要不断地向右扫描，直到遇到优先级 <strong>小于</strong> 当前优先级的运算符。</p><p>回想起我们之前定义过的各个标记，它们是以优先级从低到高排列的，即 <code>Assign</code> 的优先级最低，而 <code>Brak</code>（<code>[</code>） 的优先级最高。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="class"><span class="keyword">enum</span> {</span></span><br><span class="line">  Num = <span class="number">128</span>, Fun, Sys, Glo, Loc, Id,</span><br><span class="line">  Char, Else, Enum, If, Int, Return, Sizeof, While,</span><br><span class="line">  Assign, Cond, Lor, Lan, Or, Xor, And, Eq, Ne, Lt, Gt, Le, Ge, Shl, Shr, Add, Sub, Mul, Div, Mod, Inc, Dec, Brak</span><br><span class="line">};</span><br></pre></td></tr></tbody></table><p>所以，当我们调用 <code>expression(level)</code> 进行解析的时候，我们其实通过了参数 <code>level</code> 指定了当前的优先级。在前文的一元运算符处理中也用到了这一点。</p><p>所以，此时的二元运算符的解析的框架为：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">while</span> (token &gt;= level) {</span><br><span class="line">    <span class="comment">// parse token for binary operator and postfix operator</span></span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>解决了优先级的问题，让我们继续讲解如何把运算符编译成汇编代码吧。</p><h3 id="赋值操作" tabindex="-1"><a class="header-anchor" href="#赋值操作"><span><a href="about:blank#%E8%B5%8B%E5%80%BC%E6%93%8D%E4%BD%9C"></a>赋值操作</span></a></h3><p>赋值操作是优先级最低的运算符。考虑诸如 <code>a = (expession)</code> 的表达式，在解析 <code>=</code> 之前，我们已经为变量 <code>a</code> 生成了如下的汇编代码：</p><table><tbody><tr><td class="code"><pre><span class="line">IMM &lt;addr&gt;</span><br><span class="line">LC/LI</span><br></pre></td></tr></tbody></table><p>当解析完<code>=</code>右边的表达式后，相应的值会存放在 <code>ax</code> 中，此时，为了实际将这个值保存起来，我们需要类似下面的汇编代码：</p><table><tbody><tr><td class="code"><pre><span class="line">IMM &lt;addr&gt;</span><br><span class="line">PUSH</span><br><span class="line">SC/SI</span><br></pre></td></tr></tbody></table><p>明白了这点，也就能理解下面的源代码了：</p><table><tbody><tr><td class="code"><pre><span class="line">tmp = expr_type;</span><br><span class="line"><span class="keyword">if</span> (token == Assign) {</span><br><span class="line">    <span class="comment">// var = expr;</span></span><br><span class="line">    match(Assign);</span><br><span class="line">    <span class="keyword">if</span> (*text == LC || *text == LI) {</span><br><span class="line">        *text = PUSH; <span class="comment">// save the lvalue&#39;s pointer</span></span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%d: bad lvalue in assignment\n&quot;</span>, line);</span><br><span class="line">        <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line">    expression(Assign);</span><br><span class="line"></span><br><span class="line">    expr_type = tmp;</span><br><span class="line">    *++text = (expr_type == CHAR) ? SC : SI;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="三目运算符" tabindex="-1"><a class="header-anchor" href="#三目运算符"><span><a href="about:blank#%E4%B8%89%E7%9B%AE%E8%BF%90%E7%AE%97%E7%AC%A6"></a>三目运算符</span></a></h3><p>这是 C 语言中唯一的一个三元运算符： <code>? :</code>，它相当于一个小型的 If 语句，所以生成的代码也类似于 If 语句，这里就不多作解释。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Cond) {</span><br><span class="line">    <span class="comment">// expr ? a : b;</span></span><br><span class="line">    match(Cond);</span><br><span class="line">    *++text = JZ;</span><br><span class="line">    addr = ++text;</span><br><span class="line">    expression(Assign);</span><br><span class="line">    <span class="keyword">if</span> (token == <span class="string">&#39;:&#39;</span>) {</span><br><span class="line">        match(<span class="string">&#39;:&#39;</span>);</span><br><span class="line">    } <span class="keyword">else</span> {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%d: missing colon in conditional\n&quot;</span>, line);</span><br><span class="line">        <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line">    *addr = (<span class="type">int</span>)(text + <span class="number">3</span>);</span><br><span class="line">    *++text = JMP;</span><br><span class="line">    addr = ++text;</span><br><span class="line">    expression(Cond);</span><br><span class="line">    *addr = (<span class="type">int</span>)(text + <span class="number">1</span>);</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="逻辑运算符" tabindex="-1"><a class="header-anchor" href="#逻辑运算符"><span><a href="about:blank#%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6"></a>逻辑运算符</span></a></h3><p>这包括 <code>||</code> 和 <code>&amp;&amp;</code>。它们对应的汇编代码如下：</p><table><tbody><tr><td class="code"><pre><span class="line">&lt;expr1&gt; || &lt;expr2&gt;     &lt;expr1&gt; &amp;&amp; &lt;expr2&gt;</span><br><span class="line"></span><br><span class="line">  ...&lt;expr1&gt;...          ...&lt;expr1&gt;...</span><br><span class="line">  JNZ b                  JZ b</span><br><span class="line">  ...&lt;expr2&gt;...          ...&lt;expr2&gt;...</span><br><span class="line">b:                     b:</span><br></pre></td></tr></tbody></table><p>所以源码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Lor) {</span><br><span class="line">    <span class="comment">// logic or</span></span><br><span class="line">    match(Lor);</span><br><span class="line">    *++text = JNZ;</span><br><span class="line">    addr = ++text;</span><br><span class="line">    expression(Lan);</span><br><span class="line">    *addr = (<span class="type">int</span>)(text + <span class="number">1</span>);</span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Lan) {</span><br><span class="line">    <span class="comment">// logic and</span></span><br><span class="line">    match(Lan);</span><br><span class="line">    *++text = JZ;</span><br><span class="line">    addr = ++text;</span><br><span class="line">    expression(Or);</span><br><span class="line">    *addr = (<span class="type">int</span>)(text + <span class="number">1</span>);</span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h3 id="数学运算符" tabindex="-1"><a class="header-anchor" href="#数学运算符"><span><a href="about:blank#%E6%95%B0%E5%AD%A6%E8%BF%90%E7%AE%97%E7%AC%A6"></a>数学运算符</span></a></h3><p>它们包括 <code>|</code>, <code>^</code>, <code>&amp;</code>, <code>==</code>, <code>!=</code> <code>&lt;=</code>, <code>&gt;=</code>, <code>&lt;</code>, <code>&gt;</code>, <code>&lt;&lt;</code>, <code>&gt;&gt;</code>, <code>+</code>, <code>-</code>, <code>*</code>, <code>/</code>, <code>%</code>。它们的实现都很类似，我们以异或 <code>^</code> 为例：</p><table><tbody><tr><td class="code"><pre><span class="line">&lt;expr1&gt; ^ &lt;expr2&gt;</span><br><span class="line"></span><br><span class="line">...&lt;expr1&gt;...          &lt;- now the result is on ax</span><br><span class="line">PUSH</span><br><span class="line">...&lt;expr2&gt;...          &lt;- now the value of &lt;expr2&gt; is on ax</span><br><span class="line">XOR</span><br></pre></td></tr></tbody></table><p>所以它对应的代码为：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Xor) {</span><br><span class="line">    <span class="comment">// bitwise xor</span></span><br><span class="line">    match(Xor);</span><br><span class="line">    *++text = PUSH;</span><br><span class="line">    expression(And);</span><br><span class="line">    *++text = XOR;</span><br><span class="line">    expr_type = INT;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>其它的我们便不再详述。但这当中还有一个问题，就是指针的加减。在 C 语言中，指针加上数值等于将指针移位，且根据不同的类型移动的位移不同。如 <code>a + 1</code>，如果 <code>a</code> 是 <code>char *</code> 型，则移动一字节，而如果 <code>a</code> 是 <code>int *</code> 型，则移动 4 个字节（32位系统）。</p><p>另外，在作指针减法时，如果是两个指针相减（相同类型），则结果是两个指针间隔的元素个数。因此要有特殊的处理。</p><p>下面以加法为例，对应的汇编代码为：</p><table><tbody><tr><td class="code"><pre><span class="line">&lt;expr1&gt; + &lt;expr2&gt;</span><br><span class="line"></span><br><span class="line">normal         pointer</span><br><span class="line"></span><br><span class="line">&lt;expr1&gt;        &lt;expr1&gt;</span><br><span class="line">PUSH           PUSH</span><br><span class="line">&lt;expr2&gt;        &lt;expr2&gt;     |</span><br><span class="line">ADD            PUSH        | &lt;expr2&gt; * &lt;unit&gt;</span><br><span class="line">               IMM &lt;unit&gt;  |</span><br><span class="line">               MUL         |</span><br><span class="line">               ADD</span><br></pre></td></tr></tbody></table><p>即当 <code>&lt;expr1&gt;</code> 是指针时，要根据它的类型放大 <code>&lt;expr2&gt;</code> 的值，因此对应的源码如下：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Add) {</span><br><span class="line">    <span class="comment">// add</span></span><br><span class="line">    match(Add);</span><br><span class="line">    *++text = PUSH;</span><br><span class="line">    expression(Mul);</span><br><span class="line"></span><br><span class="line">    expr_type = tmp;</span><br><span class="line">    <span class="keyword">if</span> (expr_type &gt; PTR) {</span><br><span class="line">        <span class="comment">// pointer type, and not `char *`</span></span><br><span class="line">        *++text = PUSH;</span><br><span class="line">        *++text = IMM;</span><br><span class="line">        *++text = <span class="keyword">sizeof</span>(<span class="type">int</span>);</span><br><span class="line">        *++text = MUL;</span><br><span class="line">    }</span><br><span class="line">    *++text = ADD;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><p>相应的减法的代码就不贴了，可以自己实现看看，也可以看文末给出的链接。</p><h3 id="自增自减-1" tabindex="-1"><a class="header-anchor" href="#自增自减-1"><span><a href="about:blank#%E8%87%AA%E5%A2%9E%E8%87%AA%E5%87%8F-v2"></a>自增自减</span></a></h3><p>这次是后缀形式的，即 <code>p++</code> 或 <code>p--</code>。与前缀形式不同的是，在执行自增自减后， <code>ax</code>上需要保留原来的值。所以我们首先执行类似前缀自增自减的操作，再将 <code>ax</code> 中的值执行减/增的操作。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="comment">// 前缀形式 生成汇编代码</span></span><br><span class="line">*++text = PUSH;</span><br><span class="line">*++text = IMM;</span><br><span class="line">*++text = (expr_type &gt; PTR) ? <span class="keyword">sizeof</span>(<span class="type">int</span>) : <span class="keyword">sizeof</span>(<span class="type">char</span>);</span><br><span class="line">*++text = (tmp == Inc) ? ADD : SUB;</span><br><span class="line">*++text = (expr_type == CHAR) ? SC : SI;</span><br><span class="line"></span><br><span class="line"><span class="comment">// 后缀形式 生成汇编代码</span></span><br><span class="line">*++text = PUSH;</span><br><span class="line">*++text = IMM;</span><br><span class="line">*++text = (expr_type &gt; PTR) ? <span class="keyword">sizeof</span>(<span class="type">int</span>) : <span class="keyword">sizeof</span>(<span class="type">char</span>);</span><br><span class="line">*++text = (token == Inc) ? ADD : SUB;</span><br><span class="line">*++text = (expr_type == CHAR) ? SC : SI;</span><br><span class="line">*++text = PUSH;                                             <span class="comment">//</span></span><br><span class="line">*++text = IMM;                                              <span class="comment">// 执行相反的增/减操作</span></span><br><span class="line">*++text = (expr_type &gt; PTR) ? <span class="keyword">sizeof</span>(<span class="type">int</span>) : <span class="keyword">sizeof</span>(<span class="type">char</span>);   <span class="comment">//</span></span><br><span class="line">*++text = (token == Inc) ? SUB : ADD;                       <span class="comment">//</span></span><br></pre></td></tr></tbody></table><h3 id="数组取值操作" tabindex="-1"><a class="header-anchor" href="#数组取值操作"><span><a href="about:blank#%E6%95%B0%E7%BB%84%E5%8F%96%E5%80%BC%E6%93%8D%E4%BD%9C"></a>数组取值操作</span></a></h3><p>在学习 C 语言的时候你可能已经知道了，诸如 <code>a[10]</code> 的操作等价于 <code>*(a + 10)</code>。因此我们要做的就是生成类似的汇编代码：</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">else</span> <span class="keyword">if</span> (token == Brak) {</span><br><span class="line">    <span class="comment">// array access var[xx]</span></span><br><span class="line">    match(Brak);</span><br><span class="line">    *++text = PUSH;</span><br><span class="line">    expression(Assign);</span><br><span class="line">    match(<span class="string">&#39;]&#39;</span>);</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> (tmp &gt; PTR) {</span><br><span class="line">        <span class="comment">// pointer, `not char *`</span></span><br><span class="line">        *++text = PUSH;</span><br><span class="line">        *++text = IMM;</span><br><span class="line">        *++text = <span class="keyword">sizeof</span>(<span class="type">int</span>);</span><br><span class="line">        *++text = MUL;</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">else</span> <span class="keyword">if</span> (tmp &lt; PTR) {</span><br><span class="line">        <span class="built_in">printf</span>(<span class="string">&quot;%d: pointer type expected\n&quot;</span>, line);</span><br><span class="line">        <span class="built_in">exit</span>(<span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line">    expr_type = tmp - PTR;</span><br><span class="line">    *++text = ADD;</span><br><span class="line">    *++text = (expr_type == CHAR) ? LC : LI;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table><h2 id="代码" tabindex="-1"><a class="header-anchor" href="#代码"><span><a href="about:blank#%E4%BB%A3%E7%A0%81"></a>代码</span></a></h2><p>除了上述对表达式的解析外，我们还需要初始化虚拟机的栈，我们可以正确调用 <code>main</code> 函数，且当 <code>main</code> 函数结束时退出进程。</p><table><tbody><tr><td class="code"><pre><span class="line"><span class="type">int</span> *tmp;</span><br><span class="line"><span class="comment">// setup stack</span></span><br><span class="line">sp = (<span class="type">int</span> *)((<span class="type">int</span>)<span class="built_in">stack</span> + poolsize);</span><br><span class="line">*--sp = EXIT; <span class="comment">// call exit if main returns</span></span><br><span class="line">*--sp = PUSH; tmp = sp;</span><br><span class="line">*--sp = argc;</span><br><span class="line">*--sp = (<span class="type">int</span>)argv;</span><br><span class="line">*--sp = (<span class="type">int</span>)tmp;</span><br></pre></td></tr></tbody></table><p>当然，最后要注意的一点是：所有的变量定义必须放在语句之前。</p><p>本章的代码可以在 <a href="https://github.com/lotabout/write-a-C-interpreter/tree/step-6" target="_blank" rel="noopener noreferrer">Github<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a> 上下载，也可以直接 clone</p><table><tbody><tr><td class="code"><pre><span class="line">git clone -b step-6 https://github.com/lotabout/write-a-C-interpreter</span><br></pre></td></tr></tbody></table><p>通过 <code>gcc -o xc-tutor xc-tutor.c</code> 进行编译。并执行 <code>./xc-tutor hello.c</code> 查看结果。</p><p>正如我们保证的那样，我们的代码是自举的，能自己编译自己，所以你可以执行 <code>./xc-tutor xc-tutor.c hello.c</code>。可以看到和之前有同样的输出。</p><h2 id="小结" tabindex="-1"><a class="header-anchor" href="#小结"><span><a href="about:blank#%E5%B0%8F%E7%BB%93"></a>小结</span></a></h2><p>本章我们进行了最后的解析，解析表达式。本章有两个难点：</p><ol><li>如何通过递归调用 <code>expression</code> 来实现运算符的优先级。</li><li>如何为每个运算符生成对应的汇编代码。</li></ol><p>尽管代码看起来比较简单（虽然多），但其中用到的原理还是需要仔细推敲的。</p><p>最后，恭喜你！通过一步步的学习，自己实现了一个C语言的编译器（好吧，是解释器）。</p></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/designASimpileCCompiler/8.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/designASimpileCCompiler/7.html" aria-label="手把手教你构建 C 语言编译器（7）——语句"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->手把手教你构建 C 语言编译器（7）——语句</div></a><a class="route-link nav-link next" href="/tech/designASimpileCCompiler/9.html" aria-label="手把手教你构建 C 语言编译器（9）——总结"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">手把手教你构建 C 语言编译器（9）——总结<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/designASimpileCCompiler/9.html b/tech/designASimpileCCompiler/9.html
index b578576..247d724 100644
--- a/tech/designASimpileCCompiler/9.html
+++ b/tech/designASimpileCCompiler/9.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/designASimpileCCompiler/9.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="手把手教你构建 C 语言编译器（9）——总结"><meta property="og:description" content="转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-9/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（9）- 总结 Table of Contents 1. 虚拟机与目标代码 2. 词法分析 3. 语法分析 4. 关于编代码 5. 结语 恭喜你完成了自己的 C 语言编译..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="c"><meta property="article:tag" content="编译器"><meta property="article:tag" content="解释器"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"手把手教你构建 C 语言编译器（9）——总结","image":[""],"dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>手把手教你构建 C 语言编译器（9）——总结 | blog</title><meta name="description" content="转载声明 本文转自 https://lotabout.me/2016/write-a-C-interpreter-9/，如有侵权，请联系删除。 原文内容 手把手教你构建 C 语言编译器（9）- 总结 Table of Contents 1. 虚拟机与目标代码 2. 词法分析 3. 语法分析 4. 关于编代码 5. 结语 恭喜你完成了自己的 C 语言编译...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/9.html-CGdd1xtP.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/9.html-DOIgY3Qt.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/0.html" aria-label="手把手教你构建 C 语言编译器（0）- 前言"><!---->手把手教你构建 C 语言编译器（0）- 前言<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/1.html" aria-label="手把手教你构建 C 语言编译器（1）- 设计"><!---->手把手教你构建 C 语言编译器（1）- 设计<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/3.html" aria-label="手把手教你构建 C 语言编译器（3）——词法分析器"><!---->手把手教你构建 C 语言编译器（3）——词法分析器<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/4.html" aria-label="手把手教你构建 C 语言编译器（4）——递归下降"><!---->手把手教你构建 C 语言编译器（4）——递归下降<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/5.html" aria-label="手把手教你构建 C 语言编译器（5）——变量定义"><!---->手把手教你构建 C 语言编译器（5）——变量定义<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/6.html" aria-label="手把手教你构建 C 语言编译器（6）——函数定义"><!---->手把手教你构建 C 语言编译器（6）——函数定义<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/7.html" aria-label="手把手教你构建 C 语言编译器（7）——语句"><!---->手把手教你构建 C 语言编译器（7）——语句<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/8.html" aria-label="手把手教你构建 C 语言编译器（8）——表达式"><!---->手把手教你构建 C 语言编译器（8）——表达式<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/designASimpileCCompiler/9.html" aria-label="手把手教你构建 C 语言编译器（9）——总结"><!---->手把手教你构建 C 语言编译器（9）——总结<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/2.html" aria-label="转载声明"><!---->转载声明<!----></a></li></ul></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->手把手教你构建 C 语言编译器（9）——总结</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 5 分钟</span><meta property="timeRequired" content="PT5M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category2 clickable" role="navigation">编译原理</span><!--]--><meta property="articleSection" content="编译原理"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag4 clickable" role="navigation">c</span><span class="page-tag-item tag4 clickable" role="navigation">编译器</span><span class="page-tag-item tag4 clickable" role="navigation">解释器</span><!--]--><meta property="keywords" content="c,编译器,解释器"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#虚拟机与目标代码">虚拟机与目标代码</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#词法分析">词法分析</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#语法分析">语法分析</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#关于编代码">关于编代码</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#结语">结语</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="转载声明" tabindex="-1"><a class="header-anchor" href="#转载声明"><span>转载声明</span></a></h1><p>本文转自 <a href="https://lotabout.me/2016/write-a-C-interpreter-9/" target="_blank" rel="noopener noreferrer">https://lotabout.me/2016/write-a-C-interpreter-9/<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a>，如有侵权，请联系删除。</p><h1 id="原文内容" tabindex="-1"><a class="header-anchor" href="#原文内容"><span>原文内容</span></a></h1><h1 id="手把手教你构建-c-语言编译器-9-总结" tabindex="-1"><a class="header-anchor" href="#手把手教你构建-c-语言编译器-9-总结"><span>手把手教你构建 C 语言编译器（9）- 总结</span></a></h1><p>Table of Contents</p><ol><li><a href="about:blank#%E8%99%9A%E6%8B%9F%E6%9C%BA%E4%B8%8E%E7%9B%AE%E6%A0%87%E4%BB%A3%E7%A0%81">1. 虚拟机与目标代码</a></li><li><a href="about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90">2. 词法分析</a></li><li><a href="about:blank#%E8%AF%AD%E6%B3%95%E5%88%86%E6%9E%90">3. 语法分析</a></li><li><a href="about:blank#%E5%85%B3%E4%BA%8E%E7%BC%96%E4%BB%A3%E7%A0%81">4. 关于编代码</a></li><li><a href="about:blank#%E7%BB%93%E8%AF%AD">5. 结语</a></li></ol><p>恭喜你完成了自己的 C 语言编译器，本章中我们发一发牢骚，说一说编写编译器值得注意的一些问题；编写编译器时遇到的一些难题。</p><p>手把手教你构建 C 语言编译器系列共有10个部分：</p><ol><li><a href="http://lotabout.me/2015/write-a-C-interpreter-0/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（0）——前言<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-1/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（1）——设计<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-2/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（2）——虚拟机<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2015/write-a-C-interpreter-3/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（3）——词法分析器<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-4/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（4）——递归下降<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-5/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（5）——变量定义<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-6/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（6）——函数定义<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-7/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（7）——语句<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-8/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（8）——表达式<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="http://lotabout.me/2016/write-a-C-interpreter-9/" target="_blank" rel="noopener noreferrer">手把手教你构建 C 语言编译器（9）——总结<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li></ol><h2 id="虚拟机与目标代码" tabindex="-1"><a class="header-anchor" href="#虚拟机与目标代码"><span><a href="about:blank#%E8%99%9A%E6%8B%9F%E6%9C%BA%E4%B8%8E%E7%9B%AE%E6%A0%87%E4%BB%A3%E7%A0%81"></a>虚拟机与目标代码</span></a></h2><p>整个系列的一开始，我们就着手虚拟机的实现。不知道你是否有同感，这部分对于整个编译器的编写其实是十分重要的。我认为至少占了重要程度的50%。</p><p>这里要说明这样一个观点，学习编译原理时常常着眼于词法分析和语法分析，而忽略了同样重要的代码生成。对于学习或考试而言或许可以，但实际编译项目时，最为重要的是能“跑起来”，所以我们需要给予代码生成高度的重视。</p><p>同时我们也看到，在后期解析语句和表达式时，难点已经不再是语法分析了，而是如何为运算符生成相应的汇编代码。</p><h2 id="词法分析" tabindex="-1"><a class="header-anchor" href="#词法分析"><span><a href="about:blank#%E8%AF%8D%E6%B3%95%E5%88%86%E6%9E%90"></a>词法分析</span></a></h2><p>我们用了很暴力的手段编写了我们的词法分析器，我认为这并无不可。</p><p>但你依旧可以学习相关的知识，了解自动生成词法分析器的原理，它涉及到了“正则表达式”，“状态机”等等知识。相信这部分的知识能够很大程度上提高你的编程水平。</p><p>同时，如果今后你仍然想编写编译器，不妨试试这些自动生成工具。</p><h2 id="语法分析" tabindex="-1"><a class="header-anchor" href="#语法分析"><span><a href="about:blank#%E8%AF%AD%E6%B3%95%E5%88%86%E6%9E%90"></a>语法分析</span></a></h2><p>长期以来，语法分析对我而言一直是迷一样的存在，直到真正用递归下降的方式实现了一个。</p><p>我们用了专门的一章讲解了“递归下降”与 BNF 文法的关系。希望能减少你对理论的厌恶。至少，实现起来并不是太难。</p><p>如果有兴趣，可以学习学习这些文法，因为已经有许多自动生成的工具支持它们。这样你就不需要重复造轮子。可以看看 yacc 等工具，更先进的版本是 <code>bsion</code>。同时其它语言也有许多类似的支持。</p><p>题外话，最近知道了一个叫“PEG 文法”的表示方法，无论是读起来，还是实现起来，都比 BNF 要容易，你也可以学习看看。</p><h2 id="关于编代码" tabindex="-1"><a class="header-anchor" href="#关于编代码"><span><a href="about:blank#%E5%85%B3%E4%BA%8E%E7%BC%96%E4%BB%A3%E7%A0%81"></a>关于编代码</span></a></h2><p>这也是我自己的感慨吧。无论多好的教程，想要完全理解它，最好的方式恐怕还是要自己实现它。</p><p>只是在编写代码的过程中，我们会遇到许多的挫折，例如需要考虑许多细节，或是调试起来十分困难。但也只有真正静下心来去克服它，我们才能有所成长吧。</p><p>例如在编写表达式的解析时，大量重复的代码特别让人崩溃。还有就是调试编译器，简直痛苦地无话可说。</p><p>P.S. 如果你按这个系列自己编写代码，记得事先写一些用于输出汇编代码的函数，很有帮助的。</p><p>还有就是写这个系列的文章，开始的冲动过了之后，每写一篇都特别心烦，希望文章本身没有受我的这种情绪影响吧。</p><h2 id="结语" tabindex="-1"><a class="header-anchor" href="#结语"><span><a href="about:blank#%E7%BB%93%E8%AF%AD"></a>结语</span></a></h2><p>编程有趣又无趣，只有身在其中的我们才能体会吧。</p></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/designASimpileCCompiler/9.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/designASimpileCCompiler/8.html" aria-label="手把手教你构建 C 语言编译器（8）——表达式"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->手把手教你构建 C 语言编译器（8）——表达式</div></a><a class="route-link nav-link next" href="/tech/designASimpileCCompiler/2.html" aria-label="转载声明"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">转载声明<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/designASimpileCCompiler/index.html b/tech/designASimpileCCompiler/index.html
index c060680..8c83f31 100644
--- a/tech/designASimpileCCompiler/index.html
+++ b/tech/designASimpileCCompiler/index.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/designASimpileCCompiler/"><meta property="og:site_name" content="blog"><meta property="og:title" content="Design ASimpile CCompiler"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"Design ASimpile CCompiler"}</script><title>Design ASimpile CCompiler | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-Ak5uwHrg.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-SwHQd6yQ.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/0.html" aria-label="手把手教你构建 C 语言编译器（0）- 前言"><!---->手把手教你构建 C 语言编译器（0）- 前言<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/1.html" aria-label="手把手教你构建 C 语言编译器（1）- 设计"><!---->手把手教你构建 C 语言编译器（1）- 设计<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/3.html" aria-label="手把手教你构建 C 语言编译器（3）——词法分析器"><!---->手把手教你构建 C 语言编译器（3）——词法分析器<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/4.html" aria-label="手把手教你构建 C 语言编译器（4）——递归下降"><!---->手把手教你构建 C 语言编译器（4）——递归下降<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/5.html" aria-label="手把手教你构建 C 语言编译器（5）——变量定义"><!---->手把手教你构建 C 语言编译器（5）——变量定义<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/6.html" aria-label="手把手教你构建 C 语言编译器（6）——函数定义"><!---->手把手教你构建 C 语言编译器（6）——函数定义<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/7.html" aria-label="手把手教你构建 C 语言编译器（7）——语句"><!---->手把手教你构建 C 语言编译器（7）——语句<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/8.html" aria-label="手把手教你构建 C 语言编译器（8）——表达式"><!---->手把手教你构建 C 语言编译器（8）——表达式<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/9.html" aria-label="手把手教你构建 C 语言编译器（9）——总结"><!---->手把手教你构建 C 语言编译器（9）——总结<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/designASimpileCCompiler/2.html" aria-label="转载声明"><!---->转载声明<!----></a></li></ul></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->Design ASimpile CCompiler</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><!----></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><div class="vp-catalog-wrapper"><h2 class="vp-catalog-main-title">目录</h2><ul class="vp-catalogs"><li class="vp-catalog"><div class="vp-catalog-child-title"><a class="route-link vp-catalog-title" href="/tech/designASimpileCCompiler/0.html">手把手教你构建 C 语言编译器（0）- 前言</a></div></li><li class="vp-catalog"><div class="vp-catalog-child-title"><a class="route-link vp-catalog-title" href="/tech/designASimpileCCompiler/1.html">手把手教你构建 C 语言编译器（1）- 设计</a></div></li><li class="vp-catalog"><div class="vp-catalog-child-title"><a class="route-link vp-catalog-title" href="/tech/designASimpileCCompiler/3.html">手把手教你构建 C 语言编译器（3）——词法分析器</a></div></li><li class="vp-catalog"><div class="vp-catalog-child-title"><a class="route-link vp-catalog-title" href="/tech/designASimpileCCompiler/4.html">手把手教你构建 C 语言编译器（4）——递归下降</a></div></li><li class="vp-catalog"><div class="vp-catalog-child-title"><a class="route-link vp-catalog-title" href="/tech/designASimpileCCompiler/5.html">手把手教你构建 C 语言编译器（5）——变量定义</a></div></li><li class="vp-catalog"><div class="vp-catalog-child-title"><a class="route-link vp-catalog-title" href="/tech/designASimpileCCompiler/6.html">手把手教你构建 C 语言编译器（6）——函数定义</a></div></li><li class="vp-catalog"><div class="vp-catalog-child-title"><a class="route-link vp-catalog-title" href="/tech/designASimpileCCompiler/7.html">手把手教你构建 C 语言编译器（7）——语句</a></div></li><li class="vp-catalog"><div class="vp-catalog-child-title"><a class="route-link vp-catalog-title" href="/tech/designASimpileCCompiler/8.html">手把手教你构建 C 语言编译器（8）——表达式</a></div></li><li class="vp-catalog"><div class="vp-catalog-child-title"><a class="route-link vp-catalog-title" href="/tech/designASimpileCCompiler/9.html">手把手教你构建 C 语言编译器（9）——总结</a></div></li><li class="vp-catalog"><div class="vp-catalog-child-title"><a class="route-link vp-catalog-title" href="/tech/designASimpileCCompiler/2.html">转载声明</a></div></li></ul></div></div><!--[--><!----><!--]--><footer class="vp-page-meta"><!----><div class="vp-meta-item git-info"><!----><!----></div></footer><!----><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/docker.html b/tech/docker.html
index c0f56bc..c2b348d 100644
--- a/tech/docker.html
+++ b/tech/docker.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/docker.html"><meta property="og:site_name" content="blog"><meta property="og:description" content="GitHub Container Registry 加速 ghcr.io简介 ghcr.io 是 GitHub Container Registry 的域名。GitHub Container Registry 是 GitHub 提供的容器镜像注册表服务，允许开发者在 GitHub 上存储、管理和分享 Docker 镜像。它与 GitHub 代码仓库紧密..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="docker"><meta property="article:published_time" content="2024-09-12T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"","image":[""],"datePublished":"2024-09-12T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>blog</title><meta name="description" content="GitHub Container Registry 加速 ghcr.io简介 ghcr.io 是 GitHub Container Registry 的域名。GitHub Container Registry 是 GitHub 提供的容器镜像注册表服务，允许开发者在 GitHub 上存储、管理和分享 Docker 镜像。它与 GitHub 代码仓库紧密...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/docker.html-B-hYGcsZ.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/docker.html-DtdutZB7.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!----></h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-09-12T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category1 clickable" role="navigation">奇技淫巧</span><span class="page-category-item category2 clickable" role="navigation">docker</span><!--]--><meta property="articleSection" content="奇技淫巧,docker"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag2 clickable" role="navigation">docker</span><!--]--><meta property="keywords" content="docker"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#github-container-registry-加速">GitHub Container Registry 加速</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#ghcr-io简介">ghcr.io简介</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#镜像地址">镜像地址</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#配置方法">配置方法</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#docker-wsl2-容器目录">docker wsl2 容器目录</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h2 id="github-container-registry-加速" tabindex="-1"><a class="header-anchor" href="#github-container-registry-加速"><span>GitHub Container Registry 加速</span></a></h2><h3 id="ghcr-io简介" tabindex="-1"><a class="header-anchor" href="#ghcr-io简介"><span>ghcr.io简介</span></a></h3><ul><li>ghcr.io 是 GitHub Container Registry 的域名。GitHub Container Registry 是 GitHub 提供的容器镜像注册表服务，允许开发者在 GitHub 上存储、管理和分享 Docker 镜像。它与 GitHub 代码仓库紧密集成，可以使用相同的权限管理、团队协作和版本控制工具来管理容器镜像。</li><li>通过 GitHub Container Registry，开发者可以方便地将他们的容器镜像与代码仓库关联起来，这样就可以在同一个平台上管理代码和镜像。这种集成性使得持续集成/持续交付 (CI/CD) 流程更加简化和统一，开发团队可以更容易地构建、测试和部署应用程序。</li><li>对于使用 GitHub 作为代码托管平台的开发者来说，GitHub Container Registry 提供一个便捷且强大的容器镜像管理解决方案。通过该服务，可以更轻松地构建和部署容器化的应用程序，从而加速开发和交付周期。</li></ul><h3 id="镜像地址" tabindex="-1"><a class="header-anchor" href="#镜像地址"><span>镜像地址</span></a></h3><p>https://ghcr.nju.edu.cn</p><h3 id="配置方法" tabindex="-1"><a class="header-anchor" href="#配置方法"><span>配置方法</span></a></h3><div class="language-bash line-numbers-mode" data-ext="sh" data-title="sh"><pre class="language-bash"><code><span class="token function">sudo</span> <span class="token function">vim</span> /etc/docker/daemon.json
@@ -43,6 +43,6 @@
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div></div></div><p>拉取镜像方法</p><div class="language-bash line-numbers-mode" data-ext="sh" data-title="sh"><pre class="language-bash"><code><span class="token function">docker</span> pull ghcr.nju.edu.cn/open-webui/open-webui:main
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div></div></div><h2 id="docker-wsl2-容器目录" tabindex="-1"><a class="header-anchor" href="#docker-wsl2-容器目录"><span>docker wsl2 容器目录</span></a></h2><div class="language-text line-numbers-mode" data-ext="text" data-title="text"><pre class="language-text"><code>\\wsl$\docker-desktop-data\data\docker\containers
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div></div></div></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/docker.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><!----><a class="route-link nav-link next" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">「泛型与 OI」modint<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tech/docker_nginx\351\203\250\347\275\262web\351\241\271\347\233\256.html" "b/tech/docker_nginx\351\203\250\347\275\262web\351\241\271\347\233\256.html"
index 5fc8477..cf23a34 100644
--- "a/tech/docker_nginx\351\203\250\347\275\262web\351\241\271\347\233\256.html"
+++ "b/tech/docker_nginx\351\203\250\347\275\262web\351\241\271\347\233\256.html"
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="docker + nginx + acme.sh 部署 vue/flask 项目"><meta property="og:description" content="本文将介绍如何使用 Docker、Nginx 和 acme.sh 部署一个 Vue 和 Flask 项目。我们将详细讲解环境配置、项目结构、Nginx 配置、Docker 配置以及如何升级到 HTTPS。"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="King-sj"><meta property="article:tag" content="部署"><meta property="article:published_time" content="2024-09-16T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"docker + nginx + acme.sh 部署 vue/flask 项目","image":[""],"datePublished":"2024-09-16T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"King-sj"}]}</script><title>docker + nginx + acme.sh 部署 vue/flask 项目 | blog</title><meta name="description" content="本文将介绍如何使用 Docker、Nginx 和 acme.sh 部署一个 Vue 和 Flask 项目。我们将详细讲解环境配置、项目结构、Nginx 配置、Docker 配置以及如何升级到 HTTPS。">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->docker + nginx + acme.sh 部署 vue/flask 项目</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><span class="page-author-item">King-sj</span></span><span property="author" content="King-sj"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-09-16T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 3 分钟</span><meta property="timeRequired" content="PT3M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category4 clickable" role="navigation">nginx</span><!--]--><meta property="articleSection" content="nginx"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">部署</span><!--]--><meta property="keywords" content="部署"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#环境">环境</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#项目结构">项目结构</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#配置http服务">配置http服务</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#配置nginx">配置nginx</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#配置docker">配置docker</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#启动项目">启动项目</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#升级为https">升级为https</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#申请证书">申请证书</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#修改配置">修改配置</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#重启container">重启container</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#配置nginx反向代理-使flask支持-https">配置nginx反向代理，使flask支持 https</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#参考资料">参考资料</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="docker-nginx-acme-sh-部署-vue-flask-项目" tabindex="-1"><a class="header-anchor" href="#docker-nginx-acme-sh-部署-vue-flask-项目"><span>docker + nginx + acme.sh 部署 vue/flask 项目</span></a></h1><p>本文将介绍如何使用 Docker、Nginx 和 acme.sh 部署一个 Vue 和 Flask 项目。我们将详细讲解环境配置、项目结构、Nginx 配置、Docker 配置以及如何升级到 HTTPS。</p><!-- more --><div class="hint-container tip"><p class="hint-container-title">提示</p><p>需要先申请一个域名，本文是 bupt.online</p></div><h2 id="环境" tabindex="-1"><a class="header-anchor" href="#环境"><span>环境</span></a></h2><ul><li>Ubuntu</li><li>Docker</li><li>Docker-Compose</li><li>acme.sh</li><li>(python)</li><li>nginx</li></ul><h2 id="项目结构" tabindex="-1"><a class="header-anchor" href="#项目结构"><span>项目结构</span></a></h2><div class="language-tree line-numbers-mode" data-ext="tree" data-title="tree"><pre class="language-tree"><code>./nginx
@@ -228,6 +228,6 @@
 <span class="token punctuation">}</span>
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h3 id="重启container" tabindex="-1"><a class="header-anchor" href="#重启container"><span>重启container</span></a></h3><div class="language-bash line-numbers-mode" data-ext="sh" data-title="sh"><pre class="language-bash"><code><span class="token function">docker-compose</span> up <span class="token parameter variable">-d</span> <span class="token parameter variable">--build</span>
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div></div></div><h2 id="配置nginx反向代理-使flask支持-https" tabindex="-1"><a class="header-anchor" href="#配置nginx反向代理-使flask支持-https"><span>配置nginx反向代理，使flask支持 https</span></a></h2><p><a href="https://www.runoob.com/flask/flask-deployment.html" target="_blank" rel="noopener noreferrer">Flask 部署<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></p><p>#TODO - 添加flask+nginx配置</p><h2 id="参考资料" tabindex="-1"><a class="header-anchor" href="#参考资料"><span>参考资料</span></a></h2><ol><li><a href="https://nginx.org/en/docs/" target="_blank" rel="noopener noreferrer">Nginx Documentation<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="https://flask.palletsprojects.com/en/2.0.x/" target="_blank" rel="noopener noreferrer">Flask Documentation<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="https://www.digitalocean.com/community/tutorials/understanding-nginx-http-proxying-load-balancing-buffering-and-caching" target="_blank" rel="noopener noreferrer">Reverse Proxy Guide<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="https://letsencrypt.org/getting-started/" target="_blank" rel="noopener noreferrer">SSL Certificates<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="https://zhuanlan.zhihu.com/p/347064501" target="_blank" rel="noopener noreferrer">用acme.sh帮你免费且自动更新的HTTPS证书，省时又省力<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="https://www.cnblogs.com/vishun/p/15746849.html" target="_blank" rel="noopener noreferrer">docker部署certbot与nginx来获取ssl证书添加https及自动更新<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="https://sleele.com/2021/04/15/docker-acme-with-docker-nginx/" target="_blank" rel="noopener noreferrer">使用docker acme申请、续订泛域名证书，并自动重载docker nginx<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="https://geek-docs.com/flask/flask-questions/4_flask_can_you_add_https_functionality_to_a_python_flask_web_server.html#google_vignette" target="_blank" rel="noopener noreferrer">Flask: 如何给Python Flask Web服务器添加HTTPS功能<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li></ol></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/docker+nginx部署web项目.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><!----><a class="route-link nav-link next" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">Game Plugin<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/figure_bed.html b/tech/figure_bed.html
index cfd7e43..1ec61b7 100644
--- a/tech/figure_bed.html
+++ b/tech/figure_bed.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/figure_bed.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="github 图床"><meta property="og:description" content="参考 https://zhuanlan.zhihu.com/p/347342082"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:published_time" content="2024-11-01T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"github 图床","image":[""],"datePublished":"2024-11-01T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>github 图床 | blog</title><meta name="description" content="参考 https://zhuanlan.zhihu.com/p/347342082">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/figure_bed.html-BME-hebA.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/figure_bed.html-vyc89ngd.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->github 图床</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-11-01T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><!----></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><p>参考</p><ul><li>https://zhuanlan.zhihu.com/p/347342082</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/figure_bed.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->Game Plugin</div></a><a class="route-link nav-link next" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">github 工作流程<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tech/github \345\267\245\344\275\234\346\265\201.html" "b/tech/github \345\267\245\344\275\234\346\265\201.html"
index a84b758..85219f0 100644
--- "a/tech/github \345\267\245\344\275\234\346\265\201.html"	
+++ "b/tech/github \345\267\245\344\275\234\346\265\201.html"	
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="github 工作流程"><meta property="og:description" content="github 工作流程 十分钟学会正确的github工作流，和开源作者们使用同一套流程 相关信息 TODO"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"github 工作流程","image":[""],"dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>github 工作流程 | blog</title><meta name="description" content="github 工作流程 十分钟学会正确的github工作流，和开源作者们使用同一套流程 相关信息 TODO">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/github 工作流.html-CFTCrRk5.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/github 工作流.html-DJORqAx-.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->github 工作流程</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><!----></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="github-工作流程" tabindex="-1"><a class="header-anchor" href="#github-工作流程"><span>github 工作流程</span></a></h1><p><a href="https://www.bilibili.com/video/BV19e4y1q7JJ" target="_blank" rel="noopener noreferrer">十分钟学会正确的github工作流，和开源作者们使用同一套流程<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></p><div class="hint-container info"><p class="hint-container-title">相关信息</p><p>TODO</p></div></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/github 工作流.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/figure_bed.html" aria-label="github 图床"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->github 图床</div></a><a class="route-link nav-link next" href="/tech/python_requrements.html" aria-label="python requirements.txt"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">python requirements.txt<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/index.html b/tech/index.html
index c2913a5..dcda66d 100644
--- a/tech/index.html
+++ b/tech/index.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/"><meta property="og:site_name" content="blog"><meta property="og:title" content="技术"><meta property="og:description" content="技术 这里是所有与技术相关的文章，包括编程、工具使用、技术分享等内容。"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:published_time" content="2024-10-18T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"技术","image":[""],"datePublished":"2024-10-18T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>技术 | blog</title><meta name="description" content="技术 这里是所有与技术相关的文章，包括编程、工具使用、技术分享等内容。">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-Dakgazin.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-CqYdKjYM.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->技术</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-18T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><!----></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="技术" tabindex="-1"><a class="header-anchor" href="#技术"><span>技术</span></a></h1><p>这里是所有与技术相关的文章，包括编程、工具使用、技术分享等内容。</p><!----><div class="vp-catalog-wrapper"><h2 class="vp-catalog-main-title">目录</h2><ul class="vp-catalogs deep"><li class="vp-catalog"><h3 id class="vp-catalog-child-title"><a href="#" class="vp-catalog-header-anchor" aria-hidden="true">#</a><a class="route-link vp-catalog-title" href="/tech/docker.html"></a></h3><!----></li><li class="vp-catalog"><h3 id="「泛型与 OI」modint" class="vp-catalog-child-title"><a href="#「泛型与 OI」modint" class="vp-catalog-header-anchor" aria-hidden="true">#</a><a class="route-link vp-catalog-title" href="/tech/modint.html">「泛型与 OI」modint</a></h3><!----></li><li class="vp-catalog"><h3 id="「算术公理系统 1」自然数" class="vp-catalog-child-title"><a href="#「算术公理系统 1」自然数" class="vp-catalog-header-anchor" aria-hidden="true">#</a><a class="route-link vp-catalog-title" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html">「算术公理系统 1」自然数</a></h3><!----></li><li class="vp-catalog"><h3 id="android studio换源" class="vp-catalog-child-title"><a href="#android studio换源" class="vp-catalog-header-anchor" aria-hidden="true">#</a><a class="route-link vp-catalog-title" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html">android studio换源</a></h3><!----></li><li class="vp-catalog"><h3 id="CI/CD" class="vp-catalog-child-title"><a href="#CI/CD" class="vp-catalog-header-anchor" aria-hidden="true">#</a><a class="route-link vp-catalog-title" href="/tech/cicd.html">CI/CD</a></h3><!----></li><li class="vp-catalog"><h3 id="Design ASimpile CCompiler" class="vp-catalog-child-title has-children"><a href="#Design ASimpile CCompiler" class="vp-catalog-header-anchor" aria-hidden="true">#</a><a class="route-link vp-catalog-title" href="/tech/designASimpileCCompiler/">Design ASimpile CCompiler</a></h3><ul class="vp-child-catalogs"><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#手把手教你构建 C 语言编译器（0）- 前言" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/designASimpileCCompiler/0.html">手把手教你构建 C 语言编译器（0）- 前言</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#手把手教你构建 C 语言编译器（1）- 设计" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/designASimpileCCompiler/1.html">手把手教你构建 C 语言编译器（1）- 设计</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#手把手教你构建 C 语言编译器（3）——词法分析器" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/designASimpileCCompiler/3.html">手把手教你构建 C 语言编译器（3）——词法分析器</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#手把手教你构建 C 语言编译器（4）——递归下降" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/designASimpileCCompiler/4.html">手把手教你构建 C 语言编译器（4）——递归下降</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#手把手教你构建 C 语言编译器（5）——变量定义" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/designASimpileCCompiler/5.html">手把手教你构建 C 语言编译器（5）——变量定义</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#手把手教你构建 C 语言编译器（6）——函数定义" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/designASimpileCCompiler/6.html">手把手教你构建 C 语言编译器（6）——函数定义</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#手把手教你构建 C 语言编译器（7）——语句" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/designASimpileCCompiler/7.html">手把手教你构建 C 语言编译器（7）——语句</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#手把手教你构建 C 语言编译器（8）——表达式" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/designASimpileCCompiler/8.html">手把手教你构建 C 语言编译器（8）——表达式</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#手把手教你构建 C 语言编译器（9）——总结" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/designASimpileCCompiler/9.html">手把手教你构建 C 语言编译器（9）——总结</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#转载声明" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/designASimpileCCompiler/2.html">转载声明</a></div><!----></li></ul></li><li class="vp-catalog"><h3 id="docker + nginx + acme.sh 部署 vue/flask 项目" class="vp-catalog-child-title"><a href="#docker + nginx + acme.sh 部署 vue/flask 项目" class="vp-catalog-header-anchor" aria-hidden="true">#</a><a class="route-link vp-catalog-title" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></h3><!----></li><li class="vp-catalog"><h3 id="Game Plugin" class="vp-catalog-child-title"><a href="#Game Plugin" class="vp-catalog-header-anchor" aria-hidden="true">#</a><a class="route-link vp-catalog-title" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html">Game Plugin</a></h3><!----></li><li class="vp-catalog"><h3 id="github 图床" class="vp-catalog-child-title"><a href="#github 图床" class="vp-catalog-header-anchor" aria-hidden="true">#</a><a class="route-link vp-catalog-title" href="/tech/figure_bed.html">github 图床</a></h3><!----></li><li class="vp-catalog"><h3 id="github 工作流程" class="vp-catalog-child-title"><a href="#github 工作流程" class="vp-catalog-header-anchor" aria-hidden="true">#</a><a class="route-link vp-catalog-title" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html">github 工作流程</a></h3><!----></li><li class="vp-catalog"><h3 id="python requirements.txt" class="vp-catalog-child-title"><a href="#python requirements.txt" class="vp-catalog-header-anchor" aria-hidden="true">#</a><a class="route-link vp-catalog-title" href="/tech/python_requrements.html">python requirements.txt</a></h3><!----></li><li class="vp-catalog"><h3 id="Qt" class="vp-catalog-child-title"><a href="#Qt" class="vp-catalog-header-anchor" aria-hidden="true">#</a><a class="route-link vp-catalog-title" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html">Qt</a></h3><!----></li><li class="vp-catalog"><h3 id="Slidev" class="vp-catalog-child-title"><a href="#Slidev" class="vp-catalog-header-anchor" aria-hidden="true">#</a><a class="route-link vp-catalog-title" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html">Slidev</a></h3><!----></li><li class="vp-catalog"><h3 id="tensorflow 踩坑记录" class="vp-catalog-child-title"><a href="#tensorflow 踩坑记录" class="vp-catalog-header-anchor" aria-hidden="true">#</a><a class="route-link vp-catalog-title" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html">tensorflow 踩坑记录</a></h3><!----></li><li class="vp-catalog"><h3 id="vscode plugin" class="vp-catalog-child-title"><a href="#vscode plugin" class="vp-catalog-header-anchor" aria-hidden="true">#</a><a class="route-link vp-catalog-title" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html">vscode plugin</a></h3><!----></li><li class="vp-catalog"><h3 id="使用capacitor和ionic将vue项目迁移到mobile端" class="vp-catalog-child-title"><a href="#使用capacitor和ionic将vue项目迁移到mobile端" class="vp-catalog-header-anchor" aria-hidden="true">#</a><a class="route-link vp-catalog-title" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html">使用capacitor和ionic将vue项目迁移到mobile端</a></h3><!----></li><li class="vp-catalog"><h3 id="协程" class="vp-catalog-child-title"><a href="#协程" class="vp-catalog-header-anchor" aria-hidden="true">#</a><a class="route-link vp-catalog-title" href="/tech/%E5%8D%8F%E7%A8%8B.html">协程</a></h3><!----></li><li class="vp-catalog"><h3 id="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3" class="vp-catalog-child-title"><a href="#并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3" class="vp-catalog-header-anchor" aria-hidden="true">#</a><a class="route-link vp-catalog-title" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html">并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3</a></h3><!----></li><li class="vp-catalog"><h3 id="自建mail server" class="vp-catalog-child-title"><a href="#自建mail server" class="vp-catalog-header-anchor" aria-hidden="true">#</a><a class="route-link vp-catalog-title" href="/tech/mailserver.html">自建mail server</a></h3><!----></li><li class="vp-catalog"><h3 id="设计模式" class="vp-catalog-child-title has-children"><a href="#设计模式" class="vp-catalog-header-anchor" aria-hidden="true">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/">设计模式</a></h3><ul class="vp-child-catalogs"><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#Bridge 模式" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/bridge.html">Bridge 模式</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#builder 模式" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/builder.html">builder 模式</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#chainOfResponsibility 模式" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/chainOfResponsibility.html">chainOfResponsibility 模式</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#Command 模式" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/command.html">Command 模式</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#Composite 模式" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/composite.html">Composite 模式</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#Decorator 模式" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/decorator.html">Decorator 模式</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#facade 模式" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/facade.html">facade 模式</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#Factory Method 模式" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/factory_method.html">Factory Method 模式</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#Flyweight 模式" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/flyweight.html">Flyweight 模式</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#Interpreter 模式" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/interpreter.html">Interpreter 模式</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#Mediator 模式" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/mediator.html">Mediator 模式</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#Memento 模式" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/memento.html">Memento 模式</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#Observer 模式" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/observer.html">Observer 模式</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#Prototype 模式" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/prototype.html">Prototype 模式</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#Proxy 模式" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/proxy.html">Proxy 模式</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#Singleton 模式" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/singleton.html">Singleton 模式</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#State 模式" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/state.html">State 模式</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#Strategy 模式" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/strategy.html">Strategy 模式</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#Template Method 模式" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/template_method.html">Template Method 模式</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#Visitor 模式" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/visitor.html">Visitor 模式</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#抽象工厂模式" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/abstractFactory.html">抽象工厂模式</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#结语" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/end.html">结语</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#设计模式七大原则" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/DesignPrinciples.html">设计模式七大原则</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#迭代器模式" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/iterator.html">迭代器模式</a></div><!----></li><li class="vp-child-catalog"><div class="vp-catalog-sub-title"><a href="#适配器模式" class="vp-catalog-header-anchor">#</a><a class="route-link vp-catalog-title" href="/tech/DesignPatterns/adapter.html">适配器模式</a></div><!----></li></ul></li><li class="vp-catalog"><h3 id="闭包实现类" class="vp-catalog-child-title"><a href="#闭包实现类" class="vp-catalog-header-anchor" aria-hidden="true">#</a><a class="route-link vp-catalog-title" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html">闭包实现类</a></h3><!----></li><li class="vp-catalog"><h3 id="风格统一" class="vp-catalog-child-title"><a href="#风格统一" class="vp-catalog-header-anchor" aria-hidden="true">#</a><a class="route-link vp-catalog-title" href="/tech/style.html">风格统一</a></h3><!----></li></ul></div></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/index.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3</div></a><a class="route-link nav-link next" href="/tech/mailserver.html" aria-label="自建mail server"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">自建mail server<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/mailserver.html b/tech/mailserver.html
index f0b1562..646e296 100644
--- a/tech/mailserver.html
+++ b/tech/mailserver.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/mailserver.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="自建mail server"><meta property="og:description" content="参见: https://docker-mailserver.github.io/docker-mailserver/latest/ https://blog.csdn.net/qq_25866579/article/details/140717115 https://zhuanlan.zhihu.com/p/609639797 值得注意的是docker..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:published_time" content="2024-11-01T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"自建mail server","image":[""],"datePublished":"2024-11-01T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>自建mail server | blog</title><meta name="description" content="参见: https://docker-mailserver.github.io/docker-mailserver/latest/ https://blog.csdn.net/qq_25866579/article/details/140717115 https://zhuanlan.zhihu.com/p/609639797 值得注意的是docker...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/mailserver.html-DITZCknd.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/mailserver.html-DO5Xbwgi.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->自建mail server</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-11-01T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><!----></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#使用python-发送示例">使用python 发送示例</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><p>参见:</p><ul><li>https://docker-mailserver.github.io/docker-mailserver/latest/</li><li>https://blog.csdn.net/qq_25866579/article/details/140717115</li><li>https://zhuanlan.zhihu.com/p/609639797</li></ul><p>值得注意的是docker-mailserver 并不支持通过ui注册/修改等操作， 当可以自行实现（后端通过shell命令即可</p><h2 id="使用python-发送示例" tabindex="-1"><a class="header-anchor" href="#使用python-发送示例"><span>使用python 发送示例</span></a></h2><div class="language-python line-numbers-mode" data-ext="py" data-title="py"><pre class="language-python"><code><span class="token keyword">import</span> smtplib
@@ -68,6 +68,6 @@
 <span class="token keyword">except</span> Exception <span class="token keyword">as</span> e<span class="token punctuation">:</span>
   <span class="token keyword">print</span><span class="token punctuation">(</span><span class="token string-interpolation"><span class="token string">f&quot;Failed to send email: </span><span class="token interpolation"><span class="token punctuation">{</span>e<span class="token punctuation">}</span></span><span class="token string">&quot;</span></span><span class="token punctuation">)</span>
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><figure><img src="/assets/image-BdPl4tjs.png" alt="alt text" tabindex="0" loading="lazy"><figcaption>alt text</figcaption></figure></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/mailserver.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link active prev" href="/tech/" aria-label="技术"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->技术</div></a><a class="route-link nav-link next" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">闭包实现类<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/modint.html b/tech/modint.html
index 5926fbd..4942f93 100644
--- a/tech/modint.html
+++ b/tech/modint.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/modint.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="「泛型与 OI」modint"><meta property="og:description" content="在 OI 中，有大量的题目要求对一些数字取模，这便是本文写作的背景。 背景介绍 这些题目要么是因为答案太大，不方便输出结果，例如许多计数 dp；要么是因为答案是浮点数，出题人不愿意写一个确定精度的 Special Judge，例如很多期望概率题；要么是因为这道题目直接考察了模的性质和运用，比如大量的 998244353 类的多项式题目。"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="MODInt"><meta property="article:published_time" content="2023-08-02T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"「泛型与 OI」modint","image":[""],"datePublished":"2023-08-02T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>「泛型与 OI」modint | blog</title><meta name="description" content="在 OI 中，有大量的题目要求对一些数字取模，这便是本文写作的背景。 背景介绍 这些题目要么是因为答案太大，不方便输出结果，例如许多计数 dp；要么是因为答案是浮点数，出题人不愿意写一个确定精度的 Special Judge，例如很多期望概率题；要么是因为这道题目直接考察了模的性质和运用，比如大量的 998244353 类的多项式题目。">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/modint.html-M2GwLZ2U.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/modint.html-DNrISIPe.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->「泛型与 OI」modint</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2023-08-02T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category6 clickable" role="navigation">OI</span><!--]--><meta property="articleSection" content="OI"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">MODInt</span><!--]--><meta property="keywords" content="MODInt"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#背景介绍">背景介绍</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#过去的做法">过去的做法</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#第一种-直接取模">第一种 直接取模</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#第二种-函数取模">第二种 函数取模</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#泛型编程">泛型编程</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="「泛型与-oi」modint" tabindex="-1"><a class="header-anchor" href="#「泛型与-oi」modint"><span>「泛型与 OI」modint</span></a></h1><p>在 OI 中，有大量的题目要求对一些数字取模，这便是本文写作的背景。</p><h2 id="背景介绍" tabindex="-1"><a class="header-anchor" href="#背景介绍"><span>背景介绍</span></a></h2><p>这些题目要么是因为答案太大，不方便输出结果，例如许多计数 dp；要么是因为答案是浮点数，出题人不愿意写一个确定精度的 Special Judge，例如很多期望概率题；要么是因为这道题目直接考察了模的性质和运用，比如大量的 998244353 类的多项式题目。</p><!-- more --><h2 id="过去的做法" tabindex="-1"><a class="header-anchor" href="#过去的做法"><span>过去的做法</span></a></h2><p>在这种要求之下，取模运算就成为了编程中不可缺少的一部分。下面以式子 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="21.387ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 9452.9 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtext"><path data-c="1D68A" d="M126 306Q105 306 90 321T74 359Q74 439 211 439Q268 439 276 438Q343 426 383 390T430 306Q431 301 431 190V81Q446 79 465 78T492 76T509 72T521 60T524 38Q524 11 506 3Q502 1 466 1Q426 1 406 5T379 14T355 36L345 30Q284 -6 205 -6Q135 -6 92 39T48 141Q48 182 79 212T158 256T252 278T342 285H347V290Q347 315 325 335T267 362Q258 363 224 363Q189 363 185 362H179L178 358Q178 353 178 352T176 345T174 337T170 330T165 322T158 316T150 311T139 308T126 306ZM132 140Q132 115 157 93T224 70Q269 70 302 87T344 133Q346 139 347 175V211H339Q256 209 194 190T132 140Z"></path><path data-c="1D697" d="M89 431Q94 431 105 431T122 432Q173 432 173 399Q173 394 175 394Q176 394 190 404T233 425T298 436Q343 436 371 423Q411 402 423 365T436 265Q436 257 436 239T435 211V198V76H498Q512 67 516 60T520 38Q520 9 498 1H308Q286 9 286 32V38V45Q286 65 303 73Q309 76 329 76H351V188Q351 204 351 230T352 266Q352 321 341 341T288 361Q253 361 222 341T176 274L174 264L173 170V76H236Q250 67 254 60T258 38Q258 9 236 1H27Q4 8 4 38Q4 53 8 60T27 76H89V355H58L27 356Q4 363 4 393Q4 408 8 415T27 431H89Z" transform="translate(525,0)"></path><path data-c="1D69C" d="M72 317Q72 361 108 396T229 439Q231 439 245 439T268 440Q303 439 324 435T353 427T363 423L372 432Q380 440 397 440Q430 440 430 395Q430 390 430 380T429 366V335Q429 311 422 302T387 293Q364 293 355 300T346 316T343 336T325 353Q306 364 257 364Q209 364 178 351T147 317Q147 284 231 272Q327 256 357 247Q458 210 458 129V121Q458 74 413 34T271 -6Q246 -6 224 -3T189 5T165 14T150 22T144 26Q142 23 139 18T135 11T132 6T128 1T124 -2T119 -4T113 -5T104 -6Q84 -6 78 6T71 43Q71 48 71 60T72 79Q72 132 73 141T81 157Q90 166 115 166Q135 166 142 162T157 140Q168 108 191 90T260 70Q297 70 323 76T361 91T379 110T384 129Q384 157 346 171T247 195T165 212Q119 228 96 256T72 317Z" transform="translate(1050,0)"></path></g><g data-mml-node="mo" transform="translate(1852.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(2908.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3297.6,0)"><path data-c="1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></g><g data-mml-node="mo" transform="translate(4091.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5092,0)"><path data-c="1D466" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5804.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6804.4,0)"><path data-c="1D467" d="M347 338Q337 338 294 349T231 360Q211 360 197 356T174 346T162 335T155 324L153 320Q150 317 138 317Q117 317 117 325Q117 330 120 339Q133 378 163 406T229 440Q241 442 246 442Q271 442 291 425T329 392T367 375Q389 375 411 408T434 441Q435 442 449 442H462Q468 436 468 434Q468 430 463 420T449 399T432 377T418 358L411 349Q368 298 275 214T160 106L148 94L163 93Q185 93 227 82T290 71Q328 71 360 90T402 140Q406 149 409 151T424 153Q443 153 443 143Q443 138 442 134Q425 72 376 31T278 -11Q252 -11 232 6T193 40T155 57Q111 57 76 -3Q70 -11 59 -11H54H41Q35 -5 35 -2Q35 13 93 84Q132 129 225 214T340 322Q352 338 347 338Z"></path></g><g data-mml-node="mo" transform="translate(7269.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7880.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8880.9,0)"><path data-c="1D462" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext mathvariant="monospace">ans</mtext><mo>=</mo><mo stretchy="false">(</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo stretchy="false">)</mo><mo>×</mo><mi>u</mi></math></mjx-assistive-mml></mjx-container> 为例介绍几种写法。</p><h3 id="第一种-直接取模" tabindex="-1"><a class="header-anchor" href="#第一种-直接取模"><span>第一种 直接取模</span></a></h3><p>这种方法是直接取模，简单直接，清晰明了。</p><div class="language-cpp line-numbers-mode" data-ext="cpp" data-title="cpp"><pre class="language-cpp"><code><span class="token keyword">constexpr</span> <span class="token keyword">int</span> p<span class="token operator">=</span><span class="token number">998244353</span><span class="token punctuation">;</span>
@@ -77,6 +77,6 @@
 modint<span class="token operator">&lt;</span><span class="token keyword">int</span><span class="token punctuation">,</span><span class="token number">998244353</span><span class="token operator">&gt;</span> ans<span class="token operator">=</span><span class="token punctuation">(</span>x<span class="token operator">+</span>y<span class="token operator">+</span>z<span class="token punctuation">)</span><span class="token operator">*</span>u<span class="token punctuation">;</span>
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><p>这样使用的时候，一方面减少了心智负担，不用操心运算时忘记取模；另一方面采取了常数更小的加减法操作，运算更快。</p><p>唯一的缺点就是类型名难写，但是模数个数少的时候可以缩写，即写成：</p><div class="language-cpp line-numbers-mode" data-ext="cpp" data-title="cpp"><pre class="language-cpp"><code><span class="token keyword">typedef</span> modint<span class="token operator">&lt;</span><span class="token keyword">int</span><span class="token punctuation">,</span><span class="token number">998244353</span><span class="token operator">&gt;</span> modInt1<span class="token punctuation">;</span>
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div></div></div><p>这样就解决了类型名长的缺点。</p></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/modint.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/docker.html" aria-label="/tech/docker.html"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->/tech/docker.html</div></a><a class="route-link nav-link next" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">「算术公理系统 1」自然数<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/python_requrements.html b/tech/python_requrements.html
index ac96895..cb677e3 100644
--- a/tech/python_requrements.html
+++ b/tech/python_requrements.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/python_requrements.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="python requirements.txt"><meta property="og:description" content="Python 生成 requirements有两种方式 pip list --format=freeze > requirements.txt (推荐做法) pip freeze > requirements.txt (不推荐，会带有本地路径)"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="踩坑记录"><meta property="article:published_time" content="2024-10-29T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"python requirements.txt","image":[""],"datePublished":"2024-10-29T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>python requirements.txt | blog</title><meta name="description" content="Python 生成 requirements有两种方式 pip list --format=freeze > requirements.txt (推荐做法) pip freeze > requirements.txt (不推荐，会带有本地路径)">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/python_requrements.html-Va55tBYB.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/python_requrements.html-D_iboyN4.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->python requirements.txt</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-29T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category7 clickable" role="navigation">python</span><!--]--><meta property="articleSection" content="python"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag2 clickable" role="navigation">踩坑记录</span><!--]--><meta property="keywords" content="踩坑记录"></span></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><p>Python 生成 <code>requirements</code>有两种方式</p><ul><li><code>pip list --format=freeze &gt; requirements.txt</code> (推荐做法)</li><li><code>pip freeze &gt; requirements.txt</code> (不推荐，会带有本地路径)</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/python_requrements.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->github 工作流程</div></a><a class="route-link nav-link next" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">Qt<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tech/steam\346\250\241\347\273\204\345\274\200\345\217\221.html" "b/tech/steam\346\250\241\347\273\204\345\274\200\345\217\221.html"
index a10cfdb..9237be8 100644
--- "a/tech/steam\346\250\241\347\273\204\345\274\200\345\217\221.html"
+++ "b/tech/steam\346\250\241\347\273\204\345\274\200\345\217\221.html"
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="Game Plugin"><meta property="og:description" content="This is the content of the game plugin post. BepInEx AssetStudioAssetStudio dnSpy Harmony UnityExplorer 相关信息 TODO"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:published_time" content="2024-09-09T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"Game Plugin","image":[""],"datePublished":"2024-09-09T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>Game Plugin | blog</title><meta name="description" content="This is the content of the game plugin post. BepInEx AssetStudioAssetStudio dnSpy Harmony UnityExplorer 相关信息 TODO">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/steam模组开发.html-DQKsmuFu.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/steam模组开发.html-BnsNbJlM.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->Game Plugin</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-09-09T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><!----></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><p>This is the content of the game plugin post.</p><ul><li><a href="https://github.com/BepInEx/BepInEx" target="_blank" rel="noopener noreferrer">BepInEx<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="https://github.com/Perfare/AssetStudio" target="_blank" rel="noopener noreferrer">AssetStudioAssetStudio<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="https://github.com/dnSpy/dnSpy" target="_blank" rel="noopener noreferrer">dnSpy<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="https://github.com/pardeike/Harmony" target="_blank" rel="noopener noreferrer">Harmony<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="https://github.com/sinai-dev/UnityExplorer" target="_blank" rel="noopener noreferrer">UnityExplorer<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li></ul><div class="hint-container info"><p class="hint-container-title">相关信息</p><p>TODO</p></div></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/steam模组开发.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->docker + nginx + acme.sh 部署 vue/flask 项目</div></a><a class="route-link nav-link next" href="/tech/figure_bed.html" aria-label="github 图床"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">github 图床<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tech/style.html b/tech/style.html
index 6954e9f..740a310 100644
--- a/tech/style.html
+++ b/tech/style.html
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/style.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="风格统一"><meta property="og:description" content="风格统一 如何实现风格统一？ 可以使用*.editorconfig*文件来实现风格统一。 安装EditorConfig插件 (部分IDE默认直接支持) 在项目根目录下创建.editorconfig文件，并添加以下内容："><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:published_time" content="2024-08-25T12:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"风格统一","image":[""],"datePublished":"2024-08-25T12:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>风格统一 | blog</title><meta name="description" content="风格统一 如何实现风格统一？ 可以使用*.editorconfig*文件来实现风格统一。 安装EditorConfig插件 (部分IDE默认直接支持) 在项目根目录下创建.editorconfig文件，并添加以下内容：">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/style.html-CXxr9xzn.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/style.html-4qtN5eOW.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->风格统一</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-08-25T12:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category1 clickable" role="navigation">风格</span><!--]--><meta property="articleSection" content="风格"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag1 clickable" role="navigation">风格</span><!--]--><meta property="keywords" content="风格"></span></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="风格统一" tabindex="-1"><a class="header-anchor" href="#风格统一"><span>风格统一</span></a></h1><p>如何实现风格统一？ 可以使用*.editorconfig*文件来实现风格统一。</p><ol><li>安装EditorConfig插件 (部分IDE默认直接支持)</li><li>在项目根目录下创建.editorconfig文件，并添加以下内容：</li></ol><div class="language-text line-numbers-mode" data-ext="text" data-title="text"><pre class="language-text"><code>root = true
@@ -43,6 +43,6 @@
 trim_trailing_whitespace = true
 insert_final_newline = true
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/style.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->闭包实现类</div></a><!----></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tech/tensorflow\350\270\251\345\235\221.html" "b/tech/tensorflow\350\270\251\345\235\221.html"
index d9a17dc..f6d4859 100644
--- "a/tech/tensorflow\350\270\251\345\235\221.html"
+++ "b/tech/tensorflow\350\270\251\345\235\221.html"
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/tensorflow%E8%B8%A9%E5%9D%91.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="tensorflow 踩坑记录"><meta property="og:description" content="Pytorch 用于快速原型验证（学术研究）， TensorFlow 用于工业生产部署"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:published_time" content="2024-11-01T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"tensorflow 踩坑记录","image":[""],"datePublished":"2024-11-01T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>tensorflow 踩坑记录 | blog</title><meta name="description" content="Pytorch 用于快速原型验证（学术研究）， TensorFlow 用于工业生产部署">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/tensorflow踩坑.html-BAaphJ4H.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/tensorflow踩坑.html-CtBHw7dX.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->tensorflow 踩坑记录</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-11-01T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><!----></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><p><strong>Pytorch 用于快速原型验证（学术研究）， TensorFlow 用于工业生产部署</strong></p><!-- more --><p>近日使用 TensorFlow 完成图像去噪任务，然而速度太慢，于是寻求 GPU 资源进行加速。本以为 TensorFlow 2 能轻松使用 GPU（当然需要配置相关驱动），谁知 TensorFlow 高版本（&gt;=2.10.0）不再支持 Windows，而 Pytorch 仍然支持。最终 <s>选择了 Pytorch 进行实验</s> 寻得了Linux GPU 环境（感谢lucky&amp;agicy）。</p><p>此外，Pytorch 的动态计算图机制使得调试和开发更加灵活，适合快速迭代和原型验证。而 TensorFlow 虽然在工业部署中表现出色，但其静态计算图机制在开发过程中略显繁琐。综合考虑，决定以后在学术研究和快速原型验证阶段使用 Pytorch，而在工业生产部署阶段方才使用 TensorFlow（当然得是Linux环境）。</p></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/tensorflow踩坑.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->Slidev</div></a><a class="route-link nav-link next" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">vscode plugin<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tech/vsocde\346\217\222\344\273\266\345\274\200\345\217\221\345\260\217\350\256\260.html" "b/tech/vsocde\346\217\222\344\273\266\345\274\200\345\217\221\345\260\217\350\256\260.html"
index 895f287..c165300 100644
--- "a/tech/vsocde\346\217\222\344\273\266\345\274\200\345\217\221\345\260\217\350\256\260.html"
+++ "b/tech/vsocde\346\217\222\344\273\266\345\274\200\345\217\221\345\260\217\350\256\260.html"
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="vscode plugin"><meta property="og:description" content="vscode plugin // TODO https://code.visualstudio.com/api/get-started/your-first-extension tips 若activate function执行时间过长，会导致Activating extension 'undefined_publisher.kcodetime' fa..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"vscode plugin","image":[""],"dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>vscode plugin | blog</title><meta name="description" content="vscode plugin // TODO https://code.visualstudio.com/api/get-started/your-first-extension tips 若activate function执行时间过长，会导致Activating extension 'undefined_publisher.kcodetime' fa...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/vsocde插件开发小记.html-BytDpa8J.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->vscode plugin</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><!----></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="vscode-plugin" tabindex="-1"><a class="header-anchor" href="#vscode-plugin"><span>vscode plugin</span></a></h1><p>// TODO https://code.visualstudio.com/api/get-started/your-first-extension</p><h1 id="tips" tabindex="-1"><a class="header-anchor" href="#tips"><span>tips</span></a></h1><ul><li>若activate function执行时间过长，会导致<code>Activating extension &#39;undefined_publisher.kcodetime&#39; failed: AggregateError.</code>, 从而启动失败</li><li>若deactivate function执行时间超过5s, 会被强行终止，导致插件无法正常退出。</li><li>关闭vscode 不会触发onDidCloseTextDocument事件</li></ul></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/vsocde插件开发小记.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->tensorflow 踩坑记录</div></a><a class="route-link nav-link next" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">使用capacitor和ionic将vue项目迁移到mobile端<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tech/\343\200\214\347\256\227\346\234\257\345\205\254\347\220\206\347\263\273\347\273\237 1\343\200\215\350\207\252\347\204\266\346\225\260.html" "b/tech/\343\200\214\347\256\227\346\234\257\345\205\254\347\220\206\347\263\273\347\273\237 1\343\200\215\350\207\252\347\204\266\346\225\260.html"
index 07c94ca..6efe523 100644
--- "a/tech/\343\200\214\347\256\227\346\234\257\345\205\254\347\220\206\347\263\273\347\273\237 1\343\200\215\350\207\252\347\204\266\346\225\260.html"	
+++ "b/tech/\343\200\214\347\256\227\346\234\257\345\205\254\347\220\206\347\263\273\347\273\237 1\343\200\215\350\207\252\347\204\266\346\225\260.html"	
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="「算术公理系统 1」自然数"><meta property="og:description" content="假设存在一个算数系统的模型满足 Peano 公理，即假定 Peano 公理相容，在此承认次假设的基础之上，我们即可建立如今最常用的算术公理系统。自然数的定义则是构建此算术公理系统的第一步。"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="公理系统"><meta property="article:published_time" content="2023-07-09T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"「算术公理系统 1」自然数","image":[""],"datePublished":"2023-07-09T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>「算术公理系统 1」自然数 | blog</title><meta name="description" content="假设存在一个算数系统的模型满足 Peano 公理，即假定 Peano 公理相容，在此承认次假设的基础之上，我们即可建立如今最常用的算术公理系统。自然数的定义则是构建此算术公理系统的第一步。">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->「算术公理系统 1」自然数</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2023-07-09T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 18 分钟</span><meta property="timeRequired" content="PT18M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category3 clickable" role="navigation">数学</span><!--]--><meta property="articleSection" content="数学"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag3 clickable" role="navigation">公理系统</span><!--]--><meta property="keywords" content="公理系统"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#自然数的定义">自然数的定义</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#自然数的加法运算">自然数的加法运算</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#加法的定义">加法的定义</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#加法的性质">加法的性质</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#自然数的序">自然数的序</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#序的定义">序的定义</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#正自然数">正自然数</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#序的反对称性">序的反对称性</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#序的传递性">序的传递性</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#序的完全性">序的完全性</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#加法保序性">加法保序性</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#自然数的乘法运算">自然数的乘法运算</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#乘法的定义">乘法的定义</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#乘法的性质">乘法的性质</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#peano-公理的合理性">Peano 公理的合理性</a></li><li><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#乘法保序性">乘法保序性</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#乘法消去保序性">乘法消去保序性</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level3" href="#用图论阐述-peano-系统">用图论阐述 Peano 系统</a></li><!----><!--]--></ul></li><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="「算术公理系统-1」自然数" tabindex="-1"><a class="header-anchor" href="#「算术公理系统-1」自然数"><span>「算术公理系统 1」自然数</span></a></h1><p>假设存在一个算数系统的模型满足 Peano 公理，即假定 Peano 公理相容，在此承认次假设的基础之上，我们即可建立如今最常用的<strong>算术公理系统</strong>。<strong>自然数的定义</strong>则是构建此算术公理系统的第一步。</p><!-- more --><h2 id="自然数的定义" tabindex="-1"><a class="header-anchor" href="#自然数的定义"><span>自然数的定义</span></a></h2><p>先介绍 Peano 公理，共有五条：</p><ol><li><p><mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.05ex;" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></mjx-assistive-mml></mjx-container> 是自然数；</p></li><li><p>任何自然数的后继存在且唯一，下文用 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="6.271ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2772 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2383,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 表示 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 的后继；</p></li><li><p><mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.05ex;" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></mjx-assistive-mml></mjx-container> 不是任何自然数的后继；</p></li><li><p>不同的自然数后继不同；</p></li><li><p><mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="4.256ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 1881 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mo" transform="translate(503,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(892,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1492,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 是关于自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 的一个命题，且满足两个条件：</p><ul><li><mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="4.029ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 1781 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mo" transform="translate(503,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(892,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(1392,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 是真命题；</li><li>由 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="4.256ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 1881 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mo" transform="translate(503,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(892,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1492,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 为真命题可以推理出 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="9.17ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4053 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mo" transform="translate(503,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(892,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2286,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(2675,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3275,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3664,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo stretchy="false">(</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 为真命题。</li></ul><p>则有，对于任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container>，<mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="4.256ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 1881 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mo" transform="translate(503,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(892,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1492,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 为真命题。</p></li></ol><p>这样就定义了自然数，自然数这个新的数学对象因我们的假设而确立。</p><h2 id="自然数的加法运算" tabindex="-1"><a class="header-anchor" href="#自然数的加法运算"><span>自然数的加法运算</span></a></h2><p>自然数中最重要的运算当然是<strong>加法</strong>。</p><h3 id="加法的定义" tabindex="-1"><a class="header-anchor" href="#加法的定义"><span>加法的定义</span></a></h3><p>定义加法的运算规则：</p><ol><li>若 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是自然数，则 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="5.254ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 2322.4 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 的运算结果为 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container>，即 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="9.629ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 4256 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3656,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>+</mo><mi>n</mi><mo>=</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container>；</li><li>若 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="4.35ex" height="1.439ex" role="img" focusable="false" viewBox="0 -442 1922.7 636" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>,</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container> 都是自然数，则 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="25.064ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 11078.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7989,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9089.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10089.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10689.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo>+</mo><mi>n</mi><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo>+</mo><mi>n</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container>。</li></ol><p>下面我们需要证明对于任意两个自然数，都可以进行加法运算，也就是说，我们需要证明加法结果的存在性和唯一性。</p><h4 id="加法结果的存在性" tabindex="-1"><a class="header-anchor" href="#加法结果的存在性"><span>加法结果的存在性</span></a></h4><p><mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是任意自然数，记 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="6.032ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2666.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 表示 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="6.11ex" height="1.505ex" role="img" focusable="false" viewBox="0 -583 2700.4 665" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是否是自然数，即 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="6.11ex" height="1.505ex" role="img" focusable="false" viewBox="0 -583 2700.4 665" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是否存在。</p><p><mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是自然数，由加法运算规则 Ⅰ 有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="9.629ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 4256 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3656,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>+</mo><mi>n</mi><mo>=</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container>，进而有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="5.254ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 2322.4 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是自然数； <strong>即 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="5.177ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2288.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(1399.3,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(1899.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 得证。</strong></p><p><mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.986ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 878 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></mjx-assistive-mml></mjx-container> 和 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="6.11ex" height="1.505ex" role="img" focusable="false" viewBox="0 -583 2700.4 665" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是自然数，由 Peano 公理 Ⅱ 有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="6.9ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 3050 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 和 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="11.024ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4872.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2883.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo>+</mo><mi>n</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 是自然数； 根据加法运算规则 Ⅱ 有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="25.064ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 11078.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7989,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9089.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10089.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10689.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo>+</mo><mi>n</mi><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo>+</mo><mi>n</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container>，进有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="11.024ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4872.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是自然数； 综上所述，若 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="6.11ex" height="1.505ex" role="img" focusable="false" viewBox="0 -583 2700.4 665" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是自然数，则 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="11.024ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4872.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 也是自然数； <strong>即由 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="6.032ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2666.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 为真命题可以推出 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="10.946ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4838.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2793.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3182.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4060.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4449.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 为真命题。</strong></p><p>由 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="6.032ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2666.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 的性质和 Peano 公理 Ⅴ 有，对于任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.986ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 878 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></mjx-assistive-mml></mjx-container>，<mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="6.032ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2666.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 成立，即 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="6.11ex" height="1.505ex" role="img" focusable="false" viewBox="0 -583 2700.4 665" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是自然数，再根据 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 的任意性，得出对于任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="4.35ex" height="1.439ex" role="img" focusable="false" viewBox="0 -442 1922.7 636" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>,</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container>，<mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="6.11ex" height="1.505ex" role="img" focusable="false" viewBox="0 -583 2700.4 665" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 都是自然数。</p><h4 id="加法结果的唯一性" tabindex="-1"><a class="header-anchor" href="#加法结果的唯一性"><span>加法结果的唯一性</span></a></h4><p><mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是任意自然数，记 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="6.032ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2666.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 表示 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="6.11ex" height="1.505ex" role="img" focusable="false" viewBox="0 -583 2700.4 665" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是否唯一，即 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="6.11ex" height="1.505ex" role="img" focusable="false" viewBox="0 -583 2700.4 665" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 的结果是否唯一。</p><p><mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是自然数，由加法运算规则 Ⅰ 有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="9.629ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 4256 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3656,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>+</mo><mi>n</mi><mo>=</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container>，进而 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="5.254ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 2322.4 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是唯一的，就是 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container>； <strong>即 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="5.177ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2288.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(1399.3,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(1899.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 得证。</strong></p><p><mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.986ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 878 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></mjx-assistive-mml></mjx-container> 是自然数，<mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="6.11ex" height="1.505ex" role="img" focusable="false" viewBox="0 -583 2700.4 665" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是唯一的，由 Peano 公理 Ⅱ 有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="6.9ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 3050 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 是自然数且 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="11.024ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4872.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2883.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo>+</mo><mi>n</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 唯一； 根据加法运算规则 Ⅱ 有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="25.064ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 11078.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7989,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9089.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10089.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10689.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo>+</mo><mi>n</mi><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo>+</mo><mi>n</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container>，进有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="11.024ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4872.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 唯一； 综上所述，若 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="6.11ex" height="1.505ex" role="img" focusable="false" viewBox="0 -583 2700.4 665" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 唯一，则 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="11.024ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4872.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 也唯一； <strong>即由 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="6.032ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2666.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 为真命题可以推出 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="10.946ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4838.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2793.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3182.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4060.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4449.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 为真命题。</strong></p><p>由 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="6.032ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2666.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 的性质和 Peano 公理 Ⅴ 有，对于任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.986ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 878 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></mjx-assistive-mml></mjx-container>，<mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="6.032ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2666.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 成立，即 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="6.11ex" height="1.505ex" role="img" focusable="false" viewBox="0 -583 2700.4 665" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 唯一，再根据 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 的任意性，得出对于任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="4.35ex" height="1.439ex" role="img" focusable="false" viewBox="0 -442 1922.7 636" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>,</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container>，<mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="6.11ex" height="1.505ex" role="img" focusable="false" viewBox="0 -583 2700.4 665" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 都是唯一的。</p><h3 id="加法的性质" tabindex="-1"><a class="header-anchor" href="#加法的性质"><span>加法的性质</span></a></h3><p>在明确证明了自然数加法运算的良好性质，即任意两个自然数都可以进行加法运算，且加法运算的结果存在且唯一之后，我们终于可以对自然数加法的性质进行进一步的探索。</p><h4 id="加法交换律" tabindex="-1"><a class="header-anchor" href="#加法交换律"><span>加法交换律</span></a></h4><p>下面证明加法交换律，即对于任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="4.35ex" height="1.439ex" role="img" focusable="false" viewBox="0 -442 1922.7 636" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>,</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container>，有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="15.236ex" height="1.505ex" role="img" focusable="false" viewBox="0 -583 6734.4 665" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>+</mo><mi>m</mi><mo>=</mo><mi>m</mi><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container>。</p><p>直接证明比较困难，考虑从加法运算的定义下手，即先证明加法的两条运算规则符合交换律。</p><p>试证 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="17.9ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 7912 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3656,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4533.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5589.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6411.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(7412,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>+</mo><mi>n</mi><mo>=</mo><mi>n</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container>，首先有</p><mjx-container class="MathJax" jax="SVG" display="true" style="position:relative;"><svg style="vertical-align:-2.036ex;" xmlns="http://www.w3.org/2000/svg" width="37.243ex" height="5.204ex" role="img" focusable="false" viewBox="0 -1400 16461.4 2300" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,650)"><g data-mml-node="mtd"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(1722.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g><g data-mml-node="mtd" transform="translate(2222.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(1833.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(8778.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-650)"><g data-mml-node="mtd" transform="translate(2222.4,0)"></g><g data-mml-node="mtd" transform="translate(2222.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2055.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(3056,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(3556,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(8778.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right left right" columnspacing="0em 2em" rowspacing="3pt"><mtr><mtd><mn>0</mn><mo>+</mo><mn>0</mn></mtd><mtd><mi></mi><mo>=</mo><mn>0</mn><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅰ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mn>0</mn><mo>+</mo><mn>0</mn><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅰ</mtext></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container><p>进而当 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是自然数且 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="17.9ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 7912 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3656,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4533.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5589.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6411.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(7412,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>+</mo><mi>n</mi><mo>=</mo><mi>n</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container> 时有</p><mjx-container class="MathJax" jax="SVG" display="true" style="position:relative;"><svg style="vertical-align:-3.507ex;" xmlns="http://www.w3.org/2000/svg" width="47.524ex" height="8.145ex" role="img" focusable="false" viewBox="0 -2050 21005.4 3600" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3116.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3505.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4105.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3716.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(4105.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13322.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(4494.4,0)"></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3938.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(4939,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(5439,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5828,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(15916.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(877.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1933.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2755.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(3756,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(4494.4,0)"></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3716.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4327.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(5328,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(5828,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13322.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right left right" columnspacing="0em 2em" rowspacing="3pt"><mtr><mtd><mn>0</mn><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mtd><mtd><mi></mi><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅰ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo>+</mo><mn>0</mn><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mi>n</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>0</mn></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>+</mo><mn>0</mn><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅱ</mtext></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container><p>根据 Peano 公理 Ⅴ，得知 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="17.9ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 7912 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3656,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4533.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5589.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6411.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(7412,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>+</mo><mi>n</mi><mo>=</mo><mi>n</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container> 对任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 成立。</p><p>试证 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="39.105ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 17284.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7989,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9089.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10089.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10689.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(11356.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(12412,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(13806,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(14195,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(15073,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(15684.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(16684.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo>+</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container>，首先有</p><mjx-container class="MathJax" jax="SVG" display="true" style="position:relative;"><svg style="vertical-align:-3.507ex;" xmlns="http://www.w3.org/2000/svg" width="47.524ex" height="8.145ex" role="img" focusable="false" viewBox="0 -2050 21005.4 3600" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3116.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3505.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4105.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3716.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(4105.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13322.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(4494.4,0)"></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(3116.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(3838.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4839,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5439,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5828,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13322.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(4494.4,0)"></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(3116.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(3616.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4227.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5228,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mstyle" transform="translate(5828,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13322.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right left right" columnspacing="0em 2em" rowspacing="3pt"><mtr><mtd><mn>0</mn><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mtd><mtd><mi></mi><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅰ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mn>0</mn><mo>+</mo><mi>n</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅰ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo>+</mo><mi>n</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅱ</mtext></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container><p>进而当 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.986ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 878 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></mjx-assistive-mml></mjx-container> 是自然数且 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="39.105ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 17284.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7989,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9089.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10089.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10689.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(11356.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(12412,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(13806,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(14195,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(15073,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(15684.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(16684.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo>+</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 时有</p><mjx-container class="MathJax" jax="SVG" display="true" style="position:relative;"><svg style="vertical-align:-4.977ex;" xmlns="http://www.w3.org/2000/svg" width="68.629ex" height="11.086ex" role="img" focusable="false" viewBox="0 -2700 30333.9 4900" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1950)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(5666.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6055.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6655.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4216.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5217,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6611,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7000,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7989,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(8378,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(22650.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,650)"><g data-mml-node="mtd" transform="translate(7044.4,0)"></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4510.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4899.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5999.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7000,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7989,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(8378,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18422.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7989,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9089.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10089.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10689.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-650)"><g data-mml-node="mtd" transform="translate(7044.4,0)"></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4510.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4899.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5777.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6388.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7389,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7989,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(8378,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18422.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2883.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7989,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(8867,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(9478.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10478.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1950)"><g data-mml-node="mtd" transform="translate(7044.4,0)"></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4510.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4899.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5777.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6166.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6777.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7778,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mstyle" transform="translate(8378,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(22650.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right left right" columnspacing="0em 2em" rowspacing="3pt"><mtr><mtd><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mtd><mtd><mi></mi><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅱ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo>+</mo><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mi>m</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo>+</mo><mi>n</mi><mo stretchy="false">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo>+</mo><mi>n</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo>+</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo>+</mo><mi>n</mi></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>+</mo><mi>n</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅱ</mtext></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container><p>根据 Peano 公理 Ⅴ，得知 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="39.105ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 17284.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7600,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7989,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9089.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10089.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10689.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(11356.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(12412,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(13806,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(14195,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(15073,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(15684.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(16684.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo>+</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 对任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="4.35ex" height="1.439ex" role="img" focusable="false" viewBox="0 -442 1922.7 636" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>,</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container> 成立，将其称为新的<strong>加法运算规则 Ⅱ</strong>。</p><p>证明了加法运算规则的交换律之后，试证加法交换律 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="15.236ex" height="1.505ex" role="img" focusable="false" viewBox="0 -583 6734.4 665" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>+</mo><mi>m</mi><mo>=</mo><mi>m</mi><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container>，首先由加法运算规则 Ⅰ 有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="14.784ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 6534.4 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2878.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3934,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5034.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(6034.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>+</mo><mi>m</mi><mo>=</mo><mi>m</mi><mo>+</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container>，进而当 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是自然数且 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="15.236ex" height="1.505ex" role="img" focusable="false" viewBox="0 -583 6734.4 665" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>+</mo><mi>m</mi><mo>=</mo><mi>m</mi><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 时，有</p><mjx-container class="MathJax" jax="SVG" display="true" style="position:relative;"><svg style="vertical-align:-3.507ex;" xmlns="http://www.w3.org/2000/svg" width="49.234ex" height="8.145ex" role="img" focusable="false" viewBox="0 -2050 21761.4 3600" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2383,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(2994.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3994.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3938.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4939,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5817,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(6206,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14078.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(4872.4,0)"></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4216.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5217,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5817,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(6206,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14194,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(4872.4,0)"></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2433.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3434,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4828,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5217,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5817,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(6206,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14078.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right left right" columnspacing="0em 2em" rowspacing="3pt"><mtr><mtd><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>+</mo><mi>m</mi></mtd><mtd><mi></mi><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo>+</mo><mi>m</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅱ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo>+</mo><mi>n</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mi>n</mi><mo>+</mo><mi>m</mi><mo>=</mo><mi>m</mi><mo>+</mo><mi>n</mi></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>m</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅱ</mtext></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container><p>根据 Peano 公理 Ⅴ，得知 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="15.236ex" height="1.505ex" role="img" focusable="false" viewBox="0 -583 6734.4 665" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>+</mo><mi>m</mi><mo>=</mo><mi>m</mi><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 对任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="4.35ex" height="1.439ex" role="img" focusable="false" viewBox="0 -442 1922.7 636" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>,</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container> 成立，即加法交换律成立。</p><h4 id="加法结合律" tabindex="-1"><a class="header-anchor" href="#加法结合律"><span>加法结合律</span></a></h4><p>下面证明加法结合律，即对于任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="5.159ex" height="2.009ex" role="img" focusable="false" viewBox="0 -694 2280.3 888" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi></math></mjx-assistive-mml></mjx-container>，有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="23.894ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 10561.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5947.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6698.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(7698.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8739.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9739.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(10172.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo stretchy="false">)</mo><mo>+</mo><mi>c</mi><mo>=</mo><mi>a</mi><mo>+</mo><mo stretchy="false">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container>。</p><p>首先当 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="5.128ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 2266.6 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container> 时，有</p><mjx-container class="MathJax" jax="SVG" display="true" style="position:relative;"><svg style="vertical-align:-4.977ex;" xmlns="http://www.w3.org/2000/svg" width="48.216ex" height="11.086ex" role="img" focusable="false" viewBox="0 -2700 21311.3 4900" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1950)"><g data-mml-node="mtd"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g><g data-mml-node="mtd" transform="translate(4613.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(1333.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2473.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3474,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(3903,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4514.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(5514.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(6014.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18211.8,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,650)"><g data-mml-node="mtd" transform="translate(4613.9,0)"></g><g data-mml-node="mtd" transform="translate(4613.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3085,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(3514,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13628.3,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-650)"><g data-mml-node="mtd" transform="translate(4613.9,0)"></g><g data-mml-node="mtd" transform="translate(4613.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(3085,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3474,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4125.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(5125.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(5625.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(6014.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13628.3,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1950)"><g data-mml-node="mtd" transform="translate(4613.9,0)"></g><g data-mml-node="mtd" transform="translate(4613.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(3085,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3474,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4125.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5125.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5558.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5947.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18211.8,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right left right" columnspacing="0em 2em" rowspacing="3pt"><mtr><mtd><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo stretchy="false">)</mo><mo>+</mo><mi>c</mi></mtd><mtd><mi></mi><mo>=</mo><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo stretchy="false">)</mo><mo>+</mo><mn>0</mn><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mi>c</mi><mo>=</mo><mn>0</mn></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅰ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>a</mi><mo>+</mo><mo stretchy="false">(</mo><mi>b</mi><mo>+</mo><mn>0</mn><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅰ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>a</mi><mo>+</mo><mo stretchy="false">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mi>c</mi><mo>=</mo><mn>0</mn></mrow></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container><p>进而当 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="0.98ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 433 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></mjx-assistive-mml></mjx-container> 为自然数且 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="23.894ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 10561.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5947.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6698.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(7698.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8739.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9739.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(10172.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo stretchy="false">)</mo><mo>+</mo><mi>c</mi><mo>=</mo><mi>a</mi><mo>+</mo><mo stretchy="false">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 时有</p><mjx-container class="MathJax" jax="SVG" display="true" style="position:relative;"><svg style="vertical-align:-4.977ex;" xmlns="http://www.w3.org/2000/svg" width="66.289ex" height="11.086ex" role="img" focusable="false" viewBox="0 -2700 29299.7 4900" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1950)"><g data-mml-node="mtd"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(5574.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5963.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6396.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(6785.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mo" transform="translate(3116.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3505.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4256.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5257,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(5686,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6297.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7297.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(7730.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(8119.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(21616.7,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,650)"><g data-mml-node="mtd" transform="translate(6785.9,0)"></g><g data-mml-node="mtd" transform="translate(6785.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(3867.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(4868,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5257,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(5908.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6908.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(7341.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7730.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(8119.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(17905.3,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5947.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6698.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(7698.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8739.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9739.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(10172.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-650)"><g data-mml-node="mtd" transform="translate(6785.9,0)"></g><g data-mml-node="mtd" transform="translate(6785.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3085,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4479,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4868,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(5519.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6519.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6952.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(7341.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(21616.7,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1950)"><g data-mml-node="mtd" transform="translate(6785.9,0)"></g><g data-mml-node="mtd" transform="translate(6785.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(3085,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3474,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4125.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5125.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6519.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6908.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(7341.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7730.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(8119.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(21616.7,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right left right" columnspacing="0em 2em" rowspacing="3pt"><mtr><mtd><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo stretchy="false">)</mo><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></mtd><mtd><mi></mi><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo stretchy="false">)</mo><mo>+</mo><mi>c</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅱ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mo stretchy="false">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo stretchy="false">)</mo><mo>+</mo><mi>c</mi><mo>=</mo><mi>a</mi><mo>+</mo><mo stretchy="false">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo stretchy="false">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅱ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>a</mi><mo>+</mo><mo stretchy="false">(</mo><mi>b</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅱ</mtext></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container><p>根据 Peano 公理 Ⅴ，得知 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="23.894ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 10561.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5947.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6698.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(7698.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8739.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9739.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(10172.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo stretchy="false">)</mo><mo>+</mo><mi>c</mi><mo>=</mo><mi>a</mi><mo>+</mo><mo stretchy="false">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 对任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="5.159ex" height="2.009ex" role="img" focusable="false" viewBox="0 -694 2280.3 888" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi></math></mjx-assistive-mml></mjx-container> 成立，即加法结合律成立。</p><h4 id="加法消去律" tabindex="-1"><a class="header-anchor" href="#加法消去律"><span>加法消去律</span></a></h4><p>下面证明加法消去律，即对于任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="5.159ex" height="2.009ex" role="img" focusable="false" viewBox="0 -694 2280.3 888" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi></math></mjx-assistive-mml></mjx-container>，有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="21.379ex" height="1.756ex" role="img" focusable="false" viewBox="0 -694 9449.6 776" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5880.2,0)"><path data-c="21D4" d="M308 524Q318 526 323 526Q340 526 340 514Q340 507 336 499Q326 476 314 454T292 417T274 391T260 374L255 368Q255 367 500 367Q744 367 744 368L739 374Q734 379 726 390T707 416T685 453T663 499Q658 511 658 515Q658 525 680 525Q687 524 690 523T695 519T701 507Q766 359 902 287Q921 276 939 269T961 259T966 250Q966 246 965 244T960 240T949 236T930 228T902 213Q763 137 701 -7Q697 -16 695 -19T690 -23T680 -25Q658 -25 658 -15Q658 -11 663 1Q673 24 685 46T707 83T725 109T739 126L744 132Q744 133 500 133Q255 133 255 132L260 126Q265 121 273 110T292 84T314 47T336 1Q341 -11 341 -15Q341 -25 319 -25Q312 -24 309 -23T304 -19T298 -7Q233 141 97 213Q83 221 70 227T51 235T41 239T35 243T34 250T35 256T40 261T51 265T70 273T97 287Q235 363 299 509Q305 522 308 524ZM792 319L783 327H216Q183 294 120 256L110 250L120 244Q173 212 207 181L216 173H783L792 181Q826 212 879 244L889 250L879 256Q826 288 792 319Z"></path></g><g data-mml-node="mi" transform="translate(7158,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7964.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9020.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>+</mo><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo stretchy="false">⇔</mo><mi>a</mi><mo>=</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container>。</p><p>试证 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="21.379ex" height="1.756ex" role="img" focusable="false" viewBox="0 -694 9449.6 776" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(3847.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4598.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5598.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6309.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(7365.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8016.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9016.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>b</mi><mo stretchy="false">⇒</mo><mi>a</mi><mo>+</mo><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>c</mi></math></mjx-assistive-mml></mjx-container>。</p><p>首先当 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="5.128ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 2266.6 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container> 时有</p><mjx-container class="MathJax" jax="SVG" display="true" style="position:relative;"><svg style="vertical-align:-6.448ex;" xmlns="http://www.w3.org/2000/svg" width="37.223ex" height="14.027ex" role="img" focusable="false" viewBox="0 -3350 16452.4 6200" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,2600)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g><g data-mml-node="mtd" transform="translate(2184.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(3085,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(3585,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13352.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd" transform="translate(2184.4,0)"></g><g data-mml-node="mtd" transform="translate(2184.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mstyle" transform="translate(1862.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(8769.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(2184.4,0)"></g><g data-mml-node="mtd" transform="translate(2184.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(1762.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13327.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(2184.4,0)"></g><g data-mml-node="mtd" transform="translate(2184.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(2985,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(3485,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(8769.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-2600)"><g data-mml-node="mtd" transform="translate(2184.4,0)"></g><g data-mml-node="mtd" transform="translate(2184.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mstyle" transform="translate(3418,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13352.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right left right" columnspacing="0em 2em" rowspacing="3pt"><mtr><mtd><mi>a</mi><mo>+</mo><mi>c</mi></mtd><mtd><mi></mi><mo>=</mo><mi>a</mi><mo>+</mo><mn>0</mn><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mi>c</mi><mo>=</mo><mn>0</mn></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>a</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅰ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>b</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mi>a</mi><mo>=</mo><mi>b</mi></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>b</mi><mo>+</mo><mn>0</mn><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅰ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>c</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mi>c</mi><mo>=</mo><mn>0</mn></mrow></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container><p>进而当 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="0.98ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 433 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></mjx-assistive-mml></mjx-container> 为自然数且 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="21.379ex" height="1.756ex" role="img" focusable="false" viewBox="0 -694 9449.6 776" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(3847.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4598.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5598.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6309.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(7365.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8016.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9016.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>b</mi><mo stretchy="false">⇒</mo><mi>a</mi><mo>+</mo><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>c</mi></math></mjx-assistive-mml></mjx-container> 时有</p><mjx-container class="MathJax" jax="SVG" display="true" style="position:relative;"><svg style="vertical-align:-3.507ex;" xmlns="http://www.w3.org/2000/svg" width="52.781ex" height="8.145ex" role="img" focusable="false" viewBox="0 -2050 23329 3600" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(3867.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4868,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5301,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5690,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(15646,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(3767.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5590,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13046.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(3847.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4598.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5598.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6309.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(7365.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8016.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9016.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5590,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(15646,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right left right" columnspacing="0em 2em" rowspacing="3pt"><mtr><mtd><mi>a</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></mtd><mtd><mi></mi><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>c</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅱ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mi>a</mi><mo>=</mo><mi>b</mi><mo stretchy="false">⇒</mo><mi>a</mi><mo>+</mo><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>c</mi></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅱ</mtext></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container><p>即 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="47.402ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 20951.6 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(3847.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4598.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5598.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6309.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(7365.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8016.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9016.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9727.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(11005.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(11756.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(12756.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(14150.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(14539.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(14972.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(15639.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(16695.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(17346.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(18346.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(19740.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(20129.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(20562.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>b</mi><mo stretchy="false">⇒</mo><mi>a</mi><mo>+</mo><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo stretchy="false">⇒</mo><mi>a</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>=</mo><mi>b</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container>，根据 Peano 公理 Ⅴ，得知 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="21.379ex" height="1.756ex" role="img" focusable="false" viewBox="0 -694 9449.6 776" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(3847.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4598.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5598.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6309.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(7365.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8016.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9016.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>b</mi><mo stretchy="false">⇒</mo><mi>a</mi><mo>+</mo><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>c</mi></math></mjx-assistive-mml></mjx-container> 对任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="5.159ex" height="2.009ex" role="img" focusable="false" viewBox="0 -694 2280.3 888" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi></math></mjx-assistive-mml></mjx-container> 成立。</p><p>试证 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="21.379ex" height="1.756ex" role="img" focusable="false" viewBox="0 -694 9449.6 776" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5880.2,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(7158,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7964.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9020.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>+</mo><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo stretchy="false">⇒</mo><mi>a</mi><mo>=</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container>。</p><p>首先当 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="5.128ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 2266.6 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container> 时有</p><mjx-container class="MathJax" jax="SVG" display="true" style="position:relative;"><svg style="vertical-align:-6.448ex;" xmlns="http://www.w3.org/2000/svg" width="33.477ex" height="14.027ex" role="img" focusable="false" viewBox="0 -3350 14797 6200" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,2600)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g></g><g data-mml-node="mtd" transform="translate(529,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(3085,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(3585,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(7114,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd" transform="translate(529,0)"></g><g data-mml-node="mtd" transform="translate(529,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3085,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mstyle" transform="translate(3518,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(11697.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(529,0)"></g><g data-mml-node="mtd" transform="translate(529,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mstyle" transform="translate(3418,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(8361.6,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(529,0)"></g><g data-mml-node="mtd" transform="translate(529,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(2985,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(3485,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(11697.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-2600)"><g data-mml-node="mtd" transform="translate(529,0)"></g><g data-mml-node="mtd" transform="translate(529,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(1762.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(7114,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right left right" columnspacing="0em 2em" rowspacing="3pt"><mtr><mtd><mi>a</mi></mtd><mtd><mi></mi><mo>=</mo><mi>a</mi><mo>+</mo><mn>0</mn><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅰ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>c</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mi>c</mi><mo>=</mo><mn>0</mn></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>c</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mi>a</mi><mo>+</mo><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>c</mi></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>b</mi><mo>+</mo><mn>0</mn><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mi>c</mi><mo>=</mo><mn>0</mn></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>b</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅰ</mtext></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container><p>进而当 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="0.98ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 433 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></mjx-assistive-mml></mjx-container> 为自然数且 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="21.379ex" height="1.756ex" role="img" focusable="false" viewBox="0 -694 9449.6 776" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5880.2,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(7158,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7964.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9020.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>+</mo><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo stretchy="false">⇒</mo><mi>a</mi><mo>=</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container> 时有</p><mjx-container class="MathJax" jax="SVG" display="true" style="position:relative;"><svg style="vertical-align:-4.977ex;" xmlns="http://www.w3.org/2000/svg" width="52.554ex" height="11.086ex" role="img" focusable="false" viewBox="0 -2700 23229 4900" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1950)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5590,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18396,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">已</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">知</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">条</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">件</text></g></g></g><g data-mml-node="mtr" transform="translate(0,650)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2534.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(3767.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5590,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(15546,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-650)"><g data-mml-node="mtd" transform="translate(2172,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mstyle" transform="translate(3418,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(16615,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><path data-c="50" d="M130 622Q123 629 119 631T103 634T60 637H27V683H214Q237 683 276 683T331 684Q419 684 471 671T567 616Q624 563 624 489Q624 421 573 372T451 307Q429 302 328 301H234V181Q234 62 237 58Q245 47 304 46H337V0H326Q305 3 182 3Q47 3 38 0H27V46H60Q102 47 111 49T130 61V622ZM507 488Q507 514 506 528T500 564T483 597T450 620T397 635Q385 637 307 637H286Q237 637 234 628Q231 624 231 483V342H302H339Q390 342 423 349T481 382Q507 411 507 488Z"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(681,0)"></path><path data-c="61" d="M137 305T115 305T78 320T63 359Q63 394 97 421T218 448Q291 448 336 416T396 340Q401 326 401 309T402 194V124Q402 76 407 58T428 40Q443 40 448 56T453 109V145H493V106Q492 66 490 59Q481 29 455 12T400 -6T353 12T329 54V58L327 55Q325 52 322 49T314 40T302 29T287 17T269 6T247 -2T221 -8T190 -11Q130 -11 82 20T34 107Q34 128 41 147T68 188T116 225T194 253T304 268H318V290Q318 324 312 340Q290 411 215 411Q197 411 181 410T156 406T148 403Q170 388 170 359Q170 334 154 320ZM126 106Q126 75 150 51T209 26Q247 26 276 49T315 109Q317 116 318 175Q318 233 317 233Q309 233 296 232T251 223T193 203T147 166T126 106Z" transform="translate(1125,0)"></path><path data-c="6E" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z" transform="translate(1625,0)"></path><path data-c="6F" d="M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z" transform="translate(2181,0)"></path><path data-c="20" d="" transform="translate(2681,0)"></path><text data-variant="normal" transform="translate(2931,0) scale(1,-1)" font-size="884px" font-family="serif">公</text><text data-variant="normal" transform="translate(3931,0) scale(1,-1)" font-size="884px" font-family="serif">理</text><path data-c="20" d="" transform="translate(4931,0)"></path><text data-variant="normal" transform="translate(5181,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅳ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1950)"><g data-mml-node="mtd" transform="translate(3827.4,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(1762.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(12946.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5880.2,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(7158,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7964.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9020.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right left right" columnspacing="0em 2em" rowspacing="3pt"><mtr><mtd><mi>a</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></mtd><mtd><mi></mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>已知条件</mtext></mtd></mtr><mtr><mtd><mi>suc</mi><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>c</mi><mo stretchy="false">)</mo></mtd><mtd><mi></mi><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅱ</mtext></mtd></mtr><mtr><mtd><mi>a</mi><mo>+</mo><mi>c</mi></mtd><mtd><mi></mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>c</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>Peano 公理 Ⅳ</mtext></mtd></mtr><mtr><mtd><mi>a</mi></mtd><mtd><mi></mi><mo>=</mo><mi>b</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mi>a</mi><mo>+</mo><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo stretchy="false">⇒</mo><mi>a</mi><mo>=</mo><mi>b</mi></mrow></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container><p>即 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="47.402ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 20951.6 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(10224.2,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(11502,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(12253.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(13253.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(13964.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(15020,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(15671.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(16671.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(17382.2,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(18660,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(19466.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(20522.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>=</mo><mi>b</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">⇒</mo><mi>a</mi><mo>+</mo><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo stretchy="false">⇒</mo><mi>a</mi><mo>=</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container>，根据 Peano 公理 Ⅴ，得知 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="21.379ex" height="1.756ex" role="img" focusable="false" viewBox="0 -694 9449.6 776" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5880.2,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(7158,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7964.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9020.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>+</mo><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo stretchy="false">⇒</mo><mi>a</mi><mo>=</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container> 对任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="5.159ex" height="2.009ex" role="img" focusable="false" viewBox="0 -694 2280.3 888" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi></math></mjx-assistive-mml></mjx-container> 成立。</p><p>综上所述，加法消去律 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="21.379ex" height="1.756ex" role="img" focusable="false" viewBox="0 -694 9449.6 776" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5880.2,0)"><path data-c="21D4" d="M308 524Q318 526 323 526Q340 526 340 514Q340 507 336 499Q326 476 314 454T292 417T274 391T260 374L255 368Q255 367 500 367Q744 367 744 368L739 374Q734 379 726 390T707 416T685 453T663 499Q658 511 658 515Q658 525 680 525Q687 524 690 523T695 519T701 507Q766 359 902 287Q921 276 939 269T961 259T966 250Q966 246 965 244T960 240T949 236T930 228T902 213Q763 137 701 -7Q697 -16 695 -19T690 -23T680 -25Q658 -25 658 -15Q658 -11 663 1Q673 24 685 46T707 83T725 109T739 126L744 132Q744 133 500 133Q255 133 255 132L260 126Q265 121 273 110T292 84T314 47T336 1Q341 -11 341 -15Q341 -25 319 -25Q312 -24 309 -23T304 -19T298 -7Q233 141 97 213Q83 221 70 227T51 235T41 239T35 243T34 250T35 256T40 261T51 265T70 273T97 287Q235 363 299 509Q305 522 308 524ZM792 319L783 327H216Q183 294 120 256L110 250L120 244Q173 212 207 181L216 173H783L792 181Q826 212 879 244L889 250L879 256Q826 288 792 319Z"></path></g><g data-mml-node="mi" transform="translate(7158,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7964.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9020.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>+</mo><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo stretchy="false">⇔</mo><mi>a</mi><mo>=</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container>，对任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="5.159ex" height="2.009ex" role="img" focusable="false" viewBox="0 -694 2280.3 888" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi></math></mjx-assistive-mml></mjx-container> 成立。</p><h2 id="自然数的序" tabindex="-1"><a class="header-anchor" href="#自然数的序"><span>自然数的序</span></a></h2><p>自然数的序为两个自然数的关系。</p><h3 id="序的定义" tabindex="-1"><a class="header-anchor" href="#序的定义"><span>序的定义</span></a></h3><p>定义自然数的序即定义 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.312ex;" xmlns="http://www.w3.org/2000/svg" width="6.361ex" height="1.751ex" role="img" focusable="false" viewBox="0 -636 2811.6 774" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(877.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1933.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>≤</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container> 当且仅当存在自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.294ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 572 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></mjx-assistive-mml></mjx-container> 满足 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="10.421ex" height="1.505ex" role="img" focusable="false" viewBox="0 -583 4606 665" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(877.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1933.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3033.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>m</mi><mo>+</mo><mi>x</mi></math></mjx-assistive-mml></mjx-container>。定义 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.09ex;" xmlns="http://www.w3.org/2000/svg" width="6.361ex" height="1.312ex" role="img" focusable="false" viewBox="0 -540 2811.6 580" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(877.8,0)"><path data-c="3C" d="M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z"></path></g><g data-mml-node="mi" transform="translate(1933.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>&lt;</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container> 当且仅当 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.312ex;" xmlns="http://www.w3.org/2000/svg" width="6.361ex" height="1.751ex" role="img" focusable="false" viewBox="0 -636 2811.6 774" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(877.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1933.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>≤</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container> 且 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.486ex;" xmlns="http://www.w3.org/2000/svg" width="6.361ex" height="2.106ex" role="img" focusable="false" viewBox="0 -716 2811.6 931" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(877.8,0)"><path data-c="2260" d="M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z"></path></g><g data-mml-node="mi" transform="translate(1933.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>≠</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container>。</p><p>自然数的序是全序关系，它应该具有反对称性、传递性和完全性。</p><h3 id="正自然数" tabindex="-1"><a class="header-anchor" href="#正自然数"><span>正自然数</span></a></h3><p>在考察序的性质之前，我们预先准备以方便证明。</p><p>定义正自然数为非 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.05ex;" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></mjx-assistive-mml></mjx-container> 自然数。</p><h4 id="正自然数的性质" tabindex="-1"><a class="header-anchor" href="#正自然数的性质"><span>正自然数的性质</span></a></h4><p>正自然数与自然数相加为正自然数，即对于正自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.023ex;" xmlns="http://www.w3.org/2000/svg" width="1.197ex" height="1.02ex" role="img" focusable="false" viewBox="0 -441 529 451" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></mjx-assistive-mml></mjx-container>，其与自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="0.971ex" height="1.595ex" role="img" focusable="false" viewBox="0 -694 429 705" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></mjx-assistive-mml></mjx-container> 的和 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="4.933ex" height="1.756ex" role="img" focusable="false" viewBox="0 -694 2180.4 776" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>+</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container> 为正自然数。</p><p>首先，当 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="5.119ex" height="1.756ex" role="img" focusable="false" viewBox="0 -694 2262.6 776" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1762.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container> 时，<mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="9.308ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 4114 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(1751.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2529.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3585,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>+</mo><mn>0</mn><mo>=</mo><mi>a</mi></math></mjx-assistive-mml></mjx-container> 为正自然数。</p><p>进而当 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="0.971ex" height="1.595ex" role="img" focusable="false" viewBox="0 -694 429 705" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></mjx-assistive-mml></mjx-container> 为自然数且 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="4.933ex" height="1.756ex" role="img" focusable="false" viewBox="0 -694 2180.4 776" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>+</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container> 为正自然数时有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="22.711ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 10038.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(3963.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4630.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5686,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7080,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7469,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(8220.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9220.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(9649.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>b</mi><mo stretchy="false">)</mo><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container>，根据 Peano 公理 Ⅲ，<mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="9.847ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4352.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2534.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(3963.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 为正自然数，进而 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="9.847ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4352.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(3963.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>b</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 为正自然数。</p><p>根据 Peano 公理 Ⅴ，正自然数与自然数相加为正自然数。</p><h3 id="序的反对称性" tabindex="-1"><a class="header-anchor" href="#序的反对称性"><span>序的反对称性</span></a></h3><p>若 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.312ex;" xmlns="http://www.w3.org/2000/svg" width="5.185ex" height="1.882ex" role="img" focusable="false" viewBox="0 -694 2291.6 832" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>≤</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container> 且 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.312ex;" xmlns="http://www.w3.org/2000/svg" width="5.185ex" height="1.882ex" role="img" focusable="false" viewBox="0 -694 2291.6 832" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>≤</mo><mi>a</mi></math></mjx-assistive-mml></mjx-container>，则 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="5.185ex" height="1.756ex" role="img" focusable="false" viewBox="0 -694 2291.6 776" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container>。</p><p>由 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.312ex;" xmlns="http://www.w3.org/2000/svg" width="5.185ex" height="1.882ex" role="img" focusable="false" viewBox="0 -694 2291.6 832" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>≤</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container> 有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.339ex;" xmlns="http://www.w3.org/2000/svg" width="10.924ex" height="1.91ex" role="img" focusable="false" viewBox="0 -694 4828.6 844" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(3514,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><msub><mi>m</mi><mn>1</mn></msub></math></mjx-assistive-mml></mjx-container>，由 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.312ex;" xmlns="http://www.w3.org/2000/svg" width="5.185ex" height="1.882ex" role="img" focusable="false" viewBox="0 -694 2291.6 832" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>≤</mo><mi>a</mi></math></mjx-assistive-mml></mjx-container> 有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.339ex;" xmlns="http://www.w3.org/2000/svg" width="10.924ex" height="1.91ex" role="img" focusable="false" viewBox="0 -694 4828.6 844" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(3514,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>b</mi><mo>+</mo><msub><mi>m</mi><mn>2</mn></msub></math></mjx-assistive-mml></mjx-container>。</p><p>因此 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.339ex;" xmlns="http://www.w3.org/2000/svg" width="34.729ex" height="1.91ex" role="img" focusable="false" viewBox="0 -694 15350.1 844" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2529.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3585,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4391.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5447.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6098.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(7099,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g><g data-mml-node="mo" transform="translate(8691.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9747.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(10498.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(11498.6,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g><g data-mml-node="mo" transform="translate(13035.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(14035.6,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>+</mo><mi>a</mi><mo>=</mo><mi>a</mi><mo>=</mo><mi>b</mi><mo>+</mo><msub><mi>m</mi><mn>2</mn></msub><mo>=</mo><mi>a</mi><mo>+</mo><msub><mi>m</mi><mn>1</mn></msub><mo>+</mo><msub><mi>m</mi><mn>2</mn></msub></math></mjx-assistive-mml></mjx-container>，由加法消去律得到 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.339ex;" xmlns="http://www.w3.org/2000/svg" width="12.862ex" height="1.846ex" role="img" focusable="false" viewBox="0 -666 5685.1 816" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g><g data-mml-node="mo" transform="translate(1536.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(2537,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g><g data-mml-node="mo" transform="translate(4129.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(5185.1,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>m</mi><mn>1</mn></msub><mo>+</mo><msub><mi>m</mi><mn>2</mn></msub><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container>，根据正自然数的性质得出 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.339ex;" xmlns="http://www.w3.org/2000/svg" width="13.114ex" height="1.846ex" role="img" focusable="false" viewBox="0 -666 5796.2 816" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g><g data-mml-node="mo" transform="translate(1592.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="msub" transform="translate(2648.1,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g><g data-mml-node="mo" transform="translate(4240.4,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(5296.2,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>m</mi><mn>1</mn></msub><mo>=</mo><msub><mi>m</mi><mn>2</mn></msub><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container>，因此 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.339ex;" xmlns="http://www.w3.org/2000/svg" width="23.249ex" height="1.91ex" role="img" focusable="false" viewBox="0 -694 10276.1 844" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2613.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(3614,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(4391.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5447.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6198.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(7199,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g><g data-mml-node="mo" transform="translate(8791.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9847.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>a</mi><mo>+</mo><mn>0</mn><mo>=</mo><mi>a</mi><mo>+</mo><msub><mi>m</mi><mn>1</mn></msub><mo>=</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container>。</p><h3 id="序的传递性" tabindex="-1"><a class="header-anchor" href="#序的传递性"><span>序的传递性</span></a></h3><p>若 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.312ex;" xmlns="http://www.w3.org/2000/svg" width="5.185ex" height="1.882ex" role="img" focusable="false" viewBox="0 -694 2291.6 832" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>≤</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container> 且 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.312ex;" xmlns="http://www.w3.org/2000/svg" width="4.967ex" height="1.882ex" role="img" focusable="false" viewBox="0 -694 2195.6 832" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>≤</mo><mi>c</mi></math></mjx-assistive-mml></mjx-container>，则 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.312ex;" xmlns="http://www.w3.org/2000/svg" width="5.194ex" height="1.751ex" role="img" focusable="false" viewBox="0 -636 2295.6 774" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>≤</mo><mi>c</mi></math></mjx-assistive-mml></mjx-container>。</p><p>由 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.312ex;" xmlns="http://www.w3.org/2000/svg" width="5.185ex" height="1.882ex" role="img" focusable="false" viewBox="0 -694 2291.6 832" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>≤</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container> 有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.339ex;" xmlns="http://www.w3.org/2000/svg" width="10.924ex" height="1.91ex" role="img" focusable="false" viewBox="0 -694 4828.6 844" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(3514,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><msub><mi>m</mi><mn>1</mn></msub></math></mjx-assistive-mml></mjx-container>，由 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.312ex;" xmlns="http://www.w3.org/2000/svg" width="4.967ex" height="1.882ex" role="img" focusable="false" viewBox="0 -694 2195.6 832" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>≤</mo><mi>c</mi></math></mjx-assistive-mml></mjx-container> 有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.339ex;" xmlns="http://www.w3.org/2000/svg" width="10.707ex" height="1.91ex" role="img" focusable="false" viewBox="0 -694 4732.6 844" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1766.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2417.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(3418,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><msub><mi>m</mi><mn>2</mn></msub></math></mjx-assistive-mml></mjx-container>。</p><p>根据加法结果的存在性得到 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.339ex;" xmlns="http://www.w3.org/2000/svg" width="8.714ex" height="1.658ex" role="img" focusable="false" viewBox="0 -583 3851.6 733" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g><g data-mml-node="mo" transform="translate(1536.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(2537,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>m</mi><mn>1</mn></msub><mo>+</mo><msub><mi>m</mi><mn>2</mn></msub></math></mjx-assistive-mml></mjx-container> 是自然数，根据加法结合律得出 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="45.615ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 20161.7 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1766.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2417.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(3418,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g><g data-mml-node="mo" transform="translate(5010.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(6066.1,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6455.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7206.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(8206.6,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g><g data-mml-node="mo" transform="translate(9521.1,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(10132.3,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(11132.6,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g><g data-mml-node="mo" transform="translate(12724.9,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(13780.7,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(14531.9,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(15532.1,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="msub" transform="translate(15921.1,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g><g data-mml-node="mo" transform="translate(17457.9,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="msub" transform="translate(18458.1,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(911,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g><g data-mml-node="mo" transform="translate(19772.7,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><msub><mi>m</mi><mn>2</mn></msub><mo>=</mo><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><msub><mi>m</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mi>m</mi><mn>2</mn></msub><mo>=</mo><mi>a</mi><mo>+</mo><mo stretchy="false">(</mo><msub><mi>m</mi><mn>1</mn></msub><mo>+</mo><msub><mi>m</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container>，进而 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.312ex;" xmlns="http://www.w3.org/2000/svg" width="5.194ex" height="1.751ex" role="img" focusable="false" viewBox="0 -636 2295.6 774" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>≤</mo><mi>c</mi></math></mjx-assistive-mml></mjx-container>。</p><h3 id="序的完全性" tabindex="-1"><a class="header-anchor" href="#序的完全性"><span>序的完全性</span></a></h3><p>任意两个自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="3.173ex" height="2.009ex" role="img" focusable="false" viewBox="0 -694 1402.7 888" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container> 都有序关系。</p><p>对于 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="3.173ex" height="2.009ex" role="img" focusable="false" viewBox="0 -694 1402.7 888" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container> 两个自然数，当 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="5.119ex" height="1.756ex" role="img" focusable="false" viewBox="0 -694 2262.6 776" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1762.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container> 时有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="17.258ex" height="1.756ex" role="img" focusable="false" viewBox="0 -694 7628 776" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1862.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2584.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3585,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4391.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5447.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6098.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7099,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>0</mn><mo>+</mo><mi>a</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>a</mi></math></mjx-assistive-mml></mjx-container> 所以 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.312ex;" xmlns="http://www.w3.org/2000/svg" width="5.185ex" height="1.882ex" role="img" focusable="false" viewBox="0 -694 2291.6 832" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>≤</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container>。</p><p>当 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="0.971ex" height="1.595ex" role="img" focusable="false" viewBox="0 -694 429 705" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></mjx-assistive-mml></mjx-container> 为自然数时。若 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="5.185ex" height="1.756ex" role="img" focusable="false" viewBox="0 -694 2291.6 776" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container>，则 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="18.91ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 8358 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2212,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(2878.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3934.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4685.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5686,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(7080,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(7469,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(7969,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo stretchy="false">(</mo><mi>b</mi><mo stretchy="false">)</mo><mo>=</mo><mi>a</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container>，因此 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="10.099ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4463.6 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3C" d="M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3256.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3645.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4074.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>&lt;</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>b</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container>；若 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.09ex;" xmlns="http://www.w3.org/2000/svg" width="5.185ex" height="1.661ex" role="img" focusable="false" viewBox="0 -694 2291.6 734" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3C" d="M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>&lt;</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container>，则 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="36.234ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 16015.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2212,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(2878.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3934.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4585.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5586,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6980,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(7369,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(7869,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(8535.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9591.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(10242.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(11243,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(12343.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(13343.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(14737.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(15126.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(15626.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo stretchy="false">(</mo><mi>b</mi><mo stretchy="false">)</mo><mo>=</mo><mi>b</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo>=</mo><mi>b</mi><mo>+</mo><mi>m</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container>，因此 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="10.099ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4463.6 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3C" d="M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3256.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3645.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4074.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>&lt;</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>b</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container>；若 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.09ex;" xmlns="http://www.w3.org/2000/svg" width="5.185ex" height="1.661ex" role="img" focusable="false" viewBox="0 -694 2291.6 734" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3E" d="M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>&gt;</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container>，则 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="10.099ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4463.6 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2265" d="M83 616Q83 624 89 630T99 636Q107 636 253 568T543 431T687 361Q694 356 694 346T687 331Q685 329 395 192L107 56H101Q83 58 83 76Q83 77 83 79Q82 86 98 95Q117 105 248 167Q326 204 378 228L626 346L360 472Q291 505 200 548Q112 589 98 597T83 616ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3256.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3645.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4074.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>≥</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>b</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container>。</p><p>由 Peano 公理 Ⅴ 有任意两个自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="3.173ex" height="2.009ex" role="img" focusable="false" viewBox="0 -694 1402.7 888" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container> 都有序关系。</p><h3 id="加法保序性" tabindex="-1"><a class="header-anchor" href="#加法保序性"><span>加法保序性</span></a></h3><p>若 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.312ex;" xmlns="http://www.w3.org/2000/svg" width="5.185ex" height="1.882ex" role="img" focusable="false" viewBox="0 -694 2291.6 832" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>≤</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container>，则 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.312ex;" xmlns="http://www.w3.org/2000/svg" width="12.675ex" height="1.882ex" role="img" focusable="false" viewBox="0 -694 5602.4 832" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>+</mo><mi>c</mi><mo>≤</mo><mi>b</mi><mo>+</mo><mi>c</mi></math></mjx-assistive-mml></mjx-container>。</p><p>由 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.312ex;" xmlns="http://www.w3.org/2000/svg" width="5.185ex" height="1.882ex" role="img" focusable="false" viewBox="0 -694 2291.6 832" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>≤</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container> 有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="9.937ex" height="1.756ex" role="img" focusable="false" viewBox="0 -694 4392 776" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3514,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container>，进而 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="46.371ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 20495.8 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(651.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1651.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2362.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(3418,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3807,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4558.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5558.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6436.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7047.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(8047.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(8758.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9814.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(10565.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(11565.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(12666.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(13666.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(14377.1,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(15432.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(15821.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(16573.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(17573.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(18006.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(18617.6,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(19617.8,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>+</mo><mi>c</mi><mo>=</mo><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>m</mi><mo stretchy="false">)</mo><mo>+</mo><mi>c</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>m</mi><mo>+</mo><mi>c</mi><mo>=</mo><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>c</mi><mo stretchy="false">)</mo><mo>+</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container> 因此 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.312ex;" xmlns="http://www.w3.org/2000/svg" width="12.675ex" height="1.882ex" role="img" focusable="false" viewBox="0 -694 5602.4 832" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2462.2,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(3518,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4169.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5169.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>+</mo><mi>c</mi><mo>≤</mo><mi>b</mi><mo>+</mo><mi>c</mi></math></mjx-assistive-mml></mjx-container>。</p><h2 id="自然数的乘法运算" tabindex="-1"><a class="header-anchor" href="#自然数的乘法运算"><span>自然数的乘法运算</span></a></h2><p>自然数的乘法也十分重要。</p><h3 id="乘法的定义" tabindex="-1"><a class="header-anchor" href="#乘法的定义"><span>乘法的定义</span></a></h3><p>定义乘法的运算规则：</p><ol><li>若 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是自然数，则 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.05ex;" xmlns="http://www.w3.org/2000/svg" width="5.254ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 2322.4 688" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>×</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 的运算结果为 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.05ex;" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></mjx-assistive-mml></mjx-container>，即 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="9.403ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 4156 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(3656,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>×</mo><mi>n</mi><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container>；</li><li>若 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="4.35ex" height="1.439ex" role="img" focusable="false" viewBox="0 -442 1922.7 636" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>,</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container> 都是自然数，则 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="24.274ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 10728.9 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7306.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8306.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9128.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10128.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo>×</mo><mi>n</mi><mo>=</mo><mi>m</mi><mo>×</mo><mi>n</mi><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container>。</li></ol><p>下面我们需要证明对于任意两个自然数，都可以进行乘法运算，也就是说，我们需要证明乘法结果的存在性和唯一性。</p><h4 id="乘法结果的存在性" tabindex="-1"><a class="header-anchor" href="#乘法结果的存在性"><span>乘法结果的存在性</span></a></h4><p><mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是任意自然数，记 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="6.032ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2666.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 表示 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="6.11ex" height="1.136ex" role="img" focusable="false" viewBox="0 -491 2700.4 502" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>×</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是否是自然数，即 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="6.11ex" height="1.136ex" role="img" focusable="false" viewBox="0 -491 2700.4 502" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>×</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是否存在。</p><p><mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是自然数，由乘法运算规则 Ⅰ 有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="9.403ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 4156 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(3656,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>×</mo><mi>n</mi><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container>，进而有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.05ex;" xmlns="http://www.w3.org/2000/svg" width="5.254ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 2322.4 688" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>×</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是自然数； <strong>即 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="5.177ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2288.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(1399.3,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(1899.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 得证。</strong></p><p><mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 和 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="6.11ex" height="1.136ex" role="img" focusable="false" viewBox="0 -491 2700.4 502" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>×</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是自然数，由加法结果的存在性有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="10.233ex" height="1.505ex" role="img" focusable="false" viewBox="0 -583 4522.9 665" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2922.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3922.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>×</mo><mi>n</mi><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 存在； 根据乘法运算规则 Ⅱ 有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="24.274ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 10728.9 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7306.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8306.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9128.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10128.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo>×</mo><mi>n</mi><mo>=</mo><mi>m</mi><mo>×</mo><mi>n</mi><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container>，进有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="11.024ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4872.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo>×</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是自然数； 综上所述，若 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="6.11ex" height="1.136ex" role="img" focusable="false" viewBox="0 -491 2700.4 502" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>×</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是自然数，则 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="11.024ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4872.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo>×</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 也是自然数； <strong>即由 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="6.032ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2666.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 为真命题可以推出 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="10.946ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4838.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2793.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3182.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4060.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4449.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 为真命题。</strong></p><p>由 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="6.032ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2666.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 的性质和 Peano 公理 Ⅴ 有，对于任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.986ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 878 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></mjx-assistive-mml></mjx-container>，<mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="6.032ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2666.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 成立，即 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="6.11ex" height="1.136ex" role="img" focusable="false" viewBox="0 -491 2700.4 502" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>×</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是自然数，再根据 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 的任意性，得出对于任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="4.35ex" height="1.439ex" role="img" focusable="false" viewBox="0 -442 1922.7 636" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>,</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container>，<mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="6.11ex" height="1.136ex" role="img" focusable="false" viewBox="0 -491 2700.4 502" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>×</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 都是自然数。</p><h4 id="乘法结果的唯一性" tabindex="-1"><a class="header-anchor" href="#乘法结果的唯一性"><span>乘法结果的唯一性</span></a></h4><p><mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是任意自然数，记 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="6.032ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2666.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 表示 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="6.11ex" height="1.136ex" role="img" focusable="false" viewBox="0 -491 2700.4 502" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>×</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是否唯一，即 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="6.11ex" height="1.136ex" role="img" focusable="false" viewBox="0 -491 2700.4 502" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>×</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 的结果是否唯一。</p><p><mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是自然数，由乘法运算规则 Ⅰ 有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="9.403ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 4156 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(3656,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>×</mo><mi>n</mi><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container>，进而 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.05ex;" xmlns="http://www.w3.org/2000/svg" width="5.254ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 2322.4 688" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>×</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是唯一的，就是 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.05ex;" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></mjx-assistive-mml></mjx-container>； <strong>即 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="5.177ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2288.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(1399.3,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(1899.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 得证。</strong></p><p><mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.986ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 878 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></mjx-assistive-mml></mjx-container> 是自然数，<mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="6.11ex" height="1.136ex" role="img" focusable="false" viewBox="0 -491 2700.4 502" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>×</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是唯一的，由加法结果的唯一性有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="10.233ex" height="1.505ex" role="img" focusable="false" viewBox="0 -583 4522.9 665" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2922.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3922.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>×</mo><mi>n</mi><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 唯一； 根据乘法运算规则 Ⅱ 有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="24.274ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 10728.9 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7306.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8306.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9128.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10128.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo>×</mo><mi>n</mi><mo>=</mo><mi>m</mi><mo>×</mo><mi>n</mi><mo>+</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container>，进有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="11.024ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4872.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo>×</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 唯一； 综上所述，若 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="6.11ex" height="1.136ex" role="img" focusable="false" viewBox="0 -491 2700.4 502" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>×</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 唯一，则 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="11.024ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4872.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo>×</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 也唯一； <strong>即由 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="6.032ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2666.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 为真命题可以推出 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="10.946ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4838.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2793.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3182.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4060.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4449.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 为真命题。</strong></p><p>由 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="6.032ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2666.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 的性质和 Peano 公理 Ⅴ 有，对于任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.986ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 878 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></mjx-assistive-mml></mjx-container>，<mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="6.032ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2666.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mi" transform="translate(536,-150) scale(0.707)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1010.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1399.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2277.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 成立，即 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="6.11ex" height="1.136ex" role="img" focusable="false" viewBox="0 -491 2700.4 502" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>×</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 唯一，再根据 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 的任意性，得出对于任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="4.35ex" height="1.439ex" role="img" focusable="false" viewBox="0 -442 1922.7 636" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>,</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container>，<mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="6.11ex" height="1.136ex" role="img" focusable="false" viewBox="0 -491 2700.4 502" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>×</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 都是唯一的。</p><h3 id="乘法的性质" tabindex="-1"><a class="header-anchor" href="#乘法的性质"><span>乘法的性质</span></a></h3><p>在明确证明了自然数乘法运算的良好性质，即任意两个自然数都可以进行乘法运算，且乘法运算的结果存在且唯一之后，我们终于可以对自然数乘法的性质进行进一步的探索。</p><h4 id="乘法交换律" tabindex="-1"><a class="header-anchor" href="#乘法交换律"><span>乘法交换律</span></a></h4><p>下面证明乘法交换律，即对于任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="4.35ex" height="1.439ex" role="img" focusable="false" viewBox="0 -442 1922.7 636" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>,</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container>，有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="15.236ex" height="1.505ex" role="img" focusable="false" viewBox="0 -583 6734.4 665" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>×</mo><mi>m</mi><mo>=</mo><mi>m</mi><mo>×</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container>。</p><p>直接证明比较困难，考虑从乘法运算的定义下手，即先证明乘法的两条运算规则符合交换律。</p><p>试证 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="17.674ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 7812 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(3656,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(4433.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5489.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6311.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(7312,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>×</mo><mi>n</mi><mo>=</mo><mn>0</mn><mo>=</mo><mi>n</mi><mo>×</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container>。</p><p>首先有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="17.222ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 7612 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(1722.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2500.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(3556,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(4333.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(5389.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(6111.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(7112,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>×</mo><mn>0</mn><mo>=</mo><mn>0</mn><mo>=</mo><mn>0</mn><mo>×</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container>。</p><p>进而当 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是自然数且 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="17.674ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 7812 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(3656,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(4433.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5489.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6311.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(7312,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>×</mo><mi>n</mi><mo>=</mo><mn>0</mn><mo>=</mo><mi>n</mi><mo>×</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container> 时有</p><mjx-container class="MathJax" jax="SVG" display="true" style="position:relative;"><svg style="vertical-align:-4.977ex;" xmlns="http://www.w3.org/2000/svg" width="47.524ex" height="11.086ex" role="img" focusable="false" viewBox="0 -2700 21005.4 4900" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1950)"><g data-mml-node="mtd"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3116.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3505.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4105.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(1833.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13322.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,650)"><g data-mml-node="mtd" transform="translate(4494.4,0)"></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2155.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(3156,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(3656,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(16016.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(777.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1833.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2655.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(3656,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-650)"><g data-mml-node="mtd" transform="translate(4494.4,0)"></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2155.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(3156,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(3878.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(4878.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(5378.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13322.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1950)"><g data-mml-node="mtd" transform="translate(4494.4,0)"></g><g data-mml-node="mtd" transform="translate(4494.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3716.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4327.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(5328,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(5828,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13322.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right left right" columnspacing="0em 2em" rowspacing="3pt"><mtr><mtd><mn>0</mn><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mtd><mtd><mi></mi><mo>=</mo><mn>0</mn><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>乘法运算规则 Ⅰ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>n</mi><mo>×</mo><mn>0</mn><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mn>0</mn><mo>=</mo><mi>n</mi><mo>×</mo><mn>0</mn></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>n</mi><mo>×</mo><mn>0</mn><mo>+</mo><mn>0</mn><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅰ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>×</mo><mn>0</mn><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>乘法运算规则 Ⅱ</mtext></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container><p>根据 Peano 公理 Ⅴ，得知 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="17.674ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 7812 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2600.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(3656,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(4433.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5489.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6311.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(7312,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>×</mo><mi>n</mi><mo>=</mo><mn>0</mn><mo>=</mo><mi>n</mi><mo>×</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container> 对任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 成立。</p><p>试证 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="24.902ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 11006.9 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7306.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8306.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9128.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10128.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mi>m</mi><mo>×</mo><mi>n</mi><mo>+</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container>。</p><p>首先 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="6.135ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 2711.6 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1155.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(2211.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container> 时有</p><mjx-container class="MathJax" jax="SVG" display="true" style="position:relative;"><svg style="vertical-align:-6.448ex;" xmlns="http://www.w3.org/2000/svg" width="49.072ex" height="14.027ex" role="img" focusable="false" viewBox="0 -3350 21689.9 6200" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,2600)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2055.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3056,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4450,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4839,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5439,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5828,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18145.3,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1155.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(2211.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd" transform="translate(4872.4,0)"></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(1833.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14006.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(4872.4,0)"></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2055.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3056,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mstyle" transform="translate(3656,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14006.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(4872.4,0)"></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2055.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3056,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3878.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(4878.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(5378.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14006.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-2600)"><g data-mml-node="mtd" transform="translate(4872.4,0)"></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2433.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3434,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4256.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5256.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mstyle" transform="translate(6134.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18145.3,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1155.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(2211.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right left right" columnspacing="0em 2em" rowspacing="3pt"><mtr><mtd><mi>m</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mtd><mtd><mi></mi><mo>=</mo><mn>0</mn><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mi>m</mi><mo>=</mo><mn>0</mn></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mn>0</mn><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>乘法运算规则 Ⅰ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mn>0</mn><mo>×</mo><mi>n</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>乘法运算规则 Ⅰ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mn>0</mn><mo>×</mo><mi>n</mi><mo>+</mo><mn>0</mn><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅰ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>m</mi><mo>×</mo><mi>n</mi><mo>+</mo><mi>m</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mi>m</mi><mo>=</mo><mn>0</mn></mrow></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container><p>进而当 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.986ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 878 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></mjx-assistive-mml></mjx-container> 是自然数且 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="24.902ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 11006.9 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7306.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8306.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9128.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10128.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mi>m</mi><mo>×</mo><mi>n</mi><mo>+</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container> 时有</p><mjx-container class="MathJax" jax="SVG" display="true" style="position:relative;"><svg style="vertical-align:-6.448ex;" xmlns="http://www.w3.org/2000/svg" width="63.814ex" height="14.027ex" role="img" focusable="false" viewBox="0 -3350 28205.9 6200" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,2600)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2661,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3272.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4272.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(5666.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6055.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6655.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2433.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3434,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4828,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5217,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5817,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6428.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7428.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8822.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9211.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9811.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(10200.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(20522.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd" transform="translate(7044.4,0)"></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2433.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3434,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4256.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5256.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6356.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7356.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8750.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9139.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9739.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(10128.9,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(22572,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2922.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3922.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(7044.4,0)"></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2433.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3434,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4256.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5256.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6650.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7039.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7917.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(8528.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9528.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mstyle" transform="translate(10128.9,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(20522.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(7044.4,0)"></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2433.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3434,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4256.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5256.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6078.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7078.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8472.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8861.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9739.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(10128.9,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(22372.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">交</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">换</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">律</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-2600)"><g data-mml-node="mtd" transform="translate(7044.4,0)"></g><g data-mml-node="mtd" transform="translate(7044.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3994.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4605.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5606,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6428.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7428.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8822.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9211.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10089.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(10478.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(20522.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right left right" columnspacing="0em 2em" rowspacing="3pt"><mtr><mtd><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mtd><mtd><mi></mi><mo>=</mo><mi>m</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>乘法运算规则 Ⅱ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>m</mi><mo>×</mo><mi>n</mi><mo>+</mo><mi>m</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mi>m</mi><mo>×</mo><mi>n</mi><mo>+</mo><mi>m</mi></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>m</mi><mo>×</mo><mi>n</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo>+</mo><mi>n</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅱ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>m</mi><mo>×</mo><mi>n</mi><mo>+</mo><mi>n</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法交换律</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo>×</mo><mi>n</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>乘法运算规则 Ⅱ</mtext></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container><p>根据 Peano 公理 Ⅴ，得知 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="24.902ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 11006.9 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4483.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5150.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6206,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7306.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8306.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9128.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10128.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mi>m</mi><mo>×</mo><mi>n</mi><mo>+</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container> 对任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="4.35ex" height="1.439ex" role="img" focusable="false" viewBox="0 -442 1922.7 636" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>,</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container> 成立，将其称为新的<strong>乘法运算规则 Ⅱ</strong>。</p><p>证明了乘法运算规则的交换律之后，试证乘法交换律 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="15.236ex" height="1.505ex" role="img" focusable="false" viewBox="0 -583 6734.4 665" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>×</mo><mi>m</mi><mo>=</mo><mi>m</mi><mo>×</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container>，首先当 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="5.506ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 2433.6 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(877.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1933.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container> 时由乘法运算规则 Ⅰ 有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="14.784ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 6534.4 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(722.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1722.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2878.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3934,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5034.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(6034.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>×</mo><mi>m</mi><mo>=</mo><mi>m</mi><mo>×</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container>。</p><p>进而当 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 是自然数且 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="15.236ex" height="1.505ex" role="img" focusable="false" viewBox="0 -583 6734.4 665" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>×</mo><mi>m</mi><mo>=</mo><mi>m</mi><mo>×</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 时，有</p><mjx-container class="MathJax" jax="SVG" display="true" style="position:relative;"><svg style="vertical-align:-3.507ex;" xmlns="http://www.w3.org/2000/svg" width="49.234ex" height="8.145ex" role="img" focusable="false" viewBox="0 -2050 21761.4 3600" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2383,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(2994.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3994.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2155.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3156,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4256.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5256.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mstyle" transform="translate(6134.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14078.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(4872.4,0)"></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2433.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3434,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4256.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5256.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mstyle" transform="translate(6134.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14194,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(4872.4,0)"></g><g data-mml-node="mtd" transform="translate(4872.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2433.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3434,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4828,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5217,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5817,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(6206,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(14078.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right left right" columnspacing="0em 2em" rowspacing="3pt"><mtr><mtd><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>×</mo><mi>m</mi></mtd><mtd><mi></mi><mo>=</mo><mi>n</mi><mo>×</mo><mi>m</mi><mo>+</mo><mi>m</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>乘法运算规则 Ⅱ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>m</mi><mo>×</mo><mi>n</mi><mo>+</mo><mi>m</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mi>n</mi><mo>×</mo><mi>m</mi><mo>=</mo><mi>m</mi><mo>×</mo><mi>n</mi></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>m</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>乘法运算规则 Ⅱ</mtext></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container><p>根据 Peano 公理 Ⅴ，得知 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="15.236ex" height="1.505ex" role="img" focusable="false" viewBox="0 -583 6734.4 665" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1822.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2978.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4034,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5134.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(6134.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>×</mo><mi>m</mi><mo>=</mo><mi>m</mi><mo>×</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container> 对任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="4.35ex" height="1.439ex" role="img" focusable="false" viewBox="0 -442 1922.7 636" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>,</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container> 成立，即乘法交换律成立。</p><h4 id="乘法分配律" tabindex="-1"><a class="header-anchor" href="#乘法分配律"><span>乘法分配律</span></a></h4><p>下面证明乘法分配律，即对于任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="5.537ex" height="2.009ex" role="img" focusable="false" viewBox="0 -694 2447.3 888" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>n</mi></math></mjx-assistive-mml></mjx-container>，有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="27.013ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 11939.8 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(1822.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(2211.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2962.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3962.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4391.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5058.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6114.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6936.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7936.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(8688.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9688.3,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10510.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(11510.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>×</mo><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo stretchy="false">)</mo><mo>=</mo><mi>n</mi><mo>×</mo><mi>a</mi><mo>+</mo><mi>n</mi><mo>×</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container>。</p><p>首先当 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="5.506ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 2433.6 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(877.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1933.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container> 时，<mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="68.558ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 30302.7 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(1822.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(2211.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2962.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3962.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4391.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5058.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(6114.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(6836.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(7836.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8225.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(8977.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9977.3,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(10406.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(11073.1,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(12128.9,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(12906.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(13962.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(14684.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(15684.9,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(16462.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(17518.4,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(18240.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(19240.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(19992.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mn" transform="translate(20992.3,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(21714.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(22714.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(23421.6,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(24477.3,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(25299.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(26299.8,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(27051,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(28051.2,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(28873.4,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(29873.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>×</mo><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo>×</mo><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo>=</mo><mn>0</mn><mo>+</mo><mn>0</mn><mo>=</mo><mn>0</mn><mo>×</mo><mi>a</mi><mo>+</mo><mn>0</mn><mo>×</mo><mi>b</mi><mo>=</mo><mi>n</mi><mo>×</mo><mi>a</mi><mo>+</mo><mi>n</mi><mo>×</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container>，进而当 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></mjx-assistive-mml></mjx-container> 为自然数且 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="27.013ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 11939.8 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(1822.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(2211.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2962.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3962.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4391.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5058.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6114.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6936.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7936.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(8688.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9688.3,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10510.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(11510.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>×</mo><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo stretchy="false">)</mo><mo>=</mo><mi>n</mi><mo>×</mo><mi>a</mi><mo>+</mo><mi>n</mi><mo>×</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container> 时有</p><mjx-container class="MathJax" jax="SVG" display="true" style="position:relative;"><svg style="vertical-align:-7.919ex;" xmlns="http://www.w3.org/2000/svg" width="78.831ex" height="16.968ex" role="img" focusable="false" viewBox="0 -4000 34843.4 7500" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,3250)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2383,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(2994.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(3994.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4383.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(5134.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6134.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6563.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(6952.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2155.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(3156,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3545,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4296.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5296.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(5725.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6336.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(7336.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7725.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(8477.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9477.3,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(9906.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(10295.3,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(27160.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,1950)"><g data-mml-node="mtd" transform="translate(6952.9,0)"></g><g data-mml-node="mtd" transform="translate(6952.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2155.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3156,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(3907.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4907.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5729.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(6729.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(7381.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(8381.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8770.3,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(9521.6,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10521.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(10950.8,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(11339.8,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(22070.7,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(1822.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(2211.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2962.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3962.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4391.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5058.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6114.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6936.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7936.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(8688.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9688.3,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10510.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(11510.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,650)"><g data-mml-node="mtd" transform="translate(6952.9,0)"></g><g data-mml-node="mtd" transform="translate(6952.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2155.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3156,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(3907.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4907.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5729.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(6729.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(7381.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(8381.3,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(9132.6,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10132.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(10561.8,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(29010.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">结</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">合</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">律</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-650)"><g data-mml-node="mtd" transform="translate(6952.9,0)"></g><g data-mml-node="mtd" transform="translate(6952.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2155.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3156,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(3907.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4907.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(5658.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6658.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(7481.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8481.3,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(9132.6,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(10132.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(10561.8,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(29010.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">交</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">换</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">律</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1950)"><g data-mml-node="mtd" transform="translate(6952.9,0)"></g><g data-mml-node="mtd" transform="translate(6952.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(1333.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2544.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3545,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4296.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5296.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(5825.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6436.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mo" transform="translate(7436.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7825.9,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(8648.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(9648.3,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(10299.6,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(11299.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(11728.8,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(12117.8,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(29010.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">结</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">合</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">律</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-3250)"><g data-mml-node="mtd" transform="translate(6952.9,0)"></g><g data-mml-node="mtd" transform="translate(6952.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(2727.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3116.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3716.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4327.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5328,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6079.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7079.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8473.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8862.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(9462.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(10073.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(11073.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(11502.9,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(27160.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right left right" columnspacing="0em 2em" rowspacing="3pt"><mtr><mtd><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>×</mo><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo stretchy="false">)</mo></mtd><mtd><mi></mi><mo>=</mo><mi>n</mi><mo>×</mo><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>乘法运算规则 Ⅱ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>n</mi><mo>×</mo><mi>a</mi><mo>+</mo><mi>n</mi><mo>×</mo><mi>b</mi><mo>+</mo><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mi>n</mi><mo>×</mo><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo stretchy="false">)</mo><mo>=</mo><mi>n</mi><mo>×</mo><mi>a</mi><mo>+</mo><mi>n</mi><mo>×</mo><mi>b</mi></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>n</mi><mo>×</mo><mi>a</mi><mo>+</mo><mi>n</mi><mo>×</mo><mi>b</mi><mo>+</mo><mi>a</mi><mo>+</mo><mi>b</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法结合律</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>n</mi><mo>×</mo><mi>a</mi><mo>+</mo><mi>a</mi><mo>+</mo><mi>n</mi><mo>×</mo><mi>b</mi><mo>+</mo><mi>b</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法交换律</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mo stretchy="false">(</mo><mi>n</mi><mo>×</mo><mi>a</mi><mo>+</mo><mi>a</mi><mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false">(</mo><mi>n</mi><mo>×</mo><mi>b</mi><mo>+</mo><mi>b</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法结合律</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>×</mo><mi>a</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>×</mo><mi>b</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>乘法运算规则 Ⅱ</mtext></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container><p>根据 Peano 公理 Ⅴ，得知 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="27.013ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 11939.8 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(822.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(1822.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(2211.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2962.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3962.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4391.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5058.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(6114.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6936.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7936.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(8688.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(9688.3,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(10510.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(11510.8,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>×</mo><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo stretchy="false">)</mo><mo>=</mo><mi>n</mi><mo>×</mo><mi>a</mi><mo>+</mo><mi>n</mi><mo>×</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container> 对任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="5.537ex" height="2.009ex" role="img" focusable="false" viewBox="0 -694 2447.3 888" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(600,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1044.7,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1573.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(2018.3,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>,</mo><mi>a</mi><mo>,</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container> 成立，即乘法分配律成立。</p><h4 id="乘法结合律" tabindex="-1"><a class="header-anchor" href="#乘法结合律"><span>乘法结合律</span></a></h4><p>下面证明乘法结合律，即对于任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="5.159ex" height="2.009ex" role="img" focusable="false" viewBox="0 -694 2280.3 888" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi></math></mjx-assistive-mml></mjx-container>，有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="23.894ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 10561.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5947.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6698.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(7698.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8739.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(9739.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(10172.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>a</mi><mo>×</mo><mi>b</mi><mo stretchy="false">)</mo><mo>×</mo><mi>c</mi><mo>=</mo><mi>a</mi><mo>×</mo><mo stretchy="false">(</mo><mi>b</mi><mo>×</mo><mi>c</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container>。</p><p>首先当 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="5.128ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 2266.6 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container> 时，有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="63.368ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 28008.8 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(5947.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6336.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7087.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8516.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(9128.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(10128.3,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(10906.1,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(11961.9,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(12739.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(13795.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(14546.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(15546.9,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(16324.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(17380.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(18131.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(19131.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(19520.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(20172.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(21172.3,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(21672.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(22339.1,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(23394.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(24146.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(25146.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(25535.3,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(26186.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(27186.8,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(27619.8,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>a</mi><mo>×</mo><mi>b</mi><mo stretchy="false">)</mo><mo>×</mo><mi>c</mi><mo>=</mo><mo stretchy="false">(</mo><mi>a</mi><mo>×</mo><mi>b</mi><mo stretchy="false">)</mo><mo>×</mo><mn>0</mn><mo>=</mo><mn>0</mn><mo>=</mo><mi>a</mi><mo>×</mo><mn>0</mn><mo>=</mo><mi>a</mi><mo>×</mo><mo stretchy="false">(</mo><mi>b</mi><mo>×</mo><mn>0</mn><mo stretchy="false">)</mo><mo>=</mo><mi>a</mi><mo>×</mo><mo stretchy="false">(</mo><mi>b</mi><mo>×</mo><mi>c</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container>。</p><p>进而当 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="0.98ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 433 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></mjx-assistive-mml></mjx-container> 为自然数且 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="23.894ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 10561.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5947.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6698.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(7698.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8739.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(9739.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(10172.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>a</mi><mo>×</mo><mi>b</mi><mo stretchy="false">)</mo><mo>×</mo><mi>c</mi><mo>=</mo><mi>a</mi><mo>×</mo><mo stretchy="false">(</mo><mi>b</mi><mo>×</mo><mi>c</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 时有</p><mjx-container class="MathJax" jax="SVG" display="true" style="position:relative;"><svg style="vertical-align:-4.977ex;" xmlns="http://www.w3.org/2000/svg" width="69.074ex" height="11.086ex" role="img" focusable="false" viewBox="0 -2700 30530.6 4900" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1950)"><g data-mml-node="mtd"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(5574.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5963.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6396.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(6785.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(1333.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1722.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2473.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3474,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(3903,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4514.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5514.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6169.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7169.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7921.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8921.3,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(9350.3,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(22847.6,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,650)"><g data-mml-node="mtd" transform="translate(6785.9,0)"></g><g data-mml-node="mtd" transform="translate(6785.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(3085,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3474,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4125.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5125.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5558.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6169.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7169.9,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(7921.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(8921.3,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(9350.3,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(19136.2,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5947.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6698.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(7698.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8739.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(9739.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(10172.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-650)"><g data-mml-node="mtd" transform="translate(6785.9,0)"></g><g data-mml-node="mtd" transform="translate(6785.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(3085,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3474,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4125.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5125.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5780.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6780.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(7209.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(7598.9,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(24697.6,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">分</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">配</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">律</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1950)"><g data-mml-node="mtd" transform="translate(6785.9,0)"></g><g data-mml-node="mtd" transform="translate(6785.9,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(3085,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3474,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(4125.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5125.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6519.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6908.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(7341.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7730.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(8119.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(22847.6,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right left right" columnspacing="0em 2em" rowspacing="3pt"><mtr><mtd><mo stretchy="false">(</mo><mi>a</mi><mo>×</mo><mi>b</mi><mo stretchy="false">)</mo><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></mtd><mtd><mi></mi><mo>=</mo><mo stretchy="false">(</mo><mi>a</mi><mo>×</mo><mi>b</mi><mo stretchy="false">)</mo><mo>×</mo><mi>c</mi><mo>+</mo><mi>a</mi><mo>×</mo><mi>b</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>乘法运算规则 Ⅱ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>a</mi><mo>×</mo><mo stretchy="false">(</mo><mi>b</mi><mo>×</mo><mi>c</mi><mo stretchy="false">)</mo><mo>+</mo><mi>a</mi><mo>×</mo><mi>b</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mi>a</mi><mo>×</mo><mi>b</mi><mo stretchy="false">)</mo><mo>×</mo><mi>c</mi><mo>=</mo><mi>a</mi><mo>×</mo><mo stretchy="false">(</mo><mi>b</mi><mo>×</mo><mi>c</mi><mo stretchy="false">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>a</mi><mo>×</mo><mo stretchy="false">(</mo><mi>b</mi><mo>×</mo><mi>c</mi><mo>+</mo><mi>b</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>乘法分配律</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>a</mi><mo>×</mo><mo stretchy="false">(</mo><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>乘法运算规则 Ⅱ</mtext></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container><p>根据 Peano 公理 Ⅴ，得知 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="23.894ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 10561.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(1140.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2140.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3180.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4180.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4891.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5947.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6698.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mo" transform="translate(7698.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(8087.9,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(8739.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(9739.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(10172.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>a</mi><mo>×</mo><mi>b</mi><mo stretchy="false">)</mo><mo>×</mo><mi>c</mi><mo>=</mo><mi>a</mi><mo>×</mo><mo stretchy="false">(</mo><mi>b</mi><mo>×</mo><mi>c</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 对任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="5.159ex" height="2.009ex" role="img" focusable="false" viewBox="0 -694 2280.3 888" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi></math></mjx-assistive-mml></mjx-container> 成立，即乘法结合律成立。</p><h4 id="乘法消去律" tabindex="-1"><a class="header-anchor" href="#乘法消去律"><span>乘法消去律</span></a></h4><p>下面证明乘法消去律，即对于任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="3.173ex" height="2.009ex" role="img" focusable="false" viewBox="0 -694 1402.7 888" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container> 和 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="0.98ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 433 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></mjx-assistive-mml></mjx-container>，有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="31.207ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 13793.6 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(10224.2,0)"><path data-c="21D4" d="M308 524Q318 526 323 526Q340 526 340 514Q340 507 336 499Q326 476 314 454T292 417T274 391T260 374L255 368Q255 367 500 367Q744 367 744 368L739 374Q734 379 726 390T707 416T685 453T663 499Q658 511 658 515Q658 525 680 525Q687 524 690 523T695 519T701 507Q766 359 902 287Q921 276 939 269T961 259T966 250Q966 246 965 244T960 240T949 236T930 228T902 213Q763 137 701 -7Q697 -16 695 -19T690 -23T680 -25Q658 -25 658 -15Q658 -11 663 1Q673 24 685 46T707 83T725 109T739 126L744 132Q744 133 500 133Q255 133 255 132L260 126Q265 121 273 110T292 84T314 47T336 1Q341 -11 341 -15Q341 -25 319 -25Q312 -24 309 -23T304 -19T298 -7Q233 141 97 213Q83 221 70 227T51 235T41 239T35 243T34 250T35 256T40 261T51 265T70 273T97 287Q235 363 299 509Q305 522 308 524ZM792 319L783 327H216Q183 294 120 256L110 250L120 244Q173 212 207 181L216 173H783L792 181Q826 212 879 244L889 250L879 256Q826 288 792 319Z"></path></g><g data-mml-node="mi" transform="translate(11502,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(12308.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(13364.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>=</mo><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">⇔</mo><mi>a</mi><mo>=</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container>。</p><p>试证 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="31.207ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 13793.6 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(3847.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4598.3,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5598.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6992.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7381.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(7814.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(8481.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9537.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(10188.3,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(11188.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(12582.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(12971.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(13404.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>b</mi><mo stretchy="false">⇒</mo><mi>a</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>=</mo><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container>。</p><p>首先当 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="5.128ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 2266.6 748" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container> 时有</p><mjx-container class="MathJax" jax="SVG" display="true" style="position:relative;"><svg style="vertical-align:-12.33ex;" xmlns="http://www.w3.org/2000/svg" width="47.051ex" height="25.792ex" role="img" focusable="false" viewBox="0 -5950 20796.4 11400" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,5200)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3085,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4479,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(4868,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(5368,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5757,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(17696.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,3900)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(3085,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(3807.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4807.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mstyle" transform="translate(5336.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13113.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,2600)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2055.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3056,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mstyle" transform="translate(3585,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13113.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mstyle" transform="translate(1862.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13113.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(1762.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(17671.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(2055.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3056,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(3485,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13113.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-2600)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mn" transform="translate(2985,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(3707.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4707.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(5136.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13113.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅰ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-3900)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(4768,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(5268,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5657,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(13113.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-5200)"><g data-mml-node="mtd" transform="translate(4356.4,0)"></g><g data-mml-node="mtd" transform="translate(4356.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5590,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(17696.9,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(710.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1766.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right left right" columnspacing="0em 2em" rowspacing="3pt"><mtr><mtd><mi>a</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></mtd><mtd><mi></mi><mo>=</mo><mi>a</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mi>c</mi><mo>=</mo><mn>0</mn></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>a</mi><mo>×</mo><mn>0</mn><mo>+</mo><mi>a</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>乘法运算规则 Ⅱ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mn>0</mn><mo>+</mo><mi>a</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>乘法运算规则 Ⅰ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>a</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅰ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>b</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mi>a</mi><mo>=</mo><mi>b</mi></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mn>0</mn><mo>+</mo><mi>b</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅰ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>b</mi><mo>×</mo><mn>0</mn><mo>+</mo><mi>b</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>乘法运算规则 Ⅰ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>乘法运算规则 Ⅱ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mi>c</mi><mo>=</mo><mn>0</mn></mrow></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container><p>进而当 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="0.98ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 433 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></mjx-assistive-mml></mjx-container> 为自然数且 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="22.503ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 9946.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>=</mo><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 时有</p><mjx-container class="MathJax" jax="SVG" display="true" style="position:relative;"><svg style="vertical-align:-3.507ex;" xmlns="http://www.w3.org/2000/svg" width="72.085ex" height="8.145ex" role="img" focusable="false" viewBox="0 -2050 31861.4 3600" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4928.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5317.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5750.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(6139.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(6528.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2084.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3085,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4479,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4868,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5301,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5912.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6912.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mstyle" transform="translate(7441.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(24178.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(6528.4,0)"></g><g data-mml-node="mtd" transform="translate(6528.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5812.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(6812.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mstyle" transform="translate(7241.4,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(17290.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mrow" transform="translate(833,0)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g><g data-mml-node="mtext" transform="translate(2291.6,0)"><path data-c="A0" d=""></path><text data-variant="normal" transform="translate(250,0) scale(1,-1)" font-size="884px" font-family="serif">且</text><path data-c="A0" d="" transform="translate(1250,0)"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(3791.6,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(6528.4,0)"></g><g data-mml-node="mtd" transform="translate(6528.4,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6162,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6551,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6984,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7373,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(7762,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(24178.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right left right" columnspacing="0em 2em" rowspacing="3pt"><mtr><mtd><mi>a</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mtd><mtd><mi></mi><mo>=</mo><mi>a</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>+</mo><mi>a</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>乘法运算规则 Ⅱ</mtext></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>+</mo><mi>b</mi><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow><mrow data-mjx-texclass="ORD"><mi>a</mi><mo>=</mo><mi>b</mi></mrow><mtext> 且 </mtext><mrow data-mjx-texclass="ORD"><mi>a</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>=</mo><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></mrow></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi></mi><mo>=</mo><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>乘法运算规则 Ⅱ</mtext></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container><p>即 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="67.058ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 29639.6 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(3847.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4598.3,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5598.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6992.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7381.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(7814.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(8481.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9537.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(10188.3,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(11188.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(12582.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(12971.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(13404.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(14071.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(15349.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(16100.3,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(17100.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(18494.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(18883.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(20277.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(20666.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(21099.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(21488.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(22155.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(23211.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(23862.3,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(24862.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(26256.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(26645.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(28039.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(28428.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(28861.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(29250.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>b</mi><mo stretchy="false">⇒</mo><mi>a</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>=</mo><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">⇒</mo><mi>a</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>=</mo><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container>，根据 Peano 公理 Ⅴ，得知 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="31.207ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 13793.6 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2569.3,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(3847.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(4598.3,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(5598.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(6992.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7381.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(7814.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(8481.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(9537.1,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(10188.3,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(11188.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(12582.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(12971.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(13404.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>b</mi><mo stretchy="false">⇒</mo><mi>a</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>=</mo><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 对任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="5.159ex" height="2.009ex" role="img" focusable="false" viewBox="0 -694 2280.3 888" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi></math></mjx-assistive-mml></mjx-container> 成立。</p><p>试证 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="31.207ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 13793.6 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(10224.2,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(11502,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(12308.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(13364.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>=</mo><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">⇒</mo><mi>a</mi><mo>=</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container>，采用反证法，假设 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.486ex;" xmlns="http://www.w3.org/2000/svg" width="5.185ex" height="2.106ex" role="img" focusable="false" viewBox="0 -716 2291.6 931" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2260" d="M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>≠</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container>，则由加法运算规则 Ⅱ 可知 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="9.937ex" height="1.756ex" role="img" focusable="false" viewBox="0 -694 4392 776" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3514,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container> 或 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="9.937ex" height="1.756ex" role="img" focusable="false" viewBox="0 -694 4392 776" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3514,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container>，其中 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.486ex;" xmlns="http://www.w3.org/2000/svg" width="6.135ex" height="2.106ex" role="img" focusable="false" viewBox="0 -716 2711.6 931" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1155.8,0)"><path data-c="2260" d="M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z"></path></g><g data-mml-node="mn" transform="translate(2211.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>≠</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container>，不妨设 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.486ex;" xmlns="http://www.w3.org/2000/svg" width="17.077ex" height="2.106ex" role="img" focusable="false" viewBox="0 -716 7548.2 931" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3514,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(4392,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(4836.7,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5992.4,0)"><path data-c="2260" d="M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z"></path></g><g data-mml-node="mn" transform="translate(7048.2,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>m</mi><mo>,</mo><mi>m</mi><mo>≠</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container>。</p><p>由 Peano 公理 Ⅲ 有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="10.042ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4438.6 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2216,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(2882.8,0)"><path data-c="2260" d="M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z"></path></g><g data-mml-node="mn" transform="translate(3938.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>≠</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container>。</p><p>由 Peano 公理 Ⅲ、Ⅳ 有，任意非零自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="0.98ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 433 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></mjx-assistive-mml></mjx-container> 都有唯一的数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.294ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 572 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></mjx-assistive-mml></mjx-container> 满足 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="10.205ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4510.6 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></g><g data-mml-node="mo" transform="translate(2355,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3021.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(4077.6,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mi>c</mi></math></mjx-assistive-mml></mjx-container>，不妨记作 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="10.2ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4508.6 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="70" d="M36 -148H50Q89 -148 97 -134V-126Q97 -119 97 -107T97 -77T98 -38T98 6T98 55T98 106Q98 140 98 177T98 243T98 296T97 335T97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 61 434T98 436Q115 437 135 438T165 441T176 442H179V416L180 390L188 397Q247 441 326 441Q407 441 464 377T522 216Q522 115 457 52T310 -11Q242 -11 190 33L182 40V-45V-101Q182 -128 184 -134T195 -145Q216 -148 244 -148H260V-194H252L228 -193Q205 -192 178 -192T140 -191Q37 -191 28 -194H20V-148H36ZM424 218Q424 292 390 347T305 402Q234 402 182 337V98Q222 26 294 26Q345 26 384 80T424 218Z"></path><path data-c="72" d="M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z" transform="translate(556,0)"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(948,0)"></path></g><g data-mml-node="mo" transform="translate(1392,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1781,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2214,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(2880.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(3936.6,0)"><path data-c="1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pre</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>=</mo><mi>x</mi></math></mjx-assistive-mml></mjx-container>。</p><p>若有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="22.503ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 9946.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>=</mo><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container>，则有</p><mjx-container class="MathJax" jax="SVG" display="true" style="position:relative;"><svg style="vertical-align:-9.389ex;" xmlns="http://www.w3.org/2000/svg" width="69.571ex" height="19.91ex" role="img" focusable="false" viewBox="0 -4650 30750.4 8800" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,3900)"><g data-mml-node="mtd" transform="translate(5827.9,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(10184.3,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5590,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(25917.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">已</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">知</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">条</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">件</text></g></g></g><g data-mml-node="mtr" transform="translate(0,2600)"><g data-mml-node="mtd" transform="translate(3049.4,0)"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1040.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(2040.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2918.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(3529.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(4529.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(5923.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6312.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(6745.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(10184.3,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5590,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(25525.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(833,0)"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3514,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></g><g data-mml-node="mtr" transform="translate(0,1300)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(651.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1651.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3045.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3434.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3867.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4478.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5478.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6579.1,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7579.3,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8973.3,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9362.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9795.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(10184.3,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1333.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1984.8,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2985,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(4379,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(4768,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(5201,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mstyle" transform="translate(5590,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18917.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">交</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">换</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">律</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">、</text><text data-variant="normal" transform="translate(6000,0) scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(7000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(8000,0) scale(1,-1)" font-size="884px" font-family="serif">分</text><text data-variant="normal" transform="translate(9000,0) scale(1,-1)" font-size="884px" font-family="serif">配</text><text data-variant="normal" transform="translate(10000,0) scale(1,-1)" font-size="884px" font-family="serif">律</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(5478.9,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3494.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4316.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(10184.3,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(1833.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(24917.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">消</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">去</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">律</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(5550.4,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2755.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3755.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mtd" transform="translate(10184.3,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(1833.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(23067.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">乘</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-2600)"><g data-mml-node="mtd" transform="translate(1208.4,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2755.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3755.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(5149.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5538.9,0)"><path data-c="70" d="M36 -148H50Q89 -148 97 -134V-126Q97 -119 97 -107T97 -77T98 -38T98 6T98 55T98 106Q98 140 98 177T98 243T98 296T97 335T97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 61 434T98 436Q115 437 135 438T165 441T176 442H179V416L180 390L188 397Q247 441 326 441Q407 441 464 377T522 216Q522 115 457 52T310 -11Q242 -11 190 33L182 40V-45V-101Q182 -128 184 -134T195 -145Q216 -148 244 -148H260V-194H252L228 -193Q205 -192 178 -192T140 -191Q37 -191 28 -194H20V-148H36ZM424 218Q424 292 390 347T305 402Q234 402 182 337V98Q222 26 294 26Q345 26 384 80T424 218Z"></path><path data-c="72" d="M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z" transform="translate(556,0)"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(948,0)"></path></g><g data-mml-node="mo" transform="translate(6930.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7319.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(8197.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(8586.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(10184.3,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(1833.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(18774.3,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mrow" transform="translate(833,0)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1155.8,0)"><path data-c="2260" d="M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z"></path></g><g data-mml-node="mn" transform="translate(2211.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g><g data-mml-node="mtext" transform="translate(2711.6,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">、</text></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(3711.6,0)"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1155.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(2211.6,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3605.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3994.6,0)"><path data-c="70" d="M36 -148H50Q89 -148 97 -134V-126Q97 -119 97 -107T97 -77T98 -38T98 6T98 55T98 106Q98 140 98 177T98 243T98 296T97 335T97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 61 434T98 436Q115 437 135 438T165 441T176 442H179V416L180 390L188 397Q247 441 326 441Q407 441 464 377T522 216Q522 115 457 52T310 -11Q242 -11 190 33L182 40V-45V-101Q182 -128 184 -134T195 -145Q216 -148 244 -148H260V-194H252L228 -193Q205 -192 178 -192T140 -191Q37 -191 28 -194H20V-148H36ZM424 218Q424 292 390 347T305 402Q234 402 182 337V98Q222 26 294 26Q345 26 384 80T424 218Z"></path><path data-c="72" d="M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z" transform="translate(556,0)"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(948,0)"></path></g><g data-mml-node="mo" transform="translate(5386.6,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5775.6,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6653.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(7042.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-3900)"><g data-mml-node="mtd" transform="translate(1208.4,0)"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(1394,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1783,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2883.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(3883.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(4538.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(5538.9,0)"><path data-c="70" d="M36 -148H50Q89 -148 97 -134V-126Q97 -119 97 -107T97 -77T98 -38T98 6T98 55T98 106Q98 140 98 177T98 243T98 296T97 335T97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 61 434T98 436Q115 437 135 438T165 441T176 442H179V416L180 390L188 397Q247 441 326 441Q407 441 464 377T522 216Q522 115 457 52T310 -11Q242 -11 190 33L182 40V-45V-101Q182 -128 184 -134T195 -145Q216 -148 244 -148H260V-194H252L228 -193Q205 -192 178 -192T140 -191Q37 -191 28 -194H20V-148H36ZM424 218Q424 292 390 347T305 402Q234 402 182 337V98Q222 26 294 26Q345 26 384 80T424 218Z"></path><path data-c="72" d="M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z" transform="translate(556,0)"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(948,0)"></path></g><g data-mml-node="mo" transform="translate(6930.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7319.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(8197.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(8586.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g><g data-mml-node="mtd" transform="translate(10184.3,0)"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(1333.6,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mstyle" transform="translate(1833.6,0)"><g data-mml-node="mspace"></g></g></g><g data-mml-node="mtd" transform="translate(23067.4,0)"><g data-mml-node="mi"><path data-c="23" d="M56 347Q56 360 70 367H313L355 524Q394 676 401 686Q406 694 416 694Q434 694 436 676Q436 672 396 522Q355 374 355 369L354 367H543L585 524Q626 679 630 685Q636 694 646 694Q653 694 659 689T665 678Q665 668 626 522Q585 374 585 369L584 367H762Q777 359 777 347Q777 334 767 331T722 327H667H572L552 251L531 174Q531 173 647 173H720Q756 173 766 170T777 153T762 133H519L477 -24Q436 -179 432 -185Q426 -194 416 -194Q409 -194 403 -189T397 -177Q397 -167 436 -21Q477 125 477 131L478 133H289L247 -24Q206 -179 202 -185Q196 -194 186 -194Q179 -194 173 -189T167 -177Q167 -167 206 -21Q247 125 247 131L248 133H70Q56 140 56 153Q56 168 72 173H260L280 249L301 326Q301 327 186 327H72Q56 332 56 347ZM531 326Q531 327 437 327H342L322 251L301 174Q301 173 395 173H490L510 249L531 326Z"></path></g><g data-mml-node="mtext" transform="translate(833,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">加</text><text data-variant="normal" transform="translate(1000,0) scale(1,-1)" font-size="884px" font-family="serif">法</text><text data-variant="normal" transform="translate(2000,0) scale(1,-1)" font-size="884px" font-family="serif">运</text><text data-variant="normal" transform="translate(3000,0) scale(1,-1)" font-size="884px" font-family="serif">算</text><text data-variant="normal" transform="translate(4000,0) scale(1,-1)" font-size="884px" font-family="serif">规</text><text data-variant="normal" transform="translate(5000,0) scale(1,-1)" font-size="884px" font-family="serif">则</text><path data-c="20" d="" transform="translate(6000,0)"></path><text data-variant="normal" transform="translate(6250,0) scale(1,-1)" font-size="884px" font-family="serif">Ⅱ</text></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right left right" columnspacing="0em 2em" rowspacing="3pt"><mtr><mtd><mi>a</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></mtd><mtd><mi></mi><mo>=</mo><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>已知条件</mtext></mtd></mtr><mtr><mtd><mo stretchy="false">(</mo><mi>b</mi><mo>+</mo><mi>m</mi><mo stretchy="false">)</mo><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></mtd><mtd><mi></mi><mo>=</mo><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow data-mjx-texclass="ORD"><mi>a</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>m</mi></mrow></mtd></mtr><mtr><mtd><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>+</mo><mi>m</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></mtd><mtd><mi></mi><mo>=</mo><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>乘法交换律、乘法分配律</mtext></mtd></mtr><mtr><mtd><mi>m</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></mtd><mtd><mi></mi><mo>=</mo><mn>0</mn><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法消去律</mtext></mtd></mtr><mtr><mtd><mi>m</mi><mo>×</mo><mi>c</mi><mo>+</mo><mi>m</mi></mtd><mtd><mi></mi><mo>=</mo><mn>0</mn><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>乘法运算规则 Ⅱ</mtext></mtd></mtr><mtr><mtd><mi>m</mi><mo>×</mo><mi>c</mi><mo>+</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>pre</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mtd><mtd><mi></mi><mo>=</mo><mn>0</mn><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mrow><mrow data-mjx-texclass="ORD"><mi>m</mi><mo>≠</mo><mn>0</mn></mrow><mtext>、</mtext><mrow data-mjx-texclass="ORD"><mi>m</mi><mo>=</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>pre</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow></mrow></mtd></mtr><mtr><mtd><mi>suc</mi><mo stretchy="false">(</mo><mi>m</mi><mo>×</mo><mi>c</mi><mo>+</mo><mi>pre</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mtd><mtd><mi></mi><mo>=</mo><mn>0</mn><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle></mtd><mtd><mi mathvariant="normal">#</mi><mtext>加法运算规则 Ⅱ</mtext></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container><p>上述等式表明 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.05ex;" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></mjx-assistive-mml></mjx-container> 是 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="15.393ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 6803.9 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1100.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(2100.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(2755.7,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3755.9,0)"><path data-c="70" d="M36 -148H50Q89 -148 97 -134V-126Q97 -119 97 -107T97 -77T98 -38T98 6T98 55T98 106Q98 140 98 177T98 243T98 296T97 335T97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 61 434T98 436Q115 437 135 438T165 441T176 442H179V416L180 390L188 397Q247 441 326 441Q407 441 464 377T522 216Q522 115 457 52T310 -11Q242 -11 190 33L182 40V-45V-101Q182 -128 184 -134T195 -145Q216 -148 244 -148H260V-194H252L228 -193Q205 -192 178 -192T140 -191Q37 -191 28 -194H20V-148H36ZM424 218Q424 292 390 347T305 402Q234 402 182 337V98Q222 26 294 26Q345 26 384 80T424 218Z"></path><path data-c="72" d="M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z" transform="translate(556,0)"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(948,0)"></path></g><g data-mml-node="mo" transform="translate(5147.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5536.9,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(6414.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>×</mo><mi>c</mi><mo>+</mo><mi>pre</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 的后继，这违背了 Peano 公理 Ⅲ，由此知道假设不成立，即 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="31.207ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 13793.6 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(10224.2,0)"><path data-c="21D2" d="M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z"></path></g><g data-mml-node="mi" transform="translate(11502,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(12308.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(13364.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>=</mo><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">⇒</mo><mi>a</mi><mo>=</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container>。</p><p>综上所述，乘法消去律 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="31.207ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 13793.6 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(10224.2,0)"><path data-c="21D4" d="M308 524Q318 526 323 526Q340 526 340 514Q340 507 336 499Q326 476 314 454T292 417T274 391T260 374L255 368Q255 367 500 367Q744 367 744 368L739 374Q734 379 726 390T707 416T685 453T663 499Q658 511 658 515Q658 525 680 525Q687 524 690 523T695 519T701 507Q766 359 902 287Q921 276 939 269T961 259T966 250Q966 246 965 244T960 240T949 236T930 228T902 213Q763 137 701 -7Q697 -16 695 -19T690 -23T680 -25Q658 -25 658 -15Q658 -11 663 1Q673 24 685 46T707 83T725 109T739 126L744 132Q744 133 500 133Q255 133 255 132L260 126Q265 121 273 110T292 84T314 47T336 1Q341 -11 341 -15Q341 -25 319 -25Q312 -24 309 -23T304 -19T298 -7Q233 141 97 213Q83 221 70 227T51 235T41 239T35 243T34 250T35 256T40 261T51 265T70 273T97 287Q235 363 299 509Q305 522 308 524ZM792 319L783 327H216Q183 294 120 256L110 250L120 244Q173 212 207 181L216 173H783L792 181Q826 212 879 244L889 250L879 256Q826 288 792 319Z"></path></g><g data-mml-node="mi" transform="translate(11502,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(12308.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(13364.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>=</mo><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">⇔</mo><mi>a</mi><mo>=</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container>，对任意自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.439ex;" xmlns="http://www.w3.org/2000/svg" width="5.159ex" height="2.009ex" role="img" focusable="false" viewBox="0 -694 2280.3 888" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(529,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(973.7,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(1402.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(1847.3,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi></math></mjx-assistive-mml></mjx-container> 成立。</p><h2 id="peano-公理的合理性" tabindex="-1"><a class="header-anchor" href="#peano-公理的合理性"><span>Peano 公理的合理性</span></a></h2><p>通过上述步骤，我们成功地由 Peano 公理构建出了一个自然数代数系统。但 Peano 公理自身任有待研究。从上述步骤中我们看出 Peano 公理每一条公理都被使用过，少了任何一条都不足以构建出上述的自然数系统，这究竟是为什么呢？</p><p>下面我将阐述为什么每条公理都是必须的，通过举反例的方式。研究 Peano 公理自然不能从 Peano 公理系统内出发，我们将借助另一个公理系统——图论。</p><h3 id="乘法保序性" tabindex="-1"><a class="header-anchor" href="#乘法保序性"><span>乘法保序性</span></a></h3><p>若 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.312ex;" xmlns="http://www.w3.org/2000/svg" width="5.185ex" height="1.882ex" role="img" focusable="false" viewBox="0 -694 2291.6 832" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>≤</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container>，则 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="22.503ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 9946.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>≤</mo><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container>。</p><p>由 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.312ex;" xmlns="http://www.w3.org/2000/svg" width="5.185ex" height="1.882ex" role="img" focusable="false" viewBox="0 -694 2291.6 832" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>≤</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container> 有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="9.937ex" height="1.756ex" role="img" focusable="false" viewBox="0 -694 4392 776" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(706.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1762.6,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3514,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container>，进而 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="55.3ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 24442.8 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(651.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1651.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3045.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3434.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3867.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4534.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(5590,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(5979,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6730.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7730.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(8608.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(9219.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(10219.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(11613.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(12002.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(12435.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(13102.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(14158.4,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(14909.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(15909.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(17303.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(17692.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(18125.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(18737.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(19737.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(20837.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(21837.8,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(23231.8,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(23620.8,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(24053.8,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>m</mi><mo stretchy="false">)</mo><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>=</mo><mi>a</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>+</mo><mi>m</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 因此 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="22.503ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 9946.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>≤</mo><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container>。</p><h3 id="乘法消去保序性" tabindex="-1"><a class="header-anchor" href="#乘法消去保序性"><span>乘法消去保序性</span></a></h3><p>若 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="22.503ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 9946.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>≤</mo><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container>，则 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.312ex;" xmlns="http://www.w3.org/2000/svg" width="5.185ex" height="1.882ex" role="img" focusable="false" viewBox="0 -694 2291.6 832" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>≤</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container>。</p><p>采用反证法，假设 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.09ex;" xmlns="http://www.w3.org/2000/svg" width="5.185ex" height="1.661ex" role="img" focusable="false" viewBox="0 -694 2291.6 734" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3E" d="M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>&gt;</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container>，则存在正自然数 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.986ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 878 453" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></mjx-assistive-mml></mjx-container> 满足 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="9.937ex" height="1.756ex" role="img" focusable="false" viewBox="0 -694 4392 776" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(2513.8,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(3514,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>m</mi></math></mjx-assistive-mml></mjx-container>，有</p><mjx-container class="MathJax" jax="SVG" display="true" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="55.074ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 24342.8 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(5690,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(6079,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6730.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(7730.4,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(8608.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(9219.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(10219.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(11613.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(12002.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(12435.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(13102.7,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(14158.4,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(14809.7,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(15809.9,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(17203.9,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(17592.9,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(18025.9,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(18637.1,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(19637.3,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(20737.6,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(21737.8,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(23131.8,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(23520.8,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(23953.8,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>a</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mi>b</mi><mo>+</mo><mi>m</mi><mo stretchy="false">)</mo><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>=</mo><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>+</mo><mi>m</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container><p>由此有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="22.503ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 9946.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(651.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1651.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3045.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3434.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3867.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4534.2,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mi" transform="translate(5590,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>≤</mo><mi>a</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container>，根据序的反对称性有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="22.503ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 9946.4 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(751.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(1751.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(3145.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3534.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(3967.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4634.2,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(5690,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g><g data-mml-node="mo" transform="translate(6341.2,0)"><path data-c="D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path></g><g data-mml-node="mi" transform="translate(7341.4,0)"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(394,0)"></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" transform="translate(950,0)"></path></g><g data-mml-node="mo" transform="translate(8735.4,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(9124.4,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mo" transform="translate(9557.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo>=</mo><mi>b</mi><mo>×</mo><mi>suc</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container>，根据乘法消去律有 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.186ex;" xmlns="http://www.w3.org/2000/svg" width="5.185ex" height="1.756ex" role="img" focusable="false" viewBox="0 -694 2291.6 776" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container>，这与 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.09ex;" xmlns="http://www.w3.org/2000/svg" width="5.185ex" height="1.661ex" role="img" focusable="false" viewBox="0 -694 2291.6 734" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mo" transform="translate(806.8,0)"><path data-c="3E" d="M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z"></path></g><g data-mml-node="mi" transform="translate(1862.6,0)"><path data-c="1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>&gt;</mo><mi>b</mi></math></mjx-assistive-mml></mjx-container> 的假设矛盾，因此假设不成立，即证明了乘法消去的保序性。</p><h3 id="用图论阐述-peano-系统" tabindex="-1"><a class="header-anchor" href="#用图论阐述-peano-系统"><span>用图论阐述 Peano 系统</span></a></h3><p>自然数与有向图 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="7.78ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 3438.7 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mi"><path data-c="47" d="M56 342Q56 428 89 500T174 615T283 681T391 705Q394 705 400 705T408 704Q499 704 569 636L582 624L612 663Q639 700 643 704Q644 704 647 704T653 705H657Q660 705 666 699V419L660 413H626Q620 419 619 430Q610 512 571 572T476 651Q457 658 426 658Q401 658 376 654T316 633T254 592T205 519T177 411Q173 369 173 335Q173 259 192 201T238 111T302 58T370 31T431 24Q478 24 513 45T559 100Q562 110 562 160V212Q561 213 557 216T551 220T542 223T526 225T502 226T463 227H437V273H449L609 270Q715 270 727 273H735V227H721Q674 227 668 215Q666 211 666 108V6Q660 0 657 0Q653 0 639 10Q617 25 600 42L587 54Q571 27 524 3T406 -22Q317 -22 238 22T108 151T56 342Z"></path></g></g><g data-mml-node="mo" transform="translate(785,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(1174,0)"><g data-mml-node="mi"><path data-c="56" d="M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z"></path></g></g><g data-mml-node="mo" transform="translate(1924,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(2368.7,0)"><g data-mml-node="mi"><path data-c="45" d="M128 619Q121 626 117 628T101 631T58 634H25V680H597V676Q599 670 611 560T625 444V440H585V444Q584 447 582 465Q578 500 570 526T553 571T528 601T498 619T457 629T411 633T353 634Q266 634 251 633T233 622Q233 622 233 621Q232 619 232 497V376H286Q359 378 377 385Q413 401 416 469Q416 471 416 473V493H456V213H416V233Q415 268 408 288T383 317T349 328T297 330Q290 330 286 330H232V196V114Q232 57 237 52Q243 47 289 47H340H391Q428 47 452 50T505 62T552 92T584 146Q594 172 599 200T607 247T612 270V273H652V270Q651 267 632 137T610 3V0H25V46H58Q100 47 109 49T128 61V619Z"></path></g></g><g data-mml-node="mo" transform="translate(3049.7,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">G</mi></mrow><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">V</mi></mrow><mo>,</mo><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">E</mi></mrow><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> 同构，这个图满足如下性质：</p><ol><li>存在点 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.05ex;" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></mjx-assistive-mml></mjx-container>，即 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.375ex;" xmlns="http://www.w3.org/2000/svg" width="6.548ex" height="1.92ex" role="img" focusable="false" viewBox="0 -683 2894.1 848.6" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path></g><g data-mml-node="mn" transform="translate(518,-150) scale(0.707)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g><g data-mml-node="mo" transform="translate(1199.3,0)"><path data-c="2208" d="M84 250Q84 372 166 450T360 539Q361 539 377 539T419 540T469 540H568Q583 532 583 520Q583 511 570 501L466 500Q355 499 329 494Q280 482 242 458T183 409T147 354T129 306T124 272V270H568Q583 262 583 250T568 230H124V228Q124 207 134 177T167 112T231 48T328 7Q355 1 466 0H570Q583 -10 583 -20Q583 -32 568 -40H471Q464 -40 446 -40T417 -41Q262 -41 172 45Q84 127 84 250Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(2144.1,0)"><g data-mml-node="mi"><path data-c="56" d="M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z"></path></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>0</mn></msub><mo>∈</mo><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">V</mi></mrow></math></mjx-assistive-mml></mjx-container>；</li><li>所有点的出度为 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:0;" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.507ex" role="img" focusable="false" viewBox="0 -666 500 666" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></mjx-assistive-mml></mjx-container>，即 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="14.139ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 6249.6 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="6F" d="M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z"></path><path data-c="75" d="M383 58Q327 -10 256 -10H249Q124 -10 105 89Q104 96 103 226Q102 335 102 348T96 369Q86 385 36 385H25V408Q25 431 27 431L38 432Q48 433 67 434T105 436Q122 437 142 438T172 441T184 442H187V261Q188 77 190 64Q193 49 204 40Q224 26 264 26Q290 26 311 35T343 58T363 90T375 120T379 144Q379 145 379 161T380 201T380 248V315Q380 361 370 372T320 385H302V431Q304 431 378 436T457 442H464V264Q464 84 465 81Q468 61 479 55T524 46H542V0Q540 0 467 -5T390 -11H383V58Z" transform="translate(500,0)"></path><path data-c="74" d="M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z" transform="translate(1056,0)"></path><path data-c="44" d="M130 622Q123 629 119 631T103 634T60 637H27V683H228Q399 682 419 682T461 676Q504 667 546 641T626 573T685 470T708 336Q708 210 634 116T442 3Q429 1 228 0H27V46H60Q102 47 111 49T130 61V622ZM593 338Q593 439 571 501T493 602Q439 637 355 637H322H294Q238 637 234 628Q231 624 231 344Q231 62 232 59Q233 49 248 48T339 46H350Q456 46 515 95Q561 133 577 191T593 338Z" transform="translate(1445,0)"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(2209,0)"></path><path data-c="67" d="M329 409Q373 453 429 453Q459 453 472 434T485 396Q485 382 476 371T449 360Q416 360 412 390Q410 404 415 411Q415 412 416 414V415Q388 412 363 393Q355 388 355 386Q355 385 359 381T368 369T379 351T388 325T392 292Q392 230 343 187T222 143Q172 143 123 171Q112 153 112 133Q112 98 138 81Q147 75 155 75T227 73Q311 72 335 67Q396 58 431 26Q470 -13 470 -72Q470 -139 392 -175Q332 -206 250 -206Q167 -206 107 -175Q29 -140 29 -75Q29 -39 50 -15T92 18L103 24Q67 55 67 108Q67 155 96 193Q52 237 52 292Q52 355 102 398T223 442Q274 442 318 416L329 409ZM299 343Q294 371 273 387T221 404Q192 404 171 388T145 343Q142 326 142 292Q142 248 149 227T179 192Q196 182 222 182Q244 182 260 189T283 207T294 227T299 242Q302 258 302 292T299 343ZM403 -75Q403 -50 389 -34T348 -11T299 -2T245 0H218Q151 0 138 -6Q118 -15 107 -34T95 -74Q95 -84 101 -97T122 -127T170 -155T250 -167Q319 -167 361 -139T403 -75Z" transform="translate(2653,0)"></path></g><g data-mml-node="mo" transform="translate(3153,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3542,0)"><path data-c="1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path></g><g data-mml-node="mo" transform="translate(4027,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4693.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(5749.6,0)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>outDeg</mi><mo stretchy="false">(</mo><mi>v</mi><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn></math></mjx-assistive-mml></mjx-container>；</li><li>点 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.05ex;" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></mjx-assistive-mml></mjx-container> 入度为 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.05ex;" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></mjx-assistive-mml></mjx-container>，即 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="13.745ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 6075.1 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="69" d="M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z"></path><path data-c="6E" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z" transform="translate(278,0)"></path><path data-c="44" d="M130 622Q123 629 119 631T103 634T60 637H27V683H228Q399 682 419 682T461 676Q504 667 546 641T626 573T685 470T708 336Q708 210 634 116T442 3Q429 1 228 0H27V46H60Q102 47 111 49T130 61V622ZM593 338Q593 439 571 501T493 602Q439 637 355 637H322H294Q238 637 234 628Q231 624 231 344Q231 62 232 59Q233 49 248 48T339 46H350Q456 46 515 95Q561 133 577 191T593 338Z" transform="translate(834,0)"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(1598,0)"></path><path data-c="67" d="M329 409Q373 453 429 453Q459 453 472 434T485 396Q485 382 476 371T449 360Q416 360 412 390Q410 404 415 411Q415 412 416 414V415Q388 412 363 393Q355 388 355 386Q355 385 359 381T368 369T379 351T388 325T392 292Q392 230 343 187T222 143Q172 143 123 171Q112 153 112 133Q112 98 138 81Q147 75 155 75T227 73Q311 72 335 67Q396 58 431 26Q470 -13 470 -72Q470 -139 392 -175Q332 -206 250 -206Q167 -206 107 -175Q29 -140 29 -75Q29 -39 50 -15T92 18L103 24Q67 55 67 108Q67 155 96 193Q52 237 52 292Q52 355 102 398T223 442Q274 442 318 416L329 409ZM299 343Q294 371 273 387T221 404Q192 404 171 388T145 343Q142 326 142 292Q142 248 149 227T179 192Q196 182 222 182Q244 182 260 189T283 207T294 227T299 242Q302 258 302 292T299 343ZM403 -75Q403 -50 389 -34T348 -11T299 -2T245 0H218Q151 0 138 -6Q118 -15 107 -34T95 -74Q95 -84 101 -97T122 -127T170 -155T250 -167Q319 -167 361 -139T403 -75Z" transform="translate(2042,0)"></path></g><g data-mml-node="mo" transform="translate(2542,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="msub" transform="translate(2931,0)"><g data-mml-node="mi"><path data-c="1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path></g><g data-mml-node="mn" transform="translate(518,-150) scale(0.707)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g><g data-mml-node="mo" transform="translate(3852.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4519.3,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mn" transform="translate(5575.1,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inDeg</mi><mo stretchy="false">(</mo><msub><mi>v</mi><mn>0</mn></msub><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container>；</li><li>任意点的入度小于等于 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:0;" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.507ex" role="img" focusable="false" viewBox="0 -666 500 666" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></mjx-assistive-mml></mjx-container>，即 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="12.757ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 5638.6 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="69" d="M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z"></path><path data-c="6E" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z" transform="translate(278,0)"></path><path data-c="44" d="M130 622Q123 629 119 631T103 634T60 637H27V683H228Q399 682 419 682T461 676Q504 667 546 641T626 573T685 470T708 336Q708 210 634 116T442 3Q429 1 228 0H27V46H60Q102 47 111 49T130 61V622ZM593 338Q593 439 571 501T493 602Q439 637 355 637H322H294Q238 637 234 628Q231 624 231 344Q231 62 232 59Q233 49 248 48T339 46H350Q456 46 515 95Q561 133 577 191T593 338Z" transform="translate(834,0)"></path><path data-c="65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(1598,0)"></path><path data-c="67" d="M329 409Q373 453 429 453Q459 453 472 434T485 396Q485 382 476 371T449 360Q416 360 412 390Q410 404 415 411Q415 412 416 414V415Q388 412 363 393Q355 388 355 386Q355 385 359 381T368 369T379 351T388 325T392 292Q392 230 343 187T222 143Q172 143 123 171Q112 153 112 133Q112 98 138 81Q147 75 155 75T227 73Q311 72 335 67Q396 58 431 26Q470 -13 470 -72Q470 -139 392 -175Q332 -206 250 -206Q167 -206 107 -175Q29 -140 29 -75Q29 -39 50 -15T92 18L103 24Q67 55 67 108Q67 155 96 193Q52 237 52 292Q52 355 102 398T223 442Q274 442 318 416L329 409ZM299 343Q294 371 273 387T221 404Q192 404 171 388T145 343Q142 326 142 292Q142 248 149 227T179 192Q196 182 222 182Q244 182 260 189T283 207T294 227T299 242Q302 258 302 292T299 343ZM403 -75Q403 -50 389 -34T348 -11T299 -2T245 0H218Q151 0 138 -6Q118 -15 107 -34T95 -74Q95 -84 101 -97T122 -127T170 -155T250 -167Q319 -167 361 -139T403 -75Z" transform="translate(2042,0)"></path></g><g data-mml-node="mo" transform="translate(2542,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(2931,0)"><path data-c="1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path></g><g data-mml-node="mo" transform="translate(3416,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(4082.8,0)"><path data-c="2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path></g><g data-mml-node="mn" transform="translate(5138.6,0)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inDeg</mi><mo stretchy="false">(</mo><mi>v</mi><mo stretchy="false">)</mo><mo>≤</mo><mn>1</mn></math></mjx-assistive-mml></mjx-container>；</li><li>存在从 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.05ex;" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></mjx-assistive-mml></mjx-container> 到任意点的路径，即 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="11.157ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4931.3 1000" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="2203" d="M56 661T56 674T70 694H487Q497 686 500 679V15Q497 10 487 1L279 0H70Q56 7 56 20T70 40H460V327H84Q70 334 70 347T84 367H460V654H70Q56 661 56 674Z"></path></g><g data-mml-node="mi" transform="translate(722.7,0)"><path data-c="70" d="M36 -148H50Q89 -148 97 -134V-126Q97 -119 97 -107T97 -77T98 -38T98 6T98 55T98 106Q98 140 98 177T98 243T98 296T97 335T97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 61 434T98 436Q115 437 135 438T165 441T176 442H179V416L180 390L188 397Q247 441 326 441Q407 441 464 377T522 216Q522 115 457 52T310 -11Q242 -11 190 33L182 40V-45V-101Q182 -128 184 -134T195 -145Q216 -148 244 -148H260V-194H252L228 -193Q205 -192 178 -192T140 -191Q37 -191 28 -194H20V-148H36ZM424 218Q424 292 390 347T305 402Q234 402 182 337V98Q222 26 294 26Q345 26 384 80T424 218Z"></path><path data-c="61" d="M137 305T115 305T78 320T63 359Q63 394 97 421T218 448Q291 448 336 416T396 340Q401 326 401 309T402 194V124Q402 76 407 58T428 40Q443 40 448 56T453 109V145H493V106Q492 66 490 59Q481 29 455 12T400 -6T353 12T329 54V58L327 55Q325 52 322 49T314 40T302 29T287 17T269 6T247 -2T221 -8T190 -11Q130 -11 82 20T34 107Q34 128 41 147T68 188T116 225T194 253T304 268H318V290Q318 324 312 340Q290 411 215 411Q197 411 181 410T156 406T148 403Q170 388 170 359Q170 334 154 320ZM126 106Q126 75 150 51T209 26Q247 26 276 49T315 109Q317 116 318 175Q318 233 317 233Q309 233 296 232T251 223T193 203T147 166T126 106Z" transform="translate(556,0)"></path><path data-c="74" d="M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z" transform="translate(1056,0)"></path><path data-c="68" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z" transform="translate(1445,0)"></path></g><g data-mml-node="mo" transform="translate(2723.7,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(3112.7,0)"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(3612.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(4057.3,0)"><path data-c="1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path></g><g data-mml-node="mo" transform="translate(4542.3,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∃</mi><mi>path</mi><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mi>v</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container>。</li></ol><p>下面我们试着通过<strong>删除公理</strong>的方法来寻找反例。</p><h4 id="peano-公理-i" tabindex="-1"><a class="header-anchor" href="#peano-公理-i"><span>Peano 公理 Ⅰ</span></a></h4><p>若去除，则允许不存在 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.05ex;" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></mjx-assistive-mml></mjx-container>，可以构造出空集自然数系统。</p><h4 id="peano-公理-ii" tabindex="-1"><a class="header-anchor" href="#peano-公理-ii"><span>Peano 公理 Ⅱ</span></a></h4><p>若去除，则对点的出度无规定，可以构造出菊花图自然数系统。</p><h4 id="peano-公理-iii" tabindex="-1"><a class="header-anchor" href="#peano-公理-iii"><span>Peano 公理 Ⅲ</span></a></h4><p>若去除，则对 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.05ex;" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></mjx-assistive-mml></mjx-container> 的入度无规定，可以构造出环状自然数系统。</p><h4 id="peano-公理-iv" tabindex="-1"><a class="header-anchor" href="#peano-公理-iv"><span>Peano 公理 Ⅳ</span></a></h4><p>若去除，则对一个数可以是多个数的后继，可以构造出 <mjx-container class="MathJax" jax="SVG" style="position:relative;"><svg style="vertical-align:-0.489ex;" xmlns="http://www.w3.org/2000/svg" width="1.17ex" height="1.489ex" role="img" focusable="false" viewBox="0 -442 517 658" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D70C" d="M58 -216Q25 -216 23 -186Q23 -176 73 26T127 234Q143 289 182 341Q252 427 341 441Q343 441 349 441T359 442Q432 442 471 394T510 276Q510 219 486 165T425 74T345 13T266 -10H255H248Q197 -10 165 35L160 41L133 -71Q108 -168 104 -181T92 -202Q76 -216 58 -216ZM424 322Q424 359 407 382T357 405Q322 405 287 376T231 300Q217 269 193 170L176 102Q193 26 260 26Q298 26 334 62Q367 92 389 158T418 266T424 322Z"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ρ</mi></math></mjx-assistive-mml></mjx-container> 状自然数系统。</p><h4 id="peano-公理-v" tabindex="-1"><a class="header-anchor" href="#peano-公理-v"><span>Peano 公理 Ⅴ</span></a></h4><p>若去除，则对连通性无要求，可以构造出分段状自然数系统。</p></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/「算术公理系统 1」自然数.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->「泛型与 OI」modint</div></a><a class="route-link nav-link next" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">android studio换源<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tech/\344\275\277\347\224\250capacitor\345\222\214ionic\345\260\206vue\351\241\271\347\233\256\350\277\201\347\247\273\345\210\260mobile\347\253\257.html" "b/tech/\344\275\277\347\224\250capacitor\345\222\214ionic\345\260\206vue\351\241\271\347\233\256\350\277\201\347\247\273\345\210\260mobile\347\253\257.html"
index a4cc9d1..10b9d97 100644
--- "a/tech/\344\275\277\347\224\250capacitor\345\222\214ionic\345\260\206vue\351\241\271\347\233\256\350\277\201\347\247\273\345\210\260mobile\347\253\257.html"
+++ "b/tech/\344\275\277\347\224\250capacitor\345\222\214ionic\345\260\206vue\351\241\271\347\233\256\350\277\201\347\247\273\345\210\260mobile\347\253\257.html"
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="使用capacitor和ionic将vue项目迁移到mobile端"><meta property="og:description" content="当我们写完了vue项目后，想做一个一样的移动app，此时我们可以使用ionic无缝将其迁移到移动端。"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="mobile"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"使用capacitor和ionic将vue项目迁移到mobile端","image":[""],"dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>使用capacitor和ionic将vue项目迁移到mobile端 | blog</title><meta name="description" content="当我们写完了vue项目后，想做一个一样的移动app，此时我们可以使用ionic无缝将其迁移到移动端。">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->使用capacitor和ionic将vue项目迁移到mobile端</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag0 clickable" role="navigation">mobile</span><!--]--><meta property="keywords" content="mobile"></span></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#安装">安装</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#tips">tips</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#bug-记录">bug 记录</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="前言" tabindex="-1"><a class="header-anchor" href="#前言"><span>前言</span></a></h1><p>当我们写完了vue项目后，想做一个一样的移动app，此时我们可以使用ionic无缝将其迁移到移动端。</p><!-- more --><h2 id="安装" tabindex="-1"><a class="header-anchor" href="#安装"><span>安装</span></a></h2><p><a href="https://capacitorjs.com/" target="_blank" rel="noopener noreferrer">Capacitor<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></p><p><a href="https://ionic.nodejs.cn/" target="_blank" rel="noopener noreferrer">ionic<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></p><h2 id="tips" tabindex="-1"><a class="header-anchor" href="#tips"><span>tips</span></a></h2><p><a href="https://ionic.nodejs.cn/vue/your-first-app/deploying-mobile" target="_blank" rel="noopener noreferrer">deploy<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></p><p>每次执行更新你的 Web 目录的构建（例如 ionic build）时（默认：build)，你需要将这些更改复制到你的原生项目中：</p><p>ionic cap copy</p><p>注意：更新代码的原生部分（例如添加新插件）后，使用 sync 命令：</p><div class="language-bash line-numbers-mode" data-ext="sh" data-title="sh"><pre class="language-bash"><code>ionic cap <span class="token function">sync</span>
@@ -46,6 +46,6 @@
   }
 };
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="bug-记录" tabindex="-1"><a class="header-anchor" href="#bug-记录"><span>bug 记录</span></a></h2><ul><li>使用 vscode ionic打包后的相对路径不正确， 手动修改后可正常运行</li></ul><div class="hint-container important"><p class="hint-container-title">重要</p><p>用Android Studio时不能打开360手机助手，会和ADB冲突</p></div></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/使用capacitor和ionic将vue项目迁移到mobile端.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->vscode plugin</div></a><a class="route-link nav-link next" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">协程<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tech/\345\215\217\347\250\213(asyncio)\345\210\260\345\272\225\351\234\200\344\270\215\351\234\200\350\246\201\345\212\240\351\224\201.html" "b/tech/\345\215\217\347\250\213(asyncio)\345\210\260\345\272\225\351\234\200\344\270\215\351\234\200\350\246\201\345\212\240\351\224\201.html"
index abdb4f6..bcefae8 100644
--- "a/tech/\345\215\217\347\250\213(asyncio)\345\210\260\345\272\225\351\234\200\344\270\215\351\234\200\350\246\201\345\212\240\351\224\201.html"
+++ "b/tech/\345\215\217\347\250\213(asyncio)\345\210\260\345\272\225\351\234\200\344\270\215\351\234\200\350\246\201\345\212\240\351\224\201.html"
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><meta property="og:description" content="原文转载自「刘悦的技术博客」https://v3u.cn/a_id_208"><meta property="og:type" content="article"><meta property="og:image" content="https://segmentfault.com/img/remote/1460000041568841"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3","image":["https://segmentfault.com/img/remote/1460000041568841"],"dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3 | blog</title><meta name="description" content="原文转载自「刘悦的技术博客」https://v3u.cn/a_id_208">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 10 分钟</span><meta property="timeRequired" content="PT10M"></span><!----><!----></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#线程安全">线程安全</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#协程">协程</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#协程安全">协程安全</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#协程是否需要加锁">协程是否需要加锁</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="并发异步编程之争-协程-asyncio-到底需不需要加锁-线程-协程安全-挂起-主动切换-python3" tabindex="-1"><a class="header-anchor" href="#并发异步编程之争-协程-asyncio-到底需不需要加锁-线程-协程安全-挂起-主动切换-python3"><span><a href="https://segmentfault.com/a/1190000041568839" target="_blank" rel="noopener noreferrer">并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></span></a></h1><p>原文转载自「刘悦的技术博客」<a href="https://link.segmentfault.com/?enc=8btt3pfGP%2FRxuxLguNqhrg%3D%3D.f%2BWWJlm9AsMAbAJjJZT%2BOQBqYNXwZgTYGW7Jx9l%2BpxQ%3D" target="_blank" rel="noopener noreferrer">https://v3u.cn/a_id_208<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></p><!-- more --><p>协程与线程向来焦孟不离，但事实上是，线程更被我们所熟知，在Python编程领域，单核同时间内只能有一个线程运行，这并不是什么缺陷，这实际上是符合客观逻辑的，单核处理器本来就没法同时处理两件事情，要同时进行多件事情本来就需要正在运行的让出处理器，然后才能去处理另一件事情，左手画方右手画圆在现实中本来就不成立，只不过这个让出的过程是线程调度器主动抢占的。</p><h2 id="线程安全" tabindex="-1"><a class="header-anchor" href="#线程安全"><span>线程安全</span></a></h2><p>系统的线程调度器是假设不同的线程是毫无关系的，所以它平均地分配时间片让处理器一视同仁，雨露均沾。但是Python受限于GIL全局解释器锁，任何Python线程执行前，必须先获得GIL锁，然后，每执行100条字节码，解释器就自动释放GIL锁，让别的线程有机会执行。这个GIL全局解释器锁实际上把所有线程的执行代码都给上了锁，所以，多线程在Python中只能交替执行，即使多个线程跑在8核处理上，也只能用到1个核。</p><p>但其实，这并不是事情的全貌，就算只能用单核处理任务，多个线程之前也并不是完全独立的，它们会操作同一个资源。于是，大家又发明了同步锁，使得一段时间内只有一个线程可以操作这个资源，其他线程只能等待：</p><div class="language-mipsasm line-numbers-mode" data-ext="mipsasm" data-title="mipsasm"><pre class="language-mipsasm"><code>import threading
@@ -215,6 +215,6 @@
 0
 0
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><p>是的，无论是结果，还是过程中，都保持了其一致性，但是我们也付出了相应的代价，那就是任务又回到了线性同步执行，再也没有异步的加持了。话说回来，世界上的事情本来就是这样，本来就没有两全其美的解决方案，又要共享状态，又想多协程，还想变量安全，这可能吗？</p><h2 id="协程是否需要加锁" tabindex="-1"><a class="header-anchor" href="#协程是否需要加锁"><span>协程是否需要加锁</span></a></h2><p>结论当然就是看使用场景，如果协程在操作共享变量的过程中，没有主动放弃执行权(await)，也就是没有切换挂起状态，那就不需要加锁，执行过程本身就是安全的；可是如果在执行事务逻辑块中主动放弃执行权了，会分两种情况，如果在逻辑执行过程中我们需要判断变量状态，或者执行过程中要根据变量状态进行一些下游操作，则必须加锁，如果我们不关注执行过程中的状态，只关注最终结果一致性，则不需要加锁。是的，抛开剂量谈毒性，是不客观的，给一个健康的人注射吗啡是犯罪，但是给一个垂死的人注射吗啡，那就是最大的道德，所以说，道德不是空泛的，脱离对象孤立存在的，同理，抛开场景谈逻辑，也是不客观的，协程也不是虚空的，脱离具体场景孤立存在的，我们应该养成具体问题具体分析的辩证唯物思想，只有掌握了辩证的矛盾思维才能更全面更灵活的看待问题，才能透过现象，把握本质。</p><p>原文转载自「刘悦的技术博客」 <a href="https://link.segmentfault.com/?enc=aOuNWC7a1JCzFai3ycjkKg%3D%3D.l5t0sKltIhLGYnZPLxsFYIiEbKuxzYikfYFHmurPNGM%3D" target="_blank" rel="noopener noreferrer">https://v3u.cn/a_id_208<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></p></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/协程(asyncio)到底需不需要加锁.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->协程</div></a><a class="route-link nav-link active next" href="/tech/" aria-label="技术"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">技术<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tech/\345\215\217\347\250\213.html" "b/tech/\345\215\217\347\250\213.html"
index 15d630c..57b5e91 100644
--- "a/tech/\345\215\217\347\250\213.html"
+++ "b/tech/\345\215\217\347\250\213.html"
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/%E5%8D%8F%E7%A8%8B.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="协程"><meta property="og:description" content="协程 文档 重要 TODO"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"协程","image":[""],"dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>协程 | blog</title><meta name="description" content="协程 文档 重要 TODO">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/协程.html-LdIMvjSl.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/协程.html-BovqfV_l.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->协程</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><!----></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="协程" tabindex="-1"><a class="header-anchor" href="#协程"><span>协程</span></a></h1><p><a href="https://course.rs/advance/async/getting-started.html#:~:text=async%20%E7%AE%80%E4%BB%8B." target="_blank" rel="noopener noreferrer">文档<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></p><div class="hint-container important"><p class="hint-container-title">重要</p><p>TODO</p></div></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/协程.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->使用capacitor和ionic将vue项目迁移到mobile端</div></a><a class="route-link nav-link next" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tech/\347\250\213\345\272\217\345\221\230\347\232\204PPT.html" "b/tech/\347\250\213\345\272\217\345\221\230\347\232\204PPT.html"
index 372c92a..2fc4980 100644
--- "a/tech/\347\250\213\345\272\217\345\221\230\347\232\204PPT.html"
+++ "b/tech/\347\250\213\345\272\217\345\221\230\347\232\204PPT.html"
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="Slidev"><meta property="og:description" content="Slidev 复杂演示推荐 缺点 不支持导出pptx https://cn.sli.dev/guide Marp 简单PPT,且需要导出为pptx推荐 缺点 不支持动画 https://sspai.com/post/55718 https://segmentfault.com/a/1190000040806239 ⚠️注意事项 如果你的 VS Code..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"Slidev","image":[""],"dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>Slidev | blog</title><meta name="description" content="Slidev 复杂演示推荐 缺点 不支持导出pptx https://cn.sli.dev/guide Marp 简单PPT,且需要导出为pptx推荐 缺点 不支持动画 https://sspai.com/post/55718 https://segmentfault.com/a/1190000040806239 ⚠️注意事项 如果你的 VS Code...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/程序员的PPT.html-CmGk8DAJ.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/程序员的PPT.html-D4bbFarZ.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->Slidev</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><!----><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><!----></div><hr></div><div class="vp-toc-placeholder"><aside id="toc"><!--[--><!----><!--]--><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#缺点">缺点</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#缺点-1">缺点</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="slidev" tabindex="-1"><a class="header-anchor" href="#slidev"><span>Slidev</span></a></h1><p>复杂演示推荐</p><h2 id="缺点" tabindex="-1"><a class="header-anchor" href="#缺点"><span>缺点</span></a></h2><p>不支持导出pptx</p><p>https://cn.sli.dev/guide</p><hr><h1 id="marp" tabindex="-1"><a class="header-anchor" href="#marp"><span>Marp</span></a></h1><p>简单PPT,且需要导出为pptx推荐</p><h2 id="缺点-1" tabindex="-1"><a class="header-anchor" href="#缺点-1"><span>缺点</span></a></h2><p>不支持动画</p><hr><p>https://sspai.com/post/55718</p><p>https://segmentfault.com/a/1190000040806239</p><p>⚠️注意事项 如果你的 VS Code 安装了 Markdown 渲染插件 Markdown Preview Enhanced，需要先将这个插件「禁用」或是「卸载」，转而使用 VS Code 后来集成的 Markdown 预览功能，才能正常看到渲染后的 PPT 页面。</p></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/程序员的PPT.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->Qt</div></a><a class="route-link nav-link next" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">tensorflow 踩坑记录<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tech/\351\227\255\345\214\205\345\256\236\347\216\260\347\261\273.html" "b/tech/\351\227\255\345\214\205\345\256\236\347\216\260\347\261\273.html"
index 825f7c7..25729c6 100644
--- "a/tech/\351\227\255\345\214\205\345\256\236\347\216\260\347\261\273.html"
+++ "b/tech/\351\227\255\345\214\205\345\256\236\347\216\260\347\261\273.html"
@@ -30,8 +30,8 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="闭包实现类"><meta property="og:description" content="你是否曾经想过，不用类也能封装数据和方法？这篇文章将带你走进闭包的奇妙世界，展示如何用闭包来实现这一点。通过一个有趣的代码示例，你将看到闭包是如何捕获变量并提供类似类的功能的。准备好了吗？让我们开始这段有趣的旅程吧！"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="MODInt"><meta property="article:published_time" content="2023-08-02T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"闭包实现类","image":[""],"datePublished":"2023-08-02T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>闭包实现类 | blog</title><meta name="description" content="你是否曾经想过，不用类也能封装数据和方法？这篇文章将带你走进闭包的奇妙世界，展示如何用闭包来实现这一点。通过一个有趣的代码示例，你将看到闭包是如何捕获变量并提供类似类的功能的。准备好了吗？让我们开始这段有趣的旅程吧！">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/闭包实现类.html-DjTAmLiV.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/闭包实现类.html-CeWxsqOK.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><!----><span class="vp-sidebar-title">技术</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker.html" aria-label="/tech/docker.html"><!---->/tech/docker.html<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/modint.html" aria-label="「泛型与 OI」modint"><!---->「泛型与 OI」modint<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html" aria-label="「算术公理系统 1」自然数"><!---->「算术公理系统 1」自然数<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html" aria-label="android studio换源"><!---->android studio换源<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/cicd.html" aria-label="CI/CD"><!---->CI/CD<!----></a></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design ASimpile CCompiler</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable" type="button"><!----><span class="vp-sidebar-title">Design Patterns</span><span class="vp-arrow end"></span></button><!----></section></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html" aria-label="docker + nginx + acme.sh 部署 vue/flask 项目"><!---->docker + nginx + acme.sh 部署 vue/flask 项目<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html" aria-label="Game Plugin"><!---->Game Plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/figure_bed.html" aria-label="github 图床"><!---->github 图床<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/github%20%E5%B7%A5%E4%BD%9C%E6%B5%81.html" aria-label="github 工作流程"><!---->github 工作流程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/python_requrements.html" aria-label="python requirements.txt"><!---->python requirements.txt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html" aria-label="Qt"><!---->Qt<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%84PPT.html" aria-label="Slidev"><!---->Slidev<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html" aria-label="tensorflow 踩坑记录"><!---->tensorflow 踩坑记录<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/vsocde%E6%8F%92%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B0%8F%E8%AE%B0.html" aria-label="vscode plugin"><!---->vscode plugin<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E4%BD%BF%E7%94%A8capacitor%E5%92%8Cionic%E5%B0%86vue%E9%A1%B9%E7%9B%AE%E8%BF%81%E7%A7%BB%E5%88%B0mobile%E7%AB%AF.html" aria-label="使用capacitor和ionic将vue项目迁移到mobile端"><!---->使用capacitor和ionic将vue项目迁移到mobile端<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B.html" aria-label="协程"><!---->协程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/%E5%8D%8F%E7%A8%8B(asyncio)%E5%88%B0%E5%BA%95%E9%9C%80%E4%B8%8D%E9%9C%80%E8%A6%81%E5%8A%A0%E9%94%81.html" aria-label="并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3"><!---->并发异步编程之争：协程(asyncio)到底需不需要加锁？(线程/协程安全/挂起/主动切换)Python3<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/" aria-label="技术"><!---->技术<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/mailserver.html" aria-label="自建mail server"><!---->自建mail server<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html" aria-label="闭包实现类"><!---->闭包实现类<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tech/style.html" aria-label="风格统一"><!---->风格统一<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->闭包实现类</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2023-08-02T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>大约 2 分钟</span><meta property="timeRequired" content="PT2M"></span><span class="page-category-info" aria-label="分类🌈" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg><!--[--><span class="page-category-item category6 clickable" role="navigation">OI</span><!--]--><meta property="articleSection" content="OI"></span><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag8 clickable" role="navigation">MODInt</span><!--]--><meta property="keywords" content="MODInt"></span></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="闭包实现类" tabindex="-1"><a class="header-anchor" href="#闭包实现类"><span>闭包实现类</span></a></h1><p>你是否曾经想过，不用类也能封装数据和方法？这篇文章将带你走进闭包的奇妙世界，展示如何用闭包来实现这一点。通过一个有趣的代码示例，你将看到闭包是如何捕获变量并提供类似类的功能的。准备好了吗？让我们开始这段有趣的旅程吧！</p><!-- more --><div class="vp-code-tabs"><div class="vp-code-tabs-nav" role="tablist"><button type="button" class="vp-code-tab-nav active" role="tab" aria-controls="codetab-7-0" aria-selected="true">cpp</button><button type="button" class="vp-code-tab-nav" role="tab" aria-controls="codetab-7-1" aria-selected="false">python</button></div><!--[--><div class="vp-code-tab active" id="codetab-7-0" role="tabpanel" aria-expanded="true"><div class="vp-code-tab-title">cpp</div><!--[--><div class="language-cpp line-numbers-mode" data-ext="cpp" data-title="cpp"><pre class="language-cpp"><code><span class="token macro property"><span class="token directive-hash">#</span><span class="token directive keyword">include</span> <span class="token string">&lt;iostream&gt;</span></span>
@@ -123,6 +123,6 @@
 Rex is 5 years old, running at 10 km/h
 &quot;&quot;&quot;</span>
 </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><!--]--></div><!--]--></div><figure><img src="/assets/Closures-Bb-D5Kse.png" alt="alt text" tabindex="0" loading="lazy"><figcaption>alt text</figcaption></figure></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tech/闭包实现类.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tech/mailserver.html" aria-label="自建mail server"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->自建mail server</div></a><a class="route-link nav-link next" href="/tech/style.html" aria-label="风格统一"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">风格统一<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/timeline/index.html b/timeline/index.html
index 9c213ba..6e3efbd 100644
--- a/timeline/index.html
+++ b/timeline/index.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/timeline/"><meta property="og:site_name" content="blog"><meta property="og:title" content="时间轴"><meta property="og:type" content="website"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><script type="application/ld+json">{"@context":"https://schema.org","@type":"WebPage","name":"时间轴"}</script><title>时间轴 | blog</title><meta name="description" content="KSJ-blog">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-Bb8RnxYT.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-BOaWfYA8.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
-    <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><div class="timeline-wrapper"><ul class="timeline-content"><li class="motto">昨日不在</li><div class="vp-toc-placeholder"><aside id="toc"><!----><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#2024">2024</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#2023">2023</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!----></aside></div><!--[--><!--[--><h3 id="2024" class="timeline-year-title"><span>2024</span></h3><li class="timeline-year-list"><ul class="timeline-year-wrapper"><li class="timeline-item"><span class="timeline-date">11/1</span><a class="route-link timeline-title" href="/tech/figure_bed.html">github 图床</a></li><li class="timeline-item"><span class="timeline-date">11/1</span><a class="route-link timeline-title" href="/tech/mailserver.html">自建mail server</a></li><li class="timeline-item"><span class="timeline-date">11/1</span><a class="route-link timeline-title" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html">tensorflow 踩坑记录</a></li><li class="timeline-item"><span class="timeline-date">10/30</span><a class="route-link timeline-title" href="/essays/%E5%91%BD%E9%87%8C%E6%9C%89%E6%97%B6%E7%BB%88%E9%A1%BB%E6%9C%89.html">命里有时终须有</a></li><li class="timeline-item"><span class="timeline-date">10/29</span><a class="route-link timeline-title" href="/tech/python_requrements.html">python requirements.txt</a></li><li class="timeline-item"><span class="timeline-date">10/29</span><a class="route-link timeline-title" href="/tech/DesignPatterns/command.html">Command 模式</a></li><li class="timeline-item"><span class="timeline-date">10/29</span><a class="route-link timeline-title" href="/tech/DesignPatterns/end.html">结语</a></li><li class="timeline-item"><span class="timeline-date">10/29</span><a class="route-link timeline-title" href="/tech/DesignPatterns/interpreter.html">Interpreter 模式</a></li><li class="timeline-item"><span class="timeline-date">10/29</span><a class="route-link timeline-title" href="/tech/DesignPatterns/proxy.html">Proxy 模式</a></li><li class="timeline-item"><span class="timeline-date">10/28</span><a class="route-link timeline-title" href="/tech/DesignPatterns/flyweight.html">Flyweight 模式</a></li><li class="timeline-item"><span class="timeline-date">10/28</span><a class="route-link timeline-title" href="/tech/DesignPatterns/memento.html">Memento 模式</a></li><li class="timeline-item"><span class="timeline-date">10/28</span><a class="route-link timeline-title" href="/tech/DesignPatterns/state.html">State 模式</a></li><li class="timeline-item"><span class="timeline-date">10/26</span><a class="route-link timeline-title" href="/tech/DesignPatterns/facade.html">facade 模式</a></li><li class="timeline-item"><span class="timeline-date">10/26</span><a class="route-link timeline-title" href="/tech/DesignPatterns/mediator.html">Mediator 模式</a></li><li class="timeline-item"><span class="timeline-date">10/26</span><a class="route-link timeline-title" href="/tech/DesignPatterns/observer.html">Observer 模式</a></li><li class="timeline-item"><span class="timeline-date">10/25</span><a class="route-link timeline-title" href="/tech/DesignPatterns/abstractFactory.html">抽象工厂模式</a></li><li class="timeline-item"><span class="timeline-date">10/25</span><a class="route-link timeline-title" href="/tech/DesignPatterns/bridge.html">Bridge 模式</a></li><li class="timeline-item"><span class="timeline-date">10/25</span><a class="route-link timeline-title" href="/tech/DesignPatterns/chainOfResponsibility.html">chainOfResponsibility 模式</a></li><li class="timeline-item"><span class="timeline-date">10/25</span><a class="route-link timeline-title" href="/tech/DesignPatterns/composite.html">Composite 模式</a></li><li class="timeline-item"><span class="timeline-date">10/25</span><a class="route-link timeline-title" href="/tech/DesignPatterns/decorator.html">Decorator 模式</a></li><li class="timeline-item"><span class="timeline-date">10/25</span><a class="route-link timeline-title" href="/tech/DesignPatterns/strategy.html">Strategy 模式</a></li><li class="timeline-item"><span class="timeline-date">10/25</span><a class="route-link timeline-title" href="/tech/DesignPatterns/visitor.html">Visitor 模式</a></li><li class="timeline-item"><span class="timeline-date">10/22</span><a class="route-link timeline-title" href="/tech/DesignPatterns/builder.html">builder 模式</a></li><li class="timeline-item"><span class="timeline-date">10/22</span><a class="route-link timeline-title" href="/tech/DesignPatterns/prototype.html">Prototype 模式</a></li><li class="timeline-item"><span class="timeline-date">10/21</span><a class="route-link timeline-title" href="/tutorials/typora%E6%BF%80%E6%B4%BB.html">Typora激活教程</a></li><li class="timeline-item"><span class="timeline-date">10/21</span><a class="route-link timeline-title" href="/tech/DesignPatterns/DesignPrinciples.html">设计模式七大原则</a></li><li class="timeline-item"><span class="timeline-date">10/21</span><a class="route-link timeline-title" href="/tech/DesignPatterns/adapter.html">适配器模式</a></li><li class="timeline-item"><span class="timeline-date">10/21</span><a class="route-link timeline-title" href="/tech/DesignPatterns/factory_method.html">Factory Method 模式</a></li><li class="timeline-item"><span class="timeline-date">10/21</span><a class="route-link timeline-title" href="/tech/DesignPatterns/">设计模式</a></li><li class="timeline-item"><span class="timeline-date">10/21</span><a class="route-link timeline-title" href="/tech/DesignPatterns/iterator.html">迭代器模式</a></li><li class="timeline-item"><span class="timeline-date">10/21</span><a class="route-link timeline-title" href="/tech/DesignPatterns/singleton.html">Singleton 模式</a></li><li class="timeline-item"><span class="timeline-date">10/21</span><a class="route-link timeline-title" href="/tech/DesignPatterns/template_method.html">Template Method 模式</a></li><li class="timeline-item"><span class="timeline-date">10/18</span><a class="route-link timeline-title" href="/essays/">随笔</a></li><li class="timeline-item"><span class="timeline-date">10/18</span><a class="route-link timeline-title" href="/projects/">项目</a></li><li class="timeline-item"><span class="timeline-date">10/18</span><a class="route-link timeline-title" href="/resources/">资源</a></li><li class="timeline-item"><span class="timeline-date">10/18</span><a class="route-link timeline-title" href="/tech/">技术</a></li><li class="timeline-item"><span class="timeline-date">10/18</span><a class="route-link timeline-title" href="/tutorials/">教程</a></li><li class="timeline-item"><span class="timeline-date">9/16</span><a class="route-link timeline-title" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li><li class="timeline-item"><span class="timeline-date">9/12</span><a class="route-link timeline-title" href="/tech/docker.html"></a></li><li class="timeline-item"><span class="timeline-date">9/9</span><a class="route-link timeline-title" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html">Game Plugin</a></li><li class="timeline-item"><span class="timeline-date">8/31</span><a class="route-link timeline-title" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html">Qt</a></li><li class="timeline-item"><span class="timeline-date">8/25</span><a class="route-link timeline-title" href="/tech/style.html">风格统一</a></li><li class="timeline-item"><span class="timeline-date">8/2</span><a class="route-link timeline-title" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html">android studio换源</a></li><li class="timeline-item"><span class="timeline-date">8/2</span><a class="route-link timeline-title" href="/tech/cicd.html">CI/CD</a></li></ul></li><!--]--><!--[--><h3 id="2023" class="timeline-year-title"><span>2023</span></h3><li class="timeline-year-list"><ul class="timeline-year-wrapper"><li class="timeline-item"><span class="timeline-date">8/2</span><a class="route-link timeline-title" href="/tech/modint.html">「泛型与 OI」modint</a></li><li class="timeline-item"><span class="timeline-date">8/2</span><a class="route-link timeline-title" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html">闭包实现类</a></li><li class="timeline-item"><span class="timeline-date">7/9</span><a class="route-link timeline-title" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html">「算术公理系统 1」自然数</a></li></ul></li><!--]--><!--]--></ul></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">64</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">47</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">64</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container no-sidebar"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/intro.html" aria-label="介绍页"><span class="font-icon icon circle-info" style=""></span>介绍页<!----></a></li></ul><!--[--><!----><!--]--></aside><!--[--><div class="vp-page vp-blog"><div class="blog-page-wrapper"><main id="main-content" class="vp-blog-main"><div class="timeline-wrapper"><ul class="timeline-content"><li class="motto">昨日不在</li><div class="vp-toc-placeholder"><aside id="toc"><!----><div class="vp-toc-header">此页内容<button type="button" class="print-button" title="打印"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button><div class="arrow end"></div></div><div class="vp-toc-wrapper"><ul class="vp-toc-list"><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#2024">2024</a></li><!----><!--]--><!--[--><li class="vp-toc-item"><a class="route-link vp-toc-link level2" href="#2023">2023</a></li><!----><!--]--></ul><div class="vp-toc-marker" style="top:-1.7rem;"></div></div><!----></aside></div><!--[--><!--[--><h3 id="2024" class="timeline-year-title"><span>2024</span></h3><li class="timeline-year-list"><ul class="timeline-year-wrapper"><li class="timeline-item"><span class="timeline-date">11/7</span><a class="route-link timeline-title" href="/projects/carrobot.html">北京邮电大学创新创业智能车循迹python版</a></li><li class="timeline-item"><span class="timeline-date">11/6</span><a class="route-link timeline-title" href="/resources/compile/">编译原理相关</a></li><li class="timeline-item"><span class="timeline-date">11/1</span><a class="route-link timeline-title" href="/tech/figure_bed.html">github 图床</a></li><li class="timeline-item"><span class="timeline-date">11/1</span><a class="route-link timeline-title" href="/tech/mailserver.html">自建mail server</a></li><li class="timeline-item"><span class="timeline-date">11/1</span><a class="route-link timeline-title" href="/tech/tensorflow%E8%B8%A9%E5%9D%91.html">tensorflow 踩坑记录</a></li><li class="timeline-item"><span class="timeline-date">10/30</span><a class="route-link timeline-title" href="/essays/%E5%91%BD%E9%87%8C%E6%9C%89%E6%97%B6%E7%BB%88%E9%A1%BB%E6%9C%89.html">命里有时终须有</a></li><li class="timeline-item"><span class="timeline-date">10/29</span><a class="route-link timeline-title" href="/tech/python_requrements.html">python requirements.txt</a></li><li class="timeline-item"><span class="timeline-date">10/29</span><a class="route-link timeline-title" href="/tech/DesignPatterns/command.html">Command 模式</a></li><li class="timeline-item"><span class="timeline-date">10/29</span><a class="route-link timeline-title" href="/tech/DesignPatterns/end.html">结语</a></li><li class="timeline-item"><span class="timeline-date">10/29</span><a class="route-link timeline-title" href="/tech/DesignPatterns/interpreter.html">Interpreter 模式</a></li><li class="timeline-item"><span class="timeline-date">10/29</span><a class="route-link timeline-title" href="/tech/DesignPatterns/proxy.html">Proxy 模式</a></li><li class="timeline-item"><span class="timeline-date">10/28</span><a class="route-link timeline-title" href="/tech/DesignPatterns/flyweight.html">Flyweight 模式</a></li><li class="timeline-item"><span class="timeline-date">10/28</span><a class="route-link timeline-title" href="/tech/DesignPatterns/memento.html">Memento 模式</a></li><li class="timeline-item"><span class="timeline-date">10/28</span><a class="route-link timeline-title" href="/tech/DesignPatterns/state.html">State 模式</a></li><li class="timeline-item"><span class="timeline-date">10/26</span><a class="route-link timeline-title" href="/tech/DesignPatterns/facade.html">facade 模式</a></li><li class="timeline-item"><span class="timeline-date">10/26</span><a class="route-link timeline-title" href="/tech/DesignPatterns/mediator.html">Mediator 模式</a></li><li class="timeline-item"><span class="timeline-date">10/26</span><a class="route-link timeline-title" href="/tech/DesignPatterns/observer.html">Observer 模式</a></li><li class="timeline-item"><span class="timeline-date">10/25</span><a class="route-link timeline-title" href="/tech/DesignPatterns/abstractFactory.html">抽象工厂模式</a></li><li class="timeline-item"><span class="timeline-date">10/25</span><a class="route-link timeline-title" href="/tech/DesignPatterns/bridge.html">Bridge 模式</a></li><li class="timeline-item"><span class="timeline-date">10/25</span><a class="route-link timeline-title" href="/tech/DesignPatterns/chainOfResponsibility.html">chainOfResponsibility 模式</a></li><li class="timeline-item"><span class="timeline-date">10/25</span><a class="route-link timeline-title" href="/tech/DesignPatterns/composite.html">Composite 模式</a></li><li class="timeline-item"><span class="timeline-date">10/25</span><a class="route-link timeline-title" href="/tech/DesignPatterns/decorator.html">Decorator 模式</a></li><li class="timeline-item"><span class="timeline-date">10/25</span><a class="route-link timeline-title" href="/tech/DesignPatterns/strategy.html">Strategy 模式</a></li><li class="timeline-item"><span class="timeline-date">10/25</span><a class="route-link timeline-title" href="/tech/DesignPatterns/visitor.html">Visitor 模式</a></li><li class="timeline-item"><span class="timeline-date">10/22</span><a class="route-link timeline-title" href="/tech/DesignPatterns/builder.html">builder 模式</a></li><li class="timeline-item"><span class="timeline-date">10/22</span><a class="route-link timeline-title" href="/tech/DesignPatterns/prototype.html">Prototype 模式</a></li><li class="timeline-item"><span class="timeline-date">10/21</span><a class="route-link timeline-title" href="/tutorials/typora%E6%BF%80%E6%B4%BB.html">Typora激活教程</a></li><li class="timeline-item"><span class="timeline-date">10/21</span><a class="route-link timeline-title" href="/tech/DesignPatterns/DesignPrinciples.html">设计模式七大原则</a></li><li class="timeline-item"><span class="timeline-date">10/21</span><a class="route-link timeline-title" href="/tech/DesignPatterns/adapter.html">适配器模式</a></li><li class="timeline-item"><span class="timeline-date">10/21</span><a class="route-link timeline-title" href="/tech/DesignPatterns/factory_method.html">Factory Method 模式</a></li><li class="timeline-item"><span class="timeline-date">10/21</span><a class="route-link timeline-title" href="/tech/DesignPatterns/">设计模式</a></li><li class="timeline-item"><span class="timeline-date">10/21</span><a class="route-link timeline-title" href="/tech/DesignPatterns/iterator.html">迭代器模式</a></li><li class="timeline-item"><span class="timeline-date">10/21</span><a class="route-link timeline-title" href="/tech/DesignPatterns/singleton.html">Singleton 模式</a></li><li class="timeline-item"><span class="timeline-date">10/21</span><a class="route-link timeline-title" href="/tech/DesignPatterns/template_method.html">Template Method 模式</a></li><li class="timeline-item"><span class="timeline-date">10/18</span><a class="route-link timeline-title" href="/essays/">随笔</a></li><li class="timeline-item"><span class="timeline-date">10/18</span><a class="route-link timeline-title" href="/projects/">项目</a></li><li class="timeline-item"><span class="timeline-date">10/18</span><a class="route-link timeline-title" href="/resources/">资源</a></li><li class="timeline-item"><span class="timeline-date">10/18</span><a class="route-link timeline-title" href="/tech/">技术</a></li><li class="timeline-item"><span class="timeline-date">10/18</span><a class="route-link timeline-title" href="/tutorials/">教程</a></li><li class="timeline-item"><span class="timeline-date">9/16</span><a class="route-link timeline-title" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li><li class="timeline-item"><span class="timeline-date">9/12</span><a class="route-link timeline-title" href="/tech/docker.html"></a></li><li class="timeline-item"><span class="timeline-date">9/9</span><a class="route-link timeline-title" href="/tech/steam%E6%A8%A1%E7%BB%84%E5%BC%80%E5%8F%91.html">Game Plugin</a></li><li class="timeline-item"><span class="timeline-date">8/31</span><a class="route-link timeline-title" href="/tech/Qt6%20Maintence%20tools%E4%B8%8D%E8%83%BD%E5%AE%89%E8%A3%85Qt5.html">Qt</a></li><li class="timeline-item"><span class="timeline-date">8/25</span><a class="route-link timeline-title" href="/tech/style.html">风格统一</a></li><li class="timeline-item"><span class="timeline-date">8/2</span><a class="route-link timeline-title" href="/tech/android%20studio%E6%8D%A2%E6%BA%90.html">android studio换源</a></li><li class="timeline-item"><span class="timeline-date">8/2</span><a class="route-link timeline-title" href="/tech/cicd.html">CI/CD</a></li></ul></li><!--]--><!--[--><h3 id="2023" class="timeline-year-title"><span>2023</span></h3><li class="timeline-year-list"><ul class="timeline-year-wrapper"><li class="timeline-item"><span class="timeline-date">8/2</span><a class="route-link timeline-title" href="/tech/modint.html">「泛型与 OI」modint</a></li><li class="timeline-item"><span class="timeline-date">8/2</span><a class="route-link timeline-title" href="/tech/%E9%97%AD%E5%8C%85%E5%AE%9E%E7%8E%B0%E7%B1%BB.html">闭包实现类</a></li><li class="timeline-item"><span class="timeline-date">7/9</span><a class="route-link timeline-title" href="/tech/%E3%80%8C%E7%AE%97%E6%9C%AF%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F%201%E3%80%8D%E8%87%AA%E7%84%B6%E6%95%B0.html">「算术公理系统 1」自然数</a></li></ul></li><!--]--><!--]--></ul></div></main><aside class="vp-blog-info-wrapper"><div class="vp-blogger-info" vocab="https://schema.org/" typeof="Person"><div class="vp-blogger" style="cursor:pointer;" aria-label="个人介绍" data-balloon-pos="down" role="link"><img class="vp-blogger-avatar" src="/logo.svg" property="image" alt="Blogger Avatar" loading="lazy"><div class="vp-blogger-name" property="name">KSJ</div><div class="vp-blogger-description">一位热衷于探索全栈开发领域的技术爱好者，擅长将前端与后端技术无缝结合，致力于打造高效、优雅的解决方案。</div><meta property="url" content="/intro.html"></div><div class="vp-blog-counts"><a class="route-link vp-blog-count" href="/article/"><div class="count">66</div><div>文章</div></a><a class="route-link vp-blog-count" href="/category/"><div class="count">11</div><div>分类</div></a><a class="route-link vp-blog-count" href="/tag/"><div class="count">27</div><div>标签</div></a><a class="route-link vp-blog-count" href="/timeline/"><div class="count">49</div><div>时间轴</div></a></div><div class="vp-social-medias"><a class="vp-social-media" href="mailto:2175616761@qq.com" rel="noopener noreferrer" target="_blank" aria-label="Email" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon email-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#1384FF"/><path fill="#fff" d="M270.077 286.233H751.99c32.933 0 59.86 24.855 60.274 55.51l-301.023 157L210.217 341.88c.207-30.723 26.927-55.717 59.86-55.717zm-59.929 115.714-.276 277.756c0 30.931 27.134 56.2 60.205 56.2H751.99c33.14 0 60.274-25.269 60.274-56.2V401.81L518.283 551.492a15.88 15.88 0 0 1-14.43 0L210.148 401.947z"/></svg></a><a class="vp-social-media" href="https://github.com/King-sj" rel="noopener noreferrer" target="_blank" aria-label="GitHub" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#171515"/><path fill="#fff" d="M509.423 146.442c-200.317 0-362.756 162.42-362.756 362.8 0 160.266 103.936 296.24 248.109 344.217 18.139 3.327 24.76-7.872 24.76-17.486 0-8.613-.313-31.427-.49-61.702-100.912 21.923-122.205-48.63-122.205-48.63-16.495-41.91-40.28-53.067-40.28-53.067-32.937-22.51 2.492-22.053 2.492-22.053 36.407 2.566 55.568 37.386 55.568 37.386 32.362 55.438 84.907 39.43 105.58 30.143 3.296-23.444 12.667-39.43 23.032-48.498-80.557-9.156-165.246-40.28-165.246-179.297 0-39.604 14.135-71.988 37.342-97.348-3.731-9.178-16.18-46.063 3.556-96.009 0 0 30.46-9.754 99.76 37.19 28.937-8.048 59.97-12.071 90.823-12.211 30.807.14 61.843 4.165 90.822 12.21 69.26-46.944 99.663-37.189 99.663-37.189 19.792 49.946 7.34 86.831 3.61 96.01 23.25 25.359 37.29 57.742 37.29 97.347 0 139.366-84.82 170.033-165.637 179.013 13.026 11.2 24.628 33.342 24.628 67.182 0 48.498-.445 87.627-.445 99.521 0 9.702 6.535 20.988 24.945 17.444 144.03-48.067 247.881-183.95 247.881-344.175 0-200.378-162.442-362.798-362.802-362.798z"/></svg></a><a class="vp-social-media" href="https://wpa.qq.com/msgrd?v=3&amp;uin=2175616761&amp;site=qq&amp;menu=yes" rel="noopener noreferrer" target="_blank" aria-label="QQ" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon qq-icon" viewBox="0 0 1024 1024"><circle cx="512" cy="512" r="512" fill="#5eaade"/><path fill="#fff" d="M805.25 585.542c-15-48.188-32.25-88.688-58.781-154.97 4.125-174.093-68.25-314.905-234.938-314.905-168.562 0-239.344 143.625-234.844 314.906-26.625 66.375-43.78 106.594-58.78 154.969-31.876 102.656-21.563 145.125-13.688 146.062 16.875 2.063 65.718-77.25 65.718-77.25 0 45.938 23.625 105.844 74.813 149.063-24.75 7.593-80.344 28.03-67.125 50.437 10.688 18.094 183.938 11.531 233.906 5.906 49.969 5.625 223.219 12.188 233.906-5.906 13.22-22.312-42.468-42.844-67.125-50.437 51.188-43.313 74.813-103.22 74.813-149.063 0 0 48.844 79.313 65.719 77.25 7.969-1.031 18.281-43.5-13.594-146.062z"/></svg></a></div></div><div class="vp-blog-infos"><div class="vp-blog-type-switcher"><button type="button" class="vp-blog-type-button"><div class="icon-wrapper active" aria-label="文章" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="分类" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon category-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="category icon"><path d="M148.41 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H148.41c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.311-40.31zM147.556 553.478H429.73c22.263 0 40.311 18.048 40.311 40.31v282.176c0 22.263-18.048 40.312-40.31 40.312H147.555c-22.263 0-40.311-18.049-40.311-40.312V593.79c0-22.263 18.048-40.311 40.31-40.311zM593.927 106.992h282.176c22.263 0 40.31 18.048 40.31 40.31V429.48c0 22.263-18.047 40.31-40.31 40.31H593.927c-22.263 0-40.311-18.047-40.311-40.31V147.302c0-22.263 18.048-40.31 40.31-40.31zM730.22 920.502H623.926c-40.925 0-74.22-33.388-74.22-74.425V623.992c0-41.038 33.387-74.424 74.425-74.424h222.085c41.038 0 74.424 33.226 74.424 74.067v114.233c0 10.244-8.304 18.548-18.547 18.548s-18.548-8.304-18.548-18.548V623.635c0-20.388-16.746-36.974-37.33-36.974H624.13c-20.585 0-37.331 16.747-37.331 37.33v222.086c0 20.585 16.654 37.331 37.126 37.331H730.22c10.243 0 18.547 8.304 18.547 18.547 0 10.244-8.304 18.547-18.547 18.547z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="标签" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg></div></button><button type="button" class="vp-blog-type-button"><div class="icon-wrapper" aria-label="时间轴" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timeline-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timeline icon"><path d="M511.997 70.568c-243.797 0-441.429 197.633-441.429 441.435 0 243.797 197.632 441.429 441.43 441.429S953.431 755.8 953.431 512.002c0-243.796-197.637-441.434-441.435-441.434zm150.158 609.093-15.605 15.61c-8.621 8.615-22.596 8.615-31.215 0L472.197 552.126c-4.95-4.944-4.34-14.888-4.34-24.677V247.14c0-12.19 9.882-22.07 22.07-22.07h22.07c12.19 0 22.07 9.882 22.07 22.07v273.218l128.088 128.088c8.62 8.62 8.62 22.595 0 31.215zm0 0"></path></svg></div></button></div><div class="vp-star-article-wrapper"><div class="title"><svg xmlns="http://www.w3.org/2000/svg" class="icon article-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="article icon"><path d="M853.333 938.667H170.667A42.667 42.667 0 0 1 128 896V128a42.667 42.667 0 0 1 42.667-42.667h682.666A42.667 42.667 0 0 1 896 128v768a42.667 42.667 0 0 1-42.667 42.667zm-42.666-85.334V170.667H213.333v682.666h597.334zM298.667 256h170.666v170.667H298.667V256zm0 256h426.666v85.333H298.667V512zm0 170.667h426.666V768H298.667v-85.333zm256-384h170.666V384H554.667v-85.333z"></path></svg><span class="num">66</span>文章</div><hr><ul class="vp-star-articles"><li class="vp-star-article"><a class="route-link" href="/tech/docker_nginx%E9%83%A8%E7%BD%B2web%E9%A1%B9%E7%9B%AE.html">docker + nginx + acme.sh 部署 vue/flask 项目</a></li></ul></div></div></aside></div></div><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git a/tutorials/index.html b/tutorials/index.html
index ea3c3ef..b76ea8d 100644
--- a/tutorials/index.html
+++ b/tutorials/index.html
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tutorials/"><meta property="og:site_name" content="blog"><meta property="og:title" content="教程"><meta property="og:description" content="教程 这里是所有详细的教程和指南。"><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:published_time" content="2024-10-18T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"教程","image":[""],"datePublished":"2024-10-18T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>教程 | blog</title><meta name="description" content="教程 这里是所有详细的教程和指南。">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/index.html-BtJnl_OK.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-BuwKOD8g.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/index.html-C9AeqWIc.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/typora激活.html-DUOLfN6Y.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><span class="font-icon icon book" style=""></span><span class="vp-sidebar-title">教程</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tutorials/typora%E6%BF%80%E6%B4%BB.html" aria-label="Typora激活教程"><!---->Typora激活教程<!----></a></li><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->教程</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-18T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><!----></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="教程" tabindex="-1"><a class="header-anchor" href="#教程"><span>教程</span></a></h1><p>这里是所有详细的教程和指南。</p><!----><div class="vp-catalog-wrapper"><h2 class="vp-catalog-main-title">目录</h2><ul class="vp-catalogs"><li class="vp-catalog"><div class="vp-catalog-child-title"><a class="route-link vp-catalog-title" href="/tutorials/typora%E6%BF%80%E6%B4%BB.html">Typora激活教程</a></div></li></ul></div></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tutorials/index.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><a class="route-link nav-link prev" href="/tutorials/typora%E6%BF%80%E6%B4%BB.html" aria-label="Typora激活教程"><div class="hint"><span class="arrow start"></span>上一页</div><div class="link"><!---->Typora激活教程</div></a><!----></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>
diff --git "a/tutorials/typora\346\277\200\346\264\273.html" "b/tutorials/typora\346\277\200\346\264\273.html"
index d537c57..de9c207 100644
--- "a/tutorials/typora\346\277\200\346\264\273.html"
+++ "b/tutorials/typora\346\277\200\346\264\273.html"
@@ -30,11 +30,11 @@
     </script>
     <meta property="og:url" content="https://github.com/King-sj/tutorials/typora%E6%BF%80%E6%B4%BB.html"><meta property="og:site_name" content="blog"><meta property="og:title" content="Typora激活教程"><meta property="og:description" content="Typora 简介 Typora 是一款简洁高效的 Markdown 编辑器，支持实时预览和多种导出格式，适用于编写笔记、文档和博客等。 安装教程 Typora 官网 Typora 中文官网 工具下载：百度网盘，密码：dcqe 一路点击“下一步”进行安装。将下载的工具解压后得到的两个 exe 文件（license-gen.exe 和 node_inje..."><meta property="og:type" content="article"><meta property="og:locale" content="zh-CN"><meta property="article:author" content="KSJ"><meta property="article:tag" content="激活"><meta property="article:published_time" content="2024-10-21T00:00:00.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"Typora激活教程","image":[""],"datePublished":"2024-10-21T00:00:00.000Z","dateModified":null,"author":[{"@type":"Person","name":"KSJ","url":"https://github.com/King-sj"}]}</script><title>Typora激活教程 | blog</title><meta name="description" content="Typora 简介 Typora 是一款简洁高效的 Markdown 编辑器，支持实时预览和多种导出格式，适用于编写笔记、文档和博客等。 安装教程 Typora 官网 Typora 中文官网 工具下载：百度网盘，密码：dcqe 一路点击“下一步”进行安装。将下载的工具解压后得到的两个 exe 文件（license-gen.exe 和 node_inje...">
     <link rel="preload" href="/assets/style-Dbd0bHIw.css" as="style"><link rel="stylesheet" href="/assets/style-Dbd0bHIw.css">
-    <link rel="modulepreload" href="/assets/app-B69Gl_S-.js"><link rel="modulepreload" href="/assets/typora激活.html-BuwKOD8g.js">
-    <link rel="prefetch" href="/assets/index.html-BjAw7f-F.js" as="script"><link rel="prefetch" href="/assets/intro.html-CEHYbhC9.js" as="script"><link rel="prefetch" href="/assets/index.html-DzJoMr4P.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-DOvT7-xg.js" as="script"><link rel="prefetch" href="/assets/index.html-BjDh3PHW.js" as="script"><link rel="prefetch" href="/assets/index.html-Dv6rE_pN.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-CTk8exni.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-CxjDu5df.js" as="script"><link rel="prefetch" href="/assets/cicd.html-CedraPRV.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-4IxhKq9E.js" as="script"><link rel="prefetch" href="/assets/docker.html-B-hYGcsZ.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-BME-hebA.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-CFTCrRk5.js" as="script"><link rel="prefetch" href="/assets/index.html-Dakgazin.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DITZCknd.js" as="script"><link rel="prefetch" href="/assets/modint.html-M2GwLZ2U.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-Va55tBYB.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-DQKsmuFu.js" as="script"><link rel="prefetch" href="/assets/style.html-CXxr9xzn.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-BAaphJ4H.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-DtdCKw5q.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-CtzEDcR8.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CjY4pFX9.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-CTO2grll.js" as="script"><link rel="prefetch" href="/assets/协程.html-LdIMvjSl.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-CmGk8DAJ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-DjTAmLiV.js" as="script"><link rel="prefetch" href="/assets/index.html-BtJnl_OK.js" as="script"><link rel="prefetch" href="/assets/index.html-CXhg3e64.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BLnXHGN8.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-DS3CgVqp.js" as="script"><link rel="prefetch" href="/assets/adapter.html-B2UlYWFL.js" as="script"><link rel="prefetch" href="/assets/bridge.html-LTDknqB7.js" as="script"><link rel="prefetch" href="/assets/builder.html-Ba33pTyP.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-DhJtx4gW.js" as="script"><link rel="prefetch" href="/assets/command.html-d4IhdjVF.js" as="script"><link rel="prefetch" href="/assets/composite.html-DOBxYen3.js" as="script"><link rel="prefetch" href="/assets/decorator.html-FfT8RlFX.js" as="script"><link rel="prefetch" href="/assets/end.html-De4ifiEs.js" as="script"><link rel="prefetch" href="/assets/facade.html-Cj3lyBcS.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-B20phxz9.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-CWx8TgTS.js" as="script"><link rel="prefetch" href="/assets/index.html-B5GIg4Ij.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-CansycaD.js" as="script"><link rel="prefetch" href="/assets/iterator.html-USsHv5Pr.js" as="script"><link rel="prefetch" href="/assets/mediator.html-RBFBa63Z.js" as="script"><link rel="prefetch" href="/assets/memento.html-CbbBldep.js" as="script"><link rel="prefetch" href="/assets/observer.html-BvrPoU9w.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Boe-0El2.js" as="script"><link rel="prefetch" href="/assets/proxy.html-CSHBH0Xk.js" as="script"><link rel="prefetch" href="/assets/singleton.html-Pzh1ZzrO.js" as="script"><link rel="prefetch" href="/assets/state.html-DsXXtCU9.js" as="script"><link rel="prefetch" href="/assets/strategy.html-Cprd53d9.js" as="script"><link rel="prefetch" href="/assets/template_method.html-Do5aF6Sl.js" as="script"><link rel="prefetch" href="/assets/visitor.html-C6V612X1.js" as="script"><link rel="prefetch" href="/assets/0.html-BMihHxnS.js" as="script"><link rel="prefetch" href="/assets/1.html-B2woGSgL.js" as="script"><link rel="prefetch" href="/assets/2.html-DuLx7xSk.js" as="script"><link rel="prefetch" href="/assets/3.html-CZB5joNY.js" as="script"><link rel="prefetch" href="/assets/4.html-C8TuLMaF.js" as="script"><link rel="prefetch" href="/assets/5.html-qLlLbRlw.js" as="script"><link rel="prefetch" href="/assets/6.html-BPGbpgjm.js" as="script"><link rel="prefetch" href="/assets/7.html-DopH3hey.js" as="script"><link rel="prefetch" href="/assets/8.html-D1TnfZgI.js" as="script"><link rel="prefetch" href="/assets/9.html-CGdd1xtP.js" as="script"><link rel="prefetch" href="/assets/404.html-BC0rHQLu.js" as="script"><link rel="prefetch" href="/assets/index.html-Ak5uwHrg.js" as="script"><link rel="prefetch" href="/assets/index.html-CO8-8uSt.js" as="script"><link rel="prefetch" href="/assets/index.html-B7IKPS0E.js" as="script"><link rel="prefetch" href="/assets/index.html-BK-iNYKv.js" as="script"><link rel="prefetch" href="/assets/index.html-DDeLtmuh.js" as="script"><link rel="prefetch" href="/assets/index.html-BSJr7qwh.js" as="script"><link rel="prefetch" href="/assets/index.html-DRlrhC7d.js" as="script"><link rel="prefetch" href="/assets/index.html-BXtqeyHq.js" as="script"><link rel="prefetch" href="/assets/index.html-UrkKwESw.js" as="script"><link rel="prefetch" href="/assets/index.html-C8X5E5_U.js" as="script"><link rel="prefetch" href="/assets/index.html-CZDJXbd3.js" as="script"><link rel="prefetch" href="/assets/index.html-B71I-yvI.js" as="script"><link rel="prefetch" href="/assets/index.html-ZxSgoRoh.js" as="script"><link rel="prefetch" href="/assets/index.html-bipylPNF.js" as="script"><link rel="prefetch" href="/assets/index.html-DR-PJoSN.js" as="script"><link rel="prefetch" href="/assets/index.html-DDn6tClc.js" as="script"><link rel="prefetch" href="/assets/index.html-BvZSJ2r-.js" as="script"><link rel="prefetch" href="/assets/index.html-BKjCcFT0.js" as="script"><link rel="prefetch" href="/assets/index.html-CSRSsNOG.js" as="script"><link rel="prefetch" href="/assets/index.html-BLuB_Eoc.js" as="script"><link rel="prefetch" href="/assets/index.html-CLOegCHC.js" as="script"><link rel="prefetch" href="/assets/index.html-D2pTqZFy.js" as="script"><link rel="prefetch" href="/assets/index.html-DZYdDCPP.js" as="script"><link rel="prefetch" href="/assets/index.html-DzsdPiFk.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-BZLD09T1.js" as="script"><link rel="prefetch" href="/assets/index.html-CRzs15I0.js" as="script"><link rel="prefetch" href="/assets/index.html-CGsa9ffM.js" as="script"><link rel="prefetch" href="/assets/index.html-QNuKjuoZ.js" as="script"><link rel="prefetch" href="/assets/index.html-9q-r5JHT.js" as="script"><link rel="prefetch" href="/assets/index.html-BHNGjpbb.js" as="script"><link rel="prefetch" href="/assets/index.html-0LHdE1Bw.js" as="script"><link rel="prefetch" href="/assets/index.html-kOhwCTdr.js" as="script"><link rel="prefetch" href="/assets/index.html-BlxatHgv.js" as="script"><link rel="prefetch" href="/assets/index.html-ayClYbZ3.js" as="script"><link rel="prefetch" href="/assets/index.html-B3D_5fpm.js" as="script"><link rel="prefetch" href="/assets/index.html-CcgdDCiF.js" as="script"><link rel="prefetch" href="/assets/index.html-B2T3kUK3.js" as="script"><link rel="prefetch" href="/assets/index.html-BpjUVtkj.js" as="script"><link rel="prefetch" href="/assets/index.html-BNAyU6dK.js" as="script"><link rel="prefetch" href="/assets/index.html-VMxXqaQ8.js" as="script"><link rel="prefetch" href="/assets/index.html-DeH2SCB3.js" as="script"><link rel="prefetch" href="/assets/index.html-Dh_a7h_3.js" as="script"><link rel="prefetch" href="/assets/index.html-Bb8RnxYT.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-ChLYKTZm.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DUP77o_D.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
+    <link rel="modulepreload" href="/assets/app-B4LGNJZ0.js"><link rel="modulepreload" href="/assets/typora激活.html-DUOLfN6Y.js">
+    <link rel="prefetch" href="/assets/index.html-Bq7J9cN0.js" as="script"><link rel="prefetch" href="/assets/intro.html-DcelwrZW.js" as="script"><link rel="prefetch" href="/assets/index.html-CdwZ1P48.js" as="script"><link rel="prefetch" href="/assets/命里有时终须有.html-B46pNP68.js" as="script"><link rel="prefetch" href="/assets/carrobot.html-B7set7IG.js" as="script"><link rel="prefetch" href="/assets/index.html-jwKIpsPi.js" as="script"><link rel="prefetch" href="/assets/index.html-DtPJaw_H.js" as="script"><link rel="prefetch" href="/assets/Qt6 Maintence tools不能安装Qt5.html-DdU1Gd4z.js" as="script"><link rel="prefetch" href="/assets/android studio换源.html-DkRIM6mj.js" as="script"><link rel="prefetch" href="/assets/cicd.html-BxLHD3yn.js" as="script"><link rel="prefetch" href="/assets/docker_nginx部署web项目.html-CZONKQdf.js" as="script"><link rel="prefetch" href="/assets/docker.html-DtdutZB7.js" as="script"><link rel="prefetch" href="/assets/figure_bed.html-vyc89ngd.js" as="script"><link rel="prefetch" href="/assets/github 工作流.html-DJORqAx-.js" as="script"><link rel="prefetch" href="/assets/index.html-CqYdKjYM.js" as="script"><link rel="prefetch" href="/assets/mailserver.html-DO5Xbwgi.js" as="script"><link rel="prefetch" href="/assets/modint.html-DNrISIPe.js" as="script"><link rel="prefetch" href="/assets/python_requrements.html-D_iboyN4.js" as="script"><link rel="prefetch" href="/assets/steam模组开发.html-BnsNbJlM.js" as="script"><link rel="prefetch" href="/assets/style.html-4qtN5eOW.js" as="script"><link rel="prefetch" href="/assets/tensorflow踩坑.html-CtBHw7dX.js" as="script"><link rel="prefetch" href="/assets/vsocde插件开发小记.html-BytDpa8J.js" as="script"><link rel="prefetch" href="/assets/「算术公理系统 1」自然数.html-NHamcIiY.js" as="script"><link rel="prefetch" href="/assets/使用capacitor和ionic将vue项目迁移到mobile端.html-CKHKQibh.js" as="script"><link rel="prefetch" href="/assets/协程(asyncio)到底需不需要加锁.html-gfcHinKw.js" as="script"><link rel="prefetch" href="/assets/协程.html-BovqfV_l.js" as="script"><link rel="prefetch" href="/assets/程序员的PPT.html-D4bbFarZ.js" as="script"><link rel="prefetch" href="/assets/闭包实现类.html-CeWxsqOK.js" as="script"><link rel="prefetch" href="/assets/index.html-C9AeqWIc.js" as="script"><link rel="prefetch" href="/assets/index.html-ybZqFA4D.js" as="script"><link rel="prefetch" href="/assets/index.html-BlsqD0oa.js" as="script"><link rel="prefetch" href="/assets/DesignPrinciples.html-BAjp9viD.js" as="script"><link rel="prefetch" href="/assets/abstractFactory.html-D_oh5f2L.js" as="script"><link rel="prefetch" href="/assets/adapter.html-x6kHt0VN.js" as="script"><link rel="prefetch" href="/assets/bridge.html-DzkNbynT.js" as="script"><link rel="prefetch" href="/assets/builder.html-B7MALN7e.js" as="script"><link rel="prefetch" href="/assets/chainOfResponsibility.html-CpbeYqOk.js" as="script"><link rel="prefetch" href="/assets/command.html-Bzqk5uGA.js" as="script"><link rel="prefetch" href="/assets/composite.html-D89dw1yo.js" as="script"><link rel="prefetch" href="/assets/decorator.html-0jwtowLH.js" as="script"><link rel="prefetch" href="/assets/end.html-CkqhlgwJ.js" as="script"><link rel="prefetch" href="/assets/facade.html-BODpRH45.js" as="script"><link rel="prefetch" href="/assets/factory_method.html-NuMbQ7is.js" as="script"><link rel="prefetch" href="/assets/flyweight.html-DUTi0_Qx.js" as="script"><link rel="prefetch" href="/assets/index.html-Dj_dWWjR.js" as="script"><link rel="prefetch" href="/assets/interpreter.html-DfDQyPSV.js" as="script"><link rel="prefetch" href="/assets/iterator.html-9EjNXcsT.js" as="script"><link rel="prefetch" href="/assets/mediator.html-C5vte2nl.js" as="script"><link rel="prefetch" href="/assets/memento.html-Dw4vFzUb.js" as="script"><link rel="prefetch" href="/assets/observer.html-DCoBW7Y-.js" as="script"><link rel="prefetch" href="/assets/prototype.html-Be3THUal.js" as="script"><link rel="prefetch" href="/assets/proxy.html-DydmfTHY.js" as="script"><link rel="prefetch" href="/assets/singleton.html-CJylCsqx.js" as="script"><link rel="prefetch" href="/assets/state.html-D0BJywlY.js" as="script"><link rel="prefetch" href="/assets/strategy.html-BeQd57Ga.js" as="script"><link rel="prefetch" href="/assets/template_method.html-B7oRZ-kS.js" as="script"><link rel="prefetch" href="/assets/visitor.html-DaIekGHb.js" as="script"><link rel="prefetch" href="/assets/0.html-CC8GZdvL.js" as="script"><link rel="prefetch" href="/assets/1.html-C8e1pvTo.js" as="script"><link rel="prefetch" href="/assets/2.html-CfN7D4gf.js" as="script"><link rel="prefetch" href="/assets/3.html-D9pPtuiP.js" as="script"><link rel="prefetch" href="/assets/4.html-DavKkBaH.js" as="script"><link rel="prefetch" href="/assets/5.html-DpkUOZDe.js" as="script"><link rel="prefetch" href="/assets/6.html-4dTDTOb4.js" as="script"><link rel="prefetch" href="/assets/7.html-BzOHeKw-.js" as="script"><link rel="prefetch" href="/assets/8.html-C-sA1tiy.js" as="script"><link rel="prefetch" href="/assets/9.html-DOIgY3Qt.js" as="script"><link rel="prefetch" href="/assets/404.html-CGMXaJuv.js" as="script"><link rel="prefetch" href="/assets/index.html-SwHQd6yQ.js" as="script"><link rel="prefetch" href="/assets/index.html-TRJ6qSMT.js" as="script"><link rel="prefetch" href="/assets/index.html-BCqj2PVi.js" as="script"><link rel="prefetch" href="/assets/index.html-CE6ffKsf.js" as="script"><link rel="prefetch" href="/assets/index.html-CVNN5Fwq.js" as="script"><link rel="prefetch" href="/assets/index.html-DhCS_0vf.js" as="script"><link rel="prefetch" href="/assets/index.html-BgifGsNR.js" as="script"><link rel="prefetch" href="/assets/index.html-DOXbY5aY.js" as="script"><link rel="prefetch" href="/assets/index.html-ZzlVKqB8.js" as="script"><link rel="prefetch" href="/assets/index.html-BjeRhPA4.js" as="script"><link rel="prefetch" href="/assets/index.html-B1eL3fl0.js" as="script"><link rel="prefetch" href="/assets/index.html-DOZrz5tX.js" as="script"><link rel="prefetch" href="/assets/index.html-CL479cux.js" as="script"><link rel="prefetch" href="/assets/index.html-mplfcIL_.js" as="script"><link rel="prefetch" href="/assets/index.html-DW1c3ODz.js" as="script"><link rel="prefetch" href="/assets/index.html-CzSwk-A5.js" as="script"><link rel="prefetch" href="/assets/index.html-SMm58lXr.js" as="script"><link rel="prefetch" href="/assets/index.html-D8p9fsJ8.js" as="script"><link rel="prefetch" href="/assets/index.html-rivgPJ9m.js" as="script"><link rel="prefetch" href="/assets/index.html-DwPUACaS.js" as="script"><link rel="prefetch" href="/assets/index.html-BwXv95cV.js" as="script"><link rel="prefetch" href="/assets/index.html-DeNCk-ye.js" as="script"><link rel="prefetch" href="/assets/index.html-hPg6lxSo.js" as="script"><link rel="prefetch" href="/assets/index.html-CYOJa5u_.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Cw9y1ZOg.js" as="script"><link rel="prefetch" href="/assets/index.html-JQfnAIea.js" as="script"><link rel="prefetch" href="/assets/index.html-Dpy8imS-.js" as="script"><link rel="prefetch" href="/assets/index.html-i5A_pLCb.js" as="script"><link rel="prefetch" href="/assets/index.html-yUxPRBBH.js" as="script"><link rel="prefetch" href="/assets/index.html-DklcXGYl.js" as="script"><link rel="prefetch" href="/assets/index.html-BFj2MrdQ.js" as="script"><link rel="prefetch" href="/assets/index.html-NUfXNLwU.js" as="script"><link rel="prefetch" href="/assets/index.html-BJX9B5Ij.js" as="script"><link rel="prefetch" href="/assets/index.html-F61LMFJS.js" as="script"><link rel="prefetch" href="/assets/index.html-COyA9Sec.js" as="script"><link rel="prefetch" href="/assets/index.html-DYx5t_sy.js" as="script"><link rel="prefetch" href="/assets/index.html-CryaZFG_.js" as="script"><link rel="prefetch" href="/assets/index.html-y8ELyp0v.js" as="script"><link rel="prefetch" href="/assets/index.html-auYNF0Cp.js" as="script"><link rel="prefetch" href="/assets/index.html-DCZKDe-x.js" as="script"><link rel="prefetch" href="/assets/index.html-DERlmHfl.js" as="script"><link rel="prefetch" href="/assets/index.html-DottIbHL.js" as="script"><link rel="prefetch" href="/assets/index.html-BOaWfYA8.js" as="script"><link rel="prefetch" href="/assets/giscus--_FS5kYt.js" as="script"><link rel="prefetch" href="/assets/mermaid.core-DNo_7Q2B.js" as="script"><link rel="prefetch" href="/assets/photoswipe.esm-SzV8tJDW.js" as="script"><link rel="prefetch" href="/assets/SearchResult-DAas8KH8.js" as="script"><link rel="prefetch" href="/assets/index-BNnYFWcz.js" as="script">
   </head>
   <body>
     <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">跳至主要內容</a><!--]--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="route-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.svg" alt><!----><span class="vp-site-name hide-in-pad">blog</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><nav class="vp-nav-links"><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/" aria-label="主页"><span class="font-icon icon home" style=""></span>主页<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/tech/" aria-label="技术"><!---->技术<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/essays/" aria-label="随笔"><!---->随笔<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/projects/" aria-label="项目"><!---->项目<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link active" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></div><div class="vp-nav-item hide-in-mobile"><a class="route-link nav-link" href="/resources/" aria-label="资源"><!---->资源<!----></a></div><div class="vp-nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="友链"><span class="title"><!---->友链</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://bupt.online" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog" class="nav-link"><!---->KSJ-Blog<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://king-sj.github.io" rel="noopener noreferrer" target="_blank" aria-label="KSJ-Blog-GitHub" class="nav-link"><!---->KSJ-Blog-GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><!----><div class="vp-nav-item vp-action"><a class="vp-action-link" href="https://github.com/King-sj/KBlog" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><div class="vp-nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><!--[--><button type="button" class="search-pro-button" aria-label="搜索"><svg xmlns="http://www.w3.org/2000/svg" class="icon search-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="search icon"><path d="M192 480a256 256 0 1 1 512 0 256 256 0 0 1-512 0m631.776 362.496-143.2-143.168A318.464 318.464 0 0 0 768 480c0-176.736-143.264-320-320-320S128 303.264 128 480s143.264 320 320 320a318.016 318.016 0 0 0 184.16-58.592l146.336 146.368c12.512 12.48 32.768 12.48 45.28 0 12.48-12.512 12.48-32.768 0-45.28"></path></svg><div class="search-pro-placeholder">搜索</div><div class="search-pro-key-hints"><kbd class="search-pro-key">Ctrl</kbd><kbd class="search-pro-key">K</kbd></div></button><!--]--><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><button class="vp-sidebar-header clickable active" type="button"><span class="font-icon icon book" style=""></span><span class="vp-sidebar-title">教程</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><a class="route-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/tutorials/typora%E6%BF%80%E6%B4%BB.html" aria-label="Typora激活教程"><!---->Typora激活教程<!----></a></li><li><a class="route-link nav-link vp-sidebar-link vp-sidebar-page" href="/tutorials/" aria-label="教程"><!---->教程<!----></a></li></ul></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!--[--><!----><!--]--><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->Typora激活教程</h1><div class="page-info"><span class="page-author-info" aria-label="作者🖊" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon author-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="author icon"><path d="M649.6 633.6c86.4-48 147.2-144 147.2-249.6 0-160-128-288-288-288s-288 128-288 288c0 108.8 57.6 201.6 147.2 249.6-121.6 48-214.4 153.6-240 288-3.2 9.6 0 19.2 6.4 25.6 3.2 9.6 12.8 12.8 22.4 12.8h704c9.6 0 19.2-3.2 25.6-12.8 6.4-6.4 9.6-16 6.4-25.6-25.6-134.4-121.6-240-243.2-288z"></path></svg><span><a class="page-author-item" href="https://github.com/King-sj" target="_blank" rel="noopener noreferrer">KSJ</a></span><span property="author" content="KSJ"></span></span><!----><span class="page-date-info" aria-label="写作日期📅" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2024-10-21T00:00:00.000Z"></span><!----><span class="page-reading-time-info" aria-label="阅读时间⌛" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>小于 1 分钟</span><meta property="timeRequired" content="PT1M"></span><!----><span class="page-tag-info" aria-label="标签🏷" data-balloon-pos="up"><svg xmlns="http://www.w3.org/2000/svg" class="icon tag-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="tag icon"><path d="M939.902 458.563L910.17 144.567c-1.507-16.272-14.465-29.13-30.737-30.737L565.438 84.098h-.402c-3.215 0-5.726 1.005-7.634 2.913l-470.39 470.39a10.004 10.004 0 000 14.164l365.423 365.424c1.909 1.908 4.42 2.913 7.132 2.913s5.223-1.005 7.132-2.913l470.39-470.39c2.01-2.11 3.014-5.023 2.813-8.036zm-240.067-72.121c-35.458 0-64.286-28.828-64.286-64.286s28.828-64.285 64.286-64.285 64.286 28.828 64.286 64.285-28.829 64.286-64.286 64.286z"></path></svg><!--[--><span class="page-tag-item tag7 clickable" role="navigation">激活</span><!--]--><meta property="keywords" content="激活"></span></div><hr></div><!----><!--[--><!----><!--]--><div class="theme-hope-content"><h1 id="typora-简介" tabindex="-1"><a class="header-anchor" href="#typora-简介"><span>Typora 简介</span></a></h1><p>Typora 是一款简洁高效的 Markdown 编辑器，支持实时预览和多种导出格式，适用于编写笔记、文档和博客等。</p><h1 id="安装教程" tabindex="-1"><a class="header-anchor" href="#安装教程"><span>安装教程</span></a></h1><ul><li><a href="https://typora.io" target="_blank" rel="noopener noreferrer">Typora 官网<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li><li><a href="https://typoraio.cn" target="_blank" rel="noopener noreferrer">Typora 中文官网<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li></ul><!-- TODO: 添加自己的静态服务 --><ul><li>工具下载：<a href="https://pan.baidu.com/share/init?surl=gga2OZ732Xvig1QKn52NHQ" target="_blank" rel="noopener noreferrer">百度网盘，密码：dcqe<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span></a></li></ul><ol><li><p>一路点击“下一步”进行安装。<strong>将下载的工具解压后得到的两个 exe 文件（license-gen.exe 和 node_inject.exe）复制到 Typora 安装目录下</strong>（默认为 <code>C:\Program Files\Typora\</code>）。</p></li><li><p>以管理员身份在 Typora 安装路径打开 PowerShell。</p></li><li><p>输入 <code>node_inject.exe</code> 并回车，等待提示 &quot;done!&quot;。</p></li><li><p>输入 <code>license-gen.exe</code> 并回车，等待显示序列号。</p></li><li><p>启动 Typora，输入任意邮箱和刚才生成的序列号到激活窗口，并点击激活。</p></li></ol><h1 id="结语" tabindex="-1"><a class="header-anchor" href="#结语"><span>结语</span></a></h1><p>通过上述步骤，您可以免费安装并使用 Typora，但如有条件还请支持正版。</p></div><!--[--><!----><!--]--><footer class="vp-page-meta"><div class="vp-meta-item edit-link"><a href="https://github.com/King-sj/KBlog/edit/main/src/tutorials/typora激活.md" rel="noopener noreferrer" target="_blank" aria-label="在 GitHub 上编辑此页" class="nav-link vp-meta-label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->在 GitHub 上编辑此页<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="vp-meta-item git-info"><!----><!----></div></footer><nav class="vp-page-nav"><!----><a class="route-link nav-link active next" href="/tutorials/" aria-label="教程"><div class="hint">下一页<span class="arrow end"></span></div><div class="link">教程<!----></div></a></nav><div id="vp-comment" class="giscus-wrapper input-top" style="display:block;"><svg xmlns="http://www.w3.org/2000/svg" width="32" height="32" preserveAspectRatio="xMidYMid" viewBox="0 0 100 100"><circle cx="28" cy="75" r="11" fill="currentColor"><animate attributeName="fill-opacity" begin="0s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></circle><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 47a28 28 0 0 1 28 28"><animate attributeName="stroke-opacity" begin="0.1s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path><path fill="none" stroke="#88baf0" stroke-width="10" d="M28 25a50 50 0 0 1 50 50"><animate attributeName="stroke-opacity" begin="0.2s" dur="1s" keyTimes="0;0.2;1" repeatCount="indefinite" values="0;1;1"></animate></path></svg></div><!--[--><!----><!--]--><!--]--></main><!--]--><footer class="vp-footer-wrapper"><div class="vp-footer"><a href='https://beian.miit.gov.cn'>黔ICP备2024025117号-1</a> | 版权所有 © 2024-至今 KSJ </div><div class="vp-copyright">MPL-2.0 许可证</div></footer></div><!--]--><!--[--><!----><!----><!--]--><!--]--></div>
-    <script type="module" src="/assets/app-B69Gl_S-.js" defer></script>
+    <script type="module" src="/assets/app-B4LGNJZ0.js" defer></script>
   </body>
 </html>